Finite Group Databasebeta

← C3×C43×AGL(1,𝔽11) #28382004

Subgroups — C3×C43×AGL(1,𝔽11) #28382004

Order 14190.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C43×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C43×AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
3C3×D11×C43C511yesmaximal, characteristic, complemented, Hall
4C43×C11⋊C5C2×C311yescharacteristic, complemented, Hall
5C3×C11×C43C2×C511yescharacteristic, complemented, Hall
6C2×C3×C5×C43—111nomaximal, Hall
7D11×C43C3×C511yescharacteristic, complemented, Hall
8C3×C5×C43—111noHall
9C11×C43C2×C3×C511yescharacteristic, complemented, Hall
10C2×C5×C43—111noHall
11C3×AGL(1,𝔽11)C4311yesmaximal, characteristic, direct product factor, Hall
12C2×C3×C43—111noHall
13C5×C43—111noHall
14C3×C11⋊C5C2×C4311yescharacteristic, complemented, Hall
15C3×C43AGL(1,𝔽11)11yescharacteristic, direct product factor, Hall
16AGL(1,𝔽11)C3×C4311yescharacteristic, direct product factor, Hall
17C2×C43—111noHall
18C3×D11C5×C4311yescharacteristic, complemented, Hall
19C11⋊C5C2×C3×C4311yescharacteristic, complemented, Hall
20C43C3×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
21C3×C11C2×C5×C4311yescharacteristic, complemented, Hall
22C2×C3×C5—111noHall
23D11C3×C5×C4311yescharacteristic, complemented, Hall
24C3×C5—111noHall
25C11C2×C3×C5×C4311yescharacteristic, complemented, Sylow
26C2×C5—111noHall
27C2×C3—111noHall
28C5—111noSylow
29C3C43×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
30C2—111noSylow
subgroupG/H
center, hypercenterC3×C43AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C43
FrattiniC1G
Fitting, socleC3×C11×C43C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C43

Complements

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

NH ≅ G/Ntype
1. C3×C43×C11⋊C5C2semidirect
2. C43×AGL(1,𝔽11)C3direct (N × H)
3. C3×D11×C43C5semidirect
4. C43×C11⋊C5C2×C3semidirect
5. C3×C11×C43C2×C5semidirect
7. D11×C43C3×C5semidirect
9. C11×C43C2×C3×C5semidirect
11. C3×AGL(1,𝔽11)C43direct (N × H)
14. C3×C11⋊C5C2×C43semidirect
15. C3×C43AGL(1,𝔽11)direct (N × H)
16. AGL(1,𝔽11)C3×C43direct (N × H)
18. C3×D11C5×C43semidirect
19. C11⋊C5C2×C3×C43semidirect
20. C43C3×AGL(1,𝔽11)direct (N × H)
21. C3×C11C2×C5×C43semidirect
23. D11C3×C5×C43semidirect
25. C11C2×C3×C5×C43semidirect
29. C3C43×AGL(1,𝔽11)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C43×C11⋊C52
C43×AGL(1,𝔽11)3
C3×D11×C435
C2×C3×C5×C4311
C3×AGL(1,𝔽11)43