Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2096 conjugacy classes of subgroups.
The subgroup lattice has 425 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62479 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #60715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60648 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19746 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #19731 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #19675 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #19662 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #19653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #19645 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #19632 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C2×#1713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #19596 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #17335 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#578 | — | 2 | 2 | no | — |
| 15 | #3509 | C22 | 1 | 2 | yes | — |
| 16 | #3499 | C22 | 1 | 2 | yes | — |
| 17 | #3386 | — | 2 | 8 | no | — |
| 18 | #3353 | — | 2 | 8 | no | — |
| 19 | #3343 | — | 2 | 16 | no | — |
| 20 | #3230 | C22 | 1 | 8 | yes | — |
| 21 | #3229 | C22 | 1 | 4 | yes | — |
| 22 | #3228 | C22 | 1 | 8 | yes | — |
| 23 | #3226 | C22 | 1 | 4 | yes | — |
| 24 | #3185 | C22 | 1 | 4 | yes | — |
| 25 | #3182 | C22 | 1 | 8 | yes | — |
| 26 | #3177 | — | 2 | 4 | no | — |
| 27 | #3170 | C22 | 1 | 4 | yes | — |
| 28 | #3167 | C22 | 1 | 4 | yes | — |
| 29 | #3165 | C22 | 1 | 8 | yes | — |
| 30 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#500 | C22 | 1 | 4 | yes | — |
| 32 | #3156 | — | 2 | 4 | no | — |
| 33 | #3156 | — | 2 | 2 | no | — |
| 34 | #3152 | C22 | 1 | 4 | yes | — |
| 35 | #3152 | C22 | 1 | 2 | yes | — |
| 36 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 37 | #3147 | C22 | 1 | 2 | yes | — |
| 38 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#494 | C22 | 1 | 2 | yes | — |
| 41 | #3139 | C22 | 1 | 2 | yes | — |
| 42 | #3059 | — | 2 | 2 | no | — |
| 43 | #2965 | C22 | 1 | 2 | yes | — |
| 44 | #2950 | — | 2 | 2 | no | — |
| 45 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 46 | #1723 | C22 | 1 | 8 | yes | — |
| 47 | #1723 | C22 | 1 | 8 | yes | — |
| 48 | #1722 | C22 | 1 | 4 | yes | — |
| 49 | #1719 | C22 | 1 | 8 | yes | — |
| 50 | #1716 | C22 | 1 | 4 | yes | — |
| 51 | #1714 | C22 | 1 | 8 | yes | — |
| 52 | #1713 | C22 | 1 | 2 | yes | — |
| 53 | #1713 | C22 | 1 | 2 | yes | — |
| 54 | #1713 | C22 | 1 | 4 | yes | — |
| 55 | #1713 | C22 | 1 | 2 | yes | — |
| 56 | #1709 | C22 | 1 | 2 | yes | — |
| 57 | #1708 | C22 | 1 | 2 | yes | — |
| 58 | #1707 | C22 | 1 | 2 | yes | — |
| 59 | #1707 | C22 | 1 | 4 | yes | — |
| 60 | #1706 | C22 | 1 | 2 | yes | — |
| 61 | #1705 | C22 | 1 | 2 | yes | — |
| 62 | #1455 | C22 | 1 | 2 | yes | — |
| 63 | #1453 | C22 | 1 | 2 | yes | — |
| 64 | #1451 | C22 | 1 | 2 | yes | — |
| 65 | #1450 | C22 | 1 | 1 | yes | characteristic |
| 66 | C8×M16 | C22 | 1 | 4 | yes | — |
