← #16030254
Subgroups — #16030254
Order 3328.
2390 conjugacy classes of subgroups.
The subgroup lattice has 338 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11719175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#11719182 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13120784 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13120779 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13120772 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13120764 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #13118122 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #13117326 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C2×C13×#376 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×#6127 | C22 | 1 | 2 | yes | — |
| 11 | C22×C42×C13 | C22 | 1 | 2 | yes | — |
| 12 | C22×C42×C13 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#88184 | C22 | 1 | 4 | yes | — |
| 14 | C2×#88180 | C22 | 1 | 2 | yes | — |
| 15 | C2×#88178 | C22 | 1 | 4 | yes | — |
| 16 | #11719182 | — | 2 | 8 | no | — |
| 17 | C2×#88129 | C22 | 1 | 2 | yes | — |
| 18 | C2×#88128 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×D52 | C22 | 1 | 4 | yes | — |
| 20 | #11719175 | — | 2 | 8 | no | — |
| 21 | C2×#88124 | C22 | 1 | 2 | yes | — |
| 22 | C2×#88123 | C22 | 1 | 2 | yes | — |
| 23 | C2×#88123 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C4×Dic26 | C22 | 1 | 4 | yes | — |
| 25 | C13×#376 | C22 | 1 | 2 | yes | — |
| 26 | C13×#376 | C22 | 1 | 2 | yes | — |
| 27 | C13×#376 | C22 | 1 | 4 | yes | — |
| 28 | C2×C13×#95 | C22 | 1 | 4 | yes | — |
| 29 | #11718874 | C22 | 1 | 16 | yes | — |
| 30 | #11718600 | C22 | 1 | 8 | yes | — |
| 31 | C4×#6103 | C22 | 1 | 16 | yes | — |
| 32 | #11718590 | C22 | 1 | 8 | yes | — |
| 33 | #11718335 | C22 | 1 | 16 | yes | — |
| 34 | #11718334 | C22 | 1 | 16 | yes | — |
| 35 | #11718333 | C22 | 1 | 16 | yes | — |
| 36 | #11718320 | C22 | 1 | 16 | yes | — |
| 37 | C23×C4×C13 | C23 | 1 | 4 | yes | — |
| 38 | C23×C4×C13 | C23 | 1 | 2 | yes | — |
| 39 | C23×C4×C13 | C23 | 1 | 1 | yes | characteristic |
| 40 | C22×C22⋊D13 | C23 | 1 | 4 | yes | — |
| 41 | C2×#6127 | — | 2 | 8 | no | — |
| 42 | C2×#6127 | — | 2 | 16 | no | — |
| 43 | C22×D52 | C23 | 1 | 2 | yes | — |
| 44 | C22×D52 | C23 | 1 | 4 | yes | — |
| 45 | C22×C4×D13 | C23 | 1 | 4 | yes | — |
| 46 | C22×Dic26 | C23 | 1 | 2 | yes | — |
| 47 | C22×Dic26 | C23 | 1 | 4 | yes | — |
| 48 | C2×C42×C13 | — | 2 | 8 | no | — |
| 49 | C2×C42×C13 | D4 | 1 | 8 | yes | — |
| 50 | C2×C42×C13 | C23 | 1 | 4 | yes | — |
| 51 | C2×C42×C13 | C23 | 1 | 4 | yes | — |
| 52 | C2×C42×C13 | C23 | 1 | 2 | yes | — |
| 53 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C22⋊Dic13 | C23 | 1 | 4 | yes | — |
| 56 | #88184 | — | 2 | 16 | no | — |
| 57 | C2×#6103 | C23 | 1 | 8 | yes | — |
| 58 | C2×#6103 | C23 | 1 | 32 | yes | — |
| 59 | #88180 | — | 2 | 8 | no | — |
