Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1723 conjugacy classes of subgroups.
The subgroup lattice has 536 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61807 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61582 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20301 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20239 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20163 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20027 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #19717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #19504 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #19431 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #18727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #18617 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #18529 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #17950 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #3548 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #3506 | C22 | 1 | 2 | yes | — |
| 16 | C2×D42 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3354 | C22 | 1 | 4 | yes | complemented |
| 18 | #3346 | — | 2 | 4 | no | — |
| 19 | #3334 | C22 | 1 | 4 | yes | complemented |
| 20 | #3330 | C22 | 1 | 4 | yes | complemented |
| 21 | #3325 | C22 | 1 | 4 | yes | — |
| 22 | #3325 | C22 | 1 | 4 | yes | — |
| 23 | #3324 | — | 2 | 4 | no | — |
| 24 | #3309 | — | 2 | 4 | no | — |
| 25 | #3303 | C22 | 1 | 4 | yes | complemented |
| 26 | #3274 | — | 2 | 4 | no | — |
| 27 | #3272 | C22 | 1 | 4 | yes | — |
| 28 | #3272 | C22 | 1 | 4 | yes | — |
| 29 | #3235 | C22 | 1 | 2 | yes | complemented |
| 30 | #3231 | C22 | 1 | 2 | yes | complemented |
| 31 | #3208 | C22 | 1 | 2 | yes | — |
| 32 | #3205 | C22 | 1 | 2 | yes | — |
| 33 | #3198 | — | 2 | 4 | no | — |
| 34 | #3194 | — | 2 | 4 | no | — |
| 35 | #3185 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #3138 | C22 | 1 | 1 | yes | characteristic |
| 37 | #3110 | C22 | 1 | 2 | yes | — |
| 38 | #3101 | C22 | 1 | 2 | yes | — |
| 39 | #3100 | C22 | 1 | 2 | yes | — |
| 40 | #3098 | — | 2 | 4 | no | — |
| 41 | #3003 | — | 2 | 4 | no | — |
| 42 | #2981 | C22 | 1 | 2 | yes | complemented |
| 43 | #2975 | C22 | 1 | 2 | yes | — |
| 44 | #1720 | C22 | 1 | 2 | yes | complemented |
| 45 | #1719 | C22 | 1 | 2 | yes | complemented |
| 46 | #1714 | C22 | 1 | 2 | yes | complemented |
| 47 | #1708 | C22 | 1 | 2 | yes | complemented |
| 48 | #1703 | C22 | 1 | 4 | yes | complemented |
| 49 | #1699 | C22 | 1 | 4 | yes | complemented |
| 50 | #1697 | C22 | 1 | 4 | yes | complemented |
| 51 | #1693 | C22 | 1 | 4 | yes | complemented |
| 52 | #1691 | C22 | 1 | 4 | yes | complemented |
| 53 | #1685 | C22 | 1 | 4 | yes | complemented |
| 54 | #1677 | C22 | 1 | 4 | yes | complemented |
| 55 | #1665 | C22 | 1 | 4 | yes | complemented |
| 56 | #1654 | C22 | 1 | 4 | yes | complemented |
| 57 | #1646 | C22 | 1 | 4 | yes | complemented |
| 58 | #1639 | C22 | 1 | 4 | yes | — |
| 59 | #1639 | C22 | 1 | 4 | yes | — |
| 60 | #1635 | C22 | 1 | 4 | yes | complemented |
