Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1611 conjugacy classes of subgroups.
The subgroup lattice has 934 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596669 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5524 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10595023 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10595022 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10592705 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#5006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10591231 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10590408 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10590407 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #82936 | — | 3 | 1 | no | maximal |
| 11 | #78690 | — | 3 | 1 | no | maximal |
| 12 | C2×#3828 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×#235 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×#235 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C3×C4×D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #64330 | C22 | 1 | 4 | yes | — |
| 17 | #64308 | — | 2 | 1 | no | — |
| 18 | #64307 | — | 2 | 1 | no | — |
| 19 | #64307 | — | 2 | 1 | no | — |
| 20 | #64306 | — | 2 | 2 | no | — |
| 21 | D3×#235 | — | 2 | 2 | no | — |
| 22 | D3×#235 | — | 2 | 2 | no | — |
| 23 | #64298 | — | 2 | 1 | no | — |
| 24 | #64297 | — | 2 | 1 | no | — |
| 25 | #64297 | — | 2 | 1 | no | — |
| 26 | C32×#117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #64135 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3×#926 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C3×#897 | — | 2 | 1 | no | — |
| 30 | C3×#895 | — | 2 | 1 | no | — |
| 31 | C3×#886 | C22 | 1 | 2 | yes | complemented |
| 32 | C3×#882 | C22 | 1 | 2 | yes | complemented |
| 33 | C3×C4×D12 | — | 2 | 2 | no | — |
| 34 | #63977 | C22 | 1 | 2 | yes | complemented |
| 35 | #63976 | C22 | 1 | 2 | yes | complemented |
| 36 | #63966 | C22 | 1 | 2 | yes | complemented |
| 37 | #63961 | C22 | 1 | 2 | yes | complemented |
| 38 | #63909 | — | 2 | 1 | no | — |
| 39 | #63908 | — | 2 | 1 | no | — |
| 40 | C4×#626 | — | 2 | 2 | no | — |
| 41 | C4×#625 | — | 2 | 2 | no | — |
| 42 | #63857 | — | 2 | 1 | no | — |
| 43 | #63856 | — | 2 | 1 | no | — |
| 44 | #63633 | C22 | 1 | 4 | yes | complemented |
| 45 | C3×#806 | C22 | 1 | 4 | yes | complemented |
| 46 | #63580 | C22 | 1 | 4 | yes | complemented |
| 47 | #5964 | — | 3 | 1 | no | — |
| 48 | #5964 | — | 3 | 1 | no | — |
| 49 | C3×#525 | — | 3 | 1 | no | — |
| 50 | #5828 | — | 3 | 1 | no | — |
| 51 | #5791 | — | 3 | 1 | no | — |
| 52 | #5791 | — | 3 | 1 | no | — |
| 53 | #5524 | — | 3 | 1 | no | — |
| 54 | #5524 | D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | C3×#410 | — | 3 | 1 | no | — |
| 56 | #5240 | — | 3 | 1 | no | — |
| 57 | #5053 | — | 3 | 4 | no | — |
| 58 | #5032 | — | 3 | 4 | no | — |
| 59 | #5006 | — | 3 | 1 | no | — |
| 60 | #5006 | — | 3 | 1 | no | — |
| 61 | #5006 | — | 3 | 1 | no | — |
| 62 | #5006 | — | 6 | 1 | no | — |
| 63 | #5006 | D3 | 1 | 1 | yes | characteristic, complemented |
| 64 | #4742 | — | 3 | 4 | no | — |
| 65 | #4741 | — | 3 | 4 | no | — |
| 66 | C23×C3×D3 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×#638 | C23 | 1 | 2 | yes | — |
| 69 | #3828 | — | 2 | 1 | no | — |
| 70 | #3828 | — | 2 | 1 | no | — |
| 71 | #3828 | — | 2 | 1 | no | — |
| 72 | #3828 | — | 2 | 1 | no | — |
| 73 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic, complemented |
| 74 | C2×C4×C3⋊D3 | D4 | 1 | 2 | yes | complemented |
| 75 | C2×#634 | D4 | 1 | 1 | yes | characteristic, complemented |
| 76 | C2×C3×#67 | C23 | 1 | 2 | yes | — |
| 77 | C2×C3×#67 | C23 | 1 | 2 | yes | — |
| 78 | C22×C3×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 79 | C3×#235 | — | 2 | 1 | no | — |
| 80 | C3×#235 | — | 2 | 1 | no | — |
| 81 | C3×#235 | — | 2 | 1 | no | — |
| 82 | C3×#235 | — | 2 | 1 | no | — |
| 83 | C3×#235 | — | 2 | 1 | no | — |
| 84 | C3×#235 | — | 2 | 1 | no | — |
| 85 | C3×#235 | — | 2 | 1 | no | — |
| 86 | C3×#235 | — | 2 | 1 | no | — |
| 87 | C2×C3×D12 | — | 2 | 2 | no | — |
| 88 | C2×C3×D12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 89 | C2×C3×D12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 90 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 91 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 92 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 93 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 94 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 95 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 96 | C2×C3×C4×D3 | D4 | 1 | 2 | yes | complemented |
| 97 | C2×C3×C4×D3 | D4 | 1 | 2 | yes | complemented |
| 98 | C2×C3×Dic6 | D4 | 1 | 1 | yes | characteristic, complemented |
| 99 | C2×C3×Dic6 | D4 | 1 | 1 | yes | characteristic, complemented |
| 100 | #3811 | — | 2 | 4 | no | — |
| 101 | D3×#67 | — | 2 | 4 | no | — |
| 102 | D3×#67 | — | 2 | 4 | no | — |
| 103 | C2×#626 | — | 2 | 2 | no | — |
| 104 | C2×#625 | — | 2 | 2 | no | — |
| 105 | #3805 | — | 2 | 4 | no | — |
| 106 | #3804 | — | 2 | 4 | no | — |
| 107 | #3804 | — | 2 | 4 | no | — |
