Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6552 conjugacy classes of subgroups.
The subgroup lattice has 987 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62834 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62263 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #62259 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #62251 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #62248 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #62245 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #61791 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #61788 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #61784 | C2 | 1 | 8 | yes | maximal, complemented |
| 10 | #61668 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #61661 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #61657 | C2 | 1 | 8 | yes | maximal, complemented |
| 13 | #60948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #60946 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #60940 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #60768 | C2 | 1 | 8 | yes | maximal, complemented |
| 17 | C2×#2979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #3558 | — | 2 | 4 | no | — |
| 19 | #3558 | — | 2 | 4 | no | — |
| 20 | #3549 | C22 | 1 | 4 | yes | complemented |
| 21 | #3548 | C22 | 1 | 4 | yes | complemented |
| 22 | #3546 | — | 2 | 4 | no | — |
| 23 | #3546 | C22 | 1 | 8 | yes | complemented |
| 24 | #3537 | — | 2 | 4 | no | — |
| 25 | #3519 | — | 2 | 4 | no | — |
| 26 | #3519 | C22 | 1 | 8 | yes | complemented |
| 27 | #3511 | — | 2 | 2 | no | — |
| 28 | #3511 | C22 | 1 | 4 | yes | complemented |
| 29 | #3508 | — | 2 | 4 | no | — |
| 30 | #3506 | C22 | 1 | 4 | yes | complemented |
| 31 | #3506 | C22 | 1 | 4 | yes | complemented |
| 32 | #3498 | — | 2 | 2 | no | — |
| 33 | #3498 | C22 | 1 | 4 | yes | complemented |
| 34 | #3496 | C22 | 1 | 4 | yes | complemented |
| 35 | #3496 | C22 | 1 | 4 | yes | complemented |
| 36 | #3488 | — | 2 | 4 | no | — |
| 37 | #3488 | C22 | 1 | 8 | yes | complemented |
| 38 | #3444 | C22 | 1 | 2 | yes | complemented |
| 39 | C2×#532 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#532 | C22 | 1 | 2 | yes | complemented |
| 41 | #3357 | C22 | 1 | 8 | yes | complemented |
| 42 | #3355 | C22 | 1 | 8 | yes | complemented |
| 43 | #3354 | C22 | 1 | 8 | yes | complemented |
| 44 | #3353 | C22 | 1 | 8 | yes | complemented |
| 45 | #3341 | C22 | 1 | 4 | yes | complemented |
| 46 | #3340 | C22 | 1 | 8 | yes | complemented |
| 47 | #3339 | C22 | 1 | 8 | yes | complemented |
| 48 | #3338 | C22 | 1 | 4 | yes | complemented |
| 49 | #3334 | C22 | 1 | 8 | yes | complemented |
| 50 | #3333 | C22 | 1 | 8 | yes | complemented |
| 51 | #3332 | C22 | 1 | 8 | yes | complemented |
| 52 | #3330 | C22 | 1 | 8 | yes | complemented |
| 53 | #3325 | C22 | 1 | 8 | yes | complemented |
| 54 | #3325 | C22 | 1 | 8 | yes | complemented |
| 55 | #3324 | C22 | 1 | 8 | yes | complemented |
| 56 | #3322 | C22 | 1 | 16 | yes | complemented |
| 57 | #3305 | C22 | 1 | 8 | yes | complemented |
| 58 | #3305 | C22 | 1 | 8 | yes | complemented |
| 59 | #3302 | C22 | 1 | 8 | yes | complemented |
| 60 | #3297 | C22 | 1 | 16 | yes | complemented |
| 61 | #3295 | C22 | 1 | 8 | yes | complemented |
| 62 | #3294 | C22 | 1 | 8 | yes | complemented |
| 63 | #3294 | C22 | 1 | 8 | yes | complemented |
| 64 | #3287 | C22 | 1 | 4 | yes | complemented |
| 65 | #3284 | C22 | 1 | 8 | yes | complemented |
| 66 | #3280 | C22 | 1 | 8 | yes | complemented |
| 67 | D4×D8 | C22 | 1 | 8 | yes | complemented |
| 68 | D4×D8 | C22 | 1 | 4 | yes | complemented |
| 69 | #3274 | C22 | 1 | 8 | yes | complemented |
| 70 | #3274 | C22 | 1 | 8 | yes | complemented |
| 71 | #3273 | C22 | 1 | 8 | yes | complemented |
| 72 | #3272 | C22 | 1 | 8 | yes | complemented |
| 73 | #3249 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | #3247 | C22 | 1 | 4 | yes | complemented |
| 75 | #3247 | C22 | 1 | 4 | yes | complemented |
| 76 | #3246 | C22 | 1 | 2 | yes | complemented |
| 77 | #3245 | C22 | 1 | 2 | yes | complemented |
| 78 | #3245 | C22 | 1 | 2 | yes | complemented |
| 79 | #3245 | C22 | 1 | 1 | yes | characteristic, complemented |
| 80 | #3233 | C22 | 1 | 4 | yes | complemented |
| 81 | #3230 | C22 | 1 | 2 | yes | complemented |
| 82 | #3228 | C22 | 1 | 4 | yes | complemented |
| 83 | #3227 | C22 | 1 | 2 | yes | complemented |
| 84 | #3226 | C22 | 1 | 4 | yes | complemented |
| 85 | #3212 | C22 | 1 | 4 | yes | complemented |
| 86 | #3208 | C22 | 1 | 2 | yes | complemented |
| 87 | #3207 | C22 | 1 | 4 | yes | complemented |
| 88 | #3205 | C22 | 1 | 4 | yes | complemented |
| 89 | #3205 | C22 | 1 | 2 | yes | complemented |
| 90 | #3203 | C22 | 1 | 16 | yes | complemented |
| 91 | #3199 | C22 | 1 | 16 | yes | complemented |
| 92 | #3198 | C22 | 1 | 16 | yes | complemented |
| 93 | #3198 | C22 | 1 | 16 | yes | complemented |
| 94 | #3191 | C22 | 1 | 4 | yes | complemented |
| 95 | #3191 | C22 | 1 | 8 | yes | complemented |
| 96 | #3188 | C22 | 1 | 8 | yes | complemented |
| 97 | #3188 | C22 | 1 | 16 | yes | complemented |
| 98 | #3186 | C22 | 1 | 4 | yes | complemented |
| 99 | #3186 | C22 | 1 | 8 | yes | complemented |
| 100 | #3169 | C22 | 1 | 4 | yes | complemented |
| 101 | #3169 | C22 | 1 | 4 | yes | complemented |
| 102 | #3168 | C22 | 1 | 4 | yes | complemented |
| 103 | #3167 | C22 | 1 | 4 | yes | complemented |
| 104 | #3107 | C22 | 1 | 4 | yes | complemented |
| 105 | #3106 | C22 | 1 | 4 | yes | complemented |
| 106 | #3106 | C22 | 1 | 4 | yes | complemented |
| 107 | #3106 | C22 | 1 | 4 | yes | complemented |
| 108 | #3105 | C22 | 1 | 8 | yes | complemented |
| 109 | #3100 | C22 | 1 | 8 | yes | complemented |
