Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1607 conjugacy classes of subgroups.
The subgroup lattice has 456 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62373 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62332 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20308 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20006 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #19975 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #19937 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #19909 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #19603 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #19344 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #19332 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #18687 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #17958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #17956 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #3548 | C22 | 1 | 4 | yes | — |
| 15 | #3391 | — | 2 | 2 | no | — |
| 16 | #3391 | C22 | 1 | 4 | yes | — |
| 17 | #3380 | — | 2 | 2 | no | — |
| 18 | #3380 | C22 | 1 | 4 | yes | — |
| 19 | #3366 | — | 2 | 4 | no | — |
| 20 | #3366 | C22 | 1 | 8 | yes | — |
| 21 | #3338 | C22 | 1 | 4 | yes | — |
| 22 | #3334 | — | 2 | 2 | no | — |
| 23 | #3333 | C22 | 1 | 8 | yes | — |
| 24 | #3330 | — | 2 | 4 | no | — |
| 25 | #3287 | C22 | 1 | 4 | yes | — |
| 26 | #3283 | — | 2 | 2 | no | — |
| 27 | #3259 | — | 2 | 4 | no | — |
| 28 | #3254 | C22 | 1 | 4 | yes | — |
| 29 | #3253 | C22 | 1 | 4 | yes | — |
| 30 | #3203 | — | 2 | 4 | no | — |
| 31 | #3176 | — | 2 | 4 | no | — |
| 32 | #3170 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3169 | C22 | 1 | 2 | yes | — |
| 34 | #3169 | C22 | 1 | 2 | yes | — |
| 35 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 36 | #3147 | C22 | 1 | 2 | yes | — |
| 37 | #3061 | — | 2 | 4 | no | — |
| 38 | #2960 | C22 | 1 | 2 | yes | — |
| 39 | #2931 | C22 | 1 | 2 | yes | — |
| 40 | #1713 | C22 | 1 | 1 | yes | characteristic |
| 41 | #1712 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1709 | C22 | 1 | 2 | yes | — |
| 43 | #1706 | C22 | 1 | 2 | yes | — |
| 44 | #1706 | C22 | 1 | 2 | yes | — |
| 45 | #1698 | C22 | 1 | 8 | yes | — |
| 46 | #1697 | C22 | 1 | 8 | yes | — |
| 47 | #1676 | C22 | 1 | 4 | yes | — |
| 48 | #1675 | C22 | 1 | 4 | yes | — |
| 49 | #1668 | C22 | 1 | 4 | yes | — |
| 50 | #1667 | C22 | 1 | 4 | yes | — |
| 51 | #1632 | C22 | 1 | 8 | yes | — |
| 52 | #1631 | C22 | 1 | 8 | yes | — |
| 53 | #1622 | C22 | 1 | 8 | yes | — |
| 54 | #1621 | C22 | 1 | 8 | yes | — |
| 55 | #1591 | C22 | 1 | 2 | yes | — |
| 56 | #1591 | C22 | 1 | 2 | yes | — |
| 57 | #1589 | C22 | 1 | 2 | yes | — |
| 58 | #1589 | C22 | 1 | 2 | yes | — |
| 59 | C8×Q16 | C22 | 1 | 2 | yes | — |
| 60 | C8×Q16 | C22 | 1 | 2 | yes | — |
| 61 | C8×D8 | C22 | 1 | 2 | yes | — |
| 62 | C8×D8 | C22 | 1 | 2 | yes | — |
| 63 | #1567 | C22 | 1 | 1 | yes | characteristic |
| 64 | #1567 | C22 | 1 | 1 | yes | characteristic |
| 65 | #1560 | C22 | 1 | 4 | yes | — |
| 66 | #1493 | C22 | 1 | 2 | yes | — |
| 67 | #1492 | C22 | 1 | 2 | yes | — |
