Finite Group Databasebeta

← #11925895⋊D3 #20300007

Subgroups — #11925895⋊D3 #20300007

Order 7260.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊#11925895C211yesmaximal, characteristic, complemented
2C3⋊#11925892C211yesmaximal, characteristic, complemented
3C3×#11925895C211yesmaximal, characteristic, complemented
4#11925892⋊C2—31nomaximal, Hall
5C3×#10597243C2211yescharacteristic, complemented, Hall
6D11×D33C511yesmaximal, characteristic, complemented, Hall
7#11925895—31no—
8#11925895D311yescharacteristic, complemented
9#11925892—31no—
10C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
11C11×D33C2×C511yescharacteristic, complemented
12C3×C11×D11C2×C511yescharacteristic, complemented
13C2×C3⋊AGL(1,𝔽11)—111nomaximal
14D3×AGL(1,𝔽11)—111nomaximal
15#10597243C2×D311yescharacteristic, complemented, Hall
16D112—31noHall
17C3×C112C22×C511yescharacteristic, complemented, Hall
18C2×C3×C11⋊C5—111no—
19C3⋊AGL(1,𝔽11)—111no—
20C3⋊AGL(1,𝔽11)—111no—
21C3⋊AGL(1,𝔽11)—111no—
22C3⋊AGL(1,𝔽11)—225no—
23D3×C11⋊C5—111no—
24C3×AGL(1,𝔽11)—111no—
25C11⋊D11—31no—
26C11×D11—31no—
27C11×D11C5×D311yescharacteristic, complemented
28C2×AGL(1,𝔽11)—331no—
29C2×AGL(1,𝔽11)—331no—
30C3×C11⋊C5—111no—
31C3×C11⋊C5—111no—
32C3×C11⋊C5—225no—
33C2×D33—111no—
34D3×D11—111no—
35C112C2×C5×D311yescharacteristic, complemented, Sylow
36C2×C11⋊C5—111no—
37C2×C11⋊C5—331no—
38AGL(1,𝔽11)—111no—
39AGL(1,𝔽11)—331no—
40AGL(1,𝔽11)—331no—
41AGL(1,𝔽11)—331no—
42AGL(1,𝔽11)—665no—
43C2×C3×C11—111no—
44D33—111no—
45D33—111no—
46D33—225no—
47D33AGL(1,𝔽11)11yescharacteristic, complemented
48C3×D11AGL(1,𝔽11)11yescharacteristic, complemented
49D3×C11—111no—
50C2×C5×D3—1211noHall
51C11⋊C5—111no—
52C11⋊C5—111no—
53C11⋊C5—225no—
54C2×D11—331no—
55C2×D11—331no—
56C3×C11—25no—
57C3×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
58C3×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
59C2×C3×C5—1211no—
60C5×D3—1211no—
61C5×D3—1211no—
62C2×C11—111no—
63C2×C11—331no—
64D11—31no—
65D11—331no—
66D11—331no—
67D11—665no—
68D11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
69C22×C5—3631noHall
70C3×C5—1211noHall
71C2×D3—1211noHall
72C11—25no—
73C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
74C11C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
75C2×C5—3631no—
76C2×C5—3631no—
77C2×C5—1211no—
78C2×C3—111no—
79D3—111no—
80D3—1211no—
81C5—1211noSylow
82C22—3631noSylow
83C3#11925892⋊C211yescharacteristic, complemented, Sylow
84C2—111no—
85C2—331no—
86C2—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. C3⋊#11925895C2semidirect
2. C3⋊#11925892C2semidirect
3. C3×#11925895C2semidirect
5. C3×#10597243C22semidirect
6. D11×D33C5semidirect
8. #11925895D3semidirect
10. C3⋊(C11⋊D11)C2×C5semidirect
11. C11×D33C2×C5semidirect
12. C3×C11×D11C2×C5semidirect
15. #10597243C2×D3semidirect
17. C3×C112C22×C5semidirect
27. C11×D11C5×D3semidirect
35. C112C2×C5×D3semidirect
47. D33AGL(1,𝔽11)semidirect
48. C3×D11AGL(1,𝔽11)semidirect
57. C3×C11C2×AGL(1,𝔽11)semidirect
58. C3×C11C2×AGL(1,𝔽11)semidirect
68. D11C3⋊AGL(1,𝔽11)semidirect
73. C11D3×AGL(1,𝔽11)semidirect
74. C11C2×C3⋊AGL(1,𝔽11)semidirect
83. C3#11925892⋊C2semidirect