← #16018325
Subgroups — #16018325
Order 3328.
834 conjugacy classes of subgroups.
The subgroup lattice has 234 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11718565 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #13125264 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13117097 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13117092 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13117089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13117086 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C4×C13×C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#88158 | — | 2 | 2 | no | — |
| 9 | C2×#88158 | C22 | 1 | 4 | yes | — |
| 10 | #11719182 | — | 2 | 2 | no | — |
| 11 | C22×C13×C16 | C22 | 1 | 2 | yes | — |
| 12 | C2×C4×C8×C13 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×Dic104 | C22 | 1 | 4 | yes | — |
| 14 | #11718565 | — | 2 | 16 | no | — |
| 15 | C2×#88040 | C22 | 1 | 8 | yes | — |
| 16 | C2×D208 | C22 | 1 | 4 | yes | — |
| 17 | #11718360 | C22 | 1 | 2 | yes | — |
| 18 | #11718357 | — | 2 | 2 | no | — |
| 19 | #11718357 | C22 | 1 | 4 | yes | — |
| 20 | #11718356 | C22 | 1 | 2 | yes | — |
| 21 | #11718354 | — | 2 | 2 | no | — |
| 22 | C4×C13×C16 | C22 | 1 | 1 | yes | characteristic |
| 23 | C4×C13×C16 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×C13×C16 | C22 | 1 | 2 | yes | — |
| 25 | C2×#6127 | — | 2 | 4 | no | — |
| 26 | C22×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 27 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 28 | C2×C42×C13 | D4 | 1 | 1 | yes | characteristic |
| 29 | #88184 | — | 4 | 4 | no | — |
| 30 | C2×Dic52 | — | 2 | 2 | no | — |
| 31 | C2×Dic52 | C23 | 1 | 4 | yes | — |
| 32 | #88158 | — | 2 | 16 | no | — |
| 33 | #88158 | — | 4 | 8 | no | — |
| 34 | C2×D104 | — | 2 | 2 | no | — |
| 35 | C2×D104 | C23 | 1 | 4 | yes | — |
| 36 | C2×#6095 | — | 2 | 4 | no | — |
| 37 | C2×#6095 | — | 2 | 4 | no | — |
| 38 | #88129 | — | 2 | 4 | no | — |
| 39 | #88128 | — | 2 | 2 | no | — |
| 40 | C4×D52 | — | 4 | 4 | no | — |
| 41 | #88123 | — | 2 | 2 | no | — |
| 42 | C2×C13×C16 | D4 | 1 | 8 | yes | complemented |
| 43 | C2×C13×C16 | C23 | 1 | 2 | yes | — |
| 44 | C2×C13×C16 | C23 | 1 | 2 | yes | — |
| 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 | Dic104 | — | 2 | 8 | no | — |
| 50 | #88040 | — | 2 | 16 | no | — |
| 51 | D208 | — | 2 | 8 | no | — |
| 52 | #33713 | — | 13 | 1 | no | maximal, Sylow |
| 53 | C22×C4×C13 | D8 | 1 | 2 | yes | — |
| 54 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 55 | C2×C22⋊D13 | — | 4 | 4 | no | — |
| 56 | #6127 | — | 4 | 8 | no | — |
| 57 | #6127 | — | 4 | 8 | no | — |
| 58 | C2×D52 | — | 2 | 4 | no | — |
| 59 | C2×D52 | — | 4 | 4 | no | — |
| 60 | C2×C4×D13 | — | 4 | 4 | no | — |
| 61 | C2×Dic26 | — | 2 | 4 | no | — |
| 62 | C2×C8×C13 | D8 | 1 | 4 | yes | — |
| 63 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 64 | C2×C8×C13 | C2×D4 | 1 | 4 | yes | — |
| 65 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 67 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 68 | C42×C13 | D8 | 1 | 2 | yes | — |
| 69 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | #6103 | — | 4 | 8 | no | — |
| 72 | C4⋊Dic13 | — | 4 | 4 | no | — |
| 73 | Dic52 | — | 2 | 8 | no | — |
| 74 | Dic52 | — | 4 | 4 | no | — |
| 75 | D104 | — | 2 | 8 | no | — |
| 76 | D104 | — | 4 | 4 | no | — |