| 108 | #3802 | — | 2 | 2 | no | — |
| 109 | D3×D12 | — | 2 | 2 | no | — |
| 110 | D3×D12 | — | 2 | 2 | no | — |
| 111 | C4×D32 | — | 2 | 4 | no | — |
| 112 | #3799 | — | 2 | 2 | no | — |
| 113 | #3799 | — | 2 | 2 | no | — |
| 114 | #3798 | — | 2 | 4 | no | — |
| 115 | #3797 | — | 2 | 2 | no | — |
| 116 | #3796 | — | 2 | 2 | no | — |
| 117 | #3796 | — | 2 | 2 | no | — |
| 118 | #3795 | — | 2 | 2 | no | — |
| 119 | #3795 | — | 2 | 2 | no | — |
| 120 | D3×Dic6 | — | 2 | 2 | no | — |
| 121 | D3×Dic6 | — | 2 | 2 | no | — |
| 122 | C32×C4⋊C4 | — | 2 | 1 | no | — |
| 123 | C32×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 124 | C32×C42 | — | 2 | 1 | no | — |
| 125 | #3757 | C23 | 1 | 2 | yes | — |
| 126 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 127 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 128 | C3×#217 | C23 | 1 | 2 | yes | — |
| 129 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 130 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 131 | C3×C4⋊Dic3 | — | 2 | 1 | no | — |
| 132 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 133 | C3×C4×Dic3 | — | 2 | 1 | no | — |
| 134 | #3724 | — | 2 | 2 | no | — |
| 135 | Dic3⋊Dic3 | — | 2 | 2 | no | — |
| 136 | #3722 | — | 2 | 2 | no | — |
| 137 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 138 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 139 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 140 | #3025 | — | 9 | 1 | no | Sylow |
| 141 | C2×C3×#41 | — | 3 | 1 | no | — |
| 142 | C2×C3×#41 | — | 3 | 1 | no | — |
| 143 | C23×C3×C4 | — | 3 | 1 | no | — |
| 144 | #1010 | — | 6 | 1 | no | — |
| 145 | #1010 | — | 6 | 1 | no | — |
| 146 | #1010 | — | 6 | 1 | no | — |
| 147 | #1010 | — | 6 | 1 | no | — |
| 148 | #1009 | — | 6 | 1 | no | — |
| 149 | #1009 | — | 6 | 1 | no | — |
| 150 | #1009 | — | 6 | 1 | no | — |
| 151 | #1009 | — | 6 | 1 | no | — |
| 152 | D3×#41 | — | 6 | 2 | no | — |
| 153 | D3×#41 | — | 6 | 2 | no | — |
| 154 | D3×#41 | — | 6 | 2 | no | — |
| 155 | D3×#41 | — | 6 | 2 | no | — |
| 156 | #1007 | — | 6 | 1 | no | — |
| 157 | #1007 | — | 6 | 1 | no | — |
| 158 | #1004 | — | 3 | 4 | no | — |
| 159 | #1004 | — | 3 | 4 | no | — |
| 160 | #1004 | — | 6 | 1 | no | — |
| 161 | #1004 | — | 6 | 1 | no | — |
| 162 | C2×#235 | — | 3 | 1 | no | — |
| 163 | C2×#235 | — | 3 | 1 | no | — |
| 164 | C2×#235 | — | 6 | 1 | no | — |
| 165 | C2×#235 | — | 6 | 2 | no | — |
| 166 | C2×#235 | — | 6 | 2 | no | — |
| 167 | C2×#235 | C2×D3 | 1 | 1 | yes | characteristic |
| 168 | C2×#235 | C2×D3 | 1 | 1 | yes | characteristic |
| 169 | C22×C4×D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 170 | C3×#123 | — | 3 | 2 | no | — |
| 171 | C3×C22⋊Q8 | — | 6 | 1 | no | — |
| 172 | C3×#121 | — | 6 | 1 | no | — |
| 173 | C3×#120 | — | 3 | 2 | no | — |
| 174 | C3×C4×D4 | — | 6 | 2 | no | — |
| 175 | C3×#117 | — | 2 | 1 | no | — |
| 176 | C3×#117 | — | 3 | 1 | no | — |
| 177 | C3×#117 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 178 | C3×#117 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 179 | #953 | — | 3 | 2 | no | — |
| 180 | #953 | — | 3 | 2 | no | — |
| 181 | #946 | — | 6 | 1 | no | — |
| 182 | #938 | — | 6 | 1 | no | — |
| 183 | #937 | — | 3 | 2 | no | — |
| 184 | #935 | — | 3 | 2 | no | — |
| 185 | #930 | — | 6 | 1 | no | — |
| 186 | #930 | — | 6 | 1 | no | — |
| 187 | #929 | — | 3 | 2 | no | — |
| 188 | #929 | — | 3 | 2 | no | — |
| 189 | C4×#67 | — | 6 | 2 | no | — |
| 190 | C4×#67 | — | 6 | 2 | no | — |
| 191 | C4×#67 | — | 6 | 2 | no | — |
| 192 | #926 | — | 3 | 1 | no | — |
| 193 | #926 | — | 3 | 1 | no | — |
| 194 | #926 | — | 6 | 1 | no | — |
| 195 | #926 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 196 | #924 | — | 6 | 1 | no | — |
| 197 | #924 | — | 6 | 1 | no | — |
| 198 | #897 | — | 2 | 1 | no | — |
| 199 | #897 | — | 6 | 1 | no | — |
| 200 | #895 | — | 2 | 1 | no | — |
| 201 | #895 | — | 6 | 1 | no | — |
| 202 | #886 | — | 3 | 2 | no | — |
| 203 | #886 | C2×D3 | 1 | 2 | yes | complemented |
| 204 | #882 | — | 3 | 2 | no | — |
| 205 | #882 | C2×D3 | 1 | 2 | yes | complemented |
| 206 | C4×D12 | — | 2 | 2 | no | — |
| 207 | C4×D12 | — | 6 | 2 | no | — |
| 208 | C3×#99 | — | 3 | 4 | no | — |
| 209 | #834 | — | 3 | 4 | no | — |
| 210 | #806 | — | 3 | 4 | no | — |
| 211 | #806 | — | 3 | 4 | no | — |
| 212 | #806 | — | 3 | 4 | no | — |
| 213 | #806 | — | 6 | 4 | no | — |
| 214 | #806 | C2×D3 | 1 | 4 | yes | complemented |
| 215 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 216 | C22×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 217 | C22×C3×D3 | — | 2 | 1 | no | — |
| 218 | C22×C3×D3 | — | 2 | 1 | no | — |
| 219 | C22×C3×D3 | — | 2 | 1 | no | — |
| 220 | C22×C3×D3 | — | 4 | 2 | no | — |
| 221 | C22×C3×D3 | C2×D4 | 1 | 2 | yes | — |
| 222 | C22×C3×D3 | C2×D4 | 1 | 2 | yes | — |
| 223 | C2×D32 | — | 2 | 4 | no | — |
| 224 | C2×C32×C4 | — | 2 | 2 | no | — |
| 225 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 231 | #638 | — | 2 | 2 | no | — |
| 232 | #638 | — | 2 | 2 | no | — |
| 233 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 234 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 235 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 236 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 237 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 238 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 239 | #634 | — | 2 | 1 | no | — |
| 240 | #634 | — | 2 | 1 | no | — |
| 241 | C3×#67 | — | 2 | 2 | no | — |
| 242 | C3×#67 | — | 2 | 2 | no | — |
| 243 | C3×#67 | — | 2 | 2 | no | — |
| 244 | C3×#67 | — | 2 | 2 | no | — |
| 245 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 246 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 247 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 248 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 249 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 250 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 251 | C3×D12 | — | 2 | 1 | no | — |
| 252 | C3×D12 | — | 2 | 1 | no | — |
| 253 | C3×D12 | — | 2 | 1 | no | — |
| 254 | C3×D12 | — | 2 | 1 | no | — |
| 255 | C3×D12 | — | 4 | 4 | no | — |
| 256 | C3×C4×D3 | — | 2 | 2 | no | — |
| 257 | C3×C4×D3 | — | 2 | 2 | no | — |
| 258 | C3×C4×D3 | — | 2 | 2 | no | — |
| 259 | C3×C4×D3 | — | 2 | 2 | no | — |
| 260 | C3×C4×D3 | — | 4 | 1 | no | — |
| 261 | C3×C4×D3 | — | 4 | 1 | no | — |
| 262 | C3×C4×D3 | — | 4 | 1 | no | — |
| 263 | C3×C4×D3 | — | 4 | 1 | no | — |
| 264 | C3×Dic6 | — | 2 | 1 | no | — |
| 265 | C3×Dic6 | — | 2 | 1 | no | — |
| 266 | C3×Dic6 | — | 2 | 1 | no | — |
| 267 | C3×Dic6 | — | 2 | 1 | no | — |
| 268 | #627 | — | 2 | 4 | no | — |
| 269 | #626 | — | 2 | 4 | no | — |
| 270 | #626 | — | 2 | 4 | no | — |
| 271 | #626 | — | 4 | 4 | no | — |
| 272 | #625 | — | 2 | 4 | no | — |
| 273 | #625 | — | 4 | 4 | no | — |
| 274 | #624 | — | 2 | 4 | no | — |
| 275 | D3×Dic3 | — | 2 | 4 | no | — |
| 276 | D3×Dic3 | — | 2 | 4 | no | — |
| 277 | #585 | — | 9 | 1 | no | — |
| 278 | #525 | — | 3 | 1 | no | — |
| 279 | #525 | — | 9 | 1 | no | — |
| 280 | #525 | — | 9 | 1 | no | — |
| 281 | #458 | — | 9 | 4 | no | — |
| 282 | B(4,𝔽2) | — | 9 | 4 | no | — |
| 283 | #410 | — | 3 | 1 | no | — |
| 284 | #410 | — | 9 | 1 | no | — |
| 285 | #410 | — | 9 | 1 | no | — |
| 286 | C24×C3 | — | 3 | 1 | no | — |
| 287 | C23×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 288 | C3×#41 | — | 6 | 1 | no | — |
| 289 | C3×#41 | — | 6 | 1 | no | — |
| 290 | C3×#41 | — | 6 | 1 | no | — |
| 291 | C3×#41 | — | 6 | 1 | no | — |
| 292 | C3×#41 | — | 6 | 1 | no | — |
| 293 | C3×#41 | — | 6 | 1 | no | — |
| 294 | C3×#41 | — | 6 | 1 | no | — |
| 295 | C3×#41 | — | 6 | 1 | no | — |
| 296 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 297 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 298 | C2×C3×D4 | — | 3 | 2 | no | — |
| 299 | C2×C3×D4 | — | 3 | 2 | no | — |
| 300 | C2×C3×D4 | — | 3 | 1 | no | — |
| 301 | C2×C3×D4 | — | 3 | 1 | no | — |
| 302 | C2×C3×D4 | — | 6 | 2 | no | — |
| 303 | C22×C3×C4 | — | 2 | 1 | no | — |
| 304 | C22×C3×C4 | — | 3 | 2 | no | — |
| 305 | C22×C3×C4 | — | 3 | 2 | no | — |
| 306 | C22×C3×C4 | — | 3 | 1 | no | — |
| 307 | C22×C3×C4 | — | 6 | 1 | no | — |
| 308 | C22×C3×C4 | — | 6 | 1 | no | — |
| 309 | C22×C3×C4 | — | 6 | 1 | no | — |
| 310 | C22×C3×C4 | — | 6 | 1 | no | — |
| 311 | C22×C3×C4 | — | 6 | 1 | no | — |
| 312 | C22×C3×C4 | — | 6 | 1 | no | — |
| 313 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 314 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 315 | C2×#67 | — | 3 | 2 | no | — |
| 316 | C2×#67 | — | 3 | 2 | no | — |
| 317 | C2×#67 | — | 6 | 2 | no | — |
| 318 | C2×#67 | — | 6 | 2 | no | — |
| 319 | C2×#67 | — | 6 | 4 | no | — |
| 320 | C2×#67 | — | 6 | 4 | no | — |
| 321 | C2×#67 | — | 6 | 2 | no | — |
| 322 | C2×#67 | — | 6 | 2 | no | — |
| 323 | C2×#67 | C22×D3 | 1 | 2 | yes | — |
| 324 | C2×#67 | C22×D3 | 1 | 2 | yes | — |
| 325 | C22×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 326 | #239 | — | 6 | 2 | no | — |
| 327 | #239 | — | 6 | 2 | no | — |
| 328 | #239 | — | 6 | 2 | no | — |
| 329 | #239 | — | 6 | 2 | no | — |
| 330 | D3×Q8 | — | 6 | 2 | no | — |
| 331 | D3×Q8 | — | 6 | 2 | no | — |
| 332 | D3×Q8 | — | 6 | 2 | no | — |
| 333 | D3×Q8 | — | 6 | 2 | no | — |
| 334 | #237 | — | 6 | 2 | no | — |
| 335 | #237 | — | 6 | 2 | no | — |
| 336 | #237 | — | 6 | 2 | no | — |
| 337 | #237 | — | 6 | 2 | no | — |
| 338 | #237 | — | 6 | 4 | no | — |
| 339 | #237 | — | 6 | 4 | no | — |
| 340 | #237 | — | 6 | 4 | no | — |
| 341 | #237 | — | 6 | 4 | no | — |
| 342 | D3×D4 | — | 6 | 2 | no | — |
| 343 | D3×D4 | — | 6 | 2 | no | — |
| 344 | D3×D4 | — | 6 | 2 | no | — |
| 345 | D3×D4 | — | 6 | 2 | no | — |
| 346 | D3×D4 | — | 6 | 4 | no | — |
| 347 | D3×D4 | — | 6 | 4 | no | — |
| 348 | D3×D4 | — | 6 | 4 | no | — |
| 349 | D3×D4 | — | 6 | 4 | no | — |
| 350 | #235 | — | 2 | 1 | no | — |
| 351 | #235 | — | 2 | 1 | no | — |
| 352 | #235 | — | 2 | 1 | no | — |
| 353 | #235 | — | 2 | 1 | no | — |
| 354 | #235 | — | 2 | 1 | no | — |
| 355 | #235 | — | 2 | 1 | no | — |
| 356 | #235 | — | 2 | 1 | no | — |
| 357 | #235 | — | 2 | 1 | no | — |
| 358 | #235 | — | 6 | 2 | no | — |
| 359 | #235 | — | 6 | 2 | no | — |
| 360 | #235 | — | 6 | 4 | no | — |
| 361 | #235 | — | 6 | 4 | no | — |
