Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6362 conjugacy classes of subgroups.
The subgroup lattice has 691 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62855 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #62849 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #61344 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | #61341 | C2 | 1 | 16 | yes | maximal, complemented |
| 5 | #61334 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #61327 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #60619 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #60612 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #60490 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #60489 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #60424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#3043 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #60193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #60169 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | C2×#2949 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#137 | C22 | 1 | 2 | yes | — |
| 17 | C23×SD16 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3510 | C22 | 1 | 8 | yes | — |
| 19 | #3508 | C22 | 1 | 8 | yes | — |
| 20 | #3506 | C22 | 1 | 8 | yes | — |
| 21 | #3502 | — | 2 | 4 | no | — |
| 22 | #3502 | — | 2 | 8 | no | — |
| 23 | #3502 | C22 | 1 | 8 | yes | complemented |
| 24 | #3502 | C22 | 1 | 16 | yes | complemented |
| 25 | #3494 | — | 2 | 8 | no | — |
| 26 | #3490 | — | 2 | 4 | no | — |
| 27 | #3460 | — | 2 | 4 | no | — |
| 28 | #3458 | — | 2 | 4 | no | — |
| 29 | #3458 | C22 | 1 | 2 | yes | — |
| 30 | #3458 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3458 | C22 | 1 | 1 | yes | characteristic |
| 32 | #3449 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#535 | C22 | 1 | 2 | yes | — |
| 34 | #3428 | C22 | 1 | 2 | yes | — |
| 35 | C2×#519 | C22 | 1 | 2 | yes | — |
| 36 | C2×#519 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#518 | C22 | 1 | 1 | yes | characteristic |
| 38 | #3377 | C22 | 1 | 32 | yes | complemented |
| 39 | #3375 | C22 | 1 | 32 | yes | complemented |
| 40 | #3371 | C22 | 1 | 32 | yes | complemented |
| 41 | #3371 | C22 | 1 | 32 | yes | complemented |
| 42 | #3369 | C22 | 1 | 16 | yes | complemented |
| 43 | #3368 | C22 | 1 | 16 | yes | complemented |
| 44 | #3368 | C22 | 1 | 32 | yes | complemented |
| 45 | #3365 | C22 | 1 | 32 | yes | complemented |
| 46 | #3364 | C22 | 1 | 16 | yes | complemented |
| 47 | #3362 | C22 | 1 | 16 | yes | complemented |
| 48 | #3140 | C22 | 1 | 8 | yes | complemented |
| 49 | #3138 | C22 | 1 | 8 | yes | complemented |
| 50 | #3137 | C22 | 1 | 8 | yes | complemented |
| 51 | #3136 | C22 | 1 | 16 | yes | — |
| 52 | #3136 | C22 | 1 | 16 | yes | complemented |
| 53 | #3136 | C22 | 1 | 8 | yes | complemented |
| 54 | #3135 | C22 | 1 | 4 | yes | complemented |
| 55 | #3131 | C22 | 1 | 4 | yes | complemented |
| 56 | #3084 | C22 | 1 | 8 | yes | complemented |
| 57 | #3083 | C22 | 1 | 8 | yes | complemented |
| 58 | #3082 | C22 | 1 | 8 | yes | complemented |
| 59 | #3081 | C22 | 1 | 16 | yes | complemented |
| 60 | #3081 | C22 | 1 | 8 | yes | complemented |
| 61 | #3077 | C22 | 1 | 8 | yes | complemented |
| 62 | #3076 | C22 | 1 | 16 | yes | complemented |
| 63 | #3044 | C22 | 1 | 8 | yes | complemented |
| 64 | #3043 | C22 | 1 | 16 | yes | — |
| 65 | #3043 | C22 | 1 | 8 | yes | complemented |
| 66 | #3043 | C22 | 1 | 8 | yes | complemented |
| 67 | #3043 | C22 | 1 | 8 | yes | complemented |
| 68 | #3037 | C22 | 1 | 8 | yes | complemented |
| 69 | C2×#464 | C22 | 1 | 8 | yes | complemented |
| 70 | C2×#460 | C22 | 1 | 8 | yes | complemented |
| 71 | #2962 | C22 | 1 | 16 | yes | complemented |
| 72 | #2961 | C22 | 1 | 4 | yes | complemented |
| 73 | #2960 | C22 | 1 | 4 | yes | complemented |
| 74 | #2950 | C22 | 1 | 8 | yes | complemented |
| 75 | #2949 | C22 | 1 | 16 | yes | complemented |
| 76 | #2949 | C22 | 1 | 8 | yes | complemented |
| 77 | #2947 | C22 | 1 | 16 | yes | complemented |
