← #16732313
Subgroups — #16732313
Order 3328.
1998 conjugacy classes of subgroups.
The subgroup lattice has 334 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13128621 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13125239 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #13125218 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13125206 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #13125184 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#11718730 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13123366 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #13123264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C13×#3504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#88257 | C22 | 1 | 2 | yes | — |
| 11 | C13×#557 | — | 2 | 2 | no | — |
| 12 | C13×#554 | — | 2 | 6 | no | — |
| 13 | C13×#544 | C22 | 1 | 6 | yes | — |
| 14 | C13×#533 | C22 | 1 | 3 | yes | — |
| 15 | C2×C13×#125 | C22 | 1 | 3 | yes | — |
| 16 | C13×#520 | C22 | 1 | 2 | yes | — |
| 17 | C4×C13×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#88202 | C22 | 1 | 2 | yes | — |
| 19 | Q8×D52 | — | 2 | 2 | no | — |
| 20 | #11719260 | — | 2 | 6 | no | — |
| 21 | #11719231 | C22 | 1 | 6 | yes | — |
| 22 | #11719182 | C22 | 1 | 3 | yes | — |
| 23 | C2×#88123 | C22 | 1 | 3 | yes | — |
| 24 | #11718754 | C22 | 1 | 12 | yes | — |
| 25 | #11718750 | C22 | 1 | 12 | yes | — |
| 26 | #11718730 | C22 | 1 | 3 | yes | — |
| 27 | #11718730 | C22 | 1 | 12 | yes | — |
| 28 | #11718730 | C22 | 1 | 6 | yes | — |
| 29 | #11718730 | C22 | 1 | 3 | yes | — |
| 30 | #11718729 | C22 | 1 | 12 | yes | — |
| 31 | #11718728 | C22 | 1 | 1 | yes | characteristic |
| 32 | #11718728 | C22 | 1 | 3 | yes | — |
| 33 | #11718665 | C22 | 1 | 12 | yes | — |
| 34 | #11718663 | C22 | 1 | 12 | yes | — |
| 35 | #11718658 | C22 | 1 | 6 | yes | — |
| 36 | C2×#88050 | C22 | 1 | 12 | yes | — |
| 37 | #11718627 | C22 | 1 | 12 | yes | — |
| 38 | C4×#6099 | C22 | 1 | 3 | yes | — |
| 39 | C2×#88043 | C22 | 1 | 3 | yes | — |
| 40 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 41 | #88257 | — | 2 | 16 | no | — |
| 42 | C2×Q8×D13 | — | 2 | 2 | no | — |
| 43 | C2×#6129 | — | 2 | 6 | no | — |
| 44 | C2×#6127 | C23 | 1 | 6 | yes | — |
| 45 | C22×Dic26 | C23 | 1 | 6 | yes | — |
| 46 | C13×C4⋊Q8 | — | 2 | 6 | no | — |
| 47 | C13×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 48 | C13×#125 | — | 2 | 6 | no | — |
| 49 | C13×#125 | — | 2 | 6 | no | — |
| 50 | C13×#125 | C23 | 1 | 3 | yes | — |
| 51 | C13×#125 | C23 | 1 | 1 | yes | characteristic |
| 52 | C13×#125 | C23 | 1 | 6 | yes | — |
| 53 | C13×C22⋊Q8 | — | 2 | 6 | no | — |
| 54 | C13×C22⋊Q8 | — | 2 | 12 | no | — |
| 55 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 56 | C4×Q8×C13 | — | 2 | 6 | no | — |
| 57 | C4×Q8×C13 | D4 | 1 | 2 | yes | — |
| 58 | C4×D4×C13 | — | 2 | 6 | no | — |
