Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2190 conjugacy classes of subgroups.
The subgroup lattice has 500 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C47 | C22⋊C4 |
| commutator | C22 | C22×C42×C47 |
| Frattini, cosocle | C22×C4 | C24×C47 |
| socle | C23×C47 | #95 |
| prime radical | C25×C47 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C47 ◁ C24×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C47×#344 | C2 | direct (N × H) |
| 13. C22×M16×C47 | C4 | semidirect |
| 14. C22×M16×C47 | C4 | semidirect |
| 15. C22×M16×C47 | C4 | semidirect |
| 19. C23×C8×C47 | C4 | semidirect |
| 27. C47×#344 | C22 | direct (N × H) |
| 57. C2×M16×C47 | C2×C4 | semidirect |
| 58. C2×M16×C47 | C2×C4 | semidirect |
| 59. C2×M16×C47 | C2×C4 | semidirect |
| 67. C22×C8×C47 | C2×C4 | semidirect |
| 139. M16×C47 | C22×C4 | semidirect |
| 145. C2×C8×C47 | C22×C4 | semidirect |
| 213. C22×#344 | C47 | direct (N × H) |
| 225. C22×C47 | #344 | direct (N × H) |
| 245. C2×#344 | C2×C47 | direct (N × H) |
| 252. C2×C47 | C2×#344 | direct (N × H) |
| 262. C22×M16 | C4×C47 | semidirect |
| 263. C22×M16 | C4×C47 | semidirect |
| 264. C22×M16 | C4×C47 | semidirect |
| 268. C23×C8 | C4×C47 | semidirect |
| 276. #344 | C22×C47 | direct (N × H) |
| 277. C47 | C22×#344 | direct (N × H) |
| 307. C2×M16 | C2×C4×C47 | semidirect |
| 308. C2×M16 | C2×C4×C47 | semidirect |
| 309. C2×M16 | C2×C4×C47 | semidirect |
| 317. C22×C8 | C2×C4×C47 | semidirect |
| 389. M16 | C22×C4×C47 | semidirect |
| 395. C2×C8 | C22×C4×C47 | semidirect |
| 474. C22 | C47×#344 | direct (N × H) |
| 497. C2 | C2×C47×#344 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×M16×C47 | 2 |
| C22×#117×C47 | 2 |
| C2×C47×#344 | 2 |
| C22×#344 | 47 |