Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
34479 conjugacy classes of subgroups.
The subgroup lattice has 613 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62961 | C2 | 1 | 18 | yes | maximal, complemented |
| 2 | #62946 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #62931 | C2 | 1 | 18 | yes | maximal, complemented |
| 4 | #62916 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #62905 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #62895 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #62812 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | #62800 | C2 | 1 | 12 | yes | maximal, complemented |
| 9 | #62748 | C2 | 1 | 36 | yes | maximal, complemented |
| 10 | C2×#3480 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #62686 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×#585 | C22 | 1 | 6 | yes | complemented |
| 13 | #3562 | C22 | 1 | 144 | yes | complemented |
| 14 | #3561 | C22 | 1 | 72 | yes | complemented |
| 15 | #3560 | C22 | 1 | 144 | yes | complemented |
| 16 | #3559 | C22 | 1 | 72 | yes | complemented |
| 17 | #3558 | C22 | 1 | 72 | yes | complemented |
| 18 | #3558 | C22 | 1 | 72 | yes | complemented |
| 19 | #3554 | C22 | 1 | 72 | yes | complemented |
| 20 | #3552 | C22 | 1 | 72 | yes | complemented |
| 21 | #3546 | C22 | 1 | 72 | yes | complemented |
| 22 | #3543 | C22 | 1 | 72 | yes | complemented |
| 23 | #3537 | C22 | 1 | 72 | yes | complemented |
| 24 | #3536 | C22 | 1 | 72 | yes | complemented |
| 25 | #3534 | C22 | 1 | 144 | yes | complemented |
| 26 | #3529 | C22 | 1 | 48 | yes | complemented |
| 27 | #3522 | C22 | 1 | 24 | yes | complemented |
| 28 | #3519 | C22 | 1 | 72 | yes | complemented |
| 29 | #3517 | C22 | 1 | 24 | yes | complemented |
| 30 | #3514 | C22 | 1 | 72 | yes | complemented |
| 31 | #3511 | C22 | 1 | 36 | yes | complemented |
| 32 | #3508 | C22 | 1 | 36 | yes | complemented |
| 33 | #3503 | C22 | 1 | 12 | yes | complemented |
| 34 | #3500 | C22 | 1 | 72 | yes | complemented |
| 35 | #3499 | C22 | 1 | 36 | yes | complemented |
| 36 | #3498 | C22 | 1 | 12 | yes | complemented |
| 37 | #3498 | C22 | 1 | 36 | yes | complemented |
| 38 | #3497 | C22 | 1 | 18 | yes | complemented |
| 39 | #3497 | C22 | 1 | 18 | yes | complemented |
| 40 | #3496 | C22 | 1 | 36 | yes | complemented |
| 41 | #3496 | C22 | 1 | 36 | yes | complemented |
| 42 | #3496 | C22 | 1 | 18 | yes | complemented |
| 43 | #3496 | C22 | 1 | 18 | yes | complemented |
| 44 | #3494 | C22 | 1 | 72 | yes | complemented |
| 45 | #3488 | C22 | 1 | 24 | yes | complemented |
| 46 | #3483 | C22 | 1 | 8 | yes | complemented |
| 47 | #3481 | C22 | 1 | 72 | yes | complemented |
| 48 | #3480 | C22 | 1 | 36 | yes | complemented |
| 49 | #3480 | C22 | 1 | 12 | yes | complemented |
| 50 | #3480 | C22 | 1 | 12 | yes | complemented |
| 51 | #3480 | C22 | 1 | 36 | yes | complemented |
| 52 | C2×#559 | C22 | 1 | 9 | yes | complemented |
| 53 | C2×#557 | C22 | 1 | 3 | yes | complemented |
| 54 | C2×#556 | C22 | 1 | 9 | yes | complemented |
| 55 | C2×#553 | C22 | 1 | 18 | yes | complemented |
| 56 | D4×#41 | C22 | 1 | 72 | yes | complemented |
| 57 | D4×#41 | C22 | 1 | 72 | yes | complemented |
| 58 | C2×#550 | C22 | 1 | 3 | yes | complemented |
| 59 | C2×#548 | C22 | 1 | 6 | yes | complemented |
| 60 | #3461 | C22 | 1 | 18 | yes | complemented |
| 61 | #3461 | C22 | 1 | 18 | yes | complemented |
| 62 | #3460 | C22 | 1 | 72 | yes | complemented |
| 63 | #3460 | C22 | 1 | 18 | yes | complemented |
| 64 | #3460 | C22 | 1 | 18 | yes | complemented |
| 65 | #3459 | C22 | 1 | 48 | yes | complemented |
| 66 | #3459 | C22 | 1 | 12 | yes | complemented |
| 67 | #3459 | C22 | 1 | 12 | yes | complemented |
| 68 | #3458 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #3455 | C22 | 1 | 36 | yes | complemented |
