Finite Group Databasebeta

← C3×C59×AGL(1,𝔽11) #34085698

Subgroups — C3×C59×AGL(1,𝔽11) #34085698

Order 19470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11⋊C5×C59C211yesmaximal, characteristic, complemented, Hall
2C59×AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
3C3×D11×C59C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C59C2×C311yescharacteristic, complemented, Hall
5C3×C11×C59C2×C511yescharacteristic, complemented, Hall
6C2×C3×C5×C59—111nomaximal, Hall
7D11×C59C3×C511yescharacteristic, complemented, Hall
8C3×C5×C59—111noHall
9C11×C59C2×C3×C511yescharacteristic, complemented, Hall
10C2×C5×C59—111noHall
11C2×C3×C59—111noHall
12C3×AGL(1,𝔽11)C5911yesmaximal, characteristic, direct product factor, Hall
13C5×C59—111noHall
14C3×C59AGL(1,𝔽11)11yescharacteristic, direct product factor, Hall
15C3×C11⋊C5C2×C5911yescharacteristic, complemented, Hall
16C2×C59—111noHall
17AGL(1,𝔽11)C3×C5911yescharacteristic, direct product factor, Hall
18C3×D11C5×C5911yescharacteristic, complemented, Hall
19C59C3×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
20C11⋊C5C2×C3×C5911yescharacteristic, complemented, Hall
21C3×C11C2×C5×C5911yescharacteristic, complemented, Hall
22C2×C3×C5—111noHall
23D11C3×C5×C5911yescharacteristic, complemented, Hall
24C3×C5—111noHall
25C11C2×C3×C5×C5911yescharacteristic, complemented, Sylow
26C2×C5—111noHall
27C2×C3—111noHall
28C5—111noSylow
29C3C59×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
30C2—111noSylow
subgroupG/H
center, hypercenterC3×C59AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C59
FrattiniC1G
Fitting, socleC3×C11×C59C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C59

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C5×C59C2semidirect
2. C59×AGL(1,𝔽11)C3direct (N × H)
3. C3×D11×C59C5semidirect
4. C11⋊C5×C59C2×C3semidirect
5. C3×C11×C59C2×C5semidirect
7. D11×C59C3×C5semidirect
9. C11×C59C2×C3×C5semidirect
12. C3×AGL(1,𝔽11)C59direct (N × H)
14. C3×C59AGL(1,𝔽11)direct (N × H)
15. C3×C11⋊C5C2×C59semidirect
17. AGL(1,𝔽11)C3×C59direct (N × H)
18. C3×D11C5×C59semidirect
19. C59C3×AGL(1,𝔽11)direct (N × H)
20. C11⋊C5C2×C3×C59semidirect
21. C3×C11C2×C5×C59semidirect
23. D11C3×C5×C59semidirect
25. C11C2×C3×C5×C59semidirect
29. C3C59×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×C11⋊C5×C592
C59×AGL(1,𝔽11)3
C3×D11×C595
C2×C3×C5×C5911
C3×AGL(1,𝔽11)59