Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6750 conjugacy classes of subgroups.
The subgroup lattice has 340 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62845 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61415 | C2 | 1 | 24 | yes | maximal, complemented |
| 3 | #61408 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #61406 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #60643 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #60425 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #60191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#2951 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#575 | C22 | 1 | 6 | yes | — |
| 10 | C22×#135 | C22 | 1 | 3 | yes | — |
| 11 | #3507 | C22 | 1 | 24 | yes | complemented |
| 12 | #3506 | C22 | 1 | 24 | yes | complemented |
| 13 | #3493 | — | 2 | 12 | no | — |
| 14 | #3492 | — | 2 | 12 | no | — |
| 15 | #3459 | — | 2 | 8 | no | — |
| 16 | #3458 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3449 | C22 | 1 | 6 | yes | — |
| 18 | C2×#520 | C22 | 1 | 6 | yes | — |
| 19 | #3403 | C22 | 1 | 48 | yes | complemented |
| 20 | #3402 | C22 | 1 | 48 | yes | complemented |
| 21 | #3400 | C22 | 1 | 48 | yes | complemented |
| 22 | #3397 | C22 | 1 | 48 | yes | complemented |
| 23 | #3396 | C22 | 1 | 24 | yes | complemented |
| 24 | #3395 | C22 | 1 | 8 | yes | complemented |
| 25 | #3393 | C22 | 1 | 24 | yes | complemented |
| 26 | #3391 | C22 | 1 | 8 | yes | complemented |
| 27 | #3156 | C22 | 1 | 12 | yes | complemented |
| 28 | #3155 | C22 | 1 | 12 | yes | complemented |
| 29 | #3154 | C22 | 1 | 24 | yes | complemented |
| 30 | #3150 | C22 | 1 | 12 | yes | — |
| 31 | #3147 | C22 | 1 | 12 | yes | — |
| 32 | #3046 | C22 | 1 | 48 | yes | complemented |
| 33 | #3045 | C22 | 1 | 48 | yes | complemented |
| 34 | #3037 | C22 | 1 | 24 | yes | complemented |
| 35 | #3036 | C22 | 1 | 24 | yes | complemented |
| 36 | #2961 | C22 | 1 | 12 | yes | complemented |
| 37 | #2960 | C22 | 1 | 12 | yes | complemented |
| 38 | #2951 | C22 | 1 | 24 | yes | complemented |
| 39 | #2951 | C22 | 1 | 24 | yes | complemented |
| 40 | C2×#440 | C22 | 1 | 12 | yes | complemented |
| 41 | C2×C4×Q16 | C22 | 1 | 6 | yes | complemented |
| 42 | C2×C4×D8 | C22 | 1 | 6 | yes | complemented |
| 43 | C22×#107 | C22 | 1 | 1 | yes | characteristic |
| 44 | #2905 | C22 | 1 | 3 | yes | — |
| 45 | C2×#417 | C22 | 1 | 6 | yes | — |
| 46 | C2×#405 | C22 | 1 | 3 | yes | — |
| 47 | C22×#41 | C23 | 1 | 6 | yes | — |
| 48 | #575 | — | 4 | 24 | no | — |
| 49 | C2×#137 | C23 | 1 | 24 | yes | — |
| 50 | C2×AGL(1,ℤ/8) | C23 | 1 | 24 | yes | — |
| 51 | C2×#135 | — | 2 | 24 | no | — |
| 52 | C2×#135 | C23 | 1 | 12 | yes | — |
| 53 | C2×#135 | C23 | 1 | 12 | yes | — |
| 54 | C2×#135 | C23 | 1 | 24 | yes | — |
| 55 | C22×Q16 | C23 | 1 | 3 | yes | — |
| 56 | C22×SD16 | C23 | 1 | 6 | yes | — |
| 57 | C22×D8 | C23 | 1 | 3 | yes | — |
| 58 | C22×M16 | C23 | 1 | 3 | yes | — |
| 59 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 60 | #559 | C23 | 1 | 48 | yes | — |
| 61 | #557 | C23 | 1 | 16 | yes | — |
| 62 | #556 | — | 2 | 24 | no | — |
| 63 | #556 | C23 | 1 | 48 | yes | — |
| 64 | #555 | — | 2 | 24 | no | — |
