Finite Group DatabasebetaFinite Group Databasebeta← C5×D7×ΓL(1,𝔽8)×D11 #44568632
Order 32340.
168 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D7×ΓL(1,𝔽8)×D11 |
| commutator, cosocle, hypocenter | C72×C11 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C22×C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×ΓL(1,𝔽8)×D77 | 2 |
| C5×C11×D7×ΓL(1,𝔽8) | 2 |
| C5×C7×ΓL(1,𝔽8)×D11 | 2 |
| C5×C7×D7×D11 | 3 |
| D7×ΓL(1,𝔽8)×D11 | 5 |
| C3×C5×D7×D11 | 7 |
| C2×C5×ΓL(1,𝔽8)×D11 | 7 |
| C2×C5×D7×ΓL(1,𝔽8) | 11 |