← #16732303
Subgroups — #16732303
Order 3328.
2134 conjugacy classes of subgroups.
The subgroup lattice has 342 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13128662 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13128614 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13125237 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13125211 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13125192 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #13125182 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#11718374 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #13123363 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C13×#2875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#88256 | C22 | 1 | 2 | yes | — |
| 11 | C2×C13×#131 | C22 | 1 | 2 | yes | — |
| 12 | C4×C13×#41 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11719532 | C22 | 1 | 2 | yes | — |
| 14 | #11719282 | — | 2 | 2 | no | — |
| 15 | #11719274 | — | 2 | 2 | no | — |
| 16 | D4×D52 | — | 2 | 6 | no | — |
| 17 | #11719244 | — | 2 | 6 | no | — |
| 18 | #11719230 | C22 | 1 | 6 | yes | — |
| 19 | #11719224 | C22 | 1 | 6 | yes | complemented |
| 20 | #11719182 | C22 | 1 | 3 | yes | — |
| 21 | C2×#88128 | C22 | 1 | 3 | yes | — |
| 22 | #11719175 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×#88124 | C22 | 1 | 3 | yes | complemented |
| 24 | C13×#405 | C22 | 1 | 6 | yes | complemented |
| 25 | C4×C13×M16 | C22 | 1 | 3 | yes | complemented |
| 26 | C2×C13×#97 | C22 | 1 | 3 | yes | complemented |
| 27 | #11718794 | C22 | 1 | 12 | yes | complemented |
| 28 | #11718792 | C22 | 1 | 12 | yes | complemented |
| 29 | #11718774 | C22 | 1 | 12 | yes | complemented |
| 30 | C2×#88061 | C22 | 1 | 12 | yes | complemented |
| 31 | #11718375 | C22 | 1 | 12 | yes | complemented |
| 32 | #11718374 | C22 | 1 | 3 | yes | complemented |
| 33 | #11718374 | C22 | 1 | 12 | yes | complemented |
| 34 | #11718374 | C22 | 1 | 6 | yes | complemented |
| 35 | #11718374 | C22 | 1 | 3 | yes | complemented |
| 36 | #11718364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #11718364 | C22 | 1 | 3 | yes | complemented |
| 38 | #11718358 | C22 | 1 | 12 | yes | complemented |
| 39 | #11718355 | C22 | 1 | 12 | yes | complemented |
| 40 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 41 | #88256 | — | 2 | 16 | no | — |
| 42 | C2×#6131 | — | 2 | 2 | no | — |
| 43 | C2×D4×D13 | — | 2 | 6 | no | — |
| 44 | C2×#6127 | C23 | 1 | 6 | yes | — |
| 45 | C22×D52 | — | 2 | 6 | no | — |
| 46 | C22×D52 | C23 | 1 | 6 | yes | — |
| 47 | C13×#131 | — | 2 | 8 | no | — |
| 48 | C2×C13×M16 | C23 | 1 | 6 | yes | — |
| 49 | C22×C8×C13 | C23 | 1 | 6 | yes | — |
| 50 | C4×Q8×C13 | D4 | 1 | 2 | yes | — |
| 51 | C4×D4×C13 | D4 | 1 | 6 | yes | — |
| 52 | C13×#117 | C23 | 1 | 3 | yes | — |
| 53 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 54 | Q8×Dic13 | — | 2 | 2 | no | — |
| 55 | D4×Dic13 | — | 2 | 6 | no | — |
| 56 | #88184 | — | 2 | 6 | no | — |
