Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
1390 conjugacy classes of subgroups.
The subgroup lattice has 356 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C113 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C113 |
| Frattini, cosocle | C23×C4 | C23×C113 |
| prime radical | C25×C113 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C113 ◁ C24×C4×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C113×#1280 | C2 | direct (N × H) |
| 9. C2×C22⋊C8×C113 | C4 | semidirect |
| 22. C23×C4×C113 | C8 | semidirect |
| 36. C22⋊C8×C113 | C2×C4 | semidirect |
| 75. C22×C4×C113 | C2×C8 | semidirect |
| 167. C2×#1280 | C113 | direct (N × H) |
| 172. C2×C113 | #1280 | direct (N × H) |
| 180. #1280 | C2×C113 | direct (N × H) |
| 181. C113 | C2×#1280 | direct (N × H) |
| 187. C2×C22⋊C8 | C4×C113 | semidirect |
| 200. C23×C4 | C8×C113 | semidirect |
| 214. C22⋊C8 | C2×C4×C113 | semidirect |
| 253. C22×C4 | C2×C8×C113 | semidirect |
| 349. C2 | C113×#1280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C8×C113 | 2 |
| C22×#95×C113 | 2 |
| C113×#1280 | 2 |
| C2×#1280 | 113 |