Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1068 conjugacy classes of subgroups.
The subgroup lattice has 870 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62435 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33307 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #19621 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19352 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #19033 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #19014 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #18437 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #18428 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10132 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10129 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10102 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10088 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #9787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #9761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #8247 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3561 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3558 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3401 | — | 2 | 1 | no | — |
| 19 | #3394 | — | 2 | 1 | no | — |
| 20 | #3282 | — | 2 | 1 | no | — |
| 21 | #3282 | — | 2 | 1 | no | — |
| 22 | D4×SD16 | — | 2 | 1 | no | — |
| 23 | #3275 | — | 2 | 1 | no | — |
| 24 | #3270 | — | 2 | 1 | no | — |
| 25 | #3264 | — | 2 | 1 | no | — |
| 26 | #3239 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3227 | C22 | 1 | 1 | yes | characteristic |
| 28 | #3225 | — | 2 | 1 | no | — |
| 29 | #3224 | — | 2 | 1 | no | — |
| 30 | #3217 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3215 | C22 | 1 | 1 | yes | characteristic |
| 32 | #3213 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3208 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #3173 | — | 2 | 1 | no | — |
| 35 | #3167 | C22 | 1 | 1 | yes | characteristic |
| 36 | #3165 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #3154 | — | 2 | 1 | no | — |
| 38 | #3151 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#497 | — | 2 | 1 | no | — |
| 40 | C2×#497 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#496 | — | 2 | 1 | no | — |
| 42 | C2×#496 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#495 | — | 2 | 1 | no | — |
| 44 | C2×#495 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#492 | — | 2 | 1 | no | — |
| 46 | C2×#492 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #2966 | C22 | 1 | 1 | yes | characteristic |
| 48 | #2658 | C22 | 1 | 1 | yes | characteristic |
| 49 | #2657 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #1726 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #1715 | — | 2 | 1 | no | — |
| 52 | #1714 | — | 2 | 1 | no | — |
| 53 | #1706 | — | 2 | 1 | no | — |
| 54 | #1705 | — | 2 | 1 | no | — |
| 55 | #1686 | — | 2 | 1 | no | — |
| 56 | #1685 | — | 2 | 1 | no | — |
| 57 | #1666 | — | 2 | 1 | no | — |
| 58 | #1665 | — | 2 | 1 | no | — |
| 59 | #1661 | — | 2 | 2 | no | — |
| 60 | #1660 | — | 2 | 2 | no | — |
| 61 | #1656 | — | 2 | 2 | no | — |
| 62 | #1655 | — | 2 | 2 | no | — |
| 63 | #1618 | — | 2 | 2 | no | — |
| 64 | #1613 | — | 2 | 2 | no | — |
| 65 | #1600 | — | 2 | 2 | no | — |
| 66 | #1596 | — | 2 | 2 | no | — |
| 67 | #1568 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #1556 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #1555 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #1531 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #1530 | C22 | 1 | 1 | yes | characteristic |
| 72 | #1527 | C22 | 1 | 1 | yes | characteristic |
| 73 | #1527 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | #1524 | C22 | 1 | 1 | yes | characteristic |
| 75 | #1506 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #1505 | C22 | 1 | 1 | yes | characteristic |
| 77 | #1500 | C22 | 1 | 1 | yes | characteristic |
| 78 | #1469 | C22 | 1 | 1 | yes | characteristic |
| 79 | #1469 | C22 | 1 | 1 | yes | characteristic, complemented |
| 80 | C8×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 81 | #1302 | C22 | 1 | 1 | yes | characteristic, complemented |
| 82 | #1300 | C22 | 1 | 1 | yes | characteristic, complemented |
| 83 | C2×#137 | — | 2 | 1 | no | — |
| 84 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 85 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 86 | C2×#135 | — | 2 | 1 | no | — |
| 87 | C22×Q16 | — | 2 | 1 | no | — |
| 88 | C22×Q16 | D4 | 1 | 1 | yes | characteristic |
| 89 | C22×SD16 | — | 2 | 1 | no | — |
