← #17187708
Subgroups — #17187708
Order 4352.
674 conjugacy classes of subgroups.
The subgroup lattice has 264 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11763241 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14537658 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #14530647 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #14530642 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #14530630 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #14530494 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #14530380 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C17×#366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#10587590 | C22 | 1 | 2 | yes | — |
| 10 | #11763290 | — | 2 | 2 | no | — |
| 11 | #11763241 | C4 | 1 | 8 | yes | complemented |
| 12 | C2×Dic136 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#10587471 | C22 | 1 | 2 | yes | — |
| 14 | C2×D272 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#10587483 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11762908 | — | 2 | 4 | no | — |
| 17 | #11762903 | C22 | 1 | 4 | yes | — |
| 18 | #11762891 | C22 | 1 | 4 | yes | — |
| 19 | #11762808 | — | 2 | 2 | no | — |
| 20 | #11762764 | C22 | 1 | 1 | yes | characteristic |
| 21 | #11762612 | C22 | 1 | 4 | yes | — |
| 22 | #11762609 | C22 | 1 | 4 | yes | — |
| 23 | #11762584 | C22 | 1 | 2 | yes | — |
| 24 | C16×Dic17 | C22 | 1 | 2 | yes | — |
| 25 | C22×C16×C17 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C17×#107 | C22 | 1 | 2 | yes | — |
| 27 | C17×#366 | C22 | 1 | 2 | yes | — |
| 28 | C17×#366 | C22 | 1 | 2 | yes | — |
| 29 | C2×#63252 | — | 2 | 2 | no | — |
| 30 | C22×C8×C17 | C23 | 1 | 1 | yes | characteristic |
| 31 | C2×C4⋊C4×C17 | — | 2 | 2 | no | — |
| 32 | C4×C22⋊D17 | — | 4 | 4 | no | — |
| 33 | #10587612 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×#63223 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×Dic68 | C23 | 1 | 2 | yes | — |
| 36 | #10587590 | — | 2 | 4 | no | — |
| 37 | #10587590 | C2×C4 | 1 | 8 | yes | complemented |
| 38 | C2×D136 | C23 | 1 | 2 | yes | — |
| 39 | C2×#63219 | — | 2 | 2 | no | — |
| 40 | #10587579 | — | 2 | 4 | no | — |
| 41 | #10587578 | — | 4 | 2 | no | — |
| 42 | C4⋊C4×D17 | — | 4 | 2 | no | — |
| 43 | #10587573 | — | 2 | 4 | no | — |
| 44 | C2×C16×C17 | C2×C4 | 1 | 4 | yes | complemented |
| 45 | C2×C16×C17 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C16×C17 | C23 | 1 | 1 | yes | characteristic |
| 47 | C17×#107 | — | 2 | 2 | no | — |
| 48 | C17×#107 | C23 | 1 | 4 | yes | — |
| 49 | #10587486 | D4 | 1 | 2 | yes | — |
| 50 | C8×Dic17 | C23 | 1 | 2 | yes | — |
| 51 | #10587483 | — | 2 | 2 | no | — |
| 52 | C2×#63214 | C23 | 1 | 2 | yes | — |
| 53 | #10587481 | — | 2 | 4 | no | — |
| 54 | #10587480 | — | 2 | 4 | no | — |
| 55 | Dic136 | C2×C4 | 1 | 4 | yes | complemented |
| 56 | #10587471 | C2×C4 | 1 | 8 | yes | complemented |
| 57 | D272 | C2×C4 | 1 | 4 | yes | complemented |
| 58 | C22×C4×C17 | — | 4 | 2 | no | — |
| 59 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C22⋊D17 | — | 4 | 2 | no | — |
| 61 | #63252 | — | 2 | 8 | no | — |
| 62 | #63252 | — | 4 | 4 | no | — |
| 63 | C2×D68 | — | 2 | 2 | no | — |
| 64 | C2×C4×D17 | — | 4 | 2 | no | — |
| 65 | C2×C4×D17 | — | 4 | 4 | no | — |
| 66 | C2×Dic34 | — | 2 | 2 | no | — |
| 67 | C2×C8×C17 | C22×C4 | 1 | 2 | yes | — |
| 68 | C2×C8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C2×C8×C17 | #41 | 1 | 2 | yes | — |
| 70 | C2×C8×C17 | C24 | 1 | 1 | yes | characteristic |
| 71 | C4⋊C4×C17 | — | 2 | 4 | no | — |
| 72 | C4⋊C4×C17 | — | 4 | 2 | no | — |
| 73 | C22⋊Dic17 | D8 | 1 | 2 | yes | — |
| 74 | #63227 | — | 4 | 4 | no | — |
| 75 | C4⋊Dic17 | D8 | 1 | 1 | yes | characteristic |
| 76 | C4⋊Dic17 | D8 | 1 | 1 | yes | characteristic |
| 77 | #63225 | — | 4 | 4 | no | — |
| 78 | C4×Dic17 | — | 4 | 4 | no | — |
| 79 | C4×Dic17 | C2×D4 | 1 | 2 | yes | — |
| 80 | #63223 | — | 2 | 2 | no | — |
| 81 | C2×#3622 | C2×D4 | 1 | 2 | yes | — |
| 82 | Dic68 | — | 2 | 2 | no | — |
| 83 | Dic68 | C22×C4 | 1 | 4 | yes | — |
| 84 | D136 | — | 2 | 2 | no | — |
| 85 | D136 | C22×C4 | 1 | 4 | yes | — |
| 86 | #63219 | — | 2 | 8 | no | — |
| 87 | C16×C17 | C22×C4 | 1 | 2 | yes | — |
| 88 | C16×C17 | C22×C4 | 1 | 2 | yes | — |
| 89 | #63214 | — | 2 | 2 | no | — |
| 90 | #33459 | — | 17 | 1 | no | maximal, Sylow |
| 91 | C23×C17 | C2×D8 | 1 | 1 | yes | characteristic |
| 92 | C22×D17 | — | 4 | 2 | no | — |
| 93 | C2×C4×C17 | — | 4 | 4 | no | — |
| 94 | C2×C4×C17 | — | 16 | 2 | no | — |
| 95 | C2×C4×C17 | C4×D4 | 1 | 2 | yes | — |
| 96 | C2×C4×C17 | C2×D8 | 1 | 1 | yes | characteristic |
| 97 | C2×C4×C17 | #135 | 1 | 2 | yes | — |
| 98 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 99 | C22⋊D17 | — | 4 | 8 | no | — |
| 100 | C2×Dic17 | — | 4 | 2 | no | — |
| 101 | C2×Dic17 | C2×D8 | 1 | 2 | yes | — |
| 102 | C2×Dic17 | C2×D8 | 1 | 2 | yes | — |
| 103 | D68 | — | 2 | 4 | no | — |
| 104 | D68 | — | 4 | 2 | no | — |
| 105 | C4×D17 | — | 4 | 8 | no | — |
| 106 | C4×D17 | — | 16 | 4 | no | — |
| 107 | Dic34 | — | 2 | 4 | no | — |
| 108 | Dic34 | — | 4 | 2 | no | — |
| 109 | C8×C17 | C4×D4 | 1 | 2 | yes | — |
| 110 | C8×C17 | C23×C4 | 1 | 1 | yes | characteristic |
| 111 | C8×C17 | C2×#41 | 1 | 1 | yes | characteristic |
| 112 | #3622 | — | 2 | 2 | no | — |
| 113 | C2×#508 | — | 17 | 1 | no | — |
| 114 | #2951 | — | 17 | 2 | no | — |
| 115 | #2175 | — | 17 | 4 | no | — |
| 116 | C4×Q32 | — | 17 | 2 | no | — |
| 117 | C4×D16 | — | 17 | 2 | no | — |
| 118 | C2×#366 | D17 | 1 | 1 | yes | characteristic, complemented |
| 119 | #2139 | — | 17 | 2 | no | — |
| 120 | #2108 | — | 17 | 1 | no | — |
| 121 | C22×C17 | — | 2 | 1 | no | — |
| 122 | C22×C17 | — | 2 | 1 | no | — |
| 123 | C22×C17 | C4×D8 | 1 | 2 | yes | — |
| 124 | C22×C17 | C22×D8 | 1 | 1 | yes | characteristic |
| 125 | C2×D17 | — | 4 | 4 | no | — |
| 126 | C2×D17 | — | 8 | 2 | no | — |
| 127 | C2×D17 | — | 8 | 2 | no | — |
| 128 | C4×C17 | — | 8 | 4 | no | — |
| 129 | C4×C17 | C4×D8 | 1 | 2 | yes | — |
| 130 | C4×C17 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 131 | C4×C17 | C2×#135 | 1 | 1 | yes | characteristic |
| 132 | Dic17 | — | 2 | 2 | no | — |
| 133 | Dic17 | — | 2 | 2 | no | — |
| 134 | Dic17 | — | 4 | 4 | no | — |
| 135 | C2×#135 | — | 17 | 2 | no | — |
| 136 | #520 | — | 34 | 2 | no | — |
| 137 | #508 | — | 17 | 8 | no | — |
| 138 | C2×Q32 | — | 17 | 1 | no | — |
| 139 | C2×SD32 | — | 17 | 2 | no | — |
| 140 | C2×D16 | — | 17 | 1 | no | — |
| 141 | C2×M32 | — | 17 | 1 | no | — |
| 142 | C22×C16 | C2×D17 | 1 | 1 | yes | characteristic |
| 143 | #440 | — | 34 | 4 | no | — |
| 144 | C4×Q16 | — | 17 | 4 | no | — |
| 145 | C4×D8 | — | 17 | 4 | no | — |
| 146 | C2×#107 | C2×D17 | 1 | 2 | yes | — |
| 147 | #417 | — | 34 | 2 | no | — |
| 148 | #405 | — | 17 | 1 | no | — |
| 149 | #366 | C2×D17 | 1 | 2 | yes | — |
| 150 | #366 | C2×D17 | 1 | 2 | yes | — |
| 151 | #358 | — | 17 | 4 | no | — |
| 152 | #357 | — | 17 | 4 | no | — |
| 153 | #346 | — | 17 | 2 | no | — |
| 154 | C4×C16 | — | 17 | 2 | no | — |
| 155 | C2×C17 | — | 2 | 2 | no | — |
| 156 | C2×C17 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 157 | C2×C17 | #3415 | 1 | 1 | yes | characteristic |
| 158 | C2×C17 | #3417 | 1 | 1 | yes | characteristic |
| 159 | D17 | — | 8 | 4 | no | — |
| 160 | C2×#41 | — | 34 | 2 | no | — |
| 161 | #135 | — | 17 | 8 | no | — |
| 162 | #135 | — | 34 | 4 | no | — |
| 163 | C2×Q16 | — | 17 | 2 | no | — |
| 164 | C2×SD16 | — | 34 | 2 | no | — |
| 165 | C2×D8 | — | 17 | 2 | no | — |
| 166 | C2×M16 | — | 17 | 1 | no | — |
| 167 | C22×C8 | C22×D17 | 1 | 1 | yes | characteristic |
| 168 | C4×Q8 | — | 34 | 4 | no | — |
| 169 | C4×D4 | — | 34 | 4 | no | — |
| 170 | C4×D4 | — | 68 | 4 | no | — |
| 171 | #117 | — | 17 | 1 | no | — |
| 172 | #117 | — | 68 | 2 | no | — |
| 173 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 174 | C2×C4⋊C4 | — | 68 | 2 | no | — |
| 175 | Q32 | — | 17 | 4 | no | — |
| 176 | SD32 | — | 17 | 8 | no | — |
| 177 | D16 | — | 17 | 4 | no | — |
| 178 | M32 | — | 34 | 2 | no | — |
| 179 | C2×C16 | — | 17 | 2 | no | — |
| 180 | C2×C16 | C4×D17 | 1 | 4 | yes | complemented |
| 181 | C2×C16 | C22×D17 | 1 | 1 | yes | characteristic |
| 182 | C2×C16 | C22×D17 | 1 | 1 | yes | characteristic |
| 183 | #107 | — | 2 | 2 | no | — |
| 184 | #107 | C22×D17 | 1 | 4 | yes | — |
| 185 | #103 | — | 34 | 4 | no | — |
| 186 | #102 | — | 34 | 4 | no | — |
| 187 | #97 | — | 17 | 2 | no | — |
| 188 | C4×C8 | — | 17 | 2 | no | — |
| 189 | C17 | #33459 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 190 | #41 | — | 34 | 8 | no | — |
| 191 | #41 | — | 68 | 4 | no | — |
| 192 | C2×Q8 | — | 34 | 2 | no | — |
| 193 | C2×D4 | — | 34 | 2 | no | — |
| 194 | C2×D4 | — | 68 | 2 | no | — |
| 195 | C22×C4 | — | 4 | 2 | no | — |
| 196 | C22×C4 | — | 68 | 4 | no | — |
| 197 | C22×C4 | — | 68 | 2 | no | — |
| 198 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 199 | Q16 | — | 17 | 4 | no | — |
| 200 | Q16 | — | 34 | 2 | no | — |
| 201 | SD16 | — | 34 | 8 | no | — |
| 202 | D8 | — | 17 | 4 | no | — |
| 203 | D8 | — | 34 | 2 | no | — |
| 204 | M16 | — | 34 | 2 | no | — |
| 205 | C2×C8 | — | 17 | 2 | no | — |
| 206 | C2×C8 | C2×C4×D17 | 1 | 2 | yes | — |
| 207 | C2×C8 | D4×D17 | 1 | 1 | yes | characteristic |
| 208 | C2×C8 | #63256 | 1 | 2 | yes | — |
| 209 | C2×C8 | C23×D17 | 1 | 1 | yes | characteristic |
| 210 | C4⋊C4 | — | 2 | 4 | no | — |
| 211 | C4⋊C4 | — | 4 | 2 | no | — |
| 212 | C4⋊C4 | — | 17 | 1 | no | — |
| 213 | C4⋊C4 | — | 17 | 1 | no | — |
| 214 | C4⋊C4 | — | 68 | 4 | no | — |
| 215 | C22⋊C4 | — | 17 | 2 | no | — |
| 216 | C22⋊C4 | — | 68 | 4 | no | — |
| 217 | C42 | — | 17 | 2 | no | — |
| 218 | C42 | — | 68 | 4 | no | — |
| 219 | C16 | — | 34 | 2 | no | — |
| 220 | C16 | C2×C4×D17 | 1 | 2 | yes | — |
| 221 | C16 | C2×C4×D17 | 1 | 2 | yes | — |
| 222 | C23 | — | 68 | 2 | no | — |
| 223 | C23 | D8×D17 | 1 | 1 | yes | characteristic |
| 224 | Q8 | — | 34 | 4 | no | — |
| 225 | Q8 | — | 68 | 2 | no | — |
| 226 | D4 | — | 34 | 4 | no | — |
| 227 | D4 | — | 68 | 8 | no | — |
| 228 | D4 | — | 68 | 2 | no | — |
| 229 | C2×C4 | — | 4 | 4 | no | — |
| 230 | C2×C4 | — | 16 | 2 | no | — |
| 231 | C2×C4 | — | 272 | 4 | no | — |
| 232 | C2×C4 | — | 17 | 2 | no | — |
| 233 | C2×C4 | — | 17 | 2 | no | — |
| 234 | C2×C4 | — | 68 | 2 | no | — |
| 235 | C2×C4 | — | 68 | 8 | no | — |
| 236 | C2×C4 | #10587579 | 1 | 2 | yes | — |
| 237 | C2×C4 | D8×D17 | 1 | 1 | yes | characteristic |
| 238 | C2×C4 | #10587605 | 1 | 2 | yes | — |
| 239 | C2×C4 | C2×D4×D17 | 1 | 1 | yes | characteristic |
| 240 | C8 | — | 34 | 2 | no | — |
| 241 | C8 | #10587579 | 1 | 2 | yes | — |
| 242 | C8 | C22×C4×D17 | 1 | 1 | yes | characteristic |
| 243 | C8 | C2×#63256 | 1 | 1 | yes | characteristic |
| 244 | C22 | — | 2 | 1 | no | — |
| 245 | C22 | — | 2 | 1 | no | — |
| 246 | C22 | — | 68 | 4 | no | — |
| 247 | C22 | — | 136 | 2 | no | — |
| 248 | C22 | — | 136 | 2 | no | — |
| 249 | C22 | #11762891 | 1 | 2 | yes | — |
| 250 | C22 | C2×D8×D17 | 1 | 1 | yes | characteristic |
| 251 | C4 | — | 8 | 4 | no | — |
| 252 | C4 | — | 34 | 2 | no | — |
| 253 | C4 | — | 34 | 2 | no | — |
| 254 | C4 | — | 68 | 4 | no | — |
| 255 | C4 | #11762891 | 1 | 2 | yes | — |
| 256 | C4 | C2×#10587579 | 1 | 1 | yes | characteristic |
| 257 | C4 | C2×#10587605 | 1 | 1 | yes | characteristic |
| 258 | C2 | — | 2 | 2 | no | — |
| 259 | C2 | — | 136 | 4 | no | — |
| 260 | C2 | C2×#11762891 | 1 | 1 | yes | characteristic |
| 261 | C2 | #14541921 | 1 | 1 | yes | characteristic |
| 262 | C2 | #14541933 | 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