← #36462801
Subgroups — #36462801
Order 22784.
606 conjugacy classes of subgroups.
The subgroup lattice has 294 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #26028842 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26019984 | C2 | 1 | 2 | yes | maximal |
| 3 | #26019968 | C2 | 1 | 2 | yes | maximal |
| 4 | #26019950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×H(3,ℤ/4)×C89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C23×#10623494 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×#15667971 | C22 | 1 | 2 | yes | — |
| 8 | C2×#15667971 | C22 | 1 | 1 | yes | characteristic |
| 9 | #19151640 | — | 2 | 4 | no | — |
| 10 | #19151636 | — | 2 | 2 | no | — |
| 11 | #19151364 | — | 2 | 4 | no | — |
| 12 | #19151360 | — | 2 | 4 | no | — |
| 13 | #19151352 | — | 2 | 2 | no | — |
| 14 | C22×M16×C89 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#117×C89 | C22 | 1 | 2 | yes | — |
| 16 | H(3,ℤ/4)×C89 | C4 | 1 | 4 | yes | complemented |
| 17 | C22×#10623494 | — | 2 | 2 | no | — |
| 18 | C22×#10623494 | — | 2 | 1 | no | — |
| 19 | C22×#10623494 | — | 2 | 1 | no | — |
| 20 | C22×#10623494 | — | 2 | 2 | no | — |
| 21 | C22×#10623494 | Q8 | 1 | 2 | yes | — |
| 22 | #15667971 | — | 2 | 2 | no | — |
| 23 | #15667971 | — | 2 | 2 | no | — |
| 24 | #15667971 | — | 2 | 2 | no | — |
| 25 | #15667971 | — | 2 | 2 | no | — |
| 26 | #15667971 | — | 2 | 2 | no | — |
| 27 | #15667971 | — | 2 | 2 | no | — |
| 28 | C2×C4⋊Dic89 | — | 2 | 1 | no | — |
| 29 | C2×C4⋊Dic89 | D4 | 1 | 4 | yes | — |
| 30 | C2×C22⋊Dic89 | — | 2 | 2 | no | — |
| 31 | C2×C22⋊Dic89 | D4 | 1 | 2 | yes | — |
| 32 | C2×C4×Dic89 | — | 2 | 1 | no | — |
| 33 | C2×C4×Dic89 | — | 2 | 2 | no | — |
| 34 | #15667946 | — | 2 | 4 | no | — |
| 35 | #15667944 | — | 2 | 4 | no | — |
| 36 | C23×C4×C89 | C23 | 1 | 1 | yes | characteristic |
| 37 | C2×M16×C89 | — | 2 | 2 | no | — |
| 38 | C2×M16×C89 | — | 2 | 2 | no | — |
| 39 | C2×M16×C89 | C2×C4 | 1 | 2 | yes | — |
| 40 | C2×M16×C89 | Q8 | 1 | 2 | yes | — |
| 41 | C22×C8×C89 | D4 | 1 | 2 | yes | — |
| 42 | #117×C89 | — | 2 | 2 | no | — |
| 43 | #117×C89 | — | 2 | 2 | no | — |
| 44 | #117×C89 | — | 2 | 2 | no | — |
| 45 | #117×C89 | C2×C4 | 1 | 4 | yes | — |
| 46 | C2×C4⋊C4×C89 | — | 2 | 2 | no | — |
| 47 | C2×C22⋊C4×C89 | — | 2 | 2 | no | — |
| 48 | C2×C42×C89 | — | 2 | 2 | no | — |
| 49 | C22×Dic89 | — | 2 | 2 | no | — |
| 50 | C22×Dic89 | — | 2 | 4 | no | — |
| 51 | C2×#10623494 | — | 2 | 4 | no | — |
| 52 | C2×#10623494 | — | 2 | 2 | no | — |
| 53 | C2×#10623494 | — | 4 | 1 | no | — |
| 54 | C2×#10623494 | — | 4 | 2 | no | — |
| 55 | C2×#10623494 | — | 4 | 1 | no | — |
| 56 | C4⋊Dic89 | — | 2 | 4 | no | — |
| 57 | C4⋊Dic89 | — | 2 | 4 | no | — |
| 58 | C4⋊Dic89 | — | 4 | 2 | no | — |
| 59 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 60 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 61 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 62 | C4×Dic89 | — | 4 | 2 | no | — |
| 63 | C4×Dic89 | — | 4 | 1 | no | — |
| 64 | C4×Dic89 | — | 4 | 2 | no | — |
| 65 | C4×Dic89 | — | 4 | 1 | no | — |
| 66 | C24×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 67 | C22×C4×C89 | — | 4 | 2 | no | — |
| 68 | C22×C4×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 69 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C22×C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 71 | C22×C4×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 72 | C22×C4×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 73 | C22×C4×C89 | #41 | 1 | 2 | yes | — |
| 74 | C22×C4×C89 | #41 | 1 | 2 | yes | — |
| 75 | C22×C4×C89 | #41 | 1 | 2 | yes | — |
| 76 | C22×C4×C89 | #41 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×C89 | #41 | 1 | 1 | yes | characteristic |
| 78 | M16×C89 | — | 2 | 4 | no | — |
| 79 | M16×C89 | — | 2 | 4 | no | — |
| 80 | C2×C8×C89 | — | 2 | 2 | no | — |
| 81 | C2×C8×C89 | — | 2 | 2 | no | — |
| 82 | C2×C8×C89 | C4⋊C4 | 1 | 4 | yes | — |
| 83 | C4⋊C4×C89 | — | 2 | 4 | no | — |
| 84 | C4⋊C4×C89 | — | 4 | 2 | no | — |
| 85 | C22⋊C4×C89 | — | 2 | 4 | no | — |
| 86 | C22⋊C4×C89 | — | 4 | 2 | no | — |
| 87 | C42×C89 | — | 2 | 4 | no | — |
| 88 | C42×C89 | — | 4 | 2 | no | — |
| 89 | C23×C89 | — | 4 | 2 | no | — |
| 90 | C23×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 91 | C23×C89 | #121 | 1 | 2 | yes | — |
| 92 | C23×C89 | #121 | 1 | 1 | yes | characteristic |
| 93 | C23×C89 | #123 | 1 | 2 | yes | — |
| 94 | C23×C89 | C4⋊Q8 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C89 | — | 4 | 4 | no | — |
| 96 | C2×C4×C89 | — | 8 | 4 | no | — |
| 97 | C2×C4×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C89 | #117 | 1 | 2 | yes | — |
| 99 | C2×C4×C89 | C4×D4 | 1 | 2 | yes | — |
| 100 | C2×C4×C89 | C4×Q8 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×C89 | C22⋊Q8 | 1 | 2 | yes | — |
| 103 | C2×C4×C89 | C22⋊Q8 | 1 | 2 | yes | — |
| 104 | C2×C4×C89 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C89 | #123 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×C89 | #123 | 1 | 2 | yes | — |
| 107 | C2×C4×C89 | #124 | 1 | 2 | yes | — |
| 108 | C2×C4×C89 | #124 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×C89 | #124 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C89 | #125 | 1 | 2 | yes | — |
| 111 | C2×C4×C89 | #125 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C89 | #125 | 1 | 2 | yes | — |
