← #17983195
Subgroups — #17983195
Order 4352.
506 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 | #14546010 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14546009 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #14546008 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | Q8×#63241 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #14545976 | C2 | 1 | 2 | yes | maximal |
| 6 | #14545973 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #14545946 | C2 | 1 | 2 | yes | maximal |
| 8 | C4×#10587665 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #14545573 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#10587666 | C22 | 1 | 2 | yes | — |
| 11 | C2×#10587665 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#10587665 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11763912 | C22 | 1 | 4 | yes | — |
| 14 | C4⋊#63241 | C22 | 1 | 2 | yes | — |
| 15 | C4⋊#63241 | C22 | 1 | 2 | yes | — |
| 16 | C4⋊#63241 | C22 | 1 | 4 | yes | — |
| 17 | #11763903 | C22 | 1 | 4 | yes | — |
| 18 | C4×#63241 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×#63241 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#63241 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×#63241 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×#63241 | C22 | 1 | 4 | yes | — |
| 23 | #11763860 | C4 | 1 | 2 | yes | — |
| 24 | #11763859 | C4 | 1 | 2 | yes | — |
| 25 | #11763858 | C22 | 1 | 2 | yes | — |
| 26 | Q8×#3624 | C22 | 1 | 2 | yes | — |
| 27 | #11763816 | C4 | 1 | 2 | yes | — |
| 28 | #11763813 | C4 | 1 | 1 | yes | characteristic |
| 29 | #11763774 | C22 | 1 | 2 | yes | — |
| 30 | C4×#63242 | C22 | 1 | 1 | yes | characteristic |
| 31 | #11763364 | C4 | 1 | 1 | yes | characteristic |
| 32 | C2×#63243 | C2×C4 | 1 | 2 | yes | — |
| 33 | C2×#63242 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#63242 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×#63241 | C23 | 1 | 1 | yes | characteristic |
| 36 | C2×#63241 | C23 | 1 | 1 | yes | characteristic |
| 37 | C2×#63241 | C23 | 1 | 4 | yes | — |
| 38 | C2×#63241 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×#63241 | C23 | 1 | 1 | yes | characteristic |
| 40 | #10587666 | — | 2 | 4 | no | — |
| 41 | #10587665 | — | 2 | 2 | no | — |
| 42 | #10587665 | Q8 | 1 | 4 | yes | complemented |
| 43 | C17×C4⋊Q8 | C8 | 1 | 1 | yes | characteristic |
| 44 | #10587632 | C8 | 1 | 2 | yes | — |
| 45 | Q8×Dic17 | C2×C4 | 1 | 2 | yes | — |
| 46 | #10587583 | C8 | 1 | 2 | yes | — |
| 47 | #10587578 | C2×C4 | 1 | 2 | yes | — |
| 48 | #10587576 | C8 | 1 | 2 | yes | — |
| 49 | #10587573 | C2×C4 | 1 | 2 | yes | — |
| 50 | C42×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | #10587555 | C8 | 1 | 1 | yes | characteristic |
| 52 | #10587544 | C2×C4 | 1 | 4 | yes | — |
| 53 | #10587542 | C2×C4 | 1 | 4 | yes | — |
| 54 | C4⋊#3624 | C2×C4 | 1 | 2 | yes | — |
| 55 | C4⋊#3624 | C2×C4 | 1 | 2 | yes | — |
| 56 | C4⋊#3624 | C2×C4 | 1 | 4 | yes | — |
