Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7146 conjugacy classes of subgroups.
The subgroup lattice has 442 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62986 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61419 | C2 | 1 | 18 | yes | maximal, complemented |
| 3 | #61409 | C2 | 1 | 9 | yes | maximal, complemented |
| 4 | #61406 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | #61402 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #61393 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#3391 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #60647 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #60428 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | Q8×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C4×#576 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×#576 | C22 | 1 | 3 | yes | — |
| 13 | C2×#576 | C22 | 1 | 6 | yes | — |
| 14 | #3519 | — | 2 | 18 | no | — |
| 15 | #3517 | — | 2 | 6 | no | — |
| 16 | #3508 | C22 | 1 | 18 | yes | complemented |
| 17 | #3506 | C22 | 1 | 18 | yes | complemented |
| 18 | #3498 | C22 | 1 | 6 | yes | — |
| 19 | #3483 | — | 2 | 2 | no | — |
| 20 | #3480 | C22 | 1 | 6 | yes | complemented |
| 21 | Q8×#41 | C22 | 1 | 1 | yes | characteristic |
| 22 | D4×#41 | — | 2 | 6 | no | — |
| 23 | C2×#550 | C22 | 1 | 6 | yes | complemented |
| 24 | C4×H(5,𝔽2) | C22 | 1 | 6 | yes | — |
| 25 | #3403 | C22 | 1 | 36 | yes | complemented |
| 26 | #3399 | C22 | 1 | 36 | yes | complemented |
| 27 | #3399 | C22 | 1 | 36 | yes | complemented |
| 28 | #3397 | C22 | 1 | 36 | yes | complemented |
| 29 | #3396 | C22 | 1 | 9 | yes | complemented |
| 30 | #3396 | C22 | 1 | 18 | yes | complemented |
| 31 | #3395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #3394 | C22 | 1 | 18 | yes | complemented |
| 33 | #3393 | C22 | 1 | 9 | yes | complemented |
| 34 | #3392 | C22 | 1 | 6 | yes | complemented |
| 35 | #3391 | C22 | 1 | 3 | yes | complemented |
| 36 | #3391 | C22 | 1 | 6 | yes | complemented |
| 37 | #3391 | C22 | 1 | 18 | yes | complemented |
| 38 | #3391 | C22 | 1 | 18 | yes | complemented |
| 39 | #3391 | C22 | 1 | 6 | yes | complemented |
| 40 | #3155 | C22 | 1 | 18 | yes | complemented |
| 41 | #3155 | C22 | 1 | 18 | yes | complemented |
| 42 | #3151 | C22 | 1 | 18 | yes | complemented |
| 43 | #3147 | C22 | 1 | 9 | yes | complemented |
| 44 | C2×#493 | C22 | 1 | 9 | yes | complemented |
| 45 | #3045 | C22 | 1 | 36 | yes | complemented |
| 46 | #3041 | C22 | 1 | 36 | yes | complemented |
| 47 | #3038 | C22 | 1 | 18 | yes | complemented |
| 48 | #3036 | C22 | 1 | 18 | yes | complemented |
| 49 | #3035 | C22 | 1 | 18 | yes | complemented |
| 50 | C2×#459 | C22 | 1 | 18 | yes | complemented |
| 51 | Q8×M16 | C22 | 1 | 3 | yes | complemented |
| 52 | #2962 | C22 | 1 | 9 | yes | complemented |
| 53 | #2960 | C22 | 1 | 9 | yes | complemented |
| 54 | C2×C8×Q8 | C22 | 1 | 3 | yes | complemented |
| 55 | #2951 | C22 | 1 | 9 | yes | complemented |
| 56 | #2948 | C22 | 1 | 9 | yes | complemented |