| 113 | C2×C4×C89 | #126 | 1 | 2 | yes | — |
| 114 | C2×C4×C89 | #126 | 1 | 2 | yes | — |
| 115 | C2×Dic89 | — | 4 | 4 | no | — |
| 116 | C2×Dic89 | — | 4 | 4 | no | — |
| 117 | C2×Dic89 | — | 4 | 2 | no | — |
| 118 | C2×Dic89 | — | 8 | 4 | no | — |
| 119 | C8×C89 | — | 2 | 4 | no | — |
| 120 | #10623494 | — | 4 | 2 | no | — |
| 121 | C22×C89 | — | 2 | 2 | no | — |
| 122 | C22×C89 | — | 2 | 4 | no | — |
| 123 | C22×C89 | — | 4 | 1 | no | — |
| 124 | C22×C89 | — | 4 | 2 | no | — |
| 125 | C22×C89 | — | 4 | 1 | no | — |
| 126 | C22×C89 | #388 | 1 | 2 | yes | — |
| 127 | C22×C89 | #389 | 1 | 1 | yes | characteristic |
| 128 | C22×C89 | #394 | 1 | 1 | yes | characteristic |
| 129 | C22×C89 | #397 | 1 | 1 | yes | characteristic |
| 130 | C22×C89 | #398 | 1 | 2 | yes | — |
| 131 | C4×C89 | — | 8 | 4 | no | — |
| 132 | C4×C89 | #382 | 1 | 1 | yes | characteristic |
| 133 | C4×C89 | #385 | 1 | 1 | yes | characteristic |
| 134 | C4×C89 | #387 | 1 | 2 | yes | — |
| 135 | C4×C89 | #393 | 1 | 1 | yes | characteristic |
| 136 | C4×C89 | #400 | 1 | 1 | yes | characteristic |
| 137 | C4×C89 | #400 | 1 | 2 | yes | — |
| 138 | Dic89 | — | 8 | 2 | no | — |
| 139 | Dic89 | — | 8 | 4 | no | — |
| 140 | #11285 | — | 89 | 1 | no | maximal, Sylow |
| 141 | C2×C89 | — | 2 | 1 | no | — |
| 142 | C2×C89 | — | 2 | 2 | no | — |
| 143 | C2×C89 | — | 2 | 1 | no | — |
| 144 | C2×C89 | — | 2 | 2 | no | — |
| 145 | C2×C89 | #1442 | 1 | 1 | yes | characteristic |
| 146 | C2×C89 | #2053 | 1 | 2 | yes | — |
| 147 | #2911 | — | 89 | 1 | no | — |
| 148 | #1740 | — | 89 | 2 | no | — |
| 149 | #1735 | — | 89 | 2 | no | — |
| 150 | C2×H(3,ℤ/4) | D89 | 1 | 1 | yes | characteristic |
| 151 | #1729 | — | 89 | 1 | no | — |
| 152 | C89 | #11285 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 153 | C22×M16 | C2×D89 | 1 | 1 | yes | characteristic |
| 154 | C23×C8 | — | 89 | 1 | no | — |
| 155 | C2×#117 | — | 89 | 1 | no | — |
| 156 | C2×#117 | — | 89 | 2 | no | — |
| 157 | C2×#117 | C2×D89 | 1 | 2 | yes | — |
| 158 | #428 | — | 178 | 4 | no | — |
| 159 | #427 | — | 178 | 2 | no | — |
| 160 | #342 | — | 178 | 4 | no | — |
| 161 | #340 | — | 178 | 4 | no | — |
| 162 | H(3,ℤ/4) | Dic89 | 1 | 4 | yes | complemented |
| 163 | #336 | — | 178 | 2 | no | — |
| 164 | C23×C4 | C22×D89 | 1 | 1 | yes | characteristic |
| 165 | C2×M16 | — | 2 | 2 | no | — |
| 166 | C2×M16 | — | 2 | 2 | no | — |
| 167 | C2×M16 | Dic178 | 1 | 2 | yes | — |
| 168 | C2×M16 | C2×Dic89 | 1 | 2 | yes | — |
| 169 | C22×C8 | — | 89 | 2 | no | — |
| 170 | C22×C8 | — | 178 | 2 | no | — |
| 171 | C22×C8 | — | 178 | 1 | no | — |
| 172 | C22×C8 | — | 178 | 1 | no | — |
| 173 | C22×C8 | — | 178 | 2 | no | — |
| 174 | C22×C8 | D356 | 1 | 2 | yes | — |
| 175 | #117 | — | 2 | 2 | no | — |
| 176 | #117 | — | 2 | 2 | no | — |
| 177 | #117 | — | 2 | 2 | no | — |
| 178 | #117 | — | 178 | 2 | no | — |
| 179 | #117 | — | 178 | 2 | no | — |
| 180 | #117 | — | 178 | 2 | no | — |
| 181 | #117 | — | 178 | 2 | no | — |
| 182 | #117 | — | 178 | 2 | no | — |
| 183 | #117 | — | 178 | 2 | no | — |
| 184 | #117 | C2×Dic89 | 1 | 4 | yes | — |
| 185 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 186 | C2×C4⋊C4 | — | 89 | 4 | no | — |
| 187 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 188 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 189 | C2×C22⋊C4 | — | 89 | 2 | no | — |
| 190 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 191 | C2×C42 | — | 2 | 2 | no | — |
| 192 | C2×C42 | — | 178 | 1 | no | — |
| 193 | C2×C42 | — | 178 | 2 | no | — |
| 194 | #107 | — | 178 | 4 | no | — |
| 195 | #106 | — | 178 | 4 | no | — |
| 196 | C24 | D4×D89 | 1 | 1 | yes | characteristic |
| 197 | C22×C4 | — | 4 | 2 | no | — |
| 198 | C22×C4 | — | 178 | 2 | no | — |
| 199 | C22×C4 | — | 178 | 4 | no | — |
| 200 | C22×C4 | C22×Dic89 | 1 | 1 | yes | characteristic |
| 201 | C22×C4 | D4×D89 | 1 | 2 | yes | — |
| 202 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 203 | C22×C4 | Q8×D89 | 1 | 1 | yes | characteristic |
| 204 | C22×C4 | C2×Dic178 | 1 | 1 | yes | characteristic |
| 205 | C22×C4 | #13083573 | 1 | 2 | yes | — |
| 206 | C22×C4 | #13083573 | 1 | 1 | yes | characteristic |
| 207 | C22×C4 | #13083574 | 1 | 2 | yes | — |
| 208 | C22×C4 | #13083574 | 1 | 2 | yes | — |
| 209 | C22×C4 | #13083575 | 1 | 1 | yes | characteristic |
| 210 | M16 | — | 2 | 4 | no | — |
| 211 | M16 | — | 2 | 4 | no | — |
| 212 | C2×C8 | — | 2 | 2 | no | — |
| 213 | C2×C8 | — | 2 | 2 | no | — |
| 214 | C2×C8 | — | 356 | 1 | no | — |
| 215 | C2×C8 | — | 356 | 2 | no | — |
| 216 | C2×C8 | — | 356 | 1 | no | — |
| 217 | C2×C8 | — | 178 | 4 | no | — |
| 218 | C2×C8 | — | 178 | 2 | no | — |
| 219 | C2×C8 | C4⋊Dic89 | 1 | 4 | yes | — |
| 220 | C4⋊C4 | — | 2 | 4 | no | — |
| 221 | C4⋊C4 | — | 4 | 2 | no | — |
| 222 | C4⋊C4 | — | 356 | 2 | no | — |
| 223 | C4⋊C4 | — | 178 | 4 | no | — |
| 224 | C4⋊C4 | — | 178 | 4 | no | — |
| 225 | C22⋊C4 | — | 2 | 4 | no | — |
| 226 | C22⋊C4 | — | 4 | 2 | no | — |
| 227 | C22⋊C4 | — | 356 | 2 | no | — |
| 228 | C22⋊C4 | — | 356 | 2 | no | — |
| 229 | C22⋊C4 | — | 178 | 4 | no | — |
| 230 | C42 | — | 2 | 4 | no | — |
| 231 | C42 | — | 4 | 2 | no | — |
| 232 | C42 | — | 356 | 1 | no | — |
| 233 | C42 | — | 356 | 2 | no | — |
| 234 | C42 | — | 356 | 1 | no | — |
| 235 | C42 | — | 356 | 2 | no | — |
| 236 | C23 | — | 4 | 2 | no | — |
| 237 | C23 | D4×Dic89 | 1 | 1 | yes | characteristic |
| 238 | C23 | #15667985 | 1 | 2 | yes | — |
| 239 | C23 | #15667987 | 1 | 1 | yes | characteristic |
| 240 | C23 | #15667994 | 1 | 2 | yes | — |
| 241 | C23 | #15668011 | 1 | 1 | yes | characteristic |
| 242 | C2×C4 | — | 4 | 4 | no | — |
| 243 | C2×C4 | — | 8 | 4 | no | — |
| 244 | C2×C4 | — | 356 | 4 | no | — |
| 245 | C2×C4 | — | 356 | 4 | no | — |
| 246 | C2×C4 | — | 356 | 2 | no | — |
| 247 | C2×C4 | — | 712 | 4 | no | — |
| 248 | C2×C4 | C2×C4⋊Dic89 | 1 | 1 | yes | characteristic |
| 249 | C2×C4 | #15667971 | 1 | 2 | yes | — |
| 250 | C2×C4 | D4×Dic89 | 1 | 2 | yes | — |
| 251 | C2×C4 | Q8×Dic89 | 1 | 1 | yes | characteristic |
| 252 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 253 | C2×C4 | #15667989 | 1 | 2 | yes | — |
| 254 | C2×C4 | #15667990 | 1 | 2 | yes | — |
| 255 | C2×C4 | #15667992 | 1 | 1 | yes | characteristic |
| 256 | C2×C4 | #15667996 | 1 | 1 | yes | characteristic |
| 257 | C2×C4 | #15667997 | 1 | 2 | yes | — |
| 258 | C2×C4 | #15667998 | 1 | 2 | yes | — |
| 259 | C2×C4 | #15668000 | 1 | 1 | yes | characteristic |
| 260 | C2×C4 | #15668000 | 1 | 1 | yes | characteristic |
| 261 | C2×C4 | #15668002 | 1 | 2 | yes | — |
| 262 | C2×C4 | #15668003 | 1 | 1 | yes | characteristic |
| 263 | C2×C4 | #15668004 | 1 | 2 | yes | — |
| 264 | C2×C4 | #15668005 | 1 | 2 | yes | — |
| 265 | C2×C4 | #15668007 | 1 | 2 | yes | — |
| 266 | C8 | — | 2 | 4 | no | — |
| 267 | C8 | — | 356 | 2 | no | — |
| 268 | C22 | — | 2 | 4 | no | — |
| 269 | C22 | — | 2 | 2 | no | — |
| 270 | C22 | — | 4 | 1 | no | — |
| 271 | C22 | — | 4 | 2 | no | — |
| 272 | C22 | — | 4 | 1 | no | — |
| 273 | C22 | #19151491 | 1 | 2 | yes | — |
| 274 | C22 | #19151497 | 1 | 1 | yes | characteristic |
| 275 | C22 | #19151516 | 1 | 1 | yes | characteristic |
| 276 | C22 | #19151525 | 1 | 1 | yes | characteristic |
| 277 | C22 | #19151532 | 1 | 2 | yes | — |
| 278 | C4 | — | 8 | 4 | no | — |
| 279 | C4 | — | 712 | 2 | no | — |
| 280 | C4 | — | 712 | 4 | no | — |
| 281 | C4 | #19151464 | 1 | 1 | yes | characteristic |
| 282 | C4 | #19151473 | 1 | 1 | yes | characteristic |
| 283 | C4 | #19151484 | 1 | 2 | yes | — |
| 284 | C4 | #19151511 | 1 | 1 | yes | characteristic |
| 285 | C4 | #19151538 | 1 | 1 | yes | characteristic |
| 286 | C4 | #19151540 | 1 | 2 | yes | — |
| 287 | C2 | — | 2 | 2 | no | — |
| 288 | C2 | — | 2 | 1 | no | — |
| 289 | C2 | — | 2 | 1 | no | — |
| 290 | C2 | — | 2 | 2 | no | — |
| 291 | C2 | #26018509 | 1 | 1 | yes | characteristic |
| 292 | C2 | #26021559 | 1 | 2 | yes | — |
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