Finite Group Databasebeta

← C3⋊(C3⋊#16811772) #44501837

Subgroups — C3⋊(C3⋊#16811772) #44501837

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#13133723C211yesmaximal, characteristic, complemented, Hall
2C3⋊#16811772—34nomaximal
3C11×C3⋊D93C511yesmaximal, characteristic, complemented, Hall
4C3×#13133723D314yescomplemented
5#16811772—91noHall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C3⋊(C3⋊(D31⋊C5))—111nomaximal, Hall
8C11×D93—34no—
9#13133723C3⋊D311yescharacteristic, complemented, Hall
10C32×ΓL(1,𝔽32)—111noHall
11C3×C11×C31C5×D314yescomplemented
12C3⋊D3×C11⋊C5—311nomaximal, Hall
13C3⋊(D31⋊C5)—334no—
14C11×D31—91noHall
15C3⋊D93C11⋊C511yescharacteristic, complemented, Hall
16C32×C11⋊C5—311noHall
17C3×ΓL(1,𝔽32)—114no—
18C11×C31C5×C3⋊D311yescharacteristic, complemented, Hall
19D3×C11⋊C5—934no—
20D31⋊C5—991noHall
21C32×C31C2×C11⋊C511yescharacteristic, complemented, Hall
22C11×C3⋊D3—311noHall
23D93—34no—
24C3×C11⋊C5—314no—
25ΓL(1,𝔽32)—111noHall
26C2×C11⋊C5—2791noHall
27C32×C11D31⋊C511yescharacteristic, complemented, Hall
28C3×C31D3×C11⋊C514yescomplemented
29C5×C3⋊D3—3411noHall
30D3×C11—934no—
31D31—91noHall
32C11⋊C5—311noHall
33C32×C5—3411noHall
34C3×C11C3⋊(D31⋊C5)14yescomplemented
35C31C3⋊D3×C11⋊C511yescharacteristic, complemented, Sylow
36C5×D3—10234no—
37C2×C11—2791noHall
38C3⋊D3—311noHall
39C3×C5—3414no—
40C11C3⋊(C3⋊(D31⋊C5))11yescharacteristic, complemented, Sylow
41C2×C5—30691noHall
42C32#1681177211yescharacteristic, complemented, Sylow
43D3—934no—
44C5—3411noSylow
45C3C3⋊#1681177214yescomplemented
46C2—2791noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C31C2×C5
LCSG ▷ C32×C11×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×#13133723C2semidirect
3. C11×C3⋊D93C5semidirect
4. C3×#13133723D3semidirect
6. C32×C11×C31C2×C5semidirect
9. #13133723C3⋊D3semidirect
11. C3×C11×C31C5×D3semidirect
15. C3⋊D93C11⋊C5semidirect
18. C11×C31C5×C3⋊D3semidirect
21. C32×C31C2×C11⋊C5semidirect
27. C32×C11D31⋊C5semidirect
28. C3×C31D3×C11⋊C5semidirect
34. C3×C11C3⋊(D31⋊C5)semidirect
35. C31C3⋊D3×C11⋊C5semidirect
40. C11C3⋊(C3⋊(D31⋊C5))semidirect
42. C32#16811772semidirect
45. C3C3⋊#16811772semidirect

Maximal subgroups

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

subgroupindex
C32×#131337232
C3⋊#168117723
C11×C3⋊D935
C3⋊(C3⋊(D31⋊C5))11
C3⋊D3×C11⋊C531