← #36472485
Subgroups — #36472485
Order 22784.
274 conjugacy classes of subgroups.
The subgroup lattice has 240 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#19151427 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#19151423 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26021849 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #26021037 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #26018362 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #26018360 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C89×#1952 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#15667952 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×#13083549 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#15667948 | C22 | 1 | 1 | yes | characteristic |
| 11 | #19151641 | — | 2 | 1 | no | — |
| 12 | C2×#15667946 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19151427 | C4 | 1 | 4 | yes | complemented |
| 14 | #19151423 | — | 2 | 1 | no | — |
| 15 | #19151423 | — | 2 | 1 | no | — |
| 16 | #19151374 | — | 2 | 1 | no | — |
| 17 | C4×#13083549 | — | 2 | 1 | no | — |
| 18 | #19151366 | — | 2 | 1 | no | — |
| 19 | C2×#108×C89 | C22 | 1 | 1 | yes | characteristic |
| 20 | #428×C89 | — | 2 | 1 | no | — |
| 21 | C2×#107×C89 | C22 | 1 | 1 | yes | characteristic |
| 22 | #405×C89 | C22 | 1 | 1 | yes | characteristic |
| 23 | #343×C89 | — | 2 | 1 | no | — |
| 24 | C2×#13083558 | — | 2 | 1 | no | — |
| 25 | C2×C4⋊Dic89 | — | 2 | 1 | no | — |
| 26 | #15667952 | — | 2 | 1 | no | — |
| 27 | #15667952 | Q8 | 1 | 2 | yes | — |
| 28 | C2×#13083549 | — | 2 | 1 | no | — |
| 29 | C2×#13083549 | C2×C4 | 1 | 2 | yes | — |
| 30 | C2×#13083549 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×#13083549 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×#13083549 | Q8 | 1 | 2 | yes | — |
| 33 | #15667948 | — | 2 | 1 | no | — |
| 34 | #15667948 | C2×C4 | 1 | 2 | yes | — |
| 35 | #15667946 | — | 2 | 1 | no | — |
| 36 | #15667946 | — | 2 | 1 | no | — |
| 37 | #15667945 | — | 4 | 1 | no | — |
| 38 | #15667943 | — | 4 | 1 | no | — |
| 39 | C2×M16×C89 | — | 2 | 1 | no | — |
| 40 | C2×M16×C89 | D4 | 1 | 1 | yes | characteristic |
| 41 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 42 | #117×C89 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×C4⋊C4×C89 | — | 2 | 1 | no | — |
| 44 | #108×C89 | — | 2 | 1 | no | — |
| 45 | #108×C89 | C2×C4 | 1 | 2 | yes | — |
| 46 | #107×C89 | — | 2 | 1 | no | — |
| 47 | #107×C89 | — | 2 | 1 | no | — |
| 48 | #107×C89 | — | 4 | 1 | no | — |
| 49 | #106×C89 | — | 4 | 1 | no | — |
| 50 | #97×C89 | — | 2 | 1 | no | — |
| 51 | C4×C8×C89 | — | 2 | 1 | no | — |
| 52 | C22×Dic89 | — | 4 | 1 | no | — |
| 53 | #13083558 | — | 2 | 2 | no | — |
| 54 | #13083558 | — | 4 | 1 | no | — |
| 55 | C2×#10623494 | — | 4 | 1 | no | — |
