← #16952538
Subgroups — #16952538
Order 4352.
614 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×#11763186 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#11762611 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #14528944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C4×C16×C17 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C22×D136 | — | 2 | 1 | no | — |
| 6 | C22×D136 | C22 | 1 | 2 | yes | — |
| 7 | C2×#10587560 | — | 2 | 1 | no | — |
| 8 | #11763186 | — | 2 | 2 | no | — |
| 9 | #11763186 | C4 | 1 | 4 | yes | complemented |
| 10 | C2×#10587489 | — | 2 | 1 | no | — |
| 11 | C2×#10587489 | C22 | 1 | 2 | yes | — |
| 12 | #11762679 | — | 2 | 1 | no | — |
| 13 | #11762611 | — | 2 | 8 | no | — |
| 14 | C22×C16×C17 | C22 | 1 | 2 | yes | — |
| 15 | C2×C4×C8×C17 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×C16×C17 | — | 2 | 2 | no | — |
| 17 | C22×D68 | — | 2 | 2 | no | — |
| 18 | C22×D68 | — | 4 | 2 | no | — |
| 19 | C22×C8×C17 | D4 | 1 | 1 | yes | characteristic |
| 20 | C22×C8×C17 | C23 | 1 | 1 | yes | characteristic |
| 21 | C2×C42×C17 | D4 | 1 | 1 | yes | characteristic |
| 22 | C2×C4⋊Dic17 | — | 2 | 2 | no | — |
| 23 | C2×C4⋊Dic17 | — | 4 | 2 | no | — |
| 24 | C2×D136 | — | 2 | 4 | no | — |
| 25 | C2×D136 | — | 2 | 2 | no | — |
| 26 | C2×D136 | — | 2 | 4 | no | — |
| 27 | C2×D136 | — | 2 | 4 | no | — |
| 28 | C2×D136 | — | 4 | 2 | no | — |
| 29 | C2×D136 | — | 4 | 2 | no | — |
| 30 | C2×D136 | C2×C4 | 1 | 4 | yes | — |
| 31 | #10587560 | — | 2 | 4 | no | — |
| 32 | #10587560 | — | 4 | 2 | no | — |
| 33 | C2×C16×C17 | — | 2 | 2 | no | — |
| 34 | C2×C16×C17 | — | 2 | 2 | no | — |
| 35 | C2×C16×C17 | D4 | 1 | 4 | yes | complemented |
| 36 | C4×C8×C17 | C2×C4 | 1 | 2 | yes | — |
| 37 | C4×C8×C17 | D4 | 1 | 2 | yes | — |
| 38 | #10587489 | — | 2 | 4 | no | — |
| 39 | #10587489 | — | 4 | 2 | no | — |
| 40 | C23×D17 | — | 4 | 2 | no | — |
| 41 | C22×C4×C17 | D8 | 1 | 2 | yes | — |
| 42 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 43 | C22×Dic17 | — | 4 | 2 | no | — |
| 44 | C2×D68 | — | 2 | 4 | no | — |
| 45 | C2×D68 | — | 4 | 2 | no | — |
| 46 | C2×D68 | — | 4 | 2 | no | — |
| 47 | C2×D68 | — | 4 | 2 | no | — |
| 48 | C2×D68 | — | 4 | 2 | no | — |
| 49 | C2×D68 | — | 4 | 8 | no | — |
| 50 | C2×D68 | — | 4 | 2 | no | — |
| 51 | C2×D68 | — | 8 | 4 | no | — |
| 52 | C2×D68 | — | 8 | 4 | no | — |
| 53 | C2×C8×C17 | C22⋊C4 | 1 | 2 | yes | — |
| 54 | C2×C8×C17 | D8 | 1 | 2 | yes | — |
| 55 | C2×C8×C17 | SD16 | 1 | 2 | yes | — |
| 56 | C2×C8×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×C8×C17 | C2×D4 | 1 | 2 | yes | — |
