Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
34164 conjugacy classes of subgroups.
The subgroup lattice has 775 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63039 | C2 | 1 | 8 | yes | maximal, complemented |
| 2 | #63015 | C2 | 1 | 24 | yes | maximal, complemented |
| 3 | #62999 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | D4×2−1+4 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #62986 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | Q8×H(5,𝔽2) | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #62946 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #62944 | C2 | 1 | 18 | yes | maximal, complemented |
| 9 | #62917 | C2 | 1 | 12 | yes | maximal, complemented |
| 10 | #62913 | C2 | 1 | 12 | yes | maximal, complemented |
| 11 | #62835 | C2 | 1 | 18 | yes | maximal, complemented |
| 12 | #62800 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | #62788 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | C2×#3497 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C2×Q8×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×2−1+4 | C22 | 1 | 6 | yes | complemented |
| 17 | #3561 | C22 | 1 | 72 | yes | complemented |
| 18 | #3559 | C22 | 1 | 72 | yes | complemented |
| 19 | #3554 | C22 | 1 | 72 | yes | complemented |
| 20 | #3554 | C22 | 1 | 72 | yes | complemented |
| 21 | #3552 | C22 | 1 | 72 | yes | complemented |
| 22 | #3550 | C22 | 1 | 36 | yes | complemented |
| 23 | #3548 | C22 | 1 | 72 | yes | complemented |
| 24 | #3548 | C22 | 1 | 36 | yes | complemented |
| 25 | #3547 | C22 | 1 | 72 | yes | complemented |
| 26 | #3547 | C22 | 1 | 72 | yes | complemented |
| 27 | #3541 | C22 | 1 | 144 | yes | complemented |
| 28 | #3536 | C22 | 1 | 144 | yes | complemented |
| 29 | #3536 | C22 | 1 | 72 | yes | complemented |
| 30 | #3523 | C22 | 1 | 12 | yes | complemented |
| 31 | #3522 | C22 | 1 | 24 | yes | complemented |
| 32 | #3522 | C22 | 1 | 12 | yes | complemented |
| 33 | #3522 | C22 | 1 | 12 | yes | complemented |
| 34 | #3522 | C22 | 1 | 24 | yes | complemented |
| 35 | #3520 | C22 | 1 | 72 | yes | complemented |
| 36 | #3519 | C22 | 1 | 72 | yes | complemented |
| 37 | #3519 | C22 | 1 | 36 | yes | complemented |
| 38 | #3518 | C22 | 1 | 24 | yes | complemented |
| 39 | #3517 | C22 | 1 | 24 | yes | complemented |
| 40 | #3517 | C22 | 1 | 12 | yes | complemented |
| 41 | #3516 | C22 | 1 | 24 | yes | complemented |
| 42 | #3514 | C22 | 1 | 36 | yes | complemented |
| 43 | #3511 | C22 | 1 | 36 | yes | complemented |
| 44 | #3511 | C22 | 1 | 72 | yes | complemented |
| 45 | #3511 | C22 | 1 | 18 | yes | complemented |
| 46 | #3508 | C22 | 1 | 36 | yes | complemented |
| 47 | #3508 | C22 | 1 | 18 | yes | complemented |
| 48 | #3507 | C22 | 1 | 18 | yes | complemented |
| 49 | #3506 | C22 | 1 | 36 | yes | complemented |
| 50 | #3503 | C22 | 1 | 6 | yes | — |
| 51 | #3503 | C22 | 1 | 24 | yes | complemented |
| 52 | #3503 | C22 | 1 | 36 | yes | complemented |
| 53 | #3502 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #3501 | C22 | 1 | 72 | yes | complemented |
| 55 | #3501 | C22 | 1 | 36 | yes | complemented |
| 56 | #3499 | C22 | 1 | 24 | yes | complemented |
| 57 | #3499 | C22 | 1 | 36 | yes | complemented |
| 58 | #3498 | C22 | 1 | 6 | yes | — |
| 59 | #3497 | C22 | 1 | 6 | yes | complemented |
| 60 | #3497 | C22 | 1 | 24 | yes | complemented |
| 61 | #3497 | C22 | 1 | 24 | yes | complemented |
| 62 | #3497 | C22 | 1 | 3 | yes | complemented |
| 63 | #3497 | C22 | 1 | 18 | yes | complemented |
| 64 | #3497 | C22 | 1 | 24 | yes | complemented |
| 65 | #3497 | C22 | 1 | 18 | yes | complemented |
| 66 | #3494 | C22 | 1 | 36 | yes | complemented |
| 67 | #3492 | C22 | 1 | 18 | yes | complemented |
| 68 | #3489 | C22 | 1 | 48 | yes | complemented |
| 69 | #3489 | C22 | 1 | 72 | yes | complemented |
| 70 | #3488 | C22 | 1 | 4 | yes | — |
| 71 | #3486 | C22 | 1 | 6 | yes | complemented |
| 72 | #3486 | C22 | 1 | 48 | yes | complemented |
| 73 | #3483 | C22 | 1 | 8 | yes | complemented |
| 74 | #3483 | C22 | 1 | 12 | yes | complemented |
| 75 | #3482 | C22 | 1 | 24 | yes | complemented |
| 76 | #3481 | C22 | 1 | 36 | yes | complemented |
| 77 | #3480 | C22 | 1 | 12 | yes | complemented |
| 78 | #3480 | C22 | 1 | 12 | yes | complemented |
| 79 | Q8×#41 | C22 | 1 | 4 | yes | — |
| 80 | Q8×#41 | C22 | 1 | 8 | yes | complemented |
| 81 | Q8×#41 | C22 | 1 | 12 | yes | complemented |
| 82 | Q8×#41 | C22 | 1 | 12 | yes | complemented |
| 83 | Q8×#41 | C22 | 1 | 4 | yes | complemented |
| 84 | Q8×#41 | C22 | 1 | 12 | yes | complemented |
| 85 | C2×Q82 | C22 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×#557 | C22 | 1 | 3 | yes | complemented |
| 87 | C2×#554 | C22 | 1 | 9 | yes | complemented |
| 88 | D4×#41 | C22 | 1 | 24 | yes | complemented |
| 89 | D4×#41 | C22 | 1 | 36 | yes | complemented |
| 90 | C2×#550 | C22 | 1 | 12 | yes | complemented |
| 91 | C2×D4×Q8 | C22 | 1 | 24 | yes | complemented |
| 92 | C2×D4×Q8 | C22 | 1 | 12 | yes | complemented |
| 93 | C2×D4×Q8 | C22 | 1 | 3 | yes | complemented |
| 94 | C2×#548 | C22 | 1 | 24 | yes | complemented |
| 95 | #3461 | C22 | 1 | 18 | yes | complemented |
| 96 | #3460 | C22 | 1 | 36 | yes | complemented |
| 97 | C2×#537 | C22 | 1 | 18 | yes | complemented |
| 98 | #3444 | C22 | 1 | 18 | yes | complemented |
| 99 | C2×#533 | C22 | 1 | 9 | yes | complemented |
| 100 | C2×#532 | C22 | 1 | 18 | yes | complemented |
| 101 | C4×2−1+4 | C22 | 1 | 6 | yes | complemented |
| 102 | C4×H(5,𝔽2) | C22 | 1 | 12 | yes | — |
| 103 | C2×C4×#41 | C22 | 1 | 3 | yes | — |
| 104 | C22×C4×Q8 | C22 | 1 | 3 | yes | complemented |
| 105 | C2×2−1+4 | — | 4 | 48 | no | — |
| 106 | C2×2−1+4 | C23 | 1 | 6 | yes | — |
| 107 | C2×2−1+4 | C23 | 1 | 48 | yes | — |
| 108 | C2×2−1+4 | C23 | 1 | 36 | yes | — |
| 109 | C2×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 110 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 111 | C22×#41 | C23 | 1 | 36 | yes | — |
| 112 | C22×#41 | C23 | 1 | 24 | yes | — |
| 113 | C23×Q8 | C23 | 1 | 3 | yes | — |
| 114 | C23×Q8 | C23 | 1 | 24 | yes | — |
| 115 | #563 | C23 | 1 | 144 | yes | — |
| 116 | #562 | C23 | 1 | 288 | yes | — |
| 117 | #562 | C23 | 1 | 144 | yes | — |
| 118 | #559 | C23 | 1 | 36 | yes | — |
| 119 | #559 | C23 | 1 | 36 | yes | — |
| 120 | #559 | C23 | 1 | 36 | yes | — |
| 121 | #559 | C23 | 1 | 72 | yes | — |
| 122 | Q82 | C23 | 1 | 4 | yes | — |
| 123 | Q82 | C23 | 1 | 12 | yes | — |
| 124 | Q82 | C23 | 1 | 4 | yes | — |
| 125 | Q82 | C23 | 1 | 12 | yes | — |
| 126 | Q82 | C23 | 1 | 24 | yes | — |
| 127 | #557 | C23 | 1 | 12 | yes | — |
| 128 | #557 | C23 | 1 | 36 | yes | — |
| 129 | #557 | C23 | 1 | 12 | yes | — |
| 130 | #557 | C23 | 1 | 36 | yes | — |
| 131 | #557 | C23 | 1 | 4 | yes | — |
| 132 | #557 | C23 | 1 | 8 | yes | — |
| 133 | #556 | C23 | 1 | 36 | yes | — |
| 134 | #556 | C23 | 1 | 36 | yes | — |
| 135 | #556 | C23 | 1 | 72 | yes | — |
| 136 | #556 | C23 | 1 | 72 | yes | — |
| 137 | #555 | C23 | 1 | 72 | yes | — |
| 138 | #555 | C23 | 1 | 72 | yes | — |
| 139 | #555 | C23 | 1 | 36 | yes | — |
| 140 | #554 | C23 | 1 | 36 | yes | — |
| 141 | #554 | C23 | 1 | 72 | yes | — |
| 142 | #554 | C23 | 1 | 36 | yes | — |
| 143 | #554 | C23 | 1 | 72 | yes | — |
| 144 | #554 | C23 | 1 | 36 | yes | — |
| 145 | #554 | C23 | 1 | 72 | yes | — |
| 146 | #554 | C23 | 1 | 36 | yes | — |
| 147 | #554 | C23 | 1 | 36 | yes | — |
| 148 | #554 | C23 | 1 | 144 | yes | — |
| 149 | #554 | C23 | 1 | 144 | yes | — |
| 150 | #554 | C23 | 1 | 72 | yes | — |
| 151 | #553 | C23 | 1 | 72 | yes | — |
| 152 | #553 | C23 | 1 | 72 | yes | — |
| 153 | #553 | C23 | 1 | 72 | yes | — |
| 154 | #553 | C23 | 1 | 72 | yes | — |
| 155 | #553 | C23 | 1 | 144 | yes | — |
| 156 | #552 | C23 | 1 | 72 | yes | — |
| 157 | #552 | C23 | 1 | 72 | yes | — |
| 158 | #551 | C23 | 1 | 144 | yes | — |
| 159 | #550 | C23 | 1 | 12 | yes | — |
| 160 | #550 | C23 | 1 | 24 | yes | — |
| 161 | #550 | C23 | 1 | 72 | yes | — |
| 162 | #550 | C23 | 1 | 72 | yes | — |
| 163 | #550 | C23 | 1 | 36 | yes | — |
| 164 | #550 | C23 | 1 | 12 | yes | — |
| 165 | #550 | C23 | 1 | 8 | yes | — |
| 166 | #550 | C23 | 1 | 12 | yes | — |
| 167 | #550 | C23 | 1 | 36 | yes | — |
| 168 | #550 | C23 | 1 | 24 | yes | — |
| 169 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 170 | D4×Q8 | C23 | 1 | 36 | yes | — |
| 171 | D4×Q8 | C23 | 1 | 24 | yes | — |
| 172 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 173 | D4×Q8 | C23 | 1 | 24 | yes | — |
| 174 | D4×Q8 | C23 | 1 | 24 | yes | — |
| 175 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 176 | D4×Q8 | C23 | 1 | 144 | yes | — |
| 177 | D4×Q8 | C23 | 1 | 72 | yes | — |
| 178 | D4×Q8 | C23 | 1 | 72 | yes | — |
| 179 | D4×Q8 | C23 | 1 | 72 | yes | — |
| 180 | D4×Q8 | C23 | 1 | 24 | yes | — |
| 181 | D4×Q8 | C23 | 1 | 72 | yes | — |
| 182 | #548 | C23 | 1 | 24 | yes | — |
| 183 | #548 | C23 | 1 | 48 | yes | — |
| 184 | #548 | C23 | 1 | 144 | yes | — |
| 185 | #548 | C23 | 1 | 144 | yes | — |
| 186 | #548 | C23 | 1 | 24 | yes | — |
| 187 | #548 | C23 | 1 | 72 | yes | — |
| 188 | #548 | C23 | 1 | 8 | yes | — |
| 189 | #548 | C23 | 1 | 24 | yes | — |
| 190 | #548 | C23 | 1 | 144 | yes | — |
| 191 | #548 | C23 | 1 | 48 | yes | — |
| 192 | #547 | C23 | 1 | 72 | yes | — |
| 193 | #547 | C23 | 1 | 72 | yes | — |
| 194 | #547 | C23 | 1 | 36 | yes | — |
| 195 | #547 | C23 | 1 | 72 | yes | — |
| 196 | #547 | C23 | 1 | 144 | yes | — |
| 197 | #547 | C23 | 1 | 72 | yes | — |
| 198 | #547 | C23 | 1 | 144 | yes | — |
| 199 | #547 | C23 | 1 | 72 | yes | — |
| 200 | #546 | C23 | 1 | 144 | yes | — |