| 90 | C22×SD16 | — | 2 | 1 | no | — |
| 91 | C22×SD16 | — | 2 | 1 | no | — |
| 92 | C22×SD16 | — | 2 | 1 | no | — |
| 93 | C22×SD16 | — | 2 | 1 | no | — |
| 94 | C22×SD16 | D4 | 1 | 1 | yes | characteristic |
| 95 | C22×SD16 | D4 | 1 | 1 | yes | characteristic |
| 96 | C22×D8 | — | 2 | 1 | no | — |
| 97 | C22×D8 | D4 | 1 | 1 | yes | characteristic |
| 98 | #563 | — | 2 | 1 | no | — |
| 99 | #562 | — | 2 | 1 | no | — |
| 100 | #562 | — | 2 | 1 | no | — |
| 101 | H(3,𝔽4) | — | 2 | 1 | no | — |
| 102 | #559 | — | 2 | 1 | no | — |
| 103 | #556 | — | 2 | 1 | no | — |
| 104 | #551 | — | 4 | 1 | no | — |
| 105 | D4×Q8 | — | 2 | 1 | no | — |
| 106 | #548 | — | 2 | 1 | no | — |
| 107 | #548 | — | 2 | 1 | no | — |
| 108 | #546 | — | 2 | 1 | no | — |
| 109 | #546 | — | 2 | 1 | no | — |
| 110 | #546 | — | 4 | 1 | no | — |
| 111 | D42 | — | 2 | 1 | no | — |
| 112 | #543 | — | 2 | 1 | no | — |
| 113 | #542 | — | 2 | 1 | no | — |
| 114 | #542 | — | 2 | 1 | no | — |
| 115 | #542 | — | 4 | 1 | no | — |
| 116 | #538 | — | 2 | 1 | no | — |
| 117 | #538 | — | 2 | 1 | no | — |
| 118 | #538 | — | 4 | 1 | no | — |
| 119 | #536 | — | 2 | 1 | no | — |
| 120 | #535 | — | 2 | 1 | no | — |
| 121 | #534 | — | 2 | 1 | no | — |
| 122 | #533 | C23 | 1 | 1 | yes | characteristic |
| 123 | #532 | C23 | 1 | 1 | yes | characteristic |
| 124 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 125 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×#127 | — | 2 | 1 | no | — |
| 127 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 128 | #529 | C23 | 1 | 1 | yes | characteristic |
| 129 | C2×#124 | — | 2 | 1 | no | — |
| 130 | C2×#124 | — | 2 | 1 | no | — |
| 131 | C2×#124 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×#124 | C23 | 1 | 1 | yes | characteristic |
| 133 | #501 | — | 2 | 1 | no | — |
| 134 | #501 | — | 2 | 2 | no | — |
| 135 | #500 | — | 2 | 1 | no | — |
| 136 | #498 | — | 2 | 1 | no | — |
| 137 | #498 | — | 2 | 1 | no | — |
| 138 | #498 | D4 | 1 | 1 | yes | characteristic, complemented |
| 139 | #497 | — | 2 | 1 | no | — |
| 140 | #497 | — | 2 | 1 | no | — |
| 141 | #497 | — | 2 | 2 | no | — |
| 142 | #497 | — | 4 | 1 | no | — |
| 143 | #497 | — | 4 | 4 | no | — |
| 144 | #496 | — | 2 | 1 | no | — |
| 145 | #496 | — | 2 | 1 | no | — |
| 146 | #496 | — | 2 | 1 | no | — |
| 147 | #496 | — | 2 | 2 | no | — |
| 148 | #496 | — | 2 | 2 | no | — |
| 149 | #496 | — | 4 | 1 | no | — |
| 150 | #496 | — | 4 | 4 | no | — |
| 151 | #495 | — | 2 | 1 | no | — |
| 152 | #495 | — | 2 | 1 | no | — |
| 153 | #495 | — | 2 | 1 | no | — |
| 154 | #495 | — | 2 | 1 | no | — |
| 155 | #495 | — | 2 | 1 | no | — |
| 156 | #495 | — | 4 | 4 | no | — |
| 157 | #493 | — | 2 | 1 | no | — |
| 158 | #492 | — | 2 | 1 | no | — |
| 159 | #492 | — | 2 | 1 | no | — |
| 160 | #492 | — | 2 | 1 | no | — |
| 161 | #492 | — | 2 | 1 | no | — |
| 162 | #492 | — | 2 | 1 | no | — |
| 163 | #492 | — | 2 | 1 | no | — |
| 164 | #492 | — | 2 | 1 | no | — |
| 165 | #492 | — | 4 | 4 | no | — |
| 166 | #492 | D4 | 1 | 1 | yes | characteristic, complemented |
| 167 | #490 | — | 2 | 1 | no | — |
| 168 | #489 | — | 2 | 1 | no | — |
| 169 | #489 | — | 2 | 1 | no | — |
| 170 | #489 | — | 2 | 1 | no | — |
| 171 | #487 | D4 | 1 | 1 | yes | characteristic, complemented |
| 172 | #486 | — | 2 | 1 | no | — |
| 173 | #486 | — | 2 | 1 | no | — |
| 174 | #486 | D4 | 1 | 1 | yes | characteristic, complemented |
| 175 | #484 | — | 2 | 1 | no | — |
| 176 | #481 | — | 2 | 1 | no | — |
| 177 | #481 | — | 2 | 2 | no | — |
| 178 | #476 | — | 4 | 1 | no | — |
| 179 | #475 | — | 2 | 1 | no | — |
| 180 | #474 | — | 2 | 1 | no | — |
| 181 | #470 | — | 2 | 1 | no | — |
| 182 | #469 | — | 2 | 1 | no | — |
| 183 | #465 | — | 2 | 1 | no | — |
| 184 | #465 | — | 2 | 1 | no | — |
| 185 | #465 | — | 2 | 1 | no | — |
| 186 | #465 | — | 2 | 1 | no | — |
| 187 | #464 | — | 2 | 1 | no | — |
| 188 | #464 | — | 2 | 1 | no | — |
| 189 | #464 | — | 2 | 1 | no | — |
| 190 | #464 | — | 2 | 1 | no | — |
| 191 | #463 | — | 2 | 1 | no | — |
| 192 | #463 | — | 2 | 1 | no | — |
| 193 | #463 | — | 2 | 1 | no | — |
| 194 | #463 | — | 2 | 1 | no | — |
| 195 | #462 | — | 2 | 1 | no | — |
| 196 | #461 | — | 2 | 1 | no | — |
| 197 | #460 | — | 2 | 1 | no | — |
| 198 | #460 | — | 2 | 1 | no | — |
| 199 | #460 | — | 4 | 1 | no | — |
| 200 | #459 | — | 2 | 1 | no | — |
| 201 | #459 | — | 2 | 1 | no | — |
| 202 | #452 | — | 2 | 1 | no | — |
| 203 | #452 | — | 2 | 1 | no | — |
| 204 | #451 | — | 2 | 1 | no | — |
| 205 | #451 | — | 2 | 1 | no | — |
| 206 | #450 | — | 2 | 1 | no | — |
