Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1580 conjugacy classes of subgroups.
The subgroup lattice has 502 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62552 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #20319 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20308 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20302 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20003 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #19996 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #19925 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #19911 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C2×#1709 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #19362 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #18685 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #18682 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #17959 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #3544 | C22 | 1 | 2 | yes | — |
| 15 | #3543 | C22 | 1 | 2 | yes | complemented |
| 16 | #3375 | C22 | 1 | 4 | yes | complemented |
| 17 | #3366 | C22 | 1 | 4 | yes | complemented |
| 18 | #3362 | C22 | 1 | 4 | yes | complemented |
| 19 | #3361 | C22 | 1 | 4 | yes | complemented |
| 20 | #3333 | C22 | 1 | 4 | yes | complemented |
| 21 | #3325 | C22 | 1 | 4 | yes | complemented |
| 22 | #3310 | — | 2 | 4 | no | — |
| 23 | #3306 | — | 2 | 4 | no | — |
| 24 | #3305 | C22 | 1 | 4 | yes | complemented |
| 25 | #3296 | — | 2 | 4 | no | — |
| 26 | #3295 | C22 | 1 | 4 | yes | complemented |
| 27 | #3294 | — | 2 | 4 | no | — |
| 28 | #3241 | — | 2 | 4 | no | — |
| 29 | #3238 | C22 | 1 | 4 | yes | complemented |
| 30 | #3224 | — | 2 | 4 | no | — |
| 31 | #3217 | C22 | 1 | 4 | yes | — |
| 32 | #3179 | — | 2 | 4 | no | — |
| 33 | #3168 | C22 | 1 | 2 | yes | — |
| 34 | C2×#494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 36 | #3136 | — | 2 | 4 | no | — |
| 37 | C2×#486 | C22 | 1 | 4 | yes | complemented |
| 38 | #2966 | C22 | 1 | 4 | yes | complemented |
| 39 | #1709 | C22 | 1 | 1 | yes | characteristic |
| 40 | #1709 | C22 | 1 | 1 | yes | characteristic |
| 41 | #1709 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #1709 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #1709 | C22 | 1 | 4 | yes | complemented |
| 44 | #1698 | C22 | 1 | 4 | yes | complemented |
| 45 | #1698 | C22 | 1 | 4 | yes | complemented |
| 46 | #1697 | C22 | 1 | 4 | yes | complemented |
| 47 | #1697 | C22 | 1 | 4 | yes | complemented |
| 48 | #1678 | C22 | 1 | 4 | yes | complemented |
| 49 | #1678 | C22 | 1 | 4 | yes | complemented |
| 50 | #1677 | C22 | 1 | 4 | yes | complemented |
| 51 | #1677 | C22 | 1 | 4 | yes | complemented |
| 52 | #1634 | C22 | 1 | 2 | yes | complemented |
| 53 | #1634 | C22 | 1 | 2 | yes | complemented |
| 54 | #1633 | C22 | 1 | 2 | yes | complemented |