| 60 | C2×C4⋊Dic13 | C23 | 1 | 4 | yes | — |
| 61 | C2×C4⋊Dic13 | C23 | 1 | 4 | yes | — |
| 62 | C2×C4⋊Dic13 | C23 | 1 | 4 | yes | — |
| 63 | #88178 | — | 2 | 16 | no | — |
| 64 | C2×#6101 | C23 | 1 | 8 | yes | — |
| 65 | C2×C4×Dic13 | C23 | 1 | 4 | yes | — |
| 66 | #88129 | — | 2 | 8 | no | — |
| 67 | #88128 | — | 2 | 4 | no | — |
| 68 | C4×D52 | — | 2 | 16 | no | — |
| 69 | #88124 | — | 2 | 8 | no | — |
| 70 | #88123 | — | 2 | 8 | no | — |
| 71 | #88123 | — | 2 | 4 | no | — |
| 72 | C4×Dic26 | — | 2 | 16 | no | — |
| 73 | C13×#95 | C23 | 1 | 8 | yes | — |
| 74 | C13×#95 | C23 | 1 | 8 | yes | — |
| 75 | #88071 | C23 | 1 | 32 | yes | — |
| 76 | #34637 | — | 13 | 1 | no | maximal, Sylow |
| 77 | C24×C13 | C24 | 1 | 1 | yes | characteristic |
| 78 | C23×D13 | C24 | 1 | 4 | yes | — |
| 79 | C22×C4×C13 | — | 2 | 8 | no | — |
| 80 | C22×C4×C13 | — | 4 | 4 | no | — |
| 81 | C22×C4×C13 | — | 4 | 8 | no | — |
| 82 | C22×C4×C13 | C2×D4 | 1 | 8 | yes | — |
| 83 | C22×C4×C13 | C2×D4 | 1 | 4 | yes | — |
| 84 | C22×C4×C13 | #41 | 1 | 8 | yes | — |
| 85 | C22×C4×C13 | C24 | 1 | 8 | yes | — |
| 86 | C22×C4×C13 | C24 | 1 | 2 | yes | — |
| 87 | C22×C4×C13 | C24 | 1 | 2 | yes | — |
| 88 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 90 | C2×C22⋊D13 | — | 2 | 8 | no | — |
| 91 | C2×C22⋊D13 | — | 2 | 16 | no | — |
| 92 | C22×Dic13 | C24 | 1 | 4 | yes | — |
| 93 | C22×Dic13 | C24 | 1 | 8 | yes | — |
| 94 | #6127 | — | 4 | 32 | no | — |
| 95 | C2×D52 | — | 2 | 8 | no | — |
| 96 | C2×D52 | — | 2 | 4 | no | — |
| 97 | C2×D52 | — | 2 | 8 | no | — |
| 98 | C2×D52 | — | 4 | 8 | no | — |
| 99 | C2×C4×D13 | — | 2 | 8 | no | — |
| 100 | C2×C4×D13 | — | 2 | 16 | no | — |
| 101 | C2×Dic26 | — | 2 | 8 | no | — |
| 102 | C2×Dic26 | — | 2 | 4 | no | — |
| 103 | C2×Dic26 | — | 2 | 8 | no | — |
| 104 | C2×Dic26 | — | 4 | 8 | no | — |
| 105 | C42×C13 | — | 2 | 8 | no | — |
| 106 | C42×C13 | — | 2 | 8 | no | — |
| 107 | C42×C13 | C2×D4 | 1 | 8 | yes | — |
| 108 | C42×C13 | C2×D4 | 1 | 4 | yes | — |
| 109 | C42×C13 | C2×D4 | 1 | 4 | yes | — |
| 110 | C22⋊Dic13 | — | 2 | 8 | no | — |
| 111 | #6103 | — | 2 | 16 | no | — |
| 112 | #6103 | — | 4 | 32 | no | — |
| 113 | C4⋊Dic13 | — | 2 | 8 | no | — |
| 114 | C4⋊Dic13 | — | 2 | 8 | no | — |
| 115 | C4⋊Dic13 | — | 2 | 8 | no | — |
| 116 | #6101 | — | 2 | 16 | no | — |
| 117 | C4×Dic13 | — | 2 | 8 | no | — |
| 118 | C2×#533 | — | 13 | 1 | no | — |
| 119 | C2×#532 | — | 13 | 1 | no | — |
| 120 | #2642 | — | 13 | 2 | no | — |
| 121 | #2641 | — | 13 | 2 | no | — |
| 122 | #2640 | — | 13 | 4 | no | — |
| 123 | #2639 | — | 13 | 8 | no | — |
| 124 | #2398 | — | 13 | 8 | no | — |
| 125 | #2297 | — | 13 | 4 | no | — |
| 126 | C2×#376 | D13 | 1 | 1 | yes | characteristic, complemented |
| 127 | C23×C13 | — | 2 | 4 | no | — |
| 128 | C23×C13 | C22×D4 | 1 | 2 | yes | — |
| 129 | C23×C13 | C2×#41 | 1 | 4 | yes | — |