| 57 | #88180 | C23 | 1 | 6 | yes | — |
| 58 | C2×C4⋊Dic13 | C23 | 1 | 6 | yes | — |
| 59 | #88178 | — | 2 | 6 | no | — |
| 60 | C2×#6101 | — | 2 | 6 | no | — |
| 61 | #88149 | — | 2 | 12 | no | — |
| 62 | #88144 | — | 2 | 6 | no | — |
| 63 | #88142 | — | 2 | 6 | no | — |
| 64 | #88136 | — | 2 | 12 | no | — |
| 65 | #88132 | — | 2 | 12 | no | — |
| 66 | #88129 | C23 | 1 | 6 | yes | — |
| 67 | #88128 | — | 2 | 6 | no | — |
| 68 | #88128 | C23 | 1 | 3 | yes | — |
| 69 | #88128 | C23 | 1 | 6 | yes | — |
| 70 | C4×D52 | — | 2 | 6 | no | — |
| 71 | #88124 | — | 2 | 6 | no | — |
| 72 | #88124 | C23 | 1 | 3 | yes | — |
| 73 | #88124 | C23 | 1 | 6 | yes | — |
| 74 | #88124 | C23 | 1 | 1 | yes | characteristic |
| 75 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 76 | #88123 | C23 | 1 | 6 | yes | — |
| 77 | C4×Dic26 | — | 2 | 6 | no | — |
| 78 | C13×#97 | C23 | 1 | 1 | yes | characteristic |
| 79 | C13×#97 | C23 | 1 | 3 | yes | — |
| 80 | C13×#97 | C23 | 1 | 6 | yes | — |
| 81 | C4×C8×C13 | C23 | 1 | 6 | yes | — |
| 82 | #88061 | C23 | 1 | 12 | yes | — |
| 83 | #88061 | C23 | 1 | 24 | yes | — |
| 84 | #88061 | C23 | 1 | 12 | yes | — |
| 85 | #88056 | C23 | 1 | 4 | yes | — |
| 86 | #88056 | C23 | 1 | 12 | yes | — |
| 87 | #60626 | — | 13 | 1 | no | maximal, Sylow |
| 88 | C23×D13 | — | 2 | 6 | no | — |
| 89 | C13×#41 | #41 | 1 | 8 | yes | — |
| 90 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×D4×C13 | C2×D4 | 1 | 3 | yes | — |
| 92 | C22×C4×C13 | C2×D4 | 1 | 6 | yes | — |
| 93 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 94 | C2×C22⋊D13 | — | 2 | 6 | no | — |
| 95 | C22×Dic13 | — | 2 | 6 | no | — |
| 96 | #6131 | — | 4 | 8 | no | — |
| 97 | D4×D13 | — | 4 | 24 | no | — |
| 98 | #6127 | — | 2 | 24 | no | — |
| 99 | C2×D52 | — | 2 | 24 | no | — |
| 100 | C2×D52 | — | 2 | 6 | no | — |
| 101 | C2×D52 | — | 2 | 6 | no | — |
| 102 | C2×D52 | — | 2 | 12 | no | — |
| 103 | C2×D52 | — | 8 | 12 | no | — |
| 104 | C2×D52 | C24 | 1 | 6 | yes | — |
| 105 | C2×C4×D13 | — | 2 | 6 | no | — |
| 106 | C2×Dic26 | — | 2 | 6 | no | — |
| 107 | C2×Dic26 | C24 | 1 | 2 | yes | — |
| 108 | C13×M16 | — | 2 | 12 | no | — |
| 109 | C2×C8×C13 | — | 2 | 12 | no | — |
| 110 | C2×C8×C13 | C24 | 1 | 6 | yes | — |
| 111 | C2×C8×C13 | C24 | 1 | 2 | yes | — |
| 112 | C13×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 113 | C13×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 114 | C42×C13 | C2×D4 | 1 | 6 | yes | — |
| 115 | C42×C13 | C24 | 1 | 3 | yes | — |
| 116 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 117 | C22⋊Dic13 | — | 2 | 6 | no | — |
| 118 | #6103 | — | 2 | 12 | no | — |
| 119 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 120 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 121 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 122 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 123 | C4⋊Dic13 | C24 | 1 | 6 | yes | — |
| 124 | #6101 | — | 2 | 2 | no | — |
