← #15756056
Subgroups — #15756056
Order 3328.
378 conjugacy classes of subgroups.
The subgroup lattice has 296 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×Q8×#1055 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13114973 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13113582 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13113265 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13112732 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13112731 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C13×#1487 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×C4×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 9 | C13×#431 | C22 | 1 | 1 | yes | characteristic |
| 10 | C13×#423 | C22 | 1 | 1 | yes | characteristic |
| 11 | Q8×#1055 | — | 2 | 1 | no | — |
| 12 | Q8×#1055 | — | 2 | 1 | no | — |
| 13 | Q8×#1055 | C4 | 1 | 2 | yes | — |
| 14 | Q8×#1055 | C4 | 1 | 2 | yes | — |
| 15 | #11718586 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11718585 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4⋊#1055 | — | 2 | 1 | no | — |
| 18 | C2×C4⋊#1055 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×#1055 | — | 2 | 1 | no | — |
| 20 | C2×C4×#1055 | C22 | 1 | 1 | yes | characteristic |
| 21 | C13×Q8⋊C8 | — | 2 | 2 | no | — |
| 22 | #11718150 | — | 2 | 1 | no | — |
| 23 | #11718150 | — | 2 | 1 | no | — |
| 24 | Q8⋊#1055 | — | 2 | 2 | no | — |
| 25 | #11718072 | — | 2 | 1 | no | — |
| 26 | #11718071 | — | 2 | 1 | no | — |
| 27 | C22×Q8×C13 | Q8 | 1 | 1 | yes | characteristic |
| 28 | C2×C13×M16 | — | 2 | 1 | no | — |
| 29 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 30 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 31 | C4×Q8×C13 | C2×C4 | 1 | 2 | yes | — |
| 32 | C4×Q8×C13 | D4 | 1 | 2 | yes | — |
| 33 | C2×C13×C4⋊C4 | — | 2 | 1 | no | — |
| 34 | C2×C13×C4⋊C4 | Q8 | 1 | 1 | yes | characteristic |
| 35 | C2×C42×C13 | — | 2 | 1 | no | — |
| 36 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 37 | C2×#6099 | — | 2 | 1 | no | — |
| 38 | C22×#1055 | — | 2 | 1 | no | — |
| 39 | C22×#1055 | D4 | 1 | 1 | yes | characteristic |
| 40 | C22×#1055 | D4 | 1 | 1 | yes | characteristic |
| 41 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 42 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 43 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 44 | C13×C22⋊C8 | — | 2 | 1 | no | — |
| 45 | C4×C8×C13 | — | 2 | 1 | no | — |
| 46 | C22⋊#1055 | — | 2 | 1 | no | — |
| 47 | C4⋊#1055 | — | 2 | 1 | no | — |
| 48 | C4⋊#1055 | — | 2 | 2 | no | — |
| 49 | C4⋊#1055 | — | 2 | 2 | no | — |
| 50 | C4⋊#1055 | — | 2 | 1 | no | — |
| 51 | C4⋊#1055 | — | 2 | 1 | no | — |
| 52 | C4⋊#1055 | — | 2 | 1 | no | — |
| 53 | C4⋊#1055 | C2×C4 | 1 | 2 | yes | — |
| 54 | C4×#1055 | — | 2 | 2 | no | — |
| 55 | C4×#1055 | — | 2 | 2 | no | — |
| 56 | C4×#1055 | — | 2 | 1 | no | — |
| 57 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C4×#1055 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4×#1055 | D4 | 1 | 1 | yes | characteristic |
| 61 | #8661 | — | 13 | 1 | no | maximal, Sylow |
| 62 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 63 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 64 | C2×Q8×C13 | C4⋊C4 | 1 | 2 | yes | — |
| 65 | C22×C4×C13 | — | 2 | 1 | no | — |
