Finite Group Databasebeta

← AGL(1,𝔽11)×D141 #44526626

Subgroups — AGL(1,𝔽11)×D141 #44526626

Order 31020.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C47⋊AGL(1,𝔽11))C211yesmaximal, characteristic, complemented
2C11⋊C5×D141C211yesmaximal, characteristic, complemented
3C3×C47×AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
4D47×AGL(1,𝔽11)—31nomaximal, Hall
5C3×C47×C11⋊C5C2211yescharacteristic, complemented, Hall
6D11×D141C511yesmaximal, characteristic, complemented, Hall
7C47⋊AGL(1,𝔽11)—31no—
8C47×AGL(1,𝔽11)D311yescharacteristic, complemented
9C11⋊C5×D47—31no—
10D1551C2×C511yescharacteristic, complemented
11C11×D141C2×C511yescharacteristic, complemented
12C3×D11×C47C2×C511yescharacteristic, complemented
13C2×C5×D141—111nomaximal, Hall
14C47×C11⋊C5C2×D311yescharacteristic, complemented, Hall
15D11×D47—31noHall
16C3×C11×C47C22×C511yescharacteristic, complemented, Hall
17C2×C3×C5×C47—111no—
18C5×D141—111no—
19C5×D141—111no—
20D517—31no—
21C11×D47—31no—
22D11×C47C5×D311yescharacteristic, complemented
23C2×C5×D47—331noHall
24C3×C5×C47—111noHall
25D3×AGL(1,𝔽11)—471nomaximal, Hall
26C2×D141—111noHall
27C11×C47C2×C5×D311yescharacteristic, complemented, Hall
28C2×C5×C47—111no—
29C5×D47—331no—
30C5×D47—331no—
31C3⋊AGL(1,𝔽11)—471no—
32D3×C11⋊C5—471no—
33C3×AGL(1,𝔽11)D4711yescharacteristic, complemented
34C2×C3×C47—111no—
35D141—111no—
36D141AGL(1,𝔽11)11yescharacteristic, direct product factor
37C5×C47—111noHall
38C2×AGL(1,𝔽11)—1411noHall
39C2×D47—331noHall
40C3×C11⋊C5C2×D4711yescharacteristic, complemented, Hall
41C3×C47C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
42D3×D11—471noHall
43C2×C11⋊C5—1411no—
44AGL(1,𝔽11)—1411no—
45AGL(1,𝔽11)D14111yescharacteristic, direct product factor
46C2×C47—111no—
47D47—31no—
48D47—331no—
49D33—471no—
50C3×D11C5×D4711yescharacteristic, complemented
51D3×C11—471no—
52C2×C5×D3—5171noHall
53C11⋊C5C2×D14111yescharacteristic, complemented, Hall
54C47D3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
55C2×D11—1411noHall
56C3×C11C2×C5×D4711yescharacteristic, complemented, Hall
57C2×C3×C5—111no—
58C5×D3—5171no—
59C5×D3—5171no—
60C2×C11—1411no—
61D11—1411no—
62D11C5×D14111yescharacteristic, complemented
63C22×C5—15511noHall
64C3×C5—111noHall
65C2×D3—5171noHall
66C11C2×C5×D14111yescharacteristic, complemented, Sylow
67C2×C5—111no—
68C2×C5—15511no—
69C2×C5—15511no—
70C2×C3—111no—
71D3—5171no—
72D3—471no—
73C5—111noSylow
74C22—15511noSylow
75C3D47×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
76C2—111no—
77C2—15511no—
78C2—1411no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C47C22×C5
LCSG ▷ C3×C11×C47
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C47⋊AGL(1,𝔽11))C2semidirect
2. C11⋊C5×D141C2semidirect
3. C3×C47×AGL(1,𝔽11)C2semidirect
5. C3×C47×C11⋊C5C22semidirect
6. D11×D141C5semidirect
8. C47×AGL(1,𝔽11)D3semidirect
10. D1551C2×C5semidirect
11. C11×D141C2×C5semidirect
12. C3×D11×C47C2×C5semidirect
14. C47×C11⋊C5C2×D3semidirect
16. C3×C11×C47C22×C5semidirect
22. D11×C47C5×D3semidirect
27. C11×C47C2×C5×D3semidirect
33. C3×AGL(1,𝔽11)D47semidirect
36. D141AGL(1,𝔽11)direct (N × H)
40. C3×C11⋊C5C2×D47semidirect
41. C3×C47C2×AGL(1,𝔽11)semidirect
45. AGL(1,𝔽11)D141direct (N × H)
50. C3×D11C5×D47semidirect
53. C11⋊C5C2×D141semidirect
54. C47D3×AGL(1,𝔽11)semidirect
56. C3×C11C2×C5×D47semidirect
62. D11C5×D141semidirect
66. C11C2×C5×D141semidirect
75. C3D47×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⋊(C47⋊AGL(1,𝔽11))2
C11⋊C5×D1412
C3×C47×AGL(1,𝔽11)2
D47×AGL(1,𝔽11)3
D11×D1415
C2×C5×D14111
D3×AGL(1,𝔽11)47