Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1252 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13079069 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #13067905 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #13067208 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C11×#3549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C11×H(3,𝔽4) | C22 | 1 | 4 | yes | complemented |
| 6 | C11×#555 | — | 2 | 3 | no | — |
| 7 | D42×C11 | — | 2 | 3 | no | — |
| 8 | C11×#535 | — | 2 | 6 | no | — |
| 9 | C11×#532 | C22 | 1 | 3 | yes | — |
| 10 | C2×#67002 | — | 2 | 6 | no | — |
| 11 | C2×#66927 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #10622698 | — | 2 | 3 | no | — |
| 13 | #10622686 | — | 2 | 3 | no | — |
| 14 | #10622671 | C22 | 1 | 12 | yes | complemented |
| 15 | C4×#4318 | C22 | 1 | 3 | yes | complemented |
| 16 | #10622178 | C22 | 1 | 12 | yes | complemented |
| 17 | C2×C11×#41 | D4 | 1 | 6 | yes | — |
| 18 | C22×D4×C11 | — | 2 | 6 | no | — |
| 19 | C22×D44 | — | 2 | 3 | no | — |
| 20 | C11×C4⋊Q8 | D4 | 1 | 3 | yes | — |
| 21 | C11×#127 | — | 2 | 4 | no | — |
| 22 | C11×#127 | D4 | 1 | 3 | yes | — |
| 23 | C11×#124 | — | 2 | 12 | no | — |
| 24 | C11×#124 | C23 | 1 | 6 | yes | — |
| 25 | C11×#121 | — | 2 | 12 | no | — |
| 26 | C11×#121 | — | 2 | 6 | no | — |
| 27 | C11×#120 | — | 2 | 4 | no | — |
| 28 | C11×#120 | — | 2 | 12 | no | — |
| 29 | C4×D4×C11 | — | 2 | 6 | no | — |
| 30 | C11×#117 | — | 2 | 6 | no | — |
| 31 | C2×C42×C11 | C23 | 1 | 1 | yes | characteristic |
| 32 | #67002 | — | 4 | 24 | no | — |
| 33 | C2×#4325 | — | 2 | 12 | no | — |
| 34 | C2×#4323 | — | 2 | 12 | no | — |
| 35 | C2×#4318 | — | 2 | 3 | no | — |
| 36 | #66927 | — | 2 | 3 | no | — |
| 37 | #66927 | C23 | 1 | 2 | yes | — |
| 38 | #66867 | C23 | 1 | 6 | yes | — |
| 39 | C4×C11⋊C8 | — | 2 | 3 | no | — |
| 40 | #19073 | — | 11 | 1 | no | maximal, Sylow |
| 41 | C24×C11 | — | 2 | 4 | no | — |
| 42 | C23×D11 | — | 4 | 1 | no | — |
| 43 | C11×#41 | — | 4 | 12 | no | — |
| 44 | C2×Q8×C11 | C2×D4 | 1 | 6 | yes | — |
| 45 | C2×D4×C11 | — | 2 | 12 | no | — |
| 46 | C2×D4×C11 | — | 2 | 6 | no | — |
| 47 | C2×D4×C11 | — | 2 | 6 | no | — |
| 48 | C2×D4×C11 | — | 8 | 12 | no | — |
| 49 | C2×D4×C11 | C2×D4 | 1 | 6 | yes | — |
| 50 | C22×C4×C11 | — | 2 | 6 | no | — |
| 51 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 52 | C2×D44 | — | 2 | 6 | no | — |
| 53 | C2×D44 | — | 4 | 12 | no | — |
| 54 | C2×D44 | — | 4 | 3 | no | — |
| 55 | C11×C4⋊C4 | — | 2 | 6 | no | — |
| 56 | C11×C22⋊C4 | — | 2 | 12 | no | — |
| 57 | C11×C22⋊C4 | — | 2 | 12 | no | — |
| 58 | C42×C11 | — | 2 | 4 | no | — |
| 59 | C42×C11 | C2×D4 | 1 | 3 | yes | — |
| 60 | C42×C11 | C24 | 1 | 1 | yes | characteristic |
| 61 | #4325 | — | 4 | 24 | no | — |
| 62 | #4323 | — | 4 | 24 | no | — |
| 63 | #4318 | — | 2 | 12 | no | — |
