Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6020 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63004 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #62530 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #62360 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | #62100 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #61952 | C2 | 1 | 10 | yes | maximal, complemented |
| 7 | #61884 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #61821 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | Q16×#41 | C2 | 1 | 10 | yes | maximal, complemented |
| 10 | C2×#3363 | C2 | 1 | 5 | yes | maximal, complemented |
| 11 | C8×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #3504 | — | 2 | 10 | no | — |
| 13 | #3503 | — | 2 | 10 | no | — |
| 14 | #3503 | C22 | 1 | 10 | yes | — |
| 15 | #3503 | C22 | 1 | 10 | yes | — |
| 16 | #3502 | — | 2 | 5 | no | — |
| 17 | #3502 | — | 2 | 5 | no | — |
| 18 | #3502 | C22 | 1 | 5 | yes | — |
| 19 | #3502 | C22 | 1 | 5 | yes | — |
| 20 | Q8×#41 | C22 | 1 | 10 | yes | — |
| 21 | Q8×#41 | C22 | 1 | 10 | yes | — |
| 22 | C2×Q82 | C22 | 1 | 5 | yes | — |
| 23 | C2×#557 | C22 | 1 | 5 | yes | — |
| 24 | C4×2−1+4 | — | 2 | 1 | no | — |
| 25 | C4×2−1+4 | — | 2 | 1 | no | — |
| 26 | C4×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3395 | C22 | 1 | 20 | yes | — |
| 28 | #3395 | C22 | 1 | 10 | yes | — |
| 29 | Q8×Q16 | C22 | 1 | 10 | yes | — |
| 30 | Q8×Q16 | C22 | 1 | 20 | yes | — |
| 31 | #3363 | C22 | 1 | 20 | yes | — |
| 32 | #3363 | C22 | 1 | 20 | yes | — |
| 33 | #3363 | C22 | 1 | 20 | yes | — |
| 34 | #3363 | C22 | 1 | 10 | yes | — |
| 35 | #3363 | C22 | 1 | 20 | yes | — |
| 36 | #3363 | C22 | 1 | 10 | yes | — |
| 37 | #3338 | C22 | 1 | 30 | yes | — |
| 38 | #3299 | C22 | 1 | 60 | yes | — |
| 39 | #3299 | C22 | 1 | 30 | yes | — |
| 40 | #3299 | C22 | 1 | 10 | yes | — |
| 41 | D4×Q16 | C22 | 1 | 30 | yes | — |
| 42 | #3249 | C22 | 1 | 30 | yes | — |
| 43 | #3230 | C22 | 1 | 30 | yes | — |
| 44 | #3209 | C22 | 1 | 30 | yes | — |
| 45 | #3170 | C22 | 1 | 30 | yes | — |
| 46 | C2×#487 | C22 | 1 | 15 | yes | — |
| 47 | #3104 | C22 | 1 | 30 | yes | — |
| 48 | #3104 | C22 | 1 | 30 | yes | — |
| 49 | C2×#477 | C22 | 1 | 15 | yes | — |
| 50 | C2×#462 | C22 | 1 | 15 | yes | — |
| 51 | #2988 | C22 | 1 | 10 | yes | — |
| 52 | #2982 | C22 | 1 | 5 | yes | — |
| 53 | C8×#41 | C22 | 1 | 10 | yes | — |
| 54 | C2×C8×Q8 | C22 | 1 | 5 | yes | — |
| 55 | C2×C4×Q16 | C22 | 1 | 15 | yes | — |