| 61 | #1634 | C22 | 1 | 4 | yes | complemented |
| 62 | #1625 | C22 | 1 | 4 | yes | complemented |
| 63 | #1625 | C22 | 1 | 4 | yes | complemented |
| 64 | #1594 | C22 | 1 | 4 | yes | complemented |
| 65 | #1589 | C22 | 1 | 4 | yes | complemented |
| 66 | #1586 | C22 | 1 | 4 | yes | complemented |
| 67 | #1581 | C22 | 1 | 4 | yes | complemented |
| 68 | #1572 | C22 | 1 | 2 | yes | complemented |
| 69 | #1555 | C22 | 1 | 1 | yes | characteristic |
| 70 | #1554 | C22 | 1 | 2 | yes | complemented |
| 71 | #1544 | C22 | 1 | 1 | yes | characteristic, complemented |
| 72 | #1490 | C22 | 1 | 2 | yes | — |
| 73 | #1484 | C22 | 1 | 2 | yes | complemented |
| 74 | #1453 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | C23×D4 | — | 2 | 2 | no | — |
| 76 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 77 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 78 | #562 | — | 4 | 1 | no | — |
| 79 | #559 | — | 4 | 2 | no | — |
| 80 | #556 | — | 2 | 2 | no | — |
| 81 | #555 | C23 | 1 | 4 | yes | — |
| 82 | #554 | — | 2 | 2 | no | — |
| 83 | #553 | — | 2 | 4 | no | — |
| 84 | #550 | — | 2 | 2 | no | — |
| 85 | #550 | — | 2 | 2 | no | — |
| 86 | #547 | C23 | 1 | 4 | yes | — |
| 87 | #547 | C23 | 1 | 4 | yes | complemented |
| 88 | D42 | — | 2 | 4 | no | — |
| 89 | D42 | — | 4 | 1 | no | — |
| 90 | D42 | C23 | 1 | 4 | yes | — |
| 91 | #540 | — | 4 | 1 | no | — |
| 92 | #538 | — | 4 | 2 | no | — |
| 93 | #537 | — | 2 | 4 | no | — |
| 94 | #535 | — | 2 | 2 | no | — |
| 95 | #533 | C23 | 1 | 1 | yes | characteristic |
| 96 | #533 | C23 | 1 | 2 | yes | — |
| 97 | #532 | C23 | 1 | 2 | yes | — |
| 98 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 99 | #525 | — | 2 | 4 | no | — |
| 100 | C2×#121 | — | 2 | 2 | no | — |
| 101 | C2×#120 | — | 4 | 1 | no | — |
| 102 | #520 | — | 2 | 2 | no | — |
| 103 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 104 | #501 | — | 2 | 2 | no | — |
| 105 | #500 | C23 | 1 | 2 | yes | complemented |
| 106 | #498 | C23 | 1 | 2 | yes | complemented |
| 107 | #498 | C23 | 1 | 1 | yes | characteristic, complemented |
| 108 | #494 | C23 | 1 | 1 | yes | characteristic, complemented |
| 109 | #493 | — | 2 | 2 | no | — |
| 110 | #492 | C23 | 1 | 2 | yes | — |
| 111 | #492 | C23 | 1 | 2 | yes | — |
| 112 | #490 | — | 2 | 2 | no | — |
| 113 | #490 | — | 4 | 1 | no | — |
| 114 | #487 | C23 | 1 | 2 | yes | complemented |
| 115 | #487 | C23 | 1 | 2 | yes | complemented |
| 116 | #487 | C23 | 1 | 2 | yes | complemented |
| 117 | #486 | — | 2 | 2 | no | — |
| 118 | #486 | C23 | 1 | 2 | yes | — |
| 119 | #486 | C23 | 1 | 2 | yes | — |
| 120 | #486 | C23 | 1 | 2 | yes | — |
| 121 | #486 | C23 | 1 | 2 | yes | — |
| 122 | #485 | — | 2 | 4 | no | — |
| 123 | #485 | — | 2 | 4 | no | — |
| 124 | #484 | — | 2 | 2 | no | — |
| 125 | #484 | — | 2 | 4 | no | — |
| 126 | #483 | — | 2 | 2 | no | — |
| 127 | #482 | — | 2 | 4 | no | — |
| 128 | #482 | — | 2 | 4 | no | — |
| 129 | #482 | — | 2 | 4 | no | — |
| 130 | #482 | — | 2 | 4 | no | — |
| 131 | #481 | — | 2 | 4 | no | — |
| 132 | #480 | — | 2 | 4 | no | — |
