Finite Group DatabasebetaFinite Group Databasebeta← (C3⋊AGL(1,𝔽11))⋊D35 #37528464
Order 23100.
192 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C11 | C22×C5 |
| LCS | G ▷ C3×C5×C7×C11 | |
| UCS | C1 | |
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 |
|---|---|
| C11⋊C5×D105 | 2 |
| C5×C7×C3⋊AGL(1,𝔽11) | 2 |
| C3×C5⋊(C7⋊AGL(1,𝔽11)) | 2 |
| D35×AGL(1,𝔽11) | 3 |
| D33⋊D35 | 5 |
| D21⋊AGL(1,𝔽11) | 5 |
| D15⋊AGL(1,𝔽11) | 7 |
| C5×D3×D35 | 11 |