Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6020 conjugacy classes of subgroups.
The subgroup lattice has 816 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62999 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #62589 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #62540 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #62394 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #62357 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #62153 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #62114 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #62002 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #61964 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #61906 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #61883 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #61846 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #61821 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #61469 | C2 | 1 | 4 | yes | maximal, complemented |
| 16 | #61440 | C2 | 1 | 6 | yes | maximal, complemented |
| 17 | #61322 | C2 | 1 | 4 | yes | maximal, complemented |
| 18 | C2×#3363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #60333 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #3522 | — | 2 | 4 | no | — |
| 21 | #3522 | C22 | 1 | 4 | yes | — |
| 22 | #3518 | — | 2 | 4 | no | — |
| 23 | #3518 | C22 | 1 | 4 | yes | — |
| 24 | #3511 | — | 2 | 6 | no | — |
| 25 | #3511 | C22 | 1 | 6 | yes | — |
| 26 | #3504 | — | 2 | 6 | no | — |
| 27 | #3504 | — | 2 | 4 | no | — |
| 28 | #3503 | C22 | 1 | 6 | yes | — |
| 29 | #3503 | C22 | 1 | 4 | yes | — |
| 30 | #3502 | — | 2 | 1 | no | — |
| 31 | #3502 | — | 2 | 4 | no | — |
| 32 | #3502 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3502 | C22 | 1 | 4 | yes | — |
| 34 | #3497 | — | 2 | 1 | no | — |
| 35 | #3497 | C22 | 1 | 1 | yes | characteristic |
| 36 | #3483 | C22 | 1 | 4 | yes | — |
| 37 | #3480 | C22 | 1 | 6 | yes | — |
| 38 | Q8×#41 | C22 | 1 | 4 | yes | — |
| 39 | Q8×#41 | C22 | 1 | 6 | yes | — |
| 40 | Q8×#41 | C22 | 1 | 4 | yes | — |
| 41 | C2×Q82 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#557 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#557 | C22 | 1 | 4 | yes | — |
| 44 | C4×2−1+4 | — | 2 | 1 | no | — |
| 45 | C4×2−1+4 | — | 2 | 1 | no | — |
| 46 | C4×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 47 | #3400 | C22 | 1 | 6 | yes | — |
| 48 | #3400 | C22 | 1 | 12 | yes | — |
| 49 | #3392 | C22 | 1 | 4 | yes | — |
| 50 | #3392 | C22 | 1 | 4 | yes | — |
| 51 | #3392 | C22 | 1 | 4 | yes | — |
| 52 | #3387 | C22 | 1 | 6 | yes | — |
| 53 | #3385 | C22 | 1 | 12 | yes | — |
| 54 | Q8×Q16 | C22 | 1 | 4 | yes | — |
| 55 | Q8×Q16 | C22 | 1 | 4 | yes | — |
| 56 | Q8×SD16 | C22 | 1 | 4 | yes | — |
| 57 | #3375 | C22 | 1 | 6 | yes | — |
| 58 | #3374 | C22 | 1 | 6 | yes | — |
| 59 | #3374 | C22 | 1 | 12 | yes | — |
| 60 | #3372 | C22 | 1 | 12 | yes | — |
| 61 | #3372 | C22 | 1 | 12 | yes | — |
| 62 | #3372 | C22 | 1 | 12 | yes | — |
| 63 | #3363 | C22 | 1 | 4 | yes | — |
| 64 | #3363 | C22 | 1 | 4 | yes | — |
| 65 | #3363 | C22 | 1 | 4 | yes | — |
| 66 | #3363 | C22 | 1 | 4 | yes | — |
| 67 | #3363 | C22 | 1 | 4 | yes | — |
| 68 | #3363 | C22 | 1 | 4 | yes | — |
| 69 | #3362 | C22 | 1 | 4 | yes | — |
| 70 | #3359 | C22 | 1 | 4 | yes | — |
| 71 | #3359 | C22 | 1 | 4 | yes | — |
| 72 | #3359 | C22 | 1 | 4 | yes | — |
| 73 | #3357 | C22 | 1 | 12 | yes | — |
| 74 | #3356 | C22 | 1 | 6 | yes | — |
| 75 | #3346 | C22 | 1 | 12 | yes | — |
| 76 | #3333 | C22 | 1 | 6 | yes | — |
| 77 | #3329 | C22 | 1 | 12 | yes | — |
| 78 | #3329 | C22 | 1 | 12 | yes | — |
| 79 | #3329 | C22 | 1 | 12 | yes | — |
| 80 | #3328 | C22 | 1 | 6 | yes | — |
| 81 | #3328 | C22 | 1 | 12 | yes | — |
| 82 | #3320 | C22 | 1 | 12 | yes | — |
| 83 | #3320 | C22 | 1 | 24 | yes | — |
| 84 | #3316 | C22 | 1 | 4 | yes | — |
| 85 | #3278 | C22 | 1 | 6 | yes | — |
| 86 | #3278 | C22 | 1 | 12 | yes | — |
| 87 | #3270 | C22 | 1 | 12 | yes | — |
| 88 | #3254 | C22 | 1 | 12 | yes | — |
| 89 | #3252 | C22 | 1 | 12 | yes | — |
| 90 | #3246 | C22 | 1 | 6 | yes | — |
| 91 | #3237 | C22 | 1 | 12 | yes | — |
| 92 | #3231 | C22 | 1 | 12 | yes | — |
| 93 | #3230 | C22 | 1 | 6 | yes | — |
| 94 | #3218 | C22 | 1 | 12 | yes | — |
| 95 | #3206 | C22 | 1 | 6 | yes | — |
| 96 | #3206 | C22 | 1 | 12 | yes | — |
| 97 | #3182 | C22 | 1 | 12 | yes | — |
| 98 | #3172 | C22 | 1 | 12 | yes | — |
| 99 | #3167 | C22 | 1 | 6 | yes | — |
| 100 | #3139 | C22 | 1 | 12 | yes | — |
| 101 | C2×#487 | C22 | 1 | 3 | yes | — |
| 102 | #3116 | C22 | 1 | 12 | yes | — |
| 103 | #3112 | C22 | 1 | 12 | yes | — |
| 104 | #3108 | C22 | 1 | 12 | yes | — |
| 105 | #3107 | C22 | 1 | 12 | yes | — |
| 106 | #3104 | C22 | 1 | 6 | yes | — |
| 107 | #3103 | C22 | 1 | 6 | yes | — |
| 108 | #3078 | C22 | 1 | 12 | yes | — |
| 109 | C2×#477 | C22 | 1 | 3 | yes | — |
| 110 | #3039 | C22 | 1 | 12 | yes | — |
| 111 | C2×#462 | C22 | 1 | 3 | yes | — |
| 112 | #2991 | C22 | 1 | 4 | yes | — |
| 113 | #2989 | C22 | 1 | 6 | yes | — |
| 114 | #2984 | C22 | 1 | 4 | yes | — |
| 115 | #2982 | C22 | 1 | 1 | yes | characteristic |
| 116 | #2971 | C22 | 1 | 4 | yes | — |
| 117 | #2965 | C22 | 1 | 6 | yes | — |
| 118 | Q8×M16 | C22 | 1 | 4 | yes | — |
| 119 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 120 | C4×#137 | C22 | 1 | 12 | yes | — |
| 121 | C2×C4×Q16 | C22 | 1 | 3 | yes | — |
| 122 | C2×2−1+4 | — | 2 | 1 | no | — |
| 123 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic |
| 124 | C2×#137 | C23 | 1 | 12 | yes | — |
| 125 | C22×Q16 | C23 | 1 | 3 | yes | — |
| 126 | #559 | — | 2 | 6 | no | — |
| 127 | #559 | C23 | 1 | 6 | yes | — |
| 128 | Q82 | — | 2 | 4 | no | — |
| 129 | Q82 | — | 2 | 4 | no | — |
| 130 | Q82 | — | 2 | 6 | no | — |
| 131 | Q82 | C23 | 1 | 4 | yes | — |
| 132 | Q82 | C23 | 1 | 4 | yes | — |
| 133 | Q82 | C23 | 1 | 4 | yes | — |
| 134 | Q82 | C23 | 1 | 6 | yes | — |
| 135 | #557 | — | 2 | 4 | no | — |
| 136 | #557 | — | 2 | 12 | no | — |
| 137 | #557 | — | 2 | 4 | no | — |
| 138 | #557 | — | 2 | 4 | no | — |
| 139 | #557 | — | 2 | 6 | no | — |
| 140 | #557 | — | 2 | 4 | no | — |
| 141 | #557 | — | 2 | 12 | no | — |
| 142 | #557 | — | 2 | 4 | no | — |
| 143 | #557 | C23 | 1 | 4 | yes | — |
| 144 | #557 | C23 | 1 | 4 | yes | — |
| 145 | #557 | C23 | 1 | 4 | yes | — |
| 146 | #557 | C23 | 1 | 6 | yes | — |
| 147 | #557 | C23 | 1 | 12 | yes | — |
| 148 | #557 | C23 | 1 | 6 | yes | — |
| 149 | #556 | — | 2 | 6 | no | — |
| 150 | #556 | — | 2 | 6 | no | — |
| 151 | #556 | — | 2 | 12 | no | — |
| 152 | #556 | C23 | 1 | 6 | yes | — |
| 153 | #555 | — | 2 | 12 | no | — |
| 154 | #555 | C23 | 1 | 12 | yes | — |
| 155 | #554 | — | 2 | 12 | no | — |
| 156 | #554 | — | 2 | 6 | no | — |
| 157 | #554 | — | 2 | 12 | no | — |
| 158 | #554 | — | 2 | 12 | no | — |
| 159 | #554 | — | 2 | 6 | no | — |
| 160 | #554 | — | 2 | 12 | no | — |
| 161 | #554 | — | 2 | 12 | no | — |
| 162 | #554 | C23 | 1 | 12 | yes | — |
| 163 | #554 | C23 | 1 | 6 | yes | — |
| 164 | #554 | C23 | 1 | 4 | yes | — |
| 165 | #553 | — | 2 | 12 | no | — |
| 166 | #553 | C23 | 1 | 12 | yes | — |
| 167 | #550 | — | 2 | 4 | no | — |
| 168 | #550 | C23 | 1 | 6 | yes | — |
| 169 | #550 | C23 | 1 | 4 | yes | — |
| 170 | D4×Q8 | — | 2 | 4 | no | — |
| 171 | D4×Q8 | C23 | 1 | 6 | yes | — |
| 172 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 173 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 174 | D4×Q8 | C23 | 1 | 4 | yes | — |
| 175 | #548 | — | 2 | 4 | no | — |
| 176 | #548 | — | 2 | 4 | no | — |
| 177 | #548 | — | 2 | 4 | no | — |
| 178 | #548 | — | 2 | 12 | no | — |
| 179 | #548 | C23 | 1 | 4 | yes | — |
| 180 | #547 | — | 2 | 6 | no | — |
| 181 | #547 | — | 2 | 12 | no | — |
| 182 | #544 | — | 2 | 6 | no | — |
| 183 | #544 | — | 2 | 12 | no | — |
| 184 | #544 | — | 2 | 12 | no | — |
| 185 | #544 | — | 2 | 3 | no | — |
| 186 | #544 | — | 2 | 12 | no | — |
| 187 | #542 | — | 2 | 12 | no | — |
| 188 | #542 | — | 2 | 12 | no | — |
| 189 | #542 | — | 2 | 12 | no | — |
| 190 | #537 | — | 2 | 6 | no | — |
| 191 | #537 | — | 2 | 3 | no | — |
| 192 | #533 | — | 2 | 12 | no | — |
| 193 | #533 | — | 2 | 6 | no | — |
| 194 | #533 | — | 2 | 12 | no | — |
| 195 | #533 | — | 2 | 12 | no | — |
| 196 | #533 | C23 | 1 | 6 | yes | — |
| 197 | #533 | C23 | 1 | 12 | yes | — |
| 198 | #533 | C23 | 1 | 12 | yes | — |
| 199 | #533 | C23 | 1 | 12 | yes | — |
| 200 | #532 | — | 2 | 6 | no | — |
| 201 | #532 | — | 2 | 12 | no | — |
| 202 | #532 | C23 | 1 | 6 | yes | — |
| 203 | #532 | C23 | 1 | 12 | yes | — |
| 204 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 205 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 206 | C2×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 207 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 208 | #529 | — | 2 | 12 | no | — |
| 209 | #529 | C23 | 1 | 12 | yes | — |
| 210 | C2×#125 | — | 2 | 3 | no | — |
| 211 | C2×#125 | — | 2 | 12 | no | — |
| 212 | #520 | — | 2 | 6 | no | — |
| 213 | #520 | — | 2 | 4 | no | — |
| 214 | #520 | — | 2 | 4 | no | — |
| 215 | #520 | — | 2 | 6 | no | — |
| 216 | #520 | D4 | 1 | 6 | yes | — |
| 217 | #520 | D4 | 1 | 4 | yes | — |
| 218 | #519 | — | 2 | 4 | no | — |
| 219 | #519 | — | 2 | 1 | no | — |
| 220 | #519 | — | 2 | 4 | no | — |
| 221 | #519 | D4 | 1 | 1 | yes | characteristic |
| 222 | #519 | D4 | 1 | 4 | yes | — |
| 223 | C4×#41 | — | 2 | 6 | no | — |
| 224 | C4×#41 | — | 2 | 4 | no | — |
| 225 | C4×#41 | — | 2 | 4 | no | — |
| 226 | C4×#41 | — | 2 | 6 | no | — |
| 227 | C4×#41 | C23 | 1 | 12 | yes | — |
| 228 | C4×#41 | C23 | 1 | 6 | yes | — |
| 229 | C4×#41 | C23 | 1 | 4 | yes | — |
| 230 | C2×C4×Q8 | — | 2 | 4 | no | — |
| 231 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 232 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 233 | C2×C4×Q8 | — | 2 | 4 | no | — |
| 234 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 235 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 236 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 237 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 239 | #501 | C23 | 1 | 12 | yes | — |
| 240 | #500 | C23 | 1 | 12 | yes | — |
| 241 | #498 | C23 | 1 | 6 | yes | — |
| 242 | #497 | C23 | 1 | 12 | yes | — |
| 243 | #492 | C23 | 1 | 6 | yes | — |
| 244 | #492 | C23 | 1 | 12 | yes | — |
| 245 | #491 | C23 | 1 | 12 | yes | — |
| 246 | #491 | C23 | 1 | 24 | yes | — |
| 247 | #489 | C23 | 1 | 4 | yes | — |
| 248 | #487 | C23 | 1 | 6 | yes | — |
| 249 | #487 | C23 | 1 | 12 | yes | — |
| 250 | #487 | C23 | 1 | 12 | yes | — |
| 251 | #487 | C23 | 1 | 12 | yes | — |
| 252 | #487 | C23 | 1 | 12 | yes | — |
| 253 | #486 | C23 | 1 | 6 | yes | — |
| 254 | #485 | C23 | 1 | 12 | yes | — |
| 255 | #485 | C23 | 1 | 24 | yes | — |
| 256 | #485 | C23 | 1 | 12 | yes | — |
| 257 | #484 | C23 | 1 | 12 | yes | — |
| 258 | #483 | C23 | 1 | 4 | yes | — |
| 259 | #481 | C23 | 1 | 4 | yes | — |
| 260 | #480 | C23 | 1 | 12 | yes | — |
| 261 | #479 | C23 | 1 | 12 | yes | — |
| 262 | #479 | C23 | 1 | 24 | yes | — |
| 263 | #479 | C23 | 1 | 12 | yes | — |
| 264 | #477 | C23 | 1 | 12 | yes | — |
| 265 | #477 | C23 | 1 | 12 | yes | — |
| 266 | #477 | C23 | 1 | 12 | yes | — |
| 267 | #477 | C23 | 1 | 12 | yes | — |
| 268 | #477 | C23 | 1 | 6 | yes | — |
| 269 | #477 | C23 | 1 | 6 | yes | — |
| 270 | #476 | C23 | 1 | 12 | yes | — |
| 271 | #475 | C23 | 1 | 12 | yes | — |
| 272 | #475 | C23 | 1 | 6 | yes | — |
| 273 | #475 | C23 | 1 | 6 | yes | — |
| 274 | #475 | C23 | 1 | 4 | yes | — |
| 275 | #474 | C23 | 1 | 12 | yes | — |
| 276 | #470 | C23 | 1 | 4 | yes | — |
| 277 | #470 | C23 | 1 | 12 | yes | — |
| 278 | #468 | C23 | 1 | 12 | yes | — |
| 279 | #468 | C23 | 1 | 12 | yes | — |
| 280 | #468 | C23 | 1 | 24 | yes | — |
| 281 | #465 | C23 | 1 | 12 | yes | — |
| 282 | #465 | C23 | 1 | 4 | yes | — |
| 283 | #464 | C23 | 1 | 4 | yes | — |
| 284 | #464 | C23 | 1 | 12 | yes | — |
| 285 | #462 | C23 | 1 | 6 | yes | — |
| 286 | #462 | C23 | 1 | 12 | yes | — |
| 287 | #462 | C23 | 1 | 6 | yes | — |
| 288 | #462 | C23 | 1 | 12 | yes | — |
| 289 | #462 | C23 | 1 | 12 | yes | — |
| 290 | #461 | C23 | 1 | 12 | yes | — |
| 291 | #461 | C23 | 1 | 12 | yes | — |
| 292 | #461 | C23 | 1 | 12 | yes | — |
| 293 | #461 | C23 | 1 | 12 | yes | — |
| 294 | #461 | C23 | 1 | 24 | yes | — |
| 295 | #460 | C23 | 1 | 6 | yes | — |
| 296 | #460 | C23 | 1 | 6 | yes | — |
| 297 | #460 | C23 | 1 | 12 | yes | — |
| 298 | #452 | C23 | 1 | 12 | yes | — |
| 299 | #452 | C23 | 1 | 4 | yes | — |
| 300 | #451 | C23 | 1 | 12 | yes | — |
| 301 | #451 | C23 | 1 | 4 | yes | — |
| 302 | #448 | C23 | 1 | 12 | yes | — |
| 303 | #448 | C23 | 1 | 24 | yes | — |
| 304 | #448 | C23 | 1 | 12 | yes | — |
| 305 | #446 | C23 | 1 | 6 | yes | — |
| 306 | #446 | C23 | 1 | 6 | yes | — |
| 307 | #446 | C23 | 1 | 12 | yes | — |
| 308 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 309 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 310 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 311 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 312 | #441 | C23 | 1 | 12 | yes | — |
| 313 | #441 | C23 | 1 | 4 | yes | — |
| 314 | #440 | C23 | 1 | 12 | yes | — |
| 315 | #440 | C23 | 1 | 24 | yes | — |
| 316 | #440 | C23 | 1 | 12 | yes | — |
| 317 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 318 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 319 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 320 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 321 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 322 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 323 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 324 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 325 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 326 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 327 | #436 | C23 | 1 | 6 | yes | — |
| 328 | #436 | C23 | 1 | 12 | yes | — |
| 329 | #436 | C23 | 1 | 6 | yes | — |
| 330 | #435 | C23 | 1 | 12 | yes | — |
| 331 | #435 | C23 | 1 | 4 | yes | — |
| 332 | #432 | C23 | 1 | 12 | yes | — |
| 333 | #431 | C23 | 1 | 6 | yes | — |
| 334 | #431 | C23 | 1 | 12 | yes | — |
| 335 | #428 | C23 | 1 | 12 | yes | — |
| 336 | C2×#107 | C23 | 1 | 3 | yes | — |
| 337 | #423 | C23 | 1 | 12 | yes | — |
| 338 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 339 | #419 | C23 | 1 | 24 | yes | — |
| 340 | #419 | C23 | 1 | 12 | yes | — |
| 341 | #417 | C23 | 1 | 4 | yes | — |
| 342 | C2×#103 | C23 | 1 | 6 | yes | — |
| 343 | C2×#103 | C23 | 1 | 3 | yes | — |
| 344 | C2×#103 | C23 | 1 | 1 | yes | characteristic |
| 345 | C4×M16 | C23 | 1 | 12 | yes | — |
| 346 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 347 | 2−1+4 | — | 2 | 8 | no | — |
| 348 | 2−1+4 | — | 4 | 8 | no | — |
| 349 | C2×#41 | — | 2 | 4 | no | — |
| 350 | C2×#41 | — | 2 | 6 | no | — |
| 351 | C2×#41 | — | 2 | 12 | no | — |
| 352 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 353 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 354 | C2×#41 | C24 | 1 | 4 | yes | — |
| 355 | C22×Q8 | — | 2 | 4 | no | — |
| 356 | C22×Q8 | — | 2 | 3 | no | — |
| 357 | C22×Q8 | C2×D4 | 1 | 4 | yes | — |
| 358 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 359 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 360 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 361 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 362 | #137 | — | 4 | 24 | no | — |
| 363 | C2×Q16 | — | 4 | 6 | no | — |
| 364 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 365 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 366 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 367 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 368 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 369 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 370 | C2×SD16 | C24 | 1 | 4 | yes | — |
| 371 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 372 | C2×M16 | C24 | 1 | 12 | yes | — |
| 373 | C2×M16 | C24 | 1 | 4 | yes | — |
| 374 | C22×C8 | C24 | 1 | 3 | yes | — |
| 375 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 376 | C4⋊Q8 | — | 2 | 6 | no | — |
| 377 | C4⋊Q8 | — | 2 | 12 | no | — |
| 378 | C4⋊Q8 | — | 2 | 12 | no | — |
| 379 | C4⋊Q8 | — | 2 | 6 | no | — |
| 380 | C4⋊Q8 | — | 2 | 12 | no | — |
| 381 | C4⋊Q8 | — | 2 | 12 | no | — |
| 382 | C4⋊Q8 | — | 2 | 6 | no | — |
| 383 | C4⋊Q8 | — | 2 | 12 | no | — |
| 384 | C4⋊Q8 | — | 2 | 12 | no | — |
| 385 | C4⋊Q8 | — | 2 | 6 | no | — |
| 386 | C4⋊Q8 | — | 2 | 12 | no | — |
| 387 | C4⋊Q8 | — | 2 | 12 | no | — |
| 388 | C4⋊Q8 | — | 2 | 6 | no | — |
| 389 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 390 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 391 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 392 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 393 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 394 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 395 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 396 | #127 | — | 2 | 6 | no | — |
| 397 | #127 | C24 | 1 | 6 | yes | — |
| 398 | #126 | — | 2 | 12 | no | — |
| 399 | #126 | — | 2 | 12 | no | — |
| 400 | #126 | — | 2 | 12 | no | — |
| 401 | #125 | — | 2 | 6 | no | — |
| 402 | #125 | — | 2 | 12 | no | — |
| 403 | #125 | — | 2 | 12 | no | — |
| 404 | #125 | — | 2 | 12 | no | — |
| 405 | #125 | — | 2 | 12 | no | — |
| 406 | #125 | — | 2 | 12 | no | — |
| 407 | #125 | — | 2 | 24 | no | — |
| 408 | #125 | — | 2 | 12 | no | — |
| 409 | #125 | — | 2 | 6 | no | — |
| 410 | #125 | — | 2 | 4 | no | — |
| 411 | #125 | — | 2 | 12 | no | — |
| 412 | #125 | — | 2 | 12 | no | — |
| 413 | #125 | — | 2 | 6 | no | — |
| 414 | #125 | C24 | 1 | 12 | yes | — |
| 415 | #124 | — | 2 | 6 | no | — |
| 416 | #124 | — | 2 | 6 | no | — |
| 417 | #124 | — | 2 | 4 | no | — |
| 418 | #124 | — | 2 | 24 | no | — |
| 419 | #124 | — | 2 | 6 | no | — |
| 420 | #124 | — | 2 | 12 | no | — |
| 421 | #124 | C24 | 1 | 4 | yes | — |
| 422 | #123 | — | 2 | 12 | no | — |
| 423 | #123 | — | 2 | 12 | no | — |
| 424 | #123 | — | 2 | 12 | no | — |
| 425 | C22⋊Q8 | — | 2 | 12 | no | — |
| 426 | C22⋊Q8 | — | 2 | 12 | no | — |
| 427 | C22⋊Q8 | — | 2 | 12 | no | — |
| 428 | C22⋊Q8 | — | 2 | 6 | no | — |
| 429 | C22⋊Q8 | — | 2 | 12 | no | — |
| 430 | C22⋊Q8 | — | 2 | 12 | no | — |
| 431 | C22⋊Q8 | — | 2 | 4 | no | — |
| 432 | C22⋊Q8 | — | 2 | 12 | no | — |
| 433 | C22⋊Q8 | — | 2 | 24 | no | — |
| 434 | C22⋊Q8 | — | 2 | 4 | no | — |
| 435 | C22⋊Q8 | — | 2 | 12 | no | — |
| 436 | C22⋊Q8 | — | 2 | 4 | no | — |
| 437 | C22⋊Q8 | — | 2 | 12 | no | — |
| 438 | C22⋊Q8 | — | 2 | 12 | no | — |
| 439 | C22⋊Q8 | — | 2 | 24 | no | — |
| 440 | C22⋊Q8 | — | 2 | 12 | no | — |
| 441 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 442 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 443 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 444 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 445 | #121 | — | 2 | 4 | no | — |
| 446 | #121 | — | 2 | 12 | no | — |
| 447 | #121 | — | 2 | 12 | no | — |
| 448 | #121 | — | 2 | 6 | no | — |
| 449 | #121 | — | 2 | 12 | no | — |
| 450 | #121 | — | 2 | 12 | no | — |
| 451 | #121 | — | 2 | 12 | no | — |
| 452 | #121 | C24 | 1 | 12 | yes | — |
| 453 | #121 | C24 | 1 | 4 | yes | — |
| 454 | C4×Q8 | — | 2 | 4 | no | — |
| 455 | C4×Q8 | — | 2 | 6 | no | — |
| 456 | C4×Q8 | — | 2 | 4 | no | — |
| 457 | C4×Q8 | — | 2 | 4 | no | — |
| 458 | C4×Q8 | — | 2 | 12 | no | — |
| 459 | C4×Q8 | — | 2 | 4 | no | — |
| 460 | C4×Q8 | — | 2 | 4 | no | — |
| 461 | C4×Q8 | — | 2 | 6 | no | — |
| 462 | C4×Q8 | — | 2 | 4 | no | — |
| 463 | C4×Q8 | — | 2 | 6 | no | — |
| 464 | C4×Q8 | — | 2 | 6 | no | — |
| 465 | C4×Q8 | — | 2 | 12 | no | — |
| 466 | C4×Q8 | — | 2 | 6 | no | — |
| 467 | C4×Q8 | — | 2 | 12 | no | — |
| 468 | C4×Q8 | — | 2 | 12 | no | — |
| 469 | C4×Q8 | — | 2 | 6 | no | — |
| 470 | C4×Q8 | — | 2 | 12 | no | — |
| 471 | C4×Q8 | — | 2 | 12 | no | — |
| 472 | C4×Q8 | — | 2 | 12 | no | — |
| 473 | C4×Q8 | — | 2 | 6 | no | — |
| 474 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 475 | C4×Q8 | C2×D4 | 1 | 12 | yes | — |
| 476 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 477 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 478 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 479 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 480 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 481 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 482 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 483 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 484 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 485 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 486 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 487 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 488 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 489 | C4×D4 | — | 2 | 4 | no | — |
| 490 | C4×D4 | — | 2 | 6 | no | — |
| 491 | C4×D4 | — | 2 | 12 | no | — |
| 492 | C4×D4 | — | 2 | 6 | no | — |
| 493 | C4×D4 | — | 2 | 12 | no | — |
| 494 | C4×D4 | — | 2 | 12 | no | — |
| 495 | C4×D4 | — | 2 | 12 | no | — |
| 496 | C4×D4 | — | 2 | 12 | no | — |
| 497 | C4×D4 | — | 2 | 6 | no | — |
| 498 | C4×D4 | — | 2 | 6 | no | — |
| 499 | C4×D4 | — | 2 | 4 | no | — |
| 500 | C4×D4 | — | 2 | 12 | no | — |
| 501 | C4×D4 | — | 2 | 12 | no | — |
| 502 | C4×D4 | — | 2 | 6 | no | — |
| 503 | C4×D4 | C2×D4 | 1 | 12 | yes | — |
| 504 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 505 | C4×D4 | C2×D4 | 1 | 12 | yes | — |
| 506 | C4×D4 | C24 | 1 | 12 | yes | — |
| 507 | C4×D4 | C24 | 1 | 12 | yes | — |
| 508 | C4×D4 | C24 | 1 | 4 | yes | — |
| 509 | C4×D4 | C24 | 1 | 6 | yes | — |
| 510 | #117 | — | 2 | 12 | no | — |
| 511 | #117 | — | 2 | 12 | no | — |
| 512 | #117 | — | 2 | 6 | no | — |
| 513 | #117 | — | 2 | 12 | no | — |
| 514 | #117 | — | 2 | 12 | no | — |
| 515 | #117 | — | 2 | 12 | no | — |
| 516 | #117 | C2×D4 | 1 | 6 | yes | — |
| 517 | #117 | C2×D4 | 1 | 12 | yes | — |
| 518 | #117 | C2×D4 | 1 | 12 | yes | — |
| 519 | #117 | C24 | 1 | 12 | yes | — |
