← #16019027
Subgroups — #16019027
Order 3328.
538 conjugacy classes of subgroups.
The subgroup lattice has 294 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13125415 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#11718343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13117118 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13117060 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13117022 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13116984 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C13×#2162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11719182 | — | 2 | 1 | no | — |
| 9 | C2×#88123 | — | 2 | 1 | no | — |
| 10 | C2×C4×C8×C13 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11718776 | — | 2 | 1 | no | — |
| 12 | #11718776 | C22 | 1 | 2 | yes | — |
| 13 | C2×#88058 | — | 2 | 1 | no | — |
| 14 | C2×#88058 | C22 | 1 | 2 | yes | — |
| 15 | #11718356 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11718355 | — | 2 | 1 | no | — |
| 17 | C4×D104 | — | 2 | 1 | no | — |
| 18 | C4×D104 | C22 | 1 | 2 | yes | — |
| 19 | #11718343 | — | 2 | 1 | no | — |
| 20 | #11718343 | — | 2 | 1 | no | — |
| 21 | #11718343 | C22 | 1 | 1 | yes | characteristic |
| 22 | #11718343 | C22 | 1 | 2 | yes | — |
| 23 | #11718343 | C22 | 1 | 2 | yes | — |
| 24 | C13×C4⋊C16 | C22 | 1 | 2 | yes | — |
| 25 | C13×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 26 | C4×C13×C16 | C22 | 1 | 2 | yes | — |
| 27 | #11718101 | C22 | 1 | 8 | yes | — |
| 28 | #11718097 | C22 | 1 | 8 | yes | — |
| 29 | C2×#6127 | — | 4 | 1 | no | — |
| 30 | C22×Dic26 | — | 4 | 1 | no | — |
| 31 | C22×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 32 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 33 | C2×C42×C13 | D4 | 1 | 1 | yes | characteristic |
| 34 | #88184 | — | 2 | 2 | no | — |
| 35 | #88184 | — | 4 | 1 | no | — |
| 36 | C2×C4⋊Dic13 | — | 2 | 2 | no | — |
| 37 | C2×C4⋊Dic13 | — | 4 | 1 | no | — |
| 38 | C2×D104 | — | 2 | 1 | no | — |
| 39 | C2×D104 | C23 | 1 | 2 | yes | — |
| 40 | #88129 | — | 4 | 1 | no | — |
| 41 | #88128 | — | 2 | 1 | no | — |
| 42 | C4×D52 | — | 2 | 2 | no | — |
| 43 | C4×D52 | — | 4 | 1 | no | — |
| 44 | #88123 | — | 2 | 2 | no | — |
| 45 | #88123 | — | 2 | 2 | no | — |
| 46 | #88123 | — | 2 | 1 | no | — |
| 47 | #88123 | — | 4 | 1 | no | — |
| 48 | #88123 | — | 4 | 1 | no | — |
| 49 | C2×C13×C16 | C23 | 1 | 4 | yes | — |
| 50 | C4×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 51 | C4×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 52 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 53 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 54 | #88061 | — | 2 | 2 | no | — |
| 55 | #88061 | — | 2 | 2 | no | — |
| 56 | #88058 | — | 2 | 2 | no | — |
| 57 | #88058 | — | 2 | 2 | no | — |
| 58 | #88058 | — | 2 | 2 | no | — |
| 59 | #88058 | — | 2 | 1 | no | — |
| 60 | #88058 | C23 | 1 | 4 | yes | — |
| 61 | #88058 | C23 | 1 | 2 | yes | — |
| 62 | #33793 | — | 13 | 1 | no | maximal, Sylow |
| 63 | C22×C4×C13 | D8 | 1 | 1 | yes | characteristic |
| 64 | C22×C4×C13 | D8 | 1 | 1 | yes | characteristic |
