← #492170
Subgroups — #492170
Order 512.
397 conjugacy classes of subgroups.
The subgroup lattice has 386 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #33962 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #33930 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #20010 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19932 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #12528 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #12494 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #12477 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #12440 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #12421 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #12386 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #12358 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #12334 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #12334 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #12072 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #12059 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #3395 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3395 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3395 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3387 | — | 2 | 1 | no | — |
| 20 | #3383 | — | 2 | 1 | no | — |
| 21 | Q8×Q16 | C22 | 1 | 1 | yes | characteristic |
| 22 | #2247 | — | 2 | 1 | no | — |
| 23 | #2247 | C22 | 1 | 1 | yes | characteristic |
| 24 | #2247 | C22 | 1 | 1 | yes | characteristic |
| 25 | #2241 | — | 2 | 1 | no | — |
| 26 | #2241 | C22 | 1 | 1 | yes | characteristic |
| 27 | #2241 | C22 | 1 | 1 | yes | characteristic |
| 28 | #2227 | — | 2 | 1 | no | — |
| 29 | #2227 | C22 | 1 | 1 | yes | characteristic |
| 30 | #2209 | — | 2 | 1 | no | — |
| 31 | #2209 | — | 2 | 1 | no | — |
| 32 | #2209 | — | 2 | 1 | no | — |
| 33 | #2209 | C22 | 1 | 1 | yes | characteristic |
| 34 | #2209 | C22 | 1 | 1 | yes | characteristic |
| 35 | #2209 | C22 | 1 | 1 | yes | characteristic |
| 36 | Q8×C16 | C22 | 1 | 1 | yes | characteristic |
| 37 | Q8×C16 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×Q32 | — | 2 | 1 | no | — |
| 39 | C4×Q32 | — | 2 | 1 | no | — |
| 40 | C4×Q32 | C22 | 1 | 1 | yes | characteristic |
| 41 | #1713 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1707 | C22 | 1 | 1 | yes | characteristic |
| 43 | #1692 | — | 2 | 1 | no | — |
| 44 | #1676 | C22 | 1 | 1 | yes | characteristic |
| 45 | #1674 | — | 2 | 1 | no | — |
| 46 | #1670 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1670 | C22 | 1 | 1 | yes | characteristic |
| 48 | #1670 | C22 | 1 | 1 | yes | characteristic |
| 49 | #1648 | — | 2 | 1 | no | — |
| 50 | #1648 | — | 2 | 1 | no | — |
| 51 | #1645 | — | 2 | 1 | no | — |
| 52 | #1636 | — | 2 | 1 | no | — |
| 53 | #1591 | C22 | 1 | 1 | yes | characteristic |
| 54 | C8×Q16 | C22 | 1 | 1 | yes | characteristic |
| 55 | C8×Q16 | C22 | 1 | 1 | yes | characteristic |
| 56 | #1371 | C22 | 1 | 1 | yes | characteristic |
| 57 | #1367 | C22 | 1 | 1 | yes | characteristic |
| 58 | #1365 | C22 | 1 | 1 | yes | characteristic |