| 207 | #450 | — | 2 | 1 | no | — |
| 208 | #450 | — | 2 | 1 | no | — |
| 209 | #450 | — | 2 | 2 | no | — |
| 210 | #449 | — | 2 | 1 | no | — |
| 211 | #449 | — | 2 | 1 | no | — |
| 212 | #448 | — | 2 | 1 | no | — |
| 213 | #448 | — | 2 | 1 | no | — |
| 214 | #447 | — | 2 | 1 | no | — |
| 215 | #447 | — | 2 | 1 | no | — |
| 216 | #447 | — | 2 | 1 | no | — |
| 217 | #446 | D4 | 1 | 1 | yes | characteristic, complemented |
| 218 | C8×Q8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 219 | #442 | — | 2 | 1 | no | — |
| 220 | #441 | — | 2 | 1 | no | — |
| 221 | C4×SD16 | — | 2 | 1 | no | — |
| 222 | C4×SD16 | — | 2 | 1 | no | — |
| 223 | C4×SD16 | — | 2 | 1 | no | — |
| 224 | C4×SD16 | — | 2 | 1 | no | — |
| 225 | #436 | D4 | 1 | 1 | yes | characteristic, complemented |
| 226 | #435 | — | 2 | 1 | no | — |
| 227 | C8×D4 | — | 2 | 1 | no | — |
| 228 | C8×D4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 229 | #433 | — | 2 | 1 | no | — |
| 230 | #432 | C23 | 1 | 1 | yes | characteristic |
| 231 | #432 | C23 | 1 | 1 | yes | characteristic |
| 232 | #432 | C23 | 1 | 1 | yes | characteristic |
| 233 | #431 | C23 | 1 | 1 | yes | characteristic |
| 234 | #428 | — | 4 | 1 | no | — |
| 235 | #405 | — | 2 | 1 | no | — |
| 236 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 237 | C2×#97 | — | 2 | 1 | no | — |
| 238 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 239 | C2×C4×C8 | — | 2 | 1 | no | — |
| 240 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 241 | #399 | — | 2 | 2 | no | — |
| 242 | #399 | — | 4 | 1 | no | — |
| 243 | #392 | — | 2 | 2 | no | — |
| 244 | #392 | — | 4 | 1 | no | — |
| 245 | #376 | C23 | 1 | 1 | yes | characteristic |
| 246 | #335 | — | 2 | 1 | no | — |
| 247 | #334 | — | 2 | 1 | no | — |
| 248 | #332 | — | 2 | 1 | no | — |
| 249 | #332 | — | 2 | 1 | no | — |
| 250 | #331 | — | 2 | 1 | no | — |
| 251 | #331 | — | 2 | 1 | no | — |
| 252 | #330 | — | 2 | 2 | no | — |
| 253 | #330 | D4 | 1 | 2 | yes | complemented |
| 254 | #329 | — | 2 | 2 | no | — |
| 255 | #329 | — | 2 | 2 | no | — |
| 256 | #329 | — | 2 | 2 | no | — |
| 257 | #329 | D4 | 1 | 2 | yes | complemented |
| 258 | #328 | — | 2 | 2 | no | — |
| 259 | #328 | D4 | 1 | 2 | yes | — |
| 260 | #327 | — | 2 | 2 | no | — |
| 261 | #327 | D4 | 1 | 2 | yes | — |
| 262 | #323 | — | 2 | 2 | no | — |
| 263 | #323 | — | 2 | 2 | no | — |
| 264 | #322 | — | 2 | 1 | no | — |
| 265 | C82 | — | 2 | 1 | no | — |
| 266 | C2×#41 | — | 2 | 1 | no | — |
| 267 | C2×#41 | — | 2 | 1 | no | — |
| 268 | C2×#41 | — | 2 | 1 | no | — |
| 269 | C22×Q8 | — | 2 | 1 | no | — |
| 270 | C22×Q8 | — | 2 | 1 | no | — |
| 271 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C22×D4 | — | 2 | 1 | no | — |
| 274 | C22×D4 | — | 2 | 1 | no | — |
| 275 | C22×D4 | — | 2 | 1 | no | — |
| 276 | C22×D4 | — | 2 | 1 | no | — |
| 277 | C22×D4 | — | 4 | 2 | no | — |
| 278 | C22×D4 | — | 4 | 1 | no | — |
| 279 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | #137 | — | 8 | 2 | no | — |
| 282 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 283 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 284 | #135 | — | 8 | 2 | no | — |
| 285 | C2×Q16 | — | 2 | 1 | no | — |
| 286 | C2×Q16 | — | 2 | 1 | no | — |
| 287 | C2×Q16 | — | 2 | 1 | no | — |
| 288 | C2×Q16 | — | 2 | 1 | no | — |
| 289 | C2×Q16 | — | 4 | 2 | no | — |
| 290 | C2×Q16 | — | 4 | 2 | no | — |
| 291 | C2×Q16 | — | 4 | 2 | no | — |
| 292 | C2×Q16 | — | 4 | 2 | no | — |
| 293 | C2×SD16 | — | 2 | 1 | no | — |
| 294 | C2×SD16 | — | 2 | 1 | no | — |
| 295 | C2×SD16 | — | 2 | 1 | no | — |
| 296 | C2×SD16 | — | 2 | 1 | no | — |
| 297 | C2×SD16 | — | 2 | 1 | no | — |
| 298 | C2×SD16 | — | 2 | 1 | no | — |
| 299 | C2×SD16 | — | 2 | 1 | no | — |
| 300 | C2×SD16 | — | 2 | 1 | no | — |
| 301 | C2×SD16 | — | 2 | 1 | no | — |
| 302 | C2×SD16 | — | 2 | 1 | no | — |
| 303 | C2×SD16 | — | 4 | 2 | no | — |
| 304 | C2×SD16 | — | 4 | 2 | no | — |
| 305 | C2×SD16 | — | 4 | 2 | no | — |
| 306 | C2×SD16 | — | 4 | 2 | no | — |
| 307 | C2×SD16 | — | 4 | 2 | no | — |
| 308 | C2×SD16 | — | 4 | 2 | no | — |
| 309 | C2×SD16 | — | 4 | 2 | no | — |
| 310 | C2×SD16 | — | 4 | 2 | no | — |
| 311 | C2×SD16 | — | 4 | 2 | no | — |
| 312 | C2×SD16 | — | 4 | 2 | no | — |
| 313 | C2×SD16 | — | 4 | 2 | no | — |
| 314 | C2×SD16 | — | 4 | 2 | no | — |
| 315 | C2×SD16 | — | 4 | 2 | no | — |
| 316 | C2×SD16 | — | 4 | 2 | no | — |
| 317 | C2×SD16 | — | 4 | 1 | no | — |
| 318 | C2×SD16 | — | 4 | 1 | no | — |
| 319 | C2×SD16 | — | 4 | 1 | no | — |
| 320 | C2×SD16 | — | 4 | 1 | no | — |