| 70 | #3449 | C22 | 1 | 36 | yes | complemented |
| 71 | #3449 | C22 | 1 | 9 | yes | complemented |
| 72 | #3444 | C22 | 1 | 36 | yes | complemented |
| 73 | C2×#532 | C22 | 1 | 36 | yes | complemented |
| 74 | C2×#532 | C22 | 1 | 9 | yes | complemented |
| 75 | C2×#529 | C22 | 1 | 18 | yes | complemented |
| 76 | C4×H(5,𝔽2) | C22 | 1 | 8 | yes | complemented |
| 77 | C2×C4×#41 | C22 | 1 | 6 | yes | complemented |
| 78 | C2×C4×#41 | C22 | 1 | 9 | yes | complemented |
| 79 | C22×C4×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 80 | #585 | — | 4 | 48 | no | — |
| 81 | C2×2−1+4 | C23 | 1 | 36 | yes | — |
| 82 | C2×H(5,𝔽2) | C23 | 1 | 24 | yes | — |
| 83 | C2×H(5,𝔽2) | C23 | 1 | 36 | yes | — |
| 84 | C2×H(5,𝔽2) | C23 | 1 | 8 | yes | — |
| 85 | C22×#41 | C23 | 1 | 9 | yes | — |
| 86 | C22×#41 | C23 | 1 | 72 | yes | — |
| 87 | C22×#41 | C23 | 1 | 6 | yes | — |
| 88 | C23×Q8 | C23 | 1 | 1 | yes | characteristic |
| 89 | #563 | C23 | 1 | 144 | yes | — |
| 90 | #562 | C23 | 1 | 144 | yes | — |
| 91 | #562 | C23 | 1 | 144 | yes | — |
| 92 | H(3,𝔽4) | C23 | 1 | 48 | yes | — |
| 93 | #560 | C23 | 1 | 288 | yes | — |
| 94 | #559 | C23 | 1 | 36 | yes | — |
| 95 | #559 | C23 | 1 | 36 | yes | — |
| 96 | #559 | C23 | 1 | 72 | yes | — |
| 97 | #559 | C23 | 1 | 72 | yes | — |
| 98 | Q82 | C23 | 1 | 8 | yes | — |
| 99 | #557 | C23 | 1 | 12 | yes | — |
| 100 | #557 | C23 | 1 | 36 | yes | — |
| 101 | #556 | C23 | 1 | 36 | yes | — |
| 102 | #556 | C23 | 1 | 36 | yes | — |
| 103 | #556 | C23 | 1 | 72 | yes | — |
| 104 | #555 | C23 | 1 | 72 | yes | — |
| 105 | #554 | C23 | 1 | 72 | yes | — |
| 106 | #554 | C23 | 1 | 72 | yes | — |
| 107 | #553 | C23 | 1 | 72 | yes | — |
| 108 | #553 | C23 | 1 | 144 | yes | — |
| 109 | #553 | C23 | 1 | 72 | yes | — |
| 110 | #553 | C23 | 1 | 144 | yes | — |
| 111 | #553 | C23 | 1 | 144 | yes | — |
| 112 | #551 | C23 | 1 | 288 | yes | — |
| 113 | #550 | C23 | 1 | 12 | yes | — |
| 114 | #550 | C23 | 1 | 36 | yes | — |
| 115 | #550 | C23 | 1 | 72 | yes | — |
| 116 | #550 | C23 | 1 | 72 | yes | — |
| 117 | #550 | C23 | 1 | 24 | yes | — |
| 118 | #550 | C23 | 1 | 24 | yes | — |
| 119 | D4×Q8 | C23 | 1 | 72 | yes | — |
| 120 | D4×Q8 | C23 | 1 | 72 | yes | — |
| 121 | #548 | C23 | 1 | 24 | yes | — |
| 122 | #548 | C23 | 1 | 72 | yes | — |
| 123 | #548 | C23 | 1 | 144 | yes | — |
| 124 | #548 | C23 | 1 | 144 | yes | — |
| 125 | #547 | C23 | 1 | 144 | yes | — |
| 126 | #547 | C23 | 1 | 72 | yes | — |
| 127 | #547 | C23 | 1 | 72 | yes | — |
| 128 | #547 | C23 | 1 | 144 | yes | — |
| 129 | #546 | C23 | 1 | 288 | yes | — |
| 130 | #546 | C23 | 1 | 144 | yes | — |
| 131 | #546 | C23 | 1 | 288 | yes | — |
| 132 | #546 | C23 | 1 | 144 | yes | — |
| 133 | #546 | C23 | 1 | 144 | yes | — |
| 134 | #546 | C23 | 1 | 144 | yes | — |
| 135 | D42 | C23 | 1 | 144 | yes | — |
| 136 | D42 | C23 | 1 | 72 | yes | — |
| 137 | D42 | C23 | 1 | 144 | yes | — |
| 138 | D42 | C23 | 1 | 72 | yes | — |
| 139 | D42 | C23 | 1 | 72 | yes | — |
| 140 | #544 | C23 | 1 | 6 | yes | — |
| 141 | #544 | C23 | 1 | 6 | yes | — |
| 142 | #544 | C23 | 1 | 72 | yes | — |
| 143 | #543 | C23 | 1 | 4 | yes | — |
| 144 | #543 | C23 | 1 | 48 | yes | — |
| 145 | #542 | C23 | 1 | 72 | yes | — |
| 146 | #542 | C23 | 1 | 72 | yes | — |
| 147 | #542 | C23 | 1 | 144 | yes | — |
| 148 | #542 | C23 | 1 | 144 | yes | — |
| 149 | #541 | C23 | 1 | 72 | yes | — |
| 150 | #540 | C23 | 1 | 72 | yes | — |
| 151 | #540 | C23 | 1 | 144 | yes | — |
| 152 | #540 | C23 | 1 | 144 | yes | — |
| 153 | #539 | C23 | 1 | 72 | yes | — |
| 154 | #539 | C23 | 1 | 72 | yes | — |
| 155 | #539 | C23 | 1 | 288 | yes | — |
| 156 | #538 | C23 | 1 | 72 | yes | — |
| 157 | #538 | C23 | 1 | 72 | yes | — |
| 158 | #538 | C23 | 1 | 144 | yes | — |