| 64 | C2×C11⋊C8 | — | 2 | 6 | no | — |
| 65 | #3549 | D11 | 1 | 1 | yes | characteristic, complemented |
| 66 | #3151 | — | 11 | 3 | no | — |
| 67 | #1655 | — | 11 | 8 | no | — |
| 68 | #1525 | — | 11 | 3 | no | — |
| 69 | C23×C11 | — | 2 | 6 | no | — |
| 70 | C23×C11 | — | 8 | 12 | no | — |
| 71 | C23×C11 | #120 | 1 | 1 | yes | characteristic |
| 72 | C22×D11 | — | 4 | 2 | no | — |
| 73 | C22×D11 | — | 8 | 6 | no | — |
| 74 | Q8×C11 | — | 4 | 6 | no | — |
| 75 | D4×C11 | — | 4 | 6 | no | — |
| 76 | D4×C11 | — | 4 | 12 | no | — |
| 77 | D4×C11 | — | 8 | 6 | no | — |
| 78 | D4×C11 | — | 8 | 12 | no | — |
| 79 | C2×C4×C11 | — | 2 | 6 | no | — |
| 80 | C2×C4×C11 | — | 2 | 6 | no | — |
| 81 | C2×C4×C11 | — | 4 | 12 | no | — |
| 82 | C2×C4×C11 | #120 | 1 | 3 | yes | — |
| 83 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 84 | D44 | — | 4 | 12 | no | — |
| 85 | D44 | — | 8 | 6 | no | — |
| 86 | C11⋊C8 | — | 2 | 12 | no | — |
| 87 | C2×AGL(1,ℤ/8) | — | 22 | 6 | no | — |
| 88 | H(3,𝔽4) | C2×D11 | 1 | 4 | yes | complemented |
| 89 | #555 | — | 2 | 3 | no | — |
| 90 | D42 | — | 2 | 3 | no | — |
| 91 | #535 | — | 2 | 6 | no | — |
| 92 | #532 | C2×D11 | 1 | 3 | yes | — |
| 93 | C2×#127 | — | 11 | 1 | no | — |
| 94 | #496 | — | 11 | 12 | no | — |
| 95 | #493 | — | 22 | 3 | no | — |
| 96 | #492 | — | 22 | 3 | no | — |
| 97 | C4×M16 | — | 11 | 3 | no | — |
| 98 | #329 | — | 11 | 12 | no | — |
| 99 | C22×C11 | — | 2 | 3 | no | — |
| 100 | C22×C11 | — | 4 | 6 | no | — |
| 101 | C22×C11 | — | 4 | 12 | no | — |
| 102 | C22×C11 | — | 16 | 8 | no | — |
| 103 | C22×C11 | C2×#120 | 1 | 1 | yes | characteristic |
| 104 | C2×D11 | — | 8 | 6 | no | — |
| 105 | C2×D11 | — | 16 | 4 | no | — |
| 106 | C4×C11 | — | 2 | 3 | no | — |
| 107 | C4×C11 | — | 4 | 6 | no | — |
| 108 | C4×C11 | #453 | 1 | 6 | yes | — |
| 109 | C2×#41 | C22⋊D11 | 1 | 6 | yes | — |
| 110 | C22×D4 | — | 2 | 6 | no | — |
| 111 | C22×D4 | — | 22 | 3 | no | — |
| 112 | AGL(1,ℤ/8) | — | 44 | 24 | no | — |
| 113 | C2×SD16 | — | 22 | 12 | no | — |
| 114 | C2×D8 | — | 22 | 12 | no | — |
| 115 | C2×M16 | — | 22 | 3 | no | — |
| 116 | C4⋊Q8 | C22⋊D11 | 1 | 3 | yes | — |
| 117 | #127 | — | 2 | 4 | no | — |
| 118 | #127 | — | 11 | 2 | no | — |
| 119 | #127 | — | 22 | 3 | no | — |
| 120 | #127 | C22⋊D11 | 1 | 3 | yes | — |
| 121 | #124 | — | 2 | 12 | no | — |
| 122 | #124 | C22×D11 | 1 | 6 | yes | — |
| 123 | #121 | — | 2 | 12 | no | — |
| 124 | #121 | — | 2 | 6 | no | — |
| 125 | #120 | — | 2 | 4 | no | — |
| 126 | #120 | — | 2 | 12 | no | — |
| 127 | C4×D4 | — | 2 | 6 | no | — |
| 128 | #117 | — | 2 | 6 | no | — |
| 129 | C2×C42 | C22×D11 | 1 | 1 | yes | characteristic |
| 130 | #97 | — | 11 | 6 | no | — |
| 131 | C4×C8 | — | 22 | 3 | no | — |
| 132 | C2×C11 | — | 4 | 1 | no | — |
| 133 | C2×C11 | — | 8 | 6 | no | — |
| 134 | C2×C11 | C2×#453 | 1 | 3 | yes | — |
| 135 | D11 | — | 16 | 2 | no | — |