| 66 | C22×C4×C13 | — | 2 | 1 | no | — |
| 67 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 68 | C22×C4×C13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 69 | C22×C4×C13 | #41 | 1 | 1 | yes | characteristic |
| 70 | C13×M16 | — | 4 | 1 | no | — |
| 71 | C13×M16 | — | 4 | 1 | no | — |
| 72 | C2×C8×C13 | — | 4 | 1 | no | — |
| 73 | C2×C8×C13 | — | 4 | 1 | no | — |
| 74 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 75 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 76 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 77 | C13×C4⋊C4 | C4⋊C4 | 1 | 2 | yes | — |
| 78 | C42×C13 | — | 2 | 2 | no | — |
| 79 | C42×C13 | — | 2 | 2 | no | — |
| 80 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 81 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C42×C13 | #41 | 1 | 1 | yes | characteristic |
| 84 | #6099 | — | 4 | 1 | no | — |
| 85 | #6099 | — | 4 | 1 | no | — |
| 86 | C2×#1055 | — | 2 | 1 | no | — |
| 87 | C2×#1055 | — | 2 | 1 | no | — |
| 88 | C2×#1055 | — | 2 | 1 | no | — |
| 89 | C2×#1055 | — | 2 | 1 | no | — |
| 90 | C2×#1055 | — | 2 | 2 | no | — |
| 91 | C2×#1055 | — | 4 | 1 | no | — |
| 92 | C2×#1055 | — | 4 | 1 | no | — |
| 93 | C2×#1055 | — | 4 | 1 | no | — |
| 94 | C2×#1055 | — | 4 | 1 | no | — |
| 95 | C2×#1055 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×#1055 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C2×#1055 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 98 | C2×#1055 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 99 | C2×C8×Q8 | — | 13 | 1 | no | — |
| 100 | #1837 | — | 13 | 1 | no | — |
| 101 | #1564 | — | 13 | 1 | no | — |
| 102 | #1487 | — | 13 | 1 | no | — |
| 103 | #1487 | D13 | 1 | 1 | yes | characteristic |
| 104 | #1301 | — | 13 | 1 | no | — |
| 105 | #1301 | — | 13 | 1 | no | — |
| 106 | C23×C13 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 107 | Q8×C13 | — | 2 | 4 | no | — |
| 108 | Q8×C13 | — | 2 | 2 | no | — |
| 109 | Q8×C13 | #108 | 1 | 4 | yes | — |
| 110 | C2×C4×C13 | — | 2 | 4 | no | — |
| 111 | C2×C4×C13 | — | 2 | 2 | no | — |
| 112 | C2×C4×C13 | — | 2 | 2 | no | — |
| 113 | C2×C4×C13 | — | 2 | 2 | no | — |
| 114 | C2×C4×C13 | — | 4 | 1 | no | — |
| 115 | C2×C4×C13 | — | 4 | 2 | no | — |
| 116 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×C13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C13 | #117 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C13 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×C13 | #135 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C13 | #135 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C13 | #137 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C13 | #137 | 1 | 1 | yes | characteristic |
| 126 | C8×C13 | — | 8 | 1 | no | — |
| 127 | C8×C13 | — | 8 | 1 | no | — |
| 128 | #1055 | — | 2 | 1 | no | — |
| 129 | #1055 | — | 2 | 1 | no | — |
| 130 | #1055 | — | 2 | 1 | no | — |
| 131 | #1055 | — | 2 | 1 | no | — |
| 132 | #1055 | — | 4 | 2 | no | — |
| 133 | #1055 | — | 8 | 1 | no | — |
| 134 | #1055 | — | 8 | 1 | no | — |
| 135 | C2×C4×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 136 | C8×Q8 | — | 13 | 2 | no | — |
| 137 | C8×Q8 | — | 13 | 2 | no | — |
| 138 | C8×Q8 | — | 26 | 1 | no | — |
| 139 | C8×Q8 | — | 26 | 1 | no | — |
| 140 | #431 | — | 13 | 1 | no | — |
