Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1686 conjugacy classes of subgroups.
The subgroup lattice has 827 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61584 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61563 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×Q8×D8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #61325 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #20062 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20033 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #19782 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #19761 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #19704 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #19423 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #19385 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #19208 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #19123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #18927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #18905 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #18759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #18758 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #17906 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #17877 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #3506 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3501 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×D4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×D4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 24 | Q8×D8 | — | 2 | 2 | no | — |
| 25 | Q8×D8 | — | 2 | 2 | no | — |
| 26 | Q8×D8 | C22 | 1 | 4 | yes | — |
| 27 | Q8×D8 | C22 | 1 | 4 | yes | — |
| 28 | #3370 | — | 2 | 2 | no | — |
| 29 | #3367 | C22 | 1 | 2 | yes | — |
| 30 | #3366 | C22 | 1 | 2 | yes | — |
| 31 | #3361 | — | 2 | 2 | no | — |
| 32 | #3360 | C22 | 1 | 2 | yes | — |
| 33 | #3358 | C22 | 1 | 2 | yes | — |
| 34 | #3329 | — | 2 | 2 | no | — |
| 35 | #3328 | C22 | 1 | 4 | yes | complemented |
| 36 | #3299 | — | 2 | 2 | no | — |
| 37 | #3299 | C22 | 1 | 4 | yes | complemented |
| 38 | D4×Q16 | — | 2 | 2 | no | — |
| 39 | D4×Q16 | C22 | 1 | 4 | yes | complemented |
| 40 | #3278 | C22 | 1 | 4 | yes | complemented |
| 41 | #3276 | — | 2 | 2 | no | — |
| 42 | #3230 | C22 | 1 | 1 | yes | characteristic |
| 43 | #3227 | C22 | 1 | 1 | yes | characteristic |
| 44 | #3209 | C22 | 1 | 1 | yes | characteristic |
| 45 | #3209 | C22 | 1 | 1 | yes | characteristic |
| 46 | #3209 | C22 | 1 | 1 | yes | characteristic |
| 47 | #3206 | C22 | 1 | 1 | yes | characteristic |
| 48 | #3196 | — | 2 | 2 | no | — |
| 49 | #3189 | — | 2 | 2 | no | — |
| 50 | C2×#500 | — | 2 | 1 | no | — |
| 51 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 52 | #3136 | — | 2 | 1 | no | — |
| 53 | #3131 | C22 | 1 | 1 | yes | characteristic |
| 54 | #3104 | C22 | 1 | 1 | yes | characteristic |
| 55 | #3104 | C22 | 1 | 1 | yes | characteristic |
| 56 | #3103 | C22 | 1 | 1 | yes | characteristic |
| 57 | #3083 | — | 2 | 1 | no | — |
| 58 | #3077 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×#474 | — | 2 | 1 | no | — |
| 60 | C2×#474 | — | 2 | 1 | no | — |
| 61 | C2×#474 | C22 | 1 | 1 | yes | characteristic |
| 62 | C2×#474 | C22 | 1 | 1 | yes | characteristic |
| 63 | #3041 | — | 2 | 1 | no | — |
| 64 | #3036 | C22 | 1 | 1 | yes | characteristic |
| 65 | #3004 | — | 2 | 2 | no | — |
| 66 | C2×#451 | — | 2 | 2 | no | — |
| 67 | #2975 | C22 | 1 | 1 | yes | characteristic |
| 68 | #2972 | C22 | 1 | 1 | yes | characteristic |
| 69 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 70 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 71 | #2946 | — | 2 | 1 | no | — |
| 72 | C2×C4×D8 | — | 2 | 1 | no | — |
| 73 | C2×C4×D8 | C22 | 1 | 1 | yes | characteristic |
| 74 | #1723 | C22 | 1 | 2 | yes | complemented |
| 75 | #1722 | C22 | 1 | 2 | yes | complemented |
| 76 | #1719 | C22 | 1 | 2 | yes | complemented |
| 77 | #1718 | C22 | 1 | 2 | yes | complemented |
| 78 | #1703 | C22 | 1 | 4 | yes | complemented |
| 79 | #1694 | C22 | 1 | 4 | yes | complemented |
| 80 | #1689 | C22 | 1 | 4 | yes | complemented |
| 81 | #1684 | C22 | 1 | 2 | yes | complemented |
| 82 | #1682 | C22 | 1 | 2 | yes | complemented |
| 83 | #1680 | C22 | 1 | 2 | yes | complemented |
| 84 | #1679 | C22 | 1 | 4 | yes | complemented |
| 85 | #1678 | C22 | 1 | 2 | yes | complemented |
| 86 | #1674 | C22 | 1 | 4 | yes | complemented |
| 87 | #1665 | C22 | 1 | 4 | yes | complemented |
| 88 | #1652 | C22 | 1 | 4 | yes | complemented |
