Finite Group Databasebeta

← C3×C3⋊(ΓL(1,𝔽32)⋊D11) #44501819

Subgroups — C3×C3⋊(ΓL(1,𝔽32)⋊D11) #44501819

Order 30690.

72 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)⋊D11)C311yesmaximal, characteristic, direct product factor
3C3×ΓL(1,𝔽32)⋊D11—31nomaximal
4C3×D1023C511yesmaximal, characteristic, complemented, Hall
5C3×C11×ΓL(1,𝔽32)—21no—
6C3×C11×ΓL(1,𝔽32)D311yescharacteristic, complemented
7C3×C11×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
8ΓL(1,𝔽32)⋊D11—31noHall
9C32×C11×C31C2×C511yescharacteristic, complemented, Hall
10C3×C3⋊(D31⋊C5)—111nomaximal, Hall
11D1023C3×C511yescharacteristic, complemented
12C3×D341—31no—
13C11×ΓL(1,𝔽32)C3×D311yescharacteristic, complemented, Hall
14C32×ΓL(1,𝔽32)D1111yescharacteristic, complemented, Hall
15C3×C11×C31—21no—
16C3×C11×C31C5×D311yescharacteristic, complemented
17C3×C11×C31C2×C3×C511yescharacteristic, complemented
18C3×C5×D33—311nomaximal, Hall
19C3⋊(D31⋊C5)—111no—
20C3×D31⋊C5—331no—
21D341—31noHall
22C3×D93—111noHall
23C32×C5×C11—311noHall
24C3×ΓL(1,𝔽32)—21no—
25C3×ΓL(1,𝔽32)C3×D1111yescharacteristic, complemented
26C3×ΓL(1,𝔽32)D3311yescharacteristic, complemented
27C11×C31C3×C5×D311yescharacteristic, complemented, Hall
28C5×D33—311no—
29C3×C5×D11—931no—
30D31⋊C5—331noHall
31C32×C31C5×D1111yescharacteristic, complemented, Hall
32C3×D33—311noHall
33D93—111no—
34C3×D31—331no—
35C3×C5×C11—311no—
36C3×C5×C11—311no—
37C3×C5×C11—621no—
38ΓL(1,𝔽32)C3×D3311yescharacteristic, complemented, Hall
39C5×D11—931noHall
40C32×C11D31⋊C511yescharacteristic, complemented, Hall
41C3×C31—21no—
42C3×C31C3×C5×D1111yescharacteristic, complemented
43C3×C31C5×D3311yescharacteristic, complemented
44C3×C5×D3—3411noHall
45D33—311no—
46C3×D11—931no—
47D31—331noHall
48C5×C11—311noHall
49C32×C5—311noHall
50C3×C11—21no—
51C3×C11C3×D31⋊C511yescharacteristic, complemented
52C3×C11C3⋊(D31⋊C5)11yescharacteristic, complemented
53C31C3×C5×D3311yescharacteristic, complemented, Sylow
54C2×C3×C5—10231no—
55C5×D3—3411no—
56D11—931noHall
57C3×D3—3411noHall
58C3×C5—311no—
59C3×C5—311no—
60C3×C5—621no—
61C11C3×C3⋊(D31⋊C5)11yescharacteristic, complemented, Sylow
62C2×C5—10231noHall
63C32ΓL(1,𝔽32)⋊D1111yescharacteristic, complemented, Sylow
64C2×C3—10231no—
65D3—3411no—
66C5—311noSylow
67C3—21no—
68C3C3×ΓL(1,𝔽32)⋊D1111yescharacteristic, complemented
69C3C3⋊(ΓL(1,𝔽32)⋊D11)11yescharacteristic, direct product factor
70C2—10231noSylow
subgroupG/H
center, hypercenterC3C3⋊(ΓL(1,𝔽32)⋊D11)
commutator, cosocle, hypocenterC3×C11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1 ◁ C3

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)⋊D11)C3direct (N × H)
4. C3×D1023C5semidirect
6. C3×C11×ΓL(1,𝔽32)D3semidirect
7. C3×C11×ΓL(1,𝔽32)C2×C3semidirect
9. C32×C11×C31C2×C5semidirect
11. D1023C3×C5semidirect
13. C11×ΓL(1,𝔽32)C3×D3semidirect
14. C32×ΓL(1,𝔽32)D11semidirect
16. C3×C11×C31C5×D3semidirect
17. C3×C11×C31C2×C3×C5semidirect
25. C3×ΓL(1,𝔽32)C3×D11semidirect
26. C3×ΓL(1,𝔽32)D33semidirect
27. C11×C31C3×C5×D3semidirect
31. C32×C31C5×D11semidirect
38. ΓL(1,𝔽32)C3×D33semidirect
40. C32×C11D31⋊C5semidirect
42. C3×C31C3×C5×D11semidirect
43. C3×C31C5×D33semidirect
51. C3×C11C3×D31⋊C5semidirect
52. C3×C11C3⋊(D31⋊C5)semidirect
53. C31C3×C5×D33semidirect
61. C11C3×C3⋊(D31⋊C5)semidirect
63. C32ΓL(1,𝔽32)⋊D11semidirect
68. C3C3×ΓL(1,𝔽32)⋊D11semidirect
69. C3C3⋊(ΓL(1,𝔽32)⋊D11)direct (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)⋊D11)3
C3×ΓL(1,𝔽32)⋊D113
C3×D10235
C3×C3⋊(D31⋊C5)11
C3×C5×D3331