← #15873406
Subgroups — #15873406
Order 3328.
870 conjugacy classes of subgroups.
The subgroup lattice has 308 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11718587 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×#88180 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13115557 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13115019 | C2 | 1 | 4 | yes | maximal |
| 5 | #13114987 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13114952 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×C13×#423 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C22×C13×M16 | C22 | 1 | 2 | yes | — |
| 9 | C22×C42×C13 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#88180 | C4 | 1 | 2 | yes | — |
| 11 | C13×#423 | — | 2 | 4 | no | — |
| 12 | C2×C13×C4⋊C8 | C22 | 1 | 2 | yes | — |
| 13 | C2×C13×C4⋊C8 | C22 | 1 | 2 | yes | — |
| 14 | C4×C22⋊Dic13 | C4 | 1 | 2 | yes | — |
| 15 | C4×C22⋊Dic13 | C22 | 1 | 2 | yes | — |
| 16 | C2×C22⋊#1055 | C22 | 1 | 2 | yes | — |
| 17 | C2×#88054 | C22 | 1 | 8 | yes | — |
| 18 | C4×C4⋊Dic13 | C4 | 1 | 2 | yes | — |
| 19 | C4×C4⋊Dic13 | C22 | 1 | 2 | yes | — |
| 20 | #11718593 | C4 | 1 | 1 | yes | characteristic |
| 21 | #11718593 | C4 | 1 | 1 | yes | characteristic |
| 22 | C42×Dic13 | C22 | 1 | 2 | yes | — |
| 23 | #11718587 | — | 2 | 4 | no | — |
| 24 | C2×C4⋊#1055 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C4⋊#1055 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#88043 | C22 | 1 | 2 | yes | — |
| 27 | #11718142 | C22 | 1 | 8 | yes | — |
| 28 | C23×C4×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C23×C4×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C23×C4×C13 | C23 | 1 | 1 | yes | characteristic |
| 31 | C2×C13×M16 | — | 2 | 4 | no | — |
| 32 | C2×C13×M16 | — | 4 | 4 | no | — |
| 33 | C22×C8×C13 | C23 | 1 | 4 | yes | — |
| 34 | C2×C42×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×C42×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×C42×C13 | D4 | 1 | 4 | yes | — |
| 37 | C2×C42×C13 | Q8 | 1 | 4 | yes | — |
| 38 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×C22⋊Dic13 | C2×C4 | 1 | 4 | yes | — |
| 41 | #88180 | — | 2 | 8 | no | — |
| 42 | C2×C4⋊Dic13 | C2×C4 | 1 | 4 | yes | — |
| 43 | C2×C4×Dic13 | C2×C4 | 1 | 2 | yes | — |
| 44 | C2×C4×Dic13 | C2×C4 | 1 | 4 | yes | — |
| 45 | C2×C4×Dic13 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×C4×Dic13 | C23 | 1 | 4 | yes | — |
| 47 | C22×#1055 | C23 | 1 | 2 | yes | — |
| 48 | C22×#1055 | C23 | 1 | 2 | yes | — |
| 49 | C13×C4⋊C8 | — | 2 | 4 | no | — |
| 50 | C13×C4⋊C8 | — | 2 | 4 | no | — |
| 51 | #88071 | C2×C4 | 1 | 2 | yes | — |
| 52 | #88071 | C2×C4 | 1 | 2 | yes | — |
| 53 | #88071 | C2×C4 | 1 | 2 | yes | — |
| 54 | #88071 | C2×C4 | 1 | 2 | yes | — |
| 55 | C22⋊#1055 | — | 2 | 4 | no | — |
| 56 | #88054 | — | 4 | 8 | no | — |
| 57 | C4⋊#1055 | — | 2 | 2 | no | — |
| 58 | C4⋊#1055 | — | 2 | 2 | no | — |
| 59 | #88043 | — | 2 | 4 | no | — |
| 60 | #21978 | — | 13 | 1 | no | maximal, Sylow |
| 61 | C24×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 62 | C22×C4×C13 | — | 2 | 4 | no | — |
| 63 | C22×C4×C13 | — | 2 | 2 | no | — |
| 64 | C22×C4×C13 | — | 2 | 2 | no | — |
| 65 | C22×C4×C13 | — | 4 | 2 | no | — |
| 66 | C22×C4×C13 | C4⋊C4 | 1 | 4 | yes | — |
| 67 | C22×C4×C13 | C4⋊C4 | 1 | 4 | yes | — |
| 68 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 69 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 72 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 73 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 74 | C22×C4×C13 | C2×Q8 | 1 | 2 | yes | — |
| 75 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 76 | C22×Dic13 | C22×C4 | 1 | 4 | yes | — |
| 77 | C22×Dic13 | C22×C4 | 1 | 4 | yes | — |
| 78 | C13×M16 | — | 4 | 8 | no | — |
| 79 | C2×C8×C13 | — | 2 | 4 | no | — |
| 80 | C2×C8×C13 | — | 2 | 8 | no | — |
| 81 | C42×C13 | C4⋊C4 | 1 | 4 | yes | — |
| 82 | C42×C13 | C4⋊C4 | 1 | 4 | yes | — |
| 83 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 84 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 85 | C42×C13 | C2×Q8 | 1 | 2 | yes | — |
| 86 | C42×C13 | C2×Q8 | 1 | 2 | yes | — |
| 87 | C22⋊Dic13 | — | 2 | 8 | no | — |
| 88 | C4⋊Dic13 | — | 2 | 8 | no | — |
| 89 | C4×Dic13 | — | 2 | 4 | no | — |
| 90 | C4×Dic13 | — | 2 | 4 | no | — |
| 91 | C4×Dic13 | — | 2 | 4 | no | — |
| 92 | C4×Dic13 | — | 4 | 4 | no | — |
| 93 | C4×Dic13 | M16 | 1 | 8 | yes | complemented |
| 94 | C2×#1055 | — | 2 | 2 | no | — |
| 95 | C2×#1055 | — | 2 | 2 | no | — |
| 96 | C2×#1055 | — | 2 | 4 | no | — |
| 97 | C2×#1055 | — | 2 | 4 | no | — |
| 98 | C2×#432 | — | 13 | 1 | no | — |
| 99 | C2×#423 | D13 | 1 | 1 | yes | characteristic |
| 100 | C4×#117 | — | 13 | 1 | no | — |
| 101 | #1940 | — | 13 | 4 | no | — |
| 102 | #1851 | — | 13 | 4 | no | — |
| 103 | #1842 | — | 13 | 2 | no | — |
| 104 | #1831 | — | 13 | 2 | no | — |
| 105 | C23×C13 | — | 2 | 2 | no | — |
| 106 | C23×C13 | — | 2 | 2 | no | — |
| 107 | C23×C13 | — | 2 | 2 | no | — |
| 108 | C23×C13 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 109 | C23×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C13 | — | 2 | 2 | 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 | — | 2 | 2 | no | — |
| 115 | C2×C4×C13 | — | 2 | 2 | no | — |
| 116 | C2×C4×C13 | — | 2 | 4 | no | — |
| 117 | C2×C4×C13 | — | 2 | 8 | no | — |
| 118 | C2×C4×C13 | — | 4 | 4 | no | — |
| 119 | C2×C4×C13 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 120 | C2×C4×C13 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 121 | C2×C4×C13 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 122 | C2×C4×C13 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 123 | C2×C4×C13 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 124 | C2×C4×C13 | C2×M16 | 1 | 4 | yes | — |
| 125 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C13 | C22×Q8 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×C13 | H(5,𝔽2) | 1 | 2 | yes | — |
| 128 | C2×C4×C13 | 2−1+4 | 1 | 2 | yes | — |
| 129 | C2×Dic13 | — | 2 | 4 | no | — |
| 130 | C2×Dic13 | — | 2 | 4 | no | — |
| 131 | C2×Dic13 | — | 2 | 4 | no | — |
| 132 | C2×Dic13 | — | 2 | 4 | no | — |
| 133 | C2×Dic13 | — | 2 | 4 | no | — |
| 134 | C2×Dic13 | C2×M16 | 1 | 8 | yes | — |
| 135 | C8×C13 | — | 4 | 4 | no | — |
| 136 | #1055 | — | 4 | 2 | no | — |
| 137 | #1055 | — | 4 | 2 | no | — |
| 138 | C22×M16 | C2×D13 | 1 | 2 | yes | — |
| 139 | C2×#117 | — | 13 | 2 | no | — |
| 140 | C22×C42 | C2×D13 | 1 | 1 | yes | characteristic |
| 141 | #432 | — | 26 | 4 | no | — |
| 142 | #423 | — | 2 | 4 | no | — |
| 143 | C2×C4⋊C8 | — | 13 | 1 | no | — |
| 144 | C2×C4⋊C8 | — | 13 | 1 | no | — |
| 145 | C2×C4⋊C8 | — | 13 | 8 | no | — |
| 146 | C2×C4⋊C8 | C2×D13 | 1 | 2 | yes | — |
| 147 | C2×C4⋊C8 | C2×D13 | 1 | 2 | yes | — |
| 148 | C2×C22⋊C8 | — | 13 | 2 | no | — |
| 149 | C2×#97 | — | 13 | 2 | no | — |
| 150 | C4×C4⋊C4 | — | 13 | 2 | no | — |
| 151 | C4×C4⋊C4 | — | 13 | 2 | no | — |
| 152 | C4×C22⋊C4 | — | 13 | 2 | no | — |
| 153 | C4×C22⋊C4 | — | 13 | 2 | no | — |
| 154 | #376 | — | 13 | 1 | no | — |
| 155 | #376 | — | 13 | 1 | no | — |
| 156 | C43 | — | 13 | 2 | no | — |
| 157 | #336 | — | 13 | 8 | no | — |
| 158 | C22×C13 | — | 2 | 2 | no | — |
| 159 | C22×C13 | — | 2 | 2 | no | — |
| 160 | C22×C13 | — | 2 | 2 | no | — |
| 161 | C22×C13 | — | 4 | 4 | no | — |
| 162 | C22×C13 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 163 | C22×C13 | #520 | 1 | 2 | yes | — |
| 164 | C22×C13 | C22×M16 | 1 | 2 | yes | — |
| 165 | C22×C13 | #568 | 1 | 2 | yes | — |
| 166 | C4×C13 | — | 2 | 2 | no | — |
| 167 | C4×C13 | — | 2 | 2 | no | — |
| 168 | C4×C13 | — | 2 | 2 | no | — |
| 169 | C4×C13 | — | 2 | 2 | no | — |
| 170 | C4×C13 | #423 | 1 | 4 | yes | — |
| 171 | C4×C13 | #535 | 1 | 1 | yes | characteristic |
| 172 | C4×C13 | #536 | 1 | 1 | yes | characteristic |
| 173 | C4×C13 | #544 | 1 | 2 | yes | — |
| 174 | Dic13 | — | 2 | 8 | no | — |
| 175 | Dic13 | — | 4 | 4 | no | — |
| 176 | C23×C4 | C4×D13 | 1 | 1 | yes | characteristic |
| 177 | C23×C4 | C4×D13 | 1 | 1 | yes | characteristic |
| 178 | C23×C4 | C22×D13 | 1 | 1 | yes | characteristic |
| 179 | C2×M16 | — | 2 | 4 | no | — |
| 180 | C2×M16 | — | 4 | 4 | no | — |
| 181 | C22×C8 | — | 13 | 2 | no | — |
| 182 | C22×C8 | — | 13 | 2 | no | — |
| 183 | C22×C8 | C22×D13 | 1 | 4 | yes | — |
| 184 | #117 | — | 26 | 8 | no | — |
| 185 | C2×C4⋊C4 | — | 13 | 4 | no | — |
| 186 | C2×C22⋊C4 | — | 13 | 4 | no | — |
| 187 | C2×C42 | — | 13 | 2 | no | — |
| 188 | C2×C42 | — | 13 | 2 | no | — |
| 189 | C2×C42 | — | 13 | 4 | no | — |
| 190 | C2×C42 | — | 13 | 4 | no | — |
| 191 | C2×C42 | Dic26 | 1 | 4 | yes | — |
| 192 | C2×C42 | C4×D13 | 1 | 1 | yes | characteristic |
| 193 | C2×C42 | C4×D13 | 1 | 1 | yes | characteristic |
| 194 | C2×C42 | C22⋊D13 | 1 | 4 | yes | — |
| 195 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 196 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 197 | C4⋊C8 | — | 2 | 4 | no | — |
| 198 | C4⋊C8 | — | 2 | 4 | no | — |
| 199 | C4⋊C8 | — | 26 | 2 | no | — |
| 200 | C4⋊C8 | — | 26 | 2 | no | — |
| 201 | C4⋊C8 | — | 52 | 8 | no | — |
| 202 | C22⋊C8 | — | 26 | 4 | no | — |
| 203 | #97 | — | 26 | 4 | no | — |
| 204 | #95 | — | 13 | 2 | no | — |
| 205 | #95 | — | 13 | 2 | no | — |
| 206 | #95 | — | 13 | 2 | no | — |
| 207 | #95 | — | 13 | 2 | no | — |
| 208 | C2×C13 | — | 4 | 2 | no | — |
| 209 | C2×C13 | #2317 | 1 | 1 | yes | characteristic |
| 210 | C2×C13 | C2×#423 | 1 | 1 | yes | characteristic |
| 211 | C2×C13 | #2905 | 1 | 1 | yes | characteristic |
| 212 | C2×C13 | #2989 | 1 | 4 | yes | — |
| 213 | C24 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 214 | C22×C4 | — | 2 | 4 | no | — |
| 215 | C22×C4 | — | 2 | 2 | no | — |
| 216 | C22×C4 | — | 2 | 2 | no | — |
| 217 | C22×C4 | — | 4 | 2 | no | — |
| 218 | C22×C4 | — | 13 | 4 | no | — |
| 219 | C22×C4 | — | 13 | 4 | no | — |
| 220 | C22×C4 | #6101 | 1 | 4 | yes | — |
| 221 | C22×C4 | #6101 | 1 | 4 | yes | — |
| 222 | C22×C4 | C2×Dic26 | 1 | 2 | yes | — |
| 223 | C22×C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 224 | C22×C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 225 | C22×C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 226 | C22×C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 227 | C22×C4 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 228 | C22×C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 229 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 230 | M16 | — | 4 | 8 | no | — |
| 231 | C2×C8 | — | 2 | 8 | no | — |
| 232 | C2×C8 | — | 2 | 4 | no | — |
| 233 | C2×C8 | — | 26 | 4 | no | — |
| 234 | C2×C8 | — | 26 | 4 | no | — |
| 235 | C2×C8 | — | 26 | 2 | no | — |
| 236 | C2×C8 | — | 26 | 2 | no | — |
| 237 | C4⋊C4 | — | 26 | 8 | no | — |
| 238 | C22⋊C4 | — | 26 | 8 | no | — |
| 239 | C42 | — | 13 | 8 | no | — |
| 240 | C42 | — | 26 | 4 | no | — |
| 241 | C42 | — | 26 | 4 | no | — |
| 242 | C42 | — | 26 | 4 | no | — |
| 243 | C42 | — | 52 | 4 | no | — |
| 244 | C42 | #6101 | 1 | 4 | yes | — |
| 245 | C42 | #6101 | 1 | 4 | yes | — |
| 246 | C42 | C2×Dic26 | 1 | 2 | yes | — |
| 247 | C42 | C2×Dic26 | 1 | 2 | yes | — |
| 248 | C42 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 249 | C42 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 250 | C13 | #21978 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 251 | C23 | — | 2 | 2 | no | — |
| 252 | C23 | — | 2 | 2 | no | — |
| 253 | C23 | — | 2 | 2 | no | — |
| 254 | C23 | C2×#6101 | 1 | 2 | yes | — |
| 255 | C23 | C22×C4×D13 | 1 | 1 | yes | characteristic |
| 256 | C2×C4 | — | 2 | 2 | no | — |
| 257 | C2×C4 | — | 2 | 2 | no | — |
| 258 | C2×C4 | — | 2 | 2 | no | — |
| 259 | C2×C4 | — | 2 | 2 | no | — |
| 260 | C2×C4 | — | 2 | 4 | no | — |
| 261 | C2×C4 | — | 2 | 2 | no | — |
| 262 | C2×C4 | — | 2 | 2 | no | — |
| 263 | C2×C4 | — | 2 | 8 | no | — |
| 264 | C2×C4 | — | 4 | 4 | no | — |
| 265 | C2×C4 | — | 13 | 8 | no | — |
| 266 | C2×C4 | — | 26 | 4 | no | — |
| 267 | C2×C4 | — | 26 | 4 | no | — |
| 268 | C2×C4 | — | 26 | 4 | no | — |
| 269 | C2×C4 | — | 26 | 4 | no | — |
| 270 | C2×C4 | — | 26 | 4 | no | — |
| 271 | C2×C4 | M16×D13 | 1 | 4 | yes | — |
| 272 | C2×C4 | C2×#6101 | 1 | 2 | yes | — |
| 273 | C2×C4 | C2×#6101 | 1 | 2 | yes | — |
| 274 | C2×C4 | C2×#6101 | 1 | 2 | yes | — |
| 275 | C2×C4 | C2×#6101 | 1 | 2 | yes | — |
| 276 | C2×C4 | C2×#6101 | 1 | 2 | yes | — |
| 277 | C2×C4 | C22×Dic26 | 1 | 1 | yes | characteristic |
| 278 | C2×C4 | #88251 | 1 | 2 | yes | — |
| 279 | C2×C4 | #88254 | 1 | 2 | yes | — |
| 280 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 281 | C8 | — | 4 | 4 | no | — |
| 282 | C8 | — | 52 | 2 | no | — |
| 283 | C8 | — | 52 | 2 | no | — |
| 284 | C22 | — | 2 | 2 | no | — |
| 285 | C22 | — | 2 | 2 | no | — |
| 286 | C22 | — | 2 | 2 | no | — |
| 287 | C22 | — | 4 | 4 | no | — |
| 288 | C22 | #11719209 | 1 | 2 | yes | — |
| 289 | C22 | C2×M16×D13 | 1 | 2 | yes | — |
| 290 | C22 | #11719450 | 1 | 2 | yes | — |
| 291 | C22 | C22×#6101 | 1 | 1 | yes | characteristic |
| 292 | C4 | — | 2 | 2 | no | — |
| 293 | C4 | — | 2 | 2 | no | — |
| 294 | C4 | — | 2 | 2 | no | — |
| 295 | C4 | — | 2 | 2 | no | — |
| 296 | C4 | — | 26 | 8 | no | — |
| 297 | C4 | — | 52 | 4 | no | — |
| 298 | C4 | #11718779 | 1 | 4 | yes | — |
| 299 | C4 | #11719205 | 1 | 2 | yes | — |
| 300 | C4 | #11719510 | 1 | 1 | yes | characteristic |
| 301 | C4 | #11719521 | 1 | 1 | yes | characteristic |
| 302 | C2 | — | 4 | 2 | no | — |
| 303 | C2 | #13117460 | 1 | 1 | yes | characteristic |
| 304 | C2 | C2×#11718779 | 1 | 1 | yes | characteristic |
| 305 | C2 | #13123399 | 1 | 1 | yes | characteristic |
| 306 | C2 | #13123950 | 1 | 4 | yes | — |
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