← #15780354
Subgroups — #15780354
Order 3328.
458 conjugacy classes of subgroups.
The subgroup lattice has 342 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11718804 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#11718109 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#11718095 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13114900 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13112945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13112930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C13×#504 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×C13×#131 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#88205 | — | 2 | 1 | no | — |
| 10 | C22×Dic52 | C22 | 1 | 1 | yes | characteristic |
| 11 | C13×#504 | — | 2 | 2 | no | — |
| 12 | C13×#504 | — | 2 | 2 | no | — |
| 13 | C2×C13×M32 | — | 2 | 1 | no | — |
| 14 | C2×C13×M32 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C13×C16 | — | 2 | 1 | no | — |
| 16 | C22×C13×C16 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11718893 | — | 2 | 1 | no | — |
| 18 | #11718804 | — | 2 | 2 | no | — |
| 19 | #11718804 | C4 | 1 | 4 | yes | complemented |
| 20 | C2×#88064 | — | 2 | 1 | no | — |
| 21 | C2×#88059 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#88059 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#88058 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11718146 | — | 2 | 1 | no | — |
| 25 | #11718109 | — | 2 | 2 | no | — |
| 26 | #11718095 | — | 2 | 1 | no | — |
| 27 | #11718095 | — | 2 | 1 | no | — |
| 28 | C2×C13×#41 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×Dic26 | — | 2 | 1 | no | — |
| 30 | C13×#131 | — | 2 | 1 | no | — |
| 31 | C13×#131 | — | 2 | 1 | no | — |
| 32 | C13×#131 | C2×C4 | 1 | 2 | yes | — |
| 33 | C13×#131 | D4 | 1 | 2 | yes | — |
| 34 | C2×C13×M16 | — | 2 | 1 | no | — |
| 35 | C2×C13×M16 | D4 | 1 | 1 | yes | characteristic |
| 36 | C22×C8×C13 | — | 2 | 1 | no | — |
| 37 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 38 | #88205 | — | 2 | 4 | no | — |
| 39 | #88205 | — | 4 | 2 | no | — |
| 40 | C2×#6107 | — | 4 | 1 | no | — |
| 41 | C2×#6105 | — | 4 | 1 | no | — |
| 42 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 43 | C2×#6099 | — | 2 | 1 | no | — |
| 44 | C2×#6099 | — | 2 | 1 | no | — |
| 45 | C2×Dic52 | — | 2 | 1 | no | — |
| 46 | C2×Dic52 | — | 2 | 1 | no | — |
| 47 | C2×Dic52 | — | 2 | 1 | no | — |
| 48 | C2×Dic52 | — | 2 | 1 | no | — |
| 49 | C2×Dic52 | — | 2 | 1 | no | — |
| 50 | C2×Dic52 | C2×C4 | 1 | 2 | yes | — |
| 51 | C13×M32 | — | 2 | 4 | no | — |
| 52 | C13×M32 | — | 2 | 1 | no | — |
| 53 | C13×M32 | D4 | 1 | 2 | yes | — |
| 54 | C2×C13×C16 | — | 2 | 4 | no | — |
| 55 | C2×C13×C16 | — | 2 | 1 | no | — |
| 56 | C2×C13×C16 | — | 2 | 1 | no | — |
| 57 | C2×C13×C16 | — | 2 | 1 | no | — |
| 58 | C2×C13×C16 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C13×C16 | D4 | 1 | 1 | yes | characteristic |
| 60 | #88075 | — | 4 | 1 | no | — |
| 61 | #88072 | — | 4 | 1 | no | — |
| 62 | #88064 | — | 2 | 4 | no | — |
| 63 | #88059 | — | 2 | 1 | no | — |
| 64 | #88059 | — | 2 | 1 | no | — |
| 65 | #88059 | — | 2 | 1 | no | — |
| 66 | #88059 | C2×C4 | 1 | 2 | yes | — |
| 67 | #88058 | — | 2 | 1 | no | — |
| 68 | #88058 | — | 2 | 1 | no | — |
| 69 | #13072 | — | 13 | 1 | no | maximal, Sylow |
| 70 | C13×#41 | — | 2 | 1 | no | — |
| 71 | C13×#41 | — | 2 | 1 | no | — |
| 72 | C13×#41 | C22⋊C4 | 1 | 2 | yes | — |
| 73 | C13×#41 | SD16 | 1 | 2 | yes | — |
| 74 | C2×Q8×C13 | D8 | 1 | 1 | yes | characteristic |
| 75 | C2×D4×C13 | — | 2 | 1 | no | — |
| 76 | C2×D4×C13 | D8 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×C13 | — | 2 | 1 | no | — |
| 78 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | C22×Dic13 | — | 4 | 1 | no | — |
| 80 | C22×Dic13 | — | 4 | 1 | no | — |
| 81 | C2×Dic26 | — | 2 | 2 | no | — |
| 82 | C2×Dic26 | — | 4 | 1 | no | — |
| 83 | C2×Dic26 | — | 4 | 1 | no | — |
| 84 | C2×Dic26 | — | 4 | 1 | no | — |
| 85 | C2×Dic26 | — | 4 | 1 | no | — |
| 86 | C2×Dic26 | — | 4 | 1 | no | — |
| 87 | C13×M16 | — | 2 | 1 | no | — |
| 88 | C13×M16 | — | 2 | 2 | no | — |
| 89 | C13×M16 | — | 2 | 2 | no | — |
| 90 | C13×M16 | C22⋊C4 | 1 | 2 | yes | — |
| 91 | C2×C8×C13 | — | 2 | 1 | no | — |
| 92 | C2×C8×C13 | — | 2 | 2 | no | — |
| 93 | C2×C8×C13 | — | 2 | 2 | no | — |
| 94 | C2×C8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×C8×C13 | #41 | 1 | 1 | yes | characteristic |
| 99 | C2×C8×C13 | #41 | 1 | 1 | yes | characteristic |
| 100 | #6107 | — | 4 | 4 | no | — |
| 101 | #6105 | — | 4 | 4 | no | — |
| 102 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 103 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 104 | #6099 | — | 2 | 2 | no | — |
| 105 | #6099 | — | 4 | 1 | no | — |
| 106 | #6099 | — | 4 | 1 | no | — |
| 107 | #6099 | — | 4 | 1 | no | — |
| 108 | C2×#1055 | — | 4 | 1 | no | — |
| 109 | C2×#1055 | — | 4 | 1 | no | — |
| 110 | Dic52 | — | 2 | 2 | no | — |
| 111 | Dic52 | — | 2 | 2 | no | — |
| 112 | Dic52 | — | 4 | 1 | no | — |
| 113 | Dic52 | — | 4 | 1 | no | — |
| 114 | C13×C16 | — | 2 | 1 | no | — |
| 115 | C13×C16 | — | 2 | 2 | no | — |
| 116 | C13×C16 | — | 2 | 1 | no | — |
| 117 | C2×#504 | D13 | 1 | 1 | yes | characteristic |
| 118 | C2×#473 | — | 13 | 1 | no | — |
| 119 | C2×#362 | — | 13 | 1 | no | — |
| 120 | C2×#358 | — | 13 | 1 | no | — |
| 121 | #1816 | — | 13 | 1 | no | — |
| 122 | #1387 | — | 13 | 1 | no | — |
| 123 | #1381 | — | 13 | 1 | no | — |
| 124 | C23×C13 | — | 2 | 1 | no | — |
| 125 | C23×C13 | #135 | 1 | 1 | yes | characteristic |
| 126 | Q8×C13 | — | 2 | 1 | no | — |
| 127 | Q8×C13 | #102 | 1 | 2 | yes | — |
| 128 | D4×C13 | — | 2 | 2 | no | — |
| 129 | D4×C13 | — | 2 | 2 | no | — |
| 130 | D4×C13 | — | 2 | 1 | no | — |
| 131 | D4×C13 | #102 | 1 | 2 | yes | — |
| 132 | C2×C4×C13 | — | 2 | 1 | no | — |
| 133 | C2×C4×C13 | — | 2 | 2 | no | — |
| 134 | C2×C4×C13 | — | 2 | 2 | no | — |
| 135 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C13 | C2×SD16 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C13 | #135 | 1 | 1 | yes | characteristic |
| 141 | C2×Dic13 | — | 4 | 2 | no | — |
| 142 | C2×Dic13 | — | 8 | 1 | no | — |
| 143 | C2×Dic13 | — | 8 | 1 | no | — |
| 144 | C2×Dic13 | — | 8 | 1 | no | — |
| 145 | C2×Dic13 | — | 16 | 1 | no | — |
| 146 | Dic26 | — | 4 | 2 | no | — |
| 147 | Dic26 | — | 4 | 2 | no | — |
| 148 | Dic26 | — | 8 | 1 | no | — |
| 149 | Dic26 | — | 8 | 1 | no | — |
| 150 | C8×C13 | — | 2 | 2 | no | — |
| 151 | C8×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 152 | C8×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 153 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 154 | C8×C13 | #123 | 1 | 1 | yes | characteristic |
| 155 | #1055 | — | 4 | 2 | no | — |
| 156 | #1055 | — | 8 | 1 | no | — |
| 157 | C2×#137 | — | 26 | 1 | no | — |
| 158 | C22×Q16 | — | 13 | 1 | no | — |
| 159 | C2×#131 | C2×D13 | 1 | 1 | yes | characteristic |
| 160 | #504 | — | 2 | 2 | no | — |
| 161 | #504 | — | 2 | 2 | no | — |
| 162 | C2×M32 | — | 2 | 1 | no | — |
| 163 | C2×M32 | C2×D13 | 1 | 1 | yes | characteristic |
| 164 | C22×C16 | — | 2 | 1 | no | — |
| 165 | C22×C16 | C2×D13 | 1 | 1 | yes | characteristic |
| 166 | #473 | — | 13 | 4 | no | — |
| 167 | #473 | — | 26 | 2 | no | — |
| 168 | C2×#108 | — | 13 | 1 | no | — |
| 169 | C2×#108 | — | 13 | 1 | no | — |
| 170 | C2×#107 | — | 13 | 1 | no | — |
| 171 | #417 | — | 26 | 1 | no | — |
| 172 | C2×#101 | — | 26 | 1 | no | — |
| 173 | #362 | — | 26 | 2 | no | — |
| 174 | #358 | — | 26 | 1 | no | — |
| 175 | #358 | — | 26 | 1 | no | — |
| 176 | #343 | — | 26 | 1 | no | — |
| 177 | C22×C13 | — | 2 | 1 | no | — |
| 178 | C22×C13 | — | 2 | 1 | no | — |
| 179 | C22×C13 | — | 2 | 2 | no | — |
| 180 | C22×C13 | — | 4 | 1 | no | — |
| 181 | C22×C13 | — | 4 | 1 | no | — |
| 182 | C22×C13 | #416 | 1 | 1 | yes | characteristic |
| 183 | C22×C13 | #465 | 1 | 1 | yes | characteristic |
| 184 | C22×C13 | #466 | 1 | 1 | yes | characteristic |
| 185 | C4×C13 | — | 2 | 2 | no | — |
| 186 | C4×C13 | #386 | 1 | 1 | yes | characteristic |
| 187 | C4×C13 | C2×#102 | 1 | 1 | yes | characteristic |
| 188 | C4×C13 | #465 | 1 | 1 | yes | characteristic |
| 189 | C4×C13 | #466 | 1 | 1 | yes | characteristic |
| 190 | Dic13 | — | 8 | 2 | no | — |
| 191 | Dic13 | — | 16 | 1 | no | — |
| 192 | C2×#41 | D52 | 1 | 1 | yes | characteristic |
| 193 | C22×Q8 | — | 26 | 1 | no | — |
| 194 | #137 | — | 26 | 4 | no | — |
| 195 | #137 | — | 52 | 2 | no | — |
| 196 | C2×Q16 | — | 13 | 2 | no | — |
| 197 | C2×Q16 | — | 26 | 1 | no | — |
| 198 | C2×Q16 | — | 26 | 1 | no | — |
| 199 | C2×Q16 | — | 26 | 1 | no | — |
| 200 | C2×Q16 | — | 26 | 1 | no | — |
| 201 | C2×Q16 | — | 26 | 1 | no | — |
| 202 | C2×Q16 | — | 52 | 1 | no | — |
| 203 | C2×SD16 | — | 52 | 1 | no | — |
| 204 | #131 | — | 2 | 1 | no | — |
| 205 | #131 | — | 2 | 1 | no | — |
| 206 | #131 | C4×D13 | 1 | 2 | yes | — |
| 207 | #131 | C22⋊D13 | 1 | 2 | yes | — |
| 208 | C2×M16 | — | 2 | 1 | no | — |
| 209 | C2×M16 | — | 26 | 1 | no | — |
| 210 | C2×M16 | — | 26 | 1 | no | — |
| 211 | C2×M16 | D52 | 1 | 1 | yes | characteristic |
| 212 | C22×C8 | — | 2 | 1 | no | — |
| 213 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 214 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 215 | M32 | — | 2 | 4 | no | — |
| 216 | M32 | — | 2 | 1 | no | — |
| 217 | M32 | C22⋊D13 | 1 | 2 | yes | — |
| 218 | C2×C16 | — | 2 | 4 | no | — |
| 219 | C2×C16 | — | 2 | 1 | no | — |
| 220 | C2×C16 | — | 2 | 1 | no | — |
| 221 | C2×C16 | — | 2 | 1 | no | — |
| 222 | C2×C16 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 223 | C2×C16 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 224 | #108 | — | 13 | 2 | no | — |
| 225 | #108 | — | 26 | 1 | no | — |
| 226 | #108 | — | 26 | 1 | no | — |
| 227 | #108 | — | 26 | 1 | no | — |
| 228 | #107 | — | 26 | 1 | no | — |
| 229 | #107 | — | 26 | 1 | no | — |
| 230 | #103 | — | 52 | 1 | no | — |
| 231 | #102 | — | 52 | 1 | no | — |
| 232 | #101 | — | 26 | 4 | no | — |
| 233 | C2×C13 | — | 2 | 1 | no | — |
| 234 | C2×C13 | — | 2 | 1 | no | — |
| 235 | C2×C13 | — | 4 | 2 | no | — |
| 236 | C2×C13 | #1893 | 1 | 1 | yes | characteristic |
| 237 | C2×C13 | #2222 | 1 | 1 | yes | characteristic |
| 238 | C2×C13 | #2223 | 1 | 1 | yes | characteristic |
| 239 | #41 | — | 2 | 1 | no | — |
| 240 | #41 | — | 2 | 1 | no | — |
| 241 | #41 | #6095 | 1 | 2 | yes | — |
| 242 | #41 | #6103 | 1 | 2 | yes | — |
| 243 | C2×Q8 | — | 26 | 2 | no | — |
| 244 | C2×Q8 | — | 52 | 1 | no | — |
| 245 | C2×Q8 | — | 52 | 1 | no | — |
| 246 | C2×Q8 | — | 52 | 1 | no | — |
| 247 | C2×Q8 | — | 52 | 1 | no | — |
| 248 | C2×Q8 | — | 52 | 1 | no | — |
| 249 | C2×Q8 | D104 | 1 | 1 | yes | characteristic |
| 250 | C2×D4 | — | 2 | 1 | no | — |
| 251 | C2×D4 | D104 | 1 | 1 | yes | characteristic |
| 252 | C22×C4 | — | 2 | 1 | no | — |
| 253 | C22×C4 | — | 52 | 1 | no | — |
| 254 | C22×C4 | — | 52 | 1 | no | — |
| 255 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 256 | Q16 | — | 26 | 2 | no | — |
| 257 | Q16 | — | 26 | 2 | no | — |
| 258 | Q16 | — | 52 | 4 | no | — |
| 259 | Q16 | — | 52 | 1 | no | — |
| 260 | Q16 | — | 52 | 1 | no | — |
| 261 | SD16 | — | 52 | 4 | no | — |
| 262 | M16 | — | 2 | 1 | no | — |
| 263 | M16 | — | 2 | 2 | no | — |
| 264 | M16 | — | 2 | 2 | no | — |
| 265 | M16 | — | 26 | 2 | no | — |
| 266 | M16 | — | 52 | 1 | no | — |
| 267 | M16 | — | 52 | 1 | no | — |
| 268 | M16 | — | 52 | 1 | no | — |
| 269 | M16 | #6103 | 1 | 2 | yes | — |
| 270 | C2×C8 | — | 2 | 1 | no | — |
| 271 | C2×C8 | — | 2 | 2 | no | — |
| 272 | C2×C8 | — | 2 | 2 | no | — |
| 273 | C2×C8 | — | 52 | 1 | no | — |
| 274 | C2×C8 | — | 52 | 1 | no | — |
| 275 | C2×C8 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 276 | C2×C8 | #6127 | 1 | 1 | yes | characteristic |
| 277 | C2×C8 | #6127 | 1 | 1 | yes | characteristic |
| 278 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 279 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 280 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 281 | C4⋊C4 | — | 52 | 1 | no | — |
| 282 | C4⋊C4 | — | 52 | 1 | no | — |
| 283 | C16 | — | 2 | 1 | no | — |
| 284 | C16 | — | 2 | 2 | no | — |
| 285 | C16 | — | 2 | 1 | no | — |
| 286 | C13 | #13072 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 287 | C23 | — | 2 | 1 | no | — |
| 288 | C23 | #88158 | 1 | 1 | yes | characteristic |
| 289 | Q8 | — | 2 | 1 | no | — |
| 290 | Q8 | — | 52 | 2 | no | — |
| 291 | Q8 | — | 52 | 2 | no | — |
| 292 | Q8 | — | 104 | 1 | no | — |
| 293 | Q8 | — | 104 | 1 | no | — |
| 294 | Q8 | #88061 | 1 | 2 | yes | — |
| 295 | D4 | — | 2 | 2 | no | — |
| 296 | D4 | — | 2 | 2 | no | — |
| 297 | D4 | — | 2 | 1 | no | — |
| 298 | D4 | #88061 | 1 | 2 | yes | — |
| 299 | C2×C4 | — | 2 | 1 | no | — |
| 300 | C2×C4 | — | 2 | 2 | no | — |
| 301 | C2×C4 | — | 2 | 2 | no | — |
| 302 | C2×C4 | — | 52 | 2 | no | — |
| 303 | C2×C4 | — | 104 | 1 | no | — |
| 304 | C2×C4 | — | 104 | 1 | no | — |
| 305 | C2×C4 | — | 104 | 1 | no | — |
| 306 | C2×C4 | — | 208 | 1 | no | — |
| 307 | C2×C4 | C2×#6095 | 1 | 1 | yes | characteristic |
| 308 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 309 | C2×C4 | #88158 | 1 | 1 | yes | characteristic |
| 310 | C2×C4 | C2×#6103 | 1 | 1 | yes | characteristic |
| 311 | C2×C4 | #88184 | 1 | 1 | yes | characteristic |
| 312 | C2×C4 | #88184 | 1 | 1 | yes | characteristic |
| 313 | C8 | — | 2 | 2 | no | — |
| 314 | C8 | — | 52 | 2 | no | — |
| 315 | C8 | — | 104 | 1 | no | — |
| 316 | C8 | C4×C22⋊D13 | 1 | 1 | yes | characteristic |
| 317 | C8 | C4×C22⋊D13 | 1 | 1 | yes | characteristic |
| 318 | C8 | #88183 | 1 | 1 | yes | characteristic |
| 319 | C8 | #88207 | 1 | 1 | yes | characteristic |
| 320 | C22 | — | 2 | 1 | no | — |
| 321 | C22 | — | 2 | 1 | no | — |
| 322 | C22 | — | 2 | 2 | no | — |
| 323 | C22 | — | 4 | 1 | no | — |
| 324 | C22 | — | 4 | 1 | no | — |
| 325 | C22 | #11718774 | 1 | 1 | yes | characteristic |
| 326 | C22 | #11718775 | 1 | 1 | yes | characteristic |
| 327 | C22 | #11718776 | 1 | 1 | yes | characteristic |
| 328 | C4 | — | 2 | 2 | no | — |
| 329 | C4 | — | 104 | 2 | no | — |
| 330 | C4 | — | 208 | 1 | no | — |
| 331 | C4 | C2×#88061 | 1 | 1 | yes | characteristic |
| 332 | C4 | #11718775 | 1 | 1 | yes | characteristic |
| 333 | C4 | #11718776 | 1 | 1 | yes | characteristic |
| 334 | C4 | #11718874 | 1 | 1 | yes | characteristic |
| 335 | C2 | — | 2 | 1 | no | — |
| 336 | C2 | — | 2 | 1 | no | — |
| 337 | C2 | — | 4 | 2 | no | — |
| 338 | C2 | #13115264 | 1 | 1 | yes | characteristic |
| 339 | C2 | #13116961 | 1 | 1 | yes | characteristic |
| 340 | C2 | #13116966 | 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