Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1548 conjugacy classes of subgroups.
The subgroup lattice has 620 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62328 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #61805 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20133 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20103 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #19864 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #19773 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #19712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #19519 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #19336 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #19264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #18935 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #18841 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #17989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #17908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3549 | C22 | 1 | 2 | yes | — |
| 17 | #3507 | C22 | 1 | 2 | yes | complemented |
| 18 | #3396 | — | 2 | 1 | no | — |
| 19 | #3393 | C22 | 1 | 2 | yes | complemented |
| 20 | #3383 | — | 2 | 1 | no | — |
| 21 | #3380 | C22 | 1 | 2 | yes | complemented |
| 22 | #3365 | — | 2 | 2 | no | — |
| 23 | #3360 | C22 | 1 | 4 | yes | complemented |
| 24 | #3357 | C22 | 1 | 4 | yes | complemented |
| 25 | #3348 | — | 2 | 4 | no | — |
| 26 | #3341 | — | 2 | 1 | no | — |
| 27 | #3341 | C22 | 1 | 2 | yes | — |
| 28 | #3340 | C22 | 1 | 4 | yes | complemented |
| 29 | #3325 | — | 2 | 2 | no | — |
| 30 | #3325 | C22 | 1 | 4 | yes | — |
| 31 | #3324 | C22 | 1 | 4 | yes | complemented |
| 32 | #3310 | — | 2 | 4 | no | — |
| 33 | #3295 | C22 | 1 | 4 | yes | complemented |
| 34 | D4×D8 | — | 2 | 1 | no | — |
| 35 | D4×D8 | C22 | 1 | 2 | yes | — |
| 36 | #3253 | C22 | 1 | 2 | yes | — |
| 37 | #3250 | — | 2 | 2 | no | — |
| 38 | #3246 | C22 | 1 | 2 | yes | complemented |
| 39 | #3235 | C22 | 1 | 2 | yes | — |
| 40 | #3228 | C22 | 1 | 2 | yes | complemented |
| 41 | #3210 | C22 | 1 | 2 | yes | complemented |
| 42 | #3200 | — | 2 | 4 | no | — |
| 43 | #3199 | — | 2 | 2 | no | — |
| 44 | #3170 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 46 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 47 | #3168 | — | 2 | 2 | no | — |
| 48 | #3112 | C22 | 1 | 2 | yes | complemented |
| 49 | #3103 | C22 | 1 | 1 | yes | characteristic |
| 50 | #3096 | — | 2 | 4 | no | — |
| 51 | #3058 | — | 2 | 2 | no | — |
| 52 | #2981 | C22 | 1 | 2 | yes | complemented |
| 53 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 55 | #1723 | C22 | 1 | 2 | yes | complemented |
| 56 | #1722 | C22 | 1 | 2 | yes | complemented |
| 57 | #1720 | C22 | 1 | 2 | yes | complemented |
| 58 | #1717 | C22 | 1 | 2 | yes | — |
| 59 | #1697 | C22 | 1 | 4 | yes | complemented |
| 60 | #1695 | C22 | 1 | 2 | yes | complemented |
| 61 | #1691 | C22 | 1 | 4 | yes | complemented |
| 62 | #1689 | C22 | 1 | 2 | yes | complemented |
| 63 | #1683 | C22 | 1 | 4 | yes | complemented |
| 64 | #1681 | C22 | 1 | 4 | yes | complemented |
| 65 | #1678 | C22 | 1 | 4 | yes | complemented |
| 66 | #1676 | C22 | 1 | 2 | yes | complemented |
| 67 | #1675 | C22 | 1 | 4 | yes | complemented |
| 68 | #1668 | C22 | 1 | 2 | yes | — |
| 69 | #1646 | C22 | 1 | 4 | yes | complemented |
| 70 | #1639 | C22 | 1 | 4 | yes | complemented |
| 71 | #1638 | C22 | 1 | 4 | yes | complemented |
