← #509710
Subgroups — #509710
Order 512.
512 conjugacy classes of subgroups.
The subgroup lattice has 413 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#2252 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#2227 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #28813 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #26485 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13530 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13515 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #13505 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #13451 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #13451 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #13364 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #13148 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #13133 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #13112 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #13104 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #12936 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×Q16 | C22 | 1 | 1 | yes | characteristic |
| 20 | #2551 | — | 2 | 1 | no | — |
| 21 | #2451 | — | 2 | 1 | no | — |
| 22 | #2252 | — | 2 | 4 | no | — |
| 23 | #2227 | — | 2 | 4 | no | — |
| 24 | C2×#366 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#366 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#366 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#366 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#366 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#366 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#358 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#358 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#358 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#358 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×C4×C16 | C22 | 1 | 1 | yes | characteristic |
| 36 | #2068 | — | 2 | 1 | no | — |
| 37 | #2057 | — | 2 | 1 | no | — |
| 38 | #2057 | — | 2 | 1 | no | — |
| 39 | #2024 | — | 2 | 1 | no | — |
| 40 | #1969 | C22 | 1 | 1 | yes | characteristic |
| 41 | #1969 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1947 | — | 2 | 1 | no | — |
| 43 | #1942 | C22 | 1 | 1 | yes | characteristic |
| 44 | #1942 | C22 | 1 | 1 | yes | characteristic |
| 45 | #1942 | C22 | 1 | 1 | yes | characteristic |
| 46 | #1942 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1863 | — | 2 | 1 | no | — |
| 48 | #1845 | C22 | 1 | 1 | yes | characteristic |
| 49 | C4×#107 | C22 | 1 | 1 | yes | characteristic |
| 50 | C8×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1380 | C22 | 1 | 1 | yes | characteristic |
| 52 | #1380 | C22 | 1 | 1 | yes | characteristic |
| 53 | #1380 | C22 | 1 | 1 | yes | characteristic |
| 54 | #1380 | C22 | 1 | 1 | yes | characteristic |
| 55 | #1380 | C22 | 1 | 1 | yes | characteristic |
| 56 | #1380 | C22 | 1 | 1 | yes | characteristic |
| 57 | #1374 | C22 | 1 | 1 | yes | characteristic |
| 58 | #1374 | C22 | 1 | 1 | yes | characteristic |
| 59 | #1374 | C22 | 1 | 1 | yes | characteristic |
| 60 | #1374 | C22 | 1 | 1 | yes | characteristic |
| 61 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 63 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 64 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 65 | C2×C4⋊Q8 | — | 4 | 1 | no | — |