| 520 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 521 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 522 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 523 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 524 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 525 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 526 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 527 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 528 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 529 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 530 | C2×C4⋊C4 | C2×D4 | 1 | 12 | yes | — |
| 531 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 532 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 533 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 534 | C2×C42 | — | 2 | 12 | no | — |
| 535 | C2×C42 | — | 2 | 3 | no | — |
| 536 | C2×C42 | — | 2 | 3 | no | — |
| 537 | C2×C42 | — | 2 | 12 | no | — |
| 538 | C2×C42 | C24 | 1 | 3 | yes | — |
| 539 | C2×C42 | C24 | 1 | 12 | yes | — |
| 540 | #107 | C24 | 1 | 6 | yes | — |
| 541 | #107 | C24 | 1 | 6 | yes | — |
| 542 | #107 | C24 | 1 | 12 | yes | — |
| 543 | #107 | C24 | 1 | 12 | yes | — |
| 544 | #106 | C24 | 1 | 4 | yes | — |
| 545 | #106 | C24 | 1 | 12 | yes | — |
| 546 | #106 | C24 | 1 | 4 | yes | — |
| 547 | #106 | C24 | 1 | 4 | yes | — |
| 548 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 549 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 550 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 551 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 552 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 553 | #103 | C24 | 1 | 1 | yes | characteristic |
| 554 | #103 | C24 | 1 | 6 | yes | — |
| 555 | #103 | C24 | 1 | 24 | yes | — |
| 556 | #103 | C24 | 1 | 1 | yes | characteristic |
| 557 | #103 | C24 | 1 | 1 | yes | characteristic |
| 558 | #103 | C24 | 1 | 1 | yes | characteristic |
| 559 | #103 | C24 | 1 | 6 | yes | — |
| 560 | #103 | C24 | 1 | 4 | yes | — |
| 561 | #103 | C24 | 1 | 4 | yes | — |
| 562 | #103 | C24 | 1 | 12 | yes | — |
| 563 | #103 | C24 | 1 | 12 | yes | — |
| 564 | #103 | C24 | 1 | 12 | yes | — |
| 565 | #103 | C24 | 1 | 12 | yes | — |
| 566 | #103 | C24 | 1 | 12 | yes | — |
| 567 | #103 | C24 | 1 | 4 | yes | — |
| 568 | #102 | C24 | 1 | 4 | yes | — |
| 569 | #102 | C24 | 1 | 4 | yes | — |
| 570 | #102 | C24 | 1 | 4 | yes | — |
| 571 | #102 | C24 | 1 | 12 | yes | — |
| 572 | C22⋊C8 | C24 | 1 | 4 | yes | — |
| 573 | C22⋊C8 | C24 | 1 | 4 | yes | — |
| 574 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 575 | #97 | C24 | 1 | 4 | yes | — |
| 576 | #97 | C24 | 1 | 12 | yes | — |
| 577 | C4×C8 | C24 | 1 | 6 | yes | — |
| 578 | C4×C8 | C24 | 1 | 6 | yes | — |
| 579 | C4×C8 | C24 | 1 | 12 | yes | — |
| 580 | #41 | — | 2 | 16 | no | — |
| 581 | #41 | — | 2 | 24 | no | — |
| 582 | #41 | — | 2 | 8 | no | — |
| 583 | #41 | — | 4 | 4 | no | — |
| 584 | #41 | — | 4 | 16 | no | — |
| 585 | #41 | — | 4 | 24 | no | — |
| 586 | #41 | — | 16 | 12 | no | — |
| 587 | C2×Q8 | — | 2 | 16 | no | — |
| 588 | C2×Q8 | — | 2 | 1 | no | — |
| 589 | C2×Q8 | — | 2 | 6 | no | — |
| 590 | C2×Q8 | — | 2 | 4 | no | — |
| 591 | C2×Q8 | — | 2 | 6 | no | — |
| 592 | C2×Q8 | — | 2 | 12 | no | — |
| 593 | C2×Q8 | — | 2 | 3 | no | — |
| 594 | C2×Q8 | — | 2 | 12 | no | — |
| 595 | C2×Q8 | — | 2 | 2 | no | — |
| 596 | C2×Q8 | — | 4 | 1 | no | — |
| 597 | C2×Q8 | — | 4 | 3 | no | — |
| 598 | C2×Q8 | — | 4 | 12 | no | — |
| 599 | C2×Q8 | — | 4 | 3 | no | — |
| 600 | C2×Q8 | — | 4 | 12 | no | — |
| 601 | C2×Q8 | — | 4 | 16 | no | — |
| 602 | C2×Q8 | — | 16 | 3 | no | — |
| 603 | C2×Q8 | #137 | 1 | 8 | yes | complemented |
| 604 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 605 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 606 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 607 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 608 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 609 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 610 | C2×D4 | — | 2 | 4 | no | — |
| 611 | C2×D4 | — | 2 | 4 | no | — |
| 612 | C2×D4 | — | 2 | 12 | no | — |
| 613 | C2×D4 | — | 2 | 6 | no | — |
| 614 | C2×D4 | — | 2 | 6 | no | — |
| 615 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 616 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 617 | C2×D4 | C25 | 1 | 4 | yes | — |
| 618 | C22×C4 | — | 2 | 1 | no | — |
| 619 | C22×C4 | — | 2 | 4 | no | — |
| 620 | C22×C4 | — | 2 | 1 | no | — |
