← #62482
Subgroups — #62482
Order 256.
826 conjugacy classes of subgroups.
The subgroup lattice has 277 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #3509 | C2 | 1 | 2 | yes | maximal |
| 2 | #3390 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #3352 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #3349 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #3231 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #3231 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #3230 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #3185 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #3170 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #3165 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #3160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #2965 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #557 | — | 2 | 2 | no | — |
| 14 | #557 | C22 | 1 | 4 | yes | — |
| 15 | #556 | — | 2 | 2 | no | — |
| 16 | #556 | C22 | 1 | 4 | yes | — |
| 17 | #552 | — | 2 | 2 | no | — |
| 18 | #552 | — | 2 | 2 | no | — |
| 19 | #552 | C22 | 1 | 4 | yes | — |
| 20 | #552 | C22 | 1 | 4 | yes | — |
| 21 | #541 | — | 2 | 2 | no | — |
| 22 | #541 | — | 2 | 2 | no | — |
| 23 | #536 | — | 2 | 2 | no | — |
| 24 | #533 | C22 | 1 | 2 | yes | — |
| 25 | #533 | C22 | 1 | 2 | yes | — |
| 26 | #533 | C22 | 1 | 2 | yes | — |
| 27 | #533 | C22 | 1 | 2 | yes | — |
| 28 | #533 | C22 | 1 | 2 | yes | — |
| 29 | C2×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 30 | #519 | — | 2 | 2 | no | — |
| 31 | C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 32 | #501 | C22 | 1 | 8 | yes | — |
| 33 | #500 | C22 | 1 | 1 | yes | characteristic |
| 34 | #500 | C22 | 1 | 1 | yes | characteristic |
| 35 | #500 | C22 | 1 | 1 | yes | characteristic |
| 36 | #500 | C22 | 1 | 2 | yes | — |
| 37 | #499 | C22 | 1 | 4 | yes | — |
| 38 | #498 | C22 | 1 | 2 | yes | — |
| 39 | #498 | C22 | 1 | 2 | yes | — |
| 40 | #494 | C22 | 1 | 1 | yes | characteristic |
| 41 | #487 | C22 | 1 | 2 | yes | — |
| 42 | #487 | C22 | 1 | 2 | yes | — |
| 43 | #487 | C22 | 1 | 2 | yes | — |
| 44 | #485 | C22 | 1 | 8 | yes | — |
| 45 | #485 | C22 | 1 | 8 | yes | — |
| 46 | #484 | C22 | 1 | 8 | yes | — |
| 47 | #479 | C22 | 1 | 8 | yes | — |
| 48 | #479 | C22 | 1 | 8 | yes | — |
| 49 | #477 | C22 | 1 | 8 | yes | — |
| 50 | #470 | C22 | 1 | 8 | yes | — |
| 51 | #467 | C22 | 1 | 4 | yes | — |
| 52 | #446 | C22 | 1 | 2 | yes | — |
| 53 | #441 | C22 | 1 | 8 | yes | — |
| 54 | C4×Q16 | C22 | 1 | 4 | yes | — |
| 55 | #436 | C22 | 1 | 2 | yes | — |
| 56 | #435 | C22 | 1 | 4 | yes | — |
| 57 | #431 | C22 | 1 | 2 | yes | — |
| 58 | #431 | C22 | 1 | 1 | yes | characteristic |
| 59 | #428 | C22 | 1 | 8 | yes | — |
| 60 | #427 | C22 | 1 | 4 | yes | — |
| 61 | C4×M16 | C22 | 1 | 2 | yes | — |
| 62 | C2×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 63 | C2×#41 | D4 | 1 | 1 | yes | characteristic |
