← #16769452
Subgroups — #16769452
Order 3328.
2038 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 | #13129610 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13127989 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #13127984 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #13127977 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13127972 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#11718565 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×C13×#504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11719648 | — | 2 | 2 | no | — |
| 9 | C2×C13×#131 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11719458 | C22 | 1 | 8 | yes | complemented |
| 11 | #11719457 | C22 | 1 | 8 | yes | complemented |
| 12 | #11719456 | — | 2 | 8 | no | — |
| 13 | #11719453 | — | 2 | 6 | no | — |
| 14 | C2×#88158 | C22 | 1 | 12 | yes | complemented |
| 15 | C13×#504 | C22 | 1 | 4 | yes | complemented |
| 16 | C13×#504 | C22 | 1 | 4 | yes | complemented |
| 17 | C2×C13×M32 | C22 | 1 | 3 | yes | complemented |
| 18 | C22×C13×C16 | C22 | 1 | 3 | yes | complemented |
| 19 | #11718570 | C22 | 1 | 24 | yes | complemented |
| 20 | #11718569 | C22 | 1 | 24 | yes | complemented |
| 21 | C2×Dic104 | C22 | 1 | 6 | yes | complemented |
| 22 | #11718565 | C22 | 1 | 4 | yes | complemented |
| 23 | #11718565 | C22 | 1 | 12 | yes | complemented |
| 24 | #11718565 | C22 | 1 | 12 | yes | complemented |
| 25 | #11718565 | C22 | 1 | 12 | yes | complemented |
| 26 | C2×#88040 | C22 | 1 | 12 | yes | complemented |
| 27 | C2×D208 | C22 | 1 | 6 | yes | complemented |
| 28 | C2×C13×#41 | D4 | 1 | 1 | yes | characteristic |
| 29 | #88257 | — | 2 | 8 | no | — |
| 30 | #88256 | — | 2 | 8 | no | — |
| 31 | #41×D13 | — | 4 | 8 | no | — |
| 32 | #88254 | — | 4 | 2 | no | — |
| 33 | #88251 | — | 4 | 6 | no | — |
| 34 | C2×#6127 | — | 2 | 12 | no | — |
| 35 | C13×#131 | D4 | 1 | 4 | yes | — |
| 36 | C13×#131 | C23 | 1 | 4 | yes | — |
| 37 | C2×C13×M16 | D4 | 1 | 3 | yes | — |
| 38 | C22×C8×C13 | C23 | 1 | 3 | yes | — |
| 39 | #88163 | — | 2 | 24 | no | — |
| 40 | #88162 | — | 2 | 24 | no | — |
| 41 | C2×Dic52 | C23 | 1 | 12 | yes | — |
| 42 | #88158 | — | 2 | 12 | no | — |
| 43 | #88158 | — | 2 | 12 | no | — |
| 44 | #88158 | C23 | 1 | 8 | yes | — |
| 45 | #88158 | C23 | 1 | 24 | yes | — |
| 46 | C2×D104 | C23 | 1 | 12 | yes | — |
| 47 | C2×#6095 | — | 2 | 12 | no | — |
| 48 | C13×M32 | C23 | 1 | 12 | yes | — |
| 49 | C2×C13×C16 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C13×C16 | C23 | 1 | 3 | yes | — |
| 51 | C2×C13×C16 | C23 | 1 | 6 | yes | — |
| 52 | C2×C13×C16 | C23 | 1 | 6 | yes | — |
| 53 | Dic104 | C23 | 1 | 4 | yes | — |
| 54 | Dic104 | C23 | 1 | 12 | yes | — |
| 55 | #88040 | C23 | 1 | 8 | yes | — |
| 56 | #88040 | C23 | 1 | 24 | yes | — |
| 57 | D208 | C23 | 1 | 4 | yes | — |
| 58 | D208 | C23 | 1 | 12 | yes | — |
| 59 | #62635 | — | 13 | 1 | no | maximal, Sylow |
| 60 | C13×#41 | D8 | 1 | 4 | yes | — |
| 61 | C13×#41 | C2×D4 | 1 | 4 | yes | — |
| 62 | C2×Q8×C13 | D8 | 1 | 1 | yes | characteristic |
| 63 | C2×D4×C13 | D8 | 1 | 3 | yes | — |
| 64 | C22×C4×C13 | C2×D4 | 1 | 3 | yes | — |
| 65 | C2×C22⋊D13 | — | 4 | 12 | no | — |
| 66 | #6131 | — | 4 | 8 | no | — |
| 67 | Q8×D13 | — | 4 | 8 | no | — |
| 68 | #6129 | — | 4 | 24 | no | — |
| 69 | D4×D13 | — | 4 | 24 | no | — |
| 70 | #6127 | — | 2 | 8 | no | — |
| 71 | #6127 | — | 2 | 24 | no | — |
| 72 | #6127 | — | 4 | 12 | no | — |
| 73 | #6127 | — | 4 | 12 | no | — |
| 74 | C2×D52 | — | 2 | 12 | no | — |
| 75 | C2×C4×D13 | — | 4 | 12 | no | — |
| 76 | C2×Dic26 | — | 2 | 12 | no | — |
| 77 | C13×M16 | C2×D4 | 1 | 12 | yes | — |
| 78 | C2×C8×C13 | C2×D4 | 1 | 6 | yes | — |
| 79 | C2×C8×C13 | C2×D4 | 1 | 3 | yes | — |
| 80 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 81 | C2×C8×C13 | C24 | 1 | 6 | yes | — |
| 82 | Dic52 | — | 2 | 12 | no | — |
| 83 | Dic52 | C24 | 1 | 8 | yes | — |
| 84 | D104 | — | 2 | 12 | no | — |
| 85 | D104 | C24 | 1 | 8 | yes | — |
| 86 | #6095 | — | 2 | 8 | no | — |
| 87 | #6095 | — | 2 | 24 | no | — |
| 88 | C13×C16 | C24 | 1 | 1 | yes | characteristic |
| 89 | C13×C16 | C24 | 1 | 1 | yes | characteristic |
| 90 | C13×C16 | C24 | 1 | 6 | yes | — |
| 91 | #3584 | — | 13 | 2 | no | — |
| 92 | #3417 | — | 13 | 4 | no | — |
| 93 | #3416 | — | 13 | 8 | no | — |
| 94 | #3415 | — | 13 | 4 | no | — |
| 95 | #3414 | — | 13 | 6 | no | — |
| 96 | C2×#508 | — | 13 | 6 | no | — |
| 97 | C2×#504 | D13 | 1 | 1 | yes | characteristic, complemented |
| 98 | C23×C13 | C2×D8 | 1 | 3 | yes | — |
| 99 | C22×D13 | — | 4 | 12 | no | — |
| 100 | Q8×C13 | C2×D8 | 1 | 4 | yes | — |
| 101 | D4×C13 | C2×D8 | 1 | 12 | yes | — |
| 102 | C2×C4×C13 | C2×D8 | 1 | 6 | yes | — |
| 103 | C2×C4×C13 | C2×D8 | 1 | 3 | yes | — |
| 104 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C13 | C22×D4 | 1 | 6 | yes | — |
| 106 | C22⋊D13 | — | 4 | 8 | no | — |
| 107 | C22⋊D13 | — | 4 | 24 | no | — |
| 108 | C2×Dic13 | — | 4 | 12 | no | — |
| 109 | D52 | — | 2 | 8 | no | — |
| 110 | D52 | — | 4 | 12 | no | — |
| 111 | C4×D13 | — | 4 | 8 | no | — |
| 112 | C4×D13 | — | 4 | 24 | no | — |
| 113 | Dic26 | — | 2 | 8 | no | — |
| 114 | Dic26 | — | 4 | 12 | no | — |
| 115 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 116 | C8×C13 | C22×D4 | 1 | 6 | yes | — |
| 117 | C8×C13 | C25 | 1 | 1 | yes | characteristic |
| 118 | #585 | — | 26 | 2 | no | — |
