Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6901 conjugacy classes of subgroups.
The subgroup lattice has 672 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63001 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #61421 | C2 | 1 | 9 | yes | maximal, complemented |
| 4 | #61420 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | #61410 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | #61407 | C2 | 1 | 9 | yes | maximal, complemented |
| 7 | #61404 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #61402 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #61393 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#3392 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #60646 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #60431 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #60429 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | Q8×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C4×#577 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | C2×#577 | C22 | 1 | 3 | yes | — |
| 17 | C2×#577 | C22 | 1 | 6 | yes | — |
| 18 | #3523 | — | 2 | 3 | no | — |
| 19 | #3519 | — | 2 | 9 | no | — |
| 20 | #3517 | — | 2 | 3 | no | — |
| 21 | #3515 | — | 2 | 9 | no | — |
| 22 | #3509 | C22 | 1 | 9 | yes | complemented |
| 23 | #3508 | C22 | 1 | 9 | yes | — |
| 24 | #3507 | C22 | 1 | 9 | yes | complemented |
| 25 | #3506 | C22 | 1 | 9 | yes | — |
| 26 | #3499 | C22 | 1 | 3 | yes | — |
| 27 | #3498 | C22 | 1 | 3 | yes | — |
| 28 | #3483 | — | 2 | 1 | no | — |
| 29 | #3482 | — | 2 | 3 | no | — |
| 30 | #3480 | C22 | 1 | 3 | yes | — |
| 31 | #3480 | C22 | 1 | 3 | yes | complemented |
| 32 | Q8×#41 | — | 2 | 1 | no | — |
| 33 | Q8×#41 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#557 | C22 | 1 | 3 | yes | complemented |
| 35 | D4×#41 | — | 2 | 3 | no | — |
| 36 | C2×#550 | C22 | 1 | 3 | yes | — |
| 37 | C4×2−1+4 | C22 | 1 | 3 | yes | — |
| 38 | C4×H(5,𝔽2) | C22 | 1 | 3 | yes | — |
| 39 | #3401 | C22 | 1 | 36 | yes | complemented |
| 40 | #3400 | C22 | 1 | 18 | yes | complemented |
| 41 | #3400 | C22 | 1 | 18 | yes | complemented |
| 42 | #3399 | C22 | 1 | 18 | yes | complemented |
| 43 | #3398 | C22 | 1 | 18 | yes | complemented |
| 44 | #3397 | C22 | 1 | 18 | yes | complemented |
| 45 | #3397 | C22 | 1 | 18 | yes | complemented |
| 46 | #3396 | C22 | 1 | 9 | yes | complemented |
| 47 | #3395 | C22 | 1 | 3 | yes | complemented |
| 48 | #3394 | C22 | 1 | 9 | yes | complemented |
| 49 | #3394 | C22 | 1 | 9 | yes | complemented |
| 50 | #3394 | C22 | 1 | 18 | yes | complemented |
| 51 | #3393 | C22 | 1 | 9 | yes | complemented |
| 52 | #3392 | C22 | 1 | 3 | yes | complemented |
| 53 | #3392 | C22 | 1 | 6 | yes | complemented |
| 54 | #3392 | C22 | 1 | 18 | yes | complemented |
| 55 | #3392 | C22 | 1 | 18 | yes | complemented |
| 56 | #3392 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #3392 | C22 | 1 | 6 | yes | complemented |
| 58 | #3391 | C22 | 1 | 3 | yes | complemented |
| 59 | #3154 | C22 | 1 | 18 | yes | complemented |
| 60 | #3154 | C22 | 1 | 18 | yes | complemented |
| 61 | #3152 | C22 | 1 | 9 | yes | complemented |
| 62 | #3151 | C22 | 1 | 9 | yes | complemented |
| 63 | #3147 | C22 | 1 | 9 | yes | complemented |
| 64 | C2×#492 | C22 | 1 | 9 | yes | complemented |
| 65 | #3046 | C22 | 1 | 18 | yes | complemented |
| 66 | #3045 | C22 | 1 | 18 | yes | complemented |
| 67 | #3043 | C22 | 1 | 18 | yes | complemented |
| 68 | #3042 | C22 | 1 | 18 | yes | complemented |
| 69 | #3039 | C22 | 1 | 9 | yes | complemented |
| 70 | #3038 | C22 | 1 | 9 | yes | complemented |
| 71 | #3037 | C22 | 1 | 9 | yes | complemented |
| 72 | #3036 | C22 | 1 | 9 | yes | complemented |
| 73 | #3035 | C22 | 1 | 9 | yes | complemented |
| 74 | #3035 | C22 | 1 | 9 | yes | complemented |
| 75 | C2×#460 | C22 | 1 | 9 | yes | complemented |
| 76 | C2×#461 | C22 | 1 | 9 | yes | complemented |
| 77 | Q8×M16 | C22 | 1 | 3 | yes | complemented |
| 78 | #2962 | C22 | 1 | 9 | yes | complemented |
| 79 | #2960 | C22 | 1 | 9 | yes | complemented |
| 80 | C2×C8×Q8 | C22 | 1 | 3 | yes | complemented |
| 81 | #2952 | C22 | 1 | 9 | yes | complemented |
| 82 | #2949 | C22 | 1 | 9 | yes | complemented |
| 83 | #2947 | C22 | 1 | 9 | yes | complemented |
| 84 | #2946 | C22 | 1 | 9 | yes | complemented |
| 85 | C4×#137 | C22 | 1 | 9 | yes | complemented |
| 86 | C4×AGL(1,ℤ/8) | C22 | 1 | 9 | yes | complemented |
| 87 | C4×#135 | C22 | 1 | 9 | yes | complemented |
| 88 | C2×C4×SD16 | C22 | 1 | 9 | yes | complemented |
| 89 | #2912 | C22 | 1 | 1 | yes | characteristic |
| 90 | #2906 | C22 | 1 | 3 | yes | — |
| 91 | #2898 | C22 | 1 | 3 | yes | — |
| 92 | #2897 | C22 | 1 | 3 | yes | — |
| 93 | C4×#131 | C22 | 1 | 3 | yes | — |
| 94 | C2×2−1+4 | C23 | 1 | 3 | yes | — |
| 95 | C2×H(5,𝔽2) | C23 | 1 | 3 | yes | — |
| 96 | C22×#41 | — | 2 | 3 | no | — |
| 97 | #577 | — | 2 | 24 | no | — |
| 98 | #577 | — | 4 | 24 | no | — |
| 99 | C2×#137 | C23 | 1 | 9 | yes | — |
| 100 | C2×#137 | C23 | 1 | 18 | yes | — |
| 101 | C2×AGL(1,ℤ/8) | C23 | 1 | 9 | yes | — |
| 102 | C2×AGL(1,ℤ/8) | C23 | 1 | 18 | yes | — |
| 103 | C2×#135 | C23 | 1 | 9 | yes | — |
| 104 | C2×#135 | C23 | 1 | 18 | yes | — |
| 105 | C22×SD16 | C23 | 1 | 9 | yes | — |
| 106 | C22×SD16 | C23 | 1 | 18 | yes | — |
| 107 | C2×#131 | C23 | 1 | 3 | yes | — |
| 108 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 109 | #559 | C23 | 1 | 9 | yes | — |
| 110 | #559 | C23 | 1 | 9 | yes | — |
| 111 | #559 | C23 | 1 | 18 | yes | — |
| 112 | Q82 | D4 | 1 | 1 | yes | characteristic |
| 113 | #557 | — | 2 | 3 | no | — |
| 114 | #557 | — | 2 | 9 | no | — |
| 115 | #557 | D4 | 1 | 3 | yes | — |
| 116 | #557 | C23 | 1 | 3 | yes | — |
| 117 | #557 | C23 | 1 | 18 | yes | — |
| 118 | #557 | C23 | 1 | 1 | yes | characteristic |
| 119 | #557 | C23 | 1 | 6 | yes | — |
| 120 | #556 | — | 2 | 9 | no | — |
| 121 | #556 | C23 | 1 | 9 | yes | — |
| 122 | #556 | C23 | 1 | 9 | yes | — |
| 123 | #556 | C23 | 1 | 18 | yes | — |
| 124 | #555 | — | 2 | 9 | no | — |
| 125 | #554 | — | 2 | 9 | no | — |
| 126 | #554 | D4 | 1 | 9 | yes | — |
| 127 | #553 | — | 2 | 18 | no | — |
| 128 | #553 | — | 2 | 9 | no | — |
| 129 | #553 | — | 2 | 9 | no | — |
| 130 | #552 | — | 2 | 18 | no | — |
| 131 | #552 | — | 2 | 18 | no | — |
| 132 | #552 | — | 2 | 18 | no | — |
| 133 | #550 | — | 2 | 3 | no | — |
| 134 | #550 | — | 2 | 9 | no | — |
| 135 | #550 | — | 2 | 3 | no | — |
| 136 | #550 | — | 2 | 3 | no | — |
| 137 | #550 | C23 | 1 | 1 | yes | characteristic |
| 138 | #550 | C23 | 1 | 3 | yes | — |
| 139 | #550 | C23 | 1 | 18 | yes | — |
| 140 | #550 | C23 | 1 | 6 | yes | — |
| 141 | D4×Q8 | — | 2 | 3 | no | — |
| 142 | D4×Q8 | — | 2 | 3 | no | — |
| 143 | D4×Q8 | D4 | 1 | 3 | yes | — |
| 144 | #548 | — | 2 | 3 | no | — |
| 145 | #548 | — | 2 | 3 | no | — |
| 146 | #547 | — | 2 | 9 | no | — |
| 147 | #547 | — | 2 | 9 | no | — |
| 148 | #547 | — | 2 | 9 | no | — |
| 149 | #546 | — | 2 | 18 | no | — |
| 150 | #546 | — | 2 | 18 | no | — |
| 151 | D42 | — | 2 | 9 | no | — |
| 152 | D42 | — | 2 | 9 | no | — |
| 153 | #541 | — | 2 | 18 | no | — |
| 154 | #540 | — | 2 | 18 | no | — |
| 155 | #539 | — | 2 | 18 | no | — |
| 156 | #538 | — | 2 | 18 | no | — |
| 157 | #536 | C23 | 1 | 18 | yes | — |
| 158 | #535 | C23 | 1 | 18 | yes | — |
| 159 | #533 | — | 2 | 9 | no | — |
| 160 | #533 | — | 2 | 9 | no | — |
| 161 | #533 | C23 | 1 | 9 | yes | — |
| 162 | #532 | — | 2 | 9 | no | — |
| 163 | #532 | — | 2 | 9 | no | — |
| 164 | #532 | C23 | 1 | 9 | yes | — |
| 165 | #532 | C23 | 1 | 9 | yes | — |
| 166 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 167 | C2×#127 | C23 | 1 | 9 | yes | — |
| 168 | #529 | — | 2 | 18 | no | — |
| 169 | #529 | — | 2 | 9 | no | — |
| 170 | #529 | — | 2 | 9 | no | — |
| 171 | C2×#125 | — | 2 | 9 | no | — |
| 172 | #525 | — | 2 | 18 | no | — |
| 173 | C2×#121 | — | 2 | 9 | no | — |
| 174 | #520 | — | 2 | 3 | no | — |
| 175 | #520 | — | 2 | 9 | no | — |
| 176 | #520 | C23 | 1 | 9 | yes | — |
| 177 | #520 | C23 | 1 | 9 | yes | — |
| 178 | #520 | C23 | 1 | 1 | yes | characteristic |
| 179 | #520 | C23 | 1 | 1 | yes | characteristic |
| 180 | #519 | — | 2 | 3 | no | — |
| 181 | #519 | C23 | 1 | 9 | yes | — |
| 182 | #518 | — | 2 | 9 | no | — |
| 183 | #518 | C23 | 1 | 9 | yes | — |
| 184 | C4×#41 | — | 2 | 3 | no | — |
| 185 | C4×#41 | — | 2 | 3 | no | — |
| 186 | C4×#41 | — | 2 | 3 | no | — |
| 187 | C4×#41 | — | 2 | 9 | no | — |
| 188 | C4×#41 | C23 | 1 | 9 | yes | — |
| 189 | C4×#41 | C23 | 1 | 9 | yes | — |
| 190 | C4×#41 | C23 | 1 | 3 | yes | — |
| 191 | C2×C4×Q8 | — | 2 | 3 | no | — |
| 192 | C2×C4×Q8 | — | 2 | 3 | no | — |
| 193 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 194 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 195 | C2×C4×D4 | — | 2 | 9 | no | — |
| 196 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 197 | #497 | C23 | 1 | 36 | yes | — |
| 198 | #496 | C23 | 1 | 36 | yes | — |
| 199 | #495 | C23 | 1 | 18 | yes | — |
| 200 | #495 | C23 | 1 | 18 | yes | — |
| 201 | #494 | C23 | 1 | 9 | yes | — |
| 202 | #493 | C23 | 1 | 9 | yes | — |
| 203 | #492 | C23 | 1 | 9 | yes | — |
| 204 | #492 | C23 | 1 | 18 | yes | — |
| 205 | #492 | C23 | 1 | 18 | yes | — |
| 206 | #492 | C23 | 1 | 18 | yes | — |
| 207 | #492 | C23 | 1 | 3 | yes | — |
| 208 | #464 | C23 | 1 | 18 | yes | — |
| 209 | #464 | C23 | 1 | 18 | yes | — |
| 210 | #464 | C23 | 1 | 36 | yes | — |
| 211 | #463 | C23 | 1 | 18 | yes | — |
| 212 | #463 | C23 | 1 | 18 | yes | — |
| 213 | #463 | C23 | 1 | 36 | yes | — |
| 214 | #462 | C23 | 1 | 9 | yes | — |
| 215 | #462 | C23 | 1 | 9 | yes | — |
| 216 | #462 | C23 | 1 | 18 | yes | — |
| 217 | #461 | C23 | 1 | 9 | yes | — |
| 218 | #461 | C23 | 1 | 18 | yes | — |
| 219 | #461 | C23 | 1 | 36 | yes | — |
| 220 | #461 | C23 | 1 | 3 | yes | — |
| 221 | #461 | C23 | 1 | 18 | yes | — |
| 222 | #460 | C23 | 1 | 9 | yes | — |
| 223 | #460 | C23 | 1 | 36 | yes | — |
| 224 | #460 | C23 | 1 | 18 | yes | — |
| 225 | #460 | C23 | 1 | 3 | yes | — |
| 226 | #460 | C23 | 1 | 18 | yes | — |
| 227 | #459 | C23 | 1 | 9 | yes | — |
| 228 | #459 | C23 | 1 | 9 | yes | — |
| 229 | #459 | C23 | 1 | 18 | yes | — |
| 230 | #446 | C23 | 1 | 18 | yes | — |
| 231 | #446 | C23 | 1 | 18 | yes | — |
| 232 | C8×Q8 | C23 | 1 | 3 | yes | — |
| 233 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 234 | C8×Q8 | C23 | 1 | 9 | yes | — |
| 235 | C8×Q8 | C23 | 1 | 9 | yes | — |
| 236 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 237 | #442 | C23 | 1 | 18 | yes | — |
| 238 | #441 | C23 | 1 | 18 | yes | — |
| 239 | #440 | C23 | 1 | 18 | yes | — |
| 240 | #440 | C23 | 1 | 18 | yes | — |
| 241 | C4×Q16 | C23 | 1 | 9 | yes | — |
| 242 | C4×Q16 | C23 | 1 | 9 | yes | — |
| 243 | C4×SD16 | C23 | 1 | 9 | yes | — |
| 244 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 245 | C4×SD16 | C23 | 1 | 9 | yes | — |
| 246 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 247 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 248 | C4×SD16 | C23 | 1 | 3 | yes | — |
| 249 | C4×SD16 | C23 | 1 | 9 | yes | — |
| 250 | C4×D8 | C23 | 1 | 9 | yes | — |
| 251 | C4×D8 | C23 | 1 | 9 | yes | — |
| 252 | #428 | C23 | 1 | 3 | yes | — |
| 253 | #428 | C23 | 1 | 3 | yes | — |
| 254 | #427 | C23 | 1 | 3 | yes | — |
| 255 | C2×#106 | C23 | 1 | 3 | yes | — |
| 256 | #424 | C23 | 1 | 18 | yes | — |
| 257 | #423 | C23 | 1 | 9 | yes | — |
| 258 | C2×C4⋊C8 | C23 | 1 | 9 | yes | — |
| 259 | #419 | C23 | 1 | 9 | yes | — |
| 260 | #418 | C23 | 1 | 9 | yes | — |
| 261 | #417 | C23 | 1 | 9 | yes | — |
| 262 | #417 | C23 | 1 | 9 | yes | — |
| 263 | #416 | C23 | 1 | 9 | yes | — |
| 264 | #416 | C23 | 1 | 9 | yes | — |
| 265 | C2×#103 | C23 | 1 | 9 | yes | — |
| 266 | C2×#102 | C23 | 1 | 9 | yes | — |
| 267 | #405 | C23 | 1 | 9 | yes | — |
| 268 | #405 | C23 | 1 | 9 | yes | — |
| 269 | C4×M16 | C23 | 1 | 9 | yes | — |
| 270 | C2×C4×C8 | C23 | 1 | 9 | yes | — |
| 271 | 2−1+4 | — | 2 | 12 | no | — |
| 272 | 2−1+4 | — | 2 | 12 | no | — |
| 273 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 274 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 275 | C2×#41 | — | 2 | 1 | no | — |
| 276 | C2×#41 | — | 2 | 3 | no | — |
| 277 | C2×#41 | — | 2 | 3 | no | — |
| 278 | C2×#41 | — | 2 | 18 | no | — |
| 279 | C2×#41 | — | 2 | 6 | no | — |
| 280 | C2×#41 | — | 2 | 9 | no | — |
| 281 | C2×#41 | — | 8 | 12 | no | — |
| 282 | C2×#41 | C24 | 1 | 9 | yes | — |
| 283 | C2×#41 | C24 | 1 | 9 | yes | — |
| 284 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 285 | C22×Q8 | — | 2 | 3 | no | — |
| 286 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 287 | C22×Q8 | C24 | 1 | 9 | yes | — |
| 288 | C22×D4 | — | 2 | 9 | no | — |
| 289 | C22×D4 | — | 2 | 9 | no | — |
| 290 | C22×D4 | — | 2 | 9 | no | — |
| 291 | C22×D4 | C24 | 1 | 9 | yes | — |
| 292 | C23×C4 | — | 2 | 9 | no | — |
| 293 | #137 | — | 2 | 36 | no | — |
| 294 | #137 | — | 4 | 36 | no | — |
| 295 | AGL(1,ℤ/8) | — | 2 | 36 | no | — |
| 296 | AGL(1,ℤ/8) | — | 4 | 36 | no | — |
| 297 | #135 | — | 2 | 36 | no | — |
| 298 | #135 | — | 4 | 36 | no | — |
| 299 | C2×Q16 | C24 | 1 | 9 | yes | — |
| 300 | C2×Q16 | C24 | 1 | 18 | yes | — |
| 301 | C2×SD16 | — | 2 | 36 | no | — |
| 302 | C2×SD16 | — | 4 | 36 | no | — |
| 303 | C2×SD16 | C24 | 1 | 9 | yes | — |
| 304 | C2×SD16 | C24 | 1 | 18 | yes | — |
| 305 | C2×SD16 | C24 | 1 | 3 | yes | — |
| 306 | C2×SD16 | C24 | 1 | 18 | yes | — |
| 307 | C2×SD16 | C24 | 1 | 36 | yes | — |
| 308 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 309 | C2×D8 | C24 | 1 | 9 | yes | — |
| 310 | C2×D8 | C24 | 1 | 18 | yes | — |
| 311 | #131 | — | 2 | 12 | no | — |
| 312 | #131 | #41 | 1 | 8 | yes | complemented |
| 313 | C2×M16 | C24 | 1 | 9 | yes | — |
| 314 | C2×M16 | C24 | 1 | 3 | yes | — |
| 315 | C22×C8 | C24 | 1 | 9 | yes | — |
| 316 | C22×C8 | C24 | 1 | 3 | yes | — |
| 317 | C4⋊Q8 | — | 2 | 9 | no | — |
| 318 | C4⋊Q8 | — | 2 | 9 | no | — |
| 319 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 320 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 321 | C4⋊Q8 | C24 | 1 | 9 | yes | — |
| 322 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 323 | C4⋊Q8 | C24 | 1 | 3 | yes | — |
| 324 | #127 | — | 2 | 9 | no | — |
| 325 | #127 | — | 2 | 9 | no | — |
| 326 | #127 | C24 | 1 | 9 | yes | — |
| 327 | #127 | C24 | 1 | 18 | yes | — |
| 328 | #127 | C24 | 1 | 3 | yes | — |
| 329 | #126 | — | 2 | 18 | no | — |
| 330 | #126 | — | 2 | 36 | no | — |
| 331 | #126 | — | 2 | 18 | no | — |
| 332 | #125 | — | 2 | 9 | no | — |
| 333 | #125 | — | 2 | 18 | no | — |
| 334 | #125 | — | 2 | 36 | no | — |
| 335 | #125 | — | 2 | 3 | no | — |
| 336 | #125 | — | 2 | 18 | no | — |
| 337 | #125 | C2×D4 | 1 | 18 | yes | — |
| 338 | #124 | — | 2 | 9 | no | — |
| 339 | #124 | — | 2 | 9 | no | — |
| 340 | #124 | — | 2 | 18 | no | — |
| 341 | #124 | C24 | 1 | 18 | yes | — |
| 342 | #124 | C24 | 1 | 18 | yes | — |
| 343 | #123 | — | 2 | 36 | no | — |
| 344 | #123 | — | 2 | 18 | no | — |
| 345 | #123 | — | 2 | 18 | no | — |
| 346 | #123 | — | 2 | 36 | no | — |
| 347 | C22⋊Q8 | — | 2 | 9 | no | — |
| 348 | C22⋊Q8 | — | 2 | 9 | no | — |
| 349 | C22⋊Q8 | — | 2 | 18 | no | — |
| 350 | C22⋊Q8 | — | 2 | 18 | no | — |
| 351 | C22⋊Q8 | — | 2 | 18 | no | — |
| 352 | C22⋊Q8 | C2×D4 | 1 | 18 | yes | — |
| 353 | C22⋊Q8 | C2×D4 | 1 | 18 | yes | — |
| 354 | #121 | — | 2 | 9 | no | — |
| 355 | #121 | — | 2 | 9 | no | — |
| 356 | #121 | — | 2 | 9 | no | — |
| 357 | #121 | — | 2 | 9 | no | — |
| 358 | #121 | — | 2 | 9 | no | — |
| 359 | #121 | — | 2 | 18 | no | — |
