Finite Group Databasebeta

← C13×C11⋊(D31⋊C3) #40998249

Subgroups — C13×C11⋊(D31⋊C3) #40998249

Order 26598.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C13×C31⋊C3C211yesmaximal, characteristic, complemented, Hall
2C13×D341C311yesmaximal, characteristic, complemented, Hall
3C11×C13×C31C2×C311yescharacteristic, complemented, Hall
4C13×D31⋊C3—111nomaximal, Hall
5C11⋊(D31⋊C3)C1311yesmaximal, characteristic, direct product factor, Hall
6C13×C31⋊C3D1111yescharacteristic, complemented, Hall
7C11×C31⋊C3C2×C1311yescharacteristic, complemented, Hall
8C3×C13×D11—311nomaximal, Hall
9C13×D31—111noHall
10D341C3×C1311yescharacteristic, complemented, Hall
11C3×C11×C13—311noHall
12C13×C31C3×D1111yescharacteristic, complemented, Hall
13C11×C31C2×C3×C1311yescharacteristic, complemented, Hall
14C13×D11—311noHall
15D31⋊C3—111noHall
16C11×C13D31⋊C311yescharacteristic, complemented, Hall
17C31⋊C3C13×D1111yescharacteristic, complemented, Hall
18C2×C3×C13—3411noHall
19C3×D11—311noHall
20D31—111noHall
21C3×C13—311noHall
22C3×C11—311noHall
23C31C3×C13×D1111yescharacteristic, complemented, Sylow
24C2×C13—3411noHall
25D11—311noHall
26C13C11⋊(D31⋊C3)11yescharacteristic, direct product factor, Sylow
27C11C13×D31⋊C311yescharacteristic, complemented, Sylow
28C2×C3—3411noHall
29C3—311noSylow
30C2—3411noSylow
subgroupG/H
center, hypercenterC13C11⋊(D31⋊C3)
commutator, cosocle, hypocenterC11×C31C2×C3×C13
FrattiniC1G
Fitting, socleC11×C13×C31C2×C3
LCSG ▷ C11×C31
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C11×C13×C31⋊C3C2semidirect
2. C13×D341C3semidirect
3. C11×C13×C31C2×C3semidirect
5. C11⋊(D31⋊C3)C13direct (N × H)
6. C13×C31⋊C3D11semidirect
7. C11×C31⋊C3C2×C13semidirect
10. D341C3×C13semidirect
12. C13×C31C3×D11semidirect
13. C11×C31C2×C3×C13semidirect
16. C11×C13D31⋊C3semidirect
17. C31⋊C3C13×D11semidirect
23. C31C3×C13×D11semidirect
26. C13C11⋊(D31⋊C3)direct (N × H)
27. C11C13×D31⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11×C13×C31⋊C32
C13×D3413
C13×D31⋊C311
C11⋊(D31⋊C3)13
C3×C13×D1131