← #16018271
Subgroups — #16018271
Order 3328.
682 conjugacy classes of subgroups.
The subgroup lattice has 248 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13125350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13117077 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #13117059 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13116552 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C4×#88052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×C13×#493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C22×C13×D8 | — | 2 | 1 | no | — |
| 8 | C22×C13×D8 | C22 | 1 | 2 | yes | — |
| 9 | C2×C13×#127 | — | 2 | 1 | no | — |
| 10 | #11719175 | — | 2 | 1 | no | — |
| 11 | C13×#493 | — | 2 | 1 | no | — |
| 12 | C13×#493 | — | 2 | 1 | no | — |
| 13 | C13×#493 | C22 | 1 | 2 | yes | — |
| 14 | C13×#493 | C22 | 1 | 2 | yes | — |
| 15 | C2×C4×C8×C13 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11718767 | — | 2 | 1 | no | — |
| 17 | #11718767 | C22 | 1 | 2 | yes | — |
| 18 | C2×#88052 | C22 | 1 | 2 | yes | — |
| 19 | #11718344 | — | 2 | 1 | no | — |
| 20 | #11718344 | C22 | 1 | 2 | yes | complemented |
| 21 | #11718343 | C22 | 1 | 2 | yes | complemented |
| 22 | #11718341 | — | 2 | 1 | no | — |
| 23 | #11718154 | C22 | 1 | 16 | yes | complemented |
| 24 | #11718053 | C22 | 1 | 2 | yes | complemented |
| 25 | C4×#6090 | C22 | 1 | 2 | yes | complemented |
| 26 | C22×D4×C13 | — | 2 | 2 | no | — |
| 27 | C22×D4×C13 | — | 4 | 2 | no | — |
| 28 | C2×C13×D8 | — | 2 | 2 | no | — |
| 29 | C2×C13×D8 | — | 2 | 2 | no | — |
| 30 | C2×C13×D8 | — | 2 | 2 | no | — |
| 31 | C2×C13×D8 | — | 2 | 8 | no | — |
| 32 | C2×C13×D8 | — | 4 | 4 | no | — |
| 33 | C2×C13×D8 | C23 | 1 | 4 | yes | — |
| 34 | C22×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 35 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 36 | C13×#127 | — | 2 | 2 | no | — |
| 37 | C13×#127 | — | 2 | 2 | no | — |
| 38 | C13×#127 | — | 4 | 2 | no | — |
| 39 | C2×C42×C13 | D4 | 1 | 1 | yes | characteristic |
| 40 | #88180 | — | 2 | 2 | no | — |
| 41 | #88178 | — | 4 | 2 | no | — |
| 42 | #88124 | — | 2 | 2 | no | — |
| 43 | #88123 | — | 2 | 2 | no | — |
| 44 | C4×Dic26 | — | 4 | 2 | no | — |
| 45 | C4×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 46 | C4×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 47 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 48 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 49 | #88058 | — | 2 | 2 | no | — |
| 50 | #88058 | C23 | 1 | 4 | yes | — |
| 51 | #88057 | — | 2 | 2 | no | — |
| 52 | #88057 | — | 2 | 2 | no | — |
| 53 | #88052 | — | 2 | 4 | no | — |
| 54 | C2×#6090 | C23 | 1 | 4 | yes | — |
| 55 | #33704 | — | 13 | 1 | no | maximal, Sylow |
| 56 | C24×C13 | — | 4 | 2 | no | — |
| 57 | C2×D4×C13 | — | 2 | 4 | no | — |
| 58 | C2×D4×C13 | — | 4 | 4 | no | — |
| 59 | C2×D4×C13 | — | 4 | 4 | no | — |
| 60 | C2×D4×C13 | — | 4 | 4 | no | — |
| 61 | C2×D4×C13 | — | 4 | 2 | no | — |
| 62 | C2×D4×C13 | — | 4 | 4 | no | — |
| 63 | C2×D4×C13 | — | 8 | 8 | no | — |
| 64 | C22×C4×C13 | D8 | 1 | 2 | yes | — |
| 65 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 66 | C2×Dic26 | — | 4 | 2 | no | — |
| 67 | C13×D8 | — | 2 | 8 | no | — |
| 68 | C13×D8 | — | 4 | 4 | no | — |
| 69 | C13×D8 | — | 4 | 4 | no | — |
| 70 | C13×D8 | — | 4 | 4 | no | — |
| 71 | C2×C8×C13 | SD16 | 1 | 4 | yes | — |
| 72 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C2×C8×C13 | #41 | 1 | 4 | yes | — |
| 76 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 77 | C42×C13 | D8 | 1 | 2 | yes | — |
| 78 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C22⋊Dic13 | — | 4 | 2 | no | — |
| 81 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 82 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 83 | #6101 | — | 4 | 4 | no | — |
| 84 | C4×Dic13 | — | 4 | 2 | no | — |
| 85 | #6090 | — | 2 | 4 | no | — |
| 86 | #3160 | — | 13 | 1 | no | — |
| 87 | C2×#493 | D13 | 1 | 1 | yes | characteristic |
| 88 | #2244 | — | 13 | 4 | no | — |
| 89 | #2240 | — | 13 | 4 | no | — |
| 90 | #2140 | — | 13 | 4 | no | — |
| 91 | C4×M32 | — | 13 | 1 | no | — |
| 92 | C23×C13 | — | 4 | 4 | no | — |
| 93 | C23×C13 | — | 8 | 8 | no | — |
| 94 | C23×C13 | — | 8 | 4 | no | — |
| 95 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 96 | D4×C13 | — | 4 | 4 | no | — |
| 97 | D4×C13 | — | 4 | 4 | no | — |
| 98 | D4×C13 | — | 8 | 8 | no | — |
| 99 | D4×C13 | — | 8 | 4 | no | — |
| 100 | D4×C13 | — | 8 | 8 | no | — |
| 101 | C2×C4×C13 | — | 2 | 4 | no | — |
| 102 | C2×C4×C13 | #124 | 1 | 2 | yes | — |
| 103 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 104 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 106 | C2×C4×C13 | C2×SD16 | 1 | 2 | yes | — |
| 107 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×Dic13 | — | 4 | 4 | no | — |
| 109 | Dic26 | — | 8 | 4 | no | — |
| 110 | C8×C13 | #124 | 1 | 2 | yes | — |
| 111 | C8×C13 | C2×SD16 | 1 | 2 | yes | — |
| 112 | C8×C13 | C2×SD16 | 1 | 2 | yes | — |
| 113 | C8×C13 | C2×#41 | 1 | 2 | yes | — |
| 114 | C22×D8 | — | 2 | 1 | no | — |
| 115 | C22×D8 | C2×D13 | 1 | 2 | yes | — |
| 116 | #533 | — | 26 | 1 | no | — |
| 117 | C2×#127 | — | 2 | 1 | no | — |
| 118 | C2×M32 | — | 13 | 2 | no | — |
| 119 | #500 | — | 13 | 2 | no | — |
| 120 | #499 | — | 13 | 2 | no | — |
| 121 | #499 | — | 26 | 1 | no | — |
| 122 | #498 | — | 26 | 1 | no | — |
| 123 | #493 | — | 2 | 1 | no | — |
| 124 | #493 | — | 2 | 1 | no | — |
| 125 | #493 | C2×D13 | 1 | 2 | yes | — |
| 126 | #493 | C2×D13 | 1 | 2 | yes | — |
| 127 | #427 | — | 13 | 2 | no | — |
| 128 | #427 | — | 26 | 1 | no | — |
| 129 | C2×C4×C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 130 | #357 | — | 13 | 16 | no | — |
| 131 | #346 | — | 13 | 2 | no | — |
| 132 | C4×C16 | — | 13 | 2 | no | — |
| 133 | C22×C13 | — | 2 | 2 | no | — |
| 134 | C22×C13 | — | 8 | 4 | no | — |
| 135 | C22×C13 | — | 8 | 8 | no | — |
| 136 | C22×C13 | — | 16 | 8 | no | — |
| 137 | C22×C13 | #486 | 1 | 2 | yes | — |
| 138 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 139 | C4×C13 | — | 2 | 2 | no | — |
| 140 | C4×C13 | #486 | 1 | 2 | yes | — |
| 141 | C4×C13 | #509 | 1 | 4 | yes | — |
| 142 | C4×C13 | C2×#124 | 1 | 1 | yes | characteristic |
| 143 | C4×C13 | C22×SD16 | 1 | 1 | yes | characteristic |
| 144 | Dic13 | — | 8 | 4 | no | — |
| 145 | C22×D4 | — | 2 | 2 | no | — |
| 146 | C22×D4 | — | 4 | 2 | no | — |
| 147 | C2×D8 | — | 2 | 8 | no | — |
| 148 | C2×D8 | — | 2 | 2 | no | — |
| 149 | C2×D8 | — | 2 | 2 | no | — |
| 150 | C2×D8 | — | 2 | 2 | no | — |
| 151 | C2×D8 | — | 4 | 4 | no | — |
| 152 | C2×D8 | C22×D13 | 1 | 4 | yes | — |
| 153 | C22×C8 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 154 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 155 | C4⋊Q8 | — | 26 | 2 | no | — |
| 156 | #127 | — | 2 | 2 | no | — |
| 157 | #127 | — | 2 | 2 | no | — |
| 158 | #127 | — | 4 | 2 | no | — |
| 159 | #125 | — | 26 | 2 | no | — |
| 160 | C22⋊Q8 | — | 52 | 2 | no | — |
| 161 | C4×Q8 | — | 52 | 2 | no | — |
| 162 | #117 | — | 26 | 2 | no | — |
| 163 | C2×C42 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 164 | M32 | — | 26 | 4 | no | — |
| 165 | C2×C16 | — | 13 | 4 | no | — |
| 166 | #107 | — | 13 | 4 | no | — |
| 167 | #107 | — | 26 | 2 | no | — |
| 168 | #106 | — | 26 | 2 | no | — |
| 169 | #106 | — | 26 | 2 | no | — |
| 170 | C4×C8 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 171 | C4×C8 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 172 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 173 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 174 | C2×C13 | — | 2 | 2 | no | — |
| 175 | C2×C13 | — | 16 | 4 | no | — |
| 176 | C2×C13 | C2×#486 | 1 | 1 | yes | characteristic |
| 177 | C2×C13 | C2×#509 | 1 | 2 | yes | — |
| 178 | C24 | — | 4 | 2 | no | — |
| 179 | C2×Q8 | — | 52 | 2 | no | — |
| 180 | C2×D4 | — | 2 | 4 | no | — |
| 181 | C2×D4 | — | 4 | 4 | no | — |
| 182 | C2×D4 | — | 4 | 4 | no | — |
| 183 | C2×D4 | — | 4 | 2 | no | — |
| 184 | C2×D4 | — | 4 | 4 | no | — |
| 185 | C2×D4 | — | 4 | 4 | no | — |
| 186 | C2×D4 | — | 8 | 8 | no | — |
| 187 | C22×C4 | #6104 | 1 | 2 | yes | — |
| 188 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 189 | D8 | — | 2 | 8 | no | — |
| 190 | D8 | — | 4 | 4 | no | — |
| 191 | D8 | — | 4 | 4 | no | — |
| 192 | D8 | — | 4 | 4 | no | — |
| 193 | C2×C8 | #6105 | 1 | 4 | yes | — |
| 194 | C2×C8 | #6129 | 1 | 4 | yes | — |
| 195 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 196 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 197 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 198 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 199 | C4⋊C4 | — | 26 | 4 | no | — |
| 200 | C4⋊C4 | — | 52 | 4 | no | — |
| 201 | C4⋊C4 | — | 52 | 2 | no | — |
| 202 | C22⋊C4 | — | 52 | 2 | no | — |
| 203 | C42 | — | 52 | 2 | no | — |
| 204 | C42 | #6104 | 1 | 2 | yes | — |
| 205 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 206 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 207 | C16 | — | 26 | 4 | no | — |
| 208 | C13 | #33704 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 209 | C23 | — | 4 | 4 | no | — |
| 210 | C23 | — | 8 | 8 | no | — |
| 211 | C23 | — | 8 | 4 | no | — |
| 212 | C23 | C2×#6104 | 1 | 1 | yes | characteristic |
| 213 | Q8 | — | 104 | 4 | no | — |
| 214 | D4 | — | 4 | 4 | no | — |
| 215 | D4 | — | 4 | 4 | no | — |
| 216 | D4 | — | 8 | 8 | no | — |
| 217 | D4 | — | 8 | 4 | no | — |
| 218 | D4 | — | 8 | 8 | no | — |
| 219 | C2×C4 | — | 2 | 4 | no | — |
| 220 | C2×C4 | — | 52 | 4 | no | — |
| 221 | C2×C4 | C2×#6104 | 1 | 2 | yes | — |
| 222 | C2×C4 | C2×#6104 | 1 | 1 | yes | characteristic |
| 223 | C2×C4 | C2×#6104 | 1 | 2 | yes | — |
| 224 | C2×C4 | C2×#6105 | 1 | 2 | yes | — |
| 225 | C2×C4 | #88190 | 1 | 2 | yes | — |
| 226 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 227 | C8 | C2×#6105 | 1 | 2 | yes | — |
| 228 | C8 | C2×#6105 | 1 | 2 | yes | — |
| 229 | C8 | #88190 | 1 | 2 | yes | — |
| 230 | C8 | C2×#6129 | 1 | 2 | yes | — |
| 231 | C22 | — | 2 | 2 | no | — |
| 232 | C22 | — | 8 | 4 | no | — |
| 233 | C22 | — | 8 | 8 | no | — |
| 234 | C22 | — | 16 | 8 | no | — |
| 235 | C22 | #11718731 | 1 | 2 | yes | — |
| 236 | C22 | C22×#6104 | 1 | 1 | yes | characteristic |
| 237 | C4 | — | 2 | 2 | no | — |
| 238 | C4 | — | 104 | 4 | no | — |
| 239 | C4 | #11718731 | 1 | 2 | yes | — |
| 240 | C4 | #11718808 | 1 | 4 | yes | — |
| 241 | C4 | C22×#6105 | 1 | 1 | yes | characteristic |
| 242 | C4 | C2×#88190 | 1 | 1 | yes | characteristic |
| 243 | C2 | — | 2 | 2 | no | — |
| 244 | C2 | — | 16 | 4 | no | — |
| 245 | C2 | C2×#11718731 | 1 | 1 | yes | characteristic |
| 246 | C2 | C2×#11718808 | 1 | 2 | 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