Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6367518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #512897 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #512857 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #488929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #153641 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #153638 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #153536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #153450 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #153441 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #62144 | — | 2 | 1 | no | — |
| 11 | #61934 | — | 2 | 1 | no | — |
| 12 | #61105 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#2230 | — | 2 | 1 | no | — |
| 14 | #33571 | — | 2 | 1 | no | — |
| 15 | #33546 | — | 2 | 1 | no | — |
| 16 | #20289 | C22 | 1 | 2 | yes | complemented |
| 17 | #20156 | — | 2 | 1 | no | — |
| 18 | #20152 | — | 2 | 1 | no | — |
| 19 | #20119 | — | 2 | 2 | no | — |
| 20 | #20013 | C22 | 1 | 2 | yes | complemented |
| 21 | #19952 | — | 2 | 2 | no | — |
| 22 | #19654 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19570 | — | 2 | 1 | no | — |
| 24 | #19494 | — | 2 | 1 | no | — |
| 25 | #18688 | C22 | 1 | 1 | yes | characteristic |
| 26 | #18655 | — | 2 | 1 | no | — |
| 27 | #18480 | C22 | 1 | 1 | yes | characteristic |
| 28 | #18019 | — | 2 | 1 | no | — |
| 29 | #13684 | — | 2 | 2 | no | — |
| 30 | #13683 | C22 | 1 | 4 | yes | — |
| 31 | #13676 | C22 | 1 | 2 | yes | — |
| 32 | #13675 | — | 2 | 1 | no | — |
| 33 | #13674 | C22 | 1 | 2 | yes | — |
| 34 | #13673 | — | 2 | 1 | no | — |
| 35 | #13589 | C22 | 1 | 1 | yes | characteristic |
| 36 | #13583 | C22 | 1 | 1 | yes | characteristic |
| 37 | #13574 | — | 2 | 1 | no | — |
| 38 | #13560 | — | 2 | 1 | no | — |
| 39 | #12365 | C22 | 1 | 4 | yes | — |
| 40 | #12364 | — | 2 | 2 | no | — |
| 41 | #11922 | C22 | 1 | 1 | yes | characteristic |
| 42 | #11602 | — | 2 | 1 | no | — |
| 43 | #7536 | C22 | 1 | 4 | yes | complemented |
| 44 | #7520 | C22 | 1 | 4 | yes | complemented |
| 45 | #7518 | C22 | 1 | 2 | yes | complemented |
| 46 | #7517 | C22 | 1 | 2 | yes | complemented |
| 47 | #3584 | — | 4 | 1 | no | — |
| 48 | #3550 | D4 | 1 | 1 | yes | characteristic, complemented |
| 49 | #3509 | — | 2 | 1 | no | — |
| 50 | #3481 | D4 | 1 | 1 | yes | characteristic |
| 51 | #3400 | — | 2 | 2 | no | — |
| 52 | #3398 | — | 4 | 1 | no | — |
| 53 | #3394 | — | 2 | 2 | no | — |
| 54 | #3393 | — | 4 | 1 | no | — |
| 55 | #3381 | — | 2 | 2 | no | — |
| 56 | #3369 | — | 2 | 2 | no | — |
| 57 | #3367 | — | 4 | 1 | no | — |
| 58 | #3365 | — | 2 | 2 | no | — |
| 59 | #3363 | — | 2 | 2 | no | — |
| 60 | #3359 | — | 4 | 1 | no | — |
| 61 | #3356 | — | 2 | 2 | no | — |
| 62 | #3351 | — | 4 | 2 | no | — |
| 63 | #3324 | — | 2 | 2 | no | — |
| 64 | #3323 | — | 4 | 2 | no | — |
| 65 | #3293 | — | 2 | 1 | no | — |
| 66 | #3292 | — | 2 | 1 | no | — |
| 67 | #3291 | — | 2 | 1 | no | — |
| 68 | #3291 | C23 | 1 | 2 | yes | — |
| 69 | #3290 | — | 4 | 2 | no | — |
| 70 | #3254 | — | 2 | 1 | no | — |
| 71 | #3252 | — | 4 | 1 | no | — |
| 72 | #3233 | — | 4 | 1 | no | — |
| 73 | #3227 | — | 2 | 1 | no | — |
| 74 | #3225 | — | 4 | 2 | no | — |
| 75 | #3209 | — | 2 | 1 | no | — |
| 76 | #3206 | — | 2 | 1 | no | — |
| 77 | C2×#498 | D4 | 1 | 1 | yes | characteristic, complemented |
| 78 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 79 | #3121 | — | 4 | 2 | no | — |
| 80 | #3107 | — | 2 | 1 | no | — |
| 81 | #3106 | — | 2 | 1 | no | — |
| 82 | #3101 | — | 4 | 1 | no | — |
| 83 | #3079 | — | 2 | 1 | no | — |
| 84 | #3077 | — | 4 | 1 | no | — |
| 85 | #3067 | — | 4 | 1 | no | — |
| 86 | #3025 | — | 4 | 1 | no | — |
| 87 | #3022 | — | 4 | 1 | no | — |
| 88 | #3018 | — | 2 | 1 | no | — |
| 89 | #3018 | — | 2 | 1 | no | — |
| 90 | #2991 | — | 2 | 1 | no | — |
| 91 | #2986 | — | 2 | 1 | no | — |
| 92 | C2×#443 | — | 2 | 1 | no | — |
| 93 | #2230 | — | 2 | 4 | no | — |
| 94 | #2230 | — | 4 | 2 | no | — |
| 95 | #2205 | — | 2 | 4 | no | — |
| 96 | #2203 | — | 4 | 2 | no | — |
| 97 | #2198 | — | 2 | 2 | no | — |
| 98 | #2197 | — | 4 | 2 | no | — |
| 99 | #2196 | — | 2 | 2 | no | — |
| 100 | C2×#365 | — | 4 | 1 | no | — |
| 101 | C2×#364 | — | 2 | 1 | no | — |
| 102 | C2×#360 | — | 4 | 1 | no | — |
| 103 | #2135 | — | 4 | 1 | no | — |
| 104 | #2132 | — | 2 | 1 | no | — |
| 105 | #2126 | — | 2 | 1 | no | — |
| 106 | #2120 | — | 4 | 1 | no | — |
| 107 | #1716 | — | 2 | 1 | no | — |
| 108 | #1715 | — | 2 | 1 | no | — |
| 109 | #1708 | C23 | 1 | 2 | yes | — |