| 59 | #1362 | C22 | 1 | 1 | yes | characteristic |
| 60 | #1362 | C22 | 1 | 1 | yes | characteristic |
| 61 | #1362 | C22 | 1 | 1 | yes | characteristic |
| 62 | Q8⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 63 | Q8⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 64 | #1332 | C22 | 1 | 1 | yes | characteristic |
| 65 | #1332 | C22 | 1 | 1 | yes | characteristic |
| 66 | #1312 | C22 | 1 | 1 | yes | characteristic |
| 67 | Q82 | — | 2 | 1 | no | — |
| 68 | #557 | — | 2 | 1 | no | — |
| 69 | #557 | — | 2 | 1 | no | — |
| 70 | #557 | — | 2 | 1 | no | — |
| 71 | C2×Q32 | — | 2 | 1 | no | — |
| 72 | C2×Q32 | — | 2 | 1 | no | — |
| 73 | C2×Q32 | — | 2 | 1 | no | — |
| 74 | C2×Q32 | — | 2 | 1 | no | — |
| 75 | C2×Q32 | — | 2 | 1 | no | — |
| 76 | C2×Q32 | — | 4 | 1 | no | — |
| 77 | C2×Q32 | D4 | 1 | 1 | yes | characteristic |
| 78 | #501 | — | 4 | 1 | no | — |
| 79 | #500 | — | 2 | 1 | no | — |
| 80 | #500 | — | 2 | 1 | no | — |
| 81 | #500 | — | 2 | 1 | no | — |
| 82 | #500 | C23 | 1 | 1 | yes | characteristic |
| 83 | #499 | — | 4 | 1 | no | — |
| 84 | #498 | — | 2 | 1 | no | — |
| 85 | #494 | — | 2 | 1 | no | — |
| 86 | #494 | — | 2 | 1 | no | — |
| 87 | #494 | — | 2 | 1 | no | — |
| 88 | #494 | C23 | 1 | 1 | yes | characteristic |
| 89 | #494 | C23 | 1 | 1 | yes | characteristic |
| 90 | #494 | C23 | 1 | 1 | yes | characteristic |
| 91 | #487 | — | 2 | 1 | no | — |
| 92 | #479 | — | 4 | 1 | no | — |
| 93 | #479 | — | 4 | 1 | no | — |
| 94 | #479 | — | 4 | 1 | no | — |
| 95 | #477 | — | 2 | 1 | no | — |
| 96 | #477 | — | 2 | 1 | no | — |
| 97 | #477 | — | 4 | 1 | no | — |
| 98 | #475 | — | 2 | 1 | no | — |
| 99 | #475 | — | 2 | 1 | no | — |
| 100 | #475 | — | 2 | 1 | no | — |
| 101 | #475 | — | 4 | 1 | no | — |
| 102 | #462 | — | 2 | 1 | no | — |
| 103 | #462 | — | 2 | 1 | no | — |
| 104 | #462 | — | 2 | 1 | no | — |
| 105 | #462 | — | 4 | 1 | no | — |
| 106 | #462 | — | 4 | 1 | no | — |
| 107 | #462 | — | 4 | 1 | no | — |
| 108 | #446 | — | 2 | 1 | no | — |
| 109 | C8×Q8 | — | 2 | 1 | no | — |
| 110 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 111 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 112 | #441 | — | 4 | 1 | no | — |
| 113 | C4×Q16 | — | 2 | 1 | no | — |
| 114 | C4×Q16 | — | 2 | 1 | no | — |
| 115 | C4×Q16 | — | 2 | 1 | no | — |
| 116 | C4×Q16 | — | 2 | 1 | no | — |
| 117 | C4×Q16 | — | 4 | 1 | no | — |
| 118 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 119 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 120 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 121 | #366 | — | 2 | 1 | no | — |
| 122 | #366 | D4 | 1 | 1 | yes | characteristic |
| 123 | C4⋊C16 | — | 2 | 1 | no | — |
| 124 | C4⋊C16 | — | 2 | 1 | no | — |
| 125 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 126 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 127 | #358 | — | 2 | 1 | no | — |
| 128 | #358 | — | 2 | 1 | no | — |
| 129 | #358 | — | 2 | 1 | no | — |
| 130 | #358 | — | 2 | 1 | no | — |
| 131 | #358 | — | 2 | 1 | no | — |
| 132 | #358 | — | 2 | 1 | no | — |
| 133 | #358 | — | 4 | 1 | no | — |
| 134 | #358 | D4 | 1 | 1 | yes | characteristic |
| 135 | #358 | D4 | 1 | 1 | yes | characteristic |
| 136 | C4×C16 | — | 2 | 1 | no | — |
| 137 | C4×C16 | — | 2 | 1 | no | — |
| 138 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 139 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 140 | #335 | D4 | 1 | 1 | yes | characteristic |
| 141 | #335 | C23 | 1 | 1 | yes | characteristic |
| 142 | #335 | C23 | 1 | 1 | yes | characteristic |
| 143 | #333 | — | 2 | 1 | no | — |
| 144 | #332 | — | 2 | 1 | no | — |
| 145 | #332 | — | 2 | 1 | no | — |
| 146 | #332 | — | 2 | 1 | no | — |
| 147 | Q8⋊C8 | — | 2 | 1 | no | — |
| 148 | Q8⋊C8 | — | 2 | 1 | no | — |
| 149 | Q8⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 150 | Q8⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 151 | C82 | C23 | 1 | 1 | yes | characteristic |
| 152 | C2×Q16 | — | 2 | 1 | no | — |
| 153 | C2×Q16 | — | 2 | 1 | no | — |
| 154 | C2×Q16 | — | 2 | 1 | no | — |
| 155 | C2×Q16 | — | 2 | 1 | no | — |
| 156 | C2×Q16 | — | 2 | 1 | no | — |
| 157 | C2×Q16 | — | 2 | 1 | no | — |
| 158 | C2×Q16 | — | 4 | 1 | no | — |
| 159 | C2×Q16 | — | 4 | 1 | no | — |
| 160 | C2×Q16 | — | 4 | 1 | no | — |
| 161 | C2×Q16 | D8 | 1 | 1 | yes | characteristic |
| 162 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C4⋊Q8 | — | 2 | 1 | no | — |
| 165 | C4⋊Q8 | — | 2 | 1 | no | — |
| 166 | C4⋊Q8 | — | 2 | 1 | no | — |
| 167 | C4⋊Q8 | — | 2 | 1 | no | — |
| 168 | C4⋊Q8 | — | 4 | 1 | no | — |
| 169 | C4⋊Q8 | — | 4 | 1 | no | — |
| 170 | C4⋊Q8 | — | 4 | 1 | no | — |
| 171 | C4⋊Q8 | — | 4 | 1 | no | — |
| 172 | C4⋊Q8 | — | 4 | 1 | no | — |
| 173 | C4⋊Q8 | — | 8 | 1 | no | — |
| 174 | #125 | — | 4 | 1 | no | — |
| 175 | #125 | — | 4 | 1 | no | — |
| 176 | #125 | — | 4 | 1 | no | — |
| 177 | #125 | — | 8 | 1 | no | — |
| 178 | #125 | — | 8 | 1 | no | — |
| 179 | #125 | — | 8 | 1 | no | — |
| 180 | C4×Q8 | — | 2 | 1 | no | — |
| 181 | C4×Q8 | — | 2 | 1 | no | — |
| 182 | C4×Q8 | — | 4 | 1 | no | — |
| 183 | C4×Q8 | — | 4 | 1 | no | — |
| 184 | C4×Q8 | — | 4 | 1 | no | — |
| 185 | C4×Q8 | — | 4 | 1 | no | — |
| 186 | C4×Q8 | — | 4 | 1 | no | — |
| 187 | C4×Q8 | — | 4 | 1 | no | — |
| 188 | C4×Q8 | — | 4 | 1 | no | — |
| 189 | C4×Q8 | — | 4 | 1 | no | — |
| 190 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | Q32 | — | 4 | 1 | no | — |
| 193 | Q32 | — | 4 | 2 | no | — |
| 194 | Q32 | — | 4 | 2 | no | — |
| 195 | Q32 | — | 8 | 1 | no | — |
| 196 | Q32 | — | 8 | 1 | no | — |
| 197 | Q32 | — | 8 | 1 | no | — |
| 198 | Q32 | — | 8 | 2 | no | — |
| 199 | C2×C16 | — | 2 | 1 | no | — |
| 200 | C2×C16 | — | 2 | 1 | no | — |
| 201 | C2×C16 | — | 2 | 1 | no | — |
| 202 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | #107 | — | 2 | 1 | no | — |
| 205 | #107 | — | 2 | 1 | no | — |
| 206 | #107 | — | 4 | 1 | no | — |
| 207 | #107 | — | 4 | 1 | no | — |
| 208 | #107 | — | 4 | 1 | no | — |
| 209 | #107 | — | 4 | 1 | no | — |
| 210 | #107 | — | 8 | 1 | no | — |
| 211 | #107 | D8 | 1 | 1 | yes | characteristic |
| 212 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | #106 | — | 4 | 1 | no | — |
