Finite Group Databasebeta

← C11×C3⋊(C5⋊AGL(1,𝔽11)) #31827662

Subgroups — C11×C3⋊(C5⋊AGL(1,𝔽11)) #31827662

Order 18150.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C11×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C11×C5⋊AGL(1,𝔽11)—31nomaximal, Hall
3C11×D165C511yesmaximal, characteristic, complemented
4C11×C3⋊AGL(1,𝔽11)—51nomaximal
5C5×C11×C11⋊C5D311yescharacteristic, complemented, Hall
6C3×C5×C112C2×C511yescharacteristic, complemented
7C3×C11×C11⋊C5—22no—
8C3×C11×C11⋊C5D511yescharacteristic, complemented
9C5×C11×D15—111nomaximal
10C3⋊(C5⋊AGL(1,𝔽11))C1111yesmaximal, characteristic, direct product factor
11C11×D55—31no—
12C11×AGL(1,𝔽11)—151no—
13C3×C52×C11—221no—
14C3×C5×C11⋊C5C2×C1111yescharacteristic, complemented
15C11×D33—51noHall
16C5×C112C5×D311yescharacteristic, complemented
17C11×C11⋊C5—22no—
18C11×C11⋊C5D1511yescharacteristic, complemented
19C5×D5×C11—331no—
20C5⋊AGL(1,𝔽11)—31no—
21C3×C112C5×D511yescharacteristic, complemented, Hall
22D165C5×C1111yescharacteristic, complemented
23C11×D15—111no—
24C5×D3×C11—551no—
25C3⋊AGL(1,𝔽11)—51no—
26C52×C11—221no—
27C5×C11⋊C5D3×C1111yescharacteristic, complemented
28C11×D11—151noHall
29C3×C5×C11—101no—
30C3×C5×C11—222no—
31C3×C5×C11—221no—
32C3×C5×C11AGL(1,𝔽11)11yescharacteristic, complemented
33C3×C5×C11C2×C5×C1111yescharacteristic, complemented
34C3×C11⋊C5—22no—
35C3×C11⋊C5D5×C1111yescharacteristic, complemented
36C5×D15—111noHall
37C112C5×D1511yescharacteristic, complemented, Sylow
38C2×C5×C11—1651no—
39D55—31no—
40D5×C11—331no—
41AGL(1,𝔽11)—151no—
42C3×C52—221noHall
43D33—51no—
44D3×C11—551no—
45C5×C11—101no—
46C5×C11—221no—
47C5×C11—222no—
48C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
49C5×C11C5×D3×C1111yescharacteristic, complemented
50C11⋊C5—22no—
51C11⋊C5C11×D1511yescharacteristic, complemented
52C5×D5—331noHall
53C3×C11—101no—
54C3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
55C3×C11C5×D5×C1111yescharacteristic, complemented
56D15—111no—
57C5×D3—551no—
58C52—221noSylow
59C2×C11—1651no—
60D11—151no—
61C3×C5—221no—
62C3×C5—222no—
63C3×C5C11×AGL(1,𝔽11)11yescharacteristic, complemented
64C11—101no—
65C11C3⋊(C5⋊AGL(1,𝔽11))11yescharacteristic, direct product factor
66C11C5×C11×D1511yescharacteristic, complemented
67C2×C5—1651no—
68D5—331no—
69D3—551noHall
70C5—221no—
71C5—222no—
72C5C11×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
73C3C11×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
74C2—1651noSylow
subgroupG/H
center, hypercenterC11C3⋊(C5⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C5×C11C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C11⋊C5C2semidirect
3. C11×D165C5semidirect
5. C5×C11×C11⋊C5D3semidirect
6. C3×C5×C112C2×C5semidirect
8. C3×C11×C11⋊C5D5semidirect
10. C3⋊(C5⋊AGL(1,𝔽11))C11direct (N × H)
14. C3×C5×C11⋊C5C2×C11semidirect
16. C5×C112C5×D3semidirect
18. C11×C11⋊C5D15semidirect
21. C3×C112C5×D5semidirect
22. D165C5×C11semidirect
27. C5×C11⋊C5D3×C11semidirect
32. C3×C5×C11AGL(1,𝔽11)semidirect
33. C3×C5×C11C2×C5×C11semidirect
35. C3×C11⋊C5D5×C11semidirect
37. C112C5×D15semidirect
48. C5×C11C3⋊AGL(1,𝔽11)semidirect
49. C5×C11C5×D3×C11semidirect
51. C11⋊C5C11×D15semidirect
54. C3×C11C5⋊AGL(1,𝔽11)semidirect
55. C3×C11C5×D5×C11semidirect
63. C3×C5C11×AGL(1,𝔽11)semidirect
65. C11C3⋊(C5⋊AGL(1,𝔽11))direct (N × H)
66. C11C5×C11×D15semidirect
72. C5C11×C3⋊AGL(1,𝔽11)semidirect
73. C3C11×C5⋊AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C11×C11⋊C52
C11×C5⋊AGL(1,𝔽11)3
C11×D1655
C11×C3⋊AGL(1,𝔽11)5
C5×C11×D1511
C3⋊(C5⋊AGL(1,𝔽11))11