Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7180 conjugacy classes of subgroups.
The subgroup lattice has 811 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62916 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62463 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | #62453 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #62440 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #62431 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #62420 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #62415 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #61402 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #61393 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#3391 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #61093 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #61089 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #61084 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #60832 | C2 | 1 | 6 | yes | maximal, complemented |
| 15 | #60695 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | #60647 | C2 | 1 | 3 | yes | maximal, complemented |
| 17 | #60218 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | C2×#576 | C22 | 1 | 6 | yes | complemented |
| 19 | C2×#576 | C22 | 1 | 6 | yes | complemented |
| 20 | #3546 | — | 2 | 6 | no | — |
| 21 | #3546 | C22 | 1 | 12 | yes | complemented |
| 22 | #3543 | — | 2 | 6 | no | — |
| 23 | #3543 | C22 | 1 | 12 | yes | complemented |
| 24 | #3537 | — | 2 | 12 | no | — |
| 25 | #3517 | — | 2 | 2 | no | — |
| 26 | #3517 | C22 | 1 | 4 | yes | complemented |
| 27 | #3498 | — | 2 | 2 | no | — |
| 28 | #3498 | C22 | 1 | 6 | yes | complemented |
| 29 | #3498 | C22 | 1 | 4 | yes | complemented |
| 30 | #3498 | C22 | 1 | 6 | yes | complemented |
| 31 | #3496 | C22 | 1 | 6 | yes | complemented |
| 32 | #3488 | — | 2 | 4 | no | — |
| 33 | #3480 | C22 | 1 | 1 | yes | characteristic |
| 34 | #3480 | C22 | 1 | 2 | yes | complemented |
| 35 | C2×#550 | C22 | 1 | 2 | yes | complemented |
| 36 | #3460 | C22 | 1 | 6 | yes | complemented |
| 37 | #3399 | C22 | 1 | 12 | yes | complemented |
| 38 | #3397 | C22 | 1 | 12 | yes | complemented |
| 39 | #3396 | C22 | 1 | 3 | yes | complemented |
| 40 | #3395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #3394 | C22 | 1 | 6 | yes | complemented |
| 42 | #3393 | C22 | 1 | 3 | yes | complemented |
| 43 | #3392 | C22 | 1 | 2 | yes | complemented |
| 44 | #3392 | C22 | 1 | 4 | yes | complemented |
| 45 | #3391 | C22 | 1 | 2 | yes | complemented |
| 46 | #3391 | C22 | 1 | 6 | yes | complemented |
| 47 | #3391 | C22 | 1 | 2 | yes | complemented |
| 48 | #3391 | C22 | 1 | 6 | yes | complemented |
| 49 | #3391 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #3391 | C22 | 1 | 4 | yes | complemented |
| 51 | #3287 | C22 | 1 | 6 | yes | complemented |
| 52 | #3287 | C22 | 1 | 6 | yes | complemented |
| 53 | #3284 | C22 | 1 | 12 | yes | complemented |
| 54 | #3283 | C22 | 1 | 6 | yes | complemented |
| 55 | #3280 | C22 | 1 | 12 | yes | complemented |
| 56 | D4×D8 | C22 | 1 | 6 | yes | complemented |
| 57 | D4×D8 | C22 | 1 | 6 | yes | complemented |
| 58 | D4×D8 | C22 | 1 | 6 | yes | complemented |
| 59 | D4×D8 | C22 | 1 | 12 | yes | complemented |
| 60 | #3274 | C22 | 1 | 12 | yes | complemented |
| 61 | #3274 | C22 | 1 | 12 | yes | complemented |
| 62 | #3274 | C22 | 1 | 12 | yes | complemented |
| 63 | #3273 | C22 | 1 | 12 | yes | complemented |
| 64 | #3272 | C22 | 1 | 12 | yes | complemented |
| 65 | #3272 | C22 | 1 | 12 | yes | complemented |
| 66 | #3268 | C22 | 1 | 24 | yes | complemented |
| 67 | #3264 | C22 | 1 | 24 | yes | complemented |
| 68 | #3224 | C22 | 1 | 24 | yes | complemented |
| 69 | #3220 | C22 | 1 | 24 | yes | complemented |
| 70 | #3217 | C22 | 1 | 12 | yes | complemented |
| 71 | #3214 | C22 | 1 | 12 | yes | complemented |
| 72 | #3212 | C22 | 1 | 12 | yes | complemented |
| 73 | #3205 | C22 | 1 | 12 | yes | complemented |
| 74 | #3179 | C22 | 1 | 12 | yes | complemented |
| 75 | #3176 | C22 | 1 | 6 | yes | complemented |
| 76 | #3175 | C22 | 1 | 6 | yes | complemented |
| 77 | #3171 | C22 | 1 | 12 | yes | complemented |
| 78 | #3169 | C22 | 1 | 6 | yes | complemented |
| 79 | #3168 | C22 | 1 | 6 | yes | complemented |
| 80 | #3164 | C22 | 1 | 1 | yes | characteristic, complemented |
| 81 | #3155 | C22 | 1 | 3 | yes | complemented |
| 82 | #3155 | C22 | 1 | 6 | yes | complemented |
| 83 | #3155 | C22 | 1 | 12 | yes | complemented |
| 84 | #3155 | C22 | 1 | 12 | yes | complemented |
| 85 | #3151 | C22 | 1 | 6 | yes | complemented |
| 86 | #3151 | C22 | 1 | 12 | yes | complemented |
| 87 | #3147 | C22 | 1 | 3 | yes | complemented |
| 88 | #3147 | C22 | 1 | 6 | yes | complemented |
| 89 | C2×#493 | C22 | 1 | 3 | yes | complemented |
| 90 | C2×#493 | C22 | 1 | 6 | yes | complemented |
| 91 | #3136 | C22 | 1 | 6 | yes | complemented |