| 133 | #480 | — | 2 | 4 | no | — |
| 134 | #480 | D4 | 1 | 4 | yes | — |
| 135 | #479 | — | 2 | 4 | no | — |
| 136 | #476 | C23 | 1 | 4 | yes | — |
| 137 | #476 | C23 | 1 | 4 | yes | complemented |
| 138 | #474 | D4 | 1 | 4 | yes | — |
| 139 | #474 | C23 | 1 | 4 | yes | — |
| 140 | #474 | C23 | 1 | 4 | yes | complemented |
| 141 | #470 | — | 4 | 1 | no | — |
| 142 | #469 | — | 2 | 4 | no | — |
| 143 | #469 | — | 2 | 4 | no | — |
| 144 | #469 | — | 2 | 4 | no | — |
| 145 | #468 | — | 2 | 4 | no | — |
| 146 | #468 | — | 2 | 4 | no | — |
| 147 | #468 | — | 2 | 4 | no | — |
| 148 | #466 | — | 2 | 4 | no | — |
| 149 | #465 | — | 2 | 4 | no | — |
| 150 | #461 | C23 | 1 | 4 | yes | — |
| 151 | #461 | C23 | 1 | 4 | yes | — |
| 152 | #460 | — | 2 | 4 | no | — |
| 153 | #459 | D4 | 1 | 4 | yes | — |
| 154 | #459 | C23 | 1 | 4 | yes | — |
| 155 | #459 | C23 | 1 | 4 | yes | — |
| 156 | #450 | — | 2 | 2 | no | — |
| 157 | #450 | — | 2 | 2 | no | — |
| 158 | #450 | — | 2 | 4 | no | — |
| 159 | #450 | — | 2 | 4 | no | — |
| 160 | #450 | — | 2 | 4 | no | — |
| 161 | #449 | — | 2 | 4 | no | — |
| 162 | #449 | — | 2 | 4 | no | — |
| 163 | #449 | — | 2 | 4 | no | — |
| 164 | #449 | — | 2 | 4 | no | — |
| 165 | #447 | — | 2 | 4 | no | — |
| 166 | #447 | — | 2 | 4 | no | — |
| 167 | #447 | — | 2 | 4 | no | — |
| 168 | #447 | D4 | 1 | 4 | yes | — |
| 169 | #441 | — | 4 | 1 | no | — |
| 170 | #440 | — | 2 | 4 | no | — |
| 171 | C4×SD16 | — | 2 | 4 | no | — |
| 172 | C4×D8 | C23 | 1 | 4 | yes | — |
| 173 | C4×D8 | C23 | 1 | 4 | yes | — |
| 174 | #436 | — | 2 | 4 | no | — |
| 175 | #436 | C23 | 1 | 4 | yes | — |
| 176 | #436 | C23 | 1 | 4 | yes | — |
| 177 | #436 | C23 | 1 | 4 | yes | complemented |
| 178 | #435 | — | 2 | 4 | no | — |
| 179 | C8×D4 | C23 | 1 | 4 | yes | complemented |
| 180 | #432 | C23 | 1 | 2 | yes | — |
| 181 | #431 | C23 | 1 | 2 | yes | — |
| 182 | #431 | C23 | 1 | 2 | yes | — |
| 183 | #428 | — | 2 | 4 | no | — |
| 184 | C2×#107 | — | 2 | 4 | no | — |
| 185 | #418 | — | 2 | 4 | no | — |
| 186 | #418 | — | 2 | 4 | no | — |
| 187 | #418 | — | 4 | 1 | no | — |
| 188 | #417 | — | 2 | 4 | no | — |
| 189 | #416 | — | 2 | 4 | no | — |
| 190 | #408 | — | 2 | 4 | no | — |
| 191 | #407 | — | 2 | 4 | no | — |
| 192 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 193 | #335 | C23 | 1 | 4 | yes | complemented |
| 194 | #334 | C23 | 1 | 4 | yes | complemented |
| 195 | #333 | C23 | 1 | 4 | yes | complemented |
| 196 | #332 | C23 | 1 | 4 | yes | complemented |
| 197 | #332 | C23 | 1 | 4 | yes | complemented |
| 198 | #331 | C23 | 1 | 4 | yes | — |
| 199 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 200 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 201 | D4⋊C8 | C23 | 1 | 4 | yes | complemented |
| 202 | D4⋊C8 | C23 | 1 | 4 | yes | complemented |
| 203 | #322 | C23 | 1 | 2 | yes | complemented |
| 204 | #322 | C23 | 1 | 1 | yes | characteristic, complemented |
| 205 | C82 | C23 | 1 | 1 | yes | characteristic, complemented |
| 206 | C25 | — | 4 | 1 | no | — |
| 207 | C2×#41 | — | 2 | 2 | no | — |