| 72 | #1634 | C22 | 1 | 4 | yes | complemented |
| 73 | #1632 | C22 | 1 | 4 | yes | complemented |
| 74 | #1629 | C22 | 1 | 4 | yes | complemented |
| 75 | #1628 | C22 | 1 | 4 | yes | complemented |
| 76 | #1622 | C22 | 1 | 4 | yes | complemented |
| 77 | #1588 | C22 | 1 | 4 | yes | complemented |
| 78 | #1586 | C22 | 1 | 4 | yes | complemented |
| 79 | #1581 | C22 | 1 | 4 | yes | complemented |
| 80 | SD16⋊C8 | C22 | 1 | 4 | yes | complemented |
| 81 | #1571 | C22 | 1 | 1 | yes | characteristic, complemented |
| 82 | #1568 | C22 | 1 | 1 | yes | characteristic, complemented |
| 83 | #1559 | C22 | 1 | 2 | yes | complemented |
| 84 | #1551 | C22 | 1 | 2 | yes | complemented |
| 85 | #1496 | C22 | 1 | 2 | yes | complemented |
| 86 | #1487 | C22 | 1 | 1 | yes | characteristic, complemented |
| 87 | #1480 | C22 | 1 | 1 | yes | characteristic |
| 88 | #1452 | C22 | 1 | 1 | yes | characteristic, complemented |
| 89 | C22×D8 | — | 2 | 2 | no | — |
| 90 | C2×#131 | — | 2 | 1 | no | — |
| 91 | H(3,𝔽4) | — | 4 | 2 | no | — |
| 92 | #559 | — | 2 | 2 | no | — |
| 93 | #557 | — | 2 | 2 | no | — |
| 94 | #556 | — | 4 | 2 | no | — |
| 95 | #556 | C23 | 1 | 4 | yes | — |
| 96 | #555 | — | 2 | 2 | no | — |
| 97 | #555 | — | 2 | 2 | no | — |
| 98 | #555 | C23 | 1 | 4 | yes | — |
| 99 | #554 | C23 | 1 | 4 | yes | — |
| 100 | #552 | — | 2 | 4 | no | — |
| 101 | D42 | — | 2 | 2 | no | — |
| 102 | D42 | — | 2 | 2 | no | — |
| 103 | D42 | C23 | 1 | 4 | yes | — |
| 104 | #539 | — | 4 | 2 | no | — |
| 105 | #536 | — | 2 | 2 | no | — |
| 106 | #535 | — | 2 | 4 | no | — |
| 107 | #535 | — | 2 | 4 | no | — |
| 108 | #535 | — | 4 | 2 | no | — |
| 109 | #533 | C23 | 1 | 2 | yes | — |
| 110 | #532 | C23 | 1 | 2 | yes | — |
| 111 | #532 | C23 | 1 | 1 | yes | characteristic |
| 112 | #532 | C23 | 1 | 2 | yes | — |
| 113 | #529 | — | 2 | 4 | no | — |
| 114 | #520 | — | 2 | 2 | no | — |
| 115 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 116 | #501 | — | 2 | 2 | no | — |
| 117 | #500 | D4 | 1 | 1 | yes | characteristic |
| 118 | #500 | C23 | 1 | 1 | yes | characteristic |
| 119 | #500 | C23 | 1 | 2 | yes | — |
| 120 | #500 | C23 | 1 | 1 | yes | characteristic |
| 121 | #499 | — | 2 | 2 | no | — |
| 122 | #498 | C23 | 1 | 2 | yes | — |
| 123 | #495 | — | 2 | 2 | no | — |
| 124 | #494 | C23 | 1 | 1 | yes | characteristic |
| 125 | #494 | C23 | 1 | 2 | yes | — |
| 126 | #493 | D4 | 1 | 1 | yes | characteristic |
| 127 | #493 | C23 | 1 | 1 | yes | characteristic |
| 128 | #492 | C23 | 1 | 2 | yes | — |
| 129 | #490 | — | 2 | 2 | no | — |
| 130 | #488 | — | 2 | 4 | no | — |
| 131 | #487 | C23 | 1 | 2 | yes | — |
| 132 | #487 | C23 | 1 | 2 | yes | — |
| 133 | #486 | D4 | 1 | 2 | yes | — |
| 134 | #486 | C23 | 1 | 2 | yes | — |
| 135 | #486 | C23 | 1 | 2 | yes | — |
| 136 | #486 | C23 | 1 | 2 | yes | — |
| 137 | #486 | C23 | 1 | 2 | yes | — |
| 138 | #485 | — | 2 | 4 | no | — |
| 139 | #485 | — | 2 | 4 | no | — |
| 140 | #482 | — | 2 | 4 | no | — |
| 141 | #482 | — | 2 | 4 | no | — |
| 142 | #482 | — | 2 | 4 | no | — |
| 143 | #482 | — | 2 | 4 | no | — |
| 144 | #482 | — | 2 | 4 | no | — |
| 145 | #482 | — | 2 | 4 | no | — |
| 146 | #481 | — | 2 | 4 | no | — |
| 147 | #481 | D4 | 1 | 2 | yes | — |
| 148 | #480 | — | 2 | 2 | no | — |
| 149 | #480 | — | 2 | 4 | no | — |
| 150 | #479 | — | 2 | 4 | no | — |
| 151 | #478 | — | 2 | 4 | no | — |
| 152 | #478 | — | 2 | 4 | no | — |
| 153 | #477 | C23 | 1 | 4 | yes | — |