| 59 | C4×D4×C13 | D4 | 1 | 6 | yes | — |
| 60 | C13×#117 | C23 | 1 | 6 | yes | — |
| 61 | C13×#117 | C23 | 1 | 3 | yes | — |
| 62 | C2×C13×C4⋊C4 | — | 2 | 6 | no | — |
| 63 | C2×C13×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 64 | C2×C42×C13 | C23 | 1 | 3 | yes | — |
| 65 | #88202 | — | 2 | 8 | no | — |
| 66 | #88184 | — | 2 | 6 | no | — |
| 67 | C2×C4⋊Dic13 | — | 2 | 6 | no | — |
| 68 | C2×#6099 | C23 | 1 | 6 | yes | — |
| 69 | C22×#1055 | C23 | 1 | 6 | yes | — |
| 70 | #88151 | — | 2 | 12 | no | — |
| 71 | #88140 | — | 2 | 12 | no | — |
| 72 | #88129 | C23 | 1 | 6 | yes | — |
| 73 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4×D52 | — | 2 | 6 | no | — |
| 75 | #88123 | — | 2 | 6 | no | — |
| 76 | #88123 | C23 | 1 | 3 | yes | — |
| 77 | #88123 | C23 | 1 | 6 | yes | — |
| 78 | #88050 | C23 | 1 | 12 | yes | — |
| 79 | #88050 | C23 | 1 | 12 | yes | — |
| 80 | #88050 | C23 | 1 | 24 | yes | — |
| 81 | #88049 | C23 | 1 | 4 | yes | — |
| 82 | #88049 | C23 | 1 | 12 | yes | — |
| 83 | #88043 | C23 | 1 | 6 | yes | — |
| 84 | #88043 | C23 | 1 | 1 | yes | characteristic |
| 85 | #88043 | C23 | 1 | 3 | yes | — |
| 86 | C4×#1055 | C23 | 1 | 6 | yes | — |
| 87 | #60627 | — | 13 | 1 | no | maximal, Sylow |
| 88 | C13×#41 | #41 | 1 | 8 | yes | — |
| 89 | C2×Q8×C13 | — | 2 | 6 | no | — |
| 90 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×D4×C13 | C2×D4 | 1 | 3 | yes | — |
| 92 | C22×C4×C13 | — | 2 | 6 | no | — |
| 93 | C22×C4×C13 | C2×D4 | 1 | 6 | yes | — |
| 94 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 95 | C2×C22⋊D13 | — | 2 | 6 | no | — |
| 96 | C22×Dic13 | — | 2 | 6 | no | — |
| 97 | Q8×D13 | — | 4 | 8 | no | — |
| 98 | #6129 | — | 4 | 24 | no | — |
| 99 | #6127 | — | 2 | 24 | no | — |
| 100 | C2×D52 | — | 2 | 2 | no | — |
| 101 | C2×D52 | C24 | 1 | 2 | yes | — |
| 102 | C2×C4×D13 | — | 2 | 6 | no | — |
| 103 | C2×Dic26 | — | 2 | 24 | no | — |
| 104 | C2×Dic26 | — | 2 | 6 | no | — |
| 105 | C2×Dic26 | C24 | 1 | 6 | yes | — |
| 106 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 107 | C13×C4⋊C4 | — | 2 | 12 | no | — |
| 108 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 109 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 110 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 111 | C13×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 112 | C13×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 113 | C13×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 114 | C13×C22⋊C4 | — | 2 | 6 | no | — |
| 115 | C13×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 116 | C42×C13 | — | 2 | 6 | no | — |
| 117 | C42×C13 | C2×D4 | 1 | 6 | yes | — |
| 118 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 119 | C42×C13 | C24 | 1 | 3 | yes | — |
| 120 | #6103 | — | 2 | 12 | no | — |
| 121 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 122 | C4⋊Dic13 | — | 2 | 12 | no | — |
