Finite Group Databasebeta

← (C3⋊D3)⋊(C5⋊(C11⋊D11)) #36345346

Subgroups — (C3⋊D3)⋊(C5⋊(C11⋊D11)) #36345346

Order 21780.

616 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C3⋊(C5⋊(C11⋊D11))C212yesmaximal, complemented
2C5×C112×C3⋊D3C211yesmaximal, characteristic, complemented
3D3×C5⋊(C11⋊D11)—32nomaximal
4C32×C5×C112C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊(C11⋊D11)—51nomaximal, Hall
6C3⋊(C5⋊(C11⋊D11))D312yescomplemented
7C5×D3×C112—32no—
8C5×D3×C112—61no—
9C3×C5⋊(C11⋊D11)—32no—
10C2×C5⋊(C11⋊D11)—91noHall
11C112×C3⋊D3D511yescharacteristic, complemented
12C3×C3⋊(C11⋊D11)—52no—
13(C3⋊D3)⋊D55—1112nomaximal
14C3×C5×C112—21no—
15C3×C5×C112C2×D312yescomplemented
16D3×C11⋊D11—152no—
17C2×C5×C112—91no—
18C5⋊(C11⋊D11)—32no—
19C32×C112C2×D511yescharacteristic, complemented, Hall
20C5×C11×C3⋊D3D11112yescomplemented
21C3×D165—1124no—
22C3⋊(C11⋊D11)—52no—
23D3×C112—32no—
24D3×C112—61no—
25C3×C11⋊D11—152no—
26D3×D55—3324no—
27C5×C112D3211yescharacteristic, complemented, Hall
28C32×C5×C11C2×D11112yescomplemented
29C2×C11⋊D11—451noHall
30(C3⋊D3)⋊D11—5512no—
31C3×C112—21no—
32C3×C112D3×D512yescomplemented
33D165—1124no—
34C5×D3×C11—324no—
35C5×D3×C11—612no—
36C3×D55—3324no—
37C2×C112—91no—
38C11⋊D11—152no—
39C2×D55—9912no—
40C11×C3⋊D3D55112yescomplemented
41C3×D33—5524no—
42(C3⋊D3)⋊D5—1211noHall
43C3×C5×C11—212no—
44C3×C5×C11D3×D11124yescomplemented
45D3×D11—16524no—
46C112(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
47C2×C5×C11—912no—
48D55—3324no—
49C32×C11C2×D55112yescomplemented
50C5×C3⋊D3C11⋊D1111yescharacteristic, complemented
51C3×D15—1212no—
52D33—5524no—
53C3×D11—16524no—
54D3×C11—324no—
55D3×C11—612no—
56D3×D5—3632no—
57C5×C11(C3⋊D3)⋊D11112yescomplemented
58C32×C5C2×C11⋊D1111yescharacteristic, complemented, Hall
59C2×D11—49512no—
60D32—6051noHall
61C3×C11—212no—
62C3×C11D3×D55124yescomplemented
63D15—1212no—
64C3×D5—3632no—
65C5×D3—32no—
66C5×D3—61no—
67C2×C11—912no—
68D11—16524no—
69C2×D5—10891noHall
70C3⋊D3C5⋊(C11⋊D11)11yescharacteristic, complemented
71C3×D3—6052no—
72C3×C5—21no—
73C3×C5D3×C11⋊D1112yescomplemented
74C2×D3—18152no—
75C11(C3⋊D3)⋊D55112yescomplemented
76C2×C5—91no—
77D5—3632no—
78C32C2×C5⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
79C2×C3—18152no—
80D3—32no—
81D3—61no—
82D3—6052no—
83C5(C3⋊D3)⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
84C22—54451noSylow
85C3—21no—
86C3D3×C5⋊(C11⋊D11)12yescomplemented
87C2—91no—
88C2—18152no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C112C22
LCSG ▷ C32×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊(C5⋊(C11⋊D11))C2semidirect
2. C5×C112×C3⋊D3C2semidirect
4. C32×C5×C112C22semidirect
6. C3⋊(C5⋊(C11⋊D11))D3semidirect
11. C112×C3⋊D3D5semidirect
15. C3×C5×C112C2×D3semidirect
19. C32×C112C2×D5semidirect
20. C5×C11×C3⋊D3D11semidirect
27. C5×C112D32semidirect
28. C32×C5×C11C2×D11semidirect
32. C3×C112D3×D5semidirect
40. C11×C3⋊D3D55semidirect
44. C3×C5×C11D3×D11semidirect
46. C112(C3⋊D3)⋊D5semidirect
49. C32×C11C2×D55semidirect
50. C5×C3⋊D3C11⋊D11semidirect
57. C5×C11(C3⋊D3)⋊D11semidirect
58. C32×C5C2×C11⋊D11semidirect
62. C3×C11D3×D55semidirect
70. C3⋊D3C5⋊(C11⋊D11)semidirect
73. C3×C5D3×C11⋊D11semidirect
75. C11(C3⋊D3)⋊D55semidirect
78. C32C2×C5⋊(C11⋊D11)semidirect
83. C5(C3⋊D3)⋊(C11⋊D11)semidirect
86. C3D3×C5⋊(C11⋊D11)semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊(C5⋊(C11⋊D11))2
C5×C112×C3⋊D32
D3×C5⋊(C11⋊D11)3
(C3⋊D3)⋊(C11⋊D11)5
(C3⋊D3)⋊D5511