← #16019347
Subgroups — #16019347
Order 3328.
464 conjugacy classes of subgroups.
The subgroup lattice has 296 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13125495 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13117000 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13116997 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13116942 | C2 | 1 | 2 | yes | maximal |
| 5 | #13116925 | C2 | 1 | 2 | yes | maximal |
| 6 | #13116886 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13116883 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13116595 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C13×#3177 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C13×#541 | — | 2 | 1 | no | — |
| 11 | #11719223 | — | 2 | 1 | no | — |
| 12 | C13×#499 | C22 | 1 | 1 | yes | characteristic |
| 13 | C13×#494 | C22 | 1 | 1 | yes | characteristic |
| 14 | C13×#491 | — | 2 | 1 | no | — |
| 15 | C13×#470 | — | 2 | 1 | no | — |
| 16 | C13×#467 | C22 | 1 | 2 | yes | — |
| 17 | C13×#441 | — | 2 | 1 | no | — |
| 18 | C4×C13×Q16 | C22 | 1 | 2 | yes | — |
| 19 | C13×#405 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#88069 | C22 | 1 | 2 | yes | — |
| 21 | C2×#88069 | C22 | 1 | 2 | yes | — |
| 22 | #11718798 | — | 2 | 1 | no | — |
| 23 | #11718777 | C22 | 1 | 2 | yes | — |
| 24 | C2×#88052 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22×#6090 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11718377 | — | 2 | 1 | no | — |
| 27 | #11718364 | — | 2 | 1 | no | — |
| 28 | #11718360 | C22 | 1 | 1 | yes | characteristic |
| 29 | C4×Dic52 | C22 | 1 | 2 | yes | — |
| 30 | #11718344 | C22 | 1 | 1 | yes | characteristic |
| 31 | #11718156 | C22 | 1 | 2 | yes | — |
| 32 | #11718156 | C22 | 1 | 2 | yes | — |
| 33 | #11718084 | C22 | 1 | 2 | yes | — |
| 34 | #11718084 | C22 | 1 | 2 | yes | — |
| 35 | #11718082 | C22 | 1 | 2 | yes | — |
| 36 | #11718081 | C22 | 1 | 2 | yes | — |
| 37 | C4⋊#6090 | C22 | 1 | 2 | yes | — |
| 38 | C4⋊#6090 | C22 | 1 | 2 | yes | — |
| 39 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 40 | C2×C13×Q16 | C23 | 1 | 2 | yes | — |
| 41 | C2×C13×M16 | D4 | 1 | 1 | yes | characteristic |
| 42 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 43 | C13×C4⋊Q8 | — | 2 | 1 | no | — |
| 44 | C13×#126 | — | 4 | 2 | no | — |
| 45 | C13×#125 | — | 2 | 1 | no | — |
| 46 | C13×#125 | — | 4 | 2 | no | — |
| 47 | C13×C22⋊Q8 | — | 2 | 2 | no | — |
| 48 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 49 | C13×#117 | D4 | 1 | 1 | yes | characteristic |
| 50 | #88178 | — | 2 | 2 | no | — |
| 51 | C2×Dic52 | — | 2 | 1 | no | — |
| 52 | C2×Dic52 | C23 | 1 | 2 | yes | — |
| 53 | #88143 | — | 4 | 2 | no | — |
| 54 | #88133 | — | 4 | 2 | no | — |
| 55 | #88124 | — | 2 | 1 | no | — |
| 56 | #88123 | — | 2 | 1 | no | — |
| 57 | C4×Dic26 | — | 2 | 2 | no | — |
| 58 | C13×#107 | C23 | 1 | 2 | yes | — |
| 59 | C13×#106 | — | 2 | 1 | no | — |
| 60 | C13×#103 | — | 2 | 2 | no | — |
| 61 | C13×#103 | — | 2 | 2 | no | — |
| 62 | C13×#97 | D4 | 1 | 1 | yes | characteristic |
| 63 | C13×#97 | D4 | 1 | 1 | yes | characteristic |
| 64 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 66 | #88069 | — | 4 | 2 | no | — |