| 110 | #1705 | D4 | 1 | 2 | yes | complemented |
| 111 | #1703 | — | 2 | 2 | no | — |
| 112 | #1702 | — | 2 | 2 | no | — |
| 113 | #1692 | — | 2 | 2 | no | — |
| 114 | #1685 | — | 2 | 2 | no | — |
| 115 | #1684 | — | 2 | 2 | no | — |
| 116 | #1682 | — | 2 | 2 | no | — |
| 117 | #1672 | — | 2 | 2 | no | — |
| 118 | #1666 | — | 2 | 2 | no | — |
| 119 | #1653 | — | 2 | 2 | no | — |
| 120 | #1653 | — | 2 | 2 | no | — |
| 121 | #1652 | — | 2 | 2 | no | — |
| 122 | #1652 | — | 2 | 2 | no | — |
| 123 | #1633 | D4 | 1 | 2 | yes | complemented |
| 124 | #1632 | — | 2 | 1 | no | — |
| 125 | #1630 | — | 2 | 1 | no | — |
| 126 | #1630 | C23 | 1 | 1 | yes | characteristic |
| 127 | #1629 | C23 | 1 | 1 | yes | characteristic |
| 128 | #1623 | C23 | 1 | 2 | yes | — |
| 129 | #1622 | — | 2 | 1 | no | — |
| 130 | #1620 | — | 2 | 1 | no | — |
| 131 | #1620 | D4 | 1 | 1 | yes | characteristic |
| 132 | #1619 | D4 | 1 | 1 | yes | characteristic |
| 133 | #1590 | — | 2 | 2 | no | — |
| 134 | #1588 | — | 2 | 2 | no | — |
| 135 | #1587 | — | 2 | 2 | no | — |
| 136 | C8×Q16 | — | 2 | 2 | no | — |
| 137 | #1574 | — | 2 | 1 | no | — |
| 138 | #1560 | D4 | 1 | 1 | yes | characteristic, complemented |
| 139 | #1546 | — | 2 | 1 | no | — |
| 140 | #1543 | D4 | 1 | 1 | yes | characteristic |
| 141 | #1493 | — | 2 | 1 | no | — |
| 142 | #1476 | — | 2 | 1 | no | — |
| 143 | #1450 | D4 | 1 | 1 | yes | characteristic, complemented |
| 144 | #1411 | — | 2 | 1 | no | — |
| 145 | #1410 | C23 | 1 | 2 | yes | — |
| 146 | #1409 | C23 | 1 | 2 | yes | — |
| 147 | #1408 | — | 2 | 1 | no | — |
| 148 | #1405 | — | 2 | 4 | no | — |
| 149 | #1402 | — | 2 | 2 | no | — |
| 150 | #1402 | — | 2 | 2 | no | — |
| 151 | #1359 | — | 2 | 1 | no | — |
| 152 | #1359 | C23 | 1 | 2 | yes | — |
| 153 | #1335 | — | 2 | 4 | no | — |
| 154 | #585 | — | 2 | 1 | no | — |
| 155 | #585 | — | 2 | 1 | no | — |
| 156 | #578 | — | 4 | 2 | no | — |
| 157 | #578 | — | 8 | 1 | no | — |
| 158 | #577 | — | 4 | 2 | no | — |
| 159 | #577 | — | 4 | 2 | no | — |
| 160 | #577 | — | 8 | 1 | no | — |
| 161 | #577 | — | 8 | 1 | no | — |
| 162 | #576 | — | 4 | 2 | no | — |
| 163 | #576 | — | 8 | 1 | no | — |
| 164 | #575 | — | 4 | 1 | no | — |
| 165 | #575 | — | 4 | 1 | no | — |
| 166 | #575 | — | 8 | 2 | no | — |
| 167 | C2×#137 | — | 8 | 1 | no | — |
| 168 | C2×#135 | — | 2 | 1 | no | — |
| 169 | C2×#135 | — | 4 | 1 | no | — |
| 170 | C2×#135 | — | 8 | 2 | no | — |
| 171 | C2×#131 | — | 4 | 1 | no | — |
| 172 | #563 | — | 4 | 1 | no | — |
| 173 | #559 | — | 2 | 1 | no | — |
| 174 | #559 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | Q82 | C2×D4 | 1 | 2 | yes | — |
| 176 | #557 | — | 2 | 2 | no | — |
| 177 | #557 | — | 4 | 1 | no | — |
| 178 | #556 | — | 2 | 2 | no | — |
| 179 | #556 | — | 4 | 1 | no | — |
| 180 | #556 | — | 4 | 1 | no | — |
| 181 | #554 | — | 2 | 1 | no | — |
| 182 | #553 | — | 4 | 1 | no | — |
| 183 | #552 | — | 4 | 2 | no | — |
| 184 | #552 | — | 8 | 1 | no | — |
| 185 | #551 | — | 4 | 1 | no | — |
| 186 | D4×Q8 | — | 4 | 1 | no | — |
| 187 | #546 | — | 4 | 1 | no | — |
| 188 | D42 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | #542 | — | 4 | 2 | no | — |
| 190 | #541 | — | 8 | 1 | no | — |
| 191 | #536 | — | 4 | 1 | no | — |
| 192 | #536 | — | 4 | 1 | no | — |
| 193 | #533 | — | 2 | 1 | no | — |
| 194 | #533 | — | 4 | 1 | no | — |
| 195 | #533 | — | 4 | 1 | no | — |
| 196 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 199 | #529 | — | 4 | 1 | no | — |
| 200 | #525 | — | 4 | 1 | no | — |
| 201 | #525 | — | 8 | 1 | no | — |
| 202 | #519 | — | 4 | 1 | no | — |
| 203 | C4×#41 | — | 2 | 1 | no | — |
| 204 | C2×C4×D4 | — | 4 | 1 | no | — |
| 205 | C2×M32 | — | 4 | 1 | no | — |
| 206 | #499 | — | 4 | 2 | no | — |
| 207 | #498 | — | 2 | 2 | no | — |
| 208 | #498 | — | 2 | 1 | no | — |
| 209 | #498 | — | 4 | 1 | no | — |
| 210 | #498 | C2×D4 | 1 | 2 | yes | — |
| 211 | #497 | — | 4 | 2 | no | — |
| 212 | #495 | — | 4 | 1 | no | — |
| 213 | #495 | — | 4 | 2 | no | — |
| 214 | #494 | — | 4 | 1 | no | — |
| 215 | #494 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | #492 | — | 2 | 2 | no | — |
| 218 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | #492 | C24 | 1 | 1 | yes | characteristic |
| 220 | #489 | — | 4 | 2 | no | — |
| 221 | #488 | — | 4 | 2 | no | — |
| 222 | #487 | — | 2 | 2 | no | — |
| 223 | #487 | — | 4 | 2 | no | — |
| 224 | #487 | — | 4 | 1 | no | — |
| 225 | #486 | — | 2 | 2 | no | — |
| 226 | #485 | — | 2 | 2 | no | — |
| 227 | #485 | — | 4 | 2 | no | — |
| 228 | #483 | — | 4 | 2 | no | — |