| 215 | #106 | — | 4 | 1 | no | — |
| 216 | #106 | — | 4 | 1 | no | — |
| 217 | #106 | — | 4 | 1 | no | — |
| 218 | #106 | — | 4 | 1 | no | — |
| 219 | C4⋊C8 | — | 2 | 1 | no | — |
| 220 | C4⋊C8 | — | 2 | 1 | no | — |
| 221 | C4⋊C8 | — | 2 | 1 | no | — |
| 222 | C4⋊C8 | — | 2 | 1 | no | — |
| 223 | C4⋊C8 | — | 4 | 1 | no | — |
| 224 | C4⋊C8 | — | 4 | 1 | no | — |
| 225 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | #103 | — | 2 | 1 | no | — |
| 228 | #103 | — | 2 | 1 | no | — |
| 229 | #103 | — | 4 | 1 | no | — |
| 230 | #103 | — | 4 | 1 | no | — |
| 231 | #103 | — | 4 | 1 | no | — |
| 232 | #103 | — | 4 | 1 | no | — |
| 233 | #103 | — | 4 | 1 | no | — |
| 234 | #103 | — | 4 | 1 | no | — |
| 235 | #103 | — | 4 | 1 | no | — |
| 236 | #103 | — | 4 | 1 | no | — |
| 237 | #103 | — | 8 | 1 | no | — |
| 238 | #103 | D8 | 1 | 1 | yes | characteristic |
| 239 | #103 | D8 | 1 | 1 | yes | characteristic |
| 240 | #97 | — | 4 | 1 | no | — |
| 241 | C4×C8 | — | 2 | 1 | no | — |
| 242 | C4×C8 | — | 2 | 1 | no | — |
| 243 | C4×C8 | — | 4 | 1 | no | — |
| 244 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 247 | C2×Q8 | — | 2 | 1 | no | — |
| 248 | C2×Q8 | — | 2 | 1 | no | — |
| 249 | C2×Q8 | — | 4 | 1 | no | — |
| 250 | C2×Q8 | — | 4 | 1 | no | — |
| 251 | C2×Q8 | — | 4 | 1 | no | — |
| 252 | C2×Q8 | — | 4 | 1 | no | — |
| 253 | C2×Q8 | — | 8 | 1 | no | — |
| 254 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 255 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 256 | Q16 | — | 2 | 1 | no | — |
| 257 | Q16 | — | 2 | 1 | no | — |
| 258 | Q16 | — | 2 | 1 | no | — |
| 259 | Q16 | — | 2 | 1 | no | — |
| 260 | Q16 | — | 4 | 1 | no | — |
| 261 | Q16 | — | 4 | 1 | no | — |
| 262 | Q16 | — | 4 | 1 | no | — |
| 263 | Q16 | — | 4 | 1 | no | — |
| 264 | Q16 | — | 4 | 1 | no | — |
| 265 | Q16 | — | 4 | 1 | no | — |
| 266 | Q16 | — | 8 | 1 | no | — |
| 267 | Q16 | — | 8 | 1 | no | — |
| 268 | Q16 | — | 8 | 1 | no | — |
| 269 | Q16 | — | 16 | 1 | no | — |
| 270 | Q16 | — | 16 | 1 | no | — |
| 271 | Q16 | — | 16 | 1 | no | — |
| 272 | Q16 | Q32 | 1 | 4 | yes | complemented |
| 273 | C2×C8 | — | 2 | 1 | no | — |
| 274 | C2×C8 | — | 2 | 1 | no | — |
| 275 | C2×C8 | — | 2 | 1 | no | — |
| 276 | C2×C8 | — | 4 | 1 | no | — |
| 277 | C2×C8 | — | 4 | 1 | no | — |
| 278 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 279 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 280 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 281 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 282 | C4⋊C4 | — | 2 | 1 | no | — |
| 283 | C4⋊C4 | — | 2 | 1 | no | — |
| 284 | C4⋊C4 | — | 2 | 1 | no | — |
| 285 | C4⋊C4 | — | 2 | 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 | — | 4 | 1 | no | — |
| 295 | C4⋊C4 | — | 4 | 1 | no | — |
| 296 | C4⋊C4 | — | 8 | 1 | no | — |
| 297 | C4⋊C4 | — | 8 | 1 | no | — |
| 298 | C4⋊C4 | — | 8 | 1 | no | — |
| 299 | C4⋊C4 | — | 8 | 1 | no | — |
| 300 | C4⋊C4 | — | 8 | 1 | no | — |
| 301 | C4⋊C4 | — | 8 | 1 | no | — |
| 302 | C4⋊C4 | — | 8 | 1 | no | — |
| 303 | C4⋊C4 | — | 8 | 1 | no | — |
| 304 | C4⋊C4 | — | 8 | 1 | no | — |
