Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6656 conjugacy classes of subgroups.
The subgroup lattice has 430 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63001 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61422 | C2 | 1 | 18 | yes | maximal, complemented |
| 3 | #61411 | C2 | 1 | 9 | yes | maximal, complemented |
| 4 | #61408 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | #61404 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #61393 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#3395 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #60648 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #60432 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | Q8×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C4×#578 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×#578 | C22 | 1 | 3 | yes | — |
| 13 | C2×#578 | C22 | 1 | 6 | yes | — |
| 14 | #3523 | — | 2 | 6 | no | — |
| 15 | #3515 | — | 2 | 18 | no | — |
| 16 | #3509 | C22 | 1 | 18 | yes | — |
| 17 | #3507 | C22 | 1 | 18 | yes | — |
| 18 | #3499 | C22 | 1 | 6 | yes | — |
| 19 | #3482 | — | 2 | 6 | no | — |
| 20 | #3480 | C22 | 1 | 6 | yes | — |
| 21 | Q8×#41 | — | 2 | 2 | no | — |
| 22 | Q8×#41 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#557 | C22 | 1 | 6 | yes | — |
| 24 | C4×2−1+4 | C22 | 1 | 6 | yes | — |
| 25 | #3402 | C22 | 1 | 36 | yes | — |
| 26 | #3400 | C22 | 1 | 36 | yes | — |
| 27 | #3398 | C22 | 1 | 36 | yes | — |
| 28 | #3398 | C22 | 1 | 36 | yes | — |
| 29 | #3396 | C22 | 1 | 9 | yes | — |
| 30 | #3395 | C22 | 1 | 3 | yes | — |
| 31 | #3395 | C22 | 1 | 6 | yes | — |
| 32 | #3395 | C22 | 1 | 18 | yes | — |
| 33 | #3395 | C22 | 1 | 18 | yes | — |
| 34 | #3395 | C22 | 1 | 6 | yes | — |
| 35 | #3394 | C22 | 1 | 18 | yes | — |
| 36 | #3393 | C22 | 1 | 9 | yes | — |
| 37 | #3393 | C22 | 1 | 18 | yes | — |
| 38 | #3392 | C22 | 1 | 6 | yes | — |
| 39 | #3391 | C22 | 1 | 1 | yes | characteristic |
| 40 | #3156 | C22 | 1 | 18 | yes | — |
| 41 | #3156 | C22 | 1 | 18 | yes | — |
| 42 | #3152 | C22 | 1 | 18 | yes | — |
| 43 | #3147 | C22 | 1 | 9 | yes | — |
| 44 | C2×#494 | C22 | 1 | 9 | yes | — |
| 45 | #3046 | C22 | 1 | 36 | yes | — |
| 46 | #3044 | C22 | 1 | 36 | yes | — |
| 47 | #3039 | C22 | 1 | 18 | yes | — |
| 48 | #3037 | C22 | 1 | 18 | yes | — |
| 49 | #3035 | C22 | 1 | 18 | yes | — |
| 50 | C2×#462 | C22 | 1 | 18 | yes | — |
| 51 | Q8×M16 | C22 | 1 | 3 | yes | — |
| 52 | #2962 | C22 | 1 | 9 | yes | — |
| 53 | #2960 | C22 | 1 | 9 | yes | — |
| 54 | C2×C8×Q8 | C22 | 1 | 3 | yes | — |
| 55 | #2951 | C22 | 1 | 9 | yes | — |
| 56 | #2950 | C22 | 1 | 9 | yes | — |
| 57 | #2947 | C22 | 1 | 18 | yes | — |