| 67 | C2×C82 | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×2−1+4 | — | 2 | 2 | no | — |
| 69 | #578 | — | 4 | 16 | no | — |
| 70 | C2×#137 | — | 2 | 4 | no | — |
| 71 | C2×#137 | — | 2 | 8 | no | — |
| 72 | C2×#135 | — | 2 | 4 | no | — |
| 73 | C2×#135 | — | 2 | 2 | no | — |
| 74 | C22×Q16 | — | 2 | 4 | no | — |
| 75 | C22×Q16 | — | 2 | 2 | no | — |
| 76 | C22×Q16 | — | 2 | 2 | no | — |
| 77 | C2×#131 | D4 | 1 | 2 | yes | — |
| 78 | #557 | — | 2 | 4 | no | — |
| 79 | #556 | — | 2 | 4 | no | — |
| 80 | #552 | — | 2 | 8 | no | — |
| 81 | D4×Q8 | — | 2 | 4 | no | — |
| 82 | #547 | — | 2 | 8 | no | — |
| 83 | #547 | — | 2 | 4 | no | — |
| 84 | #541 | — | 2 | 4 | no | — |
| 85 | #536 | — | 2 | 2 | no | — |
| 86 | #536 | — | 2 | 2 | no | — |
| 87 | #536 | — | 2 | 4 | no | — |
| 88 | #533 | C23 | 1 | 2 | yes | — |
| 89 | #533 | C23 | 1 | 8 | yes | — |
| 90 | #532 | C23 | 1 | 2 | yes | — |
| 91 | #532 | C23 | 1 | 4 | yes | — |
| 92 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 93 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 94 | C2×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 95 | #519 | — | 2 | 2 | no | — |
| 96 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 97 | #501 | — | 2 | 16 | no | — |
| 98 | #500 | — | 2 | 8 | no | — |
| 99 | #500 | C23 | 1 | 8 | yes | — |
| 100 | #500 | C23 | 1 | 8 | yes | — |
| 101 | #500 | C23 | 1 | 2 | yes | — |
| 102 | #500 | C23 | 1 | 8 | yes | — |
| 103 | #499 | — | 2 | 2 | no | — |
| 104 | #498 | C23 | 1 | 2 | yes | — |
| 105 | #498 | C23 | 1 | 4 | yes | — |
| 106 | #498 | C23 | 1 | 8 | yes | — |
| 107 | #497 | — | 2 | 8 | no | — |
| 108 | #497 | — | 2 | 4 | no | — |
| 109 | #495 | — | 2 | 4 | no | — |
| 110 | #495 | — | 2 | 2 | no | — |
| 111 | #494 | — | 2 | 4 | no | — |
| 112 | #494 | — | 2 | 2 | no | — |
| 113 | #494 | — | 2 | 2 | no | — |
| 114 | #494 | C23 | 1 | 2 | yes | — |
| 115 | #494 | C23 | 1 | 1 | yes | characteristic |
| 116 | #494 | C23 | 1 | 2 | yes | — |
| 117 | #494 | C23 | 1 | 4 | yes | — |
| 118 | #494 | C23 | 1 | 2 | yes | — |
| 119 | #494 | C23 | 1 | 2 | yes | — |
| 120 | #493 | C23 | 1 | 1 | yes | characteristic |
| 121 | #492 | C23 | 1 | 2 | yes | — |
| 122 | #492 | C23 | 1 | 4 | yes | — |
| 123 | #492 | C23 | 1 | 4 | yes | — |
| 124 | #491 | — | 2 | 4 | no | — |
| 125 | #487 | C23 | 1 | 8 | yes | — |
| 126 | #487 | C23 | 1 | 4 | yes | — |
| 127 | #487 | C23 | 1 | 8 | yes | — |
| 128 | #486 | C23 | 1 | 4 | yes | — |
| 129 | #486 | C23 | 1 | 8 | yes | — |
| 130 | #484 | — | 2 | 16 | no | — |
| 131 | #483 | — | 2 | 8 | no | — |
| 132 | #482 | — | 2 | 16 | no | — |
| 133 | #480 | — | 2 | 8 | no | — |
| 134 | #478 | — | 2 | 16 | no | — |
| 135 | #477 | — | 2 | 16 | no | — |
| 136 | #475 | — | 2 | 8 | no | — |
| 137 | #474 | — | 2 | 8 | no | — |
| 138 | #470 | — | 2 | 8 | no | — |
| 139 | #468 | — | 2 | 16 | no | — |
| 140 | #467 | — | 2 | 8 | no | — |
| 141 | #465 | — | 2 | 8 | no | — |
| 142 | #446 | D4 | 1 | 4 | yes | — |
| 143 | #441 | — | 2 | 8 | no | — |
| 144 | #440 | — | 2 | 16 | no | — |