| 66 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 67 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 71 | #500 | — | 2 | 2 | no | — |
| 72 | #500 | — | 2 | 2 | no | — |
| 73 | #500 | — | 2 | 2 | no | — |
| 74 | #500 | — | 4 | 1 | no | — |
| 75 | #500 | — | 4 | 1 | no | — |
| 76 | #500 | — | 4 | 1 | no | — |
| 77 | C4×Q16 | — | 2 | 2 | no | — |
| 78 | C4×Q16 | — | 4 | 1 | no | — |
| 79 | C2×#107 | — | 2 | 1 | no | — |
| 80 | C2×#107 | — | 2 | 1 | no | — |
| 81 | C2×#107 | — | 2 | 1 | no | — |
| 82 | C2×#107 | — | 2 | 1 | no | — |
| 83 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 91 | C2×#103 | — | 2 | 1 | no | — |
| 92 | C2×#103 | — | 2 | 1 | no | — |
| 93 | C2×#103 | — | 2 | 1 | no | — |
| 94 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 97 | #398 | — | 4 | 1 | no | — |
| 98 | #395 | — | 4 | 1 | no | — |
| 99 | #395 | — | 4 | 1 | no | — |
| 100 | #395 | — | 4 | 1 | no | — |
| 101 | #391 | — | 2 | 1 | no | — |
| 102 | #391 | — | 2 | 1 | no | — |
| 103 | #391 | — | 4 | 1 | no | — |
| 104 | #389 | — | 2 | 1 | no | — |
| 105 | #389 | — | 2 | 1 | no | — |
| 106 | #389 | — | 2 | 1 | no | — |
| 107 | #389 | — | 2 | 1 | no | — |
| 108 | #389 | — | 4 | 1 | no | — |
| 109 | #387 | — | 4 | 1 | no | — |
| 110 | #384 | — | 2 | 1 | no | — |
| 111 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 112 | C4×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 113 | #366 | — | 2 | 2 | no | — |
| 114 | #366 | — | 2 | 2 | no | — |
| 115 | #366 | — | 2 | 2 | no | — |
| 116 | #366 | — | 2 | 2 | no | — |
| 117 | #366 | — | 4 | 1 | no | — |
| 118 | #366 | D4 | 1 | 4 | yes | — |
| 119 | C4⋊C16 | — | 2 | 2 | no | — |
| 120 | #358 | — | 2 | 2 | no | — |
| 121 | #358 | — | 2 | 2 | no | — |
| 122 | #358 | — | 4 | 1 | no | — |
| 123 | #358 | Q8 | 1 | 4 | yes | complemented |
| 124 | C4×C16 | — | 2 | 2 | no | — |
| 125 | #340 | — | 2 | 1 | no | — |
| 126 | #340 | — | 2 | 1 | no | — |
| 127 | #340 | — | 2 | 1 | no | — |
| 128 | #340 | — | 2 | 1 | no | — |
| 129 | #340 | — | 2 | 1 | no | — |
| 130 | #336 | D4 | 1 | 1 | yes | characteristic |
| 131 | #336 | D4 | 1 | 1 | yes | characteristic |
| 132 | C22×Q8 | — | 2 | 1 | no | — |
| 133 | C22×Q8 | — | 4 | 1 | no | — |
| 134 | C22×Q8 | — | 4 | 1 | no | — |
| 135 | C22×Q8 | — | 4 | 1 | no | — |
| 136 | C2×Q16 | — | 2 | 1 | no | — |
| 137 | C2×Q16 | — | 2 | 1 | no | — |
| 138 | C2×Q16 | — | 2 | 1 | no | — |
| 139 | C2×Q16 | — | 2 | 1 | no | — |
| 140 | C2×Q16 | — | 2 | 1 | no | — |
| 141 | C2×Q16 | C2×Q8 | 1 | 2 | yes | — |
| 142 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 146 | C4⋊Q8 | — | 4 | 2 | no | — |
| 147 | C4⋊Q8 | — | 4 | 2 | no | — |
| 148 | C4⋊Q8 | — | 4 | 2 | no | — |
| 149 | C4⋊Q8 | — | 8 | 1 | no | — |
| 150 | C4⋊Q8 | — | 8 | 1 | no | — |
| 151 | C4⋊Q8 | — | 8 | 1 | no | — |
| 152 | C4⋊Q8 | — | 8 | 4 | no | — |
| 153 | C4×Q8 | — | 4 | 2 | no | — |
| 154 | C4×Q8 | — | 8 | 1 | no | — |
| 155 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 156 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 157 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 158 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 159 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 160 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 161 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 162 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 163 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 164 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 165 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 166 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 167 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 168 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 169 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 170 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 171 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 172 | C2×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 173 | C2×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 174 | C2×C42 | — | 4 | 1 | no | — |
| 175 | C2×C42 | — | 4 | 1 | no | — |
| 176 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C16 | — | 2 | 1 | no | — |
| 180 | C2×C16 | — | 2 | 1 | no | — |
| 181 | C2×C16 | — | 2 | 1 | no | — |
| 182 | C2×C16 | — | 2 | 1 | no | — |
| 183 | C2×C16 | — | 2 | 1 | no | — |
| 184 | C2×C16 | — | 2 | 1 | no | — |
| 185 | C2×C16 | — | 2 | 1 | no | — |
| 186 | C2×C16 | — | 2 | 1 | no | — |
| 187 | C2×C16 | — | 2 | 1 | no | — |
| 188 | C2×C16 | — | 2 | 1 | no | — |
| 189 | C2×C16 | C2×D4 | 1 | 2 | yes | — |
| 190 | C2×C16 | C2×Q8 | 1 | 2 | yes | — |
| 191 | #107 | — | 2 | 1 | no | — |
| 192 | #107 | — | 2 | 1 | no | — |
| 193 | #107 | — | 2 | 1 | no | — |
| 194 | #107 | — | 2 | 1 | no | — |
| 195 | #107 | — | 2 | 1 | no | — |
| 196 | #107 | — | 2 | 1 | no | — |
| 197 | #107 | — | 2 | 1 | no | — |
| 198 | #107 | — | 2 | 1 | no | — |
| 199 | #107 | — | 2 | 1 | no | — |
| 200 | #107 | — | 2 | 1 | no | — |
| 201 | #107 | — | 2 | 1 | no | — |
| 202 | #107 | — | 4 | 2 | no | — |
| 203 | #107 | — | 4 | 2 | no | — |
| 204 | #107 | — | 4 | 2 | no | — |
| 205 | #107 | — | 8 | 1 | no | — |
| 206 | #107 | C2×D4 | 1 | 2 | yes | — |
| 207 | #107 | C2×D4 | 1 | 2 | yes | — |
| 208 | #107 | C2×Q8 | 1 | 2 | yes | — |
| 209 | C4⋊C8 | — | 2 | 2 | no | — |
| 210 | #103 | — | 4 | 2 | no | — |
| 211 | #103 | — | 4 | 2 | no | — |
| 212 | #103 | — | 8 | 1 | no | — |
| 213 | C4×C8 | — | 2 | 1 | no | — |
| 214 | C4×C8 | — | 2 | 1 | no | — |
| 215 | C4×C8 | — | 2 | 1 | no | — |
| 216 | C4×C8 | — | 2 | 1 | no | — |
| 217 | C4×C8 | — | 2 | 1 | no | — |
| 218 | C4×C8 | — | 2 | 1 | no | — |
| 219 | #95 | — | 4 | 1 | no | — |
| 220 | #95 | — | 4 | 1 | no | — |
| 221 | #95 | — | 4 | 1 | no | — |
| 222 | #95 | — | 4 | 1 | no | — |
| 223 | #95 | — | 4 | 1 | no | — |
| 224 | #95 | — | 4 | 1 | no | — |
| 225 | #95 | — | 4 | 1 | no | — |
| 226 | #95 | — | 4 | 1 | no | — |
| 227 | #95 | — | 4 | 1 | no | — |
| 228 | #95 | D8 | 1 | 1 | yes | characteristic |
| 229 | #95 | D8 | 1 | 1 | yes | characteristic |
| 230 | C2×Q8 | — | 2 | 2 | no | — |
| 231 | C2×Q8 | — | 4 | 1 | no | — |
| 232 | C2×Q8 | — | 4 | 1 | no | — |
| 233 | C2×Q8 | — | 4 | 1 | no | — |
| 234 | C2×Q8 | — | 4 | 1 | no | — |
| 235 | C2×Q8 | — | 4 | 1 | no | — |
| 236 | C2×Q8 | — | 8 | 2 | no | — |
| 237 | C2×Q8 | — | 8 | 2 | no | — |
| 238 | C2×Q8 | — | 8 | 2 | no | — |
| 239 | C2×Q8 | — | 8 | 2 | no | — |
| 240 | C2×Q8 | — | 8 | 2 | no | — |
| 241 | C2×Q8 | — | 8 | 2 | no | — |
| 242 | C2×Q8 | — | 16 | 1 | no | — |
| 243 | C2×Q8 | — | 16 | 1 | no | — |
| 244 | C2×Q8 | — | 16 | 1 | no | — |
| 245 | C22×C4 | — | 4 | 1 | no | — |
| 246 | C22×C4 | — | 4 | 1 | no | — |
| 247 | C22×C4 | — | 4 | 1 | no | — |