| 159 | #538 | C23 | 1 | 144 | yes | — |
| 160 | #538 | C23 | 1 | 288 | yes | — |
| 161 | #537 | C23 | 1 | 18 | yes | — |
| 162 | #537 | C23 | 1 | 18 | yes | — |
| 163 | #537 | C23 | 1 | 72 | yes | — |
| 164 | #537 | C23 | 1 | 72 | yes | — |
| 165 | #537 | C23 | 1 | 72 | yes | — |
| 166 | #536 | C23 | 1 | 36 | yes | — |
| 167 | #536 | C23 | 1 | 144 | yes | — |
| 168 | #535 | C23 | 1 | 36 | yes | — |
| 169 | #535 | C23 | 1 | 144 | yes | — |
| 170 | #535 | C23 | 1 | 72 | yes | — |
| 171 | #535 | C23 | 1 | 72 | yes | — |
| 172 | #534 | C23 | 1 | 36 | yes | — |
| 173 | #534 | C23 | 1 | 72 | yes | — |
| 174 | #534 | C23 | 1 | 72 | yes | — |
| 175 | #534 | C23 | 1 | 144 | yes | — |
| 176 | #533 | C23 | 1 | 12 | yes | — |
| 177 | #533 | C23 | 1 | 36 | yes | — |
| 178 | #533 | C23 | 1 | 36 | yes | — |
| 179 | #532 | C23 | 1 | 36 | yes | — |
| 180 | #532 | C23 | 1 | 36 | yes | — |
| 181 | #532 | C23 | 1 | 36 | yes | — |
| 182 | #532 | C23 | 1 | 72 | yes | — |
| 183 | #532 | C23 | 1 | 72 | yes | — |
| 184 | #532 | C23 | 1 | 36 | yes | — |
| 185 | #532 | C23 | 1 | 36 | yes | — |
| 186 | #532 | C23 | 1 | 72 | yes | — |
| 187 | #532 | C23 | 1 | 72 | yes | — |
| 188 | #532 | C23 | 1 | 72 | yes | — |
| 189 | #532 | C23 | 1 | 72 | yes | — |
| 190 | #532 | C23 | 1 | 36 | yes | — |
| 191 | #532 | C23 | 1 | 36 | yes | — |
| 192 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 193 | C2×C4⋊Q8 | C23 | 1 | 36 | yes | — |
| 194 | C2×#127 | C23 | 1 | 9 | yes | — |
| 195 | C2×#127 | C23 | 1 | 36 | yes | — |
| 196 | #529 | C23 | 1 | 72 | yes | — |
| 197 | #529 | C23 | 1 | 72 | yes | — |
| 198 | #529 | C23 | 1 | 72 | yes | — |
| 199 | #529 | C23 | 1 | 72 | yes | — |
| 200 | #529 | C23 | 1 | 72 | yes | — |
| 201 | #529 | C23 | 1 | 72 | yes | — |
| 202 | #529 | C23 | 1 | 72 | yes | — |
| 203 | #529 | C23 | 1 | 72 | yes | — |
| 204 | #529 | C23 | 1 | 72 | yes | — |
| 205 | #529 | C23 | 1 | 72 | yes | — |
| 206 | C2×#126 | C23 | 1 | 36 | yes | — |
| 207 | C2×#125 | C23 | 1 | 18 | yes | — |
| 208 | C2×#124 | C23 | 1 | 18 | yes | — |
| 209 | C2×#124 | C23 | 1 | 18 | yes | — |
| 210 | C2×#124 | C23 | 1 | 72 | yes | — |
| 211 | #525 | C23 | 1 | 72 | yes | — |
| 212 | #525 | C23 | 1 | 72 | yes | — |
| 213 | #525 | C23 | 1 | 72 | yes | — |
| 214 | #525 | C23 | 1 | 288 | yes | — |
| 215 | C2×#123 | C23 | 1 | 36 | yes | — |
| 216 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 217 | C2×#121 | C23 | 1 | 18 | yes | — |
| 218 | C2×#121 | C23 | 1 | 18 | yes | — |
| 219 | C2×#121 | C23 | 1 | 18 | yes | — |
| 220 | C2×#121 | C23 | 1 | 72 | yes | — |
| 221 | C2×#121 | C23 | 1 | 72 | yes | — |
| 222 | #520 | C23 | 1 | 24 | yes | — |
| 223 | #520 | C23 | 1 | 24 | yes | — |
| 224 | #518 | C23 | 1 | 72 | yes | — |
| 225 | C4×#41 | C23 | 1 | 12 | yes | — |
| 226 | C4×#41 | C23 | 1 | 36 | yes | — |
| 227 | C4×#41 | C23 | 1 | 36 | yes | — |
| 228 | C4×#41 | C23 | 1 | 36 | yes | — |
| 229 | C4×#41 | C23 | 1 | 36 | yes | — |
| 230 | C4×#41 | C23 | 1 | 36 | yes | — |
| 231 | C4×#41 | C23 | 1 | 12 | yes | — |
| 232 | C4×#41 | C23 | 1 | 36 | yes | — |
| 233 | C4×#41 | C23 | 1 | 24 | yes | — |
| 234 | C4×#41 | C23 | 1 | 24 | yes | — |
| 235 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 236 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 237 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 238 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 239 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 240 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 241 | C2×C4×Q8 | C23 | 1 | 6 | yes | — |
| 242 | C2×C4×D4 | C23 | 1 | 18 | yes | — |
| 243 | C2×C4×D4 | C23 | 1 | 18 | yes | — |
| 244 | C2×C4×D4 | C23 | 1 | 18 | yes | — |
| 245 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 246 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 247 | C2×C4×D4 | C23 | 1 | 18 | yes | — |
