← #16796013
Subgroups — #16796013
Order 3328.
544 conjugacy classes of subgroups.
The subgroup lattice has 346 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13131740 | C2 | 1 | 2 | yes | maximal |
| 2 | #13130462 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13130459 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13130449 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13130448 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13130396 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #13130198 | C2 | 1 | 2 | yes | maximal |
| 8 | #13130049 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #13125417 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11719327 | C22 | 1 | 2 | yes | — |
| 11 | #11719158 | C22 | 1 | 2 | yes | — |
| 12 | Q8×#1057 | C22 | 1 | 2 | yes | — |
| 13 | #11719130 | C22 | 1 | 2 | yes | — |
| 14 | #11719119 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11719119 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11719080 | — | 2 | 2 | no | — |
| 17 | #11719080 | C22 | 1 | 2 | yes | — |
| 18 | #11719078 | — | 2 | 2 | no | — |
| 19 | #11719074 | C22 | 1 | 2 | yes | — |
| 20 | #11719068 | — | 2 | 2 | no | — |
| 21 | #11719068 | — | 2 | 2 | no | — |
| 22 | C13×#467 | C4 | 1 | 1 | yes | characteristic |
| 23 | Q16×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11718842 | C4 | 1 | 1 | yes | characteristic |
| 25 | #11718777 | C4 | 1 | 1 | yes | characteristic |
| 26 | C2×C8×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 27 | #11718712 | C4 | 1 | 2 | yes | — |
| 28 | #11718535 | C4 | 1 | 1 | yes | characteristic |
| 29 | #11718534 | C22 | 1 | 1 | yes | characteristic |
| 30 | #11718453 | C4 | 1 | 2 | yes | — |
| 31 | #11718451 | C22 | 1 | 2 | yes | — |
| 32 | Q8⋊#1057 | C22 | 1 | 2 | yes | — |
| 33 | Q8⋊#1057 | C22 | 1 | 2 | yes | — |
| 34 | #11718256 | C22 | 1 | 2 | yes | — |
| 35 | #11718253 | C22 | 1 | 1 | yes | characteristic |
| 36 | #11718253 | C22 | 1 | 1 | yes | characteristic |
| 37 | #1057⋊C8 | C22 | 1 | 2 | yes | — |
| 38 | #1057⋊C8 | C22 | 1 | 2 | yes | — |
| 39 | #11718244 | C22 | 1 | 2 | yes | — |
| 40 | #11718244 | C22 | 1 | 2 | yes | — |
| 41 | C2×C13×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C22×C8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C13×C22⋊Q8 | C2×C4 | 1 | 2 | yes | — |
| 44 | Q8×Dic13 | C23 | 1 | 2 | yes | — |
| 45 | #88198 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×#6107 | C2×C4 | 1 | 2 | yes | — |
| 47 | #88178 | C2×C4 | 1 | 2 | yes | — |
| 48 | C2×C4×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×Dic52 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | #88143 | — | 2 | 2 | no | — |
| 52 | #88142 | C2×C4 | 1 | 2 | yes | — |
| 53 | #88141 | — | 2 | 2 | no | — |
| 54 | #88141 | C23 | 1 | 2 | yes | — |
| 55 | #88132 | — | 2 | 2 | no | — |
| 56 | #88131 | — | 2 | 2 | no | — |
| 57 | C22⋊#1057 | — | 2 | 2 | no | — |
| 58 | C22⋊#1057 | — | 2 | 1 | no | — |
| 59 | C22⋊#1057 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22⋊#1057 | D4 | 1 | 1 | yes | characteristic |
| 61 | #88112 | — | 2 | 2 | no | — |
| 62 | #88112 | — | 2 | 2 | no | — |
| 63 | #88110 | — | 2 | 2 | no | — |
| 64 | #88110 | — | 2 | 2 | no | — |
| 65 | #88110 | — | 2 | 2 | no | — |
| 66 | C4⋊#1057 | — | 2 | 2 | no | — |
| 67 | C4⋊#1057 | — | 2 | 2 | no | — |
| 68 | C4⋊#1057 | — | 2 | 1 | no | — |
| 69 | C4⋊#1057 | D4 | 1 | 2 | yes | — |
| 70 | C4⋊#1057 | C23 | 1 | 2 | yes | — |
| 71 | C4⋊#1057 | C23 | 1 | 2 | yes | — |
| 72 | C4×#1057 | — | 2 | 2 | no | — |
| 73 | C4×#1057 | — | 2 | 2 | no | — |
| 74 | C4×#1057 | C23 | 1 | 2 | yes | — |
| 75 | C4×#1057 | C23 | 1 | 2 | yes | — |
| 76 | C13×#107 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | C13×#103 | C2×C4 | 1 | 2 | yes | — |
| 78 | #88075 | C2×C4 | 1 | 2 | yes | — |
| 79 | #88058 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | #88056 | C2×C4 | 1 | 2 | yes | — |
| 81 | C8×Dic13 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | C8×Dic13 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C8×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 84 | C8×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 85 | #88050 | C2×C4 | 1 | 2 | yes | — |
| 86 | #88047 | C2×C4 | 1 | 2 | yes | — |
| 87 | #17991 | — | 13 | 1 | no | maximal, Sylow |
| 88 | C2×Q8×C13 | C22×C4 | 1 | 2 | yes | — |
| 89 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C22×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C22×Dic13 | #41 | 1 | 1 | yes | characteristic |
| 92 | C2×Dic26 | — | 2 | 2 | no | — |
| 93 | C2×Dic26 | C22×C4 | 1 | 2 | yes | — |
| 94 | C2×#1057 | — | 2 | 2 | no | — |
| 95 | C2×#1057 | — | 2 | 2 | no | — |
| 96 | C2×#1057 | — | 2 | 2 | no | — |
| 97 | C2×#1057 | C2×D4 | 1 | 2 | yes | — |
| 98 | C2×#1057 | C2×D4 | 1 | 2 | yes | — |
| 99 | C13×Q16 | — | 4 | 1 | no | — |
| 100 | C2×C8×C13 | — | 4 | 1 | no | — |
| 101 | C2×C8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C2×C8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 103 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 104 | C13×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 105 | C13×C22⋊C4 | — | 2 | 2 | no | — |
| 106 | C22⋊Dic13 | — | 2 | 2 | no | — |
| 107 | #6107 | — | 4 | 2 | no | — |
| 108 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 109 | C4⋊Dic13 | C22×C4 | 1 | 2 | yes | — |
| 110 | #6101 | — | 2 | 2 | no | — |
| 111 | #6101 | — | 2 | 2 | no | — |
| 112 | #6101 | — | 2 | 2 | no | — |
| 113 | #6101 | — | 2 | 2 | no | — |
| 114 | #6101 | — | 2 | 2 | no | — |
| 115 | C4×Dic13 | — | 2 | 2 | no | — |
| 116 | C4×Dic13 | — | 2 | 2 | no | — |
| 117 | C4×Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 118 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C4×Dic13 | #41 | 1 | 1 | yes | characteristic |
| 120 | C4×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 121 | C2×#1055 | — | 4 | 1 | no | — |
| 122 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | Dic52 | — | 4 | 1 | no | — |