| 154 | #476 | — | 2 | 2 | no | — |
| 155 | #476 | C23 | 1 | 4 | yes | — |
| 156 | #476 | C23 | 1 | 4 | yes | — |
| 157 | #476 | C23 | 1 | 4 | yes | — |
| 158 | #475 | — | 2 | 2 | no | — |
| 159 | #475 | D4 | 1 | 2 | yes | — |
| 160 | #474 | C23 | 1 | 4 | yes | — |
| 161 | #469 | — | 2 | 4 | no | — |
| 162 | #469 | — | 2 | 4 | no | — |
| 163 | #468 | — | 2 | 4 | no | — |
| 164 | #468 | — | 2 | 4 | no | — |
| 165 | #467 | — | 2 | 1 | no | — |
| 166 | #467 | — | 2 | 1 | no | — |
| 167 | #466 | — | 2 | 2 | no | — |
| 168 | #466 | — | 2 | 1 | no | — |
| 169 | #466 | — | 2 | 1 | no | — |
| 170 | #466 | — | 2 | 2 | no | — |
| 171 | #466 | D4 | 1 | 2 | yes | — |
| 172 | #466 | D4 | 1 | 2 | yes | — |
| 173 | #465 | — | 2 | 4 | no | — |
| 174 | #465 | — | 2 | 4 | no | — |
| 175 | #465 | — | 2 | 4 | no | — |
| 176 | #464 | — | 2 | 4 | no | — |
| 177 | #464 | — | 4 | 2 | no | — |
| 178 | #463 | — | 2 | 4 | no | — |
| 179 | #461 | C23 | 1 | 4 | yes | — |
| 180 | #460 | — | 2 | 2 | no | — |
| 181 | #460 | D4 | 1 | 2 | yes | — |
| 182 | #460 | C23 | 1 | 4 | yes | — |
| 183 | #459 | — | 2 | 2 | no | — |
| 184 | #459 | C23 | 1 | 4 | yes | — |
| 185 | #452 | — | 4 | 2 | no | — |
| 186 | #450 | — | 2 | 4 | no | — |
| 187 | #450 | — | 2 | 4 | no | — |
| 188 | #448 | — | 2 | 2 | no | — |
| 189 | #448 | D4 | 1 | 2 | yes | — |
| 190 | #447 | — | 2 | 4 | no | — |
| 191 | #447 | — | 2 | 4 | no | — |
| 192 | C8×Q8 | — | 2 | 1 | no | — |
| 193 | C8×Q8 | — | 2 | 1 | no | — |
| 194 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 195 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 196 | #440 | — | 2 | 4 | no | — |
| 197 | C4×Q16 | — | 2 | 2 | no | — |
| 198 | C4×Q16 | — | 2 | 1 | no | — |
| 199 | C4×Q16 | — | 2 | 1 | no | — |
| 200 | C4×SD16 | — | 2 | 4 | no | — |
| 201 | C4×SD16 | C23 | 1 | 4 | yes | — |
| 202 | C4×D8 | — | 2 | 2 | no | — |
| 203 | C4×D8 | — | 2 | 1 | no | — |
| 204 | C4×D8 | — | 2 | 1 | no | — |
| 205 | C4×D8 | C23 | 1 | 2 | yes | — |
| 206 | C4×D8 | C23 | 1 | 2 | yes | — |
| 207 | #436 | — | 2 | 1 | no | — |
| 208 | #436 | C23 | 1 | 4 | yes | — |
| 209 | #436 | C23 | 1 | 2 | yes | — |
| 210 | #435 | — | 2 | 4 | no | — |
| 211 | C8×D4 | — | 2 | 1 | no | — |
| 212 | C8×D4 | C23 | 1 | 4 | yes | — |
| 213 | C8×D4 | C23 | 1 | 2 | yes | — |
| 214 | #432 | C23 | 1 | 2 | yes | — |
| 215 | #431 | C23 | 1 | 1 | yes | characteristic |
| 216 | #431 | C23 | 1 | 1 | yes | characteristic |
| 217 | #428 | — | 2 | 4 | no | — |
| 218 | #427 | — | 2 | 2 | no | — |
| 219 | #427 | — | 2 | 4 | no | — |
| 220 | #423 | C23 | 1 | 1 | yes | characteristic |
| 221 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 222 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 223 | #418 | — | 2 | 4 | no | — |
| 224 | #418 | — | 2 | 4 | no | — |
| 225 | C2×#102 | — | 2 | 4 | no | — |
| 226 | #408 | — | 2 | 1 | no | — |
| 227 | #408 | — | 2 | 4 | no | — |
| 228 | C2×C4×C8 | — | 2 | 1 | no | — |
| 229 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 230 | #335 | C23 | 1 | 2 | yes | — |
| 231 | #335 | C23 | 1 | 4 | yes | — |
| 232 | #334 | C23 | 1 | 2 | yes | — |
| 233 | #333 | C23 | 1 | 4 | yes | — |
| 234 | #333 | C23 | 1 | 4 | yes | — |
| 235 | #332 | C23 | 1 | 4 | yes | — |
| 236 | #331 | C23 | 1 | 4 | yes | — |
| 237 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 238 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 239 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 240 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 241 | #322 | C23 | 1 | 2 | yes | — |
