← #34019647
Subgroups — #34019647
Order 18688.
714 conjugacy classes of subgroups.
The subgroup lattice has 308 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22626677 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22625580 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22625551 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22625529 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22625473 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22625238 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22625141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22620511 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C2×#14556679 | — | 2 | 2 | no | — |
| 10 | #17989621 | C22 | 1 | 4 | yes | — |
| 11 | #17989617 | — | 2 | 4 | no | — |
| 12 | #17989615 | C22 | 1 | 4 | yes | — |
| 13 | #17989606 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17989588 | C22 | 1 | 2 | yes | — |
| 15 | #17989562 | — | 2 | 2 | no | — |
| 16 | C4×#11924038 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17989449 | C22 | 1 | 2 | yes | — |
| 18 | #17989448 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17989448 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17989435 | C22 | 1 | 4 | yes | — |
| 21 | #17989435 | C22 | 1 | 4 | yes | — |
| 22 | #17989429 | C22 | 1 | 2 | yes | — |
| 23 | #17989428 | C22 | 1 | 2 | yes | — |
| 24 | #17989138 | C22 | 1 | 2 | yes | — |
| 25 | #17988964 | C4 | 1 | 1 | yes | characteristic |
| 26 | #17988935 | C4 | 1 | 2 | yes | — |
| 27 | #17988824 | C4 | 1 | 2 | yes | — |
| 28 | #17988824 | C4 | 1 | 2 | yes | — |
| 29 | #17988669 | C22 | 1 | 2 | yes | — |
| 30 | #17988669 | C22 | 1 | 2 | yes | — |
| 31 | C4×C8×D73 | C22 | 1 | 1 | yes | characteristic |
| 32 | #500×C73 | C4 | 1 | 1 | yes | characteristic |
| 33 | #14556679 | — | 4 | 8 | no | — |
| 34 | C2×#11924038 | — | 2 | 4 | no | — |
| 35 | C2×#11924038 | D4 | 1 | 2 | yes | — |
| 36 | C2×#11924036 | — | 2 | 4 | no | — |
| 37 | C2×#11924036 | — | 2 | 2 | no | — |
| 38 | #14556658 | — | 2 | 2 | no | — |
| 39 | C4⋊#10596833 | — | 2 | 1 | no | — |
| 40 | C4⋊#10596833 | C23 | 1 | 2 | yes | — |
| 41 | C4⋊#10596833 | C23 | 1 | 2 | yes | — |
| 42 | #14556648 | — | 2 | 4 | no | — |
| 43 | #14556648 | — | 2 | 4 | no | — |
| 44 | #14556648 | — | 2 | 1 | no | — |
| 45 | #14556646 | D4 | 1 | 2 | yes | — |
| 46 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 47 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 48 | C2×#11924029 | — | 2 | 2 | no | — |
| 49 | C2×D584 | C2×C4 | 1 | 2 | yes | — |
| 50 | C2×D584 | C2×C4 | 1 | 2 | yes | — |
| 51 | C2×C8×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C2×C8×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | #14556588 | C2×C4 | 1 | 2 | yes | — |
| 54 | #14556580 | — | 2 | 2 | no | — |
| 55 | #14556566 | — | 2 | 2 | no | — |
| 56 | #14556566 | C2×C4 | 1 | 4 | yes | — |
| 57 | #14556553 | — | 2 | 2 | no | — |
| 58 | #14556553 | C23 | 1 | 4 | yes | — |
| 59 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 60 | #14556511 | C2×C4 | 1 | 4 | yes | — |
| 61 | #14556511 | C2×C4 | 1 | 4 | yes | — |
| 62 | C4×#10596831 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C8×Dic73 | C23 | 1 | 1 | yes | characteristic |
| 64 | C8×Dic73 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4⋊Q8×C73 | C2×C4 | 1 | 2 | yes | — |
| 66 | #107×C73 | C2×C4 | 1 | 2 | yes | — |
| 67 | #107×C73 | C2×C4 | 1 | 2 | yes | — |
| 68 | C4×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | #11924038 | — | 2 | 4 | no | — |
| 70 | #11924038 | — | 4 | 8 | no | — |
| 71 | #11924036 | — | 4 | 8 | no | — |
| 72 | #11924036 | — | 4 | 4 | no | — |
| 73 | C2×#10596833 | — | 2 | 2 | no | — |
| 74 | C2×#10596833 | — | 2 | 2 | no | — |
| 75 | C2×#10596833 | — | 2 | 2 | no | — |
| 76 | C2×#10596833 | C2×D4 | 1 | 4 | yes | — |
| 77 | #11924029 | — | 4 | 4 | no | — |
| 78 | #11924029 | — | 4 | 4 | no | — |
| 79 | C2×D292 | — | 2 | 4 | no | — |
| 80 | C2×D292 | — | 2 | 2 | no | — |
| 81 | C2×D292 | — | 2 | 2 | no | — |
| 82 | C2×D292 | C22×C4 | 1 | 4 | yes | — |
| 83 | C2×C4×D73 | — | 2 | 4 | no | — |
| 84 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×D73 | #41 | 1 | 1 | yes | characteristic |
| 87 | D584 | — | 2 | 4 | no | — |
| 88 | D584 | — | 4 | 2 | no | — |
| 89 | C2×#10596831 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C2×#10596831 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | C8×D73 | — | 2 | 2 | no | — |
| 92 | C8×D73 | — | 4 | 1 | no | — |
| 93 | #11924005 | — | 2 | 4 | no | — |
| 94 | #11924005 | — | 2 | 4 | no | — |
| 95 | C4×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C4×Dic73 | #41 | 1 | 1 | yes | characteristic |
| 97 | C4×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 98 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 99 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 102 | C4⋊C4×C73 | C22×C4 | 1 | 4 | yes | — |
| 103 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 104 | C22×D73 | — | 2 | 4 | no | — |
| 105 | C22×D73 | C4×D4 | 1 | 1 | yes | characteristic |
| 106 | Q8×C73 | — | 4 | 4 | no | — |
| 107 | C2×C4×C73 | — | 2 | 4 | no | — |
| 108 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 111 | C2×Dic73 | C4×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×Dic73 | C22×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×Dic73 | C2×#41 | 1 | 1 | yes | characteristic |
| 114 | D292 | — | 2 | 4 | no | — |
| 115 | D292 | — | 2 | 4 | no | — |
| 116 | D292 | — | 4 | 8 | no | — |
| 117 | D292 | — | 4 | 4 | no | — |
| 118 | D292 | — | 8 | 2 | no | — |
| 119 | C4×D73 | — | 2 | 1 | no | — |
| 120 | C4×D73 | — | 2 | 1 | no | — |
| 121 | C4×D73 | — | 4 | 1 | no | — |
| 122 | C4×D73 | — | 4 | 4 | no | — |
| 123 | C4×D73 | — | 4 | 4 | no | — |
| 124 | C4×D73 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 125 | #10596833 | — | 2 | 4 | no | — |
| 126 | #10596833 | — | 4 | 2 | no | — |
| 127 | #10596833 | — | 4 | 2 | no | — |
| 128 | #10596833 | — | 4 | 2 | no | — |
| 129 | C8×C73 | — | 2 | 1 | no | — |
| 130 | C8×C73 | #131 | 1 | 2 | yes | complemented |
| 131 | #10596831 | — | 2 | 1 | no | — |
| 132 | #10596831 | — | 2 | 1 | no | — |
| 133 | C22×C73 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×D73 | — | 2 | 1 | no | — |
| 135 | C2×D73 | — | 2 | 1 | no | — |
| 136 | C2×D73 | — | 4 | 4 | no | — |
| 137 | C2×D73 | — | 4 | 4 | no | — |
| 138 | C2×D73 | — | 4 | 4 | no | — |
| 139 | C2×D73 | #442 | 1 | 2 | yes | — |
| 140 | C4×C73 | — | 2 | 1 | no | — |
| 141 | C4×C73 | — | 4 | 4 | no | — |
| 142 | C4×C73 | #442 | 1 | 2 | yes | — |
| 143 | C4×C73 | C2×#131 | 1 | 1 | yes | characteristic |
| 144 | C4×C73 | #568 | 1 | 1 | yes | characteristic |
| 145 | Dic73 | — | 2 | 1 | no | — |
| 146 | Dic73 | — | 2 | 1 | no | — |
| 147 | Dic73 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 148 | #18073 | — | 73 | 1 | no | maximal, Sylow |
| 149 | C2×C73 | #2935 | 1 | 1 | yes | characteristic |
| 150 | C2×C73 | C2×#442 | 1 | 1 | yes | characteristic |
| 151 | C2×C73 | #2957 | 1 | 1 | yes | characteristic |
| 152 | D73 | — | 2 | 2 | no | — |
| 153 | D73 | — | 8 | 4 | no | — |
| 154 | #3169 | — | 73 | 1 | no | — |
| 155 | #2935 | — | 73 | 2 | no | — |
| 156 | #1594 | — | 73 | 2 | no | — |
| 157 | #1586 | — | 73 | 4 | no | — |
| 158 | #1580 | — | 73 | 2 | no | — |
| 159 | C2×#334 | — | 73 | 1 | no | — |
| 160 | #1480 | — | 73 | 2 | no | — |
| 161 | #1451 | — | 73 | 1 | no | — |
| 162 | C73 | #18073 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 163 | C2×#131 | — | 146 | 2 | no | — |
| 164 | #532 | — | 73 | 2 | no | — |
| 165 | #500 | #64408 | 1 | 1 | yes | characteristic |
| 166 | #493 | — | 73 | 1 | no | — |
| 167 | #486 | — | 73 | 2 | no | — |
| 168 | #466 | — | 73 | 2 | no | — |
| 169 | #466 | — | 73 | 2 | no | — |
| 170 | C4×D8 | — | 73 | 2 | no | — |
| 171 | C4×D8 | — | 73 | 2 | no | — |
| 172 | #436 | — | 73 | 4 | no | — |
| 173 | #435 | — | 146 | 4 | no | — |
| 174 | C8×D4 | — | 73 | 4 | no | — |
| 175 | #431 | — | 73 | 1 | no | — |
| 176 | C2×C4⋊C8 | — | 73 | 2 | no | — |
| 177 | #408 | — | 146 | 2 | no | — |
| 178 | C4×M16 | — | 73 | 1 | no | — |
| 179 | C2×C4×C8 | — | 73 | 1 | no | — |
| 180 | #334 | — | 73 | 1 | no | — |
| 181 | #334 | — | 73 | 2 | no | — |
| 182 | #334 | — | 73 | 1 | no | — |
| 183 | D4⋊C8 | — | 73 | 4 | no | — |
| 184 | D4⋊C8 | — | 73 | 4 | no | — |
| 185 | #322 | — | 73 | 2 | no | — |
| 186 | #322 | — | 73 | 2 | no | — |
| 187 | C2×#41 | — | 146 | 2 | no | — |
| 188 | C2×D8 | — | 73 | 2 | no | — |
| 189 | C2×D8 | — | 73 | 2 | no | — |
| 190 | #131 | — | 292 | 8 | no | — |
| 191 | C2×M16 | — | 73 | 2 | no | — |
| 192 | C2×M16 | — | 146 | 4 | no | — |
| 193 | C22×C8 | — | 73 | 1 | no | — |
| 194 | C22×C8 | — | 73 | 1 | no | — |
| 195 | C22×C8 | — | 146 | 4 | no | — |
| 196 | C22×C8 | — | 146 | 2 | no | — |
| 197 | C4⋊Q8 | C2×#64408 | 1 | 2 | yes | — |
| 198 | #127 | — | 73 | 2 | no | — |
| 199 | #124 | — | 146 | 2 | no | — |
| 200 | #121 | — | 73 | 4 | no | — |
| 201 | #121 | — | 146 | 2 | no | — |
| 202 | C4×D4 | — | 73 | 4 | no | — |
| 203 | C4×D4 | — | 146 | 2 | no | — |
| 204 | C2×C42 | — | 73 | 1 | no | — |
| 205 | #107 | C2×#64408 | 1 | 2 | yes | — |
| 206 | #107 | C2×#64408 | 1 | 2 | yes | — |
| 207 | C4⋊C8 | — | 73 | 2 | no | — |
| 208 | C4⋊C8 | — | 73 | 2 | no | — |
| 209 | C4⋊C8 | — | 146 | 2 | no | — |
| 210 | C4⋊C8 | — | 146 | 1 | no | — |
| 211 | #102 | — | 73 | 4 | no | — |
| 212 | #102 | — | 73 | 4 | no | — |
| 213 | C22⋊C8 | — | 146 | 4 | no | — |
| 214 | C22⋊C8 | — | 146 | 4 | no | — |
| 215 | C22⋊C8 | — | 146 | 1 | no | — |
| 216 | #97 | — | 73 | 2 | no | — |
| 217 | C4×C8 | — | 73 | 2 | no | — |
| 218 | C4×C8 | — | 73 | 1 | no | — |
| 219 | C4×C8 | — | 73 | 1 | no | — |
| 220 | C4×C8 | — | 73 | 2 | no | — |
| 221 | C4×C8 | — | 73 | 1 | no | — |
| 222 | C4×C8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 223 | #41 | — | 292 | 4 | no | — |
| 224 | #41 | — | 292 | 4 | no | — |
| 225 | C2×Q8 | — | 2 | 2 | no | — |
| 226 | C2×D4 | — | 73 | 4 | no | — |
| 227 | C2×D4 | — | 146 | 4 | no | — |
| 228 | C2×D4 | — | 146 | 2 | no | — |
| 229 | C2×D4 | — | 146 | 2 | no | — |
| 230 | C22×C4 | — | 73 | 1 | no | — |
| 231 | C22×C4 | — | 73 | 1 | no | — |
| 232 | C22×C4 | — | 73 | 1 | no | — |
| 233 | C22×C4 | — | 146 | 4 | no | — |
| 234 | D8 | — | 292 | 2 | no | — |
| 235 | D8 | — | 146 | 4 | no | — |
| 236 | M16 | — | 292 | 8 | no | — |
| 237 | M16 | — | 146 | 4 | no | — |
| 238 | C2×C8 | — | 292 | 1 | no | — |
| 239 | C2×C8 | — | 292 | 4 | no | — |
| 240 | C2×C8 | — | 292 | 8 | no | — |
| 241 | C2×C8 | — | 73 | 4 | no | — |
| 242 | C2×C8 | — | 73 | 1 | no | — |
| 243 | C2×C8 | — | 73 | 1 | no | — |
| 244 | C2×C8 | — | 146 | 2 | no | — |
| 245 | C2×C8 | — | 146 | 2 | no | — |
| 246 | C2×C8 | — | 146 | 2 | no | — |
| 247 | C2×C8 | — | 146 | 2 | no | — |
| 248 | C2×C8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 249 | C2×C8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 250 | C4⋊C4 | — | 2 | 2 | no | — |
| 251 | C4⋊C4 | C22×#64408 | 1 | 4 | yes | — |
| 252 | C22⋊C4 | — | 146 | 4 | no | — |
| 253 | C22⋊C4 | — | 146 | 4 | no | — |
| 254 | C42 | — | 73 | 1 | no | — |
| 255 | C42 | — | 73 | 1 | no | — |
| 256 | C42 | — | 73 | 1 | no | — |
| 257 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 258 | C23 | — | 73 | 1 | no | — |
| 259 | C23 | — | 146 | 4 | no | — |
| 260 | Q8 | — | 4 | 4 | no | — |
| 261 | D4 | — | 292 | 8 | no | — |
| 262 | D4 | — | 292 | 4 | no | — |
| 263 | D4 | — | 584 | 2 | no | — |
| 264 | D4 | — | 146 | 4 | no | — |
| 265 | D4 | — | 146 | 4 | no | — |
| 266 | C2×C4 | — | 2 | 4 | no | — |
| 267 | C2×C4 | — | 292 | 1 | no | — |
| 268 | C2×C4 | — | 292 | 4 | no | — |
| 269 | C2×C4 | — | 292 | 4 | no | — |
| 270 | C2×C4 | — | 73 | 1 | no | — |
| 271 | C2×C4 | — | 73 | 4 | no | — |
| 272 | C2×C4 | — | 73 | 1 | no | — |
| 273 | C2×C4 | — | 73 | 1 | no | — |
| 274 | C2×C4 | — | 146 | 1 | no | — |
| 275 | C2×C4 | — | 146 | 1 | no | — |
| 276 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 277 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 278 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 279 | C8 | — | 2 | 1 | no | — |
| 280 | C8 | — | 292 | 2 | no | — |
| 281 | C8 | — | 292 | 2 | no | — |
| 282 | C8 | — | 292 | 2 | no | — |
| 283 | C8 | — | 146 | 4 | no | — |
| 284 | C8 | — | 146 | 1 | no | — |
| 285 | C8 | — | 146 | 1 | no | — |
| 286 | C8 | #14556679 | 1 | 2 | yes | complemented |
| 287 | C22 | — | 292 | 4 | no | — |
| 288 | C22 | — | 292 | 4 | no | — |
| 289 | C22 | — | 292 | 4 | no | — |
| 290 | C22 | — | 73 | 2 | no | — |
| 291 | C22 | — | 146 | 1 | no | — |
| 292 | C22 | — | 146 | 1 | no | — |
| 293 | C22 | C2×D4×#64408 | 1 | 1 | yes | characteristic |
| 294 | C4 | — | 2 | 1 | no | — |
| 295 | C4 | — | 4 | 4 | no | — |
| 296 | C4 | — | 73 | 2 | no | — |
| 297 | C4 | — | 146 | 1 | no | — |
| 298 | C4 | — | 146 | 1 | no | — |
| 299 | C4 | #17989628 | 1 | 2 | yes | — |
| 300 | C4 | C2×#14556679 | 1 | 1 | yes | characteristic |
| 301 | C4 | #17989667 | 1 | 1 | yes | characteristic |
| 302 | C2 | — | 584 | 4 | no | — |
| 303 | C2 | — | 146 | 2 | no | — |
| 304 | C2 | #22626677 | 1 | 1 | yes | characteristic |
| 305 | C2 | C2×#17989628 | 1 | 1 | yes | characteristic |
| 306 | C2 | #22626711 | 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