| 201 | #546 | C23 | 1 | 72 | yes | — |
| 202 | #546 | C23 | 1 | 144 | yes | — |
| 203 | #546 | C23 | 1 | 24 | yes | — |
| 204 | #546 | C23 | 1 | 72 | yes | — |
| 205 | #546 | C23 | 1 | 144 | yes | — |
| 206 | D42 | C23 | 1 | 24 | yes | — |
| 207 | D42 | C23 | 1 | 36 | yes | — |
| 208 | D42 | C23 | 1 | 36 | yes | — |
| 209 | #544 | C23 | 1 | 36 | yes | — |
| 210 | #544 | C23 | 1 | 6 | yes | — |
| 211 | #544 | C23 | 1 | 144 | yes | — |
| 212 | #543 | C23 | 1 | 144 | yes | — |
| 213 | #542 | C23 | 1 | 72 | yes | — |
| 214 | #542 | C23 | 1 | 72 | yes | — |
| 215 | #542 | C23 | 1 | 72 | yes | — |
| 216 | #542 | C23 | 1 | 144 | yes | — |
| 217 | #542 | C23 | 1 | 144 | yes | — |
| 218 | #542 | C23 | 1 | 144 | yes | — |
| 219 | #541 | C23 | 1 | 72 | yes | — |
| 220 | #540 | C23 | 1 | 72 | yes | — |
| 221 | #540 | C23 | 1 | 72 | yes | — |
| 222 | #540 | C23 | 1 | 144 | yes | — |
| 223 | #539 | C23 | 1 | 72 | yes | — |
| 224 | #539 | C23 | 1 | 288 | yes | — |
| 225 | #538 | C23 | 1 | 144 | yes | — |
| 226 | #538 | C23 | 1 | 144 | yes | — |
| 227 | #537 | C23 | 1 | 18 | yes | — |
| 228 | #537 | C23 | 1 | 36 | yes | — |
| 229 | #537 | C23 | 1 | 72 | yes | — |
| 230 | #537 | C23 | 1 | 144 | yes | — |
| 231 | #537 | C23 | 1 | 12 | yes | — |
| 232 | #537 | C23 | 1 | 144 | yes | — |
| 233 | #537 | C23 | 1 | 144 | yes | — |
| 234 | #536 | C23 | 1 | 36 | yes | — |
| 235 | #536 | C23 | 1 | 144 | yes | — |
| 236 | #536 | C23 | 1 | 144 | yes | — |
| 237 | #535 | C23 | 1 | 12 | yes | — |
| 238 | #535 | C23 | 1 | 36 | yes | — |
| 239 | #533 | C23 | 1 | 36 | yes | — |
| 240 | #533 | C23 | 1 | 36 | yes | — |
| 241 | #533 | C23 | 1 | 36 | yes | — |
| 242 | #533 | C23 | 1 | 36 | yes | — |
| 243 | #533 | C23 | 1 | 6 | yes | — |
| 244 | #533 | C23 | 1 | 18 | yes | — |
| 245 | #533 | C23 | 1 | 18 | yes | — |
| 246 | #533 | C23 | 1 | 72 | yes | — |
| 247 | #533 | C23 | 1 | 72 | yes | — |
| 248 | #532 | C23 | 1 | 18 | yes | — |
| 249 | #532 | C23 | 1 | 36 | yes | — |
| 250 | #532 | C23 | 1 | 36 | yes | — |
| 251 | #532 | C23 | 1 | 36 | yes | — |
| 252 | #532 | C23 | 1 | 36 | yes | — |
| 253 | #532 | C23 | 1 | 36 | yes | — |
| 254 | #532 | C23 | 1 | 36 | yes | — |
| 255 | #532 | C23 | 1 | 36 | yes | — |
| 256 | #532 | C23 | 1 | 18 | yes | — |
| 257 | #532 | C23 | 1 | 18 | yes | — |
| 258 | #532 | C23 | 1 | 72 | yes | — |
| 259 | #532 | C23 | 1 | 72 | yes | — |
| 260 | #532 | C23 | 1 | 72 | yes | — |
| 261 | C2×C4⋊Q8 | C23 | 1 | 18 | yes | — |
| 262 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 263 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 264 | C2×C4⋊Q8 | C23 | 1 | 72 | yes | — |
| 265 | C2×#127 | C23 | 1 | 18 | yes | — |
| 266 | #529 | C23 | 1 | 36 | yes | — |
| 267 | #529 | C23 | 1 | 36 | yes | — |
| 268 | #529 | C23 | 1 | 36 | yes | — |
| 269 | #529 | C23 | 1 | 36 | yes | — |
| 270 | #529 | C23 | 1 | 36 | yes | — |
| 271 | #529 | C23 | 1 | 36 | yes | — |
| 272 | #529 | C23 | 1 | 72 | yes | — |
| 273 | #529 | C23 | 1 | 72 | yes | — |
| 274 | C2×#125 | C23 | 1 | 18 | yes | — |
| 275 | C2×#124 | C23 | 1 | 36 | yes | — |
| 276 | #525 | C23 | 1 | 12 | yes | — |
| 277 | #525 | C23 | 1 | 36 | yes | — |
| 278 | #525 | C23 | 1 | 36 | yes | — |
| 279 | #525 | C23 | 1 | 144 | yes | — |
| 280 | #525 | C23 | 1 | 144 | yes | — |
| 281 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 282 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 283 | C2×C22⋊Q8 | C23 | 1 | 72 | yes | — |
| 284 | C2×C22⋊Q8 | C23 | 1 | 144 | yes | — |
| 285 | C2×#121 | C23 | 1 | 12 | yes | — |
| 286 | C2×#121 | C23 | 1 | 36 | yes | — |
| 287 | C2×#121 | C23 | 1 | 72 | yes | — |
| 288 | #520 | C23 | 1 | 4 | yes | — |
| 289 | #520 | C23 | 1 | 36 | yes | — |
| 290 | #520 | C23 | 1 | 24 | yes | — |
| 291 | #520 | C23 | 1 | 36 | yes | — |
| 292 | #520 | C23 | 1 | 24 | yes | — |
| 293 | #520 | C23 | 1 | 48 | yes | — |
| 294 | #519 | C23 | 1 | 2 | yes | — |
| 295 | #519 | C23 | 1 | 24 | yes | — |
| 296 | #518 | C23 | 1 | 36 | yes | — |
| 297 | #518 | C23 | 1 | 72 | yes | — |
| 298 | C4×#41 | C23 | 1 | 6 | yes | — |
| 299 | C4×#41 | C23 | 1 | 18 | yes | — |
| 300 | C4×#41 | C23 | 1 | 18 | yes | — |
| 301 | C4×#41 | C23 | 1 | 6 | yes | — |
| 302 | C4×#41 | C23 | 1 | 36 | yes | — |
| 303 | C4×#41 | C23 | 1 | 24 | yes | — |
| 304 | C4×#41 | C23 | 1 | 36 | yes | — |
| 305 | C4×#41 | C23 | 1 | 24 | yes | — |
| 306 | C4×#41 | C23 | 1 | 36 | yes | — |
| 307 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 308 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 309 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 310 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 311 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 312 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 313 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 314 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 315 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 316 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 317 | C2×C4×Q8 | C23 | 1 | 24 | yes | — |