| 242 | #322 | C23 | 1 | 2 | yes | — |
| 243 | C2×#41 | — | 2 | 2 | no | — |
| 244 | C2×#41 | — | 2 | 1 | no | — |
| 245 | C2×#41 | — | 2 | 2 | no | — |
| 246 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C22×D4 | — | 2 | 4 | no | — |
| 248 | C22×D4 | — | 2 | 4 | no | — |
| 249 | C22×D4 | — | 4 | 2 | no | — |
| 250 | C2×Q16 | — | 2 | 1 | no | — |
| 251 | C2×Q16 | — | 2 | 1 | no | — |
| 252 | C2×Q16 | — | 4 | 2 | no | — |
| 253 | C2×SD16 | — | 2 | 4 | no | — |
| 254 | C2×SD16 | — | 2 | 4 | no | — |
| 255 | C2×SD16 | — | 4 | 2 | no | — |
| 256 | C2×SD16 | C2×D4 | 1 | 4 | yes | — |
| 257 | C2×D8 | — | 2 | 4 | no | — |
| 258 | C2×D8 | — | 2 | 1 | no | — |
| 259 | C2×D8 | — | 2 | 1 | no | — |
| 260 | C2×D8 | — | 8 | 4 | no | — |
| 261 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 262 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 263 | #131 | — | 8 | 2 | no | — |
| 264 | C2×M16 | — | 2 | 1 | no | — |
| 265 | C2×M16 | — | 2 | 2 | no | — |
| 266 | C2×M16 | — | 2 | 4 | no | — |
| 267 | C22×C8 | — | 2 | 1 | no | — |
| 268 | C22×C8 | — | 2 | 2 | no | — |
| 269 | C22×C8 | — | 2 | 4 | no | — |
| 270 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C4⋊Q8 | — | 4 | 2 | no | — |
| 273 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 275 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 276 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 277 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 278 | #127 | — | 4 | 4 | no | — |
| 279 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | #127 | C2×D4 | 1 | 2 | yes | — |
| 281 | #127 | C24 | 1 | 2 | yes | — |
| 282 | #126 | — | 4 | 4 | no | — |
| 283 | #126 | — | 4 | 4 | no | — |
| 284 | #125 | — | 2 | 4 | no | — |
| 285 | #125 | — | 2 | 2 | no | — |
| 286 | #125 | — | 4 | 4 | no | — |
| 287 | #124 | — | 2 | 4 | no | — |
| 288 | #124 | — | 2 | 2 | no | — |
| 289 | #124 | — | 2 | 1 | no | — |
| 290 | #124 | — | 2 | 2 | no | — |
| 291 | #124 | — | 4 | 4 | no | — |
| 292 | #124 | — | 4 | 4 | no | — |
| 293 | #124 | — | 4 | 4 | no | — |
| 294 | #124 | — | 4 | 2 | no | — |
| 295 | #123 | — | 4 | 4 | no | — |
| 296 | #123 | — | 4 | 4 | no | — |
| 297 | C22⋊Q8 | — | 2 | 4 | no | — |
| 298 | C22⋊Q8 | — | 2 | 4 | no | — |
| 299 | C22⋊Q8 | — | 2 | 2 | no | — |
| 300 | C22⋊Q8 | — | 2 | 2 | no | — |
| 301 | C22⋊Q8 | — | 4 | 4 | no | — |
| 302 | #121 | — | 2 | 1 | no | — |
| 303 | #121 | — | 2 | 2 | no | — |
| 304 | #121 | — | 2 | 4 | no | — |
| 305 | #121 | — | 2 | 4 | no | — |
| 306 | #121 | — | 2 | 2 | no | — |
| 307 | #121 | — | 2 | 2 | no | — |
| 308 | #121 | — | 2 | 4 | no | — |
| 309 | #121 | — | 2 | 4 | no | — |
| 310 | #121 | — | 4 | 2 | no | — |
| 311 | #121 | — | 4 | 2 | no | — |
| 312 | #121 | C2×D4 | 1 | 4 | yes | — |
| 313 | #121 | C2×D4 | 1 | 2 | yes | — |
| 314 | #120 | — | 4 | 4 | no | — |
| 315 | #120 | — | 4 | 4 | no | — |
| 316 | #120 | — | 4 | 4 | no | — |
| 317 | #120 | — | 4 | 4 | no | — |
| 318 | C4×Q8 | — | 2 | 1 | no | — |
| 319 | C4×Q8 | — | 2 | 1 | no | — |
| 320 | C4×Q8 | — | 2 | 4 | no | — |
| 321 | C4×Q8 | — | 2 | 2 | no | — |
| 322 | C4×Q8 | — | 2 | 2 | no | — |
| 323 | C4×Q8 | — | 4 | 2 | no | — |
| 324 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 325 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 326 | C4×D4 | — | 2 | 4 | no | — |
| 327 | C4×D4 | — | 2 | 1 | no | — |