| 92 | #3062 | C22 | 1 | 6 | yes | complemented |
| 93 | #3061 | C22 | 1 | 3 | yes | complemented |
| 94 | #3058 | C22 | 1 | 3 | yes | complemented |
| 95 | #3038 | C22 | 1 | 6 | yes | complemented |
| 96 | #3036 | C22 | 1 | 6 | yes | complemented |
| 97 | #3035 | C22 | 1 | 6 | yes | complemented |
| 98 | C2×#459 | C22 | 1 | 6 | yes | complemented |
| 99 | #3012 | C22 | 1 | 12 | yes | complemented |
| 100 | #3008 | C22 | 1 | 12 | yes | complemented |
| 101 | #2971 | C22 | 1 | 2 | yes | complemented |
| 102 | #2969 | C22 | 1 | 6 | yes | complemented |
| 103 | #2966 | C22 | 1 | 6 | yes | complemented |
| 104 | C8×#41 | C22 | 1 | 2 | yes | complemented |
| 105 | Q8×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 106 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 107 | C4×AGL(1,ℤ/8) | C22 | 1 | 6 | yes | complemented |
| 108 | C4×#135 | C22 | 1 | 3 | yes | complemented |
| 109 | C2×C4×D8 | C22 | 1 | 3 | yes | complemented |
| 110 | #2935 | C22 | 1 | 3 | yes | complemented |
| 111 | #2931 | C22 | 1 | 3 | yes | complemented |
| 112 | #2925 | C22 | 1 | 3 | yes | complemented |
| 113 | C4×#131 | C22 | 1 | 3 | yes | complemented |
| 114 | C2×H(5,𝔽2) | — | 2 | 4 | no | — |
| 115 | C2×H(5,𝔽2) | C23 | 1 | 12 | yes | — |
| 116 | C22×#41 | — | 2 | 2 | no | — |
| 117 | #576 | — | 4 | 24 | no | — |
| 118 | #576 | — | 4 | 24 | no | — |
| 119 | C2×AGL(1,ℤ/8) | C23 | 1 | 6 | yes | — |
| 120 | C2×AGL(1,ℤ/8) | C23 | 1 | 12 | yes | — |
| 121 | C2×AGL(1,ℤ/8) | C23 | 1 | 24 | yes | — |
| 122 | C2×AGL(1,ℤ/8) | C23 | 1 | 24 | yes | — |
| 123 | C2×#135 | C23 | 1 | 3 | yes | — |
| 124 | C2×#135 | C23 | 1 | 6 | yes | — |
| 125 | C2×#135 | C23 | 1 | 12 | yes | — |
| 126 | C2×#135 | C23 | 1 | 12 | yes | — |
| 127 | C22×D8 | C23 | 1 | 3 | yes | — |
| 128 | C22×D8 | C23 | 1 | 6 | yes | — |
| 129 | C22×D8 | C23 | 1 | 12 | yes | — |
| 130 | C22×D8 | C23 | 1 | 12 | yes | — |
| 131 | C2×#131 | C23 | 1 | 3 | yes | — |
| 132 | C2×#131 | C23 | 1 | 3 | yes | — |
| 133 | #560 | — | 2 | 24 | no | — |
| 134 | #560 | — | 2 | 24 | no | — |
| 135 | #559 | D4 | 1 | 3 | yes | — |
| 136 | #559 | C23 | 1 | 6 | yes | — |
| 137 | #557 | D4 | 1 | 1 | yes | characteristic |
| 138 | #557 | C23 | 1 | 2 | yes | — |
| 139 | #556 | D4 | 1 | 3 | yes | — |
| 140 | #556 | C23 | 1 | 6 | yes | — |
| 141 | #553 | — | 2 | 12 | no | — |
| 142 | #553 | — | 2 | 12 | no | — |
| 143 | #553 | — | 2 | 6 | no | — |
| 144 | #553 | D4 | 1 | 6 | yes | — |
| 145 | #550 | — | 2 | 4 | no | — |
| 146 | #550 | — | 2 | 2 | no | — |
| 147 | #550 | — | 2 | 6 | no | — |
| 148 | #550 | — | 2 | 4 | no | — |
| 149 | #550 | — | 2 | 6 | no | — |
| 150 | #550 | — | 2 | 6 | no | — |
| 151 | #550 | D4 | 1 | 1 | yes | characteristic |
| 152 | #550 | C23 | 1 | 12 | yes | — |
| 153 | #550 | C23 | 1 | 12 | yes | — |
| 154 | #550 | C23 | 1 | 4 | yes | — |
| 155 | #550 | C23 | 1 | 2 | yes | — |
| 156 | #550 | C23 | 1 | 12 | yes | — |
| 157 | #548 | — | 2 | 2 | no | — |
| 158 | #548 | D4 | 1 | 2 | yes | — |
| 159 | #547 | — | 2 | 6 | no | — |
| 160 | #547 | C23 | 1 | 12 | yes | — |
| 161 | #546 | — | 2 | 12 | no | — |
| 162 | #546 | — | 2 | 12 | no | — |
| 163 | #546 | — | 2 | 12 | no | — |
| 164 | #546 | C23 | 1 | 24 | yes | — |
| 165 | D42 | — | 2 | 6 | no | — |
| 166 | D42 | — | 2 | 12 | no | — |
| 167 | D42 | — | 2 | 12 | no | — |
| 168 | D42 | — | 2 | 12 | no | — |
| 169 | D42 | — | 2 | 12 | no | — |
| 170 | D42 | — | 2 | 6 | no | — |
| 171 | D42 | — | 2 | 12 | no | — |
| 172 | D42 | — | 2 | 12 | no | — |
| 173 | D42 | — | 2 | 6 | no | — |
| 174 | D42 | C23 | 1 | 12 | yes | — |
| 175 | D42 | C23 | 1 | 12 | yes | — |
| 176 | D42 | C23 | 1 | 12 | yes | — |
| 177 | #544 | C23 | 1 | 2 | yes | — |
| 178 | #542 | — | 2 | 6 | no | — |
| 179 | #542 | C23 | 1 | 12 | yes | — |
| 180 | #540 | — | 2 | 12 | no | — |
| 181 | #540 | — | 2 | 6 | no | — |
| 182 | #540 | — | 2 | 12 | no | — |
| 183 | #540 | C23 | 1 | 12 | yes | — |
| 184 | #538 | — | 2 | 24 | no | — |
| 185 | #538 | — | 2 | 12 | no | — |
| 186 | #537 | — | 2 | 12 | no | — |
| 187 | #537 | C23 | 1 | 6 | yes | — |
| 188 | #535 | — | 2 | 12 | no | — |
| 189 | #535 | — | 2 | 12 | no | — |
| 190 | #535 | — | 2 | 12 | no | — |
| 191 | #535 | — | 2 | 12 | no | — |
| 192 | #535 | C23 | 1 | 6 | yes | — |
| 193 | #535 | C23 | 1 | 24 | yes | — |
| 194 | #535 | C23 | 1 | 6 | yes | — |
| 195 | #534 | — | 2 | 24 | no | — |
| 196 | #534 | — | 2 | 12 | no | — |
| 197 | #532 | — | 2 | 6 | no | — |
| 198 | #532 | — | 2 | 6 | no | — |
| 199 | #532 | C23 | 1 | 12 | yes | — |
| 200 | #532 | C23 | 1 | 6 | yes | — |
| 201 | #532 | C23 | 1 | 12 | yes | — |
| 202 | #532 | C23 | 1 | 3 | yes | — |
| 203 | C2×#127 | — | 2 | 6 | no | — |
| 204 | C2×#127 | C23 | 1 | 12 | yes | — |
| 205 | C2×#127 | C23 | 1 | 6 | yes | — |
| 206 | #529 | — | 2 | 6 | no | — |
| 207 | #529 | — | 2 | 6 | no | — |