| 141 | #431 | C2×D13 | 1 | 1 | yes | characteristic |
| 142 | #423 | — | 13 | 1 | no | — |
| 143 | #423 | C2×D13 | 1 | 1 | yes | characteristic |
| 144 | C2×C4⋊C8 | — | 13 | 1 | no | — |
| 145 | C2×C4⋊C8 | — | 26 | 1 | no | — |
| 146 | C2×C4×C8 | — | 13 | 1 | no | — |
| 147 | C2×C4×C8 | — | 26 | 1 | no | — |
| 148 | #341 | — | 26 | 1 | no | — |
| 149 | #341 | — | 26 | 1 | no | — |
| 150 | #335 | — | 26 | 1 | no | — |
| 151 | #334 | — | 26 | 1 | no | — |
| 152 | Q8⋊C8 | — | 2 | 2 | no | — |
| 153 | Q8⋊C8 | — | 26 | 2 | no | — |
| 154 | C22×C13 | — | 2 | 1 | no | — |
| 155 | C22×C13 | — | 2 | 1 | no | — |
| 156 | C22×C13 | #380 | 1 | 1 | yes | characteristic |
| 157 | C22×C13 | #479 | 1 | 1 | yes | characteristic |
| 158 | C22×C13 | #479 | 1 | 1 | yes | characteristic |
| 159 | C4×C13 | — | 2 | 4 | no | — |
| 160 | C4×C13 | — | 2 | 1 | no | — |
| 161 | C4×C13 | — | 2 | 1 | no | — |
| 162 | C4×C13 | — | 2 | 1 | no | — |
| 163 | C4×C13 | — | 4 | 2 | no | — |
| 164 | C4×C13 | #416 | 1 | 1 | yes | characteristic |
| 165 | C4×C13 | #419 | 1 | 1 | yes | characteristic |
| 166 | C4×C13 | C2×#108 | 1 | 2 | yes | — |
| 167 | C4×C13 | #464 | 1 | 1 | yes | characteristic |
| 168 | C4×C13 | #464 | 1 | 1 | yes | characteristic |
| 169 | C22×Q8 | Dic26 | 1 | 1 | yes | characteristic |
| 170 | C2×M16 | — | 2 | 1 | no | — |
| 171 | C2×M16 | — | 26 | 1 | no | — |
| 172 | C22×C8 | — | 13 | 1 | no | — |
| 173 | C22×C8 | — | 13 | 1 | no | — |
| 174 | C22×C8 | — | 26 | 1 | no | — |
| 175 | C4×Q8 | — | 2 | 1 | no | — |
| 176 | C4×Q8 | — | 2 | 1 | no | — |
| 177 | C4×Q8 | C4×D13 | 1 | 2 | yes | — |
| 178 | C4×Q8 | C22⋊D13 | 1 | 2 | yes | — |
| 179 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 180 | C2×C4⋊C4 | Dic26 | 1 | 1 | yes | characteristic |
| 181 | C2×C42 | — | 2 | 1 | no | — |
| 182 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 183 | C4⋊C8 | — | 2 | 1 | no | — |
| 184 | C4⋊C8 | — | 2 | 1 | no | — |
| 185 | C4⋊C8 | — | 2 | 1 | no | — |
| 186 | C4⋊C8 | — | 13 | 2 | no | — |
| 187 | C4⋊C8 | — | 26 | 2 | no | — |
| 188 | C4⋊C8 | — | 26 | 2 | no | — |
| 189 | C4⋊C8 | — | 26 | 1 | no | — |
| 190 | C4⋊C8 | — | 26 | 1 | no | — |
| 191 | C4⋊C8 | — | 26 | 1 | no | — |
| 192 | C4⋊C8 | — | 26 | 1 | no | — |
| 193 | C22⋊C8 | — | 2 | 1 | no | — |
| 194 | C22⋊C8 | — | 26 | 1 | no | — |
| 195 | C4×C8 | — | 2 | 1 | no | — |
| 196 | C4×C8 | — | 13 | 1 | no | — |
| 197 | C4×C8 | — | 13 | 1 | no | — |
| 198 | C4×C8 | — | 13 | 1 | no | — |
| 199 | C4×C8 | — | 13 | 1 | no | — |
| 200 | C4×C8 | — | 26 | 2 | no | — |
| 201 | C4×C8 | — | 26 | 2 | no | — |
| 202 | C4×C8 | — | 26 | 1 | no | — |
| 203 | C2×C13 | — | 2 | 1 | no | — |
| 204 | C2×C13 | — | 2 | 1 | no | — |
| 205 | C2×C13 | #1805 | 1 | 1 | yes | characteristic |
| 206 | C2×C13 | #1810 | 1 | 1 | yes | characteristic |
| 207 | C2×C13 | #1814 | 1 | 1 | yes | characteristic |
| 208 | C2×Q8 | — | 2 | 4 | no | — |
| 209 | C2×Q8 | — | 2 | 1 | no | — |
| 210 | C2×Q8 | #6101 | 1 | 2 | yes | — |
| 211 | C22×C4 | — | 2 | 1 | no | — |
| 212 | C22×C4 | — | 2 | 1 | no | — |
| 213 | C22×C4 | C2×Dic26 | 1 | 1 | yes | characteristic |
| 214 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 215 | C22×C4 | #6129 | 1 | 1 | yes | characteristic |
| 216 | M16 | — | 4 | 1 | no | — |
| 217 | M16 | — | 4 | 1 | no | — |
| 218 | M16 | — | 52 | 1 | no | — |
| 219 | M16 | — | 52 | 1 | no | — |
| 220 | C2×C8 | — | 4 | 1 | no | — |
| 221 | C2×C8 | — | 4 | 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 | — | 26 | 1 | no | — |
| 227 | C2×C8 | — | 26 | 1 | no | — |
| 228 | C2×C8 | — | 26 | 1 | no | — |
| 229 | C2×C8 | — | 26 | 1 | no | — |
| 230 | C2×C8 | — | 26 | 2 | no | — |
| 231 | C2×C8 | — | 52 | 1 | no | — |
| 232 | C2×C8 | — | 52 | 1 | no | — |
| 233 | C2×C8 | — | 52 | 1 | no | — |
| 234 | C2×C8 | — | 52 | 1 | no | — |
| 235 | C4⋊C4 | — | 2 | 2 | no | — |
| 236 | C4⋊C4 | — | 2 | 1 | no | — |
| 237 | C4⋊C4 | — | 2 | 2 | no | — |
| 238 | C4⋊C4 | #6101 | 1 | 2 | yes | — |
| 239 | C42 | — | 2 | 2 | no | — |
| 240 | C42 | — | 2 | 2 | no | — |
| 241 | C42 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 242 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 243 | C42 | #6129 | 1 | 1 | yes | characteristic |
| 244 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 245 | C13 | #8661 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 246 | C23 | #88132 | 1 | 1 | yes | characteristic |
| 247 | Q8 | — | 2 | 4 | no | — |
| 248 | Q8 | — | 2 | 2 | no | — |
| 249 | Q8 | #88062 | 1 | 4 | yes | — |
| 250 | C2×C4 | — | 2 | 4 | no | — |
| 251 | C2×C4 | — | 2 | 2 | no | — |
| 252 | C2×C4 | — | 2 | 2 | no | — |
| 253 | C2×C4 | — | 2 | 2 | no | — |
| 254 | C2×C4 | — | 4 | 1 | no | — |
| 255 | C2×C4 | — | 4 | 2 | no | — |
| 256 | C2×C4 | #88131 | 1 | 1 | yes | characteristic |
| 257 | C2×C4 | #88132 | 1 | 1 | yes | characteristic |
| 258 | C2×C4 | C22⋊C4×D13 | 1 | 1 | yes | characteristic |
| 259 | C2×C4 | #88169 | 1 | 1 | yes | characteristic |
| 260 | C2×C4 | #88170 | 1 | 1 | yes | characteristic |
| 261 | C2×C4 | #88172 | 1 | 1 | yes | characteristic |
| 262 | C2×C4 | #88173 | 1 | 1 | yes | characteristic |
| 263 | C2×C4 | C2×#6101 | 1 | 1 | yes | characteristic |
| 264 | C2×C4 | #88193 | 1 | 1 | yes | characteristic |
| 265 | C2×C4 | #88193 | 1 | 1 | yes | characteristic |
| 266 | C8 | — | 8 | 1 | no | — |
| 267 | C8 | — | 8 | 1 | no | — |
| 268 | C8 | — | 26 | 1 | no | — |
| 269 | C8 | — | 26 | 1 | no | — |
| 270 | C8 | — | 26 | 1 | no | — |
| 271 | C8 | — | 26 | 1 | no | — |
| 272 | C8 | — | 52 | 2 | no | — |
| 273 | C8 | — | 104 | 1 | no | — |
| 274 | C8 | — | 104 | 1 | no | — |
| 275 | C22 | — | 2 | 1 | no | — |
| 276 | C22 | — | 2 | 1 | no | — |
| 277 | C22 | #11718457 | 1 | 1 | yes | characteristic |
| 278 | C22 | #11718460 | 1 | 1 | yes | characteristic |
| 279 | C22 | #11718603 | 1 | 1 | yes | characteristic |
| 280 | C4 | — | 2 | 1 | no | — |
| 281 | C4 | — | 2 | 1 | no | — |
| 282 | C4 | — | 2 | 4 | no | — |
| 283 | C4 | — | 2 | 1 | no | — |
| 284 | C4 | — | 4 | 2 | no | — |
| 285 | C4 | #11718463 | 1 | 1 | yes | characteristic |
| 286 | C4 | #11718465 | 1 | 1 | yes | characteristic |
| 287 | C4 | C2×#88062 | 1 | 2 | yes | — |
| 288 | C4 | #11718827 | 1 | 1 | yes | characteristic |
| 289 | C4 | #11718846 | 1 | 1 | yes | characteristic |
| 290 | C2 | — | 2 | 1 | no | — |
| 291 | C2 | — | 2 | 1 | no | — |
| 292 | C2 | #13114849 | 1 | 1 | yes | characteristic |
| 293 | C2 | #13114872 | 1 | 1 | yes | characteristic |
| 294 | C2 | #13114888 | 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