| 248 | C2×C4×D4 | C23 | 1 | 72 | yes | — |
| 249 | C2×C4×D4 | C23 | 1 | 18 | yes | — |
| 250 | C2×C4×D4 | C23 | 1 | 72 | yes | — |
| 251 | C2×#117 | C23 | 1 | 3 | yes | — |
| 252 | C2×#117 | C23 | 1 | 18 | yes | — |
| 253 | C2×#117 | C23 | 1 | 18 | yes | — |
| 254 | C22×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 255 | C22×C42 | C23 | 1 | 3 | yes | — |
| 256 | C22×C42 | C23 | 1 | 18 | yes | — |
| 257 | 2−1+4 | — | 4 | 144 | no | — |
| 258 | H(5,𝔽2) | — | 4 | 96 | no | — |
| 259 | H(5,𝔽2) | — | 4 | 144 | no | — |
| 260 | H(5,𝔽2) | — | 4 | 32 | no | — |
| 261 | C2×#41 | — | 2 | 72 | no | — |
| 262 | C2×#41 | — | 4 | 288 | no | — |
| 263 | C2×#41 | — | 4 | 24 | no | — |
| 264 | C2×#41 | C24 | 1 | 12 | yes | — |
| 265 | C2×#41 | C24 | 1 | 36 | yes | — |
| 266 | C2×#41 | C24 | 1 | 36 | yes | — |
| 267 | C2×#41 | C24 | 1 | 36 | yes | — |
| 268 | C2×#41 | C24 | 1 | 24 | yes | — |
| 269 | C2×#41 | C24 | 1 | 48 | yes | — |
| 270 | C2×#41 | C24 | 1 | 144 | yes | — |
| 271 | C2×#41 | C24 | 1 | 144 | yes | — |
| 272 | C2×#41 | C24 | 1 | 24 | yes | — |
| 273 | C22×Q8 | — | 4 | 4 | no | — |
| 274 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 275 | C22×Q8 | C24 | 1 | 9 | yes | — |
| 276 | C22×Q8 | C24 | 1 | 9 | yes | — |
| 277 | C22×Q8 | C24 | 1 | 72 | yes | — |
| 278 | C22×D4 | C24 | 1 | 18 | yes | — |
| 279 | C22×D4 | C24 | 1 | 9 | yes | — |
| 280 | C22×D4 | C24 | 1 | 18 | yes | — |
| 281 | C22×D4 | C24 | 1 | 72 | yes | — |
| 282 | C22×D4 | C24 | 1 | 144 | yes | — |
| 283 | C22×D4 | C24 | 1 | 72 | yes | — |
| 284 | C22×D4 | C24 | 1 | 18 | yes | — |
| 285 | C22×D4 | C24 | 1 | 72 | yes | — |
| 286 | C23×C4 | C24 | 1 | 18 | yes | — |
| 287 | C23×C4 | C24 | 1 | 3 | yes | — |
| 288 | C23×C4 | C24 | 1 | 18 | yes | — |
| 289 | C23×C4 | C24 | 1 | 48 | yes | — |
| 290 | C23×C4 | C24 | 1 | 3 | yes | — |
| 291 | C23×C4 | C24 | 1 | 18 | yes | — |
| 292 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 293 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 294 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 295 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 296 | C4⋊Q8 | C24 | 1 | 72 | yes | — |
| 297 | C4⋊Q8 | C24 | 1 | 72 | yes | — |
| 298 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 299 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 300 | #127 | C24 | 1 | 36 | yes | — |
| 301 | #127 | C24 | 1 | 36 | yes | — |
| 302 | #127 | C24 | 1 | 36 | yes | — |
| 303 | #127 | C24 | 1 | 72 | yes | — |
| 304 | #127 | C24 | 1 | 72 | yes | — |
| 305 | #126 | C24 | 1 | 144 | yes | — |
| 306 | #126 | C24 | 1 | 144 | yes | — |
| 307 | #126 | C24 | 1 | 144 | yes | — |
| 308 | #126 | C24 | 1 | 144 | yes | — |
| 309 | #125 | C24 | 1 | 72 | yes | — |
| 310 | #125 | C24 | 1 | 72 | yes | — |
| 311 | #125 | C24 | 1 | 24 | yes | — |
| 312 | #125 | C24 | 1 | 72 | yes | — |
| 313 | #125 | C24 | 1 | 72 | yes | — |
| 314 | #124 | C24 | 1 | 72 | yes | — |
| 315 | #124 | C24 | 1 | 72 | yes | — |
| 316 | #124 | C24 | 1 | 72 | yes | — |
| 317 | #124 | C24 | 1 | 72 | yes | — |
| 318 | #124 | C24 | 1 | 72 | yes | — |
| 319 | #124 | C24 | 1 | 144 | yes | — |
| 320 | #124 | C24 | 1 | 144 | yes | — |
| 321 | #124 | C24 | 1 | 72 | yes | — |
| 322 | #124 | C24 | 1 | 72 | yes | — |
| 323 | #123 | C24 | 1 | 144 | yes | — |
| 324 | #123 | C24 | 1 | 144 | yes | — |
| 325 | #123 | C24 | 1 | 144 | yes | — |
| 326 | #123 | C24 | 1 | 144 | yes | — |
| 327 | #123 | C24 | 1 | 144 | yes | — |
| 328 | #123 | C24 | 1 | 288 | yes | — |
| 329 | #123 | C24 | 1 | 288 | yes | — |
| 330 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 331 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 332 | C22⋊Q8 | C24 | 1 | 24 | yes | — |
| 333 | C22⋊Q8 | C24 | 1 | 24 | yes | — |