| 78 | C4×#137 | C22 | 1 | 16 | yes | complemented |
| 79 | C2×#440 | C22 | 1 | 4 | yes | complemented |
| 80 | C2×C4×SD16 | C22 | 1 | 4 | yes | complemented |
| 81 | #2911 | C22 | 1 | 2 | yes | — |
| 82 | C2×#427 | C22 | 1 | 1 | yes | characteristic |
| 83 | #2905 | C22 | 1 | 1 | yes | characteristic |
| 84 | C2×#424 | C22 | 1 | 2 | yes | — |
| 85 | #2896 | C22 | 1 | 2 | yes | — |
| 86 | #2896 | C22 | 1 | 2 | yes | — |
| 87 | C2×#419 | C22 | 1 | 1 | yes | characteristic |
| 88 | C2×#418 | C22 | 1 | 2 | yes | — |
| 89 | C2×#418 | C22 | 1 | 1 | yes | characteristic |
| 90 | C2×#416 | C22 | 1 | 2 | yes | — |
| 91 | #2873 | C22 | 1 | 2 | yes | — |
| 92 | C2×#405 | C22 | 1 | 1 | yes | characteristic |
| 93 | C22×#41 | C23 | 1 | 2 | yes | — |
| 94 | C23×Q8 | C23 | 1 | 1 | yes | characteristic |
| 95 | C23×D4 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×#137 | — | 2 | 16 | no | — |
| 97 | C2×#137 | C23 | 1 | 8 | yes | — |
| 98 | C2×#137 | C23 | 1 | 8 | yes | — |
| 99 | C22×Q16 | C23 | 1 | 4 | yes | — |
| 100 | C22×SD16 | — | 2 | 8 | no | — |
| 101 | C22×SD16 | C23 | 1 | 2 | yes | — |
| 102 | C22×SD16 | C23 | 1 | 2 | yes | — |
| 103 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 104 | C22×SD16 | C23 | 1 | 8 | yes | — |
| 105 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 106 | C22×M16 | C23 | 1 | 2 | yes | — |
| 107 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 108 | #559 | C23 | 1 | 32 | yes | — |
| 109 | Q82 | — | 2 | 16 | no | — |
| 110 | Q82 | — | 2 | 8 | no | — |
| 111 | Q82 | C23 | 1 | 16 | yes | complemented |
| 112 | #557 | — | 2 | 16 | no | — |
| 113 | #557 | — | 2 | 8 | no | — |
| 114 | #557 | — | 2 | 16 | no | — |
| 115 | #557 | — | 2 | 16 | no | — |
| 116 | #557 | — | 2 | 16 | no | — |
| 117 | #557 | C23 | 1 | 16 | yes | complemented |
| 118 | #557 | C23 | 1 | 32 | yes | complemented |
| 119 | #556 | C23 | 1 | 16 | yes | — |
| 120 | #555 | — | 2 | 8 | no | — |
| 121 | #553 | — | 2 | 16 | no | — |
| 122 | #551 | — | 2 | 32 | no | — |
| 123 | #550 | C23 | 1 | 16 | yes | — |
| 124 | #547 | — | 2 | 8 | no | — |
| 125 | #546 | — | 2 | 32 | no | — |
| 126 | #544 | — | 2 | 16 | no | — |
| 127 | #544 | — | 2 | 32 | no | — |
| 128 | #544 | — | 2 | 2 | no | — |
| 129 | #544 | — | 2 | 4 | no | — |
| 130 | #544 | D4 | 1 | 4 | yes | — |
| 131 | #544 | D4 | 1 | 8 | yes | — |
| 132 | #544 | C23 | 1 | 8 | yes | — |
| 133 | #544 | C23 | 1 | 8 | yes | — |
| 134 | #544 | C23 | 1 | 8 | yes | — |
| 135 | #543 | — | 2 | 2 | no | — |
| 136 | #543 | — | 2 | 4 | no | — |
| 137 | #543 | D4 | 1 | 4 | yes | — |
| 138 | #542 | — | 2 | 16 | no | — |
| 139 | #540 | — | 2 | 16 | no | — |
| 140 | #538 | — | 2 | 16 | no | — |
| 141 | #537 | — | 2 | 2 | no | — |
| 142 | #536 | C23 | 1 | 4 | yes | — |
| 143 | #535 | — | 2 | 4 | no | — |
| 144 | #535 | — | 2 | 4 | no | — |
| 145 | #535 | C23 | 1 | 8 | yes | — |
| 146 | #535 | C23 | 1 | 8 | yes | — |
| 147 | #535 | C23 | 1 | 4 | yes | — |
| 148 | #534 | — | 2 | 2 | no | — |
| 149 | #533 | — | 2 | 16 | no | — |
| 150 | #533 | — | 2 | 32 | no | — |
| 151 | #533 | — | 2 | 4 | no | — |
| 152 | #533 | — | 2 | 4 | no | — |
| 153 | #533 | — | 2 | 4 | no | — |
| 154 | #533 | C23 | 1 | 8 | yes | — |
| 155 | #533 | C23 | 1 | 4 | yes | — |
| 156 | #533 | C23 | 1 | 4 | yes | — |
| 157 | #533 | C23 | 1 | 8 | yes | — |
| 158 | #532 | — | 2 | 16 | no | — |
| 159 | #532 | C23 | 1 | 4 | yes | — |
| 160 | C2×#127 | C23 | 1 | 4 | yes | — |
| 161 | #529 | — | 2 | 16 | no | — |
| 162 | C2×#124 | C23 | 1 | 4 | yes | — |
| 163 | #525 | — | 2 | 16 | no | — |
| 164 | #525 | — | 2 | 4 | no | — |
| 165 | C2×#121 | — | 2 | 4 | no | — |
| 166 | C2×#120 | — | 2 | 4 | no | — |
| 167 | #520 | — | 2 | 4 | no | — |
| 168 | #520 | C23 | 1 | 8 | yes | — |
| 169 | #519 | — | 2 | 4 | no | — |
| 170 | #519 | — | 2 | 4 | no | — |
| 171 | #519 | — | 2 | 4 | no | — |
| 172 | #519 | C23 | 1 | 4 | yes | — |
| 173 | #519 | C23 | 1 | 8 | yes | — |
| 174 | #519 | C23 | 1 | 8 | yes | — |
| 175 | #519 | C23 | 1 | 8 | yes | — |
| 176 | #518 | — | 2 | 4 | no | — |
| 177 | #518 | — | 2 | 4 | no | — |