| 64 | C22×Q8 | — | 2 | 2 | no | — |
| 65 | C2×Q16 | C23 | 1 | 4 | yes | — |
| 66 | C2×M16 | C23 | 1 | 4 | yes | — |
| 67 | C22×C8 | C23 | 1 | 2 | yes | — |
| 68 | C4⋊Q8 | — | 2 | 4 | no | — |
| 69 | C4⋊Q8 | — | 2 | 2 | no | — |
| 70 | C4⋊Q8 | — | 2 | 2 | no | — |
| 71 | C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 72 | C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 73 | C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 74 | C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 75 | C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 76 | #126 | — | 2 | 4 | no | — |
| 77 | #126 | — | 2 | 4 | no | — |
| 78 | #126 | — | 2 | 4 | no | — |
| 79 | #126 | — | 2 | 4 | no | — |
| 80 | #125 | — | 2 | 4 | no | — |
| 81 | #125 | — | 2 | 4 | no | — |
| 82 | #125 | — | 2 | 4 | no | — |
| 83 | #125 | — | 2 | 4 | no | — |
| 84 | #125 | — | 2 | 2 | no | — |
| 85 | #125 | — | 2 | 2 | no | — |
| 86 | #125 | — | 2 | 2 | no | — |
| 87 | #125 | C23 | 1 | 4 | yes | — |
| 88 | #125 | C23 | 1 | 4 | yes | — |
| 89 | #124 | — | 2 | 4 | no | — |
| 90 | #123 | — | 2 | 4 | no | — |
| 91 | #123 | — | 2 | 4 | no | — |
| 92 | C22⋊Q8 | — | 2 | 2 | no | — |
| 93 | C22⋊Q8 | — | 2 | 2 | no | — |
| 94 | C22⋊Q8 | — | 2 | 2 | no | — |
| 95 | C22⋊Q8 | — | 2 | 2 | no | — |
| 96 | C22⋊Q8 | — | 2 | 2 | no | — |
| 97 | C22⋊Q8 | — | 2 | 2 | no | — |
| 98 | C22⋊Q8 | — | 2 | 2 | no | — |
| 99 | C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 100 | C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 101 | C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 102 | C4×Q8 | — | 2 | 4 | no | — |
| 103 | C4×Q8 | — | 2 | 4 | no | — |
| 104 | C4×Q8 | — | 2 | 2 | no | — |
| 105 | C4×Q8 | — | 2 | 2 | no | — |
| 106 | C4×Q8 | — | 2 | 2 | no | — |
| 107 | C4×Q8 | — | 2 | 2 | no | — |
| 108 | C4×Q8 | — | 2 | 2 | no | — |
| 109 | C4×Q8 | — | 2 | 2 | no | — |
| 110 | C4×Q8 | — | 2 | 2 | no | — |
| 111 | C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 112 | C4×Q8 | C23 | 1 | 4 | yes | — |
| 113 | C4×Q8 | C23 | 1 | 4 | yes | — |
| 114 | C4×Q8 | C23 | 1 | 4 | yes | — |
| 115 | C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 116 | C4×D4 | D4 | 1 | 1 | yes | characteristic |
| 117 | C4×D4 | D4 | 1 | 2 | yes | — |
| 118 | C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 119 | C4×D4 | C23 | 1 | 2 | yes | — |
| 120 | #117 | — | 2 | 2 | no | — |
| 121 | #117 | — | 2 | 2 | no | — |
| 122 | #117 | — | 2 | 2 | no | — |
| 123 | #117 | — | 2 | 4 | no | — |
| 124 | #117 | — | 2 | 4 | no | — |
| 125 | #117 | D4 | 1 | 2 | yes | — |
| 126 | #117 | D4 | 1 | 1 | yes | characteristic |
| 127 | #117 | C23 | 1 | 4 | yes | — |
| 128 | #117 | C23 | 1 | 4 | yes | — |
| 129 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 130 | C2×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 131 | C2×C42 | C23 | 1 | 2 | yes | — |
