Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6812 conjugacy classes of subgroups.
The subgroup lattice has 436 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63040 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #63037 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #62413 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #62326 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | #62002 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #61999 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #61664 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | #61662 | C2 | 1 | 9 | yes | maximal, complemented |
| 9 | #61434 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #61087 | C2 | 1 | 9 | yes | maximal, complemented |
| 11 | #60308 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#577 | C22 | 1 | 6 | yes | complemented |
| 13 | #3550 | C22 | 1 | 9 | yes | complemented |
| 14 | #3549 | — | 2 | 9 | no | — |
| 15 | #3549 | C22 | 1 | 9 | yes | — |
| 16 | #3544 | — | 2 | 9 | no | — |
| 17 | #3522 | — | 2 | 6 | no | — |
| 18 | #3503 | C22 | 1 | 6 | yes | complemented |
| 19 | #3499 | C22 | 1 | 9 | yes | complemented |
| 20 | #3498 | — | 2 | 6 | no | — |
| 21 | #3498 | C22 | 1 | 9 | yes | — |
| 22 | #3498 | C22 | 1 | 6 | yes | — |
| 23 | #3483 | — | 2 | 1 | no | — |
| 24 | #3483 | C22 | 1 | 6 | yes | — |
| 25 | #3483 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3482 | C22 | 1 | 6 | yes | complemented |
| 27 | C2×Q82 | — | 2 | 1 | no | — |
| 28 | #3392 | C22 | 1 | 12 | yes | complemented |
| 29 | #3392 | C22 | 1 | 6 | yes | complemented |
| 30 | Q8×SD16 | C22 | 1 | 2 | yes | complemented |
| 31 | #3363 | C22 | 1 | 6 | yes | complemented |
| 32 | #3358 | C22 | 1 | 6 | yes | complemented |
| 33 | #3340 | C22 | 1 | 18 | yes | complemented |
| 34 | #3329 | C22 | 1 | 36 | yes | complemented |
| 35 | #3324 | C22 | 1 | 36 | yes | complemented |
| 36 | #3304 | C22 | 1 | 18 | yes | complemented |
| 37 | #3303 | C22 | 1 | 18 | yes | complemented |
| 38 | #3284 | C22 | 1 | 18 | yes | complemented |
| 39 | D4×SD16 | C22 | 1 | 36 | yes | complemented |
| 40 | D4×SD16 | C22 | 1 | 36 | yes | complemented |
| 41 | #3278 | C22 | 1 | 36 | yes | complemented |
| 42 | #3272 | C22 | 1 | 36 | yes | complemented |
| 43 | #3254 | C22 | 1 | 18 | yes | complemented |
| 44 | #3208 | C22 | 1 | 18 | yes | complemented |
| 45 | #3206 | C22 | 1 | 18 | yes | complemented |
| 46 | #3200 | C22 | 1 | 36 | yes | complemented |
| 47 | #3167 | C22 | 1 | 18 | yes | complemented |
| 48 | C2×#492 | C22 | 1 | 9 | yes | complemented |
| 49 | #3107 | C22 | 1 | 18 | yes | complemented |
| 50 | #3106 | C22 | 1 | 18 | yes | complemented |
| 51 | #3057 | C22 | 1 | 18 | yes | complemented |
| 52 | #3039 | C22 | 1 | 9 | yes | complemented |
| 53 | #3038 | C22 | 1 | 9 | yes | complemented |
| 54 | #3010 | C22 | 1 | 18 | yes | complemented |