| 110 | #3098 | C22 | 1 | 16 | yes | complemented |
| 111 | #3096 | C22 | 1 | 16 | yes | complemented |
| 112 | #3055 | C22 | 1 | 16 | yes | complemented |
| 113 | #3050 | C22 | 1 | 8 | yes | complemented |
| 114 | C2×#466 | C22 | 1 | 8 | yes | complemented |
| 115 | #3012 | C22 | 1 | 16 | yes | complemented |
| 116 | #3008 | C22 | 1 | 16 | yes | complemented |
| 117 | #2979 | C22 | 1 | 8 | yes | complemented |
| 118 | #2979 | C22 | 1 | 4 | yes | complemented |
| 119 | #2979 | C22 | 1 | 4 | yes | complemented |
| 120 | C2×#436 | C22 | 1 | 2 | yes | complemented |
| 121 | C2×#436 | C22 | 1 | 2 | yes | complemented |
| 122 | C2×C8×D4 | C22 | 1 | 2 | yes | complemented |
| 123 | C2×C8×D4 | C22 | 1 | 2 | yes | complemented |
| 124 | C2×#431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 125 | C2×#431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 126 | C2×#408 | C22 | 1 | 4 | yes | complemented |
| 127 | C2×H(5,𝔽2) | — | 2 | 4 | no | — |
| 128 | C2×H(5,𝔽2) | C23 | 1 | 8 | yes | — |
| 129 | C22×#41 | — | 2 | 2 | no | — |
| 130 | C22×#41 | C23 | 1 | 2 | yes | — |
| 131 | C2×AGL(1,ℤ/8) | C23 | 1 | 16 | yes | — |
| 132 | C2×#135 | C23 | 1 | 8 | yes | — |
| 133 | C22×D8 | C23 | 1 | 8 | yes | — |
| 134 | C22×M16 | C23 | 1 | 4 | yes | — |
| 135 | C23×C8 | C23 | 1 | 4 | yes | — |
| 136 | #562 | — | 2 | 8 | no | — |
| 137 | H(3,𝔽4) | — | 2 | 8 | no | — |
| 138 | #560 | — | 2 | 16 | no | — |
| 139 | #559 | — | 2 | 8 | no | — |
| 140 | #559 | — | 2 | 8 | no | — |
| 141 | #556 | — | 2 | 4 | no | — |
| 142 | #556 | C23 | 1 | 8 | yes | — |
| 143 | #555 | — | 2 | 4 | no | — |
| 144 | #555 | C23 | 1 | 8 | yes | — |
| 145 | #555 | C23 | 1 | 8 | yes | — |
| 146 | #554 | — | 2 | 4 | no | — |
| 147 | #554 | C23 | 1 | 8 | yes | — |
| 148 | #553 | — | 2 | 8 | no | — |
| 149 | #553 | — | 2 | 8 | no | — |
| 150 | #553 | — | 2 | 8 | no | — |
| 151 | #553 | C23 | 1 | 16 | yes | — |
| 152 | #550 | — | 2 | 8 | no | — |
| 153 | #550 | — | 2 | 4 | no | — |
| 154 | #550 | — | 2 | 4 | no | — |
| 155 | #550 | — | 2 | 8 | no | — |
| 156 | #550 | C23 | 1 | 8 | yes | — |
| 157 | #550 | C23 | 1 | 8 | yes | — |
| 158 | #548 | — | 2 | 8 | no | — |
| 159 | #548 | — | 2 | 8 | no | — |
| 160 | #547 | — | 2 | 4 | no | — |
| 161 | #547 | C23 | 1 | 8 | yes | — |
| 162 | #547 | C23 | 1 | 8 | yes | — |
| 163 | #547 | C23 | 1 | 8 | yes | — |
| 164 | #546 | — | 2 | 8 | no | — |
| 165 | #546 | — | 2 | 16 | no | — |
| 166 | #546 | — | 2 | 8 | no | — |
| 167 | #546 | — | 2 | 8 | no | — |
| 168 | #546 | — | 2 | 8 | no | — |
| 169 | #546 | — | 2 | 8 | no | — |
| 170 | #546 | — | 2 | 16 | no | — |
| 171 | #546 | C23 | 1 | 16 | yes | — |
| 172 | D42 | — | 2 | 16 | no | — |
| 173 | D42 | — | 2 | 8 | no | — |
| 174 | D42 | — | 2 | 8 | no | — |
| 175 | D42 | — | 2 | 4 | no | — |
| 176 | D42 | — | 2 | 4 | no | — |
| 177 | D42 | — | 2 | 8 | no | — |
| 178 | D42 | — | 2 | 8 | no | — |
| 179 | D42 | C23 | 1 | 8 | yes | — |
| 180 | D42 | C23 | 1 | 8 | yes | — |
| 181 | D42 | C23 | 1 | 8 | yes | — |
| 182 | #542 | — | 2 | 8 | no | — |
| 183 | #542 | — | 2 | 8 | no | — |
| 184 | #540 | — | 2 | 8 | no | — |
| 185 | #540 | — | 2 | 8 | no | — |
| 186 | #538 | — | 2 | 16 | no | — |
| 187 | #538 | — | 2 | 8 | no | — |
| 188 | #538 | — | 2 | 16 | no | — |
| 189 | #538 | — | 2 | 8 | no | — |
| 190 | #537 | — | 2 | 8 | no | — |
| 191 | #537 | — | 2 | 4 | no | — |
| 192 | #537 | C23 | 1 | 16 | yes | — |
| 193 | #537 | C23 | 1 | 8 | yes | — |
| 194 | #535 | — | 2 | 4 | no | — |
| 195 | #535 | — | 2 | 8 | no | — |
| 196 | #535 | — | 2 | 8 | no | — |
| 197 | #535 | — | 2 | 8 | no | — |
| 198 | #535 | — | 2 | 8 | no | — |
| 199 | #535 | C23 | 1 | 16 | yes | — |
| 200 | #535 | C23 | 1 | 8 | yes | — |
| 201 | #534 | — | 2 | 8 | no | — |
| 202 | #534 | — | 2 | 8 | no | — |
| 203 | #533 | — | 2 | 4 | no | — |
| 204 | #533 | C23 | 1 | 2 | yes | — |
| 205 | #533 | C23 | 1 | 2 | yes | — |
| 206 | #533 | C23 | 1 | 2 | yes | — |
| 207 | #532 | — | 2 | 4 | no | — |
| 208 | #532 | — | 2 | 4 | no | — |
| 209 | #532 | — | 2 | 2 | no | — |
| 210 | #532 | — | 2 | 2 | no | — |
| 211 | #532 | — | 2 | 2 | no | — |
| 212 | #532 | — | 2 | 2 | no | — |
| 213 | #532 | D4 | 1 | 4 | yes | — |
| 214 | #532 | D4 | 1 | 4 | yes | — |
| 215 | #532 | C23 | 1 | 2 | yes | — |
| 216 | #532 | C23 | 1 | 4 | yes | — |
| 217 | #532 | C23 | 1 | 4 | yes | — |
| 218 | #532 | C23 | 1 | 2 | yes | — |
| 219 | #532 | C23 | 1 | 4 | yes | — |
| 220 | #532 | C23 | 1 | 4 | yes | — |
| 221 | #532 | C23 | 1 | 2 | yes | — |
| 222 | #532 | C23 | 1 | 4 | yes | — |
| 223 | #532 | C23 | 1 | 4 | yes | — |
| 224 | C2×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 225 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 226 | C2×#127 | — | 2 | 4 | no | — |
| 227 | C2×#127 | D4 | 1 | 1 | yes | characteristic |
| 228 | C2×#127 | C23 | 1 | 2 | yes | — |
| 229 | #529 | — | 2 | 2 | no | — |
| 230 | #529 | — | 2 | 2 | no | — |
| 231 | #529 | — | 2 | 2 | no | — |
| 232 | #529 | — | 2 | 2 | no | — |
| 233 | #529 | C23 | 1 | 4 | yes | — |
| 234 | #529 | C23 | 1 | 4 | yes | — |
| 235 | C2×#124 | — | 2 | 2 | no | — |
| 236 | C2×#124 | D4 | 1 | 2 | yes | — |
| 237 | #525 | — | 2 | 2 | no | — |
| 238 | #525 | — | 2 | 2 | no | — |
| 239 | #525 | — | 2 | 8 | no | — |
| 240 | #525 | C23 | 1 | 4 | yes | — |
| 241 | #525 | C23 | 1 | 16 | yes | — |
| 242 | C2×#121 | — | 2 | 2 | no | — |
| 243 | C2×#121 | — | 2 | 8 | no | — |
| 244 | C2×#121 | D4 | 1 | 2 | yes | — |
| 245 | C2×#121 | D4 | 1 | 2 | yes | — |
| 246 | C2×#121 | C23 | 1 | 4 | yes | — |
| 247 | C2×#121 | C23 | 1 | 16 | yes | — |
| 248 | #520 | — | 2 | 4 | no | — |
| 249 | #520 | C23 | 1 | 8 | yes | — |
| 250 | #518 | — | 2 | 8 | no | — |
| 251 | C4×#41 | — | 2 | 2 | no | — |
| 252 | C4×#41 | — | 2 | 2 | no | — |
| 253 | C4×#41 | C23 | 1 | 4 | yes | — |
| 254 | C2×C4×D4 | — | 2 | 2 | no | — |
| 255 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 256 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 257 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 258 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 259 | #500 | C23 | 1 | 4 | yes | — |
| 260 | #500 | C23 | 1 | 4 | yes | — |
| 261 | #499 | C23 | 1 | 4 | yes | — |
| 262 | #498 | C23 | 1 | 4 | yes | — |
| 263 | #495 | C23 | 1 | 4 | yes | — |
| 264 | #493 | C23 | 1 | 4 | yes | — |
| 265 | #493 | C23 | 1 | 4 | yes | — |
| 266 | #492 | C23 | 1 | 4 | yes | — |
| 267 | #488 | C23 | 1 | 8 | yes | — |
| 268 | #487 | C23 | 1 | 4 | yes | — |
| 269 | #486 | C23 | 1 | 4 | yes | — |
| 270 | #486 | C23 | 1 | 8 | yes | — |
| 271 | #486 | C23 | 1 | 4 | yes | — |
| 272 | #486 | C23 | 1 | 4 | yes | — |
| 273 | #485 | C23 | 1 | 16 | yes | — |
| 274 | #485 | C23 | 1 | 8 | yes | — |
| 275 | #484 | C23 | 1 | 16 | yes | — |
| 276 | #484 | C23 | 1 | 8 | yes | — |
| 277 | #482 | C23 | 1 | 16 | yes | — |
| 278 | #482 | C23 | 1 | 16 | yes | — |
| 279 | #482 | C23 | 1 | 16 | yes | — |
| 280 | #482 | C23 | 1 | 8 | yes | — |
| 281 | #482 | C23 | 1 | 8 | yes | — |
| 282 | #482 | C23 | 1 | 8 | yes | — |
| 283 | #481 | C23 | 1 | 16 | yes | — |
| 284 | #481 | C23 | 1 | 8 | yes | — |
| 285 | #480 | C23 | 1 | 16 | yes | — |
| 286 | #480 | C23 | 1 | 16 | yes | — |
| 287 | #480 | C23 | 1 | 16 | yes | — |
| 288 | #478 | C23 | 1 | 8 | yes | — |
| 289 | #478 | C23 | 1 | 8 | yes | — |
| 290 | #477 | C23 | 1 | 4 | yes | — |
| 291 | #477 | C23 | 1 | 4 | yes | — |
| 292 | #477 | C23 | 1 | 4 | yes | — |
| 293 | #476 | C23 | 1 | 4 | yes | — |
| 294 | #476 | C23 | 1 | 4 | yes | — |
| 295 | #476 | C23 | 1 | 4 | yes | — |
| 296 | #475 | C23 | 1 | 4 | yes | — |
| 297 | #474 | C23 | 1 | 8 | yes | — |
| 298 | #474 | C23 | 1 | 4 | yes | — |
| 299 | #474 | C23 | 1 | 8 | yes | — |
| 300 | #469 | C23 | 1 | 16 | yes | — |
| 301 | #469 | C23 | 1 | 16 | yes | — |
| 302 | #468 | C23 | 1 | 16 | yes | — |
| 303 | #468 | C23 | 1 | 16 | yes | — |
| 304 | #467 | C23 | 1 | 8 | yes | — |
| 305 | #467 | C23 | 1 | 4 | yes | — |
| 306 | #466 | C23 | 1 | 16 | yes | — |
| 307 | #466 | C23 | 1 | 8 | yes | — |
| 308 | #466 | C23 | 1 | 8 | yes | — |
| 309 | #466 | C23 | 1 | 8 | yes | — |
| 310 | #466 | C23 | 1 | 4 | yes | — |
| 311 | #466 | C23 | 1 | 8 | yes | — |
| 312 | #466 | C23 | 1 | 8 | yes | — |
| 313 | #466 | C23 | 1 | 8 | yes | — |
| 314 | #466 | C23 | 1 | 8 | yes | — |
| 315 | #465 | C23 | 1 | 16 | yes | — |
| 316 | #465 | C23 | 1 | 8 | yes | — |
| 317 | #465 | C23 | 1 | 8 | yes | — |
| 318 | #465 | C23 | 1 | 8 | yes | — |
| 319 | #463 | C23 | 1 | 8 | yes | — |
| 320 | #463 | C23 | 1 | 8 | yes | — |
| 321 | #462 | C23 | 1 | 4 | yes | — |
| 322 | #461 | C23 | 1 | 4 | yes | — |
| 323 | #460 | C23 | 1 | 4 | yes | — |
| 324 | #460 | C23 | 1 | 4 | yes | — |
| 325 | #460 | C23 | 1 | 4 | yes | — |
| 326 | #459 | C23 | 1 | 8 | yes | — |
| 327 | #459 | C23 | 1 | 8 | yes | — |
| 328 | #459 | C23 | 1 | 4 | yes | — |
| 329 | #459 | C23 | 1 | 4 | yes | — |
| 330 | #459 | C23 | 1 | 4 | yes | — |
| 331 | #452 | C23 | 1 | 16 | yes | — |
| 332 | #452 | C23 | 1 | 8 | yes | — |
| 333 | #450 | C23 | 1 | 8 | yes | — |
| 334 | #450 | C23 | 1 | 16 | yes | — |
| 335 | #449 | C23 | 1 | 16 | yes | — |
| 336 | #449 | C23 | 1 | 16 | yes | — |
| 337 | #449 | C23 | 1 | 8 | yes | — |
| 338 | #449 | C23 | 1 | 8 | yes | — |
| 339 | #449 | C23 | 1 | 8 | yes | — |
| 340 | #449 | C23 | 1 | 16 | yes | — |
| 341 | #447 | C23 | 1 | 16 | yes | — |
| 342 | #447 | C23 | 1 | 8 | yes | — |
| 343 | #447 | C23 | 1 | 16 | yes | — |
| 344 | #447 | C23 | 1 | 16 | yes | — |
| 345 | #447 | C23 | 1 | 16 | yes | — |
| 346 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 347 | C4×SD16 | C23 | 1 | 8 | yes | — |
| 348 | C4×SD16 | C23 | 1 | 8 | yes | — |
| 349 | C4×SD16 | C23 | 1 | 8 | yes | — |
| 350 | C4×D8 | C23 | 1 | 8 | yes | — |
| 351 | C4×D8 | C23 | 1 | 8 | yes | — |
| 352 | C4×D8 | C23 | 1 | 4 | yes | — |
| 353 | C4×D8 | C23 | 1 | 8 | yes | — |
| 354 | C4×D8 | C23 | 1 | 8 | yes | — |
| 355 | #436 | C23 | 1 | 8 | yes | — |
| 356 | #436 | C23 | 1 | 8 | yes | — |
| 357 | #436 | C23 | 1 | 8 | yes | — |
| 358 | #436 | C23 | 1 | 8 | yes | — |
| 359 | C8×D4 | C23 | 1 | 8 | yes | — |
| 360 | C8×D4 | C23 | 1 | 4 | yes | — |
| 361 | C8×D4 | C23 | 1 | 8 | yes | — |
| 362 | C8×D4 | C23 | 1 | 8 | yes | — |
| 363 | C8×D4 | C23 | 1 | 4 | yes | — |
| 364 | #431 | C23 | 1 | 4 | yes | — |
| 365 | #431 | C23 | 1 | 4 | yes | — |
| 366 | #431 | C23 | 1 | 2 | yes | — |
| 367 | #431 | C23 | 1 | 2 | yes | — |
| 368 | #431 | C23 | 1 | 4 | yes | — |
| 369 | #428 | C23 | 1 | 16 | yes | — |
| 370 | #427 | C23 | 1 | 8 | yes | — |
| 371 | C2×#107 | C23 | 1 | 8 | yes | — |
| 372 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 373 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 374 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 375 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 376 | #418 | C23 | 1 | 16 | yes | — |
| 377 | #417 | C23 | 1 | 16 | yes | — |
| 378 | #416 | C23 | 1 | 16 | yes | — |
| 379 | C2×#102 | C23 | 1 | 16 | yes | — |
| 380 | #408 | C23 | 1 | 16 | yes | — |
| 381 | #408 | C23 | 1 | 16 | yes | — |
| 382 | C2×C22⋊C8 | C23 | 1 | 2 | yes | — |
| 383 | C2×C22⋊C8 | C23 | 1 | 2 | yes | — |
| 384 | C2×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 385 | C2×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 386 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 387 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 388 | H(5,𝔽2) | — | 8 | 16 | no | — |
