Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
716 conjugacy classes of subgroups.
The subgroup lattice has 162 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×C42 |
| commutator | C4 | C22×C42×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C22×#97 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C11×#2110 | C2 | semidirect |
| 4. C2×C11×#347 | C2 | semidirect |
| 8. C11×#504 | C4 | semidirect |
| 27. C11×M32 | C2×C4 | semidirect |
| 29. C2×C11×C16 | C2×C4 | semidirect |
| 35. #33329 | C11 | direct (N × H) |
| 58. #2110 | C2×C11 | semidirect |
| 59. C2×#347 | C2×C11 | semidirect |
| 77. #504 | C4×C11 | semidirect |
| 104. M32 | C2×C4×C11 | semidirect |
| 106. C2×C16 | C2×C4×C11 | semidirect |
| 135. C11 | #33329 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#3407 | 2 |
| C11×#2875 | 2 |
| C11×#2110 | 2 |
| C2×C11×#347 | 2 |
| #33329 | 11 |