| 55 | #1633 | C22 | 1 | 2 | yes | complemented |
| 56 | #1632 | C22 | 1 | 4 | yes | complemented |
| 57 | #1632 | C22 | 1 | 4 | yes | complemented |
| 58 | #1621 | C22 | 1 | 4 | yes | — |
| 59 | #1621 | C22 | 1 | 4 | yes | complemented |
| 60 | #1620 | C22 | 1 | 2 | yes | — |
| 61 | #1620 | C22 | 1 | 2 | yes | complemented |
| 62 | #1619 | C22 | 1 | 2 | yes | — |
| 63 | #1619 | C22 | 1 | 2 | yes | complemented |
| 64 | #1591 | C22 | 1 | 2 | yes | complemented |
| 65 | #1590 | C22 | 1 | 4 | yes | complemented |
| 66 | #1589 | C22 | 1 | 2 | yes | complemented |
| 67 | C8×Q16 | C22 | 1 | 2 | yes | complemented |
| 68 | C8×SD16 | C22 | 1 | 4 | yes | complemented |
| 69 | C8×D8 | C22 | 1 | 2 | yes | complemented |
| 70 | #1568 | C22 | 1 | 2 | yes | complemented |
| 71 | #1558 | C22 | 1 | 2 | yes | complemented |
| 72 | #1555 | C22 | 1 | 2 | yes | complemented |
| 73 | #1494 | C22 | 1 | 4 | yes | complemented |
| 74 | C2×C82 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | C22×Q16 | — | 4 | 1 | no | — |
| 76 | C22×D8 | — | 4 | 1 | no | — |
| 77 | #563 | — | 4 | 2 | no | — |
| 78 | #560 | — | 4 | 2 | no | — |
| 79 | #559 | C23 | 1 | 2 | yes | — |
| 80 | Q82 | C23 | 1 | 2 | yes | — |
| 81 | #555 | C23 | 1 | 2 | yes | — |
| 82 | #554 | C23 | 1 | 4 | yes | — |
| 83 | #552 | — | 2 | 4 | no | — |
| 84 | #550 | C23 | 1 | 4 | yes | — |
| 85 | #547 | — | 2 | 4 | no | — |
| 86 | #546 | — | 2 | 4 | no | — |
| 87 | D42 | — | 2 | 4 | no | — |
| 88 | D42 | C23 | 1 | 2 | yes | — |
| 89 | #544 | — | 2 | 4 | no | — |
| 90 | #542 | — | 2 | 4 | no | — |
| 91 | #540 | — | 2 | 4 | no | — |
| 92 | #536 | — | 4 | 2 | no | — |
| 93 | #535 | — | 2 | 4 | no | — |
| 94 | #534 | — | 4 | 2 | no | — |
| 95 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 96 | C2×#127 | C23 | 1 | 2 | yes | — |
| 97 | #529 | C23 | 1 | 4 | yes | — |
| 98 | #501 | — | 2 | 4 | no | — |
| 99 | #499 | D4 | 1 | 2 | yes | — |
| 100 | #496 | — | 2 | 4 | no | — |
| 101 | #495 | D4 | 1 | 2 | yes | — |
| 102 | #494 | — | 4 | 1 | no | — |
| 103 | #494 | C23 | 1 | 1 | yes | characteristic |
| 104 | #494 | C23 | 1 | 2 | yes | — |
| 105 | #494 | C23 | 1 | 1 | yes | characteristic |
| 106 | #493 | — | 4 | 1 | no | — |
| 107 | #493 | C23 | 1 | 1 | yes | characteristic |
| 108 | #493 | C23 | 1 | 2 | yes | — |
| 109 | #493 | C23 | 1 | 1 | yes | characteristic |
| 110 | #490 | — | 2 | 4 | no | — |
| 111 | #490 | — | 2 | 4 | no | — |
| 112 | #489 | — | 2 | 4 | no | — |
| 113 | #489 | — | 2 | 4 | no | — |
| 114 | #488 | — | 2 | 4 | no | — |
| 115 | #488 | D4 | 1 | 4 | yes | — |
| 116 | #486 | — | 2 | 4 | no | — |
| 117 | #486 | — | 2 | 4 | no | — |
| 118 | #486 | — | 2 | 4 | no | — |
| 119 | #486 | C23 | 1 | 4 | yes | — |
| 120 | #486 | C23 | 1 | 4 | yes | — |
| 121 | #486 | C23 | 1 | 4 | yes | — |
| 122 | #486 | C23 | 1 | 4 | yes | — |