| 68 | C2×C82 | C22 | 1 | 1 | yes | characteristic |
| 69 | C2×#135 | — | 2 | 4 | no | — |
| 70 | C2×#135 | — | 4 | 2 | no | — |
| 71 | C2×#131 | — | 2 | 2 | no | — |
| 72 | #562 | — | 4 | 4 | no | — |
| 73 | #554 | — | 2 | 4 | no | — |
| 74 | #554 | C23 | 1 | 8 | yes | — |
| 75 | #550 | — | 2 | 4 | no | — |
| 76 | #550 | C23 | 1 | 8 | yes | — |
| 77 | #547 | — | 2 | 4 | no | — |
| 78 | #547 | — | 2 | 4 | no | — |
| 79 | #540 | — | 2 | 8 | no | — |
| 80 | #537 | — | 2 | 8 | no | — |
| 81 | #537 | — | 4 | 4 | no | — |
| 82 | #533 | C23 | 1 | 2 | yes | — |
| 83 | #532 | C23 | 1 | 4 | yes | — |
| 84 | #532 | C23 | 1 | 2 | yes | — |
| 85 | #500 | D4 | 1 | 1 | yes | characteristic |
| 86 | #500 | D4 | 1 | 1 | yes | characteristic |
| 87 | #500 | C23 | 1 | 2 | yes | — |
| 88 | #500 | C23 | 1 | 2 | yes | — |
| 89 | #499 | — | 2 | 4 | no | — |
| 90 | #495 | — | 4 | 2 | no | — |
| 91 | #494 | D4 | 1 | 1 | yes | characteristic |
| 92 | #494 | C23 | 1 | 2 | yes | — |
| 93 | #493 | — | 2 | 4 | no | — |
| 94 | #493 | D4 | 1 | 1 | yes | characteristic |
| 95 | #493 | C23 | 1 | 2 | yes | — |
| 96 | #493 | C23 | 1 | 2 | yes | — |
| 97 | #493 | C23 | 1 | 2 | yes | — |
| 98 | #492 | C23 | 1 | 4 | yes | — |
| 99 | #490 | — | 2 | 8 | no | — |
| 100 | #487 | D4 | 1 | 2 | yes | — |
| 101 | #486 | D4 | 1 | 2 | yes | — |
| 102 | #486 | C23 | 1 | 4 | yes | — |
| 103 | #486 | C23 | 1 | 4 | yes | — |
| 104 | #484 | — | 2 | 8 | no | — |
| 105 | #480 | — | 2 | 8 | no | — |
| 106 | #478 | — | 2 | 8 | no | — |
| 107 | #478 | — | 2 | 8 | no | — |
| 108 | #477 | C23 | 1 | 8 | yes | — |
| 109 | #476 | — | 2 | 4 | no | — |
| 110 | #476 | C23 | 1 | 8 | yes | — |
| 111 | #474 | — | 2 | 4 | no | — |
| 112 | #469 | — | 2 | 8 | no | — |
| 113 | #468 | — | 2 | 8 | no | — |
| 114 | #468 | — | 2 | 8 | no | — |
| 115 | #467 | — | 2 | 4 | no | — |
| 116 | #467 | D4 | 1 | 2 | yes | — |
| 117 | #467 | D4 | 1 | 2 | yes | — |
| 118 | #466 | — | 2 | 2 | no | — |
| 119 | #466 | — | 2 | 2 | no | — |
| 120 | #466 | — | 2 | 2 | no | — |
| 121 | #466 | — | 2 | 2 | no | — |
| 122 | #466 | — | 2 | 4 | no | — |
| 123 | #466 | D4 | 1 | 2 | yes | — |
| 124 | #466 | D4 | 1 | 2 | yes | — |
| 125 | #461 | — | 2 | 4 | no | — |
| 126 | #460 | C23 | 1 | 8 | yes | — |
| 127 | #459 | — | 2 | 8 | no | — |
| 128 | #459 | — | 2 | 4 | no | — |
| 129 | #459 | — | 2 | 8 | no | — |
| 130 | #459 | C23 | 1 | 8 | yes | — |
| 131 | #452 | — | 2 | 8 | no | — |
| 132 | #449 | — | 2 | 8 | no | — |
| 133 | #446 | — | 2 | 2 | no | — |
| 134 | #446 | C23 | 1 | 4 | yes | — |
| 135 | C8×Q8 | — | 2 | 2 | no | — |
| 136 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 137 | #442 | — | 2 | 8 | no | — |
| 138 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 139 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 140 | C4×D8 | — | 2 | 4 | no | — |
| 141 | C4×D8 | — | 2 | 4 | no | — |
| 142 | C4×D8 | — | 2 | 2 | no | — |
| 143 | C4×D8 | — | 2 | 2 | no | — |
| 144 | C4×D8 | — | 2 | 2 | no | — |
| 145 | C4×D8 | — | 2 | 2 | no | — |
| 146 | C4×D8 | C23 | 1 | 2 | yes | — |
| 147 | C4×D8 | C23 | 1 | 2 | yes | — |
| 148 | #436 | — | 2 | 2 | no | — |
| 149 | #436 | C23 | 1 | 4 | yes | — |
| 150 | C8×D4 | — | 2 | 2 | no | — |
| 151 | C8×D4 | C23 | 1 | 4 | yes | — |
| 152 | C2×#107 | — | 2 | 4 | no | — |
| 153 | #424 | — | 2 | 2 | no | — |
| 154 | #423 | C23 | 1 | 2 | yes | — |
| 155 | #423 | C23 | 1 | 2 | yes | — |
| 156 | #417 | — | 2 | 8 | no | — |
| 157 | #408 | — | 2 | 2 | no | — |
| 158 | #405 | — | 2 | 2 | no | — |
| 159 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 162 | #335 | C23 | 1 | 2 | yes | — |
| 163 | #335 | C23 | 1 | 2 | yes | — |
| 164 | #335 | C23 | 1 | 2 | yes | — |
| 165 | #335 | C23 | 1 | 2 | yes | — |
| 166 | #333 | C23 | 1 | 8 | yes | — |
| 167 | #331 | C23 | 1 | 8 | yes | — |
| 168 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 169 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 170 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 171 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 172 | C82 | C23 | 1 | 1 | yes | characteristic |
| 173 | C82 | C23 | 1 | 1 | yes | characteristic |
| 174 | C82 | C23 | 1 | 1 | yes | characteristic |
| 175 | C82 | C23 | 1 | 1 | yes | characteristic |
| 176 | C2×#41 | — | 2 | 2 | no | — |
| 177 | C2×#41 | — | 2 | 8 | no | — |
| 178 | C2×#41 | — | 2 | 4 | no | — |
| 179 | C2×#41 | — | 4 | 4 | no | — |
| 180 | #135 | — | 8 | 8 | no | — |
| 181 | #135 | — | 8 | 8 | no | — |
| 182 | C2×Q16 | — | 4 | 2 | no | — |
| 183 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 184 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 185 | C2×SD16 | — | 2 | 8 | no | — |
| 186 | C2×SD16 | — | 4 | 4 | no | — |
| 187 | C2×D8 | — | 2 | 8 | no | — |
| 188 | C2×D8 | — | 2 | 2 | no | — |
| 189 | C2×D8 | — | 2 | 2 | no | — |
| 190 | C2×D8 | — | 2 | 2 | no | — |
| 191 | C2×D8 | — | 2 | 2 | no | — |
| 192 | C2×D8 | — | 4 | 2 | no | — |
| 193 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 194 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 195 | #131 | — | 8 | 4 | no | — |
| 196 | C2×M16 | — | 2 | 2 | no | — |
| 197 | C2×M16 | — | 2 | 2 | no | — |
| 198 | C2×M16 | — | 2 | 4 | no | — |
| 199 | C22×C8 | — | 2 | 1 | no | — |
| 200 | C22×C8 | — | 2 | 4 | no | — |
| 201 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 206 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 207 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 208 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 209 | #127 | — | 2 | 8 | no | — |
| 210 | #127 | C2×D4 | 1 | 2 | yes | — |
| 211 | #127 | C24 | 1 | 4 | yes | — |
| 212 | #125 | — | 2 | 8 | no | — |
| 213 | #125 | — | 2 | 2 | no | — |
| 214 | #124 | — | 2 | 2 | no | — |
| 215 | #124 | — | 2 | 4 | no | — |
| 216 | #123 | — | 4 | 8 | no | — |
| 217 | #123 | — | 4 | 8 | no | — |
| 218 | C22⋊Q8 | — | 2 | 2 | no | — |
| 219 | C22⋊Q8 | — | 2 | 8 | no | — |
| 220 | C22⋊Q8 | — | 4 | 8 | no | — |
| 221 | C22⋊Q8 | — | 4 | 8 | no | — |
| 222 | C22⋊Q8 | — | 4 | 4 | no | — |
| 223 | C22⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 224 | #121 | — | 2 | 2 | no | — |
| 225 | #121 | — | 2 | 4 | no | — |
| 226 | #121 | — | 2 | 4 | no | — |
| 227 | #121 | — | 2 | 8 | no | — |
| 228 | #121 | — | 4 | 8 | no | — |
| 229 | #121 | — | 4 | 8 | no | — |