| 56 | C4⋊Dic89 | — | 4 | 1 | no | — |
| 57 | C4⋊Dic89 | — | 4 | 1 | no | — |
| 58 | #13083549 | — | 2 | 2 | no | — |
| 59 | #13083549 | C4⋊C4 | 1 | 2 | yes | — |
| 60 | #13083549 | C4⋊C4 | 1 | 2 | yes | — |
| 61 | C22×C4×C89 | — | 4 | 1 | no | — |
| 62 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 63 | M16×C89 | — | 2 | 1 | no | — |
| 64 | M16×C89 | — | 2 | 2 | no | — |
| 65 | M16×C89 | — | 4 | 1 | no | — |
| 66 | M16×C89 | Q16 | 1 | 2 | yes | — |
| 67 | C2×C8×C89 | — | 2 | 1 | no | — |
| 68 | C2×C8×C89 | — | 4 | 1 | no | — |
| 69 | C2×C8×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C2×C8×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 72 | C2×C8×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 73 | C2×C8×C89 | #41 | 1 | 1 | yes | characteristic |
| 74 | C2×C8×C89 | #41 | 1 | 1 | yes | characteristic |
| 75 | C4⋊C4×C89 | — | 4 | 1 | no | — |
| 76 | C4⋊C4×C89 | — | 4 | 1 | no | — |
| 77 | C4⋊C4×C89 | D8 | 1 | 1 | yes | characteristic |
| 78 | C4⋊C4×C89 | D8 | 1 | 1 | yes | characteristic |
| 79 | C22⋊C4×C89 | — | 2 | 1 | no | — |
| 80 | C42×C89 | — | 2 | 1 | no | — |
| 81 | C23×C89 | #135 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×C89 | — | 2 | 1 | no | — |
| 83 | C2×C4×C89 | — | 2 | 1 | no | — |
| 84 | C2×C4×C89 | — | 8 | 1 | no | — |
| 85 | C2×C4×C89 | — | 16 | 1 | no | — |
| 86 | C2×C4×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×C89 | #121 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×C89 | C4⋊Q8 | 1 | 1 | yes | characteristic |
| 89 | C2×C4×C89 | C2×D8 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×C89 | C2×Q16 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×C89 | #135 | 1 | 1 | yes | characteristic |
| 92 | C2×Dic89 | — | 8 | 1 | no | — |
| 93 | C2×Dic89 | — | 16 | 1 | no | — |
| 94 | C8×C89 | — | 2 | 2 | no | — |
| 95 | C8×C89 | — | 4 | 2 | no | — |
| 96 | C8×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C8×C89 | C4×Q8 | 1 | 1 | yes | characteristic |
| 98 | C8×C89 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 99 | C8×C89 | #125 | 1 | 1 | yes | characteristic |
| 100 | #10623494 | — | 4 | 2 | no | — |
| 101 | C22×C89 | — | 2 | 1 | no | — |
| 102 | C22×C89 | — | 2 | 1 | no | — |
| 103 | C22×C89 | C4×Q16 | 1 | 1 | yes | characteristic |
| 104 | C22×C89 | #466 | 1 | 1 | yes | characteristic |
| 105 | C22×C89 | #499 | 1 | 1 | yes | characteristic |
| 106 | C4×C89 | — | 4 | 1 | no | — |
| 107 | C4×C89 | — | 4 | 1 | no | — |
| 108 | C4×C89 | — | 16 | 1 | no | — |
| 109 | C4×C89 | #389 | 1 | 1 | yes | characteristic |
| 110 | C4×C89 | C4×D8 | 1 | 1 | yes | characteristic |
| 111 | C4×C89 | #467 | 1 | 1 | yes | characteristic |
| 112 | C4×C89 | #500 | 1 | 1 | yes | characteristic |
| 113 | Dic89 | — | 16 | 1 | no | — |
| 114 | #13171 | — | 89 | 1 | no | maximal, Sylow |
| 115 | C2×C89 | — | 2 | 1 | no | — |
| 116 | C2×C89 | — | 2 | 1 | no | — |
| 117 | C2×C89 | #1942 | 1 | 1 | yes | characteristic |
| 118 | C2×C89 | #2221 | 1 | 1 | yes | characteristic |
| 119 | C2×C89 | #2222 | 1 | 1 | yes | characteristic |
| 120 | C2×#368 | — | 89 | 1 | no | — |
| 121 | C2×#366 | — | 89 | 1 | no | — |
| 122 | #2108 | — | 89 | 1 | no | — |
| 123 | #1952 | — | 89 | 1 | no | — |
| 124 | #1952 | D89 | 1 | 1 | yes | characteristic |
| 125 | #1387 | — | 89 | 1 | no | — |
| 126 | #1387 | — | 89 | 1 | no | — |
| 127 | C89 | #13171 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 128 | C2×M32 | — | 89 | 1 | no | — |
| 129 | C22×C16 | — | 89 | 1 | no | — |
| 130 | C2×#108 | — | 89 | 1 | no | — |
| 131 | C2×#108 | C2×D89 | 1 | 1 | yes | characteristic |
| 132 | #428 | — | 2 | 1 | no | — |
| 133 | #428 | — | 178 | 1 | no | — |
| 134 | C2×#107 | — | 89 | 1 | no | — |
| 135 | C2×#107 | C2×D89 | 1 | 1 | yes | characteristic |
| 136 | #405 | C2×D89 | 1 | 1 | yes | characteristic |
| 137 | #368 | — | 89 | 4 | no | — |
| 138 | #366 | — | 178 | 1 | no | — |
| 139 | #366 | — | 178 | 1 | no | — |
| 140 | #346 | — | 178 | 1 | no | — |
| 141 | C4×C16 | — | 178 | 1 | no | — |
| 142 | #343 | — | 2 | 1 | no | — |
| 143 | #343 | — | 178 | 1 | no | — |
| 144 | C2×M16 | — | 2 | 1 | no | — |
| 145 | C2×M16 | — | 178 | 1 | no | — |
| 146 | C2×M16 | C22⋊D89 | 1 | 1 | yes | characteristic |
| 147 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 148 | #117 | C22⋊D89 | 1 | 1 | yes | characteristic |
| 149 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 150 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 151 | M32 | — | 89 | 2 | no | — |
| 152 | M32 | — | 178 | 1 | no | — |
| 153 | C2×C16 | — | 89 | 2 | no | — |
| 154 | C2×C16 | — | 89 | 1 | no | — |
| 155 | C2×C16 | — | 89 | 1 | no | — |
| 156 | C2×C16 | — | 89 | 2 | no | — |
| 157 | C2×C16 | — | 178 | 1 | no | — |
| 158 | #108 | — | 2 | 1 | no | — |
| 159 | #108 | — | 89 | 2 | no | — |
| 160 | #108 | — | 178 | 1 | no | — |
| 161 | #108 | C4×D89 | 1 | 2 | yes | — |
| 162 | #107 | — | 2 | 1 | no | — |
| 163 | #107 | — | 2 | 1 | no | — |
| 164 | #107 | — | 4 | 1 | no | — |
| 165 | #107 | — | 356 | 1 | no | — |
| 166 | #107 | — | 178 | 1 | no | — |
| 167 | #107 | — | 178 | 1 | no | — |
| 168 | #106 | — | 4 | 1 | no | — |
| 169 | #106 | — | 356 | 1 | no | — |
| 170 | #97 | — | 2 | 1 | no | — |
| 171 | C4×C8 | — | 2 | 1 | no | — |
| 172 | C22×C4 | — | 4 | 1 | no | — |
| 173 | C22×C4 | — | 356 | 1 | no | — |
| 174 | C22×C4 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 175 | M16 | — | 2 | 1 | no | — |
| 176 | M16 | — | 2 | 2 | no | — |
| 177 | M16 | — | 4 | 1 | no | — |
| 178 | M16 | — | 356 | 1 | no | — |
| 179 | M16 | — | 178 | 2 | no | — |
| 180 | M16 | #13083564 | 1 | 2 | yes | — |
