← #16807201
Subgroups — #16807201
Order 3328.
646 conjugacy classes of subgroups.
The subgroup lattice has 284 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13131597 | C2 | 1 | 2 | yes | maximal |
| 2 | #13131233 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | Q32×#261 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13131187 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13131146 | C2 | 1 | 2 | yes | maximal |
| 6 | #13131044 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C2×D13×Q32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11719627 | — | 2 | 2 | no | — |
| 9 | C2×Q16×D13 | C22 | 1 | 2 | yes | — |
| 10 | #11719153 | — | 2 | 2 | no | — |
| 11 | #11719110 | — | 2 | 4 | no | — |
| 12 | Q16×#261 | C22 | 1 | 8 | yes | — |
| 13 | #11719092 | C22 | 1 | 2 | yes | — |
| 14 | #11719089 | C22 | 1 | 1 | yes | characteristic |
| 15 | D13⋊M32 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C13×Q32 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#88069 | C4 | 1 | 2 | yes | complemented |
| 18 | D13×Q32 | C4 | 1 | 2 | yes | complemented |
| 19 | D13×Q32 | C4 | 1 | 2 | yes | complemented |
| 20 | D13×Q32 | C22 | 1 | 2 | yes | — |
| 21 | D13×Q32 | C22 | 1 | 2 | yes | — |
| 22 | C2×Dic104 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×C16×D13 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11718280 | C22 | 1 | 8 | yes | — |
| 25 | #11718222 | C22 | 1 | 2 | yes | — |
| 26 | #11718221 | C22 | 1 | 2 | yes | — |
| 27 | #11718216 | C22 | 1 | 2 | yes | — |
| 28 | C16×#261 | C22 | 1 | 2 | yes | — |
| 29 | C2×Q8×D13 | — | 2 | 2 | no | — |
| 30 | Q8×#261 | — | 2 | 8 | no | — |
| 31 | Q8×#261 | — | 4 | 4 | no | — |
| 32 | #88237 | — | 2 | 2 | no | — |
| 33 | #88237 | — | 4 | 4 | no | — |
| 34 | #88237 | D4 | 1 | 1 | yes | characteristic |
| 35 | D13⋊M16 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×C13×Q16 | C2×C4 | 1 | 2 | yes | — |
| 37 | C2×#6107 | — | 2 | 2 | no | — |
| 38 | Q16×D13 | — | 2 | 2 | no | — |
| 39 | Q16×D13 | — | 2 | 2 | no | — |
| 40 | Q16×D13 | C2×C4 | 1 | 4 | yes | — |
| 41 | Q16×D13 | C23 | 1 | 4 | yes | — |
| 42 | C2×Dic52 | C2×C4 | 1 | 2 | yes | — |
| 43 | C2×C8×D13 | C23 | 1 | 1 | yes | characteristic |
| 44 | #88117 | — | 2 | 8 | no | — |
| 45 | #88106 | — | 2 | 1 | no | — |
| 46 | #88102 | C23 | 1 | 4 | yes | — |
| 47 | #88101 | — | 2 | 2 | no | — |
| 48 | #88100 | D4 | 1 | 2 | yes | — |
| 49 | C8×#261 | C23 | 1 | 2 | yes | — |
| 50 | #88098 | — | 2 | 1 | no | — |
| 51 | D13⋊C16 | C23 | 1 | 2 | yes | — |
| 52 | C13×Q32 | C2×C4 | 1 | 2 | yes | — |
| 53 | C13×Q32 | C2×C4 | 1 | 2 | yes | — |
| 54 | C2×C13×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | #88069 | C2×C4 | 1 | 4 | yes | — |
| 56 | #88069 | C2×C4 | 1 | 4 | yes | — |
| 57 | C2×#6090 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | Dic104 | C2×C4 | 1 | 2 | yes | — |
| 59 | Dic104 | C2×C4 | 1 | 2 | yes | — |
| 60 | C16×D13 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C16×D13 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C16×D13 | C23 | 1 | 1 | yes | characteristic |
| 63 | C16×D13 | C23 | 1 | 1 | yes | characteristic |
| 64 | #33458 | — | 13 | 1 | no | maximal, Sylow |
| 65 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 66 | Q8×D13 | — | 2 | 4 | no | — |
| 67 | Q8×D13 | — | 2 | 4 | no | — |
| 68 | Q8×D13 | — | 4 | 2 | no | — |
| 69 | Q8×D13 | — | 4 | 2 | no | — |
| 70 | C2×C4×D13 | — | 4 | 2 | no | — |
| 71 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C2×Dic26 | — | 2 | 2 | no | — |
| 73 | C2×Dic26 | — | 4 | 2 | no | — |
| 74 | C22⋊#261 | — | 4 | 2 | no | — |
| 75 | C22⋊#261 | D8 | 1 | 2 | yes | — |
| 76 | #6122 | — | 2 | 1 | no | — |
| 77 | C4⋊#261 | — | 2 | 4 | no | — |
| 78 | C4⋊#261 | — | 4 | 8 | no | — |
| 79 | C4⋊#261 | D8 | 1 | 2 | yes | — |
| 80 | C4×#261 | — | 4 | 8 | no | — |
| 81 | C4×#261 | — | 4 | 2 | no | — |
| 82 | C4×#261 | C2×D4 | 1 | 2 | yes | — |
| 83 | #6118 | — | 2 | 1 | no | — |
| 84 | D13⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 85 | C13×Q16 | — | 2 | 2 | no | — |
| 86 | C13×Q16 | C22×C4 | 1 | 4 | yes | — |
| 87 | C2×C8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 88 | #6107 | — | 2 | 4 | no | — |
| 89 | #6107 | — | 2 | 4 | no | — |
| 90 | C2×#1055 | #41 | 1 | 1 | yes | characteristic |
| 91 | Dic52 | — | 2 | 2 | no | — |
| 92 | Dic52 | C22×C4 | 1 | 4 | yes | — |
| 93 | C8×D13 | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | C8×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C8×D13 | #41 | 1 | 1 | yes | characteristic |
| 96 | C8×D13 | C24 | 1 | 1 | yes | characteristic |
| 97 | #6092 | — | 2 | 2 | no | — |
| 98 | C13×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C13×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | #6090 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | #6090 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C22×Q32 | — | 13 | 1 | no | — |
| 103 | #2950 | — | 13 | 2 | no | — |
| 104 | #2176 | — | 13 | 4 | no | — |
| 105 | C4×Q32 | — | 13 | 4 | no | — |
| 106 | #2158 | — | 13 | 1 | no | — |
| 107 | #2141 | — | 13 | 2 | no | — |
| 108 | #2108 | — | 13 | 1 | no | — |
| 109 | C22×D13 | C2×D8 | 1 | 1 | yes | characteristic |
| 110 | C2×#261 | — | 4 | 4 | no | — |
| 111 | C2×#261 | C2×D8 | 1 | 4 | yes | — |
| 112 | Q8×C13 | — | 2 | 4 | no | — |
| 113 | Q8×C13 | — | 4 | 2 | no | — |
| 114 | C2×C4×C13 | — | 4 | 2 | no | — |
| 115 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×Dic13 | — | 4 | 2 | no | — |
| 117 | C2×Dic13 | #135 | 1 | 1 | yes | characteristic |
| 118 | C4×D13 | — | 4 | 4 | no | — |
| 119 | C4×D13 | — | 4 | 4 | no | — |
| 120 | C4×D13 | C4×D4 | 1 | 1 | yes | characteristic |
| 121 | C4×D13 | C2×D8 | 1 | 1 | yes | characteristic |
| 122 | C4×D13 | #135 | 1 | 1 | yes | characteristic |
| 123 | C4×D13 | C22×D4 | 1 | 1 | yes | characteristic |
| 124 | Dic26 | — | 2 | 4 | no | — |
| 125 | Dic26 | — | 4 | 2 | no | — |
| 126 | Dic26 | — | 4 | 4 | no | — |
| 127 | Dic26 | — | 4 | 4 | no | — |
| 128 | #1057 | — | 2 | 2 | no | — |
| 129 | C8×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 130 | C8×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 131 | #1055 | C4×D4 | 1 | 1 | yes | characteristic |
| 132 | #1055 | C2×#41 | 1 | 1 | yes | characteristic |
| 133 | C22×Q16 | — | 13 | 2 | no | — |
| 134 | #519 | — | 26 | 2 | no | — |
| 135 | C2×Q32 | — | 13 | 2 | no | — |
| 136 | C2×Q32 | — | 13 | 2 | no | — |
| 137 | C2×Q32 | — | 13 | 2 | no | — |
| 138 | C2×Q32 | — | 13 | 2 | no | — |
| 139 | C2×Q32 | — | 13 | 2 | no | — |
| 140 | C2×Q32 | — | 13 | 1 | no | — |
| 141 | C2×Q32 | #261 | 1 | 1 | yes | characteristic, complemented |
| 142 | C2×M32 | — | 13 | 1 | no | — |
| 143 | C22×C16 | — | 13 | 1 | no | — |
| 144 | #441 | — | 26 | 4 | no | — |
| 145 | C4×Q16 | — | 13 | 8 | no | — |
| 146 | #427 | — | 13 | 2 | no | — |
| 147 | #419 | — | 26 | 2 | no | — |
| 148 | #405 | — | 13 | 1 | no | — |
| 149 | #367 | — | 13 | 2 | no | — |
| 150 | #366 | — | 13 | 2 | no | — |
| 151 | #358 | — | 13 | 8 | no | — |
| 152 | #346 | — | 13 | 2 | no | — |
| 153 | C4×C16 | — | 13 | 2 | no | — |
| 154 | C22×C13 | C4×D8 | 1 | 1 | yes | characteristic |
| 155 | C2×D13 | — | 2 | 2 | no | — |
| 156 | C2×D13 | C4×D8 | 1 | 1 | yes | characteristic |
| 157 | C2×D13 | C22×D8 | 1 | 1 | yes | characteristic |
| 158 | #261 | — | 2 | 4 | no | — |
| 159 | #261 | — | 8 | 4 | no | — |
| 160 | C4×C13 | — | 4 | 4 | no | — |
| 161 | C4×C13 | C4×D8 | 1 | 1 | yes | characteristic |
| 162 | C4×C13 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 163 | Dic13 | — | 4 | 4 | no | — |
| 164 | Dic13 | C4×D8 | 1 | 1 | yes | characteristic |
| 165 | Dic13 | C2×#135 | 1 | 1 | yes | characteristic |
| 166 | C22×Q8 | — | 26 | 2 | no | — |
| 167 | C2×Q16 | — | 13 | 4 | no | — |
| 168 | C2×Q16 | — | 13 | 4 | no | — |
| 169 | C2×Q16 | — | 13 | 2 | no | — |
| 170 | C2×Q16 | — | 26 | 2 | no | — |
| 171 | C2×Q16 | — | 26 | 2 | no | — |
| 172 | C2×Q16 | — | 26 | 2 | no | — |
| 173 | C2×Q16 | C2×#261 | 1 | 2 | yes | — |
| 174 | C2×M16 | — | 13 | 1 | no | — |
| 175 | C22×C8 | — | 13 | 1 | no | — |
| 176 | C4×Q8 | — | 26 | 8 | no | — |
| 177 | C4×Q8 | — | 52 | 4 | no | — |
| 178 | #117 | — | 13 | 1 | no | — |
| 179 | #117 | — | 26 | 2 | no | — |
| 180 | #117 | — | 52 | 4 | no | — |
| 181 | Q32 | — | 13 | 4 | no | — |
| 182 | Q32 | — | 13 | 4 | no | — |
| 183 | Q32 | — | 13 | 2 | no | — |
| 184 | Q32 | — | 13 | 2 | no | — |
| 185 | Q32 | C2×#261 | 1 | 2 | yes | — |
| 186 | Q32 | C2×#261 | 1 | 2 | yes | — |
| 187 | M32 | — | 26 | 1 | no | — |
| 188 | M32 | — | 26 | 1 | no | — |
| 189 | C2×C16 | — | 13 | 1 | no | — |
| 190 | C2×C16 | — | 13 | 1 | no | — |
| 191 | C2×C16 | — | 13 | 1 | no | — |
| 192 | C2×C16 | — | 13 | 1 | no | — |
| 193 | C2×C16 | — | 13 | 1 | no | — |
| 194 | C2×C16 | — | 13 | 2 | no | — |
| 195 | C2×C16 | C2×#261 | 1 | 1 | yes | characteristic |
| 196 | #107 | — | 13 | 4 | no | — |
| 197 | #106 | — | 26 | 2 | no | — |
| 198 | #103 | — | 26 | 8 | no | — |
| 199 | #97 | — | 13 | 2 | no | — |
| 200 | C4×C8 | — | 13 | 2 | no | — |
| 201 | C2×C13 | — | 2 | 1 | no | — |
| 202 | C2×C13 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 203 | D13 | — | 2 | 1 | no | — |
| 204 | D13 | #3417 | 1 | 2 | yes | — |
| 205 | C2×Q8 | — | 2 | 2 | no | — |
| 206 | C2×Q8 | — | 26 | 4 | no | — |
| 207 | C2×Q8 | — | 26 | 4 | no | — |
| 208 | C2×Q8 | — | 26 | 2 | no | — |
| 209 | C2×Q8 | — | 52 | 2 | no | — |
| 210 | C2×Q8 | — | 52 | 2 | no | — |
| 211 | C2×Q8 | — | 52 | 2 | no | — |
| 212 | C22×C4 | — | 13 | 1 | no | — |
| 213 | C22×C4 | — | 52 | 2 | no | — |
| 214 | Q16 | — | 2 | 2 | no | — |
| 215 | Q16 | — | 13 | 4 | no | — |
| 216 | Q16 | — | 26 | 4 | no | — |
| 217 | Q16 | — | 26 | 4 | no | — |
| 218 | Q16 | — | 26 | 2 | no | — |
| 219 | Q16 | C22×#261 | 1 | 4 | yes | — |
| 220 | M16 | — | 26 | 1 | no | — |
| 221 | M16 | — | 26 | 1 | no | — |
| 222 | C2×C8 | — | 13 | 1 | no | — |
| 223 | C2×C8 | — | 13 | 1 | no | — |
| 224 | C2×C8 | — | 13 | 1 | no | — |
| 225 | C2×C8 | — | 13 | 1 | no | — |
| 226 | C2×C8 | — | 13 | 1 | no | — |
| 227 | C2×C8 | — | 13 | 2 | no | — |
| 228 | C2×C8 | C22×#261 | 1 | 1 | yes | characteristic |
| 229 | C4⋊C4 | — | 13 | 2 | no | — |
| 230 | C4⋊C4 | — | 26 | 4 | no | — |
| 231 | C4⋊C4 | — | 52 | 8 | no | — |
| 232 | C22⋊C4 | — | 13 | 2 | no | — |
| 233 | C22⋊C4 | — | 52 | 2 | no | — |
| 234 | C42 | — | 13 | 2 | no | — |
| 235 | C42 | — | 52 | 2 | no | — |
| 236 | C42 | — | 52 | 8 | no | — |
| 237 | C16 | — | 13 | 1 | no | — |
| 238 | C16 | — | 13 | 1 | no | — |
| 239 | C16 | — | 26 | 2 | no | — |
| 240 | C16 | C22×#261 | 1 | 1 | yes | characteristic |
| 241 | C16 | C22×#261 | 1 | 1 | yes | characteristic |
| 242 | C13 | #33458 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 243 | C23 | — | 13 | 1 | no | — |
| 244 | Q8 | — | 2 | 4 | no | — |
| 245 | Q8 | — | 4 | 2 | no | — |
| 246 | Q8 | — | 26 | 4 | no | — |
| 247 | Q8 | — | 52 | 4 | no | — |
| 248 | Q8 | — | 52 | 4 | no | — |
| 249 | Q8 | — | 52 | 2 | no | — |
| 250 | C2×C4 | — | 4 | 2 | no | — |
| 251 | C2×C4 | — | 13 | 1 | no | — |
| 252 | C2×C4 | — | 13 | 1 | no | — |
| 253 | C2×C4 | — | 13 | 1 | no | — |
| 254 | C2×C4 | — | 13 | 1 | no | — |
| 255 | C2×C4 | — | 13 | 1 | no | — |
| 256 | C2×C4 | — | 13 | 4 | no | — |
| 257 | C2×C4 | — | 52 | 4 | no | — |
| 258 | C2×C4 | — | 52 | 4 | no | — |
| 259 | C2×C4 | — | 52 | 2 | no | — |
| 260 | C2×C4 | — | 52 | 4 | no | — |
| 261 | C2×C4 | D4×#261 | 1 | 1 | yes | characteristic |
| 262 | C8 | — | 13 | 1 | no | — |
| 263 | C8 | — | 13 | 1 | no | — |
| 264 | C8 | — | 26 | 2 | no | — |
| 265 | C8 | D4×#261 | 1 | 1 | yes | characteristic |
| 266 | C8 | C23×#261 | 1 | 1 | yes | characteristic |
| 267 | C22 | — | 13 | 1 | no | — |
| 268 | C22 | — | 13 | 1 | no | — |
| 269 | C22 | — | 26 | 2 | no | — |
| 270 | C22 | D8×#261 | 1 | 1 | yes | characteristic |
| 271 | C4 | — | 4 | 4 | no | — |
| 272 | C4 | — | 13 | 1 | no | — |
| 273 | C4 | — | 13 | 1 | no | — |
| 274 | C4 | — | 26 | 4 | no | — |
| 275 | C4 | — | 52 | 4 | no | — |
| 276 | C4 | — | 104 | 4 | no | — |
| 277 | C4 | D8×#261 | 1 | 1 | yes | characteristic |
| 278 | C4 | C2×D4×#261 | 1 | 1 | yes | characteristic |
| 279 | C2 | — | 2 | 1 | no | — |
| 280 | C2 | — | 13 | 2 | no | — |
| 281 | C2 | — | 26 | 1 | no | — |
| 282 | C2 | C2×D8×#261 | 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