| 123 | #483 | — | 2 | 4 | no | — |
| 124 | #482 | — | 2 | 4 | no | — |
| 125 | #482 | — | 2 | 4 | no | — |
| 126 | #481 | — | 2 | 4 | no | — |
| 127 | #480 | — | 2 | 4 | no | — |
| 128 | #480 | — | 2 | 4 | no | — |
| 129 | #478 | — | 2 | 4 | no | — |
| 130 | #478 | — | 2 | 4 | no | — |
| 131 | #477 | C23 | 1 | 4 | yes | — |
| 132 | #477 | C23 | 1 | 4 | yes | — |
| 133 | #476 | — | 2 | 4 | no | — |
| 134 | #476 | C23 | 1 | 4 | yes | — |
| 135 | #476 | C23 | 1 | 4 | yes | — |
| 136 | #474 | — | 2 | 4 | no | — |
| 137 | #469 | — | 2 | 4 | no | — |
| 138 | #468 | — | 2 | 4 | no | — |
| 139 | #467 | D4 | 1 | 2 | yes | — |
| 140 | #466 | — | 2 | 4 | no | — |
| 141 | #466 | D4 | 1 | 2 | yes | — |
| 142 | #465 | — | 2 | 4 | no | — |
| 143 | #465 | D4 | 1 | 4 | yes | — |
| 144 | #464 | — | 2 | 4 | no | — |
| 145 | #463 | — | 2 | 4 | no | — |
| 146 | #460 | — | 2 | 4 | no | — |
| 147 | #460 | C23 | 1 | 4 | yes | — |
| 148 | #460 | C23 | 1 | 4 | yes | — |
| 149 | #459 | — | 2 | 4 | no | — |
| 150 | #459 | C23 | 1 | 4 | yes | — |
| 151 | #459 | C23 | 1 | 4 | yes | — |
| 152 | #452 | — | 2 | 4 | no | — |
| 153 | #450 | — | 2 | 4 | no | — |
| 154 | #450 | — | 2 | 4 | no | — |
| 155 | #449 | — | 2 | 4 | no | — |
| 156 | #447 | — | 2 | 4 | no | — |
| 157 | #447 | — | 2 | 4 | no | — |
| 158 | #446 | C23 | 1 | 4 | yes | — |
| 159 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 160 | #442 | — | 2 | 4 | no | — |
| 161 | #440 | — | 2 | 4 | no | — |
| 162 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 163 | C4×SD16 | — | 2 | 4 | no | — |
| 164 | C4×SD16 | C23 | 1 | 4 | yes | — |
| 165 | C4×D8 | — | 2 | 4 | no | — |
| 166 | C4×D8 | C23 | 1 | 2 | yes | — |
| 167 | #436 | C23 | 1 | 4 | yes | — |
| 168 | #435 | — | 2 | 4 | no | — |
| 169 | C8×D4 | — | 2 | 4 | no | — |
| 170 | C8×D4 | C23 | 1 | 4 | yes | — |
| 171 | #433 | — | 2 | 4 | no | — |
| 172 | #432 | C23 | 1 | 4 | yes | — |
| 173 | #418 | — | 2 | 4 | no | — |
| 174 | #417 | — | 2 | 4 | no | — |
| 175 | #416 | — | 2 | 4 | no | — |
| 176 | C2×#102 | — | 2 | 4 | no | — |
| 177 | C2×#102 | — | 2 | 4 | no | — |
| 178 | C2×#102 | — | 2 | 4 | no | — |
| 179 | #405 | — | 2 | 4 | no | — |
| 180 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 182 | #335 | C23 | 1 | 2 | yes | — |
| 183 | #335 | C23 | 1 | 2 | yes | — |
| 184 | #334 | C23 | 1 | 4 | yes | — |
| 185 | #333 | C23 | 1 | 4 | yes | — |
| 186 | #333 | C23 | 1 | 2 | yes | — |
| 187 | #333 | C23 | 1 | 2 | yes | — |
| 188 | #331 | C23 | 1 | 2 | yes | — |
| 189 | #331 | C23 | 1 | 2 | yes | — |
| 190 | #331 | C23 | 1 | 4 | yes | — |
| 191 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 192 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 193 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 194 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 195 | C82 | C23 | 1 | 2 | yes | — |