| 65 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C22⋊D13 | — | 4 | 2 | no | — |
| 67 | C22×Dic13 | — | 4 | 2 | no | — |
| 68 | #6127 | — | 8 | 4 | no | — |
| 69 | C2×D52 | — | 2 | 2 | no | — |
| 70 | C2×D52 | — | 4 | 1 | no | — |
| 71 | C2×D52 | — | 4 | 1 | no | — |
| 72 | C2×C4×D13 | — | 4 | 2 | no | — |
| 73 | C2×Dic26 | — | 4 | 2 | no | — |
| 74 | C2×Dic26 | — | 4 | 2 | no | — |
| 75 | C2×Dic26 | — | 4 | 1 | no | — |
| 76 | C2×Dic26 | — | 8 | 4 | no | — |
| 77 | C2×C8×C13 | — | 2 | 2 | no | — |
| 78 | C2×C8×C13 | — | 2 | 2 | no | — |
| 79 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 83 | C42×C13 | D8 | 1 | 1 | yes | characteristic |
| 84 | C42×C13 | D8 | 1 | 1 | yes | characteristic |
| 85 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | #6103 | — | 4 | 2 | no | — |
| 88 | #6103 | — | 4 | 2 | no | — |
| 89 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 90 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 91 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 92 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 93 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 94 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 95 | D104 | — | 2 | 4 | no | — |
| 96 | D104 | — | 4 | 2 | no | — |
| 97 | C13×C16 | — | 2 | 4 | no | — |
| 98 | #3169 | — | 13 | 1 | no | — |
| 99 | C2×#500 | — | 13 | 1 | no | — |
| 100 | #2254 | — | 13 | 2 | no | — |
| 101 | #2240 | — | 13 | 2 | no | — |
| 102 | #2233 | — | 13 | 4 | no | — |
| 103 | #2226 | — | 13 | 4 | no | — |
| 104 | #2162 | D13 | 1 | 1 | yes | characteristic, complemented |
| 105 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 106 | C22×D13 | — | 4 | 2 | no | — |
| 107 | C2×C4×C13 | — | 2 | 1 | no | — |
| 108 | C2×C4×C13 | — | 2 | 1 | no | — |
| 109 | C2×C4×C13 | — | 2 | 2 | no | — |
| 110 | C2×C4×C13 | SD32 | 1 | 4 | yes | — |
| 111 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 113 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 114 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 117 | C22⋊D13 | — | 8 | 4 | no | — |
| 118 | C2×Dic13 | — | 4 | 4 | no | — |
| 119 | C2×Dic13 | — | 4 | 2 | no | — |
| 120 | C2×Dic13 | — | 8 | 4 | no | — |
| 121 | D52 | — | 4 | 2 | no | — |
| 122 | D52 | — | 4 | 2 | no | — |
| 123 | D52 | — | 8 | 2 | no | — |
| 124 | D52 | — | 8 | 2 | no | — |
| 125 | C4×D13 | — | 8 | 4 | no | — |
| 126 | Dic26 | — | 8 | 4 | no | — |
| 127 | Dic26 | — | 8 | 2 | no | — |
| 128 | Dic26 | — | 8 | 4 | no | — |
| 129 | C8×C13 | — | 2 | 1 | no | — |
| 130 | C8×C13 | — | 2 | 1 | no | — |
| 131 | C8×C13 | #137 | 1 | 2 | yes | — |
| 132 | C8×C13 | 2−1+4 | 1 | 2 | yes | — |
| 133 | #532 | — | 26 | 1 | no | — |
| 134 | C2×C4⋊Q8 | — | 26 | 1 | no | — |
| 135 | #500 | — | 13 | 2 | no | — |
| 136 | #500 | — | 13 | 2 | no | — |
| 137 | #500 | — | 13 | 1 | no | — |
| 138 | #500 | — | 26 | 1 | no | — |
| 139 | #500 | — | 26 | 1 | no | — |
| 140 | #493 | — | 13 | 1 | no | — |
| 141 | #486 | — | 26 | 1 | no | — |
| 142 | #466 | — | 13 | 2 | no | — |
| 143 | #466 | — | 26 | 1 | no | — |
| 144 | C4×D8 | — | 13 | 2 | no | — |
| 145 | C4×D8 | — | 26 | 1 | no | — |
| 146 | C2×#107 | — | 13 | 2 | no | — |
| 147 | C2×#107 | — | 26 | 1 | no | — |