| 178 | #518 | C23 | 1 | 8 | yes | — |
| 179 | #518 | C23 | 1 | 4 | yes | — |
| 180 | C4×#41 | — | 2 | 4 | no | — |
| 181 | C4×#41 | C23 | 1 | 8 | yes | — |
| 182 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 183 | C2×C4×Q8 | — | 2 | 4 | no | — |
| 184 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 185 | C2×C4×Q8 | C23 | 1 | 8 | yes | — |
| 186 | C2×C4×D4 | — | 2 | 2 | no | — |
| 187 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 188 | C2×#117 | — | 2 | 4 | no | — |
| 189 | C2×#117 | — | 2 | 2 | no | — |
| 190 | C2×#117 | — | 2 | 4 | no | — |
| 191 | C2×#117 | C23 | 1 | 2 | yes | — |
| 192 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 193 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 194 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 195 | C2×#117 | C23 | 1 | 2 | yes | — |
| 196 | C22×C22⋊C4 | — | 2 | 2 | no | — |
| 197 | #491 | C23 | 1 | 8 | yes | complemented |
| 198 | #490 | C23 | 1 | 32 | yes | — |
| 199 | #490 | C23 | 1 | 8 | yes | complemented |
| 200 | #489 | C23 | 1 | 32 | yes | — |
| 201 | #489 | C23 | 1 | 16 | yes | complemented |
| 202 | #488 | C23 | 1 | 32 | yes | — |
| 203 | #488 | C23 | 1 | 16 | yes | complemented |
| 204 | #487 | C23 | 1 | 8 | yes | complemented |
| 205 | #486 | C23 | 1 | 32 | yes | — |
| 206 | #486 | C23 | 1 | 8 | yes | complemented |
| 207 | #479 | C23 | 1 | 16 | yes | complemented |
| 208 | #479 | C23 | 1 | 16 | yes | complemented |
| 209 | #478 | C23 | 1 | 32 | yes | — |
| 210 | #478 | C23 | 1 | 16 | yes | complemented |
| 211 | #478 | C23 | 1 | 16 | yes | complemented |
| 212 | #477 | C23 | 1 | 16 | yes | complemented |
| 213 | #476 | C23 | 1 | 16 | yes | — |
| 214 | #476 | C23 | 1 | 16 | yes | complemented |
| 215 | #475 | C23 | 1 | 16 | yes | complemented |
| 216 | #474 | C23 | 1 | 16 | yes | — |
| 217 | #474 | C23 | 1 | 16 | yes | complemented |
| 218 | #464 | C23 | 1 | 32 | yes | — |
| 219 | #464 | C23 | 1 | 32 | yes | — |
| 220 | #464 | C23 | 1 | 32 | yes | complemented |
| 221 | #462 | C23 | 1 | 16 | yes | complemented |
| 222 | #460 | C23 | 1 | 32 | yes | — |
| 223 | #460 | C23 | 1 | 32 | yes | — |
| 224 | #460 | C23 | 1 | 16 | yes | complemented |
| 225 | #446 | C23 | 1 | 16 | yes | complemented |
| 226 | #446 | C23 | 1 | 32 | yes | complemented |
| 227 | C8×Q8 | C23 | 1 | 16 | yes | complemented |
| 228 | #441 | C23 | 1 | 32 | yes | complemented |
| 229 | #440 | C23 | 1 | 32 | yes | — |
| 230 | #440 | C23 | 1 | 32 | yes | complemented |
| 231 | C4×Q16 | C23 | 1 | 32 | yes | complemented |
| 232 | C4×SD16 | C23 | 1 | 16 | yes | — |
| 233 | C4×SD16 | C23 | 1 | 16 | yes | — |
| 234 | C4×SD16 | C23 | 1 | 32 | yes | complemented |
| 235 | #428 | C23 | 1 | 8 | yes | — |
| 236 | #428 | C23 | 1 | 8 | yes | — |
| 237 | #427 | C23 | 1 | 8 | yes | — |
| 238 | #427 | C23 | 1 | 8 | yes | — |
| 239 | C2×#107 | C23 | 1 | 2 | yes | — |
| 240 | C2×#106 | C23 | 1 | 2 | yes | — |
| 241 | #424 | C23 | 1 | 8 | yes | — |
| 242 | #424 | C23 | 1 | 8 | yes | — |
| 243 | #424 | C23 | 1 | 4 | yes | — |
| 244 | #424 | C23 | 1 | 4 | yes | — |
| 245 | #423 | C23 | 1 | 4 | yes | — |
| 246 | C2×C4⋊C8 | C23 | 1 | 8 | yes | — |
| 247 | #419 | C23 | 1 | 4 | yes | — |
| 248 | #419 | C23 | 1 | 4 | yes | — |
| 249 | #419 | C23 | 1 | 8 | yes | — |
| 250 | #418 | C23 | 1 | 8 | yes | — |
| 251 | #418 | C23 | 1 | 4 | yes | — |
| 252 | #418 | C23 | 1 | 8 | yes | — |
| 253 | #418 | C23 | 1 | 8 | yes | — |
| 254 | #418 | C23 | 1 | 4 | yes | — |
| 255 | #417 | C23 | 1 | 8 | yes | — |
| 256 | #417 | C23 | 1 | 8 | yes | — |
| 257 | #416 | C23 | 1 | 8 | yes | — |
| 258 | #416 | C23 | 1 | 8 | yes | — |
| 259 | #416 | C23 | 1 | 4 | yes | — |
| 260 | #416 | C23 | 1 | 4 | yes | — |
| 261 | #416 | C23 | 1 | 8 | yes | — |
| 262 | C2×#103 | C23 | 1 | 4 | yes | — |
| 263 | C2×#103 | C23 | 1 | 4 | yes | — |
| 264 | C2×#102 | C23 | 1 | 8 | yes | — |
| 265 | C2×#102 | C23 | 1 | 4 | yes | — |
| 266 | C2×#102 | C23 | 1 | 4 | yes | — |
| 267 | #405 | C23 | 1 | 8 | yes | — |
| 268 | #405 | C23 | 1 | 8 | yes | — |
| 269 | #405 | C23 | 1 | 8 | yes | — |