| 58 | C4×#137 | C22 | 1 | 18 | yes | — |
| 59 | C4×#135 | C22 | 1 | 9 | yes | — |
| 60 | C2×C4×Q16 | C22 | 1 | 9 | yes | — |
| 61 | #2913 | C22 | 1 | 1 | yes | characteristic |
| 62 | #2906 | C22 | 1 | 3 | yes | — |
| 63 | #2898 | C22 | 1 | 6 | yes | — |
| 64 | C4×#131 | C22 | 1 | 3 | yes | — |
| 65 | C2×2−1+4 | C23 | 1 | 6 | yes | — |
| 66 | #578 | — | 2 | 24 | no | — |
| 67 | #578 | — | 4 | 24 | no | — |
| 68 | C2×#137 | C23 | 1 | 18 | yes | — |
| 69 | C2×#137 | C23 | 1 | 36 | yes | — |
| 70 | C2×#135 | C23 | 1 | 9 | yes | — |
| 71 | C2×#135 | C23 | 1 | 18 | yes | — |
| 72 | C22×Q16 | C23 | 1 | 9 | yes | — |
| 73 | C22×Q16 | C23 | 1 | 18 | yes | — |
| 74 | C2×#131 | C23 | 1 | 3 | yes | — |
| 75 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 76 | #559 | C23 | 1 | 18 | yes | — |
| 77 | Q82 | D4 | 1 | 1 | yes | characteristic |
| 78 | #557 | — | 2 | 6 | no | — |
| 79 | #557 | — | 2 | 18 | no | — |
| 80 | #557 | D4 | 1 | 3 | yes | — |
| 81 | #557 | C23 | 1 | 6 | yes | — |
| 82 | #557 | C23 | 1 | 36 | yes | — |
| 83 | #557 | C23 | 1 | 12 | yes | — |
| 84 | #556 | — | 2 | 18 | no | — |
| 85 | #556 | C23 | 1 | 18 | yes | — |
| 86 | #556 | C23 | 1 | 36 | yes | — |
| 87 | #554 | — | 2 | 18 | no | — |
| 88 | #554 | D4 | 1 | 9 | yes | — |
| 89 | #553 | — | 2 | 18 | no | — |
| 90 | #552 | — | 2 | 36 | no | — |
| 91 | #552 | — | 2 | 36 | no | — |
| 92 | #552 | — | 2 | 36 | no | — |
| 93 | #550 | C23 | 1 | 2 | yes | — |
| 94 | D4×Q8 | — | 2 | 6 | no | — |
| 95 | D4×Q8 | — | 2 | 6 | no | — |
| 96 | D4×Q8 | D4 | 1 | 3 | yes | — |
| 97 | #548 | — | 2 | 6 | no | — |
| 98 | #547 | — | 2 | 18 | no | — |
| 99 | #547 | — | 2 | 18 | no | — |
| 100 | #541 | — | 2 | 36 | no | — |
| 101 | #539 | — | 2 | 36 | no | — |
| 102 | #536 | C23 | 1 | 36 | yes | — |
| 103 | #533 | — | 2 | 18 | no | — |
| 104 | #533 | — | 2 | 18 | no | — |
| 105 | #533 | C23 | 1 | 9 | yes | — |
| 106 | #532 | C23 | 1 | 18 | yes | — |
| 107 | C2×C4⋊Q8 | C23 | 1 | 18 | yes | — |
| 108 | #529 | — | 2 | 36 | no | — |
| 109 | #529 | — | 2 | 18 | no | — |
| 110 | C2×#125 | — | 2 | 18 | no | — |
| 111 | #520 | — | 2 | 18 | no | — |
| 112 | #520 | C23 | 1 | 18 | yes | — |
| 113 | #520 | C23 | 1 | 2 | yes | — |
| 114 | #519 | — | 2 | 6 | no | — |
| 115 | #519 | C23 | 1 | 18 | yes | — |
| 116 | C4×#41 | — | 2 | 6 | no | — |
| 117 | C4×#41 | — | 2 | 18 | no | — |
| 118 | C4×#41 | C23 | 1 | 18 | yes | — |
| 119 | C4×#41 | C23 | 1 | 3 | yes | — |
| 120 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 121 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 122 | C2×C4×Q8 | C23 | 1 | 18 | yes | — |
| 123 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 124 | #497 | C23 | 1 | 72 | yes | — |