| 196 | C82 | C23 | 1 | 1 | yes | characteristic |
| 197 | C82 | C23 | 1 | 1 | yes | characteristic |
| 198 | C2×#41 | — | 2 | 4 | no | — |
| 199 | C2×#41 | — | 4 | 2 | no | — |
| 200 | C22×Q8 | — | 2 | 2 | no | — |
| 201 | C22×D4 | — | 2 | 4 | no | — |
| 202 | C22×D4 | — | 2 | 4 | no | — |
| 203 | C22×D4 | — | 2 | 2 | no | — |
| 204 | C22×D4 | — | 4 | 2 | no | — |
| 205 | C2×Q16 | — | 4 | 1 | no | — |
| 206 | C2×Q16 | — | 4 | 2 | no | — |
| 207 | C2×Q16 | — | 4 | 1 | no | — |
| 208 | C2×Q16 | — | 8 | 4 | no | — |
| 209 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 210 | C2×SD16 | — | 2 | 4 | no | — |
| 211 | C2×SD16 | — | 2 | 4 | no | — |
| 212 | C2×SD16 | C2×D4 | 1 | 4 | yes | — |
| 213 | C2×D8 | — | 2 | 4 | no | — |
| 214 | C2×D8 | — | 2 | 4 | no | — |
| 215 | C2×D8 | — | 4 | 1 | no | — |
| 216 | C2×D8 | — | 4 | 2 | no | — |
| 217 | C2×D8 | — | 4 | 1 | no | — |
| 218 | C2×D8 | — | 8 | 4 | no | — |
| 219 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 220 | C2×M16 | — | 2 | 4 | no | — |
| 221 | C22×C8 | — | 2 | 1 | no | — |
| 222 | C22×C8 | — | 2 | 4 | no | — |
| 223 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 224 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 225 | C4⋊Q8 | — | 2 | 4 | no | — |
| 226 | C4⋊Q8 | — | 2 | 4 | no | — |
| 227 | C4⋊Q8 | — | 2 | 2 | no | — |
| 228 | C4⋊Q8 | — | 4 | 2 | no | — |
| 229 | C4⋊Q8 | — | 4 | 2 | no | — |
| 230 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 231 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 232 | #127 | — | 2 | 4 | no | — |
| 233 | #127 | — | 2 | 4 | no | — |
| 234 | #127 | — | 2 | 2 | no | — |
| 235 | #127 | C24 | 1 | 2 | yes | — |
| 236 | #127 | C24 | 1 | 2 | yes | — |
| 237 | #126 | — | 2 | 4 | no | — |
| 238 | #126 | — | 4 | 4 | no | — |
| 239 | #125 | — | 2 | 4 | no | — |
| 240 | #125 | — | 4 | 4 | no | — |
| 241 | #125 | C2×D4 | 1 | 4 | yes | — |
| 242 | #124 | — | 2 | 4 | no | — |
| 243 | #124 | — | 4 | 2 | no | — |
| 244 | #124 | — | 4 | 2 | no | — |
| 245 | #124 | C2×D4 | 1 | 4 | yes | — |
| 246 | #123 | — | 2 | 4 | no | — |
| 247 | #123 | — | 4 | 4 | no | — |
| 248 | #123 | — | 4 | 4 | no | — |
| 249 | #123 | — | 4 | 2 | no | — |
| 250 | #123 | — | 4 | 2 | no | — |
| 251 | #123 | — | 4 | 4 | no | — |
| 252 | C22⋊Q8 | — | 2 | 4 | no | — |
| 253 | C22⋊Q8 | — | 4 | 4 | no | — |
| 254 | C22⋊Q8 | — | 4 | 4 | no | — |
| 255 | C22⋊Q8 | — | 4 | 4 | no | — |
| 256 | C22⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 257 | #121 | — | 2 | 4 | no | — |
| 258 | #121 | — | 2 | 4 | no | — |
| 259 | #121 | — | 2 | 4 | no | — |
| 260 | #121 | — | 4 | 4 | no | — |
| 261 | #121 | — | 4 | 4 | no | — |
| 262 | #121 | — | 4 | 4 | no | — |
| 263 | #121 | — | 4 | 4 | no | — |
| 264 | #121 | C2×D4 | 1 | 4 | yes | — |
| 265 | #120 | — | 4 | 2 | no | — |