| 58 | C2×C8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C8×C17 | #41 | 1 | 2 | yes | — |
| 60 | C42×C17 | C22⋊C4 | 1 | 2 | yes | — |
| 61 | C42×C17 | SD16 | 1 | 2 | yes | — |
| 62 | C4⋊Dic17 | — | 4 | 2 | no | — |
| 63 | C4⋊Dic17 | — | 4 | 2 | no | — |
| 64 | C4⋊Dic17 | — | 8 | 4 | no | — |
| 65 | D136 | — | 2 | 8 | no | — |
| 66 | D136 | — | 4 | 8 | no | — |
| 67 | D136 | — | 4 | 4 | no | — |
| 68 | C16×C17 | — | 2 | 4 | no | — |
| 69 | #13202 | — | 17 | 1 | no | maximal, Sylow |
| 70 | C23×C17 | C2×D8 | 1 | 1 | yes | characteristic |
| 71 | C22×D17 | — | 4 | 4 | no | — |
| 72 | C22×D17 | — | 8 | 2 | no | — |
| 73 | C22×D17 | — | 8 | 2 | no | — |
| 74 | C22×D17 | — | 8 | 4 | no | — |
| 75 | C22×D17 | — | 8 | 4 | no | — |
| 76 | C2×C4×C17 | #102 | 1 | 4 | yes | — |
| 77 | C2×C4×C17 | D16 | 1 | 4 | yes | — |
| 78 | C2×C4×C17 | SD32 | 1 | 4 | yes | — |
| 79 | C2×C4×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 80 | C2×C4×C17 | #124 | 1 | 1 | yes | characteristic |
| 81 | C2×C4×C17 | #127 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×C17 | C2×D8 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C17 | C2×SD16 | 1 | 1 | yes | characteristic |
| 84 | C2×C4×C17 | C2×SD16 | 1 | 1 | yes | characteristic |
| 85 | C2×Dic17 | — | 8 | 2 | no | — |
| 86 | C2×Dic17 | — | 8 | 4 | no | — |
| 87 | D68 | — | 4 | 4 | no | — |
| 88 | D68 | — | 4 | 4 | no | — |
| 89 | D68 | — | 8 | 16 | no | — |
| 90 | D68 | — | 8 | 2 | no | — |
| 91 | D68 | — | 8 | 2 | no | — |
| 92 | C8×C17 | #102 | 1 | 4 | yes | — |
| 93 | C8×C17 | C4×D4 | 1 | 2 | yes | — |
| 94 | C8×C17 | #121 | 1 | 2 | yes | — |
| 95 | C2×#493 | — | 17 | 1 | no | — |
| 96 | C2×#357 | — | 17 | 4 | no | — |
| 97 | C2×C4×C16 | D17 | 1 | 1 | yes | characteristic, complemented |
| 98 | #1845 | — | 17 | 1 | no | — |
| 99 | C22×C17 | C2×#102 | 1 | 1 | yes | characteristic |
| 100 | C22×C17 | #486 | 1 | 1 | yes | characteristic |
| 101 | C22×C17 | #493 | 1 | 1 | yes | characteristic |
| 102 | C22×C17 | C2×D16 | 1 | 2 | yes | — |
| 103 | C22×C17 | C2×SD32 | 1 | 2 | yes | — |
| 104 | C2×D17 | — | 8 | 8 | no | — |
| 105 | C2×D17 | — | 8 | 4 | no | — |
| 106 | C2×D17 | — | 16 | 4 | no | — |
| 107 | C2×D17 | — | 16 | 2 | no | — |
| 108 | C2×D17 | — | 16 | 2 | no | — |
| 109 | C4×C17 | #357 | 1 | 8 | yes | complemented |
| 110 | C4×C17 | #390 | 1 | 1 | yes | characteristic |
| 111 | C4×C17 | C2×#102 | 1 | 1 | yes | characteristic |
| 112 | C4×C17 | #486 | 1 | 1 | yes | characteristic |
| 113 | C4×C17 | #492 | 1 | 1 | yes | characteristic |
| 114 | Dic17 | — | 16 | 2 | no | — |
| 115 | C22×D8 | — | 17 | 2 | no | — |
| 116 | C22×D8 | — | 34 | 1 | no | — |
| 117 | C2×#127 | — | 34 | 1 | no | — |
| 118 | C22×C16 | C2×D17 | 1 | 2 | yes | — |
| 119 | #493 | — | 17 | 4 | no | — |
| 120 | #493 | — | 34 | 2 | no | — |
| 121 | C2×#107 | — | 17 | 2 | no | — |
| 122 | C2×#107 | — | 34 | 1 | no | — |
| 123 | C2×C4×C8 | C2×D17 | 1 | 1 | yes | characteristic |
| 124 | #384 | — | 34 | 1 | no | — |
| 125 | #357 | — | 34 | 8 | no | — |
| 126 | C4×C16 | — | 2 | 2 | no | — |
| 127 | C2×C17 | #1957 | 1 | 1 | yes | characteristic |
| 128 | C2×C17 | C2×#357 | 1 | 2 | yes | — |
| 129 | C2×C17 | #2240 | 1 | 2 | yes | — |
| 130 | C2×C17 | #2246 | 1 | 1 | yes | characteristic |
| 131 | C2×C17 | #2248 | 1 | 1 | yes | characteristic |
| 132 | D17 | — | 16 | 4 | no | — |
| 133 | C22×D4 | — | 34 | 2 | no | — |
| 134 | C22×D4 | — | 68 | 2 | no | — |
| 135 | C2×D8 | — | 17 | 4 | no | — |
| 136 | C2×D8 | — | 34 | 4 | no | — |
| 137 | C2×D8 | — | 34 | 4 | no | — |
| 138 | C2×D8 | — | 34 | 2 | no | — |
| 139 | C2×D8 | — | 34 | 4 | no | — |
| 140 | C2×D8 | — | 68 | 2 | no | — |
| 141 | C2×D8 | — | 68 | 2 | no | — |
| 142 | C22×C8 | D68 | 1 | 1 | yes | characteristic |
| 143 | C22×C8 | C22×D17 | 1 | 1 | yes | characteristic |
| 144 | #127 | — | 34 | 4 | no | — |
| 145 | #127 | — | 68 | 2 | no | — |
| 146 | C2×C4⋊C4 | — | 34 | 2 | no | — |
| 147 | C2×C4⋊C4 | — | 68 | 2 | no | — |
| 148 | C2×C42 | D68 | 1 | 1 | yes | characteristic |
| 149 | C2×C16 | — | 2 | 2 | no | — |
| 150 | C2×C16 | — | 2 | 2 | no | — |
| 151 | C2×C16 | D68 | 1 | 4 | yes | complemented |
| 152 | #107 | — | 34 | 4 | no | — |
| 153 | #107 | — | 68 | 2 | no | — |
| 154 | C4×C8 | C4×D17 | 1 | 2 | yes | — |
| 155 | C4×C8 | C22⋊D17 | 1 | 2 | yes | — |
| 156 | C17 | #13202 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 157 | C24 | — | 68 | 2 | no | — |
| 158 | C2×D4 | — | 34 | 4 | no | — |
| 159 | C2×D4 | — | 68 | 8 | no | — |
| 160 | C2×D4 | — | 68 | 2 | no | — |
| 161 | C2×D4 | — | 68 | 2 | no | — |
| 162 | C2×D4 | — | 68 | 2 | no | — |
| 163 | C2×D4 | — | 68 | 2 | no | — |
| 164 | C2×D4 | — | 68 | 2 | no | — |
| 165 | C2×D4 | — | 136 | 4 | no | — |
| 166 | C2×D4 | — | 136 | 4 | no | — |
| 167 | C22×C4 | — | 68 | 2 | no | — |
| 168 | C22×C4 | D136 | 1 | 2 | yes | — |
| 169 | C22×C4 | C2×D68 | 1 | 1 | yes | characteristic |
| 170 | D8 | — | 34 | 8 | no | — |
| 171 | D8 | — | 68 | 8 | no | — |
| 172 | D8 | — | 68 | 4 | no | — |
| 173 | C2×C8 | #63219 | 1 | 2 | yes | — |
| 174 | C2×C8 | D136 | 1 | 2 | yes | — |
| 175 | C2×C8 | #63227 | 1 | 2 | yes | — |
| 176 | C2×C8 | C2×C4×D17 | 1 | 1 | yes | characteristic |
| 177 | C2×C8 | C2×D68 | 1 | 2 | yes | — |
| 178 | C2×C8 | #63252 | 1 | 2 | yes | — |
| 179 | C2×C8 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 180 | C4⋊C4 | — | 68 | 2 | no | — |
| 181 | C4⋊C4 | — | 68 | 2 | no | — |
| 182 | C4⋊C4 | — | 136 | 4 | no | — |
| 183 | C42 | #63219 | 1 | 2 | yes | — |
| 184 | C42 | #63227 | 1 | 2 | yes | — |
| 185 | C16 | — | 2 | 4 | no | — |
| 186 | C23 | — | 68 | 4 | no | — |
| 187 | C23 | — | 136 | 4 | no | — |
| 188 | C23 | — | 136 | 4 | no | — |
| 189 | C23 | — | 136 | 2 | no | — |
| 190 | C23 | — | 136 | 2 | no | — |
| 191 | C23 | C2×D136 | 1 | 1 | yes | characteristic |
| 192 | D4 | — | 68 | 4 | no | — |
| 193 | D4 | — | 68 | 4 | no | — |
| 194 | D4 | — | 136 | 16 | no | — |
| 195 | D4 | — | 136 | 2 | no | — |
| 196 | D4 | — | 136 | 2 | no | — |
| 197 | C2×C4 | — | 136 | 4 | no | — |
| 198 | C2×C4 | — | 136 | 2 | no | — |
| 199 | C2×C4 | D272 | 1 | 4 | yes | — |
| 200 | C2×C4 | #10587471 | 1 | 4 | yes | — |
| 201 | C2×C4 | #10587492 | 1 | 4 | yes | — |
| 202 | C2×C4 | #10587560 | 1 | 1 | yes | characteristic |
| 203 | C2×C4 | #10587561 | 1 | 1 | yes | characteristic |
| 204 | C2×C4 | C2×#63219 | 1 | 1 | yes | characteristic |
| 205 | C2×C4 | C2×#63219 | 1 | 1 | yes | characteristic |
| 206 | C2×C4 | C2×D136 | 1 | 1 | yes | characteristic |
| 207 | C2×C4 | C2×#63227 | 1 | 1 | yes | characteristic |
| 208 | C8 | #10587492 | 1 | 4 | yes | — |
| 209 | C8 | C4×D68 | 1 | 2 | yes | — |
| 210 | C8 | #10587616 | 1 | 2 | yes | — |
| 211 | C22 | — | 272 | 4 | no | — |
| 212 | C22 | — | 272 | 2 | no | — |
| 213 | C22 | — | 272 | 2 | no | — |
| 214 | C22 | — | 136 | 4 | no | — |
| 215 | C22 | — | 136 | 8 | no | — |
| 216 | C22 | C2×#10587492 | 1 | 1 | yes | characteristic |
| 217 | C22 | #11763156 | 1 | 1 | yes | characteristic |
| 218 | C22 | #11763186 | 1 | 1 | yes | characteristic |
| 219 | C22 | C2×D272 | 1 | 2 | yes | — |
| 220 | C22 | C2×#10587471 | 1 | 2 | yes | — |
| 221 | C4 | — | 272 | 2 | no | — |
| 222 | C4 | #11762611 | 1 | 8 | yes | complemented |
| 223 | C4 | #11762711 | 1 | 1 | yes | characteristic |
| 224 | C4 | C2×#10587492 | 1 | 1 | yes | characteristic |
| 225 | C4 | #11763156 | 1 | 1 | yes | characteristic |
| 226 | C4 | #11763182 | 1 | 1 | yes | characteristic |
| 227 | C2 | — | 272 | 4 | no | — |
| 228 | C2 | #14529590 | 1 | 1 | yes | characteristic |
| 229 | C2 | C2×#11762611 | 1 | 2 | yes | — |
| 230 | C2 | #14531008 | 1 | 2 | yes | — |
| 231 | C2 | #14531034 | 1 | 1 | yes | characteristic |
| 232 | C2 | #14531040 | 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