Finite Group Databasebeta

← D33×AGL(1,𝔽11) #20300018

Subgroups — D33×AGL(1,𝔽11) #20300018

Order 7260.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×D33C211yesmaximal, characteristic, complemented
2C3⋊((C11⋊C5)⋊D11)C211yesmaximal, characteristic, complemented
3C3×C11×AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
4D11×AGL(1,𝔽11)—31nomaximal, Hall
5C3×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
6D11×D33C511yesmaximal, characteristic, complemented, Hall
7D11×C11⋊C5—31no—
8(C11⋊C5)⋊D11—31no—
9C11×AGL(1,𝔽11)D311yescharacteristic, complemented
10C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
11C11×D33C2×C511yescharacteristic, complemented
12C3×C11×D11C2×C511yescharacteristic, complemented
13C2×C5×D33—111nomaximal
14D3×AGL(1,𝔽11)—111nomaximal
15C11×C11⋊C5C2×D311yescharacteristic, complemented, Hall
16D112—31noHall
17C3×C112C22×C511yescharacteristic, complemented, Hall
18C2×C3×C5×C11—111no—
19C5×D33—111no—
20C5×D33—111no—
21C3⋊AGL(1,𝔽11)—111no—
22D3×C11⋊C5—111no—
23C3×AGL(1,𝔽11)D1111yescharacteristic, complemented
24C11⋊D11—31no—
25C11×D11—31no—
26C11×D11C5×D311yescharacteristic, complemented
27C2×C5×D11—331no—
28C2×AGL(1,𝔽11)—331no—
29C3×C5×C11—111no—
30C3×C11⋊C5C2×D1111yescharacteristic, complemented
31C2×D33—111no—
32D3×D11—111no—
33C112C2×C5×D311yescharacteristic, complemented, Sylow
34C2×C5×C11—111no—
35C5×D11—331no—
36C5×D11—331no—
37C2×C11⋊C5—331no—
38AGL(1,𝔽11)—331no—
39AGL(1,𝔽11)D3311yescharacteristic, direct product factor
40C2×C3×C11—111no—
41D33—111no—
42D33—111no—
43D33—1101no—
44D33AGL(1,𝔽11)11yescharacteristic, direct product factor
45C3×D11C5×D1111yescharacteristic, complemented
46D3×C11—111no—
47C2×C5×D3—1211noHall
48C5×C11—111no—
49C11⋊C5C2×D3311yescharacteristic, complemented
50C2×D11—331no—
51C2×D11—331no—
52C3×C11—101no—
53C3×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
54C3×C11C2×C5×D1111yescharacteristic, complemented
55C2×C3×C5—111no—
56C5×D3—1211no—
57C5×D3—1211no—
58C2×C11—111no—
59C2×C11—331no—
60D11—31no—
61D11—331no—
62D11—331no—
63D11—3301no—
64D11C5×D3311yescharacteristic, complemented
65C22×C5—3631noHall
66C3×C5—111noHall
67C2×D3—1211noHall
68C11—101no—
69C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
70C11C2×C5×D3311yescharacteristic, complemented
71C2×C5—111no—
72C2×C5—3631no—
73C2×C5—3631no—
74C2×C3—111no—
75D3—111no—
76D3—1211no—
77C5—111noSylow
78C22—3631noSylow
79C3D11×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
80C2—111no—
81C2—331no—
82C2—3631no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C112C22×C5
LCSG ▷ C3×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×D33C2semidirect
2. C3⋊((C11⋊C5)⋊D11)C2semidirect
3. C3×C11×AGL(1,𝔽11)C2semidirect
5. C3×C11×C11⋊C5C22semidirect
6. D11×D33C5semidirect
9. C11×AGL(1,𝔽11)D3semidirect
10. C3⋊(C11⋊D11)C2×C5semidirect
11. C11×D33C2×C5semidirect
12. C3×C11×D11C2×C5semidirect
15. C11×C11⋊C5C2×D3semidirect
17. C3×C112C22×C5semidirect
23. C3×AGL(1,𝔽11)D11semidirect
26. C11×D11C5×D3semidirect
30. C3×C11⋊C5C2×D11semidirect
33. C112C2×C5×D3semidirect
39. AGL(1,𝔽11)D33direct (N × H)
44. D33AGL(1,𝔽11)direct (N × H)
45. C3×D11C5×D11semidirect
49. C11⋊C5C2×D33semidirect
53. C3×C11C2×AGL(1,𝔽11)semidirect
54. C3×C11C2×C5×D11semidirect
64. D11C5×D33semidirect
69. C11D3×AGL(1,𝔽11)semidirect
70. C11C2×C5×D33semidirect
79. C3D11×AGL(1,𝔽11)semidirect