← #17969118
Subgroups — #17969118
Order 4352.
914 conjugacy classes of subgroups.
The subgroup lattice has 284 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | Q8×#63242 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×Q8×#595 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14544581 | C2 | 1 | 3 | yes | maximal |
| 4 | #14544578 | C2 | 1 | 3 | yes | maximal |
| 5 | #14544571 | C2 | 1 | 3 | yes | maximal |
| 6 | #14544497 | C2 | 1 | 3 | yes | maximal |
| 7 | C8×Q8×D17 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×Q8×#595 | C4 | 1 | 2 | yes | — |
| 9 | #11763858 | C4 | 1 | 6 | yes | complemented |
| 10 | Q8×#3624 | C4 | 1 | 2 | yes | complemented |
| 11 | #11763810 | C22 | 1 | 3 | yes | — |
| 12 | C2×#10587532 | C22 | 1 | 6 | yes | — |
| 13 | C4×#63242 | C22 | 1 | 3 | yes | — |
| 14 | C4⋊C4×#595 | C4 | 1 | 6 | yes | — |
| 15 | C4×C4⋊#595 | C22 | 1 | 3 | yes | — |
| 16 | C42×#595 | C22 | 1 | 3 | yes | — |
| 17 | #11763674 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11763674 | C22 | 1 | 3 | yes | — |
| 19 | #11763674 | C22 | 1 | 3 | yes | — |
| 20 | #11763674 | C22 | 1 | 3 | yes | — |
| 21 | C4×Q8×D17 | C22 | 1 | 1 | yes | characteristic |
| 22 | Q8×#3622 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C8×Dic34 | C4 | 1 | 3 | yes | complemented |
| 24 | #11762933 | C4 | 1 | 3 | yes | complemented |
| 25 | C4⋊C8×D17 | C22 | 1 | 3 | yes | — |
| 26 | C4×C8×D17 | C22 | 1 | 3 | yes | — |
| 27 | C8×Q8×C17 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×Q8×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | Q8×#595 | — | 2 | 8 | no | — |
| 30 | C2×C4⋊#595 | C2×C4 | 1 | 6 | yes | — |
| 31 | C2×C4×#595 | C2×C4 | 1 | 6 | yes | — |
| 32 | C2×C4×#595 | C2×C4 | 1 | 6 | yes | — |
| 33 | C2×C4×#595 | C23 | 1 | 1 | yes | characteristic |
| 34 | C2×C4×#595 | C23 | 1 | 3 | yes | — |
| 35 | C2×#63242 | C23 | 1 | 1 | yes | characteristic |
| 36 | C2×#63242 | C23 | 1 | 3 | yes | — |
| 37 | C4×Q8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | Q8×Dic17 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C2×C8×D17 | C23 | 1 | 3 | yes | — |
| 40 | C2×C8×D17 | C23 | 1 | 1 | yes | characteristic |
| 41 | C4⋊C4×D17 | C2×C4 | 1 | 3 | yes | — |
| 42 | #10587573 | C2×C4 | 1 | 3 | yes | — |
| 43 | C42×D17 | C23 | 1 | 3 | yes | — |
| 44 | C4×Dic34 | C2×C4 | 1 | 3 | yes | — |
| 45 | (C2×#595)⋊C4 | C2×C4 | 1 | 6 | yes | — |
| 46 | #10587544 | C2×C4 | 1 | 6 | yes | — |
| 47 | C4⋊#3624 | C2×C4 | 1 | 6 | yes | — |
| 48 | C4×#3624 | C2×C4 | 1 | 6 | yes | — |
| 49 | C4×#3624 | C2×C4 | 1 | 6 | yes | — |
| 50 | #10587532 | — | 4 | 6 | no | — |
| 51 | C17×C4⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 52 | C4×C8×C17 | C2×C4 | 1 | 3 | yes | — |
| 53 | #10587485 | C2×C4 | 1 | 6 | yes | — |
| 54 | C8×Dic17 | C2×C4 | 1 | 3 | yes | — |
| 55 | C8×Dic17 | C2×C4 | 1 | 3 | yes | — |
| 56 | C4⋊#3622 | C2×C4 | 1 | 3 | yes | — |
| 57 | C4×#3622 | C2×C4 | 1 | 3 | yes | — |
| 58 | C22×#595 | C22×C4 | 1 | 6 | yes | — |
| 59 | C22×#595 | C22×C4 | 1 | 2 | yes | — |
| 60 | C2×Q8×C17 | C42 | 1 | 1 | yes | characteristic |
| 61 | Q8×D17 | M16 | 1 | 8 | yes | — |
| 62 | C2×C4×D17 | C22×C4 | 1 | 3 | yes | — |
| 63 | C2×C4×D17 | C22×C4 | 1 | 3 | yes | — |
| 64 | C2×C4×D17 | C24 | 1 | 1 | yes | characteristic |
| 65 | C2×Dic34 | C42 | 1 | 3 | yes | — |
| 66 | C2×#3624 | C22×C4 | 1 | 2 | yes | — |
| 67 | C2×#3624 | C22×C4 | 1 | 6 | yes | — |
| 68 | C4⋊#595 | — | 2 | 12 | no | — |
| 69 | C4×#595 | — | 2 | 12 | no | — |
| 70 | C4×#595 | — | 2 | 12 | no | — |
| 71 | C4×#595 | — | 2 | 3 | no | — |
| 72 | C4×#595 | — | 2 | 3 | no | — |
| 73 | C4×#595 | — | 2 | 1 | no | — |
| 74 | C4×#595 | — | 2 | 1 | no | — |
| 75 | #63242 | — | 2 | 3 | no | — |
| 76 | #63242 | — | 2 | 1 | no | — |
| 77 | #63242 | — | 2 | 1 | no | — |
| 78 | #63242 | — | 2 | 3 | no | — |
| 79 | C2×C8×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 80 | C2×C8×C17 | C22×C4 | 1 | 3 | yes | — |
| 81 | C4⋊C4×C17 | C42 | 1 | 3 | yes | — |
| 82 | C42×C17 | C22×C4 | 1 | 3 | yes | — |
| 83 | C4⋊Dic17 | C42 | 1 | 3 | yes | — |
| 84 | #63225 | C42 | 1 | 6 | yes | — |
| 85 | C4×Dic17 | C22×C4 | 1 | 3 | yes | — |
| 86 | C4×Dic17 | C22×C4 | 1 | 3 | yes | — |
| 87 | C4×Dic17 | C22×C4 | 1 | 3 | yes | — |
| 88 | C2×#3622 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C2×#3622 | C22×C4 | 1 | 3 | yes | — |
| 90 | C8×D17 | — | 2 | 3 | no | — |
| 91 | C8×D17 | — | 2 | 1 | no | — |
| 92 | C8×D17 | — | 2 | 1 | no | — |
| 93 | C8×D17 | — | 2 | 3 | no | — |
| 94 | #20572 | — | 17 | 1 | no | maximal, Sylow |
| 95 | C22×D17 | C23×C4 | 1 | 1 | yes | characteristic |
| 96 | C2×#595 | — | 2 | 2 | no | — |
| 97 | C2×#595 | — | 2 | 2 | no | — |
| 98 | C2×#595 | — | 2 | 6 | no | — |
| 99 | C2×#595 | — | 2 | 6 | no | — |
| 100 | C2×#595 | — | 2 | 6 | no | — |
| 101 | C2×#595 | #131 | 1 | 4 | yes | — |
| 102 | Q8×C17 | #97 | 1 | 4 | yes | complemented |
| 103 | C2×C4×C17 | C2×C42 | 1 | 3 | yes | — |
| 104 | C2×C4×C17 | C2×C42 | 1 | 3 | yes | — |
| 105 | C2×C4×C17 | C23×C4 | 1 | 1 | yes | characteristic |
| 106 | C2×Dic17 | C2×C42 | 1 | 3 | yes | — |
| 107 | C2×Dic17 | C2×C42 | 1 | 3 | yes | — |
| 108 | C2×Dic17 | C23×C4 | 1 | 1 | yes | characteristic |
| 109 | C4×D17 | — | 2 | 6 | no | — |
| 110 | C4×D17 | C2×M16 | 1 | 12 | yes | — |
| 111 | C4×D17 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 112 | C4×D17 | 2−1+4 | 1 | 1 | yes | characteristic |
| 113 | C4×D17 | 2−1+4 | 1 | 1 | yes | characteristic |
| 114 | C4×D17 | 2−1+4 | 1 | 1 | yes | characteristic |
| 115 | Dic34 | #97 | 1 | 12 | yes | complemented |
| 116 | #3624 | — | 2 | 2 | no | — |
| 117 | #3624 | — | 2 | 6 | no | — |
| 118 | C8×C17 | — | 2 | 1 | no | — |
| 119 | C8×C17 | — | 2 | 3 | no | — |
| 120 | #3622 | — | 2 | 1 | no | — |
| 121 | #3622 | — | 2 | 3 | no | — |
| 122 | C2×C8×Q8 | — | 17 | 1 | no | — |
| 123 | C2×C8×Q8 | — | 17 | 1 | no | — |
| 124 | C42×Q8 | — | 17 | 1 | no | — |
| 125 | #1770 | — | 17 | 3 | no | — |
| 126 | #1770 | — | 17 | 3 | no | — |
| 127 | #1767 | — | 17 | 3 | no | — |
| 128 | #1744 | — | 17 | 3 | no | — |
| 129 | C22×C17 | C22×C42 | 1 | 1 | yes | characteristic |
| 130 | C2×D17 | #519 | 1 | 1 | yes | characteristic |
| 131 | C2×D17 | #520 | 1 | 1 | yes | characteristic |
| 132 | C2×D17 | C22×M16 | 1 | 2 | yes | — |
| 133 | C2×D17 | C2×#131 | 1 | 2 | yes | — |
| 134 | #595 | — | 2 | 4 | no | — |
| 135 | #595 | — | 4 | 6 | no | — |
| 136 | C4×C17 | — | 2 | 3 | no | — |
| 137 | C4×C17 | C2×#97 | 1 | 6 | yes | — |
| 138 | C4×C17 | #519 | 1 | 1 | yes | characteristic |
| 139 | C4×C17 | #520 | 1 | 1 | yes | characteristic |
| 140 | Dic17 | — | 2 | 3 | no | — |
| 141 | Dic17 | C2×#97 | 1 | 6 | yes | — |
| 142 | Dic17 | #519 | 1 | 1 | yes | characteristic |
| 143 | Dic17 | #520 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×Q8 | — | 17 | 1 | no | — |
| 145 | C2×C4×Q8 | — | 17 | 2 | no | — |
| 146 | C8×Q8 | — | 17 | 2 | no | — |
| 147 | C8×Q8 | — | 17 | 6 | no | — |
| 148 | C8×Q8 | — | 17 | 1 | no | — |
| 149 | C8×Q8 | — | 17 | 3 | no | — |
| 150 | C8×Q8 | — | 17 | 3 | no | — |
| 151 | C8×Q8 | #595 | 1 | 1 | yes | characteristic, complemented |
| 152 | C2×C4⋊C8 | — | 17 | 3 | no | — |
| 153 | C2×C4⋊C8 | — | 17 | 3 | no | — |
| 154 | C2×#97 | — | 17 | 6 | no | — |
| 155 | C2×C4×C8 | — | 17 | 3 | no | — |
| 156 | C2×C4×C8 | — | 17 | 3 | no | — |
| 157 | C4×C4⋊C4 | — | 17 | 3 | no | — |
| 158 | C4×C4⋊C4 | — | 17 | 6 | no | — |
| 159 | C43 | — | 17 | 3 | no | — |
| 160 | #336 | — | 17 | 1 | no | — |
| 161 | #336 | — | 17 | 3 | no | — |
| 162 | #336 | — | 17 | 3 | no | — |
| 163 | #336 | — | 17 | 3 | no | — |
| 164 | C2×C17 | #2276 | 1 | 1 | yes | characteristic |
| 165 | C2×C17 | C22×#97 | 1 | 1 | yes | characteristic |
| 166 | C2×C17 | C4×#131 | 1 | 1 | yes | characteristic |
| 167 | D17 | #2984 | 1 | 2 | yes | — |
| 168 | D17 | #2991 | 1 | 2 | yes | — |
| 169 | C22×Q8 | — | 17 | 1 | no | — |
| 170 | C22×C8 | — | 17 | 1 | no | — |
| 171 | C22×C8 | — | 17 | 3 | no | — |
| 172 | C22×C8 | — | 17 | 1 | no | — |
| 173 | C22×C8 | — | 17 | 3 | no | — |
| 174 | C4×Q8 | — | 17 | 1 | no | — |
| 175 | C4×Q8 | — | 17 | 3 | no | — |
| 176 | C4×Q8 | — | 17 | 3 | no | — |
| 177 | C4×Q8 | — | 34 | 8 | no | — |
| 178 | C4×Q8 | C2×#595 | 1 | 1 | yes | characteristic |
| 179 | C2×C4⋊C4 | — | 17 | 3 | no | — |
| 180 | C2×C4⋊C4 | — | 17 | 6 | no | — |
| 181 | C2×C42 | — | 17 | 3 | no | — |
| 182 | C2×C42 | — | 17 | 6 | no | — |
| 183 | C2×C42 | — | 17 | 6 | no | — |
| 184 | C2×C42 | — | 17 | 1 | no | — |
| 185 | C2×C42 | — | 17 | 3 | no | — |
| 186 | C4⋊C8 | — | 17 | 6 | no | — |
| 187 | C4⋊C8 | — | 17 | 6 | no | — |
| 188 | C4⋊C8 | — | 17 | 6 | no | — |
| 189 | C4⋊C8 | — | 17 | 3 | no | — |
| 190 | C4⋊C8 | C2×#595 | 1 | 3 | yes | — |
| 191 | #97 | — | 68 | 6 | no | — |
| 192 | C4×C8 | — | 17 | 6 | no | — |
| 193 | C4×C8 | — | 17 | 6 | no | — |
| 194 | C4×C8 | — | 17 | 3 | no | — |
| 195 | C4×C8 | — | 17 | 3 | no | — |
| 196 | C4×C8 | — | 17 | 3 | no | — |
| 197 | C4×C8 | C2×#595 | 1 | 3 | yes | — |
| 198 | #95 | — | 17 | 6 | no | — |
| 199 | C17 | #20572 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 200 | C2×Q8 | — | 17 | 8 | no | — |
| 201 | C2×Q8 | — | 17 | 3 | no | — |
| 202 | C2×Q8 | C4×#595 | 1 | 1 | yes | characteristic |
| 203 | C22×C4 | — | 17 | 3 | no | — |
| 204 | C22×C4 | — | 17 | 1 | no | — |
| 205 | C22×C4 | — | 17 | 2 | no | — |
| 206 | C22×C4 | — | 17 | 3 | no | — |
| 207 | C22×C4 | — | 17 | 6 | no | — |
| 208 | C2×C8 | — | 17 | 2 | no | — |
| 209 | C2×C8 | — | 17 | 6 | no | — |
| 210 | C2×C8 | — | 17 | 1 | no | — |
| 211 | C2×C8 | — | 17 | 3 | no | — |
| 212 | C2×C8 | — | 34 | 3 | no | — |
| 213 | C2×C8 | — | 34 | 1 | no | — |
| 214 | C2×C8 | — | 34 | 1 | no | — |
| 215 | C2×C8 | — | 34 | 3 | no | — |
| 216 | C2×C8 | — | 34 | 3 | no | — |
| 217 | C2×C8 | — | 34 | 1 | no | — |
| 218 | C2×C8 | — | 34 | 3 | no | — |
| 219 | C2×C8 | — | 34 | 1 | no | — |
| 220 | C2×C8 | C22×#595 | 1 | 1 | yes | characteristic |
| 221 | C2×C8 | C22×#595 | 1 | 3 | yes | — |
| 222 | C4⋊C4 | — | 17 | 6 | no | — |
| 223 | C4⋊C4 | — | 17 | 3 | no | — |
| 224 | C4⋊C4 | — | 34 | 12 | no | — |
| 225 | C4⋊C4 | C4×#595 | 1 | 3 | yes | — |
| 226 | C42 | — | 17 | 3 | no | — |
| 227 | C42 | — | 17 | 3 | no | — |
| 228 | C42 | — | 17 | 3 | no | — |
| 229 | C42 | — | 34 | 3 | no | — |
| 230 | C42 | — | 34 | 3 | no | — |
| 231 | C42 | — | 34 | 1 | no | — |
| 232 | C42 | — | 34 | 1 | no | — |
| 233 | C42 | — | 34 | 12 | no | — |
| 234 | C42 | — | 34 | 12 | no | — |
| 235 | C42 | C22×#595 | 1 | 3 | yes | — |
| 236 | C23 | — | 17 | 1 | no | — |
| 237 | Q8 | — | 17 | 12 | no | — |
| 238 | Q8 | #10587532 | 1 | 4 | yes | complemented |
| 239 | C2×C4 | — | 17 | 1 | no | — |
| 240 | C2×C4 | — | 17 | 3 | no | — |
| 241 | C2×C4 | — | 17 | 12 | no | — |
| 242 | C2×C4 | — | 17 | 1 | no | — |
| 243 | C2×C4 | — | 17 | 1 | no | — |
| 244 | C2×C4 | — | 17 | 1 | no | — |
| 245 | C2×C4 | — | 17 | 1 | no | — |
| 246 | C2×C4 | — | 17 | 4 | no | — |
| 247 | C2×C4 | — | 17 | 3 | no | — |
| 248 | C2×C4 | — | 34 | 6 | no | — |
| 249 | C2×C4 | — | 34 | 2 | no | — |
| 250 | C2×C4 | — | 34 | 2 | no | — |
| 251 | C2×C4 | — | 34 | 6 | no | — |
| 252 | C2×C4 | — | 34 | 6 | no | — |
| 253 | C2×C4 | — | 34 | 6 | no | — |
| 254 | C2×C4 | C2×C4×#595 | 1 | 3 | yes | — |
| 255 | C2×C4 | C2×C4×#595 | 1 | 3 | yes | — |
| 256 | C2×C4 | C23×#595 | 1 | 1 | yes | characteristic |
| 257 | C8 | — | 2 | 1 | no | — |
| 258 | C8 | — | 2 | 3 | no | — |
| 259 | C8 | — | 34 | 6 | no | — |
| 260 | C8 | — | 34 | 2 | no | — |
| 261 | C8 | — | 34 | 1 | no | — |
| 262 | C8 | — | 34 | 3 | no | — |
| 263 | C22 | — | 17 | 1 | no | — |
| 264 | C22 | — | 17 | 1 | no | — |
| 265 | C22 | — | 17 | 2 | no | — |
| 266 | C22 | — | 17 | 2 | no | — |
| 267 | C22 | C22×C4×#595 | 1 | 1 | yes | characteristic |
| 268 | C4 | — | 2 | 3 | no | — |
| 269 | C4 | — | 17 | 1 | no | — |
| 270 | C4 | — | 17 | 1 | no | — |
| 271 | C4 | — | 17 | 6 | no | — |
| 272 | C4 | — | 34 | 4 | no | — |
| 273 | C4 | — | 34 | 3 | no | — |
| 274 | C4 | — | 68 | 6 | no | — |
| 275 | C4 | C2×#10587532 | 1 | 6 | yes | — |
| 276 | C4 | #11763877 | 1 | 1 | yes | characteristic |
| 277 | C4 | #11763878 | 1 | 1 | yes | characteristic |
| 278 | C2 | — | 17 | 2 | no | — |
| 279 | C2 | — | 17 | 2 | no | — |
| 280 | C2 | #14545224 | 1 | 1 | yes | characteristic |
| 281 | C2 | C22×#10587532 | 1 | 1 | yes | characteristic |
| 282 | C2 | #131×#595 | 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