| 57 | C4×#3624 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C4×#3624 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C4×#3624 | C23 | 1 | 1 | yes | characteristic |
| 60 | C4×#3624 | C23 | 1 | 1 | yes | characteristic |
| 61 | C4×#3624 | C23 | 1 | 4 | yes | — |
| 62 | C2×Q8×C17 | C2×C8 | 1 | 2 | yes | — |
| 63 | C2×C4×D17 | C2×C8 | 1 | 1 | yes | characteristic |
| 64 | C2×C4×D17 | C2×C8 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×D17 | C22×C4 | 1 | 1 | yes | characteristic |
| 66 | C2×Dic34 | C2×C8 | 1 | 2 | yes | — |
| 67 | C2×#3624 | C22×C4 | 1 | 1 | yes | characteristic |
| 68 | C2×#3624 | C22×C4 | 1 | 1 | yes | characteristic |
| 69 | C2×#3624 | C22×C4 | 1 | 4 | yes | — |
| 70 | C2×#3624 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | C2×#3624 | C24 | 1 | 1 | yes | characteristic |
| 72 | #63243 | — | 2 | 4 | no | — |
| 73 | #63242 | — | 2 | 2 | no | — |
| 74 | #63242 | C2×Q8 | 1 | 2 | yes | — |
| 75 | #63242 | #41 | 1 | 2 | yes | — |
| 76 | #63241 | — | 2 | 1 | no | — |
| 77 | #63241 | — | 2 | 1 | no | — |
| 78 | #63241 | — | 2 | 4 | no | — |
| 79 | #63241 | C2×Q8 | 1 | 2 | yes | — |
| 80 | #63241 | C2×Q8 | 1 | 2 | yes | — |
| 81 | C4⋊C4×C17 | C2×C8 | 1 | 2 | yes | — |
| 82 | C4⋊C4×C17 | C2×C8 | 1 | 2 | yes | — |
| 83 | C42×C17 | C2×C8 | 1 | 1 | yes | characteristic |
| 84 | #63227 | C2×C8 | 1 | 4 | yes | — |
| 85 | C4⋊Dic17 | C2×C8 | 1 | 2 | yes | — |
| 86 | C4⋊Dic17 | C2×C8 | 1 | 2 | yes | — |
| 87 | C4⋊Dic17 | C2×C8 | 1 | 4 | yes | — |
| 88 | #63225 | C2×C8 | 1 | 4 | yes | — |
| 89 | C4×Dic17 | C2×C8 | 1 | 1 | yes | characteristic |
| 90 | C4×Dic17 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | C4×Dic17 | C22×C4 | 1 | 1 | yes | characteristic |
| 92 | C4×Dic17 | C22×C4 | 1 | 4 | yes | — |
| 93 | #33474 | — | 17 | 1 | no | maximal, Sylow |
| 94 | C22×D17 | C22×C8 | 1 | 1 | yes | characteristic |
| 95 | Q8×C17 | — | 2 | 4 | no | — |
| 96 | C2×C4×C17 | C22×C8 | 1 | 4 | yes | — |
| 97 | C2×C4×C17 | C22×C8 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C17 | C22×C8 | 1 | 1 | yes | characteristic |
| 99 | C2×C4×C17 | C22×C8 | 1 | 1 | yes | characteristic |
| 100 | C2×Dic17 | C22×C8 | 1 | 4 | yes | — |
| 101 | C2×Dic17 | C22×C8 | 1 | 1 | yes | characteristic |
| 102 | C2×Dic17 | C22×C8 | 1 | 1 | yes | characteristic |
| 103 | C2×Dic17 | C23×C4 | 1 | 1 | yes | characteristic |
| 104 | C4×D17 | — | 2 | 2 | no | — |
| 105 | C4×D17 | — | 2 | 2 | no | — |
| 106 | C4×D17 | C4×Q8 | 1 | 2 | yes | — |
| 107 | C4×D17 | #131 | 1 | 2 | yes | — |
| 108 | Dic34 | — | 2 | 4 | no | — |
| 109 | #3624 | — | 2 | 1 | no | — |
| 110 | #3624 | — | 2 | 1 | no | — |
| 111 | #3624 | — | 2 | 4 | no | — |
| 112 | #3624 | C4×Q8 | 1 | 2 | yes | — |
| 113 | #3624 | C22×Q8 | 1 | 1 | yes | characteristic |
| 114 | #3624 | C2×#41 | 1 | 1 | yes | characteristic |
| 115 | #2960 | — | 17 | 1 | no | — |
| 116 | #2183 | — | 17 | 2 | no | — |
| 117 | #2183 | — | 17 | 2 | no | — |
| 118 | Q8×C16 | — | 17 | 2 | no | — |
| 119 | Q8×C16 | — | 17 | 2 | no | — |
| 120 | #2151 | — | 17 | 2 | no | — |
| 121 | #2150 | — | 17 | 1 | no | — |
| 122 | #2108 | — | 17 | 2 | no | — |
| 123 | C2×C4×C16 | — | 17 | 1 | no | — |
| 124 | C22×C17 | C23×C8 | 1 | 1 | yes | characteristic |
| 125 | C2×D17 | — | 2 | 1 | no | — |
| 126 | C2×D17 | — | 2 | 1 | no | — |
| 127 | C2×D17 | C8×Q8 | 1 | 2 | yes | — |
| 128 | C4×C17 | — | 2 | 4 | no | — |
| 129 | C4×C17 | C8×Q8 | 1 | 2 | yes | — |
| 130 | C4×C17 | #504 | 1 | 2 | yes | — |
| 131 | C4×C17 | #504 | 1 | 2 | yes | — |
| 132 | Dic17 | — | 2 | 4 | no | — |
| 133 | Dic17 | — | 2 | 1 | no | — |
| 134 | Dic17 | — | 2 | 1 | no | — |
| 135 | Dic17 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 136 | Dic17 | C2×#131 | 1 | 1 | yes | characteristic |
| 137 | #533 | — | 17 | 1 | no | — |
| 138 | C2×M32 | — | 17 | 2 | no | — |
| 139 | C22×C16 | — | 17 | 1 | no | — |
| 140 | C22×C16 | — | 17 | 1 | no | — |
| 141 | #446 | — | 17 | 2 | no | — |
| 142 | #446 | — | 17 | 2 | no | — |
| 143 | C8×Q8 | — | 17 | 2 | no | — |
| 144 | C8×Q8 | — | 17 | 2 | no | — |
| 145 | #424 | — | 17 | 2 | no | — |
| 146 | #423 | — | 17 | 1 | no | — |
| 147 | #405 | — | 17 | 2 | no | — |
| 148 | C2×C4×C8 | — | 17 | 1 | no | — |
| 149 | C4⋊C16 | — | 17 | 2 | no | — |
| 150 | C4⋊C16 | — | 17 | 2 | no | — |
| 151 | C4⋊C16 | — | 17 | 4 | no | — |
| 152 | C4⋊C16 | — | 17 | 4 | no | — |
| 153 | #346 | — | 17 | 4 | no | — |
| 154 | C4×C16 | — | 17 | 1 | no | — |
| 155 | C4×C16 | — | 17 | 1 | no | — |
| 156 | C4×C16 | — | 17 | 1 | no | — |
| 157 | C4×C16 | — | 17 | 1 | no | — |
| 158 | C4×C16 | — | 17 | 4 | no | — |
| 159 | C2×C17 | C2×C8×Q8 | 1 | 1 | yes | characteristic |
| 160 | C2×C17 | C2×#504 | 1 | 1 | yes | characteristic |
| 161 | C2×C17 | C2×#504 | 1 | 1 | yes | characteristic |
| 162 | D17 | — | 2 | 2 | no | — |
| 163 | C2×M16 | — | 17 | 2 | no | — |
| 164 | C22×C8 | — | 17 | 1 | no | — |
| 165 | C22×C8 | — | 17 | 1 | no | — |
| 166 | C4⋊Q8 | — | 17 | 1 | no | — |
| 167 | C4⋊Q8 | #3633 | 1 | 1 | yes | characteristic |
| 168 | #125 | — | 17 | 2 | no | — |
| 169 | C22⋊Q8 | — | 17 | 2 | no | — |
| 170 | C22⋊Q8 | — | 17 | 2 | no | — |
| 171 | C4×Q8 | — | 17 | 2 | no | — |
| 172 | C4×Q8 | — | 17 | 2 | no | — |
| 173 | #117 | — | 17 | 2 | no | — |
| 174 | C2×C42 | — | 17 | 1 | no | — |
| 175 | M32 | — | 34 | 4 | no | — |
| 176 | C2×C16 | — | 17 | 4 | no | — |
| 177 | C2×C16 | — | 17 | 1 | no | — |
| 178 | C2×C16 | — | 17 | 1 | no | — |
| 179 | C2×C16 | — | 17 | 1 | no | — |
| 180 | C2×C16 | — | 17 | 1 | no | — |
| 181 | C2×C16 | — | 17 | 4 | no | — |
| 182 | C2×C16 | — | 34 | 2 | no | — |
| 183 | C4⋊C8 | — | 17 | 2 | no | — |
| 184 | C4⋊C8 | — | 17 | 2 | no | — |
| 185 | C4⋊C8 | — | 17 | 4 | no | — |
| 186 | C4⋊C8 | — | 17 | 4 | no | — |
| 187 | #97 | — | 17 | 4 | no | — |
| 188 | C4×C8 | — | 17 | 1 | no | — |
| 189 | C4×C8 | — | 17 | 1 | no | — |
| 190 | C4×C8 | — | 17 | 4 | no | — |
| 191 | C4×C8 | — | 17 | 1 | no | — |
| 192 | C4×C8 | — | 17 | 1 | no | — |
| 193 | C17 | #33474 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 194 | C2×Q8 | — | 17 | 2 | no | — |
| 195 | C2×Q8 | C2×#3633 | 1 | 2 | yes | — |
| 196 | C22×C4 | — | 17 | 1 | no | — |
| 197 | C22×C4 | — | 17 | 1 | no | — |
| 198 | C22×C4 | — | 17 | 1 | no | — |
| 199 | M16 | — | 34 | 4 | no | — |
| 200 | C2×C8 | — | 17 | 2 | no | — |
| 201 | C2×C8 | — | 17 | 2 | no | — |
| 202 | C2×C8 | — | 17 | 1 | no | — |
| 203 | C2×C8 | — | 17 | 1 | no | — |
| 204 | C2×C8 | — | 17 | 1 | no | — |
| 205 | C2×C8 | — | 17 | 1 | no | — |
| 206 | C2×C8 | — | 17 | 4 | no | — |
| 207 | C2×C8 | — | 34 | 2 | no | — |
| 208 | C4⋊C4 | — | 17 | 2 | no | — |
| 209 | C4⋊C4 | — | 17 | 4 | no | — |
| 210 | C4⋊C4 | — | 17 | 4 | no | — |
| 211 | C4⋊C4 | — | 17 | 2 | no | — |
| 212 | C4⋊C4 | C2×#3633 | 1 | 2 | yes | — |
| 213 | C4⋊C4 | C2×#3633 | 1 | 2 | yes | — |
| 214 | C22⋊C4 | — | 17 | 4 | no | — |
| 215 | C42 | — | 17 | 1 | no | — |
| 216 | C42 | — | 17 | 1 | no | — |
| 217 | C42 | — | 17 | 4 | no | — |
| 218 | C42 | — | 17 | 1 | no | — |
| 219 | C42 | C2×#3633 | 1 | 1 | yes | characteristic |
| 220 | C16 | — | 17 | 2 | no | — |
| 221 | C16 | — | 17 | 2 | no | — |
| 222 | C16 | — | 34 | 1 | no | — |
| 223 | C16 | — | 34 | 1 | no | — |
| 224 | C16 | — | 34 | 4 | no | — |
| 225 | C23 | — | 17 | 1 | no | — |
| 226 | Q8 | — | 2 | 4 | no | — |
| 227 | Q8 | — | 34 | 4 | no | — |
| 228 | C2×C4 | — | 17 | 1 | no | — |
| 229 | C2×C4 | — | 17 | 2 | no | — |
| 230 | C2×C4 | — | 17 | 2 | no | — |
| 231 | C2×C4 | — | 17 | 1 | no | — |
| 232 | C2×C4 | — | 17 | 1 | no | — |
| 233 | C2×C4 | — | 17 | 4 | no | — |
| 234 | C2×C4 | — | 34 | 2 | no | — |
| 235 | C2×C4 | — | 34 | 2 | no | — |
| 236 | C2×C4 | C22×#3633 | 1 | 4 | yes | — |
| 237 | C2×C4 | C22×#3633 | 1 | 1 | yes | characteristic |
| 238 | C2×C4 | C22×#3633 | 1 | 1 | yes | characteristic |
| 239 | C2×C4 | C22×#3633 | 1 | 1 | yes | characteristic |
| 240 | C8 | — | 17 | 1 | no | — |
| 241 | C8 | — | 17 | 1 | no | — |
| 242 | C8 | — | 17 | 2 | no | — |
| 243 | C8 | — | 34 | 1 | no | — |
| 244 | C8 | — | 34 | 1 | no | — |
| 245 | C8 | — | 34 | 4 | no | — |
| 246 | C22 | — | 17 | 2 | no | — |
| 247 | C22 | — | 34 | 1 | no | — |
| 248 | C22 | — | 34 | 1 | no | — |
| 249 | C22 | C23×#3633 | 1 | 1 | yes | characteristic |
| 250 | C4 | — | 2 | 4 | no | — |
| 251 | C4 | — | 17 | 1 | no | — |
| 252 | C4 | — | 17 | 1 | no | — |
| 253 | C4 | — | 34 | 1 | no | — |
| 254 | C4 | — | 34 | 1 | no | — |
| 255 | C4 | — | 34 | 4 | no | — |
| 256 | C4 | Q8×#3633 | 1 | 2 | yes | — |
| 257 | C4 | #11763930 | 1 | 2 | yes | — |
| 258 | C4 | #11763931 | 1 | 2 | yes | — |
| 259 | C2 | — | 34 | 2 | no | — |
| 260 | C2 | C2×Q8×#3633 | 1 | 1 | yes | characteristic |
| 261 | C2 | C2×#11763930 | 1 | 1 | yes | characteristic |
| 262 | C2 | C2×#11763931 | 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