← #17023130
Subgroups — #17023130
Order 4352.
704 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #14539916 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14539740 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #14539370 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14528460 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #14528457 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #14528443 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #14528422 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #14527076 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C17×#3169 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11763366 | C22 | 1 | 2 | yes | — |
| 11 | #11763214 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11763212 | C22 | 1 | 2 | yes | — |
| 13 | #11763205 | C22 | 1 | 2 | yes | — |
| 14 | #11763189 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11763188 | C22 | 1 | 2 | yes | — |
| 16 | #11763181 | C22 | 1 | 2 | yes | — |
| 17 | #11763160 | C22 | 1 | 2 | yes | — |
| 18 | #11763159 | C22 | 1 | 2 | yes | — |
| 19 | #11763155 | C22 | 1 | 2 | yes | — |
| 20 | #11763155 | C22 | 1 | 2 | yes | — |
| 21 | #11763155 | C22 | 1 | 2 | yes | — |
| 22 | #11763130 | — | 2 | 4 | no | — |
| 23 | #11763109 | — | 2 | 4 | no | — |
| 24 | #11763050 | — | 2 | 2 | no | — |
| 25 | #11763028 | — | 2 | 4 | no | — |
| 26 | #11762971 | — | 2 | 4 | no | — |
| 27 | C4×Dic68 | — | 2 | 2 | no | — |
| 28 | #11762862 | C22 | 1 | 1 | yes | characteristic |
| 29 | #11762862 | C22 | 1 | 1 | yes | characteristic |
| 30 | #11762531 | C22 | 1 | 2 | yes | — |
| 31 | #11762531 | C22 | 1 | 2 | yes | — |
| 32 | C17×#532 | C22 | 1 | 2 | yes | — |
| 33 | C17×#500 | C22 | 1 | 1 | yes | characteristic |
| 34 | C17×#493 | C22 | 1 | 1 | yes | characteristic |
| 35 | C17×#486 | C22 | 1 | 2 | yes | — |
| 36 | C17×#466 | — | 2 | 2 | no | — |
| 37 | C4×D8×C17 | — | 2 | 2 | no | — |
| 38 | C2×C4×C8×C17 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#41×C17 | — | 2 | 2 | no | — |
| 40 | C2×D8×C17 | — | 2 | 2 | no | — |
| 41 | C22×C8×C17 | D4 | 1 | 2 | yes | — |
| 42 | C17×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 43 | C17×#127 | C23 | 1 | 2 | yes | — |
| 44 | C17×#124 | — | 2 | 2 | no | — |
| 45 | C17×#121 | — | 2 | 2 | no | — |
| 46 | C17×#121 | — | 2 | 2 | no | — |
| 47 | C4×D4×C17 | — | 2 | 2 | no | — |
| 48 | C4×D4×C17 | — | 2 | 2 | no | — |
| 49 | C2×C42×C17 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×#63231 | — | 2 | 4 | no | — |
| 51 | C2×#63229 | — | 2 | 4 | no | — |
| 52 | #10587612 | — | 2 | 2 | no | — |
| 53 | #10587610 | — | 2 | 2 | no | — |
| 54 | #10587610 | — | 2 | 2 | no | — |
| 55 | C2×Dic68 | — | 2 | 2 | no | — |
| 56 | #10587556 | — | 2 | 2 | no | — |
| 57 | #10587555 | C23 | 1 | 2 | yes | — |
| 58 | #10587555 | C23 | 1 | 2 | yes | — |
| 59 | C4×Dic34 | — | 2 | 2 | no | — |
| 60 | C4×Dic34 | — | 2 | 2 | no | — |
| 61 | C17×#107 | — | 2 | 2 | no | — |
| 62 | C17×#102 | — | 2 | 4 | no | — |
| 63 | C4×C8×C17 | D4 | 1 | 2 | yes | — |
| 64 | C4×C8×C17 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4×C8×C17 | C23 | 1 | 1 | yes | characteristic |
| 66 | #10587506 | — | 2 | 4 | no | — |
| 67 | #10587503 | — | 2 | 4 | no | — |
| 68 | #10587503 | — | 2 | 4 | no | — |
| 69 | #10587503 | — | 2 | 4 | no | — |
| 70 | C22⋊#3622 | D4 | 1 | 2 | yes | — |
| 71 | C22⋊#3622 | D4 | 1 | 2 | yes | — |
| 72 | #10587489 | — | 2 | 2 | no | — |
| 73 | #10587487 | — | 2 | 4 | no | — |
| 74 | #10587479 | — | 2 | 4 | no | — |
| 75 | #10587478 | — | 2 | 4 | no | — |
| 76 | C4⋊#3622 | D4 | 1 | 2 | yes | — |
| 77 | C4⋊#3622 | D4 | 1 | 2 | yes | — |
| 78 | C4×#3622 | C23 | 1 | 2 | yes | — |
| 79 | C4×#3622 | C23 | 1 | 2 | yes | — |
| 80 | #41×C17 | — | 8 | 4 | no | — |
| 81 | C2×Q8×C17 | — | 2 | 2 | no | — |
| 82 | C2×D4×C17 | — | 2 | 2 | no | — |
| 83 | C2×D4×C17 | — | 2 | 2 | no | — |
| 84 | C2×D4×C17 | — | 2 | 2 | no | — |
| 85 | C2×D4×C17 | — | 4 | 2 | no | — |
| 86 | C22×C4×C17 | — | 4 | 2 | no | — |
| 87 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C2×Dic34 | — | 2 | 2 | no | — |
| 91 | C2×Dic34 | — | 2 | 2 | no | — |
| 92 | D8×C17 | — | 4 | 4 | no | — |
| 93 | C2×C8×C17 | — | 4 | 2 | no | — |
| 94 | C2×C8×C17 | C2×D4 | 1 | 2 | yes | — |
| 95 | C2×C8×C17 | C2×D4 | 1 | 2 | yes | — |
| 96 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 97 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 98 | C22⋊C4×C17 | — | 4 | 2 | no | — |
| 99 | C22⋊C4×C17 | — | 4 | 2 | no | — |
| 100 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C42×C17 | C24 | 1 | 1 | yes | characteristic |
| 104 | C22⋊Dic17 | — | 4 | 2 | no | — |
| 105 | #63231 | — | 8 | 4 | no | — |
| 106 | #63229 | — | 8 | 4 | no | — |
| 107 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 108 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 109 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 110 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 111 | #63225 | — | 4 | 2 | no | — |
| 112 | #63225 | — | 4 | 2 | no | — |
| 113 | C4×Dic17 | — | 4 | 2 | no | — |
| 114 | C2×#3622 | C2×D4 | 1 | 4 | yes | — |
| 115 | C2×#3622 | C2×D4 | 1 | 4 | yes | — |
| 116 | Dic68 | — | 4 | 4 | no | — |
| 117 | #19712 | — | 17 | 1 | no | maximal, Sylow |
| 118 | C23×C17 | — | 4 | 2 | no | — |
| 119 | C23×C17 | #127 | 1 | 1 | yes | characteristic |
| 120 | Q8×C17 | — | 4 | 4 | no | — |
| 121 | D4×C17 | — | 4 | 4 | no | — |
| 122 | D4×C17 | — | 4 | 4 | no | — |
| 123 | D4×C17 | — | 4 | 4 | no | — |
| 124 | D4×C17 | — | 8 | 4 | no | — |
| 125 | C2×C4×C17 | — | 2 | 2 | no | — |
| 126 | C2×C4×C17 | — | 2 | 2 | no | — |
| 127 | C2×C4×C17 | — | 2 | 2 | no | — |
| 128 | C2×C4×C17 | — | 4 | 2 | no | — |
| 129 | C2×C4×C17 | — | 8 | 4 | no | — |
| 130 | C2×C4×C17 | #127 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C17 | #127 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C17 | #127 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×Dic17 | — | 4 | 2 | no | — |
| 137 | C2×Dic17 | — | 4 | 2 | no | — |
| 138 | Dic34 | — | 4 | 4 | no | — |
| 139 | Dic34 | — | 4 | 4 | no | — |
| 140 | C8×C17 | — | 2 | 2 | no | — |
| 141 | C8×C17 | — | 2 | 2 | no | — |
| 142 | #3622 | — | 2 | 4 | no | — |
| 143 | #3622 | — | 2 | 4 | no | — |
| 144 | #3228 | — | 17 | 2 | no | — |
| 145 | #3210 | — | 17 | 2 | no | — |
| 146 | #3170 | — | 17 | 1 | no | — |
| 147 | #3169 | D17 | 1 | 1 | yes | characteristic |
| 148 | #1723 | — | 17 | 2 | no | — |
| 149 | #1722 | — | 17 | 2 | no | — |
| 150 | #1720 | — | 17 | 2 | no | — |
| 151 | #1717 | — | 17 | 2 | no | — |
| 152 | #1452 | — | 17 | 1 | no | — |
| 153 | C22×C17 | — | 2 | 1 | no | — |
| 154 | C22×C17 | — | 2 | 1 | no | — |
| 155 | C22×C17 | — | 2 | 1 | no | — |
| 156 | C22×C17 | — | 8 | 2 | no | — |
| 157 | C22×C17 | — | 8 | 2 | no | — |
| 158 | C22×C17 | — | 8 | 2 | no | — |
| 159 | C22×C17 | C2×#127 | 1 | 1 | yes | characteristic |
| 160 | C4×C17 | — | 2 | 1 | no | — |
| 161 | C4×C17 | — | 2 | 1 | no | — |
| 162 | C4×C17 | — | 2 | 1 | no | — |
| 163 | C4×C17 | — | 8 | 2 | no | — |
| 164 | C4×C17 | #575 | 1 | 2 | yes | — |
| 165 | C4×C17 | #576 | 1 | 2 | yes | — |
| 166 | C4×C17 | #578 | 1 | 2 | yes | — |
| 167 | Dic17 | — | 8 | 2 | no | — |
| 168 | Dic17 | — | 8 | 2 | no | — |
| 169 | #533 | — | 17 | 2 | no | — |
| 170 | #532 | C2×D17 | 1 | 2 | yes | — |
| 171 | #500 | — | 17 | 2 | no | — |
| 172 | #500 | — | 17 | 1 | no | — |
| 173 | #500 | C2×D17 | 1 | 1 | yes | characteristic |
| 174 | #498 | — | 17 | 2 | no | — |
| 175 | #494 | — | 17 | 2 | no | — |
| 176 | #494 | — | 17 | 1 | no | — |
| 177 | #493 | C2×D17 | 1 | 1 | yes | characteristic |
| 178 | #492 | — | 17 | 2 | no | — |
| 179 | #487 | — | 17 | 2 | no | — |
| 180 | #487 | — | 17 | 2 | no | — |
| 181 | #486 | — | 17 | 2 | no | — |
| 182 | #486 | — | 17 | 2 | no | — |
| 183 | #486 | — | 17 | 2 | no | — |
| 184 | #486 | C2×D17 | 1 | 2 | yes | — |
| 185 | #482 | — | 34 | 4 | no | — |
| 186 | #478 | — | 34 | 4 | no | — |
| 187 | #467 | — | 34 | 2 | no | — |
| 188 | #466 | — | 2 | 2 | no | — |
| 189 | #464 | — | 34 | 4 | no | — |
| 190 | #452 | — | 34 | 4 | no | — |
| 191 | C4×Q16 | — | 34 | 2 | no | — |
| 192 | C4×D8 | — | 2 | 2 | no | — |
| 193 | #431 | — | 17 | 1 | no | — |
| 194 | #431 | — | 17 | 1 | no | — |
| 195 | C2×C4×C8 | C2×D17 | 1 | 1 | yes | characteristic |
| 196 | #322 | — | 17 | 2 | no | — |
| 197 | #322 | — | 17 | 2 | no | — |
| 198 | C2×C17 | — | 4 | 1 | no | — |
| 199 | C2×C17 | — | 16 | 2 | no | — |
| 200 | C2×C17 | #3150 | 1 | 1 | yes | characteristic |
| 201 | C2×C17 | #3155 | 1 | 1 | yes | characteristic |
| 202 | C2×C17 | #3156 | 1 | 1 | yes | characteristic |
| 203 | C2×#41 | — | 2 | 2 | no | — |
| 204 | C2×Q16 | — | 34 | 4 | no | — |
| 205 | C2×Q16 | — | 34 | 2 | no | — |
| 206 | C2×SD16 | — | 34 | 4 | no | — |
| 207 | C2×D8 | — | 2 | 2 | no | — |
| 208 | C22×C8 | C22⋊D17 | 1 | 2 | yes | — |
| 209 | C4⋊Q8 | — | 17 | 2 | no | — |
| 210 | C4⋊Q8 | — | 17 | 2 | no | — |
| 211 | C4⋊Q8 | C22×D17 | 1 | 2 | yes | — |
| 212 | #127 | C22×D17 | 1 | 2 | yes | — |
| 213 | #125 | — | 34 | 2 | no | — |
| 214 | #124 | — | 2 | 2 | no | — |
| 215 | C22⋊Q8 | — | 34 | 2 | no | — |
| 216 | C22⋊Q8 | — | 34 | 2 | no | — |
| 217 | #121 | — | 2 | 2 | no | — |
| 218 | #121 | — | 2 | 2 | no | — |
| 219 | C4×Q8 | — | 34 | 2 | no | — |
| 220 | C4×Q8 | — | 34 | 2 | no | — |
| 221 | C4×D4 | — | 2 | 2 | no | — |
| 222 | C4×D4 | — | 2 | 2 | no | — |
| 223 | #117 | — | 34 | 2 | no | — |
| 224 | C2×C42 | C22×D17 | 1 | 1 | yes | characteristic |
| 225 | #107 | — | 2 | 2 | no | — |
| 226 | #107 | — | 34 | 4 | no | — |
| 227 | #107 | — | 34 | 2 | no | — |
| 228 | #106 | — | 34 | 4 | no | — |
| 229 | C4⋊C8 | — | 17 | 2 | no | — |
| 230 | C4⋊C8 | — | 17 | 2 | no | — |
| 231 | #103 | — | 34 | 4 | no | — |
| 232 | #103 | — | 34 | 4 | no | — |
| 233 | #102 | — | 2 | 4 | no | — |
| 234 | #102 | — | 34 | 4 | no | — |
| 235 | #102 | — | 34 | 4 | no | — |
| 236 | #102 | — | 34 | 4 | no | — |
| 237 | C22⋊C8 | — | 17 | 2 | no | — |
| 238 | C22⋊C8 | — | 17 | 2 | no | — |
| 239 | C4×C8 | — | 17 | 2 | no | — |
| 240 | C4×C8 | — | 17 | 2 | no | — |
| 241 | C4×C8 | C22⋊D17 | 1 | 2 | yes | — |
| 242 | C4×C8 | C22×D17 | 1 | 1 | yes | characteristic |
| 243 | C4×C8 | C22×D17 | 1 | 1 | yes | characteristic |
| 244 | C17 | #19712 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 245 | #41 | — | 8 | 4 | no | — |
| 246 | C2×Q8 | — | 2 | 2 | no | — |
| 247 | C2×Q8 | — | 34 | 2 | no | — |
| 248 | C2×Q8 | — | 34 | 2 | no | — |
| 249 | C2×D4 | — | 2 | 2 | no | — |
| 250 | C2×D4 | — | 2 | 2 | no | — |
| 251 | C2×D4 | — | 2 | 2 | no | — |
| 252 | C2×D4 | — | 4 | 2 | no | — |
| 253 | C22×C4 | — | 4 | 2 | no | — |
| 254 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 255 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 256 | C22×C4 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 257 | Q16 | — | 68 | 4 | no | — |
| 258 | Q16 | — | 136 | 4 | no | — |
| 259 | SD16 | — | 136 | 4 | no | — |
| 260 | D8 | — | 4 | 4 | no | — |
| 261 | C2×C8 | — | 4 | 2 | no | — |
| 262 | C2×C8 | — | 17 | 4 | no | — |
