Here is a list of the 230 3-dimensional space groups, organized by crystal system.

Each space group is labeled according to its number, abbreviated Hermann–Mauguin notation (international symbol) and full H-M notation, as well as the space group’s parent point group, Bravais lattice, crystal family, and crystal system.

#### Outline

### Triclinic Space Groups

Space Group (Number) | ShortName of a Space Group | Point Group(H-M HermannMauguin Notation) | Crystal System | Crystal Family | Bravais Lattice |

1 | Triclinic | Triclinic | Triclinic | ||

2 | Triclinic | Triclinic | Triclinic |

### Monoclinic Space Groups

Space Group(Number) | ShortName of a Space Group | Point Group (Hermann-Mauguin Notation) | CrystalSystem | CrystalFamily | BravaisLattice |

3 | Monoclinic | Monoclinic | Simple Monoclinic | ||

4 | Monoclinic | Monoclinic | Simple Monoclinic | ||

5 | Monoclinic | Monoclinic | Base-Centered Monoclinic | ||

6 | Monoclinic | Monoclinic | Simple Monoclinic | ||

7 | Monoclinic | Monoclinic | Simple Monoclinic | ||

8 | Monoclinic | Monoclinic | Base-Centered Monoclinic | ||

9 | Monoclinic | Monoclinic | Base-Centered Monoclinic | ||

10 | Monoclinic | Monoclinic | Simple Monoclinic | ||

11 | Monoclinic | Monoclinic | Simple Monoclinic | ||

12 | Monoclinic | Monoclinic | Base-Centered Monoclinic | ||

13 | Monoclinic | Monoclinic | Simple Monoclinic | ||

14 | Monoclinic | Monoclinic | Simple Monoclinic | ||

15 | Monoclinic | Monoclinic | Base-Centered Monoclinic |

### Orthorhombic Space Groups

Space Group(Number) | ShortName of a Space Group | Point Group(H-M HermannMauguin Notation) | CrystalSystem | CrystalFamily | BravaisLattice |

16 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

17 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

18 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

19 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

20 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

21 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

22 | Orthorhombic | Orthorhombic | Face-Centered Orthorhombic | ||

23 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

24 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

25 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

26 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

27 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

28 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

29 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

30 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

31 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

32 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

33 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

34 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

35 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

36 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

37 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

38 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

39 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

40 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

41 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

42 | Orthorhombic | Orthorhombic | Face-Centered Orthorhombic | ||

43 | Orthorhombic | Orthorhombic | Face-Centered Orthorhombic | ||

44 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

45 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

46 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

47 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

48 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

49 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

50 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

51 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

52 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

53 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

54 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

55 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

56 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

57 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

58 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

59 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

60 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

61 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

62 | Orthorhombic | Orthorhombic | Simple Orthorhombic | ||

63 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

64 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

65 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

66 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

67 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

68 | Orthorhombic | Orthorhombic | Base-Centered Orthorhombic | ||

69 | Orthorhombic | Orthorhombic | Face-Centered Orthorhombic | ||

70 | Orthorhombic | Orthorhombic | Face-Centered Orthorhombic | ||

71 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

72 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

73 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic | ||

74 | Orthorhombic | Orthorhombic | Body-Centered Orthorhombic |

### Tetragonal Space Groups

Space Group(Number) | ShortName of a Space Group | Point Group(H-M HermannMauguin Notation) | CrystalSystem | CrystalFamily | BravaisLattice |