| 208 | #529 | C23 | 1 | 12 | yes | — |
| 209 | #529 | C23 | 1 | 6 | yes | — |
| 210 | #525 | — | 2 | 12 | no | — |
| 211 | C2×#121 | — | 2 | 12 | no | — |
| 212 | C2×#121 | — | 2 | 6 | no | — |
| 213 | #520 | — | 2 | 4 | no | — |
| 214 | C4×#41 | — | 2 | 2 | no | — |
| 215 | C4×#41 | C23 | 1 | 6 | yes | — |
| 216 | C4×#41 | C23 | 1 | 2 | yes | — |
| 217 | C4×#41 | C23 | 1 | 3 | yes | — |
| 218 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 220 | #501 | C23 | 1 | 4 | yes | — |
| 221 | #500 | C23 | 1 | 2 | yes | — |
| 222 | #499 | C23 | 1 | 2 | yes | — |
| 223 | #496 | C23 | 1 | 24 | yes | — |
| 224 | #496 | C23 | 1 | 12 | yes | — |
| 225 | #496 | C23 | 1 | 24 | yes | — |
| 226 | #495 | C23 | 1 | 6 | yes | — |
| 227 | #495 | C23 | 1 | 6 | yes | — |
| 228 | #495 | C23 | 1 | 6 | yes | — |
| 229 | #495 | C23 | 1 | 12 | yes | — |
| 230 | #494 | C23 | 1 | 3 | yes | — |
| 231 | #493 | C23 | 1 | 6 | yes | — |
| 232 | #493 | C23 | 1 | 6 | yes | — |
| 233 | #493 | C23 | 1 | 6 | yes | — |
| 234 | #493 | C23 | 1 | 6 | yes | — |
| 235 | #493 | C23 | 1 | 3 | yes | — |
| 236 | #493 | C23 | 1 | 12 | yes | — |
| 237 | #493 | C23 | 1 | 6 | yes | — |
| 238 | #493 | C23 | 1 | 12 | yes | — |
| 239 | #492 | C23 | 1 | 6 | yes | — |
| 240 | #492 | C23 | 1 | 12 | yes | — |
| 241 | #490 | C23 | 1 | 12 | yes | — |
| 242 | #489 | C23 | 1 | 12 | yes | — |
| 243 | #488 | C23 | 1 | 12 | yes | — |
| 244 | #486 | C23 | 1 | 12 | yes | — |
| 245 | #469 | C23 | 1 | 12 | yes | — |
| 246 | #469 | C23 | 1 | 12 | yes | — |
| 247 | #468 | C23 | 1 | 12 | yes | — |
| 248 | #468 | C23 | 1 | 12 | yes | — |
| 249 | #467 | C23 | 1 | 6 | yes | — |
| 250 | #466 | C23 | 1 | 6 | yes | — |
| 251 | #466 | C23 | 1 | 6 | yes | — |
| 252 | #466 | C23 | 1 | 6 | yes | — |
| 253 | #466 | C23 | 1 | 12 | yes | — |
| 254 | #465 | C23 | 1 | 12 | yes | — |
| 255 | #464 | C23 | 1 | 12 | yes | — |
| 256 | #463 | C23 | 1 | 12 | yes | — |
| 257 | #463 | C23 | 1 | 24 | yes | — |
| 258 | #462 | C23 | 1 | 6 | yes | — |
| 259 | #461 | C23 | 1 | 6 | yes | — |
| 260 | #461 | C23 | 1 | 12 | yes | — |
| 261 | #460 | C23 | 1 | 6 | yes | — |
| 262 | #460 | C23 | 1 | 12 | yes | — |
| 263 | #460 | C23 | 1 | 12 | yes | — |
| 264 | #459 | C23 | 1 | 12 | yes | — |
| 265 | #459 | C23 | 1 | 12 | yes | — |
| 266 | #459 | C23 | 1 | 24 | yes | — |
| 267 | #459 | C23 | 1 | 6 | yes | — |
| 268 | #459 | C23 | 1 | 12 | yes | — |
| 269 | #459 | C23 | 1 | 12 | yes | — |
| 270 | #459 | C23 | 1 | 12 | yes | — |
| 271 | #452 | C23 | 1 | 24 | yes | — |
| 272 | #450 | C23 | 1 | 24 | yes | — |
| 273 | #449 | C23 | 1 | 24 | yes | — |
| 274 | #449 | C23 | 1 | 24 | yes | — |
| 275 | #449 | C23 | 1 | 24 | yes | — |
| 276 | #447 | C23 | 1 | 24 | yes | — |
| 277 | #447 | C23 | 1 | 24 | yes | — |
| 278 | #447 | C23 | 1 | 24 | yes | — |
| 279 | #446 | C23 | 1 | 6 | yes | — |
| 280 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 281 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 282 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 283 | C8×Q8 | C23 | 1 | 3 | yes | — |
| 284 | C8×Q8 | C23 | 1 | 3 | yes | — |
| 285 | #442 | C23 | 1 | 12 | yes | — |
| 286 | #440 | C23 | 1 | 12 | yes | — |
| 287 | C4×Q16 | C23 | 1 | 3 | yes | — |
| 288 | C4×Q16 | C23 | 1 | 3 | yes | — |
| 289 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 290 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 291 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 292 | C4×D8 | C23 | 1 | 6 | yes | — |
| 293 | C4×D8 | C23 | 1 | 6 | yes | — |
| 294 | C4×D8 | C23 | 1 | 6 | yes | — |
| 295 | C4×D8 | C23 | 1 | 6 | yes | — |
| 296 | C4×D8 | C23 | 1 | 3 | yes | — |
| 297 | C4×D8 | C23 | 1 | 12 | yes | — |
| 298 | C4×D8 | C23 | 1 | 3 | yes | — |
| 299 | #436 | C23 | 1 | 6 | yes | — |
| 300 | #436 | C23 | 1 | 6 | yes | — |
| 301 | #436 | C23 | 1 | 6 | yes | — |
| 302 | #435 | C23 | 1 | 12 | yes | — |
| 303 | C8×D4 | C23 | 1 | 6 | yes | — |
| 304 | C8×D4 | C23 | 1 | 6 | yes | — |
| 305 | C8×D4 | C23 | 1 | 6 | yes | — |
| 306 | #433 | C23 | 1 | 12 | yes | — |
| 307 | #432 | C23 | 1 | 6 | yes | — |
| 308 | #431 | C23 | 1 | 6 | yes | — |
| 309 | #428 | C23 | 1 | 2 | yes | — |
| 310 | #427 | C23 | 1 | 1 | yes | characteristic |
| 311 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 312 | #423 | C23 | 1 | 3 | yes | — |
| 313 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 314 | #418 | C23 | 1 | 6 | yes | — |
| 315 | #417 | C23 | 1 | 6 | yes | — |
| 316 | #416 | C23 | 1 | 6 | yes | — |
| 317 | C2×#102 | C23 | 1 | 6 | yes | — |
| 318 | #408 | C23 | 1 | 6 | yes | — |
| 319 | #405 | C23 | 1 | 1 | yes | characteristic |
| 320 | #405 | C23 | 1 | 3 | yes | — |
| 321 | #405 | C23 | 1 | 6 | yes | — |
| 322 | #405 | C23 | 1 | 6 | yes | — |
| 323 | C4×M16 | C23 | 1 | 6 | yes | — |
| 324 | C4×M16 | C23 | 1 | 3 | yes | — |