| 328 | C4×D4 | — | 2 | 2 | no | — |
| 329 | C4×D4 | — | 2 | 2 | no | — |
| 330 | C4×D4 | — | 2 | 2 | no | — |
| 331 | C4×D4 | — | 4 | 2 | no | — |
| 332 | C4×D4 | — | 4 | 4 | no | — |
| 333 | C4×D4 | C24 | 1 | 2 | yes | — |
| 334 | C4×D4 | C24 | 1 | 4 | yes | — |
| 335 | #117 | — | 2 | 2 | no | — |
| 336 | #117 | — | 2 | 4 | no | — |
| 337 | #117 | — | 2 | 4 | no | — |
| 338 | #117 | — | 2 | 4 | no | — |
| 339 | #117 | — | 4 | 4 | no | — |
| 340 | #117 | — | 4 | 2 | no | — |
| 341 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 342 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 343 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 344 | C2×C42 | — | 2 | 1 | no | — |
| 345 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 346 | #107 | — | 2 | 1 | no | — |
| 347 | #107 | — | 2 | 4 | no | — |
| 348 | #107 | — | 2 | 1 | no | — |
| 349 | #107 | — | 2 | 1 | no | — |
| 350 | #107 | — | 2 | 1 | no | — |
| 351 | #107 | — | 2 | 4 | no | — |
| 352 | #107 | — | 2 | 4 | no | — |
| 353 | #107 | C2×D4 | 1 | 2 | yes | — |
| 354 | #107 | C2×D4 | 1 | 2 | yes | — |
| 355 | #106 | — | 2 | 4 | no | — |
| 356 | #106 | — | 2 | 4 | no | — |
| 357 | #106 | — | 2 | 4 | no | — |
| 358 | #106 | — | 2 | 4 | no | — |
| 359 | #106 | C2×D4 | 1 | 4 | yes | — |
| 360 | C4⋊C8 | — | 2 | 2 | no | — |
| 361 | C4⋊C8 | — | 2 | 2 | no | — |
| 362 | C4⋊C8 | — | 2 | 1 | no | — |
| 363 | C4⋊C8 | — | 2 | 1 | no | — |
| 364 | C4⋊C8 | — | 2 | 1 | no | — |
| 365 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 366 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 367 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 368 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 369 | #103 | — | 2 | 4 | no | — |
| 370 | #103 | — | 2 | 2 | no | — |
| 371 | #103 | — | 2 | 2 | no | — |
| 372 | #103 | — | 2 | 4 | no | — |
| 373 | #103 | — | 4 | 2 | no | — |
| 374 | #103 | C2×D4 | 1 | 4 | yes | — |
| 375 | #102 | — | 2 | 4 | no | — |
| 376 | #102 | — | 2 | 4 | no | — |
| 377 | #102 | — | 2 | 4 | no | — |
| 378 | #102 | — | 2 | 4 | no | — |
| 379 | #102 | — | 2 | 4 | no | — |
| 380 | #102 | — | 2 | 2 | no | — |
| 381 | #102 | — | 2 | 4 | no | — |
| 382 | #102 | — | 2 | 2 | no | — |
| 383 | #102 | — | 2 | 4 | no | — |
| 384 | #102 | — | 2 | 4 | no | — |
| 385 | #102 | — | 4 | 2 | no | — |
| 386 | #102 | C2×D4 | 1 | 4 | yes | — |
| 387 | #102 | C2×D4 | 1 | 4 | yes | — |
| 388 | #102 | C2×D4 | 1 | 4 | yes | — |
| 389 | C22⋊C8 | — | 2 | 2 | no | — |
| 390 | C22⋊C8 | — | 2 | 1 | no | — |
| 391 | C22⋊C8 | — | 2 | 2 | no | — |
| 392 | C22⋊C8 | — | 2 | 4 | no | — |
| 393 | C22⋊C8 | — | 2 | 2 | no | — |
| 394 | C22⋊C8 | — | 2 | 4 | no | — |
| 395 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 396 | #97 | — | 2 | 2 | no | — |
| 397 | C4×C8 | — | 2 | 2 | no | — |
| 398 | C4×C8 | — | 2 | 2 | no | — |
| 399 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 400 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 401 | C4×C8 | C24 | 1 | 2 | yes | — |
| 402 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 403 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 404 | C4×C8 | C24 | 1 | 2 | yes | — |
| 405 | C24 | — | 4 | 4 | no | — |
| 406 | #41 | — | 8 | 1 | no | — |
| 407 | #41 | — | 8 | 4 | no | — |
| 408 | #41 | — | 8 | 1 | no | — |
| 409 | #41 | — | 16 | 2 | no | — |
| 410 | C2×Q8 | — | 2 | 1 | no | — |
| 411 | C2×Q8 | — | 2 | 2 | no | — |
| 412 | C2×Q8 | — | 2 | 1 | no | — |
| 413 | C2×Q8 | — | 2 | 2 | no | — |
