← #36472447
Subgroups — #36472447
Order 22784.
318 conjugacy classes of subgroups.
The subgroup lattice has 276 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#19151419 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#19151418 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26022007 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | M32×Dic89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C8×#13083553 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #26018333 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C89×#1376 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#15667952 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#15667952 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#15667941 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×C8×Dic89 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C8×Dic89 | C22 | 1 | 1 | yes | characteristic |
| 13 | C4×#13083553 | C4 | 1 | 1 | yes | characteristic |
| 14 | #19151419 | — | 2 | 2 | no | — |
| 15 | #19151418 | — | 2 | 2 | no | — |
| 16 | #19151416 | — | 2 | 1 | no | — |
| 17 | #19151416 | — | 2 | 1 | no | — |
| 18 | #19151373 | — | 2 | 1 | no | — |
| 19 | C16×Dic89 | — | 2 | 1 | no | — |
| 20 | #19151353 | C4 | 1 | 1 | yes | characteristic |
| 21 | #19151352 | C4 | 1 | 1 | yes | characteristic |
| 22 | C2×M32×C89 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×M32×C89 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C4×C8×C89 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22×#10623494 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C22×#10623494 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×#13083553 | — | 2 | 1 | no | — |
| 28 | C2×C4×Dic89 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C2×C4×Dic89 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #15667952 | — | 2 | 1 | no | — |
| 31 | #15667952 | — | 2 | 1 | no | — |
| 32 | #15667952 | — | 2 | 1 | no | — |
| 33 | #15667952 | D4 | 1 | 2 | yes | — |
| 34 | C2×#13083549 | — | 2 | 1 | no | — |
| 35 | C2×#13083549 | — | 2 | 1 | no | — |
| 36 | #15667941 | C8 | 1 | 2 | yes | — |
| 37 | #15667941 | C8 | 1 | 2 | yes | — |
| 38 | C8×Dic89 | — | 2 | 1 | no | — |
| 39 | C8×Dic89 | — | 2 | 1 | no | — |
| 40 | C8×Dic89 | D4 | 1 | 1 | yes | characteristic |
| 41 | C8×Dic89 | D4 | 1 | 1 | yes | characteristic |
| 42 | C8×Dic89 | Q8 | 1 | 1 | yes | characteristic |
| 43 | C8×Dic89 | Q8 | 1 | 1 | yes | characteristic |
| 44 | #15667919 | — | 2 | 1 | no | — |
| 45 | C22×C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C42×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | M32×C89 | — | 2 | 1 | no | — |
| 49 | M32×C89 | — | 2 | 1 | no | — |
| 50 | M32×C89 | — | 2 | 1 | no | — |
| 51 | M32×C89 | Q8 | 1 | 2 | yes | — |
| 52 | C2×C16×C89 | — | 2 | 1 | no | — |
| 53 | C2×C16×C89 | — | 2 | 1 | no | — |
| 54 | C4×C8×C89 | — | 2 | 1 | no | — |
| 55 | C4×C8×C89 | — | 2 | 1 | no | — |
| 56 | C22×Dic89 | — | 2 | 1 | no | — |
| 57 | C22×Dic89 | M16 | 1 | 1 | yes | characteristic |
| 58 | C22×Dic89 | M16 | 1 | 1 | yes | characteristic |
| 59 | C2×#10623494 | — | 2 | 1 | no | — |
| 60 | C2×#10623494 | — | 2 | 1 | no | — |
| 61 | C2×#10623494 | — | 2 | 1 | no | — |
| 62 | C2×#10623494 | — | 2 | 1 | no | — |
| 63 | C2×#10623494 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 64 | C2×#10623494 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 65 | C2×#10623494 | C2×C8 | 1 | 2 | yes | — |
| 66 | #13083553 | — | 2 | 4 | no | — |
| 67 | C4×Dic89 | — | 2 | 1 | no | — |
| 68 | C4×Dic89 | — | 2 | 1 | no | — |
| 69 | C4×Dic89 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 70 | C4×Dic89 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 71 | C4×Dic89 | C2×C8 | 1 | 1 | yes | characteristic |
| 72 | C4×Dic89 | C2×C8 | 1 | 1 | yes | characteristic |
| 73 | #13083549 | — | 2 | 2 | no | — |
| 74 | #13083549 | — | 4 | 1 | no | — |
| 75 | C22×C4×C89 | — | 2 | 1 | no | — |
| 76 | C22×C4×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 77 | C2×C8×C89 | — | 2 | 1 | no | — |
| 78 | C2×C8×C89 | — | 2 | 1 | no | — |
| 79 | C2×C8×C89 | C2×C8 | 1 | 2 | yes | — |
| 80 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C8×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 83 | C2×C8×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 84 | C2×C8×C89 | #41 | 1 | 1 | yes | characteristic |
| 85 | C2×C8×C89 | #41 | 1 | 1 | yes | characteristic |
| 86 | C42×C89 | — | 2 | 1 | no | — |
| 87 | C42×C89 | — | 2 | 1 | no | — |
| 88 | C16×C89 | — | 2 | 2 | no | — |
| 89 | C16×C89 | — | 4 | 1 | no | — |
| 90 | C23×C89 | C2×M16 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×C89 | — | 2 | 2 | no | — |
| 92 | C2×C4×C89 | — | 4 | 1 | no | — |
| 93 | C2×C4×C89 | — | 4 | 1 | no | — |
| 94 | C2×C4×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C4×C89 | C4×Q8 | 1 | 1 | yes | characteristic |
| 97 | C2×C4×C89 | C22×C8 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C89 | #131 | 1 | 1 | yes | characteristic |
| 99 | C2×C4×C89 | #131 | 1 | 1 | yes | characteristic |
| 100 | C2×Dic89 | — | 2 | 2 | no | — |
| 101 | C2×Dic89 | — | 2 | 2 | no | — |
| 102 | C2×Dic89 | — | 4 | 1 | no | — |
| 103 | C2×Dic89 | — | 4 | 1 | no | — |
| 104 | C2×Dic89 | — | 4 | 1 | no | — |
| 105 | C2×Dic89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 106 | C2×Dic89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 107 | C2×Dic89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 108 | C2×Dic89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 109 | C8×C89 | — | 2 | 2 | no | — |
| 110 | C8×C89 | #121 | 1 | 1 | yes | characteristic |
| 111 | C8×C89 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 112 | C8×C89 | #125 | 1 | 1 | yes | characteristic |
| 113 | C8×C89 | C4⋊Q8 | 1 | 1 | yes | characteristic |
| 114 | #10623494 | — | 2 | 1 | no | — |
| 115 | #10623494 | — | 2 | 1 | no | — |
| 116 | #10623494 | — | 2 | 2 | no | — |
| 117 | C22×C89 | — | 2 | 1 | no | — |
| 118 | C22×C89 | — | 2 | 1 | no | — |
| 119 | C22×C89 | C2×C4⋊C8 | 1 | 1 | yes | characteristic |
| 120 | C22×C89 | #436 | 1 | 1 | yes | characteristic |
| 121 | C22×C89 | #446 | 1 | 1 | yes | characteristic |
| 122 | C4×C89 | — | 4 | 2 | no | — |
| 123 | C4×C89 | #389 | 1 | 1 | yes | characteristic |
| 124 | C4×C89 | #424 | 1 | 1 | yes | characteristic |
| 125 | C4×C89 | C8×D4 | 1 | 1 | yes | characteristic |
| 126 | C4×C89 | C8×Q8 | 1 | 1 | yes | characteristic |
| 127 | Dic89 | — | 2 | 1 | no | — |
| 128 | Dic89 | — | 2 | 1 | no | — |
| 129 | Dic89 | — | 2 | 1 | no | — |
| 130 | Dic89 | — | 4 | 2 | no | — |
| 131 | Dic89 | #364 | 1 | 2 | yes | complemented |
| 132 | #13163 | — | 89 | 1 | no | maximal, Sylow |
| 133 | C2×C89 | — | 2 | 1 | no | — |
| 134 | C2×C89 | — | 2 | 1 | no | — |
| 135 | C2×C89 | #1939 | 1 | 1 | yes | characteristic |
| 136 | C2×C89 | C2×#364 | 1 | 1 | yes | characteristic |
| 137 | C2×C89 | #2153 | 1 | 1 | yes | characteristic |
| 138 | C2×#364 | — | 89 | 1 | no | — |
| 139 | C2×#364 | — | 89 | 1 | no | — |
| 140 | #2150 | — | 89 | 1 | no | — |
| 141 | C4×M32 | — | 89 | 1 | no | — |
| 142 | C8×C4⋊C4 | — | 89 | 1 | no | — |
| 143 | #1376 | — | 89 | 1 | no | — |
| 144 | #1376 | D89 | 1 | 1 | yes | characteristic |
| 145 | C89 | #13163 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 146 | C2×M32 | — | 89 | 1 | no | — |
| 147 | C2×M32 | — | 89 | 1 | no | — |
| 148 | C2×M32 | C2×D89 | 1 | 1 | yes | characteristic |
| 149 | C2×M32 | C2×D89 | 1 | 1 | yes | characteristic |
| 150 | C2×C4⋊C8 | — | 89 | 1 | no | — |
| 151 | C2×C4×C8 | — | 89 | 1 | no | — |
| 152 | C2×C4×C8 | — | 89 | 1 | no | — |
| 153 | C2×C4×C8 | C2×D89 | 1 | 1 | yes | characteristic |
| 154 | C4×C4⋊C4 | — | 89 | 1 | no | — |
| 155 | #364 | — | 178 | 2 | no | — |
| 156 | #364 | — | 178 | 2 | no | — |
| 157 | C4⋊C16 | — | 178 | 1 | no | — |
| 158 | C4⋊C16 | — | 178 | 1 | no | — |
| 159 | #346 | — | 178 | 1 | no | — |
| 160 | C4×C16 | — | 178 | 1 | no | — |
| 161 | #336 | — | 89 | 1 | no | — |
| 162 | #336 | — | 89 | 1 | no | — |
| 163 | C22×C8 | — | 89 | 1 | no | — |
| 164 | C22×C8 | — | 89 | 1 | no | — |
| 165 | C22×C8 | C4×D89 | 1 | 1 | yes | characteristic |
| 166 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 167 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 168 | C2×C42 | — | 89 | 1 | no | — |
| 169 | C2×C42 | — | 89 | 1 | no | — |
| 170 | C2×C42 | C4×D89 | 1 | 1 | yes | characteristic |
| 171 | M32 | — | 2 | 1 | no | — |
| 172 | M32 | — | 2 | 1 | no | — |
| 173 | M32 | — | 2 | 1 | no | — |
| 174 | M32 | — | 89 | 2 | no | — |
| 175 | M32 | — | 178 | 1 | no | — |
| 176 | M32 | — | 178 | 1 | no | — |
| 177 | M32 | — | 178 | 1 | no | — |
| 178 | M32 | Dic178 | 1 | 2 | yes | — |
| 179 | C2×C16 | — | 2 | 1 | no | — |
| 180 | C2×C16 | — | 2 | 1 | no | — |
| 181 | C2×C16 | — | 178 | 1 | no | — |
| 182 | C2×C16 | — | 178 | 1 | no | — |
| 183 | C4⋊C8 | — | 89 | 2 | no | — |
| 184 | C4⋊C8 | — | 89 | 2 | no | — |
| 185 | C4×C8 | — | 2 | 1 | no | — |
| 186 | C4×C8 | — | 2 | 1 | no | — |
| 187 | C4×C8 | — | 89 | 1 | no | — |
| 188 | C4×C8 | — | 89 | 1 | no | — |
| 189 | C4×C8 | — | 89 | 1 | no | — |
| 190 | C4×C8 | — | 89 | 1 | no | — |
| 191 | C4×C8 | — | 178 | 1 | no | — |
| 192 | C4×C8 | — | 178 | 1 | no | — |
| 193 | #95 | — | 178 | 1 | no | — |
| 194 | C22×C4 | — | 2 | 1 | no | — |
| 195 | C22×C4 | — | 89 | 1 | no | — |
| 196 | C22×C4 | — | 89 | 1 | no | — |
| 197 | C22×C4 | — | 178 | 1 | no | — |
| 198 | C22×C4 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 199 | C2×C8 | — | 2 | 1 | no | — |
| 200 | C2×C8 | — | 2 | 1 | no | — |
| 201 | C2×C8 | — | 89 | 2 | no | — |
| 202 | C2×C8 | — | 89 | 1 | no | — |
| 203 | C2×C8 | — | 89 | 1 | no | — |
| 204 | C2×C8 | — | 178 | 1 | no | — |
| 205 | C2×C8 | — | 178 | 1 | no | — |
| 206 | C2×C8 | — | 178 | 1 | no | — |
| 207 | C2×C8 | — | 178 | 1 | no | — |
| 208 | C2×C8 | C8×D89 | 1 | 2 | yes | — |
| 209 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 210 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 211 | C2×C8 | Q8×D89 | 1 | 1 | yes | characteristic |
| 212 | C2×C8 | C2×Dic178 | 1 | 1 | yes | characteristic |
| 213 | C2×C8 | #13083573 | 1 | 1 | yes | characteristic |
| 214 | C2×C8 | #13083574 | 1 | 1 | yes | characteristic |
| 215 | C4⋊C4 | — | 178 | 4 | no | — |
| 216 | C42 | — | 2 | 1 | no | — |
| 217 | C42 | — | 2 | 1 | no | — |
| 218 | C42 | — | 89 | 1 | no | — |
| 219 | C42 | — | 89 | 1 | no | — |
| 220 | C42 | — | 89 | 1 | no | — |
| 221 | C42 | — | 89 | 1 | no | — |
| 222 | C42 | — | 178 | 1 | no | — |
| 223 | C42 | — | 178 | 1 | no | — |
| 224 | C16 | — | 2 | 2 | no | — |
| 225 | C16 | — | 4 | 1 | no | — |
| 226 | C16 | — | 356 | 1 | no | — |
| 227 | C16 | — | 178 | 2 | no | — |
| 228 | C23 | M16×D89 | 1 | 1 | yes | characteristic |
| 229 | C2×C4 | — | 2 | 2 | no | — |
| 230 | C2×C4 | — | 4 | 1 | no | — |
| 231 | C2×C4 | — | 4 | 1 | no | — |
| 232 | C2×C4 | — | 89 | 1 | no | — |
| 233 | C2×C4 | — | 89 | 1 | no | — |
| 234 | C2×C4 | — | 89 | 1 | no | — |
| 235 | C2×C4 | — | 89 | 1 | no | — |
| 236 | C2×C4 | — | 356 | 1 | no | — |
| 237 | C2×C4 | — | 356 | 1 | no | — |
| 238 | C2×C4 | — | 356 | 1 | no | — |
| 239 | C2×C4 | — | 178 | 2 | no | — |
| 240 | C2×C4 | — | 178 | 2 | no | — |
| 241 | C2×C4 | C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 242 | C2×C4 | #15667972 | 1 | 1 | yes | characteristic |
| 243 | C2×C4 | C4×Dic178 | 1 | 1 | yes | characteristic |
| 244 | C2×C4 | C2×C8×D89 | 1 | 1 | yes | characteristic |
| 245 | C2×C4 | #15668018 | 1 | 1 | yes | characteristic |
| 246 | C2×C4 | #15668020 | 1 | 1 | yes | characteristic |
| 247 | C8 | — | 2 | 2 | no | — |
| 248 | C8 | — | 178 | 1 | no | — |
| 249 | C8 | — | 178 | 1 | no | — |
| 250 | C8 | — | 178 | 2 | no | — |
| 251 | C8 | #15667985 | 1 | 1 | yes | characteristic |
| 252 | C8 | #15667989 | 1 | 1 | yes | characteristic |
| 253 | C8 | #15668002 | 1 | 1 | yes | characteristic |
| 254 | C8 | #15668011 | 1 | 1 | yes | characteristic |
| 255 | C22 | — | 2 | 1 | no | — |
| 256 | C22 | — | 2 | 1 | no | — |
| 257 | C22 | C4⋊C8×D89 | 1 | 1 | yes | characteristic |
| 258 | C22 | #19151673 | 1 | 1 | yes | characteristic |
| 259 | C22 | #19151726 | 1 | 1 | yes | characteristic |
| 260 | C4 | — | 4 | 2 | no | — |
| 261 | C4 | — | 89 | 2 | no | — |
| 262 | C4 | — | 356 | 2 | no | — |
| 263 | C4 | — | 178 | 1 | no | — |
| 264 | C4 | — | 178 | 1 | no | — |
| 265 | C4 | — | 178 | 1 | no | — |
| 266 | C4 | #19151495 | 1 | 1 | yes | characteristic |
| 267 | C4 | #19151623 | 1 | 1 | yes | characteristic |
| 268 | C4 | #19151661 | 1 | 1 | yes | characteristic |
| 269 | C4 | C8×Dic178 | 1 | 1 | yes | characteristic |
| 270 | C2 | — | 2 | 1 | no | — |
| 271 | C2 | — | 2 | 1 | no | — |
| 272 | C2 | #26020969 | 1 | 1 | yes | characteristic |
| 273 | C2 | #364×D89 | 1 | 1 | yes | characteristic |
| 274 | C2 | #26022016 | 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