| 181 | C2×C8 | — | 2 | 1 | no | — |
| 182 | C2×C8 | — | 4 | 1 | no | — |
| 183 | C2×C8 | — | 356 | 1 | no | — |
| 184 | C2×C8 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 185 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 186 | C2×C8 | Q8×D89 | 1 | 1 | yes | characteristic |
| 187 | C2×C8 | Q8×D89 | 1 | 1 | yes | characteristic |
| 188 | C2×C8 | #13083573 | 1 | 1 | yes | characteristic |
| 189 | C2×C8 | #13083574 | 1 | 1 | yes | characteristic |
| 190 | C4⋊C4 | — | 4 | 1 | no | — |
| 191 | C4⋊C4 | — | 4 | 1 | no | — |
| 192 | C4⋊C4 | — | 356 | 1 | no | — |
| 193 | C4⋊C4 | — | 356 | 1 | no | — |
| 194 | C4⋊C4 | #13083559 | 1 | 1 | yes | characteristic |
| 195 | C4⋊C4 | #13083559 | 1 | 1 | yes | characteristic |
| 196 | C22⋊C4 | — | 2 | 1 | no | — |
| 197 | C42 | — | 2 | 1 | no | — |
| 198 | C16 | — | 89 | 2 | no | — |
| 199 | C16 | — | 89 | 2 | no | — |
| 200 | C16 | — | 178 | 2 | no | — |
| 201 | C23 | #15668032 | 1 | 1 | yes | characteristic |
| 202 | C2×C4 | — | 2 | 1 | no | — |
| 203 | C2×C4 | — | 2 | 1 | no | — |
| 204 | C2×C4 | — | 8 | 1 | no | — |
| 205 | C2×C4 | — | 16 | 1 | no | — |
| 206 | C2×C4 | — | 1424 | 1 | no | — |
| 207 | C2×C4 | — | 712 | 1 | no | — |
| 208 | C2×C4 | C4×C22⋊D89 | 1 | 1 | yes | characteristic |
| 209 | C2×C4 | #15667984 | 1 | 1 | yes | characteristic |
| 210 | C2×C4 | #15668010 | 1 | 1 | yes | characteristic |
| 211 | C2×C4 | C2×#13083559 | 1 | 1 | yes | characteristic |
| 212 | C2×C4 | C2×#13083564 | 1 | 1 | yes | characteristic |
| 213 | C2×C4 | #15668032 | 1 | 1 | yes | characteristic |
| 214 | C8 | — | 2 | 2 | no | — |
| 215 | C8 | — | 4 | 2 | no | — |
| 216 | C8 | — | 356 | 2 | no | — |
| 217 | C8 | C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 218 | C8 | #15667977 | 1 | 1 | yes | characteristic |
| 219 | C8 | #15667990 | 1 | 1 | yes | characteristic |
| 220 | C8 | #15668002 | 1 | 1 | yes | characteristic |
| 221 | C22 | — | 2 | 1 | no | — |
| 222 | C22 | — | 2 | 1 | no | — |
| 223 | C22 | C4×#13083564 | 1 | 1 | yes | characteristic |
| 224 | C22 | #19151832 | 1 | 1 | yes | characteristic |
| 225 | C22 | #19151997 | 1 | 1 | yes | characteristic |
| 226 | C4 | — | 4 | 1 | no | — |
| 227 | C4 | — | 4 | 1 | no | — |
| 228 | C4 | — | 16 | 1 | no | — |
| 229 | C4 | — | 1424 | 1 | no | — |
| 230 | C4 | #19151493 | 1 | 1 | yes | characteristic |
| 231 | C4 | C4×#13083559 | 1 | 1 | yes | characteristic |
| 232 | C4 | #19151837 | 1 | 1 | yes | characteristic |
| 233 | C4 | #19152001 | 1 | 1 | yes | characteristic |
| 234 | C2 | — | 2 | 1 | no | — |
| 235 | C2 | — | 2 | 1 | no | — |
| 236 | C2 | #26020982 | 1 | 1 | yes | characteristic |
| 237 | C2 | #26022370 | 1 | 1 | yes | characteristic |
| 238 | C2 | #26022375 | 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