| 208 | C2×#41 | — | 2 | 4 | no | — |
| 209 | C2×#41 | — | 2 | 4 | no | — |
| 210 | C22×D4 | — | 2 | 4 | no | — |
| 211 | C22×D4 | — | 2 | 4 | no | — |
| 212 | C22×D4 | — | 2 | 2 | no | — |
| 213 | C22×D4 | — | 2 | 1 | no | — |
| 214 | C22×D4 | — | 4 | 4 | no | — |
| 215 | C22×D4 | — | 4 | 2 | no | — |
| 216 | C22×D4 | — | 8 | 8 | no | — |
| 217 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 218 | C23×C4 | — | 2 | 2 | no | — |
| 219 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 220 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 221 | C2×Q16 | — | 4 | 1 | no | — |
| 222 | C2×SD16 | — | 2 | 4 | no | — |
| 223 | C2×SD16 | — | 2 | 4 | no | — |
| 224 | C2×SD16 | — | 2 | 4 | no | — |
| 225 | C2×SD16 | — | 2 | 4 | no | — |
| 226 | C2×D8 | — | 2 | 4 | no | — |
| 227 | C2×D8 | — | 2 | 4 | no | — |
| 228 | C2×D8 | C2×D4 | 1 | 4 | yes | — |
| 229 | C2×D8 | C2×D4 | 1 | 4 | yes | — |
| 230 | C2×M16 | — | 2 | 1 | no | — |
| 231 | C2×M16 | — | 2 | 4 | no | — |
| 232 | C2×M16 | — | 2 | 4 | no | — |
| 233 | C2×M16 | — | 2 | 4 | no | — |
| 234 | C22×C8 | — | 2 | 4 | no | — |
| 235 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 236 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 237 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 238 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 239 | #127 | — | 2 | 2 | no | — |
| 240 | #127 | — | 2 | 1 | no | — |
| 241 | #127 | — | 4 | 2 | no | — |
| 242 | #127 | — | 4 | 1 | no | — |
| 243 | #127 | C2×D4 | 1 | 2 | yes | — |
| 244 | #127 | C24 | 1 | 2 | yes | — |
| 245 | #126 | — | 4 | 4 | no | — |
| 246 | #125 | — | 2 | 2 | no | — |
| 247 | #125 | — | 2 | 1 | no | — |
| 248 | #125 | — | 4 | 1 | no | — |
| 249 | #124 | — | 2 | 2 | no | — |
| 250 | #124 | — | 4 | 4 | no | — |
| 251 | #124 | — | 4 | 2 | no | — |
| 252 | #123 | — | 4 | 4 | no | — |
| 253 | #123 | — | 4 | 4 | no | — |
| 254 | #123 | — | 4 | 4 | no | — |
| 255 | C22⋊Q8 | — | 2 | 2 | no | — |
| 256 | C22⋊Q8 | — | 2 | 2 | no | — |
| 257 | C22⋊Q8 | — | 2 | 2 | no | — |
| 258 | C22⋊Q8 | — | 2 | 4 | no | — |
| 259 | C22⋊Q8 | — | 2 | 4 | no | — |
| 260 | C22⋊Q8 | — | 4 | 4 | no | — |
| 261 | #121 | — | 2 | 2 | no | — |
| 262 | #121 | — | 2 | 4 | no | — |
| 263 | #121 | — | 2 | 4 | no | — |
| 264 | #121 | — | 2 | 4 | no | — |
| 265 | #121 | — | 2 | 4 | no | — |
| 266 | #121 | — | 2 | 4 | no | — |
| 267 | #121 | — | 2 | 4 | no | — |
| 268 | #121 | — | 4 | 4 | no | — |
| 269 | #121 | — | 4 | 4 | no | — |
| 270 | #121 | — | 4 | 4 | no | — |
| 271 | #121 | — | 4 | 4 | no | — |
| 272 | #121 | C2×D4 | 1 | 4 | yes | — |
| 273 | #120 | — | 4 | 4 | no | — |
| 274 | #120 | — | 4 | 4 | no | — |
| 275 | #120 | — | 4 | 4 | no | — |
| 276 | C4×Q8 | — | 2 | 2 | no | — |
| 277 | C4×Q8 | — | 2 | 2 | no | — |
| 278 | C4×Q8 | — | 2 | 2 | no | — |
| 279 | C4×Q8 | — | 4 | 2 | no | — |
| 280 | C4×D4 | — | 2 | 2 | no | — |
| 281 | C4×D4 | — | 2 | 2 | no | — |
| 282 | C4×D4 | — | 2 | 2 | no | — |
| 283 | C4×D4 | — | 4 | 4 | no | — |
| 284 | C4×D4 | — | 4 | 2 | no | — |
| 285 | C4×D4 | — | 4 | 2 | no | — |
| 286 | C4×D4 | — | 4 | 4 | no | — |
| 287 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 288 | C4×D4 | C24 | 1 | 4 | yes | — |
| 289 | C4×D4 | C24 | 1 | 4 | yes | — |
| 290 | #117 | — | 2 | 2 | no | — |
| 291 | #117 | — | 2 | 1 | no | — |
| 292 | #117 | — | 2 | 4 | no | — |
| 293 | #117 | — | 2 | 4 | no | — |
| 294 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 295 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 296 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 297 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 298 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 299 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 300 | #107 | — | 2 | 4 | no | — |
| 301 | #107 | — | 2 | 4 | no | — |
| 302 | #107 | — | 2 | 4 | no | — |
| 303 | #107 | C2×D4 | 1 | 4 | yes | — |
| 304 | #107 | C2×D4 | 1 | 4 | yes | — |
| 305 | #106 | — | 2 | 4 | no | — |
| 306 | #106 | — | 2 | 4 | no | — |
| 307 | #106 | — | 2 | 4 | no | — |
| 308 | #106 | — | 4 | 1 | no | — |
| 309 | C4⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 310 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 311 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 312 | #103 | — | 2 | 4 | no | — |
| 313 | #103 | — | 2 | 4 | no | — |
| 314 | #103 | — | 2 | 4 | no | — |
| 315 | #103 | — | 2 | 4 | no | — |
| 316 | #103 | — | 4 | 2 | no | — |
| 317 | #102 | — | 2 | 4 | no | — |
| 318 | #102 | — | 2 | 4 | no | — |
| 319 | #102 | — | 2 | 4 | no | — |
| 320 | #102 | — | 2 | 4 | no | — |
| 321 | #102 | — | 2 | 4 | no | — |
| 322 | #102 | — | 2 | 4 | no | — |
| 323 | #102 | — | 2 | 4 | no | — |
| 324 | #102 | — | 2 | 4 | no | — |
| 325 | #102 | — | 4 | 2 | no | — |
| 326 | #102 | — | 4 | 2 | no | — |
| 327 | #102 | C2×D4 | 1 | 4 | yes | — |
| 328 | #102 | C2×D4 | 1 | 4 | yes | — |
| 329 | #102 | C2×D4 | 1 | 4 | yes | — |
| 330 | #102 | C2×D4 | 1 | 4 | yes | — |
| 331 | C22⋊C8 | — | 2 | 2 | no | — |
| 332 | C22⋊C8 | — | 2 | 2 | no | — |
| 333 | C22⋊C8 | — | 2 | 4 | no | — |
| 334 | C22⋊C8 | — | 2 | 4 | no | — |
| 335 | C22⋊C8 | — | 2 | 4 | no | — |
| 336 | C22⋊C8 | — | 2 | 4 | no | — |
| 337 | C22⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 338 | #97 | — | 2 | 2 | no | — |
| 339 | #97 | — | 2 | 1 | no | — |
| 340 | C4×C8 | — | 2 | 2 | no | — |
| 341 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 342 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 343 | C4×C8 | C24 | 1 | 2 | yes | — |
| 344 | C4×C8 | C24 | 1 | 2 | yes | — |
| 345 | C24 | — | 2 | 2 | no | — |
| 346 | C24 | — | 4 | 4 | no | — |
| 347 | C24 | — | 4 | 1 | no | — |
| 348 | C24 | — | 8 | 8 | no | — |
| 349 | C24 | — | 16 | 2 | no | — |
| 350 | #41 | — | 8 | 4 | no | — |
| 351 | #41 | — | 8 | 4 | no | — |
| 352 | #41 | — | 8 | 4 | no | — |
| 353 | #41 | — | 8 | 4 | no | — |
| 354 | #41 | — | 8 | 4 | no | — |
| 355 | C2×Q8 | — | 2 | 2 | no | — |
| 356 | C2×Q8 | — | 2 | 2 | no | — |
| 357 | C2×Q8 | — | 2 | 2 | no | — |
| 358 | C2×Q8 | — | 2 | 2 | no | — |
| 359 | C2×D4 | — | 2 | 4 | no | — |
| 360 | C2×D4 | — | 2 | 2 | no | — |
| 361 | C2×D4 | — | 2 | 2 | no | — |
| 362 | C2×D4 | — | 2 | 2 | no | — |
| 363 | C2×D4 | — | 2 | 2 | no | — |
| 364 | C2×D4 | — | 2 | 2 | no | — |
| 365 | C2×D4 | — | 2 | 2 | no | — |
| 366 | C2×D4 | — | 4 | 4 | no | — |
| 367 | C2×D4 | — | 4 | 4 | no | — |
| 368 | C2×D4 | — | 4 | 4 | no | — |
| 369 | C2×D4 | — | 4 | 8 | no | — |
| 370 | C2×D4 | — | 4 | 8 | no | — |
| 371 | C2×D4 | — | 4 | 4 | no | — |
| 372 | C2×D4 | — | 4 | 4 | no | — |
| 373 | C2×D4 | — | 4 | 4 | no | — |
| 374 | C2×D4 | — | 4 | 2 | no | — |
| 375 | C2×D4 | — | 4 | 1 | no | — |
| 376 | C2×D4 | — | 8 | 4 | no | — |
| 377 | C2×D4 | — | 8 | 4 | no | — |
| 378 | C2×D4 | — | 8 | 4 | no | — |
| 379 | C2×D4 | — | 8 | 2 | no | — |
| 380 | C2×D4 | — | 8 | 16 | no | — |
| 381 | C2×D4 | — | 8 | 8 | no | — |
| 382 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 383 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 384 | C22×C4 | — | 2 | 2 | no | — |
| 385 | C22×C4 | — | 2 | 4 | no | — |
| 386 | C22×C4 | — | 2 | 4 | no | — |
| 387 | C22×C4 | — | 2 | 4 | no | — |
| 388 | C22×C4 | — | 4 | 4 | no | — |
| 389 | C22×C4 | — | 4 | 4 | no | — |
| 390 | C22×C4 | — | 8 | 4 | no | — |
| 391 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 392 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 393 | Q16 | — | 8 | 2 | no | — |
| 394 | SD16 | — | 4 | 8 | no | — |
| 395 | SD16 | — | 8 | 4 | no | — |
| 396 | SD16 | — | 8 | 4 | no | — |
| 397 | SD16 | — | 8 | 4 | no | — |
| 398 | D8 | — | 4 | 4 | no | — |
| 399 | D8 | — | 4 | 4 | no | — |
| 400 | D8 | — | 8 | 4 | no | — |
| 401 | D8 | — | 8 | 4 | no | — |
| 402 | M16 | — | 8 | 4 | no | — |
| 403 | M16 | — | 8 | 4 | no | — |
| 404 | M16 | — | 8 | 4 | no | — |
| 405 | M16 | — | 8 | 1 | no | — |
| 406 | C2×C8 | — | 2 | 4 | no | — |
| 407 | C2×C8 | — | 2 | 4 | no | — |
| 408 | C2×C8 | — | 2 | 1 | no | — |
| 409 | C2×C8 | — | 2 | 1 | no | — |
| 410 | C2×C8 | — | 8 | 4 | no | — |
| 411 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 412 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 413 | C4⋊C4 | — | 2 | 2 | no | — |
| 414 | C4⋊C4 | — | 2 | 2 | no | — |
| 415 | C4⋊C4 | — | 2 | 2 | no | — |
| 416 | C4⋊C4 | — | 2 | 2 | no | — |
| 417 | C4⋊C4 | — | 2 | 2 | no | — |
| 418 | C4⋊C4 | — | 2 | 2 | no | — |
| 419 | C4⋊C4 | — | 2 | 2 | no | — |
| 420 | C4⋊C4 | — | 2 | 2 | no | — |
| 421 | C4⋊C4 | — | 4 | 4 | no | — |
| 422 | C4⋊C4 | — | 4 | 4 | no | — |
| 423 | C4⋊C4 | — | 4 | 2 | no | — |
| 424 | C4⋊C4 | — | 4 | 2 | no | — |
| 425 | C4⋊C4 | — | 4 | 2 | no | — |
| 426 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 427 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 428 | C22⋊C4 | — | 2 | 4 | no | — |
| 429 | C22⋊C4 | — | 2 | 4 | no | — |
| 430 | C22⋊C4 | — | 2 | 4 | no | — |
| 431 | C22⋊C4 | — | 2 | 4 | no | — |
| 432 | C22⋊C4 | — | 4 | 4 | no | — |
| 433 | C22⋊C4 | — | 4 | 4 | no | — |
| 434 | C22⋊C4 | — | 4 | 4 | no | — |
| 435 | C22⋊C4 | — | 4 | 4 | no | — |
| 436 | C22⋊C4 | — | 4 | 4 | no | — |
| 437 | C22⋊C4 | — | 4 | 2 | no | — |
| 438 | C22⋊C4 | — | 4 | 1 | no | — |
