Finite Group Databasebeta

← C3×C11×C3⋊AGL(1,𝔽11) #24926151

Subgroups — C3×C11×C3⋊AGL(1,𝔽11) #24926151

Order 10890.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C11×C3⋊AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor
3C3×C11×AGL(1,𝔽11)—31nomaximal
4C3×C11×D33C511yesmaximal, characteristic, complemented, Hall
5C3×C11×C11⋊C5—21no—
6C3×C11×C11⋊C5D311yescharacteristic, complemented
7C3×C11×C11⋊C5C2×C311yescharacteristic, complemented
8C11×AGL(1,𝔽11)—31noHall
9C32×C112C2×C511yescharacteristic, complemented, Hall
10C3×C5×D3×C11—111nomaximal
11C3×C3⋊AGL(1,𝔽11)C1111yesmaximal, characteristic, direct product factor
12C11×D33C3×C511yescharacteristic, complemented
13C3×C11×D11—31no—
14C11×C11⋊C5C3×D311yescharacteristic, complemented, Hall
15C32×C5×C11—111no—
16C32×C11⋊C5C2×C1111yescharacteristic, complemented
17C3×C112—21no—
18C3×C112C5×D311yescharacteristic, complemented
19C3×C112C2×C3×C511yescharacteristic, complemented
20C2×C3×C5×C11—331no—
21C5×D3×C11—111no—
22C3⋊AGL(1,𝔽11)C3×C1111yescharacteristic, direct product factor
23C3×AGL(1,𝔽11)—31no—
24C11×D11—31noHall
25C3×D33C5×C1111yescharacteristic, complemented
26C3×D3×C11—111no—
27C3×C5×C11—111no—
28C3×C5×C11—111no—
29C3×C5×C11—221no—
30C3×C11⋊C5—21no—
31C3×C11⋊C5D3×C1111yescharacteristic, complemented
32C3×C11⋊C5C2×C3×C1111yescharacteristic, complemented
33C112C3×C5×D311yescharacteristic, complemented, Sylow
34C2×C5×C11—331no—
35AGL(1,𝔽11)—31no—
36C32×C11—101no—
37C32×C11AGL(1,𝔽11)11yescharacteristic, complemented
38C32×C11C2×C5×C1111yescharacteristic, complemented
39C3×C5×D3—111noHall
40C2×C3×C11—331no—
41D33C3×C5×C1111yescharacteristic, complemented
42C3×D11—31no—
43D3×C11—111no—
44C5×C11—111no—
45C11⋊C5C3×D3×C1111yescharacteristic, complemented
46C32×C5—111noHall
47C3×C11—21no—
48C3×C11—21no—
49C3×C11—102no—
50C3×C11—101no—
51C3×C11—101no—
52C3×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
53C3×C11C3⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
54C3×C11C5×D3×C1111yescharacteristic, complemented
55C3×C11C2×C3×C5×C1111yescharacteristic, complemented
56C2×C3×C5—331no—
57C5×D3—111no—
58C2×C11—331no—
59D11—31no—
60C3×D3—111noHall
61C3×C5—111no—
62C3×C5—111no—
63C3×C5—221no—
64C11—101no—
65C11C3×C3⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
66C11C3×C5×D3×C1111yescharacteristic, complemented
67C2×C5—331noHall
68C32C11×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
69C2×C3—331no—
70D3—111no—
71C5—111noSylow
72C3—21no—
73C3C3×C11×AGL(1,𝔽11)11yescharacteristic, complemented
74C3C11×C3⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
75C2—331noSylow
subgroupG/H
center, hypercenterC3×C11C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×C11⋊C5C2semidirect
2. C11×C3⋊AGL(1,𝔽11)C3direct (N × H)
4. C3×C11×D33C5semidirect
6. C3×C11×C11⋊C5D3semidirect
7. C3×C11×C11⋊C5C2×C3semidirect
9. C32×C112C2×C5semidirect
11. C3×C3⋊AGL(1,𝔽11)C11direct (N × H)
12. C11×D33C3×C5semidirect
14. C11×C11⋊C5C3×D3semidirect
16. C32×C11⋊C5C2×C11semidirect
18. C3×C112C5×D3semidirect
19. C3×C112C2×C3×C5semidirect
22. C3⋊AGL(1,𝔽11)C3×C11direct (N × H)
25. C3×D33C5×C11semidirect
31. C3×C11⋊C5D3×C11semidirect
32. C3×C11⋊C5C2×C3×C11semidirect
33. C112C3×C5×D3semidirect
37. C32×C11AGL(1,𝔽11)semidirect
38. C32×C11C2×C5×C11semidirect
41. D33C3×C5×C11semidirect
45. C11⋊C5C3×D3×C11semidirect
52. C3×C11C3×AGL(1,𝔽11)semidirect
53. C3×C11C3⋊AGL(1,𝔽11)direct (N × H)
54. C3×C11C5×D3×C11semidirect
55. C3×C11C2×C3×C5×C11semidirect
65. C11C3×C3⋊AGL(1,𝔽11)direct (N × H)
66. C11C3×C5×D3×C11semidirect
68. C32C11×AGL(1,𝔽11)semidirect
73. C3C3×C11×AGL(1,𝔽11)semidirect
74. C3C11×C3⋊AGL(1,𝔽11)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×C11⋊C52
C11×C3⋊AGL(1,𝔽11)3
C3×C11×AGL(1,𝔽11)3
C3×C11×D335
C3×C5×D3×C1111
C3×C3⋊AGL(1,𝔽11)11