| 89 | #1651 | C22 | 1 | 4 | yes | complemented |
| 90 | #1649 | C22 | 1 | 4 | yes | complemented |
| 91 | #1649 | C22 | 1 | 4 | yes | complemented |
| 92 | #1644 | C22 | 1 | 4 | yes | complemented |
| 93 | #1641 | C22 | 1 | 4 | yes | complemented |
| 94 | #1637 | C22 | 1 | 4 | yes | complemented |
| 95 | #1627 | C22 | 1 | 4 | yes | complemented |
| 96 | #1587 | C22 | 1 | 4 | yes | complemented |
| 97 | #1586 | C22 | 1 | 4 | yes | — |
| 98 | #1581 | C22 | 1 | 4 | yes | — |
| 99 | #1579 | C22 | 1 | 4 | yes | complemented |
| 100 | #1570 | C22 | 1 | 1 | yes | characteristic |
| 101 | #1564 | C22 | 1 | 1 | yes | characteristic |
| 102 | #1549 | C22 | 1 | 1 | yes | characteristic |
| 103 | #1549 | C22 | 1 | 1 | yes | characteristic |
| 104 | #1542 | C22 | 1 | 1 | yes | characteristic |
| 105 | #1540 | C22 | 1 | 1 | yes | characteristic |
| 106 | #1487 | C22 | 1 | 1 | yes | characteristic |
| 107 | #1481 | C22 | 1 | 1 | yes | characteristic |
| 108 | #1478 | C22 | 1 | 1 | yes | characteristic |
| 109 | #1478 | C22 | 1 | 1 | yes | characteristic |
| 110 | #1452 | C22 | 1 | 1 | yes | characteristic |
| 111 | C23×Q8 | — | 2 | 1 | no | — |
| 112 | C23×Q8 | — | 2 | 1 | no | — |
| 113 | C2×#137 | — | 2 | 4 | no | — |
| 114 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 115 | C22×Q16 | — | 2 | 4 | no | — |
| 116 | C22×D8 | D4 | 1 | 1 | yes | characteristic |
| 117 | #559 | — | 2 | 2 | no | — |
| 118 | #556 | C23 | 1 | 2 | yes | — |
| 119 | #555 | — | 2 | 1 | no | — |
| 120 | #554 | — | 2 | 1 | no | — |
| 121 | #554 | — | 2 | 2 | no | — |
| 122 | #554 | — | 4 | 1 | no | — |
| 123 | #554 | C23 | 1 | 2 | yes | — |
| 124 | #553 | — | 4 | 1 | no | — |
| 125 | #550 | C23 | 1 | 2 | yes | — |
| 126 | D4×Q8 | — | 2 | 2 | no | — |
| 127 | D4×Q8 | — | 2 | 2 | no | — |
| 128 | D4×Q8 | — | 2 | 1 | no | — |
| 129 | D4×Q8 | — | 2 | 2 | no | — |
| 130 | D4×Q8 | — | 2 | 2 | no | — |
| 131 | D4×Q8 | — | 4 | 1 | no | — |
| 132 | D4×Q8 | — | 4 | 1 | no | — |
| 133 | D4×Q8 | C23 | 1 | 4 | yes | — |
| 134 | D4×Q8 | C23 | 1 | 2 | yes | — |
| 135 | D4×Q8 | C23 | 1 | 4 | yes | — |
| 136 | #547 | — | 2 | 1 | no | — |
| 137 | #544 | — | 2 | 1 | no | — |
| 138 | #543 | — | 4 | 1 | no | — |
| 139 | #538 | — | 4 | 1 | no | — |
| 140 | #535 | — | 2 | 1 | no | — |
| 141 | #533 | C23 | 1 | 1 | yes | characteristic |
| 142 | #533 | C23 | 1 | 1 | yes | characteristic |
| 143 | #532 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 145 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 146 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 147 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 148 | #525 | — | 2 | 2 | no | — |
| 149 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 150 | C2×C22⋊Q8 | — | 2 | 1 | no | — |
| 151 | C2×C22⋊Q8 | — | 2 | 1 | no | — |
| 152 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 153 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 154 | #520 | — | 2 | 1 | no | — |
| 155 | #518 | — | 2 | 1 | no | — |
| 156 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×D4 | — | 2 | 1 | no | — |
| 158 | C2×C4×D4 | — | 2 | 1 | no | — |
| 159 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 161 | #500 | — | 2 | 4 | no | — |
| 162 | #500 | — | 2 | 4 | no | — |
| 163 | #500 | — | 2 | 1 | no | — |
| 164 | #500 | — | 2 | 1 | no | — |
| 165 | #500 | C23 | 1 | 2 | yes | — |
| 166 | #500 | C23 | 1 | 2 | yes | — |
| 167 | #500 | C23 | 1 | 2 | yes | — |
| 168 | #498 | C23 | 1 | 2 | yes | — |
| 169 | #494 | — | 2 | 1 | no | — |
| 170 | #494 | — | 2 | 1 | no | — |
| 171 | #494 | C23 | 1 | 2 | yes | — |
| 172 | #492 | C23 | 1 | 2 | yes | — |
| 173 | #490 | — | 2 | 2 | no | — |
| 174 | #489 | — | 2 | 2 | no | — |
| 175 | #488 | — | 2 | 2 | no | — |
| 176 | #488 | — | 2 | 1 | no | — |
| 177 | #488 | — | 2 | 1 | no | — |
| 178 | #487 | — | 2 | 1 | no | — |
| 179 | #487 | — | 2 | 1 | no | — |
| 180 | #487 | C23 | 1 | 2 | yes | — |
| 181 | #487 | C23 | 1 | 1 | yes | characteristic |
| 182 | #487 | C23 | 1 | 1 | yes | characteristic |
| 183 | #487 | C23 | 1 | 2 | yes | — |
| 184 | #487 | C23 | 1 | 2 | yes | — |
| 185 | #486 | — | 2 | 2 | no | — |
| 186 | #486 | C23 | 1 | 1 | yes | characteristic |
| 187 | #486 | C23 | 1 | 1 | yes | characteristic |
| 188 | #486 | C23 | 1 | 2 | yes | — |
| 189 | #485 | — | 2 | 4 | no | — |
| 190 | #484 | — | 2 | 1 | no | — |
| 191 | #484 | — | 2 | 4 | no | — |
| 192 | #484 | — | 4 | 1 | no | — |
| 193 | #484 | D4 | 1 | 2 | yes | — |
| 194 | #481 | — | 2 | 1 | no | — |
| 195 | #481 | — | 4 | 1 | no | — |
| 196 | #479 | — | 2 | 2 | no | — |