| 389 | H(5,𝔽2) | — | 8 | 8 | no | — |
| 390 | H(5,𝔽2) | — | 8 | 8 | no | — |
| 391 | C2×#41 | — | 2 | 8 | no | — |
| 392 | C2×#41 | — | 2 | 8 | no | — |
| 393 | C2×#41 | — | 2 | 8 | no | — |
| 394 | C2×#41 | — | 2 | 2 | no | — |
| 395 | C2×#41 | — | 2 | 4 | no | — |
| 396 | C2×#41 | — | 2 | 2 | no | — |
| 397 | C2×#41 | — | 2 | 4 | no | — |
| 398 | C2×#41 | — | 2 | 4 | no | — |
| 399 | C2×#41 | — | 2 | 4 | no | — |
| 400 | C2×#41 | — | 8 | 8 | no | — |
| 401 | C2×#41 | — | 8 | 2 | no | — |
| 402 | C2×#41 | — | 8 | 2 | no | — |
| 403 | C2×#41 | C2×D4 | 1 | 8 | yes | — |
| 404 | C2×#41 | C24 | 1 | 4 | yes | — |
| 405 | C2×#41 | C24 | 1 | 16 | yes | — |
| 406 | C2×#41 | C24 | 1 | 8 | yes | — |
| 407 | C22×Q8 | — | 2 | 2 | no | — |
| 408 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 409 | C22×D4 | — | 2 | 4 | no | — |
| 410 | C22×D4 | — | 2 | 16 | no | — |
| 411 | C22×D4 | — | 2 | 8 | no | — |
| 412 | C22×D4 | — | 2 | 16 | no | — |
| 413 | C22×D4 | — | 2 | 8 | no | — |
| 414 | C22×D4 | — | 2 | 8 | no | — |
| 415 | C22×D4 | — | 2 | 8 | no | — |
| 416 | C22×D4 | — | 2 | 2 | no | — |
| 417 | C22×D4 | — | 2 | 2 | no | — |
| 418 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 419 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 420 | C22×D4 | C2×D4 | 1 | 4 | yes | — |
| 421 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 422 | C22×D4 | C24 | 1 | 4 | yes | — |
| 423 | C22×D4 | C24 | 1 | 16 | yes | — |
| 424 | C23×C4 | — | 2 | 4 | no | — |
| 425 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 426 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 427 | C23×C4 | C24 | 1 | 4 | yes | — |
| 428 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 429 | AGL(1,ℤ/8) | — | 8 | 16 | no | — |
| 430 | #135 | — | 8 | 8 | no | — |
| 431 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 432 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 433 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 434 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 435 | C2×D8 | — | 8 | 8 | no | — |
| 436 | C2×D8 | C24 | 1 | 4 | yes | — |
| 437 | C2×D8 | C24 | 1 | 8 | yes | — |
| 438 | C2×D8 | C24 | 1 | 8 | yes | — |
| 439 | C2×D8 | C24 | 1 | 8 | yes | — |
| 440 | C2×D8 | C24 | 1 | 8 | yes | — |
| 441 | C2×M16 | — | 8 | 4 | no | — |
| 442 | C2×M16 | C24 | 1 | 16 | yes | — |
| 443 | C22×C8 | — | 8 | 4 | no | — |
| 444 | C22×C8 | C24 | 1 | 2 | yes | — |
| 445 | C22×C8 | C24 | 1 | 2 | yes | — |
| 446 | C22×C8 | C24 | 1 | 8 | yes | — |
| 447 | C22×C8 | C24 | 1 | 8 | yes | — |
| 448 | C22×C8 | C24 | 1 | 2 | yes | — |
| 449 | C22×C8 | C24 | 1 | 2 | yes | — |
| 450 | C4⋊Q8 | — | 2 | 2 | no | — |
| 451 | C4⋊Q8 | — | 2 | 2 | no | — |
| 452 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 453 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 454 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 455 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 456 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 457 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 458 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 459 | #127 | — | 2 | 8 | no | — |
| 460 | #127 | — | 2 | 8 | no | — |
| 461 | #127 | — | 2 | 8 | no | — |
| 462 | #127 | — | 2 | 16 | no | — |
| 463 | #127 | — | 2 | 2 | no | — |
| 464 | #127 | — | 2 | 2 | no | — |
| 465 | #127 | C2×D4 | 1 | 4 | yes | — |
| 466 | #127 | C2×D4 | 1 | 4 | yes | — |
| 467 | #127 | C24 | 1 | 4 | yes | — |
| 468 | #127 | C24 | 1 | 4 | yes | — |
| 469 | #127 | C24 | 1 | 2 | yes | — |
| 470 | #126 | — | 2 | 16 | no | — |
| 471 | #126 | — | 2 | 16 | no | — |
| 472 | #126 | — | 2 | 4 | no | — |
| 473 | #126 | — | 2 | 4 | no | — |
| 474 | #125 | — | 2 | 8 | no | — |
| 475 | #125 | — | 2 | 2 | no | — |
| 476 | #125 | — | 2 | 2 | no | — |
| 477 | #125 | C24 | 1 | 4 | yes | — |
| 478 | #124 | — | 2 | 8 | no | — |
| 479 | #124 | — | 2 | 16 | no | — |
| 480 | #124 | — | 2 | 8 | no | — |
| 481 | #124 | — | 2 | 16 | no | — |
| 482 | #124 | — | 2 | 16 | no | — |
| 483 | #124 | — | 2 | 4 | no | — |
| 484 | #124 | — | 2 | 4 | no | — |
| 485 | #124 | — | 2 | 4 | no | — |
| 486 | #124 | — | 2 | 4 | no | — |
| 487 | #124 | — | 2 | 2 | no | — |
| 488 | #124 | — | 2 | 2 | no | — |
| 489 | #124 | C2×D4 | 1 | 8 | yes | — |
| 490 | #124 | C2×D4 | 1 | 8 | yes | — |
| 491 | #124 | C24 | 1 | 4 | yes | — |
| 492 | #123 | — | 2 | 4 | no | — |
| 493 | #123 | — | 2 | 4 | no | — |
| 494 | #123 | — | 2 | 4 | no | — |
| 495 | #123 | — | 2 | 16 | no | — |
| 496 | #123 | — | 2 | 16 | no | — |
| 497 | #123 | — | 2 | 16 | no | — |
| 498 | #123 | — | 2 | 16 | no | — |
| 499 | #123 | — | 2 | 16 | no | — |
| 500 | #123 | — | 2 | 16 | no | — |
| 501 | C22⋊Q8 | — | 2 | 8 | no | — |
| 502 | C22⋊Q8 | — | 2 | 16 | no | — |
| 503 | C22⋊Q8 | — | 2 | 2 | no | — |
| 504 | C22⋊Q8 | — | 2 | 2 | no | — |
| 505 | C22⋊Q8 | — | 2 | 2 | no | — |
| 506 | C22⋊Q8 | — | 2 | 2 | no | — |
| 507 | C22⋊Q8 | — | 2 | 8 | no | — |
| 508 | C22⋊Q8 | — | 2 | 8 | no | — |
| 509 | C22⋊Q8 | — | 2 | 16 | no | — |
| 510 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 511 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 512 | C22⋊Q8 | C24 | 1 | 16 | yes | — |
| 513 | #121 | — | 2 | 16 | no | — |
| 514 | #121 | — | 2 | 8 | no | — |
| 515 | #121 | — | 2 | 8 | no | — |
| 516 | #121 | — | 2 | 8 | no | — |
| 517 | #121 | — | 2 | 8 | no | — |
| 518 | #121 | — | 2 | 16 | no | — |
| 519 | #121 | — | 2 | 16 | no | — |
| 520 | #121 | — | 2 | 16 | no | — |
| 521 | #121 | — | 2 | 16 | no | — |
| 522 | #121 | — | 2 | 2 | no | — |
| 523 | #121 | — | 2 | 4 | no | — |
| 524 | #121 | — | 2 | 4 | no | — |
| 525 | #121 | — | 2 | 4 | no | — |
| 526 | #121 | — | 2 | 4 | no | — |
| 527 | #121 | — | 2 | 4 | no | — |
