Finite Group Databasebeta

← C32×ΓL(1,𝔽32)⋊D11 #44501795

Subgroups — C32×ΓL(1,𝔽32)⋊D11 #44501795

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×ΓL(1,𝔽32)C211yesmaximal, characteristic, complemented, Hall
2C3×ΓL(1,𝔽32)⋊D11C314yesmaximal, direct product factor
3C32×D341C511yesmaximal, characteristic, complemented, Hall
4C3×C11×ΓL(1,𝔽32)C2×C314yescomplemented
5ΓL(1,𝔽32)⋊D11C3211yescharacteristic, direct product factor, Hall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C32×D31⋊C5—111nomaximal, Hall
8C3×D341C3×C514yescomplemented
9C11×ΓL(1,𝔽32)C2×C3211yescharacteristic, complemented, Hall
10C32×ΓL(1,𝔽32)D1111yescharacteristic, complemented, Hall
11C3×C11×C31C2×C3×C514yescomplemented
12C32×C5×D11—311nomaximal, Hall
13C3×D31⋊C5—114no—
14D341C32×C511yescharacteristic, complemented, Hall
15C32×D31—111noHall
16C32×C5×C11—311noHall
17C3×ΓL(1,𝔽32)C3×D1114yescomplemented
18C11×C31C2×C32×C511yescharacteristic, complemented, Hall
19C3×C5×D11—314no—
20D31⋊C5—111noHall
21C32×C31C5×D1111yescharacteristic, complemented, Hall
22C32×D11—311noHall
23C3×D31—114no—
24C3×C5×C11—314no—
25ΓL(1,𝔽32)C32×D1111yescharacteristic, complemented, Hall
26C5×D11—311noHall
27C32×C11D31⋊C511yescharacteristic, complemented, Hall
28C3×C31C3×C5×D1114yescomplemented
29C2×C32×C5—3411noHall
30C3×D11—314no—
31D31—111noHall
32C5×C11—311noHall
33C32×C5—311noHall
34C3×C11C3×D31⋊C514yescomplemented
35C31C32×C5×D1111yescharacteristic, complemented, Sylow
36C2×C3×C5—3414no—
37D11—311noHall
38C2×C32—3411noHall
39C3×C5—314no—
40C11C32×D31⋊C511yescharacteristic, complemented, Sylow
41C2×C5—3411noHall
42C32ΓL(1,𝔽32)⋊D1111yescharacteristic, direct product factor, Sylow
43C2×C3—3414no—
44C5—311noSylow
45C3C3×ΓL(1,𝔽32)⋊D1114yesdirect product factor
46C2—3411noSylow
subgroupG/H
center, hypercenterC32ΓL(1,𝔽32)⋊D11
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C11×ΓL(1,𝔽32)C2semidirect
2. C3×ΓL(1,𝔽32)⋊D11C3direct (N × H)
3. C32×D341C5semidirect
4. C3×C11×ΓL(1,𝔽32)C2×C3semidirect
5. ΓL(1,𝔽32)⋊D11C32direct (N × H)
6. C32×C11×C31C2×C5semidirect
8. C3×D341C3×C5semidirect
9. C11×ΓL(1,𝔽32)C2×C32semidirect
10. C32×ΓL(1,𝔽32)D11semidirect
11. C3×C11×C31C2×C3×C5semidirect
14. D341C32×C5semidirect
17. C3×ΓL(1,𝔽32)C3×D11semidirect
18. C11×C31C2×C32×C5semidirect
21. C32×C31C5×D11semidirect
25. ΓL(1,𝔽32)C32×D11semidirect
27. C32×C11D31⋊C5semidirect
28. C3×C31C3×C5×D11semidirect
34. C3×C11C3×D31⋊C5semidirect
35. C31C32×C5×D11semidirect
40. C11C32×D31⋊C5semidirect
42. C32ΓL(1,𝔽32)⋊D11direct (N × H)
45. C3C3×ΓL(1,𝔽32)⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×ΓL(1,𝔽32)2
C3×ΓL(1,𝔽32)⋊D113
C32×D3415
C32×D31⋊C511
C32×C5×D1131