| 305 | C4⋊C4 | — | 8 | 1 | no | — |
| 306 | C4⋊C4 | — | 8 | 1 | no | — |
| 307 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 308 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 309 | C42 | — | 2 | 1 | no | — |
| 310 | C42 | — | 2 | 1 | no | — |
| 311 | C42 | — | 4 | 1 | no | — |
| 312 | C42 | — | 4 | 1 | no | — |
| 313 | C42 | — | 8 | 1 | no | — |
| 314 | C42 | — | 8 | 1 | no | — |
| 315 | C42 | — | 8 | 1 | no | — |
| 316 | C42 | — | 8 | 1 | no | — |
| 317 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 318 | C16 | — | 2 | 1 | no | — |
| 319 | C16 | — | 2 | 1 | no | — |
| 320 | C16 | — | 4 | 1 | no | — |
| 321 | C16 | — | 4 | 1 | no | — |
| 322 | C16 | — | 4 | 1 | no | — |
| 323 | Q8 | — | 2 | 1 | no | — |
| 324 | Q8 | — | 2 | 1 | no | — |
| 325 | Q8 | — | 4 | 1 | no | — |
| 326 | Q8 | — | 4 | 1 | no | — |
| 327 | Q8 | — | 4 | 1 | no | — |
| 328 | Q8 | — | 4 | 1 | no | — |
| 329 | Q8 | — | 8 | 1 | no | — |
| 330 | Q8 | — | 8 | 1 | no | — |
| 331 | Q8 | — | 8 | 1 | no | — |
| 332 | Q8 | — | 8 | 1 | no | — |
| 333 | Q8 | — | 8 | 1 | no | — |
| 334 | Q8 | — | 8 | 1 | no | — |
| 335 | Q8 | — | 16 | 1 | no | — |
| 336 | Q8 | — | 32 | 1 | no | — |
| 337 | Q8 | C2×Q32 | 1 | 2 | yes | — |
| 338 | Q8 | C2×Q32 | 1 | 2 | yes | — |
| 339 | C2×C4 | — | 2 | 1 | no | — |
| 340 | C2×C4 | — | 2 | 1 | no | — |
| 341 | C2×C4 | — | 2 | 1 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 4 | 1 | no | — |
| 344 | C2×C4 | — | 4 | 1 | no | — |
| 345 | C2×C4 | — | 4 | 1 | no | — |
| 346 | C2×C4 | — | 4 | 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 | D42 | 1 | 1 | yes | characteristic |
| 352 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 353 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 354 | C8 | — | 2 | 1 | no | — |
| 355 | C8 | — | 2 | 1 | no | — |
| 356 | C8 | — | 4 | 1 | no | — |
| 357 | C8 | — | 4 | 1 | no | — |
| 358 | C8 | — | 4 | 1 | no | — |
| 359 | C8 | — | 8 | 1 | no | — |
| 360 | C8 | — | 8 | 1 | no | — |
| 361 | C8 | C2×Q32 | 1 | 2 | yes | — |
| 362 | C8 | #575 | 1 | 1 | yes | characteristic |
| 363 | C8 | #577 | 1 | 1 | yes | characteristic |
| 364 | C22 | D4×D8 | 1 | 1 | yes | characteristic |
| 365 | C4 | — | 2 | 2 | no | — |
| 366 | C4 | — | 2 | 2 | no | — |
| 367 | C4 | — | 2 | 1 | no | — |
| 368 | C4 | — | 4 | 1 | no | — |
| 369 | C4 | — | 4 | 1 | no | — |
| 370 | C4 | — | 8 | 1 | no | — |
| 371 | C4 | — | 8 | 1 | no | — |
| 372 | C4 | — | 8 | 1 | no | — |
| 373 | C4 | — | 8 | 1 | no | — |
| 374 | C4 | — | 16 | 1 | no | — |
| 375 | C4 | — | 16 | 1 | no | — |
| 376 | C4 | — | 16 | 1 | no | — |
| 377 | C4 | — | 16 | 1 | no | — |
| 378 | C4 | #3271 | 1 | 1 | yes | characteristic |
| 379 | C4 | #3288 | 1 | 1 | yes | characteristic |
| 380 | C4 | C22×Q32 | 1 | 1 | yes | characteristic |
| 381 | C4 | #3417 | 1 | 1 | yes | characteristic |
| 382 | C2 | #19762 | 1 | 1 | yes | characteristic |
| 383 | C2 | D4×Q32 | 1 | 1 | yes | characteristic |
| 384 | C2 | #33855 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 272. Q16 | Q32 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta