Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1766 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×#3383 | C2 | direct (N × H) |
| 41. C2×C11×Q16 | Q8 | semidirect |
| 82. C2×#3383 | C11 | direct (N × H) |
| 99. C11×Q16 | C2×Q8 | semidirect |
| 124. #3383 | C2×C11 | direct (N × H) |
| 204. C2×Q16 | Q8×C11 | semidirect |
| 245. C2×C11 | #3383 | direct (N × H) |
| 265. Q16 | C2×Q8×C11 | semidirect |
| 289. C11 | C2×#3383 | direct (N × H) |
| 331. C2 | C11×#3383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#557 | 2 |
| C11×#3383 | 2 |
| C2×C11×#500 | 2 |
| C2×C11×#499 | 2 |
| C2×C11×#479 | 2 |
| C2×C11×#475 | 2 |
| C2×C8×Q8×C11 | 2 |
| C2×C4×C11×Q16 | 2 |
| C2×#3383 | 11 |