| 125 | #3170 | — | 13 | 1 | no | — |
| 126 | #2985 | — | 13 | 2 | no | — |
| 127 | #1587 | — | 13 | 2 | no | — |
| 128 | #1587 | — | 13 | 2 | no | — |
| 129 | #1584 | — | 13 | 2 | no | — |
| 130 | #1584 | — | 13 | 2 | no | — |
| 131 | #1568 | — | 13 | 1 | no | — |
| 132 | #1497 | — | 13 | 2 | no | — |
| 133 | #1452 | — | 13 | 1 | no | — |
| 134 | C23×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 135 | Q8×C13 | — | 2 | 2 | no | — |
| 136 | Q8×C13 | — | 2 | 2 | no | — |
| 137 | C2×C4×C13 | — | 2 | 1 | no | — |
| 138 | C2×C4×C13 | — | 2 | 1 | no | — |
| 139 | C2×C4×C13 | — | 2 | 2 | no | — |
| 140 | C2×C4×C13 | — | 2 | 2 | no | — |
| 141 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 143 | C2×Dic13 | — | 2 | 2 | no | — |
| 144 | C2×Dic13 | — | 2 | 2 | no | — |
| 145 | C2×Dic13 | — | 2 | 2 | no | — |
| 146 | C2×Dic13 | — | 4 | 1 | no | — |
| 147 | C2×Dic13 | C4×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×Dic13 | C4×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×Dic13 | C22×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×Dic13 | C2×#41 | 1 | 1 | yes | characteristic |
| 151 | Dic26 | — | 2 | 2 | no | — |
| 152 | Dic26 | — | 2 | 2 | no | — |
| 153 | Dic26 | — | 8 | 2 | no | — |
| 154 | #1057 | — | 2 | 2 | no | — |
| 155 | #1057 | — | 2 | 2 | no | — |
| 156 | #1057 | — | 4 | 2 | no | — |
| 157 | #1057 | — | 4 | 2 | no | — |
| 158 | #1057 | — | 4 | 2 | no | — |
| 159 | C8×C13 | — | 2 | 1 | no | — |
| 160 | C8×C13 | — | 2 | 1 | no | — |
| 161 | #1055 | — | 2 | 1 | no | — |
| 162 | #1055 | — | 2 | 1 | no | — |
| 163 | #533 | — | 13 | 2 | no | — |
| 164 | #500 | — | 13 | 1 | no | — |
| 165 | #494 | — | 13 | 1 | no | — |
| 166 | #487 | — | 13 | 2 | no | — |
| 167 | #467 | — | 13 | 1 | no | — |
| 168 | #467 | — | 13 | 2 | no | — |
| 169 | #467 | #261 | 1 | 1 | yes | characteristic |
| 170 | #446 | — | 13 | 2 | no | — |
| 171 | #446 | — | 13 | 2 | no | — |
| 172 | #446 | — | 26 | 2 | no | — |
| 173 | #446 | — | 26 | 2 | no | — |
| 174 | C8×Q8 | — | 13 | 2 | no | — |
| 175 | C8×Q8 | — | 13 | 2 | no | — |
| 176 | C4×Q16 | — | 13 | 1 | no | — |
| 177 | C4×Q16 | — | 13 | 1 | no | — |
| 178 | C4×Q16 | — | 13 | 2 | no | — |
| 179 | #433 | — | 26 | 2 | no | — |
| 180 | #433 | — | 26 | 2 | no | — |
| 181 | #432 | — | 13 | 2 | no | — |
| 182 | #431 | — | 13 | 1 | no | — |
| 183 | #431 | — | 13 | 1 | no | — |
| 184 | C2×C4×C8 | — | 13 | 1 | no | — |
| 185 | #335 | — | 13 | 2 | no | — |
| 186 | #334 | — | 13 | 1 | no | — |
| 187 | #334 | — | 13 | 1 | no | — |
| 188 | Q8⋊C8 | — | 13 | 2 | no | — |
| 189 | Q8⋊C8 | — | 13 | 2 | no | — |
| 190 | Q8⋊C8 | — | 13 | 2 | no | — |
| 191 | Q8⋊C8 | — | 13 | 2 | no | — |
| 192 | #322 | — | 13 | 2 | no | — |
| 193 | #322 | — | 13 | 2 | no | — |
| 194 | C22×C13 | — | 2 | 1 | no | — |
| 195 | C22×C13 | — | 2 | 1 | no | — |
| 196 | C22×C13 | — | 2 | 1 | no | — |
| 197 | C22×C13 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 198 | C4×C13 | — | 2 | 1 | no | — |