| 125 | #495 | C23 | 1 | 18 | yes | — |
| 126 | #495 | C23 | 1 | 18 | yes | — |
| 127 | #494 | C23 | 1 | 9 | yes | — |
| 128 | #494 | C23 | 1 | 18 | yes | — |
| 129 | #494 | C23 | 1 | 18 | yes | — |
| 130 | #494 | C23 | 1 | 18 | yes | — |
| 131 | #493 | C23 | 1 | 3 | yes | — |
| 132 | #492 | C23 | 1 | 18 | yes | — |
| 133 | #464 | C23 | 1 | 36 | yes | — |
| 134 | #464 | C23 | 1 | 72 | yes | — |
| 135 | #463 | C23 | 1 | 36 | yes | — |
| 136 | #462 | C23 | 1 | 18 | yes | — |
| 137 | #462 | C23 | 1 | 36 | yes | — |
| 138 | #462 | C23 | 1 | 72 | yes | — |
| 139 | #462 | C23 | 1 | 36 | yes | — |
| 140 | #461 | C23 | 1 | 18 | yes | — |
| 141 | #461 | C23 | 1 | 36 | yes | — |
| 142 | #460 | C23 | 1 | 18 | yes | — |
| 143 | #459 | C23 | 1 | 6 | yes | — |
| 144 | #446 | C23 | 1 | 18 | yes | — |
| 145 | #446 | C23 | 1 | 18 | yes | — |
| 146 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 147 | C8×Q8 | C23 | 1 | 3 | yes | — |
| 148 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 149 | C8×Q8 | C23 | 1 | 9 | yes | — |
| 150 | C8×Q8 | C23 | 1 | 9 | yes | — |
| 151 | #441 | C23 | 1 | 36 | yes | — |
| 152 | #440 | C23 | 1 | 36 | yes | — |
| 153 | C4×Q16 | C23 | 1 | 18 | yes | — |
| 154 | C4×Q16 | C23 | 1 | 9 | yes | — |
| 155 | C4×Q16 | C23 | 1 | 9 | yes | — |
| 156 | C4×Q16 | C23 | 1 | 18 | yes | — |
| 157 | C4×Q16 | C23 | 1 | 18 | yes | — |
| 158 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 159 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 160 | C4×D8 | C23 | 1 | 3 | yes | — |
| 161 | C4×D8 | C23 | 1 | 9 | yes | — |
| 162 | #428 | C23 | 1 | 6 | yes | — |
| 163 | #427 | C23 | 1 | 3 | yes | — |
| 164 | C2×#107 | C23 | 1 | 3 | yes | — |
| 165 | #424 | C23 | 1 | 18 | yes | — |
| 166 | #423 | C23 | 1 | 9 | yes | — |
| 167 | C2×C4⋊C8 | C23 | 1 | 9 | yes | — |
| 168 | #419 | C23 | 1 | 18 | yes | — |
| 169 | #417 | C23 | 1 | 18 | yes | — |
| 170 | #416 | C23 | 1 | 18 | yes | — |
| 171 | C2×#103 | C23 | 1 | 18 | yes | — |
| 172 | #405 | C23 | 1 | 9 | yes | — |
| 173 | #405 | C23 | 1 | 9 | yes | — |
| 174 | C4×M16 | C23 | 1 | 9 | yes | — |
| 175 | C2×C4×C8 | C23 | 1 | 9 | yes | — |
| 176 | 2−1+4 | — | 2 | 24 | no | — |
| 177 | 2−1+4 | — | 2 | 24 | no | — |
| 178 | C2×#41 | — | 2 | 2 | no | — |
| 179 | C2×#41 | — | 2 | 18 | no | — |
| 180 | C2×#41 | C24 | 1 | 18 | yes | — |
| 181 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 182 | C22×Q8 | — | 2 | 6 | no | — |
| 183 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 184 | C22×Q8 | C24 | 1 | 18 | yes | — |
| 185 | #137 | — | 2 | 72 | no | — |
| 186 | #137 | — | 4 | 72 | no | — |
| 187 | #135 | — | 2 | 36 | no | — |
| 188 | #135 | — | 4 | 36 | no | — |
| 189 | C2×Q16 | — | 2 | 36 | no | — |
| 190 | C2×Q16 | — | 4 | 36 | no | — |
| 191 | C2×Q16 | C24 | 1 | 9 | yes | — |
| 192 | C2×Q16 | C24 | 1 | 18 | yes | — |
| 193 | C2×Q16 | C24 | 1 | 18 | yes | — |
| 194 | C2×Q16 | C24 | 1 | 36 | yes | — |
| 195 | C2×SD16 | C24 | 1 | 18 | yes | — |
| 196 | C2×SD16 | C24 | 1 | 36 | yes | — |
| 197 | C2×D8 | C24 | 1 | 3 | yes | — |
| 198 | C2×D8 | C24 | 1 | 6 | yes | — |
| 199 | #131 | — | 2 | 12 | no | — |
| 200 | #131 | #41 | 1 | 8 | yes | complemented |
| 201 | C2×M16 | C24 | 1 | 9 | yes | — |
| 202 | C2×M16 | C24 | 1 | 3 | yes | — |
| 203 | C22×C8 | C24 | 1 | 9 | yes | — |
| 204 | C22×C8 | C24 | 1 | 3 | yes | — |
| 205 | C4⋊Q8 | — | 2 | 18 | no | — |
| 206 | C4⋊Q8 | — | 2 | 18 | no | — |
| 207 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 208 | C4⋊Q8 | C2×D4 | 1 | 9 | yes | — |
| 209 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 210 | C4⋊Q8 | C24 | 1 | 36 | yes | — |
| 211 | #127 | C24 | 1 | 6 | yes | — |
| 212 | #126 | — | 2 | 72 | no | — |
| 213 | #126 | — | 2 | 36 | no | — |
| 214 | #125 | — | 2 | 18 | no | — |
| 215 | #125 | — | 2 | 36 | no | — |
| 216 | #125 | — | 2 | 72 | no | — |
| 217 | #125 | — | 2 | 36 | no | — |
| 218 | #125 | C2×D4 | 1 | 18 | yes | — |
| 219 | #124 | — | 2 | 18 | no | — |
| 220 | #124 | C24 | 1 | 36 | yes | — |
| 221 | #123 | — | 2 | 36 | no | — |
| 222 | #123 | — | 2 | 72 | no | — |
| 223 | C22⋊Q8 | — | 2 | 18 | no | — |
| 224 | C22⋊Q8 | — | 2 | 36 | no | — |
| 225 | C22⋊Q8 | — | 2 | 36 | no | — |
| 226 | C22⋊Q8 | — | 2 | 36 | no | — |
| 227 | C22⋊Q8 | C2×D4 | 1 | 18 | yes | — |
| 228 | C22⋊Q8 | C2×D4 | 1 | 18 | yes | — |
| 229 | #121 | — | 2 | 18 | no | — |
| 230 | #121 | — | 2 | 18 | no | — |
| 231 | #121 | — | 2 | 6 | no | — |
| 232 | C4×Q8 | — | 2 | 2 | no | — |
| 233 | C4×Q8 | — | 2 | 6 | no | — |
| 234 | C4×Q8 | — | 2 | 36 | no | — |
| 235 | C4×Q8 | — | 2 | 12 | no | — |
| 236 | C4×Q8 | — | 2 | 18 | no | — |
| 237 | C4×Q8 | — | 2 | 18 | no | — |
| 238 | C4×Q8 | — | 2 | 18 | no | — |
| 239 | C4×Q8 | — | 2 | 18 | no | — |
| 240 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 241 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 242 | C4×Q8 | C2×D4 | 1 | 9 | yes | — |
| 243 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 244 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 245 | C4×Q8 | C24 | 1 | 36 | yes | — |
| 246 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 247 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 248 | C4×Q8 | C24 | 1 | 9 | yes | — |
| 249 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 250 | C4×D4 | — | 2 | 6 | no | — |
| 251 | C4×D4 | — | 2 | 18 | no | — |
| 252 | C4×D4 | — | 2 | 18 | no | — |
| 253 | C4×D4 | — | 2 | 18 | no | — |
| 254 | C4×D4 | — | 2 | 36 | no | — |
| 255 | C4×D4 | — | 2 | 18 | no | — |
| 256 | C4×D4 | — | 2 | 18 | no | — |
| 257 | C4×D4 | C2×D4 | 1 | 9 | yes | — |
| 258 | C4×D4 | C2×D4 | 1 | 9 | yes | — |
| 259 | C4×D4 | C24 | 1 | 6 | yes | — |
| 260 | C4×D4 | C24 | 1 | 18 | yes | — |
| 261 | #117 | — | 2 | 18 | no | — |
| 262 | #117 | — | 2 | 18 | no | — |
| 263 | #117 | — | 2 | 36 | no | — |
| 264 | #117 | — | 2 | 36 | no | — |
| 265 | #117 | — | 2 | 18 | no | — |
| 266 | #117 | C24 | 1 | 6 | yes | — |
| 267 | #117 | C24 | 1 | 9 | yes | — |
| 268 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 269 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 270 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 271 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 272 | C2×C4⋊C4 | C2×D4 | 1 | 9 | yes | — |
| 273 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 274 | C2×C42 | — | 2 | 18 | no | — |
| 275 | C2×C42 | — | 2 | 18 | no | — |
| 276 | C2×C42 | C24 | 1 | 9 | yes | — |
| 277 | #107 | C24 | 1 | 3 | yes | — |
| 278 | #107 | C24 | 1 | 6 | yes | — |
| 279 | #107 | C24 | 1 | 1 | yes | characteristic |
| 280 | #106 | C24 | 1 | 6 | yes | — |
| 281 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 282 | C4⋊C8 | C24 | 1 | 9 | yes | — |
| 283 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 284 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 285 | #103 | C24 | 1 | 18 | yes | — |
| 286 | #103 | C24 | 1 | 36 | yes | — |
| 287 | #103 | C24 | 1 | 18 | yes | — |
| 288 | #102 | C24 | 1 | 6 | yes | — |
| 289 | #102 | C24 | 1 | 18 | yes | — |
| 290 | #97 | C24 | 1 | 18 | yes | — |
| 291 | C4×C8 | C24 | 1 | 3 | yes | — |
| 292 | C4×C8 | C24 | 1 | 9 | yes | — |
| 293 | C4×C8 | C24 | 1 | 9 | yes | — |
| 294 | C4×C8 | C24 | 1 | 9 | yes | — |
| 295 | #41 | — | 2 | 36 | no | — |
| 296 | #41 | — | 2 | 36 | no | — |
| 297 | #41 | — | 4 | 8 | no | — |
| 298 | #41 | — | 4 | 72 | no | — |
| 299 | #41 | C2×#41 | 1 | 4 | yes | — |
| 300 | #41 | H(5,𝔽2) | 1 | 4 | yes | — |
| 301 | C2×Q8 | — | 2 | 12 | no | — |
| 302 | C2×Q8 | — | 2 | 18 | no | — |
| 303 | C2×Q8 | — | 2 | 36 | no | — |
| 304 | C2×Q8 | — | 2 | 36 | no | — |
| 305 | C2×Q8 | — | 4 | 24 | no | — |
| 306 | C2×Q8 | C22×D4 | 1 | 9 | yes | — |
| 307 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 308 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 309 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 310 | C2×Q8 | C25 | 1 | 18 | yes | — |
| 311 | C2×D4 | — | 2 | 18 | no | — |
| 312 | C2×D4 | — | 2 | 6 | no | — |
| 313 | C2×D4 | — | 2 | 6 | no | — |
| 314 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 315 | C2×D4 | C25 | 1 | 6 | yes | — |
