Finite Group Databasebeta

← C11×C29⋊(D13⋊C3) #38733467

Subgroups — C11×C29⋊(D13⋊C3) #38733467

Order 24882.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C29×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11×D377C311yesmaximal, characteristic, complemented, Hall
3C11×C13×C29C2×C311yescharacteristic, complemented, Hall
4C29⋊(D13⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
5C3×C11×D29—131nomaximal, Hall
6C29×C13⋊C3C2×C1111yescharacteristic, complemented, Hall
7C3×C11×C29—131noHall
8C11×D13⋊C3—291nomaximal, Hall
9D377C3×C1111yescharacteristic, complemented, Hall
10C11×D29—131noHall
11C11×C13⋊C3D2911yescharacteristic, complemented, Hall
12C13×C29C2×C3×C1111yescharacteristic, complemented, Hall
13C11×C29D13⋊C311yescharacteristic, complemented, Hall
14C11×D13—291noHall
15C3×D29—131noHall
16C11×C13C3×D2911yescharacteristic, complemented, Hall
17C3×C29—131noHall
18D13⋊C3—291noHall
19C2×C3×C11—3771noHall
20D29—131noHall
21C13⋊C3C11×D2911yescharacteristic, complemented, Hall
22C3×C11—131noHall
23C29C11×D13⋊C311yescharacteristic, complemented, Sylow
24D13—291noHall
25C2×C11—3771noHall
26C13C3×C11×D2911yescharacteristic, complemented, Sylow
27C11C29⋊(D13⋊C3)11yescharacteristic, direct product factor, Sylow
28C2×C3—3771noHall
29C3—131noSylow
30C2—3771noSylow
subgroupG/H
center, hypercenterC11C29⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C29C2×C3×C11
FrattiniC1G
Fitting, socleC11×C13×C29C2×C3
LCSG ▷ C13×C29
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C29×C13⋊C3C2semidirect
2. C11×D377C3semidirect
3. C11×C13×C29C2×C3semidirect
4. C29⋊(D13⋊C3)C11direct (N × H)
6. C29×C13⋊C3C2×C11semidirect
9. D377C3×C11semidirect
11. C11×C13⋊C3D29semidirect
12. C13×C29C2×C3×C11semidirect
13. C11×C29D13⋊C3semidirect
16. C11×C13C3×D29semidirect
21. C13⋊C3C11×D29semidirect
23. C29C11×D13⋊C3semidirect
26. C13C3×C11×D29semidirect
27. C11C29⋊(D13⋊C3)direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×C29×C13⋊C32
C11×D3773
C29⋊(D13⋊C3)11
C3×C11×D2913
C11×D13⋊C329