| 55 | #3009 | C22 | 1 | 18 | yes | complemented |
| 56 | #2991 | C22 | 1 | 6 | yes | complemented |
| 57 | #2979 | C22 | 1 | 9 | yes | complemented |
| 58 | C8×#41 | C22 | 1 | 6 | yes | complemented |
| 59 | C4×#135 | C22 | 1 | 9 | yes | complemented |
| 60 | #2931 | C22 | 1 | 9 | yes | complemented |
| 61 | C2×2−1+4 | C23 | 1 | 6 | yes | — |
| 62 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 63 | C2×H(5,𝔽2) | C23 | 1 | 6 | yes | — |
| 64 | #577 | — | 4 | 24 | no | — |
| 65 | C2×#137 | C23 | 1 | 18 | yes | — |
| 66 | C2×AGL(1,ℤ/8) | C23 | 1 | 18 | yes | — |
| 67 | C2×#135 | C23 | 1 | 9 | yes | — |
| 68 | C22×SD16 | C23 | 1 | 18 | yes | — |
| 69 | C22×SD16 | C23 | 1 | 18 | yes | — |
| 70 | C2×#131 | C23 | 1 | 6 | yes | — |
| 71 | #563 | — | 2 | 18 | no | — |
| 72 | H(3,𝔽4) | — | 2 | 18 | no | — |
| 73 | #559 | — | 2 | 9 | no | — |
| 74 | Q82 | — | 2 | 9 | no | — |
| 75 | Q82 | — | 2 | 6 | no | — |
| 76 | Q82 | D4 | 1 | 1 | yes | characteristic |
| 77 | Q82 | C23 | 1 | 2 | yes | — |
| 78 | #557 | C23 | 1 | 6 | yes | — |
| 79 | #556 | C23 | 1 | 18 | yes | — |
| 80 | #555 | — | 2 | 9 | no | — |
| 81 | #555 | — | 2 | 18 | no | — |
| 82 | #555 | D4 | 1 | 9 | yes | — |
| 83 | #555 | C23 | 1 | 18 | yes | — |
| 84 | #554 | — | 2 | 18 | no | — |
| 85 | #552 | — | 2 | 18 | no | — |
| 86 | #550 | — | 2 | 6 | no | — |
| 87 | #550 | — | 2 | 6 | no | — |
| 88 | #550 | D4 | 1 | 6 | yes | — |
| 89 | #550 | C23 | 1 | 18 | yes | — |
| 90 | #550 | C23 | 1 | 6 | yes | — |
| 91 | D4×Q8 | C23 | 1 | 36 | yes | — |
| 92 | D4×Q8 | C23 | 1 | 2 | yes | — |
| 93 | #548 | — | 2 | 6 | no | — |
| 94 | #547 | — | 2 | 36 | no | — |
| 95 | #547 | C23 | 1 | 18 | yes | — |
| 96 | D42 | — | 2 | 9 | no | — |
| 97 | D42 | — | 2 | 36 | no | — |
| 98 | D42 | — | 2 | 18 | no | — |
| 99 | D42 | C23 | 1 | 36 | yes | — |
| 100 | #544 | — | 2 | 18 | no | — |
| 101 | #542 | — | 2 | 36 | no | — |
| 102 | #536 | — | 2 | 18 | no | — |
| 103 | #536 | C23 | 1 | 18 | yes | — |
| 104 | #535 | — | 2 | 18 | no | — |
| 105 | #535 | — | 2 | 36 | no | — |
| 106 | #535 | — | 2 | 18 | no | — |
| 107 | #535 | C23 | 1 | 18 | yes | — |
| 108 | #533 | C23 | 1 | 18 | yes | — |
| 109 | #532 | — | 2 | 9 | no | — |
| 110 | #532 | — | 2 | 9 | no | — |
| 111 | #532 | — | 2 | 18 | no | — |
| 112 | #532 | C23 | 1 | 18 | yes | — |
| 113 | #532 | C23 | 1 | 9 | yes | — |
| 114 | C2×C4⋊Q8 | — | 2 | 9 | no | — |
| 115 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 116 | C2×#127 | — | 2 | 9 | no | — |
| 117 | C2×#127 | C23 | 1 | 9 | yes | — |
| 118 | #529 | — | 2 | 18 | no | — |
| 119 | #520 | — | 2 | 6 | no | — |
| 120 | C4×#41 | — | 2 | 6 | no | — |
| 121 | C4×#41 | C23 | 1 | 9 | yes | — |
| 122 | C4×#41 | C23 | 1 | 9 | yes | — |
| 123 | C4×#41 | C23 | 1 | 6 | yes | — |
| 124 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 125 | #498 | C23 | 1 | 6 | yes | — |
| 126 | #492 | C23 | 1 | 18 | yes | — |
| 127 | #492 | C23 | 1 | 36 | yes | — |