| 65 | #554 | — | 2 | 24 | no | — |
| 66 | #553 | — | 2 | 48 | no | — |
| 67 | #552 | — | 2 | 48 | no | — |
| 68 | #550 | C23 | 1 | 16 | yes | — |
| 69 | #547 | — | 2 | 24 | no | — |
| 70 | #544 | D4 | 1 | 6 | yes | — |
| 71 | #544 | D4 | 1 | 6 | yes | — |
| 72 | #543 | D4 | 1 | 4 | yes | — |
| 73 | #539 | — | 2 | 48 | no | — |
| 74 | #538 | — | 2 | 48 | no | — |
| 75 | #537 | — | 2 | 6 | no | — |
| 76 | #537 | — | 2 | 6 | no | — |
| 77 | #536 | C23 | 1 | 24 | yes | — |
| 78 | #535 | C23 | 1 | 24 | yes | — |
| 79 | #534 | — | 2 | 12 | no | — |
| 80 | #533 | C23 | 1 | 12 | yes | — |
| 81 | #532 | C23 | 1 | 24 | yes | — |
| 82 | #529 | — | 2 | 48 | no | — |
| 83 | #525 | — | 2 | 48 | no | — |
| 84 | #525 | — | 2 | 24 | no | — |
| 85 | #520 | — | 2 | 24 | no | — |
| 86 | #520 | C23 | 1 | 48 | yes | — |
| 87 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 88 | C2×C4×D4 | — | 2 | 12 | no | — |
| 89 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 90 | C2×#117 | — | 2 | 6 | no | — |
| 91 | C2×#117 | C23 | 1 | 3 | yes | — |
| 92 | C22×C4⋊C4 | — | 2 | 6 | no | — |
| 93 | C22×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 94 | #497 | C23 | 1 | 48 | yes | — |
| 95 | #496 | C23 | 1 | 48 | yes | — |
| 96 | #495 | C23 | 1 | 24 | yes | — |
| 97 | #495 | C23 | 1 | 24 | yes | — |
| 98 | #494 | C23 | 1 | 12 | yes | — |
| 99 | #493 | C23 | 1 | 12 | yes | — |
| 100 | #492 | C23 | 1 | 24 | yes | — |
| 101 | #464 | C23 | 1 | 96 | yes | — |
| 102 | #463 | C23 | 1 | 96 | yes | — |
| 103 | #462 | C23 | 1 | 48 | yes | — |
| 104 | #461 | C23 | 1 | 48 | yes | — |
| 105 | #460 | C23 | 1 | 48 | yes | — |
| 106 | #459 | C23 | 1 | 48 | yes | — |
| 107 | #446 | C23 | 1 | 24 | yes | — |
| 108 | #446 | C23 | 1 | 24 | yes | — |
| 109 | C8×Q8 | C23 | 1 | 8 | yes | — |
| 110 | C8×Q8 | C23 | 1 | 8 | yes | — |
| 111 | #440 | C23 | 1 | 96 | yes | — |
| 112 | C4×Q16 | C23 | 1 | 24 | yes | — |
| 113 | C4×Q16 | C23 | 1 | 24 | yes | — |
| 114 | C4×D8 | C23 | 1 | 24 | yes | — |
| 115 | C4×D8 | C23 | 1 | 24 | yes | — |
| 116 | C2×#107 | C23 | 1 | 6 | yes | — |
| 117 | C2×#107 | C23 | 1 | 6 | yes | — |
| 118 | #424 | C23 | 1 | 24 | yes | — |
| 119 | #423 | C23 | 1 | 12 | yes | — |
| 120 | #417 | C23 | 1 | 48 | yes | — |
| 121 | C2×#103 | C23 | 1 | 12 | yes | — |
| 122 | C2×#102 | C23 | 1 | 12 | yes | — |
| 123 | #405 | C23 | 1 | 12 | yes | — |
| 124 | #405 | C23 | 1 | 12 | yes | — |
| 125 | C2×#97 | C23 | 1 | 6 | yes | — |
| 126 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 127 | C2×#41 | — | 2 | 16 | no | — |
| 128 | C2×#41 | — | 2 | 12 | no | — |
| 129 | C2×#41 | — | 2 | 24 | no | — |
| 130 | C2×#41 | — | 2 | 24 | no | — |
| 131 | C2×#41 | C24 | 1 | 24 | yes | — |
| 132 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 133 | C22×D4 | — | 2 | 6 | no | — |
| 134 | C22×D4 | C24 | 1 | 6 | yes | — |
| 135 | C23×C4 | — | 2 | 2 | no | — |
| 136 | C23×C4 | — | 2 | 6 | no | — |
| 137 | C23×C4 | — | 2 | 12 | no | — |
| 138 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 139 | #137 | — | 4 | 48 | no | — |
| 140 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 141 | #135 | — | 2 | 48 | no | — |
| 142 | #135 | — | 2 | 48 | no | — |