| 528 | #121 | — | 2 | 4 | no | — |
| 529 | #121 | — | 2 | 16 | no | — |
| 530 | #121 | — | 2 | 16 | no | — |
| 531 | #121 | — | 2 | 2 | no | — |
| 532 | #121 | — | 2 | 2 | no | — |
| 533 | #121 | — | 2 | 2 | no | — |
| 534 | #121 | — | 2 | 8 | no | — |
| 535 | #121 | — | 2 | 8 | no | — |
| 536 | #121 | — | 2 | 8 | no | — |
| 537 | #121 | — | 2 | 16 | no | — |
| 538 | #121 | — | 2 | 16 | no | — |
| 539 | #121 | — | 2 | 16 | no | — |
| 540 | #121 | C2×D4 | 1 | 8 | yes | — |
| 541 | #121 | C2×D4 | 1 | 8 | yes | — |
| 542 | #121 | C2×D4 | 1 | 8 | yes | — |
| 543 | #121 | C2×D4 | 1 | 8 | yes | — |
| 544 | #121 | C24 | 1 | 4 | yes | — |
| 545 | #121 | C24 | 1 | 8 | yes | — |
| 546 | #121 | C24 | 1 | 8 | yes | — |
| 547 | #121 | C24 | 1 | 16 | yes | — |
| 548 | #121 | C24 | 1 | 16 | yes | — |
| 549 | #121 | C24 | 1 | 4 | yes | — |
| 550 | #121 | C24 | 1 | 16 | yes | — |
| 551 | #120 | — | 2 | 4 | no | — |
| 552 | #120 | — | 2 | 16 | no | — |
| 553 | #120 | — | 2 | 16 | no | — |
| 554 | #120 | — | 2 | 16 | no | — |
| 555 | #120 | — | 2 | 16 | no | — |
| 556 | #120 | — | 2 | 16 | no | — |
| 557 | #120 | — | 2 | 16 | no | — |
| 558 | #120 | — | 2 | 16 | no | — |
| 559 | #120 | — | 2 | 16 | no | — |
| 560 | C4×Q8 | — | 2 | 8 | no | — |
| 561 | C4×Q8 | — | 2 | 8 | no | — |
| 562 | C4×Q8 | — | 2 | 2 | no | — |
| 563 | C4×Q8 | — | 2 | 2 | no | — |
| 564 | C4×Q8 | — | 2 | 2 | no | — |
| 565 | C4×Q8 | — | 2 | 2 | no | — |
| 566 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 567 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 568 | C4×D4 | — | 2 | 8 | no | — |
| 569 | C4×D4 | — | 2 | 16 | no | — |
| 570 | C4×D4 | — | 2 | 8 | no | — |
| 571 | C4×D4 | — | 2 | 4 | no | — |
| 572 | C4×D4 | — | 2 | 4 | no | — |
| 573 | C4×D4 | — | 2 | 4 | no | — |
| 574 | C4×D4 | — | 2 | 4 | no | — |
| 575 | C4×D4 | — | 2 | 4 | no | — |
| 576 | C4×D4 | — | 2 | 4 | no | — |
| 577 | C4×D4 | — | 2 | 16 | no | — |
| 578 | C4×D4 | — | 2 | 16 | no | — |
| 579 | C4×D4 | — | 2 | 8 | no | — |
| 580 | C4×D4 | — | 2 | 8 | no | — |
| 581 | C4×D4 | — | 2 | 16 | no | — |
| 582 | C4×D4 | — | 2 | 4 | no | — |
| 583 | C4×D4 | — | 2 | 4 | no | — |
| 584 | C4×D4 | — | 2 | 4 | no | — |
| 585 | C4×D4 | — | 2 | 4 | no | — |
| 586 | C4×D4 | — | 2 | 4 | no | — |
| 587 | C4×D4 | — | 2 | 4 | no | — |
| 588 | C4×D4 | — | 2 | 2 | no | — |
| 589 | C4×D4 | — | 2 | 2 | no | — |
| 590 | C4×D4 | — | 2 | 2 | no | — |
| 591 | C4×D4 | — | 2 | 2 | no | — |
| 592 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 593 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 594 | C4×D4 | C2×D4 | 1 | 8 | yes | — |
| 595 | C4×D4 | C24 | 1 | 8 | yes | — |
| 596 | C4×D4 | C24 | 1 | 8 | yes | — |
| 597 | C4×D4 | C24 | 1 | 4 | yes | — |
| 598 | C4×D4 | C24 | 1 | 4 | yes | — |
| 599 | C4×D4 | C24 | 1 | 8 | yes | — |
| 600 | C4×D4 | C24 | 1 | 4 | yes | — |
| 601 | C4×D4 | C24 | 1 | 4 | yes | — |
| 602 | #117 | — | 2 | 2 | no | — |
| 603 | #117 | — | 2 | 2 | no | — |
| 604 | #117 | — | 2 | 8 | no | — |
| 605 | #117 | — | 2 | 8 | no | — |
| 606 | #117 | — | 2 | 4 | no | — |
| 607 | #117 | — | 2 | 4 | no | — |
| 608 | #117 | — | 2 | 4 | no | — |
| 609 | #117 | C24 | 1 | 4 | yes | — |
| 610 | #117 | C24 | 1 | 16 | yes | — |
| 611 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 612 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 613 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 614 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 615 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 616 | C2×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 617 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 618 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 619 | C2×C22⋊C4 | — | 2 | 16 | no | — |
| 620 | C2×C22⋊C4 | — | 2 | 16 | no | — |
| 621 | C2×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 622 | C2×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 623 | C2×C42 | — | 2 | 4 | no | — |
| 624 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 625 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 626 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 627 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 628 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 629 | C2×C42 | C24 | 1 | 2 | yes | — |
| 630 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 631 | C2×C42 | C24 | 1 | 2 | yes | — |
| 632 | #107 | C24 | 1 | 8 | yes | — |
| 633 | #107 | C24 | 1 | 4 | yes | — |
| 634 | #107 | C24 | 1 | 8 | yes | — |
| 635 | #107 | C24 | 1 | 4 | yes | — |
| 636 | #107 | C24 | 1 | 8 | yes | — |
| 637 | #107 | C24 | 1 | 8 | yes | — |
| 638 | #106 | C24 | 1 | 8 | yes | — |
| 639 | #106 | C24 | 1 | 8 | yes | — |
| 640 | #106 | C24 | 1 | 8 | yes | — |
| 641 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 642 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 643 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 644 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 645 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 646 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 647 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 648 | #103 | C24 | 1 | 8 | yes | — |
| 649 | #103 | C24 | 1 | 8 | yes | — |
| 650 | #103 | C24 | 1 | 8 | yes | — |
| 651 | #103 | C24 | 1 | 8 | yes | — |
| 652 | #102 | C24 | 1 | 8 | yes | — |
| 653 | #102 | C24 | 1 | 8 | yes | — |
| 654 | #102 | C24 | 1 | 8 | yes | — |
| 655 | #102 | C24 | 1 | 16 | yes | — |
| 656 | #102 | C24 | 1 | 8 | yes | — |
| 657 | #102 | C24 | 1 | 8 | yes | — |
| 658 | #102 | C24 | 1 | 16 | yes | — |
| 659 | #102 | C24 | 1 | 8 | yes | — |
| 660 | #102 | C24 | 1 | 8 | yes | — |
| 661 | #102 | C24 | 1 | 8 | yes | — |
| 662 | C22⋊C8 | C24 | 1 | 4 | yes | — |
