Finite Group Databasebeta

← C11×C11⋊(D13⋊C3) #22628071

Subgroups — C11×C11⋊(D13⋊C3) #22628071

Order 9438.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C112×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11×D143C311yesmaximal, characteristic, complemented, Hall
3C112×C13C2×C311yescharacteristic, complemented, Hall
4C11⋊(D13⋊C3)C1111yesmaximal, characteristic, direct product factor
5C11×D13⋊C3—111nomaximal
6C3×C11×D11—131nomaximal, Hall
7C11×C13⋊C3—25no—
8C11×C13⋊C3D1111yescharacteristic, complemented
9C11×C13⋊C3C2×C1111yescharacteristic, complemented
10C3×C112—131noHall
11D143C3×C1111yescharacteristic, complemented
12C11×D13—111no—
13C11×D11—131noHall
14C11×C13—25no—
15C11×C13C3×D1111yescharacteristic, complemented
16C11×C13C2×C3×C1111yescharacteristic, complemented
17C112D13⋊C311yescharacteristic, complemented, Sylow
18D13⋊C3—111noHall
19C2×C3×C11—1431no—
20C3×D11—131no—
21C13⋊C3C11×D1111yescharacteristic, complemented, Hall
22C3×C11—131no—
23C3×C11—131no—
24C3×C11—265no—
25D13—111noHall
26C2×C11—1431no—
27D11—131no—
28C13C3×C11×D1111yescharacteristic, complemented, Sylow
29C11—25no—
30C11C11×D13⋊C311yescharacteristic, complemented
31C11C11⋊(D13⋊C3)11yescharacteristic, direct product factor
32C2×C3—1431noHall
33C3—131noSylow
34C2—1431noSylow
subgroupG/H
center, hypercenterC11C11⋊(D13⋊C3)
commutator, hypocenterC11×C13C2×C3×C11
FrattiniC1G
Fitting, socleC112×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C11

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C112×C13⋊C3C2semidirect
2. C11×D143C3semidirect
3. C112×C13C2×C3semidirect
4. C11⋊(D13⋊C3)C11direct (N × H)
8. C11×C13⋊C3D11semidirect
9. C11×C13⋊C3C2×C11semidirect
11. D143C3×C11semidirect
15. C11×C13C3×D11semidirect
16. C11×C13C2×C3×C11semidirect
17. C112D13⋊C3semidirect
21. C13⋊C3C11×D11semidirect
28. C13C3×C11×D11semidirect
30. C11C11×D13⋊C3semidirect
31. C11C11⋊(D13⋊C3)direct (N × H)