| 414 | C2×Q8 | — | 2 | 2 | no | — |
| 415 | C2×Q8 | — | 2 | 2 | no | — |
| 416 | C2×Q8 | — | 4 | 2 | no | — |
| 417 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 418 | C2×D4 | — | 2 | 4 | no | — |
| 419 | C2×D4 | — | 2 | 2 | no | — |
| 420 | C2×D4 | — | 2 | 1 | no | — |
| 421 | C2×D4 | — | 2 | 2 | no | — |
| 422 | C2×D4 | — | 2 | 2 | no | — |
| 423 | C2×D4 | — | 2 | 1 | no | — |
| 424 | C2×D4 | — | 2 | 2 | no | — |
| 425 | C2×D4 | — | 2 | 2 | no | — |
| 426 | C2×D4 | — | 2 | 2 | no | — |
| 427 | C2×D4 | — | 4 | 4 | no | — |
| 428 | C2×D4 | — | 4 | 4 | no | — |
| 429 | C2×D4 | — | 4 | 4 | no | — |
| 430 | C2×D4 | — | 4 | 2 | no | — |
| 431 | C2×D4 | — | 8 | 4 | no | — |
| 432 | C2×D4 | — | 8 | 4 | no | — |
| 433 | C2×D4 | — | 8 | 4 | no | — |
| 434 | C2×D4 | — | 8 | 4 | no | — |
| 435 | C2×D4 | — | 16 | 4 | no | — |
| 436 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 437 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 438 | C22×C4 | — | 2 | 1 | no | — |
| 439 | C22×C4 | — | 2 | 1 | no | — |
| 440 | C22×C4 | — | 2 | 4 | no | — |
| 441 | C22×C4 | — | 2 | 2 | no | — |
| 442 | C22×C4 | — | 4 | 4 | no | — |
| 443 | C22×C4 | — | 4 | 2 | no | — |
| 444 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 445 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 446 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 447 | Q16 | — | 4 | 2 | no | — |
| 448 | Q16 | — | 8 | 1 | no | — |
| 449 | Q16 | — | 16 | 2 | no | — |
| 450 | SD16 | — | 4 | 4 | no | — |
| 451 | SD16 | — | 8 | 4 | no | — |
| 452 | SD16 | — | 8 | 4 | no | — |
| 453 | SD16 | — | 16 | 2 | no | — |
| 454 | D8 | — | 4 | 2 | no | — |
| 455 | D8 | — | 4 | 2 | no | — |
| 456 | D8 | — | 4 | 2 | no | — |
| 457 | D8 | — | 8 | 1 | no | — |
| 458 | D8 | — | 8 | 4 | no | — |
| 459 | M16 | — | 8 | 4 | no | — |
| 460 | M16 | — | 8 | 2 | no | — |
| 461 | M16 | — | 8 | 1 | no | — |
| 462 | C2×C8 | — | 2 | 2 | no | — |
| 463 | C2×C8 | — | 2 | 4 | no | — |
| 464 | C2×C8 | — | 2 | 2 | no | — |
| 465 | C2×C8 | — | 2 | 2 | no | — |
| 466 | C2×C8 | — | 4 | 1 | no | — |
| 467 | C2×C8 | — | 4 | 1 | no | — |
| 468 | C2×C8 | — | 4 | 4 | no | — |
| 469 | C2×C8 | — | 8 | 4 | no | — |
| 470 | C2×C8 | — | 8 | 1 | no | — |
| 471 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 472 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 473 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 474 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 475 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 476 | C4⋊C4 | — | 2 | 2 | no | — |
| 477 | C4⋊C4 | — | 2 | 1 | no | — |
| 478 | C4⋊C4 | — | 2 | 1 | no | — |
| 479 | C4⋊C4 | — | 2 | 2 | no | — |
| 480 | C4⋊C4 | — | 2 | 2 | no | — |
| 481 | C4⋊C4 | — | 2 | 2 | no | — |
| 482 | C4⋊C4 | — | 2 | 2 | no | — |
| 483 | C4⋊C4 | — | 2 | 2 | no | — |
| 484 | C4⋊C4 | — | 2 | 2 | no | — |
| 485 | C4⋊C4 | — | 2 | 2 | no | — |
| 486 | C4⋊C4 | — | 2 | 2 | no | — |
| 487 | C4⋊C4 | — | 4 | 4 | no | — |
| 488 | C4⋊C4 | — | 4 | 4 | no | — |
| 489 | C4⋊C4 | — | 4 | 4 | no | — |
| 490 | C4⋊C4 | — | 4 | 2 | no | — |
| 491 | C4⋊C4 | — | 4 | 2 | no | — |
| 492 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 493 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 494 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 495 | C22⋊C4 | — | 2 | 4 | no | — |
| 496 | C22⋊C4 | — | 2 | 2 | no | — |
| 497 | C22⋊C4 | — | 2 | 2 | no | — |
| 498 | C22⋊C4 | — | 2 | 4 | no | — |