| 439 | C42 | — | 4 | 4 | no | — |
| 440 | C42 | — | 4 | 1 | no | — |
| 441 | C42 | — | 4 | 2 | no | — |
| 442 | C42 | C22×D4 | 1 | 2 | yes | — |
| 443 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 444 | C42 | C25 | 1 | 1 | yes | characteristic |
| 445 | C23 | — | 2 | 4 | no | — |
| 446 | C23 | — | 2 | 4 | no | — |
| 447 | C23 | — | 4 | 4 | no | — |
| 448 | C23 | — | 4 | 2 | no | — |
| 449 | C23 | — | 8 | 2 | no | — |
| 450 | C23 | — | 8 | 2 | no | — |
| 451 | C23 | — | 8 | 4 | no | — |
| 452 | C23 | — | 8 | 2 | no | — |
| 453 | C23 | — | 8 | 8 | no | — |
| 454 | C23 | — | 8 | 8 | no | — |
| 455 | C23 | — | 16 | 4 | no | — |
| 456 | C23 | — | 16 | 16 | no | — |
| 457 | C23 | D42 | 1 | 1 | yes | characteristic |
| 458 | Q8 | — | 4 | 4 | no | — |
| 459 | Q8 | — | 4 | 4 | no | — |
| 460 | Q8 | — | 8 | 2 | no | — |
| 461 | Q8 | — | 8 | 2 | no | — |
| 462 | D4 | — | 2 | 4 | no | — |
| 463 | D4 | — | 2 | 4 | no | — |
| 464 | D4 | — | 2 | 4 | no | — |
| 465 | D4 | — | 2 | 4 | no | — |
| 466 | D4 | — | 4 | 4 | no | — |
| 467 | D4 | — | 4 | 4 | no | — |
| 468 | D4 | — | 4 | 4 | no | — |
| 469 | D4 | — | 8 | 2 | no | — |
| 470 | D4 | — | 8 | 2 | no | — |
| 471 | D4 | — | 8 | 2 | no | — |
| 472 | D4 | — | 8 | 4 | no | — |
| 473 | D4 | — | 8 | 4 | no | — |
| 474 | D4 | — | 8 | 8 | no | — |
| 475 | D4 | — | 8 | 8 | no | — |
| 476 | D4 | — | 16 | 1 | no | — |
| 477 | D4 | — | 16 | 4 | no | — |
| 478 | D4 | — | 16 | 4 | no | — |
| 479 | D4 | — | 16 | 4 | no | — |
| 480 | C2×C4 | — | 2 | 4 | no | — |
| 481 | C2×C4 | — | 2 | 4 | no | — |
| 482 | C2×C4 | — | 2 | 4 | no | — |
| 483 | C2×C4 | — | 4 | 1 | no | — |
| 484 | C2×C4 | — | 4 | 4 | no | — |
| 485 | C2×C4 | — | 4 | 4 | no | — |
| 486 | C2×C4 | — | 4 | 4 | no | — |
| 487 | C2×C4 | — | 4 | 4 | no | — |
| 488 | C2×C4 | — | 4 | 2 | no | — |
| 489 | C2×C4 | — | 4 | 2 | no | — |
| 490 | C2×C4 | — | 4 | 2 | no | — |
| 491 | C2×C4 | — | 8 | 4 | no | — |
| 492 | C2×C4 | — | 8 | 2 | no | — |
| 493 | C2×C4 | — | 16 | 4 | no | — |
| 494 | C2×C4 | — | 16 | 4 | no | — |
| 495 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 496 | C2×C4 | D42 | 1 | 2 | yes | — |
| 497 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 498 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 499 | C8 | — | 2 | 4 | no | — |
| 500 | C8 | — | 2 | 4 | no | — |
| 501 | C8 | — | 4 | 1 | no | — |
| 502 | C8 | — | 4 | 1 | no | — |
| 503 | C8 | — | 4 | 4 | no | — |
| 504 | C8 | — | 4 | 4 | no | — |
| 505 | C22 | — | 2 | 2 | no | — |
| 506 | C22 | — | 2 | 1 | no | — |
| 507 | C22 | — | 4 | 4 | no | — |
| 508 | C22 | — | 4 | 4 | no | — |
| 509 | C22 | — | 4 | 4 | no | — |
| 510 | C22 | — | 4 | 4 | no | — |
| 511 | C22 | — | 4 | 4 | no | — |
| 512 | C22 | — | 4 | 4 | no | — |
| 513 | C22 | — | 8 | 8 | no | — |
| 514 | C22 | — | 8 | 2 | no | — |
| 515 | C22 | — | 8 | 2 | no | — |
| 516 | C22 | — | 8 | 2 | no | — |
| 517 | C22 | — | 16 | 4 | no | — |
| 518 | C22 | — | 16 | 16 | no | — |
| 519 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 520 | C4 | — | 2 | 2 | no | — |
| 521 | C4 | — | 2 | 1 | no | — |