| 229 | #482 | — | 4 | 2 | no | — |
| 230 | #482 | — | 4 | 1 | no | — |
| 231 | #481 | — | 4 | 2 | no | — |
| 232 | #479 | — | 4 | 2 | no | — |
| 233 | #478 | — | 4 | 2 | no | — |
| 234 | #478 | — | 4 | 2 | no | — |
| 235 | #477 | — | 2 | 2 | no | — |
| 236 | #477 | — | 2 | 1 | no | — |
| 237 | #477 | — | 4 | 2 | no | — |
| 238 | #477 | — | 4 | 1 | no | — |
| 239 | #476 | — | 2 | 1 | no | — |
| 240 | #476 | — | 4 | 1 | no | — |
| 241 | #476 | — | 4 | 1 | no | — |
| 242 | #476 | — | 4 | 1 | no | — |
| 243 | #475 | — | 2 | 1 | no | — |
| 244 | #475 | — | 2 | 2 | no | — |
| 245 | #475 | — | 4 | 2 | no | — |
| 246 | #474 | — | 2 | 1 | no | — |
| 247 | #474 | — | 2 | 2 | no | — |
| 248 | #474 | — | 4 | 1 | no | — |
| 249 | #473 | — | 4 | 2 | no | — |
| 250 | #472 | — | 4 | 2 | no | — |
| 251 | #471 | — | 4 | 2 | no | — |
| 252 | #471 | — | 4 | 2 | no | — |
| 253 | #470 | — | 4 | 2 | no | — |
| 254 | #468 | — | 4 | 2 | no | — |
| 255 | #468 | — | 4 | 2 | no | — |
| 256 | #464 | — | 4 | 2 | no | — |
| 257 | #464 | — | 4 | 2 | no | — |
| 258 | #464 | — | 4 | 2 | no | — |
| 259 | #464 | — | 4 | 2 | no | — |
| 260 | #463 | — | 4 | 2 | no | — |
| 261 | #462 | — | 2 | 1 | no | — |
| 262 | #462 | — | 2 | 2 | no | — |
| 263 | #462 | — | 2 | 2 | no | — |
| 264 | #462 | — | 4 | 2 | no | — |
| 265 | #461 | — | 2 | 1 | no | — |
| 266 | #461 | — | 4 | 2 | no | — |
| 267 | #461 | — | 4 | 1 | no | — |
| 268 | #461 | — | 4 | 1 | no | — |
| 269 | #461 | — | 4 | 1 | no | — |
| 270 | #460 | — | 2 | 1 | no | — |
| 271 | #460 | — | 2 | 2 | no | — |
| 272 | #459 | — | 2 | 1 | no | — |
| 273 | #458 | — | 4 | 2 | no | — |
| 274 | #458 | — | 8 | 1 | no | — |
| 275 | B(4,𝔽2) | — | 4 | 2 | no | — |
| 276 | B(4,𝔽2) | — | 8 | 1 | no | — |
| 277 | #456 | — | 2 | 2 | no | — |
| 278 | #456 | — | 4 | 1 | no | — |
| 279 | #456 | — | 4 | 4 | no | — |
| 280 | #455 | — | 2 | 2 | no | — |
| 281 | #455 | — | 4 | 1 | no | — |
| 282 | #455 | — | 8 | 2 | no | — |
| 283 | #454 | — | 2 | 2 | no | — |
| 284 | #454 | — | 4 | 1 | no | — |
| 285 | #453 | — | 2 | 2 | no | — |
| 286 | #453 | — | 4 | 1 | no | — |
| 287 | #452 | — | 2 | 2 | no | — |
| 288 | #451 | — | 4 | 2 | no | — |
| 289 | #450 | — | 4 | 2 | no | — |
| 290 | #449 | — | 4 | 1 | no | — |
| 291 | #448 | — | 4 | 2 | no | — |
| 292 | #446 | — | 2 | 2 | no | — |
| 293 | #446 | — | 4 | 1 | no | — |
| 294 | C8×Q8 | — | 2 | 2 | no | — |
| 295 | C8×Q8 | — | 2 | 2 | no | — |
| 296 | C8×Q8 | — | 4 | 1 | no | — |
| 297 | #443 | — | 2 | 2 | no | — |
| 298 | #443 | — | 2 | 2 | no | — |
| 299 | #443 | — | 4 | 1 | no | — |
| 300 | #443 | — | 4 | 1 | no | — |
| 301 | #441 | — | 4 | 2 | no | — |
| 302 | #440 | — | 4 | 2 | no | — |
| 303 | C4×Q16 | — | 2 | 2 | no | — |
| 304 | C4×Q16 | — | 4 | 2 | no | — |
| 305 | C4×SD16 | — | 2 | 2 | no | — |
| 306 | C4×SD16 | — | 4 | 2 | no | — |
| 307 | C4×SD16 | — | 4 | 2 | no | — |
| 308 | C4×SD16 | — | 4 | 1 | no | — |
| 309 | C4×SD16 | — | 4 | 2 | no | — |
| 310 | C4×D8 | — | 4 | 1 | no | — |
| 311 | #436 | — | 2 | 2 | no | — |
| 312 | #436 | — | 4 | 2 | no | — |
| 313 | #433 | — | 4 | 2 | no | — |
| 314 | #431 | — | 2 | 1 | no | — |
| 315 | #431 | — | 2 | 1 | no | — |
| 316 | #431 | — | 4 | 1 | no | — |
| 317 | C2×#108 | — | 2 | 1 | no | — |
| 318 | #428 | — | 4 | 2 | no | — |
| 319 | #428 | — | 4 | 1 | no | — |
| 320 | C2×#106 | — | 4 | 1 | no | — |
| 321 | #423 | — | 2 | 1 | no | — |
| 322 | #423 | — | 4 | 1 | no | — |
| 323 | #421 | — | 8 | 1 | no | — |
| 324 | C2×#104 | — | 4 | 1 | no | — |
| 325 | #418 | — | 4 | 2 | no | — |
| 326 | #417 | — | 4 | 1 | no | — |
| 327 | #413 | — | 2 | 1 | no | — |
| 328 | #413 | — | 2 | 1 | no | — |
| 329 | #413 | — | 4 | 1 | no | — |
| 330 | #410 | — | 4 | 1 | no | — |
| 331 | #410 | — | 8 | 1 | no | — |
| 332 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | #365 | — | 4 | 4 | no | — |
| 334 | #364 | — | 2 | 2 | no | — |
| 335 | #364 | — | 4 | 1 | no | — |
| 336 | #360 | — | 4 | 4 | no | — |
| 337 | #356 | — | 2 | 2 | no | — |
| 338 | #356 | — | 4 | 4 | no | — |
| 339 | #355 | — | 4 | 1 | no | — |
| 340 | #354 | — | 4 | 1 | no | — |
| 341 | #353 | — | 2 | 2 | no | — |
| 342 | #352 | — | 4 | 2 | no | — |
| 343 | AΣL(1,𝔽16) | — | 4 | 2 | no | — |
| 344 | #335 | — | 2 | 2 | no | — |
| 345 | #334 | — | 2 | 2 | no | — |
| 346 | #333 | — | 2 | 1 | no | — |
| 347 | #333 | C2×D4 | 1 | 2 | yes | — |
| 348 | #332 | — | 2 | 2 | no | — |
| 349 | #332 | — | 2 | 2 | no | — |
| 350 | #331 | — | 2 | 1 | no | — |
| 351 | #331 | C2×D4 | 1 | 1 | yes | characteristic |
| 352 | #331 | C2×D4 | 1 | 1 | yes | characteristic |
