Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C5×C7×AGL(1,𝔽11) #37528554
Order 23100.
320 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5×C7 | AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11 | C22×C3×C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C3×C5×C7 | |
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 |
|---|---|
| C2×C3×C5×C7×C11⋊C5 | 2 |
| C3×C5×C7×AGL(1,𝔽11) | 2 |
| C2×C5×C7×AGL(1,𝔽11) | 3 |
| C2×C3×C5×C7×D11 | 5 |
| C2×C3×C7×AGL(1,𝔽11) | 5 |
| C2×C3×C5×AGL(1,𝔽11) | 7 |
| C22×C3×C52×C7 | 11 |