| 522 | C4 | — | 2 | 1 | no | — |
| 523 | C4 | — | 4 | 4 | no | — |
| 524 | C4 | — | 4 | 4 | no | — |
| 525 | C4 | — | 8 | 2 | no | — |
| 526 | C4 | — | 8 | 2 | no | — |
| 527 | C4 | — | 8 | 2 | no | — |
| 528 | C4 | #3585 | 1 | 4 | yes | — |
| 529 | C2 | — | 4 | 1 | no | — |
| 530 | C2 | — | 8 | 4 | no | — |
| 531 | C2 | — | 8 | 4 | no | — |
| 532 | C2 | — | 16 | 2 | no | — |
| 533 | C2 | #61058 | 1 | 2 | yes | — |
| 534 | C2 | #61109 | 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. #61807 | C2 | semidirect |
| 2. #61582 | C2 | semidirect |
| 3. #20301 | C2 | semidirect |
| 4. #20239 | C2 | semidirect |
| 5. #20163 | C2 | semidirect |
| 6. #20027 | C2 | semidirect |
| 7. #19717 | C2 | semidirect |
| 8. #19504 | C2 | semidirect |
| 9. #19431 | C2 | semidirect |
| 10. #18727 | C2 | semidirect |
| 11. #18617 | C2 | semidirect |
| 12. #18529 | C2 | semidirect |
| 13. #17950 | C2 | semidirect |
| 14. #3548 | C22 | semidirect |
| 17. #3354 | C22 | semidirect |
| 19. #3334 | C22 | semidirect |
| 20. #3330 | C22 | semidirect |
| 25. #3303 | C22 | semidirect |
| 29. #3235 | C22 | semidirect |
| 30. #3231 | C22 | semidirect |
| 35. #3185 | C22 | semidirect |
| 42. #2981 | C22 | semidirect |
| 44. #1720 | C22 | semidirect |
| 45. #1719 | C22 | semidirect |
| 46. #1714 | C22 | semidirect |
| 47. #1708 | C22 | semidirect |
| 48. #1703 | C22 | semidirect |
| 49. #1699 | C22 | semidirect |
| 50. #1697 | C22 | semidirect |
| 51. #1693 | C22 | semidirect |
| 52. #1691 | C22 | semidirect |
| 53. #1685 | C22 | semidirect |
| 54. #1677 | C22 | semidirect |
| 55. #1665 | C22 | semidirect |
| 56. #1654 | C22 | semidirect |
| 57. #1646 | C22 | semidirect |
| 60. #1635 | C22 | semidirect |
| 61. #1634 | C22 | semidirect |
| 62. #1625 | C22 | semidirect |
| 63. #1625 | C22 | semidirect |
| 64. #1594 | C22 | semidirect |
| 65. #1589 | C22 | semidirect |
| 66. #1586 | C22 | semidirect |
| 67. #1581 | C22 | semidirect |
| 68. #1572 | C22 | semidirect |
| 70. #1554 | C22 | semidirect |
| 71. #1544 | C22 | semidirect |
| 73. #1484 | C22 | semidirect |
| 74. #1453 | C22 | semidirect |
| 87. #547 | C23 | semidirect |
| 105. #500 | C23 | semidirect |
| 106. #498 | C23 | semidirect |
| 107. #498 | C23 | semidirect |
| 108. #494 | C23 | semidirect |
| 114. #487 | C23 | semidirect |
| 115. #487 | C23 | semidirect |
| 116. #487 | C23 | semidirect |
| 137. #476 | C23 | semidirect |
| 140. #474 | C23 | semidirect |
| 177. #436 | C23 | semidirect |
| 179. C8×D4 | C23 | semidirect |
| 193. #335 | C23 | semidirect |
| 194. #334 | C23 | semidirect |
| 195. #333 | C23 | semidirect |
| 196. #332 | C23 | semidirect |
| 197. #332 | C23 | semidirect |
| 201. D4⋊C8 | C23 | semidirect |
| 202. D4⋊C8 | C23 | semidirect |
| 203. #322 | C23 | semidirect |
| 204. #322 | C23 | semidirect |
| 205. C82 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61807 | 2 |
| #61582 | 2 |
| #20301 | 2 |
| #20239 | 2 |
| #20163 | 2 |
| #20027 | 2 |
| #19717 | 2 |
| #19504 | 2 |
| #19431 | 2 |
| #18727 | 2 |
| #18617 | 2 |
| #18529 | 2 |
| #17950 | 2 |