| 145 | C4×Q16 | — | 2 | 8 | no | — |
| 146 | C4×SD16 | — | 2 | 8 | no | — |
| 147 | #436 | D4 | 1 | 4 | yes | — |
| 148 | #435 | D4 | 1 | 8 | yes | — |
| 149 | #431 | C23 | 1 | 2 | yes | — |
| 150 | #431 | C23 | 1 | 4 | yes | — |
| 151 | #428 | — | 2 | 16 | no | — |
| 152 | #427 | — | 2 | 2 | no | — |
| 153 | C2×#107 | — | 2 | 8 | no | — |
| 154 | #419 | — | 2 | 4 | no | — |
| 155 | #405 | D4 | 1 | 4 | yes | — |
| 156 | #405 | D4 | 1 | 2 | yes | — |
| 157 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 158 | C4×M16 | C23 | 1 | 2 | yes | — |
| 159 | C4×M16 | C23 | 1 | 4 | yes | — |
| 160 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 162 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 163 | #322 | C23 | 1 | 4 | yes | — |
| 164 | #322 | C23 | 1 | 4 | yes | — |
| 165 | #322 | C23 | 1 | 2 | yes | — |
| 166 | C82 | C23 | 1 | 2 | yes | — |
| 167 | C82 | C23 | 1 | 1 | yes | characteristic |
| 168 | C82 | C23 | 1 | 1 | yes | characteristic |
| 169 | C82 | C23 | 1 | 2 | yes | — |
| 170 | 2−1+4 | — | 4 | 16 | no | — |
| 171 | C2×#41 | — | 2 | 4 | no | — |
| 172 | C2×#41 | — | 2 | 2 | no | — |
| 173 | C2×#41 | — | 4 | 4 | no | — |
| 174 | C2×#41 | — | 4 | 2 | no | — |
| 175 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C22×Q8 | — | 2 | 2 | no | — |
| 177 | C22×Q8 | — | 2 | 4 | no | — |
| 178 | C22×Q8 | — | 2 | 2 | no | — |
| 179 | C22×Q8 | — | 4 | 2 | no | — |
| 180 | #137 | — | 4 | 16 | no | — |
| 181 | #137 | — | 4 | 32 | no | — |
| 182 | #135 | — | 4 | 16 | no | — |
| 183 | #135 | — | 4 | 8 | no | — |
| 184 | C2×Q16 | — | 2 | 2 | no | — |
| 185 | C2×Q16 | — | 2 | 4 | no | — |
| 186 | C2×Q16 | — | 2 | 8 | no | — |
| 187 | C2×Q16 | — | 2 | 4 | no | — |
| 188 | C2×Q16 | — | 2 | 4 | no | — |
| 189 | C2×Q16 | — | 2 | 4 | no | — |
| 190 | C2×Q16 | — | 4 | 16 | no | — |
| 191 | C2×Q16 | — | 4 | 8 | no | — |
| 192 | C2×Q16 | — | 4 | 8 | no | — |
| 193 | C2×SD16 | — | 2 | 8 | no | — |
| 194 | C2×SD16 | — | 2 | 4 | no | — |
| 195 | C2×SD16 | — | 2 | 8 | no | — |
| 196 | C2×D8 | — | 2 | 2 | no | — |
| 197 | #131 | — | 2 | 8 | no | — |
| 198 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 199 | C2×M16 | C2×D4 | 1 | 4 | yes | — |
| 200 | C2×M16 | C2×D4 | 1 | 8 | yes | — |
| 201 | C22×C8 | C2×D4 | 1 | 4 | yes | — |
| 202 | C22×C8 | C2×D4 | 1 | 4 | yes | — |
| 203 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 204 | C4⋊Q8 | — | 2 | 4 | no | — |
| 205 | C4⋊Q8 | — | 2 | 8 | no | — |
| 206 | C4⋊Q8 | — | 2 | 4 | no | — |
| 207 | C4⋊Q8 | — | 2 | 4 | no | — |
| 208 | C4⋊Q8 | — | 2 | 2 | no | — |
| 209 | C4⋊Q8 | — | 2 | 2 | no | — |
| 210 | C4⋊Q8 | — | 4 | 2 | no | — |
| 211 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 212 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 213 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 214 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 215 | #127 | C24 | 1 | 2 | yes | — |
| 216 | #126 | — | 4 | 8 | no | — |
| 217 | #125 | — | 2 | 2 | no | — |
| 218 | #125 | — | 2 | 8 | no | — |
| 219 | #125 | — | 4 | 8 | no | — |
| 220 | #124 | — | 2 | 4 | no | — |
| 221 | #124 | — | 2 | 2 | no | — |
| 222 | #124 | — | 4 | 2 | no | — |
| 223 | #123 | — | 4 | 4 | no | — |
| 224 | #123 | — | 4 | 4 | no | — |
| 225 | #123 | — | 4 | 8 | no | — |
| 226 | C22⋊Q8 | — | 2 | 8 | no | — |
| 227 | C22⋊Q8 | — | 2 | 4 | no | — |
| 228 | C22⋊Q8 | — | 2 | 8 | no | — |
| 229 | C22⋊Q8 | — | 4 | 4 | no | — |
| 230 | C22⋊Q8 | — | 4 | 8 | no | — |
| 231 | #121 | — | 2 | 4 | no | — |
| 232 | #121 | — | 2 | 8 | no | — |
| 233 | C4×Q8 | — | 2 | 8 | no | — |
| 234 | C4×Q8 | — | 2 | 8 | no | — |
| 235 | C4×Q8 | — | 2 | 4 | no | — |
| 236 | C4×Q8 | — | 4 | 4 | no | — |
| 237 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 238 | C4×D4 | — | 2 | 4 | no | — |
| 239 | C4×D4 | — | 2 | 8 | no | — |
| 240 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 241 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 242 | #117 | — | 2 | 2 | no | — |
| 243 | #117 | — | 2 | 8 | no | — |
| 244 | #117 | — | 4 | 4 | no | — |
| 245 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | #117 | C2×D4 | 1 | 2 | yes | — |
| 247 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 248 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 249 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 250 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 251 | C2×C42 | C24 | 1 | 2 | yes | — |
| 252 | #107 | — | 2 | 16 | no | — |
| 253 | #107 | — | 2 | 16 | no | — |
| 254 | #107 | — | 2 | 4 | no | — |
| 255 | #107 | — | 2 | 16 | no | — |
| 256 | #106 | — | 2 | 4 | no | — |
| 257 | #106 | — | 2 | 8 | no | — |
| 258 | #106 | — | 2 | 16 | no | — |
| 259 | C4⋊C8 | C2×D4 | 1 | 8 | yes | — |
| 260 | C4⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 261 | #103 | — | 2 | 16 | no | — |
| 262 | #103 | — | 2 | 8 | no | — |
| 263 | #103 | — | 2 | 16 | no | — |
| 264 | #102 | — | 2 | 8 | no | — |
| 265 | #102 | — | 2 | 16 | no | — |
| 266 | C22⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 267 | C22⋊C8 | C2×D4 | 1 | 8 | yes | — |
| 268 | #97 | C2×D4 | 1 | 4 | yes | — |
| 269 | #97 | C2×D4 | 1 | 2 | yes | — |
| 270 | #97 | C2×D4 | 1 | 8 | yes | — |
| 271 | C4×C8 | C2×D4 | 1 | 4 | yes | — |
| 272 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 273 | C4×C8 | C2×D4 | 1 | 4 | yes | — |
| 274 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 275 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 276 | C4×C8 | C24 | 1 | 2 | yes | — |
| 277 | C4×C8 | C24 | 1 | 2 | yes | — |
| 278 | C4×C8 | C24 | 1 | 4 | yes | — |
| 279 | C4×C8 | C24 | 1 | 2 | yes | — |
| 280 | #41 | — | 2 | 4 | no | — |
| 281 | #41 | — | 4 | 16 | no | — |
| 282 | #41 | — | 4 | 8 | no | — |
| 283 | #41 | — | 8 | 16 | no | — |
| 284 | #41 | — | 8 | 8 | no | — |
| 285 | C2×Q8 | — | 2 | 4 | no | — |
| 286 | C2×Q8 | — | 2 | 4 | no | — |
| 287 | C2×Q8 | — | 2 | 4 | no | — |
| 288 | C2×Q8 | — | 2 | 2 | no | — |
| 289 | C2×Q8 | — | 4 | 16 | no | — |
| 290 | C2×Q8 | — | 4 | 2 | no | — |
| 291 | C2×Q8 | — | 4 | 4 | no | — |
| 292 | C2×Q8 | — | 4 | 2 | no | — |
| 293 | C2×Q8 | — | 4 | 8 | no | — |
| 294 | C2×Q8 | — | 4 | 8 | no | — |
| 295 | C2×Q8 | — | 8 | 8 | no | — |
| 296 | C2×Q8 | #127 | 1 | 1 | yes | characteristic |
| 297 | C2×D4 | — | 2 | 4 | no | — |
| 298 | C2×D4 | — | 2 | 2 | no | — |
| 299 | C2×D4 | — | 4 | 4 | no | — |
| 300 | C2×D4 | — | 4 | 2 | no | — |
| 301 | C2×D4 | #127 | 1 | 2 | yes | — |
| 302 | C2×D4 | #127 | 1 | 1 | yes | characteristic |
| 303 | C22×C4 | — | 4 | 2 | no | — |
| 304 | C22×C4 | — | 4 | 4 | no | — |
| 305 | C22×C4 | — | 4 | 2 | no | — |
| 306 | C22×C4 | — | 4 | 4 | no | — |
| 307 | C22×C4 | — | 4 | 2 | no | — |
| 308 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 309 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 310 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 311 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 312 | Q16 | — | 4 | 16 | no | — |
| 313 | Q16 | — | 4 | 8 | no | — |
| 314 | Q16 | — | 4 | 8 | no | — |
| 315 | Q16 | — | 4 | 4 | no | — |
| 316 | Q16 | — | 4 | 8 | no | — |
| 317 | Q16 | — | 4 | 8 | no | — |
| 318 | SD16 | — | 4 | 16 | no | — |
| 319 | SD16 | — | 4 | 8 | no | — |
| 320 | SD16 | — | 4 | 16 | no | — |
| 321 | D8 | — | 4 | 4 | no | — |
| 322 | M16 | — | 2 | 4 | no | — |
| 323 | M16 | — | 2 | 8 | no | — |
| 324 | M16 | — | 2 | 16 | no | — |
| 325 | C2×C8 | — | 2 | 8 | no | — |
| 326 | C2×C8 | — | 2 | 8 | no | — |
| 327 | C2×C8 | AGL(1,ℤ/8) | 1 | 8 | yes | — |
| 328 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 329 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 330 | C2×C8 | C22×D4 | 1 | 8 | yes | — |
| 331 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 332 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 333 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 334 | C4⋊C4 | — | 2 | 4 | no | — |
| 335 | C4⋊C4 | — | 2 | 8 | no | — |
| 336 | C4⋊C4 | — | 2 | 4 | no | — |
| 337 | C4⋊C4 | — | 2 | 4 | no | — |
| 338 | C4⋊C4 | — | 2 | 8 | no | — |
| 339 | C4⋊C4 | — | 4 | 8 | no | — |
| 340 | C4⋊C4 | — | 4 | 4 | no | — |
| 341 | C4⋊C4 | — | 4 | 4 | no | — |
| 342 | C4⋊C4 | — | 4 | 8 | no | — |
| 343 | C4⋊C4 | — | 4 | 8 | no | — |
| 344 | C4⋊C4 | — | 4 | 4 | no | — |
| 345 | C4⋊C4 | #127 | 1 | 2 | yes | — |
| 346 | C4⋊C4 | #127 | 1 | 4 | yes | — |
| 347 | C22⋊C4 | — | 4 | 2 | no | — |
| 348 | C22⋊C4 | — | 4 | 8 | no | — |
| 349 | C22⋊C4 | — | 4 | 8 | no | — |
| 350 | C22⋊C4 | — | 4 | 4 | no | — |
| 351 | C22⋊C4 | #127 | 1 | 2 | yes | — |
| 352 | C22⋊C4 | #127 | 1 | 4 | yes | — |
| 353 | C42 | — | 4 | 8 | no | — |
| 354 | C42 | — | 4 | 2 | no | — |
| 355 | C42 | C22×D4 | 1 | 2 | yes | — |
| 356 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 357 | C42 | C22×D4 | 1 | 2 | yes | — |
| 358 | C42 | C22×D4 | 1 | 4 | yes | — |
| 359 | C42 | C25 | 1 | 1 | yes | characteristic |
| 360 | C23 | — | 4 | 2 | no | — |
| 361 | C23 | C2×#127 | 1 | 2 | yes | — |
| 362 | C23 | C2×#127 | 1 | 1 | yes | characteristic |
| 363 | Q8 | — | 2 | 2 | no | — |
| 364 | Q8 | — | 4 | 8 | no | — |
| 365 | Q8 | — | 4 | 4 | no | — |
| 366 | Q8 | — | 4 | 8 | no | — |
| 367 | Q8 | — | 4 | 8 | no | — |
| 368 | Q8 | — | 8 | 8 | no | — |
| 369 | Q8 | — | 8 | 4 | no | — |
| 370 | Q8 | — | 8 | 4 | no | — |
| 371 | D4 | — | 2 | 4 | no | — |
| 372 | D4 | — | 2 | 2 | no | — |
| 373 | D4 | — | 4 | 4 | no | — |
| 374 | D4 | — | 4 | 8 | no | — |
| 375 | D4 | — | 8 | 8 | no | — |
| 376 | D4 | — | 8 | 4 | no | — |
| 377 | C2×C4 | — | 2 | 4 | no | — |
| 378 | C2×C4 | — | 2 | 4 | no | — |
| 379 | C2×C4 | — | 2 | 8 | no | — |
| 380 | C2×C4 | — | 4 | 4 | no | — |
| 381 | C2×C4 | — | 4 | 4 | no | — |
| 382 | C2×C4 | — | 4 | 4 | no | — |
| 383 | C2×C4 | — | 4 | 2 | no | — |
| 384 | C2×C4 | — | 8 | 8 | no | — |
| 385 | C2×C4 | — | 8 | 8 | no | — |
| 386 | C2×C4 | — | 8 | 4 | no | — |
| 387 | C2×C4 | — | 8 | 4 | no | — |
| 388 | C2×C4 | — | 8 | 4 | no | — |
| 389 | C2×C4 | C2×#127 | 1 | 4 | yes | — |
| 390 | C2×C4 | C2×#127 | 1 | 2 | yes | — |
| 391 | C2×C4 | C2×#127 | 1 | 2 | yes | — |
| 392 | C2×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 394 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 395 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 396 | C8 | — | 2 | 4 | no | — |
| 397 | C8 | — | 2 | 4 | no | — |
| 398 | C8 | — | 2 | 8 | no | — |
| 399 | C8 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 400 | C8 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 401 | C8 | #578 | 1 | 8 | yes | complemented |
| 402 | C22 | — | 2 | 2 | no | — |
| 403 | C22 | — | 2 | 2 | no | — |
| 404 | C22 | — | 2 | 4 | no | — |
| 405 | C22 | — | 8 | 2 | no | — |
| 406 | C22 | — | 8 | 4 | no | — |
| 407 | C22 | #3151 | 1 | 2 | yes | — |
| 408 | C22 | C22×#127 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 2 | no | — |
| 410 | C4 | — | 2 | 2 | no | — |
| 411 | C4 | — | 2 | 4 | no | — |
| 412 | C4 | — | 8 | 4 | no | — |
| 413 | C4 | — | 8 | 2 | no | — |
| 414 | C4 | — | 8 | 4 | no | — |
| 415 | C4 | — | 8 | 4 | no | — |
| 416 | C4 | #3151 | 1 | 2 | yes | — |
| 417 | C4 | C22×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 418 | C4 | C2×#578 | 1 | 4 | yes | — |
| 419 | C2 | — | 2 | 2 | no | — |
| 420 | C2 | — | 4 | 2 | no | — |
| 421 | C2 | — | 16 | 2 | no | — |
| 422 | C2 | C2×#3151 | 1 | 1 | yes | characteristic |
| 423 | C2 | #60648 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#127 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | #60648 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62479 | C2 | semidirect |
| 2. #60715 | C2 | semidirect |
| 4. #19746 | C2 | semidirect |
| 5. #19731 | C2 | semidirect |
| 6. #19675 | C2 | semidirect |
| 7. #19662 | C2 | semidirect |
| 8. #19653 | C2 | semidirect |
| 9. #19645 | C2 | semidirect |
| 10. #19632 | C2 | semidirect |
| 11. C2×#1713 | C2 | semidirect |
| 12. #19596 | C2 | semidirect |
| 13. #17335 | C2 | semidirect |
| 401. C8 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62479 | 2 |
| #60715 | 2 |
| #60648 | 2 |
| #19746 | 2 |
| #19731 | 2 |
| #19675 | 2 |
| #19662 | 2 |
| #19653 | 2 |
| #19645 | 2 |
| #19632 | 2 |
| C2×#1713 | 2 |
| #19596 | 2 |
| #17335 | 2 |