Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
7022 conjugacy classes of subgroups.
The subgroup lattice has 188 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| socle | C23×C11 | C25 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#3458 | C2 | direct (N × H) |
| 2. C2×C11×#544 | C2 | semidirect |
| 4. C2×C11×#533 | C2 | semidirect |
| 7. C11×#544 | C22 | semidirect |
| 9. C11×#533 | C22 | semidirect |
| 10. C2×C11×C4⋊Q8 | C22 | semidirect |
| 11. C2×C11×#125 | C22 | semidirect |
| 13. C2×C4×Q8×C11 | C22 | semidirect |
| 22. C23×C4×C11 | Q8 | semidirect |
| 27. C11×C4⋊Q8 | C23 | semidirect |
| 28. C11×#125 | C23 | semidirect |
| 30. C4×Q8×C11 | C23 | semidirect |
| 41. C2×#3458 | C11 | direct (N × H) |
| 51. C22×C4×C11 | C2×Q8 | semidirect |
| 63. #3458 | C2×C11 | direct (N × H) |
| 64. C2×#544 | C2×C11 | semidirect |
| 66. C2×#533 | C2×C11 | semidirect |
| 86. #544 | C22×C11 | semidirect |
| 88. #533 | C22×C11 | semidirect |
| 89. C2×C4⋊Q8 | C22×C11 | semidirect |
| 90. C2×#125 | C22×C11 | semidirect |
| 92. C2×C4×Q8 | C22×C11 | semidirect |
| 111. C23×C4 | Q8×C11 | semidirect |
| 116. C4⋊Q8 | C23×C11 | semidirect |
| 117. #125 | C23×C11 | semidirect |
| 119. C4×Q8 | C23×C11 | semidirect |
| 131. C2×C11 | #3458 | direct (N × H) |
| 143. C22×C4 | C2×Q8×C11 | semidirect |
| 155. C11 | C2×#3458 | direct (N × H) |
| 184. C2 | C11×#3458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#3458 | 2 |
| C2×C11×#544 | 2 |
| C2×C11×#543 | 2 |
| C2×C11×#533 | 2 |
| C22×C11×#117 | 2 |
| C2×#3458 | 11 |