| 130 | C23×C13 | C25 | 1 | 1 | yes | characteristic |
| 131 | C22×D13 | — | 2 | 4 | no | — |
| 132 | C22×D13 | — | 2 | 8 | no | — |
| 133 | C22×D13 | — | 2 | 16 | no | — |
| 134 | C2×C4×C13 | — | 2 | 4 | no | — |
| 135 | C2×C4×C13 | — | 2 | 4 | no | — |
| 136 | C2×C4×C13 | — | 2 | 8 | no | — |
| 137 | C2×C4×C13 | — | 2 | 16 | no | — |
| 138 | C2×C4×C13 | — | 4 | 8 | no | — |
| 139 | C2×C4×C13 | — | 4 | 16 | no | — |
| 140 | C2×C4×C13 | #124 | 1 | 16 | yes | — |
| 141 | C2×C4×C13 | C22×D4 | 1 | 4 | yes | — |
| 142 | C2×C4×C13 | C22×D4 | 1 | 4 | yes | — |
| 143 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 144 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 145 | C2×C4×C13 | C2×#41 | 1 | 4 | yes | — |
| 146 | C2×C4×C13 | C2×#41 | 1 | 4 | yes | — |
| 147 | C22⋊D13 | — | 4 | 16 | no | — |
| 148 | C2×Dic13 | — | 2 | 8 | no | — |
| 149 | C2×Dic13 | — | 2 | 4 | no | — |
| 150 | C2×Dic13 | — | 2 | 8 | no | — |
| 151 | C2×Dic13 | — | 2 | 16 | no | — |
| 152 | D52 | — | 4 | 16 | no | — |
| 153 | D52 | — | 4 | 8 | no | — |
| 154 | C4×D13 | — | 4 | 16 | no | — |
| 155 | Dic26 | — | 4 | 16 | no | — |
| 156 | Dic26 | — | 4 | 8 | no | — |
| 157 | C22×#41 | — | 13 | 2 | no | — |
| 158 | #533 | — | 26 | 8 | no | — |
| 159 | #532 | — | 26 | 8 | no | — |
| 160 | C2×C4⋊Q8 | — | 13 | 2 | no | — |
| 161 | C2×C4⋊Q8 | — | 13 | 1 | no | — |
| 162 | C2×#127 | — | 13 | 1 | no | — |
| 163 | C2×#125 | — | 13 | 2 | no | — |
| 164 | C2×#124 | — | 13 | 2 | no | — |
| 165 | C2×C22⋊Q8 | — | 13 | 4 | no | — |
| 166 | C2×#121 | — | 13 | 4 | no | — |
| 167 | C2×C4×Q8 | — | 13 | 4 | no | — |
| 168 | C2×C4×D4 | — | 13 | 4 | no | — |
| 169 | C2×#117 | — | 13 | 2 | no | — |
| 170 | C22×C42 | C2×D13 | 1 | 2 | yes | — |
| 171 | C22×C42 | C2×D13 | 1 | 1 | yes | characteristic |
| 172 | #400 | — | 13 | 16 | no | — |
| 173 | #397 | — | 13 | 16 | no | — |
| 174 | #394 | — | 13 | 16 | no | — |
| 175 | #393 | — | 13 | 16 | no | — |
| 176 | #391 | — | 13 | 8 | no | — |
| 177 | #390 | — | 13 | 8 | no | — |
| 178 | #386 | — | 13 | 16 | no | — |
| 179 | C4×C22⋊C4 | — | 13 | 16 | no | — |
| 180 | #376 | C2×D13 | 1 | 2 | yes | — |
| 181 | #376 | C2×D13 | 1 | 2 | yes | — |
| 182 | #376 | C2×D13 | 1 | 4 | yes | — |
| 183 | C2×#95 | C2×D13 | 1 | 4 | yes | — |
| 184 | C22×C13 | — | 2 | 4 | no | — |
| 185 | C22×C13 | — | 2 | 8 | no | — |
| 186 | C22×C13 | C2×#124 | 1 | 4 | yes | — |
| 187 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 188 | C22×C13 | C22×#41 | 1 | 2 | yes | — |
| 189 | C22×C13 | #585 | 1 | 4 | yes | — |
| 190 | C2×D13 | — | 4 | 4 | no | — |
| 191 | C2×D13 | — | 4 | 8 | no | — |
| 192 | C2×D13 | — | 4 | 16 | no | — |
| 193 | C4×C13 | — | 2 | 4 | no | — |
| 194 | C4×C13 | — | 2 | 4 | no | — |
| 195 | C4×C13 | — | 4 | 8 | no | — |
| 196 | C4×C13 | C2×#124 | 1 | 4 | yes | — |
| 197 | C4×C13 | C2×#124 | 1 | 4 | yes | — |
| 198 | Dic13 | — | 4 | 4 | no | — |
| 199 | Dic13 | — | 4 | 8 | no | — |
| 200 | C2×#41 | — | 26 | 8 | no | — |
| 201 | C2×#41 | — | 26 | 16 | no | — |
| 202 | C22×Q8 | — | 13 | 2 | no | — |
| 203 | C22×Q8 | — | 13 | 4 | no | — |
| 204 | C22×D4 | — | 13 | 4 | no | — |
| 205 | C22×D4 | — | 13 | 2 | no | — |
| 206 | C22×D4 | — | 13 | 4 | no | — |
| 207 | C23×C4 | — | 13 | 4 | no | — |
| 208 | C23×C4 | C22×D13 | 1 | 4 | yes | — |
| 209 | C23×C4 | C22×D13 | 1 | 2 | yes | — |
| 210 | C23×C4 | C22×D13 | 1 | 1 | yes | characteristic |
| 211 | C4⋊Q8 | — | 26 | 4 | no | — |
| 212 | C4⋊Q8 | — | 26 | 8 | no | — |
| 213 | #127 | — | 26 | 4 | no | — |
| 214 | #125 | — | 26 | 8 | no | — |
| 215 | #124 | — | 26 | 8 | no | — |
| 216 | C22⋊Q8 | — | 26 | 16 | no | — |
| 217 | #121 | — | 26 | 16 | no | — |
| 218 | C4×Q8 | — | 26 | 16 | no | — |
| 219 | C4×D4 | — | 26 | 16 | no | — |
| 220 | #117 | — | 26 | 8 | no | — |
| 221 | C2×C4⋊C4 | — | 13 | 4 | no | — |
| 222 | C2×C4⋊C4 | — | 13 | 4 | no | — |
| 223 | C2×C4⋊C4 | — | 13 | 8 | no | — |
| 224 | C2×C4⋊C4 | — | 13 | 4 | no | — |
| 225 | C2×C22⋊C4 | — | 13 | 4 | no | — |
| 226 | C2×C22⋊C4 | — | 13 | 8 | no | — |
| 227 | C2×C22⋊C4 | — | 13 | 32 | no | — |
| 228 | C2×C42 | — | 2 | 8 | no | — |
| 229 | C2×C42 | — | 13 | 4 | no | — |
| 230 | C2×C42 | D52 | 1 | 8 | yes | — |
| 231 | C2×C42 | C22×D13 | 1 | 4 | yes | — |
| 232 | C2×C42 | C22×D13 | 1 | 4 | yes | — |
| 233 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 234 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 235 | C2×C42 | C22×D13 | 1 | 2 | yes | — |
| 236 | #95 | — | 13 | 32 | no | — |
| 237 | #95 | C22×D13 | 1 | 8 | yes | — |
| 238 | #95 | C22×D13 | 1 | 8 | yes | — |
| 239 | C2×C13 | — | 2 | 4 | no | — |
| 240 | C2×C13 | C22×#124 | 1 | 1 | yes | characteristic |
| 241 | C2×C13 | #3449 | 1 | 2 | yes | — |
| 242 | C2×C13 | #3455 | 1 | 4 | yes | — |
| 243 | D13 | — | 8 | 4 | no | — |
| 244 | C24 | — | 13 | 4 | no | — |
| 245 | C24 | C23×D13 | 1 | 1 | yes | characteristic |
| 246 | #41 | — | 52 | 32 | no | — |
| 247 | C2×Q8 | — | 26 | 8 | no | — |
| 248 | C2×Q8 | — | 26 | 4 | no | — |
| 249 | C2×Q8 | — | 26 | 8 | no | — |
| 250 | C2×Q8 | — | 52 | 8 | no | — |
| 251 | C2×D4 | — | 26 | 8 | no | — |
| 252 | C2×D4 | — | 26 | 16 | no | — |
| 253 | C2×D4 | — | 26 | 8 | no | — |
| 254 | C2×D4 | — | 26 | 4 | no | — |
| 255 | C2×D4 | — | 26 | 8 | no | — |
| 256 | C2×D4 | — | 52 | 8 | no | — |
| 257 | C22×C4 | — | 2 | 8 | no | — |
| 258 | C22×C4 | — | 4 | 4 | no | — |
| 259 | C22×C4 | — | 4 | 8 | no | — |
| 260 | C22×C4 | — | 13 | 4 | no | — |
| 261 | C22×C4 | — | 13 | 8 | no | — |
| 262 | C22×C4 | — | 26 | 8 | no | — |
| 263 | C22×C4 | — | 26 | 16 | no | — |
| 264 | C22×C4 | C2×D52 | 1 | 8 | yes | — |
| 265 | C22×C4 | C2×D52 | 1 | 4 | yes | — |
| 266 | C22×C4 | #6127 | 1 | 8 | yes | — |
| 267 | C22×C4 | C23×D13 | 1 | 8 | yes | — |