| 143 | #135 | — | 4 | 48 | no | — |
| 144 | C2×Q16 | — | 2 | 12 | no | — |
| 145 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 146 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 147 | C2×Q16 | C24 | 1 | 24 | yes | — |
| 148 | C2×SD16 | — | 2 | 24 | no | — |
| 149 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 150 | C2×SD16 | C24 | 1 | 48 | yes | — |
| 151 | C2×D8 | — | 2 | 12 | no | — |
| 152 | C2×D8 | C24 | 1 | 6 | yes | — |
| 153 | C2×D8 | C24 | 1 | 6 | yes | — |
| 154 | C2×D8 | C24 | 1 | 24 | yes | — |
| 155 | C2×M16 | — | 2 | 12 | no | — |
| 156 | C2×M16 | C24 | 1 | 12 | yes | — |
| 157 | C22×C8 | #41 | 1 | 8 | yes | complemented |
| 158 | C22×C8 | C24 | 1 | 6 | yes | — |
| 159 | C22×C8 | C24 | 1 | 3 | yes | — |
| 160 | C22×C8 | C24 | 1 | 3 | yes | — |
| 161 | C4⋊Q8 | C2×D4 | 1 | 12 | yes | — |
| 162 | C4⋊Q8 | C2×D4 | 1 | 12 | yes | — |
| 163 | C4⋊Q8 | C24 | 1 | 24 | yes | — |
| 164 | #127 | C24 | 1 | 24 | yes | — |
| 165 | #126 | — | 2 | 96 | no | — |
| 166 | #125 | — | 2 | 48 | no | — |
| 167 | #125 | C2×D4 | 1 | 24 | yes | — |
| 168 | #124 | — | 2 | 48 | no | — |
| 169 | #124 | C24 | 1 | 48 | yes | — |
| 170 | #123 | — | 2 | 96 | no | — |
| 171 | #123 | — | 2 | 48 | no | — |
| 172 | C22⋊Q8 | — | 2 | 48 | no | — |
| 173 | C22⋊Q8 | — | 2 | 24 | no | — |
| 174 | C22⋊Q8 | — | 2 | 24 | no | — |
| 175 | C22⋊Q8 | C2×D4 | 1 | 24 | yes | — |
| 176 | C22⋊Q8 | C2×D4 | 1 | 24 | yes | — |
| 177 | #121 | — | 2 | 24 | no | — |
| 178 | #121 | — | 2 | 24 | no | — |
| 179 | #121 | — | 2 | 24 | no | — |
| 180 | #121 | — | 2 | 24 | no | — |
| 181 | #121 | — | 2 | 48 | no | — |
| 182 | #120 | — | 2 | 48 | no | — |
| 183 | C4×Q8 | — | 2 | 16 | no | — |
| 184 | C4×Q8 | — | 2 | 24 | no | — |
| 185 | C4×Q8 | C24 | 1 | 48 | yes | — |
| 186 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 187 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 188 | C4×D4 | — | 2 | 48 | no | — |
| 189 | C4×D4 | — | 2 | 96 | no | — |
| 190 | C4×D4 | — | 2 | 24 | no | — |
| 191 | C4×D4 | — | 2 | 24 | no | — |
| 192 | C4×D4 | — | 2 | 24 | no | — |
| 193 | C4×D4 | C24 | 1 | 48 | yes | — |
| 194 | #117 | — | 2 | 48 | no | — |
| 195 | #117 | — | 2 | 48 | no | — |
| 196 | #117 | C2×D4 | 1 | 12 | yes | — |
| 197 | #117 | C24 | 1 | 12 | yes | — |
| 198 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 199 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 200 | C2×C4⋊C4 | — | 2 | 48 | no | — |
| 201 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 202 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 203 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 204 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 205 | C2×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 206 | C2×C42 | — | 2 | 12 | no | — |
| 207 | C2×C42 | C24 | 1 | 6 | yes | — |
| 208 | #107 | C24 | 1 | 4 | yes | — |
| 209 | #107 | C24 | 1 | 12 | yes | — |
| 210 | C4⋊C8 | C24 | 1 | 24 | yes | — |
| 211 | C4⋊C8 | C24 | 1 | 24 | yes | — |
| 212 | #103 | C24 | 1 | 48 | yes | — |
| 213 | #102 | C24 | 1 | 48 | yes | — |
| 214 | #97 | C24 | 1 | 24 | yes | — |
| 215 | C4×C8 | C24 | 1 | 12 | yes | — |
| 216 | C4×C8 | C24 | 1 | 12 | yes | — |
| 217 | C24 | — | 2 | 6 | no | — |
