Order 12032.
1934 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D47 |
| commutator, socle, prime radical, cosocle | C24×C47 | C24 |
| Fitting | C2×C47×#389 | C2 |
| hypercenter | C2×#389 | D47 |
| hypocenter | C47 | #15143 |
| LCS | G ▷ C24×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C2×#389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 43. C2×C4×Dic47 | Q8 | semidirect |
| 46. C47⋊#95 | Q8 | semidirect |
| 58. C2×C4⋊C4×C47 | Q8 | semidirect |
| 151. C2×Dic47 | C4⋊Q8 | semidirect |
| 175. C4×C47 | #395 | semidirect |
| 212. C47 | #15143 | semidirect |
| 239. C2×C4⋊C4 | Dic94 | semidirect |
| 363. C4 | #15689043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094024 | 2 |
| C2×#15689043 | 2 |
| C2×#15688992 | 2 |
| #20241652 | 2 |
| #20241617 | 2 |
| C4×C47⋊#95 | 2 |
| C2×C47×#389 | 2 |
| #15143 | 47 |