| 199 | C4×C13 | — | 4 | 2 | no | — |
| 200 | C4×C13 | — | 4 | 2 | no | — |
| 201 | C4×C13 | #568 | 1 | 1 | yes | characteristic |
| 202 | C4×C13 | #568 | 1 | 1 | yes | characteristic |
| 203 | Dic13 | — | 2 | 1 | no | — |
| 204 | Dic13 | — | 2 | 1 | no | — |
| 205 | Dic13 | — | 2 | 1 | no | — |
| 206 | Dic13 | — | 4 | 2 | no | — |
| 207 | Dic13 | — | 4 | 2 | no | — |
| 208 | Dic13 | #578 | 1 | 2 | yes | — |
| 209 | C2×Q16 | — | 13 | 2 | no | — |
| 210 | C2×Q16 | — | 13 | 1 | no | — |
| 211 | C2×Q16 | C2×#261 | 1 | 1 | yes | characteristic |
| 212 | C22×C8 | — | 13 | 1 | no | — |
| 213 | C22×C8 | C2×#261 | 1 | 1 | yes | characteristic |
| 214 | C4⋊Q8 | — | 13 | 2 | no | — |
| 215 | C4⋊Q8 | — | 13 | 2 | no | — |
| 216 | #125 | — | 26 | 2 | no | — |
| 217 | C22⋊Q8 | — | 13 | 2 | no | — |
| 218 | C22⋊Q8 | — | 26 | 2 | no | — |
| 219 | C22⋊Q8 | C2×#261 | 1 | 2 | yes | — |
| 220 | C4×Q8 | — | 13 | 2 | no | — |
| 221 | C4×Q8 | — | 13 | 2 | no | — |
| 222 | C4×Q8 | — | 26 | 2 | no | — |
| 223 | #117 | — | 26 | 2 | no | — |
| 224 | C2×C42 | — | 13 | 1 | no | — |
| 225 | #107 | — | 13 | 1 | no | — |
| 226 | #107 | — | 13 | 2 | no | — |
| 227 | #107 | C2×#261 | 1 | 1 | yes | characteristic |
| 228 | C4⋊C8 | — | 13 | 2 | no | — |
| 229 | C4⋊C8 | — | 13 | 2 | no | — |
| 230 | C4⋊C8 | — | 13 | 2 | no | — |
| 231 | C4⋊C8 | — | 26 | 1 | no | — |
| 232 | C4⋊C8 | — | 26 | 2 | no | — |
| 233 | C4⋊C8 | — | 26 | 2 | no | — |
| 234 | C4⋊C8 | — | 26 | 2 | no | — |
| 235 | C4⋊C8 | — | 26 | 2 | no | — |
| 236 | #103 | — | 13 | 2 | no | — |
| 237 | #103 | — | 13 | 2 | no | — |
| 238 | #103 | — | 13 | 2 | no | — |
| 239 | #103 | C2×#261 | 1 | 2 | yes | — |
| 240 | C22⋊C8 | — | 13 | 1 | no | — |
| 241 | C22⋊C8 | — | 13 | 1 | no | — |
| 242 | C22⋊C8 | — | 26 | 1 | no | — |
| 243 | C22⋊C8 | — | 26 | 2 | no | — |
| 244 | #97 | — | 26 | 2 | no | — |
| 245 | #97 | — | 26 | 2 | no | — |
| 246 | #97 | — | 26 | 2 | no | — |
| 247 | C4×C8 | — | 13 | 2 | no | — |
| 248 | C4×C8 | — | 13 | 1 | no | — |
| 249 | C4×C8 | — | 13 | 1 | no | — |
| 250 | C4×C8 | — | 13 | 1 | no | — |
| 251 | C4×C8 | — | 13 | 1 | no | — |
| 252 | C4×C8 | — | 13 | 2 | no | — |
| 253 | C4×C8 | — | 26 | 2 | no | — |
| 254 | C4×C8 | — | 26 | 2 | no | — |
| 255 | C2×C13 | — | 4 | 1 | no | — |
| 256 | C2×C13 | #2932 | 1 | 1 | yes | characteristic |
| 257 | C2×C13 | #2950 | 1 | 1 | yes | characteristic |
| 258 | C2×C13 | #2957 | 1 | 1 | yes | characteristic |
| 259 | C2×Q8 | — | 13 | 2 | no | — |
| 260 | C2×Q8 | — | 26 | 2 | no | — |
| 261 | C2×Q8 | C22×#261 | 1 | 2 | yes | — |
| 262 | C22×C4 | — | 13 | 1 | no | — |
| 263 | C22×C4 | — | 13 | 1 | no | — |
| 264 | C22×C4 | C22×#261 | 1 | 1 | yes | characteristic |
| 265 | Q16 | — | 4 | 1 | no | — |
| 266 | Q16 | — | 52 | 1 | no | — |
| 267 | Q16 | — | 52 | 2 | no | — |
| 268 | C2×C8 | — | 4 | 1 | no | — |
| 269 | C2×C8 | — | 13 | 2 | no | — |
| 270 | C2×C8 | — | 13 | 2 | no | — |