| 321 | C2×SD16 | — | 4 | 1 | no | — |
| 322 | C2×SD16 | — | 8 | 2 | no | — |
| 323 | C2×D8 | — | 2 | 1 | no | — |
| 324 | C2×D8 | — | 2 | 1 | no | — |
| 325 | C2×D8 | — | 2 | 1 | no | — |
| 326 | C2×D8 | — | 2 | 1 | no | — |
| 327 | C2×D8 | — | 4 | 2 | no | — |
| 328 | C2×D8 | — | 4 | 2 | no | — |
| 329 | C2×D8 | — | 4 | 2 | no | — |
| 330 | C2×D8 | — | 4 | 2 | no | — |
| 331 | C2×D8 | — | 4 | 2 | no | — |
| 332 | C2×D8 | — | 4 | 1 | no | — |
| 333 | C2×M16 | — | 2 | 1 | no | — |
| 334 | C2×M16 | — | 2 | 1 | no | — |
| 335 | C22×C8 | — | 2 | 1 | no | — |
| 336 | C22×C8 | — | 2 | 1 | no | — |
| 337 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 338 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 339 | C4⋊Q8 | — | 2 | 1 | no | — |
| 340 | C4⋊Q8 | — | 2 | 1 | no | — |
| 341 | C4⋊Q8 | — | 2 | 1 | no | — |
| 342 | C4⋊Q8 | — | 2 | 1 | no | — |
| 343 | C4⋊Q8 | — | 2 | 1 | no | — |
| 344 | C4⋊Q8 | — | 4 | 2 | no | — |
| 345 | C4⋊Q8 | — | 4 | 2 | no | — |
| 346 | C4⋊Q8 | — | 4 | 1 | no | — |
| 347 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 348 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 349 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 350 | #127 | — | 2 | 1 | no | — |
| 351 | #127 | — | 2 | 1 | no | — |
| 352 | #127 | — | 2 | 1 | no | — |
| 353 | #127 | — | 2 | 1 | no | — |
| 354 | #127 | — | 2 | 1 | no | — |
| 355 | #127 | — | 4 | 2 | no | — |
| 356 | #127 | — | 4 | 2 | no | — |
| 357 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 358 | #126 | — | 2 | 1 | no | — |
| 359 | #126 | — | 4 | 1 | no | — |
| 360 | #126 | — | 4 | 1 | no | — |
| 361 | #126 | — | 4 | 1 | no | — |
| 362 | #126 | — | 4 | 1 | no | — |
| 363 | #125 | — | 2 | 1 | no | — |
| 364 | #125 | C2×D4 | 1 | 1 | yes | characteristic |
| 365 | #124 | — | 2 | 1 | no | — |
| 366 | #124 | — | 2 | 1 | no | — |
| 367 | #124 | — | 2 | 1 | no | — |
| 368 | #124 | — | 2 | 1 | no | — |
| 369 | #124 | — | 2 | 1 | no | — |
| 370 | #124 | — | 2 | 1 | no | — |
| 371 | #124 | — | 2 | 1 | no | — |
| 372 | #124 | — | 2 | 1 | no | — |
| 373 | #124 | — | 2 | 1 | no | — |
| 374 | #124 | — | 2 | 1 | no | — |
| 375 | #124 | — | 2 | 1 | no | — |
| 376 | #124 | — | 4 | 2 | no | — |
| 377 | #124 | — | 4 | 2 | no | — |
| 378 | #124 | — | 4 | 2 | no | — |
| 379 | #124 | — | 4 | 2 | no | — |
| 380 | #124 | — | 4 | 1 | no | — |
| 381 | #124 | — | 4 | 1 | no | — |
| 382 | #124 | — | 4 | 1 | no | — |
| 383 | #124 | — | 4 | 1 | no | — |
| 384 | #124 | — | 4 | 1 | no | — |
| 385 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 386 | #123 | — | 2 | 1 | no | — |
| 387 | #123 | — | 4 | 1 | no | — |
| 388 | #123 | — | 4 | 1 | no | — |
| 389 | #123 | — | 4 | 1 | no | — |
| 390 | #123 | — | 4 | 1 | no | — |
| 391 | #123 | — | 4 | 1 | no | — |
| 392 | #123 | — | 4 | 1 | no | — |
| 393 | #123 | — | 4 | 1 | no | — |
| 394 | #123 | — | 4 | 1 | no | — |
| 395 | C22⋊Q8 | — | 2 | 1 | no | — |
| 396 | C22⋊Q8 | — | 2 | 1 | no | — |
| 397 | C22⋊Q8 | — | 2 | 1 | no | — |
| 398 | C22⋊Q8 | — | 2 | 1 | no | — |
| 399 | C22⋊Q8 | — | 4 | 1 | no | — |
| 400 | C22⋊Q8 | — | 4 | 1 | no | — |
| 401 | C22⋊Q8 | — | 4 | 1 | no | — |
| 402 | C22⋊Q8 | — | 4 | 1 | no | — |
| 403 | C22⋊Q8 | — | 4 | 1 | no | — |
| 404 | C22⋊Q8 | — | 4 | 1 | no | — |
| 405 | C22⋊Q8 | — | 4 | 1 | no | — |
| 406 | C22⋊Q8 | — | 4 | 1 | no | — |
| 407 | C22⋊Q8 | — | 4 | 1 | no | — |
| 408 | C22⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 409 | #121 | — | 2 | 1 | no | — |
| 410 | #121 | — | 2 | 1 | no | — |
| 411 | #121 | — | 2 | 1 | no | — |
| 412 | #121 | — | 2 | 1 | no | — |
| 413 | #121 | — | 4 | 1 | no | — |
| 414 | #121 | — | 4 | 1 | no | — |
| 415 | #121 | — | 4 | 1 | no | — |
| 416 | #121 | — | 4 | 1 | no | — |
| 417 | #121 | — | 4 | 1 | no | — |
| 418 | #121 | — | 4 | 1 | no | — |
| 419 | #121 | — | 4 | 1 | no | — |
| 420 | #121 | C2×D4 | 1 | 1 | yes | characteristic |
| 421 | #120 | — | 4 | 1 | no | — |
| 422 | #120 | — | 4 | 1 | no | — |
| 423 | #120 | — | 4 | 1 | no | — |
| 424 | #120 | — | 4 | 1 | no | — |
| 425 | #120 | — | 4 | 1 | no | — |
| 426 | #120 | — | 4 | 1 | no | — |
| 427 | C4×Q8 | — | 2 | 1 | no | — |
| 428 | C4×Q8 | — | 2 | 1 | no | — |
| 429 | C4×Q8 | — | 2 | 1 | no | — |
| 430 | C4×Q8 | — | 2 | 1 | no | — |
| 431 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 432 | C4×D4 | — | 2 | 1 | no | — |
| 433 | C4×D4 | — | 2 | 1 | no | — |
| 434 | C4×D4 | — | 2 | 1 | no | — |
| 435 | C4×D4 | — | 2 | 1 | no | — |
| 436 | C4×D4 | — | 2 | 1 | no | — |
| 437 | C4×D4 | — | 4 | 1 | no | — |
| 438 | C4×D4 | — | 4 | 1 | no | — |