| 128 | #487 | C23 | 1 | 18 | yes | — |
| 129 | #486 | C23 | 1 | 18 | yes | — |
| 130 | #485 | C23 | 1 | 36 | yes | — |
| 131 | #482 | C23 | 1 | 36 | yes | — |
| 132 | #477 | C23 | 1 | 18 | yes | — |
| 133 | #476 | C23 | 1 | 6 | yes | — |
| 134 | #475 | C23 | 1 | 6 | yes | — |
| 135 | #474 | C23 | 1 | 18 | yes | — |
| 136 | #468 | C23 | 1 | 72 | yes | — |
| 137 | #465 | C23 | 1 | 36 | yes | — |
| 138 | #465 | C23 | 1 | 36 | yes | — |
| 139 | #462 | C23 | 1 | 18 | yes | — |
| 140 | #461 | C23 | 1 | 36 | yes | — |
| 141 | #461 | C23 | 1 | 18 | yes | — |
| 142 | #460 | C23 | 1 | 18 | yes | — |
| 143 | #460 | C23 | 1 | 36 | yes | — |
| 144 | #459 | C23 | 1 | 18 | yes | — |
| 145 | #452 | C23 | 1 | 36 | yes | — |
| 146 | #450 | C23 | 1 | 72 | yes | — |
| 147 | #449 | C23 | 1 | 36 | yes | — |
| 148 | #448 | C23 | 1 | 72 | yes | — |
| 149 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 150 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 151 | C4×Q16 | C23 | 1 | 18 | yes | — |
| 152 | C4×SD16 | C23 | 1 | 36 | yes | — |
| 153 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 154 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 155 | C4×D8 | C23 | 1 | 18 | yes | — |
| 156 | #436 | C23 | 1 | 36 | yes | — |
| 157 | C8×D4 | C23 | 1 | 18 | yes | — |
| 158 | C8×D4 | C23 | 1 | 18 | yes | — |
| 159 | #431 | C23 | 1 | 18 | yes | — |
| 160 | #427 | C23 | 1 | 9 | yes | — |
| 161 | #423 | C23 | 1 | 9 | yes | — |
| 162 | #419 | C23 | 1 | 18 | yes | — |
| 163 | #418 | C23 | 1 | 18 | yes | — |
| 164 | #416 | C23 | 1 | 9 | yes | — |
| 165 | #416 | C23 | 1 | 9 | yes | — |
| 166 | #408 | C23 | 1 | 18 | yes | — |
| 167 | C2×C4×C8 | C23 | 1 | 9 | yes | — |
| 168 | 2−1+4 | — | 4 | 12 | no | — |
| 169 | 2−1+4 | — | 8 | 6 | no | — |
| 170 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 171 | H(5,𝔽2) | — | 8 | 6 | no | — |
| 172 | H(5,𝔽2) | — | 8 | 24 | no | — |
| 173 | C2×#41 | — | 2 | 6 | no | — |
| 174 | C2×#41 | — | 2 | 6 | no | — |
| 175 | C2×#41 | — | 2 | 18 | no | — |
| 176 | C2×#41 | — | 2 | 18 | no | — |
| 177 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 178 | C2×#41 | C24 | 1 | 9 | yes | — |
| 179 | C2×#41 | C24 | 1 | 9 | yes | — |
| 180 | C2×#41 | C24 | 1 | 6 | yes | — |
| 181 | C22×Q8 | — | 2 | 2 | no | — |
| 182 | C22×Q8 | — | 2 | 6 | no | — |
| 183 | C22×Q8 | C24 | 1 | 18 | yes | — |
| 184 | C22×D4 | — | 2 | 18 | no | — |
| 185 | C22×D4 | — | 2 | 36 | no | — |
| 186 | C22×D4 | — | 2 | 18 | no | — |
| 187 | C22×D4 | C24 | 1 | 18 | yes | — |
| 188 | #137 | — | 4 | 36 | no | — |
| 189 | AGL(1,ℤ/8) | — | 4 | 36 | no | — |
| 190 | #135 | — | 2 | 36 | no | — |
| 191 | C2×Q16 | C24 | 1 | 9 | yes | — |
| 192 | C2×SD16 | — | 4 | 36 | no | — |
| 193 | C2×SD16 | — | 8 | 18 | no | — |
| 194 | C2×SD16 | C24 | 1 | 9 | yes | — |
| 195 | C2×SD16 | C24 | 1 | 36 | yes | — |
| 196 | C2×SD16 | C24 | 1 | 36 | yes | — |
