← #16017621
Subgroups — #16017621
Order 3328.
520 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13125376 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13123704 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13117002 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13116998 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13116986 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13116976 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13116624 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #13116618 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #13116596 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#11718156 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C13×#2141 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C22×C13×Q16 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11719517 | — | 2 | 1 | no | — |
| 14 | #11719224 | — | 2 | 1 | no | — |
| 15 | C2×C13×M32 | C22 | 1 | 1 | yes | characteristic |
| 16 | C13×#427 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11718886 | — | 2 | 1 | no | — |
| 18 | #11718845 | — | 2 | 2 | no | — |
| 19 | Q16×Dic13 | C22 | 1 | 2 | yes | — |
| 20 | Q16×Dic13 | C22 | 1 | 2 | yes | — |
| 21 | #11718767 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#88058 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11718762 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×#6090 | C22 | 1 | 1 | yes | characteristic |
| 25 | #11718656 | — | 2 | 1 | no | — |
| 26 | #11718539 | C22 | 1 | 2 | yes | — |
| 27 | #11718535 | C22 | 1 | 2 | yes | — |
| 28 | #11718517 | — | 2 | 2 | no | — |
| 29 | C13×#358 | C22 | 1 | 2 | yes | — |
| 30 | C13×#358 | C22 | 1 | 2 | yes | — |
| 31 | #11718156 | C22 | 1 | 2 | yes | — |
| 32 | #11718156 | C22 | 1 | 2 | yes | — |
| 33 | #11718097 | C22 | 1 | 2 | yes | — |
| 34 | #11718096 | C22 | 1 | 2 | yes | — |
| 35 | #11718093 | C22 | 1 | 2 | yes | — |
| 36 | #11718093 | C22 | 1 | 2 | yes | — |
| 37 | #11718082 | C22 | 1 | 1 | yes | characteristic |
| 38 | #11718082 | C22 | 1 | 1 | yes | characteristic |
| 39 | #11718081 | C22 | 1 | 1 | yes | characteristic |
| 40 | #11718081 | C22 | 1 | 1 | yes | characteristic |
| 41 | C22×Q8×C13 | — | 2 | 1 | no | — |
| 42 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 43 | C2×C13×Q16 | — | 2 | 2 | no | — |
| 44 | C2×C13×Q16 | Q8 | 1 | 4 | yes | complemented |
| 45 | C2×C13×Q16 | C23 | 1 | 2 | yes | — |
| 46 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 47 | C13×#117 | — | 2 | 1 | no | — |
| 48 | Q8×Dic13 | — | 2 | 2 | no | — |
| 49 | Q8×Dic13 | — | 2 | 2 | no | — |
| 50 | Q8×Dic13 | — | 4 | 1 | no | — |
| 51 | Q8×Dic13 | — | 4 | 1 | no | — |
| 52 | #88180 | — | 2 | 1 | no | — |
| 53 | #88180 | — | 4 | 2 | no | — |
| 54 | #88180 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 56 | C2×#6099 | D4 | 1 | 1 | yes | characteristic |
| 57 | #88144 | — | 2 | 2 | no | — |
| 58 | #88142 | — | 2 | 2 | no | — |
| 59 | #88132 | — | 4 | 2 | no | — |
| 60 | #88124 | — | 4 | 1 | no | — |
| 61 | #88123 | — | 4 | 1 | no | — |
| 62 | C13×M32 | — | 2 | 2 | no | — |
| 63 | C2×C13×C16 | C23 | 1 | 2 | yes | — |
| 64 | C13×#107 | C23 | 1 | 1 | yes | characteristic |
| 65 | C13×#107 | C23 | 1 | 1 | yes | characteristic |
| 66 | C13×#106 | — | 2 | 1 | no | — |
| 67 | #88075 | — | 2 | 2 | no | — |
| 68 | #88075 | — | 2 | 2 | no | — |
| 69 | #88058 | — | 2 | 1 | no | — |
| 70 | #88058 | C23 | 1 | 2 | yes | — |
| 71 | #88058 | C23 | 1 | 1 | yes | characteristic |
| 72 | #88058 | C23 | 1 | 1 | yes | characteristic |
| 73 | #88057 | — | 2 | 1 | no | — |
| 74 | #88055 | D4 | 1 | 2 | yes | — |
| 75 | C8×Dic13 | C23 | 1 | 2 | yes | — |
| 76 | C2×#6090 | — | 2 | 2 | no | — |
| 77 | C2×#6090 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×#6090 | C23 | 1 | 1 | yes | characteristic |
| 79 | #88048 | — | 2 | 2 | no | — |
| 80 | #88047 | — | 2 | 2 | no | — |
| 81 | #33632 | — | 13 | 1 | no | maximal, Sylow |
| 82 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 83 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 84 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 85 | C2×Q8×C13 | — | 4 | 2 | no | — |
| 86 | C22×C4×C13 | — | 4 | 1 | no | — |
| 87 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C22×Dic13 | — | 4 | 1 | no | — |
| 89 | C2×Dic26 | — | 4 | 2 | no | — |
| 90 | C13×Q16 | — | 2 | 4 | no | — |
| 91 | C13×Q16 | — | 2 | 2 | no | — |
| 92 | C13×Q16 | C2×Q8 | 1 | 4 | yes | — |
| 93 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C13 | C2×Q8 | 1 | 2 | yes | — |
| 95 | C2×C8×C13 | #41 | 1 | 2 | yes | — |
| 96 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 97 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 98 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 99 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 100 | C42×C13 | — | 4 | 1 | no | — |
| 101 | C22⋊Dic13 | — | 4 | 1 | no | — |
| 102 | C22⋊Dic13 | D8 | 1 | 2 | yes | — |
| 103 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 104 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 105 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 106 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 107 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 108 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 109 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 110 | C4⋊Dic13 | D8 | 1 | 1 | yes | characteristic |
| 111 | C4⋊Dic13 | D8 | 1 | 1 | yes | characteristic |
| 112 | #6101 | — | 4 | 2 | no | — |
| 113 | #6101 | — | 4 | 2 | no | — |
| 114 | C4×Dic13 | — | 4 | 1 | no | — |
| 115 | C4×Dic13 | — | 4 | 2 | no | — |
| 116 | C4×Dic13 | — | 4 | 2 | no | — |
| 117 | C4×Dic13 | C2×D4 | 1 | 2 | yes | — |
| 118 | #6099 | — | 2 | 2 | no | — |
| 119 | C2×#1055 | C2×D4 | 1 | 2 | yes | — |
| 120 | C13×C16 | — | 2 | 2 | no | — |
| 121 | #6090 | — | 2 | 1 | no | — |
| 122 | #6090 | — | 2 | 1 | no | — |
| 123 | #3164 | — | 13 | 1 | no | — |
| 124 | #2950 | — | 13 | 1 | no | — |
| 125 | #2229 | — | 13 | 2 | no | — |
| 126 | #2229 | — | 13 | 2 | no | — |
| 127 | #2227 | — | 13 | 2 | no | — |
| 128 | #2225 | — | 13 | 2 | no | — |
| 129 | #2159 | — | 13 | 1 | no | — |
| 130 | #2158 | — | 13 | 1 | no | — |
| 131 | #2151 | — | 13 | 1 | no | — |
| 132 | #2141 | D13 | 1 | 1 | yes | characteristic |
| 133 | C2×#358 | — | 13 | 1 | no | — |
| 134 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 135 | Q8×C13 | — | 2 | 4 | no | — |
| 136 | Q8×C13 | — | 4 | 2 | no | — |
| 137 | Q8×C13 | — | 4 | 4 | no | — |
| 138 | C2×C4×C13 | — | 4 | 2 | no | — |
| 139 | C2×C4×C13 | — | 4 | 4 | no | — |
| 140 | C2×C4×C13 | — | 4 | 1 | no | — |
| 141 | C2×C4×C13 | — | 4 | 1 | no | — |
| 142 | C2×C4×C13 | C22⋊Q8 | 1 | 2 | yes | — |
| 143 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C13 | #137 | 1 | 2 | yes | — |
| 145 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×Dic13 | — | 4 | 1 | no | — |
| 147 | C2×Dic13 | — | 4 | 1 | no | — |
| 148 | C2×Dic13 | — | 4 | 2 | no | — |
| 149 | C2×Dic13 | — | 16 | 1 | no | — |
| 150 | C2×Dic13 | C2×D8 | 1 | 2 | yes | — |
| 151 | C2×Dic13 | C2×D8 | 1 | 2 | yes | — |
| 152 | Dic26 | — | 16 | 2 | no | — |
| 153 | C8×C13 | C22⋊Q8 | 1 | 2 | yes | — |
| 154 | C8×C13 | C22×Q8 | 1 | 1 | yes | characteristic |
| 155 | C8×C13 | C2×#41 | 1 | 1 | yes | characteristic |
| 156 | #1055 | — | 2 | 2 | no | — |
| 157 | C22×Q16 | C2×D13 | 1 | 1 | yes | characteristic |
| 158 | #544 | — | 26 | 1 | no | — |
| 159 | #519 | — | 26 | 1 | no | — |
| 160 | C2×M32 | C2×D13 | 1 | 1 | yes | characteristic |
| 161 | C22×C16 | — | 13 | 1 | no | — |
| 162 | #501 | — | 26 | 2 | no | — |
| 163 | #500 | — | 13 | 2 | no | — |
| 164 | #499 | — | 13 | 2 | no | — |
| 165 | #441 | — | 26 | 2 | no | — |
| 166 | C4×Q16 | — | 13 | 2 | no | — |
| 167 | C4×Q16 | — | 13 | 2 | no | — |
| 168 | #428 | — | 26 | 1 | no | — |
| 169 | #427 | — | 13 | 1 | no | — |
| 170 | #427 | C2×D13 | 1 | 1 | yes | characteristic |
| 171 | C2×#107 | — | 13 | 1 | no | — |
| 172 | #419 | — | 26 | 1 | no | — |
| 173 | #405 | — | 13 | 1 | no | — |
| 174 | #367 | — | 13 | 2 | no | — |
| 175 | #367 | — | 13 | 1 | no | — |
| 176 | #367 | — | 13 | 1 | no | — |
| 177 | #366 | — | 13 | 2 | no | — |
| 178 | #366 | — | 13 | 1 | no | — |
| 179 | #366 | — | 13 | 1 | no | — |
| 180 | C4⋊C16 | — | 13 | 2 | no | — |
| 181 | C4⋊C16 | — | 13 | 2 | no | — |
| 182 | #358 | — | 13 | 2 | no | — |
| 183 | #358 | — | 13 | 2 | no | — |
| 184 | #358 | C2×D13 | 1 | 2 | yes | — |
| 185 | #358 | C2×D13 | 1 | 2 | yes | — |
| 186 | C22×C13 | — | 2 | 1 | no | — |
| 187 | C22×C13 | — | 2 | 1 | no | — |
| 188 | C22×C13 | #474 | 1 | 2 | yes | — |
| 189 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 190 | C4×C13 | — | 4 | 4 | no | — |
| 191 | C4×C13 | — | 8 | 1 | no | — |
| 192 | C4×C13 | — | 8 | 1 | no | — |
| 193 | C4×C13 | #474 | 1 | 2 | yes | — |
| 194 | C4×C13 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 195 | C4×C13 | C2×#137 | 1 | 1 | yes | characteristic |
| 196 | Dic13 | — | 2 | 2 | no | — |
| 197 | Dic13 | — | 2 | 2 | no | — |
| 198 | Dic13 | — | 8 | 2 | no | — |
| 199 | Dic13 | — | 8 | 1 | no | — |
| 200 | Dic13 | — | 8 | 1 | no | — |
| 201 | C22×Q8 | — | 2 | 1 | no | — |
| 202 | C2×Q16 | — | 2 | 1 | no | — |
| 203 | C2×Q16 | — | 2 | 2 | no | — |
| 204 | C2×Q16 | Dic26 | 1 | 4 | yes | complemented |
| 205 | C2×Q16 | C22×D13 | 1 | 2 | yes | — |
| 206 | C2×M16 | — | 13 | 1 | no | — |
| 207 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 208 | C4⋊Q8 | — | 26 | 2 | no | — |
| 209 | C4⋊Q8 | — | 52 | 1 | no | — |
| 210 | #125 | — | 26 | 2 | no | — |
| 211 | #125 | — | 52 | 1 | no | — |
| 212 | C22⋊Q8 | — | 52 | 2 | no | — |
| 213 | C4×Q8 | — | 26 | 2 | no | — |
| 214 | C4×Q8 | — | 26 | 2 | no | — |
| 215 | C4×Q8 | — | 52 | 1 | no | — |
| 216 | C4×Q8 | — | 52 | 1 | no | — |
| 217 | #117 | — | 2 | 1 | no | — |
| 218 | #117 | — | 13 | 1 | no | — |
| 219 | #117 | — | 26 | 1 | no | — |
| 220 | #117 | — | 52 | 2 | no | — |
| 221 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 222 | M32 | — | 2 | 2 | no | — |
| 223 | C2×C16 | — | 13 | 1 | no | — |
| 224 | C2×C16 | — | 13 | 1 | no | — |
| 225 | C2×C16 | — | 26 | 2 | no | — |
| 226 | C2×C16 | C22×D13 | 1 | 2 | yes | — |
| 227 | #107 | — | 13 | 2 | no | — |
| 228 | #107 | — | 13 | 1 | no | — |
| 229 | #107 | — | 13 | 1 | no | — |
| 230 | #107 | — | 26 | 2 | no | — |
| 231 | #107 | — | 26 | 1 | no | — |
| 232 | #107 | C22×D13 | 1 | 1 | yes | characteristic |
| 233 | #107 | C22×D13 | 1 | 1 | yes | characteristic |
| 234 | #106 | — | 2 | 1 | no | — |
| 235 | #106 | — | 26 | 2 | no | — |
| 236 | #106 | — | 26 | 1 | no | — |
| 237 | #103 | — | 26 | 2 | no | — |
| 238 | #103 | — | 26 | 2 | no | — |
| 239 | #97 | — | 13 | 2 | no | — |
| 240 | C4×C8 | — | 13 | 2 | no | — |
| 241 | C2×C13 | — | 2 | 2 | no | — |
| 242 | C2×C13 | C2×#474 | 1 | 1 | yes | characteristic |
| 243 | C2×C13 | #3416 | 1 | 1 | yes | characteristic |
| 244 | C2×C13 | #3417 | 1 | 1 | yes | characteristic |
| 245 | C2×Q8 | — | 2 | 4 | no | — |
| 246 | C2×Q8 | — | 2 | 2 | no | — |
| 247 | C2×Q8 | — | 4 | 1 | no | — |
| 248 | C2×Q8 | — | 4 | 2 | no | — |
| 249 | C2×Q8 | — | 52 | 2 | no | — |
| 250 | C22×C4 | — | 4 | 1 | no | — |
| 251 | C22×C4 | — | 52 | 1 | no | — |
| 252 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 253 | Q16 | — | 2 | 4 | no | — |
| 254 | Q16 | — | 2 | 2 | no | — |
| 255 | Q16 | C2×Dic26 | 1 | 4 | yes | — |
| 256 | M16 | — | 26 | 2 | no | — |
| 257 | C2×C8 | — | 13 | 2 | no | — |
| 258 | C2×C8 | C2×Dic26 | 1 | 2 | yes | — |
| 259 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 260 | C2×C8 | #6129 | 1 | 2 | yes | — |
| 261 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 262 | C4⋊C4 | — | 2 | 1 | no | — |
| 263 | C4⋊C4 | — | 2 | 1 | no | — |
| 264 | C4⋊C4 | — | 13 | 1 | no | — |
| 265 | C4⋊C4 | — | 13 | 1 | no | — |
| 266 | C4⋊C4 | — | 26 | 1 | no | — |
| 267 | C4⋊C4 | — | 26 | 1 | no | — |
| 268 | C4⋊C4 | — | 26 | 2 | no | — |
| 269 | C4⋊C4 | — | 52 | 2 | no | — |
| 270 | C4⋊C4 | — | 52 | 2 | no | — |
| 271 | C4⋊C4 | — | 52 | 2 | no | — |
| 272 | C4⋊C4 | — | 52 | 2 | no | — |
| 273 | C4⋊C4 | — | 52 | 2 | no | — |
| 274 | C4⋊C4 | — | 52 | 1 | no | — |
| 275 | C22⋊C4 | — | 4 | 1 | no | — |
| 276 | C22⋊C4 | — | 13 | 2 | no | — |
| 277 | C22⋊C4 | — | 52 | 1 | no | — |
| 278 | C42 | — | 4 | 1 | no | — |
| 279 | C42 | — | 13 | 2 | no | — |
| 280 | C42 | — | 52 | 2 | no | — |
| 281 | C42 | — | 52 | 2 | no | — |
| 282 | C42 | — | 52 | 1 | no | — |
| 283 | C16 | — | 2 | 2 | no | — |
| 284 | C16 | — | 26 | 1 | no | — |
| 285 | C16 | — | 26 | 1 | no | — |
| 286 | C13 | #33632 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 287 | C23 | D8×D13 | 1 | 1 | yes | characteristic |
| 288 | Q8 | — | 2 | 4 | no | — |
| 289 | Q8 | — | 4 | 4 | no | — |
| 290 | Q8 | — | 4 | 2 | no | — |
| 291 | Q8 | — | 208 | 2 | no | — |
| 292 | C2×C4 | — | 4 | 4 | no | — |
| 293 | C2×C4 | — | 4 | 2 | no | — |
| 294 | C2×C4 | — | 4 | 1 | no | — |
| 295 | C2×C4 | — | 4 | 1 | no | — |
| 296 | C2×C4 | — | 13 | 2 | no | — |
| 297 | C2×C4 | — | 13 | 2 | no | — |
| 298 | C2×C4 | — | 52 | 1 | no | — |
| 299 | C2×C4 | — | 52 | 1 | no | — |
| 300 | C2×C4 | — | 52 | 2 | no | — |
| 301 | C2×C4 | — | 208 | 1 | no | — |
| 302 | C2×C4 | #88132 | 1 | 2 | yes | — |
| 303 | C2×C4 | D8×D13 | 1 | 1 | yes | characteristic |
| 304 | C2×C4 | #88169 | 1 | 2 | yes | — |
| 305 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 306 | C8 | — | 26 | 2 | no | — |
| 307 | C8 | #88132 | 1 | 2 | yes | — |
| 308 | C8 | C22×Dic26 | 1 | 1 | yes | characteristic |
| 309 | C8 | C2×#6129 | 1 | 1 | yes | characteristic |
| 310 | C22 | — | 2 | 1 | no | — |
| 311 | C22 | — | 2 | 1 | no | — |
| 312 | C22 | #11718420 | 1 | 2 | yes | — |
| 313 | C22 | C2×D8×D13 | 1 | 1 | yes | characteristic |
| 314 | C4 | — | 4 | 4 | no | — |
| 315 | C4 | — | 8 | 1 | no | — |
| 316 | C4 | — | 8 | 1 | no | — |
| 317 | C4 | — | 26 | 2 | no | — |
| 318 | C4 | — | 26 | 2 | no | — |
| 319 | C4 | — | 104 | 1 | no | — |
| 320 | C4 | — | 104 | 2 | no | — |
| 321 | C4 | — | 104 | 1 | no | — |
| 322 | C4 | #11718420 | 1 | 2 | yes | — |
| 323 | C4 | C2×#88132 | 1 | 1 | yes | characteristic |
| 324 | C4 | C2×#88169 | 1 | 1 | yes | characteristic |
| 325 | C2 | — | 2 | 2 | no | — |
| 326 | C2 | C2×#11718420 | 1 | 1 | yes | characteristic |
| 327 | C2 | #13127981 | 1 | 1 | yes | characteristic |
| 328 | C2 | #13127988 | 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