| 325 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 326 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 327 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 328 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 329 | H(5,𝔽2) | — | 8 | 16 | no | — |
| 330 | C2×#41 | — | 2 | 2 | no | — |
| 331 | C2×#41 | — | 2 | 4 | no | — |
| 332 | C2×#41 | — | 2 | 12 | no | — |
| 333 | C2×#41 | — | 2 | 12 | no | — |
| 334 | C2×#41 | — | 2 | 12 | no | — |
| 335 | C2×#41 | — | 8 | 8 | no | — |
| 336 | C2×#41 | C2×D4 | 1 | 2 | yes | — |
| 337 | C2×#41 | C24 | 1 | 6 | yes | — |
| 338 | C2×#41 | C24 | 1 | 24 | yes | — |
| 339 | C2×#41 | C24 | 1 | 3 | yes | — |
| 340 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 341 | C22×D4 | — | 2 | 24 | no | — |
| 342 | C22×D4 | — | 2 | 12 | no | — |
| 343 | C22×D4 | — | 2 | 12 | no | — |
| 344 | C22×D4 | — | 2 | 12 | no | — |
| 345 | C22×D4 | — | 2 | 12 | no | — |
| 346 | C22×D4 | — | 2 | 6 | no | — |
| 347 | C22×D4 | — | 2 | 12 | no | — |
| 348 | C22×D4 | — | 2 | 6 | no | — |
| 349 | C22×D4 | — | 2 | 12 | no | — |
| 350 | C22×D4 | C24 | 1 | 6 | yes | — |
| 351 | C22×D4 | C24 | 1 | 24 | yes | — |
| 352 | C23×C4 | — | 2 | 6 | no | — |
| 353 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 354 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 355 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 356 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 357 | #135 | — | 2 | 12 | no | — |
| 358 | #135 | — | 4 | 24 | no | — |
| 359 | #135 | — | 4 | 24 | no | — |
| 360 | #135 | — | 4 | 12 | no | — |
| 361 | C2×Q16 | C24 | 1 | 3 | yes | — |
| 362 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 363 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 364 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 365 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 366 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 367 | C2×D8 | — | 2 | 12 | no | — |
| 368 | C2×D8 | — | 4 | 24 | no | — |
| 369 | C2×D8 | — | 4 | 24 | no | — |
| 370 | C2×D8 | — | 4 | 12 | no | — |
| 371 | C2×D8 | C24 | 1 | 3 | yes | — |
| 372 | C2×D8 | C24 | 1 | 6 | yes | — |
| 373 | C2×D8 | C24 | 1 | 12 | yes | — |
| 374 | C2×D8 | C24 | 1 | 6 | yes | — |
| 375 | C2×D8 | C24 | 1 | 6 | yes | — |
| 376 | C2×D8 | C24 | 1 | 12 | yes | — |
| 377 | C2×D8 | C24 | 1 | 24 | yes | — |
| 378 | C2×D8 | C24 | 1 | 12 | yes | — |
| 379 | #131 | — | 2 | 12 | no | — |
| 380 | #131 | — | 2 | 12 | no | — |
| 381 | C2×M16 | C24 | 1 | 3 | yes | — |
| 382 | C2×M16 | C24 | 1 | 6 | yes | — |
| 383 | C2×M16 | C24 | 1 | 6 | yes | — |
| 384 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 385 | C22×C8 | C24 | 1 | 3 | yes | — |
| 386 | C22×C8 | C24 | 1 | 6 | yes | — |
| 387 | C22×C8 | C24 | 1 | 6 | yes | — |
| 388 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 389 | C4⋊Q8 | — | 2 | 2 | no | — |
| 390 | C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 391 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 392 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 393 | #127 | — | 2 | 6 | no | — |
| 394 | #127 | — | 2 | 12 | no | — |
| 395 | #127 | — | 2 | 12 | no | — |
| 396 | #127 | — | 2 | 6 | no | — |
| 397 | #127 | — | 2 | 6 | no | — |
| 398 | #127 | — | 2 | 12 | no | — |
| 399 | #127 | — | 2 | 12 | no | — |
| 400 | #127 | C2×D4 | 1 | 3 | yes | — |
| 401 | #127 | C24 | 1 | 12 | yes | — |
| 402 | #127 | C24 | 1 | 6 | yes | — |
| 403 | #127 | C24 | 1 | 12 | yes | — |
| 404 | #127 | C24 | 1 | 12 | yes | — |
| 405 | #126 | — | 2 | 12 | no | — |
| 406 | #126 | — | 2 | 12 | no | — |
| 407 | #126 | — | 2 | 12 | no | — |
| 408 | #126 | C2×D4 | 1 | 12 | yes | — |
| 409 | #125 | — | 2 | 2 | no | — |
| 410 | #125 | — | 2 | 6 | no | — |
| 411 | #125 | C2×D4 | 1 | 6 | yes | — |
| 412 | #125 | C24 | 1 | 4 | yes | — |
| 413 | #124 | — | 2 | 6 | no | — |
| 414 | #124 | — | 2 | 6 | no | — |
| 415 | #124 | — | 2 | 12 | no | — |
| 416 | #124 | — | 2 | 12 | no | — |
| 417 | #124 | C2×D4 | 1 | 6 | yes | — |
| 418 | #124 | C2×D4 | 1 | 6 | yes | — |
| 419 | #124 | C24 | 1 | 12 | yes | — |
| 420 | #124 | C24 | 1 | 12 | yes | — |
| 421 | #123 | — | 2 | 12 | no | — |
| 422 | #123 | — | 2 | 12 | no | — |
| 423 | #123 | — | 2 | 12 | no | — |
| 424 | #123 | — | 2 | 12 | no | — |
| 425 | #123 | — | 2 | 24 | no | — |
| 426 | #123 | — | 2 | 12 | no | — |
| 427 | #123 | — | 2 | 24 | no | — |
| 428 | #123 | C2×D4 | 1 | 12 | yes | — |
| 429 | C22⋊Q8 | — | 2 | 6 | no | — |
| 430 | C22⋊Q8 | — | 2 | 6 | no | — |
| 431 | C22⋊Q8 | — | 2 | 12 | no | — |
| 432 | C22⋊Q8 | — | 2 | 4 | no | — |
| 433 | C22⋊Q8 | C2×D4 | 1 | 6 | yes | — |
| 434 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 435 | #121 | — | 2 | 12 | no | — |
| 436 | #121 | — | 2 | 12 | no | — |
| 437 | #121 | — | 2 | 6 | no | — |
| 438 | #121 | — | 2 | 6 | no | — |
| 439 | #121 | — | 2 | 6 | no | — |
| 440 | #121 | — | 2 | 12 | no | — |
| 441 | #121 | — | 2 | 12 | no | — |
| 442 | #121 | — | 2 | 12 | no | — |
| 443 | #121 | — | 2 | 24 | no | — |
| 444 | #121 | — | 2 | 12 | no | — |
| 445 | #121 | — | 2 | 12 | no | — |
| 446 | #121 | — | 2 | 12 | no | — |
| 447 | #121 | — | 2 | 6 | no | — |
| 448 | #121 | — | 2 | 6 | no | — |
| 449 | #121 | — | 2 | 12 | no | — |
| 450 | #121 | — | 2 | 6 | no | — |
| 451 | #121 | — | 2 | 12 | no | — |
| 452 | #121 | — | 2 | 24 | no | — |
| 453 | #121 | — | 2 | 24 | no | — |
| 454 | #121 | — | 2 | 24 | no | — |
| 455 | #121 | — | 2 | 12 | no | — |
| 456 | #121 | — | 2 | 12 | no | — |
| 457 | #121 | — | 2 | 24 | no | — |
| 458 | #121 | — | 2 | 24 | no | — |
| 459 | #121 | C2×D4 | 1 | 6 | yes | — |
| 460 | #121 | C2×D4 | 1 | 6 | yes | — |
| 461 | #121 | C2×D4 | 1 | 6 | yes | — |
| 462 | #121 | C24 | 1 | 12 | yes | — |
| 463 | #121 | C24 | 1 | 12 | yes | — |
| 464 | #121 | C24 | 1 | 12 | yes | — |
| 465 | #120 | — | 2 | 12 | no | — |
| 466 | #120 | — | 2 | 24 | no | — |
| 467 | #120 | — | 2 | 12 | no | — |
| 468 | #120 | — | 2 | 24 | no | — |
| 469 | #120 | — | 2 | 24 | no | — |
| 470 | #120 | — | 2 | 24 | no | — |
| 471 | #120 | — | 2 | 24 | no | — |
| 472 | #120 | — | 2 | 24 | no | — |
| 473 | C4×Q8 | — | 2 | 2 | no | — |
| 474 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 475 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 476 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 477 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 478 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 479 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 480 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 481 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 482 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 483 | C4×D4 | — | 2 | 6 | no | — |
| 484 | C4×D4 | — | 2 | 6 | no | — |
| 485 | C4×D4 | — | 2 | 12 | no | — |
| 486 | C4×D4 | — | 2 | 6 | no | — |
| 487 | C4×D4 | — | 2 | 12 | no | — |
| 488 | C4×D4 | — | 2 | 12 | no | — |
| 489 | C4×D4 | — | 2 | 6 | no | — |
| 490 | C4×D4 | — | 2 | 6 | no | — |
| 491 | C4×D4 | — | 2 | 6 | no | — |
| 492 | C4×D4 | — | 2 | 12 | no | — |
| 493 | C4×D4 | — | 2 | 12 | no | — |
| 494 | C4×D4 | — | 2 | 6 | no | — |
| 495 | C4×D4 | — | 2 | 12 | no | — |
| 496 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 497 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 498 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 499 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 500 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 501 | C4×D4 | C24 | 1 | 12 | yes | — |
| 502 | C4×D4 | C24 | 1 | 12 | yes | — |
| 503 | C4×D4 | C24 | 1 | 6 | yes | — |
| 504 | C4×D4 | C24 | 1 | 6 | yes | — |
| 505 | C4×D4 | C24 | 1 | 6 | yes | — |
| 506 | C4×D4 | C24 | 1 | 6 | yes | — |
| 507 | #117 | — | 2 | 6 | no | — |
| 508 | #117 | — | 2 | 6 | no | — |
| 509 | #117 | — | 2 | 12 | no | — |
| 510 | #117 | C2×D4 | 1 | 6 | yes | — |
| 511 | #117 | C24 | 1 | 2 | yes | — |
| 512 | #117 | C24 | 1 | 1 | yes | characteristic |
| 513 | #117 | C24 | 1 | 6 | yes | — |
| 514 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 515 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 516 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 517 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 518 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 519 | C2×C42 | — | 2 | 6 | no | — |
| 520 | C2×C42 | C24 | 1 | 3 | yes | — |
| 521 | C2×C42 | C24 | 1 | 6 | yes | — |
| 522 | #107 | C24 | 1 | 2 | yes | — |
| 523 | #107 | C24 | 1 | 2 | yes | — |
| 524 | #107 | C24 | 1 | 1 | yes | characteristic |
| 525 | #107 | C24 | 1 | 1 | yes | characteristic |
| 526 | #107 | C24 | 1 | 4 | yes | — |
| 527 | #106 | C24 | 1 | 2 | yes | — |
| 528 | #106 | C24 | 1 | 4 | yes | — |
| 529 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 530 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 531 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 532 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 533 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 534 | #103 | C24 | 1 | 6 | yes | — |
| 535 | #103 | C24 | 1 | 6 | yes | — |
| 536 | #103 | C24 | 1 | 12 | yes | — |
| 537 | #102 | C24 | 1 | 12 | yes | — |
| 538 | #102 | C24 | 1 | 12 | yes | — |
| 539 | #102 | C24 | 1 | 6 | yes | — |
| 540 | #102 | C24 | 1 | 6 | yes | — |
| 541 | #102 | C24 | 1 | 12 | yes | — |
| 542 | #102 | C24 | 1 | 12 | yes | — |
| 543 | #102 | C24 | 1 | 12 | yes | — |
| 544 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 545 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 546 | #97 | C24 | 1 | 2 | yes | — |
| 547 | #97 | C24 | 1 | 6 | yes | — |
| 548 | #97 | C24 | 1 | 6 | yes | — |
| 549 | C4×C8 | C24 | 1 | 2 | yes | — |
| 550 | C4×C8 | C24 | 1 | 3 | yes | — |
| 551 | C4×C8 | C24 | 1 | 6 | yes | — |
| 552 | C4×C8 | C24 | 1 | 3 | yes | — |
| 553 | C4×C8 | C24 | 1 | 6 | yes | — |
| 554 | C4×C8 | C24 | 1 | 3 | yes | — |
| 555 | C4×C8 | C24 | 1 | 3 | yes | — |
| 556 | C24 | — | 2 | 6 | no | — |
| 557 | C24 | — | 2 | 24 | no | — |
| 558 | #41 | — | 2 | 8 | no | — |
| 559 | #41 | — | 2 | 6 | no | — |
| 560 | #41 | — | 2 | 6 | no | — |
| 561 | #41 | — | 2 | 12 | no | — |
| 562 | #41 | — | 2 | 12 | no | — |
| 563 | #41 | — | 4 | 24 | no | — |
| 564 | #41 | — | 4 | 24 | no | — |
| 565 | #41 | — | 4 | 16 | no | — |
| 566 | #41 | — | 4 | 8 | no | — |
| 567 | #41 | — | 8 | 24 | no | — |
| 568 | #41 | — | 8 | 24 | no | — |
| 569 | #41 | — | 8 | 24 | no | — |
| 570 | C2×Q8 | — | 2 | 4 | no | — |
| 571 | C2×Q8 | — | 2 | 4 | no | — |
| 572 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 573 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 574 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 575 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 576 | C2×D4 | — | 2 | 6 | no | — |
| 577 | C2×D4 | — | 2 | 12 | no | — |
| 578 | C2×D4 | — | 2 | 12 | no | — |
| 579 | C2×D4 | — | 2 | 24 | no | — |
| 580 | C2×D4 | — | 2 | 12 | no | — |
| 581 | C2×D4 | — | 2 | 6 | no | — |
| 582 | C2×D4 | — | 2 | 12 | no | — |
| 583 | C2×D4 | — | 2 | 6 | no | — |
| 584 | C2×D4 | — | 2 | 6 | no | — |
| 585 | C2×D4 | — | 2 | 12 | no | — |
| 586 | C2×D4 | — | 2 | 12 | no | — |
| 587 | C2×D4 | — | 2 | 12 | no | — |
| 588 | C2×D4 | — | 2 | 12 | no | — |
| 589 | C2×D4 | — | 2 | 24 | no | — |
| 590 | C2×D4 | — | 2 | 12 | no | — |
| 591 | C2×D4 | — | 2 | 12 | no | — |
| 592 | C2×D4 | — | 2 | 12 | no | — |
| 593 | C2×D4 | — | 4 | 24 | no | — |
| 594 | C2×D4 | — | 4 | 24 | no | — |
| 595 | C2×D4 | — | 8 | 12 | no | — |
| 596 | C2×D4 | — | 8 | 24 | no | — |
| 597 | C2×D4 | — | 8 | 24 | no | — |
| 598 | C2×D4 | — | 8 | 24 | no | — |
| 599 | C2×D4 | — | 8 | 24 | no | — |
| 600 | C2×D4 | — | 8 | 48 | no | — |
| 601 | C2×D4 | — | 16 | 6 | no | — |
| 602 | C2×D4 | — | 16 | 12 | no | — |
| 603 | C2×D4 | — | 16 | 12 | no | — |
| 604 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 605 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 606 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 607 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 608 | C2×D4 | C25 | 1 | 6 | yes | — |
| 609 | C2×D4 | C25 | 1 | 12 | yes | — |
| 610 | C22×C4 | — | 2 | 2 | no | — |
| 611 | C22×C4 | — | 2 | 6 | no | — |
| 612 | C22×C4 | — | 2 | 6 | no | — |
| 613 | C22×C4 | — | 2 | 12 | no | — |
| 614 | C22×C4 | — | 2 | 6 | no | — |
| 615 | C22×C4 | — | 2 | 12 | no | — |
| 616 | C22×C4 | — | 2 | 24 | no | — |
| 617 | C22×C4 | — | 8 | 12 | no | — |
| 618 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 619 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 620 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 621 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 622 | C22×C4 | C25 | 1 | 6 | yes | — |
| 623 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 624 | Q16 | — | 2 | 6 | no | — |
| 625 | Q16 | — | 4 | 6 | no | — |
| 626 | SD16 | — | 2 | 12 | no | — |
| 627 | SD16 | — | 2 | 24 | no | — |
| 628 | SD16 | — | 4 | 24 | no | — |
| 629 | SD16 | — | 4 | 12 | no | — |
| 630 | D8 | — | 2 | 12 | no | — |
| 631 | D8 | — | 2 | 12 | no | — |
| 632 | D8 | — | 2 | 6 | no | — |
| 633 | D8 | — | 2 | 24 | no | — |
| 634 | D8 | — | 4 | 6 | no | — |
| 635 | D8 | — | 4 | 12 | no | — |
| 636 | D8 | — | 4 | 24 | no | — |
| 637 | D8 | — | 4 | 12 | no | — |
| 638 | M16 | — | 2 | 6 | no | — |
| 639 | M16 | — | 2 | 12 | no | — |
| 640 | M16 | — | 2 | 12 | no | — |
| 641 | M16 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 642 | C2×C8 | — | 2 | 6 | no | — |
| 643 | C2×C8 | — | 2 | 12 | no | — |
| 644 | C2×C8 | — | 2 | 12 | no | — |
| 645 | C2×C8 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 646 | C2×C8 | C25 | 1 | 3 | yes | — |
| 647 | C2×C8 | C25 | 1 | 6 | yes | — |
| 648 | C2×C8 | C25 | 1 | 3 | yes | — |
| 649 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 650 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 651 | C2×C8 | C25 | 1 | 2 | yes | — |
| 652 | C4⋊C4 | — | 2 | 6 | no | — |
| 653 | C4⋊C4 | — | 2 | 12 | no | — |
| 654 | C4⋊C4 | — | 2 | 2 | no | — |
| 655 | C4⋊C4 | — | 2 | 4 | no | — |
| 656 | C4⋊C4 | — | 2 | 6 | no | — |
| 657 | C4⋊C4 | — | 2 | 6 | no | — |
| 658 | C4⋊C4 | — | 2 | 4 | no | — |
| 659 | C4⋊C4 | — | 2 | 4 | no | — |
| 660 | C4⋊C4 | — | 2 | 6 | no | — |
| 661 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 662 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 663 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 664 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 665 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 666 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 667 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 668 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 669 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 670 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 671 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 672 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 673 | C22⋊C4 | — | 2 | 12 | no | — |