| 663 | C22⋊C8 | C24 | 1 | 8 | yes | — |
| 664 | C22⋊C8 | C24 | 1 | 4 | yes | — |
| 665 | C22⋊C8 | C24 | 1 | 8 | yes | — |
| 666 | C22⋊C8 | C24 | 1 | 16 | yes | — |
| 667 | C22⋊C8 | C24 | 1 | 8 | yes | — |
| 668 | C4×C8 | C24 | 1 | 4 | yes | — |
| 669 | C4×C8 | C24 | 1 | 4 | yes | — |
| 670 | C4×C8 | C24 | 1 | 4 | yes | — |
| 671 | C4×C8 | C24 | 1 | 4 | yes | — |
| 672 | C24 | — | 2 | 4 | no | — |
| 673 | C24 | — | 2 | 16 | no | — |
| 674 | C24 | C22×D4 | 1 | 4 | yes | — |
| 675 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 676 | #41 | — | 4 | 8 | no | — |
| 677 | #41 | — | 4 | 8 | no | — |
| 678 | #41 | — | 4 | 4 | no | — |
| 679 | #41 | — | 4 | 4 | no | — |
| 680 | #41 | — | 4 | 16 | no | — |
| 681 | #41 | — | 4 | 16 | no | — |
| 682 | #41 | — | 4 | 16 | no | — |
| 683 | #41 | — | 4 | 8 | no | — |
| 684 | #41 | — | 8 | 4 | no | — |
| 685 | #41 | — | 8 | 8 | no | — |
| 686 | #41 | — | 8 | 8 | no | — |
| 687 | #41 | — | 8 | 8 | no | — |
| 688 | #41 | — | 8 | 8 | no | — |
| 689 | #41 | — | 8 | 16 | no | — |
| 690 | #41 | — | 8 | 16 | no | — |
| 691 | #41 | — | 8 | 16 | no | — |
| 692 | C2×Q8 | — | 2 | 2 | no | — |
| 693 | C2×Q8 | — | 2 | 4 | no | — |
| 694 | C2×Q8 | — | 2 | 2 | no | — |
| 695 | C2×Q8 | — | 2 | 4 | no | — |
| 696 | C2×Q8 | — | 8 | 4 | no | — |
| 697 | C2×Q8 | — | 8 | 2 | no | — |
| 698 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 699 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 700 | C2×D4 | — | 2 | 8 | no | — |
| 701 | C2×D4 | — | 2 | 4 | no | — |
| 702 | C2×D4 | — | 2 | 4 | no | — |
| 703 | C2×D4 | — | 2 | 4 | no | — |
| 704 | C2×D4 | — | 2 | 16 | no | — |
| 705 | C2×D4 | — | 2 | 16 | no | — |
| 706 | C2×D4 | — | 2 | 8 | no | — |
| 707 | C2×D4 | — | 2 | 16 | no | — |
| 708 | C2×D4 | — | 2 | 16 | no | — |
| 709 | C2×D4 | — | 2 | 8 | no | — |
| 710 | C2×D4 | — | 2 | 4 | no | — |
| 711 | C2×D4 | — | 2 | 2 | no | — |
| 712 | C2×D4 | — | 2 | 4 | no | — |
| 713 | C2×D4 | — | 2 | 4 | no | — |
| 714 | C2×D4 | — | 2 | 2 | no | — |
| 715 | C2×D4 | — | 2 | 4 | no | — |
| 716 | C2×D4 | — | 2 | 4 | no | — |
| 717 | C2×D4 | — | 2 | 16 | no | — |
| 718 | C2×D4 | — | 4 | 4 | no | — |
| 719 | C2×D4 | — | 4 | 4 | no | — |
| 720 | C2×D4 | — | 4 | 4 | no | — |
| 721 | C2×D4 | — | 4 | 16 | no | — |
| 722 | C2×D4 | — | 4 | 16 | no | — |
| 723 | C2×D4 | — | 8 | 4 | no | — |
| 724 | C2×D4 | — | 8 | 4 | no | — |
| 725 | C2×D4 | — | 8 | 16 | no | — |
| 726 | C2×D4 | — | 8 | 16 | no | — |
| 727 | C2×D4 | — | 8 | 16 | no | — |
| 728 | C2×D4 | — | 8 | 2 | no | — |
| 729 | C2×D4 | — | 8 | 4 | no | — |
| 730 | C2×D4 | — | 8 | 16 | no | — |
| 731 | C2×D4 | — | 8 | 8 | no | — |
| 732 | C2×D4 | — | 8 | 32 | no | — |
| 733 | C2×D4 | — | 8 | 32 | no | — |
| 734 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 735 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 736 | C2×D4 | C22×D4 | 1 | 16 | yes | — |
| 737 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 738 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 739 | C2×D4 | C25 | 1 | 4 | yes | — |
| 740 | C2×D4 | C25 | 1 | 8 | yes | — |
| 741 | C22×C4 | — | 2 | 4 | no | — |
| 742 | C22×C4 | — | 2 | 4 | no | — |
| 743 | C22×C4 | — | 2 | 16 | no | — |
| 744 | C22×C4 | — | 2 | 4 | no | — |
| 745 | C22×C4 | — | 2 | 4 | no | — |
| 746 | C22×C4 | — | 2 | 4 | no | — |
| 747 | C22×C4 | — | 2 | 8 | no | — |
| 748 | C22×C4 | — | 2 | 8 | no | — |
| 749 | C22×C4 | — | 2 | 16 | no | — |
| 750 | C22×C4 | — | 4 | 4 | no | — |
| 751 | C22×C4 | — | 4 | 4 | no | — |
| 752 | C22×C4 | — | 4 | 2 | no | — |
| 753 | C22×C4 | — | 4 | 1 | no | — |
| 754 | C22×C4 | — | 4 | 1 | no | — |
| 755 | C22×C4 | — | 8 | 8 | no | — |
| 756 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 757 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 758 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 759 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 760 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 761 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 762 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 763 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 764 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 765 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 766 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 767 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 768 | C22×C4 | C25 | 1 | 2 | yes | — |
| 769 | C22×C4 | C25 | 1 | 8 | yes | — |
| 770 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 771 | Q16 | — | 4 | 4 | no | — |
| 772 | SD16 | — | 4 | 8 | no | — |
| 773 | SD16 | — | 4 | 8 | no | — |
| 774 | SD16 | — | 4 | 8 | no | — |
| 775 | D8 | — | 4 | 8 | no | — |
| 776 | D8 | — | 4 | 4 | no | — |
| 777 | D8 | — | 4 | 8 | no | — |
| 778 | D8 | — | 4 | 8 | no | — |
| 779 | D8 | — | 4 | 8 | no | — |
| 780 | M16 | — | 4 | 16 | no | — |
| 781 | C2×C8 | — | 4 | 2 | no | — |
| 782 | C2×C8 | — | 4 | 2 | no | — |
| 783 | C2×C8 | — | 4 | 8 | no | — |
| 784 | C2×C8 | — | 4 | 8 | no | — |
| 785 | C2×C8 | — | 4 | 2 | no | — |
| 786 | C2×C8 | — | 4 | 2 | no | — |
| 787 | C2×C8 | C25 | 1 | 2 | yes | — |
| 788 | C2×C8 | C25 | 1 | 4 | yes | — |
| 789 | C2×C8 | C25 | 1 | 4 | yes | — |
| 790 | C2×C8 | C25 | 1 | 4 | yes | — |
| 791 | C2×C8 | C25 | 1 | 2 | yes | — |
| 792 | C4⋊C4 | — | 2 | 2 | no | — |
| 793 | C4⋊C4 | — | 2 | 4 | no | — |
| 794 | C4⋊C4 | — | 2 | 4 | no | — |
| 795 | C4⋊C4 | — | 2 | 16 | no | — |
| 796 | C4⋊C4 | — | 2 | 4 | no | — |
| 797 | C4⋊C4 | — | 2 | 16 | no | — |
| 798 | C4⋊C4 | — | 2 | 2 | no | — |
| 799 | C4⋊C4 | — | 2 | 4 | no | — |
| 800 | C4⋊C4 | — | 2 | 4 | no | — |
| 801 | C4⋊C4 | — | 2 | 4 | no | — |
| 802 | C4⋊C4 | — | 2 | 4 | no | — |
| 803 | C4⋊C4 | — | 2 | 2 | no | — |