| 353 | Q8⋊C8 | — | 2 | 1 | no | — |
| 354 | Q8⋊C8 | — | 2 | 2 | no | — |
| 355 | Q8⋊C8 | — | 2 | 1 | no | — |
| 356 | Q8⋊C8 | — | 2 | 2 | no | — |
| 357 | D4⋊C8 | — | 2 | 1 | no | — |
| 358 | D4⋊C8 | — | 2 | 1 | no | — |
| 359 | #322 | — | 2 | 1 | no | — |
| 360 | C82 | C2×D4 | 1 | 2 | yes | — |
| 361 | 2−1+4 | — | 2 | 2 | no | — |
| 362 | 2−1+4 | — | 4 | 1 | no | — |
| 363 | 2−1+4 | — | 8 | 1 | no | — |
| 364 | 2−1+4 | — | 8 | 1 | no | — |
| 365 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 366 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 367 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 368 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 369 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 370 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 371 | C2×#41 | — | 2 | 1 | no | — |
| 372 | C2×#41 | — | 2 | 1 | no | — |
| 373 | C2×#41 | — | 2 | 1 | no | — |
| 374 | C2×#41 | — | 4 | 1 | no | — |
| 375 | C2×#41 | — | 8 | 1 | no | — |
| 376 | C2×#41 | — | 8 | 1 | no | — |
| 377 | C2×#41 | — | 8 | 2 | no | — |
| 378 | C2×#41 | — | 8 | 2 | no | — |
| 379 | C22×Q8 | — | 4 | 1 | no | — |
| 380 | C22×Q8 | — | 4 | 1 | no | — |
| 381 | C22×D4 | — | 4 | 1 | no | — |
| 382 | C23×C4 | — | 4 | 1 | no | — |
| 383 | #137 | — | 4 | 2 | no | — |
| 384 | #137 | — | 4 | 2 | no | — |
| 385 | #137 | — | 8 | 2 | no | — |
| 386 | #137 | — | 8 | 2 | no | — |
| 387 | #137 | — | 8 | 2 | no | — |
| 388 | #137 | — | 8 | 2 | no | — |
| 389 | #137 | — | 8 | 1 | no | — |
| 390 | #137 | — | 8 | 1 | no | — |
| 391 | #137 | — | 8 | 4 | no | — |
| 392 | #137 | — | 16 | 2 | no | — |
| 393 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 394 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 395 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 396 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 397 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 398 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 399 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 400 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 401 | #135 | — | 2 | 2 | no | — |
| 402 | #135 | — | 2 | 2 | no | — |
| 403 | #135 | — | 4 | 1 | no | — |
| 404 | #135 | — | 4 | 1 | no | — |
| 405 | #135 | — | 8 | 1 | no | — |
| 406 | #135 | — | 8 | 1 | no | — |
| 407 | #135 | — | 8 | 1 | no | — |
| 408 | #135 | — | 8 | 1 | no | — |
| 409 | #135 | — | 8 | 2 | no | — |
| 410 | #135 | — | 8 | 2 | no | — |
| 411 | #135 | — | 8 | 2 | no | — |
| 412 | #135 | — | 8 | 2 | no | — |
| 413 | #135 | — | 8 | 2 | no | — |
| 414 | #135 | — | 8 | 2 | no | — |
| 415 | C2×Q16 | — | 2 | 1 | no | — |
| 416 | C2×Q16 | — | 2 | 2 | no | — |
| 417 | C2×Q16 | — | 4 | 1 | no | — |
| 418 | C2×Q16 | — | 4 | 2 | no | — |
| 419 | C2×Q16 | — | 4 | 2 | no | — |
| 420 | C2×Q16 | — | 8 | 2 | no | — |
| 421 | C2×Q16 | — | 16 | 1 | no | — |
| 422 | C2×SD16 | — | 2 | 2 | no | — |
| 423 | C2×SD16 | — | 4 | 1 | no | — |
| 424 | C2×SD16 | — | 4 | 1 | no | — |
| 425 | C2×SD16 | — | 4 | 1 | no | — |
| 426 | C2×SD16 | — | 4 | 2 | no | — |
| 427 | C2×SD16 | — | 4 | 2 | no | — |
| 428 | C2×SD16 | — | 4 | 1 | no | — |
| 429 | C2×SD16 | — | 4 | 2 | no | — |
| 430 | C2×SD16 | — | 8 | 2 | no | — |
| 431 | C2×SD16 | — | 8 | 2 | no | — |
| 432 | C2×SD16 | — | 16 | 1 | no | — |
| 433 | C2×D8 | — | 2 | 1 | no | — |
| 434 | C2×D8 | — | 4 | 1 | no | — |
| 435 | C2×D8 | — | 4 | 1 | no | — |
| 436 | C2×D8 | — | 8 | 2 | no | — |
| 437 | #131 | — | 4 | 2 | no | — |
| 438 | #131 | — | 4 | 2 | no | — |
| 439 | #131 | — | 8 | 1 | no | — |
| 440 | #131 | — | 8 | 1 | no | — |
| 441 | C2×M16 | — | 4 | 2 | no | — |
| 442 | C2×M16 | — | 4 | 1 | no | — |
| 443 | C2×M16 | — | 4 | 1 | no | — |
| 444 | C2×M16 | — | 8 | 1 | no | — |
| 445 | C2×M16 | — | 8 | 1 | no | — |
| 446 | C22×C8 | — | 2 | 1 | no | — |
| 447 | C22×C8 | — | 8 | 1 | no | — |
| 448 | C4⋊Q8 | — | 2 | 1 | no | — |
| 449 | C4⋊Q8 | — | 2 | 1 | no | — |
| 450 | C4⋊Q8 | — | 2 | 2 | no | — |
| 451 | C4⋊Q8 | — | 4 | 1 | no | — |
| 452 | C4⋊Q8 | — | 4 | 1 | no | — |
| 453 | C4⋊Q8 | — | 4 | 2 | no | — |
| 454 | C4⋊Q8 | — | 4 | 2 | no | — |
| 455 | C4⋊Q8 | — | 4 | 2 | no | — |
| 456 | C4⋊Q8 | — | 4 | 1 | no | — |
| 457 | C4⋊Q8 | #120 | 1 | 1 | yes | characteristic |
| 458 | C4⋊Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 459 | #127 | #120 | 1 | 1 | yes | characteristic |
| 460 | #127 | C22×D4 | 1 | 1 | yes | characteristic |
| 461 | #126 | — | 8 | 1 | no | — |
| 462 | #126 | — | 8 | 2 | no | — |
| 463 | #126 | — | 8 | 2 | no | — |
| 464 | #126 | — | 8 | 2 | no | — |
| 465 | #125 | — | 4 | 1 | no | — |