| 674 | C22⋊C4 | — | 2 | 2 | no | — |
| 675 | C22⋊C4 | — | 2 | 12 | no | — |
| 676 | C22⋊C4 | — | 2 | 12 | no | — |
| 677 | C22⋊C4 | — | 2 | 12 | no | — |
| 678 | C22⋊C4 | — | 2 | 12 | no | — |
| 679 | C22⋊C4 | — | 2 | 12 | no | — |
| 680 | C22⋊C4 | — | 2 | 12 | no | — |
| 681 | C22⋊C4 | — | 2 | 12 | no | — |
| 682 | C22⋊C4 | — | 2 | 6 | no | — |
| 683 | C22⋊C4 | — | 2 | 6 | no | — |
| 684 | C22⋊C4 | — | 2 | 12 | no | — |
| 685 | C22⋊C4 | — | 2 | 12 | no | — |
| 686 | C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 687 | C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 688 | C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 689 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 690 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 691 | C42 | — | 2 | 2 | no | — |
| 692 | C42 | — | 2 | 6 | no | — |
| 693 | C42 | — | 2 | 6 | no | — |
| 694 | C42 | C22×D4 | 1 | 3 | yes | — |
| 695 | C42 | C22×D4 | 1 | 6 | yes | — |
| 696 | C42 | C22×D4 | 1 | 3 | yes | — |
| 697 | C42 | C22×D4 | 1 | 6 | yes | — |
| 698 | C42 | C25 | 1 | 2 | yes | — |
| 699 | C42 | C25 | 1 | 3 | yes | — |
| 700 | C42 | C25 | 1 | 3 | yes | — |
| 701 | C23 | — | 2 | 6 | no | — |
| 702 | C23 | — | 2 | 12 | no | — |
| 703 | C23 | — | 4 | 12 | no | — |
| 704 | C23 | — | 8 | 6 | no | — |
| 705 | C23 | — | 8 | 6 | no | — |
| 706 | C23 | — | 8 | 24 | no | — |
| 707 | C23 | — | 8 | 24 | no | — |
| 708 | C23 | — | 8 | 24 | no | — |
| 709 | C23 | C23×D4 | 1 | 6 | yes | — |
| 710 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 711 | Q8 | — | 2 | 6 | no | — |
| 712 | Q8 | — | 2 | 6 | no | — |
| 713 | Q8 | — | 2 | 6 | no | — |
| 714 | Q8 | — | 2 | 6 | no | — |
| 715 | Q8 | — | 8 | 4 | no | — |
| 716 | Q8 | #576 | 1 | 4 | yes | complemented |
| 717 | D4 | — | 2 | 12 | no | — |
| 718 | D4 | — | 2 | 12 | no | — |
| 719 | D4 | — | 2 | 6 | no | — |
| 720 | D4 | — | 2 | 12 | no | — |
| 721 | D4 | — | 2 | 6 | no | — |
| 722 | D4 | — | 2 | 6 | no | — |
| 723 | D4 | — | 2 | 12 | no | — |
| 724 | D4 | — | 4 | 6 | no | — |
| 725 | D4 | — | 4 | 12 | no | — |
| 726 | D4 | — | 4 | 12 | no | — |
| 727 | D4 | — | 4 | 12 | no | — |
| 728 | D4 | — | 4 | 24 | no | — |
| 729 | D4 | — | 8 | 24 | no | — |
| 730 | D4 | — | 8 | 12 | no | — |
| 731 | D4 | — | 8 | 12 | no | — |
| 732 | D4 | — | 8 | 6 | no | — |
| 733 | D4 | — | 8 | 12 | no | — |
| 734 | D4 | — | 8 | 12 | no | — |
| 735 | D4 | — | 8 | 12 | no | — |
| 736 | D4 | — | 8 | 24 | no | — |
| 737 | D4 | — | 8 | 12 | no | — |
| 738 | D4 | — | 8 | 12 | no | — |
| 739 | D4 | — | 8 | 12 | no | — |
| 740 | C2×C4 | — | 2 | 6 | no | — |
| 741 | C2×C4 | — | 2 | 6 | no | — |
| 742 | C2×C4 | — | 2 | 6 | no | — |
| 743 | C2×C4 | — | 2 | 12 | no | — |
| 744 | C2×C4 | — | 2 | 2 | no | — |
| 745 | C2×C4 | — | 2 | 2 | no | — |
| 746 | C2×C4 | — | 2 | 6 | no | — |
| 747 | C2×C4 | — | 2 | 4 | no | — |
| 748 | C2×C4 | — | 4 | 6 | no | — |
| 749 | C2×C4 | — | 4 | 3 | no | — |
| 750 | C2×C4 | — | 4 | 12 | no | — |
| 751 | C2×C4 | — | 4 | 24 | no | — |
| 752 | C2×C4 | — | 4 | 12 | no | — |
| 753 | C2×C4 | — | 8 | 12 | no | — |
| 754 | C2×C4 | — | 8 | 24 | no | — |
| 755 | C2×C4 | — | 8 | 6 | no | — |
| 756 | C2×C4 | — | 8 | 2 | no | — |
| 757 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 758 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 759 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 760 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 761 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 762 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 763 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 764 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 765 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 766 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 767 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 768 | C8 | — | 2 | 3 | no | — |
| 769 | C8 | — | 2 | 3 | no | — |
| 770 | C8 | — | 2 | 6 | no | — |
| 771 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 772 | C8 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 773 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 774 | C22 | — | 2 | 1 | no | — |
| 775 | C22 | — | 2 | 1 | no | — |
| 776 | C22 | — | 2 | 6 | no | — |
| 777 | C22 | — | 2 | 6 | no | — |
| 778 | C22 | — | 2 | 6 | no | — |
| 779 | C22 | — | 4 | 6 | no | — |
| 780 | C22 | — | 4 | 12 | no | — |
| 781 | C22 | — | 4 | 12 | no | — |
| 782 | C22 | — | 4 | 6 | no | — |
| 783 | C22 | — | 4 | 6 | no | — |
| 784 | C22 | — | 4 | 12 | no | — |
| 785 | C22 | — | 16 | 12 | no | — |
| 786 | C22 | — | 32 | 24 | no | — |
| 787 | C22 | #3498 | 1 | 2 | yes | — |