| 123 | #6099 | — | 2 | 12 | no | — |
| 124 | C2×#1055 | — | 2 | 12 | no | — |
| 125 | C2×#1055 | C24 | 1 | 2 | yes | — |
| 126 | C2×#1055 | C24 | 1 | 6 | yes | — |
| 127 | #3504 | D13 | 1 | 1 | yes | characteristic, complemented |
| 128 | #3499 | — | 13 | 1 | no | — |
| 129 | #3142 | — | 13 | 3 | no | — |
| 130 | #3139 | — | 13 | 3 | no | — |
| 131 | #3137 | — | 13 | 12 | no | — |
| 132 | #3135 | — | 13 | 3 | no | — |
| 133 | C2×#491 | — | 13 | 3 | no | — |
| 134 | #2898 | — | 13 | 4 | no | — |
| 135 | #2875 | — | 13 | 1 | no | — |
| 136 | C23×C13 | C22×D4 | 1 | 3 | yes | — |
| 137 | C22×D13 | — | 2 | 2 | no | — |
| 138 | Q8×C13 | — | 8 | 6 | no | — |
| 139 | Q8×C13 | #124 | 1 | 4 | yes | — |
| 140 | D4×C13 | #124 | 1 | 12 | yes | — |
| 141 | C2×C4×C13 | — | 2 | 2 | no | — |
| 142 | C2×C4×C13 | — | 2 | 6 | no | — |
| 143 | C2×C4×C13 | — | 4 | 6 | no | — |
| 144 | C2×C4×C13 | — | 8 | 6 | no | — |
| 145 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 146 | C2×C4×C13 | C22×D4 | 1 | 6 | yes | — |
| 147 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 148 | C2×C4×C13 | C2×#41 | 1 | 12 | yes | — |
| 149 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 150 | C22⋊D13 | — | 4 | 12 | no | — |
| 151 | C2×Dic13 | — | 2 | 6 | no | — |
| 152 | C2×Dic13 | — | 4 | 12 | no | — |
| 153 | D52 | — | 2 | 4 | no | — |
| 154 | D52 | — | 4 | 4 | no | — |
| 155 | C4×D13 | — | 4 | 12 | no | — |
| 156 | Dic26 | — | 2 | 12 | no | — |
| 157 | Dic26 | — | 4 | 12 | no | — |
| 158 | #1055 | — | 2 | 2 | no | — |
| 159 | #1055 | — | 2 | 6 | no | — |
| 160 | C2×2−1+4 | — | 13 | 2 | no | — |
| 161 | C2×#131 | — | 13 | 2 | no | — |
| 162 | #557 | — | 2 | 2 | no | — |
| 163 | #554 | — | 2 | 6 | no | — |
| 164 | D4×Q8 | — | 26 | 2 | no | — |
| 165 | #547 | — | 26 | 6 | no | — |
| 166 | #544 | C2×D13 | 1 | 6 | yes | — |
| 167 | #536 | — | 13 | 6 | no | — |
| 168 | #533 | C2×D13 | 1 | 3 | yes | — |
| 169 | #532 | — | 13 | 3 | no | — |
| 170 | C2×C4⋊Q8 | — | 13 | 3 | no | — |
| 171 | C2×#125 | C2×D13 | 1 | 3 | yes | — |
| 172 | #520 | C2×D13 | 1 | 2 | yes | — |
| 173 | C4×#41 | C2×D13 | 1 | 1 | yes | characteristic |
| 174 | #491 | — | 13 | 3 | no | — |
| 175 | #491 | — | 13 | 12 | no | — |
| 176 | #491 | — | 13 | 6 | no | — |
| 177 | #491 | — | 13 | 3 | no | — |
| 178 | #490 | — | 13 | 1 | no | — |
| 179 | #490 | — | 13 | 3 | no | — |
| 180 | #489 | — | 13 | 12 | no | — |
| 181 | #488 | — | 13 | 12 | no | — |
| 182 | #487 | — | 13 | 12 | no | — |
| 183 | #419 | — | 13 | 12 | no | — |
| 184 | #417 | — | 13 | 12 | no | — |
| 185 | #416 | — | 13 | 12 | no | — |
| 186 | C2×#103 | — | 13 | 12 | no | — |
| 187 | #405 | — | 13 | 6 | no | — |
| 188 | C4×M16 | — | 13 | 3 | no | — |
| 189 | C2×#97 | — | 13 | 3 | no | — |
| 190 | C22×C13 | — | 2 | 6 | no | — |
| 191 | C22×C13 | C2×#124 | 1 | 6 | yes | — |
| 192 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×D13 | — | 4 | 4 | no | — |