| 499 | C22⋊C4 | — | 4 | 4 | no | — |
| 500 | C22⋊C4 | — | 4 | 4 | no | — |
| 501 | C22⋊C4 | — | 4 | 4 | no | — |
| 502 | C22⋊C4 | — | 4 | 4 | no | — |
| 503 | C22⋊C4 | — | 4 | 4 | no | — |
| 504 | C22⋊C4 | — | 4 | 4 | no | — |
| 505 | C22⋊C4 | — | 4 | 2 | no | — |
| 506 | C22⋊C4 | — | 4 | 2 | no | — |
| 507 | C22⋊C4 | — | 4 | 2 | no | — |
| 508 | C42 | — | 2 | 2 | no | — |
| 509 | C42 | — | 2 | 2 | no | — |
| 510 | C42 | — | 4 | 4 | no | — |
| 511 | C42 | — | 4 | 4 | no | — |
| 512 | C42 | — | 4 | 2 | no | — |
| 513 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 514 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 515 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 516 | C42 | C25 | 1 | 1 | yes | characteristic |
| 517 | C23 | — | 2 | 4 | no | — |
| 518 | C23 | — | 2 | 2 | no | — |
| 519 | C23 | — | 4 | 2 | no | — |
| 520 | C23 | — | 16 | 4 | no | — |
| 521 | C23 | — | 16 | 4 | no | — |
| 522 | C23 | — | 16 | 4 | no | — |
| 523 | C23 | D42 | 1 | 1 | yes | characteristic |
| 524 | Q8 | — | 2 | 2 | no | — |
| 525 | Q8 | — | 2 | 2 | no | — |
| 526 | Q8 | — | 4 | 2 | no | — |
| 527 | Q8 | — | 4 | 2 | no | — |
| 528 | Q8 | — | 4 | 2 | no | — |
| 529 | Q8 | — | 8 | 2 | no | — |
| 530 | Q8 | — | 8 | 1 | no | — |
| 531 | Q8 | — | 8 | 2 | no | — |
| 532 | Q8 | — | 8 | 2 | no | — |
| 533 | D4 | — | 2 | 4 | no | — |
| 534 | D4 | — | 2 | 4 | no | — |
| 535 | D4 | — | 2 | 4 | no | — |
| 536 | D4 | — | 4 | 2 | no | — |
| 537 | D4 | — | 4 | 4 | no | — |
| 538 | D4 | — | 4 | 2 | no | — |
| 539 | D4 | — | 4 | 2 | no | — |
| 540 | D4 | — | 8 | 2 | no | — |
| 541 | D4 | — | 8 | 2 | no | — |
| 542 | D4 | — | 8 | 1 | no | — |
| 543 | D4 | — | 8 | 2 | no | — |
| 544 | D4 | — | 8 | 4 | no | — |
| 545 | D4 | — | 8 | 2 | no | — |
| 546 | D4 | — | 16 | 4 | no | — |
| 547 | D4 | — | 16 | 4 | no | — |
| 548 | D4 | — | 16 | 2 | no | — |
| 549 | D4 | — | 16 | 4 | no | — |
| 550 | C2×C4 | — | 2 | 2 | no | — |
| 551 | C2×C4 | — | 2 | 1 | no | — |
| 552 | C2×C4 | — | 2 | 1 | no | — |
| 553 | C2×C4 | — | 2 | 2 | no | — |
| 554 | C2×C4 | — | 2 | 2 | no | — |
| 555 | C2×C4 | — | 2 | 2 | no | — |
| 556 | C2×C4 | — | 2 | 4 | no | — |
| 557 | C2×C4 | — | 4 | 1 | no | — |
| 558 | C2×C4 | — | 4 | 2 | no | — |
| 559 | C2×C4 | — | 4 | 4 | no | — |
| 560 | C2×C4 | — | 4 | 4 | no | — |
| 561 | C2×C4 | — | 4 | 2 | no | — |
| 562 | C2×C4 | — | 4 | 2 | no | — |
| 563 | C2×C4 | — | 4 | 2 | no | — |
| 564 | C2×C4 | — | 4 | 2 | no | — |
| 565 | C2×C4 | — | 4 | 2 | no | — |
| 566 | C2×C4 | — | 8 | 4 | no | — |
| 567 | C2×C4 | — | 8 | 1 | no | — |
| 568 | C2×C4 | — | 16 | 4 | no | — |
| 569 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 570 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 571 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 572 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 573 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 574 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 575 | C8 | — | 2 | 4 | no | — |
| 576 | C8 | — | 2 | 1 | no | — |
| 577 | C8 | — | 2 | 1 | no | — |
| 578 | C8 | — | 2 | 1 | no | — |
| 579 | C8 | — | 2 | 1 | no | — |
| 580 | C8 | — | 4 | 2 | no | — |
| 581 | C8 | — | 4 | 4 | no | — |
| 582 | C8 | — | 4 | 2 | no | — |
| 583 | C8 | — | 4 | 2 | no | — |
| 584 | C22 | — | 2 | 1 | no | — |
| 585 | C22 | — | 2 | 1 | no | — |
| 586 | C22 | — | 2 | 1 | no | — |
| 587 | C22 | — | 4 | 4 | no | — |
| 588 | C22 | — | 4 | 2 | no | — |
| 589 | C22 | — | 4 | 2 | no | — |