| 788 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 789 | C4 | — | 2 | 6 | no | — |
| 790 | C4 | — | 2 | 2 | no | — |
| 791 | C4 | — | 2 | 3 | no | — |
| 792 | C4 | — | 2 | 2 | no | — |
| 793 | C4 | — | 2 | 3 | no | — |
| 794 | C4 | — | 2 | 3 | no | — |
| 795 | C4 | — | 4 | 6 | no | — |
| 796 | C4 | — | 4 | 4 | no | — |
| 797 | C4 | — | 4 | 2 | no | — |
| 798 | C4 | — | 4 | 2 | no | — |
| 799 | C4 | #3498 | 1 | 2 | yes | — |
| 800 | C4 | C2×#576 | 1 | 6 | yes | — |
| 801 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 802 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 803 | C2 | — | 2 | 2 | no | — |
| 804 | C2 | — | 4 | 6 | no | — |
| 805 | C2 | — | 8 | 12 | no | — |
| 806 | C2 | — | 8 | 6 | no | — |
| 807 | C2 | C2×#3498 | 1 | 1 | yes | characteristic |
| 808 | C2 | C22×#576 | 1 | 1 | yes | characteristic |
| 809 | C2 | #63091 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #3480 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62916 | C2 | semidirect |
| 2. #62463 | C2 | semidirect |
| 3. #62453 | C2 | semidirect |
| 4. #62440 | C2 | semidirect |
| 5. #62431 | C2 | semidirect |
| 6. #62420 | C2 | semidirect |
| 7. #62415 | C2 | semidirect |
| 8. #61402 | C2 | semidirect |
| 9. #61393 | C2 | semidirect |
| 10. C2×#3391 | C2 | semidirect |
| 11. #61093 | C2 | semidirect |
| 12. #61089 | C2 | semidirect |
| 13. #61084 | C2 | semidirect |
| 14. #60832 | C2 | semidirect |
| 15. #60695 | C2 | semidirect |
| 16. #60647 | C2 | semidirect |
| 17. #60218 | C2 | semidirect |
| 18. C2×#576 | C22 | semidirect |
| 19. C2×#576 | C22 | semidirect |
| 21. #3546 | C22 | semidirect |
| 23. #3543 | C22 | semidirect |
| 26. #3517 | C22 | semidirect |
| 28. #3498 | C22 | semidirect |
| 29. #3498 | C22 | semidirect |
| 30. #3498 | C22 | semidirect |
| 31. #3496 | C22 | semidirect |
| 34. #3480 | C22 | semidirect |
| 35. C2×#550 | C22 | semidirect |
| 36. #3460 | C22 | semidirect |
| 37. #3399 | C22 | semidirect |
| 38. #3397 | C22 | semidirect |
| 39. #3396 | C22 | semidirect |
| 40. #3395 | C22 | semidirect |
| 41. #3394 | C22 | semidirect |
| 42. #3393 | C22 | semidirect |
| 43. #3392 | C22 | semidirect |
| 44. #3392 | C22 | semidirect |
| 45. #3391 | C22 | semidirect |
| 46. #3391 | C22 | semidirect |
| 47. #3391 | C22 | semidirect |
| 48. #3391 | C22 | semidirect |
| 49. #3391 | C22 | semidirect |
| 50. #3391 | C22 | semidirect |
| 51. #3287 | C22 | semidirect |
| 52. #3287 | C22 | semidirect |
| 53. #3284 | C22 | semidirect |
| 54. #3283 | C22 | semidirect |
| 55. #3280 | C22 | semidirect |
| 56. D4×D8 | C22 | semidirect |
| 57. D4×D8 | C22 | semidirect |
| 58. D4×D8 | C22 | semidirect |
| 59. D4×D8 | C22 | semidirect |
| 60. #3274 | C22 | semidirect |
| 61. #3274 | C22 | semidirect |
| 62. #3274 | C22 | semidirect |
| 63. #3273 | C22 | semidirect |
| 64. #3272 | C22 | semidirect |
| 65. #3272 | C22 | semidirect |
| 66. #3268 | C22 | semidirect |
| 67. #3264 | C22 | semidirect |
| 68. #3224 | C22 | semidirect |
| 69. #3220 | C22 | semidirect |
| 70. #3217 | C22 | semidirect |
| 71. #3214 | C22 | semidirect |
| 72. #3212 | C22 | semidirect |
| 73. #3205 | C22 | semidirect |
| 74. #3179 | C22 | semidirect |
| 75. #3176 | C22 | semidirect |
| 76. #3175 | C22 | semidirect |
| 77. #3171 | C22 | semidirect |
| 78. #3169 | C22 | semidirect |
| 79. #3168 | C22 | semidirect |
| 80. #3164 | C22 | semidirect |
| 81. #3155 | C22 | semidirect |
| 82. #3155 | C22 | semidirect |
| 83. #3155 | C22 | semidirect |
| 84. #3155 | C22 | semidirect |
| 85. #3151 | C22 | semidirect |
| 86. #3151 | C22 | semidirect |
| 87. #3147 | C22 | semidirect |
| 88. #3147 | C22 | semidirect |
| 89. C2×#493 | C22 | semidirect |
| 90. C2×#493 | C22 | semidirect |
| 91. #3136 | C22 | semidirect |
| 92. #3062 | C22 | semidirect |
| 93. #3061 | C22 | semidirect |
| 94. #3058 | C22 | semidirect |
| 95. #3038 | C22 | semidirect |
| 96. #3036 | C22 | semidirect |
| 97. #3035 | C22 | semidirect |
| 98. C2×#459 | C22 | semidirect |
| 99. #3012 | C22 | semidirect |
| 100. #3008 | C22 | semidirect |
| 101. #2971 | C22 | semidirect |
| 102. #2969 | C22 | semidirect |
| 103. #2966 | C22 | semidirect |
| 104. C8×#41 | C22 | semidirect |
| 105. Q8×M16 | C22 | semidirect |
| 106. C2×C8×Q8 | C22 | semidirect |
| 107. C4×AGL(1,ℤ/8) | C22 | semidirect |
| 108. C4×#135 | C22 | semidirect |
| 109. C2×C4×D8 | C22 | semidirect |
| 110. #2935 | C22 | semidirect |
| 111. #2931 | C22 | semidirect |
| 112. #2925 | C22 | semidirect |
| 113. C4×#131 | C22 | semidirect |
| 641. M16 | H(5,𝔽2) | semidirect |
| 645. C2×C8 | H(5,𝔽2) | semidirect |
| 716. Q8 | #576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62916 | 2 |
| #62463 | 2 |
| #62453 | 2 |
| #62440 | 2 |
| #62431 | 2 |
| #62420 | 2 |
| #62415 | 2 |
| #61402 | 2 |
| #61393 | 2 |
| C2×#3391 | 2 |
| #61093 | 2 |
| #61089 | 2 |
| #61084 | 2 |
| #60832 | 2 |
| #60695 | 2 |
| #60647 | 2 |
| #60218 | 2 |