| 266 | #120 | — | 4 | 2 | no | — |
| 267 | #120 | — | 4 | 4 | no | — |
| 268 | #120 | — | 4 | 4 | no | — |
| 269 | C4×Q8 | — | 2 | 4 | no | — |
| 270 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 271 | C4×D4 | — | 2 | 4 | no | — |
| 272 | C4×D4 | — | 2 | 4 | no | — |
| 273 | C4×D4 | — | 2 | 4 | no | — |
| 274 | C4×D4 | — | 2 | 4 | no | — |
| 275 | C4×D4 | C24 | 1 | 4 | yes | — |
| 276 | #117 | — | 2 | 4 | no | — |
| 277 | #117 | — | 2 | 4 | no | — |
| 278 | #117 | — | 4 | 2 | no | — |
| 279 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 280 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 281 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 282 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 283 | #107 | — | 2 | 4 | no | — |
| 284 | #107 | — | 2 | 4 | no | — |
| 285 | #107 | C2×D4 | 1 | 2 | yes | — |
| 286 | #107 | C2×D4 | 1 | 2 | yes | — |
| 287 | #106 | — | 2 | 4 | no | — |
| 288 | #106 | — | 2 | 4 | no | — |
| 289 | #106 | C2×D4 | 1 | 4 | yes | — |
| 290 | C4⋊C8 | — | 2 | 4 | no | — |
| 291 | C4⋊C8 | — | 2 | 4 | no | — |
| 292 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 293 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 294 | #103 | — | 2 | 4 | no | — |
| 295 | #103 | — | 2 | 4 | no | — |
| 296 | #103 | C2×D4 | 1 | 4 | yes | — |
| 297 | #103 | C2×D4 | 1 | 4 | yes | — |
| 298 | #102 | — | 2 | 4 | no | — |
| 299 | #102 | — | 2 | 4 | no | — |
| 300 | #102 | — | 2 | 4 | no | — |
| 301 | #102 | — | 2 | 4 | no | — |
| 302 | #102 | — | 2 | 4 | no | — |
| 303 | #102 | — | 2 | 4 | no | — |
| 304 | #102 | — | 2 | 4 | no | — |
| 305 | #102 | — | 2 | 4 | no | — |
| 306 | #102 | — | 2 | 4 | no | — |
| 307 | #102 | — | 2 | 4 | no | — |
| 308 | #102 | — | 2 | 4 | no | — |
| 309 | #102 | — | 2 | 4 | no | — |
| 310 | #102 | — | 2 | 4 | no | — |
| 311 | #102 | — | 2 | 4 | no | — |
| 312 | #102 | C2×D4 | 1 | 4 | yes | — |
| 313 | #102 | C2×D4 | 1 | 4 | yes | — |
| 314 | C22⋊C8 | — | 2 | 4 | no | — |
| 315 | C22⋊C8 | — | 2 | 4 | no | — |
| 316 | C22⋊C8 | — | 2 | 4 | no | — |
| 317 | #97 | — | 2 | 4 | no | — |
| 318 | #97 | — | 2 | 4 | no | — |
| 319 | C4×C8 | — | 2 | 4 | no | — |
| 320 | C4×C8 | — | 2 | 1 | no | — |
| 321 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 322 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 323 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 324 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 325 | C4×C8 | C24 | 1 | 2 | yes | — |
| 326 | C4×C8 | C24 | 1 | 2 | yes | — |
| 327 | C24 | — | 4 | 2 | no | — |
| 328 | C24 | — | 4 | 2 | no | — |
| 329 | #41 | — | 8 | 4 | no | — |
| 330 | #41 | — | 8 | 4 | no | — |
| 331 | #41 | — | 16 | 4 | no | — |
| 332 | C2×Q8 | — | 2 | 2 | no | — |
| 333 | C2×Q8 | — | 2 | 2 | no | — |
| 334 | C2×Q8 | — | 4 | 2 | no | — |
| 335 | C2×Q8 | — | 4 | 2 | no | — |