| 248 | C22×C4 | — | 4 | 1 | no | — |
| 249 | C22×C4 | — | 4 | 1 | no | — |
| 250 | C22×C4 | — | 4 | 1 | no | — |
| 251 | C22×C4 | — | 4 | 1 | no | — |
| 252 | C22×C4 | — | 4 | 1 | no | — |
| 253 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 254 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 255 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 256 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 257 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 258 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 259 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | Q16 | — | 2 | 2 | no | — |
| 261 | Q16 | — | 2 | 2 | no | — |
| 262 | Q16 | — | 4 | 1 | no | — |
| 263 | Q16 | — | 4 | 1 | no | — |
| 264 | C2×C8 | — | 2 | 1 | no | — |
| 265 | C2×C8 | — | 2 | 1 | no | — |
| 266 | C2×C8 | — | 2 | 1 | no | — |
| 267 | C2×C8 | — | 2 | 1 | no | — |
| 268 | C2×C8 | — | 2 | 1 | no | — |
| 269 | C2×C8 | — | 2 | 1 | no | — |
| 270 | C2×C8 | — | 2 | 1 | no | — |
| 271 | C2×C8 | — | 2 | 1 | no | — |
| 272 | C2×C8 | #137 | 1 | 2 | yes | — |
| 273 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 275 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 276 | C2×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 277 | C2×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 278 | C2×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 279 | C4⋊C4 | — | 2 | 2 | no | — |
| 280 | C4⋊C4 | — | 2 | 2 | no | — |
| 281 | C4⋊C4 | — | 2 | 2 | no | — |
| 282 | C4⋊C4 | — | 2 | 2 | no | — |
| 283 | C4⋊C4 | — | 4 | 1 | no | — |
| 284 | C4⋊C4 | — | 4 | 1 | no | — |
| 285 | C4⋊C4 | — | 4 | 1 | no | — |
| 286 | C4⋊C4 | — | 4 | 1 | no | — |
| 287 | C4⋊C4 | — | 4 | 1 | no | — |
| 288 | C4⋊C4 | — | 4 | 1 | no | — |
| 289 | C4⋊C4 | — | 4 | 1 | no | — |
| 290 | C4⋊C4 | — | 4 | 1 | no | — |
| 291 | C4⋊C4 | — | 4 | 1 | no | — |
| 292 | C4⋊C4 | — | 4 | 1 | no | — |
| 293 | C4⋊C4 | — | 4 | 1 | no | — |
| 294 | C4⋊C4 | — | 8 | 2 | no | — |
| 295 | C4⋊C4 | — | 8 | 2 | no | — |
| 296 | C4⋊C4 | — | 8 | 2 | no | — |
| 297 | C4⋊C4 | — | 8 | 2 | no | — |
| 298 | C4⋊C4 | — | 8 | 2 | no | — |
| 299 | C4⋊C4 | — | 8 | 2 | no | — |
| 300 | C4⋊C4 | — | 8 | 2 | no | — |
| 301 | C4⋊C4 | — | 16 | 1 | no | — |
| 302 | C4⋊C4 | — | 16 | 1 | no | — |
| 303 | C4⋊C4 | — | 16 | 1 | no | — |
| 304 | C4⋊C4 | Q32 | 1 | 4 | yes | — |
| 305 | C42 | — | 2 | 1 | no | — |
| 306 | C42 | — | 2 | 1 | no | — |
| 307 | C42 | — | 2 | 1 | no | — |
| 308 | C42 | — | 2 | 1 | no | — |
| 309 | C42 | — | 2 | 1 | no | — |
| 310 | C42 | — | 2 | 1 | no | — |
| 311 | C42 | — | 8 | 2 | no | — |
| 312 | C42 | — | 8 | 2 | no | — |
| 313 | C16 | — | 2 | 2 | no | — |
| 314 | C16 | — | 2 | 2 | no | — |
| 315 | C16 | — | 4 | 1 | no | — |
| 316 | C16 | — | 4 | 1 | no | — |
| 317 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 318 | Q8 | — | 4 | 2 | no | — |
| 319 | Q8 | — | 4 | 2 | no | — |
| 320 | Q8 | — | 8 | 1 | no | — |
| 321 | Q8 | — | 8 | 1 | no | — |
| 322 | Q8 | — | 16 | 4 | no | — |
| 323 | Q8 | — | 16 | 4 | no | — |
| 324 | Q8 | — | 16 | 4 | no | — |
| 325 | C2×C4 | — | 2 | 1 | no | — |
| 326 | C2×C4 | — | 2 | 1 | no | — |
| 327 | C2×C4 | — | 2 | 1 | no | — |
| 328 | C2×C4 | — | 2 | 1 | no | — |
| 329 | C2×C4 | — | 2 | 1 | no | — |
| 330 | C2×C4 | — | 2 | 1 | no | — |
| 331 | C2×C4 | — | 2 | 1 | no | — |
| 332 | C2×C4 | — | 2 | 1 | no | — |
| 333 | C2×C4 | — | 2 | 1 | no | — |
| 334 | C2×C4 | — | 2 | 1 | no | — |
| 335 | C2×C4 | — | 2 | 1 | no | — |
| 336 | C2×C4 | — | 2 | 1 | no | — |
| 337 | C2×C4 | — | 2 | 1 | no | — |
| 338 | C2×C4 | — | 2 | 1 | no | — |
| 339 | C2×C4 | — | 4 | 2 | no | — |
| 340 | C2×C4 | — | 4 | 2 | no | — |
| 341 | C2×C4 | — | 4 | 2 | no | — |
| 342 | C2×C4 | — | 4 | 2 | no | — |
| 343 | C2×C4 | — | 8 | 1 | no | — |
| 344 | C2×C4 | — | 8 | 1 | no | — |
| 345 | C2×C4 | — | 8 | 1 | no | — |
| 346 | C2×C4 | — | 8 | 1 | no | — |
| 347 | C2×C4 | — | 8 | 1 | no | — |
| 348 | C2×C4 | — | 8 | 1 | no | — |
| 349 | C2×C4 | — | 8 | 1 | no | — |
| 350 | C2×C4 | — | 8 | 1 | no | — |
| 351 | C2×C4 | — | 8 | 1 | no | — |
| 352 | C2×C4 | — | 8 | 1 | no | — |
| 353 | C2×C4 | — | 8 | 1 | no | — |
| 354 | C2×C4 | — | 8 | 1 | no | — |
| 355 | C2×C4 | — | 8 | 1 | no | — |
| 356 | C2×C4 | — | 8 | 1 | no | — |
| 357 | C2×C4 | — | 8 | 1 | no | — |
| 358 | C2×C4 | — | 8 | 1 | no | — |
| 359 | C2×C4 | — | 8 | 1 | no | — |
| 360 | C2×C4 | — | 8 | 1 | no | — |
| 361 | C2×C4 | — | 8 | 1 | no | — |
| 362 | C2×C4 | — | 8 | 1 | no | — |
| 363 | C2×C4 | C2×Q32 | 1 | 2 | yes | — |
| 364 | C2×C4 | C2×Q32 | 1 | 2 | yes | — |
| 365 | C2×C4 | C2×Q32 | 1 | 2 | yes | — |
| 366 | C2×C4 | #509 | 1 | 2 | yes | — |
| 367 | C2×C4 | #536 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | D4×Q8 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | C2×#137 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 372 | C2×C4 | #578 | 1 | 1 | yes | characteristic |
| 373 | C8 | — | 2 | 2 | no | — |
| 374 | C8 | — | 4 | 1 | no | — |
| 375 | C8 | — | 4 | 1 | no | — |
| 376 | C8 | #536 | 1 | 1 | yes | characteristic |
| 377 | C8 | #544 | 1 | 1 | yes | characteristic |
| 378 | C8 | D4×Q8 | 1 | 1 | yes | characteristic |
| 379 | C8 | #563 | 1 | 1 | yes | characteristic |
| 380 | C22 | #3226 | 1 | 1 | yes | characteristic |
| 381 | C22 | D4×D8 | 1 | 1 | yes | characteristic |
| 382 | C22 | Q8×D8 | 1 | 1 | yes | characteristic |
| 383 | C22 | C22×Q32 | 1 | 1 | yes | characteristic |
| 384 | C22 | C2×#509 | 1 | 1 | yes | characteristic |
| 385 | C22 | #3415 | 1 | 1 | yes | characteristic |
| 386 | C22 | #3417 | 1 | 1 | yes | characteristic |
| 387 | C4 | — | 2 | 2 | no | — |
| 388 | C4 | — | 2 | 2 | no | — |
| 389 | C4 | — | 2 | 2 | no | — |
| 390 | C4 | — | 2 | 2 | no | — |
| 391 | C4 | — | 4 | 1 | no | — |
| 392 | C4 | — | 4 | 1 | no | — |
| 393 | C4 | — | 8 | 2 | no | — |
| 394 | C4 | — | 8 | 2 | no | — |
| 395 | C4 | — | 8 | 2 | no | — |
| 396 | C4 | — | 8 | 2 | no | — |
| 397 | C4 | — | 16 | 1 | no | — |
| 398 | C4 | — | 16 | 1 | no | — |
| 399 | C4 | — | 16 | 1 | no | — |
| 400 | C4 | — | 16 | 1 | no | — |
| 401 | C4 | #2677 | 1 | 1 | yes | characteristic |
| 402 | C4 | #3243 | 1 | 1 | yes | characteristic |
| 403 | C4 | #3270 | 1 | 1 | yes | characteristic |
| 404 | C4 | #3385 | 1 | 1 | yes | characteristic |
| 405 | C2 | #30946 | 1 | 1 | yes | characteristic |
| 406 | C2 | #33796 | 1 | 1 | yes | characteristic |
| 407 | C2 | #33809 | 1 | 1 | yes | characteristic |
| 408 | C2 | #33830 | 1 | 1 | yes | characteristic |
| 409 | C2 | D4×Q32 | 1 | 1 | yes | characteristic |
| 410 | C2 | Q8×Q32 | 1 | 1 | yes | characteristic |
| 411 | C2 | #33953 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 123. #358 | Q8 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta