Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3158 conjugacy classes of subgroups.
The subgroup lattice has 392 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C11 | C24 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C11×#2365 | C2 | direct (N × H) |
| 11. C2×C11×C4⋊Q8 | C4 | semidirect |
| 48. C11×C4⋊Q8 | C2×C4 | semidirect |
| 56. C2×C11×C4⋊C4 | Q8 | semidirect |
| 76. C2×#2365 | C11 | direct (N × H) |
| 120. C11×C4⋊C4 | C2×Q8 | semidirect |
| 127. #2365 | C2×C11 | direct (N × H) |
| 164. C2×C4×C11 | C4×Q8 | semidirect |
| 176. C2×C4⋊Q8 | C4×C11 | semidirect |
| 222. C4×C11 | C2×C4×Q8 | semidirect |
| 235. C4⋊Q8 | C2×C4×C11 | semidirect |
| 243. C2×C4⋊C4 | Q8×C11 | semidirect |
| 263. C2×C11 | #2365 | direct (N × H) |
| 314. C4⋊C4 | C2×Q8×C11 | semidirect |
| 319. C11 | C2×#2365 | direct (N × H) |
| 350. C2×C4 | C4×Q8×C11 | semidirect |
| 382. C4 | C2×C4×Q8×C11 | semidirect |
| 383. C2 | C11×#2365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×C4⋊Q8 | 2 |
| C22×C4×Q8×C11 | 2 |
| C11×#2365 | 2 |
| C2×C11×#391 | 2 |
| C2×C11×#389 | 2 |
| C2×C11×#387 | 2 |
| C2×C4×C11×C4⋊C4 | 2 |
| C2×#2365 | 11 |