| 334 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 335 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 336 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 337 | C22⋊Q8 | C24 | 1 | 72 | yes | — |
| 338 | C22⋊Q8 | C24 | 1 | 288 | yes | — |
| 339 | C22⋊Q8 | C24 | 1 | 288 | yes | — |
| 340 | #121 | C24 | 1 | 72 | yes | — |
| 341 | #121 | C24 | 1 | 72 | yes | — |
| 342 | #121 | C24 | 1 | 72 | yes | — |
| 343 | #121 | C24 | 1 | 72 | yes | — |
| 344 | #121 | C24 | 1 | 72 | yes | — |
| 345 | #121 | C24 | 1 | 72 | yes | — |
| 346 | #121 | C24 | 1 | 72 | yes | — |
| 347 | #121 | C24 | 1 | 72 | yes | — |
| 348 | #121 | C24 | 1 | 144 | yes | — |
| 349 | #121 | C24 | 1 | 144 | yes | — |
| 350 | #121 | C24 | 1 | 144 | yes | — |
| 351 | #121 | C24 | 1 | 144 | yes | — |
| 352 | #121 | C24 | 1 | 72 | yes | — |
| 353 | #121 | C24 | 1 | 72 | yes | — |
| 354 | #121 | C24 | 1 | 72 | yes | — |
| 355 | #121 | C24 | 1 | 72 | yes | — |
| 356 | #121 | C24 | 1 | 288 | yes | — |
| 357 | #121 | C24 | 1 | 288 | yes | — |
| 358 | #120 | C24 | 1 | 144 | yes | — |
| 359 | #120 | C24 | 1 | 288 | yes | — |
| 360 | #120 | C24 | 1 | 288 | yes | — |
| 361 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 362 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 363 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 364 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 365 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 366 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 367 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 368 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 369 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 370 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 371 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 372 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 373 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 374 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 375 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 376 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 377 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 378 | C4×D4 | C24 | 1 | 36 | yes | — |
| 379 | C4×D4 | C24 | 1 | 72 | yes | — |
| 380 | C4×D4 | C24 | 1 | 72 | yes | — |
| 381 | C4×D4 | C24 | 1 | 72 | yes | — |
| 382 | C4×D4 | C24 | 1 | 36 | yes | — |
| 383 | C4×D4 | C24 | 1 | 36 | yes | — |
| 384 | C4×D4 | C24 | 1 | 72 | yes | — |
| 385 | C4×D4 | C24 | 1 | 72 | yes | — |
| 386 | C4×D4 | C24 | 1 | 36 | yes | — |
| 387 | C4×D4 | C24 | 1 | 36 | yes | — |
| 388 | C4×D4 | C24 | 1 | 36 | yes | — |
| 389 | C4×D4 | C24 | 1 | 36 | yes | — |
| 390 | C4×D4 | C24 | 1 | 72 | yes | — |
| 391 | C4×D4 | C24 | 1 | 72 | yes | — |
| 392 | C4×D4 | C24 | 1 | 72 | yes | — |
| 393 | C4×D4 | C24 | 1 | 36 | yes | — |
| 394 | C4×D4 | C24 | 1 | 36 | yes | — |
| 395 | C4×D4 | C24 | 1 | 36 | yes | — |
| 396 | C4×D4 | C24 | 1 | 144 | yes | — |
| 397 | C4×D4 | C24 | 1 | 144 | yes | — |
| 398 | C4×D4 | C24 | 1 | 72 | yes | — |
| 399 | C4×D4 | C24 | 1 | 144 | yes | — |
| 400 | C4×D4 | C24 | 1 | 144 | yes | — |
| 401 | C4×D4 | C24 | 1 | 72 | yes | — |
| 402 | C4×D4 | C24 | 1 | 72 | yes | — |
| 403 | #117 | C24 | 1 | 12 | yes | — |
| 404 | #117 | C24 | 1 | 12 | yes | — |
| 405 | #117 | C24 | 1 | 36 | yes | — |
| 406 | #117 | C24 | 1 | 72 | yes | — |
| 407 | #117 | C24 | 1 | 72 | yes | — |
| 408 | #117 | C24 | 1 | 36 | yes | — |
| 409 | #117 | C24 | 1 | 72 | yes | — |
| 410 | #117 | C24 | 1 | 72 | yes | — |
| 411 | #117 | C24 | 1 | 72 | yes | — |