| 590 | C22 | — | 4 | 4 | no | — |
| 591 | C22 | — | 4 | 4 | no | — |
| 592 | C22 | — | 4 | 2 | no | — |
| 593 | C22 | — | 8 | 2 | no | — |
| 594 | C22 | — | 8 | 2 | no | — |
| 595 | C22 | — | 8 | 2 | no | — |
| 596 | C22 | — | 32 | 8 | no | — |
| 597 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 598 | C4 | — | 2 | 1 | no | — |
| 599 | C4 | — | 2 | 1 | no | — |
| 600 | C4 | — | 2 | 1 | no | — |
| 601 | C4 | — | 2 | 1 | no | — |
| 602 | C4 | — | 4 | 4 | no | — |
| 603 | C4 | — | 4 | 2 | no | — |
| 604 | C4 | — | 4 | 2 | no | — |
| 605 | C4 | — | 4 | 2 | no | — |
| 606 | C4 | — | 8 | 2 | no | — |
| 607 | C4 | — | 8 | 2 | no | — |
| 608 | C4 | — | 8 | 2 | no | — |
| 609 | C4 | #3584 | 1 | 2 | yes | — |
| 610 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 611 | C4 | #3586 | 1 | 1 | yes | characteristic |
| 612 | C2 | — | 4 | 1 | no | — |
| 613 | C2 | — | 8 | 4 | no | — |
| 614 | C2 | — | 8 | 2 | no | — |
| 615 | C2 | — | 16 | 2 | no | — |
| 616 | C2 | #61051 | 1 | 1 | yes | characteristic |
| 617 | C2 | #61080 | 1 | 1 | yes | characteristic |
| 618 | C2 | #61106 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | #62328 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62361 | C2 | semidirect |
| 3. #61805 | C2 | semidirect |
| 4. #20133 | C2 | semidirect |
| 5. #20103 | C2 | semidirect |
| 6. #19864 | C2 | semidirect |
| 7. #19773 | C2 | semidirect |
| 8. #19712 | C2 | semidirect |
| 9. #19519 | C2 | semidirect |
| 10. #19336 | C2 | semidirect |
| 11. #19264 | C2 | semidirect |
| 12. #18935 | C2 | semidirect |
| 13. #18841 | C2 | semidirect |
| 14. #17989 | C2 | semidirect |
| 15. #17908 | C2 | semidirect |
| 17. #3507 | C22 | semidirect |
| 19. #3393 | C22 | semidirect |
| 21. #3380 | C22 | semidirect |
| 23. #3360 | C22 | semidirect |
| 24. #3357 | C22 | semidirect |
| 28. #3340 | C22 | semidirect |
| 31. #3324 | C22 | semidirect |
| 33. #3295 | C22 | semidirect |
| 38. #3246 | C22 | semidirect |
| 40. #3228 | C22 | semidirect |
| 41. #3210 | C22 | semidirect |
| 44. #3170 | C22 | semidirect |
| 48. #3112 | C22 | semidirect |
| 52. #2981 | C22 | semidirect |
| 53. C2×C8×Q8 | C22 | semidirect |
| 55. #1723 | C22 | semidirect |
| 56. #1722 | C22 | semidirect |
| 57. #1720 | C22 | semidirect |
| 59. #1697 | C22 | semidirect |
| 60. #1695 | C22 | semidirect |
| 61. #1691 | C22 | semidirect |
| 62. #1689 | C22 | semidirect |
| 63. #1683 | C22 | semidirect |
| 64. #1681 | C22 | semidirect |
| 65. #1678 | C22 | semidirect |
| 66. #1676 | C22 | semidirect |
| 67. #1675 | C22 | semidirect |
| 69. #1646 | C22 | semidirect |
| 70. #1639 | C22 | semidirect |
| 71. #1638 | C22 | semidirect |
| 72. #1634 | C22 | semidirect |
| 73. #1632 | C22 | semidirect |
| 74. #1629 | C22 | semidirect |
| 75. #1628 | C22 | semidirect |
| 76. #1622 | C22 | semidirect |
| 77. #1588 | C22 | semidirect |
| 78. #1586 | C22 | semidirect |
| 79. #1581 | C22 | semidirect |
| 80. SD16⋊C8 | C22 | semidirect |
| 81. #1571 | C22 | semidirect |
| 82. #1568 | C22 | semidirect |
| 83. #1559 | C22 | semidirect |
| 84. #1551 | C22 | semidirect |
| 85. #1496 | C22 | semidirect |
| 86. #1487 | C22 | semidirect |
| 88. #1452 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62361 | 2 |
| #62328 | 2 |
| #61805 | 2 |
| #20133 | 2 |
| #20103 | 2 |
| #19864 | 2 |
| #19773 | 2 |
| #19712 | 2 |
| #19519 | 2 |
| #19336 | 2 |
| #19264 | 2 |
| #18935 | 2 |
| #18841 | 2 |
| #17989 | 2 |
| #17908 | 2 |