Finite Group DatabasebetaFinite Group Databasebeta← C5×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)) #46831542
Order 34650.
288 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 76 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 | C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)) |
| commutator, cosocle, hypocenter | C3×C7×C11 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C11 | C2×C3×C5 |
| LCS | G ▷ C3×C7×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 |
|---|---|
| C3×C5×ΓL(1,𝔽8)×C11⋊C5 | 2 |
| C5×C3⋊(C7⋊AGL(1,𝔽11)) | 3 |
| C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11) | 3 |
| C5×C3⋊(C11⋊AGL(1,𝔽7)) | 5 |
| C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)) | 5 |
| C3×C5×C3⋊AGL(1,𝔽11) | 7 |
| C52×C3⋊AGL(1,𝔽7) | 11 |