| 412 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 413 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 414 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 415 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 416 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 417 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 418 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 419 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 420 | C2×C4⋊C4 | C24 | 1 | 72 | yes | — |
| 421 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 422 | C2×C4⋊C4 | C24 | 1 | 72 | yes | — |
| 423 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 424 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 425 | C2×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 426 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 427 | C2×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 428 | C2×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 429 | C2×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 430 | C2×C42 | C24 | 1 | 6 | yes | — |
| 431 | C2×C42 | C24 | 1 | 9 | yes | — |
| 432 | C2×C42 | C24 | 1 | 18 | yes | — |
| 433 | C2×C42 | C24 | 1 | 9 | yes | — |
| 434 | C2×C42 | C24 | 1 | 18 | yes | — |
| 435 | C2×C42 | C24 | 1 | 36 | yes | — |
| 436 | C2×C42 | C24 | 1 | 36 | yes | — |
| 437 | C2×C42 | C24 | 1 | 9 | yes | — |
| 438 | C2×C42 | C24 | 1 | 9 | yes | — |
| 439 | C2×C42 | C24 | 1 | 36 | yes | — |
| 440 | C2×C42 | C24 | 1 | 36 | yes | — |
| 441 | C24 | C25 | 1 | 18 | yes | — |
| 442 | C24 | C25 | 1 | 48 | yes | — |
| 443 | C24 | C25 | 1 | 1 | yes | characteristic |
| 444 | #41 | — | 2 | 48 | no | — |
| 445 | #41 | — | 2 | 144 | no | — |
| 446 | #41 | — | 2 | 144 | no | — |
| 447 | #41 | — | 4 | 96 | no | — |
| 448 | #41 | — | 4 | 48 | no | — |
| 449 | #41 | — | 4 | 288 | no | — |
| 450 | #41 | — | 4 | 72 | no | — |
| 451 | #41 | — | 4 | 288 | no | — |
| 452 | #41 | — | 8 | 24 | no | — |
| 453 | C2×Q8 | — | 2 | 12 | no | — |
| 454 | C2×Q8 | — | 2 | 36 | no | — |
| 455 | C2×Q8 | — | 4 | 18 | no | — |
| 456 | C2×Q8 | — | 4 | 144 | no | — |
| 457 | C2×Q8 | C25 | 1 | 9 | yes | — |
| 458 | C2×Q8 | C25 | 1 | 36 | yes | — |
| 459 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 460 | C2×Q8 | C25 | 1 | 8 | yes | — |
| 461 | C2×Q8 | C25 | 1 | 8 | yes | — |
| 462 | C2×Q8 | C25 | 1 | 48 | yes | — |
| 463 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 464 | C2×D4 | — | 2 | 72 | no | — |
| 465 | C2×D4 | — | 2 | 36 | no | — |
| 466 | C2×D4 | — | 4 | 36 | no | — |
| 467 | C2×D4 | — | 4 | 144 | no | — |
| 468 | C2×D4 | — | 4 | 144 | no | — |
| 469 | C2×D4 | — | 4 | 288 | no | — |
| 470 | C2×D4 | — | 8 | 18 | no | — |
| 471 | C2×D4 | — | 8 | 72 | no | — |
| 472 | C2×D4 | C25 | 1 | 36 | yes | — |
| 473 | C2×D4 | C25 | 1 | 72 | yes | — |
| 474 | C2×D4 | C25 | 1 | 36 | yes | — |
| 475 | C2×D4 | C25 | 1 | 36 | yes | — |
| 476 | C2×D4 | C25 | 1 | 72 | yes | — |
| 477 | C2×D4 | C25 | 1 | 72 | yes | — |
| 478 | C2×D4 | C25 | 1 | 72 | yes | — |
| 479 | C2×D4 | C25 | 1 | 144 | yes | — |
| 480 | C22×C4 | — | 2 | 72 | no | — |
| 481 | C22×C4 | — | 4 | 6 | no | — |
| 482 | C22×C4 | — | 4 | 36 | no | — |
| 483 | C22×C4 | — | 4 | 96 | no | — |
| 484 | C22×C4 | — | 8 | 3 | no | — |
| 485 | C22×C4 | — | 8 | 18 | no | — |
| 486 | C22×C4 | H(5,𝔽2) | 1 | 8 | yes | complemented |
| 487 | C22×C4 | C25 | 1 | 9 | yes | — |
| 488 | C22×C4 | C25 | 1 | 18 | yes | — |
| 489 | C22×C4 | C25 | 1 | 36 | yes | — |
| 490 | C22×C4 | C25 | 1 | 36 | yes | — |
| 491 | C22×C4 | C25 | 1 | 36 | yes | — |
| 492 | C22×C4 | C25 | 1 | 9 | yes | — |
| 493 | C22×C4 | C25 | 1 | 6 | yes | — |
| 494 | C22×C4 | C25 | 1 | 6 | yes | — |
| 495 | C22×C4 | C25 | 1 | 9 | yes | — |
| 496 | C22×C4 | C25 | 1 | 36 | yes | — |
| 497 | C22×C4 | C25 | 1 | 36 | yes | — |
| 498 | C22×C4 | C25 | 1 | 9 | yes | — |
| 499 | C22×C4 | C25 | 1 | 36 | yes | — |
| 500 | C22×C4 | C25 | 1 | 144 | yes | — |
| 501 | C22×C4 | C25 | 1 | 3 | yes | — |
| 502 | C22×C4 | C25 | 1 | 3 | yes | — |