| 197 | #478 | — | 2 | 2 | no | — |
| 198 | #478 | — | 2 | 2 | no | — |
| 199 | #477 | — | 2 | 2 | no | — |
| 200 | #477 | — | 4 | 1 | no | — |
| 201 | #477 | D4 | 1 | 2 | yes | — |
| 202 | #477 | C23 | 1 | 2 | yes | — |
| 203 | #476 | — | 4 | 1 | no | — |
| 204 | #476 | C23 | 1 | 2 | yes | — |
| 205 | #475 | C23 | 1 | 2 | yes | — |
| 206 | #474 | — | 2 | 2 | no | — |
| 207 | #474 | — | 2 | 2 | no | — |
| 208 | #474 | — | 2 | 2 | no | — |
| 209 | #474 | — | 2 | 4 | no | — |
| 210 | #474 | — | 2 | 4 | no | — |
| 211 | #474 | — | 2 | 4 | no | — |
| 212 | #474 | — | 2 | 4 | no | — |
| 213 | #474 | C23 | 1 | 2 | yes | — |
| 214 | #474 | C23 | 1 | 4 | yes | — |
| 215 | #474 | C23 | 1 | 4 | yes | — |
| 216 | #470 | — | 2 | 4 | no | — |
| 217 | #468 | — | 2 | 4 | no | — |
| 218 | #467 | — | 2 | 4 | no | — |
| 219 | #467 | — | 2 | 4 | no | — |
| 220 | #463 | — | 2 | 2 | no | — |
| 221 | #463 | — | 2 | 2 | no | — |
| 222 | #463 | — | 2 | 2 | no | — |
| 223 | #462 | — | 2 | 2 | no | — |
| 224 | #462 | D4 | 1 | 2 | yes | — |
| 225 | #462 | C23 | 1 | 4 | yes | — |
| 226 | #462 | C23 | 1 | 2 | yes | — |
| 227 | #462 | C23 | 1 | 4 | yes | — |
| 228 | #461 | — | 2 | 2 | no | — |
| 229 | #461 | C23 | 1 | 2 | yes | — |
| 230 | #460 | C23 | 1 | 2 | yes | — |
| 231 | #459 | — | 2 | 2 | no | — |
| 232 | #459 | — | 2 | 2 | no | — |
| 233 | #459 | C23 | 1 | 2 | yes | — |
| 234 | #452 | — | 2 | 4 | no | — |
| 235 | #451 | — | 2 | 1 | no | — |
| 236 | #451 | — | 2 | 4 | no | — |
| 237 | #451 | — | 2 | 4 | no | — |
| 238 | #451 | — | 2 | 2 | no | — |
| 239 | #451 | — | 2 | 2 | no | — |
| 240 | #451 | — | 2 | 4 | no | — |
| 241 | #451 | — | 2 | 4 | no | — |
| 242 | #451 | — | 2 | 2 | no | — |
| 243 | #451 | D4 | 1 | 2 | yes | — |
| 244 | #448 | — | 2 | 1 | no | — |
| 245 | #448 | — | 2 | 4 | no | — |
| 246 | #448 | — | 2 | 2 | no | — |
| 247 | #446 | — | 2 | 1 | no | — |
| 248 | #446 | C23 | 1 | 2 | yes | — |
| 249 | C8×Q8 | — | 2 | 1 | no | — |
| 250 | C8×Q8 | — | 2 | 1 | no | — |
| 251 | C8×Q8 | — | 2 | 1 | no | — |
| 252 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 253 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 254 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 255 | #442 | — | 2 | 2 | no | — |
| 256 | #440 | — | 2 | 2 | no | — |
| 257 | C4×Q16 | — | 2 | 2 | no | — |
| 258 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 259 | C4×SD16 | — | 2 | 2 | no | — |
| 260 | C4×SD16 | — | 2 | 2 | no | — |
| 261 | C4×D8 | — | 2 | 4 | no | — |
| 262 | C4×D8 | — | 2 | 4 | no | — |
| 263 | C4×D8 | — | 2 | 2 | no | — |
| 264 | C4×D8 | D4 | 1 | 2 | yes | — |
| 265 | C4×D8 | D4 | 1 | 2 | yes | — |
| 266 | C4×D8 | C23 | 1 | 2 | yes | — |
| 267 | C4×D8 | C23 | 1 | 2 | yes | — |
| 268 | #436 | — | 2 | 2 | no | — |
| 269 | #436 | C23 | 1 | 4 | yes | — |
| 270 | C8×D4 | — | 2 | 2 | no | — |
| 271 | C8×D4 | C23 | 1 | 4 | yes | — |
| 272 | #431 | C23 | 1 | 1 | yes | characteristic |
| 273 | #431 | C23 | 1 | 1 | yes | characteristic |
| 274 | #431 | C23 | 1 | 1 | yes | characteristic |
| 275 | #431 | C23 | 1 | 1 | yes | characteristic |
| 276 | #428 | — | 2 | 1 | no | — |
| 277 | C2×#107 | — | 2 | 1 | no | — |
| 278 | C2×#107 | — | 2 | 1 | no | — |
| 279 | C2×#107 | — | 2 | 1 | no | — |
| 280 | C2×#107 | — | 2 | 1 | no | — |
| 281 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 282 | #424 | — | 2 | 1 | no | — |
| 283 | #423 | C23 | 1 | 1 | yes | characteristic |
| 284 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 285 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 286 | #419 | — | 2 | 4 | no | — |
| 287 | #418 | — | 2 | 1 | no | — |
| 288 | #417 | — | 2 | 1 | no | — |
| 289 | #416 | — | 2 | 1 | no | — |
| 290 | #416 | — | 2 | 1 | no | — |
| 291 | C2×#103 | — | 2 | 4 | no | — |
| 292 | C2×#102 | — | 2 | 1 | no | — |
| 293 | C2×#102 | — | 2 | 1 | no | — |
| 294 | C2×#102 | D4 | 1 | 1 | yes | characteristic |
| 295 | C2×#102 | D4 | 1 | 1 | yes | characteristic |
| 296 | #407 | — | 2 | 2 | no | — |
| 297 | C2×C22⋊C8 | — | 2 | 2 | no | — |
| 298 | #405 | — | 2 | 1 | no | — |
| 299 | C2×C4×C8 | — | 2 | 1 | no | — |
| 300 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 301 | #335 | C23 | 1 | 2 | yes | — |
| 302 | #334 | C23 | 1 | 2 | yes | — |
| 303 | #334 | C23 | 1 | 4 | yes | — |
| 304 | #333 | C23 | 1 | 2 | yes | — |
| 305 | #332 | C23 | 1 | 2 | yes | — |
| 306 | #332 | C23 | 1 | 2 | yes | — |
| 307 | #332 | C23 | 1 | 4 | yes | — |
| 308 | #332 | C23 | 1 | 4 | yes | — |
| 309 | #331 | C23 | 1 | 2 | yes | — |
| 310 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 311 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 312 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 313 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 314 | #322 | C23 | 1 | 2 | yes | — |
| 315 | #322 | C23 | 1 | 2 | yes | — |
| 316 | C2×#41 | — | 2 | 2 | no | — |
| 317 | C2×#41 | — | 2 | 1 | no | — |
| 318 | C22×Q8 | — | 2 | 4 | no | — |
| 319 | C22×Q8 | — | 2 | 4 | no | — |
| 320 | C22×Q8 | — | 2 | 2 | no | — |
| 321 | C22×Q8 | — | 2 | 1 | no | — |
| 322 | C22×Q8 | — | 2 | 1 | no | — |
| 323 | C22×Q8 | — | 4 | 1 | no | — |
| 324 | C22×Q8 | — | 4 | 1 | no | — |
| 325 | C22×Q8 | — | 4 | 2 | no | — |
| 326 | C22×Q8 | — | 4 | 2 | no | — |
| 327 | C22×Q8 | — | 8 | 4 | no | — |
| 328 | C22×Q8 | — | 8 | 4 | no | — |
| 329 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 330 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 331 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 332 | C23×C4 | — | 2 | 1 | no | — |
| 333 | C23×C4 | — | 2 | 1 | no | — |
| 334 | C23×C4 | — | 4 | 1 | no | — |
| 335 | C23×C4 | — | 4 | 1 | no | — |
| 336 | #137 | — | 8 | 8 | no | — |
| 337 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 338 | C2×Q16 | — | 2 | 2 | no | — |
| 339 | C2×Q16 | — | 2 | 4 | no | — |
| 340 | C2×Q16 | — | 2 | 4 | no | — |
| 341 | C2×Q16 | — | 2 | 4 | no | — |
| 342 | C2×Q16 | — | 8 | 8 | no | — |
| 343 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 344 | C2×SD16 | — | 2 | 2 | no | — |
| 345 | C2×SD16 | — | 2 | 2 | no | — |
| 346 | C2×SD16 | — | 2 | 4 | no | — |
| 347 | C2×D8 | — | 2 | 4 | no | — |
| 348 | C2×D8 | — | 2 | 2 | no | — |
| 349 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 350 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 351 | C2×M16 | — | 2 | 1 | no | — |
| 352 | C2×M16 | — | 2 | 4 | no | — |
| 353 | C22×C8 | — | 2 | 1 | no | — |
| 354 | C22×C8 | — | 2 | 4 | no | — |
| 355 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 356 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 357 | C4⋊Q8 | — | 2 | 4 | no | — |
| 358 | C4⋊Q8 | — | 2 | 4 | no | — |
| 359 | C4⋊Q8 | — | 2 | 2 | no | — |
| 360 | C4⋊Q8 | — | 2 | 1 | no | — |
| 361 | C4⋊Q8 | — | 2 | 1 | no | — |
| 362 | C4⋊Q8 | — | 2 | 1 | no | — |
| 363 | C4⋊Q8 | — | 2 | 1 | no | — |
| 364 | C4⋊Q8 | — | 2 | 1 | no | — |
| 365 | C4⋊Q8 | — | 2 | 1 | no | — |
| 366 | C4⋊Q8 | — | 4 | 2 | no | — |
| 367 | C4⋊Q8 | — | 4 | 2 | no | — |
| 368 | C4⋊Q8 | — | 4 | 1 | no | — |
| 369 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 370 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 371 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 372 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 373 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 374 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 375 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 376 | #127 | — | 2 | 2 | no | — |
| 377 | #127 | C24 | 1 | 1 | yes | characteristic |
| 378 | #126 | — | 4 | 2 | no | — |
| 379 | #125 | — | 2 | 2 | no | — |
| 380 | #125 | — | 2 | 1 | no | — |
| 381 | #125 | — | 2 | 1 | no | — |
| 382 | #125 | — | 4 | 1 | no | — |
| 383 | #124 | — | 2 | 2 | no | — |
| 384 | #124 | — | 2 | 1 | no | — |
| 385 | #124 | — | 4 | 2 | no | — |
| 386 | #123 | — | 4 | 2 | no | — |
| 387 | #123 | — | 4 | 2 | no | — |
| 388 | C22⋊Q8 | — | 2 | 1 | no | — |
| 389 | C22⋊Q8 | — | 2 | 2 | no | — |
| 390 | C22⋊Q8 | — | 2 | 2 | no | — |
| 391 | C22⋊Q8 | — | 2 | 1 | no | — |
| 392 | C22⋊Q8 | — | 2 | 1 | no | — |
| 393 | C22⋊Q8 | — | 2 | 4 | no | — |
| 394 | C22⋊Q8 | — | 2 | 4 | no | — |
| 395 | C22⋊Q8 | — | 2 | 2 | no | — |
| 396 | C22⋊Q8 | — | 4 | 4 | no | — |
| 397 | C22⋊Q8 | — | 4 | 4 | no | — |
| 398 | C22⋊Q8 | — | 4 | 2 | no | — |
| 399 | C22⋊Q8 | — | 4 | 2 | no | — |
| 400 | C22⋊Q8 | — | 4 | 4 | no | — |
| 401 | C22⋊Q8 | — | 4 | 4 | no | — |
| 402 | C22⋊Q8 | — | 4 | 2 | no | — |
| 403 | C22⋊Q8 | — | 4 | 2 | no | — |
| 404 | C22⋊Q8 | — | 4 | 2 | no | — |
| 405 | C22⋊Q8 | — | 4 | 2 | no | — |
| 406 | C22⋊Q8 | — | 4 | 2 | no | — |
| 407 | C22⋊Q8 | — | 4 | 2 | no | — |
| 408 | C22⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 409 | #121 | — | 2 | 1 | no | — |
| 410 | #121 | — | 2 | 1 | no | — |
| 411 | #121 | — | 2 | 2 | no | — |
| 412 | #121 | — | 4 | 2 | no | — |
| 413 | #121 | — | 4 | 1 | no | — |
| 414 | #121 | — | 4 | 1 | no | — |
| 415 | #120 | — | 4 | 2 | no | — |
| 416 | C4×Q8 | — | 2 | 1 | no | — |
| 417 | C4×Q8 | — | 2 | 1 | no | — |
| 418 | C4×Q8 | — | 2 | 1 | no | — |
| 419 | C4×Q8 | — | 2 | 2 | no | — |
| 420 | C4×Q8 | — | 2 | 1 | no | — |
| 421 | C4×Q8 | — | 2 | 1 | no | — |
| 422 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 423 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 424 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 425 | C4×D4 | — | 2 | 4 | no | — |
| 426 | C4×D4 | — | 2 | 4 | no | — |
| 427 | C4×D4 | — | 2 | 2 | no | — |
| 428 | C4×D4 | — | 2 | 2 | no | — |
| 429 | C4×D4 | — | 2 | 2 | no | — |
| 430 | C4×D4 | — | 2 | 1 | no | — |
| 431 | C4×D4 | — | 2 | 1 | no | — |
| 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 | — | 4 | 2 | no | — |
| 437 | C4×D4 | — | 4 | 2 | no | — |
| 438 | C4×D4 | — | 4 | 2 | no | — |
| 439 | C4×D4 | — | 4 | 2 | no | — |
| 440 | C4×D4 | — | 4 | 1 | no | — |
| 441 | C4×D4 | — | 4 | 1 | no | — |
| 442 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 443 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 444 | C4×D4 | C24 | 1 | 2 | yes | — |
| 445 | C4×D4 | C24 | 1 | 2 | yes | — |
| 446 | #117 | — | 2 | 1 | no | — |
| 447 | #117 | — | 2 | 1 | no | — |
| 448 | #117 | — | 2 | 2 | no | — |
| 449 | #117 | — | 4 | 1 | no | — |
| 450 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 451 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 452 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 453 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 454 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 455 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 456 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 457 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 458 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 459 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 460 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 461 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 462 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 463 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 464 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 465 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 466 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 467 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 468 | C2×C42 | — | 2 | 1 | no | — |
| 469 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 470 | #107 | — | 2 | 2 | no | — |
| 471 | #107 | — | 2 | 2 | no | — |
| 472 | #107 | — | 2 | 2 | no | — |
| 473 | #107 | — | 2 | 2 | no | — |
| 474 | #107 | — | 2 | 4 | no | — |
| 475 | #107 | — | 2 | 4 | no | — |
| 476 | #107 | — | 2 | 2 | no | — |
| 477 | #107 | — | 2 | 2 | no | — |
| 478 | #107 | — | 4 | 2 | no | — |
| 479 | #107 | C2×D4 | 1 | 2 | yes | — |
| 480 | #107 | C2×D4 | 1 | 2 | yes | — |
| 481 | #107 | C2×D4 | 1 | 4 | yes | — |
| 482 | #106 | — | 2 | 2 | no | — |
| 483 | #106 | — | 2 | 2 | no | — |
| 484 | #106 | — | 4 | 2 | no | — |
| 485 | C4⋊C8 | — | 2 | 2 | no | — |
| 486 | C4⋊C8 | — | 2 | 2 | no | — |
| 487 | C4⋊C8 | — | 2 | 2 | no | — |
| 488 | C4⋊C8 | — | 2 | 2 | no | — |
| 489 | C4⋊C8 | — | 2 | 1 | no | — |
| 490 | C4⋊C8 | — | 2 | 1 | no | — |
| 491 | C4⋊C8 | — | 2 | 1 | no | — |
| 492 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 493 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 494 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 495 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 496 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 497 | #103 | — | 2 | 2 | no | — |
| 498 | #103 | — | 2 | 2 | no | — |
| 499 | #103 | — | 2 | 4 | no | — |
| 500 | #103 | — | 2 | 1 | no | — |
| 501 | #103 | — | 2 | 1 | no | — |
| 502 | #103 | — | 2 | 1 | no | — |
| 503 | #103 | — | 2 | 1 | no | — |
| 504 | #103 | — | 2 | 4 | no | — |
| 505 | #103 | — | 2 | 4 | no | — |
| 506 | #103 | — | 2 | 2 | no | — |
| 507 | #103 | — | 2 | 4 | no | — |
| 508 | #103 | — | 2 | 2 | no | — |
| 509 | #103 | — | 4 | 2 | no | — |
| 510 | #103 | C2×D4 | 1 | 4 | yes | — |
| 511 | #103 | C2×D4 | 1 | 4 | yes | — |
| 512 | #102 | — | 2 | 4 | no | — |
| 513 | #102 | — | 2 | 4 | no | — |
| 514 | #102 | — | 2 | 2 | no | — |
| 515 | #102 | — | 2 | 2 | no | — |
| 516 | #102 | — | 2 | 1 | no | — |
| 517 | #102 | — | 2 | 1 | no | — |
| 518 | #102 | — | 2 | 1 | no | — |
| 519 | #102 | — | 2 | 1 | no | — |
| 520 | #102 | — | 2 | 2 | no | — |
| 521 | #102 | — | 2 | 2 | no | — |
| 522 | #102 | — | 4 | 2 | no | — |
| 523 | #102 | C2×D4 | 1 | 2 | yes | — |
| 524 | #102 | C2×D4 | 1 | 2 | yes | — |
| 525 | #102 | C2×D4 | 1 | 2 | yes | — |
| 526 | #102 | C2×D4 | 1 | 2 | yes | — |
| 527 | C22⋊C8 | — | 2 | 1 | no | — |