| 148 | C2×C4×C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 149 | #367 | — | 13 | 8 | no | — |
| 150 | C4⋊C16 | C2×D13 | 1 | 2 | yes | — |
| 151 | #357 | — | 13 | 8 | no | — |
| 152 | C22⋊C16 | C2×D13 | 1 | 2 | yes | — |
| 153 | C4×C16 | C2×D13 | 1 | 2 | yes | — |
| 154 | C22×C13 | — | 2 | 1 | no | — |
| 155 | C22×C13 | — | 2 | 1 | no | — |
| 156 | C22×C13 | C2×SD32 | 1 | 2 | yes | — |
| 157 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 158 | C2×D13 | — | 8 | 2 | no | — |
| 159 | C2×D13 | — | 8 | 2 | no | — |
| 160 | C2×D13 | — | 8 | 2 | no | — |
| 161 | C4×C13 | — | 2 | 1 | no | — |
| 162 | C4×C13 | — | 2 | 1 | no | — |
| 163 | C4×C13 | C2×SD32 | 1 | 2 | yes | — |
| 164 | C4×C13 | C2×SD32 | 1 | 2 | yes | — |
| 165 | C4×C13 | #509 | 1 | 2 | yes | — |
| 166 | C4×C13 | #536 | 1 | 1 | yes | characteristic |
| 167 | C4×C13 | C2×#137 | 1 | 1 | yes | characteristic |
| 168 | Dic13 | — | 8 | 2 | no | — |
| 169 | Dic13 | — | 8 | 4 | no | — |
| 170 | C2×#41 | — | 52 | 1 | no | — |
| 171 | C22×Q8 | — | 52 | 1 | no | — |
| 172 | C2×D8 | — | 13 | 2 | no | — |
| 173 | C2×D8 | — | 26 | 1 | no | — |
| 174 | C22×C8 | D52 | 1 | 1 | yes | characteristic |
| 175 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 176 | C4⋊Q8 | — | 26 | 2 | no | — |
| 177 | C4⋊Q8 | — | 26 | 2 | no | — |
| 178 | C4⋊Q8 | — | 26 | 1 | no | — |
| 179 | C4⋊Q8 | — | 52 | 1 | no | — |
| 180 | C4⋊Q8 | — | 52 | 1 | no | — |
| 181 | #127 | — | 26 | 1 | no | — |
| 182 | #124 | — | 52 | 1 | no | — |
| 183 | #121 | — | 26 | 2 | no | — |
| 184 | #121 | — | 52 | 1 | no | — |
| 185 | C4×D4 | — | 26 | 2 | no | — |
| 186 | C4×D4 | — | 52 | 1 | no | — |
| 187 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 188 | C2×C4⋊C4 | — | 52 | 1 | no | — |
| 189 | C2×C42 | D52 | 1 | 1 | yes | characteristic |
| 190 | C2×C16 | C22×D13 | 1 | 4 | yes | — |
| 191 | #107 | — | 13 | 4 | no | — |
| 192 | #107 | — | 13 | 2 | no | — |
| 193 | #107 | — | 26 | 2 | no | — |
| 194 | #107 | — | 26 | 2 | no | — |
| 195 | #107 | — | 26 | 2 | no | — |
| 196 | #107 | — | 26 | 1 | no | — |
| 197 | #102 | — | 26 | 2 | no | — |
| 198 | #102 | — | 26 | 2 | no | — |
| 199 | C4×C8 | D52 | 1 | 1 | yes | characteristic |
| 200 | C4×C8 | D52 | 1 | 1 | yes | characteristic |
| 201 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 202 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 203 | C2×C13 | — | 2 | 2 | no | — |
| 204 | C2×C13 | #3226 | 1 | 1 | yes | characteristic |
| 205 | C2×C13 | C22×SD32 | 1 | 1 | yes | characteristic |
| 206 | C2×C13 | C2×#509 | 1 | 1 | yes | characteristic |
| 207 | D13 | — | 16 | 2 | no | — |
| 208 | #41 | — | 104 | 4 | no | — |
| 209 | C2×Q8 | — | 52 | 1 | no | — |
| 210 | C2×Q8 | — | 52 | 2 | no | — |
| 211 | C2×Q8 | — | 52 | 2 | no | — |
| 212 | C2×Q8 | — | 104 | 4 | no | — |
| 213 | C2×D4 | — | 26 | 2 | no | — |
| 214 | C2×D4 | — | 52 | 2 | no | — |
| 215 | C2×D4 | — | 52 | 1 | no | — |
| 216 | C2×D4 | — | 52 | 1 | no | — |
| 217 | C22×C4 | — | 52 | 2 | no | — |
| 218 | C22×C4 | — | 52 | 2 | no | — |
| 219 | C22×C4 | D104 | 1 | 1 | yes | characteristic |
| 220 | C22×C4 | D104 | 1 | 1 | yes | characteristic |