| 439 | C4×D4 | — | 4 | 1 | no | — |
| 440 | C4×D4 | — | 4 | 1 | no | — |
| 441 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 442 | #117 | — | 2 | 1 | no | — |
| 443 | #117 | — | 2 | 1 | no | — |
| 444 | #117 | — | 4 | 1 | no | — |
| 445 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 446 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 447 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 448 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 449 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 450 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 451 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 452 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 453 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 454 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 455 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 456 | C2×C42 | — | 2 | 1 | no | — |
| 457 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 458 | #107 | — | 4 | 2 | no | — |
| 459 | #107 | — | 4 | 1 | no | — |
| 460 | #106 | — | 2 | 1 | no | — |
| 461 | #106 | — | 2 | 1 | no | — |
| 462 | #106 | — | 4 | 2 | no | — |
| 463 | #106 | — | 4 | 2 | no | — |
| 464 | #106 | — | 4 | 1 | no | — |
| 465 | C4⋊C8 | — | 2 | 1 | no | — |
| 466 | C4⋊C8 | — | 2 | 1 | no | — |
| 467 | C4⋊C8 | — | 2 | 1 | no | — |
| 468 | C4⋊C8 | — | 2 | 1 | no | — |
| 469 | C4⋊C8 | — | 2 | 1 | no | — |
| 470 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 471 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 472 | #103 | — | 2 | 1 | no | — |
| 473 | #103 | — | 2 | 1 | no | — |
| 474 | #103 | — | 2 | 1 | no | — |
| 475 | #103 | — | 2 | 1 | no | — |
| 476 | #103 | — | 2 | 1 | no | — |
| 477 | #103 | — | 2 | 1 | no | — |
| 478 | #103 | — | 4 | 1 | no | — |
| 479 | #102 | — | 2 | 1 | no | — |
| 480 | #102 | — | 2 | 1 | no | — |
| 481 | #102 | — | 2 | 1 | no | — |
| 482 | #102 | — | 2 | 1 | no | — |
| 483 | #102 | — | 2 | 1 | no | — |
| 484 | #102 | — | 2 | 1 | no | — |
| 485 | #102 | — | 4 | 2 | no | — |
| 486 | #102 | — | 4 | 2 | no | — |
| 487 | #102 | — | 4 | 1 | no | — |
| 488 | #102 | — | 4 | 1 | no | — |
| 489 | #102 | — | 4 | 1 | no | — |
| 490 | C22⋊C8 | — | 2 | 1 | no | — |
| 491 | C22⋊C8 | — | 2 | 1 | no | — |
| 492 | C22⋊C8 | — | 2 | 1 | no | — |
| 493 | C22⋊C8 | — | 2 | 1 | no | — |
| 494 | C22⋊C8 | — | 2 | 1 | no | — |
| 495 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 496 | #97 | — | 2 | 4 | no | — |
| 497 | #97 | — | 2 | 1 | no | — |
| 498 | #97 | — | 2 | 1 | no | — |
| 499 | #97 | — | 2 | 1 | no | — |
| 500 | #97 | — | 2 | 1 | no | — |
| 501 | #97 | — | 2 | 1 | no | — |
| 502 | #97 | C2×D4 | 1 | 2 | yes | — |
| 503 | #97 | C2×D4 | 1 | 2 | yes | — |
| 504 | C4×C8 | — | 2 | 4 | no | — |
| 505 | C4×C8 | — | 2 | 1 | no | — |
| 506 | C4×C8 | — | 2 | 1 | no | — |
| 507 | C4×C8 | — | 2 | 1 | no | — |
| 508 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 509 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 510 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 511 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 512 | #95 | — | 2 | 1 | no | — |
| 513 | #95 | C2×D4 | 1 | 2 | yes | — |
| 514 | C24 | — | 2 | 1 | no | — |
| 515 | C24 | — | 2 | 1 | no | — |
| 516 | C24 | — | 4 | 1 | no | — |
| 517 | C24 | — | 4 | 1 | no | — |
| 518 | #41 | — | 8 | 2 | no | — |
| 519 | #41 | — | 8 | 1 | no | — |
| 520 | #41 | — | 8 | 1 | no | — |
| 521 | #41 | — | 8 | 1 | no | — |
| 522 | #41 | — | 8 | 1 | no | — |
| 523 | C2×Q8 | — | 2 | 1 | no | — |
| 524 | C2×Q8 | — | 2 | 1 | no | — |
| 525 | C2×Q8 | — | 2 | 1 | no | — |
| 526 | C2×Q8 | — | 2 | 1 | no | — |
| 527 | C2×Q8 | — | 2 | 1 | no | — |
| 528 | C2×Q8 | — | 2 | 1 | no | — |
| 529 | C2×Q8 | — | 2 | 1 | no | — |
| 530 | C2×Q8 | — | 4 | 1 | no | — |
| 531 | C2×Q8 | — | 4 | 1 | no | — |
| 532 | C2×Q8 | — | 4 | 1 | no | — |
| 533 | C2×Q8 | — | 4 | 1 | no | — |
| 534 | C2×Q8 | — | 4 | 1 | no | — |
| 535 | C2×Q8 | — | 4 | 1 | no | — |
| 536 | C2×Q8 | — | 4 | 1 | no | — |
| 537 | C2×Q8 | — | 4 | 1 | no | — |
| 538 | C2×Q8 | — | 4 | 1 | no | — |
| 539 | C2×Q8 | — | 4 | 1 | no | — |
| 540 | C2×Q8 | — | 4 | 1 | no | — |
| 541 | C2×Q8 | — | 8 | 1 | no | — |
| 542 | C2×Q8 | — | 8 | 1 | no | — |
| 543 | C2×Q8 | #127 | 1 | 1 | yes | characteristic |
| 544 | C2×D4 | — | 2 | 1 | no | — |
| 545 | C2×D4 | — | 2 | 1 | no | — |
| 546 | C2×D4 | — | 2 | 1 | no | — |
| 547 | C2×D4 | — | 2 | 1 | no | — |
| 548 | C2×D4 | — | 2 | 1 | no | — |
| 549 | C2×D4 | — | 2 | 1 | no | — |
| 550 | C2×D4 | — | 2 | 1 | no | — |