| 132 | C2×C42 | C23 | 1 | 1 | yes | characteristic |
| 133 | #107 | C23 | 1 | 4 | yes | — |
| 134 | #107 | C23 | 1 | 4 | yes | — |
| 135 | #107 | C23 | 1 | 4 | yes | — |
| 136 | #107 | C23 | 1 | 8 | yes | — |
| 137 | #106 | C23 | 1 | 8 | yes | — |
| 138 | #106 | C23 | 1 | 8 | yes | — |
| 139 | C4⋊C8 | C23 | 1 | 4 | yes | — |
| 140 | C4⋊C8 | C23 | 1 | 2 | yes | — |
| 141 | #103 | C23 | 1 | 8 | yes | — |
| 142 | #103 | C23 | 1 | 8 | yes | — |
| 143 | #103 | C23 | 1 | 8 | yes | — |
| 144 | C22⋊C8 | C23 | 1 | 2 | yes | — |
| 145 | C22⋊C8 | C23 | 1 | 4 | yes | — |
| 146 | #97 | C23 | 1 | 4 | yes | — |
| 147 | C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 148 | C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 149 | C4×C8 | C23 | 1 | 2 | yes | — |
| 150 | C4×C8 | C23 | 1 | 2 | yes | — |
| 151 | #41 | — | 4 | 2 | no | — |
| 152 | C2×Q8 | — | 2 | 2 | no | — |
| 153 | C2×Q8 | — | 2 | 2 | no | — |
| 154 | C2×Q8 | — | 2 | 2 | no | — |
| 155 | C2×Q8 | — | 2 | 4 | no | — |
| 156 | C2×Q8 | — | 4 | 8 | no | — |
| 157 | C2×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×Q8 | C24 | 1 | 4 | yes | — |
| 159 | C2×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×D4 | C2×D4 | 1 | 2 | yes | — |
| 161 | C22×C4 | — | 2 | 4 | no | — |
| 162 | C22×C4 | C2×D4 | 1 | 2 | yes | — |
| 163 | C22×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×C4 | C2×D4 | 1 | 2 | yes | — |
| 165 | C22×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C22×C4 | C24 | 1 | 2 | yes | — |
| 167 | C22×C4 | C24 | 1 | 1 | yes | characteristic |
| 168 | Q16 | — | 2 | 8 | no | — |
| 169 | M16 | — | 2 | 8 | no | — |
| 170 | C2×C8 | — | 2 | 4 | no | — |
| 171 | C2×C8 | C24 | 1 | 2 | yes | — |
| 172 | C2×C8 | C24 | 1 | 4 | yes | — |
| 173 | C2×C8 | C24 | 1 | 2 | yes | — |
| 174 | C4⋊C4 | — | 2 | 2 | no | — |
| 175 | C4⋊C4 | — | 2 | 2 | no | — |
| 176 | C4⋊C4 | — | 2 | 4 | no | — |
| 177 | C4⋊C4 | — | 2 | 4 | no | — |
| 178 | C4⋊C4 | — | 2 | 2 | no | — |
| 179 | C4⋊C4 | — | 2 | 2 | no | — |
| 180 | C4⋊C4 | — | 2 | 2 | no | — |
| 181 | C4⋊C4 | — | 2 | 4 | no | — |
| 182 | C4⋊C4 | — | 2 | 4 | no | — |
| 183 | C4⋊C4 | — | 2 | 4 | no | — |
| 184 | C4⋊C4 | — | 2 | 4 | no | — |
| 185 | C4⋊C4 | — | 2 | 4 | no | — |
| 186 | C4⋊C4 | — | 2 | 4 | no | — |
| 187 | C4⋊C4 | — | 2 | 4 | no | — |
| 188 | C4⋊C4 | — | 2 | 4 | no | — |
| 189 | C4⋊C4 | — | 2 | 4 | no | — |
| 190 | C4⋊C4 | — | 2 | 4 | no | — |
| 191 | C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 192 | C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 194 | C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C4⋊C4 | C24 | 1 | 4 | yes | — |
| 196 | C4⋊C4 | C24 | 1 | 4 | yes | — |
| 197 | C4⋊C4 | C24 | 1 | 4 | yes | — |
| 198 | C22⋊C4 | — | 2 | 4 | no | — |
| 199 | C22⋊C4 | — | 2 | 4 | no | — |
| 200 | C22⋊C4 | — | 2 | 4 | no | — |
| 201 | C22⋊C4 | — | 2 | 4 | no | — |