| 218 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 219 | #41 | — | 2 | 48 | no | — |
| 220 | #41 | — | 2 | 48 | no | — |
| 221 | #41 | — | 4 | 48 | no | — |
| 222 | #41 | — | 16 | 16 | no | — |
| 223 | C2×Q8 | — | 2 | 6 | no | — |
| 224 | C2×Q8 | — | 2 | 12 | no | — |
| 225 | C2×Q8 | — | 2 | 12 | no | — |
| 226 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 227 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 228 | C2×Q8 | C25 | 1 | 12 | yes | — |
| 229 | C2×D4 | — | 2 | 24 | no | — |
| 230 | C2×D4 | — | 2 | 6 | no | — |
| 231 | C2×D4 | — | 2 | 24 | no | — |
| 232 | C2×D4 | — | 2 | 24 | no | — |
| 233 | C2×D4 | — | 2 | 12 | no | — |
| 234 | C2×D4 | — | 2 | 12 | no | — |
| 235 | C2×D4 | — | 4 | 24 | no | — |
| 236 | C2×D4 | C25 | 1 | 12 | yes | — |
| 237 | C22×C4 | — | 2 | 6 | no | — |
| 238 | C22×C4 | — | 2 | 12 | no | — |
| 239 | C22×C4 | — | 2 | 24 | no | — |
| 240 | C22×C4 | — | 2 | 48 | no | — |
| 241 | C22×C4 | — | 4 | 24 | no | — |
| 242 | C22×C4 | — | 16 | 12 | no | — |
| 243 | C22×C4 | — | 16 | 2 | no | — |
| 244 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 245 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 246 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 247 | C22×C4 | C2×#41 | 1 | 4 | yes | — |
| 248 | C22×C4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 249 | C22×C4 | C25 | 1 | 3 | yes | — |
| 250 | Q16 | — | 2 | 12 | no | — |
| 251 | Q16 | — | 2 | 12 | no | — |
| 252 | Q16 | — | 4 | 24 | no | — |
| 253 | SD16 | — | 2 | 48 | no | — |
| 254 | SD16 | — | 4 | 48 | no | — |
| 255 | D8 | — | 2 | 12 | no | — |
| 256 | D8 | — | 2 | 12 | no | — |
| 257 | D8 | — | 4 | 24 | no | — |
| 258 | M16 | — | 2 | 24 | no | — |
| 259 | C2×C8 | — | 2 | 12 | no | — |
| 260 | C2×C8 | C2×#41 | 1 | 12 | yes | — |
| 261 | C2×C8 | C2×#41 | 1 | 12 | yes | — |
| 262 | C2×C8 | C25 | 1 | 12 | yes | — |
| 263 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 264 | C2×C8 | C25 | 1 | 3 | yes | — |
| 265 | C4⋊C4 | — | 2 | 12 | no | — |
| 266 | C4⋊C4 | — | 2 | 48 | no | — |
| 267 | C4⋊C4 | — | 2 | 24 | no | — |
| 268 | C4⋊C4 | — | 2 | 24 | no | — |
| 269 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 270 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 271 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 272 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 273 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 274 | C22⋊C4 | — | 2 | 48 | no | — |
| 275 | C22⋊C4 | — | 2 | 48 | no | — |
| 276 | C22⋊C4 | — | 2 | 48 | no | — |
| 277 | C22⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 278 | C42 | — | 2 | 48 | no | — |
| 279 | C42 | C22×D4 | 1 | 12 | yes | — |
| 280 | C42 | C25 | 1 | 12 | yes | — |
| 281 | C23 | — | 2 | 12 | no | — |
| 282 | C23 | — | 4 | 1 | no | — |
| 283 | C23 | — | 4 | 1 | no | — |
| 284 | C23 | — | 4 | 12 | no | — |
| 285 | C23 | — | 8 | 6 | no | — |
| 286 | C23 | — | 8 | 6 | no | — |
| 287 | C23 | #550 | 1 | 4 | yes | — |
| 288 | C23 | C23×D4 | 1 | 3 | yes | — |
| 289 | Q8 | — | 2 | 12 | no | — |
| 290 | Q8 | — | 2 | 12 | no | — |
| 291 | Q8 | — | 4 | 8 | no | — |
| 292 | Q8 | — | 4 | 8 | no | — |
| 293 | Q8 | — | 4 | 12 | no | — |
