← #31725383
Subgroups — #31725383
Order 17152.
3114 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16864213 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #22573994 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22570703 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #22570668 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #22570637 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#16863776 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C4×#131×C67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14524090 | C22 | 1 | 4 | yes | — |
| 9 | #16864213 | — | 2 | 32 | no | — |
| 10 | C2×#14524076 | C22 | 1 | 24 | yes | — |
| 11 | C2×#14524065 | C22 | 1 | 12 | yes | — |
| 12 | C22×Dic268 | C22 | 1 | 12 | yes | — |
| 13 | Q8×D268 | — | 2 | 4 | no | — |
| 14 | #16864050 | — | 2 | 12 | no | — |
| 15 | #16863972 | C22 | 1 | 12 | yes | — |
| 16 | #16863946 | C22 | 1 | 6 | yes | — |
| 17 | C2×#14524043 | C22 | 1 | 6 | yes | — |
| 18 | #16863790 | C22 | 1 | 24 | yes | — |
| 19 | #16863780 | C22 | 1 | 12 | yes | — |
| 20 | #16863776 | C22 | 1 | 3 | yes | — |
| 21 | #16863776 | C22 | 1 | 6 | yes | — |
| 22 | #16863776 | C22 | 1 | 12 | yes | — |
| 23 | #16863773 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16863769 | C22 | 1 | 6 | yes | — |
| 25 | C2×#131×C67 | C22 | 1 | 2 | yes | — |
| 26 | C4×#41×C67 | C22 | 1 | 1 | yes | characteristic |
| 27 | #405×C67 | C22 | 1 | 6 | yes | — |
| 28 | C4×M16×C67 | C22 | 1 | 3 | yes | — |
| 29 | C2×C4×C8×C67 | C22 | 1 | 3 | yes | — |
| 30 | #14524090 | — | 2 | 32 | no | — |
| 31 | C2×#11761628 | C23 | 1 | 12 | yes | — |
| 32 | C2×#11761627 | — | 2 | 12 | no | — |
| 33 | C22×Dic134 | C23 | 1 | 12 | yes | — |
| 34 | C2×Q8×D67 | — | 2 | 4 | no | — |
| 35 | #14524076 | — | 2 | 96 | no | — |
| 36 | #14524065 | — | 2 | 48 | no | — |
| 37 | C2×Dic268 | — | 2 | 48 | no | — |
| 38 | C2×Dic268 | C23 | 1 | 12 | yes | — |
| 39 | C2×Dic268 | C23 | 1 | 24 | yes | — |
| 40 | C2×#11761617 | C23 | 1 | 24 | yes | — |
| 41 | C2×D536 | C23 | 1 | 4 | yes | — |
| 42 | #14524043 | — | 2 | 12 | no | — |
| 43 | #14524043 | C23 | 1 | 6 | yes | — |
| 44 | #14524043 | C23 | 1 | 12 | yes | — |
| 45 | #14524040 | C23 | 1 | 2 | yes | — |
| 46 | #14524031 | C23 | 1 | 12 | yes | — |
| 47 | #14524027 | — | 2 | 24 | no | — |
| 48 | #14524023 | — | 2 | 24 | no | — |
| 49 | #14524017 | — | 2 | 12 | no | — |
| 50 | C4×D268 | — | 2 | 12 | no | — |
| 51 | C2×C4⋊Dic67 | — | 2 | 12 | no | — |
| 52 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 53 | #131×C67 | D4 | 1 | 16 | yes | complemented |
| 54 | C2×M16×C67 | C23 | 1 | 6 | yes | — |
| 55 | C22×C8×C67 | C23 | 1 | 6 | yes | — |
| 56 | C4×Q8×C67 | D4 | 1 | 2 | yes | — |
| 57 | C4×D4×C67 | D4 | 1 | 6 | yes | — |
| 58 | #117×C67 | C23 | 1 | 3 | yes | — |
| 59 | C2×C42×C67 | C23 | 1 | 3 | yes | — |
| 60 | #97×C67 | C23 | 1 | 6 | yes | — |
| 61 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 62 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 63 | C4×C8×C67 | C23 | 1 | 6 | yes | — |
| 64 | #11761628 | — | 2 | 48 | no | — |
| 65 | #11761627 | — | 4 | 48 | no | — |
| 66 | C2×Dic134 | — | 2 | 48 | no | — |
| 67 | C2×Dic134 | — | 2 | 12 | no | — |
| 68 | C2×Dic134 | C24 | 1 | 12 | yes | — |
| 69 | Q8×D67 | — | 4 | 16 | no | — |
| 70 | C2×D268 | — | 2 | 4 | no | — |
| 71 | C2×D268 | C24 | 1 | 4 | yes | — |
| 72 | C2×C22⋊D67 | — | 2 | 12 | no | — |
| 73 | C22×Dic67 | — | 2 | 12 | no | — |
| 74 | C2×C4×D67 | — | 2 | 12 | no | — |
| 75 | Dic268 | — | 2 | 24 | no | — |
| 76 | Dic268 | — | 2 | 48 | no | — |
| 77 | #11761617 | — | 2 | 48 | no | — |
| 78 | D536 | — | 2 | 8 | no | — |
| 79 | C4⋊Dic67 | — | 2 | 12 | no | — |
| 80 | C4⋊Dic67 | — | 2 | 24 | no | — |
| 81 | (C2×D67)⋊C4 | — | 2 | 24 | no | — |
| 82 | #41×C67 | C2×D4 | 1 | 8 | yes | — |
| 83 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C2×D4×C67 | C2×D4 | 1 | 3 | yes | — |
| 85 | C22×C4×C67 | C2×D4 | 1 | 6 | yes | — |
| 86 | C22×C4×C67 | C24 | 1 | 3 | yes | — |
| 87 | M16×C67 | C2×D4 | 1 | 24 | yes | — |
| 88 | C2×C8×C67 | C2×D4 | 1 | 24 | yes | — |
| 89 | C2×C8×C67 | C24 | 1 | 2 | yes | — |
| 90 | C2×C8×C67 | C24 | 1 | 6 | yes | — |
| 91 | C4⋊C4×C67 | C2×D4 | 1 | 6 | yes | — |
| 92 | C22⋊C4×C67 | C2×D4 | 1 | 6 | yes | — |
| 93 | C42×C67 | C2×D4 | 1 | 6 | yes | — |
| 94 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 95 | C42×C67 | C24 | 1 | 3 | yes | — |
| 96 | C23×C67 | C22×D4 | 1 | 3 | yes | — |
| 97 | C22×D67 | — | 2 | 4 | no | — |
| 98 | Q8×C67 | #127 | 1 | 4 | yes | — |
| 99 | D4×C67 | #127 | 1 | 12 | yes | — |
| 100 | C2×C4×C67 | — | 2 | 12 | no | — |
| 101 | C2×C4×C67 | C22×D4 | 1 | 6 | yes | — |
| 102 | C2×C4×C67 | C22×D4 | 1 | 3 | yes | — |
| 103 | C2×C4×C67 | C22×D4 | 1 | 12 | yes | — |
| 104 | C2×C4×C67 | C22×D4 | 1 | 2 | yes | — |
| 105 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 106 | C22⋊D67 | — | 4 | 24 | no | — |
| 107 | C2×Dic67 | — | 2 | 12 | no | — |
| 108 | C2×Dic67 | — | 4 | 24 | no | — |
| 109 | D268 | — | 2 | 8 | no | — |
| 110 | D268 | — | 4 | 8 | no | — |
| 111 | C4×D67 | — | 4 | 24 | no | — |
| 112 | Dic134 | — | 2 | 24 | no | — |
| 113 | Dic134 | — | 4 | 24 | no | — |
| 114 | C8×C67 | C22×D4 | 1 | 4 | yes | — |
| 115 | C8×C67 | C22×D4 | 1 | 12 | yes | — |
| 116 | C22×C67 | — | 2 | 6 | no | — |
| 117 | C22×C67 | C2×#127 | 1 | 6 | yes | — |
| 118 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×D67 | — | 4 | 4 | no | — |
| 120 | C2×D67 | — | 4 | 8 | no | — |
| 121 | C4×C67 | — | 2 | 6 | no | — |
| 122 | C4×C67 | C2×#127 | 1 | 6 | yes | — |
| 123 | C4×C67 | #578 | 1 | 4 | yes | complemented |
| 124 | C4×C67 | C23×D4 | 1 | 2 | yes | — |
| 125 | Dic67 | — | 4 | 12 | no | — |
| 126 | #60648 | — | 67 | 1 | no | maximal, Sylow |
| 127 | C2×C67 | — | 2 | 6 | no | — |
| 128 | C2×C67 | C22×#127 | 1 | 1 | yes | characteristic |
| 129 | C2×C67 | C2×#578 | 1 | 2 | yes | — |
| 130 | D67 | — | 8 | 4 | no | — |
| 131 | C2×#578 | — | 67 | 4 | no | — |
| 132 | #3499 | — | 67 | 2 | no | — |
| 133 | #3156 | — | 67 | 12 | no | — |
| 134 | #3152 | — | 67 | 6 | no | — |
| 135 | #3147 | — | 67 | 3 | no | — |
| 136 | C2×#494 | — | 67 | 3 | no | — |
| 137 | C4×#131 | D67 | 1 | 1 | yes | characteristic, complemented |
| 138 | C67 | #60648 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 139 | C2×2−1+4 | — | 67 | 4 | no | — |
| 140 | #578 | — | 134 | 32 | no | — |
| 141 | C2×#137 | — | 67 | 24 | no | — |
| 142 | C2×#135 | — | 67 | 12 | no | — |
| 143 | C22×Q16 | — | 67 | 12 | no | — |
| 144 | C2×#131 | C2×D67 | 1 | 2 | yes | — |
| 145 | D4×Q8 | — | 134 | 4 | no | — |
| 146 | #547 | — | 134 | 12 | no | — |
| 147 | #536 | — | 67 | 12 | no | — |
| 148 | #532 | — | 67 | 6 | no | — |
| 149 | C2×C4⋊Q8 | — | 67 | 6 | no | — |
| 150 | C4×#41 | C2×D67 | 1 | 1 | yes | characteristic |
| 151 | #497 | — | 67 | 24 | no | — |
| 152 | #495 | — | 67 | 12 | no | — |
| 153 | #494 | — | 67 | 3 | no | — |
| 154 | #494 | — | 67 | 6 | no | — |
| 155 | #494 | — | 67 | 12 | no | — |
| 156 | #493 | — | 67 | 1 | no | — |
| 157 | #492 | — | 67 | 6 | no | — |
| 158 | #405 | C2×D67 | 1 | 6 | yes | — |
| 159 | C4×M16 | C2×D67 | 1 | 3 | yes | — |
| 160 | C2×C4×C8 | C2×D67 | 1 | 3 | yes | — |
| 161 | 2−1+4 | — | 134 | 32 | no | — |
| 162 | C2×#41 | — | 67 | 12 | no | — |
| 163 | C2×#41 | — | 134 | 12 | no | — |
| 164 | C2×#41 | C22×D67 | 1 | 1 | yes | characteristic |
| 165 | C22×Q8 | — | 67 | 12 | no | — |
| 166 | C22×Q8 | — | 134 | 4 | no | — |
| 167 | #137 | — | 134 | 96 | no | — |
| 168 | #135 | — | 134 | 48 | no | — |
| 169 | C2×Q16 | — | 67 | 12 | no | — |
| 170 | C2×Q16 | — | 67 | 24 | no | — |
| 171 | C2×Q16 | — | 134 | 48 | no | — |
| 172 | C2×SD16 | — | 67 | 24 | no | — |
| 173 | C2×D8 | — | 67 | 4 | no | — |
| 174 | #131 | D268 | 1 | 16 | yes | complemented |
| 175 | C2×M16 | C22×D67 | 1 | 6 | yes | — |
| 176 | C22×C8 | C22×D67 | 1 | 6 | yes | — |
| 177 | C4⋊Q8 | — | 67 | 6 | no | — |
| 178 | C4⋊Q8 | — | 67 | 12 | no | — |
| 179 | C4⋊Q8 | — | 134 | 12 | no | — |
| 180 | #127 | — | 67 | 2 | no | — |
| 181 | #124 | — | 67 | 12 | no | — |
| 182 | #123 | — | 134 | 24 | no | — |
| 183 | C22⋊Q8 | — | 134 | 24 | no | — |
| 184 | #121 | — | 134 | 12 | no | — |
| 185 | C4×Q8 | D268 | 1 | 2 | yes | — |
| 186 | C4×D4 | — | 134 | 12 | no | — |
| 187 | C4×D4 | D268 | 1 | 6 | yes | — |
| 188 | #117 | C22×D67 | 1 | 3 | yes | — |
| 189 | C2×C4⋊C4 | — | 134 | 12 | no | — |
| 190 | C2×C42 | C22×D67 | 1 | 3 | yes | — |
| 191 | #97 | C22×D67 | 1 | 6 | yes | — |
| 192 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 193 | C4×C8 | C22×D67 | 1 | 3 | yes | — |
| 194 | C4×C8 | C22×D67 | 1 | 6 | yes | — |
| 195 | #41 | — | 268 | 48 | no | — |
| 196 | #41 | — | 134 | 48 | no | — |
| 197 | #41 | C2×D268 | 1 | 8 | yes | — |
| 198 | C2×Q8 | — | 268 | 16 | no | — |
| 199 | C2×Q8 | — | 67 | 12 | no | — |
| 200 | C2×Q8 | — | 134 | 48 | no | — |
| 201 | C2×Q8 | — | 134 | 12 | no | — |
| 202 | C2×Q8 | C2×D268 | 1 | 1 | yes | characteristic |
| 203 | C2×D4 | — | 67 | 4 | no | — |
| 204 | C2×D4 | — | 134 | 12 | no | — |
| 205 | C2×D4 | — | 134 | 4 | no | — |
| 206 | C2×D4 | C2×D268 | 1 | 3 | yes | — |
| 207 | C22×C4 | — | 134 | 12 | no | — |
| 208 | C22×C4 | — | 134 | 12 | no | — |
| 209 | C22×C4 | C2×D268 | 1 | 6 | yes | — |
| 210 | C22×C4 | C23×D67 | 1 | 3 | yes | — |
| 211 | Q16 | — | 134 | 24 | no | — |
| 212 | Q16 | — | 134 | 48 | no | — |
| 213 | SD16 | — | 134 | 48 | no | — |
| 214 | D8 | — | 134 | 8 | no | — |
| 215 | M16 | C2×D268 | 1 | 24 | yes | — |
| 216 | C2×C8 | C2×D268 | 1 | 24 | yes | — |
| 217 | C2×C8 | C23×D67 | 1 | 2 | yes | — |
| 218 | C2×C8 | C23×D67 | 1 | 6 | yes | — |
| 219 | C4⋊C4 | — | 134 | 12 | no | — |
| 220 | C4⋊C4 | — | 134 | 24 | no | — |
| 221 | C4⋊C4 | C2×D268 | 1 | 6 | yes | — |
| 222 | C22⋊C4 | — | 134 | 24 | no | — |
| 223 | C22⋊C4 | C2×D268 | 1 | 6 | yes | — |
| 224 | C42 | C2×D268 | 1 | 6 | yes | — |
| 225 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 226 | C42 | C23×D67 | 1 | 3 | yes | — |
| 227 | C23 | — | 134 | 4 | no | — |
| 228 | C23 | C22×D268 | 1 | 3 | yes | — |
| 229 | Q8 | — | 268 | 24 | no | — |
| 230 | Q8 | — | 134 | 24 | no | — |
| 231 | Q8 | #14524040 | 1 | 4 | yes | — |
| 232 | D4 | — | 268 | 24 | no | — |
| 233 | D4 | — | 268 | 8 | no | — |
| 234 | D4 | — | 134 | 8 | no | — |
| 235 | D4 | #14524040 | 1 | 12 | yes | — |
| 236 | C2×C4 | — | 2 | 12 | no | — |
| 237 | C2×C4 | — | 268 | 24 | no | — |
| 238 | C2×C4 | — | 268 | 24 | no | — |
| 239 | C2×C4 | — | 134 | 12 | no | — |
| 240 | C2×C4 | C22×D268 | 1 | 6 | yes | — |
| 241 | C2×C4 | C22×D268 | 1 | 3 | yes | — |
| 242 | C2×C4 | C22×D268 | 1 | 12 | yes | — |
| 243 | C2×C4 | C22×D268 | 1 | 2 | yes | — |
| 244 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 245 | C8 | C22×D268 | 1 | 4 | yes | — |
| 246 | C8 | C22×D268 | 1 | 12 | yes | — |
| 247 | C22 | — | 2 | 6 | no | — |
| 248 | C22 | — | 268 | 8 | no | — |
| 249 | C22 | — | 268 | 4 | no | — |
| 250 | C22 | C2×#14524040 | 1 | 6 | yes | — |
| 251 | C22 | C23×D268 | 1 | 1 | yes | characteristic |
| 252 | C4 | — | 2 | 6 | no | — |
| 253 | C4 | — | 268 | 12 | no | — |
| 254 | C4 | C2×#14524040 | 1 | 6 | yes | — |
| 255 | C4 | #16864213 | 1 | 4 | yes | complemented |
| 256 | C4 | C23×D268 | 1 | 2 | yes | — |
| 257 | C2 | — | 2 | 6 | no | — |
| 258 | C2 | — | 536 | 4 | no | — |
| 259 | C2 | C22×#14524040 | 1 | 1 | yes | characteristic |
| 260 | C2 | C2×#16864213 | 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