| 270 | C4×M16 | C23 | 1 | 8 | yes | — |
| 271 | C2×#97 | C23 | 1 | 2 | yes | — |
| 272 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 273 | C25 | — | 2 | 1 | no | — |
| 274 | C2×#41 | — | 2 | 16 | no | — |
| 275 | C2×#41 | — | 2 | 2 | no | — |
| 276 | C2×#41 | — | 2 | 2 | no | — |
| 277 | C2×#41 | — | 2 | 8 | no | — |
| 278 | C2×#41 | — | 2 | 8 | no | — |
| 279 | C2×#41 | C24 | 1 | 4 | yes | — |
| 280 | C2×#41 | C24 | 1 | 4 | yes | — |
| 281 | C22×Q8 | — | 2 | 1 | no | — |
| 282 | C22×Q8 | — | 2 | 2 | no | — |
| 283 | C22×Q8 | — | 2 | 4 | no | — |
| 284 | C22×Q8 | #41 | 1 | 8 | yes | complemented |
| 285 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 286 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 287 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 288 | C22×D4 | — | 2 | 2 | no | — |
| 289 | C22×D4 | — | 2 | 1 | no | — |
| 290 | C22×D4 | — | 2 | 2 | no | — |
| 291 | C22×D4 | — | 2 | 8 | no | — |
| 292 | C22×D4 | — | 2 | 4 | no | — |
| 293 | C22×D4 | — | 2 | 4 | no | — |
| 294 | C22×D4 | C24 | 1 | 2 | yes | — |
| 295 | C22×D4 | C24 | 1 | 4 | yes | — |
| 296 | C22×D4 | C24 | 1 | 2 | yes | — |
| 297 | C23×C4 | — | 2 | 1 | no | — |
| 298 | C23×C4 | — | 2 | 2 | no | — |
| 299 | C23×C4 | — | 2 | 4 | no | — |
| 300 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 301 | #137 | — | 2 | 32 | no | — |
| 302 | #137 | — | 2 | 32 | no | — |
| 303 | C2×Q16 | — | 2 | 16 | no | — |
| 304 | C2×Q16 | C24 | 1 | 16 | yes | — |
| 305 | C2×SD16 | — | 2 | 32 | no | — |
| 306 | C2×SD16 | — | 2 | 8 | no | — |
| 307 | C2×SD16 | — | 2 | 8 | no | — |
| 308 | C2×SD16 | — | 2 | 16 | no | — |
| 309 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 310 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 311 | C2×SD16 | C24 | 1 | 16 | yes | — |
| 312 | C2×M16 | — | 2 | 8 | no | — |
| 313 | C2×M16 | — | 2 | 4 | no | — |
| 314 | C2×M16 | C24 | 1 | 4 | yes | — |
| 315 | C2×M16 | C24 | 1 | 4 | yes | — |
| 316 | C2×M16 | C24 | 1 | 4 | yes | — |
| 317 | C22×C8 | — | 2 | 4 | no | — |
| 318 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 319 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 320 | C22×C8 | C24 | 1 | 4 | yes | — |
| 321 | C22×C8 | C24 | 1 | 4 | yes | — |
| 322 | C22×C8 | C24 | 1 | 2 | yes | — |
| 323 | C4⋊Q8 | — | 2 | 16 | no | — |
| 324 | C4⋊Q8 | — | 2 | 32 | no | — |
| 325 | C4⋊Q8 | — | 2 | 16 | no | — |
| 326 | C4⋊Q8 | — | 2 | 32 | no | — |
| 327 | C4⋊Q8 | — | 2 | 8 | no | — |
| 328 | C4⋊Q8 | — | 2 | 8 | no | — |
| 329 | C4⋊Q8 | — | 2 | 8 | no | — |
| 330 | C4⋊Q8 | C2×D4 | 1 | 16 | yes | — |
| 331 | C4⋊Q8 | C2×D4 | 1 | 8 | yes | — |
| 332 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 333 | C4⋊Q8 | C24 | 1 | 8 | yes | — |
| 334 | C4⋊Q8 | C24 | 1 | 16 | yes | — |
| 335 | #127 | — | 2 | 8 | no | — |
| 336 | #127 | C24 | 1 | 16 | yes | — |
| 337 | #127 | C24 | 1 | 4 | yes | — |
| 338 | #126 | — | 2 | 32 | no | — |
| 339 | #125 | — | 2 | 32 | no | — |
| 340 | #125 | — | 2 | 32 | no | — |
| 341 | #125 | — | 2 | 32 | no | — |
| 342 | #125 | — | 2 | 8 | no | — |
| 343 | #125 | — | 2 | 8 | no | — |
| 344 | #125 | — | 2 | 8 | no | — |
| 345 | #125 | C2×D4 | 1 | 16 | yes | — |
| 346 | #125 | C2×D4 | 1 | 8 | yes | — |
| 347 | #125 | C24 | 1 | 8 | yes | — |
| 348 | #125 | C24 | 1 | 16 | yes | — |
| 349 | #124 | — | 2 | 32 | no | — |
| 350 | #124 | — | 2 | 8 | no | — |
| 351 | #124 | C24 | 1 | 16 | yes | — |
| 352 | #124 | C24 | 1 | 8 | yes | — |
| 353 | #123 | — | 2 | 32 | no | — |
| 354 | #123 | — | 2 | 32 | no | — |
| 355 | #123 | — | 2 | 8 | no | — |
| 356 | C22⋊Q8 | — | 2 | 16 | no | — |
| 357 | C22⋊Q8 | — | 2 | 16 | no | — |
| 358 | C22⋊Q8 | — | 2 | 8 | no | — |
| 359 | C22⋊Q8 | — | 2 | 8 | no | — |
| 360 | C22⋊Q8 | — | 2 | 16 | no | — |
| 361 | C22⋊Q8 | — | 2 | 16 | no | — |
| 362 | C22⋊Q8 | — | 2 | 16 | no | — |
| 363 | C22⋊Q8 | C2×D4 | 1 | 16 | yes | — |
| 364 | C22⋊Q8 | C2×D4 | 1 | 32 | yes | — |
| 365 | #121 | — | 2 | 8 | no | — |
| 366 | #121 | — | 2 | 16 | no | — |
| 367 | #121 | — | 2 | 16 | no | — |
| 368 | #121 | — | 2 | 8 | no | — |
| 369 | #121 | — | 2 | 16 | no | — |
| 370 | #121 | — | 2 | 32 | no | — |
| 371 | #120 | — | 2 | 16 | no | — |
| 372 | #120 | — | 2 | 16 | no | — |
| 373 | #120 | — | 2 | 8 | no | — |
| 374 | C4×Q8 | — | 2 | 16 | no | — |
| 375 | C4×Q8 | — | 2 | 16 | no | — |
| 376 | C4×Q8 | — | 2 | 16 | no | — |
| 377 | C4×Q8 | — | 2 | 16 | no | — |
| 378 | C4×Q8 | — | 2 | 8 | no | — |
| 379 | C4×Q8 | — | 2 | 16 | no | — |
| 380 | C4×Q8 | — | 2 | 32 | no | — |
| 381 | C4×Q8 | — | 2 | 16 | no | — |
| 382 | C4×Q8 | — | 2 | 8 | no | — |
| 383 | C4×Q8 | — | 2 | 16 | no | — |
| 384 | C4×Q8 | — | 2 | 8 | no | — |
| 385 | C4×Q8 | C24 | 1 | 16 | yes | — |
| 386 | C4×Q8 | C24 | 1 | 32 | yes | — |
| 387 | C4×Q8 | C24 | 1 | 16 | yes | — |
| 388 | C4×Q8 | C24 | 1 | 16 | yes | — |
| 389 | C4×D4 | — | 2 | 16 | no | — |
| 390 | C4×D4 | — | 2 | 16 | no | — |
| 391 | C4×D4 | — | 2 | 8 | no | — |
| 392 | C4×D4 | — | 2 | 32 | no | — |
| 393 | C4×D4 | — | 2 | 16 | no | — |
| 394 | C4×D4 | — | 2 | 8 | no | — |
| 395 | C4×D4 | — | 2 | 8 | no | — |
| 396 | C4×D4 | C24 | 1 | 16 | yes | — |
| 397 | C4×D4 | C24 | 1 | 16 | yes | — |
| 398 | #117 | — | 2 | 2 | no | — |
| 399 | #117 | — | 2 | 2 | no | — |
| 400 | #117 | — | 2 | 2 | no | — |
| 401 | #117 | — | 2 | 2 | no | — |
| 402 | #117 | — | 2 | 8 | no | — |
| 403 | #117 | — | 2 | 16 | no | — |
| 404 | #117 | — | 2 | 8 | no | — |
| 405 | #117 | — | 2 | 16 | no | — |
| 406 | #117 | — | 2 | 16 | no | — |
| 407 | #117 | — | 2 | 16 | no | — |
| 408 | #117 | — | 2 | 8 | no | — |
| 409 | #117 | C2×D4 | 1 | 4 | yes | — |
| 410 | #117 | C2×D4 | 1 | 4 | yes | — |
| 411 | #117 | C2×D4 | 1 | 4 | yes | — |
| 412 | #117 | C24 | 1 | 4 | yes | — |
| 413 | #117 | C24 | 1 | 4 | yes | — |
| 414 | #117 | C24 | 1 | 4 | yes | — |
| 415 | #117 | C24 | 1 | 4 | yes | — |
| 416 | #117 | C24 | 1 | 4 | yes | — |
| 417 | #117 | C24 | 1 | 4 | yes | — |
| 418 | #117 | C24 | 1 | 4 | yes | — |
| 419 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 420 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 421 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 422 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 423 | C2×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 424 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 425 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 426 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 427 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 428 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 429 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 430 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 431 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 432 | C2×C22⋊C4 | — | 2 | 16 | no | — |
| 433 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 434 | C2×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 435 | C2×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 436 | C2×C42 | — | 2 | 8 | no | — |
| 437 | C2×C42 | — | 2 | 4 | no | — |
| 438 | C2×C42 | — | 2 | 1 | no | — |
| 439 | C2×C42 | — | 2 | 1 | no | — |
| 440 | C2×C42 | — | 2 | 2 | no | — |
| 441 | C2×C42 | — | 2 | 8 | no | — |
| 442 | C2×C42 | C24 | 1 | 2 | yes | — |
| 443 | C2×C42 | C24 | 1 | 4 | yes | — |
| 444 | #107 | C24 | 1 | 8 | yes | — |
| 445 | #107 | C24 | 1 | 16 | yes | — |
| 446 | #106 | C24 | 1 | 4 | yes | — |
| 447 | #106 | C24 | 1 | 4 | yes | — |
| 448 | #106 | C24 | 1 | 16 | yes | — |
| 449 | C4⋊C8 | C24 | 1 | 16 | yes | — |
| 450 | C4⋊C8 | C24 | 1 | 16 | yes | — |
| 451 | C4⋊C8 | C24 | 1 | 16 | yes | — |
| 452 | #103 | C24 | 1 | 8 | yes | — |
| 453 | #103 | C24 | 1 | 8 | yes | — |
| 454 | #103 | C24 | 1 | 16 | yes | — |
| 455 | #103 | C24 | 1 | 16 | yes | — |
| 456 | #103 | C24 | 1 | 16 | yes | — |
| 457 | #102 | C24 | 1 | 8 | yes | — |
| 458 | #102 | C24 | 1 | 8 | yes | — |
| 459 | #102 | C24 | 1 | 16 | yes | — |
| 460 | #102 | C24 | 1 | 32 | yes | — |
| 461 | #102 | C24 | 1 | 16 | yes | — |
| 462 | #102 | C24 | 1 | 16 | yes | — |
| 463 | #97 | C24 | 1 | 8 | yes | — |
| 464 | #97 | C24 | 1 | 16 | yes | — |