| 77 | #6095 | — | 4 | 8 | no | — |
| 78 | #6095 | — | 4 | 8 | no | — |
| 79 | C13×C16 | C2×D4 | 1 | 4 | yes | — |
| 80 | C13×C16 | C2×D4 | 1 | 4 | yes | — |
| 81 | C2×#508 | — | 13 | 4 | no | — |
| 82 | #3147 | — | 13 | 2 | no | — |
| 83 | #2249 | — | 13 | 4 | no | — |
| 84 | #2248 | — | 13 | 2 | no | — |
| 85 | #2247 | — | 13 | 1 | no | — |
| 86 | #2246 | — | 13 | 1 | no | — |
| 87 | C2×C4×C16 | D13 | 1 | 1 | yes | characteristic, complemented |
| 88 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 89 | C22×D13 | — | 4 | 4 | no | — |
| 90 | C2×C4×C13 | — | 2 | 4 | no | — |
| 91 | C2×C4×C13 | #127 | 1 | 2 | yes | — |
| 92 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 93 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 94 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 96 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 97 | C22⋊D13 | — | 8 | 8 | no | — |
| 98 | C2×Dic13 | — | 4 | 4 | no | — |
| 99 | D52 | — | 4 | 4 | no | — |
| 100 | D52 | — | 4 | 4 | no | — |
| 101 | D52 | — | 8 | 8 | no | — |
| 102 | C4×D13 | — | 8 | 8 | no | — |
| 103 | Dic26 | — | 4 | 4 | no | — |
| 104 | Dic26 | — | 4 | 4 | no | — |
| 105 | C8×C13 | #127 | 1 | 2 | yes | — |
| 106 | C8×C13 | C2×D8 | 1 | 2 | yes | — |
| 107 | C8×C13 | C2×D8 | 1 | 2 | yes | — |
| 108 | C8×C13 | C22×D4 | 1 | 2 | yes | — |
| 109 | C2×#135 | — | 13 | 4 | no | — |
| 110 | C2×#135 | — | 26 | 2 | no | — |
| 111 | #532 | — | 26 | 2 | no | — |
| 112 | #508 | — | 26 | 16 | no | — |
| 113 | C2×Q32 | — | 13 | 4 | no | — |
| 114 | C2×SD32 | — | 13 | 8 | no | — |
| 115 | C2×D16 | — | 13 | 4 | no | — |
| 116 | C22×C16 | C2×D13 | 1 | 2 | yes | — |
| 117 | #495 | — | 13 | 4 | no | — |
| 118 | #495 | — | 26 | 2 | no | — |
| 119 | #494 | — | 13 | 2 | no | — |
| 120 | #493 | — | 13 | 2 | no | — |
| 121 | #492 | — | 26 | 2 | no | — |
| 122 | C2×C4×C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 123 | C4×C16 | C2×D13 | 1 | 1 | yes | characteristic |
| 124 | C4×C16 | C2×D13 | 1 | 1 | yes | characteristic |
| 125 | C4×C16 | C2×D13 | 1 | 2 | yes | — |
| 126 | C22×C13 | — | 2 | 2 | no | — |
| 127 | C22×C13 | #493 | 1 | 2 | yes | — |
| 128 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 129 | C2×D13 | — | 8 | 4 | no | — |
| 130 | C2×D13 | — | 8 | 8 | no | — |
| 131 | C4×C13 | — | 2 | 2 | no | — |
| 132 | C4×C13 | #493 | 1 | 2 | yes | — |
| 133 | C4×C13 | #508 | 1 | 4 | yes | complemented |
| 134 | C4×C13 | C2×#127 | 1 | 1 | yes | characteristic |
| 135 | C4×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 136 | Dic13 | — | 8 | 4 | no | — |
| 137 | C2×#41 | — | 26 | 4 | no | — |
| 138 | #135 | — | 26 | 16 | no | — |
| 139 | #135 | — | 52 | 8 | no | — |
| 140 | C2×Q16 | — | 13 | 4 | no | — |
| 141 | C2×Q16 | — | 26 | 2 | no | — |
| 142 | C2×SD16 | — | 26 | 4 | no | — |
| 143 | C2×SD16 | — | 26 | 4 | no | — |
| 144 | C2×D8 | — | 13 | 4 | no | — |
| 145 | C2×D8 | — | 26 | 2 | no | — |
| 146 | C22×C8 | D52 | 1 | 1 | yes | characteristic |
| 147 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 148 | C4⋊Q8 | — | 26 | 2 | no | — |
| 149 | #127 | — | 26 | 2 | no | — |
| 150 | #124 | — | 26 | 4 | no | — |
| 151 | #121 | — | 52 | 4 | no | — |
| 152 | C4×D4 | — | 52 | 4 | no | — |
| 153 | C2×C42 | D52 | 1 | 1 | yes | characteristic |
| 154 | Q32 | — | 26 | 8 | no | — |
| 155 | SD32 | — | 26 | 16 | no | — |
| 156 | D16 | — | 26 | 8 | no | — |