| 336 | C2×Q8 | — | 8 | 4 | no | — |
| 337 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 338 | C2×D4 | — | 2 | 4 | no | — |
| 339 | C2×D4 | — | 2 | 4 | no | — |
| 340 | C2×D4 | — | 2 | 4 | no | — |
| 341 | C2×D4 | — | 2 | 2 | no | — |
| 342 | C2×D4 | — | 2 | 2 | no | — |
| 343 | C2×D4 | — | 4 | 4 | no | — |
| 344 | C2×D4 | — | 4 | 4 | no | — |
| 345 | C2×D4 | — | 4 | 4 | no | — |
| 346 | C2×D4 | — | 4 | 2 | no | — |
| 347 | C2×D4 | — | 4 | 2 | no | — |
| 348 | C2×D4 | — | 4 | 4 | no | — |
| 349 | C2×D4 | — | 8 | 4 | no | — |
| 350 | C2×D4 | — | 8 | 4 | no | — |
| 351 | C2×D4 | — | 8 | 4 | no | — |
| 352 | C2×D4 | — | 8 | 4 | no | — |
| 353 | C2×D4 | — | 8 | 4 | no | — |
| 354 | C2×D4 | — | 16 | 4 | no | — |
| 355 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 356 | C22×C4 | — | 2 | 4 | no | — |
| 357 | C22×C4 | — | 4 | 4 | no | — |
| 358 | C22×C4 | — | 4 | 2 | no | — |
| 359 | C22×C4 | — | 4 | 4 | no | — |
| 360 | C22×C4 | — | 4 | 2 | no | — |
| 361 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 362 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 363 | Q16 | — | 4 | 2 | no | — |
| 364 | Q16 | — | 8 | 2 | no | — |
| 365 | Q16 | — | 8 | 4 | no | — |
| 366 | Q16 | — | 8 | 2 | no | — |
| 367 | SD16 | — | 4 | 4 | no | — |
| 368 | SD16 | — | 8 | 4 | no | — |
| 369 | SD16 | — | 8 | 4 | no | — |
| 370 | D8 | — | 4 | 2 | no | — |
| 371 | D8 | — | 8 | 2 | no | — |
| 372 | D8 | — | 8 | 4 | no | — |
| 373 | D8 | — | 8 | 2 | no | — |
| 374 | D8 | — | 8 | 4 | no | — |
| 375 | D8 | — | 8 | 4 | no | — |
| 376 | M16 | — | 8 | 4 | no | — |
| 377 | C2×C8 | — | 2 | 4 | no | — |
| 378 | C2×C8 | — | 2 | 1 | no | — |
| 379 | C2×C8 | — | 2 | 1 | no | — |
| 380 | C2×C8 | — | 2 | 4 | no | — |
| 381 | C2×C8 | — | 2 | 4 | no | — |
| 382 | C2×C8 | — | 4 | 2 | no | — |
| 383 | C2×C8 | — | 4 | 2 | no | — |
| 384 | C2×C8 | — | 8 | 4 | no | — |
| 385 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 386 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 387 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 388 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 389 | C4⋊C4 | — | 2 | 4 | no | — |
| 390 | C4⋊C4 | — | 2 | 4 | no | — |
| 391 | C4⋊C4 | — | 2 | 4 | no | — |
| 392 | C4⋊C4 | — | 2 | 4 | no | — |
| 393 | C4⋊C4 | — | 2 | 4 | no | — |
| 394 | C4⋊C4 | — | 2 | 4 | no | — |
| 395 | C4⋊C4 | — | 4 | 4 | no | — |
| 396 | C4⋊C4 | — | 4 | 4 | no | — |
| 397 | C4⋊C4 | — | 4 | 4 | no | — |
| 398 | C4⋊C4 | — | 4 | 4 | no | — |
| 399 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 400 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 401 | C22⋊C4 | — | 2 | 4 | no | — |
| 402 | C22⋊C4 | — | 2 | 4 | no | — |
| 403 | C22⋊C4 | — | 2 | 4 | no | — |
| 404 | C22⋊C4 | — | 2 | 4 | no | — |
| 405 | C22⋊C4 | — | 2 | 4 | no | — |
| 406 | C22⋊C4 | — | 4 | 2 | no | — |
| 407 | C22⋊C4 | — | 4 | 2 | no | — |