| 551 | C2×D4 | — | 2 | 1 | no | — |
| 552 | C2×D4 | — | 4 | 1 | no | — |
| 553 | C2×D4 | — | 4 | 1 | no | — |
| 554 | C2×D4 | — | 4 | 1 | no | — |
| 555 | C2×D4 | — | 4 | 1 | no | — |
| 556 | C2×D4 | — | 4 | 1 | no | — |
| 557 | C2×D4 | — | 4 | 1 | no | — |
| 558 | C2×D4 | — | 4 | 1 | no | — |
| 559 | C2×D4 | — | 4 | 1 | no | — |
| 560 | C2×D4 | — | 4 | 1 | no | — |
| 561 | C2×D4 | — | 4 | 1 | no | — |
| 562 | C2×D4 | — | 4 | 1 | no | — |
| 563 | C2×D4 | — | 4 | 1 | no | — |
| 564 | C2×D4 | — | 4 | 1 | no | — |
| 565 | C2×D4 | — | 4 | 1 | no | — |
| 566 | C2×D4 | — | 4 | 1 | no | — |
| 567 | C2×D4 | — | 4 | 1 | no | — |
| 568 | C2×D4 | — | 4 | 1 | no | — |
| 569 | C2×D4 | — | 4 | 1 | no | — |
| 570 | C2×D4 | — | 4 | 1 | no | — |
| 571 | C2×D4 | — | 4 | 1 | no | — |
| 572 | C2×D4 | — | 4 | 1 | no | — |
| 573 | C2×D4 | — | 4 | 1 | no | — |
| 574 | C2×D4 | — | 8 | 2 | no | — |
| 575 | C2×D4 | — | 8 | 4 | no | — |
| 576 | C2×D4 | — | 8 | 1 | no | — |
| 577 | C2×D4 | — | 8 | 1 | no | — |
| 578 | C2×D4 | — | 16 | 1 | no | — |
| 579 | C2×D4 | — | 16 | 2 | no | — |
| 580 | C2×D4 | — | 16 | 2 | no | — |
| 581 | C2×D4 | — | 16 | 2 | no | — |
| 582 | C2×D4 | #127 | 1 | 1 | yes | characteristic |
| 583 | C22×C4 | — | 2 | 2 | no | — |
| 584 | C22×C4 | — | 2 | 1 | no | — |
| 585 | C22×C4 | — | 2 | 1 | no | — |
| 586 | C22×C4 | — | 2 | 1 | no | — |
| 587 | C22×C4 | — | 4 | 1 | no | — |
| 588 | C22×C4 | — | 4 | 1 | no | — |
| 589 | C22×C4 | — | 4 | 1 | no | — |
| 590 | C22×C4 | — | 4 | 1 | no | — |
| 591 | C22×C4 | — | 4 | 1 | no | — |
| 592 | C22×C4 | — | 4 | 1 | no | — |
| 593 | C22×C4 | — | 4 | 1 | no | — |
| 594 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 595 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 596 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 597 | Q16 | — | 4 | 2 | no | — |
| 598 | Q16 | — | 8 | 1 | no | — |
| 599 | Q16 | — | 8 | 4 | no | — |
| 600 | Q16 | — | 8 | 1 | no | — |
| 601 | Q16 | — | 8 | 1 | no | — |
| 602 | SD16 | — | 4 | 2 | no | — |
| 603 | SD16 | — | 4 | 2 | no | — |
| 604 | SD16 | — | 4 | 2 | no | — |
| 605 | SD16 | — | 4 | 2 | no | — |
| 606 | SD16 | — | 8 | 1 | no | — |
| 607 | SD16 | — | 8 | 1 | no | — |
| 608 | SD16 | — | 8 | 4 | no | — |
| 609 | SD16 | — | 8 | 4 | no | — |
| 610 | SD16 | — | 8 | 2 | no | — |
| 611 | SD16 | — | 8 | 2 | no | — |
| 612 | SD16 | — | 8 | 4 | no | — |
| 613 | SD16 | — | 8 | 1 | no | — |
| 614 | SD16 | — | 8 | 1 | no | — |
| 615 | SD16 | — | 8 | 1 | no | — |
| 616 | SD16 | — | 8 | 1 | no | — |
| 617 | SD16 | — | 8 | 2 | no | — |
| 618 | SD16 | — | 8 | 2 | no | — |
| 619 | SD16 | — | 16 | 2 | no | — |
| 620 | SD16 | — | 16 | 1 | no | — |
| 621 | D8 | — | 4 | 2 | no | — |
| 622 | D8 | — | 8 | 1 | no | — |
| 623 | D8 | — | 8 | 4 | no | — |
| 624 | D8 | — | 8 | 4 | no | — |
| 625 | D8 | — | 8 | 1 | no | — |
| 626 | D8 | — | 8 | 1 | no | — |
| 627 | D8 | — | 16 | 1 | no | — |
| 628 | M16 | — | 2 | 4 | no | — |
| 629 | M16 | — | 4 | 2 | no | — |
| 630 | C2×C8 | — | 2 | 2 | no | — |
| 631 | C2×C8 | — | 2 | 2 | no | — |
| 632 | C2×C8 | — | 2 | 2 | no | — |
| 633 | C2×C8 | — | 2 | 2 | no | — |
| 634 | C2×C8 | — | 2 | 2 | no | — |
| 635 | C2×C8 | — | 2 | 2 | no | — |
| 636 | C2×C8 | — | 2 | 1 | no | — |
| 637 | C2×C8 | — | 2 | 1 | no | — |
| 638 | C2×C8 | — | 2 | 2 | no | — |
| 639 | C2×C8 | — | 4 | 2 | no | — |
| 640 | C2×C8 | — | 4 | 1 | no | — |
| 641 | C2×C8 | — | 4 | 1 | no | — |
| 642 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 643 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 644 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 645 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 646 | C4⋊C4 | — | 2 | 1 | no | — |
| 647 | C4⋊C4 | — | 2 | 1 | no | — |
| 648 | C4⋊C4 | — | 2 | 1 | no | — |
| 649 | C4⋊C4 | — | 2 | 1 | no | — |
| 650 | C4⋊C4 | — | 2 | 1 | no | — |
| 651 | C4⋊C4 | — | 2 | 1 | no | — |
| 652 | C4⋊C4 | — | 2 | 1 | no | — |
| 653 | C4⋊C4 | — | 2 | 1 | no | — |
| 654 | C4⋊C4 | — | 2 | 1 | no | — |
| 655 | C4⋊C4 | — | 2 | 1 | no | — |
| 656 | C4⋊C4 | — | 4 | 1 | no | — |
| 657 | C4⋊C4 | — | 4 | 1 | no | — |
| 658 | C4⋊C4 | — | 4 | 1 | no | — |
| 659 | C4⋊C4 | — | 4 | 1 | no | — |
| 660 | C4⋊C4 | — | 4 | 1 | no | — |
| 661 | C4⋊C4 | — | 4 | 1 | no | — |
| 662 | C4⋊C4 | — | 4 | 1 | no | — |
| 663 | C4⋊C4 | — | 4 | 1 | no | — |
| 664 | C4⋊C4 | — | 4 | 1 | no | — |
| 665 | C4⋊C4 | — | 4 | 1 | no | — |
| 666 | C4⋊C4 | — | 4 | 1 | no | — |
| 667 | C4⋊C4 | — | 4 | 1 | no | — |
| 668 | C4⋊C4 | — | 8 | 4 | no | — |
| 669 | C4⋊C4 | #127 | 1 | 1 | yes | characteristic |