| 197 | C2×SD16 | C24 | 1 | 1 | yes | characteristic |
| 198 | C2×D8 | C24 | 1 | 9 | yes | — |
| 199 | #131 | — | 4 | 12 | no | — |
| 200 | C2×M16 | C24 | 1 | 18 | yes | — |
| 201 | C22×C8 | C24 | 1 | 9 | yes | — |
| 202 | C22×C8 | C24 | 1 | 9 | yes | — |
| 203 | C4⋊Q8 | — | 2 | 18 | no | — |
| 204 | C4⋊Q8 | — | 2 | 36 | no | — |
| 205 | C4⋊Q8 | — | 2 | 6 | no | — |
| 206 | C4⋊Q8 | — | 2 | 9 | no | — |
| 207 | C4⋊Q8 | — | 2 | 9 | no | — |
| 208 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 209 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 210 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 211 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 212 | #127 | — | 2 | 18 | no | — |
| 213 | #127 | — | 2 | 18 | no | — |
| 214 | #127 | — | 2 | 9 | no | — |
| 215 | #127 | — | 2 | 9 | no | — |
| 216 | #127 | C2×D4 | 1 | 9 | yes | — |
| 217 | #127 | C24 | 1 | 18 | yes | — |
| 218 | #126 | — | 2 | 36 | no | — |
| 219 | #125 | — | 2 | 18 | no | — |
| 220 | #125 | — | 2 | 18 | no | — |
| 221 | #124 | — | 2 | 18 | no | — |
| 222 | #124 | — | 2 | 18 | no | — |
| 223 | #124 | — | 2 | 18 | no | — |
| 224 | #124 | — | 2 | 36 | no | — |
| 225 | #124 | — | 2 | 18 | no | — |
| 226 | #124 | C2×D4 | 1 | 18 | yes | — |
| 227 | #123 | — | 2 | 36 | no | — |
| 228 | #123 | — | 2 | 36 | no | — |
| 229 | C22⋊Q8 | — | 2 | 18 | no | — |
| 230 | C22⋊Q8 | — | 2 | 6 | no | — |
| 231 | C22⋊Q8 | — | 2 | 72 | no | — |
| 232 | C22⋊Q8 | C24 | 1 | 36 | yes | — |
| 233 | #121 | — | 2 | 18 | no | — |
| 234 | #121 | — | 2 | 18 | no | — |
| 235 | #121 | — | 2 | 18 | no | — |
| 236 | #121 | — | 2 | 18 | no | — |
| 237 | #121 | — | 2 | 36 | no | — |
| 238 | #121 | — | 2 | 36 | no | — |
| 239 | #121 | C2×D4 | 1 | 36 | yes | — |
| 240 | #121 | C24 | 1 | 36 | yes | — |
| 241 | #120 | — | 2 | 36 | no | — |
| 242 | #120 | — | 2 | 72 | no | — |
| 243 | C4×Q8 | — | 2 | 6 | no | — |
| 244 | C4×Q8 | — | 2 | 2 | no | — |
| 245 | C4×Q8 | — | 2 | 18 | no | — |
| 246 | C4×Q8 | — | 2 | 18 | no | — |
| 247 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 248 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 249 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 250 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 251 | C4×D4 | — | 2 | 36 | no | — |
| 252 | C4×D4 | — | 2 | 18 | no | — |
| 253 | C4×D4 | — | 2 | 18 | no | — |
| 254 | C4×D4 | — | 2 | 18 | no | — |
| 255 | C4×D4 | — | 2 | 18 | no | — |
| 256 | C4×D4 | C2×D4 | 1 | 18 | yes | — |
| 257 | C4×D4 | C24 | 1 | 6 | yes | — |
| 258 | C4×D4 | C24 | 1 | 18 | yes | — |
| 259 | C4×D4 | C24 | 1 | 18 | yes | — |
| 260 | #117 | — | 2 | 18 | no | — |
| 261 | #117 | — | 2 | 18 | no | — |
| 262 | #117 | — | 2 | 9 | no | — |
| 263 | #117 | — | 2 | 9 | no | — |
| 264 | #117 | C2×D4 | 1 | 18 | yes | — |
| 265 | #117 | C24 | 1 | 9 | yes | — |
| 266 | #117 | C24 | 1 | 9 | yes | — |
| 267 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 268 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 269 | C2×C42 | — | 2 | 9 | no | — |
| 270 | C2×C42 | — | 2 | 9 | no | — |
| 271 | C2×C42 | C24 | 1 | 9 | yes | — |
| 272 | #107 | C24 | 1 | 18 | yes | — |
| 273 | #106 | C24 | 1 | 6 | yes | — |
| 274 | #106 | C24 | 1 | 12 | yes | — |
| 275 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 276 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 277 | #103 | C24 | 1 | 6 | yes | — |
| 278 | #103 | C24 | 1 | 18 | yes | — |
| 279 | #103 | C24 | 1 | 36 | yes | — |
| 280 | #102 | C24 | 1 | 6 | yes | — |
| 281 | #102 | C24 | 1 | 18 | yes | — |
| 282 | #102 | C24 | 1 | 36 | yes | — |
| 283 | C22⋊C8 | C24 | 1 | 36 | yes | — |
| 284 | C4×C8 | C24 | 1 | 6 | yes | — |
| 285 | C4×C8 | C24 | 1 | 18 | yes | — |
| 286 | C24 | — | 2 | 18 | no | — |
| 287 | #41 | — | 2 | 24 | no | — |
| 288 | #41 | — | 2 | 18 | no | — |
| 289 | #41 | — | 2 | 18 | no | — |
| 290 | #41 | — | 4 | 6 | no | — |
| 291 | #41 | — | 4 | 6 | no | — |
| 292 | #41 | — | 4 | 9 | no | — |
| 293 | #41 | — | 4 | 9 | no | — |
| 294 | #41 | — | 4 | 24 | no | — |
| 295 | #41 | — | 8 | 36 | no | — |
| 296 | #41 | — | 8 | 12 | no | — |
| 297 | #41 | — | 8 | 36 | no | — |
| 298 | C2×Q8 | — | 2 | 6 | no | — |
| 299 | C2×Q8 | — | 2 | 18 | no | — |
| 300 | C2×Q8 | — | 2 | 6 | no | — |
| 301 | C2×Q8 | — | 4 | 18 | no | — |
| 302 | C2×Q8 | — | 4 | 18 | no | — |
| 303 | C2×Q8 | — | 4 | 8 | no | — |
| 304 | C2×Q8 | — | 8 | 12 | no | — |
| 305 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 306 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 307 | C2×Q8 | C25 | 1 | 9 | yes | — |
| 308 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 309 | C2×D4 | — | 2 | 9 | no | — |
| 310 | C2×D4 | — | 2 | 9 | no | — |
| 311 | C2×D4 | — | 2 | 36 | no | — |
| 312 | C2×D4 | — | 2 | 18 | no | — |
| 313 | C2×D4 | — | 2 | 18 | no | — |
| 314 | C2×D4 | — | 2 | 18 | no | — |
| 315 | C2×D4 | — | 4 | 18 | no | — |
| 316 | C2×D4 | — | 4 | 18 | no | — |
| 317 | C2×D4 | — | 8 | 36 | no | — |
| 318 | C2×D4 | — | 8 | 72 | no | — |
| 319 | C2×D4 | — | 8 | 36 | no | — |
| 320 | C2×D4 | C22×D4 | 1 | 18 | yes | — |
| 321 | C2×D4 | C22×D4 | 1 | 18 | yes | — |
| 322 | C2×D4 | C25 | 1 | 9 | yes | — |
| 323 | C2×D4 | C25 | 1 | 1 | yes | characteristic |
| 324 | C22×C4 | — | 2 | 18 | no | — |
| 325 | C22×C4 | — | 2 | 6 | no | — |
| 326 | C22×C4 | — | 2 | 9 | no | — |
| 327 | C22×C4 | — | 2 | 9 | no | — |
| 328 | C22×C4 | — | 2 | 18 | no | — |
| 329 | C22×C4 | C22×D4 | 1 | 18 | yes | — |
| 330 | C22×C4 | C25 | 1 | 9 | yes | — |
| 331 | Q16 | — | 2 | 18 | no | — |
| 332 | SD16 | — | 2 | 18 | no | — |
| 333 | SD16 | — | 4 | 36 | no | — |
| 334 | SD16 | — | 4 | 36 | no | — |
| 335 | SD16 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 336 | D8 | — | 2 | 18 | no | — |
| 337 | M16 | — | 4 | 18 | no | — |
| 338 | C2×C8 | — | 2 | 18 | no | — |
| 339 | C2×C8 | — | 4 | 9 | no | — |
| 340 | C2×C8 | C25 | 1 | 6 | yes | — |
| 341 | C2×C8 | C25 | 1 | 9 | yes | — |
| 342 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 343 | C4⋊C4 | — | 2 | 18 | no | — |
| 344 | C4⋊C4 | — | 2 | 18 | no | — |
| 345 | C4⋊C4 | — | 2 | 36 | no | — |
| 346 | C4⋊C4 | — | 2 | 6 | no | — |
| 347 | C4⋊C4 | — | 2 | 6 | no | — |
| 348 | C4⋊C4 | — | 2 | 6 | no | — |
| 349 | C4⋊C4 | — | 2 | 18 | no | — |
| 350 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 351 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 352 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 353 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 354 | C22⋊C4 | — | 2 | 36 | no | — |
| 355 | C22⋊C4 | — | 2 | 9 | no | — |
| 356 | C22⋊C4 | — | 2 | 9 | no | — |
| 357 | C22⋊C4 | — | 2 | 6 | no | — |
| 358 | C22⋊C4 | — | 2 | 36 | no | — |
| 359 | C22⋊C4 | — | 2 | 18 | no | — |
| 360 | C22⋊C4 | C22×D4 | 1 | 36 | yes | — |
| 361 | C42 | — | 2 | 6 | no | — |
| 362 | C42 | — | 2 | 9 | no | — |
| 363 | C42 | — | 2 | 18 | no | — |
| 364 | C42 | — | 2 | 9 | no | — |
| 365 | C42 | C22×D4 | 1 | 9 | yes | — |
| 366 | C42 | C22×D4 | 1 | 9 | yes | — |
| 367 | C42 | C25 | 1 | 6 | yes | — |
| 368 | C23 | — | 2 | 1 | no | — |
| 369 | C23 | — | 2 | 9 | no | — |
| 370 | C23 | — | 8 | 18 | no | — |
| 371 | C23 | — | 8 | 36 | no | — |
| 372 | C23 | C23×D4 | 1 | 9 | yes | — |
| 373 | Q8 | — | 2 | 1 | no | — |
| 374 | Q8 | — | 2 | 9 | no | — |
| 375 | Q8 | — | 2 | 9 | no | — |
| 376 | Q8 | — | 4 | 6 | no | — |
| 377 | Q8 | — | 4 | 12 | no | — |
| 378 | Q8 | — | 8 | 18 | no | — |
| 379 | Q8 | — | 8 | 6 | no | — |
| 380 | Q8 | #577 | 1 | 8 | yes | complemented |
| 381 | Q8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 382 | D4 | — | 2 | 9 | no | — |
| 383 | D4 | — | 2 | 1 | no | — |
| 384 | D4 | — | 2 | 9 | no | — |
| 385 | D4 | — | 2 | 36 | no | — |
| 386 | D4 | — | 4 | 18 | no | — |
| 387 | D4 | — | 4 | 18 | no | — |
| 388 | D4 | — | 4 | 18 | no | — |
| 389 | D4 | — | 4 | 36 | no | — |
| 390 | D4 | — | 8 | 18 | no | — |
| 391 | D4 | — | 8 | 18 | no | — |
| 392 | D4 | — | 8 | 36 | no | — |
| 393 | D4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 394 | C2×C4 | — | 2 | 1 | no | — |
| 395 | C2×C4 | — | 2 | 9 | no | — |
| 396 | C2×C4 | — | 2 | 9 | no | — |
| 397 | C2×C4 | — | 2 | 36 | no | — |
| 398 | C2×C4 | — | 2 | 6 | no | — |
| 399 | C2×C4 | — | 2 | 6 | no | — |
| 400 | C2×C4 | — | 2 | 9 | no | — |
| 401 | C2×C4 | — | 4 | 18 | no | — |
| 402 | C2×C4 | — | 4 | 18 | no | — |
| 403 | C2×C4 | — | 4 | 36 | no | — |
| 404 | C2×C4 | — | 4 | 12 | no | — |
| 405 | C2×C4 | — | 8 | 18 | no | — |
| 406 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 407 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 408 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 409 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 410 | C8 | — | 2 | 9 | no | — |
| 411 | C8 | — | 2 | 6 | no | — |
| 412 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 413 | C22 | — | 2 | 9 | no | — |
| 414 | C22 | — | 2 | 2 | no | — |
| 415 | C22 | — | 2 | 18 | no | — |
| 416 | C22 | — | 4 | 2 | no | — |
| 417 | C22 | — | 4 | 9 | no | — |
| 418 | C22 | — | 4 | 18 | no | — |
| 419 | C22 | — | 32 | 18 | no | — |
| 420 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 421 | C4 | — | 2 | 9 | no | — |
| 422 | C4 | — | 2 | 2 | no | — |
| 423 | C4 | — | 2 | 6 | no | — |
| 424 | C4 | — | 4 | 9 | no | — |
| 425 | C4 | — | 4 | 6 | no | — |
| 426 | C4 | — | 4 | 6 | no | — |
| 427 | C4 | C2×#577 | 1 | 12 | yes | — |
| 428 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 429 | C4 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 430 | C2 | — | 4 | 9 | no | — |
| 431 | C2 | — | 4 | 2 | no | — |
| 432 | C2 | — | 8 | 9 | no | — |
| 433 | C2 | D4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 434 | C2 | C22×#577 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #3483 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63040 | C2 | semidirect |
| 2. #63037 | C2 | semidirect |
| 3. #62413 | C2 | semidirect |
| 4. #62326 | C2 | semidirect |
| 5. #62002 | C2 | semidirect |
| 6. #61999 | C2 | semidirect |
| 7. #61664 | C2 | semidirect |
| 8. #61662 | C2 | semidirect |
| 9. #61434 | C2 | semidirect |
| 10. #61087 | C2 | semidirect |
| 11. #60308 | C2 | semidirect |
| 12. C2×#577 | C22 | semidirect |
| 13. #3550 | C22 | semidirect |
| 18. #3503 | C22 | semidirect |
| 19. #3499 | C22 | semidirect |
| 26. #3482 | C22 | semidirect |
| 28. #3392 | C22 | semidirect |
| 29. #3392 | C22 | semidirect |
| 30. Q8×SD16 | C22 | semidirect |
| 31. #3363 | C22 | semidirect |
| 32. #3358 | C22 | semidirect |
| 33. #3340 | C22 | semidirect |
| 34. #3329 | C22 | semidirect |
| 35. #3324 | C22 | semidirect |
| 36. #3304 | C22 | semidirect |
| 37. #3303 | C22 | semidirect |
| 38. #3284 | C22 | semidirect |
| 39. D4×SD16 | C22 | semidirect |
| 40. D4×SD16 | C22 | semidirect |
| 41. #3278 | C22 | semidirect |
| 42. #3272 | C22 | semidirect |
| 43. #3254 | C22 | semidirect |
| 44. #3208 | C22 | semidirect |
| 45. #3206 | C22 | semidirect |
| 46. #3200 | C22 | semidirect |
| 47. #3167 | C22 | semidirect |
| 48. C2×#492 | C22 | semidirect |
| 49. #3107 | C22 | semidirect |
| 50. #3106 | C22 | semidirect |
| 51. #3057 | C22 | semidirect |
| 52. #3039 | C22 | semidirect |
| 53. #3038 | C22 | semidirect |
| 54. #3010 | C22 | semidirect |
| 55. #3009 | C22 | semidirect |
| 56. #2991 | C22 | semidirect |
| 57. #2979 | C22 | semidirect |
| 58. C8×#41 | C22 | semidirect |
| 59. C4×#135 | C22 | semidirect |
| 60. #2931 | C22 | semidirect |
| 335. SD16 | H(5,𝔽2) | semidirect |
| 380. Q8 | #577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63040 | 2 |
| #63037 | 2 |
| #62413 | 2 |
| #62326 | 2 |
| #62002 | 2 |
| #61999 | 2 |
| #61664 | 2 |
| #61662 | 2 |
| #61434 | 2 |
| #61087 | 2 |
| #60308 | 2 |