Finite Group DatabasebetaFinite Group Databasebeta← (C11⋊C5)⋊#10596873 #44568445
Order 32340.
144 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 36 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 | C2 | (C11⋊C5)⋊#64423 |
| commutator, hypocenter | C72×C11 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C72×C11 | C2×C3×C5 |
| prime radical | C2×C11⋊C5×#3861 | C2 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C7⋊(Dic11⋊C5) | C3 | semidirect |
| 3. C11⋊C5×#3861 | C4 | semidirect |
| 4. C11⋊#10596873 | C5 | semidirect |
| 10. C72×C11⋊C5 | C3×C4 | semidirect |
| 14. C7×Dic77 | C3×C5 | semidirect |
| 15. C11×#3861 | C4×C5 | semidirect |
| 16. C7⋊(Dic11⋊C5) | ΓL(1,𝔽8) | semidirect |
| 32. C72×C11 | C3×C4×C5 | semidirect |
| 40. C7×C11⋊C5 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 41. C7×C11⋊C5 | C4×ΓL(1,𝔽8) | semidirect |
| 43. Dic77 | C5×ΓL(1,𝔽8) | semidirect |
| 59. #3861 | Dic11⋊C5 | semidirect |
| 71. C7×C11 | C5×ΓL(1,𝔽8)⋊C4 | semidirect |
| 72. C7×C11 | C4×C5×ΓL(1,𝔽8) | semidirect |
| 78. C11⋊C5 | #10596873 | semidirect |
| 79. C72 | C3×Dic11⋊C5 | semidirect |
| 101. C11 | C5×#10596873 | semidirect |
| 104. C7 | ΓL(1,𝔽8)×Dic11⋊C5 | semidirect |
| 105. C7 | ΓL(1,𝔽8)⋊(Dic11⋊C5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11⋊C5×#3861 | 2 |
| C7×C7⋊(Dic11⋊C5) | 3 |
| C11⋊#10596873 | 5 |
| ΓL(1,𝔽8)⋊(Dic11⋊C5) | 7 |
| ΓL(1,𝔽8)×Dic11⋊C5 | 7 |
| C5×#10596873 | 11 |