| 56 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic |
| 57 | C22×Q16 | C23 | 1 | 15 | yes | — |
| 58 | Q82 | — | 2 | 20 | no | — |
| 59 | Q82 | — | 2 | 10 | no | — |
| 60 | Q82 | C23 | 1 | 10 | yes | — |
| 61 | Q82 | C23 | 1 | 20 | yes | — |
| 62 | Q82 | C23 | 1 | 10 | yes | — |
| 63 | #557 | — | 2 | 20 | no | — |
| 64 | #557 | — | 2 | 10 | no | — |
| 65 | #557 | — | 2 | 10 | no | — |
| 66 | #557 | — | 2 | 10 | no | — |
| 67 | #557 | — | 2 | 20 | no | — |
| 68 | #557 | — | 2 | 20 | no | — |
| 69 | #557 | C23 | 1 | 10 | yes | — |
| 70 | #557 | C23 | 1 | 20 | yes | — |
| 71 | #557 | C23 | 1 | 10 | yes | — |
| 72 | #554 | — | 2 | 30 | no | — |
| 73 | #554 | — | 2 | 30 | no | — |
| 74 | #554 | — | 2 | 30 | no | — |
| 75 | #554 | C23 | 1 | 10 | yes | — |
| 76 | #554 | C23 | 1 | 30 | yes | — |
| 77 | D4×Q8 | — | 2 | 30 | no | — |
| 78 | D4×Q8 | C23 | 1 | 10 | yes | — |
| 79 | D4×Q8 | C23 | 1 | 30 | yes | — |
| 80 | #544 | — | 2 | 30 | no | — |
| 81 | #544 | — | 2 | 30 | no | — |
| 82 | #544 | — | 2 | 15 | no | — |
| 83 | #544 | — | 2 | 15 | no | — |
| 84 | #533 | — | 2 | 30 | no | — |
| 85 | #533 | — | 2 | 30 | no | — |
| 86 | #533 | C23 | 1 | 30 | yes | — |
| 87 | #533 | C23 | 1 | 30 | yes | — |
| 88 | C2×C4⋊Q8 | — | 2 | 15 | no | — |
| 89 | C2×C4⋊Q8 | C23 | 1 | 15 | yes | — |
| 90 | C2×C4⋊Q8 | C23 | 1 | 15 | yes | — |
| 91 | C2×#125 | — | 2 | 15 | no | — |
| 92 | #520 | — | 2 | 10 | no | — |
| 93 | #520 | — | 2 | 10 | no | — |
| 94 | #520 | D4 | 1 | 10 | yes | — |
| 95 | #519 | — | 2 | 5 | no | — |
| 96 | #519 | — | 2 | 5 | no | — |
| 97 | #519 | D4 | 1 | 5 | yes | — |
| 98 | C4×#41 | — | 2 | 10 | no | — |
| 99 | C4×#41 | — | 2 | 10 | no | — |
| 100 | C4×#41 | C23 | 1 | 10 | yes | — |
| 101 | C2×C4×Q8 | — | 2 | 5 | no | — |
| 102 | C2×C4×Q8 | — | 2 | 5 | no | — |
| 103 | C2×C4×Q8 | C23 | 1 | 15 | yes | — |
| 104 | C2×C4×Q8 | C23 | 1 | 15 | yes | — |
| 105 | C2×C4×Q8 | C23 | 1 | 5 | yes | — |
| 106 | #500 | C23 | 1 | 30 | yes | — |
| 107 | #494 | C23 | 1 | 30 | yes | — |
| 108 | #487 | C23 | 1 | 30 | yes | — |
| 109 | #487 | C23 | 1 | 60 | yes | — |
| 110 | #487 | C23 | 1 | 10 | yes | — |
| 111 | #484 | C23 | 1 | 20 | yes | — |
| 112 | #484 | C23 | 1 | 60 | yes | — |
| 113 | #477 | C23 | 1 | 30 | yes | — |
| 114 | #477 | C23 | 1 | 60 | yes | — |
| 115 | #477 | C23 | 1 | 30 | yes | — |
| 116 | #477 | C23 | 1 | 10 | yes | — |
| 117 | #477 | C23 | 1 | 30 | yes | — |
| 118 | #467 | C23 | 1 | 60 | yes | — |
| 119 | #467 | C23 | 1 | 20 | yes | — |
| 120 | #462 | C23 | 1 | 10 | yes | — |