| 294 | D4 | — | 2 | 12 | no | — |
| 295 | D4 | — | 2 | 12 | no | — |
| 296 | D4 | — | 4 | 48 | no | — |
| 297 | D4 | — | 4 | 12 | no | — |
| 298 | D4 | — | 8 | 24 | no | — |
| 299 | D4 | — | 8 | 24 | no | — |
| 300 | C2×C4 | — | 2 | 8 | no | — |
| 301 | C2×C4 | — | 2 | 12 | no | — |
| 302 | C2×C4 | — | 4 | 6 | no | — |
| 303 | C2×C4 | — | 4 | 6 | no | — |
| 304 | C2×C4 | — | 4 | 12 | no | — |
| 305 | C2×C4 | — | 4 | 48 | no | — |
| 306 | C2×C4 | — | 8 | 48 | no | — |
| 307 | C2×C4 | — | 8 | 12 | no | — |
| 308 | C2×C4 | #550 | 1 | 12 | yes | — |
| 309 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 310 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 311 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 312 | C2×C4 | C22×#41 | 1 | 6 | yes | — |
| 313 | C2×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 314 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 315 | C8 | — | 2 | 12 | no | — |
| 316 | C8 | C22×#41 | 1 | 2 | yes | — |
| 317 | C8 | C22×#41 | 1 | 6 | yes | — |
| 318 | C22 | — | 2 | 3 | no | — |
| 319 | C22 | — | 2 | 3 | no | — |
| 320 | C22 | — | 4 | 4 | no | — |
| 321 | C22 | — | 4 | 12 | no | — |
| 322 | C22 | — | 4 | 12 | no | — |
| 323 | C22 | — | 4 | 12 | no | — |
| 324 | C22 | — | 8 | 24 | no | — |
| 325 | C22 | C2×#550 | 1 | 6 | yes | — |
| 326 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 327 | C4 | — | 2 | 12 | no | — |
| 328 | C4 | — | 2 | 12 | no | — |
| 329 | C4 | — | 4 | 8 | no | — |
| 330 | C4 | — | 4 | 12 | no | — |
| 331 | C4 | C2×#550 | 1 | 6 | yes | — |
| 332 | C4 | C23×#41 | 1 | 1 | yes | characteristic |
| 333 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 334 | C2 | — | 2 | 6 | no | — |
| 335 | C2 | — | 8 | 12 | no | — |
| 336 | C2 | C22×#550 | 1 | 1 | yes | characteristic |
| 337 | C2 | #63091 | 1 | 1 | yes | characteristic |
| 338 | 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 ◁ #3458 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62845 | C2 | semidirect |
| 2. #61415 | C2 | semidirect |
| 3. #61408 | C2 | semidirect |
| 4. #61406 | C2 | semidirect |
| 5. #60643 | C2 | semidirect |
| 6. #60425 | C2 | semidirect |
| 7. #60191 | C2 | semidirect |
| 8. C2×#2951 | C2 | semidirect |
| 11. #3507 | C22 | semidirect |
| 12. #3506 | C22 | semidirect |
| 19. #3403 | C22 | semidirect |
| 20. #3402 | C22 | semidirect |
| 21. #3400 | C22 | semidirect |
| 22. #3397 | C22 | semidirect |
| 23. #3396 | C22 | semidirect |
| 24. #3395 | C22 | semidirect |
| 25. #3393 | C22 | semidirect |
| 26. #3391 | C22 | semidirect |
| 27. #3156 | C22 | semidirect |
| 28. #3155 | C22 | semidirect |
| 29. #3154 | C22 | semidirect |
| 32. #3046 | C22 | semidirect |
| 33. #3045 | C22 | semidirect |
| 34. #3037 | C22 | semidirect |
| 35. #3036 | C22 | semidirect |
| 36. #2961 | C22 | semidirect |
| 37. #2960 | C22 | semidirect |
| 38. #2951 | C22 | semidirect |
| 39. #2951 | C22 | semidirect |
| 40. C2×#440 | C22 | semidirect |
| 41. C2×C4×Q16 | C22 | semidirect |
| 42. C2×C4×D8 | C22 | semidirect |
| 157. C22×C8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62845 | 2 |
| #61415 | 2 |
| #61408 | 2 |
| #61406 | 2 |
| #60643 | 2 |
| #60425 | 2 |
| #60191 | 2 |
| C2×#2951 | 2 |