| 360 | #121 | — | 2 | 36 | no | — |
| 361 | #121 | — | 2 | 3 | no | — |
| 362 | #121 | — | 2 | 18 | no | — |
| 363 | #121 | — | 2 | 18 | no | — |
| 364 | #121 | — | 2 | 18 | no | — |
| 365 | #120 | — | 2 | 36 | no | — |
| 366 | C4×Q8 | — | 2 | 1 | no | — |
| 367 | C4×Q8 | — | 2 | 3 | no | — |
| 368 | C4×Q8 | — | 2 | 18 | no | — |
| 369 | C4×Q8 | — | 2 | 1 | no | — |
| 370 | C4×Q8 | — | 2 | 1 | no | — |
| 371 | C4×Q8 | — | 2 | 6 | no | — |
| 372 | C4×Q8 | — | 2 | 9 | no | — |
| 373 | C4×Q8 | — | 2 | 9 | no | — |
| 374 | C4×Q8 | — | 2 | 9 | no | — |
| 375 | C4×Q8 | — | 2 | 9 | no | — |
| 376 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 377 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 378 | C4×Q8 | C2×D4 | 1 | 9 | yes | — |
| 379 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 380 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 381 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 382 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 383 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 384 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 385 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 386 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 387 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 388 | C4×D4 | — | 2 | 3 | no | — |
| 389 | C4×D4 | — | 2 | 3 | no | — |
| 390 | C4×D4 | — | 2 | 9 | no | — |
| 391 | C4×D4 | — | 2 | 9 | no | — |
| 392 | C4×D4 | — | 2 | 9 | no | — |
| 393 | C4×D4 | — | 2 | 9 | no | — |
| 394 | C4×D4 | — | 2 | 9 | no | — |
| 395 | C4×D4 | — | 2 | 9 | no | — |
| 396 | C4×D4 | — | 2 | 9 | no | — |
| 397 | C4×D4 | — | 2 | 9 | no | — |
| 398 | C4×D4 | — | 2 | 18 | no | — |
| 399 | C4×D4 | — | 2 | 18 | no | — |
| 400 | C4×D4 | — | 2 | 18 | no | — |
| 401 | C4×D4 | — | 2 | 9 | no | — |
| 402 | C4×D4 | — | 2 | 9 | no | — |
| 403 | C4×D4 | — | 2 | 9 | no | — |
| 404 | C4×D4 | — | 2 | 9 | no | — |
| 405 | C4×D4 | — | 2 | 9 | no | — |
| 406 | C4×D4 | — | 2 | 9 | no | — |
| 407 | C4×D4 | C2×D4 | 1 | 9 | yes | — |
| 408 | C4×D4 | C2×D4 | 1 | 9 | yes | — |
| 409 | C4×D4 | C24 | 1 | 9 | yes | — |
| 410 | C4×D4 | C24 | 1 | 18 | yes | — |
| 411 | C4×D4 | C24 | 1 | 3 | yes | — |
| 412 | C4×D4 | C24 | 1 | 9 | yes | — |
| 413 | C4×D4 | C24 | 1 | 9 | yes | — |
| 414 | #117 | — | 2 | 9 | no | — |
| 415 | #117 | — | 2 | 9 | no | — |
| 416 | #117 | — | 2 | 9 | no | — |
| 417 | #117 | — | 2 | 9 | no | — |
| 418 | #117 | — | 2 | 18 | no | — |
| 419 | #117 | — | 2 | 18 | no | — |
| 420 | #117 | — | 2 | 9 | no | — |
| 421 | #117 | — | 2 | 9 | no | — |
| 422 | #117 | C24 | 1 | 3 | yes | — |
| 423 | #117 | C24 | 1 | 3 | yes | — |
| 424 | #117 | C24 | 1 | 9 | yes | — |
| 425 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 426 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 427 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 428 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 429 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 430 | C2×C4⋊C4 | C2×D4 | 1 | 9 | yes | — |
| 431 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 432 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 433 | C2×C22⋊C4 | — | 2 | 9 | no | — |
| 434 | C2×C22⋊C4 | — | 2 | 18 | no | — |
| 435 | C2×C42 | — | 2 | 9 | no | — |
| 436 | C2×C42 | — | 2 | 9 | no | — |
| 437 | C2×C42 | — | 2 | 9 | no | — |
| 438 | C2×C42 | C24 | 1 | 9 | yes | — |
| 439 | #107 | C24 | 1 | 3 | yes | — |
| 440 | #107 | C24 | 1 | 3 | yes | — |
| 441 | #106 | C24 | 1 | 3 | yes | — |
| 442 | #106 | C24 | 1 | 6 | yes | — |
| 443 | #106 | C24 | 1 | 1 | yes | characteristic |
| 444 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 445 | C4⋊C8 | C24 | 1 | 9 | yes | — |
| 446 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 447 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 448 | #103 | C24 | 1 | 9 | yes | — |
| 449 | #103 | C24 | 1 | 18 | yes | — |
| 450 | #103 | C24 | 1 | 3 | yes | — |
| 451 | #103 | C24 | 1 | 9 | yes | — |
| 452 | #103 | C24 | 1 | 9 | yes | — |
| 453 | #102 | C24 | 1 | 9 | yes | — |
| 454 | #102 | C24 | 1 | 18 | yes | — |
| 455 | #102 | C24 | 1 | 3 | yes | — |
| 456 | #102 | C24 | 1 | 9 | yes | — |
| 457 | #102 | C24 | 1 | 9 | yes | — |
| 458 | #97 | C24 | 1 | 18 | yes | — |
| 459 | C4×C8 | C24 | 1 | 3 | yes | — |
| 460 | C4×C8 | C24 | 1 | 9 | yes | — |
| 461 | C4×C8 | C24 | 1 | 9 | yes | — |
| 462 | C4×C8 | C24 | 1 | 9 | yes | — |
| 463 | C24 | — | 2 | 9 | no | — |
| 464 | #41 | — | 2 | 18 | no | — |
| 465 | #41 | — | 2 | 18 | no | — |
| 466 | #41 | — | 2 | 18 | no | — |
| 467 | #41 | — | 2 | 18 | no | — |
| 468 | #41 | — | 4 | 12 | no | — |
| 469 | #41 | — | 4 | 4 | no | — |
| 470 | #41 | — | 4 | 12 | no | — |
| 471 | #41 | — | 4 | 36 | no | — |
| 472 | #41 | — | 8 | 36 | no | — |
| 473 | #41 | — | 16 | 6 | no | — |
| 474 | #41 | C2×#41 | 1 | 4 | yes | — |
| 475 | #41 | H(5,𝔽2) | 1 | 4 | yes | — |
| 476 | C2×Q8 | — | 2 | 12 | no | — |
| 477 | C2×Q8 | — | 2 | 9 | no | — |
| 478 | C2×Q8 | — | 2 | 18 | no | — |
| 479 | C2×Q8 | — | 2 | 18 | no | — |
| 480 | C2×Q8 | — | 4 | 12 | no | — |
| 481 | C2×Q8 | C22×D4 | 1 | 9 | yes | — |
| 482 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 483 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 484 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 485 | C2×Q8 | C25 | 1 | 3 | yes | — |
| 486 | C2×Q8 | C25 | 1 | 9 | yes | — |
| 487 | C2×D4 | — | 2 | 9 | no | — |
| 488 | C2×D4 | — | 2 | 9 | no | — |
| 489 | C2×D4 | — | 2 | 3 | no | — |
| 490 | C2×D4 | — | 2 | 9 | no | — |
| 491 | C2×D4 | — | 2 | 9 | no | — |
| 492 | C2×D4 | — | 2 | 3 | no | — |
| 493 | C2×D4 | — | 2 | 18 | no | — |
| 494 | C2×D4 | — | 2 | 9 | no | — |
| 495 | C2×D4 | — | 2 | 18 | no | — |
| 496 | C2×D4 | — | 2 | 18 | no | — |
| 497 | C2×D4 | — | 2 | 18 | no | — |
| 498 | C2×D4 | — | 4 | 36 | no | — |
| 499 | C2×D4 | — | 8 | 18 | no | — |
| 500 | C2×D4 | — | 16 | 9 | no | — |
| 501 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 502 | C2×D4 | C25 | 1 | 3 | yes | — |
| 503 | C2×D4 | C25 | 1 | 9 | yes | — |
| 504 | C22×C4 | — | 2 | 9 | no | — |
| 505 | C22×C4 | — | 2 | 3 | no | — |
| 506 | C22×C4 | — | 2 | 3 | no | — |
| 507 | C22×C4 | — | 2 | 3 | no | — |
| 508 | C22×C4 | — | 2 | 9 | no | — |
| 509 | C22×C4 | — | 2 | 9 | no | — |
| 510 | C22×C4 | — | 2 | 9 | no | — |
| 511 | C22×C4 | — | 2 | 9 | no | — |
| 512 | C22×C4 | — | 2 | 9 | no | — |
| 513 | C22×C4 | — | 2 | 18 | no | — |
| 514 | C22×C4 | — | 8 | 18 | no | — |
| 515 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 516 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 517 | C22×C4 | C25 | 1 | 3 | yes | — |
| 518 | Q16 | — | 2 | 18 | no | — |
| 519 | Q16 | — | 4 | 18 | no | — |
| 520 | SD16 | — | 2 | 18 | no | — |
| 521 | SD16 | — | 2 | 36 | no | — |
| 522 | SD16 | — | 2 | 6 | no | — |
| 523 | SD16 | — | 4 | 18 | no | — |
| 524 | SD16 | — | 4 | 36 | no | — |
| 525 | SD16 | — | 4 | 6 | no | — |
| 526 | D8 | — | 2 | 18 | no | — |
| 527 | D8 | — | 4 | 18 | no | — |
| 528 | M16 | — | 2 | 18 | no | — |
| 529 | M16 | C2×#41 | 1 | 12 | yes | complemented |
| 530 | C2×C8 | — | 2 | 18 | no | — |
| 531 | C2×C8 | C2×#41 | 1 | 12 | yes | complemented |
| 532 | C2×C8 | C25 | 1 | 3 | yes | — |
| 533 | C2×C8 | C25 | 1 | 9 | yes | — |
| 534 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 535 | C2×C8 | C25 | 1 | 3 | yes | — |
| 536 | C4⋊C4 | — | 2 | 3 | no | — |
| 537 | C4⋊C4 | — | 2 | 3 | no | — |
| 538 | C4⋊C4 | — | 2 | 9 | no | — |
| 539 | C4⋊C4 | — | 2 | 9 | no | — |
| 540 | C4⋊C4 | — | 2 | 18 | no | — |
| 541 | C4⋊C4 | — | 2 | 9 | no | — |
| 542 | C4⋊C4 | — | 2 | 9 | no | — |
| 543 | C4⋊C4 | — | 2 | 18 | no | — |
| 544 | C4⋊C4 | — | 2 | 18 | no | — |
| 545 | C4⋊C4 | — | 2 | 3 | no | — |
| 546 | C4⋊C4 | — | 2 | 3 | no | — |
| 547 | C4⋊C4 | — | 2 | 9 | no | — |
| 548 | C4⋊C4 | — | 2 | 3 | no | — |
| 549 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 550 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 551 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 552 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 553 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 554 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 555 | C4⋊C4 | C25 | 1 | 3 | yes | — |
| 556 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 557 | C4⋊C4 | C25 | 1 | 3 | yes | — |
| 558 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 559 | C22⋊C4 | — | 2 | 3 | no | — |
| 560 | C22⋊C4 | — | 2 | 3 | no | — |
| 561 | C22⋊C4 | — | 2 | 9 | no | — |
| 562 | C22⋊C4 | — | 2 | 9 | no | — |
| 563 | C22⋊C4 | — | 2 | 18 | no | — |
| 564 | C22⋊C4 | — | 2 | 3 | no | — |
| 565 | C22⋊C4 | — | 2 | 9 | no | — |
| 566 | C22⋊C4 | — | 2 | 18 | no | — |
| 567 | C22⋊C4 | — | 2 | 18 | no | — |
| 568 | C22⋊C4 | — | 2 | 18 | no | — |
| 569 | C22⋊C4 | — | 2 | 18 | no | — |
| 570 | C22⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 571 | C42 | — | 2 | 3 | no | — |
| 572 | C42 | — | 2 | 3 | no | — |
| 573 | C42 | — | 2 | 3 | no | — |
| 574 | C42 | — | 2 | 9 | no | — |
| 575 | C42 | — | 2 | 9 | no | — |
| 576 | C42 | — | 2 | 9 | no | — |
| 577 | C42 | — | 2 | 18 | no | — |
| 578 | C42 | C22×D4 | 1 | 9 | yes | — |
| 579 | C42 | C22×D4 | 1 | 9 | yes | — |
| 580 | C42 | C25 | 1 | 3 | yes | — |
| 581 | C42 | C25 | 1 | 9 | yes | — |
| 582 | C23 | — | 2 | 3 | no | — |
| 583 | C23 | — | 2 | 9 | no | — |
| 584 | C23 | — | 4 | 18 | no | — |
| 585 | C23 | — | 8 | 9 | no | — |
| 586 | C23 | — | 8 | 9 | no | — |
| 587 | C23 | C23×D4 | 1 | 3 | yes | — |
| 588 | Q8 | — | 2 | 18 | no | — |
| 589 | Q8 | — | 2 | 9 | no | — |
| 590 | Q8 | — | 2 | 3 | no | — |
| 591 | Q8 | — | 2 | 9 | no | — |
| 592 | Q8 | — | 2 | 3 | no | — |
| 593 | Q8 | — | 4 | 6 | no | — |
| 594 | Q8 | — | 4 | 18 | no | — |
| 595 | Q8 | #550 | 1 | 4 | yes | — |
| 596 | Q8 | #577 | 1 | 4 | yes | complemented |
| 597 | D4 | — | 2 | 3 | no | — |
| 598 | D4 | — | 2 | 9 | no | — |
| 599 | D4 | — | 2 | 3 | no | — |
| 600 | D4 | — | 2 | 9 | no | — |
| 601 | D4 | — | 4 | 18 | no | — |
| 602 | D4 | — | 4 | 18 | no | — |
| 603 | D4 | — | 4 | 18 | no | — |
| 604 | D4 | — | 4 | 18 | no | — |
| 605 | D4 | — | 4 | 6 | no | — |
| 606 | D4 | — | 8 | 3 | no | — |
| 607 | D4 | — | 8 | 18 | no | — |
| 608 | D4 | — | 8 | 9 | no | — |
| 609 | D4 | — | 8 | 18 | no | — |
| 610 | D4 | #550 | 1 | 12 | yes | — |
| 611 | C2×C4 | — | 2 | 18 | no | — |
| 612 | C2×C4 | — | 2 | 1 | no | — |
| 613 | C2×C4 | — | 2 | 3 | no | — |
| 614 | C2×C4 | — | 2 | 1 | no | — |
| 615 | C2×C4 | — | 2 | 3 | no | — |
| 616 | C2×C4 | — | 2 | 3 | no | — |
| 617 | C2×C4 | — | 2 | 9 | no | — |
| 618 | C2×C4 | — | 4 | 9 | no | — |
| 619 | C2×C4 | — | 4 | 18 | no | — |
| 620 | C2×C4 | — | 4 | 18 | no | — |
| 621 | C2×C4 | — | 4 | 18 | no | — |
| 622 | C2×C4 | — | 4 | 18 | no | — |
| 623 | C2×C4 | — | 4 | 6 | no | — |
| 624 | C2×C4 | — | 8 | 9 | no | — |
| 625 | C2×C4 | — | 8 | 18 | no | — |
| 626 | C2×C4 | — | 8 | 9 | no | — |
| 627 | C2×C4 | — | 8 | 3 | no | — |
| 628 | C2×C4 | — | 8 | 3 | no | — |
| 629 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 630 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 631 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 632 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 633 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 634 | C2×C4 | C22×#41 | 1 | 6 | yes | — |
| 635 | C2×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 636 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 637 | C8 | — | 2 | 3 | no | — |
| 638 | C8 | — | 2 | 9 | no | — |
| 639 | C8 | C22×#41 | 1 | 2 | yes | — |
| 640 | C8 | C22×#41 | 1 | 6 | yes | — |
| 641 | C22 | — | 2 | 3 | no | — |
| 642 | C22 | — | 2 | 3 | no | — |