| 202 | C22⋊C4 | — | 2 | 4 | no | — |
| 203 | C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 204 | C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 205 | C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 206 | C42 | — | 2 | 4 | no | — |
| 207 | C42 | — | 2 | 4 | no | — |
| 208 | C42 | — | 2 | 4 | no | — |
| 209 | C42 | — | 2 | 4 | no | — |
| 210 | C42 | — | 2 | 4 | no | — |
| 211 | C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C42 | C2×D4 | 1 | 2 | yes | — |
| 213 | C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C42 | C2×D4 | 1 | 2 | yes | — |
| 215 | C42 | C24 | 1 | 1 | yes | characteristic |
| 216 | C42 | C24 | 1 | 1 | yes | characteristic |
| 217 | C42 | C24 | 1 | 2 | yes | — |
| 218 | C23 | C22×D4 | 1 | 1 | yes | characteristic |
| 219 | C23 | C22×D4 | 1 | 2 | yes | — |
| 220 | Q8 | — | 2 | 8 | no | — |
| 221 | Q8 | — | 4 | 1 | no | — |
| 222 | Q8 | — | 4 | 8 | no | — |
| 223 | Q8 | — | 4 | 4 | no | — |
| 224 | Q8 | — | 4 | 4 | no | — |
| 225 | Q8 | — | 4 | 4 | no | — |
| 226 | D4 | — | 4 | 1 | no | — |
| 227 | D4 | — | 4 | 2 | no | — |
| 228 | C2×C4 | — | 2 | 4 | no | — |
| 229 | C2×C4 | — | 2 | 2 | no | — |
| 230 | C2×C4 | — | 2 | 4 | no | — |
| 231 | C2×C4 | — | 2 | 2 | no | — |
| 232 | C2×C4 | — | 2 | 2 | no | — |
| 233 | C2×C4 | — | 2 | 4 | no | — |
| 234 | C2×C4 | — | 2 | 4 | no | — |
| 235 | C2×C4 | — | 2 | 4 | no | — |
| 236 | C2×C4 | — | 2 | 4 | no | — |
| 237 | C2×C4 | — | 2 | 4 | no | — |
| 238 | C2×C4 | — | 4 | 8 | no | — |
| 239 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×C4 | C22×D4 | 1 | 2 | yes | — |
| 242 | C2×C4 | C22×D4 | 1 | 2 | yes | — |
| 243 | C2×C4 | C22×D4 | 1 | 2 | yes | — |
| 244 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C4 | C25 | 1 | 1 | yes | characteristic |
| 248 | C8 | — | 2 | 2 | no | — |
| 249 | C8 | — | 2 | 4 | no | — |
| 250 | C8 | 2−1+4 | 1 | 4 | yes | — |
| 251 | C22 | — | 2 | 1 | no | — |
| 252 | C22 | — | 2 | 2 | no | — |
| 253 | C22 | — | 2 | 2 | no | — |
| 254 | C22 | — | 2 | 1 | no | — |
| 255 | C22 | — | 2 | 1 | no | — |
| 256 | C22 | — | 2 | 2 | no | — |
| 257 | C22 | C23×D4 | 1 | 1 | yes | characteristic |
| 258 | C4 | — | 2 | 1 | no | — |
| 259 | C4 | — | 2 | 2 | no | — |
| 260 | C4 | — | 2 | 1 | no | — |
| 261 | C4 | — | 2 | 2 | no | — |
| 262 | C4 | — | 2 | 1 | no | — |
| 263 | C4 | — | 2 | 2 | no | — |
| 264 | C4 | — | 4 | 4 | no | — |
| 265 | C4 | — | 4 | 4 | no | — |
| 266 | C4 | — | 4 | 4 | no | — |
| 267 | C4 | — | 4 | 4 | no | — |
| 268 | C4 | #575 | 1 | 2 | yes | — |
| 269 | C4 | #578 | 1 | 2 | yes | — |
| 270 | C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 271 | C2 | — | 4 | 2 | no | — |
| 272 | C2 | — | 4 | 1 | no | — |
| 273 | C2 | #3499 | 1 | 1 | yes | characteristic |
| 274 | C2 | C2×#575 | 1 | 1 | yes | characteristic |
| 275 | C2 | C2×#578 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta