← #36708944
Subgroups — #36708944
Order 22784.
674 conjugacy classes of subgroups.
The subgroup lattice has 300 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#19152014 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26029918 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #26022362 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #26022340 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #26022335 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#19151424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #26021964 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#508×C89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#15668018 | C22 | 1 | 1 | yes | characteristic |
| 10 | #19152176 | — | 2 | 2 | no | — |
| 11 | #19152014 | — | 2 | 4 | no | — |
| 12 | C2×#15667952 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#15667951 | C22 | 1 | 2 | yes | — |
| 14 | C2×C16×D89 | C22 | 1 | 2 | yes | — |
| 15 | #19151841 | — | 2 | 4 | no | — |
| 16 | #19151836 | C22 | 1 | 4 | yes | — |
| 17 | #19151831 | C22 | 1 | 4 | yes | — |
| 18 | C2×#15667946 | C22 | 1 | 2 | yes | — |
| 19 | #19151599 | — | 2 | 2 | no | — |
| 20 | #19151424 | C22 | 1 | 2 | yes | — |
| 21 | #19151424 | C22 | 1 | 2 | yes | — |
| 22 | #19151402 | C22 | 1 | 4 | yes | — |
| 23 | #19151399 | C22 | 1 | 4 | yes | — |
| 24 | C2×#135×C89 | C22 | 1 | 2 | yes | — |
| 25 | #508×C89 | — | 2 | 4 | no | — |
| 26 | C2×Q32×C89 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×SD32×C89 | C22 | 1 | 2 | yes | — |
| 28 | C2×D16×C89 | C22 | 1 | 1 | yes | characteristic |
| 29 | C22×C16×C89 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#13083574 | D4 | 1 | 1 | yes | characteristic |
| 31 | #15668018 | — | 2 | 2 | no | — |
| 32 | #15668018 | — | 2 | 2 | no | — |
| 33 | C2×#13083558 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×#13083557 | D4 | 1 | 2 | yes | — |
| 35 | C2×C8×D89 | C23 | 1 | 2 | yes | — |
| 36 | #15667991 | — | 4 | 2 | no | — |
| 37 | #15667988 | — | 2 | 4 | no | — |
| 38 | #15667986 | — | 4 | 2 | no | — |
| 39 | #15667984 | — | 4 | 4 | no | — |
| 40 | #15667983 | — | 2 | 4 | no | — |
| 41 | C2×C4⋊Dic89 | — | 2 | 2 | no | — |
| 42 | #15667952 | — | 2 | 2 | no | — |
| 43 | #15667951 | — | 2 | 4 | no | — |
| 44 | C2×#13083549 | C23 | 1 | 2 | yes | — |
| 45 | C16×D89 | — | 2 | 4 | no | — |
| 46 | #15667946 | — | 2 | 2 | no | — |
| 47 | #15667946 | C23 | 1 | 4 | yes | — |
| 48 | #15667936 | — | 2 | 4 | no | — |
| 49 | #15667933 | — | 2 | 4 | no | — |
| 50 | C2×#41×C89 | — | 2 | 2 | no | — |
| 51 | #135×C89 | — | 2 | 4 | no | — |
| 52 | #135×C89 | — | 2 | 4 | no | — |
| 53 | C2×Q16×C89 | C23 | 1 | 2 | yes | — |
| 54 | C2×SD16×C89 | — | 2 | 2 | no | — |
| 55 | C2×D8×C89 | C23 | 1 | 2 | yes | — |
| 56 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 57 | Q32×C89 | — | 2 | 2 | no | — |
| 58 | SD32×C89 | — | 2 | 4 | no | — |
| 59 | D16×C89 | — | 2 | 2 | no | — |
| 60 | C2×C16×C89 | D4 | 1 | 4 | yes | complemented |
| 61 | C2×C16×C89 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C16×C89 | C23 | 1 | 1 | yes | characteristic |
| 63 | #13083574 | — | 2 | 2 | no | — |
| 64 | #13083574 | — | 2 | 2 | no | — |
| 65 | C2×Dic178 | D8 | 1 | 1 | yes | characteristic |
| 66 | C2×D356 | D8 | 1 | 1 | yes | characteristic |
| 67 | C2×C22⋊D89 | — | 4 | 4 | no | — |
| 68 | C2×C22⋊D89 | D8 | 1 | 2 | yes | — |
| 69 | C22×Dic89 | — | 4 | 2 | no | — |
| 70 | C2×C4×D89 | C2×D4 | 1 | 2 | yes | — |
| 71 | #13083558 | — | 2 | 2 | no | — |
| 72 | #13083557 | — | 2 | 4 | no | — |
| 73 | C2×#10623494 | C2×D4 | 1 | 2 | yes | — |
| 74 | C8×D89 | — | 2 | 2 | no | — |
| 75 | C8×D89 | — | 2 | 2 | no | — |
| 76 | C4⋊Dic89 | — | 2 | 4 | no | — |
| 77 | C4⋊Dic89 | — | 4 | 2 | no | — |
| 78 | #13083553 | — | 4 | 4 | no | — |
| 79 | C22⋊Dic89 | — | 4 | 4 | no | — |
| 80 | #13083551 | — | 4 | 4 | no | — |
| 81 | #13083549 | — | 2 | 2 | no | — |
| 82 | #41×C89 | — | 4 | 4 | no | — |
| 83 | #41×C89 | — | 4 | 4 | no | — |
| 84 | C2×Q8×C89 | — | 2 | 2 | no | — |
| 85 | C2×D4×C89 | — | 2 | 2 | no | — |
| 86 | C2×D4×C89 | — | 4 | 2 | no | — |
| 87 | C22×C4×C89 | — | 4 | 2 | no | — |
| 88 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | Q16×C89 | — | 2 | 2 | no | — |
| 90 | Q16×C89 | — | 2 | 2 | no | — |
| 91 | SD16×C89 | — | 4 | 4 | no | — |
| 92 | D8×C89 | — | 2 | 2 | no | — |
| 93 | D8×C89 | — | 2 | 2 | no | — |
| 94 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C2×C8×C89 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×C8×C89 | #41 | 1 | 2 | yes | — |
| 97 | C2×C8×C89 | C24 | 1 | 1 | yes | characteristic |
| 98 | C16×C89 | C2×D4 | 1 | 2 | yes | — |
| 99 | C16×C89 | C2×D4 | 1 | 2 | yes | — |
| 100 | C23×C89 | — | 4 | 2 | no | — |
| 101 | C23×C89 | C2×D8 | 1 | 1 | yes | characteristic |
| 102 | C22×D89 | C2×D8 | 1 | 2 | yes | — |
| 103 | Q8×C89 | — | 4 | 2 | no | — |
| 104 | Q8×C89 | — | 4 | 2 | no | — |
| 105 | D4×C89 | — | 4 | 2 | no | — |
| 106 | D4×C89 | — | 4 | 2 | no | — |
| 107 | D4×C89 | — | 8 | 4 | no | — |
| 108 | C2×C4×C89 | — | 4 | 2 | no | — |
| 109 | C2×C4×C89 | — | 8 | 4 | no | — |
| 110 | C2×C4×C89 | #121 | 1 | 2 | yes | — |
| 111 | C2×C4×C89 | C2×D8 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C89 | #135 | 1 | 2 | yes | — |
| 113 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 114 | C22⋊D89 | — | 2 | 4 | no | — |
| 115 | C22⋊D89 | — | 16 | 4 | no | — |
| 116 | C2×Dic89 | — | 4 | 4 | no | — |
| 117 | C2×Dic89 | — | 16 | 2 | no | — |
| 118 | C2×Dic89 | C2×D8 | 1 | 2 | yes | — |
| 119 | D356 | — | 2 | 2 | no | — |
| 120 | C4×D89 | — | 2 | 2 | no | — |
| 121 | C4×D89 | — | 2 | 2 | no | — |
| 122 | Dic178 | — | 2 | 2 | no | — |
| 123 | C8×C89 | #121 | 1 | 2 | yes | — |
| 124 | C8×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 125 | C8×C89 | C2×#41 | 1 | 1 | yes | characteristic |
| 126 | #10623494 | — | 2 | 2 | no | — |
| 127 | C22×C89 | — | 2 | 1 | no | — |
| 128 | C22×C89 | — | 2 | 1 | no | — |
| 129 | C22×C89 | — | 8 | 2 | no | — |
| 130 | C22×C89 | — | 8 | 2 | no | — |
| 131 | C22×C89 | — | 8 | 2 | no | — |
| 132 | C22×C89 | #466 | 1 | 2 | yes | — |
| 133 | C22×C89 | C22×D8 | 1 | 1 | yes | characteristic |
| 134 | C2×D89 | — | 2 | 2 | no | — |
| 135 | C2×D89 | — | 2 | 2 | no | — |
| 136 | C2×D89 | — | 2 | 2 | no | — |
| 137 | C4×C89 | — | 8 | 2 | no | — |
| 138 | C4×C89 | #466 | 1 | 2 | yes | — |
| 139 | C4×C89 | C2×#121 | 1 | 1 | yes | characteristic |
| 140 | C4×C89 | C2×#135 | 1 | 1 | yes | characteristic |
| 141 | Dic89 | — | 2 | 2 | no | — |
| 142 | Dic89 | — | 8 | 4 | no | — |
| 143 | #33610 | — | 89 | 1 | no | maximal, Sylow |
| 144 | C2×C89 | — | 2 | 2 | no | — |
| 145 | C2×C89 | — | 16 | 2 | no | — |
| 146 | C2×C89 | C2×#466 | 1 | 1 | yes | characteristic |
| 147 | C2×C89 | #3415 | 1 | 1 | yes | characteristic |
| 148 | C2×C89 | #3417 | 1 | 1 | yes | characteristic |
| 149 | D89 | — | 4 | 2 | no | — |
| 150 | C2×#508 | D89 | 1 | 1 | yes | characteristic, complemented |
| 151 | C2×#504 | — | 89 | 1 | no | — |
| 152 | #3061 | — | 89 | 2 | no | — |
| 153 | #2220 | — | 89 | 4 | no | — |
| 154 | #2216 | — | 89 | 2 | no | — |
| 155 | #2215 | — | 89 | 2 | no | — |
| 156 | C2×#366 | — | 89 | 1 | no | — |
| 157 | #2139 | — | 89 | 2 | no | — |
| 158 | C89 | #33610 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 159 | C2×#135 | C2×D89 | 1 | 2 | yes | — |
| 160 | C2×#131 | — | 89 | 1 | no | — |
| 161 | #537 | — | 178 | 2 | no | — |
| 162 | #508 | — | 2 | 4 | no | — |
| 163 | C2×Q32 | C2×D89 | 1 | 1 | yes | characteristic |
| 164 | C2×SD32 | C2×D89 | 1 | 2 | yes | — |
| 165 | C2×D16 | C2×D89 | 1 | 1 | yes | characteristic |
| 166 | #504 | — | 178 | 4 | no | — |
| 167 | C2×M32 | — | 89 | 1 | no | — |
| 168 | C2×M32 | — | 89 | 2 | no | — |
| 169 | C22×C16 | — | 89 | 2 | no | — |
| 170 | C22×C16 | C2×D89 | 1 | 1 | yes | characteristic |
| 171 | #468 | — | 178 | 4 | no | — |
| 172 | #467 | — | 89 | 4 | no | — |
| 173 | #466 | — | 89 | 4 | no | — |
| 174 | C2×#107 | — | 89 | 2 | no | — |
| 175 | #417 | — | 178 | 2 | no | — |
| 176 | #366 | — | 89 | 2 | no | — |
| 177 | #366 | — | 89 | 2 | no | — |
| 178 | #358 | — | 89 | 4 | no | — |
| 179 | #357 | — | 89 | 4 | no | — |
| 180 | C2×#41 | — | 2 | 2 | no | — |
| 181 | C2×#41 | — | 89 | 1 | no | — |
| 182 | #135 | — | 2 | 4 | no | — |
| 183 | #135 | — | 2 | 4 | no | — |
| 184 | C2×Q16 | C22×D89 | 1 | 2 | yes | — |
| 185 | C2×SD16 | — | 2 | 2 | no | — |
| 186 | C2×D8 | C22×D89 | 1 | 2 | yes | — |
| 187 | #131 | — | 178 | 2 | no | — |
| 188 | #131 | — | 178 | 2 | no | — |
| 189 | C2×M16 | — | 89 | 1 | no | — |
| 190 | C2×M16 | — | 89 | 2 | no | — |
| 191 | C22×C8 | — | 89 | 2 | no | — |
| 192 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 193 | C22⋊Q8 | — | 356 | 2 | no | — |
| 194 | C22⋊Q8 | — | 178 | 4 | no | — |
| 195 | #121 | — | 356 | 2 | no | — |
| 196 | #121 | — | 356 | 4 | no | — |
| 197 | #121 | — | 178 | 4 | no | — |
| 198 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 199 | Q32 | — | 2 | 2 | no | — |
| 200 | SD32 | — | 2 | 4 | no | — |
| 201 | D16 | — | 2 | 2 | no | — |
| 202 | M32 | — | 178 | 2 | no | — |
| 203 | M32 | — | 178 | 4 | no | — |
| 204 | C2×C16 | — | 89 | 2 | no | — |
| 205 | C2×C16 | — | 178 | 4 | no | — |
| 206 | C2×C16 | C22⋊D89 | 1 | 4 | yes | complemented |
| 207 | C2×C16 | C22×D89 | 1 | 1 | yes | characteristic |
| 208 | C2×C16 | C22×D89 | 1 | 1 | yes | characteristic |
| 209 | #107 | — | 89 | 4 | no | — |
| 210 | #107 | — | 178 | 2 | no | — |
| 211 | #103 | — | 178 | 4 | no | — |
| 212 | #102 | — | 178 | 4 | no | — |
| 213 | #41 | — | 4 | 4 | no | — |
| 214 | #41 | — | 4 | 4 | no | — |
| 215 | #41 | — | 178 | 2 | no | — |
| 216 | #41 | — | 178 | 2 | no | — |
| 217 | C2×Q8 | — | 2 | 2 | no | — |
| 218 | C2×Q8 | — | 89 | 1 | no | — |
| 219 | C2×D4 | — | 2 | 2 | no | — |
| 220 | C2×D4 | — | 4 | 2 | no | — |
| 221 | C2×D4 | — | 89 | 2 | no | — |
| 222 | C2×D4 | — | 89 | 1 | no | — |
| 223 | C2×D4 | — | 356 | 4 | no | — |
| 224 | C22×C4 | — | 4 | 2 | no | — |
| 225 | C22×C4 | — | 89 | 2 | no | — |
| 226 | C22×C4 | — | 356 | 2 | no | — |
| 227 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 228 | Q16 | — | 2 | 2 | no | — |
| 229 | Q16 | — | 2 | 2 | no | — |
| 230 | SD16 | — | 4 | 4 | no | — |
| 231 | D8 | — | 2 | 2 | no | — |
| 232 | D8 | — | 2 | 2 | no | — |
| 233 | M16 | — | 178 | 2 | no | — |
| 234 | M16 | — | 178 | 4 | no | — |
| 235 | C2×C8 | — | 89 | 2 | no | — |
| 236 | C2×C8 | — | 178 | 2 | no | — |
| 237 | C2×C8 | — | 178 | 2 | no | — |
| 238 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 239 | C2×C8 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 240 | C2×C8 | #13083573 | 1 | 2 | yes | — |
| 241 | C2×C8 | C23×D89 | 1 | 1 | yes | characteristic |
| 242 | C4⋊C4 | — | 356 | 4 | no | — |
| 243 | C4⋊C4 | — | 356 | 2 | no | — |
| 244 | C4⋊C4 | — | 178 | 4 | no | — |
| 245 | C22⋊C4 | — | 356 | 4 | no | — |
| 246 | C22⋊C4 | — | 356 | 4 | no | — |
| 247 | C16 | — | 178 | 2 | no | — |
| 248 | C16 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 249 | C16 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 250 | C23 | — | 4 | 2 | no | — |
| 251 | C23 | — | 89 | 2 | no | — |
| 252 | C23 | D8×D89 | 1 | 1 | yes | characteristic |
| 253 | Q8 | — | 4 | 2 | no | — |
| 254 | Q8 | — | 4 | 2 | no | — |
| 255 | Q8 | — | 178 | 2 | no | — |
| 256 | D4 | — | 4 | 2 | no | — |
| 257 | D4 | — | 4 | 2 | no | — |
| 258 | D4 | — | 8 | 4 | no | — |
| 259 | D4 | — | 1424 | 4 | no | — |
| 260 | D4 | — | 178 | 4 | no | — |
| 261 | D4 | — | 178 | 2 | no | — |
| 262 | C2×C4 | — | 4 | 2 | no | — |
| 263 | C2×C4 | — | 8 | 4 | no | — |
| 264 | C2×C4 | — | 89 | 2 | no | — |
| 265 | C2×C4 | — | 356 | 4 | no | — |
| 266 | C2×C4 | — | 1424 | 2 | no | — |
| 267 | C2×C4 | — | 178 | 2 | no | — |
| 268 | C2×C4 | — | 178 | 2 | no | — |
| 269 | C2×C4 | #15667983 | 1 | 2 | yes | — |
| 270 | C2×C4 | D8×D89 | 1 | 1 | yes | characteristic |
| 271 | C2×C4 | #15668031 | 1 | 2 | yes | — |
| 272 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 273 | C8 | — | 178 | 2 | no | — |
| 274 | C8 | #15667983 | 1 | 2 | yes | — |
| 275 | C8 | C22×C22⋊D89 | 1 | 1 | yes | characteristic |
| 276 | C8 | C2×#13083573 | 1 | 1 | yes | characteristic |
| 277 | C22 | — | 2 | 1 | no | — |
| 278 | C22 | — | 2 | 1 | no | — |
| 279 | C22 | — | 8 | 2 | no | — |
| 280 | C22 | — | 8 | 2 | no | — |
| 281 | C22 | — | 8 | 2 | no | — |
| 282 | C22 | — | 178 | 2 | no | — |
| 283 | C22 | — | 178 | 2 | no | — |
| 284 | C22 | — | 178 | 2 | no | — |
| 285 | C22 | #19151831 | 1 | 2 | yes | — |
| 286 | C22 | C2×D8×D89 | 1 | 1 | yes | characteristic |
| 287 | C4 | — | 8 | 2 | no | — |
| 288 | C4 | — | 178 | 2 | no | — |
| 289 | C4 | — | 712 | 4 | no | — |
| 290 | C4 | #19151831 | 1 | 2 | yes | — |
| 291 | C4 | C2×#15667983 | 1 | 1 | yes | characteristic |
| 292 | C4 | C2×#15668031 | 1 | 1 | yes | characteristic |
| 293 | C2 | — | 2 | 2 | no | — |
| 294 | C2 | — | 16 | 2 | no | — |
| 295 | C2 | — | 356 | 2 | no | — |
| 296 | C2 | C2×#19151831 | 1 | 1 | yes | characteristic |
| 297 | C2 | #26033390 | 1 | 1 | yes | characteristic |
| 298 | C2 | #26033402 | 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