| 221 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 222 | D8 | — | 26 | 4 | no | — |
| 223 | D8 | — | 52 | 2 | no | — |
| 224 | C2×C8 | — | 2 | 2 | no | — |
| 225 | C2×C8 | — | 2 | 2 | no | — |
| 226 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 227 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 228 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 229 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 230 | C4⋊C4 | — | 26 | 2 | no | — |
| 231 | C4⋊C4 | — | 26 | 4 | no | — |
| 232 | C4⋊C4 | — | 52 | 2 | no | — |
| 233 | C4⋊C4 | — | 52 | 2 | no | — |
| 234 | C4⋊C4 | — | 52 | 2 | no | — |
| 235 | C4⋊C4 | — | 52 | 1 | no | — |
| 236 | C22⋊C4 | — | 52 | 2 | no | — |
| 237 | C22⋊C4 | — | 52 | 2 | no | — |
| 238 | C42 | D104 | 1 | 1 | yes | characteristic |
| 239 | C42 | D104 | 1 | 1 | yes | characteristic |
| 240 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 241 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 242 | C16 | — | 2 | 4 | no | — |
| 243 | C13 | #33793 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 244 | C23 | — | 52 | 2 | no | — |
| 245 | C23 | C2×D104 | 1 | 1 | yes | characteristic |
| 246 | Q8 | — | 104 | 4 | no | — |
| 247 | Q8 | — | 104 | 2 | no | — |
| 248 | Q8 | — | 104 | 4 | no | — |
| 249 | D4 | — | 52 | 2 | no | — |
| 250 | D4 | — | 52 | 2 | no | — |
| 251 | D4 | — | 104 | 4 | no | — |
| 252 | D4 | — | 104 | 2 | no | — |
| 253 | D4 | — | 104 | 2 | no | — |
| 254 | C2×C4 | — | 2 | 1 | no | — |
| 255 | C2×C4 | — | 2 | 1 | no | — |
| 256 | C2×C4 | — | 2 | 2 | no | — |
| 257 | C2×C4 | — | 52 | 2 | no | — |
| 258 | C2×C4 | — | 52 | 4 | no | — |
| 259 | C2×C4 | — | 104 | 4 | no | — |
| 260 | C2×C4 | — | 104 | 4 | no | — |
| 261 | C2×C4 | #88040 | 1 | 4 | yes | — |
| 262 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 263 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 264 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 265 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 266 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 267 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 268 | C8 | — | 2 | 1 | no | — |
| 269 | C8 | — | 2 | 1 | no | — |
| 270 | C8 | #88163 | 1 | 2 | yes | — |
| 271 | C8 | #88257 | 1 | 2 | yes | — |
| 272 | C22 | — | 2 | 1 | no | — |
| 273 | C22 | — | 2 | 1 | no | — |
| 274 | C22 | — | 104 | 2 | no | — |
| 275 | C22 | — | 104 | 2 | no | — |
| 276 | C22 | — | 104 | 2 | no | — |
| 277 | C22 | C2×#88040 | 1 | 2 | yes | — |
| 278 | C22 | C22×D104 | 1 | 1 | yes | characteristic |
| 279 | C4 | — | 2 | 1 | no | — |
| 280 | C4 | — | 2 | 1 | no | — |
| 281 | C4 | — | 104 | 2 | no | — |
| 282 | C4 | — | 104 | 4 | no | — |
| 283 | C4 | C2×#88040 | 1 | 2 | yes | — |
| 284 | C4 | C2×#88040 | 1 | 2 | yes | — |
| 285 | C4 | #11718569 | 1 | 2 | yes | — |
| 286 | C4 | #11719231 | 1 | 1 | yes | characteristic |
| 287 | C4 | C2×#88163 | 1 | 1 | yes | characteristic |
| 288 | C2 | — | 2 | 2 | no | — |
| 289 | C2 | — | 208 | 2 | no | — |
| 290 | C2 | #13125959 | 1 | 1 | yes | characteristic |
| 291 | C2 | C22×#88040 | 1 | 1 | yes | characteristic |
| 292 | C2 | C2×#11718569 | 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