| 318 | C2×C4×Q8 | C23 | 1 | 6 | yes | — |
| 319 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 320 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 321 | C2×C4×D4 | C23 | 1 | 36 | yes | — |
| 322 | C2×C4×D4 | C23 | 1 | 72 | yes | — |
| 323 | C2×C4×D4 | C23 | 1 | 36 | yes | — |
| 324 | C2×#117 | C23 | 1 | 9 | yes | — |
| 325 | C22×C4⋊C4 | C23 | 1 | 9 | yes | — |
| 326 | C22×C42 | C23 | 1 | 9 | yes | — |
| 327 | 2−1+4 | — | 2 | 48 | no | — |
| 328 | 2−1+4 | — | 4 | 192 | no | — |
| 329 | 2−1+4 | — | 4 | 144 | no | — |
| 330 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 331 | C2×#41 | — | 2 | 8 | no | — |
| 332 | C2×#41 | — | 4 | 144 | no | — |
| 333 | C2×#41 | — | 4 | 96 | no | — |
| 334 | C2×#41 | C24 | 1 | 3 | yes | — |
| 335 | C2×#41 | C24 | 1 | 3 | yes | — |
| 336 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 337 | C2×#41 | C24 | 1 | 12 | yes | — |
| 338 | C2×#41 | C24 | 1 | 8 | yes | — |
| 339 | C2×#41 | C24 | 1 | 36 | yes | — |
| 340 | C2×#41 | C24 | 1 | 24 | yes | — |
| 341 | C2×#41 | C24 | 1 | 72 | yes | — |
| 342 | C2×#41 | C24 | 1 | 144 | yes | — |
| 343 | C2×#41 | C24 | 1 | 72 | yes | — |
| 344 | C2×#41 | C24 | 1 | 72 | yes | — |
| 345 | C2×#41 | C24 | 1 | 36 | yes | — |
| 346 | C2×#41 | C24 | 1 | 48 | yes | — |
| 347 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 348 | C22×Q8 | — | 2 | 24 | no | — |
| 349 | C22×Q8 | — | 4 | 96 | no | — |
| 350 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 351 | C22×Q8 | C24 | 1 | 9 | yes | — |
| 352 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 353 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 354 | C22×Q8 | C24 | 1 | 24 | yes | — |
| 355 | C22×Q8 | C24 | 1 | 36 | yes | — |
| 356 | C22×Q8 | C24 | 1 | 144 | yes | — |
| 357 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 358 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 359 | C22×D4 | C24 | 1 | 3 | yes | — |
| 360 | C22×D4 | C24 | 1 | 12 | yes | — |
| 361 | C22×D4 | C24 | 1 | 24 | yes | — |
| 362 | C22×D4 | C24 | 1 | 24 | yes | — |
| 363 | C22×D4 | C24 | 1 | 36 | yes | — |
| 364 | C22×D4 | C24 | 1 | 36 | yes | — |
| 365 | C23×C4 | C24 | 1 | 9 | yes | — |
| 366 | C23×C4 | C24 | 1 | 3 | yes | — |
| 367 | C23×C4 | C24 | 1 | 72 | yes | — |
| 368 | C23×C4 | C24 | 1 | 9 | yes | — |
| 369 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 370 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 371 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 372 | C4⋊Q8 | C24 | 1 | 72 | yes | — |
| 373 | C4⋊Q8 | C24 | 1 | 72 | yes | — |
| 374 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 375 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 376 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 377 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 378 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 379 | C4⋊Q8 | C24 | 1 | 144 | yes | — |
| 380 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 381 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 382 | C4⋊Q8 | C24 | 1 | 24 | yes | — |
| 383 | #127 | C24 | 1 | 18 | yes | — |
| 384 | #127 | C24 | 1 | 36 | yes | — |
| 385 | #127 | C24 | 1 | 36 | yes | — |
| 386 | #127 | C24 | 1 | 36 | yes | — |
| 387 | #127 | C24 | 1 | 24 | yes | — |
| 388 | #126 | C24 | 1 | 72 | yes | — |
| 389 | #126 | C24 | 1 | 72 | yes | — |
| 390 | #126 | C24 | 1 | 144 | yes | — |
| 391 | #126 | C24 | 1 | 144 | yes | — |
| 392 | #125 | C24 | 1 | 72 | yes | — |
| 393 | #125 | C24 | 1 | 72 | yes | — |
| 394 | #125 | C24 | 1 | 12 | yes | — |
| 395 | #125 | C24 | 1 | 24 | yes | — |
| 396 | #125 | C24 | 1 | 36 | yes | — |
| 397 | #125 | C24 | 1 | 36 | yes | — |
| 398 | #125 | C24 | 1 | 72 | yes | — |
| 399 | #125 | C24 | 1 | 144 | yes | — |
| 400 | #124 | C24 | 1 | 36 | yes | — |
| 401 | #124 | C24 | 1 | 72 | yes | — |
| 402 | #124 | C24 | 1 | 72 | yes | — |
| 403 | #124 | C24 | 1 | 72 | yes | — |
| 404 | #124 | C24 | 1 | 24 | yes | — |
| 405 | #124 | C24 | 1 | 36 | yes | — |
| 406 | #124 | C24 | 1 | 36 | yes | — |
| 407 | #124 | C24 | 1 | 72 | yes | — |
| 408 | #124 | C24 | 1 | 144 | yes | — |
| 409 | #124 | C24 | 1 | 144 | yes | — |
| 410 | #123 | C24 | 1 | 24 | yes | — |
| 411 | #123 | C24 | 1 | 72 | yes | — |
| 412 | #123 | C24 | 1 | 72 | yes | — |
| 413 | #123 | C24 | 1 | 288 | yes | — |
| 414 | #123 | C24 | 1 | 144 | yes | — |
| 415 | #123 | C24 | 1 | 144 | yes | — |
| 416 | #123 | C24 | 1 | 144 | yes | — |
| 417 | #123 | C24 | 1 | 144 | yes | — |
| 418 | C22⋊Q8 | C24 | 1 | 36 | yes | — |
| 419 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 420 | C22⋊Q8 | C24 | 1 | 144 | yes | — |
| 421 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 422 | C22⋊Q8 | C24 | 1 | 144 | yes | — |
| 423 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 424 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 425 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 426 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 427 | C22⋊Q8 | C24 | 1 | 288 | yes | — |
| 428 | C22⋊Q8 | C24 | 1 | 288 | yes | — |
| 429 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 430 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 431 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 432 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 433 | C22⋊Q8 | C24 | 1 | 36 | yes | — |
| 434 | C22⋊Q8 | C24 | 1 | 36 | yes | — |
| 435 | C22⋊Q8 | C24 | 1 | 144 | yes | — |
| 436 | C22⋊Q8 | C24 | 1 | 24 | yes | — |
| 437 | C22⋊Q8 | C24 | 1 | 144 | yes | — |
| 438 | C22⋊Q8 | C24 | 1 | 144 | yes | — |
| 439 | #121 | C24 | 1 | 12 | yes | — |
| 440 | #121 | C24 | 1 | 36 | yes | — |
| 441 | #121 | C24 | 1 | 72 | yes | — |
| 442 | #121 | C24 | 1 | 144 | yes | — |
| 443 | #121 | C24 | 1 | 24 | yes | — |
| 444 | #121 | C24 | 1 | 24 | yes | — |
| 445 | #121 | C24 | 1 | 24 | yes | — |
| 446 | #121 | C24 | 1 | 72 | yes | — |
| 447 | #121 | C24 | 1 | 72 | yes | — |
| 448 | #121 | C24 | 1 | 72 | yes | — |
| 449 | #121 | C24 | 1 | 288 | yes | — |
| 450 | #121 | C24 | 1 | 36 | yes | — |
| 451 | #121 | C24 | 1 | 48 | yes | — |
| 452 | #121 | C24 | 1 | 12 | yes | — |
| 453 | #121 | C24 | 1 | 36 | yes | — |
| 454 | #121 | C24 | 1 | 36 | yes | — |
| 455 | #121 | C24 | 1 | 144 | yes | — |
| 456 | #121 | C24 | 1 | 72 | yes | — |
| 457 | #121 | C24 | 1 | 72 | yes | — |
| 458 | #121 | C24 | 1 | 24 | yes | — |
| 459 | #121 | C24 | 1 | 144 | yes | — |
| 460 | #121 | C24 | 1 | 144 | yes | — |
| 461 | #120 | C24 | 1 | 24 | yes | — |
| 462 | #120 | C24 | 1 | 144 | yes | — |
| 463 | #120 | C24 | 1 | 48 | yes | — |
| 464 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 465 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 466 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 467 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 468 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 469 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 470 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 471 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 472 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 473 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 474 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 475 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 476 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 477 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 478 | C4×Q8 | C24 | 1 | 72 | yes | — |
| 479 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 480 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 481 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 482 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 483 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 484 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 485 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 486 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 487 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 488 | C4×Q8 | C24 | 1 | 48 | yes | — |
| 489 | C4×D4 | C24 | 1 | 18 | yes | — |
| 490 | C4×D4 | C24 | 1 | 24 | yes | — |
| 491 | C4×D4 | C24 | 1 | 72 | yes | — |
| 492 | C4×D4 | C24 | 1 | 72 | yes | — |
| 493 | C4×D4 | C24 | 1 | 36 | yes | — |
| 494 | C4×D4 | C24 | 1 | 36 | yes | — |
| 495 | C4×D4 | C24 | 1 | 18 | yes | — |
| 496 | C4×D4 | C24 | 1 | 36 | yes | — |
| 497 | C4×D4 | C24 | 1 | 18 | yes | — |
| 498 | C4×D4 | C24 | 1 | 36 | yes | — |
| 499 | C4×D4 | C24 | 1 | 18 | yes | — |
| 500 | C4×D4 | C24 | 1 | 144 | yes | — |
| 501 | C4×D4 | C24 | 1 | 72 | yes | — |
| 502 | C4×D4 | C24 | 1 | 72 | yes | — |
| 503 | C4×D4 | C24 | 1 | 72 | yes | — |
| 504 | C4×D4 | C24 | 1 | 72 | yes | — |
| 505 | C4×D4 | C24 | 1 | 72 | yes | — |
| 506 | C4×D4 | C24 | 1 | 72 | yes | — |
| 507 | C4×D4 | C24 | 1 | 24 | yes | — |
| 508 | C4×D4 | C24 | 1 | 24 | yes | — |
| 509 | C4×D4 | C24 | 1 | 36 | yes | — |
| 510 | C4×D4 | C24 | 1 | 72 | yes | — |
| 511 | C4×D4 | C24 | 1 | 36 | yes | — |
| 512 | C4×D4 | C24 | 1 | 72 | yes | — |
| 513 | C4×D4 | C24 | 1 | 72 | yes | — |
| 514 | C4×D4 | C24 | 1 | 36 | yes | — |
| 515 | C4×D4 | C24 | 1 | 72 | yes | — |
| 516 | C4×D4 | C24 | 1 | 72 | yes | — |
| 517 | C4×D4 | C24 | 1 | 36 | yes | — |
| 518 | C4×D4 | C24 | 1 | 144 | yes | — |
| 519 | #117 | C24 | 1 | 18 | yes | — |
| 520 | #117 | C24 | 1 | 18 | yes | — |
| 521 | #117 | C24 | 1 | 18 | yes | — |
| 522 | #117 | C24 | 1 | 18 | yes | — |
| 523 | #117 | C24 | 1 | 12 | yes | — |
| 524 | #117 | C24 | 1 | 12 | yes | — |
| 525 | #117 | C24 | 1 | 72 | yes | — |
| 526 | #117 | C24 | 1 | 72 | yes | — |
| 527 | #117 | C24 | 1 | 72 | yes | — |
| 528 | #117 | C24 | 1 | 72 | yes | — |
| 529 | #117 | C24 | 1 | 72 | yes | — |
| 530 | #117 | C24 | 1 | 36 | yes | — |
| 531 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 532 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 533 | C2×C4⋊C4 | C24 | 1 | 36 | yes | — |
| 534 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 535 | C2×C4⋊C4 | C24 | 1 | 36 | yes | — |
| 536 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 537 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 538 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 539 | C2×C4⋊C4 | C24 | 1 | 72 | yes | — |
| 540 | C2×C4⋊C4 | C24 | 1 | 36 | yes | — |
| 541 | C2×C4⋊C4 | C24 | 1 | 72 | yes | — |
| 542 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 543 | C2×C4⋊C4 | C24 | 1 | 144 | yes | — |
| 544 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 545 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 546 | C2×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 547 | C2×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 548 | C2×C42 | C24 | 1 | 9 | yes | — |
| 549 | C2×C42 | C24 | 1 | 18 | yes | — |
| 550 | C2×C42 | C24 | 1 | 18 | yes | — |
| 551 | C2×C42 | C24 | 1 | 9 | yes | — |
| 552 | C2×C42 | C24 | 1 | 9 | yes | — |
| 553 | C2×C42 | C24 | 1 | 72 | yes | — |
| 554 | C2×C42 | C24 | 1 | 3 | yes | — |
| 555 | C2×C42 | C24 | 1 | 18 | yes | — |
| 556 | C2×C42 | C24 | 1 | 18 | yes | — |
| 557 | C24 | C25 | 1 | 3 | yes | — |
| 558 | C24 | C25 | 1 | 24 | yes | — |
| 559 | #41 | — | 2 | 96 | no | — |
| 560 | #41 | — | 2 | 4 | no | — |
| 561 | #41 | — | 2 | 32 | no | — |
| 562 | #41 | — | 2 | 12 | no | — |
| 563 | #41 | — | 2 | 144 | no | — |
| 564 | #41 | — | 2 | 12 | no | — |
| 565 | #41 | — | 2 | 48 | no | — |
| 566 | #41 | — | 4 | 144 | no | — |
| 567 | #41 | — | 4 | 144 | no | — |
| 568 | #41 | — | 4 | 144 | no | — |
| 569 | #41 | — | 4 | 288 | no | — |
| 570 | #41 | — | 8 | 36 | no | — |
| 571 | #41 | — | 8 | 48 | no | — |
| 572 | #41 | 2−1+4 | 1 | 8 | yes | complemented |
| 573 | C2×Q8 | — | 2 | 48 | no | — |
| 574 | C2×Q8 | — | 2 | 48 | no | — |
| 575 | C2×Q8 | — | 2 | 96 | no | — |
| 576 | C2×Q8 | — | 2 | 4 | no | — |
| 577 | C2×Q8 | — | 2 | 36 | no | — |
| 578 | C2×Q8 | — | 4 | 72 | no | — |
| 579 | C2×Q8 | — | 4 | 288 | no | — |
| 580 | C2×Q8 | — | 8 | 6 | no | — |
| 581 | C2×Q8 | H(5,𝔽2) | 1 | 8 | yes | complemented |
| 582 | C2×Q8 | C25 | 1 | 3 | yes | — |
| 583 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 584 | C2×Q8 | C25 | 1 | 36 | yes | — |
| 585 | C2×Q8 | C25 | 1 | 36 | yes | — |
| 586 | C2×Q8 | C25 | 1 | 12 | yes | — |
| 587 | C2×Q8 | C25 | 1 | 24 | yes | — |
| 588 | C2×Q8 | C25 | 1 | 72 | yes | — |
| 589 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 590 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 591 | C2×D4 | — | 2 | 12 | no | — |
| 592 | C2×D4 | — | 2 | 96 | no | — |
| 593 | C2×D4 | — | 2 | 48 | no | — |
| 594 | C2×D4 | — | 4 | 72 | no | — |
| 595 | C2×D4 | — | 4 | 48 | no | — |
| 596 | C2×D4 | — | 8 | 36 | no | — |
| 597 | C2×D4 | C25 | 1 | 6 | yes | — |
| 598 | C2×D4 | C25 | 1 | 24 | yes | — |
| 599 | C2×D4 | C25 | 1 | 24 | yes | — |
| 600 | C2×D4 | C25 | 1 | 3 | yes | — |
| 601 | C2×D4 | C25 | 1 | 12 | yes | — |
| 602 | C2×D4 | C25 | 1 | 24 | yes | — |
| 603 | C2×D4 | C25 | 1 | 36 | yes | — |
| 604 | C2×D4 | C25 | 1 | 24 | yes | — |
| 605 | C2×D4 | C25 | 1 | 72 | yes | — |
| 606 | C2×D4 | C25 | 1 | 36 | yes | — |
| 607 | C2×D4 | C25 | 1 | 72 | yes | — |
| 608 | C2×D4 | C25 | 1 | 48 | yes | — |
| 609 | C2×D4 | C25 | 1 | 3 | yes | — |
| 610 | C22×C4 | — | 2 | 36 | no | — |
| 611 | C22×C4 | — | 2 | 12 | no | — |
| 612 | C22×C4 | — | 4 | 144 | no | — |
| 613 | C22×C4 | — | 8 | 9 | no | — |
| 614 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 615 | C22×C4 | C25 | 1 | 3 | yes | — |
| 616 | C22×C4 | C25 | 1 | 3 | yes | — |
| 617 | C22×C4 | C25 | 1 | 3 | yes | — |
| 618 | C22×C4 | C25 | 1 | 3 | yes | — |
| 619 | C22×C4 | C25 | 1 | 24 | yes | — |
| 620 | C22×C4 | C25 | 1 | 9 | yes | — |
| 621 | C22×C4 | C25 | 1 | 18 | yes | — |
| 622 | C22×C4 | C25 | 1 | 18 | yes | — |
| 623 | C22×C4 | C25 | 1 | 72 | yes | — |
| 624 | C22×C4 | C25 | 1 | 3 | yes | — |
| 625 | C22×C4 | C25 | 1 | 18 | yes | — |
| 626 | C22×C4 | C25 | 1 | 9 | yes | — |
| 627 | C22×C4 | C25 | 1 | 18 | yes | — |
| 628 | C22×C4 | C25 | 1 | 72 | yes | — |
| 629 | C22×C4 | C25 | 1 | 24 | yes | — |
| 630 | C22×C4 | C25 | 1 | 144 | yes | — |
| 631 | C22×C4 | C25 | 1 | 3 | yes | — |
| 632 | C22×C4 | C25 | 1 | 3 | yes | — |
| 633 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 634 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 635 | C4⋊C4 | C25 | 1 | 18 | yes | — |