| 643 | C22 | — | 4 | 9 | no | — |
| 644 | C22 | — | 4 | 3 | no | — |
| 645 | C22 | — | 4 | 3 | no | — |
| 646 | C22 | — | 4 | 9 | no | — |
| 647 | C22 | — | 4 | 3 | no | — |
| 648 | C22 | — | 4 | 9 | no | — |
| 649 | C22 | — | 16 | 18 | no | — |
| 650 | C22 | C2×#550 | 1 | 6 | yes | — |
| 651 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 652 | C4 | — | 2 | 9 | no | — |
| 653 | C4 | — | 2 | 3 | no | — |
| 654 | C4 | — | 2 | 9 | no | — |
| 655 | C4 | — | 4 | 1 | no | — |
| 656 | C4 | — | 4 | 3 | no | — |
| 657 | C4 | — | 4 | 3 | no | — |
| 658 | C4 | — | 4 | 1 | no | — |
| 659 | C4 | — | 4 | 3 | no | — |
| 660 | C4 | — | 4 | 9 | no | — |
| 661 | C4 | C2×#550 | 1 | 6 | yes | — |
| 662 | C4 | C2×#577 | 1 | 6 | yes | — |
| 663 | C4 | C23×#41 | 1 | 1 | yes | characteristic |
| 664 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 665 | C2 | — | 2 | 6 | no | — |
| 666 | C2 | — | 8 | 3 | no | — |
| 667 | C2 | — | 8 | 9 | no | — |
| 668 | C2 | C22×#550 | 1 | 1 | yes | characteristic |
| 669 | C2 | C22×#577 | 1 | 1 | yes | characteristic |
| 670 | C2 | #63092 | 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 ◁ Q8×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63001 | C2 | semidirect |
| 2. #62986 | C2 | semidirect |
| 3. #61421 | C2 | semidirect |
| 4. #61420 | C2 | semidirect |
| 5. #61410 | C2 | semidirect |
| 6. #61407 | C2 | semidirect |
| 7. #61404 | C2 | semidirect |
| 8. #61402 | C2 | semidirect |
| 9. #61393 | C2 | semidirect |
| 10. C2×#3392 | C2 | semidirect |
| 11. #60646 | C2 | semidirect |
| 12. #60431 | C2 | semidirect |
| 13. #60429 | C2 | semidirect |
| 14. Q8×#131 | C2 | semidirect |
| 15. C4×#577 | C2 | semidirect |
| 22. #3509 | C22 | semidirect |
| 24. #3507 | C22 | semidirect |
| 31. #3480 | C22 | semidirect |
| 34. C2×#557 | C22 | semidirect |
| 39. #3401 | C22 | semidirect |
| 40. #3400 | C22 | semidirect |
| 41. #3400 | C22 | semidirect |
| 42. #3399 | C22 | semidirect |
| 43. #3398 | C22 | semidirect |
| 44. #3397 | C22 | semidirect |
| 45. #3397 | C22 | semidirect |
| 46. #3396 | C22 | semidirect |
| 47. #3395 | C22 | semidirect |
| 48. #3394 | C22 | semidirect |
| 49. #3394 | C22 | semidirect |
| 50. #3394 | C22 | semidirect |
| 51. #3393 | C22 | semidirect |
| 52. #3392 | C22 | semidirect |
| 53. #3392 | C22 | semidirect |
| 54. #3392 | C22 | semidirect |
| 55. #3392 | C22 | semidirect |
| 56. #3392 | C22 | semidirect |
| 57. #3392 | C22 | semidirect |
| 58. #3391 | C22 | semidirect |
| 59. #3154 | C22 | semidirect |
| 60. #3154 | C22 | semidirect |
| 61. #3152 | C22 | semidirect |
| 62. #3151 | C22 | semidirect |
| 63. #3147 | C22 | semidirect |
| 64. C2×#492 | C22 | semidirect |
| 65. #3046 | C22 | semidirect |
| 66. #3045 | C22 | semidirect |
| 67. #3043 | C22 | semidirect |
| 68. #3042 | C22 | semidirect |
| 69. #3039 | C22 | semidirect |
| 70. #3038 | C22 | semidirect |
| 71. #3037 | C22 | semidirect |
| 72. #3036 | C22 | semidirect |
| 73. #3035 | C22 | semidirect |
| 74. #3035 | C22 | semidirect |
| 75. C2×#460 | C22 | semidirect |
| 76. C2×#461 | C22 | semidirect |
| 77. Q8×M16 | C22 | semidirect |
| 78. #2962 | C22 | semidirect |
| 79. #2960 | C22 | semidirect |
| 80. C2×C8×Q8 | C22 | semidirect |
| 81. #2952 | C22 | semidirect |
| 82. #2949 | C22 | semidirect |
| 83. #2947 | C22 | semidirect |
| 84. #2946 | C22 | semidirect |
| 85. C4×#137 | C22 | semidirect |
| 86. C4×AGL(1,ℤ/8) | C22 | semidirect |
| 87. C4×#135 | C22 | semidirect |
| 88. C2×C4×SD16 | C22 | semidirect |
| 312. #131 | #41 | semidirect |
| 529. M16 | C2×#41 | semidirect |
| 531. C2×C8 | C2×#41 | semidirect |
| 596. Q8 | #577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63001 | 2 |
| #62986 | 2 |
| #61421 | 2 |
| #61420 | 2 |
| #61410 | 2 |
| #61407 | 2 |
| #61404 | 2 |
| #61402 | 2 |
| #61393 | 2 |
| C2×#3392 | 2 |
| #60646 | 2 |
| #60431 | 2 |
| #60429 | 2 |
| Q8×#131 | 2 |
| C4×#577 | 2 |