| 230 | #121 | — | 4 | 8 | no | — |
| 231 | #121 | — | 4 | 8 | no | — |
| 232 | #121 | — | 4 | 4 | no | — |
| 233 | #121 | C2×D4 | 1 | 4 | yes | — |
| 234 | C4×Q8 | — | 2 | 2 | no | — |
| 235 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 236 | C4×D4 | — | 2 | 8 | no | — |
| 237 | C4×D4 | — | 2 | 8 | no | — |
| 238 | C4×D4 | — | 2 | 2 | no | — |
| 239 | C4×D4 | — | 2 | 4 | no | — |
| 240 | C4×D4 | — | 2 | 4 | no | — |
| 241 | C4×D4 | C24 | 1 | 4 | yes | — |
| 242 | #117 | — | 2 | 2 | no | — |
| 243 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 244 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 245 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 246 | #107 | — | 2 | 2 | no | — |
| 247 | #107 | — | 2 | 2 | no | — |
| 248 | #107 | — | 2 | 2 | no | — |
| 249 | #107 | — | 2 | 2 | no | — |
| 250 | #107 | — | 2 | 8 | no | — |
| 251 | #107 | C2×D4 | 1 | 2 | yes | — |
| 252 | #107 | C2×D4 | 1 | 2 | yes | — |
| 253 | #107 | C2×D4 | 1 | 2 | yes | — |
| 254 | #107 | C2×D4 | 1 | 2 | yes | — |
| 255 | #106 | — | 2 | 8 | no | — |
| 256 | C4⋊C8 | — | 2 | 4 | no | — |
| 257 | C4⋊C8 | — | 2 | 4 | no | — |
| 258 | C4⋊C8 | — | 2 | 2 | no | — |
| 259 | C4⋊C8 | — | 2 | 2 | no | — |
| 260 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 261 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 262 | #103 | — | 2 | 8 | no | — |
| 263 | #103 | C2×D4 | 1 | 4 | yes | — |
| 264 | #103 | C2×D4 | 1 | 4 | yes | — |
| 265 | #102 | — | 2 | 8 | no | — |
| 266 | #102 | — | 2 | 4 | no | — |
| 267 | #102 | — | 2 | 4 | no | — |
| 268 | #102 | — | 2 | 4 | no | — |
| 269 | #102 | — | 2 | 4 | no | — |
| 270 | #102 | — | 2 | 8 | no | — |
| 271 | #102 | — | 2 | 8 | no | — |
| 272 | #102 | C2×D4 | 1 | 4 | yes | — |
| 273 | #102 | C2×D4 | 1 | 4 | yes | — |
| 274 | C22⋊C8 | — | 2 | 4 | no | — |
| 275 | C22⋊C8 | — | 2 | 4 | no | — |
| 276 | #97 | — | 2 | 4 | no | — |
| 277 | C4×C8 | — | 2 | 4 | no | — |
| 278 | C4×C8 | — | 2 | 1 | no | — |
| 279 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 283 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 284 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 285 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 286 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 287 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 288 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 289 | #41 | — | 8 | 2 | no | — |
| 290 | #41 | — | 8 | 2 | no | — |
| 291 | #41 | — | 8 | 8 | no | — |
| 292 | #41 | — | 8 | 8 | no | — |
| 293 | #41 | — | 8 | 8 | no | — |
| 294 | #41 | — | 16 | 8 | no | — |
| 295 | C2×Q8 | — | 2 | 2 | no | — |
| 296 | C2×Q8 | — | 2 | 2 | no | — |
| 297 | C2×Q8 | — | 2 | 4 | no | — |
| 298 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 299 | C2×D4 | — | 2 | 4 | no | — |
| 300 | C2×D4 | — | 2 | 2 | no | — |
| 301 | C2×D4 | — | 2 | 2 | no | — |
| 302 | C2×D4 | — | 2 | 4 | no | — |
| 303 | C2×D4 | — | 2 | 4 | no | — |
| 304 | C2×D4 | — | 2 | 4 | no | — |
| 305 | C2×D4 | — | 4 | 8 | no | — |
| 306 | C2×D4 | — | 4 | 8 | no | — |
| 307 | C2×D4 | — | 4 | 4 | no | — |
| 308 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 309 | C22×C4 | — | 2 | 4 | no | — |