75 | Tetragonal | Tetragonal | Simple Tetragonal | ||

76 | Tetragonal | Tetragonal | Simple Tetragonal | ||

77 | Tetragonal | Tetragonal | Simple Tetragonal | ||

78 | Tetragonal | Tetragonal | Simple Tetragonal | ||

79 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

80 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

81 | Tetragonal | Tetragonal | Simple Tetragonal | ||

82 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

83 | Tetragonal | Tetragonal | Simple Tetragonal | ||

84 | Tetragonal | Tetragonal | Simple Tetragonal | ||

85 | Tetragonal | Tetragonal | Simple Tetragonal | ||

86 | Tetragonal | Tetragonal | Simple Tetragonal | ||

87 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

88 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

89 | Tetragonal | Tetragonal | Simple Tetragonal | ||

90 | Tetragonal | Tetragonal | Simple Tetragonal | ||

91 | Tetragonal | Tetragonal | Simple Tetragonal | ||

92 | Tetragonal | Tetragonal | Simple Tetragonal | ||

93 | Tetragonal | Tetragonal | Simple Tetragonal | ||

94 | Tetragonal | Tetragonal | Simple Tetragonal | ||

95 | Tetragonal | Tetragonal | Simple Tetragonal | ||

96 | Tetragonal | Tetragonal | Simple Tetragonal | ||

97 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

98 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

99 | Tetragonal | Tetragonal | Simple Tetragonal | ||

100 | Tetragonal | Tetragonal | Simple Tetragonal | ||

101 | Tetragonal | Tetragonal | Simple Tetragonal | ||

102 | Tetragonal | Tetragonal | Simple Tetragonal | ||

103 | Tetragonal | Tetragonal | Simple Tetragonal | ||

104 | Tetragonal | Tetragonal | Simple Tetragonal | ||

105 | Tetragonal | Tetragonal | Simple Tetragonal | ||

106 | Tetragonal | Tetragonal | Simple Tetragonal | ||

107 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

108 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

109 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

110 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

111 | Tetragonal | Tetragonal | Simple Tetragonal | ||

112 | Tetragonal | Tetragonal | Simple Tetragonal | ||

113 | Tetragonal | Tetragonal | Simple Tetragonal | ||

114 | Tetragonal | Tetragonal | Simple Tetragonal | ||

115 | Tetragonal | Tetragonal | Simple Tetragonal | ||

116 | Tetragonal | Tetragonal | Simple Tetragonal | ||

117 | Tetragonal | Tetragonal | Simple Tetragonal | ||

118 | Tetragonal | Tetragonal | Simple Tetragonal | ||

119 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

120 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

121 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

122 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

123 | Tetragonal | Tetragonal | Simple Tetragonal | ||

124 | Tetragonal | Tetragonal | Simple Tetragonal | ||

125 | Tetragonal | Tetragonal | Simple Tetragonal | ||

126 | Tetragonal | Tetragonal | Simple Tetragonal | ||

127 | Tetragonal | Tetragonal | Simple Tetragonal | ||

128 | Tetragonal | Tetragonal | Simple Tetragonal | ||

129 | Tetragonal | Tetragonal | Simple Tetragonal | ||

130 | Tetragonal | Tetragonal | Simple Tetragonal | ||

131 | Tetragonal | Tetragonal | Simple Tetragonal | ||

132 | Tetragonal | Tetragonal | Simple Tetragonal | ||

133 | Tetragonal | Tetragonal | Simple Tetragonal | ||

134 | Tetragonal | Tetragonal | Simple Tetragonal | ||

135 | Tetragonal | Tetragonal | Simple Tetragonal | ||

136 | Tetragonal | Tetragonal | Simple Tetragonal | ||

137 | Tetragonal | Tetragonal | Simple Tetragonal | ||

138 | Tetragonal | Tetragonal | Simple Tetragonal | ||

139 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

140 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

141 | Tetragonal | Tetragonal | Body-Centered Tetragonal | ||

142 | Tetragonal | Tetragonal | Body-Centered Tetragonal |

### Trigonal Space Groups

Space Group(Number) | ShortName of a Space Group | Point Group(H-M HermannMauguin Notation) | CrystalSystem | CrystalFamily | BravaisLattice |

143 | Trigonal | Hexagonal | Hexagonal | ||

144 | Trigonal | Hexagonal | Hexagonal | ||

145 | Trigonal | Hexagonal | Hexagonal | ||

146 | Trigonal | Hexagonal | Rhombohedral | ||

147 | Trigonal | Hexagonal | Hexagonal | ||

148 | Trigonal | Hexagonal | Rhombohedral | ||

149 | Trigonal | Hexagonal | Hexagonal | ||

150 | Trigonal | Hexagonal | Hexagonal | ||

151 | Trigonal | Hexagonal | Hexagonal | ||

152 | Trigonal | Hexagonal | Hexagonal | ||

153 | Trigonal | Hexagonal | Hexagonal | ||

154 | Trigonal | Hexagonal | Hexagonal | ||

155 | Trigonal | Hexagonal | Rhombohedral | ||

156 | Trigonal | Hexagonal | Hexagonal | ||

157 | Trigonal | Hexagonal | Hexagonal | ||

158 | Trigonal | Hexagonal | Hexagonal | ||

159 | Trigonal | Hexagonal | Hexagonal | ||

160 | Trigonal | Hexagonal | Rhombohedral | ||

161 | Trigonal | Hexagonal | Rhombohedral | ||

162 | Trigonal | Hexagonal | Hexagonal | ||

163 | Trigonal | Hexagonal | Hexagonal | ||

164 | Trigonal | Hexagonal | Hexagonal | ||

165 | Trigonal | Hexagonal | Hexagonal | ||

166 | Trigonal | Hexagonal | Rhombohedral | ||

167 | Trigonal | Hexagonal | Rhombohedral |

### Hexagonal Space Groups

Space Group(Number) | ShortName of a Space Group | Point Group(H-M HermannMauguin Notation) | CrystalSystem | CrystalFamily | BravaisLattice |