| 466 | #125 | — | 4 | 2 | no | — |
| 467 | #125 | — | 4 | 1 | no | — |
| 468 | #125 | — | 8 | 1 | no | — |
| 469 | #125 | — | 8 | 2 | no | — |
| 470 | #125 | — | 8 | 2 | no | — |
| 471 | #124 | — | 2 | 1 | no | — |
| 472 | #124 | — | 2 | 1 | no | — |
| 473 | #124 | — | 4 | 1 | no | — |
| 474 | #124 | — | 4 | 2 | no | — |
| 475 | #124 | — | 4 | 2 | no | — |
| 476 | #124 | — | 4 | 2 | no | — |
| 477 | #123 | — | 4 | 1 | no | — |
| 478 | #123 | — | 4 | 1 | no | — |
| 479 | #123 | — | 8 | 1 | no | — |
| 480 | #123 | — | 8 | 1 | no | — |
| 481 | #123 | — | 8 | 2 | no | — |
| 482 | #123 | — | 8 | 1 | no | — |
| 483 | #123 | — | 8 | 2 | no | — |
| 484 | C22⋊Q8 | — | 2 | 2 | no | — |
| 485 | C22⋊Q8 | — | 4 | 1 | no | — |
| 486 | C22⋊Q8 | — | 4 | 1 | no | — |
| 487 | C22⋊Q8 | — | 4 | 2 | no | — |
| 488 | C22⋊Q8 | — | 8 | 1 | no | — |
| 489 | C22⋊Q8 | — | 8 | 2 | no | — |
| 490 | C22⋊Q8 | — | 8 | 1 | no | — |
| 491 | C22⋊Q8 | — | 8 | 1 | no | — |
| 492 | C22⋊Q8 | — | 8 | 1 | no | — |
| 493 | C22⋊Q8 | — | 8 | 1 | no | — |
| 494 | C22⋊Q8 | — | 16 | 1 | no | — |
| 495 | #121 | — | 4 | 1 | no | — |
| 496 | #121 | — | 4 | 1 | no | — |
| 497 | #121 | — | 4 | 1 | no | — |
| 498 | #121 | — | 8 | 1 | no | — |
| 499 | #121 | — | 16 | 1 | no | — |
| 500 | #120 | — | 4 | 1 | no | — |
| 501 | #120 | — | 4 | 1 | no | — |
| 502 | #120 | — | 8 | 2 | no | — |
| 503 | C4×Q8 | — | 2 | 1 | no | — |
| 504 | C4×Q8 | — | 2 | 1 | no | — |
| 505 | C4×Q8 | — | 2 | 2 | no | — |
| 506 | C4×Q8 | — | 4 | 1 | no | — |
| 507 | C4×Q8 | — | 4 | 2 | no | — |
| 508 | C4×Q8 | — | 4 | 2 | no | — |
| 509 | C4×Q8 | — | 4 | 2 | no | — |
| 510 | C4×Q8 | — | 4 | 2 | no | — |
| 511 | C4×Q8 | — | 8 | 1 | no | — |
| 512 | C4×Q8 | — | 8 | 1 | no | — |
| 513 | C4×Q8 | — | 8 | 1 | no | — |
| 514 | C4×D4 | — | 2 | 1 | no | — |
| 515 | C4×D4 | — | 2 | 1 | no | — |
| 516 | C4×D4 | — | 4 | 1 | no | — |
| 517 | C4×D4 | — | 4 | 1 | no | — |
| 518 | C4×D4 | — | 4 | 1 | no | — |
| 519 | C4×D4 | — | 4 | 1 | no | — |
| 520 | C4×D4 | — | 4 | 1 | no | — |
| 521 | C4×D4 | — | 4 | 2 | no | — |
| 522 | C4×D4 | — | 4 | 1 | no | — |
| 523 | C4×D4 | — | 8 | 1 | no | — |
| 524 | C4×D4 | — | 8 | 1 | no | — |
| 525 | C4×D4 | — | 16 | 2 | no | — |
| 526 | #117 | — | 2 | 1 | no | — |
| 527 | #117 | — | 4 | 1 | no | — |
| 528 | #117 | — | 4 | 1 | no | — |
| 529 | #117 | — | 4 | 1 | no | — |
| 530 | #117 | — | 4 | 1 | no | — |
| 531 | #117 | — | 4 | 2 | no | — |
| 532 | #117 | — | 8 | 2 | no | — |
| 533 | #117 | — | 8 | 1 | no | — |
| 534 | #117 | — | 8 | 1 | no | — |
| 535 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 536 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 537 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 538 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 539 | C2×C42 | — | 4 | 1 | no | — |
| 540 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 541 | M32 | — | 4 | 2 | no | — |
| 542 | M32 | — | 8 | 1 | no | — |
| 543 | C2×C16 | — | 8 | 1 | no | — |
| 544 | #108 | — | 2 | 2 | no | — |
| 545 | #108 | — | 4 | 1 | no | — |
| 546 | #107 | — | 2 | 2 | no | — |
| 547 | #107 | — | 4 | 2 | no | — |
| 548 | #107 | — | 4 | 2 | no | — |
| 549 | #107 | — | 4 | 1 | no | — |
| 550 | #106 | — | 2 | 2 | no | — |
| 551 | #106 | — | 4 | 2 | no | — |
| 552 | #106 | — | 4 | 1 | no | — |
| 553 | #106 | — | 4 | 2 | no | — |
| 554 | #106 | — | 4 | 2 | no | — |
| 555 | #106 | — | 4 | 2 | no | — |
| 556 | #106 | — | 8 | 1 | no | — |
| 557 | C4⋊C8 | — | 2 | 1 | no | — |
| 558 | C4⋊C8 | — | 2 | 1 | no | — |
| 559 | C4⋊C8 | — | 2 | 1 | no | — |
| 560 | C4⋊C8 | — | 2 | 1 | no | — |
| 561 | C4⋊C8 | — | 2 | 2 | no | — |
| 562 | C4⋊C8 | — | 4 | 1 | no | — |
| 563 | C4⋊C8 | — | 4 | 2 | no | — |
| 564 | C4⋊C8 | — | 4 | 2 | no | — |
| 565 | C4⋊C8 | — | 4 | 2 | no | — |
| 566 | #104 | — | 4 | 2 | no | — |
| 567 | #104 | — | 4 | 2 | no | — |
| 568 | #104 | — | 8 | 4 | no | — |
| 569 | #103 | — | 2 | 2 | no | — |
| 570 | #103 | — | 2 | 2 | no | — |
| 571 | #103 | — | 2 | 2 | no | — |
| 572 | #103 | — | 4 | 2 | no | — |
| 573 | #103 | — | 4 | 2 | no | — |
| 574 | #103 | — | 4 | 2 | no | — |
| 575 | #103 | — | 4 | 2 | no | — |
| 576 | #103 | — | 4 | 2 | no | — |
| 577 | #103 | — | 4 | 1 | no | — |
| 578 | #103 | — | 4 | 2 | no | — |
| 579 | #102 | — | 2 | 2 | no | — |
| 580 | #102 | — | 4 | 2 | no | — |
| 581 | #102 | — | 4 | 1 | no | — |
| 582 | #102 | — | 4 | 1 | no | — |
| 583 | #102 | — | 4 | 2 | no | — |
| 584 | #102 | — | 4 | 2 | no | — |
| 585 | #102 | — | 4 | 2 | no | — |
| 586 | #102 | — | 4 | 1 | no | — |
| 587 | #101 | — | 2 | 2 | no | — |