| 194 | C2×D13 | — | 4 | 2 | no | — |
| 195 | C4×C13 | — | 2 | 2 | no | — |
| 196 | C4×C13 | — | 2 | 6 | no | — |
| 197 | C4×C13 | — | 4 | 6 | no | — |
| 198 | C4×C13 | — | 4 | 2 | no | — |
| 199 | C4×C13 | C2×#124 | 1 | 6 | yes | — |
| 200 | C4×C13 | C22×#41 | 1 | 2 | yes | — |
| 201 | Dic13 | — | 4 | 6 | no | — |
| 202 | 2−1+4 | — | 26 | 16 | no | — |
| 203 | C2×#41 | — | 13 | 6 | no | — |
| 204 | C2×#41 | — | 26 | 6 | no | — |
| 205 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 206 | C22×Q8 | — | 13 | 6 | no | — |
| 207 | C22×Q8 | — | 26 | 2 | no | — |
| 208 | #131 | — | 26 | 8 | no | — |
| 209 | C2×M16 | — | 13 | 6 | no | — |
| 210 | C22×C8 | — | 13 | 6 | no | — |
| 211 | C4⋊Q8 | — | 2 | 6 | no | — |
| 212 | C4⋊Q8 | — | 13 | 3 | no | — |
| 213 | C4⋊Q8 | — | 13 | 6 | no | — |
| 214 | C4⋊Q8 | — | 26 | 6 | no | — |
| 215 | C4⋊Q8 | C22×D13 | 1 | 6 | yes | — |
| 216 | #127 | — | 13 | 1 | no | — |
| 217 | #125 | — | 2 | 6 | no | — |
| 218 | #125 | — | 2 | 6 | no | — |
| 219 | #125 | C22×D13 | 1 | 3 | yes | — |
| 220 | #125 | C22×D13 | 1 | 6 | yes | — |
| 221 | #125 | C22×D13 | 1 | 1 | yes | characteristic |
| 222 | #124 | — | 13 | 6 | no | — |
| 223 | #123 | — | 26 | 12 | no | — |
| 224 | C22⋊Q8 | — | 2 | 6 | no | — |
| 225 | C22⋊Q8 | — | 2 | 12 | no | — |
| 226 | C22⋊Q8 | — | 26 | 12 | no | — |
| 227 | #121 | — | 26 | 6 | no | — |
| 228 | C4×Q8 | — | 2 | 2 | no | — |
| 229 | C4×Q8 | — | 2 | 6 | no | — |
| 230 | C4×Q8 | C22⋊D13 | 1 | 2 | yes | — |
| 231 | C4×D4 | — | 2 | 6 | no | — |
| 232 | C4×D4 | — | 26 | 6 | no | — |
| 233 | C4×D4 | C22⋊D13 | 1 | 6 | yes | — |
| 234 | #117 | C22×D13 | 1 | 6 | yes | — |
| 235 | #117 | C22×D13 | 1 | 3 | yes | — |
| 236 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 237 | C2×C4⋊C4 | — | 26 | 6 | no | — |
| 238 | C2×C4⋊C4 | C22×D13 | 1 | 6 | yes | — |
| 239 | C2×C42 | C22×D13 | 1 | 3 | yes | — |
| 240 | #103 | — | 13 | 12 | no | — |
| 241 | #103 | — | 13 | 24 | no | — |
| 242 | #103 | — | 13 | 12 | no | — |
| 243 | #102 | — | 13 | 4 | no | — |
| 244 | #102 | — | 13 | 12 | no | — |
| 245 | #97 | — | 13 | 1 | no | — |
| 246 | #97 | — | 13 | 3 | no | — |
| 247 | #97 | — | 13 | 6 | no | — |
| 248 | C4×C8 | — | 13 | 6 | no | — |
| 249 | C2×C13 | — | 2 | 6 | no | — |
| 250 | C2×C13 | C22×#124 | 1 | 1 | yes | characteristic |
| 251 | C2×C13 | #3586 | 1 | 2 | yes | — |
| 252 | D13 | — | 8 | 2 | no | — |
| 253 | #41 | — | 26 | 24 | no | — |
| 254 | #41 | — | 52 | 24 | no | — |
| 255 | #41 | #6131 | 1 | 8 | yes | — |
| 256 | C2×Q8 | — | 2 | 6 | no | — |
| 257 | C2×Q8 | — | 13 | 6 | no | — |
| 258 | C2×Q8 | — | 26 | 6 | no | — |
| 259 | C2×Q8 | — | 26 | 24 | no | — |
| 260 | C2×Q8 | — | 52 | 8 | no | — |
| 261 | C2×Q8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 262 | C2×D4 | — | 13 | 2 | no | — |
| 263 | C2×D4 | — | 26 | 6 | no | — |
