Finite Group Databasebeta

← C3⋊D3×#13133722 #44501840

Subgroups — C3⋊D3×#13133722 #44501840

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#13133722C211yesmaximal, characteristic, complemented, Hall
2D3×#13133722—34nomaximal
3C11×C3⋊D3×C31C511yesmaximal, characteristic, complemented, Hall
4C3×#13133722D314yescomplemented
5C2×#13133722—91noHall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C3⋊D3×ΓL(1,𝔽32)—111nomaximal, Hall
8D3×C11×C31—34no—
9#13133722C3⋊D311yescharacteristic, direct product factor, Hall
10C32×ΓL(1,𝔽32)—111noHall
11C3×C11×C31C5×D314yescomplemented
12C3⋊D3×C11⋊C5—311nomaximal, Hall
13D3×ΓL(1,𝔽32)—334no—
14C2×C11×C31—91noHall
15C3⋊D3×C31C11⋊C511yescharacteristic, complemented, Hall
16C32×C11⋊C5—311noHall
17C3×ΓL(1,𝔽32)—114no—
18C11×C31C5×C3⋊D311yescharacteristic, complemented, Hall
19D3×C11⋊C5—934no—
20C2×ΓL(1,𝔽32)—991noHall
21C32×C31C2×C11⋊C511yescharacteristic, complemented, Hall
22C11×C3⋊D3ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
23D3×C31—34no—
24C3×C11⋊C5—314no—
25ΓL(1,𝔽32)—111noHall
26C2×C11⋊C5—2791noHall
27C32×C11C2×ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
28C3×C31D3×C11⋊C514yescomplemented
29C5×C3⋊D3—3411noHall
30D3×C11—34no—
31C2×C31—91noHall
32C11⋊C5—311noHall
33C32×C5—3411noHall
34C3×C11D3×ΓL(1,𝔽32)14yescomplemented
35C31C3⋊D3×C11⋊C511yescharacteristic, complemented, Sylow
36C5×D3—10234no—
37C2×C11—91noHall
38C3⋊D3#1313372211yescharacteristic, direct product factor, Hall
39C3×C5—3414no—
40C11C3⋊D3×ΓL(1,𝔽32)11yescharacteristic, complemented, Sylow
41C2×C5—30691noHall
42C32C2×#1313372211yescharacteristic, complemented, Sylow
43D3—34no—
44C5—3411noSylow
45C3D3×#1313372214yescomplemented
46C2—91noSylow
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×#13133722C2semidirect
3. C11×C3⋊D3×C31C5semidirect
4. C3×#13133722D3semidirect
6. C32×C11×C31C2×C5semidirect
9. #13133722C3⋊D3direct (N × H)
11. C3×C11×C31C5×D3semidirect
15. C3⋊D3×C31C11⋊C5semidirect
18. C11×C31C5×C3⋊D3semidirect
21. C32×C31C2×C11⋊C5semidirect
22. C11×C3⋊D3ΓL(1,𝔽32)semidirect
27. C32×C11C2×ΓL(1,𝔽32)semidirect
28. C3×C31D3×C11⋊C5semidirect
34. C3×C11D3×ΓL(1,𝔽32)semidirect
35. C31C3⋊D3×C11⋊C5semidirect
38. C3⋊D3#13133722direct (N × H)
40. C11C3⋊D3×ΓL(1,𝔽32)semidirect
42. C32C2×#13133722semidirect
45. C3D3×#13133722semidirect

Maximal subgroups

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

subgroupindex
C32×#131337222
D3×#131337223
C11×C3⋊D3×C315
C3⋊D3×ΓL(1,𝔽32)11
C3⋊D3×C11⋊C531