Finite Group Databasebeta

← C7×(C3⋊D3)⋊(C11⋊D11) #44479212

Subgroups — C7×(C3⋊D3)⋊(C11⋊D11) #44479212

Order 30492.

616 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C3⋊(C11⋊D11)C212yesmaximal, complemented
2C7×C112×C3⋊D3C211yesmaximal, characteristic, complemented
3D3×C7×C11⋊D11—32nomaximal
4C32×C7×C112C2211yescharacteristic, complemented, Hall
5C7×C3⋊(C11⋊D11)D312yescomplemented
6D3×C7×C112—32no—
7D3×C7×C112—61no—
8C3×C7×C11⋊D11—32no—
9(C3⋊D3)⋊(C11⋊D11)C711yesmaximal, characteristic, direct product factor, Hall
10C2×C7×C11⋊D11—91noHall
11C7×(C3⋊D3)⋊D11—1112nomaximal
12C3×C7×C112—21no—
13C3×C7×C112C2×D312yescomplemented
14C112×C3⋊D3C2×C711yescharacteristic, complemented
15C3×C3⋊(C11⋊D11)C2×C712yescomplemented
16C2×C7×C112—91no—
17C7×C11⋊D11—32no—
18D3×C11⋊D11—32no—
19C7×C11×C3⋊D3D11112yescomplemented
20C3×C7×D33—1124no—
21C32×C112C22×C711yescharacteristic, complemented, Hall
22D3×C7×D11—3324no—
23C7×C112D3211yescharacteristic, complemented, Hall
24C3⋊(C11⋊D11)D3×C712yescomplemented
25D3×C112—32no—
26D3×C112—61no—
27C3×C11⋊D11—32no—
28C32×C7×C11C2×D11112yescomplemented
29C2×C11⋊D11—91noHall
30C7×D33—1124no—
31D3×C7×C11—324no—
32D3×C7×C11—612no—
33C3×C7×D11—3324no—
34(C3⋊D3)⋊D11—1112no—
35C3×C112—21no—
36C3×C112C2×D3×C712yescomplemented
37C2×C7×D11—9912no—
38D32×C7—1211noHall
39C2×C112—91no—
40C11⋊D11—32no—
41C3×C7×C11—212no—
42C3×C7×C11D3×D11124yescomplemented
43C11×C3⋊D3C7×D11112yescomplemented
44C3×D33—1124no—
45C2×C7×C11—912no—
46C7×D11—3324no—
47D3×D11—3324no—
48C7×C3⋊D3C11⋊D1111yescharacteristic, complemented
49C3×D3×C7—1212no—
50C112D32×C711yescharacteristic, complemented, Sylow
51C32×C11C2×C7×D11112yescomplemented
52C2×D3×C7—3632no—
53C7×C11(C3⋊D3)⋊D11112yescomplemented
54D33—1124no—
55C3×D11—3324no—
56D3×C11—324no—
57D3×C11—612no—
58C32×C7C2×C11⋊D1111yescharacteristic, complemented, Hall
59C2×D11—9912no—
60C2×C3×C7—3632no—
61D3×C7—32no—
62D3×C7—61no—
63D3×C7—1212no—
64D32—1211noHall
65C3×C11—212no—
66C3×C11D3×C7×D11124yescomplemented
67C22×C7—10891noHall
68C2×C11—912no—
69D11—3324no—
70C3×C7—21no—
71C3×C7D3×C11⋊D1112yescomplemented
72C3⋊D3C7×C11⋊D1111yescharacteristic, complemented
73C3×D3—1212no—
74C2×C7—91no—
75C2×C7—3632no—
76C2×D3—3632no—
77C11C7×(C3⋊D3)⋊D11112yescomplemented
78C32C2×C7×C11⋊D1111yescharacteristic, complemented, Sylow
79C7(C3⋊D3)⋊(C11⋊D11)11yescharacteristic, direct product factor, Sylow
80C2×C3—3632no—
81D3—32no—
82D3—61no—
83D3—1212no—
84C22—10891noSylow
85C3—21no—
86C3D3×C7×C11⋊D1112yescomplemented
87C2—91no—
88C2—3632no—
subgroupG/H
center, hypercenterC7(C3⋊D3)⋊(C11⋊D11)
commutator, cosocle, hypocenterC32×C112C22×C7
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C112
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C3⋊(C11⋊D11)C2semidirect
2. C7×C112×C3⋊D3C2semidirect
4. C32×C7×C112C22semidirect
5. C7×C3⋊(C11⋊D11)D3semidirect
9. (C3⋊D3)⋊(C11⋊D11)C7direct (N × H)
13. C3×C7×C112C2×D3semidirect
14. C112×C3⋊D3C2×C7semidirect
15. C3×C3⋊(C11⋊D11)C2×C7semidirect
19. C7×C11×C3⋊D3D11semidirect
21. C32×C112C22×C7semidirect
23. C7×C112D32semidirect
24. C3⋊(C11⋊D11)D3×C7semidirect
28. C32×C7×C11C2×D11semidirect
36. C3×C112C2×D3×C7semidirect
42. C3×C7×C11D3×D11semidirect
43. C11×C3⋊D3C7×D11semidirect
48. C7×C3⋊D3C11⋊D11semidirect
50. C112D32×C7semidirect
51. C32×C11C2×C7×D11semidirect
53. C7×C11(C3⋊D3)⋊D11semidirect
58. C32×C7C2×C11⋊D11semidirect
66. C3×C11D3×C7×D11semidirect
71. C3×C7D3×C11⋊D11semidirect
72. C3⋊D3C7×C11⋊D11semidirect
77. C11C7×(C3⋊D3)⋊D11semidirect
78. C32C2×C7×C11⋊D11semidirect
79. C7(C3⋊D3)⋊(C11⋊D11)direct (N × H)
86. C3D3×C7×C11⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C3⋊(C11⋊D11)2
C7×C112×C3⋊D32
D3×C7×C11⋊D113
(C3⋊D3)⋊(C11⋊D11)7
C7×(C3⋊D3)⋊D1111