| 465 | C4×C8 | C24 | 1 | 8 | yes | — |
| 466 | C4×C8 | C24 | 1 | 16 | yes | — |
| 467 | C24 | — | 2 | 4 | no | — |
| 468 | C24 | — | 2 | 2 | no | — |
| 469 | C24 | — | 2 | 2 | no | — |
| 470 | C24 | — | 4 | 4 | no | — |
| 471 | C24 | — | 16 | 2 | no | — |
| 472 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 473 | #41 | — | 2 | 8 | no | — |
| 474 | #41 | — | 2 | 8 | no | — |
| 475 | #41 | — | 2 | 8 | no | — |
| 476 | #41 | — | 2 | 8 | no | — |
| 477 | #41 | — | 4 | 8 | no | — |
| 478 | #41 | — | 4 | 8 | no | — |
| 479 | #41 | — | 16 | 16 | no | — |
| 480 | C2×Q8 | — | 2 | 16 | no | — |
| 481 | C2×Q8 | — | 2 | 8 | no | — |
| 482 | C2×Q8 | — | 2 | 4 | no | — |
| 483 | C2×Q8 | — | 2 | 2 | no | — |
| 484 | C2×Q8 | — | 2 | 2 | no | — |
| 485 | C2×Q8 | — | 2 | 16 | no | — |
| 486 | C2×Q8 | — | 2 | 8 | no | — |
| 487 | C2×Q8 | — | 2 | 4 | no | — |
| 488 | C2×Q8 | — | 2 | 8 | no | — |
| 489 | C2×Q8 | — | 2 | 4 | no | — |
| 490 | C2×Q8 | — | 2 | 4 | no | — |
| 491 | C2×Q8 | C22×D4 | 1 | 16 | yes | — |
| 492 | C2×Q8 | C2×#41 | 1 | 16 | yes | — |
| 493 | C2×Q8 | C2×#41 | 1 | 8 | yes | — |
| 494 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 495 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 496 | C2×D4 | — | 2 | 4 | no | — |
| 497 | C2×D4 | — | 2 | 4 | no | — |
| 498 | C2×D4 | — | 2 | 2 | no | — |
| 499 | C2×D4 | — | 2 | 4 | no | — |
| 500 | C2×D4 | — | 2 | 2 | no | — |
| 501 | C2×D4 | — | 2 | 8 | no | — |
| 502 | C2×D4 | — | 2 | 32 | no | — |
| 503 | C2×D4 | — | 2 | 8 | no | — |
| 504 | C2×D4 | — | 2 | 4 | no | — |
| 505 | C2×D4 | — | 2 | 4 | no | — |
| 506 | C2×D4 | — | 2 | 4 | no | — |
| 507 | C2×D4 | — | 2 | 8 | no | — |
| 508 | C2×D4 | — | 2 | 4 | no | — |
| 509 | C2×D4 | — | 4 | 8 | no | — |
| 510 | C2×D4 | — | 4 | 8 | no | — |
| 511 | C2×D4 | — | 4 | 4 | no | — |
| 512 | C2×D4 | — | 16 | 8 | no | — |
| 513 | C2×D4 | C25 | 1 | 4 | yes | — |
| 514 | C2×D4 | C25 | 1 | 4 | yes | — |
| 515 | C22×C4 | — | 2 | 8 | no | — |
| 516 | C22×C4 | — | 2 | 4 | no | — |
| 517 | C22×C4 | — | 2 | 2 | no | — |
| 518 | C22×C4 | — | 2 | 2 | no | — |
| 519 | C22×C4 | — | 2 | 4 | no | — |
| 520 | C22×C4 | — | 2 | 2 | no | — |
| 521 | C22×C4 | — | 2 | 2 | no | — |
| 522 | C22×C4 | — | 2 | 4 | no | — |
| 523 | C22×C4 | — | 2 | 4 | no | — |
| 524 | C22×C4 | — | 2 | 16 | no | — |
| 525 | C22×C4 | — | 2 | 16 | no | — |
| 526 | C22×C4 | — | 4 | 8 | no | — |
| 527 | C22×C4 | — | 16 | 4 | no | — |
| 528 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 529 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 530 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 531 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 532 | C22×C4 | C2×#41 | 1 | 4 | yes | — |
| 533 | C22×C4 | 2−1+4 | 1 | 4 | yes | — |
| 534 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 535 | C22×C4 | C25 | 1 | 2 | yes | — |
| 536 | Q16 | — | 2 | 32 | no | — |
| 537 | SD16 | — | 2 | 16 | no | — |
| 538 | SD16 | — | 2 | 16 | no | — |
| 539 | SD16 | — | 2 | 32 | no | — |
| 540 | M16 | — | 2 | 8 | no | — |
| 541 | M16 | — | 2 | 8 | no | — |
| 542 | M16 | — | 2 | 8 | no | — |
| 543 | C2×C8 | — | 2 | 8 | no | — |
| 544 | C2×C8 | — | 2 | 2 | no | — |
| 545 | C2×C8 | — | 2 | 2 | no | — |
| 546 | C2×C8 | — | 2 | 8 | no | — |
| 547 | C2×C8 | — | 2 | 4 | no | — |
| 548 | C2×C8 | C25 | 1 | 4 | yes | — |
| 549 | C2×C8 | C25 | 1 | 2 | yes | — |
| 550 | C2×C8 | C25 | 1 | 8 | yes | — |
| 551 | C2×C8 | C25 | 1 | 2 | yes | — |
| 552 | C4⋊C4 | — | 2 | 2 | no | — |
| 553 | C4⋊C4 | — | 2 | 16 | no | — |
| 554 | C4⋊C4 | — | 2 | 32 | no | — |
| 555 | C4⋊C4 | — | 2 | 16 | no | — |
| 556 | C4⋊C4 | — | 2 | 4 | no | — |
| 557 | C4⋊C4 | — | 2 | 2 | no | — |
| 558 | C4⋊C4 | — | 2 | 8 | no | — |
| 559 | C4⋊C4 | — | 2 | 16 | no | — |
| 560 | C4⋊C4 | — | 2 | 8 | no | — |
| 561 | C4⋊C4 | — | 2 | 16 | no | — |
| 562 | C4⋊C4 | — | 2 | 16 | no | — |
| 563 | C4⋊C4 | — | 2 | 16 | no | — |
| 564 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 565 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 566 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 567 | C4⋊C4 | C22×D4 | 1 | 16 | yes | — |
