← #18088221
Subgroups — #18088221
Order 4864.
644 conjugacy classes of subgroups.
The subgroup lattice has 304 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #14572053 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14563367 | C2 | 1 | 2 | yes | maximal |
| 3 | #14563344 | C2 | 1 | 2 | yes | maximal |
| 4 | C2×#11926301 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×C19×H(3,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C22×#64520 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×#10597372 | C22 | 1 | 2 | yes | — |
| 8 | C2×#10597372 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11926502 | — | 2 | 2 | no | — |
| 10 | #11926499 | C4 | 1 | 4 | yes | complemented |
| 11 | M16×Dic19 | — | 2 | 2 | no | — |
| 12 | #11926310 | — | 2 | 4 | no | — |
| 13 | #11926303 | C4 | 1 | 8 | yes | complemented |
| 14 | #11926301 | — | 2 | 2 | no | — |
| 15 | C22×M16×C19 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C19×#117 | C22 | 1 | 2 | yes | — |
| 17 | C19×H(3,ℤ/4) | — | 2 | 2 | no | — |
| 18 | C23×C4×C19 | C23 | 1 | 1 | yes | characteristic |
| 19 | C2×M16×C19 | — | 2 | 2 | no | — |
| 20 | C2×M16×C19 | — | 2 | 2 | no | — |
| 21 | C2×M16×C19 | D4 | 1 | 2 | yes | — |
| 22 | C2×M16×C19 | D4 | 1 | 2 | yes | — |
| 23 | C22×C8×C19 | C2×C4 | 1 | 2 | yes | — |
| 24 | C19×#117 | — | 2 | 2 | no | — |
| 25 | C19×#117 | — | 2 | 2 | no | — |
| 26 | C19×#117 | — | 2 | 2 | no | — |
| 27 | C19×#117 | C2×C4 | 1 | 4 | yes | — |
| 28 | C2×C4⋊C4×C19 | — | 2 | 2 | no | — |
| 29 | C2×C22⋊C4×C19 | — | 2 | 2 | no | — |
| 30 | C2×C42×C19 | — | 2 | 2 | no | — |
| 31 | C2×C22⋊Dic19 | — | 2 | 2 | no | — |
| 32 | C2×C22⋊Dic19 | D4 | 1 | 2 | yes | — |
| 33 | #10597372 | — | 2 | 1 | no | — |
| 34 | #10597372 | — | 2 | 1 | no | — |
| 35 | #10597372 | — | 2 | 2 | no | — |
| 36 | #10597372 | — | 2 | 2 | no | — |
| 37 | #10597372 | — | 2 | 2 | no | — |
| 38 | #10597372 | — | 2 | 2 | no | — |
| 39 | #10597372 | C2×C4 | 1 | 2 | yes | — |
| 40 | #10597372 | Q8 | 1 | 2 | yes | — |
| 41 | C2×C4⋊Dic19 | — | 2 | 1 | no | — |
| 42 | C2×C4⋊Dic19 | — | 2 | 2 | no | — |
| 43 | C2×C4×Dic19 | — | 2 | 1 | no | — |
| 44 | C2×C4×Dic19 | C2×C4 | 1 | 4 | yes | — |
| 45 | C2×#64520 | — | 2 | 1 | no | — |
| 46 | C2×#64520 | — | 2 | 2 | no | — |
| 47 | C2×#64520 | C2×C4 | 1 | 4 | yes | — |
| 48 | C2×#64520 | C2×C4 | 1 | 2 | yes | — |
| 49 | C22×C19⋊C8 | — | 2 | 1 | no | — |
| 50 | #10597272 | — | 2 | 4 | no | — |
| 51 | C8×Dic19 | — | 2 | 4 | no | — |
| 52 | C24×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 53 | C22×C4×C19 | — | 4 | 2 | no | — |
| 54 | C22×C4×C19 | C22×C4 | 1 | 1 | yes | characteristic |
| 55 | C22×C4×C19 | C22×C4 | 1 | 2 | yes | — |
| 56 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 57 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 58 | C22×C4×C19 | C2×Q8 | 1 | 1 | yes | characteristic |
| 59 | C22×C4×C19 | #41 | 1 | 2 | yes | — |
| 60 | C22×C4×C19 | #41 | 1 | 1 | yes | characteristic |
| 61 | C22×C4×C19 | #41 | 1 | 2 | yes | — |
| 62 | C22×C4×C19 | #41 | 1 | 2 | yes | — |
| 63 | C22×C4×C19 | #41 | 1 | 1 | yes | characteristic |
| 64 | C22×Dic19 | — | 2 | 2 | no | — |
| 65 | C22×Dic19 | — | 2 | 4 | no | — |
| 66 | M16×C19 | — | 2 | 4 | no | — |
| 67 | M16×C19 | — | 2 | 4 | no | — |
| 68 | C2×C8×C19 | — | 2 | 2 | no | — |
| 69 | C2×C8×C19 | — | 2 | 2 | no | — |
| 70 | C2×C8×C19 | C22⋊C4 | 1 | 4 | yes | — |
| 71 | C4⋊C4×C19 | — | 2 | 4 | no | — |
| 72 | C4⋊C4×C19 | — | 4 | 2 | no | — |
| 73 | C22⋊C4×C19 | — | 2 | 4 | no | — |
| 74 | C22⋊C4×C19 | — | 4 | 2 | no | — |
| 75 | C42×C19 | — | 2 | 4 | no | — |
| 76 | C42×C19 | — | 4 | 2 | no | — |
| 77 | C22⋊Dic19 | — | 2 | 2 | no | — |
| 78 | C22⋊Dic19 | — | 4 | 2 | no | — |
| 79 | C22⋊Dic19 | — | 4 | 2 | no | — |
| 80 | C22⋊Dic19 | C4⋊C4 | 1 | 4 | yes | — |
| 81 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 82 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 83 | C4⋊Dic19 | — | 4 | 2 | no | — |
| 84 | C4⋊Dic19 | — | 4 | 2 | no | — |
| 85 | C4×Dic19 | — | 2 | 2 | no | — |
| 86 | C4×Dic19 | — | 2 | 2 | no | — |
| 87 | C4×Dic19 | — | 2 | 4 | no | — |
| 88 | C4×Dic19 | — | 2 | 4 | no | — |
| 89 | #64520 | — | 2 | 2 | no | — |
| 90 | #64520 | — | 2 | 4 | no | — |
| 91 | #64520 | C42 | 1 | 4 | yes | — |
| 92 | C2×C19⋊C8 | — | 2 | 2 | no | — |
| 93 | C2×C19⋊C8 | — | 2 | 4 | no | — |
| 94 | #10811 | — | 19 | 1 | no | maximal, Sylow |
| 95 | C23×C19 | — | 8 | 1 | no | — |
| 96 | C23×C19 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C23×C19 | C4×D4 | 1 | 2 | yes | — |
| 98 | C23×C19 | #121 | 1 | 1 | yes | characteristic |
| 99 | C23×C19 | #121 | 1 | 1 | yes | characteristic |
| 100 | C23×C19 | #124 | 1 | 2 | yes | — |
| 101 | C2×C4×C19 | — | 4 | 4 | no | — |
| 102 | C2×C4×C19 | — | 8 | 4 | no | — |
| 103 | C2×C4×C19 | C2×C42 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C19 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C19 | #117 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×C19 | #117 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×C19 | #117 | 1 | 2 | yes | — |
| 108 | C2×C4×C19 | #117 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×C19 | #117 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C19 | #117 | 1 | 2 | yes | — |
| 111 | C2×C4×C19 | C4×D4 | 1 | 2 | yes | — |
| 112 | C2×C4×C19 | C4×D4 | 1 | 2 | yes | — |
| 113 | C2×C4×C19 | C4×Q8 | 1 | 2 | yes | — |
| 114 | C2×C4×C19 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C19 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C19 | #123 | 1 | 2 | yes | — |
| 117 | C2×C4×C19 | #123 | 1 | 2 | yes | — |
| 118 | C2×C4×C19 | #125 | 1 | 2 | yes | — |
| 119 | C2×C4×C19 | #126 | 1 | 2 | yes | — |
| 120 | C2×C4×C19 | #126 | 1 | 2 | yes | — |
| 121 | C2×Dic19 | — | 2 | 4 | no | — |
| 122 | C2×Dic19 | — | 4 | 4 | no | — |
| 123 | C2×Dic19 | — | 8 | 2 | no | — |
| 124 | C2×Dic19 | — | 8 | 4 | no | — |
| 125 | C8×C19 | — | 2 | 4 | no | — |
| 126 | C19⋊C8 | — | 2 | 4 | no | — |
| 127 | #2873 | — | 19 | 1 | no | — |
| 128 | #1740 | — | 19 | 2 | no | — |
| 129 | #1733 | — | 19 | 2 | no | — |
| 130 | C2×H(3,ℤ/4) | — | 19 | 1 | no | — |
| 131 | C2×H(3,ℤ/4) | D19 | 1 | 1 | yes | characteristic |
| 132 | C22×C19 | — | 4 | 2 | no | — |
| 133 | C22×C19 | — | 4 | 1 | no | — |
| 134 | C22×C19 | — | 4 | 2 | no | — |
| 135 | C22×C19 | — | 4 | 1 | no | — |
| 136 | C22×C19 | — | 4 | 1 | no | — |
| 137 | C22×C19 | C4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 138 | C22×C19 | #380 | 1 | 1 | yes | characteristic |
| 139 | C22×C19 | #382 | 1 | 1 | yes | characteristic |
| 140 | C22×C19 | #388 | 1 | 2 | yes | — |
| 141 | C22×C19 | #388 | 1 | 2 | yes | — |
| 142 | C4×C19 | — | 8 | 4 | no | — |
| 143 | C4×C19 | #376 | 1 | 1 | yes | characteristic |
| 144 | C4×C19 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 145 | C4×C19 | #381 | 1 | 1 | yes | characteristic |
| 146 | C4×C19 | #383 | 1 | 1 | yes | characteristic |
| 147 | C4×C19 | #387 | 1 | 2 | yes | — |
| 148 | C4×C19 | #387 | 1 | 2 | yes | — |
| 149 | Dic19 | — | 4 | 4 | no | — |
| 150 | Dic19 | — | 8 | 4 | no | — |
| 151 | C22×M16 | — | 19 | 1 | no | — |
| 152 | C22×M16 | C2×D19 | 1 | 1 | yes | characteristic |
| 153 | C2×#117 | — | 19 | 2 | no | — |
| 154 | C2×#117 | — | 19 | 1 | no | — |
| 155 | C2×#117 | C2×D19 | 1 | 2 | yes | — |
| 156 | #405 | — | 19 | 4 | no | — |
| 157 | #405 | — | 38 | 2 | no | — |
| 158 | C4×M16 | — | 38 | 2 | no | — |
| 159 | #342 | — | 38 | 4 | no | — |
| 160 | #339 | — | 19 | 8 | no | — |
| 161 | H(3,ℤ/4) | — | 2 | 2 | no | — |
| 162 | H(3,ℤ/4) | — | 38 | 2 | no | — |
| 163 | C2×C19 | — | 2 | 1 | no | — |
| 164 | C2×C19 | — | 2 | 2 | no | — |
| 165 | C2×C19 | — | 2 | 2 | no | — |
| 166 | C2×C19 | — | 2 | 1 | no | — |
| 167 | C2×C19 | — | 2 | 1 | no | — |
| 168 | C2×C19 | #1434 | 1 | 1 | yes | characteristic |
| 169 | C23×C4 | C22×D19 | 1 | 1 | yes | characteristic |
| 170 | C2×M16 | — | 2 | 2 | no | — |
| 171 | C2×M16 | — | 2 | 2 | no | — |
| 172 | C2×M16 | — | 19 | 4 | no | — |
| 173 | C2×M16 | — | 19 | 2 | no | — |
| 174 | C2×M16 | — | 38 | 1 | no | — |
| 175 | C2×M16 | — | 38 | 2 | no | — |
| 176 | C2×M16 | D76 | 1 | 2 | yes | — |
| 177 | C2×M16 | C22⋊D19 | 1 | 2 | yes | — |
| 178 | C22×C8 | — | 38 | 1 | no | — |
| 179 | C22×C8 | C4×D19 | 1 | 2 | yes | — |
| 180 | #117 | — | 2 | 2 | no | — |
| 181 | #117 | — | 2 | 2 | no | — |
| 182 | #117 | — | 2 | 2 | no | — |
| 183 | #117 | — | 19 | 2 | no | — |
| 184 | #117 | — | 19 | 2 | no | — |
| 185 | #117 | — | 38 | 1 | no | — |
| 186 | #117 | — | 38 | 1 | no | — |
| 187 | #117 | — | 38 | 2 | no | — |
| 188 | #117 | — | 38 | 2 | no | — |
| 189 | #117 | — | 38 | 2 | no | — |
| 190 | #117 | — | 38 | 2 | no | — |
| 191 | #117 | C4×D19 | 1 | 4 | yes | — |
| 192 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 193 | C2×C4⋊C4 | — | 38 | 1 | no | — |
| 194 | C2×C4⋊C4 | — | 38 | 2 | no | — |
| 195 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 196 | C2×C22⋊C4 | — | 19 | 2 | no | — |
| 197 | C2×C22⋊C4 | — | 38 | 2 | no | — |
| 198 | C2×C42 | — | 2 | 2 | no | — |
| 199 | C2×C42 | — | 19 | 4 | no | — |
| 200 | C2×C42 | — | 38 | 1 | no | — |
| 201 | #97 | — | 38 | 4 | no | — |
| 202 | C4×C8 | — | 38 | 4 | no | — |
| 203 | C19 | #10811 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 204 | C24 | D4×D19 | 1 | 1 | yes | characteristic |
| 205 | C22×C4 | — | 4 | 2 | no | — |
| 206 | C22×C4 | — | 38 | 2 | no | — |
| 207 | C22×C4 | — | 38 | 4 | no | — |
| 208 | C22×C4 | C2×C4×D19 | 1 | 1 | yes | characteristic |
| 209 | C22×C4 | C2×C4×D19 | 1 | 2 | yes | — |
| 210 | C22×C4 | C2×D76 | 1 | 1 | yes | characteristic |
| 211 | C22×C4 | #64541 | 1 | 2 | yes | — |
| 212 | C22×C4 | #64543 | 1 | 2 | yes | — |
| 213 | C22×C4 | #64543 | 1 | 2 | yes | — |
| 214 | C22×C4 | #64543 | 1 | 1 | yes | characteristic |
| 215 | C22×C4 | Q8×D19 | 1 | 1 | yes | characteristic |
| 216 | C22×C4 | #64545 | 1 | 1 | yes | characteristic |
| 217 | C22×C4 | C2×C22⋊D19 | 1 | 1 | yes | characteristic |
| 218 | M16 | — | 2 | 4 | no | — |
| 219 | M16 | — | 2 | 4 | no | — |
| 220 | M16 | — | 19 | 4 | no | — |
| 221 | M16 | — | 38 | 2 | no | — |
| 222 | M16 | — | 38 | 4 | no | — |
| 223 | C2×C8 | — | 2 | 2 | no | — |
| 224 | C2×C8 | — | 2 | 2 | no | — |
| 225 | C2×C8 | — | 38 | 2 | no | — |
| 226 | C2×C8 | — | 38 | 4 | no | — |
| 227 | C2×C8 | (C2×D19)⋊C4 | 1 | 4 | yes | — |
| 228 | C4⋊C4 | — | 2 | 4 | no | — |
| 229 | C4⋊C4 | — | 4 | 2 | no | — |
| 230 | C4⋊C4 | — | 38 | 2 | no | — |
| 231 | C4⋊C4 | — | 38 | 2 | no | — |
| 232 | C4⋊C4 | — | 76 | 2 | no | — |
| 233 | C4⋊C4 | — | 76 | 2 | no | — |
| 234 | C22⋊C4 | — | 2 | 4 | no | — |
| 235 | C22⋊C4 | — | 4 | 2 | no | — |
| 236 | C22⋊C4 | — | 19 | 4 | no | — |
| 237 | C22⋊C4 | — | 38 | 2 | no | — |
| 238 | C22⋊C4 | — | 76 | 2 | no | — |
| 239 | C22⋊C4 | — | 76 | 2 | no | — |
| 240 | C42 | — | 2 | 4 | no | — |
| 241 | C42 | — | 4 | 2 | no | — |
| 242 | C42 | — | 38 | 2 | no | — |
| 243 | C42 | — | 38 | 2 | no | — |
| 244 | C42 | — | 38 | 4 | no | — |
| 245 | C42 | — | 38 | 4 | no | — |
| 246 | C23 | — | 8 | 1 | no | — |
| 247 | C23 | (C22⋊D19)⋊C4 | 1 | 2 | yes | — |
| 248 | C23 | #10597331 | 1 | 2 | yes | — |
| 249 | C23 | C4⋊C4×D19 | 1 | 1 | yes | characteristic |
| 250 | C23 | #10597341 | 1 | 1 | yes | characteristic |
| 251 | C23 | #10597384 | 1 | 1 | yes | characteristic |
| 252 | C2×C4 | — | 4 | 4 | no | — |
| 253 | C2×C4 | — | 8 | 4 | no | — |
| 254 | C2×C4 | — | 38 | 4 | no | — |
| 255 | C2×C4 | — | 76 | 4 | no | — |
| 256 | C2×C4 | — | 152 | 2 | no | — |
| 257 | C2×C4 | — | 152 | 4 | no | — |
| 258 | C2×C4 | C42×D19 | 1 | 1 | yes | characteristic |
| 259 | C2×C4 | #10597318 | 1 | 1 | yes | characteristic |
| 260 | C2×C4 | C4×D76 | 1 | 2 | yes | — |
| 261 | C2×C4 | #10597323 | 1 | 1 | yes | characteristic |
| 262 | C2×C4 | #10597323 | 1 | 2 | yes | — |
| 263 | C2×C4 | #10597323 | 1 | 1 | yes | characteristic |
| 264 | C2×C4 | #10597325 | 1 | 2 | yes | — |
| 265 | C2×C4 | #10597332 | 1 | 2 | yes | — |
| 266 | C2×C4 | #10597333 | 1 | 2 | yes | — |
| 267 | C2×C4 | #10597335 | 1 | 2 | yes | — |
| 268 | C2×C4 | #10597338 | 1 | 1 | yes | characteristic |
| 269 | C2×C4 | #10597338 | 1 | 2 | yes | — |
| 270 | C2×C4 | #10597343 | 1 | 1 | yes | characteristic |
| 271 | C2×C4 | #10597344 | 1 | 2 | yes | — |
| 272 | C2×C4 | C2×(C2×D19)⋊C4 | 1 | 1 | yes | characteristic |
| 273 | C2×C4 | C4×C22⋊D19 | 1 | 2 | yes | — |
| 274 | C2×C4 | #10597381 | 1 | 2 | yes | — |
| 275 | C2×C4 | #10597392 | 1 | 1 | yes | characteristic |
| 276 | C8 | — | 2 | 4 | no | — |
| 277 | C8 | — | 38 | 4 | no | — |
| 278 | C22 | — | 4 | 2 | no | — |
| 279 | C22 | — | 4 | 2 | no | — |
| 280 | C22 | — | 4 | 1 | no | — |
| 281 | C22 | — | 4 | 1 | no | — |
| 282 | C22 | — | 4 | 1 | no | — |
| 283 | C22 | #11926395 | 1 | 1 | yes | characteristic |
| 284 | C22 | #11926401 | 1 | 1 | yes | characteristic |
| 285 | C22 | #11926408 | 1 | 1 | yes | characteristic |
| 286 | C22 | #11926432 | 1 | 2 | yes | — |
| 287 | C22 | #11926436 | 1 | 2 | yes | — |
| 288 | C4 | — | 8 | 4 | no | — |
| 289 | C4 | — | 76 | 4 | no | — |
| 290 | C4 | — | 152 | 4 | no | — |
| 291 | C4 | #11926389 | 1 | 1 | yes | characteristic |
| 292 | C4 | C4×(C2×D19)⋊C4 | 1 | 1 | yes | characteristic |
| 293 | C4 | #11926405 | 1 | 1 | yes | characteristic |
| 294 | C4 | #11926411 | 1 | 1 | yes | characteristic |
| 295 | C4 | #11926425 | 1 | 2 | yes | — |
| 296 | C4 | #11926429 | 1 | 2 | yes | — |
| 297 | C2 | — | 2 | 2 | no | — |
| 298 | C2 | — | 2 | 1 | no | — |
| 299 | C2 | — | 2 | 2 | no | — |
| 300 | C2 | — | 2 | 1 | no | — |
| 301 | C2 | — | 2 | 1 | no | — |
| 302 | C2 | #14561859 | 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