| 119 | #578 | — | 13 | 8 | no | — |
| 120 | #577 | — | 26 | 8 | no | — |
| 121 | #576 | — | 13 | 8 | no | — |
| 122 | #575 | — | 26 | 6 | no | — |
| 123 | C2×#135 | — | 13 | 12 | no | — |
| 124 | C2×#131 | C2×D13 | 1 | 1 | yes | characteristic |
| 125 | #510 | — | 13 | 24 | no | — |
| 126 | #509 | — | 13 | 24 | no | — |
| 127 | #508 | — | 13 | 4 | no | — |
| 128 | #508 | — | 13 | 12 | no | — |
| 129 | #508 | — | 13 | 12 | no | — |
| 130 | #508 | — | 13 | 12 | no | — |
| 131 | C2×Q32 | — | 13 | 6 | no | — |
| 132 | C2×SD32 | — | 13 | 12 | no | — |
| 133 | C2×D16 | — | 13 | 6 | no | — |
| 134 | #504 | C2×D13 | 1 | 4 | yes | complemented |
| 135 | #504 | C2×D13 | 1 | 4 | yes | complemented |
| 136 | C2×M32 | C2×D13 | 1 | 3 | yes | complemented |
| 137 | C22×C16 | C2×D13 | 1 | 3 | yes | complemented |
| 138 | C22×C13 | — | 4 | 3 | no | — |
| 139 | C22×C13 | C22×D8 | 1 | 6 | yes | — |
| 140 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 141 | C2×D13 | — | 4 | 8 | no | — |
| 142 | C2×D13 | — | 16 | 12 | no | — |
| 143 | C4×C13 | C22×D8 | 1 | 6 | yes | — |
| 144 | C4×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 145 | C4×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 146 | Dic13 | — | 4 | 8 | no | — |
| 147 | 2−1+4 | — | 26 | 8 | no | — |
| 148 | 2−1+4 | — | 52 | 2 | no | — |
| 149 | H(5,𝔽2) | — | 26 | 8 | no | — |
| 150 | H(5,𝔽2) | — | 52 | 6 | no | — |
| 151 | C2×#41 | — | 26 | 12 | no | — |
| 152 | C2×#41 | — | 52 | 8 | no | — |
| 153 | C2×#41 | D52 | 1 | 1 | yes | characteristic |
| 154 | #137 | — | 26 | 24 | no | — |
| 155 | AGL(1,ℤ/8) | — | 26 | 24 | no | — |
| 156 | #135 | — | 13 | 8 | no | — |
| 157 | #135 | — | 13 | 24 | no | — |
| 158 | #135 | — | 26 | 12 | no | — |
| 159 | #135 | — | 26 | 12 | no | — |
| 160 | C2×Q16 | — | 13 | 12 | no | — |
| 161 | C2×SD16 | — | 26 | 12 | no | — |
| 162 | C2×D8 | — | 13 | 12 | no | — |
| 163 | #131 | D52 | 1 | 4 | yes | — |
| 164 | #131 | C22×D13 | 1 | 4 | yes | — |
| 165 | C2×M16 | D52 | 1 | 3 | yes | — |
| 166 | C22×C8 | C22×D13 | 1 | 3 | yes | — |
| 167 | Q32 | — | 13 | 4 | no | — |
| 168 | Q32 | — | 13 | 12 | no | — |
| 169 | SD32 | — | 13 | 8 | no | — |
| 170 | SD32 | — | 13 | 24 | no | — |
| 171 | D16 | — | 13 | 4 | no | — |
| 172 | D16 | — | 13 | 12 | no | — |
| 173 | M32 | C22×D13 | 1 | 12 | yes | — |
| 174 | C2×C16 | C22×D13 | 1 | 1 | yes | characteristic |
| 175 | C2×C16 | C22×D13 | 1 | 3 | yes | — |
| 176 | C2×C16 | C22×D13 | 1 | 6 | yes | — |
| 177 | C2×C16 | C22×D13 | 1 | 6 | yes | — |
| 178 | C2×C13 | — | 2 | 6 | no | — |
| 179 | C2×C13 | — | 2 | 1 | no | — |
| 180 | C2×C13 | C23×D8 | 1 | 1 | yes | characteristic |
| 181 | D13 | — | 8 | 8 | no | — |
| 182 | #41 | — | 26 | 8 | no | — |
| 183 | #41 | — | 26 | 24 | no | — |
| 184 | #41 | — | 52 | 8 | no | — |
| 185 | #41 | — | 52 | 24 | no | — |
| 186 | #41 | — | 52 | 12 | no | — |
| 187 | #41 | — | 52 | 12 | no | — |
| 188 | #41 | D104 | 1 | 4 | yes | — |
| 189 | #41 | C2×D52 | 1 | 4 | yes | — |
| 190 | C2×Q8 | — | 26 | 12 | no | — |
| 191 | C2×Q8 | — | 52 | 8 | no | — |
| 192 | C2×Q8 | D104 | 1 | 1 | yes | characteristic |
| 193 | C2×D4 | — | 26 | 12 | no | — |
| 194 | C2×D4 | — | 52 | 12 | no | — |
| 195 | C2×D4 | — | 52 | 24 | no | — |
| 196 | C2×D4 | D104 | 1 | 3 | yes | — |
| 197 | C22×C4 | — | 52 | 12 | no | — |
| 198 | C22×C4 | C2×D52 | 1 | 3 | yes | — |
| 199 | Q16 | — | 13 | 8 | no | — |
| 200 | Q16 | — | 26 | 12 | no | — |
| 201 | SD16 | — | 26 | 8 | no | — |
| 202 | SD16 | — | 26 | 24 | no | — |
| 203 | D8 | — | 13 | 8 | no | — |
| 204 | D8 | — | 26 | 12 | no | — |
| 205 | M16 | C2×D52 | 1 | 12 | yes | — |
| 206 | C2×C8 | C2×D52 | 1 | 3 | yes | — |
| 207 | C2×C8 | C2×D52 | 1 | 6 | yes | — |
| 208 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 209 | C2×C8 | C23×D13 | 1 | 6 | yes | — |
| 210 | C16 | C23×D13 | 1 | 1 | yes | characteristic |
| 211 | C16 | C23×D13 | 1 | 1 | yes | characteristic |
| 212 | C16 | C23×D13 | 1 | 6 | yes | — |
| 213 | C13 | #62635 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 214 | C23 | — | 52 | 12 | no | — |
| 215 | C23 | C2×D104 | 1 | 3 | yes | — |
| 216 | Q8 | — | 26 | 8 | no | — |
| 217 | Q8 | — | 52 | 12 | no | — |
| 218 | Q8 | C2×D104 | 1 | 4 | yes | — |
| 219 | D4 | — | 26 | 8 | no | — |
| 220 | D4 | — | 52 | 24 | no | — |
| 221 | D4 | — | 52 | 8 | no | — |
| 222 | D4 | — | 52 | 12 | no | — |
| 223 | D4 | C2×D104 | 1 | 12 | yes | — |
| 224 | C2×C4 | — | 52 | 12 | no | — |
| 225 | C2×C4 | — | 52 | 24 | no | — |
| 226 | C2×C4 | — | 52 | 8 | no | — |
| 227 | C2×C4 | C2×D104 | 1 | 3 | yes | — |
| 228 | C2×C4 | C2×D104 | 1 | 6 | yes | — |
| 229 | C2×C4 | C22×D52 | 1 | 6 | yes | — |
| 230 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 231 | C8 | C22×D52 | 1 | 1 | yes | characteristic |
| 232 | C8 | C22×D52 | 1 | 6 | yes | — |
| 233 | C8 | C24×D13 | 1 | 1 | yes | characteristic |
| 234 | C22 | — | 4 | 3 | no | — |
| 235 | C22 | — | 52 | 8 | no | — |
| 236 | C22 | — | 208 | 12 | no | — |
| 237 | C22 | C22×D104 | 1 | 6 | yes | — |
| 238 | C22 | C22×D104 | 1 | 1 | yes | characteristic |
| 239 | C4 | — | 52 | 8 | no | — |
| 240 | C4 | C22×D104 | 1 | 6 | yes | — |
| 241 | C4 | C22×D104 | 1 | 1 | yes | characteristic |
| 242 | C4 | C23×D52 | 1 | 1 | yes | characteristic |
| 243 | C2 | — | 2 | 1 | no | — |
| 244 | C2 | — | 2 | 6 | no | — |
| 245 | C2 | — | 104 | 8 | no | — |
| 246 | C2 | C23×D104 | 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