| 57 | #2946 | C22 | 1 | 18 | yes | complemented |
| 58 | C4×AGL(1,ℤ/8) | C22 | 1 | 18 | yes | complemented |
| 59 | C4×#135 | C22 | 1 | 9 | yes | complemented |
| 60 | C2×C4×D8 | C22 | 1 | 9 | yes | complemented |
| 61 | #2913 | C22 | 1 | 1 | yes | characteristic |
| 62 | #2906 | C22 | 1 | 3 | yes | — |
| 63 | #2897 | C22 | 1 | 6 | yes | — |
| 64 | C4×#131 | C22 | 1 | 3 | yes | — |
| 65 | C2×H(5,𝔽2) | C23 | 1 | 6 | yes | — |
| 66 | C22×#41 | — | 2 | 6 | no | — |
| 67 | #576 | — | 2 | 24 | no | — |
| 68 | #576 | — | 4 | 24 | no | — |
| 69 | C2×AGL(1,ℤ/8) | C23 | 1 | 18 | yes | — |
| 70 | C2×AGL(1,ℤ/8) | C23 | 1 | 36 | yes | — |
| 71 | C2×#135 | C23 | 1 | 9 | yes | — |
| 72 | C2×#135 | C23 | 1 | 18 | yes | — |
| 73 | C22×D8 | C23 | 1 | 9 | yes | — |
| 74 | C22×D8 | C23 | 1 | 18 | yes | — |
| 75 | C2×#131 | C23 | 1 | 3 | yes | — |
| 76 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 77 | #559 | C23 | 1 | 18 | yes | — |
| 78 | #559 | C23 | 1 | 36 | yes | — |
| 79 | Q82 | D4 | 1 | 1 | yes | characteristic |
| 80 | #557 | D4 | 1 | 3 | yes | — |
| 81 | #557 | C23 | 1 | 2 | yes | — |
| 82 | #556 | C23 | 1 | 18 | yes | — |
| 83 | #555 | — | 2 | 18 | no | — |
| 84 | #554 | D4 | 1 | 9 | yes | — |
| 85 | #553 | — | 2 | 36 | no | — |
| 86 | #553 | — | 2 | 18 | no | — |
| 87 | #550 | — | 2 | 6 | no | — |
| 88 | #550 | — | 2 | 18 | no | — |
| 89 | #550 | — | 2 | 6 | no | — |
| 90 | #550 | — | 2 | 6 | no | — |
| 91 | #550 | C23 | 1 | 6 | yes | — |
| 92 | #550 | C23 | 1 | 36 | yes | — |
| 93 | #550 | C23 | 1 | 12 | yes | — |
| 94 | D4×Q8 | D4 | 1 | 3 | yes | — |
| 95 | #548 | — | 2 | 6 | no | — |
| 96 | #547 | — | 2 | 18 | no | — |
| 97 | #546 | — | 2 | 36 | no | — |
| 98 | #546 | — | 2 | 36 | no | — |
| 99 | D42 | — | 2 | 18 | no | — |
| 100 | D42 | — | 2 | 18 | no | — |
| 101 | #540 | — | 2 | 36 | no | — |
| 102 | #538 | — | 2 | 36 | no | — |
| 103 | #535 | C23 | 1 | 36 | yes | — |
| 104 | #533 | C23 | 1 | 9 | yes | — |
| 105 | #532 | — | 2 | 18 | no | — |
| 106 | #532 | — | 2 | 18 | no | — |
| 107 | #532 | C23 | 1 | 18 | yes | — |
| 108 | C2×#127 | C23 | 1 | 18 | yes | — |
| 109 | #529 | — | 2 | 18 | no | — |
| 110 | #525 | — | 2 | 36 | no | — |
| 111 | C2×#121 | — | 2 | 18 | no | — |
| 112 | #520 | — | 2 | 6 | no | — |
| 113 | #520 | C23 | 1 | 18 | yes | — |
| 114 | #520 | C23 | 1 | 2 | yes | — |
| 115 | #518 | — | 2 | 18 | no | — |
| 116 | #518 | C23 | 1 | 18 | yes | — |
| 117 | C4×#41 | — | 2 | 6 | no | — |
| 118 | C4×#41 | — | 2 | 6 | no | — |
| 119 | C4×#41 | C23 | 1 | 18 | yes | — |
| 120 | C4×#41 | C23 | 1 | 3 | yes | — |
| 121 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 122 | C2×C4×D4 | — | 2 | 18 | no | — |
| 123 | C2×C4×D4 | C23 | 1 | 18 | yes | — |
| 124 | #496 | C23 | 1 | 72 | yes | — |
| 125 | #495 | C23 | 1 | 18 | yes | — |
| 126 | #495 | C23 | 1 | 18 | yes | — |
| 127 | #494 | C23 | 1 | 3 | yes | — |
| 128 | #493 | C23 | 1 | 9 | yes | — |
| 129 | #493 | C23 | 1 | 18 | yes | — |
| 130 | #493 | C23 | 1 | 18 | yes | — |
| 131 | #493 | C23 | 1 | 18 | yes | — |
