Finite Group Databasebeta

← C3×((C31⋊C3)⋊C5)⋊D11 #44501747

Subgroups — C3×((C31⋊C3)⋊C5)⋊D11 #44501747

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×(C31⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2((C31⋊C3)⋊C5)⋊D11C313yesmaximal, direct product factor
3C3×ΓL(1,𝔽32)⋊D11C311yesmaximal, characteristic, complemented
4C3×C11⋊(D31⋊C3)C511yesmaximal, characteristic, complemented, Hall
5C11×(C31⋊C3)⋊C5C2×C313yescomplemented
6C3×C11×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
7ΓL(1,𝔽32)⋊D11C3211yescharacteristic, complemented, Hall
8C3×C11×C31⋊C3C2×C511yescharacteristic, complemented, Hall
9C3×AGL(1,𝔽31)—111nomaximal, Hall
10C11⋊(D31⋊C3)C3×C513yescomplemented
11C3×D341C3×C511yescharacteristic, complemented
12C11×ΓL(1,𝔽32)C2×C3211yescharacteristic, complemented, Hall
13C3×(C31⋊C3)⋊C5D1111yescharacteristic, complemented, Hall
14C3×C11×C31C2×C3×C511yescharacteristic, complemented
15C11×C31⋊C3C2×C3×C513yescomplemented
16C32×C5×D11—311nomaximal, Hall
17C3×D31⋊C5—111no—
18AGL(1,𝔽31)—113no—
19D341C32×C511yescharacteristic, complemented, Hall
20C3×D31⋊C3—111noHall
21C32×C5×C11—311noHall
22C3×ΓL(1,𝔽32)C3×D1111yescharacteristic, complemented
23(C31⋊C3)⋊C5C3×D1113yescomplemented
24C11×C31C2×C32×C511yescharacteristic, complemented, Hall
25C3×C5×D11—311no—
26C3×C5×D11—313no—
27D31⋊C5—111noHall
28C3×C31⋊C3C5×D1111yescharacteristic, complemented, Hall
29C32×D11—311noHall
30C3×D31—111no—
31D31⋊C3—113no—
32C3×C5×C11—313no—
33C3×C5×C11—311no—
34ΓL(1,𝔽32)C32×D1111yescharacteristic, complemented, Hall
35C5×D11—311noHall
36C32×C11—311noHall
37C3×C31C3×C5×D1111yescharacteristic, complemented
38C31⋊C3C3×C5×D1113yescomplemented
39C2×C32×C5—3411noHall
40C3×D11—313no—
41C3×D11—311no—
42D31—111noHall
43C5×C11—311noHall
44C32×C5—311noHall
45C3×C11—313no—
46C3×C11AGL(1,𝔽31)11yescharacteristic, complemented
47C31C32×C5×D1111yescharacteristic, complemented, Sylow
48C2×C3×C5—3413no—
49C2×C3×C5—3411no—
50D11—311noHall
51C2×C32—3411noHall
52C3×C5—313no—
53C3×C5—311no—
54C11C3×AGL(1,𝔽31)11yescharacteristic, complemented, Sylow
55C2×C5—3411noHall
56C32—311noSylow
57C2×C3—3413no—
58C2×C3—3411no—
59C5—311noSylow
60C3—313no—
61C3((C31⋊C3)⋊C5)⋊D1111yescharacteristic, direct product factor
62C2—3411noSylow
subgroupG/H
center, hypercenterC3((C31⋊C3)⋊C5)⋊D11
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C11×(C31⋊C3)⋊C5C2semidirect
2. ((C31⋊C3)⋊C5)⋊D11C3direct (N × H)
3. C3×ΓL(1,𝔽32)⋊D11C3semidirect
4. C3×C11⋊(D31⋊C3)C5semidirect
5. C11×(C31⋊C3)⋊C5C2×C3semidirect
6. C3×C11×ΓL(1,𝔽32)C2×C3semidirect
7. ΓL(1,𝔽32)⋊D11C32semidirect
8. C3×C11×C31⋊C3C2×C5semidirect
10. C11⋊(D31⋊C3)C3×C5semidirect
11. C3×D341C3×C5semidirect
12. C11×ΓL(1,𝔽32)C2×C32semidirect
13. C3×(C31⋊C3)⋊C5D11semidirect
14. C3×C11×C31C2×C3×C5semidirect
15. C11×C31⋊C3C2×C3×C5semidirect
19. D341C32×C5semidirect
22. C3×ΓL(1,𝔽32)C3×D11semidirect
23. (C31⋊C3)⋊C5C3×D11semidirect
24. C11×C31C2×C32×C5semidirect
28. C3×C31⋊C3C5×D11semidirect
34. ΓL(1,𝔽32)C32×D11semidirect
37. C3×C31C3×C5×D11semidirect
38. C31⋊C3C3×C5×D11semidirect
46. C3×C11AGL(1,𝔽31)semidirect
47. C31C32×C5×D11semidirect
54. C11C3×AGL(1,𝔽31)semidirect
61. C3((C31⋊C3)⋊C5)⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×(C31⋊C3)⋊C52
((C31⋊C3)⋊C5)⋊D113
C3×ΓL(1,𝔽32)⋊D113
C3×C11⋊(D31⋊C3)5
C3×AGL(1,𝔽31)11
C32×C5×D1131