| 67 | #88069 | — | 4 | 2 | no | — |
| 68 | #88058 | C23 | 1 | 2 | yes | — |
| 69 | #88057 | — | 2 | 1 | no | — |
| 70 | #88056 | — | 2 | 2 | no | — |
| 71 | #88056 | — | 2 | 2 | no | — |
| 72 | #88052 | — | 4 | 1 | no | — |
| 73 | C2×#6090 | — | 4 | 1 | no | — |
| 74 | C2×#6090 | C23 | 1 | 2 | yes | — |
| 75 | C2×#6090 | C23 | 1 | 2 | yes | — |
| 76 | #33827 | — | 13 | 1 | no | maximal, Sylow |
| 77 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 78 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | C2×Dic26 | — | 2 | 2 | no | — |
| 80 | C13×Q16 | — | 2 | 2 | no | — |
| 81 | C13×Q16 | — | 2 | 2 | no | — |
| 82 | C13×Q16 | — | 4 | 2 | no | — |
| 83 | C13×M16 | — | 4 | 1 | no | — |
| 84 | C2×C8×C13 | — | 2 | 1 | no | — |
| 85 | C2×C8×C13 | — | 2 | 1 | no | — |
| 86 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 90 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 91 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 92 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 93 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 94 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 95 | C13×C4⋊C4 | D8 | 1 | 2 | yes | — |
| 96 | C13×C22⋊C4 | — | 4 | 2 | no | — |
| 97 | C13×C22⋊C4 | D8 | 1 | 2 | yes | — |
| 98 | C42×C13 | — | 4 | 2 | no | — |
| 99 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C22⋊Dic13 | — | 4 | 2 | no | — |
| 102 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 103 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 104 | #6101 | — | 4 | 2 | no | — |
| 105 | #6101 | — | 4 | 2 | no | — |
| 106 | #6101 | — | 4 | 2 | no | — |
| 107 | C4×Dic13 | — | 4 | 2 | no | — |
| 108 | Dic52 | — | 2 | 2 | no | — |
| 109 | Dic52 | — | 2 | 2 | no | — |
| 110 | Dic52 | — | 4 | 2 | no | — |
| 111 | #6090 | — | 2 | 2 | no | — |
| 112 | #6090 | — | 2 | 2 | no | — |
| 113 | #3177 | — | 13 | 1 | no | — |
| 114 | #3177 | D13 | 1 | 1 | yes | characteristic |
| 115 | #2229 | — | 13 | 2 | no | — |
| 116 | #2229 | — | 13 | 2 | no | — |
| 117 | #2219 | — | 13 | 2 | no | — |
| 118 | #2216 | — | 13 | 2 | no | — |
| 119 | #2209 | — | 13 | 2 | no | — |
| 120 | #2209 | — | 13 | 2 | no | — |
| 121 | #2151 | — | 13 | 1 | no | — |
| 122 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 123 | Q8×C13 | — | 4 | 2 | no | — |
| 124 | Q8×C13 | — | 4 | 2 | no | — |
| 125 | C2×C4×C13 | — | 2 | 1 | no | — |
| 126 | C2×C4×C13 | — | 2 | 1 | no | — |
| 127 | C2×C4×C13 | — | 4 | 2 | no | — |
| 128 | C2×C4×C13 | — | 4 | 2 | no | — |
| 129 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 130 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 132 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×Dic13 | — | 4 | 2 | no | — |
| 134 | C2×Dic13 | — | 4 | 2 | no | — |
| 135 | Dic26 | — | 4 | 2 | no | — |
| 136 | Dic26 | — | 4 | 2 | no | — |
| 137 | C8×C13 | — | 2 | 1 | no | — |
| 138 | C8×C13 | — | 2 | 1 | no | — |
| 139 | C8×C13 | — | 2 | 1 | no | — |
| 140 | C8×C13 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 141 | C8×C13 | 2−1+4 | 1 | 1 | yes | characteristic |
| 142 | #541 | — | 2 | 1 | no | — |
| 143 | #541 | — | 26 | 1 | no | — |