| 528 | C22⋊C8 | — | 2 | 1 | no | — |
| 529 | C22⋊C8 | — | 2 | 1 | no | — |
| 530 | C22⋊C8 | — | 2 | 4 | no | — |
| 531 | C22⋊C8 | — | 2 | 4 | no | — |
| 532 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 533 | #97 | — | 2 | 2 | no | — |
| 534 | C4×C8 | — | 2 | 2 | no | — |
| 535 | C4×C8 | — | 2 | 2 | no | — |
| 536 | C4×C8 | — | 2 | 2 | no | — |
| 537 | C4×C8 | — | 2 | 1 | no | — |
| 538 | C4×C8 | — | 2 | 1 | no | — |
| 539 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 540 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 541 | C4×C8 | C24 | 1 | 2 | yes | — |
| 542 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 543 | C4×C8 | C24 | 1 | 2 | yes | — |
| 544 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 545 | C24 | — | 2 | 1 | no | — |
| 546 | C24 | — | 2 | 1 | no | — |
| 547 | #41 | — | 4 | 2 | no | — |
| 548 | #41 | — | 4 | 2 | no | — |
| 549 | #41 | — | 8 | 4 | no | — |
| 550 | C2×Q8 | — | 2 | 4 | no | — |
| 551 | C2×Q8 | — | 2 | 1 | no | — |
| 552 | C2×Q8 | — | 2 | 1 | no | — |
| 553 | C2×Q8 | — | 2 | 1 | no | — |
| 554 | C2×Q8 | — | 2 | 2 | no | — |
| 555 | C2×Q8 | — | 2 | 2 | no | — |
| 556 | C2×Q8 | — | 2 | 1 | no | — |
| 557 | C2×Q8 | — | 2 | 1 | no | — |
| 558 | C2×Q8 | — | 4 | 4 | no | — |
| 559 | C2×Q8 | — | 4 | 4 | no | — |
| 560 | C2×Q8 | — | 4 | 2 | no | — |
| 561 | C2×Q8 | — | 4 | 1 | no | — |
| 562 | C2×Q8 | — | 4 | 1 | no | — |
| 563 | C2×Q8 | — | 4 | 8 | no | — |
| 564 | C2×Q8 | — | 4 | 8 | no | — |
| 565 | C2×Q8 | — | 8 | 2 | no | — |
| 566 | C2×Q8 | — | 8 | 2 | no | — |
| 567 | C2×Q8 | — | 8 | 4 | no | — |
| 568 | C2×Q8 | — | 8 | 4 | no | — |
| 569 | C2×Q8 | — | 8 | 4 | no | — |
| 570 | C2×Q8 | — | 8 | 4 | no | — |
| 571 | C2×Q8 | — | 8 | 4 | no | — |
| 572 | C2×Q8 | — | 8 | 8 | no | — |
| 573 | C2×Q8 | — | 8 | 8 | no | — |
| 574 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 575 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 576 | C2×D4 | — | 2 | 1 | no | — |
| 577 | C2×D4 | — | 2 | 1 | no | — |
| 578 | C2×D4 | — | 2 | 2 | no | — |
| 579 | C2×D4 | — | 2 | 2 | no | — |
| 580 | C2×D4 | — | 2 | 2 | no | — |
| 581 | C2×D4 | — | 2 | 1 | no | — |
| 582 | C2×D4 | — | 2 | 1 | no | — |
| 583 | C2×D4 | — | 2 | 1 | no | — |
| 584 | C2×D4 | — | 4 | 2 | no | — |
| 585 | C2×D4 | — | 4 | 2 | no | — |
| 586 | C2×D4 | — | 4 | 1 | no | — |
| 587 | C2×D4 | #137 | 1 | 4 | yes | complemented |
| 588 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 589 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 590 | C22×C4 | — | 2 | 1 | no | — |
| 591 | C22×C4 | — | 2 | 1 | no | — |
| 592 | C22×C4 | — | 2 | 1 | no | — |
| 593 | C22×C4 | — | 2 | 1 | no | — |
| 594 | C22×C4 | — | 2 | 2 | no | — |
| 595 | C22×C4 | — | 2 | 2 | no | — |
| 596 | C22×C4 | — | 2 | 2 | no | — |
| 597 | C22×C4 | — | 2 | 2 | no | — |
| 598 | C22×C4 | — | 4 | 2 | no | — |
| 599 | C22×C4 | — | 4 | 4 | no | — |
| 600 | C22×C4 | — | 4 | 4 | no | — |
| 601 | C22×C4 | — | 4 | 2 | no | — |
| 602 | C22×C4 | — | 4 | 2 | no | — |
| 603 | C22×C4 | — | 4 | 1 | no | — |
| 604 | C22×C4 | — | 4 | 1 | no | — |
| 605 | C22×C4 | — | 4 | 1 | no | — |
| 606 | C22×C4 | — | 8 | 2 | no | — |
| 607 | C22×C4 | — | 8 | 2 | no | — |
| 608 | C22×C4 | — | 8 | 4 | no | — |
| 609 | C22×C4 | — | 8 | 4 | no | — |
| 610 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 611 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 612 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 613 | Q16 | — | 2 | 8 | no | — |
| 614 | Q16 | — | 4 | 4 | no | — |
| 615 | Q16 | — | 8 | 4 | no | — |
| 616 | Q16 | — | 8 | 4 | no | — |
| 617 | Q16 | — | 8 | 4 | no | — |
| 618 | SD16 | — | 4 | 4 | no | — |
| 619 | SD16 | — | 4 | 4 | no | — |
| 620 | SD16 | — | 8 | 4 | no | — |
| 621 | D8 | — | 2 | 4 | no | — |
| 622 | D8 | — | 2 | 4 | no | — |
| 623 | D8 | — | 4 | 4 | no | — |
| 624 | M16 | — | 4 | 2 | no | — |
| 625 | M16 | — | 8 | 4 | no | — |
| 626 | C2×C8 | — | 2 | 2 | no | — |
| 627 | C2×C8 | — | 2 | 2 | no | — |
| 628 | C2×C8 | — | 2 | 2 | no | — |
| 629 | C2×C8 | — | 2 | 2 | no | — |
| 630 | C2×C8 | — | 2 | 2 | no | — |
| 631 | C2×C8 | — | 2 | 2 | no | — |
| 632 | C2×C8 | — | 2 | 2 | no | — |
| 633 | C2×C8 | — | 4 | 2 | no | — |
| 634 | C2×C8 | — | 8 | 4 | no | — |
| 635 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 636 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 637 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 638 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 639 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 640 | C4⋊C4 | — | 2 | 2 | no | — |
