Finite Group Databasebeta

← C3×C11×ΓL(1,𝔽8)×C47 #45654663

Subgroups — C3×C11×ΓL(1,𝔽8)×C47 #45654663

Order 32571.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×ΓL(1,𝔽8)×C47C313yesmaximal, direct product factor
2C3×C7×C11×C47C311yesmaximal, characteristic, complemented
3C32×C11×C47—71nomaximal, Hall
4C7×C11×C47C3211yescharacteristic, complemented, Hall
5C3×ΓL(1,𝔽8)×C47C1111yesmaximal, characteristic, direct product factor, Hall
6C3×C11×C47—73no—
7C3×C11×C47ΓL(1,𝔽8)11yescharacteristic, direct product factor
8C3×C7×C47C3×C1111yescharacteristic, complemented
9ΓL(1,𝔽8)×C47C3×C1113yesdirect product factor
10C3×C11×ΓL(1,𝔽8)C4711yesmaximal, characteristic, direct product factor, Hall
11C11×C47C3×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
12C32×C47—71noHall
13C7×C47C32×C1111yescharacteristic, complemented, Hall
14C3×C7×C11C3×C4711yescharacteristic, complemented
15C11×ΓL(1,𝔽8)C3×C4713yesdirect product factor
16C3×C47—73no—
17C3×C47C11×ΓL(1,𝔽8)11yescharacteristic, direct product factor
18C32×C11—71noHall
19C7×C11C32×C4711yescharacteristic, complemented, Hall
20C3×ΓL(1,𝔽8)C11×C4711yescharacteristic, direct product factor, Hall
21C47C3×C11×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
22C3×C11—73no—
23C3×C11ΓL(1,𝔽8)×C4711yescharacteristic, direct product factor
24C3×C7C3×C11×C4711yescharacteristic, complemented
25ΓL(1,𝔽8)C3×C11×C4713yesdirect product factor
26C11C3×ΓL(1,𝔽8)×C4711yescharacteristic, direct product factor, Sylow
27C32—71noSylow
28C7C32×C11×C4711yescharacteristic, complemented, Sylow
29C3—73no—
30C3C11×ΓL(1,𝔽8)×C4711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC3×C11×C47ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C11×C47
FrattiniC1G
Fitting, socleC3×C7×C11×C47C3
LCSG ▷ C7
UCSC1 ◁ C3×C11×C47

Complements

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

NH ≅ G/Ntype
1. C11×ΓL(1,𝔽8)×C47C3direct (N × H)
2. C3×C7×C11×C47C3semidirect
4. C7×C11×C47C32semidirect
5. C3×ΓL(1,𝔽8)×C47C11direct (N × H)
7. C3×C11×C47ΓL(1,𝔽8)direct (N × H)
8. C3×C7×C47C3×C11semidirect
9. ΓL(1,𝔽8)×C47C3×C11direct (N × H)
10. C3×C11×ΓL(1,𝔽8)C47direct (N × H)
11. C11×C47C3×ΓL(1,𝔽8)direct (N × H)
13. C7×C47C32×C11semidirect
14. C3×C7×C11C3×C47semidirect
15. C11×ΓL(1,𝔽8)C3×C47direct (N × H)
17. C3×C47C11×ΓL(1,𝔽8)direct (N × H)
19. C7×C11C32×C47semidirect
20. C3×ΓL(1,𝔽8)C11×C47direct (N × H)
21. C47C3×C11×ΓL(1,𝔽8)direct (N × H)
23. C3×C11ΓL(1,𝔽8)×C47direct (N × H)
24. C3×C7C3×C11×C47semidirect
25. ΓL(1,𝔽8)C3×C11×C47direct (N × H)
26. C11C3×ΓL(1,𝔽8)×C47direct (N × H)
28. C7C32×C11×C47semidirect
30. C3C11×ΓL(1,𝔽8)×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C11×ΓL(1,𝔽8)×C473
C3×C7×C11×C473
C32×C11×C477
C3×ΓL(1,𝔽8)×C4711
C3×C11×ΓL(1,𝔽8)47