| 268 | C22×C4 | C23×D13 | 1 | 2 | yes | — |
| 269 | C22×C4 | C23×D13 | 1 | 2 | yes | — |
| 270 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 271 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 272 | C4⋊C4 | — | 26 | 8 | no | — |
| 273 | C4⋊C4 | — | 26 | 8 | no | — |
| 274 | C4⋊C4 | — | 26 | 16 | no | — |
| 275 | C4⋊C4 | — | 26 | 8 | no | — |
| 276 | C22⋊C4 | — | 26 | 8 | no | — |
| 277 | C22⋊C4 | — | 26 | 16 | no | — |
| 278 | C22⋊C4 | — | 52 | 32 | no | — |
| 279 | C42 | — | 2 | 8 | no | — |
| 280 | C42 | — | 2 | 8 | no | — |
| 281 | C42 | — | 26 | 8 | no | — |
| 282 | C42 | C2×D52 | 1 | 8 | yes | — |
| 283 | C42 | C2×D52 | 1 | 4 | yes | — |
| 284 | C42 | C2×D52 | 1 | 4 | yes | — |
| 285 | C13 | #34637 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 286 | C23 | — | 2 | 4 | no | — |
| 287 | C23 | — | 26 | 4 | no | — |
| 288 | C23 | — | 26 | 8 | no | — |
| 289 | C23 | — | 26 | 16 | no | — |
| 290 | C23 | C22×D52 | 1 | 2 | yes | — |
| 291 | C23 | C2×#6127 | 1 | 4 | yes | — |
| 292 | C23 | C24×D13 | 1 | 1 | yes | characteristic |
| 293 | Q8 | — | 52 | 16 | no | — |
| 294 | Q8 | — | 52 | 8 | no | — |
| 295 | D4 | — | 52 | 16 | no | — |
| 296 | D4 | — | 52 | 16 | no | — |
| 297 | D4 | — | 52 | 8 | no | — |
| 298 | C2×C4 | — | 2 | 4 | no | — |
| 299 | C2×C4 | — | 2 | 4 | no | — |
| 300 | C2×C4 | — | 2 | 8 | no | — |
| 301 | C2×C4 | — | 2 | 16 | no | — |
| 302 | C2×C4 | — | 4 | 8 | no | — |
| 303 | C2×C4 | — | 4 | 16 | no | — |
| 304 | C2×C4 | — | 26 | 8 | no | — |
| 305 | C2×C4 | — | 26 | 4 | no | — |
| 306 | C2×C4 | — | 26 | 8 | no | — |
| 307 | C2×C4 | — | 26 | 16 | no | — |
| 308 | C2×C4 | — | 52 | 16 | no | — |
| 309 | C2×C4 | #88129 | 1 | 16 | yes | — |
| 310 | C2×C4 | C22×D52 | 1 | 4 | yes | — |
| 311 | C2×C4 | C22×D52 | 1 | 4 | yes | — |
| 312 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 313 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 314 | C2×C4 | C2×#6127 | 1 | 4 | yes | — |
| 315 | C2×C4 | C2×#6127 | 1 | 4 | yes | — |
| 316 | C22 | — | 2 | 8 | no | — |
| 317 | C22 | — | 2 | 4 | no | — |
| 318 | C22 | — | 52 | 16 | no | — |
| 319 | C22 | — | 52 | 4 | no | — |
| 320 | C22 | — | 52 | 8 | no | — |
| 321 | C22 | C2×#88129 | 1 | 4 | yes | — |
| 322 | C22 | C23×D52 | 1 | 1 | yes | characteristic |
| 323 | C22 | C22×#6127 | 1 | 2 | yes | — |
| 324 | C22 | #11719648 | 1 | 4 | yes | — |
| 325 | C4 | — | 2 | 4 | no | — |
| 326 | C4 | — | 2 | 4 | no | — |
| 327 | C4 | — | 4 | 8 | no | — |
| 328 | C4 | — | 52 | 4 | no | — |
| 329 | C4 | — | 52 | 8 | no | — |
| 330 | C4 | C2×#88129 | 1 | 4 | yes | — |
| 331 | C4 | C2×#88129 | 1 | 4 | yes | — |
| 332 | C2 | — | 2 | 4 | no | — |
| 333 | C2 | — | 104 | 4 | no | — |
| 334 | C2 | C22×#88129 | 1 | 1 | yes | characteristic |
| 335 | C2 | #13128169 | 1 | 2 | yes | — |
| 336 | C2 | #13128226 | 1 | 4 | 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