Finite Group Databasebeta

← C3×C109×AGL(1,𝔽11) #49112581

Subgroups — C3×C109×AGL(1,𝔽11) #49112581

Order 35970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11⋊C5×C109C211yesmaximal, characteristic, complemented, Hall
2C109×AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
3C3×D11×C109C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C109C2×C311yescharacteristic, complemented, Hall
5C3×C11×C109C2×C511yescharacteristic, complemented, Hall
6C2×C3×C5×C109—111nomaximal, Hall
7D11×C109C3×C511yescharacteristic, complemented, Hall
8C3×C5×C109—111noHall
9C11×C109C2×C3×C511yescharacteristic, complemented, Hall
10C2×C5×C109—111noHall
11C2×C3×C109—111noHall
12C5×C109—111noHall
13C3×AGL(1,𝔽11)C10911yesmaximal, characteristic, direct product factor, Hall
14C3×C109AGL(1,𝔽11)11yescharacteristic, direct product factor, Hall
15C2×C109—111noHall
16C3×C11⋊C5C2×C10911yescharacteristic, complemented, Hall
17AGL(1,𝔽11)C3×C10911yescharacteristic, direct product factor, Hall
18C109C3×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
19C3×D11C5×C10911yescharacteristic, complemented, Hall
20C11⋊C5C2×C3×C10911yescharacteristic, complemented, Hall
21C3×C11C2×C5×C10911yescharacteristic, complemented, Hall
22C2×C3×C5—111noHall
23D11C3×C5×C10911yescharacteristic, complemented, Hall
24C3×C5—111noHall
25C11C2×C3×C5×C10911yescharacteristic, complemented, Sylow
26C2×C5—111noHall
27C2×C3—111noHall
28C5—111noSylow
29C3C109×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
30C2—111noSylow
subgroupG/H
center, hypercenterC3×C109AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C109
FrattiniC1G
Fitting, socleC3×C11×C109C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C109

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C5×C109C2semidirect
2. C109×AGL(1,𝔽11)C3direct (N × H)
3. C3×D11×C109C5semidirect
4. C11⋊C5×C109C2×C3semidirect
5. C3×C11×C109C2×C5semidirect
7. D11×C109C3×C5semidirect
9. C11×C109C2×C3×C5semidirect
13. C3×AGL(1,𝔽11)C109direct (N × H)
14. C3×C109AGL(1,𝔽11)direct (N × H)
16. C3×C11⋊C5C2×C109semidirect
17. AGL(1,𝔽11)C3×C109direct (N × H)
18. C109C3×AGL(1,𝔽11)direct (N × H)
19. C3×D11C5×C109semidirect
20. C11⋊C5C2×C3×C109semidirect
21. C3×C11C2×C5×C109semidirect
23. D11C3×C5×C109semidirect
25. C11C2×C3×C5×C109semidirect
29. C3C109×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×C1092
C109×AGL(1,𝔽11)3
C3×D11×C1095
C2×C3×C5×C10911
C3×AGL(1,𝔽11)109