| 132 | #492 | C23 | 1 | 18 | yes | — |
| 133 | #464 | C23 | 1 | 36 | yes | — |
| 134 | #463 | C23 | 1 | 36 | yes | — |
| 135 | #463 | C23 | 1 | 72 | yes | — |
| 136 | #462 | C23 | 1 | 6 | yes | — |
| 137 | #461 | C23 | 1 | 18 | yes | — |
| 138 | #460 | C23 | 1 | 18 | yes | — |
| 139 | #460 | C23 | 1 | 36 | yes | — |
| 140 | #459 | C23 | 1 | 18 | yes | — |
| 141 | #459 | C23 | 1 | 36 | yes | — |
| 142 | #459 | C23 | 1 | 72 | yes | — |
| 143 | #459 | C23 | 1 | 36 | yes | — |
| 144 | #446 | C23 | 1 | 18 | yes | — |
| 145 | #446 | C23 | 1 | 18 | yes | — |
| 146 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 147 | C8×Q8 | C23 | 1 | 3 | yes | — |
| 148 | C8×Q8 | C23 | 1 | 9 | yes | — |
| 149 | C8×Q8 | C23 | 1 | 9 | yes | — |
| 150 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 151 | #442 | C23 | 1 | 36 | yes | — |
| 152 | #440 | C23 | 1 | 36 | yes | — |
| 153 | C4×Q16 | C23 | 1 | 9 | yes | — |
| 154 | C4×Q16 | C23 | 1 | 3 | yes | — |
| 155 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 156 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 157 | C4×D8 | C23 | 1 | 9 | yes | — |
| 158 | C4×D8 | C23 | 1 | 18 | yes | — |
| 159 | C4×D8 | C23 | 1 | 9 | yes | — |
| 160 | C4×D8 | C23 | 1 | 18 | yes | — |
| 161 | C4×D8 | C23 | 1 | 18 | yes | — |
| 162 | #428 | C23 | 1 | 6 | yes | — |
| 163 | #427 | C23 | 1 | 3 | yes | — |
| 164 | C2×#107 | C23 | 1 | 3 | yes | — |
| 165 | #424 | C23 | 1 | 18 | yes | — |
| 166 | #423 | C23 | 1 | 9 | yes | — |
| 167 | C2×C4⋊C8 | C23 | 1 | 9 | yes | — |
| 168 | #418 | C23 | 1 | 18 | yes | — |
| 169 | #417 | C23 | 1 | 18 | yes | — |
| 170 | #416 | C23 | 1 | 18 | yes | — |
| 171 | C2×#102 | C23 | 1 | 18 | yes | — |
| 172 | #405 | C23 | 1 | 9 | yes | — |
| 173 | #405 | C23 | 1 | 9 | yes | — |
| 174 | C4×M16 | C23 | 1 | 9 | yes | — |
| 175 | C2×C4×C8 | C23 | 1 | 9 | yes | — |
| 176 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 177 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 178 | C2×#41 | — | 2 | 6 | no | — |
| 179 | C2×#41 | — | 2 | 6 | no | — |
| 180 | C2×#41 | — | 2 | 36 | no | — |
| 181 | C2×#41 | — | 2 | 12 | no | — |
| 182 | C2×#41 | — | 8 | 24 | no | — |
| 183 | C2×#41 | C24 | 1 | 18 | yes | — |
| 184 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 185 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 186 | C22×D4 | — | 2 | 18 | no | — |
| 187 | C22×D4 | — | 2 | 18 | no | — |
| 188 | C22×D4 | — | 2 | 18 | no | — |
| 189 | C22×D4 | C24 | 1 | 18 | yes | — |
| 190 | C23×C4 | — | 2 | 18 | no | — |
| 191 | AGL(1,ℤ/8) | — | 2 | 72 | no | — |
| 192 | AGL(1,ℤ/8) | — | 4 | 72 | no | — |
| 193 | #135 | — | 2 | 36 | no | — |
| 194 | #135 | — | 4 | 36 | no | — |
| 195 | C2×Q16 | C24 | 1 | 3 | yes | — |
| 196 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 197 | C2×SD16 | C24 | 1 | 18 | yes | — |
| 198 | C2×SD16 | C24 | 1 | 36 | yes | — |
| 199 | C2×D8 | — | 2 | 36 | no | — |
| 200 | C2×D8 | — | 4 | 36 | no | — |
| 201 | C2×D8 | C24 | 1 | 9 | yes | — |
| 202 | C2×D8 | C24 | 1 | 18 | yes | — |
| 203 | C2×D8 | C24 | 1 | 18 | yes | — |
| 204 | C2×D8 | C24 | 1 | 36 | yes | — |
| 205 | #131 | — | 2 | 12 | no | — |
| 206 | #131 | #41 | 1 | 8 | yes | complemented |
| 207 | C2×M16 | C24 | 1 | 9 | yes | — |
| 208 | C2×M16 | C24 | 1 | 3 | yes | — |
| 209 | C22×C8 | C24 | 1 | 9 | yes | — |
| 210 | C22×C8 | C24 | 1 | 3 | yes | — |
| 211 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 212 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 213 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 214 | #127 | — | 2 | 18 | no | — |
| 215 | #127 | — | 2 | 18 | no | — |
| 216 | #127 | C24 | 1 | 18 | yes | — |
| 217 | #127 | C24 | 1 | 36 | yes | — |
| 218 | #126 | — | 2 | 36 | no | — |
| 219 | #125 | — | 2 | 6 | no | — |
| 220 | #125 | C2×D4 | 1 | 18 | yes | — |
| 221 | #124 | — | 2 | 18 | no | — |
| 222 | #124 | — | 2 | 36 | no | — |
| 223 | #124 | C24 | 1 | 36 | yes | — |
| 224 | #123 | — | 2 | 72 | no | — |
| 225 | #123 | — | 2 | 36 | no | — |
| 226 | C22⋊Q8 | — | 2 | 18 | no | — |
| 227 | C22⋊Q8 | C2×D4 | 1 | 18 | yes | — |
| 228 | C22⋊Q8 | C2×D4 | 1 | 18 | yes | — |
| 229 | #121 | — | 2 | 18 | no | — |
| 230 | #121 | — | 2 | 18 | no | — |
| 231 | #121 | — | 2 | 18 | no | — |
| 232 | #121 | — | 2 | 36 | no | — |
| 233 | #121 | — | 2 | 72 | no | — |
| 234 | #121 | — | 2 | 36 | no | — |
| 235 | #121 | — | 2 | 36 | no | — |
| 236 | #121 | — | 2 | 36 | no | — |
| 237 | #120 | — | 2 | 72 | no | — |
| 238 | C4×Q8 | — | 2 | 2 | no | — |
| 239 | C4×Q8 | — | 2 | 2 | no | — |
| 240 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 241 | C4×Q8 | C2×D4 | 1 | 9 | yes | — |
| 242 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 243 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 244 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 245 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 246 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 247 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 248 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 249 | C4×D4 | — | 2 | 6 | no | — |
| 250 | C4×D4 | — | 2 | 18 | no | — |
| 251 | C4×D4 | — | 2 | 18 | no | — |
| 252 | C4×D4 | — | 2 | 18 | no | — |
| 253 | C4×D4 | — | 2 | 18 | no | — |
| 254 | C4×D4 | — | 2 | 18 | no | — |
| 255 | C4×D4 | — | 2 | 36 | no | — |
| 256 | C4×D4 | — | 2 | 36 | no | — |
| 257 | C4×D4 | — | 2 | 18 | no | — |
| 258 | C4×D4 | — | 2 | 18 | no | — |
| 259 | C4×D4 | — | 2 | 18 | no | — |
| 260 | C4×D4 | — | 2 | 18 | no | — |
| 261 | C4×D4 | C2×D4 | 1 | 9 | yes | — |
| 262 | C4×D4 | C2×D4 | 1 | 9 | yes | — |
| 263 | C4×D4 | C24 | 1 | 18 | yes | — |
| 264 | C4×D4 | C24 | 1 | 36 | yes | — |
| 265 | C4×D4 | C24 | 1 | 18 | yes | — |
| 266 | #117 | — | 2 | 18 | no | — |
| 267 | #117 | — | 2 | 18 | no | — |
| 268 | #117 | — | 2 | 18 | no | — |
| 269 | #117 | C24 | 1 | 6 | yes | — |
| 270 | #117 | C24 | 1 | 9 | yes | — |
| 271 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 272 | C2×C4⋊C4 | C2×D4 | 1 | 9 | yes | — |
| 273 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 274 | C2×C22⋊C4 | — | 2 | 18 | no | — |
| 275 | C2×C22⋊C4 | — | 2 | 36 | no | — |
| 276 | C2×C42 | — | 2 | 18 | no | — |
| 277 | C2×C42 | C24 | 1 | 9 | yes | — |
| 278 | #107 | C24 | 1 | 3 | yes | — |
| 279 | #107 | C24 | 1 | 6 | yes | — |
| 280 | #107 | C24 | 1 | 1 | yes | characteristic |
| 281 | #106 | C24 | 1 | 6 | yes | — |
| 282 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 283 | C4⋊C8 | C24 | 1 | 9 | yes | — |
| 284 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 285 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 286 | #103 | C24 | 1 | 6 | yes | — |
| 287 | #103 | C24 | 1 | 18 | yes | — |
| 288 | #102 | C24 | 1 | 18 | yes | — |
| 289 | #102 | C24 | 1 | 36 | yes | — |
| 290 | #102 | C24 | 1 | 18 | yes | — |
| 291 | #97 | C24 | 1 | 18 | yes | — |
| 292 | C4×C8 | C24 | 1 | 3 | yes | — |
| 293 | C4×C8 | C24 | 1 | 9 | yes | — |
| 294 | C4×C8 | C24 | 1 | 9 | yes | — |
| 295 | C4×C8 | C24 | 1 | 9 | yes | — |
| 296 | C24 | — | 2 | 18 | no | — |
| 297 | #41 | — | 2 | 36 | no | — |
| 298 | #41 | — | 2 | 36 | no | — |
| 299 | #41 | — | 4 | 24 | no | — |
| 300 | #41 | — | 4 | 24 | no | — |
| 301 | #41 | — | 8 | 72 | no | — |
| 302 | #41 | — | 16 | 12 | no | — |
| 303 | #41 | C2×#41 | 1 | 4 | yes | — |
| 304 | #41 | H(5,𝔽2) | 1 | 4 | yes | — |
| 305 | C2×Q8 | — | 2 | 12 | no | — |
| 306 | C2×Q8 | C22×D4 | 1 | 9 | yes | — |
| 307 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 308 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 309 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 310 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 311 | C2×D4 | — | 2 | 18 | no | — |
| 312 | C2×D4 | — | 2 | 18 | no | — |
| 313 | C2×D4 | — | 2 | 18 | no | — |
| 314 | C2×D4 | — | 2 | 36 | no | — |
| 315 | C2×D4 | — | 2 | 18 | no | — |
| 316 | C2×D4 | — | 2 | 36 | no | — |
| 317 | C2×D4 | — | 2 | 36 | no | — |
| 318 | C2×D4 | — | 2 | 36 | no | — |
| 319 | C2×D4 | — | 4 | 72 | no | — |
| 320 | C2×D4 | — | 8 | 36 | no | — |
| 321 | C2×D4 | — | 16 | 18 | no | — |
| 322 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 323 | C2×D4 | C25 | 1 | 18 | yes | — |
| 324 | C22×C4 | — | 2 | 6 | no | — |
| 325 | C22×C4 | — | 2 | 18 | no | — |
| 326 | C22×C4 | — | 2 | 18 | no | — |
| 327 | C22×C4 | — | 2 | 18 | no | — |
| 328 | C22×C4 | — | 2 | 36 | no | — |
| 329 | C22×C4 | — | 8 | 36 | no | — |
| 330 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 331 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 332 | C22×C4 | C25 | 1 | 3 | yes | — |
| 333 | Q16 | — | 2 | 6 | no | — |
| 334 | Q16 | — | 4 | 6 | no | — |
| 335 | SD16 | — | 2 | 36 | no | — |
| 336 | SD16 | — | 4 | 36 | no | — |
| 337 | D8 | — | 2 | 18 | no | — |
| 338 | D8 | — | 2 | 36 | no | — |
| 339 | D8 | — | 4 | 18 | no | — |
| 340 | D8 | — | 4 | 36 | no | — |
| 341 | M16 | — | 2 | 18 | no | — |
| 342 | M16 | C2×#41 | 1 | 12 | yes | complemented |
| 343 | C2×C8 | — | 2 | 18 | no | — |
| 344 | C2×C8 | C2×#41 | 1 | 12 | yes | complemented |
| 345 | C2×C8 | C25 | 1 | 3 | yes | — |
| 346 | C2×C8 | C25 | 1 | 9 | yes | — |
| 347 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 348 | C2×C8 | C25 | 1 | 3 | yes | — |
| 349 | C4⋊C4 | — | 2 | 6 | no | — |
| 350 | C4⋊C4 | — | 2 | 18 | no | — |
| 351 | C4⋊C4 | — | 2 | 6 | no | — |
| 352 | C4⋊C4 | — | 2 | 6 | no | — |
| 353 | C4⋊C4 | — | 2 | 6 | no | — |
| 354 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 355 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 356 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 357 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 358 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 359 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 360 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 361 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 362 | C22⋊C4 | — | 2 | 6 | no | — |
| 363 | C22⋊C4 | — | 2 | 18 | no | — |
| 364 | C22⋊C4 | — | 2 | 18 | no | — |
| 365 | C22⋊C4 | — | 2 | 36 | no | — |
| 366 | C22⋊C4 | — | 2 | 36 | no | — |
| 367 | C22⋊C4 | — | 2 | 36 | no | — |
| 368 | C22⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 369 | C42 | — | 2 | 6 | no | — |
| 370 | C42 | — | 2 | 6 | no | — |
| 371 | C42 | — | 2 | 18 | no | — |
| 372 | C42 | C22×D4 | 1 | 9 | yes | — |
| 373 | C42 | C22×D4 | 1 | 9 | yes | — |
| 374 | C42 | C25 | 1 | 3 | yes | — |
| 375 | C42 | C25 | 1 | 9 | yes | — |
| 376 | C23 | — | 2 | 18 | no | — |
| 377 | C23 | — | 4 | 36 | no | — |
| 378 | C23 | — | 8 | 18 | no | — |
| 379 | C23 | — | 8 | 18 | no | — |
| 380 | C23 | C23×D4 | 1 | 3 | yes | — |
| 381 | Q8 | — | 2 | 18 | no | — |
| 382 | Q8 | — | 2 | 6 | no | — |
| 383 | Q8 | — | 2 | 6 | no | — |
| 384 | Q8 | — | 4 | 6 | no | — |
| 385 | Q8 | #550 | 1 | 4 | yes | — |
| 386 | Q8 | #576 | 1 | 4 | yes | complemented |
| 387 | D4 | — | 2 | 18 | no | — |
| 388 | D4 | — | 2 | 18 | no | — |
| 389 | D4 | — | 4 | 36 | no | — |
| 390 | D4 | — | 4 | 36 | no | — |
| 391 | D4 | — | 4 | 36 | no | — |
| 392 | D4 | — | 8 | 36 | no | — |
| 393 | D4 | — | 8 | 18 | no | — |
| 394 | D4 | — | 8 | 36 | no | — |
| 395 | D4 | #550 | 1 | 12 | yes | — |
| 396 | C2×C4 | — | 2 | 18 | no | — |
| 397 | C2×C4 | — | 2 | 2 | no | — |
| 398 | C2×C4 | — | 2 | 6 | no | — |
| 399 | C2×C4 | — | 2 | 6 | no | — |
| 400 | C2×C4 | — | 4 | 9 | no | — |
| 401 | C2×C4 | — | 4 | 36 | no | — |
| 402 | C2×C4 | — | 4 | 36 | no | — |
| 403 | C2×C4 | — | 8 | 36 | no | — |
| 404 | C2×C4 | — | 8 | 18 | no | — |
| 405 | C2×C4 | — | 8 | 6 | no | — |
| 406 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 407 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 408 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 409 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 410 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 411 | C2×C4 | C22×#41 | 1 | 6 | yes | — |
| 412 | C2×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 413 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 414 | C8 | — | 2 | 3 | no | — |
| 415 | C8 | — | 2 | 9 | no | — |
| 416 | C8 | C22×#41 | 1 | 2 | yes | — |
| 417 | C8 | C22×#41 | 1 | 6 | yes | — |
| 418 | C22 | — | 2 | 3 | no | — |
| 419 | C22 | — | 2 | 3 | no | — |
| 420 | C22 | — | 4 | 18 | no | — |
| 421 | C22 | — | 4 | 18 | no | — |
| 422 | C22 | — | 4 | 18 | no | — |
| 423 | C22 | — | 16 | 36 | no | — |
| 424 | C22 | C2×#550 | 1 | 6 | yes | — |
| 425 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 426 | C4 | — | 2 | 9 | no | — |
| 427 | C4 | — | 2 | 3 | no | — |
| 428 | C4 | — | 2 | 9 | no | — |
| 429 | C4 | — | 4 | 6 | no | — |
| 430 | C4 | — | 4 | 2 | no | — |
| 431 | C4 | — | 4 | 6 | no | — |
| 432 | C4 | C2×#550 | 1 | 6 | yes | — |
| 433 | C4 | C2×#576 | 1 | 6 | yes | — |
| 434 | C4 | C23×#41 | 1 | 1 | yes | characteristic |
| 435 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 436 | C2 | — | 2 | 6 | no | — |
| 437 | C2 | — | 8 | 18 | no | — |
| 438 | C2 | C22×#550 | 1 | 1 | yes | characteristic |
| 439 | C2 | C22×#576 | 1 | 1 | yes | characteristic |
| 440 | C2 | #63091 | 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. #62986 | C2 | semidirect |
| 2. #61419 | C2 | semidirect |
| 3. #61409 | C2 | semidirect |
| 4. #61406 | C2 | semidirect |
| 5. #61402 | C2 | semidirect |
| 6. #61393 | C2 | semidirect |
| 7. C2×#3391 | C2 | semidirect |
| 8. #60647 | C2 | semidirect |
| 9. #60428 | C2 | semidirect |
| 10. Q8×#131 | C2 | semidirect |
| 11. C4×#576 | C2 | semidirect |
| 16. #3508 | C22 | semidirect |
| 17. #3506 | C22 | semidirect |
| 20. #3480 | C22 | semidirect |
| 23. C2×#550 | C22 | semidirect |
| 25. #3403 | C22 | semidirect |
| 26. #3399 | C22 | semidirect |
| 27. #3399 | C22 | semidirect |
| 28. #3397 | C22 | semidirect |
| 29. #3396 | C22 | semidirect |
| 30. #3396 | C22 | semidirect |
| 31. #3395 | C22 | semidirect |
| 32. #3394 | C22 | semidirect |
| 33. #3393 | C22 | semidirect |
| 34. #3392 | C22 | semidirect |
| 35. #3391 | C22 | semidirect |
| 36. #3391 | C22 | semidirect |
| 37. #3391 | C22 | semidirect |
| 38. #3391 | C22 | semidirect |
| 39. #3391 | C22 | semidirect |
| 40. #3155 | C22 | semidirect |
| 41. #3155 | C22 | semidirect |
| 42. #3151 | C22 | semidirect |
| 43. #3147 | C22 | semidirect |
| 44. C2×#493 | C22 | semidirect |
| 45. #3045 | C22 | semidirect |
| 46. #3041 | C22 | semidirect |
| 47. #3038 | C22 | semidirect |
| 48. #3036 | C22 | semidirect |
| 49. #3035 | C22 | semidirect |
| 50. C2×#459 | C22 | semidirect |
| 51. Q8×M16 | C22 | semidirect |
| 52. #2962 | C22 | semidirect |
| 53. #2960 | C22 | semidirect |
| 54. C2×C8×Q8 | C22 | semidirect |
| 55. #2951 | C22 | semidirect |
| 56. #2948 | C22 | semidirect |
| 57. #2946 | C22 | semidirect |
| 58. C4×AGL(1,ℤ/8) | C22 | semidirect |
| 59. C4×#135 | C22 | semidirect |
| 60. C2×C4×D8 | C22 | semidirect |
| 206. #131 | #41 | semidirect |
| 342. M16 | C2×#41 | semidirect |
| 344. C2×C8 | C2×#41 | semidirect |
| 386. Q8 | #576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62986 | 2 |
| #61419 | 2 |
| #61409 | 2 |
| #61406 | 2 |
| #61402 | 2 |
| #61393 | 2 |
| C2×#3391 | 2 |
| #60647 | 2 |
| #60428 | 2 |
| Q8×#131 | 2 |
| C4×#576 | 2 |