Finite Group Databasebeta

← C11×C3⋊AGL(1,𝔽31) #44501749

Subgroups — C11×C3⋊AGL(1,𝔽31) #44501749

Order 30690.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×(C31⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2C11×AGL(1,𝔽31)—31nomaximal
3C11×C3⋊(D31⋊C5)C311yesmaximal, characteristic, complemented
4C11×C3⋊(D31⋊C3)C511yesmaximal, characteristic, complemented, Hall
5C11×(C31⋊C3)⋊C5—21no—
6C11×(C31⋊C3)⋊C5D311yescharacteristic, complemented
7C3×C11×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
8C11×D31⋊C5—31noHall
9C3×C11×C31⋊C3C2×C511yescharacteristic, complemented, Hall
10C3⋊AGL(1,𝔽31)C1111yesmaximal, characteristic, direct product factor, Hall
11C11×D31⋊C3—31no—
12C11×D93C3×C511yescharacteristic, complemented
13C11×ΓL(1,𝔽32)C3×D311yescharacteristic, complemented, Hall
14C3×(C31⋊C3)⋊C5C2×C1111yescharacteristic, complemented, Hall
15C3×C11×C31C2×C3×C511yescharacteristic, complemented
16C11×C31⋊C3—21no—
17C11×C31⋊C3C5×D311yescharacteristic, complemented
18C3×C5×D3×C11—311nomaximal, Hall
19C3⋊(D31⋊C5)C3×C1111yescharacteristic, complemented
20AGL(1,𝔽31)—31no—
21C11×D31—31noHall
22C3⋊(D31⋊C3)C5×C1111yescharacteristic, complemented, Hall
23C32×C5×C11—311noHall
24C3×ΓL(1,𝔽32)C2×C3×C1111yescharacteristic, complemented
25(C31⋊C3)⋊C5—21no—
26(C31⋊C3)⋊C5D3×C1111yescharacteristic, complemented
27C11×C31C3×C5×D311yescharacteristic, complemented, Hall
28C2×C3×C5×C11—931no—
29C5×D3×C11—311no—
30D31⋊C5—31noHall
31C3×C31⋊C3C2×C5×C1111yescharacteristic, complemented, Hall
32C3×D3×C11—311noHall
33D93C3×C5×C1111yescharacteristic, complemented
34D31⋊C3—31no—
35C3×C5×C11—311no—
36C3×C5×C11—311no—
37C3×C5×C11—621no—
38ΓL(1,𝔽32)C3×D3×C1111yescharacteristic, complemented, Hall
39C2×C5×C11—931noHall
40C32×C11—311noHall
41C3×C31C2×C3×C5×C1111yescharacteristic, complemented
42C31⋊C3—21no—
43C31⋊C3C5×D3×C1111yescharacteristic, complemented
44C3×C5×D3—311noHall
45C2×C3×C11—931no—
46D3×C11—311no—
47D31—31noHall
48C5×C11—311noHall
49C32×C5—311noHall
50C3×C11—311no—
51C3×C11—621no—
52C3×C11AGL(1,𝔽31)11yescharacteristic, complemented
53C31C3×C5×D3×C1111yescharacteristic, complemented, Sylow
54C2×C3×C5—931no—
55C5×D3—311no—
56C2×C11—931noHall
57C3×D3—311noHall
58C3×C5—311no—
59C3×C5—311no—
60C3×C5—621no—
61C11C3⋊AGL(1,𝔽31)11yescharacteristic, direct product factor, Sylow
62C2×C5—931noHall
63C32—311noSylow
64C2×C3—931no—
65D3—311no—
66C5—311noSylow
67C3—311no—
68C3—621no—
69C3C11×AGL(1,𝔽31)11yescharacteristic, complemented
70C2—931noSylow
subgroupG/H
center, hypercenterC11C3⋊AGL(1,𝔽31)
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×(C31⋊C3)⋊C5C2semidirect
3. C11×C3⋊(D31⋊C5)C3semidirect
4. C11×C3⋊(D31⋊C3)C5semidirect
6. C11×(C31⋊C3)⋊C5D3semidirect
7. C3×C11×ΓL(1,𝔽32)C2×C3semidirect
9. C3×C11×C31⋊C3C2×C5semidirect
10. C3⋊AGL(1,𝔽31)C11direct (N × H)
12. C11×D93C3×C5semidirect
13. C11×ΓL(1,𝔽32)C3×D3semidirect
14. C3×(C31⋊C3)⋊C5C2×C11semidirect
15. C3×C11×C31C2×C3×C5semidirect
17. C11×C31⋊C3C5×D3semidirect
19. C3⋊(D31⋊C5)C3×C11semidirect
22. C3⋊(D31⋊C3)C5×C11semidirect
24. C3×ΓL(1,𝔽32)C2×C3×C11semidirect
26. (C31⋊C3)⋊C5D3×C11semidirect
27. C11×C31C3×C5×D3semidirect
31. C3×C31⋊C3C2×C5×C11semidirect
33. D93C3×C5×C11semidirect
38. ΓL(1,𝔽32)C3×D3×C11semidirect
41. C3×C31C2×C3×C5×C11semidirect
43. C31⋊C3C5×D3×C11semidirect
52. C3×C11AGL(1,𝔽31)semidirect
53. C31C3×C5×D3×C11semidirect
61. C11C3⋊AGL(1,𝔽31)direct (N × H)
69. C3C11×AGL(1,𝔽31)semidirect

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
C11×AGL(1,𝔽31)3
C11×C3⋊(D31⋊C5)3
C11×C3⋊(D31⋊C3)5
C3⋊AGL(1,𝔽31)11
C3×C5×D3×C1131