| 568 | C4⋊C4 | C22×D4 | 1 | 32 | yes | — |
| 569 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 570 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 571 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 572 | C22⋊C4 | — | 2 | 4 | no | — |
| 573 | C22⋊C4 | — | 2 | 4 | no | — |
| 574 | C22⋊C4 | — | 2 | 4 | no | — |
| 575 | C22⋊C4 | — | 2 | 4 | no | — |
| 576 | C22⋊C4 | — | 2 | 16 | no | — |
| 577 | C22⋊C4 | — | 2 | 16 | no | — |
| 578 | C22⋊C4 | — | 2 | 32 | no | — |
| 579 | C22⋊C4 | — | 2 | 16 | no | — |
| 580 | C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 581 | C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 582 | C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 583 | C42 | — | 2 | 4 | no | — |
| 584 | C42 | — | 2 | 16 | no | — |
| 585 | C42 | — | 2 | 32 | no | — |
| 586 | C42 | — | 2 | 16 | no | — |
| 587 | C42 | — | 2 | 4 | no | — |
| 588 | C42 | — | 2 | 4 | no | — |
| 589 | C42 | — | 2 | 4 | no | — |
| 590 | C42 | C22×D4 | 1 | 8 | yes | — |
| 591 | C42 | C22×D4 | 1 | 4 | yes | — |
| 592 | C42 | C25 | 1 | 4 | yes | — |
| 593 | C42 | C25 | 1 | 8 | yes | — |
| 594 | C23 | — | 2 | 4 | no | — |
| 595 | C23 | — | 2 | 4 | no | — |
| 596 | C23 | — | 4 | 2 | no | — |
| 597 | C23 | — | 4 | 4 | no | — |
| 598 | C23 | — | 4 | 4 | no | — |
| 599 | C23 | — | 4 | 8 | no | — |
| 600 | C23 | — | 8 | 4 | no | — |
| 601 | C23 | — | 8 | 4 | no | — |
| 602 | C23 | — | 8 | 8 | no | — |
| 603 | C23 | — | 16 | 8 | no | — |
| 604 | C23 | #548 | 1 | 4 | yes | — |
| 605 | C23 | C23×D4 | 1 | 2 | yes | — |
| 606 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 607 | Q8 | — | 2 | 4 | no | — |
| 608 | Q8 | — | 2 | 8 | no | — |
| 609 | Q8 | — | 2 | 16 | no | — |
| 610 | Q8 | — | 2 | 4 | no | — |
| 611 | Q8 | — | 2 | 4 | no | — |
| 612 | Q8 | — | 4 | 16 | no | — |
| 613 | Q8 | — | 4 | 4 | no | — |
| 614 | Q8 | — | 8 | 8 | no | — |
| 615 | Q8 | — | 8 | 16 | no | — |
| 616 | Q8 | C22×#41 | 1 | 8 | yes | — |
| 617 | D4 | — | 2 | 4 | no | — |
| 618 | D4 | — | 2 | 4 | no | — |
| 619 | D4 | — | 2 | 4 | no | — |
| 620 | D4 | — | 2 | 4 | no | — |
| 621 | D4 | — | 4 | 8 | no | — |
| 622 | D4 | — | 4 | 8 | no | — |
| 623 | D4 | — | 4 | 4 | no | — |
| 624 | D4 | — | 4 | 8 | no | — |
| 625 | D4 | — | 4 | 4 | no | — |
| 626 | D4 | — | 8 | 32 | no | — |
| 627 | D4 | — | 8 | 8 | no | — |
| 628 | C2×C4 | — | 2 | 4 | no | — |
| 629 | C2×C4 | — | 2 | 16 | no | — |
| 630 | C2×C4 | — | 2 | 8 | no | — |
| 631 | C2×C4 | — | 2 | 4 | no | — |
| 632 | C2×C4 | — | 2 | 8 | no | — |
| 633 | C2×C4 | — | 2 | 4 | no | — |
| 634 | C2×C4 | — | 2 | 4 | no | — |
| 635 | C2×C4 | — | 4 | 4 | no | — |
| 636 | C2×C4 | — | 4 | 8 | no | — |
| 637 | C2×C4 | — | 4 | 4 | no | — |
| 638 | C2×C4 | — | 4 | 8 | no | — |
| 639 | C2×C4 | — | 4 | 8 | no | — |
| 640 | C2×C4 | — | 8 | 16 | no | — |
| 641 | C2×C4 | — | 8 | 16 | no | — |
| 642 | C2×C4 | — | 8 | 2 | no | — |
| 643 | C2×C4 | — | 8 | 4 | no | — |
| 644 | C2×C4 | — | 8 | 2 | no | — |
| 645 | C2×C4 | #548 | 1 | 8 | yes | — |
| 646 | C2×C4 | #548 | 1 | 4 | yes | — |
| 647 | C2×C4 | C23×D4 | 1 | 16 | yes | — |
| 648 | C2×C4 | C23×D4 | 1 | 8 | yes | — |
| 649 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 650 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 651 | C2×C4 | C22×#41 | 1 | 4 | yes | — |
| 652 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 653 | C2×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 654 | C2×C4 | C2×2−1+4 | 1 | 4 | yes | — |
| 655 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 656 | C8 | — | 2 | 2 | no | — |
| 657 | C8 | — | 2 | 2 | no | — |
| 658 | C8 | — | 2 | 8 | no | — |
| 659 | C8 | — | 2 | 4 | no | — |
| 660 | C22 | — | 2 | 2 | no | — |
| 661 | C22 | — | 2 | 4 | no | — |
| 662 | C22 | — | 4 | 4 | no | — |
| 663 | C22 | — | 4 | 8 | no | — |
| 664 | C22 | — | 4 | 8 | no | — |
| 665 | C22 | — | 4 | 4 | no | — |
| 666 | C22 | — | 4 | 4 | no | — |
| 667 | C22 | — | 8 | 8 | no | — |
| 668 | C22 | — | 16 | 4 | no | — |
| 669 | C22 | — | 16 | 8 | no | — |