| 136 | C24 | — | 2 | 4 | no | — |
| 137 | C24 | — | 44 | 1 | no | — |
| 138 | #41 | — | 4 | 12 | no | — |
| 139 | C2×Q8 | C2×C22⋊D11 | 1 | 6 | yes | — |
| 140 | C2×D4 | — | 2 | 12 | no | — |
| 141 | C2×D4 | — | 2 | 6 | no | — |
| 142 | C2×D4 | — | 2 | 6 | no | — |
| 143 | C2×D4 | — | 8 | 12 | no | — |
| 144 | C2×D4 | — | 22 | 6 | no | — |
| 145 | C2×D4 | — | 44 | 12 | no | — |
| 146 | C2×D4 | — | 44 | 3 | no | — |
| 147 | C2×D4 | C2×C22⋊D11 | 1 | 6 | yes | — |
| 148 | C22×C4 | — | 2 | 6 | no | — |
| 149 | C22×C4 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 150 | SD16 | — | 44 | 24 | no | — |
| 151 | D8 | — | 44 | 24 | no | — |
| 152 | M16 | — | 22 | 12 | no | — |
| 153 | C2×C8 | — | 22 | 6 | no | — |
| 154 | C4⋊C4 | — | 2 | 6 | no | — |
| 155 | C22⋊C4 | — | 2 | 12 | no | — |
| 156 | C22⋊C4 | — | 2 | 12 | no | — |
| 157 | C42 | — | 2 | 4 | no | — |
| 158 | C42 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 159 | C42 | C23×D11 | 1 | 1 | yes | characteristic |
| 160 | C11 | #19073 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 161 | C23 | — | 2 | 6 | no | — |
| 162 | C23 | — | 8 | 12 | no | — |
| 163 | C23 | — | 44 | 2 | no | — |
| 164 | C23 | — | 88 | 6 | no | — |
| 165 | C23 | #67006 | 1 | 1 | yes | characteristic |
| 166 | Q8 | — | 4 | 6 | no | — |
| 167 | D4 | — | 4 | 6 | no | — |
| 168 | D4 | — | 4 | 12 | no | — |
| 169 | D4 | — | 8 | 6 | no | — |
| 170 | D4 | — | 8 | 12 | no | — |
| 171 | D4 | — | 44 | 12 | no | — |
| 172 | D4 | — | 88 | 6 | no | — |
| 173 | C2×C4 | — | 2 | 6 | no | — |
| 174 | C2×C4 | — | 2 | 6 | no | — |
| 175 | C2×C4 | — | 4 | 12 | no | — |
| 176 | C2×C4 | #67006 | 1 | 3 | yes | — |
| 177 | C2×C4 | C22×C22⋊D11 | 1 | 3 | yes | — |
| 178 | C8 | — | 22 | 12 | no | — |
| 179 | C22 | — | 2 | 3 | no | — |
| 180 | C22 | — | 4 | 6 | no | — |
| 181 | C22 | — | 4 | 12 | no | — |
| 182 | C22 | — | 16 | 8 | no | — |
| 183 | C22 | — | 88 | 6 | no | — |
| 184 | C22 | — | 176 | 4 | no | — |
| 185 | C22 | C2×#67006 | 1 | 1 | yes | characteristic |
| 186 | C4 | — | 2 | 3 | no | — |
| 187 | C4 | — | 4 | 6 | no | — |
| 188 | C4 | #10622854 | 1 | 6 | yes | — |
| 189 | C2 | — | 4 | 1 | no | — |
| 190 | C2 | — | 8 | 6 | no | — |
| 191 | C2 | — | 176 | 2 | no | — |
| 192 | C2 | C2×#10622854 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13079069 | C2 | semidirect |
| 2. #13067905 | C2 | semidirect |
| 3. #13067208 | C2 | semidirect |
| 4. C11×#3549 | C2 | semidirect |
| 5. C11×H(3,𝔽4) | C22 | semidirect |
| 11. C2×#66927 | C22 | semidirect |
| 14. #10622671 | C22 | semidirect |
| 15. C4×#4318 | C22 | semidirect |
| 16. #10622178 | C22 | semidirect |
| 65. #3549 | D11 | semidirect |
| 88. H(3,𝔽4) | C2×D11 | semidirect |
| 160. C11 | #19073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079069 | 2 |
| #13067905 | 2 |
| #13067208 | 2 |
| C11×#3549 | 2 |
| #19073 | 11 |