| 621 | C22×C4 | — | 2 | 12 | no | — |
| 622 | C22×C4 | — | 2 | 3 | no | — |
| 623 | C22×C4 | — | 2 | 3 | no | — |
| 624 | C22×C4 | — | 2 | 4 | no | — |
| 625 | C22×C4 | — | 2 | 12 | no | — |
| 626 | C22×C4 | — | 2 | 12 | no | — |
| 627 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 628 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 629 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 630 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 631 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 632 | C22×C4 | C25 | 1 | 4 | yes | — |
| 633 | Q16 | — | 2 | 12 | no | — |
| 634 | Q16 | — | 2 | 8 | no | — |
| 635 | Q16 | — | 4 | 6 | no | — |
| 636 | Q16 | — | 4 | 4 | no | — |
| 637 | SD16 | — | 4 | 4 | no | — |
| 638 | SD16 | — | 4 | 12 | no | — |
| 639 | SD16 | — | 4 | 12 | no | — |
| 640 | SD16 | — | 4 | 12 | no | — |
| 641 | M16 | — | 4 | 4 | no | — |
| 642 | M16 | — | 4 | 12 | no | — |
| 643 | C2×C8 | — | 4 | 1 | no | — |
| 644 | C2×C8 | — | 4 | 3 | no | — |
| 645 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 646 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 647 | C2×C8 | C25 | 1 | 4 | yes | — |
| 648 | C2×C8 | C25 | 1 | 4 | yes | — |
| 649 | C2×C8 | C25 | 1 | 6 | yes | — |
| 650 | C4⋊C4 | — | 2 | 4 | no | — |
| 651 | C4⋊C4 | — | 2 | 6 | no | — |
| 652 | C4⋊C4 | — | 2 | 12 | no | — |
| 653 | C4⋊C4 | — | 2 | 12 | no | — |
| 654 | C4⋊C4 | — | 2 | 12 | no | — |
| 655 | C4⋊C4 | — | 2 | 6 | no | — |
| 656 | C4⋊C4 | — | 2 | 12 | no | — |
| 657 | C4⋊C4 | — | 2 | 12 | no | — |
| 658 | C4⋊C4 | — | 2 | 12 | no | — |
| 659 | C4⋊C4 | — | 2 | 6 | no | — |
| 660 | C4⋊C4 | — | 2 | 6 | no | — |
| 661 | C4⋊C4 | — | 2 | 12 | no | — |
| 662 | C4⋊C4 | — | 2 | 6 | no | — |
| 663 | C4⋊C4 | — | 2 | 12 | no | — |
| 664 | C4⋊C4 | — | 2 | 6 | no | — |
| 665 | C4⋊C4 | — | 2 | 4 | no | — |
| 666 | C4⋊C4 | — | 2 | 1 | no | — |
| 667 | C4⋊C4 | — | 2 | 3 | no | — |
| 668 | C4⋊C4 | — | 2 | 4 | no | — |
| 669 | C4⋊C4 | — | 2 | 4 | no | — |
| 670 | C4⋊C4 | — | 2 | 4 | no | — |
| 671 | C4⋊C4 | — | 2 | 6 | no | — |
| 672 | C4⋊C4 | — | 2 | 6 | no | — |
| 673 | C4⋊C4 | — | 2 | 12 | no | — |
| 674 | C4⋊C4 | — | 2 | 4 | no | — |
| 675 | C4⋊C4 | — | 2 | 12 | no | — |
| 676 | C4⋊C4 | — | 2 | 4 | no | — |
| 677 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 678 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 679 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 680 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 681 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 682 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 683 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 684 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 685 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 686 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 687 | C22⋊C4 | — | 2 | 4 | no | — |
| 688 | C22⋊C4 | — | 2 | 12 | no | — |
| 689 | C22⋊C4 | — | 2 | 4 | no | — |
| 690 | C22⋊C4 | — | 2 | 12 | no | — |
| 691 | C22⋊C4 | — | 2 | 4 | no | — |
| 692 | C22⋊C4 | — | 2 | 12 | no | — |
| 693 | C22⋊C4 | — | 2 | 4 | no | — |
| 694 | C22⋊C4 | — | 2 | 12 | no | — |
| 695 | C22⋊C4 | — | 2 | 12 | no | — |
| 696 | C22⋊C4 | — | 2 | 4 | no | — |
| 697 | C22⋊C4 | — | 2 | 4 | no | — |
| 698 | C22⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 699 | C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 700 | C22⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 701 | C42 | — | 2 | 4 | no | — |
| 702 | C42 | — | 2 | 6 | no | — |
| 703 | C42 | — | 2 | 4 | no | — |
| 704 | C42 | — | 2 | 6 | no | — |
| 705 | C42 | — | 2 | 12 | no | — |
| 706 | C42 | — | 2 | 6 | no | — |
| 707 | C42 | — | 2 | 12 | no | — |
| 708 | C42 | — | 2 | 12 | no | — |
| 709 | C42 | — | 2 | 6 | no | — |
| 710 | C42 | C22×D4 | 1 | 12 | yes | — |
| 711 | C42 | C22×D4 | 1 | 12 | yes | — |
| 712 | C42 | C22×D4 | 1 | 6 | yes | — |
| 713 | C42 | C25 | 1 | 6 | yes | — |
| 714 | C42 | C25 | 1 | 4 | yes | — |
| 715 | C23 | — | 2 | 4 | no | — |
| 716 | C23 | C23×D4 | 1 | 4 | yes | — |
| 717 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 718 | Q8 | — | 2 | 1 | no | — |
| 719 | Q8 | — | 2 | 12 | no | — |
| 720 | Q8 | — | 2 | 4 | no | — |
| 721 | Q8 | — | 2 | 6 | no | — |
| 722 | Q8 | — | 2 | 1 | no | — |
| 723 | Q8 | — | 2 | 6 | no | — |
| 724 | Q8 | — | 2 | 4 | no | — |
| 725 | Q8 | — | 2 | 1 | no | — |
| 726 | Q8 | — | 4 | 2 | no | — |
| 727 | Q8 | — | 4 | 12 | no | — |