| 125 | #6101 | — | 2 | 6 | no | — |
| 126 | #6101 | — | 2 | 12 | no | — |
| 127 | C4×Dic13 | — | 2 | 6 | no | — |
| 128 | #3504 | — | 13 | 1 | no | — |
| 129 | #3498 | — | 13 | 1 | no | — |
| 130 | #3142 | — | 13 | 3 | no | — |
| 131 | #3138 | — | 13 | 3 | no | — |
| 132 | #3136 | — | 13 | 12 | no | — |
| 133 | #3135 | — | 13 | 3 | no | — |
| 134 | C2×#490 | — | 13 | 3 | no | — |
| 135 | #2897 | — | 13 | 4 | no | — |
| 136 | #2875 | D13 | 1 | 1 | yes | characteristic, complemented |
| 137 | C23×C13 | C22×D4 | 1 | 3 | yes | — |
| 138 | C22×D13 | — | 2 | 6 | no | — |
| 139 | C22×D13 | — | 4 | 12 | no | — |
| 140 | C22×D13 | — | 8 | 12 | no | — |
| 141 | Q8×C13 | #124 | 1 | 4 | yes | — |
| 142 | D4×C13 | #124 | 1 | 12 | yes | — |
| 143 | C2×C4×C13 | — | 4 | 6 | no | — |
| 144 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 145 | C2×C4×C13 | C22×D4 | 1 | 6 | yes | — |
| 146 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 147 | C2×C4×C13 | C2×#41 | 1 | 12 | yes | — |
| 148 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 149 | C22⋊D13 | — | 4 | 12 | no | — |
| 150 | C2×Dic13 | — | 2 | 2 | no | — |
| 151 | C2×Dic13 | — | 2 | 6 | no | — |
| 152 | C2×Dic13 | — | 2 | 2 | no | — |
| 153 | C2×Dic13 | — | 8 | 6 | no | — |
| 154 | D52 | — | 2 | 12 | no | — |
| 155 | D52 | — | 4 | 12 | no | — |
| 156 | D52 | — | 4 | 12 | no | — |
| 157 | D52 | — | 8 | 12 | no | — |
| 158 | C4×D13 | — | 4 | 12 | no | — |
| 159 | Dic26 | — | 2 | 4 | no | — |
| 160 | Dic26 | — | 8 | 6 | no | — |
| 161 | C8×C13 | — | 2 | 2 | no | — |
| 162 | C8×C13 | — | 2 | 6 | no | — |
| 163 | C2×H(5,𝔽2) | — | 13 | 2 | no | — |
| 164 | C2×#131 | C2×D13 | 1 | 2 | yes | — |
| 165 | #557 | — | 26 | 2 | no | — |
| 166 | #554 | — | 26 | 6 | no | — |
| 167 | #550 | — | 26 | 2 | no | — |
| 168 | D42 | — | 26 | 6 | no | — |
| 169 | #544 | — | 13 | 6 | no | — |
| 170 | #535 | — | 13 | 6 | no | — |
| 171 | #533 | — | 13 | 3 | no | — |
| 172 | #532 | — | 13 | 3 | no | — |
| 173 | C2×#127 | — | 13 | 3 | no | — |
| 174 | C2×#125 | — | 13 | 3 | no | — |
| 175 | #520 | — | 13 | 2 | no | — |
| 176 | C4×#41 | C2×D13 | 1 | 1 | yes | characteristic |
| 177 | #491 | — | 13 | 1 | no | — |
| 178 | #491 | — | 13 | 3 | no | — |
| 179 | #490 | — | 13 | 3 | no | — |
| 180 | #490 | — | 13 | 12 | no | — |
| 181 | #490 | — | 13 | 6 | no | — |
| 182 | #490 | — | 13 | 3 | no | — |
| 183 | #489 | — | 13 | 12 | no | — |
| 184 | #488 | — | 13 | 12 | no | — |
| 185 | #486 | — | 13 | 12 | no | — |
| 186 | #418 | — | 13 | 12 | no | — |
| 187 | #417 | — | 13 | 12 | no | — |
| 188 | #416 | — | 13 | 12 | no | — |
| 189 | C2×#102 | — | 13 | 12 | no | — |
| 190 | #405 | C2×D13 | 1 | 6 | yes | complemented |
| 191 | C4×M16 | C2×D13 | 1 | 3 | yes | complemented |
| 192 | C2×#97 | C2×D13 | 1 | 3 | yes | complemented |
| 193 | C22×C13 | — | 2 | 6 | no | — |
| 194 | C22×C13 | C2×#124 | 1 | 6 | yes | — |
| 195 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×D13 | — | 4 | 12 | no | — |