| 316 | C22×C4 | — | 2 | 18 | no | — |
| 317 | C22×C4 | — | 2 | 6 | no | — |
| 318 | C22×C4 | — | 2 | 6 | no | — |
| 319 | C22×C4 | — | 2 | 18 | no | — |
| 320 | C22×C4 | — | 2 | 18 | no | — |
| 321 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 322 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 323 | C22×C4 | C25 | 1 | 3 | yes | — |
| 324 | Q16 | — | 2 | 18 | no | — |
| 325 | Q16 | — | 2 | 36 | no | — |
| 326 | Q16 | — | 4 | 18 | no | — |
| 327 | Q16 | — | 4 | 36 | no | — |
| 328 | SD16 | — | 2 | 36 | no | — |
| 329 | SD16 | — | 4 | 36 | no | — |
| 330 | D8 | — | 2 | 6 | no | — |
| 331 | D8 | — | 4 | 6 | no | — |
| 332 | M16 | — | 2 | 18 | no | — |
| 333 | M16 | C2×#41 | 1 | 12 | yes | — |
| 334 | C2×C8 | — | 2 | 18 | no | — |
| 335 | C2×C8 | C2×#41 | 1 | 12 | yes | — |
| 336 | C2×C8 | C25 | 1 | 3 | yes | — |
| 337 | C2×C8 | C25 | 1 | 9 | yes | — |
| 338 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 339 | C2×C8 | C25 | 1 | 3 | yes | — |
| 340 | C4⋊C4 | — | 2 | 6 | no | — |
| 341 | C4⋊C4 | — | 2 | 18 | no | — |
| 342 | C4⋊C4 | — | 2 | 36 | no | — |
| 343 | C4⋊C4 | — | 2 | 18 | no | — |
| 344 | C4⋊C4 | — | 2 | 18 | no | — |
| 345 | C4⋊C4 | — | 2 | 36 | no | — |
| 346 | C4⋊C4 | — | 2 | 36 | no | — |
| 347 | C4⋊C4 | — | 2 | 18 | no | — |
| 348 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 349 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 350 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 351 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 352 | C4⋊C4 | C22×D4 | 1 | 9 | yes | — |
| 353 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 354 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 355 | C4⋊C4 | C25 | 1 | 6 | yes | — |
| 356 | C22⋊C4 | — | 2 | 6 | no | — |
| 357 | C22⋊C4 | — | 2 | 6 | no | — |
| 358 | C22⋊C4 | — | 2 | 18 | no | — |
| 359 | C22⋊C4 | — | 2 | 36 | no | — |
| 360 | C22⋊C4 | — | 2 | 36 | no | — |
| 361 | C22⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 362 | C42 | — | 2 | 6 | no | — |
| 363 | C42 | — | 2 | 18 | no | — |
| 364 | C42 | — | 2 | 18 | no | — |
| 365 | C42 | — | 2 | 36 | no | — |
| 366 | C42 | C22×D4 | 1 | 9 | yes | — |
| 367 | C42 | C22×D4 | 1 | 9 | yes | — |
| 368 | C42 | C25 | 1 | 3 | yes | — |
| 369 | C42 | C25 | 1 | 9 | yes | — |
| 370 | C23 | — | 2 | 6 | no | — |
| 371 | C23 | C23×D4 | 1 | 3 | yes | — |
| 372 | Q8 | — | 2 | 18 | no | — |
| 373 | Q8 | — | 2 | 18 | no | — |
| 374 | Q8 | — | 2 | 18 | no | — |
| 375 | Q8 | — | 4 | 6 | no | — |
| 376 | Q8 | — | 4 | 36 | no | — |
| 377 | Q8 | #550 | 1 | 4 | yes | — |
| 378 | Q8 | #578 | 1 | 4 | yes | complemented |
| 379 | D4 | — | 2 | 6 | no | — |
| 380 | D4 | — | 2 | 6 | no | — |
| 381 | D4 | — | 4 | 36 | no | — |