| 728 | Q8 | — | 8 | 4 | no | — |
| 729 | Q8 | — | 8 | 6 | no | — |
| 730 | Q8 | — | 8 | 12 | no | — |
| 731 | Q8 | — | 8 | 3 | no | — |
| 732 | Q8 | — | 8 | 12 | no | — |
| 733 | Q8 | C2×#137 | 1 | 16 | yes | — |
| 734 | Q8 | #585 | 1 | 2 | yes | — |
| 735 | D4 | — | 2 | 8 | no | — |
| 736 | D4 | — | 2 | 4 | no | — |
| 737 | D4 | — | 2 | 4 | no | — |
| 738 | D4 | — | 2 | 12 | no | — |
| 739 | D4 | — | 4 | 8 | no | — |
| 740 | D4 | — | 4 | 8 | no | — |
| 741 | D4 | — | 4 | 12 | no | — |
| 742 | D4 | — | 8 | 6 | no | — |
| 743 | D4 | — | 8 | 12 | no | — |
| 744 | C2×C4 | — | 2 | 1 | no | — |
| 745 | C2×C4 | — | 2 | 1 | no | — |
| 746 | C2×C4 | — | 2 | 4 | no | — |
| 747 | C2×C4 | — | 2 | 1 | no | — |
| 748 | C2×C4 | — | 2 | 4 | no | — |
| 749 | C2×C4 | — | 2 | 24 | no | — |
| 750 | C2×C4 | — | 2 | 1 | no | — |
| 751 | C2×C4 | — | 2 | 1 | no | — |
| 752 | C2×C4 | — | 2 | 4 | no | — |
| 753 | C2×C4 | — | 2 | 1 | no | — |
| 754 | C2×C4 | — | 2 | 4 | no | — |
| 755 | C2×C4 | — | 2 | 6 | no | — |
| 756 | C2×C4 | — | 2 | 4 | no | — |
| 757 | C2×C4 | — | 2 | 6 | no | — |
| 758 | C2×C4 | — | 4 | 3 | no | — |
| 759 | C2×C4 | — | 4 | 12 | no | — |
| 760 | C2×C4 | — | 4 | 8 | no | — |
| 761 | C2×C4 | — | 4 | 2 | no | — |
| 762 | C2×C4 | — | 4 | 24 | no | — |
| 763 | C2×C4 | — | 8 | 12 | no | — |
| 764 | C2×C4 | — | 8 | 1 | no | — |
| 765 | C2×C4 | — | 8 | 4 | no | — |
| 766 | C2×C4 | — | 8 | 3 | no | — |
| 767 | C2×C4 | — | 8 | 12 | no | — |
| 768 | C2×C4 | — | 8 | 3 | no | — |
| 769 | C2×C4 | C2×#137 | 1 | 12 | yes | — |
| 770 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 771 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 772 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 773 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 774 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 775 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 776 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 777 | C8 | — | 2 | 6 | no | — |
| 778 | C8 | — | 2 | 4 | no | — |
| 779 | C8 | — | 2 | 1 | no | — |
| 780 | C8 | — | 2 | 1 | no | — |
| 781 | C8 | — | 2 | 4 | no | — |
| 782 | C22 | — | 2 | 1 | no | — |
| 783 | C22 | — | 2 | 1 | no | — |
| 784 | C22 | — | 2 | 4 | no | — |
| 785 | C22 | — | 2 | 4 | no | — |
| 786 | C22 | — | 2 | 4 | no | — |
| 787 | C22 | — | 4 | 4 | no | — |
| 788 | C22 | — | 4 | 4 | no | — |
| 789 | C22 | — | 4 | 4 | no | — |
| 790 | C22 | C22×#137 | 1 | 2 | yes | — |
| 791 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 792 | C4 | — | 2 | 4 | no | — |
| 793 | C4 | — | 2 | 1 | no | — |
| 794 | C4 | — | 2 | 2 | no | — |
| 795 | C4 | — | 2 | 4 | no | — |
| 796 | C4 | — | 2 | 4 | no | — |
| 797 | C4 | — | 2 | 6 | no | — |
| 798 | C4 | — | 4 | 1 | no | — |
| 799 | C4 | — | 4 | 4 | no | — |
| 800 | C4 | — | 4 | 6 | no | — |
| 801 | C4 | — | 4 | 4 | no | — |
| 802 | C4 | — | 4 | 1 | no | — |
| 803 | C4 | — | 4 | 6 | no | — |
| 804 | C4 | — | 4 | 1 | no | — |
| 805 | C4 | — | 4 | 4 | no | — |
| 806 | C4 | C22×#137 | 1 | 12 | yes | — |
| 807 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 808 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 809 | C2 | — | 2 | 2 | no | — |
| 810 | C2 | — | 4 | 4 | no | — |
| 811 | C2 | — | 8 | 4 | no | — |
| 812 | C2 | #63002 | 1 | 1 | yes | characteristic |
| 813 | C2 | C23×#137 | 1 | 1 | yes | characteristic |
| 814 | C2 | #63092 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | #62999 | C2 |
| 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. #63004 | C2 | semidirect |
| 3. #62589 | C2 | semidirect |
| 4. #62540 | C2 | semidirect |
| 5. #62394 | C2 | semidirect |
| 6. #62357 | C2 | semidirect |
| 7. #62153 | C2 | semidirect |
| 8. #62114 | C2 | semidirect |
| 9. #62002 | C2 | semidirect |
| 10. #61964 | C2 | semidirect |
| 11. #61906 | C2 | semidirect |
| 12. #61883 | C2 | semidirect |
| 13. #61846 | C2 | semidirect |
| 14. #61821 | C2 | semidirect |
| 15. #61469 | C2 | semidirect |
| 16. #61440 | C2 | semidirect |
| 17. #61322 | C2 | semidirect |
| 18. C2×#3363 | C2 | semidirect |
| 19. #60333 | C2 | semidirect |
| 603. C2×Q8 | #137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63004 | 2 |
| #62999 | 2 |
| #62589 | 2 |
| #62540 | 2 |
| #62394 | 2 |
| #62357 | 2 |
| #62153 | 2 |
| #62114 | 2 |
| #62002 | 2 |
| #61964 | 2 |
| #61906 | 2 |
| #61883 | 2 |
| #61846 | 2 |
| #61821 | 2 |
| #61469 | 2 |
| #61440 | 2 |
| #61322 | 2 |
| C2×#3363 | 2 |
| #60333 | 2 |