Finite Group Databasebeta

← C32×(C11⋊C5)⋊D31 #44501789

Subgroups — C32×(C11⋊C5)⋊D31 #44501789

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C31×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C3×(C11⋊C5)⋊D31C314yesmaximal, direct product factor
3C32×D341C511yesmaximal, characteristic, complemented, Hall
4C3×C31×C11⋊C5C2×C314yescomplemented
5(C11⋊C5)⋊D31C3211yescharacteristic, direct product factor, Hall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C32×C5×D31—111nomaximal, Hall
8C3×D341C3×C514yescomplemented
9C31×C11⋊C5C2×C3211yescharacteristic, complemented, Hall
10C32×C5×C31—111noHall
11C3×C11×C31C2×C3×C514yescomplemented
12C32×AGL(1,𝔽11)—311nomaximal, Hall
13C3×C5×D31—114no—
14D341C32×C511yescharacteristic, complemented, Hall
15C32×D31—111noHall
16C32×C11⋊C5D3111yescharacteristic, complemented, Hall
17C3×C5×C31—114no—
18C11×C31C2×C32×C511yescharacteristic, complemented, Hall
19C3×AGL(1,𝔽11)—314no—
20C5×D31—111noHall
21C32×C31AGL(1,𝔽11)11yescharacteristic, complemented, Hall
22C32×D11—311noHall
23C3×D31—114no—
24C3×C11⋊C5C3×D3114yescomplemented
25C5×C31—111noHall
26AGL(1,𝔽11)—311noHall
27C32×C11C5×D3111yescharacteristic, complemented, Hall
28C3×C31C3×AGL(1,𝔽11)14yescomplemented
29C2×C32×C5—3411noHall
30C3×D11—314no—
31D31—111noHall
32C11⋊C5C32×D3111yescharacteristic, complemented, Hall
33C32×C5—111noHall
34C3×C11C3×C5×D3114yescomplemented
35C31C32×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
36C2×C3×C5—3414no—
37D11—311noHall
38C2×C32—3411noHall
39C3×C5—114no—
40C11C32×C5×D3111yescharacteristic, complemented, Sylow
41C2×C5—3411noHall
42C32(C11⋊C5)⋊D3111yescharacteristic, direct product factor, Sylow
43C2×C3—3414no—
44C5—111noSylow
45C3C3×(C11⋊C5)⋊D3114yesdirect product factor
46C2—3411noSylow
subgroupG/H
center, hypercenterC32(C11⋊C5)⋊D31
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×C31×C11⋊C5C2semidirect
2. C3×(C11⋊C5)⋊D31C3direct (N × H)
3. C32×D341C5semidirect
4. C3×C31×C11⋊C5C2×C3semidirect
5. (C11⋊C5)⋊D31C32direct (N × H)
6. C32×C11×C31C2×C5semidirect
8. C3×D341C3×C5semidirect
9. C31×C11⋊C5C2×C32semidirect
11. C3×C11×C31C2×C3×C5semidirect
14. D341C32×C5semidirect
16. C32×C11⋊C5D31semidirect
18. C11×C31C2×C32×C5semidirect
21. C32×C31AGL(1,𝔽11)semidirect
24. C3×C11⋊C5C3×D31semidirect
27. C32×C11C5×D31semidirect
28. C3×C31C3×AGL(1,𝔽11)semidirect
32. C11⋊C5C32×D31semidirect
34. C3×C11C3×C5×D31semidirect
35. C31C32×AGL(1,𝔽11)semidirect
40. C11C32×C5×D31semidirect
42. C32(C11⋊C5)⋊D31direct (N × H)
45. C3C3×(C11⋊C5)⋊D31direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C31×C11⋊C52
C3×(C11⋊C5)⋊D313
C32×D3415
C32×C5×D3111
C32×AGL(1,𝔽11)31