| 263 | C2×C8 | — | 17 | 4 | no | — |
| 264 | C2×C8 | C2×C22⋊D17 | 1 | 2 | yes | — |
| 265 | C2×C8 | C2×C22⋊D17 | 1 | 2 | yes | — |
| 266 | C4⋊C4 | — | 2 | 2 | no | — |
| 267 | C4⋊C4 | — | 2 | 2 | no | — |
| 268 | C4⋊C4 | — | 34 | 2 | no | — |
| 269 | C4⋊C4 | — | 34 | 2 | no | — |
| 270 | C4⋊C4 | — | 34 | 2 | no | — |
| 271 | C4⋊C4 | — | 34 | 2 | no | — |
| 272 | C4⋊C4 | — | 68 | 2 | no | — |
| 273 | C4⋊C4 | — | 68 | 2 | no | — |
| 274 | C22⋊C4 | — | 4 | 2 | no | — |
| 275 | C22⋊C4 | — | 4 | 2 | no | — |
| 276 | C22⋊C4 | — | 68 | 2 | no | — |
| 277 | C42 | — | 68 | 2 | no | — |
| 278 | C42 | D4×D17 | 1 | 1 | yes | characteristic |
| 279 | C42 | D4×D17 | 1 | 1 | yes | characteristic |
| 280 | C42 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 281 | C42 | C23×D17 | 1 | 1 | yes | characteristic |
| 282 | C23 | — | 4 | 2 | no | — |
| 283 | C23 | #10587626 | 1 | 1 | yes | characteristic |
| 284 | Q8 | — | 4 | 4 | no | — |
| 285 | Q8 | — | 68 | 4 | no | — |
| 286 | Q8 | — | 68 | 4 | no | — |
| 287 | D4 | — | 4 | 4 | no | — |
| 288 | D4 | — | 4 | 4 | no | — |
| 289 | D4 | — | 4 | 4 | no | — |
| 290 | D4 | — | 8 | 4 | no | — |
| 291 | C2×C4 | — | 2 | 2 | no | — |
| 292 | C2×C4 | — | 2 | 2 | no | — |
| 293 | C2×C4 | — | 2 | 2 | no | — |
| 294 | C2×C4 | — | 4 | 2 | no | — |
| 295 | C2×C4 | — | 8 | 4 | no | — |
| 296 | C2×C4 | — | 68 | 2 | no | — |
| 297 | C2×C4 | — | 68 | 2 | no | — |
| 298 | C2×C4 | #10587626 | 1 | 1 | yes | characteristic |
| 299 | C2×C4 | #10587626 | 1 | 1 | yes | characteristic |
| 300 | C2×C4 | #10587626 | 1 | 1 | yes | characteristic |
| 301 | C2×C4 | C2×D4×D17 | 1 | 1 | yes | characteristic |
| 302 | C2×C4 | C2×D4×D17 | 1 | 1 | yes | characteristic |
| 303 | C2×C4 | C22×C22⋊D17 | 1 | 1 | yes | characteristic |
| 304 | C8 | — | 2 | 2 | no | — |
| 305 | C8 | — | 2 | 2 | no | — |
| 306 | C8 | — | 34 | 4 | no | — |
| 307 | C8 | — | 34 | 4 | no | — |
| 308 | C22 | — | 2 | 1 | no | — |
| 309 | C22 | — | 2 | 1 | no | — |
| 310 | C22 | — | 2 | 1 | no | — |
| 311 | C22 | — | 8 | 2 | no | — |
| 312 | C22 | — | 8 | 2 | no | — |
| 313 | C22 | — | 8 | 2 | no | — |
| 314 | C22 | C2×#10587626 | 1 | 1 | yes | characteristic |
| 315 | C4 | — | 2 | 1 | no | — |
| 316 | C4 | — | 2 | 1 | no | — |
| 317 | C4 | — | 2 | 1 | no | — |
| 318 | C4 | — | 8 | 2 | no | — |
| 319 | C4 | — | 136 | 2 | no | — |
| 320 | C4 | — | 136 | 2 | no | — |
| 321 | C4 | #11763607 | 1 | 2 | yes | — |
| 322 | C4 | #11763610 | 1 | 2 | yes | — |
| 323 | C4 | #11763623 | 1 | 2 | yes | — |
| 324 | C2 | — | 4 | 1 | no | — |
| 325 | C2 | — | 16 | 2 | no | — |
| 326 | C2 | #14539229 | 1 | 1 | yes | characteristic |
| 327 | C2 | #14539265 | 1 | 1 | yes | characteristic |
| 328 | C2 | #14539279 | 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