| 310 | C22×C4 | — | 4 | 8 | no | — |
| 311 | C22×C4 | — | 4 | 8 | no | — |
| 312 | C22×C4 | — | 4 | 4 | no | — |
| 313 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 315 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 316 | Q16 | — | 2 | 4 | no | — |
| 317 | Q16 | — | 4 | 2 | no | — |
| 318 | Q16 | — | 8 | 4 | no | — |
| 319 | SD16 | — | 8 | 8 | no | — |
| 320 | SD16 | — | 8 | 8 | no | — |
| 321 | D8 | — | 2 | 4 | no | — |
| 322 | D8 | — | 4 | 2 | no | — |
| 323 | D8 | — | 4 | 4 | no | — |
| 324 | D8 | — | 4 | 4 | no | — |
| 325 | D8 | — | 8 | 2 | no | — |
| 326 | D8 | — | 8 | 2 | no | — |
| 327 | D8 | — | 8 | 4 | no | — |
| 328 | D8 | — | 8 | 8 | no | — |
| 329 | M16 | — | 8 | 4 | no | — |
| 330 | M16 | — | 8 | 2 | no | — |
| 331 | M16 | — | 8 | 2 | no | — |
| 332 | C2×C8 | — | 2 | 4 | no | — |
| 333 | C2×C8 | — | 2 | 1 | no | — |
| 334 | C2×C8 | — | 2 | 1 | no | — |
| 335 | C2×C8 | — | 2 | 2 | no | — |
| 336 | C2×C8 | — | 2 | 2 | no | — |
| 337 | C2×C8 | — | 2 | 4 | no | — |
| 338 | C2×C8 | — | 2 | 4 | no | — |
| 339 | C2×C8 | — | 4 | 1 | no | — |
| 340 | C2×C8 | — | 4 | 1 | no | — |
| 341 | C2×C8 | — | 4 | 8 | no | — |
| 342 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 344 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 345 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 346 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 347 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 348 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 350 | C4⋊C4 | — | 2 | 2 | no | — |
| 351 | C4⋊C4 | — | 2 | 2 | no | — |
| 352 | C4⋊C4 | — | 2 | 2 | no | — |
| 353 | C4⋊C4 | — | 2 | 2 | no | — |
| 354 | C4⋊C4 | — | 2 | 4 | no | — |
| 355 | C4⋊C4 | — | 2 | 4 | no | — |
| 356 | C4⋊C4 | — | 2 | 4 | no | — |
| 357 | C4⋊C4 | — | 2 | 4 | no | — |
| 358 | C4⋊C4 | — | 4 | 8 | no | — |
| 359 | C4⋊C4 | — | 4 | 8 | no | — |
| 360 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 361 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 362 | C22⋊C4 | — | 2 | 4 | no | — |
| 363 | C22⋊C4 | — | 2 | 4 | no | — |
| 364 | C22⋊C4 | — | 2 | 4 | no | — |
| 365 | C22⋊C4 | — | 4 | 8 | no | — |
| 366 | C22⋊C4 | — | 4 | 8 | no | — |
| 367 | C22⋊C4 | — | 4 | 4 | no | — |
| 368 | C22⋊C4 | — | 4 | 4 | no | — |
| 369 | C42 | — | 2 | 4 | no | — |
| 370 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 371 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 372 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 373 | C42 | C25 | 1 | 1 | yes | characteristic |
| 374 | C23 | — | 2 | 4 | no | — |
| 375 | C23 | — | 4 | 4 | no | — |
| 376 | C23 | D42 | 1 | 1 | yes | characteristic |
| 377 | Q8 | — | 2 | 4 | no | — |
| 378 | Q8 | — | 2 | 4 | no | — |
| 379 | Q8 | — | 4 | 4 | no | — |
| 380 | Q8 | — | 8 | 2 | no | — |
| 381 | Q8 | — | 8 | 4 | no | — |
| 382 | D4 | — | 2 | 4 | no | — |
| 383 | D4 | — | 2 | 4 | no | — |
| 384 | D4 | — | 4 | 4 | no | — |
| 385 | D4 | — | 4 | 4 | no | — |
| 386 | D4 | — | 4 | 4 | no | — |
| 387 | D4 | — | 4 | 4 | no | — |
| 388 | D4 | — | 4 | 4 | no | — |
| 389 | D4 | — | 8 | 2 | no | — |
| 390 | D4 | — | 8 | 4 | no | — |
| 391 | D4 | — | 8 | 4 | no | — |
| 392 | D4 | — | 16 | 8 | no | — |
| 393 | D4 | — | 16 | 8 | no | — |
| 394 | D4 | — | 16 | 4 | no | — |
| 395 | C2×C4 | — | 2 | 1 | no | — |
| 396 | C2×C4 | — | 2 | 1 | no | — |
| 397 | C2×C4 | — | 2 | 2 | no | — |
| 398 | C2×C4 | — | 2 | 1 | no | — |
| 399 | C2×C4 | — | 2 | 1 | no | — |
| 400 | C2×C4 | — | 2 | 4 | no | — |
| 401 | C2×C4 | — | 2 | 4 | no | — |
| 402 | C2×C4 | — | 2 | 4 | no | — |
| 403 | C2×C4 | — | 4 | 4 | no | — |
| 404 | C2×C4 | — | 4 | 4 | no | — |
| 405 | C2×C4 | — | 4 | 4 | no | — |
| 406 | C2×C4 | — | 8 | 8 | no | — |
| 407 | C2×C4 | — | 16 | 8 | no | — |
| 408 | C2×C4 | — | 16 | 8 | no | — |
| 409 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 411 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 412 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 413 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 414 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 415 | C8 | — | 2 | 2 | no | — |
| 416 | C8 | — | 2 | 2 | no | — |
| 417 | C8 | — | 2 | 1 | no | — |
| 418 | C8 | — | 2 | 1 | no | — |
| 419 | C8 | — | 2 | 1 | no | — |
| 420 | C8 | — | 2 | 1 | no | — |
| 421 | C8 | — | 2 | 1 | no | — |
| 422 | C8 | — | 2 | 1 | no | — |
| 423 | C8 | — | 4 | 4 | no | — |
| 424 | C8 | — | 4 | 4 | no | — |
| 425 | C8 | #576 | 1 | 2 | yes | — |
| 426 | C8 | #578 | 1 | 2 | yes | — |
| 427 | C22 | — | 2 | 1 | no | — |
| 428 | C22 | — | 2 | 1 | no | — |
| 429 | C22 | — | 2 | 1 | no | — |
| 430 | C22 | — | 4 | 4 | no | — |
| 431 | C22 | — | 4 | 4 | no | — |
| 432 | C22 | — | 4 | 4 | no | — |
| 433 | C22 | — | 8 | 4 | no | — |
| 434 | C22 | — | 8 | 4 | no | — |
| 435 | C22 | — | 8 | 4 | no | — |
| 436 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 437 | C4 | — | 2 | 1 | no | — |
| 438 | C4 | — | 2 | 1 | no | — |
| 439 | C4 | — | 2 | 1 | no | — |
| 440 | C4 | — | 4 | 4 | no | — |
| 441 | C4 | — | 4 | 4 | no | — |
| 442 | C4 | — | 4 | 4 | no | — |
| 443 | C4 | — | 8 | 4 | no | — |
| 444 | C4 | #3292 | 1 | 2 | yes | — |
| 445 | C4 | C2×#576 | 1 | 1 | yes | characteristic |
| 446 | C4 | C2×#578 | 1 | 1 | yes | characteristic |
| 447 | C4 | #3584 | 1 | 1 | yes | characteristic |
| 448 | C4 | #3584 | 1 | 1 | yes | characteristic |
| 449 | C2 | — | 4 | 1 | no | — |
| 450 | C2 | — | 8 | 4 | no | — |
| 451 | C2 | — | 16 | 4 | no | — |
| 452 | C2 | #61084 | 1 | 1 | yes | characteristic |
| 453 | C2 | #61086 | 1 | 1 | yes | characteristic |
| 454 | 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. #62373 | C2 | semidirect |
| 2. #62332 | C2 | semidirect |
| 3. #20308 | C2 | semidirect |
| 4. #20006 | C2 | semidirect |
| 5. #19975 | C2 | semidirect |
| 6. #19937 | C2 | semidirect |
| 7. #19909 | C2 | semidirect |
| 8. #19603 | C2 | semidirect |
| 9. #19344 | C2 | semidirect |
| 10. #19332 | C2 | semidirect |
| 11. #18687 | C2 | semidirect |
| 12. #17958 | C2 | semidirect |
| 13. #17956 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62373 | 2 |
| #62332 | 2 |
| #20308 | 2 |
| #20006 | 2 |
| #19975 | 2 |
| #19937 | 2 |
| #19909 | 2 |
| #19603 | 2 |
| #19344 | 2 |
| #19332 | 2 |
| #18687 | 2 |
| #17958 | 2 |
| #17956 | 2 |