| 670 | C4⋊C4 | #127 | 1 | 1 | yes | characteristic |
| 671 | C22⋊C4 | — | 2 | 1 | no | — |
| 672 | C22⋊C4 | — | 2 | 1 | no | — |
| 673 | C22⋊C4 | — | 2 | 1 | no | — |
| 674 | C22⋊C4 | — | 2 | 1 | no | — |
| 675 | C22⋊C4 | — | 2 | 1 | no | — |
| 676 | C22⋊C4 | — | 4 | 1 | no | — |
| 677 | C22⋊C4 | — | 4 | 1 | no | — |
| 678 | C22⋊C4 | — | 4 | 1 | no | — |
| 679 | C22⋊C4 | — | 4 | 1 | no | — |
| 680 | C22⋊C4 | — | 4 | 1 | no | — |
| 681 | C22⋊C4 | — | 4 | 1 | no | — |
| 682 | C22⋊C4 | — | 4 | 1 | no | — |
| 683 | C22⋊C4 | — | 4 | 1 | no | — |
| 684 | C22⋊C4 | — | 4 | 1 | no | — |
| 685 | C22⋊C4 | — | 4 | 1 | no | — |
| 686 | C22⋊C4 | — | 4 | 1 | no | — |
| 687 | C22⋊C4 | — | 4 | 1 | no | — |
| 688 | C22⋊C4 | — | 4 | 1 | no | — |
| 689 | C22⋊C4 | — | 4 | 1 | no | — |
| 690 | C22⋊C4 | — | 4 | 1 | no | — |
| 691 | C22⋊C4 | — | 4 | 1 | no | — |
| 692 | C22⋊C4 | — | 4 | 1 | no | — |
| 693 | C22⋊C4 | — | 4 | 1 | no | — |
| 694 | C22⋊C4 | — | 4 | 1 | no | — |
| 695 | C22⋊C4 | — | 4 | 1 | no | — |
| 696 | C22⋊C4 | — | 4 | 1 | no | — |
| 697 | C22⋊C4 | — | 8 | 4 | no | — |
| 698 | C22⋊C4 | — | 8 | 4 | no | — |
| 699 | C42 | — | 2 | 2 | no | — |
| 700 | C42 | — | 2 | 2 | no | — |
| 701 | C42 | — | 2 | 1 | no | — |
| 702 | C42 | — | 4 | 1 | no | — |
| 703 | C42 | — | 4 | 1 | no | — |
| 704 | C42 | — | 4 | 1 | no | — |
| 705 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 706 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 707 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 708 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 709 | C23 | — | 2 | 1 | no | — |
| 710 | C23 | — | 4 | 1 | no | — |
| 711 | C23 | — | 4 | 1 | no | — |
| 712 | C23 | — | 4 | 1 | no | — |
| 713 | C23 | — | 4 | 2 | no | — |
| 714 | C23 | — | 4 | 2 | no | — |
| 715 | C23 | — | 8 | 1 | no | — |
| 716 | C23 | — | 8 | 1 | no | — |
| 717 | C23 | — | 8 | 1 | no | — |
| 718 | C23 | — | 8 | 1 | no | — |
| 719 | C23 | — | 8 | 1 | no | — |
| 720 | C23 | — | 8 | 1 | no | — |
| 721 | C23 | — | 8 | 2 | no | — |
| 722 | C23 | — | 8 | 1 | no | — |
| 723 | C23 | — | 8 | 2 | no | — |
| 724 | C23 | — | 16 | 1 | no | — |
| 725 | C23 | — | 16 | 1 | no | — |
| 726 | C23 | — | 16 | 1 | no | — |
| 727 | C23 | D42 | 1 | 1 | yes | characteristic |
| 728 | Q8 | — | 4 | 1 | no | — |
| 729 | Q8 | — | 4 | 1 | no | — |
| 730 | Q8 | — | 4 | 1 | no | — |
| 731 | Q8 | — | 4 | 1 | no | — |
| 732 | Q8 | — | 4 | 1 | no | — |
| 733 | Q8 | — | 4 | 1 | no | — |
| 734 | Q8 | — | 4 | 1 | no | — |
| 735 | Q8 | — | 8 | 1 | no | — |
| 736 | Q8 | — | 8 | 1 | no | — |
| 737 | Q8 | — | 8 | 1 | no | — |
| 738 | Q8 | — | 8 | 1 | no | — |
| 739 | Q8 | — | 8 | 1 | no | — |
| 740 | Q8 | — | 8 | 1 | no | — |
| 741 | Q8 | — | 8 | 1 | no | — |
| 742 | Q8 | — | 8 | 1 | no | — |
| 743 | Q8 | — | 16 | 1 | no | — |
| 744 | D4 | — | 4 | 1 | no | — |
| 745 | D4 | — | 4 | 2 | no | — |
| 746 | D4 | — | 4 | 1 | no | — |
| 747 | D4 | — | 4 | 1 | no | — |
| 748 | D4 | — | 4 | 1 | no | — |
| 749 | D4 | — | 4 | 1 | no | — |
| 750 | D4 | — | 4 | 1 | no | — |
| 751 | D4 | — | 4 | 1 | no | — |
| 752 | D4 | — | 8 | 1 | no | — |
| 753 | D4 | — | 8 | 1 | no | — |
| 754 | D4 | — | 8 | 1 | no | — |
| 755 | D4 | — | 8 | 1 | no | — |
| 756 | D4 | — | 8 | 1 | no | — |
| 757 | D4 | — | 8 | 2 | no | — |
| 758 | D4 | — | 8 | 1 | no | — |
| 759 | D4 | — | 8 | 1 | no | — |
| 760 | D4 | — | 8 | 2 | no | — |
| 761 | D4 | — | 8 | 1 | no | — |
| 762 | D4 | — | 8 | 2 | no | — |
| 763 | D4 | — | 8 | 1 | no | — |
| 764 | D4 | — | 8 | 1 | no | — |
| 765 | D4 | — | 16 | 1 | no | — |
| 766 | D4 | — | 16 | 1 | no | — |
| 767 | D4 | — | 16 | 1 | no | — |
| 768 | D4 | — | 16 | 1 | no | — |
| 769 | D4 | — | 16 | 8 | no | — |
| 770 | D4 | — | 16 | 1 | no | — |
| 771 | D4 | — | 16 | 1 | no | — |
| 772 | D4 | — | 16 | 1 | no | — |
| 773 | D4 | — | 16 | 1 | no | — |
| 774 | C2×C4 | — | 2 | 2 | no | — |
| 775 | C2×C4 | — | 2 | 1 | no | — |
| 776 | C2×C4 | — | 2 | 1 | no | — |
| 777 | C2×C4 | — | 2 | 4 | no | — |
| 778 | C2×C4 | — | 2 | 1 | no | — |
| 779 | C2×C4 | — | 2 | 1 | no | — |
| 780 | C2×C4 | — | 2 | 1 | no | — |
| 781 | C2×C4 | — | 4 | 1 | no | — |
| 782 | C2×C4 | — | 4 | 2 | no | — |
| 783 | C2×C4 | — | 4 | 2 | no | — |
| 784 | C2×C4 | — | 4 | 1 | no | — |
| 785 | C2×C4 | — | 4 | 1 | no | — |
| 786 | C2×C4 | — | 4 | 1 | no | — |
| 787 | C2×C4 | — | 4 | 1 | no | — |
| 788 | C2×C4 | — | 4 | 1 | no | — |
| 789 | C2×C4 | — | 4 | 1 | no | — |
| 790 | C2×C4 | — | 4 | 1 | no | — |
| 791 | C2×C4 | — | 8 | 1 | no | — |
| 792 | C2×C4 | — | 8 | 1 | no | — |
| 793 | C2×C4 | — | 8 | 1 | no | — |
| 794 | C2×C4 | — | 8 | 1 | no | — |
| 795 | C2×C4 | — | 8 | 1 | no | — |
| 796 | C2×C4 | — | 16 | 1 | no | — |
| 797 | C2×C4 | — | 16 | 1 | no | — |
| 798 | C2×C4 | — | 16 | 1 | no | — |
| 799 | C2×C4 | — | 16 | 1 | no | — |
| 800 | C2×C4 | — | 16 | 1 | no | — |
| 801 | C2×C4 | — | 16 | 1 | no | — |
| 802 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 803 | C2×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 804 | C2×C4 | #535 | 1 | 1 | yes | characteristic |
| 805 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 806 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 807 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 808 | C8 | — | 2 | 4 | no | — |
| 809 | C8 | — | 2 | 4 | no | — |
| 810 | C8 | — | 2 | 1 | no | — |
| 811 | C8 | — | 2 | 1 | no | — |
| 812 | C8 | — | 4 | 2 | no | — |
| 813 | C8 | — | 4 | 1 | no | — |
| 814 | C8 | — | 4 | 1 | no | — |
| 815 | C8 | — | 8 | 1 | no | — |
| 816 | C8 | — | 8 | 1 | no | — |
| 817 | C8 | #453 | 1 | 2 | yes | — |
| 818 | C8 | #453 | 1 | 2 | yes | — |
| 819 | C22 | — | 2 | 1 | no | — |
| 820 | C22 | — | 2 | 1 | no | — |
| 821 | C22 | — | 4 | 1 | no | — |
| 822 | C22 | — | 4 | 1 | no | — |
| 823 | C22 | — | 4 | 1 | no | — |
| 824 | C22 | — | 8 | 1 | no | — |
| 825 | C22 | — | 8 | 1 | no | — |
| 826 | C22 | — | 8 | 1 | no | — |
| 827 | C22 | — | 8 | 1 | no | — |
| 828 | C22 | — | 8 | 1 | no | — |
| 829 | C22 | — | 8 | 1 | no | — |
| 830 | C22 | — | 8 | 1 | no | — |
| 831 | C22 | — | 8 | 1 | no | — |
| 832 | C22 | — | 8 | 1 | no | — |
| 833 | C22 | — | 16 | 2 | no | — |
| 834 | C22 | — | 16 | 2 | no | — |
| 835 | C22 | — | 16 | 2 | no | — |
| 836 | C22 | — | 16 | 2 | no | — |
| 837 | C22 | — | 16 | 1 | no | — |
| 838 | C22 | — | 16 | 1 | no | — |
| 839 | C22 | — | 16 | 1 | no | — |
| 840 | C22 | — | 32 | 2 | no | — |
| 841 | C22 | #2433 | 1 | 1 | yes | characteristic |
| 842 | C22 | #3291 | 1 | 2 | yes | — |
| 843 | C4 | — | 2 | 1 | no | — |
| 844 | C4 | — | 2 | 1 | no | — |
| 845 | C4 | — | 2 | 1 | no | — |
| 846 | C4 | — | 2 | 1 | no | — |
| 847 | C4 | — | 2 | 1 | no | — |
| 848 | C4 | — | 4 | 4 | no | — |
| 849 | C4 | — | 4 | 1 | no | — |
| 850 | C4 | — | 4 | 1 | no | — |
| 851 | C4 | — | 4 | 1 | no | — |
| 852 | C4 | — | 8 | 1 | no | — |
| 853 | C4 | — | 8 | 1 | no | — |
| 854 | C4 | — | 8 | 1 | no | — |
| 855 | C4 | — | 8 | 1 | no | — |
| 856 | C4 | — | 8 | 1 | no | — |
| 857 | C4 | — | 16 | 1 | no | — |
| 858 | C4 | C2×#453 | 1 | 1 | yes | characteristic |
| 859 | C4 | C2×#453 | 1 | 1 | yes | characteristic |
| 860 | C2 | — | 2 | 2 | no | — |
| 861 | C2 | — | 8 | 1 | no | — |
| 862 | C2 | — | 16 | 1 | no | — |
| 863 | C2 | — | 16 | 1 | no | — |
| 864 | C2 | — | 16 | 1 | no | — |
| 865 | C2 | — | 32 | 1 | no | — |
| 866 | C2 | #25747 | 1 | 1 | yes | characteristic |
| 867 | C2 | #25798 | 1 | 1 | yes | characteristic |
| 868 | C2 | #25802 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #2433 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62435 | C2 | semidirect |
| 2. #33307 | C2 | semidirect |
| 3. #19621 | C2 | semidirect |
| 4. #19352 | C2 | semidirect |
| 5. #19033 | C2 | semidirect |
| 6. #19014 | C2 | semidirect |
| 7. #18437 | C2 | semidirect |
| 8. #18428 | C2 | semidirect |
| 9. #10132 | C2 | semidirect |
| 10. #10129 | C2 | semidirect |
| 11. #10102 | C2 | semidirect |
| 12. #10088 | C2 | semidirect |
| 13. #9787 | C2 | semidirect |
| 14. #9761 | C2 | semidirect |
| 15. #8247 | C2 | semidirect |
| 33. #3208 | C22 | semidirect |
| 36. #3165 | C22 | semidirect |
| 40. C2×#497 | C22 | semidirect |
| 46. C2×#492 | C22 | semidirect |
| 49. #2657 | C22 | semidirect |
| 50. #1726 | C22 | semidirect |
| 67. #1568 | C22 | semidirect |
| 68. #1556 | C22 | semidirect |
| 69. #1555 | C22 | semidirect |
| 70. #1531 | C22 | semidirect |
| 73. #1527 | C22 | semidirect |
| 75. #1506 | C22 | semidirect |
| 79. #1469 | C22 | semidirect |
| 80. C8×M16 | C22 | semidirect |
| 81. #1302 | C22 | semidirect |
| 82. #1300 | C22 | semidirect |
| 138. #498 | D4 | semidirect |
| 166. #492 | D4 | semidirect |
| 171. #487 | D4 | semidirect |
| 174. #486 | D4 | semidirect |
| 217. #446 | D4 | semidirect |
| 218. C8×Q8 | D4 | semidirect |
| 225. #436 | D4 | semidirect |
| 228. C8×D4 | D4 | semidirect |
| 253. #330 | D4 | semidirect |
| 257. #329 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62435 | 2 |
| #33307 | 2 |
| #19621 | 2 |
| #19352 | 2 |
| #19033 | 2 |
| #19014 | 2 |
| #18437 | 2 |
| #18428 | 2 |
| #10132 | 2 |
| #10129 | 2 |
| #10102 | 2 |
| #10088 | 2 |
| #9787 | 2 |
| #9761 | 2 |
| #8247 | 2 |