Finite Group DatabasebetaFinite Group Databasebeta← C2×ΓL(1,𝔽8)×C127⋊C3 #30630701
Order 16002.
48 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)×C127⋊C3 |
| commutator, cosocle, hypocenter | C7×C127 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C127 | C32 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. ΓL(1,𝔽8)×C127⋊C3 | C2 | direct (N × H) |
| 2. C2×#14581887 | C3 | semidirect |
| 3. C2×#14581888 | C3 | semidirect |
| 4. C2×ΓL(1,𝔽8)×C127 | C3 | semidirect |
| 5. C2×C7×C127⋊C3 | C3 | semidirect |
| 6. #14581888 | C2×C3 | semidirect |
| 7. #14581887 | C2×C3 | semidirect |
| 8. C7×C127⋊C3 | C2×C3 | semidirect |
| 9. ΓL(1,𝔽8)×C127 | C2×C3 | semidirect |
| 11. C2×C7×C127 | C32 | semidirect |
| 13. C7×C127 | C2×C32 | semidirect |
| 17. C2×C127⋊C3 | ΓL(1,𝔽8) | direct (N × H) |
| 21. C127⋊C3 | C2×ΓL(1,𝔽8) | direct (N × H) |
| 22. C2×C127 | C3×ΓL(1,𝔽8) | semidirect |
| 23. C127 | C2×C3×ΓL(1,𝔽8) | semidirect |
| 29. C2×ΓL(1,𝔽8) | C127⋊C3 | direct (N × H) |
| 33. ΓL(1,𝔽8) | C2×C127⋊C3 | direct (N × H) |
| 35. C2×C7 | C3×C127⋊C3 | semidirect |
| 37. C7 | C2×C3×C127⋊C3 | semidirect |
| 46. C2 | ΓL(1,𝔽8)×C127⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×C127⋊C3 | 2 |
| C2×#14581887 | 3 |
| C2×#14581888 | 3 |
| C2×ΓL(1,𝔽8)×C127 | 3 |
| C2×C7×C127⋊C3 | 3 |
| C2×C3×C127⋊C3 | 7 |
| C2×C3×ΓL(1,𝔽8) | 127 |