Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1143 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 1143 conjugacy classes of subgroups — too many to draw. Only its 75 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 | #6367483 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #153521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #153455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #153435 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #152595 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #152584 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #137560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #61979 | — | 2 | 1 | no | — |
| 9 | #61661 | — | 2 | 1 | no | — |
| 10 | #23196 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #20310 | — | 2 | 1 | no | — |
| 12 | #20138 | C4 | 1 | 2 | yes | complemented |
| 13 | #20053 | C4 | 1 | 2 | yes | complemented |
| 14 | #20024 | — | 2 | 2 | no | — |
| 15 | D82 | — | 2 | 1 | no | — |
| 16 | #19911 | — | 2 | 2 | no | — |
| 17 | #19661 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19554 | — | 2 | 1 | no | — |
| 19 | #19484 | — | 2 | 1 | no | — |
| 20 | #18686 | C22 | 1 | 1 | yes | characteristic |
| 21 | #18620 | — | 2 | 1 | no | — |
| 22 | #18480 | C22 | 1 | 1 | yes | characteristic |
| 23 | #18015 | — | 2 | 1 | no | — |
| 24 | #13589 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #13583 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #13261 | — | 2 | 1 | no | — |
| 27 | #12778 | — | 2 | 1 | no | — |
| 28 | #12765 | — | 2 | 1 | no | — |
| 29 | #11920 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #7527 | — | 2 | 2 | no | — |
| 31 | #7521 | — | 2 | 2 | no | — |
| 32 | #7516 | — | 2 | 1 | no | — |
| 33 | #7515 | — | 2 | 1 | no | — |
| 34 | #7488 | — | 2 | 1 | no | — |
| 35 | #7482 | — | 2 | 1 | no | — |
| 36 | #7181 | — | 2 | 1 | no | — |
| 37 | #3549 | D4 | 1 | 1 | yes | characteristic |
| 38 | #3498 | — | 2 | 1 | no | — |
| 39 | #3481 | D4 | 1 | 1 | yes | characteristic |
| 40 | #3399 | — | 2 | 2 | no | — |
| 41 | #3366 | — | 2 | 2 | no | — |
| 42 | #3325 | — | 2 | 2 | no | — |
| 43 | #3325 | — | 4 | 1 | no | — |
| 44 | #3318 | — | 4 | 2 | no | — |
| 45 | #3305 | — | 2 | 2 | no | — |
| 46 | #3305 | — | 4 | 1 | no | — |
| 47 | #3295 | — | 2 | 2 | no | — |
| 48 | D4×D8 | — | 2 | 2 | no | — |
| 49 | D4×D8 | — | 2 | 2 | no | — |
| 50 | D4×D8 | — | 4 | 1 | no | — |
| 51 | #3274 | — | 2 | 2 | no | — |
| 52 | #3274 | — | 4 | 1 | no | — |
| 53 | #3264 | — | 4 | 2 | no | — |
| 54 | #3253 | — | 2 | 1 | no | — |
| 55 | #3247 | — | 4 | 1 | no | — |
| 56 | #3217 | — | 4 | 1 | no | — |
| 57 | #3205 | — | 2 | 1 | no | — |
| 58 | #3205 | — | 2 | 1 | no | — |
| 59 | #3205 | — | 2 | 1 | no | — |
| 60 | #3199 | — | 4 | 2 | no | — |
| 61 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#493 | D4 | 1 | 1 | yes | characteristic |
| 63 | #3109 | — | 4 | 1 | no | — |
| 64 | #3106 | — | 2 | 1 | no | — |
| 65 | #3106 | — | 2 | 1 | no | — |
| 66 | #3038 | — | 2 | 1 | no | — |
| 67 | C2×#459 | — | 4 | 1 | no | — |
| 68 | #3008 | — | 4 | 2 | no | — |
| 69 | #2990 | — | 2 | 1 | no | — |
| 70 | #2979 | — | 2 | 1 | no | — |
| 71 | #2957 | — | 4 | 1 | no | — |
| 72 | C2×#364 | — | 2 | 1 | no | — |
| 73 | C2×#361 | — | 4 | 1 | no | — |
| 74 | #2140 | — | 4 | 1 | no | — |
| 75 | #2132 | — | 2 | 1 | no | — |
| 76 | #2128 | — | 4 | 1 | no | — |
| 77 | #2126 | — | 2 | 1 | no | — |
| 78 | #2120 | — | 4 | 1 | no | — |
| 79 | #1976 | — | 4 | 1 | no | — |
| 80 | #1910 | — | 4 | 1 | no | — |
| 81 | #1891 | — | 4 | 1 | no | — |
| 82 | #1884 | — | 2 | 1 | no | — |
| 83 | #1884 | — | 2 | 1 | no | — |
| 84 | #1772 | — | 2 | 1 | no | — |
| 85 | #1721 | C2×C4 | 1 | 2 | yes | — |
| 86 | #1721 | D4 | 1 | 2 | yes | — |
| 87 | #1712 | — | 2 | 1 | no | — |
| 88 | #1709 | — | 2 | 1 | no | — |
| 89 | #1698 | — | 2 | 2 | no | — |
| 90 | #1697 | — | 2 | 2 | no | — |
| 91 | #1688 | — | 2 | 2 | no | — |
| 92 | #1687 | — | 2 | 2 | no | — |
| 93 | #1677 | — | 2 | 2 | no | — |
| 94 | #1677 | — | 2 | 2 | no | — |
| 95 | #1667 | — | 2 | 2 | no | — |
| 96 | #1667 | — | 2 | 2 | no | — |
| 97 | #1634 | D4 | 1 | 2 | yes | — |
| 98 | #1632 | — | 2 | 1 | no | — |
| 99 | #1630 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | #1629 | — | 2 | 1 | no | — |
| 101 | #1629 | C2×C4 | 1 | 1 | yes | characteristic |
| 102 | #1624 | C2×C4 | 1 | 2 | yes | — |
| 103 | #1622 | — | 2 | 1 | no | — |
| 104 | #1621 | — | 2 | 2 | no | — |
| 105 | #1621 | — | 2 | 2 | no | — |
| 106 | #1620 | D4 | 1 | 1 | yes | characteristic |
| 107 | #1619 | — | 2 | 2 | no | — |
| 108 | #1619 | — | 2 | 2 | no | — |
| 109 | #1619 | — | 2 | 1 | no | — |
| 110 | #1619 | D4 | 1 | 1 | yes | characteristic |
| 111 | #1590 | — | 2 | 2 | no | — |
| 112 | #1586 | — | 2 | 2 | no | — |
| 113 | #1585 | — | 2 | 2 | no | — |
| 114 | C8×D8 | — | 2 | 2 | no | — |
| 115 | #1574 | — | 2 | 1 | no | — |
| 116 | #1560 | D4 | 1 | 1 | yes | characteristic |
| 117 | #1545 | — | 2 | 1 | no | — |
| 118 | #1543 | D4 | 1 | 1 | yes | characteristic |
| 119 | #1492 | — | 2 | 1 | no | — |
| 120 | #1476 | — | 2 | 1 | no | — |
| 121 | #1450 | D4 | 1 | 1 | yes | characteristic |
| 122 | #1411 | — | 2 | 1 | no | — |
| 123 | #1410 | — | 2 | 1 | no | — |
| 124 | #1409 | — | 2 | 1 | no | — |
| 125 | #1408 | — | 2 | 1 | no | — |
| 126 | #1358 | — | 2 | 1 | no | — |
| 127 | #1357 | — | 2 | 1 | no | — |
| 128 | C2×H(5,𝔽2) | — | 4 | 1 | no | — |
| 129 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 130 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 131 | C2×#135 | — | 4 | 1 | no | — |
| 132 | C22×D8 | — | 4 | 1 | no | — |
| 133 | C22×D8 | — | 4 | 2 | no | — |
| 134 | C22×D8 | — | 4 | 2 | no | — |
| 135 | #568 | — | 2 | 1 | no | — |
| 136 | #568 | — | 2 | 1 | no | — |
| 137 | H(3,𝔽4) | — | 4 | 1 | no | — |
| 138 | #559 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | #555 | — | 4 | 1 | no | — |
| 140 | #555 | C22⋊C4 | 1 | 2 | yes | — |
| 141 | #554 | — | 2 | 1 | no | — |
| 142 | #553 | — | 4 | 1 | no | — |
| 143 | #551 | — | 4 | 1 | no | — |
| 144 | #550 | — | 2 | 2 | no | — |
| 145 | #550 | — | 4 | 1 | no | — |
| 146 | #546 | — | 4 | 1 | no | — |
| 147 | D42 | — | 2 | 2 | no | — |
| 148 | D42 | — | 2 | 1 | no | — |
| 149 | D42 | — | 4 | 1 | no | — |
| 150 | D42 | — | 4 | 2 | no | — |
| 151 | D42 | — | 4 | 1 | no | — |
| 152 | D42 | — | 8 | 1 | no | — |
| 153 | D42 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 154 | #535 | — | 4 | 1 | no | — |
| 155 | #535 | — | 4 | 2 | no | — |
| 156 | #535 | — | 4 | 1 | no | — |
| 157 | #535 | — | 8 | 1 | no | — |
| 158 | #532 | — | 2 | 1 | no | — |
| 159 | #532 | — | 4 | 1 | no | — |
| 160 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×#127 | — | 2 | 1 | no | — |
| 163 | C2×#127 | — | 4 | 1 | no | — |
| 164 | #529 | — | 4 | 1 | no | — |
| 165 | #525 | — | 4 | 1 | no | — |
| 166 | C4×#41 | — | 2 | 1 | no | — |
| 167 | C2×C4×D4 | — | 4 | 1 | no | — |
| 168 | C2×M32 | — | 4 | 1 | no | — |
| 169 | #496 | — | 4 | 2 | no | — |
| 170 | #495 | — | 4 | 1 | no | — |
| 171 | #494 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | #493 | — | 2 | 2 | no | — |
| 173 | #493 | — | 2 | 2 | no | — |
| 174 | #493 | — | 2 | 1 | no | — |
| 175 | #493 | — | 4 | 1 | no | — |
| 176 | #493 | — | 4 | 1 | no | — |
| 177 | #493 | C22⋊C4 | 1 | 2 | yes | — |
| 178 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | #492 | C22×C4 | 1 | 1 | yes | characteristic |
| 180 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | #490 | — | 4 | 2 | no | — |
| 182 | #486 | — | 2 | 2 | no | — |
| 183 | #486 | — | 2 | 2 | no | — |
| 184 | #486 | — | 4 | 1 | no | — |
| 185 | #482 | — | 2 | 2 | no | — |
| 186 | #482 | — | 4 | 2 | no | — |
| 187 | #482 | — | 4 | 2 | no | — |
| 188 | #482 | — | 4 | 1 | no | — |
| 189 | #481 | — | 4 | 2 | no | — |
| 190 | #478 | — | 4 | 2 | no | — |
| 191 | #477 | — | 2 | 1 | no | — |
| 192 | #477 | — | 2 | 1 | no | — |
| 193 | #476 | — | 2 | 1 | no | — |
| 194 | #476 | — | 2 | 1 | no | — |
| 195 | #476 | — | 2 | 2 | no | — |
| 196 | #476 | — | 4 | 1 | no | — |
| 197 | #469 | — | 4 | 2 | no | — |
| 198 | #469 | — | 4 | 2 | no | — |
| 199 | #469 | — | 4 | 2 | no | — |
| 200 | #466 | — | 4 | 2 | no | — |
| 201 | #466 | — | 4 | 2 | no | — |
| 202 | #466 | — | 4 | 2 | no | — |
| 203 | #465 | — | 4 | 2 | no | — |
| 204 | #463 | — | 4 | 2 | no | — |
| 205 | #460 | — | 2 | 1 | no | — |
| 206 | #460 | — | 2 | 2 | no | — |
| 207 | #460 | — | 2 | 1 | no | — |
| 208 | #460 | — | 4 | 1 | no | — |
| 209 | #459 | — | 2 | 1 | no | — |
| 210 | #459 | — | 2 | 2 | no | — |
| 211 | #459 | — | 2 | 2 | no | — |
| 212 | #459 | — | 2 | 2 | no | — |
| 213 | #459 | — | 2 | 2 | no | — |
| 214 | #459 | — | 2 | 1 | no | — |
| 215 | #459 | — | 4 | 2 | no | — |
| 216 | #459 | — | 4 | 1 | no | — |
| 217 | #459 | — | 4 | 1 | no | — |
| 218 | #459 | — | 4 | 1 | no | — |
| 219 | #459 | — | 4 | 1 | no | — |
| 220 | #459 | — | 4 | 1 | no | — |
| 221 | #459 | — | 4 | 1 | no | — |
| 222 | #459 | — | 4 | 2 | no | — |
| 223 | #450 | — | 4 | 2 | no | — |
| 224 | #449 | — | 2 | 2 | no | — |
| 225 | #449 | — | 4 | 2 | no | — |
| 226 | #449 | — | 4 | 2 | no | — |
| 227 | #449 | — | 4 | 1 | no | — |
| 228 | #447 | — | 4 | 2 | no | — |
| 229 | #447 | — | 4 | 2 | no | — |
| 230 | #447 | — | 4 | 2 | no | — |
| 231 | #447 | — | 4 | 2 | no | — |
| 232 | #447 | — | 4 | 2 | no | — |
| 233 | #447 | — | 4 | 2 | no | — |
| 234 | #447 | — | 4 | 2 | no | — |
| 235 | #447 | — | 4 | 2 | no | — |
| 236 | #447 | — | 4 | 2 | no | — |
| 237 | #446 | — | 2 | 2 | no | — |
| 238 | #444 | — | 8 | 2 | no | — |
| 239 | #443 | — | 8 | 2 | no | — |
| 240 | #442 | — | 4 | 2 | no | — |
| 241 | #442 | — | 4 | 2 | no | — |
| 242 | C4×SD16 | — | 2 | 2 | no | — |
| 243 | C4×SD16 | — | 4 | 1 | no | — |
| 244 | C4×D8 | — | 2 | 2 | no | — |
| 245 | C4×D8 | — | 4 | 1 | no | — |
| 246 | #436 | — | 2 | 2 | no | — |
| 247 | #436 | — | 4 | 1 | no | — |
| 248 | #435 | — | 4 | 2 | no | — |
| 249 | C8×D4 | — | 2 | 2 | no | — |
| 250 | C8×D4 | — | 2 | 2 | no | — |
| 251 | C8×D4 | — | 4 | 1 | no | — |
| 252 | #432 | — | 4 | 1 | no | — |
| 253 | #431 | — | 2 | 1 | no | — |
| 254 | #431 | — | 2 | 1 | no | — |
| 255 | C2×#108 | — | 2 | 1 | no | — |
| 256 | #427 | — | 2 | 1 | no | — |
| 257 | #423 | — | 2 | 1 | no | — |
| 258 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 259 | #421 | — | 4 | 1 | no | — |
| 260 | #421 | — | 4 | 1 | no | — |
| 261 | #418 | — | 4 | 2 | no | — |
| 262 | #418 | — | 4 | 1 | no | — |
| 263 | #418 | — | 8 | 1 | no | — |
| 264 | #416 | — | 4 | 2 | no | — |
| 265 | C2×#102 | — | 4 | 2 | no | — |
| 266 | #413 | — | 4 | 1 | no | — |
| 267 | #410 | — | 2 | 1 | no | — |
| 268 | #410 | — | 2 | 1 | no | — |
| 269 | #410 | — | 4 | 1 | no | — |
| 270 | #408 | — | 4 | 2 | no | — |
| 271 | #407 | — | 8 | 1 | no | — |
| 272 | #405 | — | 4 | 1 | no | — |
| 273 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | #364 | — | 4 | 1 | no | — |
| 275 | #364 | — | 4 | 1 | no | — |
| 276 | #361 | — | 8 | 2 | no | — |
| 277 | #357 | — | 8 | 2 | no | — |
| 278 | #356 | — | 4 | 1 | no | — |
| 279 | #355 | — | 4 | 1 | no | — |
| 280 | #354 | — | 4 | 1 | no | — |
| 281 | #353 | — | 4 | 1 | no | — |
| 282 | #353 | — | 8 | 2 | no | — |
| 283 | #352 | — | 8 | 1 | no | — |
| 284 | AΣL(1,𝔽16) | — | 8 | 1 | no | — |
| 285 | #344 | — | 8 | 1 | no | — |
| 286 | #339 | — | 4 | 1 | no | — |
| 287 | H(3,ℤ/4) | — | 8 | 1 | no | — |
| 288 | #335 | — | 2 | 2 | no | — |
| 289 | #334 | — | 2 | 2 | no | — |
| 290 | #333 | — | 2 | 1 | no | — |
| 291 | #333 | C22⋊C4 | 1 | 2 | yes | — |
| 292 | #331 | — | 2 | 2 | no | — |
| 293 | #331 | — | 2 | 2 | no | — |
| 294 | #331 | — | 2 | 1 | no | — |
| 295 | #331 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 296 | #331 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 297 | Q8⋊C8 | — | 2 | 1 | no | — |
| 298 | Q8⋊C8 | — | 2 | 1 | no | — |
| 299 | D4⋊C8 | — | 2 | 2 | no | — |
| 300 | D4⋊C8 | — | 2 | 1 | no | — |
| 301 | D4⋊C8 | — | 2 | 1 | no | — |
| 302 | D4⋊C8 | — | 2 | 2 | no | — |
| 303 | #322 | C22⋊C4 | 1 | 2 | yes | — |
| 304 | C82 | — | 2 | 1 | no | — |
| 305 | H(5,𝔽2) | — | 16 | 2 | no | — |
| 306 | H(5,𝔽2) | — | 16 | 2 | no | — |
| 307 | C2×#41 | — | 2 | 1 | no | — |
| 308 | C2×#41 | — | 2 | 1 | no | — |
| 309 | C2×#41 | — | 2 | 1 | no | — |
| 310 | C2×#41 | — | 4 | 1 | no | — |
| 311 | C2×#41 | — | 4 | 2 | no | — |
| 312 | C2×#41 | — | 8 | 1 | no | — |
| 313 | C22×D4 | — | 4 | 1 | no | — |
| 314 | C22×D4 | — | 4 | 1 | no | — |
| 315 | C22×D4 | — | 4 | 1 | no | — |
| 316 | C22×D4 | — | 4 | 2 | no | — |
| 317 | C22×D4 | — | 4 | 2 | no | — |
| 318 | C22×D4 | — | 4 | 2 | no | — |
| 319 | C22×D4 | — | 4 | 1 | no | — |
| 320 | C22×D4 | — | 4 | 1 | no | — |
| 321 | C22×D4 | — | 8 | 1 | no | — |
| 322 | C22×D4 | — | 8 | 1 | no | — |
| 323 | C22×D4 | — | 8 | 2 | no | — |
| 324 | C23×C4 | — | 4 | 1 | no | — |
| 325 | AGL(1,ℤ/8) | — | 16 | 2 | no | — |
| 326 | AGL(1,ℤ/8) | — | 16 | 4 | no | — |
| 327 | #135 | — | 8 | 1 | no | — |
| 328 | #135 | — | 8 | 1 | no | — |
| 329 | #135 | — | 8 | 1 | no | — |
| 330 | #135 | — | 8 | 1 | no | — |
| 331 | C2×Q16 | — | 4 | 1 | no | — |
| 332 | C2×SD16 | — | 2 | 2 | no | — |
| 333 | C2×SD16 | — | 4 | 1 | no | — |
| 334 | C2×SD16 | — | 4 | 1 | no | — |
| 335 | C2×SD16 | — | 4 | 1 | no | — |
| 336 | C2×SD16 | — | 4 | 2 | no | — |
| 337 | C2×D8 | — | 2 | 2 | no | — |
| 338 | C2×D8 | — | 4 | 1 | no | — |
| 339 | C2×D8 | — | 4 | 2 | no | — |
| 340 | C2×D8 | — | 4 | 2 | no | — |
| 341 | C2×D8 | — | 4 | 2 | no | — |
| 342 | C2×D8 | — | 4 | 2 | no | — |
| 343 | C2×D8 | — | 4 | 2 | no | — |
| 344 | C2×D8 | — | 4 | 1 | no | — |
| 345 | C2×D8 | — | 4 | 2 | no | — |
| 346 | C2×D8 | — | 4 | 2 | no | — |
| 347 | C2×D8 | — | 4 | 2 | no | — |
| 348 | C2×D8 | — | 4 | 2 | no | — |
| 349 | C2×D8 | — | 8 | 1 | no | — |
| 350 | C2×D8 | — | 8 | 1 | no | — |
| 351 | C2×D8 | — | 8 | 1 | no | — |
| 352 | C2×D8 | — | 8 | 1 | no | — |
| 353 | C2×D8 | — | 8 | 1 | no | — |
| 354 | C2×D8 | — | 16 | 4 | no | — |
| 355 | C2×D8 | — | 16 | 4 | no | — |
| 356 | #131 | — | 8 | 2 | no | — |
| 357 | #131 | — | 8 | 2 | no | — |
| 358 | C2×M16 | — | 4 | 2 | no | — |
| 359 | C2×M16 | — | 4 | 1 | no | — |
| 360 | C2×M16 | — | 4 | 1 | no | — |
| 361 | C2×M16 | — | 8 | 1 | no | — |
| 362 | C2×M16 | — | 8 | 1 | no | — |
| 363 | C2×M16 | — | 8 | 1 | no | — |
| 364 | C22×C8 | — | 2 | 1 | no | — |
| 365 | C22×C8 | — | 4 | 2 | no | — |
| 366 | C22×C8 | — | 4 | 2 | no | — |
| 367 | C4⋊Q8 | — | 2 | 1 | no | — |
| 368 | C4⋊Q8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 369 | C4⋊Q8 | #120 | 1 | 1 | yes | characteristic |
| 370 | #127 | — | 2 | 1 | no | — |
| 371 | #127 | — | 2 | 2 | no | — |
| 372 | #127 | — | 4 | 1 | no | — |
| 373 | #127 | — | 4 | 1 | no | — |
| 374 | #127 | — | 4 | 2 | no | — |
| 375 | #127 | — | 4 | 2 | no | — |
| 376 | #127 | — | 4 | 1 | no | — |
| 377 | #127 | — | 8 | 1 | no | — |
| 378 | #127 | — | 8 | 1 | no | — |
| 379 | #127 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 380 | #127 | #120 | 1 | 1 | yes | characteristic |
| 381 | #126 | — | 8 | 1 | no | — |
| 382 | #125 | — | 4 | 1 | no | — |
| 383 | #124 | — | 2 | 1 | no | — |
| 384 | #124 | — | 2 | 1 | no | — |
| 385 | #124 | — | 4 | 1 | no | — |
| 386 | #124 | — | 4 | 2 | no | — |
| 387 | #124 | — | 4 | 1 | no | — |
| 388 | #124 | — | 8 | 2 | no | — |
| 389 | #124 | — | 8 | 1 | no | — |
| 390 | #123 | — | 4 | 1 | no | — |
| 391 | #123 | — | 4 | 1 | no | — |
| 392 | #123 | — | 8 | 1 | no | — |
| 393 | C22⋊Q8 | — | 4 | 1 | no | — |
| 394 | C22⋊Q8 | — | 8 | 1 | no | — |
| 395 | #121 | — | 2 | 2 | no | — |
| 396 | #121 | — | 4 | 1 | no | — |
| 397 | #121 | — | 4 | 1 | no | — |
| 398 | #121 | — | 4 | 2 | no | — |
| 399 | #121 | — | 4 | 2 | no | — |
| 400 | #121 | — | 4 | 2 | no | — |
| 401 | #121 | — | 4 | 2 | no | — |
| 402 | #121 | — | 4 | 1 | no | — |
| 403 | #121 | — | 4 | 1 | no | — |
| 404 | #121 | — | 4 | 2 | no | — |
| 405 | #121 | — | 8 | 2 | no | — |
| 406 | #121 | — | 8 | 2 | no | — |
| 407 | #121 | — | 8 | 1 | no | — |
| 408 | #121 | — | 8 | 1 | no | — |
| 409 | #121 | — | 8 | 1 | no | — |
| 410 | #120 | — | 4 | 1 | no | — |
| 411 | #120 | — | 4 | 1 | no | — |
| 412 | #120 | — | 8 | 1 | no | — |
| 413 | #120 | — | 8 | 2 | no | — |
| 414 | #120 | — | 8 | 2 | no | — |
| 415 | #120 | — | 8 | 2 | no | — |
| 416 | #120 | — | 8 | 2 | no | — |
| 417 | #120 | — | 8 | 1 | no | — |
| 418 | C4×Q8 | — | 2 | 1 | no | — |
| 419 | C4×Q8 | — | 2 | 1 | no | — |
| 420 | C4×D4 | — | 2 | 1 | no | — |
| 421 | C4×D4 | — | 2 | 1 | no | — |
| 422 | C4×D4 | — | 2 | 2 | no | — |
| 423 | C4×D4 | — | 4 | 1 | no | — |
| 424 | C4×D4 | — | 4 | 1 | no | — |
| 425 | C4×D4 | — | 4 | 1 | no | — |
| 426 | C4×D4 | — | 4 | 1 | no | — |
| 427 | C4×D4 | — | 4 | 1 | no | — |
| 428 | C4×D4 | — | 4 | 1 | no | — |
| 429 | C4×D4 | — | 4 | 2 | no | — |
| 430 | C4×D4 | — | 4 | 1 | no | — |
| 431 | C4×D4 | — | 8 | 1 | no | — |
| 432 | C4×D4 | — | 8 | 1 | no | — |
| 433 | C4×D4 | — | 8 | 1 | no | — |
| 434 | #117 | — | 2 | 1 | no | — |
| 435 | #117 | — | 4 | 1 | no | — |
| 436 | #117 | — | 4 | 1 | no | — |
| 437 | #117 | — | 4 | 1 | no | — |
| 438 | #117 | — | 4 | 2 | no | — |
| 439 | #117 | — | 4 | 1 | no | — |
| 440 | #117 | — | 8 | 1 | no | — |
| 441 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 442 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 443 | C2×C42 | — | 4 | 1 | no | — |
| 444 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 445 | M32 | — | 8 | 1 | no | — |
| 446 | M32 | — | 8 | 1 | no | — |
| 447 | C2×C16 | — | 8 | 1 | no | — |
| 448 | #108 | — | 2 | 2 | no | — |
| 449 | #108 | — | 4 | 1 | no | — |
| 450 | #107 | — | 2 | 2 | no | — |
| 451 | #107 | — | 4 | 1 | no | — |
| 452 | #107 | — | 4 | 1 | no | — |
| 453 | #106 | — | 2 | 2 | no | — |
| 454 | #106 | — | 4 | 1 | no | — |
| 455 | #106 | — | 4 | 2 | no | — |
| 456 | #106 | — | 4 | 1 | no | — |
| 457 | C4⋊C8 | — | 2 | 1 | no | — |
| 458 | C4⋊C8 | — | 2 | 1 | no | — |
| 459 | C4⋊C8 | — | 2 | 2 | no | — |
| 460 | C4⋊C8 | — | 2 | 1 | no | — |
| 461 | C4⋊C8 | — | 2 | 1 | no | — |
| 462 | C4⋊C8 | — | 4 | 1 | no | — |
| 463 | C4⋊C8 | — | 4 | 2 | no | — |
| 464 | #104 | — | 8 | 2 | no | — |
| 465 | #104 | — | 8 | 2 | no | — |
| 466 | #103 | — | 2 | 2 | no | — |
| 467 | #103 | — | 4 | 1 | no | — |
| 468 | #102 | — | 2 | 2 | no | — |
| 469 | #102 | — | 2 | 2 | no | — |
| 470 | #102 | — | 2 | 2 | no | — |
| 471 | #102 | — | 4 | 2 | no | — |
| 472 | #102 | — | 4 | 2 | no | — |
| 473 | #102 | — | 4 | 2 | no | — |
| 474 | #102 | — | 4 | 2 | no | — |
| 475 | #102 | — | 4 | 1 | no | — |
| 476 | #102 | — | 4 | 1 | no | — |
| 477 | #102 | — | 4 | 2 | no | — |
| 478 | #102 | — | 4 | 2 | no | — |
| 479 | #102 | — | 4 | 2 | no | — |
| 480 | #102 | — | 4 | 2 | no | — |
| 481 | #102 | — | 4 | 2 | no | — |
| 482 | #102 | — | 4 | 2 | no | — |
| 483 | #102 | — | 4 | 1 | no | — |
| 484 | #102 | — | 16 | 2 | no | — |
| 485 | #101 | — | 8 | 1 | no | — |
| 486 | #100 | — | 8 | 1 | no | — |
| 487 | #99 | — | 8 | 1 | no | — |
| 488 | #99 | — | 8 | 1 | no | — |
| 489 | #99 | — | 8 | 1 | no | — |
| 490 | #99 | — | 8 | 1 | no | — |
| 491 | C22⋊C8 | — | 2 | 2 | no | — |
| 492 | C22⋊C8 | — | 4 | 2 | no | — |
| 493 | C22⋊C8 | — | 4 | 2 | no | — |
| 494 | C22⋊C8 | — | 4 | 2 | no | — |
| 495 | C22⋊C8 | — | 4 | 1 | no | — |
| 496 | C22⋊C8 | — | 16 | 2 | no | — |
| 497 | #97 | — | 4 | 2 | no | — |
| 498 | #97 | — | 8 | 1 | no | — |
| 499 | C4×C8 | — | 2 | 2 | no | — |
| 500 | C4×C8 | — | 2 | 1 | no | — |
| 501 | C4×C8 | — | 4 | 1 | no | — |
| 502 | C4×C8 | — | 8 | 1 | no | — |
| 503 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 504 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 505 | C24 | — | 4 | 1 | no | — |
| 506 | C24 | — | 8 | 1 | no | — |
| 507 | C24 | — | 8 | 2 | no | — |
| 508 | C24 | — | 8 | 1 | no | — |
| 509 | #41 | — | 4 | 2 | no | — |
| 510 | #41 | — | 8 | 1 | no | — |
| 511 | #41 | — | 8 | 1 | no | — |
| 512 | #41 | — | 8 | 1 | no | — |
| 513 | #41 | — | 8 | 1 | no | — |
| 514 | #41 | — | 8 | 1 | no | — |
| 515 | #41 | — | 8 | 4 | no | — |
| 516 | #41 | — | 16 | 1 | no | — |
| 517 | #41 | — | 16 | 1 | no | — |
| 518 | #41 | — | 16 | 2 | no | — |
| 519 | #41 | — | 16 | 4 | no | — |
| 520 | C2×Q8 | — | 2 | 1 | no | — |
| 521 | C2×Q8 | — | 2 | 1 | no | — |
| 522 | C2×Q8 | — | 2 | 1 | no | — |
| 523 | C2×Q8 | — | 4 | 1 | no | — |
| 524 | C2×D4 | — | 2 | 1 | no | — |
| 525 | C2×D4 | — | 2 | 2 | no | — |
| 526 | C2×D4 | — | 2 | 1 | no | — |
| 527 | C2×D4 | — | 2 | 1 | no | — |
| 528 | C2×D4 | — | 4 | 1 | no | — |
| 529 | C2×D4 | — | 4 | 1 | no | — |
| 530 | C2×D4 | — | 4 | 2 | no | — |
| 531 | C2×D4 | — | 4 | 2 | no | — |
| 532 | C2×D4 | — | 4 | 1 | no | — |
| 533 | C2×D4 | — | 4 | 1 | no | — |
| 534 | C2×D4 | — | 4 | 2 | no | — |
| 535 | C2×D4 | — | 4 | 1 | no | — |
| 536 | C2×D4 | — | 4 | 1 | no | — |
| 537 | C2×D4 | — | 4 | 2 | no | — |
| 538 | C2×D4 | — | 4 | 1 | no | — |
| 539 | C2×D4 | — | 4 | 2 | no | — |
| 540 | C2×D4 | — | 8 | 1 | no | — |
| 541 | C2×D4 | — | 8 | 1 | no | — |
| 542 | C2×D4 | — | 8 | 1 | no | — |
| 543 | C2×D4 | — | 8 | 2 | no | — |
| 544 | C2×D4 | — | 8 | 2 | no | — |
| 545 | C2×D4 | — | 8 | 2 | no | — |
| 546 | C2×D4 | — | 8 | 2 | no | — |
| 547 | C2×D4 | — | 8 | 2 | no | — |
| 548 | C2×D4 | — | 8 | 2 | no | — |
| 549 | C2×D4 | — | 8 | 4 | no | — |
| 550 | C2×D4 | — | 8 | 1 | no | — |
| 551 | C2×D4 | — | 16 | 1 | no | — |
| 552 | C2×D4 | — | 16 | 1 | no | — |
| 553 | C2×D4 | — | 16 | 1 | no | — |
| 554 | C2×D4 | — | 16 | 1 | no | — |
| 555 | C2×D4 | — | 16 | 1 | no | — |
| 556 | C2×D4 | — | 16 | 1 | no | — |
| 557 | C2×D4 | — | 16 | 1 | no | — |
| 558 | C2×D4 | — | 16 | 2 | no | — |
| 559 | C2×D4 | — | 16 | 2 | no | — |
| 560 | C2×D4 | — | 16 | 2 | no | — |
| 561 | C2×D4 | — | 16 | 2 | no | — |
| 562 | C2×D4 | — | 16 | 2 | no | — |
| 563 | C2×D4 | — | 16 | 1 | no | — |
| 564 | C2×D4 | — | 16 | 1 | no | — |
| 565 | C2×D4 | — | 16 | 4 | no | — |
| 566 | C2×D4 | — | 16 | 8 | no | — |
| 567 | C2×D4 | — | 32 | 1 | no | — |
| 568 | C2×D4 | — | 32 | 1 | no | — |
| 569 | C22×C4 | — | 2 | 1 | no | — |
| 570 | C22×C4 | — | 4 | 1 | no | — |
| 571 | C22×C4 | — | 4 | 2 | no | — |
| 572 | C22×C4 | — | 4 | 1 | no | — |
| 573 | C22×C4 | — | 4 | 1 | no | — |
| 574 | C22×C4 | — | 4 | 1 | no | — |
| 575 | C22×C4 | — | 4 | 1 | no | — |
| 576 | C22×C4 | — | 4 | 1 | no | — |
| 577 | C22×C4 | — | 8 | 2 | no | — |
| 578 | C22×C4 | — | 8 | 1 | no | — |
| 579 | C22×C4 | — | 16 | 1 | no | — |
| 580 | C22×C4 | — | 16 | 1 | no | — |
| 581 | C22×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 582 | Q16 | — | 8 | 1 | no | — |
| 583 | Q16 | — | 8 | 1 | no | — |
| 584 | SD16 | — | 8 | 1 | no | — |
| 585 | SD16 | — | 8 | 1 | no | — |
| 586 | SD16 | — | 8 | 1 | no | — |
| 587 | SD16 | — | 8 | 1 | no | — |
| 588 | SD16 | — | 8 | 2 | no | — |
| 589 | SD16 | — | 8 | 2 | no | — |
| 590 | SD16 | — | 16 | 2 | no | — |
| 591 | D8 | — | 4 | 4 | no | — |
| 592 | D8 | — | 8 | 1 | no | — |
| 593 | D8 | — | 8 | 1 | no | — |
| 594 | D8 | — | 8 | 2 | no | — |
| 595 | D8 | — | 8 | 2 | no | — |
| 596 | D8 | — | 8 | 2 | no | — |
| 597 | D8 | — | 8 | 4 | no | — |
| 598 | D8 | — | 16 | 1 | no | — |
| 599 | D8 | — | 16 | 1 | no | — |
| 600 | D8 | — | 16 | 2 | no | — |
| 601 | D8 | — | 16 | 2 | no | — |
| 602 | D8 | — | 16 | 2 | no | — |
| 603 | D8 | — | 16 | 2 | no | — |
| 604 | D8 | — | 16 | 2 | no | — |
| 605 | D8 | — | 16 | 2 | no | — |
| 606 | D8 | — | 16 | 2 | no | — |
| 607 | M16 | — | 4 | 2 | no | — |
| 608 | M16 | — | 8 | 1 | no | — |
| 609 | M16 | — | 16 | 2 | no | — |
| 610 | M16 | — | 16 | 1 | no | — |
| 611 | M16 | — | 16 | 1 | no | — |
| 612 | M16 | — | 16 | 1 | no | — |
| 613 | M16 | — | 16 | 1 | no | — |
| 614 | M16 | — | 16 | 1 | no | — |
| 615 | C2×C8 | — | 2 | 1 | no | — |
| 616 | C2×C8 | — | 2 | 1 | no | — |
| 617 | C2×C8 | — | 2 | 1 | no | — |
| 618 | C2×C8 | — | 2 | 1 | no | — |
| 619 | C2×C8 | — | 2 | 1 | no | — |
| 620 | C2×C8 | — | 2 | 1 | no | — |
| 621 | C2×C8 | — | 2 | 2 | no | — |
| 622 | C2×C8 | — | 2 | 2 | no | — |
| 623 | C2×C8 | — | 4 | 1 | no | — |
| 624 | C2×C8 | — | 4 | 1 | no | — |
| 625 | C2×C8 | — | 4 | 2 | no | — |
| 626 | C2×C8 | — | 8 | 1 | no | — |
| 627 | C2×C8 | — | 8 | 2 | no | — |
| 628 | C2×C8 | — | 8 | 2 | no | — |
| 629 | C2×C8 | — | 16 | 2 | no | — |
| 630 | C2×C8 | — | 16 | 2 | no | — |
| 631 | C2×C8 | — | 16 | 1 | no | — |
| 632 | C4⋊C4 | — | 2 | 1 | no | — |
| 633 | C4⋊C4 | — | 2 | 1 | no | — |
| 634 | C4⋊C4 | — | 2 | 2 | no | — |
| 635 | C4⋊C4 | — | 4 | 1 | no | — |
| 636 | C4⋊C4 | — | 4 | 1 | no | — |
| 637 | C4⋊C4 | — | 4 | 1 | no | — |
| 638 | C4⋊C4 | — | 4 | 1 | no | — |
| 639 | C4⋊C4 | — | 4 | 1 | no | — |
| 640 | C4⋊C4 | — | 8 | 1 | no | — |
| 641 | C4⋊C4 | — | 8 | 1 | no | — |
| 642 | C4⋊C4 | — | 8 | 1 | no | — |
| 643 | C4⋊C4 | — | 16 | 1 | no | — |
| 644 | C22⋊C4 | — | 4 | 1 | no | — |
| 645 | C22⋊C4 | — | 4 | 2 | no | — |
| 646 | C22⋊C4 | — | 4 | 1 | no | — |
| 647 | C22⋊C4 | — | 4 | 1 | no | — |
| 648 | C22⋊C4 | — | 4 | 2 | no | — |
| 649 | C22⋊C4 | — | 4 | 1 | no | — |
| 650 | C22⋊C4 | — | 4 | 1 | no | — |
| 651 | C22⋊C4 | — | 8 | 1 | no | — |
| 652 | C22⋊C4 | — | 8 | 1 | no | — |
| 653 | C22⋊C4 | — | 8 | 1 | no | — |
| 654 | C22⋊C4 | — | 8 | 1 | no | — |
| 655 | C22⋊C4 | — | 8 | 1 | no | — |
| 656 | C22⋊C4 | — | 8 | 2 | no | — |
| 657 | C22⋊C4 | — | 8 | 2 | no | — |
| 658 | C22⋊C4 | — | 8 | 2 | no | — |
| 659 | C22⋊C4 | — | 8 | 1 | no | — |
| 660 | C22⋊C4 | — | 16 | 1 | no | — |
| 661 | C42 | — | 2 | 1 | no | — |
| 662 | C42 | — | 4 | 1 | no | — |
| 663 | C42 | — | 4 | 1 | no | — |
| 664 | C42 | — | 4 | 2 | no | — |
| 665 | C42 | — | 4 | 1 | no | — |
| 666 | C42 | — | 8 | 1 | no | — |
| 667 | C42 | — | 16 | 1 | no | — |
| 668 | C42 | #379 | 1 | 1 | yes | characteristic |
| 669 | C42 | #458 | 1 | 1 | yes | characteristic |
| 670 | C16 | — | 16 | 1 | no | — |
| 671 | C23 | — | 4 | 1 | no | — |
| 672 | C23 | — | 4 | 2 | no | — |
| 673 | C23 | — | 4 | 1 | no | — |
| 674 | C23 | — | 4 | 1 | no | — |
| 675 | C23 | — | 8 | 2 | no | — |
| 676 | C23 | — | 16 | 2 | no | — |
| 677 | C23 | — | 16 | 4 | no | — |
| 678 | C23 | — | 16 | 2 | no | — |
| 679 | C23 | — | 16 | 1 | no | — |
| 680 | C23 | — | 32 | 1 | no | — |
| 681 | C23 | — | 32 | 1 | no | — |
| 682 | C23 | — | 32 | 1 | no | — |
| 683 | C23 | — | 32 | 2 | no | — |
| 684 | C23 | — | 32 | 2 | no | — |
| 685 | C23 | — | 32 | 2 | no | — |
| 686 | C23 | #2196 | 1 | 1 | yes | characteristic |
| 687 | Q8 | — | 4 | 1 | no | — |
| 688 | Q8 | — | 4 | 1 | no | — |
| 689 | Q8 | — | 8 | 1 | no | — |
| 690 | Q8 | — | 8 | 1 | no | — |
| 691 | Q8 | — | 16 | 1 | no | — |
| 692 | D4 | — | 2 | 2 | no | — |
| 693 | D4 | — | 4 | 1 | no | — |
| 694 | D4 | — | 4 | 2 | no | — |
| 695 | D4 | — | 4 | 2 | no | — |
| 696 | D4 | — | 8 | 1 | no | — |
| 697 | D4 | — | 8 | 1 | no | — |
| 698 | D4 | — | 8 | 1 | no | — |
| 699 | D4 | — | 8 | 2 | no | — |
| 700 | D4 | — | 8 | 1 | no | — |
| 701 | D4 | — | 8 | 1 | no | — |
| 702 | D4 | — | 8 | 2 | no | — |
| 703 | D4 | — | 8 | 1 | no | — |
| 704 | D4 | — | 8 | 2 | no | — |
| 705 | D4 | — | 8 | 2 | no | — |
| 706 | D4 | — | 8 | 2 | no | — |
| 707 | D4 | — | 8 | 1 | no | — |
| 708 | D4 | — | 8 | 1 | no | — |
| 709 | D4 | — | 16 | 2 | no | — |
| 710 | D4 | — | 16 | 1 | no | — |
| 711 | D4 | — | 16 | 2 | no | — |
| 712 | D4 | — | 16 | 1 | no | — |
| 713 | D4 | — | 16 | 1 | no | — |
| 714 | D4 | — | 16 | 2 | no | — |
| 715 | D4 | — | 16 | 2 | no | — |
| 716 | D4 | — | 16 | 4 | no | — |
| 717 | D4 | — | 16 | 2 | no | — |
| 718 | D4 | — | 16 | 4 | no | — |
| 719 | D4 | — | 16 | 1 | no | — |
| 720 | D4 | — | 16 | 1 | no | — |
| 721 | D4 | — | 32 | 1 | no | — |
| 722 | D4 | — | 32 | 2 | no | — |
| 723 | D4 | — | 32 | 2 | no | — |
| 724 | D4 | — | 32 | 2 | no | — |
| 725 | C2×C4 | — | 2 | 1 | no | — |
| 726 | C2×C4 | — | 2 | 1 | no | — |
| 727 | C2×C4 | — | 2 | 1 | no | — |
| 728 | C2×C4 | — | 2 | 1 | no | — |
| 729 | C2×C4 | — | 4 | 1 | no | — |
| 730 | C2×C4 | — | 4 | 1 | no | — |
| 731 | C2×C4 | — | 4 | 1 | no | — |
| 732 | C2×C4 | — | 4 | 1 | no | — |
| 733 | C2×C4 | — | 4 | 1 | no | — |
| 734 | C2×C4 | — | 4 | 1 | no | — |
| 735 | C2×C4 | — | 4 | 2 | no | — |
| 736 | C2×C4 | — | 4 | 1 | no | — |
| 737 | C2×C4 | — | 8 | 1 | no | — |
| 738 | C2×C4 | — | 8 | 2 | no | — |
| 739 | C2×C4 | — | 8 | 2 | no | — |
| 740 | C2×C4 | — | 8 | 1 | no | — |
| 741 | C2×C4 | — | 8 | 2 | no | — |
| 742 | C2×C4 | — | 8 | 1 | no | — |
| 743 | C2×C4 | — | 8 | 1 | no | — |
| 744 | C2×C4 | — | 8 | 1 | no | — |
| 745 | C2×C4 | — | 8 | 1 | no | — |
| 746 | C2×C4 | — | 8 | 1 | no | — |
| 747 | C2×C4 | — | 8 | 1 | no | — |
| 748 | C2×C4 | — | 16 | 4 | no | — |
| 749 | C2×C4 | — | 16 | 1 | no | — |
| 750 | C2×C4 | — | 16 | 1 | no | — |
| 751 | C2×C4 | — | 32 | 1 | no | — |
| 752 | C2×C4 | — | 32 | 1 | no | — |
| 753 | C2×C4 | #1790 | 1 | 1 | yes | characteristic |
| 754 | C2×C4 | #2196 | 1 | 1 | yes | characteristic |
| 755 | C8 | — | 2 | 1 | no | — |
| 756 | C8 | — | 2 | 1 | no | — |
| 757 | C8 | — | 2 | 1 | no | — |
| 758 | C8 | — | 2 | 1 | no | — |
| 759 | C8 | — | 4 | 2 | no | — |
| 760 | C8 | — | 4 | 2 | no | — |
| 761 | C8 | — | 8 | 1 | no | — |
| 762 | C8 | — | 8 | 2 | no | — |
| 763 | C8 | — | 8 | 1 | no | — |
| 764 | C8 | — | 8 | 2 | no | — |
| 765 | C8 | — | 32 | 1 | no | — |
| 766 | C22 | — | 2 | 1 | no | — |
| 767 | C22 | — | 4 | 1 | no | — |
| 768 | C22 | — | 4 | 2 | no | — |
| 769 | C22 | — | 8 | 1 | no | — |
| 770 | C22 | — | 8 | 2 | no | — |
| 771 | C22 | — | 8 | 2 | no | — |
| 772 | C22 | — | 8 | 1 | no | — |
| 773 | C22 | — | 8 | 1 | no | — |
| 774 | C22 | — | 8 | 1 | no | — |
| 775 | C22 | — | 8 | 2 | no | — |
| 776 | C22 | — | 16 | 1 | no | — |
| 777 | C22 | — | 16 | 1 | no | — |
| 778 | C22 | — | 16 | 2 | no | — |
| 779 | C22 | — | 16 | 2 | no | — |
| 780 | C22 | — | 16 | 2 | no | — |
| 781 | C22 | — | 16 | 2 | no | — |
| 782 | C22 | — | 32 | 1 | no | — |
| 783 | C22 | — | 64 | 2 | no | — |
| 784 | C22 | — | 64 | 4 | no | — |
| 785 | C22 | — | 64 | 2 | no | — |
| 786 | C22 | #12759 | 1 | 1 | yes | characteristic |
| 787 | C4 | — | 2 | 1 | no | — |
| 788 | C4 | — | 2 | 1 | no | — |
| 789 | C4 | — | 2 | 1 | no | — |
| 790 | C4 | — | 4 | 1 | no | — |
| 791 | C4 | — | 8 | 1 | no | — |
| 792 | C4 | — | 8 | 2 | no | — |
| 793 | C4 | — | 8 | 1 | no | — |
| 794 | C4 | — | 8 | 1 | no | — |
| 795 | C4 | — | 8 | 1 | no | — |
| 796 | C4 | — | 8 | 1 | no | — |
| 797 | C4 | — | 32 | 1 | no | — |
| 798 | C4 | — | 64 | 1 | no | — |
| 799 | C4 | #13673 | 1 | 1 | yes | characteristic |
| 800 | C4 | #13675 | 1 | 1 | yes | characteristic |
| 801 | C2 | — | 2 | 1 | no | — |
| 802 | C2 | — | 4 | 1 | no | — |
| 803 | C2 | — | 8 | 2 | no | — |
| 804 | C2 | — | 16 | 1 | no | — |
| 805 | C2 | — | 16 | 2 | no | — |
| 806 | C2 | — | 16 | 1 | no | — |
| 807 | C2 | — | 32 | 2 | no | — |
| 808 | C2 | #152185 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #152185 |
| commutator | #492 | C22×C4 |
| Frattini, cosocle | #3147 | C23 |
| prime radical | #6367483 | C2 |
| LCS | G ▷ #492 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #3147 ◁ G | |
| LECS | G ▷ #3147 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #153521 | C2 | semidirect |
| 3. #153455 | C2 | semidirect |
| 4. #153435 | C2 | semidirect |
| 5. #152595 | C2 | semidirect |
| 6. #152584 | C2 | semidirect |
| 7. #137560 | C2 | semidirect |
| 10. #23196 | C22 | semidirect |
| 12. #20138 | C4 | semidirect |
| 13. #20053 | C4 | semidirect |
| 24. #13589 | C22 | semidirect |
| 25. #13583 | C22 | semidirect |
| 29. #11920 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6367483 | 2 |
| #153521 | 2 |
| #153455 | 2 |
| #153435 | 2 |
| #152595 | 2 |
| #152584 | 2 |
| #137560 | 2 |