← #16019113
Subgroups — #16019113
Order 3328.
456 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13125422 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13125350 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13117122 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13117082 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13117045 | C2 | 1 | 4 | yes | maximal |
| 6 | #13116989 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13116979 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C13×#2163 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #11719175 | — | 2 | 1 | no | — |
| 10 | #11719175 | — | 2 | 1 | no | — |
| 11 | C2×C4×C8×C13 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11718777 | — | 2 | 1 | no | — |
| 13 | #11718777 | C22 | 1 | 2 | yes | — |
| 14 | #11718767 | — | 2 | 1 | no | — |
| 15 | #11718767 | C22 | 1 | 2 | yes | — |
| 16 | #11718360 | C22 | 1 | 1 | yes | characteristic |
| 17 | C4×Dic52 | — | 2 | 1 | no | — |
| 18 | C4×Dic52 | C22 | 1 | 2 | yes | — |
| 19 | #11718344 | — | 2 | 1 | no | — |
| 20 | #11718344 | C22 | 1 | 2 | yes | — |
| 21 | #11718343 | C22 | 1 | 1 | yes | characteristic |
| 22 | #11718343 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11718343 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11718342 | — | 2 | 1 | no | — |
| 25 | #11718341 | — | 2 | 1 | no | — |
| 26 | C13×C4⋊C16 | C22 | 1 | 2 | yes | — |
| 27 | C13×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 28 | C13×#346 | C22 | 1 | 2 | yes | — |
| 29 | #11718097 | C22 | 1 | 4 | yes | — |
| 30 | #11718096 | C22 | 1 | 4 | yes | — |
| 31 | #11718095 | C22 | 1 | 4 | yes | — |
| 32 | #11718095 | C22 | 1 | 4 | yes | — |
| 33 | C22×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 34 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×C42×C13 | D4 | 1 | 1 | yes | characteristic |
| 36 | #88180 | — | 2 | 2 | no | — |
| 37 | #88180 | — | 4 | 1 | no | — |
| 38 | #88178 | — | 2 | 2 | no | — |
| 39 | #88178 | — | 4 | 1 | no | — |
| 40 | #88178 | — | 4 | 1 | no | — |
| 41 | #88178 | — | 4 | 1 | no | — |
| 42 | C2×Dic52 | — | 2 | 1 | no | — |
| 43 | C2×Dic52 | C23 | 1 | 2 | yes | — |
| 44 | #88124 | — | 2 | 2 | no | — |
| 45 | #88124 | — | 4 | 1 | no | — |
| 46 | #88123 | — | 2 | 1 | no | — |
| 47 | #88123 | — | 2 | 1 | no | — |
| 48 | #88123 | — | 2 | 1 | no | — |
| 49 | #88123 | — | 2 | 1 | no | — |
| 50 | C4×Dic26 | — | 2 | 2 | no | — |
| 51 | C4×Dic26 | — | 4 | 1 | no | — |
| 52 | C4×Dic26 | — | 4 | 1 | no | — |
| 53 | C4×Dic26 | — | 4 | 1 | no | — |
| 54 | C2×C13×C16 | C23 | 1 | 4 | yes | — |
| 55 | C4×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 56 | C4×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 57 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 58 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 59 | #88058 | — | 2 | 1 | no | — |
| 60 | #88058 | — | 2 | 1 | no | — |
| 61 | #88058 | — | 2 | 1 | no | — |
| 62 | #88058 | C23 | 1 | 2 | yes | — |
| 63 | #88058 | C23 | 1 | 2 | yes | — |
| 64 | #88058 | C23 | 1 | 2 | yes | — |
| 65 | #88057 | — | 2 | 2 | no | — |
| 66 | #88057 | — | 2 | 2 | no | — |
| 67 | #88056 | — | 2 | 2 | no | — |
| 68 | #88056 | — | 2 | 2 | no | — |
| 69 | #33803 | — | 13 | 1 | no | maximal, Sylow |
| 70 | C22×C4×C13 | D8 | 1 | 1 | yes | characteristic |
| 71 | C22×C4×C13 | D8 | 1 | 1 | yes | characteristic |
| 72 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C2×Dic26 | — | 2 | 2 | no | — |
| 74 | C2×Dic26 | — | 4 | 1 | no | — |
| 75 | C2×Dic26 | — | 4 | 1 | no | — |
| 76 | C2×Dic26 | — | 4 | 1 | 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 | C22⋊Dic13 | — | 4 | 2 | no | — |
| 88 | C22⋊Dic13 | — | 4 | 2 | no | — |
| 89 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 90 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 91 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 92 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 93 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 94 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 95 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 96 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 97 | #6101 | — | 4 | 2 | no | — |
| 98 | #6101 | — | 4 | 2 | no | — |
| 99 | #6101 | — | 4 | 2 | no | — |
| 100 | #6101 | — | 4 | 2 | no | — |
| 101 | C4×Dic13 | — | 4 | 2 | no | — |
| 102 | C4×Dic13 | — | 4 | 2 | no | — |
| 103 | Dic52 | — | 2 | 4 | no | — |
| 104 | Dic52 | — | 4 | 2 | no | — |
| 105 | C13×C16 | — | 2 | 4 | no | — |
| 106 | #3170 | — | 13 | 1 | no | — |
| 107 | #3160 | — | 13 | 1 | no | — |
| 108 | #2255 | — | 13 | 2 | no | — |
| 109 | #2245 | — | 13 | 2 | no | — |
| 110 | #2237 | — | 13 | 4 | no | — |
| 111 | #2227 | — | 13 | 2 | no | — |
| 112 | #2225 | — | 13 | 2 | no | — |
| 113 | #2163 | D13 | 1 | 1 | yes | characteristic |
| 114 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C13 | — | 2 | 1 | no | — |
| 116 | C2×C4×C13 | — | 2 | 1 | no | — |
| 117 | C2×C4×C13 | — | 2 | 2 | no | — |
| 118 | C2×C4×C13 | — | 4 | 1 | no | — |
| 119 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×Dic13 | — | 4 | 2 | no | — |
| 126 | C2×Dic13 | — | 4 | 2 | no | — |
| 127 | C2×Dic13 | — | 4 | 2 | no | — |
| 128 | C2×Dic13 | — | 4 | 2 | no | — |
| 129 | Dic26 | — | 4 | 2 | no | — |
| 130 | Dic26 | — | 4 | 2 | no | — |
| 131 | Dic26 | — | 8 | 2 | no | — |
| 132 | Dic26 | — | 8 | 2 | no | — |
| 133 | Dic26 | — | 8 | 2 | no | — |
| 134 | C8×C13 | — | 2 | 1 | no | — |
| 135 | C8×C13 | — | 2 | 1 | no | — |
| 136 | C8×C13 | #137 | 1 | 2 | yes | — |
| 137 | C8×C13 | 2−1+4 | 1 | 2 | yes | — |
| 138 | #533 | — | 26 | 1 | no | — |
| 139 | #533 | — | 26 | 1 | no | — |
| 140 | #500 | — | 13 | 1 | no | — |
| 141 | #500 | — | 13 | 1 | no | — |
| 142 | #500 | — | 13 | 1 | no | — |
| 143 | #499 | — | 13 | 2 | no | — |
| 144 | #499 | — | 26 | 1 | no | — |
| 145 | #498 | — | 26 | 1 | no | — |
| 146 | #494 | — | 13 | 1 | no | — |
| 147 | #487 | — | 26 | 1 | no | — |
| 148 | #467 | — | 13 | 2 | no | — |
| 149 | #467 | — | 26 | 1 | no | — |
| 150 | C4×Q16 | — | 13 | 2 | no | — |
| 151 | C4×Q16 | — | 26 | 1 | no | — |
| 152 | #427 | — | 13 | 2 | no | — |
| 153 | #427 | — | 26 | 1 | no | — |