| 804 | C4⋊C4 | — | 2 | 2 | no | — |
| 805 | C4⋊C4 | — | 2 | 4 | no | — |
| 806 | C4⋊C4 | — | 2 | 4 | no | — |
| 807 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 808 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 809 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 810 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 811 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 812 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 813 | C22⋊C4 | — | 2 | 16 | no | — |
| 814 | C22⋊C4 | — | 2 | 4 | no | — |
| 815 | C22⋊C4 | — | 2 | 4 | no | — |
| 816 | C22⋊C4 | — | 2 | 4 | no | — |
| 817 | C22⋊C4 | — | 2 | 16 | no | — |
| 818 | C22⋊C4 | — | 2 | 4 | no | — |
| 819 | C22⋊C4 | — | 2 | 4 | no | — |
| 820 | C22⋊C4 | — | 2 | 8 | no | — |
| 821 | C22⋊C4 | — | 2 | 16 | no | — |
| 822 | C22⋊C4 | — | 2 | 16 | no | — |
| 823 | C22⋊C4 | — | 2 | 8 | no | — |
| 824 | C22⋊C4 | — | 2 | 8 | no | — |
| 825 | C22⋊C4 | — | 2 | 8 | no | — |
| 826 | C22⋊C4 | — | 2 | 4 | no | — |
| 827 | C22⋊C4 | — | 2 | 4 | no | — |
| 828 | C22⋊C4 | — | 2 | 16 | no | — |
| 829 | C22⋊C4 | — | 2 | 4 | no | — |
| 830 | C22⋊C4 | — | 2 | 4 | no | — |
| 831 | C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 832 | C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 833 | C22⋊C4 | C22×D4 | 1 | 16 | yes | — |
| 834 | C42 | — | 2 | 4 | no | — |
| 835 | C42 | — | 2 | 4 | no | — |
| 836 | C42 | — | 2 | 4 | no | — |
| 837 | C42 | — | 2 | 16 | no | — |
| 838 | C42 | C22×D4 | 1 | 2 | yes | — |
| 839 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 840 | C42 | C22×D4 | 1 | 2 | yes | — |
| 841 | C42 | C22×D4 | 1 | 2 | yes | — |
| 842 | C42 | C22×D4 | 1 | 2 | yes | — |
| 843 | C42 | C22×D4 | 1 | 2 | yes | — |
| 844 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 845 | C42 | C25 | 1 | 1 | yes | characteristic |
| 846 | C42 | C25 | 1 | 2 | yes | — |
| 847 | C42 | C25 | 1 | 1 | yes | characteristic |
| 848 | C23 | — | 2 | 2 | no | — |
| 849 | C23 | — | 2 | 8 | no | — |
| 850 | C23 | — | 2 | 4 | no | — |
| 851 | C23 | — | 2 | 8 | no | — |
| 852 | C23 | — | 4 | 1 | no | — |
| 853 | C23 | — | 4 | 4 | no | — |
| 854 | C23 | — | 4 | 1 | no | — |
| 855 | C23 | — | 4 | 4 | no | — |
| 856 | C23 | — | 4 | 8 | no | — |
| 857 | C23 | — | 8 | 4 | no | — |
| 858 | C23 | — | 8 | 4 | no | — |
| 859 | C23 | — | 8 | 16 | no | — |
| 860 | C23 | — | 8 | 16 | no | — |
| 861 | C23 | — | 8 | 16 | no | — |
| 862 | C23 | C23×D4 | 1 | 8 | yes | — |
| 863 | C23 | C23×D4 | 1 | 2 | yes | — |
| 864 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 865 | Q8 | — | 2 | 4 | no | — |
| 866 | Q8 | — | 2 | 4 | no | — |
| 867 | Q8 | — | 4 | 8 | no | — |
| 868 | Q8 | — | 4 | 8 | no | — |
| 869 | Q8 | — | 4 | 4 | no | — |
| 870 | Q8 | — | 8 | 4 | no | — |
| 871 | Q8 | — | 8 | 2 | no | — |
| 872 | D4 | — | 2 | 8 | no | — |
| 873 | D4 | — | 2 | 4 | no | — |
| 874 | D4 | — | 2 | 8 | no | — |
| 875 | D4 | — | 2 | 8 | no | — |
| 876 | D4 | — | 2 | 4 | no | — |
| 877 | D4 | — | 2 | 16 | no | — |
| 878 | D4 | — | 4 | 4 | no | — |
| 879 | D4 | — | 4 | 8 | no | — |
| 880 | D4 | — | 4 | 16 | no | — |
| 881 | D4 | — | 4 | 8 | no | — |
| 882 | D4 | — | 4 | 8 | no | — |
| 883 | D4 | — | 4 | 8 | no | — |
| 884 | D4 | — | 4 | 16 | no | — |
| 885 | D4 | — | 4 | 8 | no | — |
| 886 | D4 | — | 4 | 4 | no | — |
| 887 | D4 | — | 4 | 8 | no | — |
| 888 | D4 | — | 8 | 16 | no | — |
| 889 | D4 | — | 8 | 4 | no | — |
| 890 | D4 | — | 8 | 4 | no | — |
| 891 | D4 | — | 8 | 2 | no | — |
| 892 | D4 | — | 8 | 16 | no | — |
| 893 | D4 | — | 8 | 16 | no | — |
| 894 | D4 | — | 8 | 16 | no | — |
| 895 | D4 | — | 8 | 16 | no | — |
| 896 | D4 | — | 8 | 8 | no | — |
| 897 | D4 | — | 8 | 4 | no | — |
| 898 | C2×C4 | — | 2 | 2 | no | — |
| 899 | C2×C4 | — | 2 | 2 | no | — |
| 900 | C2×C4 | — | 2 | 4 | no | — |
| 901 | C2×C4 | — | 2 | 1 | no | — |
| 902 | C2×C4 | — | 2 | 1 | no | — |
| 903 | C2×C4 | — | 2 | 8 | no | — |
| 904 | C2×C4 | — | 2 | 8 | no | — |
| 905 | C2×C4 | — | 2 | 2 | no | — |
| 906 | C2×C4 | — | 2 | 2 | no | — |
| 907 | C2×C4 | — | 2 | 4 | no | — |
| 908 | C2×C4 | — | 2 | 4 | no | — |
| 909 | C2×C4 | — | 2 | 4 | no | — |
| 910 | C2×C4 | — | 2 | 8 | no | — |
| 911 | C2×C4 | — | 2 | 4 | no | — |
| 912 | C2×C4 | — | 2 | 4 | no | — |
| 913 | C2×C4 | — | 4 | 2 | no | — |
| 914 | C2×C4 | — | 4 | 1 | no | — |
| 915 | C2×C4 | — | 4 | 1 | no | — |
| 916 | C2×C4 | — | 4 | 4 | no | — |
| 917 | C2×C4 | — | 4 | 8 | no | — |
| 918 | C2×C4 | — | 4 | 2 | no | — |
| 919 | C2×C4 | — | 4 | 8 | no | — |
| 920 | C2×C4 | — | 4 | 8 | no | — |
| 921 | C2×C4 | — | 4 | 16 | no | — |
| 922 | C2×C4 | — | 4 | 8 | no | — |
| 923 | C2×C4 | — | 8 | 8 | no | — |
| 924 | C2×C4 | — | 8 | 16 | no | — |
| 925 | C2×C4 | — | 8 | 4 | no | — |
| 926 | C2×C4 | — | 8 | 16 | no | — |
| 927 | C2×C4 | #576 | 1 | 4 | yes | — |
| 928 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 929 | C2×C4 | C23×D4 | 1 | 8 | yes | — |
| 930 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 931 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 932 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 933 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 934 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 935 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 936 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 937 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 938 | C8 | — | 2 | 2 | no | — |
| 939 | C8 | — | 2 | 4 | no | — |
| 940 | C8 | — | 2 | 2 | no | — |
| 941 | C8 | — | 2 | 4 | no | — |
| 942 | C8 | — | 2 | 4 | no | — |
| 943 | C22 | — | 2 | 1 | no | — |
| 944 | C22 | — | 2 | 1 | no | — |
| 945 | C22 | — | 2 | 2 | no | — |
| 946 | C22 | — | 2 | 8 | no | — |
| 947 | C22 | — | 2 | 2 | no | — |