| 197 | C2×D13 | — | 4 | 6 | no | — |
| 198 | C2×D13 | — | 16 | 12 | no | — |
| 199 | C4×C13 | — | 2 | 6 | no | — |
| 200 | C4×C13 | — | 2 | 2 | no | — |
| 201 | C4×C13 | C2×#124 | 1 | 6 | yes | — |
| 202 | C4×C13 | C22×#41 | 1 | 2 | yes | — |
| 203 | Dic13 | — | 4 | 2 | no | — |
| 204 | Dic13 | — | 4 | 6 | no | — |
| 205 | Dic13 | — | 4 | 2 | no | — |
| 206 | H(5,𝔽2) | — | 26 | 16 | no | — |
| 207 | C2×#41 | — | 13 | 6 | no | — |
| 208 | C2×#41 | — | 26 | 2 | no | — |
| 209 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 210 | C22×D4 | — | 13 | 6 | no | — |
| 211 | C22×D4 | — | 26 | 6 | no | — |
| 212 | C22×D4 | — | 26 | 6 | no | — |
| 213 | #131 | — | 2 | 8 | no | — |
| 214 | C2×M16 | C22×D13 | 1 | 6 | yes | — |
| 215 | C22×C8 | C22×D13 | 1 | 6 | yes | — |
| 216 | C4⋊Q8 | — | 13 | 6 | no | — |
| 217 | C4⋊Q8 | — | 13 | 1 | no | — |
| 218 | C4⋊Q8 | — | 26 | 6 | no | — |
| 219 | #127 | — | 13 | 3 | no | — |
| 220 | #127 | — | 13 | 6 | no | — |
| 221 | #127 | — | 26 | 6 | no | — |
| 222 | #125 | — | 13 | 3 | no | — |
| 223 | #125 | — | 13 | 6 | no | — |
| 224 | #125 | — | 13 | 1 | no | — |
| 225 | #125 | — | 26 | 6 | no | — |
| 226 | #125 | — | 26 | 6 | no | — |
| 227 | #124 | — | 13 | 6 | no | — |
| 228 | C22⋊Q8 | — | 26 | 6 | no | — |
| 229 | C22⋊Q8 | — | 26 | 12 | no | — |
| 230 | #121 | — | 26 | 6 | no | — |
| 231 | #121 | — | 26 | 12 | no | — |
| 232 | #120 | — | 26 | 12 | no | — |
| 233 | C4×Q8 | — | 26 | 2 | no | — |
| 234 | C4×Q8 | — | 26 | 6 | no | — |
| 235 | C4×Q8 | D52 | 1 | 2 | yes | — |
| 236 | C4×D4 | — | 26 | 6 | no | — |
| 237 | C4×D4 | — | 26 | 6 | no | — |
| 238 | C4×D4 | D52 | 1 | 6 | yes | — |
| 239 | #117 | — | 13 | 6 | no | — |
| 240 | #117 | C22×D13 | 1 | 3 | yes | — |
| 241 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 242 | C2×C4⋊C4 | — | 26 | 6 | no | — |
| 243 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 244 | #103 | — | 13 | 4 | no | — |
| 245 | #103 | — | 13 | 12 | no | — |
| 246 | #102 | — | 13 | 12 | no | — |
| 247 | #102 | — | 13 | 24 | no | — |
| 248 | #102 | — | 13 | 12 | no | — |
| 249 | #97 | C22×D13 | 1 | 1 | yes | characteristic |
| 250 | #97 | C22×D13 | 1 | 3 | yes | — |
| 251 | #97 | C22×D13 | 1 | 6 | yes | — |
| 252 | C4×C8 | C22×D13 | 1 | 6 | yes | — |
| 253 | C2×C13 | — | 2 | 6 | no | — |
| 254 | C2×C13 | C22×#124 | 1 | 1 | yes | characteristic |
| 255 | C2×C13 | #3585 | 1 | 2 | yes | — |
| 256 | D13 | — | 8 | 6 | no | — |
| 257 | C24 | — | 26 | 6 | no | — |
| 258 | #41 | — | 26 | 24 | no | — |
| 259 | #41 | — | 52 | 8 | no | — |
| 260 | #41 | #6127 | 1 | 8 | yes | — |
| 261 | C2×Q8 | — | 13 | 2 | no | — |
| 262 | C2×Q8 | — | 26 | 6 | no | — |
| 263 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 264 | C2×D4 | — | 13 | 6 | no | — |
| 265 | C2×D4 | — | 26 | 6 | no | — |
| 266 | C2×D4 | — | 26 | 6 | no | — |
| 267 | C2×D4 | — | 26 | 6 | no | — |
| 268 | C2×D4 | — | 26 | 12 | no | — |
| 269 | C2×D4 | — | 26 | 24 | no | — |
| 270 | C2×D4 | — | 52 | 24 | no | — |
| 271 | C2×D4 | — | 104 | 12 | no | — |
| 272 | C2×D4 | C2×D52 | 1 | 3 | yes | — |
| 273 | C22×C4 | — | 26 | 6 | no | — |
| 274 | C22×C4 | — | 26 | 6 | no | — |
| 275 | C22×C4 | C2×D52 | 1 | 6 | yes | — |
| 276 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 277 | M16 | — | 2 | 12 | no | — |
| 278 | C2×C8 | — | 2 | 12 | no | — |
| 279 | C2×C8 | C23×D13 | 1 | 6 | yes | — |
| 280 | C2×C8 | C23×D13 | 1 | 2 | yes | — |
| 281 | C4⋊C4 | — | 13 | 6 | no | — |
| 282 | C4⋊C4 | — | 13 | 2 | no | — |
| 283 | C4⋊C4 | — | 26 | 6 | no | — |
| 284 | C4⋊C4 | — | 26 | 6 | no | — |
| 285 | C4⋊C4 | — | 26 | 12 | no | — |
| 286 | C4⋊C4 | — | 26 | 2 | no | — |
| 287 | C4⋊C4 | — | 26 | 2 | no | — |
| 288 | C4⋊C4 | — | 26 | 6 | no | — |
| 289 | C4⋊C4 | C2×D52 | 1 | 6 | yes | — |
| 290 | C22⋊C4 | — | 26 | 6 | no | — |
| 291 | C22⋊C4 | — | 26 | 12 | no | — |
| 292 | C22⋊C4 | C2×D52 | 1 | 6 | yes | — |
| 293 | C42 | — | 26 | 6 | no | — |
| 294 | C42 | C2×D52 | 1 | 6 | yes | — |
| 295 | C42 | C23×D13 | 1 | 3 | yes | — |
| 296 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 297 | C13 | #60626 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 298 | C23 | — | 26 | 6 | no | — |
| 299 | C23 | — | 52 | 12 | no | — |
| 300 | C23 | — | 104 | 12 | no | — |
| 301 | C23 | C22×D52 | 1 | 3 | yes | — |
| 302 | Q8 | — | 26 | 4 | no | — |
| 303 | Q8 | — | 104 | 6 | no | — |
| 304 | Q8 | #88129 | 1 | 4 | yes | — |
| 305 | D4 | — | 26 | 12 | no | — |
| 306 | D4 | — | 52 | 12 | no | — |
| 307 | D4 | — | 52 | 12 | no | — |
| 308 | D4 | — | 52 | 12 | no | — |
| 309 | D4 | — | 104 | 12 | no | — |
| 310 | D4 | #88129 | 1 | 12 | yes | — |
| 311 | C2×C4 | — | 4 | 6 | no | — |
| 312 | C2×C4 | — | 26 | 2 | no | — |
| 313 | C2×C4 | — | 26 | 6 | no | — |
| 314 | C2×C4 | — | 26 | 2 | no | — |
| 315 | C2×C4 | — | 52 | 12 | no | — |
| 316 | C2×C4 | — | 104 | 6 | no | — |
| 317 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 318 | C2×C4 | C22×D52 | 1 | 6 | yes | — |
| 319 | C2×C4 | C22×D52 | 1 | 3 | yes | — |
| 320 | C2×C4 | C2×#6127 | 1 | 12 | yes | — |
| 321 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 322 | C8 | — | 2 | 2 | no | — |
| 323 | C8 | — | 2 | 6 | no | — |
| 324 | C22 | — | 2 | 6 | no | — |
| 325 | C22 | — | 52 | 12 | no | — |
| 326 | C22 | — | 52 | 6 | no | — |
| 327 | C22 | — | 208 | 12 | no | — |
| 328 | C22 | C2×#88129 | 1 | 6 | yes | — |
| 329 | C22 | C23×D52 | 1 | 1 | yes | characteristic |
| 330 | C4 | — | 2 | 2 | no | — |
| 331 | C4 | — | 2 | 6 | no | — |
| 332 | C4 | — | 52 | 6 | no | — |
| 333 | C4 | — | 52 | 2 | no | — |
| 334 | C4 | — | 52 | 2 | no | — |
| 335 | C4 | C2×#88129 | 1 | 6 | yes | — |
| 336 | C4 | C22×#6127 | 1 | 2 | yes | — |
| 337 | C2 | — | 2 | 6 | no | — |
| 338 | C2 | — | 104 | 6 | no | — |
| 339 | C2 | C22×#88129 | 1 | 1 | yes | characteristic |
| 340 | C2 | #13129617 | 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