| 144 | C2×Q32 | — | 13 | 2 | no | — |
| 145 | C2×Q32 | — | 13 | 2 | no | — |
| 146 | C2×M32 | — | 13 | 1 | no | — |
| 147 | C22×C16 | — | 13 | 1 | no | — |
| 148 | #499 | — | 13 | 1 | no | — |
| 149 | #499 | C2×D13 | 1 | 1 | yes | characteristic |
| 150 | #494 | — | 13 | 1 | no | — |
| 151 | #494 | C2×D13 | 1 | 1 | yes | characteristic |
| 152 | #491 | — | 2 | 1 | no | — |
| 153 | #491 | — | 26 | 1 | no | — |
| 154 | #470 | — | 2 | 1 | no | — |
| 155 | #470 | — | 26 | 1 | no | — |
| 156 | #467 | — | 13 | 2 | no | — |
| 157 | #467 | C2×D13 | 1 | 2 | yes | — |
| 158 | #441 | — | 2 | 1 | no | — |
| 159 | #441 | — | 26 | 1 | no | — |
| 160 | C4×Q16 | — | 13 | 2 | no | — |
| 161 | C4×Q16 | C2×D13 | 1 | 2 | yes | — |
| 162 | #405 | C2×D13 | 1 | 1 | yes | characteristic |
| 163 | #367 | — | 13 | 2 | no | — |
| 164 | #366 | — | 13 | 2 | no | — |
| 165 | C4⋊C16 | — | 13 | 2 | no | — |
| 166 | C4⋊C16 | — | 13 | 2 | no | — |
| 167 | #358 | — | 13 | 2 | no | — |
| 168 | #358 | — | 13 | 2 | no | — |
| 169 | #358 | — | 13 | 2 | no | — |
| 170 | #358 | — | 13 | 2 | no | — |
| 171 | C22×C13 | — | 2 | 2 | no | — |
| 172 | C22×C13 | — | 2 | 1 | no | — |
| 173 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 174 | C4×C13 | — | 2 | 2 | no | — |
| 175 | C4×C13 | — | 2 | 2 | no | — |
| 176 | C4×C13 | — | 2 | 1 | no | — |
| 177 | C4×C13 | — | 8 | 2 | no | — |
| 178 | C4×C13 | — | 8 | 2 | no | — |
| 179 | C4×C13 | #537 | 1 | 1 | yes | characteristic |
| 180 | C4×C13 | #575 | 1 | 1 | yes | characteristic |
| 181 | Dic13 | — | 8 | 2 | no | — |
| 182 | Dic13 | — | 8 | 2 | no | — |
| 183 | C2×Q16 | — | 2 | 1 | no | — |
| 184 | C2×Q16 | — | 13 | 2 | no | — |
| 185 | C2×Q16 | — | 26 | 1 | no | — |
| 186 | C2×Q16 | C22×D13 | 1 | 2 | yes | — |
| 187 | C2×M16 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 188 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 189 | C4⋊Q8 | — | 2 | 1 | no | — |
| 190 | C4⋊Q8 | — | 26 | 1 | no | — |
| 191 | #126 | — | 4 | 2 | no | — |
| 192 | #126 | — | 52 | 2 | no | — |
| 193 | #125 | — | 2 | 1 | no | — |
| 194 | #125 | — | 4 | 2 | no | — |
| 195 | #125 | — | 26 | 1 | no | — |
| 196 | #125 | — | 52 | 2 | no | — |
| 197 | C22⋊Q8 | — | 2 | 2 | no | — |
| 198 | C22⋊Q8 | — | 26 | 2 | no | — |
| 199 | C4×Q8 | — | 2 | 2 | no | — |
| 200 | C4×Q8 | — | 26 | 2 | no | — |
| 201 | #117 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 202 | Q32 | — | 52 | 2 | no | — |
| 203 | Q32 | — | 52 | 2 | no | — |
| 204 | M32 | — | 52 | 1 | no | — |
| 205 | C2×C16 | — | 13 | 2 | no | — |
| 206 | C2×C16 | — | 13 | 2 | no | — |
| 207 | C2×C16 | — | 52 | 1 | no | — |
| 208 | #107 | — | 13 | 2 | no | — |
| 209 | #107 | C22×D13 | 1 | 2 | yes | — |
| 210 | #106 | — | 2 | 1 | no | — |
| 211 | #106 | — | 26 | 1 | no | — |
| 212 | #103 | — | 2 | 2 | no | — |
| 213 | #103 | — | 2 | 2 | no | — |
| 214 | #103 | — | 26 | 2 | no | — |
| 215 | #103 | — | 26 | 2 | no | — |
| 216 | #97 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 217 | #97 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 218 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 219 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 220 | C2×C13 | — | 4 | 1 | no | — |
| 221 | C2×C13 | #3245 | 1 | 1 | yes | characteristic |
| 222 | C2×C13 | #3417 | 1 | 2 | yes | — |
| 223 | C2×Q8 | — | 2 | 2 | no | — |
| 224 | C2×Q8 | — | 26 | 2 | no | — |
| 225 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 226 | Q16 | — | 2 | 2 | no | — |
| 227 | Q16 | — | 2 | 2 | no | — |
| 228 | Q16 | — | 4 | 2 | no | — |
| 229 | Q16 | — | 26 | 2 | no | — |
| 230 | Q16 | — | 26 | 2 | no | — |
| 231 | Q16 | — | 52 | 2 | no | — |
| 232 | M16 | — | 4 | 1 | no | — |
| 233 | C2×C8 | — | 2 | 1 | no | — |
| 234 | C2×C8 | — | 2 | 1 | no | — |
| 235 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 236 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 237 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 238 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 239 | C4⋊C4 | — | 2 | 2 | no | — |
| 240 | C4⋊C4 | — | 4 | 2 | no | — |
| 241 | C4⋊C4 | — | 4 | 2 | no | — |
| 242 | C4⋊C4 | — | 4 | 2 | no | — |
| 243 | C4⋊C4 | — | 4 | 2 | no | — |
| 244 | C4⋊C4 | — | 26 | 2 | no | — |
| 245 | C4⋊C4 | — | 52 | 2 | no | — |
| 246 | C4⋊C4 | — | 52 | 2 | no | — |
| 247 | C4⋊C4 | — | 52 | 2 | no | — |
| 248 | C4⋊C4 | — | 52 | 2 | no | — |
| 249 | C4⋊C4 | #6104 | 1 | 2 | yes | — |
| 250 | C22⋊C4 | — | 4 | 2 | no | — |
| 251 | C22⋊C4 | — | 52 | 2 | no | — |
| 252 | C22⋊C4 | #6104 | 1 | 2 | yes | — |
| 253 | C42 | — | 4 | 2 | no | — |
| 254 | C42 | — | 52 | 2 | no | — |
| 255 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 256 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 257 | C16 | — | 26 | 2 | no | — |
| 258 | C16 | — | 26 | 2 | no | — |
| 259 | C13 | #33827 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 260 | C23 | C2×#6104 | 1 | 1 | yes | characteristic |
| 261 | Q8 | — | 4 | 2 | no | — |
| 262 | Q8 | — | 4 | 2 | no | — |
| 263 | Q8 | — | 52 | 2 | no | — |
| 264 | Q8 | — | 52 | 2 | no | — |
| 265 | C2×C4 | — | 2 | 1 | no | — |
| 266 | C2×C4 | — | 2 | 1 | no | — |
| 267 | C2×C4 | — | 4 | 2 | no | — |
| 268 | C2×C4 | — | 4 | 2 | no | — |
| 269 | C2×C4 | — | 52 | 2 | no | — |
| 270 | C2×C4 | — | 52 | 2 | no | — |
| 271 | C2×C4 | C2×#6104 | 1 | 2 | yes | — |
| 272 | C2×C4 | C2×#6104 | 1 | 2 | yes | — |
| 273 | C2×C4 | C2×#6104 | 1 | 1 | yes | characteristic |
| 274 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 275 | C8 | — | 2 | 1 | no | — |
| 276 | C8 | — | 2 | 1 | no | — |
| 277 | C8 | — | 2 | 1 | no | — |
| 278 | C8 | #88256 | 1 | 1 | yes | characteristic |
| 279 | C8 | #88257 | 1 | 1 | yes | characteristic |
| 280 | C22 | — | 2 | 2 | no | — |
| 281 | C22 | — | 2 | 1 | no | — |
| 282 | C22 | C22×#6104 | 1 | 1 | yes | characteristic |
| 283 | C4 | — | 2 | 2 | no | — |
| 284 | C4 | — | 2 | 2 | no | — |
| 285 | C4 | — | 2 | 1 | no | — |
| 286 | C4 | — | 8 | 2 | no | — |
| 287 | C4 | — | 8 | 2 | no | — |
| 288 | C4 | — | 104 | 2 | no | — |
| 289 | C4 | — | 104 | 2 | no | — |
| 290 | C4 | #11719527 | 1 | 1 | yes | characteristic |
| 291 | C4 | #11719538 | 1 | 1 | yes | characteristic |
| 292 | C2 | — | 4 | 1 | no | — |
| 293 | C2 | #13126143 | 1 | 1 | yes | characteristic |
| 294 | C2 | #13127987 | 1 | 2 | yes | — |
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