| 641 | C4⋊C4 | — | 2 | 1 | no | — |
| 642 | C4⋊C4 | — | 2 | 1 | no | — |
| 643 | C4⋊C4 | — | 2 | 2 | no | — |
| 644 | C4⋊C4 | — | 2 | 1 | no | — |
| 645 | C4⋊C4 | — | 2 | 1 | no | — |
| 646 | C4⋊C4 | — | 2 | 1 | no | — |
| 647 | C4⋊C4 | — | 2 | 1 | no | — |
| 648 | C4⋊C4 | — | 2 | 2 | no | — |
| 649 | C4⋊C4 | — | 2 | 2 | no | — |
| 650 | C4⋊C4 | — | 2 | 1 | no | — |
| 651 | C4⋊C4 | — | 2 | 1 | no | — |
| 652 | C4⋊C4 | — | 2 | 2 | no | — |
| 653 | C4⋊C4 | — | 2 | 2 | no | — |
| 654 | C4⋊C4 | — | 2 | 1 | no | — |
| 655 | C4⋊C4 | — | 2 | 1 | no | — |
| 656 | C4⋊C4 | — | 2 | 2 | no | — |
| 657 | C4⋊C4 | — | 2 | 2 | no | — |
| 658 | C4⋊C4 | — | 2 | 1 | no | — |
| 659 | C4⋊C4 | — | 2 | 1 | no | — |
| 660 | C4⋊C4 | — | 4 | 2 | no | — |
| 661 | C4⋊C4 | — | 4 | 2 | no | — |
| 662 | C4⋊C4 | — | 4 | 2 | no | — |
| 663 | C4⋊C4 | — | 4 | 2 | no | — |
| 664 | C4⋊C4 | — | 4 | 4 | no | — |
| 665 | C4⋊C4 | — | 4 | 4 | no | — |
| 666 | C4⋊C4 | — | 4 | 1 | no | — |
| 667 | C4⋊C4 | — | 4 | 1 | no | — |
| 668 | C4⋊C4 | — | 4 | 1 | no | — |
| 669 | C4⋊C4 | — | 4 | 1 | no | — |
| 670 | C4⋊C4 | — | 4 | 1 | no | — |
| 671 | C4⋊C4 | — | 4 | 1 | no | — |
| 672 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 673 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 674 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 675 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 676 | C22⋊C4 | — | 2 | 2 | no | — |
| 677 | C22⋊C4 | — | 2 | 2 | no | — |
| 678 | C22⋊C4 | — | 2 | 2 | no | — |
| 679 | C22⋊C4 | — | 2 | 2 | no | — |
| 680 | C22⋊C4 | — | 2 | 2 | no | — |
| 681 | C22⋊C4 | — | 4 | 2 | no | — |
| 682 | C22⋊C4 | — | 4 | 4 | no | — |
| 683 | C22⋊C4 | — | 4 | 4 | no | — |
| 684 | C22⋊C4 | — | 4 | 2 | no | — |
| 685 | C22⋊C4 | — | 4 | 2 | no | — |
| 686 | C22⋊C4 | — | 4 | 2 | no | — |
| 687 | C22⋊C4 | — | 4 | 2 | no | — |
| 688 | C22⋊C4 | — | 4 | 1 | no | — |
| 689 | C22⋊C4 | — | 4 | 1 | no | — |
| 690 | C22⋊C4 | — | 4 | 1 | no | — |
| 691 | C42 | — | 2 | 2 | no | — |
| 692 | C42 | — | 2 | 2 | no | — |
| 693 | C42 | — | 2 | 2 | no | — |
| 694 | C42 | — | 4 | 2 | no | — |
| 695 | C42 | — | 4 | 1 | no | — |
| 696 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 697 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 698 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 699 | C42 | C25 | 1 | 1 | yes | characteristic |
| 700 | C23 | — | 2 | 2 | no | — |
| 701 | C23 | — | 2 | 4 | no | — |
| 702 | C23 | — | 2 | 2 | no | — |
| 703 | C23 | — | 4 | 2 | no | — |
| 704 | C23 | — | 4 | 1 | no | — |
| 705 | C23 | — | 8 | 1 | no | — |
| 706 | C23 | — | 8 | 1 | no | — |
| 707 | C23 | — | 8 | 1 | no | — |
| 708 | C23 | — | 8 | 1 | no | — |
| 709 | C23 | D42 | 1 | 1 | yes | characteristic |
| 710 | Q8 | — | 2 | 4 | no | — |
| 711 | Q8 | — | 2 | 2 | no | — |
| 712 | Q8 | — | 2 | 4 | no | — |
| 713 | Q8 | — | 4 | 1 | no | — |
| 714 | Q8 | — | 4 | 4 | no | — |
| 715 | Q8 | — | 4 | 2 | no | — |
| 716 | Q8 | — | 4 | 4 | no | — |
| 717 | Q8 | — | 4 | 1 | no | — |
| 718 | Q8 | — | 8 | 1 | no | — |
| 719 | Q8 | — | 8 | 8 | no | — |
| 720 | Q8 | — | 8 | 8 | no | — |
| 721 | Q8 | — | 8 | 1 | no | — |
| 722 | Q8 | — | 8 | 2 | no | — |
| 723 | Q8 | — | 8 | 2 | no | — |
| 724 | Q8 | — | 16 | 2 | no | — |
| 725 | Q8 | #576 | 1 | 4 | yes | — |
| 726 | D4 | — | 2 | 4 | no | — |
| 727 | D4 | — | 2 | 2 | no | — |
| 728 | D4 | — | 2 | 2 | no | — |
| 729 | D4 | — | 2 | 2 | no | — |
| 730 | D4 | — | 4 | 2 | no | — |
| 731 | D4 | — | 4 | 1 | no | — |
| 732 | D4 | — | 4 | 2 | no | — |
| 733 | D4 | — | 4 | 1 | no | — |
| 734 | D4 | — | 8 | 1 | no | — |
| 735 | D4 | — | 8 | 2 | no | — |
| 736 | D4 | — | 16 | 2 | no | — |
| 737 | D4 | — | 16 | 2 | no | — |
| 738 | D4 | C2×#137 | 1 | 4 | yes | — |
| 739 | C2×C4 | — | 2 | 4 | no | — |
| 740 | C2×C4 | — | 2 | 2 | no | — |
| 741 | C2×C4 | — | 2 | 2 | no | — |
| 742 | C2×C4 | — | 2 | 2 | no | — |
| 743 | C2×C4 | — | 2 | 2 | no | — |
| 744 | C2×C4 | — | 2 | 2 | no | — |
| 745 | C2×C4 | — | 2 | 2 | no | — |
| 746 | C2×C4 | — | 2 | 2 | no | — |
| 747 | C2×C4 | — | 4 | 1 | no | — |
| 748 | C2×C4 | — | 4 | 2 | no | — |
| 749 | C2×C4 | — | 4 | 4 | no | — |
| 750 | C2×C4 | — | 4 | 4 | no | — |
| 751 | C2×C4 | — | 4 | 1 | no | — |
| 752 | C2×C4 | — | 4 | 1 | no | — |
| 753 | C2×C4 | — | 4 | 1 | no | — |
| 754 | C2×C4 | — | 4 | 2 | no | — |
| 755 | C2×C4 | — | 4 | 2 | no | — |
| 756 | C2×C4 | — | 8 | 2 | no | — |
| 757 | C2×C4 | — | 8 | 2 | no | — |
| 758 | C2×C4 | — | 8 | 8 | no | — |
| 759 | C2×C4 | — | 8 | 8 | no | — |
| 760 | C2×C4 | — | 8 | 1 | no | — |
| 761 | C2×C4 | — | 8 | 1 | no | — |
| 762 | C2×C4 | — | 8 | 2 | no | — |
| 763 | C2×C4 | — | 8 | 2 | no | — |
| 764 | C2×C4 | — | 8 | 2 | no | — |
| 765 | C2×C4 | — | 16 | 2 | no | — |
| 766 | C2×C4 | — | 16 | 2 | no | — |
| 767 | C2×C4 | — | 16 | 2 | no | — |
| 768 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 769 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 770 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 771 | C2×C4 | C2×#137 | 1 | 2 | yes | — |
| 772 | C2×C4 | #578 | 1 | 2 | yes | — |
| 773 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 774 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 775 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 776 | C8 | — | 2 | 1 | no | — |
| 777 | C8 | — | 2 | 1 | no | — |
| 778 | C8 | — | 2 | 4 | no | — |
| 779 | C8 | — | 2 | 1 | no | — |
| 780 | C8 | — | 2 | 1 | no | — |
| 781 | C8 | — | 4 | 2 | no | — |
| 782 | C8 | — | 4 | 2 | no | — |
| 783 | C8 | — | 4 | 2 | no | — |
| 784 | C8 | — | 4 | 2 | no | — |
| 785 | C8 | — | 4 | 2 | no | — |
| 786 | C22 | — | 2 | 1 | no | — |
| 787 | C22 | — | 2 | 1 | no | — |
| 788 | C22 | — | 2 | 4 | no | — |
| 789 | C22 | — | 4 | 2 | no | — |
| 790 | C22 | — | 4 | 2 | no | — |
| 791 | C22 | — | 4 | 2 | no | — |
| 792 | C22 | — | 4 | 2 | no | — |
| 793 | C22 | — | 4 | 2 | no | — |
| 794 | C22 | — | 8 | 4 | no | — |
| 795 | C22 | — | 8 | 4 | no | — |
| 796 | C22 | — | 8 | 1 | no | — |
| 797 | C22 | — | 8 | 1 | no | — |
| 798 | C22 | — | 8 | 1 | no | — |
| 799 | C22 | #3270 | 1 | 2 | yes | — |
| 800 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 801 | C4 | — | 2 | 4 | no | — |
| 802 | C4 | — | 2 | 1 | no | — |
| 803 | C4 | — | 2 | 1 | no | — |
| 804 | C4 | — | 2 | 1 | no | — |
| 805 | C4 | — | 4 | 2 | no | — |
| 806 | C4 | — | 4 | 2 | no | — |
| 807 | C4 | — | 4 | 2 | no | — |
| 808 | C4 | — | 4 | 2 | no | — |
| 809 | C4 | — | 4 | 2 | no | — |
| 810 | C4 | — | 8 | 1 | no | — |
| 811 | C4 | — | 8 | 2 | no | — |
| 812 | C4 | — | 8 | 2 | no | — |
| 813 | C4 | — | 8 | 1 | no | — |
| 814 | C4 | — | 8 | 1 | no | — |
| 815 | C4 | #3270 | 1 | 2 | yes | — |
| 816 | C4 | C22×#137 | 1 | 1 | yes | characteristic |
| 817 | C4 | C2×#576 | 1 | 2 | yes | — |
| 818 | C4 | C2×#578 | 1 | 1 | yes | characteristic |
| 819 | C2 | — | 2 | 2 | no | — |
| 820 | C2 | — | 4 | 4 | no | — |
| 821 | C2 | — | 8 | 2 | no | — |
| 822 | C2 | — | 16 | 1 | no | — |
| 823 | C2 | C2×#3270 | 1 | 1 | yes | characteristic |
| 824 | C2 | #61049 | 1 | 1 | yes | characteristic |
| 825 | C2 | #61108 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | #61325 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61584 | C2 | semidirect |
| 2. #61563 | C2 | semidirect |
| 3. C2×Q8×D8 | C2 | semidirect |
| 5. #20062 | C2 | semidirect |
| 6. #20033 | C2 | semidirect |
| 7. #19782 | C2 | semidirect |
| 8. #19761 | C2 | semidirect |
| 9. #19704 | C2 | semidirect |
| 10. #19423 | C2 | semidirect |
| 11. #19385 | C2 | semidirect |
| 12. #19208 | C2 | semidirect |
| 13. #19123 | C2 | semidirect |
| 14. #18927 | C2 | semidirect |
| 15. #18905 | C2 | semidirect |
| 16. #18759 | C2 | semidirect |
| 17. #18758 | C2 | semidirect |
| 18. #17906 | C2 | semidirect |
| 19. #17877 | C2 | semidirect |
| 35. #3328 | C22 | semidirect |
| 37. #3299 | C22 | semidirect |
| 39. D4×Q16 | C22 | semidirect |
| 40. #3278 | C22 | semidirect |
| 74. #1723 | C22 | semidirect |
| 75. #1722 | C22 | semidirect |
| 76. #1719 | C22 | semidirect |
| 77. #1718 | C22 | semidirect |
| 78. #1703 | C22 | semidirect |
| 79. #1694 | C22 | semidirect |
| 80. #1689 | C22 | semidirect |
| 81. #1684 | C22 | semidirect |
| 82. #1682 | C22 | semidirect |
| 83. #1680 | C22 | semidirect |
| 84. #1679 | C22 | semidirect |
| 85. #1678 | C22 | semidirect |
| 86. #1674 | C22 | semidirect |
| 87. #1665 | C22 | semidirect |
| 88. #1652 | C22 | semidirect |
| 89. #1651 | C22 | semidirect |
| 90. #1649 | C22 | semidirect |
| 91. #1649 | C22 | semidirect |
| 92. #1644 | C22 | semidirect |
| 93. #1641 | C22 | semidirect |
| 94. #1637 | C22 | semidirect |
| 95. #1627 | C22 | semidirect |
| 96. #1587 | C22 | semidirect |
| 99. #1579 | C22 | semidirect |
| 587. C2×D4 | #137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61584 | 2 |
| #61563 | 2 |
| C2×Q8×D8 | 2 |
| #61325 | 2 |
| #20062 | 2 |
| #20033 | 2 |
| #19782 | 2 |
| #19761 | 2 |
| #19704 | 2 |
| #19423 | 2 |
| #19385 | 2 |
| #19208 | 2 |
| #19123 | 2 |
| #18927 | 2 |
| #18905 | 2 |
| #18759 | 2 |
| #18758 | 2 |
| #17906 | 2 |
| #17877 | 2 |