| 157 | C2×C16 | D52 | 1 | 8 | yes | complemented |
| 158 | C2×C16 | C22×D13 | 1 | 2 | yes | — |
| 159 | C2×C16 | C22×D13 | 1 | 2 | yes | — |
| 160 | C4×C8 | D52 | 1 | 1 | yes | characteristic |
| 161 | C4×C8 | D52 | 1 | 1 | yes | characteristic |
| 162 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 163 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 164 | C2×C13 | — | 2 | 2 | no | — |
| 165 | C2×C13 | C2×#493 | 1 | 1 | yes | characteristic |
| 166 | C2×C13 | C2×#508 | 1 | 2 | yes | — |
| 167 | D13 | — | 16 | 4 | no | — |
| 168 | #41 | — | 52 | 8 | no | — |
| 169 | #41 | — | 52 | 8 | no | — |
| 170 | C2×Q8 | — | 26 | 4 | no | — |
| 171 | C2×D4 | — | 26 | 4 | no | — |
| 172 | C2×D4 | — | 52 | 4 | no | — |
| 173 | C2×D4 | — | 52 | 4 | no | — |
| 174 | C22×C4 | — | 52 | 4 | no | — |
| 175 | C22×C4 | D104 | 1 | 2 | yes | — |
| 176 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 177 | Q16 | — | 26 | 8 | no | — |
| 178 | Q16 | — | 52 | 4 | no | — |
| 179 | SD16 | — | 52 | 8 | no | — |
| 180 | SD16 | — | 52 | 8 | no | — |
| 181 | D8 | — | 26 | 8 | no | — |
| 182 | D8 | — | 52 | 4 | no | — |
| 183 | C2×C8 | D104 | 1 | 4 | yes | — |
| 184 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 185 | C2×C8 | C2×D52 | 1 | 4 | yes | — |
| 186 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 187 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 188 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 189 | C4⋊C4 | — | 52 | 4 | no | — |
| 190 | C22⋊C4 | — | 52 | 8 | no | — |
| 191 | C42 | D104 | 1 | 2 | yes | — |
| 192 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 193 | C42 | C2×D52 | 1 | 1 | yes | characteristic |
| 194 | C16 | C2×D52 | 1 | 4 | yes | — |
| 195 | C16 | C2×D52 | 1 | 4 | yes | — |
| 196 | C13 | #33713 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 197 | C23 | — | 52 | 4 | no | — |
| 198 | C23 | C2×D104 | 1 | 1 | yes | characteristic |
| 199 | Q8 | — | 52 | 4 | no | — |
| 200 | Q8 | — | 52 | 4 | no | — |
| 201 | D4 | — | 52 | 4 | no | — |
| 202 | D4 | — | 52 | 4 | no | — |
| 203 | D4 | — | 104 | 8 | no | — |
| 204 | D4 | — | 104 | 8 | no | — |
| 205 | C2×C4 | — | 2 | 4 | no | — |
| 206 | C2×C4 | — | 52 | 4 | no | — |
| 207 | C2×C4 | — | 104 | 8 | no | — |
| 208 | C2×C4 | #88128 | 1 | 2 | yes | — |
| 209 | C2×C4 | C2×D104 | 1 | 2 | yes | — |
| 210 | C2×C4 | C2×D104 | 1 | 2 | yes | — |
| 211 | C2×C4 | C2×D104 | 1 | 2 | yes | — |
| 212 | C2×C4 | C2×D104 | 1 | 1 | yes | characteristic |
| 213 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 214 | C8 | #88128 | 1 | 2 | yes | — |
| 215 | C8 | C2×D104 | 1 | 2 | yes | — |
| 216 | C8 | C2×D104 | 1 | 2 | yes | — |
| 217 | C8 | C22×D52 | 1 | 2 | yes | — |
| 218 | C22 | — | 2 | 2 | no | — |
| 219 | C22 | — | 104 | 8 | no | — |
| 220 | C22 | — | 104 | 4 | no | — |
| 221 | C22 | #11718356 | 1 | 2 | yes | — |
| 222 | C22 | C22×D104 | 1 | 1 | yes | characteristic |
| 223 | C4 | — | 2 | 2 | no | — |
| 224 | C4 | — | 104 | 4 | no | — |
| 225 | C4 | #11718356 | 1 | 2 | yes | — |
| 226 | C4 | #11718565 | 1 | 4 | yes | complemented |
| 227 | C4 | C2×#88128 | 1 | 1 | yes | characteristic |
| 228 | C4 | C22×D104 | 1 | 1 | yes | characteristic |
| 229 | C2 | — | 2 | 2 | no | — |
| 230 | C2 | — | 208 | 4 | no | — |
| 231 | C2 | C2×#11718356 | 1 | 1 | yes | characteristic |
| 232 | C2 | C2×#11718565 | 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