| 362 | #235 | — | 6 | 2 | no | — |
| 363 | #235 | — | 6 | 2 | no | — |
| 364 | #235 | — | 6 | 4 | no | — |
| 365 | #235 | — | 6 | 4 | no | — |
| 366 | #235 | — | 6 | 1 | no | — |
| 367 | #235 | — | 6 | 1 | no | — |
| 368 | #235 | — | 6 | 1 | no | — |
| 369 | #235 | — | 6 | 1 | no | — |
| 370 | #235 | — | 6 | 1 | no | — |
| 371 | #235 | — | 6 | 1 | no | — |
| 372 | #235 | — | 6 | 1 | no | — |
| 373 | #235 | — | 6 | 1 | no | — |
| 374 | #235 | — | 12 | 1 | no | — |
| 375 | #235 | — | 12 | 1 | no | — |
| 376 | #235 | — | 12 | 1 | no | — |
| 377 | #235 | — | 12 | 1 | no | — |
| 378 | C2×D12 | — | 2 | 2 | no | — |
| 379 | C2×D12 | — | 3 | 1 | no | — |
| 380 | C2×D12 | — | 3 | 1 | no | — |
| 381 | C2×D12 | — | 6 | 1 | no | — |
| 382 | C2×D12 | — | 6 | 2 | no | — |
| 383 | C2×D12 | — | 6 | 2 | no | — |
| 384 | C2×D12 | — | 6 | 2 | no | — |
| 385 | C2×D12 | D12 | 1 | 1 | yes | characteristic, complemented |
| 386 | C2×D12 | #67 | 1 | 1 | yes | characteristic, complemented |
| 387 | C2×C4×D3 | — | 2 | 1 | no | — |
| 388 | C2×C4×D3 | — | 2 | 1 | no | — |
| 389 | C2×C4×D3 | — | 2 | 1 | no | — |
| 390 | C2×C4×D3 | — | 2 | 1 | no | — |
| 391 | C2×C4×D3 | — | 2 | 1 | no | — |
| 392 | C2×C4×D3 | — | 2 | 1 | no | — |
| 393 | C2×C4×D3 | — | 3 | 2 | no | — |
| 394 | C2×C4×D3 | — | 3 | 2 | no | — |
| 395 | C2×C4×D3 | — | 6 | 2 | no | — |
| 396 | C2×C4×D3 | — | 6 | 4 | no | — |
| 397 | C2×C4×D3 | — | 6 | 4 | no | — |
| 398 | C2×C4×D3 | D12 | 1 | 2 | yes | complemented |
| 399 | C2×C4×D3 | #67 | 1 | 2 | yes | complemented |
| 400 | C2×Dic6 | — | 3 | 1 | no | — |
| 401 | C2×Dic6 | — | 3 | 1 | no | — |
| 402 | C2×Dic6 | — | 6 | 1 | no | — |
| 403 | C2×Dic6 | — | 6 | 2 | no | — |
| 404 | C2×Dic6 | — | 6 | 2 | no | — |
| 405 | C2×Dic6 | D12 | 1 | 1 | yes | characteristic, complemented |
| 406 | C2×Dic6 | #67 | 1 | 1 | yes | characteristic, complemented |
| 407 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 408 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 409 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 410 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 411 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 412 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 413 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 414 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 415 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 416 | C3×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 417 | C3×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 418 | C3×C42 | — | 2 | 1 | no | — |
| 419 | C3×C42 | — | 2 | 1 | no | — |
| 420 | C3×C42 | — | 4 | 1 | no | — |
| 421 | C3×C42 | — | 6 | 1 | no | — |
| 422 | #217 | — | 3 | 2 | no | — |
| 423 | #217 | — | 3 | 2 | no | — |
| 424 | #217 | — | 6 | 2 | no | — |
| 425 | #217 | — | 6 | 2 | no | — |
| 426 | #217 | — | 6 | 2 | no | — |
| 427 | #217 | — | 6 | 2 | no | — |
| 428 | #217 | C22×D3 | 1 | 2 | yes | — |
| 429 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 430 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 431 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 432 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 433 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 434 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 435 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 436 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 437 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 438 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 439 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 440 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 441 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 442 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 443 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 444 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 445 | C4×Dic3 | — | 2 | 1 | no | — |
| 446 | C4×Dic3 | — | 6 | 1 | no | — |
| 447 | C4×Dic3 | — | 6 | 1 | no | — |
| 448 | C4×Dic3 | — | 12 | 1 | no | — |
| 449 | C22×C32 | — | 4 | 1 | no | — |
| 450 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 451 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 452 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 453 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 454 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 455 | C2×C3×D3 | — | 2 | 2 | no | — |
| 456 | C2×C3×D3 | — | 2 | 2 | no | — |
| 457 | C2×C3×D3 | — | 2 | 2 | no | — |
| 458 | C2×C3×D3 | — | 2 | 2 | no | — |
| 459 | C2×C3×D3 | — | 2 | 2 | no | — |
| 460 | C2×C3×D3 | — | 4 | 1 | no | — |
| 461 | C2×C3×D3 | — | 4 | 1 | no | — |
| 462 | C2×C3×D3 | — | 4 | 1 | no | — |
| 463 | C2×C3×D3 | — | 4 | 1 | no | — |
| 464 | C2×C3×D3 | — | 4 | 2 | no | — |
| 465 | C2×C3×D3 | — | 4 | 2 | no | — |
| 466 | D32 | — | 8 | 4 | no | — |
| 467 | C32×C4 | — | 4 | 2 | no | — |
| 468 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 469 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 470 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 471 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 472 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 473 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 474 | C3×Dic3 | — | 2 | 2 | no | — |
| 475 | C3×Dic3 | — | 2 | 2 | no | — |
| 476 | C3×Dic3 | — | 4 | 2 | no | — |
| 477 | C3×Dic3 | — | 4 | 1 | no | — |
| 478 | 2−1+4 | — | 18 | 1 | no | — |
| 479 | 2−1+4 | — | 18 | 1 | no | — |
| 480 | 2−1+4 | — | 18 | 1 | no | — |
| 481 | H(5,𝔽2) | — | 9 | 4 | no | — |
| 482 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 483 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 484 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 485 | C2×#41 | — | 3 | 1 | no | — |
| 486 | C2×#41 | — | 3 | 1 | no | — |
| 487 | C2×#41 | — | 9 | 1 | no | — |
| 488 | C2×#41 | — | 18 | 2 | no | — |
| 489 | C2×#41 | — | 18 | 2 | no | — |
| 490 | C2×#41 | — | 18 | 2 | no | — |
| 491 | C23×C4 | — | 3 | 1 | no | — |
| 492 | #123 | — | 3 | 2 | no | — |
| 493 | #123 | — | 9 | 2 | no | — |
| 494 | #123 | — | 9 | 2 | no | — |
| 495 | C22⋊Q8 | — | 6 | 1 | no | — |
| 496 | C22⋊Q8 | — | 18 | 1 | no | — |
| 497 | C22⋊Q8 | — | 18 | 1 | no | — |
| 498 | #121 | — | 6 | 1 | no | — |
| 499 | #121 | — | 18 | 1 | no | — |
| 500 | #121 | — | 18 | 1 | no | — |
| 501 | #120 | — | 3 | 2 | no | — |
| 502 | #120 | — | 9 | 2 | no | — |
| 503 | #120 | — | 9 | 2 | no | — |
| 504 | C4×D4 | — | 6 | 2 | no | — |
| 505 | C4×D4 | — | 18 | 2 | no | — |
| 506 | C4×D4 | — | 18 | 2 | no | — |
| 507 | #117 | — | 3 | 1 | no | — |
| 508 | #117 | — | 9 | 1 | no | — |
| 509 | #117 | D32 | 1 | 1 | yes | characteristic, complemented |
| 510 | #99 | — | 3 | 4 | no | — |
| 511 | #99 | — | 9 | 4 | no | — |
| 512 | #99 | — | 9 | 4 | no | — |
| 513 | C23×C3 | — | 2 | 1 | no | — |
| 514 | C23×C3 | — | 3 | 2 | no | — |
| 515 | C23×C3 | — | 3 | 2 | no | — |
| 516 | C23×C3 | — | 6 | 1 | no | — |
| 517 | C23×C3 | — | 6 | 1 | no | — |
| 518 | C23×C3 | — | 6 | 1 | no | — |
| 519 | C23×C3 | — | 12 | 2 | no | — |
| 520 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 521 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 522 | C22×D3 | — | 2 | 1 | no | — |
| 523 | C22×D3 | — | 2 | 1 | no | — |
| 524 | C22×D3 | — | 2 | 1 | no | — |
| 525 | C22×D3 | — | 3 | 2 | no | — |
| 526 | C22×D3 | — | 3 | 2 | no | — |
| 527 | C22×D3 | — | 4 | 2 | no | — |
| 528 | C22×D3 | — | 6 | 2 | no | — |
| 529 | C22×D3 | — | 6 | 4 | no | — |
| 530 | C22×D3 | — | 6 | 4 | no | — |
| 531 | C22×D3 | C2×D12 | 1 | 2 | yes | — |
| 532 | C22×D3 | C2×#67 | 1 | 2 | yes | — |
| 533 | C3×Q8 | — | 6 | 1 | no | — |
| 534 | C3×Q8 | — | 6 | 1 | no | — |
| 535 | C3×Q8 | — | 6 | 1 | no | — |
| 536 | C3×Q8 | — | 6 | 1 | no | — |
| 537 | C3×D4 | — | 6 | 2 | no | — |
| 538 | C3×D4 | — | 6 | 2 | no | — |
| 539 | C3×D4 | — | 6 | 2 | no | — |
| 540 | C3×D4 | — | 6 | 2 | no | — |
| 541 | C3×D4 | — | 6 | 1 | no | — |
| 542 | C3×D4 | — | 6 | 1 | no | — |
| 543 | C3×D4 | — | 6 | 1 | no | — |
| 544 | C3×D4 | — | 6 | 1 | no | — |
| 545 | C3×D4 | — | 12 | 4 | no | — |
| 546 | C2×C3×C4 | — | 2 | 2 | no | — |
| 547 | C2×C3×C4 | — | 2 | 2 | no | — |
| 548 | C2×C3×C4 | — | 2 | 1 | no | — |
| 549 | C2×C3×C4 | — | 2 | 1 | no | — |
| 550 | C2×C3×C4 | — | 2 | 1 | no | — |
| 551 | C2×C3×C4 | — | 2 | 1 | no | — |
| 552 | C2×C3×C4 | — | 2 | 1 | no | — |
| 553 | C2×C3×C4 | — | 2 | 1 | no | — |
| 554 | C2×C3×C4 | — | 3 | 2 | no | — |
| 555 | C2×C3×C4 | — | 3 | 2 | no | — |
| 556 | C2×C3×C4 | — | 4 | 2 | no | — |
| 557 | C2×C3×C4 | — | 6 | 2 | no | — |
| 558 | C2×C3×C4 | — | 6 | 2 | no | — |
| 559 | C2×C3×C4 | — | 6 | 2 | no | — |
| 560 | C2×C3×C4 | — | 6 | 2 | no | — |
| 561 | C2×C3×C4 | — | 6 | 1 | no | — |
| 562 | C2×C3×C4 | — | 6 | 1 | no | — |
| 563 | C2×C3×C4 | — | 6 | 2 | no | — |
| 564 | C2×C3×C4 | — | 6 | 1 | no | — |
| 565 | C2×C3×C4 | — | 12 | 1 | no | — |
| 566 | C2×C3×C4 | — | 12 | 1 | no | — |
| 567 | C2×C3×C4 | — | 12 | 1 | no | — |
| 568 | C2×C3×C4 | — | 12 | 1 | no | — |
| 569 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 570 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 571 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 572 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 573 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 574 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 575 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 576 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 577 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 578 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 579 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 580 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 581 | #67 | — | 2 | 2 | no | — |
| 582 | #67 | — | 2 | 2 | no | — |
| 583 | #67 | — | 2 | 2 | no | — |
| 584 | #67 | — | 2 | 2 | no | — |
| 585 | #67 | — | 6 | 4 | no | — |
| 586 | #67 | — | 6 | 4 | no | — |
| 587 | #67 | — | 6 | 4 | no | — |
| 588 | #67 | — | 6 | 4 | no | — |
| 589 | #67 | — | 6 | 2 | no | — |
| 590 | #67 | — | 6 | 2 | no | — |
| 591 | #67 | — | 6 | 2 | no | — |
| 592 | #67 | — | 6 | 2 | no | — |
| 593 | #67 | — | 12 | 2 | no | — |
| 594 | #67 | — | 12 | 2 | no | — |
| 595 | #67 | — | 12 | 4 | no | — |
| 596 | #67 | — | 12 | 4 | no | — |
| 597 | #67 | — | 12 | 4 | no | — |
| 598 | C2×Dic3 | — | 2 | 2 | no | — |
| 599 | C2×Dic3 | — | 2 | 1 | no | — |
| 600 | C2×Dic3 | — | 2 | 1 | no | — |
| 601 | C2×Dic3 | — | 2 | 1 | no | — |
| 602 | C2×Dic3 | — | 3 | 2 | no | — |
| 603 | C2×Dic3 | — | 3 | 2 | no | — |
| 604 | C2×Dic3 | — | 6 | 2 | no | — |
| 605 | C2×Dic3 | — | 6 | 4 | no | — |
| 606 | C2×Dic3 | — | 6 | 4 | no | — |
| 607 | C2×Dic3 | — | 6 | 2 | no | — |
| 608 | C2×Dic3 | — | 6 | 2 | no | — |
| 609 | C2×Dic3 | — | 12 | 2 | no | — |
| 610 | C2×Dic3 | C2×D12 | 1 | 2 | yes | — |
| 611 | C2×Dic3 | C2×#67 | 1 | 2 | yes | — |
| 612 | D12 | — | 2 | 1 | no | — |
| 613 | D12 | — | 2 | 1 | no | — |
| 614 | D12 | — | 2 | 1 | no | — |
| 615 | D12 | — | 2 | 1 | no | — |
| 616 | D12 | — | 4 | 4 | no | — |
| 617 | D12 | — | 6 | 4 | no | — |
| 618 | D12 | — | 6 | 4 | no | — |
| 619 | D12 | — | 6 | 1 | no | — |
| 620 | D12 | — | 6 | 1 | no | — |
| 621 | D12 | — | 6 | 1 | no | — |
| 622 | D12 | — | 6 | 1 | no | — |
| 623 | D12 | — | 12 | 1 | no | — |
| 624 | D12 | — | 12 | 1 | no | — |
| 625 | D12 | — | 12 | 4 | no | — |
| 626 | C4×D3 | — | 2 | 2 | no | — |
| 627 | C4×D3 | — | 2 | 2 | no | — |
| 628 | C4×D3 | — | 2 | 2 | no | — |
| 629 | C4×D3 | — | 2 | 2 | no | — |
| 630 | C4×D3 | — | 4 | 1 | no | — |
| 631 | C4×D3 | — | 4 | 1 | no | — |
| 632 | C4×D3 | — | 4 | 1 | no | — |
| 633 | C4×D3 | — | 4 | 1 | no | — |
| 634 | C4×D3 | — | 6 | 4 | no | — |
| 635 | C4×D3 | — | 6 | 4 | no | — |
| 636 | C4×D3 | — | 6 | 4 | no | — |
| 637 | C4×D3 | — | 6 | 4 | no | — |
| 638 | C4×D3 | — | 6 | 2 | no | — |
| 639 | C4×D3 | — | 6 | 2 | no | — |
| 640 | C4×D3 | — | 6 | 2 | no | — |
| 641 | C4×D3 | — | 6 | 2 | no | — |
| 642 | C4×D3 | — | 12 | 2 | no | — |
| 643 | C4×D3 | — | 12 | 2 | no | — |
| 644 | Dic6 | — | 2 | 1 | no | — |
| 645 | Dic6 | — | 2 | 1 | no | — |
| 646 | Dic6 | — | 2 | 1 | no | — |
| 647 | Dic6 | — | 2 | 1 | no | — |
| 648 | Dic6 | — | 6 | 4 | no | — |
| 649 | Dic6 | — | 6 | 4 | no | — |
| 650 | Dic6 | — | 6 | 1 | no | — |
| 651 | Dic6 | — | 6 | 1 | no | — |
| 652 | Dic6 | — | 6 | 1 | no | — |
| 653 | Dic6 | — | 6 | 1 | no | — |
| 654 | Dic6 | — | 12 | 1 | no | — |
| 655 | Dic6 | — | 12 | 1 | no | — |
| 656 | C2×C32 | — | 2 | 1 | no | — |
| 657 | C2×C32 | — | 2 | 1 | no | — |
| 658 | C2×C32 | — | 2 | 1 | no | — |
| 659 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 660 | C3⋊D3 | — | 4 | 2 | no | — |
| 661 | C3×D3 | — | 4 | 2 | no | — |
| 662 | C3×D3 | — | 4 | 2 | no | — |
| 663 | C3×D3 | — | 4 | 2 | no | — |
| 664 | C24 | — | 3 | 1 | no | — |
| 665 | #41 | — | 6 | 1 | no | — |
| 666 | #41 | — | 6 | 1 | no | — |
| 667 | #41 | — | 6 | 1 | no | — |
| 668 | #41 | — | 6 | 1 | no | — |
| 669 | #41 | — | 6 | 1 | no | — |
| 670 | #41 | — | 6 | 1 | no | — |
| 671 | #41 | — | 6 | 1 | no | — |
| 672 | #41 | — | 6 | 1 | no | — |
| 673 | #41 | — | 18 | 4 | no | — |
| 674 | #41 | — | 18 | 4 | no | — |
| 675 | #41 | — | 18 | 4 | no | — |
| 676 | #41 | — | 18 | 2 | no | — |
| 677 | #41 | — | 18 | 2 | no | — |
| 678 | #41 | — | 18 | 2 | no | — |
| 679 | #41 | — | 18 | 2 | no | — |
| 680 | #41 | — | 18 | 4 | no | — |
| 681 | #41 | — | 18 | 2 | no | — |
| 682 | #41 | — | 18 | 2 | no | — |
| 683 | #41 | — | 18 | 1 | no | — |
| 684 | #41 | — | 18 | 1 | no | — |
| 685 | #41 | — | 18 | 1 | no | — |
| 686 | #41 | — | 18 | 1 | no | — |
| 687 | C2×Q8 | — | 3 | 1 | no | — |
| 688 | C2×Q8 | — | 3 | 1 | no | — |
| 689 | C2×Q8 | — | 9 | 1 | no | — |
| 690 | C2×Q8 | — | 18 | 2 | no | — |
| 691 | C2×Q8 | — | 18 | 2 | no | — |
| 692 | C2×Q8 | — | 18 | 2 | no | — |
| 693 | C2×D4 | — | 3 | 2 | no | — |
| 694 | C2×D4 | — | 3 | 2 | no | — |
| 695 | C2×D4 | — | 3 | 1 | no | — |
| 696 | C2×D4 | — | 3 | 1 | no | — |
| 697 | C2×D4 | — | 6 | 2 | no | — |
| 698 | C2×D4 | — | 9 | 2 | no | — |
| 699 | C2×D4 | — | 9 | 1 | no | — |
| 700 | C2×D4 | — | 18 | 2 | no | — |
| 701 | C2×D4 | — | 18 | 2 | no | — |
| 702 | C2×D4 | — | 18 | 2 | no | — |
| 703 | C2×D4 | — | 18 | 4 | no | — |
| 704 | C2×D4 | — | 18 | 2 | no | — |
| 705 | C2×D4 | — | 18 | 4 | no | — |
| 706 | C2×D4 | — | 18 | 4 | no | — |
| 707 | C2×D4 | — | 18 | 2 | no | — |
| 708 | C22×C4 | — | 3 | 2 | no | — |
| 709 | C22×C4 | — | 3 | 2 | no | — |
| 710 | C22×C4 | — | 3 | 1 | no | — |
| 711 | C22×C4 | — | 6 | 1 | no | — |
| 712 | C22×C4 | — | 6 | 1 | no | — |
| 713 | C22×C4 | — | 6 | 1 | no | — |
| 714 | C22×C4 | — | 6 | 1 | no | — |
| 715 | C22×C4 | — | 6 | 1 | no | — |
| 716 | C22×C4 | — | 6 | 1 | no | — |
| 717 | C22×C4 | — | 9 | 2 | no | — |
| 718 | C22×C4 | — | 18 | 4 | no | — |
| 719 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 720 | C4⋊C4 | — | 2 | 1 | no | — |
| 721 | C4⋊C4 | — | 6 | 2 | no | — |
| 722 | C4⋊C4 | — | 6 | 1 | no | — |
| 723 | C4⋊C4 | — | 18 | 2 | no | — |
| 724 | C4⋊C4 | — | 18 | 2 | no | — |
| 725 | C4⋊C4 | — | 18 | 1 | no | — |
| 726 | C22⋊C4 | — | 3 | 2 | no | — |
| 727 | C22⋊C4 | — | 6 | 2 | no | — |
| 728 | C22⋊C4 | — | 6 | 2 | no | — |
| 729 | C22⋊C4 | — | 9 | 2 | no | — |
| 730 | C22⋊C4 | — | 18 | 2 | no | — |
| 731 | C22⋊C4 | — | 18 | 2 | no | — |
| 732 | C22⋊C4 | — | 18 | 2 | no | — |
| 733 | C22⋊C4 | — | 18 | 2 | no | — |
| 734 | C22⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 735 | C42 | — | 2 | 1 | no | — |
| 736 | C42 | — | 6 | 1 | no | — |
| 737 | C42 | — | 18 | 1 | no | — |
| 738 | C22×C3 | — | 2 | 1 | no | — |
| 739 | C22×C3 | — | 2 | 1 | no | — |
| 740 | C22×C3 | — | 2 | 1 | no | — |
| 741 | C22×C3 | — | 4 | 1 | no | — |
| 742 | C22×C3 | — | 4 | 1 | no | — |
| 743 | C22×C3 | — | 6 | 2 | no | — |
| 744 | C22×C3 | — | 6 | 2 | no | — |
| 745 | C22×C3 | — | 6 | 2 | no | — |
| 746 | C22×C3 | — | 6 | 2 | no | — |
| 747 | C22×C3 | — | 6 | 2 | no | — |
| 748 | C22×C3 | — | 8 | 1 | no | — |
| 749 | C22×C3 | — | 12 | 2 | no | — |
| 750 | C22×C3 | — | 12 | 2 | no | — |
| 751 | C22×C3 | — | 12 | 1 | no | — |
| 752 | C22×C3 | — | 12 | 1 | no | — |
| 753 | C22×C3 | — | 12 | 1 | no | — |
| 754 | C22×C3 | — | 12 | 1 | no | — |
| 755 | C22×C3 | C22×D12 | 1 | 1 | yes | characteristic |
| 756 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 757 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 758 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 759 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 760 | C22×C3 | C22×#67 | 1 | 1 | yes | characteristic |
| 761 | C2×D3 | — | 2 | 2 | no | — |
| 762 | C2×D3 | — | 2 | 2 | no | — |
| 763 | C2×D3 | — | 2 | 2 | no | — |
| 764 | C2×D3 | — | 2 | 2 | no | — |
| 765 | C2×D3 | — | 2 | 2 | no | — |
| 766 | C2×D3 | — | 4 | 1 | no | — |
| 767 | C2×D3 | — | 4 | 1 | no | — |
| 768 | C2×D3 | — | 4 | 1 | no | — |
| 769 | C2×D3 | — | 4 | 1 | no | — |
| 770 | C2×D3 | — | 4 | 2 | no | — |
| 771 | C2×D3 | — | 4 | 2 | no | — |
| 772 | C2×D3 | — | 6 | 2 | no | — |
| 773 | C2×D3 | — | 6 | 2 | no | — |
| 774 | C2×D3 | — | 12 | 2 | no | — |
| 775 | C2×D3 | — | 12 | 2 | no | — |
| 776 | C2×D3 | — | 12 | 2 | no | — |
| 777 | C2×D3 | — | 24 | 2 | no | — |
| 778 | C2×D3 | — | 24 | 4 | no | — |
| 779 | C2×D3 | — | 24 | 4 | no | — |
| 780 | C3×C4 | — | 2 | 1 | no | — |
| 781 | C3×C4 | — | 2 | 1 | no | — |
| 782 | C3×C4 | — | 2 | 1 | no | — |
| 783 | C3×C4 | — | 2 | 1 | no | — |
| 784 | C3×C4 | — | 4 | 2 | no | — |
| 785 | C3×C4 | — | 4 | 2 | no | — |
| 786 | C3×C4 | — | 6 | 2 | no | — |
| 787 | C3×C4 | — | 6 | 2 | no | — |
| 788 | C3×C4 | — | 8 | 2 | no | — |
| 789 | C3×C4 | — | 12 | 2 | no | — |
| 790 | C3×C4 | — | 12 | 1 | no | — |
| 791 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 792 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 793 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 794 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 795 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 796 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 797 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 798 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 799 | Dic3 | — | 2 | 2 | no | — |
| 800 | Dic3 | — | 2 | 2 | no | — |
| 801 | Dic3 | — | 4 | 2 | no | — |
| 802 | Dic3 | — | 4 | 1 | no | — |
| 803 | Dic3 | — | 6 | 2 | no | — |
| 804 | Dic3 | — | 6 | 2 | no | — |
| 805 | Dic3 | — | 12 | 2 | no | — |
| 806 | Dic3 | — | 12 | 2 | no | — |
| 807 | Dic3 | — | 12 | 2 | no | — |
| 808 | Dic3 | — | 24 | 2 | no | — |
| 809 | C32 | #3025 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 810 | C23 | — | 3 | 2 | no | — |
| 811 | C23 | — | 3 | 2 | no | — |
| 812 | C23 | — | 6 | 1 | no | — |
| 813 | C23 | — | 6 | 1 | no | — |
| 814 | C23 | — | 6 | 1 | no | — |
| 815 | C23 | — | 9 | 2 | no | — |
| 816 | C23 | — | 12 | 2 | no | — |
| 817 | C23 | — | 18 | 4 | no | — |
| 818 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 819 | Q8 | — | 6 | 1 | no | — |
| 820 | Q8 | — | 6 | 1 | no | — |
| 821 | Q8 | — | 6 | 1 | no | — |
| 822 | Q8 | — | 6 | 1 | no | — |
| 823 | Q8 | — | 18 | 4 | no | — |
| 824 | Q8 | — | 18 | 1 | no | — |
| 825 | Q8 | — | 18 | 1 | no | — |
| 826 | D4 | — | 6 | 2 | no | — |
| 827 | D4 | — | 6 | 2 | no | — |
| 828 | D4 | — | 6 | 2 | no | — |
| 829 | D4 | — | 6 | 2 | no | — |
| 830 | D4 | — | 6 | 1 | no | — |
| 831 | D4 | — | 6 | 1 | no | — |
| 832 | D4 | — | 6 | 1 | no | — |
| 833 | D4 | — | 6 | 1 | no | — |
| 834 | D4 | — | 12 | 4 | no | — |
| 835 | D4 | — | 18 | 4 | no | — |
| 836 | D4 | — | 18 | 4 | no | — |
| 837 | D4 | — | 18 | 4 | no | — |
| 838 | D4 | — | 18 | 2 | no | — |
| 839 | D4 | — | 18 | 2 | no | — |
| 840 | D4 | — | 18 | 1 | no | — |
| 841 | D4 | — | 18 | 1 | no | — |
| 842 | D4 | — | 36 | 4 | no | — |
| 843 | D4 | — | 36 | 4 | no | — |
| 844 | C2×C4 | — | 2 | 2 | no | — |
| 845 | C2×C4 | — | 3 | 2 | no | — |
| 846 | C2×C4 | — | 3 | 2 | no | — |
| 847 | C2×C4 | — | 6 | 2 | no | — |
| 848 | C2×C4 | — | 6 | 2 | no | — |
| 849 | C2×C4 | — | 6 | 2 | no | — |
| 850 | C2×C4 | — | 6 | 2 | no | — |
| 851 | C2×C4 | — | 6 | 1 | no | — |
| 852 | C2×C4 | — | 6 | 2 | no | — |
| 853 | C2×C4 | — | 6 | 1 | no | — |
| 854 | C2×C4 | — | 6 | 1 | no | — |
| 855 | C2×C4 | — | 9 | 2 | no | — |
| 856 | C2×C4 | — | 12 | 1 | no | — |
| 857 | C2×C4 | — | 12 | 1 | no | — |
| 858 | C2×C4 | — | 12 | 1 | no | — |
| 859 | C2×C4 | — | 12 | 1 | no | — |
| 860 | C2×C4 | — | 18 | 4 | no | — |
| 861 | C2×C4 | — | 18 | 4 | no | — |
| 862 | C2×C4 | — | 18 | 4 | no | — |
| 863 | C2×C4 | — | 18 | 2 | no | — |
| 864 | C2×C4 | — | 18 | 2 | no | — |