| 271 | C2×C8 | — | 13 | 1 | no | — |
| 272 | C2×C8 | — | 13 | 1 | no | — |
| 273 | C2×C8 | — | 26 | 2 | no | — |
| 274 | C2×C8 | — | 26 | 2 | no | — |
| 275 | C2×C8 | — | 26 | 2 | no | — |
| 276 | C2×C8 | — | 52 | 1 | no | — |
| 277 | C2×C8 | C22×#261 | 1 | 1 | yes | characteristic |
| 278 | C2×C8 | C22×#261 | 1 | 1 | yes | characteristic |
| 279 | C4⋊C4 | — | 2 | 2 | no | — |
| 280 | C4⋊C4 | — | 13 | 2 | no | — |
| 281 | C4⋊C4 | — | 26 | 2 | no | — |
| 282 | C4⋊C4 | — | 26 | 2 | no | — |
| 283 | C4⋊C4 | — | 26 | 2 | no | — |
| 284 | C4⋊C4 | — | 26 | 2 | no | — |
| 285 | C4⋊C4 | — | 26 | 2 | no | — |
| 286 | C4⋊C4 | — | 26 | 2 | no | — |
| 287 | C4⋊C4 | C22×#261 | 1 | 2 | yes | — |
| 288 | C22⋊C4 | — | 2 | 2 | no | — |
| 289 | C22⋊C4 | — | 26 | 2 | no | — |
| 290 | C42 | — | 13 | 1 | no | — |
| 291 | C42 | — | 13 | 1 | no | — |
| 292 | C42 | — | 13 | 1 | no | — |
| 293 | C42 | — | 13 | 1 | no | — |
| 294 | C42 | — | 26 | 2 | no | — |
| 295 | C42 | — | 26 | 2 | no | — |
| 296 | C13 | #17991 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 297 | C23 | D4×#261 | 1 | 1 | yes | characteristic |
| 298 | Q8 | — | 2 | 2 | no | — |
| 299 | Q8 | — | 2 | 2 | no | — |
| 300 | Q8 | — | 26 | 2 | no | — |
| 301 | Q8 | — | 26 | 2 | no | — |
| 302 | Q8 | — | 104 | 2 | no | — |
| 303 | C2×C4 | — | 2 | 1 | no | — |
| 304 | C2×C4 | — | 2 | 1 | no | — |
| 305 | C2×C4 | — | 2 | 2 | no | — |
| 306 | C2×C4 | — | 2 | 2 | no | — |
| 307 | C2×C4 | — | 13 | 1 | no | — |
| 308 | C2×C4 | — | 13 | 1 | no | — |
| 309 | C2×C4 | — | 13 | 1 | no | — |
| 310 | C2×C4 | — | 13 | 1 | no | — |
| 311 | C2×C4 | — | 26 | 2 | no | — |
| 312 | C2×C4 | — | 26 | 2 | no | — |
| 313 | C2×C4 | — | 26 | 2 | no | — |
| 314 | C2×C4 | — | 52 | 1 | no | — |
| 315 | C2×C4 | D4×#261 | 1 | 1 | yes | characteristic |
| 316 | C2×C4 | C23×#261 | 1 | 1 | yes | characteristic |
| 317 | C8 | — | 2 | 1 | no | — |
| 318 | C8 | — | 2 | 1 | no | — |
| 319 | C8 | — | 26 | 2 | no | — |
| 320 | C8 | — | 26 | 2 | no | — |
| 321 | C8 | — | 26 | 1 | no | — |
| 322 | C8 | — | 26 | 1 | no | — |
| 323 | C8 | — | 52 | 2 | no | — |
| 324 | C8 | — | 52 | 2 | no | — |
| 325 | C8 | — | 52 | 2 | no | — |
| 326 | C22 | — | 2 | 1 | no | — |
| 327 | C22 | — | 2 | 1 | no | — |
| 328 | C22 | — | 2 | 1 | no | — |
| 329 | C22 | C2×D4×#261 | 1 | 1 | yes | characteristic |
| 330 | C4 | — | 2 | 1 | no | — |
| 331 | C4 | — | 4 | 2 | no | — |
| 332 | C4 | — | 4 | 2 | no | — |
| 333 | C4 | — | 13 | 2 | no | — |
| 334 | C4 | — | 26 | 1 | no | — |
| 335 | C4 | — | 26 | 1 | no | — |
| 336 | C4 | — | 26 | 1 | no | — |
| 337 | C4 | — | 52 | 2 | no | — |
| 338 | C4 | — | 52 | 2 | no | — |
| 339 | C4 | #11719621 | 1 | 1 | yes | characteristic |
| 340 | C4 | #11719629 | 1 | 1 | yes | characteristic |
| 341 | C2 | — | 4 | 1 | no | — |
| 342 | C2 | #13131564 | 1 | 1 | yes | characteristic |
| 343 | C2 | #13131597 | 1 | 1 | yes | characteristic |
| 344 | C2 | #13131615 | 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