| 408 | C22⋊C4 | — | 4 | 4 | no | — |
| 409 | C22⋊C4 | — | 4 | 4 | no | — |
| 410 | C22⋊C4 | — | 4 | 4 | no | — |
| 411 | C22⋊C4 | — | 4 | 4 | no | — |
| 412 | C42 | — | 2 | 4 | no | — |
| 413 | C42 | — | 4 | 2 | no | — |
| 414 | C42 | — | 4 | 2 | no | — |
| 415 | C42 | C22×D4 | 1 | 2 | yes | — |
| 416 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 417 | C42 | C25 | 1 | 1 | yes | characteristic |
| 418 | C23 | — | 2 | 4 | no | — |
| 419 | C23 | — | 4 | 2 | no | — |
| 420 | C23 | — | 4 | 2 | no | — |
| 421 | C23 | — | 8 | 4 | no | — |
| 422 | C23 | — | 16 | 4 | no | — |
| 423 | C23 | — | 16 | 4 | no | — |
| 424 | C23 | — | 16 | 2 | no | — |
| 425 | C23 | D42 | 1 | 1 | yes | characteristic |
| 426 | Q8 | — | 2 | 4 | no | — |
| 427 | Q8 | — | 2 | 4 | no | — |
| 428 | Q8 | — | 8 | 2 | no | — |
| 429 | Q8 | — | 8 | 2 | no | — |
| 430 | Q8 | — | 16 | 2 | no | — |
| 431 | Q8 | — | 16 | 2 | no | — |
| 432 | D4 | — | 2 | 4 | no | — |
| 433 | D4 | — | 2 | 4 | no | — |
| 434 | D4 | — | 4 | 8 | no | — |
| 435 | D4 | — | 4 | 4 | no | — |
| 436 | D4 | — | 4 | 4 | no | — |
| 437 | D4 | — | 4 | 4 | no | — |
| 438 | D4 | — | 4 | 4 | no | — |
| 439 | D4 | — | 8 | 2 | no | — |
| 440 | D4 | — | 8 | 2 | no | — |
| 441 | D4 | — | 16 | 4 | no | — |
| 442 | D4 | — | 16 | 2 | no | — |
| 443 | D4 | — | 16 | 4 | no | — |
| 444 | D4 | — | 16 | 4 | no | — |
| 445 | D4 | — | 16 | 4 | no | — |
| 446 | D4 | — | 16 | 2 | no | — |
| 447 | C2×C4 | — | 2 | 2 | no | — |
| 448 | C2×C4 | — | 2 | 2 | no | — |
| 449 | C2×C4 | — | 2 | 2 | no | — |
| 450 | C2×C4 | — | 2 | 4 | no | — |
| 451 | C2×C4 | — | 2 | 4 | no | — |
| 452 | C2×C4 | — | 2 | 4 | no | — |
| 453 | C2×C4 | — | 4 | 4 | no | — |
| 454 | C2×C4 | — | 4 | 4 | no | — |
| 455 | C2×C4 | — | 4 | 2 | no | — |
| 456 | C2×C4 | — | 4 | 2 | no | — |
| 457 | C2×C4 | — | 8 | 4 | no | — |
| 458 | C2×C4 | — | 16 | 2 | no | — |
| 459 | C2×C4 | — | 16 | 4 | no | — |
| 460 | C2×C4 | — | 16 | 4 | no | — |
| 461 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | D42 | 1 | 2 | yes | — |
| 463 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 464 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 465 | C8 | — | 2 | 2 | no | — |
| 466 | C8 | — | 2 | 2 | no | — |
| 467 | C8 | — | 2 | 2 | no | — |
| 468 | C8 | — | 2 | 2 | no | — |
| 469 | C8 | — | 2 | 2 | no | — |
| 470 | C8 | — | 2 | 2 | no | — |
| 471 | C8 | — | 4 | 4 | no | — |
| 472 | C8 | — | 4 | 4 | no | — |
| 473 | C22 | — | 2 | 2 | no | — |
| 474 | C22 | — | 4 | 4 | no | — |
| 475 | C22 | — | 4 | 4 | no | — |
| 476 | C22 | — | 4 | 4 | no | — |
| 477 | C22 | — | 8 | 4 | no | — |
| 478 | C22 | — | 8 | 4 | no | — |
| 479 | C22 | — | 8 | 2 | no | — |
| 480 | C22 | — | 8 | 2 | no | — |
| 481 | C22 | — | 32 | 4 | no | — |
| 482 | C22 | — | 32 | 4 | no | — |
| 483 | C22 | #3292 | 1 | 2 | yes | — |