| 382 | D4 | — | 4 | 12 | no | — |
| 383 | D4 | — | 8 | 6 | no | — |
| 384 | D4 | #550 | 1 | 12 | yes | — |
| 385 | C2×C4 | — | 2 | 18 | no | — |
| 386 | C2×C4 | — | 2 | 2 | no | — |
| 387 | C2×C4 | — | 2 | 6 | no | — |
| 388 | C2×C4 | — | 2 | 18 | no | — |
| 389 | C2×C4 | — | 4 | 9 | no | — |
| 390 | C2×C4 | — | 4 | 36 | no | — |
| 391 | C2×C4 | — | 4 | 36 | no | — |
| 392 | C2×C4 | — | 4 | 12 | no | — |
| 393 | C2×C4 | — | 8 | 18 | no | — |
| 394 | C2×C4 | — | 8 | 6 | no | — |
| 395 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 396 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 397 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 398 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 399 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 400 | C2×C4 | C22×#41 | 1 | 6 | yes | — |
| 401 | C2×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 402 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 403 | C8 | — | 2 | 3 | no | — |
| 404 | C8 | — | 2 | 9 | no | — |
| 405 | C8 | C22×#41 | 1 | 2 | yes | — |
| 406 | C8 | C22×#41 | 1 | 6 | yes | — |
| 407 | C22 | — | 2 | 3 | no | — |
| 408 | C22 | — | 2 | 3 | no | — |
| 409 | C22 | — | 4 | 6 | no | — |
| 410 | C22 | — | 4 | 6 | no | — |
| 411 | C22 | — | 4 | 6 | no | — |
| 412 | C22 | C2×#550 | 1 | 6 | yes | — |
| 413 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 414 | C4 | — | 2 | 9 | no | — |
| 415 | C4 | — | 2 | 3 | no | — |
| 416 | C4 | — | 2 | 9 | no | — |
| 417 | C4 | — | 4 | 2 | no | — |
| 418 | C4 | — | 4 | 6 | no | — |
| 419 | C4 | — | 4 | 18 | no | — |
| 420 | C4 | C2×#550 | 1 | 6 | yes | — |
| 421 | C4 | C2×#578 | 1 | 6 | yes | — |
| 422 | C4 | C23×#41 | 1 | 1 | yes | characteristic |
| 423 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 424 | C2 | — | 2 | 6 | no | — |
| 425 | C2 | — | 8 | 6 | no | — |
| 426 | C2 | C22×#550 | 1 | 1 | yes | characteristic |
| 427 | C2 | C22×#578 | 1 | 1 | yes | characteristic |
| 428 | C2 | #63093 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ Q8×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63001 | C2 | semidirect |
| 2. #61422 | C2 | semidirect |
| 3. #61411 | C2 | semidirect |
| 4. #61408 | C2 | semidirect |
| 5. #61404 | C2 | semidirect |
| 6. #61393 | C2 | semidirect |
| 7. C2×#3395 | C2 | semidirect |
| 8. #60648 | C2 | semidirect |
| 9. #60432 | C2 | semidirect |
| 10. Q8×#131 | C2 | semidirect |
| 11. C4×#578 | C2 | semidirect |
| 200. #131 | #41 | semidirect |
| 378. Q8 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63001 | 2 |
| #61422 | 2 |
| #61411 | 2 |
| #61408 | 2 |
| #61404 | 2 |
| #61393 | 2 |
| C2×#3395 | 2 |
| #60648 | 2 |
| #60432 | 2 |
| Q8×#131 | 2 |
| C4×#578 | 2 |