168 | Hexagonal | Hexagonal | Hexagonal | ||

169 | Hexagonal | Hexagonal | Hexagonal | ||

170 | Hexagonal | Hexagonal | Hexagonal | ||

171 | Hexagonal | Hexagonal | Hexagonal | ||

172 | Hexagonal | Hexagonal | Hexagonal | ||

173 | Hexagonal | Hexagonal | Hexagonal | ||

174 | Hexagonal | Hexagonal | Hexagonal | ||

175 | Hexagonal | Hexagonal | Hexagonal | ||

176 | Hexagonal | Hexagonal | Hexagonal | ||

177 | Hexagonal | Hexagonal | Hexagonal | ||

178 | Hexagonal | Hexagonal | Hexagonal | ||

179 | Hexagonal | Hexagonal | Hexagonal | ||

180 | Hexagonal | Hexagonal | Hexagonal | ||

181 | Hexagonal | Hexagonal | Hexagonal | ||

182 | Hexagonal | Hexagonal | Hexagonal | ||

183 | Hexagonal | Hexagonal | Hexagonal | ||

184 | Hexagonal | Hexagonal | Hexagonal | ||

185 | Hexagonal | Hexagonal | Hexagonal | ||

186 | Hexagonal | Hexagonal | Hexagonal | ||

187 | Hexagonal | Hexagonal | Hexagonal | ||

188 | Hexagonal | Hexagonal | Hexagonal | ||

189 | Hexagonal | Hexagonal | Hexagonal | ||

190 | Hexagonal | Hexagonal | Hexagonal | ||

191 | Hexagonal | Hexagonal | Hexagonal | ||

192 | Hexagonal | Hexagonal | Hexagonal | ||

193 | Hexagonal | Hexagonal | Hexagonal | ||

194 | Hexagonal | Hexagonal | Hexagonal |

### Cubic Space Groups

Space Group(Number) | ShortName of a Space Group | Point Group(H-M HermannMauguin Notation) | CrystalSystem | CrystalFamily | BravaisLattice |

195 | Cubic | Cubic | Simple Cubic | ||

196 | Cubic | Cubic | Face-Centered Cubic | ||

197 | Cubic | Cubic | Body-Centered Cubic | ||

198 | Cubic | Cubic | Simple Cubic | ||

199 | Cubic | Cubic | Body-Centered Cubic | ||

200 | Cubic | Cubic | Simple Cubic | ||

201 | Cubic | Cubic | Simple Cubic | ||

202 | Cubic | Cubic | Face-Centered Cubic | ||

203 | Cubic | Cubic | Face-Centered Cubic | ||

204 | Cubic | Cubic | Body-Centered Cubic | ||

205 | Cubic | Cubic | Simple Cubic | ||

206 | Cubic | Cubic | Body-Centered Cubic | ||

207 | Cubic | Cubic | Simple Cubic | ||

208 | Cubic | Cubic | Simple Cubic | ||

209 | Cubic | Cubic | Face-Centered Cubic | ||

210 | Cubic | Cubic | Face-Centered Cubic | ||

211 | Cubic | Cubic | Body-Centered Cubic | ||

212 | Cubic | Cubic | Simple Cubic | ||

213 | Cubic | Cubic | Simple Cubic | ||

214 | Cubic | Cubic | Body-Centered Cubic | ||

215 | Cubic | Cubic | Simple Cubic | ||

216 | Cubic | Cubic | Face-Centered Cubic | ||

217 | Cubic | Cubic | Body-Centered Cubic | ||

218 | Cubic | Cubic | Simple Cubic | ||

219 | Cubic | Cubic | Face-Centered Cubic | ||

220 | Cubic | Cubic | Body-Centered Cubic | ||

221 | Cubic | Cubic | Simple Cubic | ||

222 | Cubic | Cubic | Simple Cubic | ||

223 | Cubic | Cubic | Simple Cubic | ||

224 | Cubic | Cubic | Simple Cubic | ||

225 | Cubic | Cubic | Face-Centered Cubic | ||

226 | Cubic | Cubic | Face-Centered Cubic | ||

227 | Cubic | Cubic | Face-Centered Cubic | ||

228 | Cubic | Cubic | Face-Centered Cubic | ||

229 | Cubic | Cubic | Body-Centered Cubic | ||

230 | Cubic | Cubic | Body-Centered Cubic |

### References and Further Reading

If you have a hard time interpreting the space group symbols, check out this article which explains the various crystallography notation systems, including H-M notation.

If you want to see the other crystallography-related articles I’ve written, here is this list, in recommended reading order:

Introduction to Bravais Lattices

What is the Difference Between “Crystal Structure” and “Bravais Lattice”

Atomic Packing Factor

How to Read Miller Indices

How to Read Hexagonal Miller-Bravais Indices

Close-Packed Crystals and Stacking Order

Interstitial Sites

Primitive Cells

How to Read Crystallography Notation

What are Point Groups

List of Point Groups

What are Space Groups

List of Space Groups

The 7 Crystal Systems

If you are interested in more details about any specific crystal structure, I have written individual articles about simple crystal structures which correspond to each of the 14 Bravais lattices:

1. Simple Cubic

2. Face-Centered Cubic

2a. Diamond Cubic

3. Body-Centered Cubic

4. Simple Hexagonal

4a. Hexagonal Close-Packed

4b. Double Hexagonal Close-Packed (La-type)

5. Rhombohedral

5a. Rhombohedral Close-Packed (Sm-type)

6. Simple Tetragonal

7. Body-Centered Tetragonal

7a. Diamond Tetragonal (White Tin)

8. Simple Orthorhombic

9. Base-Centered Orthorhombic

10. Face-Centered Orthorhombic

11. Body-Centered Orthorhombic

12. Simple Monoclinic

13. Base-Centered Monoclinic

14. Triclinic