← #14673954
Subgroups — #14673954
Order 2816.
238 conjugacy classes of subgroups.
The subgroup lattice has 160 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#10622085 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×D11×C32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13070211 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13066749 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C4×C11⋊C32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C32×Dic11 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C11×#1397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#66862 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×C16×D11 | C22 | 1 | 1 | yes | characteristic |
| 10 | #10622302 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×C11×C32 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C11×C32 | C22 | 1 | 1 | yes | characteristic |
| 13 | C4×C11×C16 | C22 | 1 | 1 | yes | characteristic |
| 14 | #10622140 | C4 | 1 | 1 | yes | characteristic |
| 15 | C16×Dic11 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C11⋊C32 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C11⋊C32 | C22 | 1 | 1 | yes | characteristic |
| 18 | #10622099 | C4 | 1 | 1 | yes | characteristic |
| 19 | #10622085 | C4 | 1 | 4 | yes | complemented |
| 20 | D11×C32 | C4 | 1 | 4 | yes | complemented |
| 21 | C2×#4313 | C8 | 1 | 1 | yes | characteristic |
| 22 | C2×C8×D11 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | #66925 | C8 | 1 | 1 | yes | characteristic |
| 24 | C2×C11×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 26 | C4×C8×C11 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | #66879 | C8 | 1 | 1 | yes | characteristic |
| 28 | C8×Dic11 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C2×C11⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C11⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | #66867 | C8 | 1 | 1 | yes | characteristic |
| 32 | #66862 | C8 | 1 | 4 | yes | — |
| 33 | C16×D11 | C2×C4 | 1 | 2 | yes | — |
| 34 | C16×D11 | C2×C4 | 1 | 2 | yes | — |
| 35 | C11×C32 | C2×C4 | 1 | 2 | yes | — |
| 36 | C11×C32 | C2×C4 | 1 | 2 | yes | — |
| 37 | C11⋊C32 | C2×C4 | 1 | 2 | yes | — |
| 38 | C11⋊C32 | C2×C4 | 1 | 2 | yes | — |
| 39 | #13549 | — | 11 | 1 | no | maximal, Sylow |
| 40 | C2×C4×D11 | C2×C8 | 1 | 1 | yes | characteristic |
| 41 | C2×C8×C11 | C2×C8 | 1 | 1 | yes | characteristic |
| 42 | C2×C8×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 43 | C42×C11 | C2×C8 | 1 | 1 | yes | characteristic |
| 44 | (C2×D11)⋊C4 | C16 | 1 | 2 | yes | — |
| 45 | Dic11⋊C4 | C16 | 1 | 2 | yes | — |
| 46 | C4×Dic11 | C2×C8 | 1 | 1 | yes | characteristic |
| 47 | C2×C11⋊C8 | C2×C8 | 1 | 1 | yes | characteristic |
| 48 | C2×C11⋊C8 | C2×C8 | 1 | 1 | yes | characteristic |
| 49 | #4313 | C16 | 1 | 4 | yes | — |
| 50 | C8×D11 | C42 | 1 | 2 | yes | — |
| 51 | C8×D11 | C2×C8 | 1 | 2 | yes | — |
| 52 | C11×C16 | C2×C8 | 1 | 2 | yes | — |
| 53 | C11×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 54 | C11×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 55 | C11⋊C16 | C42 | 1 | 2 | yes | — |
| 56 | C11⋊C16 | C2×C8 | 1 | 2 | yes | — |
| 57 | C2×M64 | — | 11 | 1 | no | — |
| 58 | C22×C32 | — | 11 | 1 | no | — |
| 59 | #2108 | — | 11 | 1 | no | — |
| 60 | #1397 | — | 11 | 1 | no | — |
| 61 | #1397 | D11 | 1 | 1 | yes | characteristic, complemented |
| 62 | C4×C32 | — | 11 | 1 | no | — |
| 63 | C4×C32 | — | 11 | 1 | no | — |
| 64 | C22×D11 | C2×C16 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×C11 | C2×C16 | 1 | 2 | yes | — |
| 66 | C2×C4×C11 | C22×C8 | 1 | 1 | yes | characteristic |
| 67 | C2×Dic11 | C2×C16 | 1 | 2 | yes | — |
| 68 | C2×Dic11 | C2×C16 | 1 | 1 | yes | characteristic |
| 69 | C4×D11 | C4×C8 | 1 | 2 | yes | — |
| 70 | C4×D11 | C2×C16 | 1 | 2 | yes | — |
| 71 | C8×C11 | C2×C16 | 1 | 2 | yes | — |
| 72 | C8×C11 | C2×C42 | 1 | 1 | yes | characteristic |
| 73 | C8×C11 | C22×C8 | 1 | 1 | yes | characteristic |
| 74 | C11⋊C8 | C4×C8 | 1 | 2 | yes | — |
| 75 | C11⋊C8 | C2×C16 | 1 | 2 | yes | — |
| 76 | C2×M32 | — | 11 | 1 | no | — |
| 77 | C22×C16 | — | 11 | 1 | no | — |
| 78 | #405 | — | 11 | 1 | no | — |
| 79 | M64 | — | 11 | 4 | no | — |
| 80 | C2×C32 | — | 11 | 1 | no | — |
| 81 | C2×C32 | — | 11 | 1 | no | — |
| 82 | C2×C32 | — | 11 | 4 | no | — |
| 83 | C2×C32 | C2×D11 | 1 | 1 | yes | characteristic |
| 84 | C2×C32 | C2×D11 | 1 | 1 | yes | characteristic |
| 85 | #346 | — | 11 | 1 | no | — |
| 86 | #346 | — | 11 | 1 | no | — |
| 87 | C4×C16 | — | 11 | 1 | no | — |
| 88 | C4×C16 | C2×D11 | 1 | 1 | yes | characteristic |
| 89 | C22×C11 | C22×C16 | 1 | 1 | yes | characteristic |
| 90 | C2×D11 | — | 2 | 2 | no | — |
| 91 | C2×D11 | C4×C16 | 1 | 2 | yes | — |
| 92 | C4×C11 | — | 2 | 2 | no | — |
| 93 | C4×C11 | C2×C4×C8 | 1 | 1 | yes | characteristic |
| 94 | C4×C11 | C22×C16 | 1 | 1 | yes | characteristic |
| 95 | Dic11 | — | 2 | 2 | no | — |
| 96 | Dic11 | C4×C16 | 1 | 2 | yes | — |
| 97 | C2×M16 | — | 11 | 1 | no | — |
| 98 | C22×C8 | — | 11 | 1 | no | — |
| 99 | #117 | — | 11 | 1 | no | — |
| 100 | M32 | — | 11 | 4 | no | — |
| 101 | C2×C16 | — | 11 | 1 | no | — |
| 102 | C2×C16 | — | 11 | 1 | no | — |
| 103 | C2×C16 | — | 11 | 2 | no | — |
| 104 | C2×C16 | — | 11 | 2 | no | — |
| 105 | C2×C16 | C4×D11 | 1 | 1 | yes | characteristic |
| 106 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 107 | #97 | — | 11 | 1 | no | — |
| 108 | #97 | — | 11 | 1 | no | — |
| 109 | C4×C8 | — | 11 | 1 | no | — |
| 110 | C4×C8 | C4×D11 | 1 | 1 | yes | characteristic |
| 111 | C32 | — | 11 | 2 | no | — |
| 112 | C32 | — | 11 | 2 | no | — |
| 113 | C32 | C4×D11 | 1 | 2 | yes | — |
| 114 | C32 | C4×D11 | 1 | 2 | yes | — |
| 115 | C2×C11 | C2×C4×C16 | 1 | 1 | yes | characteristic |
| 116 | C2×C11 | #2258 | 1 | 2 | yes | — |
| 117 | D11 | — | 2 | 2 | no | — |
| 118 | C22×C4 | — | 11 | 1 | no | — |
| 119 | M16 | — | 11 | 4 | no | — |
| 120 | C2×C8 | — | 11 | 1 | no | — |
| 121 | C2×C8 | — | 11 | 1 | no | — |
| 122 | C2×C8 | — | 11 | 2 | no | — |
| 123 | C2×C8 | — | 11 | 2 | no | — |
| 124 | C2×C8 | C8×D11 | 1 | 1 | yes | characteristic |
| 125 | C2×C8 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 126 | C4⋊C4 | — | 11 | 2 | no | — |
| 127 | C22⋊C4 | — | 11 | 2 | no | — |
| 128 | C42 | — | 11 | 1 | no | — |
| 129 | C42 | C8×D11 | 1 | 1 | yes | characteristic |
| 130 | C16 | — | 11 | 2 | no | — |
| 131 | C16 | — | 11 | 2 | no | — |
| 132 | C16 | C8×D11 | 1 | 2 | yes | — |
| 133 | C16 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 134 | C16 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 135 | C11 | #13549 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 136 | C23 | — | 11 | 1 | no | — |
| 137 | C2×C4 | — | 11 | 1 | no | — |
| 138 | C2×C4 | — | 11 | 2 | no | — |
| 139 | C2×C4 | — | 11 | 2 | no | — |
| 140 | C2×C4 | — | 11 | 2 | no | — |
| 141 | C2×C4 | C16×D11 | 1 | 2 | yes | — |
| 142 | C2×C4 | C2×C8×D11 | 1 | 1 | yes | characteristic |
| 143 | C8 | — | 11 | 2 | no | — |
| 144 | C8 | — | 11 | 2 | no | — |
| 145 | C8 | C16×D11 | 1 | 2 | yes | — |
| 146 | C8 | C42×D11 | 1 | 1 | yes | characteristic |
| 147 | C8 | C2×C8×D11 | 1 | 1 | yes | characteristic |
| 148 | C22 | — | 11 | 2 | no | — |
| 149 | C22 | — | 22 | 2 | no | — |
| 150 | C22 | C2×C16×D11 | 1 | 1 | yes | characteristic |
| 151 | C4 | — | 2 | 2 | no | — |
| 152 | C4 | — | 11 | 2 | no | — |
| 153 | C4 | — | 22 | 2 | no | — |
| 154 | C4 | C4×C8×D11 | 1 | 1 | yes | characteristic |
| 155 | C4 | C2×C16×D11 | 1 | 1 | yes | characteristic |
| 156 | C2 | — | 22 | 2 | no | — |
| 157 | C2 | C4×C16×D11 | 1 | 1 | yes | characteristic |
| 158 | C2 | #13070911 | 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