Finite Group Databasebeta

← C3×(C11⋊C5)⋊D101 #45686804

Subgroups — C3×(C11⋊C5)⋊D101 #45686804

Order 33330.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11⋊C5×C101C211yesmaximal, characteristic, complemented, Hall
2(C11⋊C5)⋊D101C311yesmaximal, characteristic, direct product factor, Hall
3C3×D1111C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C101C2×C311yescharacteristic, complemented, Hall
5C3×C11×C101C2×C511yescharacteristic, complemented, Hall
6C3×C5×D101—111nomaximal, Hall
7D1111C3×C511yescharacteristic, complemented, Hall
8C3×C5×C101—111noHall
9C11×C101C2×C3×C511yescharacteristic, complemented, Hall
10C5×D101—111noHall
11C3×D101—111noHall
12C5×C101—111noHall
13C3×AGL(1,𝔽11)—1011nomaximal, Hall
14C3×C101AGL(1,𝔽11)11yescharacteristic, complemented, Hall
15D101—111noHall
16C3×C11⋊C5D10111yescharacteristic, complemented, Hall
17AGL(1,𝔽11)—1011noHall
18C101C3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
19C3×D11—1011noHall
20C11⋊C5C3×D10111yescharacteristic, complemented, Hall
21C3×C11C5×D10111yescharacteristic, complemented, Hall
22C2×C3×C5—11111noHall
23D11—1011noHall
24C3×C5—111noHall
25C11C3×C5×D10111yescharacteristic, complemented, Sylow
26C2×C5—11111noHall
27C2×C3—11111noHall
28C5—111noSylow
29C3(C11⋊C5)⋊D10111yescharacteristic, direct product factor, Sylow
30C2—11111noSylow
subgroupG/H
center, hypercenterC3(C11⋊C5)⋊D101
commutator, cosocle, hypocenterC11×C101C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C101C2×C5
LCSG ▷ C11×C101
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C5×C101C2semidirect
2. (C11⋊C5)⋊D101C3direct (N × H)
3. C3×D1111C5semidirect
4. C11⋊C5×C101C2×C3semidirect
5. C3×C11×C101C2×C5semidirect
7. D1111C3×C5semidirect
9. C11×C101C2×C3×C5semidirect
14. C3×C101AGL(1,𝔽11)semidirect
16. C3×C11⋊C5D101semidirect
18. C101C3×AGL(1,𝔽11)semidirect
20. C11⋊C5C3×D101semidirect
21. C3×C11C5×D101semidirect
25. C11C3×C5×D101semidirect
29. C3(C11⋊C5)⋊D101direct (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×C1012
(C11⋊C5)⋊D1013
C3×D11115
C3×C5×D10111
C3×AGL(1,𝔽11)101