Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6228 conjugacy classes of subgroups.
The subgroup lattice has 774 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63009 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62419 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #62418 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #62416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #62364 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #62361 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #61956 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | #61950 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #61948 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #61887 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #61882 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #61433 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | #61427 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | D8×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #61393 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | C2×#3393 | C2 | 1 | 3 | yes | maximal, complemented |
| 17 | C8×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #3523 | C22 | 1 | 4 | yes | complemented |
| 19 | #3521 | — | 2 | 12 | no | — |
| 20 | #3518 | — | 2 | 4 | no | — |
| 21 | #3514 | C22 | 1 | 12 | yes | complemented |
| 22 | #3511 | C22 | 1 | 6 | yes | complemented |
| 23 | #3507 | C22 | 1 | 6 | yes | complemented |
| 24 | #3503 | C22 | 1 | 2 | yes | — |
| 25 | #3495 | — | 2 | 6 | no | — |
| 26 | #3493 | — | 2 | 6 | no | — |
| 27 | #3489 | — | 2 | 2 | no | — |
| 28 | #3482 | C22 | 1 | 12 | yes | complemented |
| 29 | #3480 | C22 | 1 | 4 | yes | complemented |
| 30 | #3475 | C22 | 1 | 6 | yes | complemented |
| 31 | C2×#556 | C22 | 1 | 6 | yes | complemented |
| 32 | D4×#41 | C22 | 1 | 2 | yes | — |
| 33 | C4×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 34 | #3428 | — | 2 | 2 | no | — |
| 35 | #3396 | C22 | 1 | 6 | yes | complemented |
| 36 | #3395 | C22 | 1 | 2 | yes | complemented |
| 37 | #3395 | C22 | 1 | 2 | yes | complemented |
| 38 | #3394 | C22 | 1 | 12 | yes | complemented |
| 39 | #3394 | C22 | 1 | 12 | yes | complemented |
| 40 | #3393 | C22 | 1 | 6 | yes | — |
| 41 | #3393 | C22 | 1 | 3 | yes | — |
| 42 | #3393 | C22 | 1 | 12 | yes | complemented |
| 43 | #3393 | C22 | 1 | 6 | yes | complemented |
| 44 | #3393 | C22 | 1 | 6 | yes | complemented |
| 45 | #3393 | C22 | 1 | 12 | yes | complemented |
| 46 | #3393 | C22 | 1 | 6 | yes | complemented |
| 47 | #3392 | C22 | 1 | 4 | yes | complemented |
| 48 | #3391 | C22 | 1 | 1 | yes | characteristic |
| 49 | #3383 | C22 | 1 | 6 | yes | complemented |
| 50 | #3380 | C22 | 1 | 3 | yes | complemented |
| 51 | Q8×D8 | C22 | 1 | 1 | yes | characteristic |
| 52 | #3365 | C22 | 1 | 12 | yes | complemented |
| 53 | #3364 | C22 | 1 | 12 | yes | complemented |
| 54 | #3364 | C22 | 1 | 12 | yes | complemented |
| 55 | #3360 | C22 | 1 | 12 | yes | complemented |
| 56 | #3360 | C22 | 1 | 6 | yes | complemented |
| 57 | #3359 | C22 | 1 | 4 | yes | complemented |
| 58 | #3358 | C22 | 1 | 2 | yes | — |
| 59 | #3341 | C22 | 1 | 1 | yes | characteristic |
| 60 | #3336 | C22 | 1 | 6 | yes | complemented |
| 61 | #3334 | C22 | 1 | 3 | yes | — |
| 62 | #3303 | C22 | 1 | 6 | yes | complemented |
| 63 | #3300 | C22 | 1 | 24 | yes | complemented |
| 64 | #3298 | C22 | 1 | 12 | yes | complemented |
| 65 | #3296 | C22 | 1 | 12 | yes | complemented |
| 66 | #3294 | C22 | 1 | 6 | yes | — |
| 67 | D4×Q16 | C22 | 1 | 6 | yes | complemented |
| 68 | D4×Q16 | C22 | 1 | 6 | yes | complemented |
| 69 | #3285 | C22 | 1 | 12 | yes | complemented |
| 70 | #3285 | C22 | 1 | 12 | yes | complemented |
| 71 | #3283 | C22 | 1 | 3 | yes | complemented |
| 72 | #3283 | C22 | 1 | 6 | yes | complemented |
| 73 | #3282 | C22 | 1 | 24 | yes | complemented |
| 74 | D4×SD16 | C22 | 1 | 12 | yes | complemented |
| 75 | #3280 | C22 | 1 | 6 | yes | — |
| 76 | D4×D8 | C22 | 1 | 3 | yes | — |
| 77 | #3250 | C22 | 1 | 12 | yes | complemented |
| 78 | #3248 | C22 | 1 | 12 | yes | complemented |
| 79 | #3246 | C22 | 1 | 6 | yes | complemented |
| 80 | #3212 | C22 | 1 | 12 | yes | complemented |
| 81 | #3211 | C22 | 1 | 24 | yes | complemented |
| 82 | #3210 | C22 | 1 | 12 | yes | complemented |
| 83 | #3209 | C22 | 1 | 6 | yes | complemented |
| 84 | #3206 | C22 | 1 | 6 | yes | complemented |
| 85 | #3170 | C22 | 1 | 3 | yes | complemented |
| 86 | #3170 | C22 | 1 | 6 | yes | complemented |
| 87 | #3169 | C22 | 1 | 3 | yes | — |
| 88 | #3168 | C22 | 1 | 6 | yes | — |
| 89 | #3168 | C22 | 1 | 12 | yes | complemented |
| 90 | #3147 | C22 | 1 | 6 | yes | complemented |
| 91 | C2×#495 | C22 | 1 | 6 | yes | — |
| 92 | C2×#494 | C22 | 1 | 3 | yes | complemented |
| 93 | #3108 | C22 | 1 | 24 | yes | complemented |
| 94 | #3107 | C22 | 1 | 12 | yes | complemented |
| 95 | #3102 | C22 | 1 | 12 | yes | complemented |
| 96 | #3101 | C22 | 1 | 6 | yes | complemented |
| 97 | #3100 | C22 | 1 | 6 | yes | — |
| 98 | #3035 | C22 | 1 | 12 | yes | complemented |
| 99 | C2×#464 | C22 | 1 | 12 | yes | complemented |
| 100 | C2×#461 | C22 | 1 | 6 | yes | complemented |
| 101 | #2988 | C22 | 1 | 1 | yes | characteristic |
| 102 | #2988 | C22 | 1 | 6 | yes | complemented |
| 103 | #2988 | C22 | 1 | 3 | yes | complemented |
| 104 | #2982 | C22 | 1 | 3 | yes | complemented |
| 105 | #2982 | C22 | 1 | 2 | yes | complemented |
| 106 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 107 | C8×#41 | C22 | 1 | 3 | yes | complemented |
| 108 | C8×#41 | C22 | 1 | 6 | yes | complemented |
| 109 | C2×C8×Q8 | C22 | 1 | 3 | yes | complemented |
| 110 | C2×C8×Q8 | C22 | 1 | 2 | yes | complemented |
| 111 | C4×#135 | C22 | 1 | 6 | yes | complemented |
| 112 | C2×C4×Q16 | C22 | 1 | 6 | yes | complemented |
| 113 | C2×C4×D8 | C22 | 1 | 3 | yes | — |
| 114 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic |
| 115 | C22×#41 | — | 2 | 2 | no | — |
| 116 | C2×#135 | C23 | 1 | 6 | yes | — |
| 117 | C2×#135 | C23 | 1 | 12 | yes | — |
| 118 | C22×Q16 | C23 | 1 | 6 | yes | — |
| 119 | C22×Q16 | C23 | 1 | 6 | yes | — |
| 120 | C22×SD16 | C23 | 1 | 12 | yes | — |
| 121 | C22×D8 | C23 | 1 | 3 | yes | — |
| 122 | #559 | C23 | 1 | 12 | yes | — |
| 123 | Q82 | — | 2 | 2 | no | — |
| 124 | #557 | C23 | 1 | 4 | yes | — |
| 125 | #557 | C23 | 1 | 12 | yes | — |
| 126 | #556 | — | 2 | 12 | no | — |
| 127 | #556 | — | 2 | 12 | no | — |
| 128 | #556 | — | 2 | 12 | no | — |
| 129 | #556 | — | 2 | 12 | no | — |
| 130 | #556 | C23 | 1 | 6 | yes | — |
| 131 | #556 | C23 | 1 | 12 | yes | — |
| 132 | #556 | C23 | 1 | 12 | yes | — |
| 133 | #556 | C23 | 1 | 12 | yes | — |
| 134 | #555 | — | 2 | 6 | no | — |
| 135 | #555 | — | 2 | 12 | no | — |
| 136 | #555 | C23 | 1 | 2 | yes | — |
| 137 | #554 | — | 2 | 6 | no | — |
| 138 | #554 | — | 2 | 6 | no | — |
| 139 | #554 | C23 | 1 | 6 | yes | — |
| 140 | #553 | — | 2 | 6 | no | — |
| 141 | #553 | — | 2 | 12 | no | — |
| 142 | #553 | — | 2 | 12 | no | — |
| 143 | #552 | — | 2 | 6 | no | — |
| 144 | #552 | — | 2 | 12 | no | — |
| 145 | #552 | — | 2 | 24 | no | — |
| 146 | #552 | — | 2 | 12 | no | — |
| 147 | #552 | C23 | 1 | 12 | yes | — |
| 148 | #551 | — | 2 | 12 | no | — |
| 149 | #551 | — | 2 | 24 | no | — |
| 150 | #550 | C23 | 1 | 2 | yes | — |
| 151 | D4×Q8 | — | 2 | 4 | no | — |
| 152 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 153 | D4×Q8 | C23 | 1 | 2 | yes | — |
| 154 | #548 | — | 2 | 4 | no | — |
| 155 | #548 | — | 2 | 2 | no | — |
| 156 | #548 | C23 | 1 | 24 | yes | — |
| 157 | #547 | — | 2 | 12 | no | — |
| 158 | #547 | C23 | 1 | 6 | yes | — |
| 159 | #547 | C23 | 1 | 6 | yes | — |
| 160 | #546 | — | 2 | 12 | no | — |
| 161 | #546 | — | 2 | 6 | no | — |
| 162 | #546 | C23 | 1 | 12 | yes | — |
| 163 | D42 | C23 | 1 | 6 | yes | — |
| 164 | #544 | — | 2 | 6 | no | — |
| 165 | #542 | — | 2 | 12 | no | — |
| 166 | #542 | — | 2 | 12 | no | — |
| 167 | #541 | — | 2 | 12 | no | — |
| 168 | #539 | — | 2 | 12 | no | — |
| 169 | #538 | — | 2 | 24 | no | — |
| 170 | #537 | — | 2 | 6 | no | — |
| 171 | #536 | — | 2 | 6 | no | — |
| 172 | #533 | — | 2 | 12 | no | — |
| 173 | #533 | C23 | 1 | 6 | yes | — |
| 174 | #533 | C23 | 1 | 12 | yes | — |
| 175 | #532 | C23 | 1 | 12 | yes | — |
| 176 | #532 | C23 | 1 | 6 | yes | — |
| 177 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 178 | #529 | — | 2 | 12 | no | — |
| 179 | #529 | — | 2 | 24 | no | — |
| 180 | #529 | — | 2 | 12 | no | — |
| 181 | #529 | C23 | 1 | 12 | yes | — |
| 182 | #529 | C23 | 1 | 24 | yes | — |
| 183 | C2×#126 | — | 2 | 12 | no | — |
| 184 | C2×#124 | C23 | 1 | 12 | yes | — |
| 185 | #525 | — | 2 | 6 | no | — |
| 186 | #525 | — | 2 | 6 | no | — |
| 187 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 188 | #520 | — | 2 | 2 | no | — |
| 189 | #520 | — | 2 | 6 | no | — |
| 190 | #520 | — | 2 | 6 | no | — |
| 191 | #520 | D4 | 1 | 1 | yes | characteristic |
| 192 | #520 | D4 | 1 | 3 | yes | — |
| 193 | #520 | D4 | 1 | 6 | yes | — |
| 194 | #519 | — | 2 | 4 | no | — |
| 195 | #519 | D4 | 1 | 3 | yes | — |
| 196 | #519 | D4 | 1 | 2 | yes | — |
| 197 | #518 | — | 2 | 12 | no | — |
| 198 | C4×#41 | — | 2 | 4 | no | — |
| 199 | C4×#41 | — | 2 | 12 | no | — |
| 200 | C4×#41 | C23 | 1 | 12 | yes | — |
| 201 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 202 | C4×#41 | C23 | 1 | 3 | yes | — |
| 203 | C4×#41 | C23 | 1 | 6 | yes | — |
| 204 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 205 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 206 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 207 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 208 | C2×#117 | — | 2 | 6 | no | — |
| 209 | C2×#117 | — | 2 | 6 | no | — |
| 210 | #500 | C23 | 1 | 3 | yes | — |
| 211 | #500 | C23 | 1 | 1 | yes | characteristic |
| 212 | #499 | C23 | 1 | 6 | yes | — |
| 213 | #495 | C23 | 1 | 6 | yes | — |
| 214 | #495 | C23 | 1 | 24 | yes | — |
| 215 | #495 | C23 | 1 | 12 | yes | — |
| 216 | #495 | C23 | 1 | 12 | yes | — |
| 217 | #494 | C23 | 1 | 3 | yes | — |
| 218 | #494 | C23 | 1 | 6 | yes | — |
| 219 | #494 | C23 | 1 | 6 | yes | — |
| 220 | #494 | C23 | 1 | 6 | yes | — |
| 221 | #493 | C23 | 1 | 3 | yes | — |
| 222 | #492 | C23 | 1 | 12 | yes | — |
| 223 | #488 | C23 | 1 | 12 | yes | — |
| 224 | #488 | C23 | 1 | 24 | yes | — |
| 225 | #487 | C23 | 1 | 12 | yes | — |
| 226 | #487 | C23 | 1 | 6 | yes | — |
| 227 | #486 | C23 | 1 | 6 | yes | — |
| 228 | #485 | C23 | 1 | 12 | yes | — |
| 229 | #483 | C23 | 1 | 12 | yes | — |
| 230 | #482 | C23 | 1 | 4 | yes | — |
| 231 | #480 | C23 | 1 | 12 | yes | — |
| 232 | #479 | C23 | 1 | 12 | yes | — |
| 233 | #479 | C23 | 1 | 24 | yes | — |
| 234 | #478 | C23 | 1 | 12 | yes | — |
| 235 | #476 | C23 | 1 | 2 | yes | — |
| 236 | #476 | C23 | 1 | 6 | yes | — |
| 237 | #475 | C23 | 1 | 12 | yes | — |
| 238 | #474 | C23 | 1 | 6 | yes | — |
| 239 | #474 | C23 | 1 | 6 | yes | — |
| 240 | #467 | C23 | 1 | 6 | yes | — |
| 241 | #467 | C23 | 1 | 6 | yes | — |
| 242 | #467 | C23 | 1 | 12 | yes | — |
| 243 | #467 | C23 | 1 | 6 | yes | — |
| 244 | #466 | C23 | 1 | 6 | yes | — |
| 245 | #466 | C23 | 1 | 2 | yes | — |
| 246 | #466 | C23 | 1 | 6 | yes | — |
| 247 | #465 | C23 | 1 | 12 | yes | — |
| 248 | #465 | C23 | 1 | 24 | yes | — |
| 249 | #464 | C23 | 1 | 12 | yes | — |
| 250 | #464 | C23 | 1 | 24 | yes | — |
| 251 | #464 | C23 | 1 | 24 | yes | — |
| 252 | #464 | C23 | 1 | 24 | yes | — |
| 253 | #464 | C23 | 1 | 24 | yes | — |
| 254 | #463 | C23 | 1 | 12 | yes | — |
| 255 | #463 | C23 | 1 | 24 | yes | — |
| 256 | #462 | C23 | 1 | 12 | yes | — |
| 257 | #462 | C23 | 1 | 12 | yes | — |
| 258 | #461 | C23 | 1 | 6 | yes | — |
| 259 | #461 | C23 | 1 | 6 | yes | — |
| 260 | #461 | C23 | 1 | 12 | yes | — |
| 261 | #461 | C23 | 1 | 12 | yes | — |
| 262 | #461 | C23 | 1 | 12 | yes | — |
| 263 | #460 | C23 | 1 | 12 | yes | — |
| 264 | #459 | C23 | 1 | 6 | yes | — |
| 265 | #459 | C23 | 1 | 6 | yes | — |
| 266 | #452 | C23 | 1 | 12 | yes | — |
| 267 | #452 | C23 | 1 | 24 | yes | — |
| 268 | #451 | C23 | 1 | 24 | yes | — |
| 269 | #450 | C23 | 1 | 12 | yes | — |
| 270 | #449 | C23 | 1 | 12 | yes | — |
| 271 | #448 | C23 | 1 | 24 | yes | — |
| 272 | #447 | C23 | 1 | 12 | yes | — |
| 273 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 274 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 275 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 276 | C8×Q8 | C23 | 1 | 3 | yes | — |
| 277 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 278 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 279 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 280 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 281 | C8×Q8 | C23 | 1 | 3 | yes | — |
| 282 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 283 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 284 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 285 | C4×Q16 | C23 | 1 | 24 | yes | — |
| 286 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 287 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 288 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 289 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 290 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 291 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 292 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 293 | C4×D8 | C23 | 1 | 3 | yes | — |
| 294 | C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 295 | C4×D8 | C23 | 1 | 6 | yes | — |
| 296 | C4×D8 | C23 | 1 | 6 | yes | — |
| 297 | C4×D8 | C23 | 1 | 6 | yes | — |
| 298 | C4×D8 | C23 | 1 | 3 | yes | — |
| 299 | C4×D8 | C23 | 1 | 3 | yes | — |
| 300 | C4×D8 | C23 | 1 | 6 | yes | — |
| 301 | C8×D4 | C23 | 1 | 3 | yes | — |
| 302 | C8×D4 | C23 | 1 | 6 | yes | — |
| 303 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 304 | C8×D4 | C23 | 1 | 3 | yes | — |
| 305 | C8×D4 | C23 | 1 | 6 | yes | — |
| 306 | C8×D4 | C23 | 1 | 12 | yes | — |
| 307 | C8×D4 | C23 | 1 | 3 | yes | — |
| 308 | C8×D4 | C23 | 1 | 6 | yes | — |
| 309 | #431 | C23 | 1 | 3 | yes | — |
| 310 | #431 | C23 | 1 | 3 | yes | — |
| 311 | #431 | C23 | 1 | 6 | yes | — |
| 312 | #431 | C23 | 1 | 6 | yes | — |
| 313 | #431 | C23 | 1 | 12 | yes | — |
| 314 | #427 | C23 | 1 | 2 | yes | — |
| 315 | C2×#107 | C23 | 1 | 3 | yes | — |
| 316 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 317 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 318 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 319 | #416 | C23 | 1 | 12 | yes | — |
| 320 | C2×#103 | C23 | 1 | 12 | yes | — |
| 321 | C2×#102 | C23 | 1 | 6 | yes | — |
| 322 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 323 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 324 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 325 | 2−1+4 | — | 2 | 8 | no | — |
| 326 | C2×#41 | — | 2 | 2 | no | — |
| 327 | C2×#41 | — | 2 | 6 | no | — |
| 328 | C2×#41 | — | 2 | 6 | no | — |
| 329 | C2×#41 | — | 4 | 16 | no | — |
| 330 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 331 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 332 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | C2×#41 | C24 | 1 | 12 | yes | — |
| 334 | C22×Q8 | — | 2 | 2 | no | — |
| 335 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 336 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 337 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 338 | C22×D4 | — | 2 | 6 | no | — |
| 339 | C22×D4 | C24 | 1 | 6 | yes | — |
| 340 | C23×C4 | — | 2 | 6 | no | — |
| 341 | #135 | — | 4 | 12 | no | — |
| 342 | #135 | — | 8 | 12 | no | — |
| 343 | C2×Q16 | — | 4 | 12 | no | — |
| 344 | C2×Q16 | — | 8 | 6 | no | — |
| 345 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 346 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 347 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 348 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 349 | C2×SD16 | — | 8 | 12 | no | — |
| 350 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 351 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 352 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 353 | C2×D8 | — | 4 | 6 | no | — |
| 354 | C2×D8 | C24 | 1 | 1 | yes | characteristic |
| 355 | C2×D8 | C24 | 1 | 3 | yes | — |
| 356 | C2×D8 | C24 | 1 | 6 | yes | — |
| 357 | C2×D8 | C24 | 1 | 6 | yes | — |
| 358 | C22×C8 | C24 | 1 | 3 | yes | — |
| 359 | C22×C8 | C24 | 1 | 2 | yes | — |
| 360 | C22×C8 | C24 | 1 | 6 | yes | — |
| 361 | C22×C8 | C24 | 1 | 3 | yes | — |
| 362 | C22×C8 | C24 | 1 | 6 | yes | — |
| 363 | C4⋊Q8 | — | 2 | 12 | no | — |
| 364 | C4⋊Q8 | — | 2 | 12 | no | — |
| 365 | C4⋊Q8 | — | 2 | 6 | no | — |
| 366 | C4⋊Q8 | — | 2 | 6 | no | — |
| 367 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 368 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 369 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 370 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 371 | #127 | C24 | 1 | 6 | yes | — |
| 372 | #126 | — | 2 | 12 | no | — |
| 373 | #126 | — | 2 | 24 | no | — |
| 374 | #126 | — | 2 | 24 | no | — |
| 375 | #126 | — | 2 | 24 | no | — |
| 376 | #126 | — | 2 | 12 | no | — |
| 377 | #126 | — | 2 | 24 | no | — |
| 378 | #126 | — | 2 | 12 | no | — |
| 379 | #125 | — | 2 | 12 | no | — |
| 380 | #125 | — | 2 | 24 | no | — |
| 381 | #125 | — | 2 | 12 | no | — |
| 382 | #125 | — | 2 | 12 | no | — |
| 383 | #125 | — | 2 | 6 | no | — |
| 384 | #125 | C24 | 1 | 12 | yes | — |
| 385 | #124 | — | 2 | 12 | no | — |
| 386 | #124 | — | 2 | 4 | no | — |
| 387 | #124 | — | 2 | 24 | no | — |
| 388 | #124 | — | 2 | 24 | no | — |
| 389 | #124 | — | 2 | 6 | no | — |
| 390 | #124 | C24 | 1 | 12 | yes | — |
| 391 | #124 | C24 | 1 | 24 | yes | — |
| 392 | #123 | — | 2 | 12 | no | — |
| 393 | #123 | — | 2 | 24 | no | — |
| 394 | #123 | — | 2 | 12 | no | — |
| 395 | #123 | — | 2 | 24 | no | — |
| 396 | #123 | — | 2 | 12 | no | — |
| 397 | #123 | — | 2 | 12 | no | — |
| 398 | #123 | — | 2 | 12 | no | — |
| 399 | C22⋊Q8 | — | 2 | 6 | no | — |
| 400 | C22⋊Q8 | — | 2 | 12 | no | — |
| 401 | C22⋊Q8 | — | 2 | 12 | no | — |
| 402 | C22⋊Q8 | — | 2 | 12 | no | — |
| 403 | C22⋊Q8 | — | 2 | 6 | no | — |
| 404 | C22⋊Q8 | — | 2 | 12 | no | — |
| 405 | C22⋊Q8 | — | 2 | 6 | no | — |
| 406 | C22⋊Q8 | — | 2 | 6 | no | — |
| 407 | C22⋊Q8 | — | 2 | 6 | no | — |
| 408 | C22⋊Q8 | — | 2 | 12 | no | — |
| 409 | C22⋊Q8 | — | 2 | 24 | no | — |
| 410 | C22⋊Q8 | — | 2 | 24 | no | — |
| 411 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 412 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 413 | #121 | — | 2 | 2 | no | — |
| 414 | #121 | — | 2 | 6 | no | — |
| 415 | #121 | — | 2 | 24 | no | — |
| 416 | #121 | — | 2 | 12 | no | — |
| 417 | #121 | — | 2 | 12 | no | — |
| 418 | #121 | — | 2 | 6 | no | — |
| 419 | #121 | — | 2 | 6 | no | — |
| 420 | #121 | — | 2 | 6 | no | — |
| 421 | #121 | — | 2 | 12 | no | — |
| 422 | #121 | C24 | 1 | 4 | yes | — |
| 423 | #121 | C24 | 1 | 12 | yes | — |
| 424 | #120 | — | 2 | 12 | no | — |
| 425 | #120 | — | 2 | 12 | no | — |
| 426 | C4×Q8 | — | 2 | 4 | no | — |
| 427 | C4×Q8 | — | 2 | 12 | no | — |
| 428 | C4×Q8 | — | 2 | 24 | no | — |
| 429 | C4×Q8 | — | 2 | 12 | no | — |
| 430 | C4×Q8 | — | 2 | 6 | no | — |
| 431 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 432 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 433 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 434 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 435 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 436 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 437 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 438 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 439 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 440 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 441 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 442 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 443 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 444 | C4×D4 | — | 2 | 12 | no | — |
| 445 | C4×D4 | — | 2 | 24 | no | — |
| 446 | C4×D4 | — | 2 | 12 | no | — |
| 447 | C4×D4 | — | 2 | 12 | no | — |
| 448 | C4×D4 | — | 2 | 12 | no | — |
| 449 | C4×D4 | — | 2 | 12 | no | — |
| 450 | C4×D4 | — | 2 | 24 | no | — |
| 451 | C4×D4 | — | 2 | 6 | no | — |
| 452 | C4×D4 | — | 2 | 6 | no | — |
| 453 | C4×D4 | — | 2 | 12 | no | — |
| 454 | C4×D4 | — | 2 | 6 | no | — |
| 455 | C4×D4 | — | 2 | 12 | no | — |
| 456 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 457 | C4×D4 | C2×D4 | 1 | 12 | yes | — |
| 458 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 459 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 460 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 461 | C4×D4 | C24 | 1 | 2 | yes | — |
| 462 | C4×D4 | C24 | 1 | 6 | yes | — |
| 463 | C4×D4 | C24 | 1 | 6 | yes | — |
| 464 | C4×D4 | C24 | 1 | 6 | yes | — |
| 465 | C4×D4 | C24 | 1 | 12 | yes | — |
| 466 | C4×D4 | C24 | 1 | 3 | yes | — |
| 467 | C4×D4 | C24 | 1 | 6 | yes | — |
| 468 | C4×D4 | C24 | 1 | 1 | yes | characteristic |
| 469 | #117 | — | 2 | 6 | no | — |
| 470 | #117 | — | 2 | 12 | no | — |
| 471 | #117 | — | 2 | 2 | no | — |
| 472 | #117 | — | 2 | 6 | no | — |
| 473 | #117 | — | 2 | 12 | no | — |
| 474 | #117 | — | 2 | 12 | no | — |
| 475 | #117 | — | 2 | 12 | no | — |
| 476 | #117 | — | 2 | 12 | no | — |
| 477 | #117 | — | 2 | 12 | no | — |
| 478 | #117 | — | 2 | 12 | no | — |
| 479 | #117 | — | 2 | 24 | no | — |
| 480 | #117 | C2×D4 | 1 | 3 | yes | — |
| 481 | #117 | C2×D4 | 1 | 3 | yes | — |
| 482 | #117 | C2×D4 | 1 | 6 | yes | — |
| 483 | #117 | C2×D4 | 1 | 12 | yes | — |
| 484 | #117 | C2×D4 | 1 | 6 | yes | — |
| 485 | #117 | C24 | 1 | 4 | yes | — |
| 486 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 487 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 488 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 489 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 490 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 491 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 492 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 493 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 494 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 495 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 496 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 497 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 498 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 499 | C2×C42 | — | 2 | 12 | no | — |
| 500 | C2×C42 | — | 2 | 12 | no | — |
| 501 | C2×C42 | C24 | 1 | 3 | yes | — |
| 502 | C2×C42 | C24 | 1 | 6 | yes | — |
| 503 | C2×C42 | C24 | 1 | 6 | yes | — |
| 504 | #107 | C24 | 1 | 1 | yes | characteristic |
| 505 | #107 | C24 | 1 | 3 | yes | — |
| 506 | #107 | C24 | 1 | 6 | yes | — |
| 507 | #107 | C24 | 1 | 2 | yes | — |
| 508 | #107 | C24 | 1 | 6 | yes | — |
| 509 | #107 | C24 | 1 | 2 | yes | — |
| 510 | #106 | C24 | 1 | 4 | yes | — |
| 511 | #106 | C24 | 1 | 12 | yes | — |
| 512 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 513 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 514 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 515 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 516 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 517 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 518 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 519 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 520 | #103 | C24 | 1 | 12 | yes | — |
| 521 | #103 | C24 | 1 | 24 | yes | — |
| 522 | #103 | C24 | 1 | 12 | yes | — |
| 523 | #103 | C24 | 1 | 12 | yes | — |
| 524 | #103 | C24 | 1 | 12 | yes | — |
| 525 | #102 | C24 | 1 | 2 | yes | — |
| 526 | #102 | C24 | 1 | 6 | yes | — |
| 527 | #102 | C24 | 1 | 6 | yes | — |
| 528 | #102 | C24 | 1 | 6 | yes | — |
| 529 | #102 | C24 | 1 | 12 | yes | — |
| 530 | #102 | C24 | 1 | 12 | yes | — |
| 531 | #102 | C24 | 1 | 4 | yes | — |
| 532 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 533 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 534 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 535 | C22⋊C8 | C24 | 1 | 2 | yes | — |
| 536 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 537 | C4×C8 | C24 | 1 | 3 | yes | — |
| 538 | C4×C8 | C24 | 1 | 6 | yes | — |
| 539 | C4×C8 | C24 | 1 | 3 | yes | — |
| 540 | C4×C8 | C24 | 1 | 3 | yes | — |
| 541 | C4×C8 | C24 | 1 | 6 | yes | — |
| 542 | C4×C8 | C24 | 1 | 12 | yes | — |
| 543 | C4×C8 | C24 | 1 | 6 | yes | — |
| 544 | C24 | — | 2 | 6 | no | — |
| 545 | #41 | — | 2 | 24 | no | — |
| 546 | #41 | — | 2 | 12 | no | — |
| 547 | #41 | — | 4 | 12 | no | — |
| 548 | #41 | — | 4 | 12 | no | — |
| 549 | #41 | — | 4 | 8 | no | — |
| 550 | #41 | — | 4 | 24 | no | — |
| 551 | #41 | — | 4 | 24 | no | — |
| 552 | #41 | #135 | 1 | 8 | yes | complemented |
| 553 | C2×Q8 | — | 2 | 8 | no | — |
| 554 | C2×Q8 | — | 2 | 12 | no | — |
| 555 | C2×Q8 | — | 2 | 6 | no | — |
| 556 | C2×Q8 | — | 2 | 2 | no | — |
| 557 | C2×Q8 | — | 2 | 12 | no | — |
| 558 | C2×Q8 | — | 4 | 12 | no | — |
| 559 | C2×Q8 | — | 4 | 12 | no | — |
| 560 | C2×Q8 | — | 4 | 8 | no | — |
| 561 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 562 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 563 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 564 | C2×Q8 | C25 | 1 | 12 | yes | — |
| 565 | C2×D4 | — | 2 | 12 | no | — |
| 566 | C2×D4 | — | 2 | 4 | no | — |
| 567 | C2×D4 | — | 2 | 12 | no | — |
| 568 | C2×D4 | — | 2 | 6 | no | — |
| 569 | C2×D4 | — | 2 | 6 | no | — |
| 570 | C2×D4 | — | 2 | 6 | no | — |
| 571 | C2×D4 | — | 4 | 6 | no | — |
| 572 | C2×D4 | — | 4 | 6 | no | — |
| 573 | C2×D4 | — | 4 | 24 | no | — |
| 574 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 575 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 576 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 577 | C2×D4 | C25 | 1 | 2 | yes | — |
| 578 | C2×D4 | C25 | 1 | 6 | yes | — |
| 579 | C22×C4 | — | 2 | 6 | no | — |
| 580 | C22×C4 | — | 2 | 12 | no | — |
| 581 | C22×C4 | — | 2 | 6 | no | — |
| 582 | C22×C4 | — | 2 | 6 | no | — |
| 583 | C22×C4 | — | 2 | 2 | no | — |
| 584 | C22×C4 | — | 2 | 6 | no | — |
| 585 | C22×C4 | — | 2 | 12 | no | — |
| 586 | C22×C4 | — | 2 | 12 | no | — |
| 587 | C22×C4 | — | 4 | 24 | no | — |
| 588 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 589 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 590 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 591 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 592 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 593 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 594 | C22×C4 | C25 | 1 | 3 | yes | — |
| 595 | C22×C4 | C25 | 1 | 2 | yes | — |
| 596 | Q16 | — | 2 | 12 | no | — |
| 597 | Q16 | — | 4 | 12 | no | — |
| 598 | Q16 | — | 4 | 6 | no | — |
| 599 | Q16 | — | 4 | 12 | no | — |
| 600 | SD16 | — | 4 | 12 | no | — |
| 601 | SD16 | — | 4 | 24 | no | — |
| 602 | SD16 | — | 4 | 12 | no | — |
| 603 | D8 | — | 2 | 2 | no | — |
| 604 | D8 | — | 2 | 6 | no | — |
| 605 | D8 | — | 4 | 6 | no | — |
| 606 | D8 | — | 4 | 6 | no | — |
| 607 | C2×C8 | — | 2 | 6 | no | — |
| 608 | C2×C8 | — | 2 | 4 | no | — |
| 609 | C2×C8 | — | 4 | 6 | no | — |
| 610 | C2×C8 | — | 4 | 3 | no | — |
| 611 | C2×C8 | — | 4 | 6 | no | — |
| 612 | C2×C8 | C25 | 1 | 3 | yes | — |
| 613 | C2×C8 | C25 | 1 | 2 | yes | — |
| 614 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 615 | C2×C8 | C25 | 1 | 3 | yes | — |
| 616 | C2×C8 | C25 | 1 | 6 | yes | — |
| 617 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 618 | C4⋊C4 | — | 2 | 2 | no | — |
| 619 | C4⋊C4 | — | 2 | 6 | no | — |
| 620 | C4⋊C4 | — | 2 | 12 | no | — |
| 621 | C4⋊C4 | — | 2 | 6 | no | — |
| 622 | C4⋊C4 | — | 2 | 12 | no | — |
| 623 | C4⋊C4 | — | 2 | 12 | no | — |
| 624 | C4⋊C4 | — | 2 | 12 | no | — |
| 625 | C4⋊C4 | — | 2 | 12 | no | — |
| 626 | C4⋊C4 | — | 2 | 24 | no | — |
| 627 | C4⋊C4 | — | 2 | 6 | no | — |
| 628 | C4⋊C4 | — | 2 | 6 | no | — |
| 629 | C4⋊C4 | — | 2 | 12 | no | — |
| 630 | C4⋊C4 | — | 2 | 12 | no | — |
| 631 | C4⋊C4 | — | 2 | 12 | no | — |
| 632 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 633 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 634 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 635 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 636 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 637 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 638 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 639 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 640 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 641 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 642 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 643 | C22⋊C4 | — | 2 | 12 | no | — |
| 644 | C22⋊C4 | — | 2 | 12 | no | — |
| 645 | C22⋊C4 | — | 2 | 4 | no | — |
| 646 | C22⋊C4 | — | 2 | 12 | no | — |
| 647 | C22⋊C4 | — | 2 | 4 | no | — |
| 648 | C22⋊C4 | — | 2 | 2 | no | — |
| 649 | C22⋊C4 | — | 2 | 12 | no | — |
| 650 | C22⋊C4 | — | 2 | 24 | no | — |
| 651 | C22⋊C4 | — | 2 | 6 | no | — |
| 652 | C22⋊C4 | — | 2 | 24 | no | — |
| 653 | C22⋊C4 | — | 2 | 6 | no | — |
| 654 | C22⋊C4 | — | 2 | 6 | no | — |
| 655 | C22⋊C4 | — | 2 | 12 | no | — |
| 656 | C22⋊C4 | — | 2 | 12 | no | — |
| 657 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 658 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 659 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 660 | C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 661 | C42 | — | 2 | 4 | no | — |
| 662 | C42 | — | 2 | 12 | no | — |
| 663 | C42 | — | 2 | 24 | no | — |
| 664 | C42 | — | 2 | 12 | no | — |
| 665 | C42 | C22×D4 | 1 | 6 | yes | — |
| 666 | C42 | C22×D4 | 1 | 6 | yes | — |
| 667 | C42 | C22×D4 | 1 | 12 | yes | — |
| 668 | C42 | C22×D4 | 1 | 3 | yes | — |
| 669 | C42 | C22×D4 | 1 | 3 | yes | — |
| 670 | C42 | C25 | 1 | 1 | yes | characteristic |
| 671 | C42 | C25 | 1 | 3 | yes | — |
| 672 | C42 | C25 | 1 | 6 | yes | — |
| 673 | C23 | — | 2 | 2 | no | — |
| 674 | C23 | — | 2 | 6 | no | — |
| 675 | C23 | — | 4 | 12 | no | — |
| 676 | C23 | — | 8 | 6 | no | — |
| 677 | C23 | — | 8 | 6 | no | — |
| 678 | C23 | C23×D4 | 1 | 2 | yes | — |
| 679 | C23 | C23×D4 | 1 | 3 | yes | — |
| 680 | Q8 | — | 2 | 12 | no | — |
| 681 | Q8 | — | 2 | 6 | no | — |
| 682 | Q8 | — | 2 | 12 | no | — |
| 683 | Q8 | — | 2 | 12 | no | — |
| 684 | Q8 | — | 4 | 12 | no | — |
| 685 | Q8 | — | 8 | 2 | no | — |
| 686 | Q8 | — | 8 | 12 | no | — |
| 687 | Q8 | C2×#135 | 1 | 4 | yes | — |
| 688 | D4 | — | 2 | 12 | no | — |
| 689 | D4 | — | 2 | 2 | no | — |
| 690 | D4 | — | 2 | 6 | no | — |
| 691 | D4 | — | 2 | 6 | no | — |
| 692 | D4 | — | 2 | 2 | no | — |
| 693 | D4 | — | 2 | 2 | no | — |
| 694 | D4 | — | 4 | 24 | no | — |
| 695 | D4 | — | 4 | 12 | no | — |
| 696 | D4 | — | 8 | 6 | no | — |
| 697 | D4 | — | 8 | 6 | no | — |
| 698 | D4 | — | 8 | 4 | no | — |
| 699 | D4 | — | 8 | 12 | no | — |
| 700 | D4 | C2×#135 | 1 | 12 | yes | — |
| 701 | C2×C4 | — | 2 | 12 | no | — |
| 702 | C2×C4 | — | 2 | 3 | no | — |
| 703 | C2×C4 | — | 2 | 2 | no | — |
| 704 | C2×C4 | — | 2 | 3 | no | — |
| 705 | C2×C4 | — | 2 | 2 | no | — |
| 706 | C2×C4 | — | 2 | 12 | no | — |
| 707 | C2×C4 | — | 2 | 2 | no | — |
| 708 | C2×C4 | — | 2 | 4 | no | — |
| 709 | C2×C4 | — | 2 | 12 | no | — |
| 710 | C2×C4 | — | 2 | 6 | no | — |
| 711 | C2×C4 | — | 4 | 6 | no | — |
| 712 | C2×C4 | — | 4 | 6 | no | — |
| 713 | C2×C4 | — | 4 | 3 | no | — |
| 714 | C2×C4 | — | 4 | 12 | no | — |
| 715 | C2×C4 | — | 4 | 4 | no | — |
| 716 | C2×C4 | — | 4 | 12 | no | — |
| 717 | C2×C4 | — | 4 | 12 | no | — |
| 718 | C2×C4 | — | 4 | 12 | no | — |
| 719 | C2×C4 | — | 8 | 12 | no | — |
| 720 | C2×C4 | — | 8 | 12 | no | — |
| 721 | C2×C4 | — | 8 | 12 | no | — |
| 722 | C2×C4 | C2×#135 | 1 | 12 | yes | — |
| 723 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 724 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 725 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 726 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 727 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 728 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 729 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 730 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 731 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 732 | C8 | — | 2 | 3 | no | — |
| 733 | C8 | — | 2 | 2 | no | — |
| 734 | C8 | — | 2 | 3 | no | — |
| 735 | C8 | — | 2 | 6 | no | — |
| 736 | C8 | — | 2 | 1 | no | — |
| 737 | C8 | #585 | 1 | 2 | yes | — |
| 738 | C22 | — | 2 | 3 | no | — |
| 739 | C22 | — | 2 | 3 | no | — |
| 740 | C22 | — | 2 | 2 | no | — |
| 741 | C22 | — | 2 | 2 | no | — |
| 742 | C22 | — | 2 | 2 | no | — |
| 743 | C22 | — | 4 | 6 | no | — |
| 744 | C22 | — | 4 | 2 | no | — |
| 745 | C22 | — | 4 | 2 | no | — |
| 746 | C22 | — | 4 | 6 | no | — |
| 747 | C22 | — | 4 | 6 | no | — |
| 748 | C22 | — | 4 | 2 | no | — |
| 749 | C22 | — | 16 | 12 | no | — |
| 750 | C22 | C22×#135 | 1 | 6 | yes | — |
| 751 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 752 | C4 | — | 2 | 2 | no | — |
| 753 | C4 | — | 2 | 3 | no | — |
| 754 | C4 | — | 2 | 6 | no | — |
| 755 | C4 | — | 2 | 6 | no | — |
| 756 | C4 | — | 2 | 3 | no | — |
| 757 | C4 | — | 2 | 1 | no | — |
| 758 | C4 | — | 4 | 12 | no | — |
| 759 | C4 | — | 4 | 2 | no | — |
| 760 | C4 | — | 4 | 6 | no | — |
| 761 | C4 | — | 4 | 4 | no | — |
| 762 | C4 | C22×#135 | 1 | 6 | yes | — |
| 763 | C4 | C22×#135 | 1 | 2 | yes | — |
| 764 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 765 | C4 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 766 | C2 | — | 2 | 6 | no | — |
| 767 | C2 | — | 4 | 2 | no | — |
| 768 | C2 | — | 8 | 6 | no | — |
| 769 | C2 | — | 8 | 2 | no | — |
| 770 | C2 | #63003 | 1 | 1 | yes | characteristic |
| 771 | C2 | C23×#135 | 1 | 1 | yes | characteristic |
| 772 | C2 | #63093 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×2−1+4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63009 | C2 | semidirect |
| 2. #62419 | C2 | semidirect |
| 3. #62418 | C2 | semidirect |
| 4. #62416 | C2 | semidirect |
| 5. #62364 | C2 | semidirect |
| 6. #62361 | C2 | semidirect |
| 7. #61956 | C2 | semidirect |
| 8. #61950 | C2 | semidirect |
| 9. #61948 | C2 | semidirect |
| 10. #61887 | C2 | semidirect |
| 11. #61882 | C2 | semidirect |
| 12. #61433 | C2 | semidirect |
| 13. #61427 | C2 | semidirect |
| 14. D8×#41 | C2 | semidirect |
| 15. #61393 | C2 | semidirect |
| 16. C2×#3393 | C2 | semidirect |
| 17. C8×2−1+4 | C2 | semidirect |
| 18. #3523 | C22 | semidirect |
| 21. #3514 | C22 | semidirect |
| 22. #3511 | C22 | semidirect |
| 23. #3507 | C22 | semidirect |
| 28. #3482 | C22 | semidirect |
| 29. #3480 | C22 | semidirect |
| 30. #3475 | C22 | semidirect |
| 31. C2×#556 | C22 | semidirect |
| 35. #3396 | C22 | semidirect |
| 36. #3395 | C22 | semidirect |
| 37. #3395 | C22 | semidirect |
| 38. #3394 | C22 | semidirect |
| 39. #3394 | C22 | semidirect |
| 42. #3393 | C22 | semidirect |
| 43. #3393 | C22 | semidirect |
| 44. #3393 | C22 | semidirect |
| 45. #3393 | C22 | semidirect |
| 46. #3393 | C22 | semidirect |
| 47. #3392 | C22 | semidirect |
| 49. #3383 | C22 | semidirect |
| 50. #3380 | C22 | semidirect |
| 52. #3365 | C22 | semidirect |
| 53. #3364 | C22 | semidirect |
| 54. #3364 | C22 | semidirect |
| 55. #3360 | C22 | semidirect |
| 56. #3360 | C22 | semidirect |
| 57. #3359 | C22 | semidirect |
| 60. #3336 | C22 | semidirect |
| 62. #3303 | C22 | semidirect |
| 63. #3300 | C22 | semidirect |
| 64. #3298 | C22 | semidirect |
| 65. #3296 | C22 | semidirect |
| 67. D4×Q16 | C22 | semidirect |
| 68. D4×Q16 | C22 | semidirect |
| 69. #3285 | C22 | semidirect |
| 70. #3285 | C22 | semidirect |
| 71. #3283 | C22 | semidirect |
| 72. #3283 | C22 | semidirect |
| 73. #3282 | C22 | semidirect |
| 74. D4×SD16 | C22 | semidirect |
| 77. #3250 | C22 | semidirect |
| 78. #3248 | C22 | semidirect |
| 79. #3246 | C22 | semidirect |
| 80. #3212 | C22 | semidirect |
| 81. #3211 | C22 | semidirect |
| 82. #3210 | C22 | semidirect |
| 83. #3209 | C22 | semidirect |
| 84. #3206 | C22 | semidirect |
| 85. #3170 | C22 | semidirect |
| 86. #3170 | C22 | semidirect |
| 89. #3168 | C22 | semidirect |
| 90. #3147 | C22 | semidirect |
| 92. C2×#494 | C22 | semidirect |
| 93. #3108 | C22 | semidirect |
| 94. #3107 | C22 | semidirect |
| 95. #3102 | C22 | semidirect |
| 96. #3101 | C22 | semidirect |
| 98. #3035 | C22 | semidirect |
| 99. C2×#464 | C22 | semidirect |
| 100. C2×#461 | C22 | semidirect |
| 102. #2988 | C22 | semidirect |
| 103. #2988 | C22 | semidirect |
| 104. #2982 | C22 | semidirect |
| 105. #2982 | C22 | semidirect |
| 107. C8×#41 | C22 | semidirect |
| 108. C8×#41 | C22 | semidirect |
| 109. C2×C8×Q8 | C22 | semidirect |
| 110. C2×C8×Q8 | C22 | semidirect |
| 111. C4×#135 | C22 | semidirect |
| 112. C2×C4×Q16 | C22 | semidirect |
| 552. #41 | #135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63009 | 2 |
| #62419 | 2 |
| #62418 | 2 |
| #62416 | 2 |
| #62364 | 2 |
| #62361 | 2 |
| #61956 | 2 |
| #61950 | 2 |
| #61948 | 2 |
| #61887 | 2 |
| #61882 | 2 |
| #61433 | 2 |
| #61427 | 2 |
| D8×#41 | 2 |
| #61393 | 2 |
| C2×#3393 | 2 |
| C8×2−1+4 | 2 |