| 636 | C4⋊C4 | C25 | 1 | 36 | yes | — |
| 637 | C4⋊C4 | C25 | 1 | 24 | yes | — |
| 638 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 639 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 640 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 641 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 642 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 643 | C4⋊C4 | C25 | 1 | 36 | yes | — |
| 644 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 645 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 646 | C4⋊C4 | C25 | 1 | 18 | yes | — |
| 647 | C4⋊C4 | C25 | 1 | 18 | yes | — |
| 648 | C4⋊C4 | C25 | 1 | 18 | yes | — |
| 649 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 650 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 651 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 652 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 653 | C4⋊C4 | C25 | 1 | 24 | yes | — |
| 654 | C4⋊C4 | C25 | 1 | 24 | yes | — |
| 655 | C22⋊C4 | C25 | 1 | 24 | yes | — |
| 656 | C22⋊C4 | C25 | 1 | 36 | yes | — |
| 657 | C22⋊C4 | C25 | 1 | 24 | yes | — |
| 658 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 659 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 660 | C22⋊C4 | C25 | 1 | 144 | yes | — |
| 661 | C22⋊C4 | C25 | 1 | 36 | yes | — |
| 662 | C22⋊C4 | C25 | 1 | 48 | yes | — |
| 663 | C22⋊C4 | C25 | 1 | 8 | yes | — |
| 664 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 665 | C22⋊C4 | C25 | 1 | 24 | yes | — |
| 666 | C22⋊C4 | C25 | 1 | 24 | yes | — |
| 667 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 668 | C42 | C25 | 1 | 18 | yes | — |
| 669 | C42 | C25 | 1 | 6 | yes | — |
| 670 | C42 | C25 | 1 | 6 | yes | — |
| 671 | C42 | C25 | 1 | 18 | yes | — |
| 672 | C42 | C25 | 1 | 24 | yes | — |
| 673 | C42 | C25 | 1 | 24 | yes | — |
| 674 | C42 | C25 | 1 | 18 | yes | — |
| 675 | C42 | C25 | 1 | 18 | yes | — |
| 676 | C42 | C25 | 1 | 18 | yes | — |
| 677 | C42 | C25 | 1 | 18 | yes | — |
| 678 | C42 | C25 | 1 | 72 | yes | — |
| 679 | C23 | — | 2 | 6 | no | — |
| 680 | C23 | — | 2 | 6 | no | — |
| 681 | C23 | — | 2 | 48 | no | — |
| 682 | C23 | — | 4 | 3 | no | — |
| 683 | C23 | — | 4 | 24 | no | — |
| 684 | C23 | — | 4 | 24 | no | — |
| 685 | C23 | C26 | 1 | 24 | yes | — |
| 686 | C23 | C26 | 1 | 3 | yes | — |
| 687 | C23 | C26 | 1 | 1 | yes | characteristic |
| 688 | C23 | C26 | 1 | 3 | yes | — |
| 689 | Q8 | — | 2 | 72 | no | — |
| 690 | Q8 | — | 2 | 72 | no | — |
| 691 | Q8 | — | 2 | 6 | no | — |
| 692 | Q8 | — | 2 | 8 | no | — |
| 693 | Q8 | — | 4 | 72 | no | — |
| 694 | Q8 | — | 4 | 24 | no | — |
| 695 | Q8 | — | 4 | 12 | no | — |
| 696 | Q8 | C2×H(5,𝔽2) | 1 | 16 | yes | — |
| 697 | Q8 | C2×2−1+4 | 1 | 4 | yes | complemented |
| 698 | D4 | — | 2 | 48 | no | — |
| 699 | D4 | — | 2 | 48 | no | — |
| 700 | D4 | — | 2 | 12 | no | — |
| 701 | D4 | — | 2 | 72 | no | — |
| 702 | D4 | — | 2 | 48 | no | — |
| 703 | D4 | — | 2 | 24 | no | — |
| 704 | D4 | — | 2 | 6 | no | — |
| 705 | D4 | — | 4 | 48 | no | — |
| 706 | D4 | — | 4 | 72 | no | — |
| 707 | D4 | — | 4 | 36 | no | — |
| 708 | D4 | — | 4 | 72 | no | — |
| 709 | D4 | — | 4 | 24 | no | — |
| 710 | D4 | C2×2−1+4 | 1 | 12 | yes | complemented |
| 711 | C2×C4 | — | 2 | 18 | no | — |
| 712 | C2×C4 | — | 2 | 6 | no | — |
| 713 | C2×C4 | — | 2 | 36 | no | — |
| 714 | C2×C4 | — | 2 | 36 | no | — |
| 715 | C2×C4 | — | 2 | 144 | no | — |
| 716 | C2×C4 | — | 2 | 2 | no | — |
| 717 | C2×C4 | — | 2 | 6 | no | — |
| 718 | C2×C4 | — | 2 | 6 | no | — |
| 719 | C2×C4 | — | 2 | 6 | no | — |
| 720 | C2×C4 | — | 2 | 48 | no | — |
| 721 | C2×C4 | — | 4 | 24 | no | — |
| 722 | C2×C4 | — | 4 | 144 | no | — |
| 723 | C2×C4 | — | 4 | 3 | no | — |
| 724 | C2×C4 | — | 4 | 18 | no | — |
| 725 | C2×C4 | — | 4 | 9 | no | — |
| 726 | C2×C4 | — | 4 | 18 | no | — |
| 727 | C2×C4 | — | 4 | 72 | no | — |
| 728 | C2×C4 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 729 | C2×C4 | C2×2−1+4 | 1 | 12 | yes | complemented |
| 730 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 731 | C2×C4 | C26 | 1 | 3 | yes | — |
| 732 | C2×C4 | C26 | 1 | 8 | yes | — |
| 733 | C2×C4 | C26 | 1 | 18 | yes | — |
| 734 | C2×C4 | C26 | 1 | 6 | yes | — |
| 735 | C2×C4 | C26 | 1 | 8 | yes | — |
| 736 | C2×C4 | C26 | 1 | 24 | yes | — |
| 737 | C2×C4 | C26 | 1 | 18 | yes | — |
| 738 | C2×C4 | C26 | 1 | 6 | yes | — |
| 739 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 740 | C2×C4 | C26 | 1 | 3 | yes | — |
| 741 | C22 | — | 2 | 3 | no | — |
| 742 | C22 | — | 2 | 1 | no | — |
| 743 | C22 | — | 2 | 1 | no | — |
| 744 | C22 | — | 2 | 3 | no | — |
| 745 | C22 | — | 2 | 3 | no | — |
| 746 | C22 | — | 2 | 24 | no | — |
| 747 | C22 | — | 2 | 3 | no | — |
| 748 | C22 | — | 2 | 24 | no | — |
| 749 | C22 | — | 2 | 3 | no | — |