| 670 | C22 | C2×#548 | 1 | 4 | yes | — |
| 671 | C22 | C2×#548 | 1 | 2 | yes | — |
| 672 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 673 | C4 | — | 2 | 8 | no | — |
| 674 | C4 | — | 2 | 16 | no | — |
| 675 | C4 | — | 2 | 8 | no | — |
| 676 | C4 | — | 4 | 4 | no | — |
| 677 | C4 | — | 4 | 4 | no | — |
| 678 | C4 | — | 4 | 8 | no | — |
| 679 | C4 | — | 4 | 4 | no | — |
| 680 | C4 | C2×#548 | 1 | 2 | yes | — |
| 681 | C4 | C2×#548 | 1 | 4 | yes | — |
| 682 | C4 | C23×#41 | 1 | 1 | yes | characteristic |
| 683 | C4 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 684 | C2 | — | 2 | 2 | no | — |
| 685 | C2 | — | 2 | 4 | no | — |
| 686 | C2 | — | 8 | 4 | no | — |
| 687 | C2 | — | 8 | 4 | no | — |
| 688 | C2 | C22×#548 | 1 | 1 | yes | characteristic |
| 689 | C2 | #63092 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | #62855 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #3458 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #62849 | C2 | semidirect |
| 3. #61344 | C2 | semidirect |
| 4. #61341 | C2 | semidirect |
| 5. #61334 | C2 | semidirect |
| 6. #61327 | C2 | semidirect |
| 7. #60619 | C2 | semidirect |
| 8. #60612 | C2 | semidirect |
| 9. #60490 | C2 | semidirect |
| 10. #60489 | C2 | semidirect |
| 11. #60424 | C2 | semidirect |
| 12. C2×#3043 | C2 | semidirect |
| 13. #60193 | C2 | semidirect |
| 14. #60169 | C2 | semidirect |
| 15. C2×#2949 | C2 | semidirect |
| 23. #3502 | C22 | semidirect |
| 24. #3502 | C22 | semidirect |
| 38. #3377 | C22 | semidirect |
| 39. #3375 | C22 | semidirect |
| 40. #3371 | C22 | semidirect |
| 41. #3371 | C22 | semidirect |
| 42. #3369 | C22 | semidirect |
| 43. #3368 | C22 | semidirect |
| 44. #3368 | C22 | semidirect |
| 45. #3365 | C22 | semidirect |
| 46. #3364 | C22 | semidirect |
| 47. #3362 | C22 | semidirect |
| 48. #3140 | C22 | semidirect |
| 49. #3138 | C22 | semidirect |
| 50. #3137 | C22 | semidirect |
| 52. #3136 | C22 | semidirect |
| 53. #3136 | C22 | semidirect |
| 54. #3135 | C22 | semidirect |
| 55. #3131 | C22 | semidirect |
| 56. #3084 | C22 | semidirect |
| 57. #3083 | C22 | semidirect |
| 58. #3082 | C22 | semidirect |
| 59. #3081 | C22 | semidirect |
| 60. #3081 | C22 | semidirect |
| 61. #3077 | C22 | semidirect |
| 62. #3076 | C22 | semidirect |
| 63. #3044 | C22 | semidirect |
| 65. #3043 | C22 | semidirect |
| 66. #3043 | C22 | semidirect |
| 67. #3043 | C22 | semidirect |
| 68. #3037 | C22 | semidirect |
| 69. C2×#464 | C22 | semidirect |
| 70. C2×#460 | C22 | semidirect |
| 71. #2962 | C22 | semidirect |
| 72. #2961 | C22 | semidirect |
| 73. #2960 | C22 | semidirect |
| 74. #2950 | C22 | semidirect |
| 75. #2949 | C22 | semidirect |
| 76. #2949 | C22 | semidirect |
| 77. #2947 | C22 | semidirect |
| 78. C4×#137 | C22 | semidirect |
| 79. C2×#440 | C22 | semidirect |
| 80. C2×C4×SD16 | C22 | semidirect |
| 111. Q82 | C23 | semidirect |
| 117. #557 | C23 | semidirect |
| 118. #557 | C23 | semidirect |
| 197. #491 | C23 | semidirect |
| 199. #490 | C23 | semidirect |
| 201. #489 | C23 | semidirect |
| 203. #488 | C23 | semidirect |
| 204. #487 | C23 | semidirect |
| 206. #486 | C23 | semidirect |
| 207. #479 | C23 | semidirect |
| 208. #479 | C23 | semidirect |
| 210. #478 | C23 | semidirect |
| 211. #478 | C23 | semidirect |
| 212. #477 | C23 | semidirect |
| 214. #476 | C23 | semidirect |
| 215. #475 | C23 | semidirect |
| 217. #474 | C23 | semidirect |
| 220. #464 | C23 | semidirect |
| 221. #462 | C23 | semidirect |
| 224. #460 | C23 | semidirect |
| 225. #446 | C23 | semidirect |
| 226. #446 | C23 | semidirect |
| 227. C8×Q8 | C23 | semidirect |
| 228. #441 | C23 | semidirect |
| 230. #440 | C23 | semidirect |
| 231. C4×Q16 | C23 | semidirect |
| 234. C4×SD16 | C23 | semidirect |
| 284. C22×Q8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62855 | 2 |
| #62849 | 2 |
| #61344 | 2 |
| #61341 | 2 |
| #61334 | 2 |
| #61327 | 2 |
| #60619 | 2 |
| #60612 | 2 |
| #60490 | 2 |
| #60489 | 2 |
| #60424 | 2 |
| C2×#3043 | 2 |
| #60193 | 2 |
| #60169 | 2 |
| C2×#2949 | 2 |