| 948 | C22 | — | 2 | 8 | no | — |
| 949 | C22 | — | 2 | 2 | no | — |
| 950 | C22 | — | 2 | 8 | no | — |
| 951 | C22 | — | 4 | 8 | no | — |
| 952 | C22 | — | 4 | 4 | no | — |
| 953 | C22 | — | 4 | 4 | no | — |
| 954 | C22 | — | 4 | 8 | no | — |
| 955 | C22 | — | 4 | 4 | no | — |
| 956 | C22 | — | 4 | 8 | no | — |
| 957 | C22 | — | 8 | 2 | no | — |
| 958 | C22 | — | 8 | 8 | no | — |
| 959 | C22 | — | 16 | 8 | no | — |
| 960 | C22 | — | 32 | 16 | no | — |
| 961 | C22 | C2×#576 | 1 | 2 | yes | — |
| 962 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 963 | C4 | — | 2 | 1 | no | — |
| 964 | C4 | — | 2 | 1 | no | — |
| 965 | C4 | — | 2 | 1 | no | — |
| 966 | C4 | — | 2 | 2 | no | — |
| 967 | C4 | — | 2 | 1 | no | — |
| 968 | C4 | — | 2 | 2 | no | — |
| 969 | C4 | — | 2 | 8 | no | — |
| 970 | C4 | — | 4 | 4 | no | — |
| 971 | C4 | — | 4 | 8 | no | — |
| 972 | C4 | — | 4 | 4 | no | — |
| 973 | C4 | — | 4 | 4 | no | — |
| 974 | C4 | C2×#576 | 1 | 4 | yes | — |
| 975 | C4 | #3584 | 1 | 2 | yes | — |
| 976 | C4 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 977 | C4 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 978 | C2 | — | 2 | 2 | no | — |
| 979 | C2 | — | 4 | 2 | no | — |
| 980 | C2 | — | 4 | 8 | no | — |
| 981 | C2 | — | 8 | 8 | no | — |
| 982 | C2 | — | 8 | 4 | no | — |
| 983 | C2 | #62842 | 1 | 1 | yes | characteristic |
| 984 | C2 | C22×#576 | 1 | 1 | yes | characteristic |
| 985 | C2 | C2×#3584 | 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 ◁ C2×#532 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62834 | C2 | semidirect |
| 2. #62263 | C2 | semidirect |
| 3. #62259 | C2 | semidirect |
| 4. #62251 | C2 | semidirect |
| 5. #62248 | C2 | semidirect |
| 6. #62245 | C2 | semidirect |
| 7. #61791 | C2 | semidirect |
| 8. #61788 | C2 | semidirect |
| 9. #61784 | C2 | semidirect |
| 10. #61668 | C2 | semidirect |
| 11. #61661 | C2 | semidirect |
| 12. #61657 | C2 | semidirect |
| 13. #60948 | C2 | semidirect |
| 14. #60946 | C2 | semidirect |
| 15. #60940 | C2 | semidirect |
| 16. #60768 | C2 | semidirect |
| 17. C2×#2979 | C2 | semidirect |
| 20. #3549 | C22 | semidirect |
| 21. #3548 | C22 | semidirect |
| 23. #3546 | C22 | semidirect |
| 26. #3519 | C22 | semidirect |
| 28. #3511 | C22 | semidirect |
| 30. #3506 | C22 | semidirect |
| 31. #3506 | C22 | semidirect |
| 33. #3498 | C22 | semidirect |
| 34. #3496 | C22 | semidirect |
| 35. #3496 | C22 | semidirect |
| 37. #3488 | C22 | semidirect |
| 38. #3444 | C22 | semidirect |
| 40. C2×#532 | C22 | semidirect |
| 41. #3357 | C22 | semidirect |
| 42. #3355 | C22 | semidirect |
| 43. #3354 | C22 | semidirect |
| 44. #3353 | C22 | semidirect |
| 45. #3341 | C22 | semidirect |
| 46. #3340 | C22 | semidirect |
| 47. #3339 | C22 | semidirect |
| 48. #3338 | C22 | semidirect |
| 49. #3334 | C22 | semidirect |
| 50. #3333 | C22 | semidirect |
| 51. #3332 | C22 | semidirect |
| 52. #3330 | C22 | semidirect |
| 53. #3325 | C22 | semidirect |
| 54. #3325 | C22 | semidirect |
| 55. #3324 | C22 | semidirect |
| 56. #3322 | C22 | semidirect |
| 57. #3305 | C22 | semidirect |
| 58. #3305 | C22 | semidirect |
| 59. #3302 | C22 | semidirect |
| 60. #3297 | C22 | semidirect |
| 61. #3295 | C22 | semidirect |
| 62. #3294 | C22 | semidirect |
| 63. #3294 | C22 | semidirect |
| 64. #3287 | C22 | semidirect |
| 65. #3284 | C22 | semidirect |
| 66. #3280 | C22 | semidirect |
| 67. D4×D8 | C22 | semidirect |
| 68. D4×D8 | C22 | semidirect |
| 69. #3274 | C22 | semidirect |
| 70. #3274 | C22 | semidirect |
| 71. #3273 | C22 | semidirect |
| 72. #3272 | C22 | semidirect |
| 73. #3249 | C22 | semidirect |
| 74. #3247 | C22 | semidirect |
| 75. #3247 | C22 | semidirect |
| 76. #3246 | C22 | semidirect |
| 77. #3245 | C22 | semidirect |
| 78. #3245 | C22 | semidirect |
| 79. #3245 | C22 | semidirect |
| 80. #3233 | C22 | semidirect |
| 81. #3230 | C22 | semidirect |
| 82. #3228 | C22 | semidirect |
| 83. #3227 | C22 | semidirect |
| 84. #3226 | C22 | semidirect |
| 85. #3212 | C22 | semidirect |
| 86. #3208 | C22 | semidirect |
| 87. #3207 | C22 | semidirect |
| 88. #3205 | C22 | semidirect |
| 89. #3205 | C22 | semidirect |
| 90. #3203 | C22 | semidirect |
| 91. #3199 | C22 | semidirect |
| 92. #3198 | C22 | semidirect |
| 93. #3198 | C22 | semidirect |
| 94. #3191 | C22 | semidirect |
| 95. #3191 | C22 | semidirect |
| 96. #3188 | C22 | semidirect |
| 97. #3188 | C22 | semidirect |
| 98. #3186 | C22 | semidirect |
| 99. #3186 | C22 | semidirect |
| 100. #3169 | C22 | semidirect |
| 101. #3169 | C22 | semidirect |
| 102. #3168 | C22 | semidirect |
| 103. #3167 | C22 | semidirect |
| 104. #3107 | C22 | semidirect |
| 105. #3106 | C22 | semidirect |
| 106. #3106 | C22 | semidirect |
| 107. #3106 | C22 | semidirect |
| 108. #3105 | C22 | semidirect |
| 109. #3100 | C22 | semidirect |
| 110. #3098 | C22 | semidirect |
| 111. #3096 | C22 | semidirect |
| 112. #3055 | C22 | semidirect |
| 113. #3050 | C22 | semidirect |
| 114. C2×#466 | C22 | semidirect |
| 115. #3012 | C22 | semidirect |
| 116. #3008 | C22 | semidirect |
| 117. #2979 | C22 | semidirect |
| 118. #2979 | C22 | semidirect |
| 119. #2979 | C22 | semidirect |
| 120. C2×#436 | C22 | semidirect |
| 121. C2×#436 | C22 | semidirect |
| 122. C2×C8×D4 | C22 | semidirect |
| 123. C2×C8×D4 | C22 | semidirect |
| 124. C2×#431 | C22 | semidirect |
| 125. C2×#431 | C22 | semidirect |
| 126. C2×#408 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62834 | 2 |
| #62263 | 2 |
| #62259 | 2 |
| #62251 | 2 |
| #62248 | 2 |
| #62245 | 2 |
| #61791 | 2 |
| #61788 | 2 |
| #61784 | 2 |
| #61668 | 2 |
| #61661 | 2 |
| #61657 | 2 |
| #60948 | 2 |
| #60946 | 2 |
| #60940 | 2 |
| #60768 | 2 |
| C2×#2979 | 2 |