| 484 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 485 | C4 | — | 2 | 2 | no | — |
| 486 | C4 | — | 2 | 1 | no | — |
| 487 | C4 | — | 2 | 1 | no | — |
| 488 | C4 | — | 4 | 4 | no | — |
| 489 | C4 | — | 4 | 4 | no | — |
| 490 | C4 | — | 4 | 4 | no | — |
| 491 | C4 | — | 8 | 2 | no | — |
| 492 | C4 | — | 8 | 2 | no | — |
| 493 | C4 | #3584 | 1 | 2 | yes | — |
| 494 | C4 | #3584 | 1 | 2 | yes | — |
| 495 | C2 | — | 2 | 2 | no | — |
| 496 | C2 | — | 8 | 4 | no | — |
| 497 | C2 | — | 16 | 2 | no | — |
| 498 | C2 | — | 16 | 2 | no | — |
| 499 | C2 | #61088 | 1 | 2 | yes | — |
| 500 | C2 | C2×#3292 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| 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. #62552 | C2 | semidirect |
| 2. #20319 | C2 | semidirect |
| 3. #20308 | C2 | semidirect |
| 4. #20302 | C2 | semidirect |
| 5. #20003 | C2 | semidirect |
| 6. #19996 | C2 | semidirect |
| 7. #19925 | C2 | semidirect |
| 8. #19911 | C2 | semidirect |
| 9. C2×#1709 | C2 | semidirect |
| 10. #19362 | C2 | semidirect |
| 11. #18685 | C2 | semidirect |
| 12. #18682 | C2 | semidirect |
| 13. #17959 | C2 | semidirect |
| 15. #3543 | C22 | semidirect |
| 16. #3375 | C22 | semidirect |
| 17. #3366 | C22 | semidirect |
| 18. #3362 | C22 | semidirect |
| 19. #3361 | C22 | semidirect |
| 20. #3333 | C22 | semidirect |
| 21. #3325 | C22 | semidirect |
| 24. #3305 | C22 | semidirect |
| 26. #3295 | C22 | semidirect |
| 29. #3238 | C22 | semidirect |
| 34. C2×#494 | C22 | semidirect |
| 37. C2×#486 | C22 | semidirect |
| 38. #2966 | C22 | semidirect |
| 41. #1709 | C22 | semidirect |
| 42. #1709 | C22 | semidirect |
| 43. #1709 | C22 | semidirect |
| 44. #1698 | C22 | semidirect |
| 45. #1698 | C22 | semidirect |
| 46. #1697 | C22 | semidirect |
| 47. #1697 | C22 | semidirect |
| 48. #1678 | C22 | semidirect |
| 49. #1678 | C22 | semidirect |
| 50. #1677 | C22 | semidirect |
| 51. #1677 | C22 | semidirect |
| 52. #1634 | C22 | semidirect |
| 53. #1634 | C22 | semidirect |
| 54. #1633 | C22 | semidirect |
| 55. #1633 | C22 | semidirect |
| 56. #1632 | C22 | semidirect |
| 57. #1632 | C22 | semidirect |
| 59. #1621 | C22 | semidirect |
| 61. #1620 | C22 | semidirect |
| 63. #1619 | C22 | semidirect |
| 64. #1591 | C22 | semidirect |
| 65. #1590 | C22 | semidirect |
| 66. #1589 | C22 | semidirect |
| 67. C8×Q16 | C22 | semidirect |
| 68. C8×SD16 | C22 | semidirect |
| 69. C8×D8 | C22 | semidirect |
| 70. #1568 | C22 | semidirect |
| 71. #1558 | C22 | semidirect |
| 72. #1555 | C22 | semidirect |
| 73. #1494 | C22 | semidirect |
| 74. C2×C82 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62552 | 2 |
| #20319 | 2 |
| #20308 | 2 |
| #20302 | 2 |
| #20003 | 2 |
| #19996 | 2 |
| #19925 | 2 |
| #19911 | 2 |
| C2×#1709 | 2 |
| #19362 | 2 |
| #18685 | 2 |
| #18682 | 2 |
| #17959 | 2 |