| 750 | C22 | — | 2 | 24 | no | — |
| 751 | C22 | — | 4 | 12 | no | — |
| 752 | C22 | — | 8 | 48 | no | — |
| 753 | C22 | C22×H(5,𝔽2) | 1 | 2 | yes | — |
| 754 | C22 | C22×2−1+4 | 1 | 6 | yes | — |
| 755 | C22 | C27 | 1 | 1 | yes | characteristic |
| 756 | C4 | — | 2 | 24 | no | — |
| 757 | C4 | — | 2 | 18 | no | — |
| 758 | C4 | — | 2 | 1 | no | — |
| 759 | C4 | — | 2 | 8 | no | — |
| 760 | C4 | — | 2 | 3 | no | — |
| 761 | C4 | — | 2 | 8 | no | — |
| 762 | C4 | — | 2 | 6 | no | — |
| 763 | C4 | — | 2 | 18 | no | — |
| 764 | C4 | C22×H(5,𝔽2) | 1 | 12 | yes | — |
| 765 | C4 | C22×2−1+4 | 1 | 6 | yes | — |
| 766 | C4 | C22×2−1+4 | 1 | 2 | yes | — |
| 767 | C2 | — | 2 | 2 | no | — |
| 768 | C2 | — | 2 | 6 | no | — |
| 769 | C2 | — | 4 | 3 | no | — |
| 770 | C2 | — | 4 | 24 | no | — |
| 771 | C2 | C23×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 772 | C2 | C23×2−1+4 | 1 | 1 | yes | characteristic |
| 773 | C2 | #63103 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22 | C27 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63039 | C2 | semidirect |
| 2. #63015 | C2 | semidirect |
| 3. #62999 | C2 | semidirect |
| 4. D4×2−1+4 | C2 | semidirect |
| 5. #62986 | C2 | semidirect |
| 6. Q8×H(5,𝔽2) | C2 | semidirect |
| 7. #62946 | C2 | semidirect |
| 8. #62944 | C2 | semidirect |
| 9. #62917 | C2 | semidirect |
| 10. #62913 | C2 | semidirect |
| 11. #62835 | C2 | semidirect |
| 12. #62800 | C2 | semidirect |
| 13. #62788 | C2 | semidirect |
| 14. C2×#3497 | C2 | semidirect |
| 15. C2×Q8×#41 | C2 | semidirect |
| 16. C22×2−1+4 | C22 | semidirect |
| 17. #3561 | C22 | semidirect |
| 18. #3559 | C22 | semidirect |
| 19. #3554 | C22 | semidirect |
| 20. #3554 | C22 | semidirect |
| 21. #3552 | C22 | semidirect |
| 22. #3550 | C22 | semidirect |
| 23. #3548 | C22 | semidirect |
| 24. #3548 | C22 | semidirect |
| 25. #3547 | C22 | semidirect |
| 26. #3547 | C22 | semidirect |
| 27. #3541 | C22 | semidirect |
| 28. #3536 | C22 | semidirect |
| 29. #3536 | C22 | semidirect |
| 30. #3523 | C22 | semidirect |
| 31. #3522 | C22 | semidirect |
| 32. #3522 | C22 | semidirect |
| 33. #3522 | C22 | semidirect |
| 34. #3522 | C22 | semidirect |
| 35. #3520 | C22 | semidirect |
| 36. #3519 | C22 | semidirect |
| 37. #3519 | C22 | semidirect |
| 38. #3518 | C22 | semidirect |
| 39. #3517 | C22 | semidirect |
| 40. #3517 | C22 | semidirect |
| 41. #3516 | C22 | semidirect |
| 42. #3514 | C22 | semidirect |
| 43. #3511 | C22 | semidirect |
| 44. #3511 | C22 | semidirect |
| 45. #3511 | C22 | semidirect |
| 46. #3508 | C22 | semidirect |
| 47. #3508 | C22 | semidirect |
| 48. #3507 | C22 | semidirect |
| 49. #3506 | C22 | semidirect |
| 51. #3503 | C22 | semidirect |
| 52. #3503 | C22 | semidirect |
| 53. #3502 | C22 | semidirect |
| 54. #3501 | C22 | semidirect |
| 55. #3501 | C22 | semidirect |
| 56. #3499 | C22 | semidirect |
| 57. #3499 | C22 | semidirect |
| 59. #3497 | C22 | semidirect |
| 60. #3497 | C22 | semidirect |
| 61. #3497 | C22 | semidirect |
| 62. #3497 | C22 | semidirect |
| 63. #3497 | C22 | semidirect |
| 64. #3497 | C22 | semidirect |
| 65. #3497 | C22 | semidirect |
| 66. #3494 | C22 | semidirect |
| 67. #3492 | C22 | semidirect |
| 68. #3489 | C22 | semidirect |
| 69. #3489 | C22 | semidirect |
| 71. #3486 | C22 | semidirect |
| 72. #3486 | C22 | semidirect |
| 73. #3483 | C22 | semidirect |
| 74. #3483 | C22 | semidirect |
| 75. #3482 | C22 | semidirect |
| 76. #3481 | C22 | semidirect |
| 77. #3480 | C22 | semidirect |
| 78. #3480 | C22 | semidirect |
| 80. Q8×#41 | C22 | semidirect |
| 81. Q8×#41 | C22 | semidirect |
| 82. Q8×#41 | C22 | semidirect |
| 83. Q8×#41 | C22 | semidirect |
| 84. Q8×#41 | C22 | semidirect |
| 85. C2×Q82 | C22 | semidirect |
| 86. C2×#557 | C22 | semidirect |
| 87. C2×#554 | C22 | semidirect |
| 88. D4×#41 | C22 | semidirect |
| 89. D4×#41 | C22 | semidirect |
| 90. C2×#550 | C22 | semidirect |
| 91. C2×D4×Q8 | C22 | semidirect |
| 92. C2×D4×Q8 | C22 | semidirect |
| 93. C2×D4×Q8 | C22 | semidirect |
| 94. C2×#548 | C22 | semidirect |
| 95. #3461 | C22 | semidirect |
| 96. #3460 | C22 | semidirect |
| 97. C2×#537 | C22 | semidirect |
| 98. #3444 | C22 | semidirect |
| 99. C2×#533 | C22 | semidirect |
| 100. C2×#532 | C22 | semidirect |
| 101. C4×2−1+4 | C22 | semidirect |
| 104. C22×C4×Q8 | C22 | semidirect |
| 572. #41 | 2−1+4 | semidirect |
| 581. C2×Q8 | H(5,𝔽2) | semidirect |
| 697. Q8 | C2×2−1+4 | semidirect |
| 710. D4 | C2×2−1+4 | semidirect |
| 729. C2×C4 | C2×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63039 | 2 |
| #63015 | 2 |
| #62999 | 2 |
| D4×2−1+4 | 2 |
| #62986 | 2 |
| Q8×H(5,𝔽2) | 2 |
| #62946 | 2 |
| #62944 | 2 |
| #62917 | 2 |
| #62913 | 2 |
| #62835 | 2 |
| #62800 | 2 |
| #62788 | 2 |
| C2×#3497 | 2 |
| C2×Q8×#41 | 2 |