| 588 | #101 | — | 4 | 1 | no | — |
| 589 | #101 | — | 4 | 2 | no | — |
| 590 | #100 | — | 2 | 2 | no | — |
| 591 | #100 | — | 4 | 1 | no | — |
| 592 | #100 | — | 8 | 1 | no | — |
| 593 | #99 | — | 4 | 2 | no | — |
| 594 | #99 | — | 8 | 2 | no | — |
| 595 | #99 | — | 8 | 2 | no | — |
| 596 | #99 | — | 8 | 1 | no | — |
| 597 | C22⋊C8 | — | 2 | 2 | no | — |
| 598 | C22⋊C8 | — | 4 | 2 | no | — |
| 599 | C22⋊C8 | — | 4 | 1 | no | — |
| 600 | #97 | — | 4 | 2 | no | — |
| 601 | C4×C8 | — | 2 | 2 | no | — |
| 602 | C4×C8 | — | 2 | 1 | no | — |
| 603 | C4×C8 | — | 4 | 1 | no | — |
| 604 | C4×C8 | — | 4 | 2 | no | — |
| 605 | C4×C8 | — | 4 | 2 | no | — |
| 606 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 607 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 608 | C24 | — | 4 | 1 | no | — |
| 609 | #41 | — | 4 | 2 | no | — |
| 610 | #41 | — | 4 | 2 | no | — |
| 611 | #41 | — | 8 | 1 | no | — |
| 612 | #41 | — | 8 | 1 | no | — |
| 613 | #41 | — | 8 | 1 | no | — |
| 614 | #41 | — | 8 | 1 | no | — |
| 615 | #41 | — | 8 | 1 | no | — |
| 616 | #41 | — | 8 | 1 | no | — |
| 617 | #41 | — | 8 | 1 | no | — |
| 618 | #41 | — | 8 | 2 | no | — |
| 619 | #41 | — | 8 | 1 | no | — |
| 620 | #41 | — | 8 | 2 | no | — |
| 621 | #41 | — | 8 | 2 | no | — |
| 622 | #41 | — | 8 | 2 | no | — |
| 623 | #41 | — | 8 | 2 | no | — |
| 624 | #41 | — | 8 | 2 | no | — |
| 625 | #41 | — | 16 | 1 | no | — |
| 626 | #41 | — | 16 | 1 | no | — |
| 627 | #41 | — | 16 | 2 | no | — |
| 628 | #41 | — | 16 | 2 | no | — |
| 629 | #41 | — | 16 | 1 | no | — |
| 630 | #41 | — | 16 | 1 | no | — |
| 631 | C2×Q8 | — | 2 | 1 | no | — |
| 632 | C2×Q8 | — | 2 | 2 | no | — |
| 633 | C2×Q8 | — | 2 | 1 | no | — |
| 634 | C2×Q8 | — | 2 | 1 | no | — |
| 635 | C2×Q8 | — | 4 | 1 | no | — |
| 636 | C2×Q8 | — | 4 | 2 | no | — |
| 637 | C2×Q8 | — | 4 | 1 | no | — |
| 638 | C2×Q8 | — | 4 | 2 | no | — |
| 639 | C2×Q8 | — | 8 | 1 | no | — |
| 640 | C2×Q8 | — | 8 | 1 | no | — |
| 641 | C2×Q8 | — | 8 | 2 | no | — |
| 642 | C2×Q8 | — | 8 | 2 | no | — |
| 643 | C2×Q8 | — | 8 | 1 | no | — |
| 644 | C2×Q8 | — | 16 | 1 | no | — |
| 645 | C2×Q8 | — | 16 | 1 | no | — |
| 646 | C2×Q8 | — | 16 | 1 | no | — |
| 647 | C2×Q8 | — | 16 | 1 | no | — |
| 648 | C2×D4 | — | 2 | 1 | no | — |
| 649 | C2×D4 | — | 2 | 1 | no | — |
| 650 | C2×D4 | — | 2 | 1 | no | — |
| 651 | C2×D4 | — | 4 | 1 | no | — |
| 652 | C2×D4 | — | 4 | 1 | no | — |
| 653 | C2×D4 | — | 4 | 1 | no | — |
| 654 | C2×D4 | — | 4 | 1 | no | — |
| 655 | C2×D4 | — | 4 | 1 | no | — |
| 656 | C2×D4 | — | 4 | 1 | no | — |
| 657 | C2×D4 | — | 8 | 1 | no | — |
| 658 | C2×D4 | — | 8 | 2 | no | — |
| 659 | C2×D4 | — | 8 | 2 | no | — |
| 660 | C2×D4 | — | 8 | 2 | no | — |
| 661 | C2×D4 | — | 8 | 1 | no | — |
| 662 | C2×D4 | — | 8 | 1 | no | — |
| 663 | C2×D4 | — | 8 | 2 | no | — |
| 664 | C2×D4 | — | 8 | 1 | no | — |
| 665 | C2×D4 | — | 16 | 1 | no | — |
| 666 | C2×D4 | — | 16 | 1 | no | — |
| 667 | C2×D4 | — | 16 | 2 | no | — |
| 668 | C2×D4 | — | 16 | 2 | no | — |
| 669 | C2×D4 | — | 16 | 2 | no | — |
| 670 | C22×C4 | — | 2 | 1 | no | — |
| 671 | C22×C4 | — | 4 | 1 | no | — |
| 672 | C22×C4 | — | 4 | 1 | no | — |
| 673 | C22×C4 | — | 4 | 1 | no | — |
| 674 | C22×C4 | — | 4 | 1 | no | — |
| 675 | C22×C4 | — | 4 | 1 | no | — |
| 676 | C22×C4 | — | 4 | 1 | no | — |
| 677 | C22×C4 | — | 8 | 1 | no | — |
| 678 | C22×C4 | — | 8 | 1 | no | — |
| 679 | C22×C4 | — | 8 | 1 | no | — |
| 680 | C22×C4 | — | 8 | 2 | no | — |
| 681 | C22×C4 | — | 8 | 1 | no | — |
| 682 | C22×C4 | — | 16 | 1 | no | — |
| 683 | C22×C4 | — | 16 | 1 | no | — |
| 684 | C22×C4 | — | 16 | 1 | no | — |
| 685 | C22×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 686 | Q16 | — | 2 | 2 | no | — |
| 687 | Q16 | — | 4 | 1 | no | — |
| 688 | Q16 | — | 8 | 1 | no | — |
| 689 | Q16 | — | 8 | 1 | no | — |
| 690 | Q16 | — | 8 | 2 | no | — |
| 691 | Q16 | — | 8 | 2 | no | — |
| 692 | Q16 | — | 8 | 2 | no | — |
| 693 | Q16 | — | 16 | 2 | no | — |
| 694 | Q16 | — | 16 | 2 | no | — |
| 695 | Q16 | — | 16 | 4 | no | — |
| 696 | SD16 | — | 4 | 2 | no | — |
| 697 | SD16 | — | 4 | 2 | no | — |
| 698 | SD16 | — | 8 | 1 | no | — |
| 699 | SD16 | — | 8 | 1 | no | — |
| 700 | SD16 | — | 8 | 1 | no | — |
| 701 | SD16 | — | 8 | 1 | no | — |
| 702 | SD16 | — | 8 | 2 | no | — |
| 703 | SD16 | — | 8 | 2 | no | — |
| 704 | SD16 | — | 8 | 2 | no | — |
| 705 | SD16 | — | 8 | 2 | no | — |
| 706 | SD16 | — | 8 | 2 | no | — |
| 707 | SD16 | — | 16 | 2 | no | — |
| 708 | SD16 | — | 16 | 2 | no | — |
| 709 | SD16 | — | 16 | 2 | no | — |