| 264 | C2×D4 | — | 26 | 2 | no | — |
| 265 | C2×D4 | C2×C22⋊D13 | 1 | 3 | yes | — |
| 266 | C22×C4 | — | 2 | 6 | no | — |
| 267 | C22×C4 | — | 26 | 6 | no | — |
| 268 | C22×C4 | — | 26 | 6 | no | — |
| 269 | C22×C4 | C2×C22⋊D13 | 1 | 6 | yes | — |
| 270 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 271 | M16 | — | 26 | 12 | no | — |
| 272 | C2×C8 | — | 13 | 6 | no | — |
| 273 | C2×C8 | — | 13 | 2 | no | — |
| 274 | C2×C8 | — | 26 | 12 | no | — |
| 275 | C4⋊C4 | — | 2 | 6 | no | — |
| 276 | C4⋊C4 | — | 2 | 12 | no | — |
| 277 | C4⋊C4 | — | 2 | 6 | no | — |
| 278 | C4⋊C4 | — | 2 | 2 | no | — |
| 279 | C4⋊C4 | — | 2 | 6 | no | — |
| 280 | C4⋊C4 | — | 26 | 6 | no | — |
| 281 | C4⋊C4 | — | 26 | 12 | no | — |
| 282 | C4⋊C4 | C2×C22⋊D13 | 1 | 6 | yes | — |
| 283 | C4⋊C4 | C23×D13 | 1 | 6 | yes | — |
| 284 | C4⋊C4 | C23×D13 | 1 | 2 | yes | — |
| 285 | C22⋊C4 | — | 2 | 6 | no | — |
| 286 | C22⋊C4 | — | 26 | 12 | no | — |
| 287 | C22⋊C4 | C2×C22⋊D13 | 1 | 6 | yes | — |
| 288 | C42 | — | 2 | 6 | no | — |
| 289 | C42 | C2×C22⋊D13 | 1 | 6 | yes | — |
| 290 | C42 | C23×D13 | 1 | 3 | yes | — |
| 291 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 292 | C13 | #60627 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 293 | C23 | — | 26 | 2 | no | — |
| 294 | C23 | C22×C22⋊D13 | 1 | 3 | yes | — |
| 295 | Q8 | — | 8 | 6 | no | — |
| 296 | Q8 | — | 26 | 12 | no | — |
| 297 | Q8 | — | 52 | 12 | no | — |
| 298 | Q8 | #88201 | 1 | 4 | yes | — |
| 299 | D4 | — | 26 | 4 | no | — |
| 300 | D4 | — | 52 | 4 | no | — |
| 301 | D4 | — | 52 | 12 | no | — |
| 302 | D4 | #88201 | 1 | 12 | yes | — |
| 303 | C2×C4 | — | 2 | 2 | no | — |
| 304 | C2×C4 | — | 2 | 6 | no | — |
| 305 | C2×C4 | — | 4 | 6 | no | — |
| 306 | C2×C4 | — | 8 | 6 | no | — |
| 307 | C2×C4 | — | 26 | 6 | no | — |
| 308 | C2×C4 | — | 52 | 12 | no | — |
| 309 | C2×C4 | — | 52 | 12 | no | — |
| 310 | C2×C4 | C2×#6131 | 1 | 12 | yes | — |
| 311 | C2×C4 | C22×C22⋊D13 | 1 | 2 | yes | — |
| 312 | C2×C4 | C22×C22⋊D13 | 1 | 6 | yes | — |
| 313 | C2×C4 | C22×C22⋊D13 | 1 | 3 | yes | — |
| 314 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 315 | C8 | — | 26 | 2 | no | — |
| 316 | C8 | — | 26 | 6 | no | — |
| 317 | C22 | — | 2 | 6 | no | — |
| 318 | C22 | — | 52 | 2 | no | — |
| 319 | C22 | — | 52 | 4 | no | — |
| 320 | C22 | C2×#88201 | 1 | 6 | yes | — |
| 321 | C22 | C23×C22⋊D13 | 1 | 1 | yes | characteristic |
| 322 | C4 | — | 2 | 2 | no | — |
| 323 | C4 | — | 2 | 6 | no | — |
| 324 | C4 | — | 4 | 6 | no | — |
| 325 | C4 | — | 4 | 2 | no | — |
| 326 | C4 | — | 52 | 6 | no | — |
| 327 | C4 | C2×#88201 | 1 | 6 | yes | — |
| 328 | C4 | C22×#6131 | 1 | 2 | yes | — |
| 329 | C2 | — | 2 | 6 | no | — |
| 330 | C2 | — | 104 | 2 | no | — |
| 331 | C2 | C22×#88201 | 1 | 1 | yes | characteristic |
| 332 | C2 | #13129622 | 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