| 503 | C4⋊C4 | C25 | 1 | 36 | yes | — |
| 504 | C4⋊C4 | C25 | 1 | 3 | yes | — |
| 505 | C4⋊C4 | C25 | 1 | 9 | yes | — |
| 506 | C4⋊C4 | C25 | 1 | 18 | yes | — |
| 507 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 508 | C4⋊C4 | C25 | 1 | 18 | yes | — |
| 509 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 510 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 511 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 512 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 513 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 514 | C4⋊C4 | C25 | 1 | 72 | yes | — |
| 515 | C4⋊C4 | C25 | 1 | 36 | yes | — |
| 516 | C4⋊C4 | C25 | 1 | 24 | yes | — |
| 517 | C4⋊C4 | C25 | 1 | 24 | yes | — |
| 518 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 519 | C22⋊C4 | C25 | 1 | 144 | yes | — |
| 520 | C22⋊C4 | C25 | 1 | 144 | yes | — |
| 521 | C22⋊C4 | C25 | 1 | 144 | yes | — |
| 522 | C22⋊C4 | C25 | 1 | 24 | yes | — |
| 523 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 524 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 525 | C22⋊C4 | C25 | 1 | 72 | yes | — |
| 526 | C42 | C25 | 1 | 12 | yes | — |
| 527 | C42 | C25 | 1 | 9 | yes | — |
| 528 | C42 | C25 | 1 | 9 | yes | — |
| 529 | C42 | C25 | 1 | 36 | yes | — |
| 530 | C42 | C25 | 1 | 36 | yes | — |
| 531 | C42 | C25 | 1 | 18 | yes | — |
| 532 | C42 | C25 | 1 | 36 | yes | — |
| 533 | C42 | C25 | 1 | 36 | yes | — |
| 534 | C42 | C25 | 1 | 3 | yes | — |
| 535 | C42 | C25 | 1 | 9 | yes | — |
| 536 | C42 | C25 | 1 | 12 | yes | — |
| 537 | C23 | — | 2 | 36 | no | — |
| 538 | C23 | — | 4 | 1 | no | — |
| 539 | C23 | — | 4 | 1 | no | — |
| 540 | C23 | — | 4 | 18 | no | — |
| 541 | C23 | — | 4 | 18 | no | — |
| 542 | C23 | — | 4 | 48 | no | — |
| 543 | C23 | — | 4 | 48 | no | — |
| 544 | C23 | — | 4 | 48 | no | — |
| 545 | C23 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 546 | C23 | C26 | 1 | 36 | yes | — |
| 547 | C23 | C26 | 1 | 3 | yes | — |
| 548 | Q8 | — | 2 | 72 | no | — |
| 549 | Q8 | — | 2 | 18 | no | — |
| 550 | Q8 | — | 4 | 6 | no | — |
| 551 | Q8 | — | 4 | 48 | no | — |
| 552 | Q8 | — | 4 | 8 | no | — |
| 553 | Q8 | — | 4 | 8 | no | — |
| 554 | Q8 | #585 | 1 | 4 | yes | complemented |
| 555 | D4 | — | 2 | 144 | no | — |
| 556 | D4 | — | 2 | 72 | no | — |
| 557 | D4 | — | 2 | 72 | no | — |
| 558 | D4 | — | 4 | 144 | no | — |
| 559 | D4 | — | 4 | 72 | no | — |
| 560 | D4 | — | 4 | 36 | no | — |
| 561 | D4 | — | 4 | 72 | no | — |
| 562 | D4 | — | 4 | 72 | no | — |
| 563 | C2×C4 | — | 2 | 36 | no | — |
| 564 | C2×C4 | — | 2 | 72 | no | — |
| 565 | C2×C4 | — | 2 | 72 | no | — |
| 566 | C2×C4 | — | 2 | 18 | no | — |
| 567 | C2×C4 | — | 2 | 72 | no | — |
| 568 | C2×C4 | — | 4 | 6 | no | — |
| 569 | C2×C4 | — | 4 | 144 | no | — |
| 570 | C2×C4 | — | 4 | 9 | no | — |
| 571 | C2×C4 | — | 4 | 36 | no | — |
| 572 | C2×C4 | — | 4 | 9 | no | — |
| 573 | C2×C4 | — | 4 | 6 | no | — |
| 574 | C2×C4 | — | 4 | 9 | no | — |
| 575 | C2×C4 | — | 4 | 36 | no | — |
| 576 | C2×C4 | — | 4 | 36 | no | — |
| 577 | C2×C4 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 578 | C2×C4 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 579 | C2×C4 | C26 | 1 | 3 | yes | — |
| 580 | C2×C4 | C26 | 1 | 9 | yes | — |
| 581 | C2×C4 | C26 | 1 | 12 | yes | — |
| 582 | C2×C4 | C26 | 1 | 12 | yes | — |
| 583 | C2×C4 | C26 | 1 | 9 | yes | — |
| 584 | C2×C4 | C26 | 1 | 36 | yes | — |
| 585 | C2×C4 | C26 | 1 | 3 | yes | — |
| 586 | C2×C4 | C26 | 1 | 3 | yes | — |
| 587 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 588 | C22 | — | 2 | 3 | no | — |
| 589 | C22 | — | 2 | 3 | no | — |
| 590 | C22 | — | 2 | 36 | no | — |
| 591 | C22 | — | 2 | 36 | no | — |
| 592 | C22 | — | 2 | 36 | no | — |
| 593 | C22 | — | 4 | 4 | no | — |
| 594 | C22 | — | 8 | 36 | no | — |
| 595 | C22 | — | 16 | 48 | no | — |
| 596 | C22 | C22×H(5,𝔽2) | 1 | 6 | yes | — |
| 597 | C22 | C27 | 1 | 1 | yes | characteristic |
| 598 | C4 | — | 2 | 36 | no | — |
| 599 | C4 | — | 2 | 12 | no | — |
| 600 | C4 | — | 2 | 9 | no | — |
| 601 | C4 | — | 2 | 3 | no | — |
| 602 | C4 | — | 2 | 9 | no | — |
| 603 | C4 | — | 2 | 12 | no | — |
| 604 | C4 | C22×H(5,𝔽2) | 1 | 2 | yes | — |
| 605 | C4 | C22×H(5,𝔽2) | 1 | 6 | yes | — |
| 606 | C4 | C2×#585 | 1 | 6 | yes | — |
| 607 | C2 | — | 2 | 6 | no | — |
| 608 | C2 | — | 4 | 36 | no | — |
| 609 | C2 | C23×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 610 | C2 | C22×#585 | 1 | 1 | yes | characteristic |
| 611 | C2 | #63103 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C26 |
| commutator, Frattini, socle, cosocle | C22 | C27 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62961 | C2 | semidirect |
| 2. #62946 | C2 | semidirect |
| 3. #62931 | C2 | semidirect |
| 4. #62916 | C2 | semidirect |
| 5. #62905 | C2 | semidirect |
| 6. #62895 | C2 | semidirect |
| 7. #62812 | C2 | semidirect |
| 8. #62800 | C2 | semidirect |
| 9. #62748 | C2 | semidirect |
| 10. C2×#3480 | C2 | semidirect |
| 11. #62686 | C2 | semidirect |
| 12. C2×#585 | C22 | semidirect |
| 13. #3562 | C22 | semidirect |
| 14. #3561 | C22 | semidirect |
| 15. #3560 | C22 | semidirect |
| 16. #3559 | C22 | semidirect |
| 17. #3558 | C22 | semidirect |
| 18. #3558 | C22 | semidirect |
| 19. #3554 | C22 | semidirect |
| 20. #3552 | C22 | semidirect |
| 21. #3546 | C22 | semidirect |
| 22. #3543 | C22 | semidirect |
| 23. #3537 | C22 | semidirect |
| 24. #3536 | C22 | semidirect |
| 25. #3534 | C22 | semidirect |
| 26. #3529 | C22 | semidirect |
| 27. #3522 | C22 | semidirect |
| 28. #3519 | C22 | semidirect |
| 29. #3517 | C22 | semidirect |
| 30. #3514 | C22 | semidirect |
| 31. #3511 | C22 | semidirect |
| 32. #3508 | C22 | semidirect |
| 33. #3503 | C22 | semidirect |
| 34. #3500 | C22 | semidirect |
| 35. #3499 | C22 | semidirect |
| 36. #3498 | C22 | semidirect |
| 37. #3498 | C22 | semidirect |
| 38. #3497 | C22 | semidirect |
| 39. #3497 | C22 | semidirect |
| 40. #3496 | C22 | semidirect |
| 41. #3496 | C22 | semidirect |
| 42. #3496 | C22 | semidirect |
| 43. #3496 | C22 | semidirect |
| 44. #3494 | C22 | semidirect |
| 45. #3488 | C22 | semidirect |
| 46. #3483 | C22 | semidirect |
| 47. #3481 | C22 | semidirect |
| 48. #3480 | C22 | semidirect |
| 49. #3480 | C22 | semidirect |
| 50. #3480 | C22 | semidirect |
| 51. #3480 | C22 | semidirect |
| 52. C2×#559 | C22 | semidirect |
| 53. C2×#557 | C22 | semidirect |
| 54. C2×#556 | C22 | semidirect |
| 55. C2×#553 | C22 | semidirect |
| 56. D4×#41 | C22 | semidirect |
| 57. D4×#41 | C22 | semidirect |
| 58. C2×#550 | C22 | semidirect |
| 59. C2×#548 | C22 | semidirect |
| 60. #3461 | C22 | semidirect |
| 61. #3461 | C22 | semidirect |
| 62. #3460 | C22 | semidirect |
| 63. #3460 | C22 | semidirect |
| 64. #3460 | C22 | semidirect |
| 65. #3459 | C22 | semidirect |
| 66. #3459 | C22 | semidirect |
| 67. #3459 | C22 | semidirect |
| 68. #3458 | C22 | semidirect |
| 69. #3455 | C22 | semidirect |
| 70. #3449 | C22 | semidirect |
| 71. #3449 | C22 | semidirect |
| 72. #3444 | C22 | semidirect |
| 73. C2×#532 | C22 | semidirect |
| 74. C2×#532 | C22 | semidirect |
| 75. C2×#529 | C22 | semidirect |
| 76. C4×H(5,𝔽2) | C22 | semidirect |
| 77. C2×C4×#41 | C22 | semidirect |
| 78. C2×C4×#41 | C22 | semidirect |
| 79. C22×C4×Q8 | C22 | semidirect |
| 486. C22×C4 | H(5,𝔽2) | semidirect |
| 554. Q8 | #585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62961 | 2 |
| #62946 | 2 |
| #62931 | 2 |
| #62916 | 2 |
| #62905 | 2 |
| #62895 | 2 |
| #62812 | 2 |
| #62800 | 2 |
| #62748 | 2 |
| C2×#3480 | 2 |
| #62686 | 2 |