| 710 | SD16 | — | 16 | 1 | no | — |
| 711 | SD16 | — | 16 | 4 | no | — |
| 712 | D8 | — | 2 | 2 | no | — |
| 713 | D8 | — | 4 | 1 | no | — |
| 714 | D8 | — | 8 | 1 | no | — |
| 715 | D8 | — | 8 | 1 | no | — |
| 716 | D8 | — | 8 | 2 | no | — |
| 717 | D8 | — | 8 | 2 | no | — |
| 718 | D8 | — | 16 | 1 | no | — |
| 719 | M16 | — | 4 | 2 | no | — |
| 720 | M16 | — | 8 | 2 | no | — |
| 721 | M16 | — | 8 | 2 | no | — |
| 722 | M16 | — | 8 | 1 | no | — |
| 723 | M16 | — | 8 | 2 | no | — |
| 724 | M16 | — | 16 | 2 | no | — |
| 725 | M16 | — | 16 | 1 | no | — |
| 726 | M16 | — | 16 | 1 | no | — |
| 727 | C2×C8 | — | 2 | 1 | no | — |
| 728 | C2×C8 | — | 2 | 1 | no | — |
| 729 | C2×C8 | — | 2 | 1 | no | — |
| 730 | C2×C8 | — | 2 | 1 | no | — |
| 731 | C2×C8 | — | 2 | 1 | no | — |
| 732 | C2×C8 | — | 2 | 1 | no | — |
| 733 | C2×C8 | — | 2 | 2 | no | — |
| 734 | C2×C8 | — | 2 | 2 | no | — |
| 735 | C2×C8 | — | 4 | 1 | no | — |
| 736 | C2×C8 | — | 4 | 1 | no | — |
| 737 | C2×C8 | — | 4 | 2 | no | — |
| 738 | C2×C8 | — | 8 | 2 | no | — |
| 739 | C2×C8 | — | 8 | 2 | no | — |
| 740 | C2×C8 | — | 8 | 1 | no | — |
| 741 | C2×C8 | — | 16 | 1 | no | — |
| 742 | C4⋊C4 | — | 2 | 2 | no | — |
| 743 | C4⋊C4 | — | 2 | 1 | no | — |
| 744 | C4⋊C4 | — | 2 | 1 | no | — |
| 745 | C4⋊C4 | — | 4 | 1 | no | — |
| 746 | C4⋊C4 | — | 4 | 1 | no | — |
| 747 | C4⋊C4 | — | 4 | 1 | no | — |
| 748 | C4⋊C4 | — | 4 | 1 | no | — |
| 749 | C4⋊C4 | — | 4 | 1 | no | — |
| 750 | C4⋊C4 | — | 4 | 2 | no | — |
| 751 | C4⋊C4 | — | 4 | 2 | no | — |
| 752 | C4⋊C4 | — | 4 | 1 | no | — |
| 753 | C4⋊C4 | — | 4 | 1 | no | — |
| 754 | C4⋊C4 | — | 4 | 2 | no | — |
| 755 | C4⋊C4 | — | 4 | 2 | no | — |
| 756 | C4⋊C4 | — | 8 | 1 | no | — |
| 757 | C4⋊C4 | — | 8 | 1 | no | — |
| 758 | C4⋊C4 | — | 8 | 1 | no | — |
| 759 | C4⋊C4 | — | 8 | 2 | no | — |
| 760 | C4⋊C4 | — | 8 | 2 | no | — |
| 761 | C4⋊C4 | — | 8 | 2 | no | — |
| 762 | C4⋊C4 | — | 8 | 2 | no | — |
| 763 | C4⋊C4 | — | 8 | 2 | no | — |
| 764 | C4⋊C4 | — | 8 | 1 | no | — |
| 765 | C4⋊C4 | — | 16 | 1 | no | — |
| 766 | C4⋊C4 | — | 16 | 2 | no | — |
| 767 | C22⋊C4 | — | 4 | 1 | no | — |
| 768 | C22⋊C4 | — | 4 | 1 | no | — |
| 769 | C22⋊C4 | — | 4 | 2 | no | — |
| 770 | C22⋊C4 | — | 4 | 1 | no | — |
| 771 | C22⋊C4 | — | 4 | 1 | no | — |
| 772 | C22⋊C4 | — | 4 | 1 | no | — |
| 773 | C22⋊C4 | — | 8 | 1 | no | — |
| 774 | C22⋊C4 | — | 8 | 1 | no | — |
| 775 | C22⋊C4 | — | 8 | 1 | no | — |
| 776 | C22⋊C4 | — | 8 | 1 | no | — |
| 777 | C22⋊C4 | — | 8 | 1 | no | — |
| 778 | C22⋊C4 | — | 8 | 2 | no | — |
| 779 | C22⋊C4 | — | 8 | 2 | no | — |
| 780 | C22⋊C4 | — | 8 | 2 | no | — |
| 781 | C22⋊C4 | — | 8 | 2 | no | — |
| 782 | C22⋊C4 | — | 16 | 2 | no | — |
| 783 | C22⋊C4 | — | 16 | 2 | no | — |
| 784 | C42 | — | 2 | 1 | no | — |
| 785 | C42 | — | 4 | 1 | no | — |
| 786 | C42 | — | 4 | 2 | no | — |
| 787 | C42 | — | 4 | 1 | no | — |
| 788 | C42 | — | 4 | 2 | no | — |
| 789 | C42 | — | 4 | 1 | no | — |
| 790 | C42 | — | 8 | 2 | no | — |
| 791 | C42 | — | 8 | 2 | no | — |
| 792 | C42 | — | 16 | 1 | no | — |
| 793 | C42 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 794 | C42 | C2×#120 | 1 | 1 | yes | characteristic |
| 795 | C16 | — | 8 | 2 | no | — |
| 796 | C23 | — | 4 | 1 | no | — |
| 797 | C23 | — | 4 | 1 | no | — |
| 798 | C23 | — | 4 | 1 | no | — |
| 799 | C23 | — | 8 | 1 | no | — |
| 800 | C23 | — | 8 | 2 | no | — |
| 801 | C23 | — | 16 | 1 | no | — |
| 802 | C23 | — | 16 | 1 | no | — |
| 803 | C23 | — | 16 | 2 | no | — |
| 804 | C23 | #2196 | 1 | 1 | yes | characteristic |
| 805 | Q8 | — | 4 | 2 | no | — |
| 806 | Q8 | — | 4 | 2 | no | — |
| 807 | Q8 | — | 4 | 2 | no | — |
| 808 | Q8 | — | 4 | 1 | no | — |
| 809 | Q8 | — | 4 | 1 | no | — |
| 810 | Q8 | — | 8 | 1 | no | — |
| 811 | Q8 | — | 8 | 1 | no | — |
| 812 | Q8 | — | 8 | 2 | no | — |
| 813 | Q8 | — | 8 | 2 | no | — |
| 814 | Q8 | — | 8 | 2 | no | — |
| 815 | Q8 | — | 8 | 1 | no | — |
| 816 | Q8 | — | 8 | 1 | no | — |
| 817 | Q8 | — | 8 | 1 | no | — |
| 818 | Q8 | — | 16 | 2 | no | — |
| 819 | Q8 | — | 16 | 2 | no | — |
| 820 | Q8 | — | 16 | 1 | no | — |
| 821 | D4 | — | 4 | 2 | no | — |
| 822 | D4 | — | 4 | 1 | no | — |
| 823 | D4 | — | 4 | 1 | no | — |
| 824 | D4 | — | 8 | 1 | no | — |
| 825 | D4 | — | 8 | 1 | no | — |
| 826 | D4 | — | 8 | 1 | no | — |
| 827 | D4 | — | 8 | 1 | no | — |
| 828 | D4 | — | 8 | 1 | no | — |
| 829 | D4 | — | 8 | 1 | no | — |
| 830 | D4 | — | 8 | 2 | no | — |
| 831 | D4 | — | 8 | 2 | no | — |
| 832 | D4 | — | 8 | 2 | no | — |
| 833 | D4 | — | 8 | 1 | no | — |
| 834 | D4 | — | 16 | 1 | no | — |
