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Index of groups of order 64
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Hall-Senior number:
1 Abelian(2,2,2,2,2,2)
2 Abelian(4,2,2,2,2)
3 Abelian(4,4,2,2)
4 Abelian(8,2,2,2)
5 Abelian(4,4,4)
6 Abelian(8,4,2)
7 Abelian(16,2,2)
8 Abelian(8,8)
9 Abelian(16,4)
10 Abelian(32,2)
11 Cyclic(64)
12 Abelian(2,2,2) x Dihedral(8)
13 Abelian(2,2,2) x Quaternion(8)
14 Abelian(2,2) x AlmostExtraSpecial(16)
15 Abelian(2,2) x Group(16)#9
16 Abelian(2,2) x Group(16)#10
17 Abelian(2,2) x Group(16)#11
18 Abelian(4,2) x Dihedral(8)
19 Abelian(4,2) x Quaternion(8)
20 Cyclic(2) x Group(32)#16
21 Cyclic(2) x Group(32)#17
22 Cyclic(2) x Group(32)#18
23 Cyclic(2) x Group(32)#19
24 Cyclic(2) x Group(32)#20
25 Cyclic(2) x Group(32)#21
26 Cyclic(2) x Group(32)#22
27 Cyclic(4) x AlmostExtraSpecial(16)
28 Cyclic(4) x Group(16)#9
29 Cyclic(4) x Group(16)#10
30
31 Cyclic(4) x Group(16)#11
32
33
34 Cyclic(8) x Dihedral(8)
35 Cyclic(8) x Quarternion(8)
36
37
38
39
40
41
42
43 Abelian(2,2) x Dihedral(16)
44 Abelian(2,2) x Semidihedral(16)
45 Abelian(2,2) x Quaternion(16)
46 Cyclic(2) x Group(32)#26
47 Cyclic(2) x Group(32)#27
48 Cyclic(2) x Group(32)#28
49 Cyclic(2) x Group(32)#29
50 Cyclic(2) x Group(32)#30
51 Cyclic(2) x Group(32)#31
52 Cyclic(2) x Group(32)#32
53
54
55 Cyclic(4) x Dihedral(16)
56 Cyclic(4) x Semidihedral(16)
57 Cyclic(4) x Quaternion(16)
58
59
60
61
62
63
64
65
66
67
68 Cyclic(2) x Group(32)#33
69 Cyclic(2) x Group(32)#34
70 Cyclic(2) x Group(32)#35
71 Cyclic(2) x Group(32)#36
72 Cyclic(2) x Group(32)#37
73 Cyclic(2) x Group(32)#38
74 Cyclic(2) x Group(32)#39
75 Cyclic(2) x Group(32)#40
76 Cyclic(2) x Group(32)#41
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103 Cyclic(2) x Extraspecial Dihedral(8)*Dihedral(8)
104 Cyclic(2) x Extraspecial Dihedral(8)*Quaternion(8)
105 AlmostExtraspecial(64)
106
107
108
109
110 Cyclic(2) x Group(32)#44
111 Cyclic(2) x Group(32)#45
112
113
114
115
116
117
118
119
120
121
122
123 Cyclic(2) x Group(32)#46
124 Cyclic(2) x Group(32)#47
125 Cyclic(2) x Group(32)#48
126
127
128
129
130
131
132
133
134 Cyclic(2) x Dihedral(32)
135 Cyclic(2) x Semidihedral(32)
136 Cyclic(2) x Quaternion(32)
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153 The Sylow 2-subgroup of Suzuki group Sz(8)
154 Dihedral(8) x Dihedral(8)
155 Dihedral(8) x Quaternion(8)
156 Quaternion(8) x Quaternion(8)
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183 The Sylow 2-subgroup of PSL(3,4)
184
185
186
187 The Sylow 2-subgroup of SU(3,4)
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259 The Sylow2-subgroup of A8,PSU(4,2) and PSP(5,4)
260
261 The Sylow2-subgroup of M12 and G(2,5)
262
263
264
265 Dihedral(64)
266 Semidihedral(64)
267 Quaternion(64)
Index of groups of order 4
Index of groups of order 8
Index of groups of order 16
Index of groups of order 32
Index of groups of order 64