| 154 | C2×C4×C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 155 | #367 | — | 13 | 4 | no | — |
| 156 | #366 | — | 13 | 4 | no | — |
| 157 | C4⋊C16 | C2×D13 | 1 | 2 | yes | — |
| 158 | #358 | — | 13 | 4 | no | — |
| 159 | #358 | — | 13 | 4 | no | — |
| 160 | C22⋊C16 | C2×D13 | 1 | 2 | yes | — |
| 161 | #346 | C2×D13 | 1 | 2 | yes | — |
| 162 | C22×C13 | — | 2 | 1 | no | — |
| 163 | C22×C13 | — | 2 | 1 | no | — |
| 164 | C22×C13 | — | 2 | 1 | no | — |
| 165 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 166 | C4×C13 | — | 2 | 1 | no | — |
| 167 | C4×C13 | — | 2 | 1 | no | — |
| 168 | C4×C13 | — | 2 | 1 | no | — |
| 169 | C4×C13 | — | 2 | 1 | no | — |
| 170 | C4×C13 | #510 | 1 | 2 | yes | — |
| 171 | C4×C13 | #536 | 1 | 1 | yes | characteristic |
| 172 | C4×C13 | C2×#137 | 1 | 1 | yes | characteristic |
| 173 | Dic13 | — | 8 | 2 | no | — |
| 174 | Dic13 | — | 8 | 2 | no | — |
| 175 | Dic13 | — | 8 | 2 | no | — |
| 176 | Dic13 | — | 8 | 2 | no | — |
| 177 | C2×Q16 | — | 13 | 2 | no | — |
| 178 | C2×Q16 | — | 26 | 1 | no | — |
| 179 | C22×C8 | D52 | 1 | 1 | yes | characteristic |
| 180 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 181 | C4⋊Q8 | — | 26 | 1 | no | — |
| 182 | C4⋊Q8 | — | 26 | 1 | no | — |
| 183 | C4⋊Q8 | — | 26 | 1 | no | — |
| 184 | C4⋊Q8 | — | 26 | 1 | no | — |
| 185 | #125 | — | 26 | 2 | no | — |
| 186 | #125 | — | 52 | 1 | no | — |
| 187 | C22⋊Q8 | — | 26 | 2 | no | — |
| 188 | C22⋊Q8 | — | 52 | 1 | no | — |
| 189 | C22⋊Q8 | — | 52 | 1 | no | — |
| 190 | C22⋊Q8 | — | 52 | 1 | no | — |
| 191 | C4×Q8 | — | 26 | 2 | no | — |
| 192 | C4×Q8 | — | 52 | 1 | no | — |
| 193 | C4×Q8 | — | 52 | 1 | no | — |
| 194 | C4×Q8 | — | 52 | 1 | no | — |
| 195 | #117 | — | 26 | 2 | no | — |
| 196 | #117 | — | 52 | 1 | no | — |
| 197 | C2×C42 | D52 | 1 | 1 | yes | characteristic |
| 198 | C2×C16 | C22×D13 | 1 | 4 | yes | — |
| 199 | #107 | — | 13 | 2 | no | — |
| 200 | #107 | — | 13 | 2 | no | — |
| 201 | #107 | — | 13 | 2 | no | — |
| 202 | #107 | — | 26 | 1 | no | — |
| 203 | #107 | — | 26 | 1 | no | — |
| 204 | #107 | — | 26 | 1 | no | — |
| 205 | #106 | — | 26 | 2 | no | — |
| 206 | #106 | — | 26 | 2 | no | — |
| 207 | #103 | — | 26 | 2 | no | — |
| 208 | #103 | — | 26 | 2 | no | — |
| 209 | C4×C8 | D52 | 1 | 1 | yes | characteristic |
| 210 | C4×C8 | D52 | 1 | 1 | yes | characteristic |
| 211 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 212 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 213 | C2×C13 | — | 4 | 1 | no | — |
| 214 | C2×C13 | #3226 | 1 | 1 | yes | characteristic |
| 215 | C2×C13 | C2×#510 | 1 | 1 | yes | characteristic |
| 216 | C2×C13 | #3414 | 1 | 1 | yes | characteristic |
| 217 | C2×Q8 | — | 26 | 2 | no | — |
| 218 | C2×Q8 | — | 52 | 1 | no | — |
| 219 | C2×Q8 | — | 52 | 1 | no | — |
| 220 | C2×Q8 | — | 52 | 1 | no | — |
| 221 | C22×C4 | D104 | 1 | 1 | yes | characteristic |
| 222 | C22×C4 | D104 | 1 | 1 | yes | characteristic |
| 223 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 224 | Q16 | — | 26 | 4 | no | — |
| 225 | Q16 | — | 52 | 2 | no | — |
| 226 | C2×C8 | — | 2 | 2 | no | — |
| 227 | C2×C8 | — | 2 | 2 | no | — |
| 228 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 229 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 230 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 231 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 232 | C4⋊C4 | — | 26 | 2 | no | — |
| 233 | C4⋊C4 | — | 26 | 2 | no | — |
| 234 | C4⋊C4 | — | 26 | 2 | no | — |
| 235 | C4⋊C4 | — | 52 | 1 | no | — |
| 236 | C4⋊C4 | — | 52 | 1 | no | — |
| 237 | C4⋊C4 | — | 52 | 2 | no | — |
| 238 | C4⋊C4 | — | 52 | 2 | no | — |
| 239 | C4⋊C4 | — | 52 | 2 | no | — |
| 240 | C4⋊C4 | — | 52 | 2 | no | — |
| 241 | C4⋊C4 | — | 52 | 1 | no | — |
| 242 | C4⋊C4 | — | 52 | 1 | no | — |
| 243 | C4⋊C4 | — | 52 | 1 | no | — |
| 244 | C22⋊C4 | — | 52 | 2 | no | — |
| 245 | C22⋊C4 | — | 52 | 2 | no | — |
| 246 | C42 | — | 52 | 2 | no | — |
| 247 | C42 | — | 52 | 2 | no | — |
| 248 | C42 | D104 | 1 | 1 | yes | characteristic |
| 249 | C42 | D104 | 1 | 1 | yes | characteristic |
| 250 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 251 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 252 | C16 | — | 2 | 4 | no | — |
| 253 | C13 | #33803 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 254 | C23 | C2×D104 | 1 | 1 | yes | characteristic |
| 255 | Q8 | — | 52 | 2 | no | — |
| 256 | Q8 | — | 52 | 2 | no | — |
| 257 | Q8 | — | 104 | 2 | no | — |
| 258 | Q8 | — | 104 | 2 | no | — |
| 259 | Q8 | — | 104 | 2 | no | — |
| 260 | C2×C4 | — | 2 | 1 | no | — |
| 261 | C2×C4 | — | 2 | 1 | no | — |
| 262 | C2×C4 | — | 2 | 2 | no | — |
| 263 | C2×C4 | — | 4 | 1 | no | — |
| 264 | C2×C4 | — | 52 | 2 | no | — |
| 265 | C2×C4 | — | 52 | 2 | no | — |
| 266 | C2×C4 | — | 52 | 2 | no | — |
| 267 | C2×C4 | — | 52 | 2 | no | — |
| 268 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 269 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 270 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 271 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 272 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 273 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 274 | C8 | — | 2 | 1 | no | — |
| 275 | C8 | — | 2 | 1 | no | — |
| 276 | C8 | #88163 | 1 | 2 | yes | — |
| 277 | C8 | #88257 | 1 | 2 | yes | — |
| 278 | C22 | — | 2 | 1 | no | — |
| 279 | C22 | — | 2 | 1 | no | — |
| 280 | C22 | — | 2 | 1 | no | — |
| 281 | C22 | C22×D104 | 1 | 1 | yes | characteristic |
| 282 | C4 | — | 2 | 1 | no | — |
| 283 | C4 | — | 2 | 1 | no | — |
| 284 | C4 | — | 2 | 1 | no | — |
| 285 | C4 | — | 2 | 1 | no | — |
| 286 | C4 | — | 104 | 2 | no | — |
| 287 | C4 | — | 104 | 2 | no | — |
| 288 | C4 | — | 104 | 2 | no | — |
| 289 | C4 | — | 104 | 2 | no | — |
| 290 | C4 | #11718570 | 1 | 2 | yes | — |
| 291 | C4 | #11719231 | 1 | 1 | yes | characteristic |
| 292 | C4 | C2×#88163 | 1 | 1 | yes | characteristic |
| 293 | C2 | — | 4 | 1 | no | — |
| 294 | C2 | #13125959 | 1 | 1 | yes | characteristic |
| 295 | C2 | C2×#11718570 | 1 | 1 | yes | characteristic |
| 296 | C2 | #13127972 | 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