| 835 | D4 | — | 16 | 1 | no | — |
| 836 | D4 | — | 16 | 1 | no | — |
| 837 | D4 | — | 16 | 2 | no | — |
| 838 | D4 | — | 16 | 1 | no | — |
| 839 | D4 | — | 16 | 2 | no | — |
| 840 | D4 | — | 16 | 2 | no | — |
| 841 | D4 | — | 32 | 4 | no | — |
| 842 | C2×C4 | — | 2 | 1 | no | — |
| 843 | C2×C4 | — | 2 | 1 | no | — |
| 844 | C2×C4 | — | 2 | 1 | no | — |
| 845 | C2×C4 | — | 2 | 1 | no | — |
| 846 | C2×C4 | — | 4 | 1 | no | — |
| 847 | C2×C4 | — | 4 | 1 | no | — |
| 848 | C2×C4 | — | 4 | 1 | no | — |
| 849 | C2×C4 | — | 4 | 1 | no | — |
| 850 | C2×C4 | — | 4 | 2 | no | — |
| 851 | C2×C4 | — | 4 | 1 | no | — |
| 852 | C2×C4 | — | 4 | 1 | no | — |
| 853 | C2×C4 | — | 4 | 2 | no | — |
| 854 | C2×C4 | — | 4 | 1 | no | — |
| 855 | C2×C4 | — | 8 | 2 | no | — |
| 856 | C2×C4 | — | 8 | 1 | no | — |
| 857 | C2×C4 | — | 8 | 1 | no | — |
| 858 | C2×C4 | — | 8 | 1 | no | — |
| 859 | C2×C4 | — | 8 | 1 | no | — |
| 860 | C2×C4 | — | 8 | 1 | no | — |
| 861 | C2×C4 | — | 8 | 1 | no | — |
| 862 | C2×C4 | — | 8 | 1 | no | — |
| 863 | C2×C4 | — | 8 | 1 | no | — |
| 864 | C2×C4 | — | 8 | 1 | no | — |
| 865 | C2×C4 | — | 8 | 2 | no | — |
| 866 | C2×C4 | — | 8 | 2 | no | — |
| 867 | C2×C4 | — | 8 | 2 | no | — |
| 868 | C2×C4 | — | 16 | 1 | no | — |
| 869 | C2×C4 | — | 16 | 2 | no | — |
| 870 | C2×C4 | — | 16 | 2 | no | — |
| 871 | C2×C4 | — | 16 | 1 | no | — |
| 872 | C2×C4 | — | 16 | 1 | no | — |
| 873 | C2×C4 | — | 16 | 2 | no | — |
| 874 | C2×C4 | — | 16 | 2 | no | — |
| 875 | C2×C4 | — | 32 | 1 | no | — |
| 876 | C2×C4 | — | 32 | 1 | no | — |
| 877 | C2×C4 | #2196 | 1 | 1 | yes | characteristic |
| 878 | C2×C4 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 879 | C8 | — | 2 | 1 | no | — |
| 880 | C8 | — | 2 | 1 | no | — |
| 881 | C8 | — | 2 | 1 | no | — |
| 882 | C8 | — | 2 | 1 | no | — |
| 883 | C8 | — | 4 | 2 | no | — |
| 884 | C8 | — | 4 | 2 | no | — |
| 885 | C8 | — | 8 | 2 | no | — |
| 886 | C8 | — | 8 | 1 | no | — |
| 887 | C8 | — | 8 | 1 | no | — |
| 888 | C8 | — | 8 | 2 | no | — |
| 889 | C8 | — | 16 | 2 | no | — |
| 890 | C22 | — | 2 | 1 | no | — |
| 891 | C22 | — | 4 | 1 | no | — |
| 892 | C22 | — | 8 | 1 | no | — |
| 893 | C22 | — | 8 | 1 | no | — |
| 894 | C22 | — | 8 | 1 | no | — |
| 895 | C22 | — | 8 | 2 | no | — |
| 896 | C22 | — | 8 | 1 | no | — |
| 897 | C22 | — | 8 | 1 | no | — |
| 898 | C22 | — | 16 | 1 | no | — |
| 899 | C22 | — | 16 | 1 | no | — |
| 900 | C22 | — | 16 | 2 | no | — |
| 901 | C22 | — | 32 | 1 | no | — |
| 902 | C22 | — | 32 | 2 | no | — |
| 903 | C22 | — | 32 | 1 | no | — |
| 904 | C22 | — | 64 | 1 | no | — |
| 905 | C22 | C2×#2196 | 1 | 1 | yes | characteristic |
| 906 | C4 | — | 2 | 1 | no | — |
| 907 | C4 | — | 2 | 1 | no | — |
| 908 | C4 | — | 2 | 1 | no | — |
| 909 | C4 | — | 4 | 1 | no | — |
| 910 | C4 | — | 8 | 1 | no | — |
| 911 | C4 | — | 8 | 1 | no | — |
| 912 | C4 | — | 8 | 2 | no | — |
| 913 | C4 | — | 8 | 1 | no | — |
| 914 | C4 | — | 8 | 1 | no | — |
| 915 | C4 | — | 8 | 1 | no | — |
| 916 | C4 | — | 8 | 2 | no | — |
| 917 | C4 | — | 8 | 2 | no | — |
| 918 | C4 | — | 16 | 2 | no | — |
| 919 | C4 | — | 32 | 2 | no | — |
| 920 | C4 | #13674 | 1 | 1 | yes | characteristic |
| 921 | C4 | #13674 | 1 | 1 | yes | characteristic |
| 922 | C2 | — | 2 | 1 | no | — |
| 923 | C2 | — | 4 | 1 | no | — |
| 924 | C2 | — | 16 | 1 | no | — |
| 925 | C2 | — | 16 | 1 | no | — |
| 926 | C2 | — | 16 | 1 | no | — |
| 927 | C2 | — | 16 | 2 | no | — |
| 928 | C2 | C2×#13674 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×#13674 |
| commutator, Frattini, cosocle | #492 | C24 |
| prime radical | #512857 | C2 |
| LCS | G ▷ #492 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #3147 ◁ G | |
| LECS | G ▷ #492 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6367518 | C2 | semidirect |
| 2. #512897 | C2 | semidirect |
| 4. #488929 | C2 | semidirect |
| 5. #153641 | C2 | semidirect |
| 6. #153638 | C2 | semidirect |
| 7. #153536 | C2 | semidirect |
| 8. #153450 | C2 | semidirect |
| 9. #153441 | C2 | semidirect |
| 16. #20289 | C22 | semidirect |
| 20. #20013 | C22 | semidirect |
| 43. #7536 | C22 | semidirect |
| 44. #7520 | C22 | semidirect |
| 45. #7518 | C22 | semidirect |
| 46. #7517 | C22 | semidirect |
| 48. #3550 | D4 | semidirect |
| 77. C2×#498 | D4 | semidirect |
| 110. #1705 | D4 | semidirect |
| 123. #1633 | D4 | semidirect |
| 138. #1560 | D4 | semidirect |
| 143. #1450 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6367518 | 2 |
| #512897 | 2 |
| #512857 | 2 |
| #488929 | 2 |
| #153641 | 2 |
| #153638 | 2 |
| #153536 | 2 |
| #153450 | 2 |
| #153441 | 2 |