| 121 | #462 | C23 | 1 | 30 | yes | — |
| 122 | #462 | C23 | 1 | 30 | yes | — |
| 123 | #462 | C23 | 1 | 30 | yes | — |
| 124 | #462 | C23 | 1 | 60 | yes | — |
| 125 | #451 | C23 | 1 | 20 | yes | — |
| 126 | #451 | C23 | 1 | 60 | yes | — |
| 127 | C8×Q8 | C23 | 1 | 10 | yes | — |
| 128 | C8×Q8 | C23 | 1 | 20 | yes | — |
| 129 | C8×Q8 | C23 | 1 | 10 | yes | — |
| 130 | C4×Q16 | C23 | 1 | 30 | yes | — |
| 131 | C4×Q16 | C23 | 1 | 30 | yes | — |
| 132 | C4×Q16 | C23 | 1 | 60 | yes | — |
| 133 | C4×Q16 | C23 | 1 | 30 | yes | — |
| 134 | C4×Q16 | C23 | 1 | 10 | yes | — |
| 135 | C8×D4 | C23 | 1 | 30 | yes | — |
| 136 | C8×D4 | C23 | 1 | 10 | yes | — |
| 137 | #431 | C23 | 1 | 30 | yes | — |
| 138 | C2×#107 | C23 | 1 | 15 | yes | — |
| 139 | C2×C4⋊C8 | C23 | 1 | 15 | yes | — |
| 140 | C2×#103 | C23 | 1 | 30 | yes | — |
| 141 | C2×#103 | C23 | 1 | 15 | yes | — |
| 142 | C2×#103 | C23 | 1 | 5 | yes | — |
| 143 | C2×C4×C8 | C23 | 1 | 15 | yes | — |
| 144 | 2−1+4 | Q16 | 1 | 16 | yes | complemented |
| 145 | C2×#41 | C2×D4 | 1 | 10 | yes | — |
| 146 | C22×Q8 | — | 2 | 15 | no | — |
| 147 | C22×Q8 | C2×D4 | 1 | 5 | yes | — |
| 148 | C22×Q8 | C24 | 1 | 5 | yes | — |
| 149 | C22×Q8 | C24 | 1 | 15 | yes | — |
| 150 | C2×Q16 | — | 4 | 30 | no | — |
| 151 | C2×Q16 | C24 | 1 | 10 | yes | — |
| 152 | C2×Q16 | C24 | 1 | 30 | yes | — |
| 153 | C2×Q16 | C24 | 1 | 20 | yes | — |
| 154 | C22×C8 | C24 | 1 | 15 | yes | — |
| 155 | C22×C8 | C24 | 1 | 5 | yes | — |
| 156 | C4⋊Q8 | — | 2 | 30 | no | — |
| 157 | C4⋊Q8 | — | 2 | 60 | no | — |
| 158 | C4⋊Q8 | — | 2 | 10 | no | — |
| 159 | C4⋊Q8 | — | 2 | 30 | no | — |
| 160 | C4⋊Q8 | — | 2 | 30 | no | — |
| 161 | C4⋊Q8 | — | 2 | 30 | no | — |
| 162 | C4⋊Q8 | — | 2 | 30 | no | — |
| 163 | C4⋊Q8 | C24 | 1 | 30 | yes | — |
| 164 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 165 | C4⋊Q8 | C24 | 1 | 30 | yes | — |
| 166 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 167 | #125 | — | 2 | 30 | no | — |
| 168 | #125 | — | 2 | 60 | no | — |
| 169 | #125 | — | 2 | 10 | no | — |
| 170 | #125 | — | 2 | 30 | no | — |
| 171 | #125 | — | 2 | 30 | no | — |
| 172 | #125 | — | 2 | 30 | no | — |
| 173 | #125 | — | 2 | 30 | no | — |
| 174 | C22⋊Q8 | — | 2 | 30 | no | — |
| 175 | C22⋊Q8 | — | 2 | 30 | no | — |
| 176 | C22⋊Q8 | — | 2 | 20 | no | — |
| 177 | C22⋊Q8 | — | 2 | 20 | no | — |
| 178 | C22⋊Q8 | — | 2 | 60 | no | — |
| 179 | C22⋊Q8 | — | 2 | 60 | no | — |
| 180 | C22⋊Q8 | C24 | 1 | 20 | yes | — |
| 181 | C22⋊Q8 | C24 | 1 | 20 | yes | — |
| 182 | C4×Q8 | — | 2 | 10 | no | — |
| 183 | C4×Q8 | — | 2 | 10 | no | — |
| 184 | C4×Q8 | — | 2 | 20 | no | — |
| 185 | C4×Q8 | — | 2 | 20 | no | — |
| 186 | C4×Q8 | — | 2 | 10 | no | — |
| 187 | C4×Q8 | — | 2 | 10 | no | — |
| 188 | C4×Q8 | — | 2 | 30 | no | — |
| 189 | C4×Q8 | — | 2 | 30 | no | — |
| 190 | C4×Q8 | — | 2 | 30 | no | — |
| 191 | C4×Q8 | — | 2 | 30 | no | — |
| 192 | C4×Q8 | C2×D4 | 1 | 20 | yes | — |
| 193 | C4×Q8 | C2×D4 | 1 | 10 | yes | — |
| 194 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 195 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 196 | C4×Q8 | C24 | 1 | 30 | yes | — |
| 197 | C4×Q8 | C24 | 1 | 30 | yes | — |
| 198 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 199 | C4×D4 | — | 2 | 10 | no | — |
| 200 | C4×D4 | — | 2 | 10 | no | — |
| 201 | C4×D4 | — | 2 | 30 | no | — |
| 202 | C4×D4 | — | 2 | 30 | no | — |
| 203 | C4×D4 | C2×D4 | 1 | 30 | yes | — |
| 204 | C4×D4 | C24 | 1 | 10 | yes | — |
| 205 | #117 | — | 2 | 30 | no | — |
| 206 | #117 | — | 2 | 30 | no | — |
| 207 | #117 | C2×D4 | 1 | 30 | yes | — |
| 208 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 209 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 210 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 211 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 212 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 213 | C2×C4⋊C4 | C2×D4 | 1 | 15 | yes | — |
| 214 | C2×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 215 | C2×C4⋊C4 | C24 | 1 | 15 | yes | — |
| 216 | C2×C42 | — | 2 | 15 | no | — |
| 217 | C2×C42 | — | 2 | 15 | no | — |
| 218 | C2×C42 | C24 | 1 | 15 | yes | — |
| 219 | #107 | C24 | 1 | 10 | yes | — |
| 220 | #107 | C24 | 1 | 30 | yes | — |
| 221 | #107 | C24 | 1 | 20 | yes | — |
| 222 | C4⋊C8 | C24 | 1 | 30 | yes | — |
| 223 | C4⋊C8 | C24 | 1 | 10 | yes | — |
| 224 | #103 | C24 | 1 | 1 | yes | characteristic |
| 225 | #103 | C24 | 1 | 10 | yes | — |
| 226 | #103 | C24 | 1 | 60 | yes | — |
| 227 | #103 | C24 | 1 | 5 | yes | — |
| 228 | #103 | C24 | 1 | 5 | yes | — |
| 229 | #103 | C24 | 1 | 5 | yes | — |
| 230 | #103 | C24 | 1 | 30 | yes | — |
| 231 | #103 | C24 | 1 | 20 | yes | — |
| 232 | C22⋊C8 | C24 | 1 | 20 | yes | — |
| 233 | C4×C8 | C24 | 1 | 10 | yes | — |
| 234 | C4×C8 | C24 | 1 | 30 | yes | — |
| 235 | #41 | C2×Q16 | 1 | 80 | yes | complemented |
| 236 | C2×Q8 | — | 2 | 5 | no | — |
| 237 | C2×Q8 | — | 2 | 10 | no | — |
| 238 | C2×Q8 | — | 2 | 15 | no | — |
| 239 | C2×Q8 | — | 2 | 30 | no | — |
| 240 | C2×Q8 | — | 2 | 10 | no | — |
| 241 | C2×Q8 | — | 4 | 5 | no | — |
| 242 | C2×Q8 | — | 4 | 15 | no | — |
| 243 | C2×Q8 | — | 4 | 15 | no | — |
| 244 | C2×Q8 | — | 16 | 15 | no | — |
| 245 | C2×Q8 | C2×Q16 | 1 | 40 | yes | complemented |
| 246 | C2×Q8 | C22×D4 | 1 | 10 | yes | — |
| 247 | C2×Q8 | C25 | 1 | 10 | yes | — |
| 248 | C2×Q8 | C25 | 1 | 5 | yes | — |
| 249 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 250 | C2×D4 | C22×D4 | 1 | 10 | yes | — |
| 251 | C22×C4 | — | 2 | 5 | no | — |
| 252 | C22×C4 | — | 2 | 5 | no | — |
| 253 | C22×C4 | — | 2 | 15 | no | — |
| 254 | C22×C4 | — | 2 | 15 | no | — |
| 255 | C22×C4 | C22×D4 | 1 | 15 | yes | — |
| 256 | C22×C4 | C22×D4 | 1 | 15 | yes | — |
| 257 | C22×C4 | C25 | 1 | 5 | yes | — |
| 258 | Q16 | — | 2 | 20 | no | — |
| 259 | Q16 | — | 4 | 30 | no | — |
| 260 | Q16 | — | 4 | 20 | no | — |
| 261 | C2×C8 | — | 4 | 5 | no | — |
| 262 | C2×C8 | — | 4 | 15 | no | — |
| 263 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 264 | C2×C8 | C25 | 1 | 5 | yes | — |
| 265 | C2×C8 | C25 | 1 | 10 | yes | — |
| 266 | C4⋊C4 | — | 2 | 10 | no | — |
| 267 | C4⋊C4 | — | 2 | 10 | no | — |
| 268 | C4⋊C4 | — | 2 | 30 | no | — |
| 269 | C4⋊C4 | — | 2 | 30 | no | — |
| 270 | C4⋊C4 | — | 2 | 30 | no | — |
| 271 | C4⋊C4 | — | 2 | 30 | no | — |
| 272 | C4⋊C4 | — | 2 | 30 | no | — |
| 273 | C4⋊C4 | — | 2 | 5 | no | — |
| 274 | C4⋊C4 | — | 2 | 15 | no | — |
| 275 | C4⋊C4 | — | 2 | 10 | no | — |
| 276 | C4⋊C4 | — | 2 | 10 | no | — |
| 277 | C4⋊C4 | — | 2 | 10 | no | — |
| 278 | C4⋊C4 | — | 2 | 20 | no | — |
| 279 | C4⋊C4 | — | 2 | 20 | no | — |
| 280 | C4⋊C4 | C22×D4 | 1 | 30 | yes | — |
| 281 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 282 | C4⋊C4 | C25 | 1 | 10 | yes | — |
| 283 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 284 | C4⋊C4 | C25 | 1 | 5 | yes | — |
| 285 | C22⋊C4 | — | 2 | 20 | no | — |
| 286 | C22⋊C4 | — | 2 | 20 | no | — |
| 287 | C22⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 288 | C42 | — | 2 | 10 | no | — |
| 289 | C42 | — | 2 | 10 | no | — |
| 290 | C42 | — | 2 | 30 | no | — |
| 291 | C42 | — | 2 | 30 | no | — |
| 292 | C42 | C22×D4 | 1 | 30 | yes | — |
| 293 | C42 | C25 | 1 | 10 | yes | — |
| 294 | C23 | C23×D4 | 1 | 5 | yes | — |
| 295 | Q8 | — | 2 | 1 | no | — |
| 296 | Q8 | — | 2 | 10 | no | — |
| 297 | Q8 | — | 2 | 5 | no | — |
| 298 | Q8 | — | 2 | 5 | no | — |
| 299 | Q8 | — | 2 | 10 | no | — |
| 300 | Q8 | — | 4 | 10 | no | — |
| 301 | Q8 | — | 8 | 10 | no | — |
| 302 | Q8 | — | 8 | 15 | no | — |
| 303 | Q8 | — | 8 | 30 | no | — |
| 304 | Q8 | C22×Q16 | 1 | 40 | yes | — |
| 305 | Q8 | #585 | 1 | 2 | yes | — |
| 306 | D4 | C22×Q16 | 1 | 40 | yes | — |
| 307 | C2×C4 | — | 2 | 1 | no | — |
| 308 | C2×C4 | — | 2 | 5 | no | — |
| 309 | C2×C4 | — | 2 | 5 | no | — |
| 310 | C2×C4 | — | 2 | 1 | no | — |
| 311 | C2×C4 | — | 2 | 5 | no | — |
| 312 | C2×C4 | — | 2 | 5 | no | — |
| 313 | C2×C4 | — | 2 | 10 | no | — |
| 314 | C2×C4 | — | 2 | 10 | no | — |
| 315 | C2×C4 | — | 4 | 15 | no | — |
| 316 | C2×C4 | — | 4 | 10 | no | — |
| 317 | C2×C4 | — | 8 | 5 | no | — |
| 318 | C2×C4 | — | 8 | 15 | no | — |
| 319 | C2×C4 | — | 8 | 15 | no | — |
| 320 | C2×C4 | C22×Q16 | 1 | 60 | yes | — |
| 321 | C2×C4 | C23×D4 | 1 | 5 | yes | — |
| 322 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 323 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 324 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 325 | C8 | — | 2 | 10 | no | — |
| 326 | C8 | — | 2 | 1 | no | — |
| 327 | C8 | — | 2 | 5 | no | — |
| 328 | C22 | — | 2 | 5 | no | — |
| 329 | C22 | — | 2 | 5 | no | — |
| 330 | C22 | C23×Q16 | 1 | 10 | yes | — |
| 331 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 332 | C4 | — | 2 | 5 | no | — |
| 333 | C4 | — | 2 | 2 | no | — |
| 334 | C4 | — | 2 | 10 | no | — |
| 335 | C4 | — | 4 | 5 | no | — |
| 336 | C4 | — | 4 | 10 | no | — |
| 337 | C4 | — | 4 | 1 | no | — |
| 338 | C4 | — | 4 | 10 | no | — |
| 339 | C4 | — | 4 | 5 | no | — |
| 340 | C4 | C23×Q16 | 1 | 20 | yes | — |
| 341 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 342 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 343 | C2 | — | 2 | 10 | no | — |
| 344 | C2 | #63002 | 1 | 1 | yes | characteristic |
| 345 | C2 | C24×Q16 | 1 | 1 | yes | characteristic |
| 346 | C2 | #63092 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | C2×2−1+4 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×2−1+4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #62530 | C2 | semidirect |
| 4. #62360 | C2 | semidirect |
| 5. #62100 | C2 | semidirect |
| 6. #61952 | C2 | semidirect |
| 7. #61884 | C2 | semidirect |
| 8. #61821 | C2 | semidirect |
| 9. Q16×#41 | C2 | semidirect |
| 10. C2×#3363 | C2 | semidirect |
| 144. 2−1+4 | Q16 | semidirect |
| 235. #41 | C2×Q16 | semidirect |
| 245. C2×Q8 | C2×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63004 | 2 |
| Q8×2−1+4 | 2 |
| #62530 | 2 |
| #62360 | 2 |
| #62100 | 2 |
| #61952 | 2 |
| #61884 | 2 |
| #61821 | 2 |
| Q16×#41 | 2 |
| C2×#3363 | 2 |
| C8×2−1+4 | 2 |