| 865 | C2×C4 | — | 18 | 2 | no | — |
| 866 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 867 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 868 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 869 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 870 | C2×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 871 | C2×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 872 | C2×C3 | — | 2 | 1 | no | — |
| 873 | C2×C3 | — | 2 | 1 | no | — |
| 874 | C2×C3 | — | 2 | 1 | no | — |
| 875 | C2×C3 | — | 2 | 1 | no | — |
| 876 | C2×C3 | — | 2 | 1 | no | — |
| 877 | C2×C3 | — | 2 | 1 | no | — |
| 878 | C2×C3 | — | 2 | 1 | no | — |
| 879 | C2×C3 | — | 4 | 1 | no | — |
| 880 | C2×C3 | — | 4 | 1 | no | — |
| 881 | C2×C3 | — | 4 | 1 | no | — |
| 882 | C2×C3 | — | 12 | 2 | no | — |
| 883 | C2×C3 | — | 12 | 2 | no | — |
| 884 | C2×C3 | — | 12 | 2 | no | — |
| 885 | C2×C3 | C2×#882 | 1 | 1 | yes | characteristic |
| 886 | C2×C3 | C2×#937 | 1 | 1 | yes | characteristic |
| 887 | D3 | — | 4 | 2 | no | — |
| 888 | D3 | — | 4 | 2 | no | — |
| 889 | D3 | — | 4 | 2 | no | — |
| 890 | D3 | — | 12 | 2 | no | — |
| 891 | D3 | — | 12 | 2 | no | — |
| 892 | D3 | — | 24 | 2 | no | — |
| 893 | C22 | — | 4 | 1 | no | — |
| 894 | C22 | — | 6 | 2 | no | — |
| 895 | C22 | — | 6 | 2 | no | — |
| 896 | C22 | — | 6 | 2 | no | — |
| 897 | C22 | — | 6 | 2 | no | — |
| 898 | C22 | — | 6 | 2 | no | — |
| 899 | C22 | — | 12 | 2 | no | — |
| 900 | C22 | — | 12 | 2 | no | — |
| 901 | C22 | — | 12 | 1 | no | — |
| 902 | C22 | — | 12 | 1 | no | — |
| 903 | C22 | — | 12 | 1 | no | — |
| 904 | C22 | — | 12 | 1 | no | — |
| 905 | C22 | — | 18 | 2 | no | — |
| 906 | C22 | — | 36 | 2 | no | — |
| 907 | C22 | — | 72 | 4 | no | — |
| 908 | C22 | C2×D3×D12 | 1 | 1 | yes | characteristic |
| 909 | C22 | C2×#3802 | 1 | 1 | yes | characteristic |
| 910 | C22 | C2×D3×#67 | 1 | 1 | yes | characteristic |
| 911 | C4 | — | 4 | 2 | no | — |
| 912 | C4 | — | 6 | 2 | no | — |
| 913 | C4 | — | 6 | 2 | no | — |
| 914 | C4 | — | 12 | 2 | no | — |
| 915 | C4 | — | 12 | 1 | no | — |
| 916 | C4 | — | 18 | 2 | no | — |
| 917 | C4 | — | 36 | 2 | no | — |
| 918 | C4 | #63922 | 1 | 1 | yes | characteristic |
| 919 | C4 | #63922 | 1 | 1 | yes | characteristic |
| 920 | C4 | #63922 | 1 | 1 | yes | characteristic |
| 921 | C4 | #63922 | 1 | 1 | yes | characteristic |
| 922 | C3 | — | 2 | 1 | no | — |
| 923 | C3 | #78690 | 1 | 1 | yes | characteristic, complemented |
| 924 | C3 | #82936 | 1 | 1 | yes | characteristic, complemented |
| 925 | C2 | — | 2 | 1 | no | — |
| 926 | C2 | — | 2 | 1 | no | — |
| 927 | C2 | — | 2 | 1 | no | — |
| 928 | C2 | — | 12 | 2 | no | — |
| 929 | C2 | — | 12 | 2 | no | — |
| 930 | C2 | — | 12 | 2 | no | — |
| 931 | C2 | — | 36 | 2 | no | — |
| 932 | C2 | C2×#63922 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #63922 |
| commutator, cosocle | C23×C32 | C24 |
| Frattini | C23 | C22×D32 |
| Fitting | C32×#117 | C22 |
| socle | C2×C32 | C2×#120 |
| hypercenter | #117 | D32 |
| hypocenter | C32 | #3025 |
| LCS | G ▷ C23×C32 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596669 | C2 | semidirect |
| 2. C3×#5524 | C2 | semidirect |
| 3. #10595023 | C2 | semidirect |
| 4. #10595022 | C2 | semidirect |
| 5. #10592705 | C2 | semidirect |
| 6. C3×#5006 | C2 | semidirect |
| 7. #10591231 | C2 | semidirect |
| 8. #10590408 | C2 | semidirect |
| 9. #10590407 | C2 | semidirect |
| 15. C22×C3×C4×D3 | C22 | semidirect |
| 26. C32×#117 | C22 | semidirect |
| 27. #64135 | C22 | semidirect |
| 28. C3×#926 | C22 | semidirect |
| 31. C3×#886 | C22 | semidirect |
| 32. C3×#882 | C22 | semidirect |
| 34. #63977 | C22 | semidirect |
| 35. #63976 | C22 | semidirect |
| 36. #63966 | C22 | semidirect |
| 37. #63961 | C22 | semidirect |
| 44. #63633 | C22 | semidirect |
| 45. C3×#806 | C22 | semidirect |
| 46. #63580 | C22 | semidirect |
| 54. #5524 | D3 | semidirect |
| 63. #5006 | D3 | semidirect |
| 73. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 74. C2×C4×C3⋊D3 | D4 | semidirect |
| 75. C2×#634 | D4 | semidirect |
| 88. C2×C3×D12 | D4 | semidirect |
| 89. C2×C3×D12 | D4 | semidirect |
| 96. C2×C3×C4×D3 | D4 | semidirect |
| 97. C2×C3×C4×D3 | D4 | semidirect |
| 98. C2×C3×Dic6 | D4 | semidirect |
| 99. C2×C3×Dic6 | D4 | semidirect |
| 169. C22×C4×D3 | C2×D3 | semidirect |
| 177. C3×#117 | C2×D3 | semidirect |
| 178. C3×#117 | C2×D3 | semidirect |
| 195. #926 | C2×D3 | semidirect |
| 203. #886 | C2×D3 | semidirect |
| 205. #882 | C2×D3 | semidirect |
| 214. #806 | C2×D3 | semidirect |
| 385. C2×D12 | D12 | semidirect |
| 386. C2×D12 | #67 | semidirect |
| 398. C2×C4×D3 | D12 | semidirect |
| 399. C2×C4×D3 | #67 | semidirect |
| 405. C2×Dic6 | D12 | semidirect |
| 406. C2×Dic6 | #67 | semidirect |
| 509. #117 | D32 | semidirect |
| 809. C32 | #3025 | semidirect |
| 923. C3 | #78690 | semidirect |
| 924. C3 | #82936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596669 | 2 |
| C3×#5524 | 2 |
| #10595023 | 2 |
| #10595022 | 2 |
| #10592705 | 2 |
| C3×#5006 | 2 |
| #10591231 | 2 |
| #10590408 | 2 |
| #10590407 | 2 |
| #82936 | 3 |
| #78690 | 3 |