Finite Group Databasebeta

← C7×C3⋊(C11⋊(D19⋊C3)) #39911885

Subgroups — C7×C3⋊(C11⋊(D19⋊C3)) #39911885

Order 26334.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C11×C19⋊C3C211yesmaximal, characteristic, complemented, Hall
2C7×C11⋊(D19⋊C3)—31nomaximal
3C7×D627C311yesmaximal, characteristic, complemented
4C7×C11×C19⋊C3—21no—
5C7×C11×C19⋊C3D311yescharacteristic, complemented
6C3×C7×C11×C19C2×C311yescharacteristic, complemented
7C3⋊(C11⋊(D19⋊C3))C711yesmaximal, characteristic, direct product factor, Hall
8C7×D209—31noHall
9C7×C3⋊(D19⋊C3)—111nomaximal, Hall
10C3×C11×C19⋊C3C2×C711yescharacteristic, complemented, Hall
11C7×C11×C19C3×D311yescharacteristic, complemented, Hall
12C3×C7×D33—191nomaximal, Hall
13D627C3×C711yescharacteristic, complemented
14C11⋊(D19⋊C3)—31no—
15C3×C7×C19⋊C3D1111yescharacteristic, complemented, Hall
16C7×D57—111no—
17C7×D19⋊C3—331no—
18C32×C7×C11—191noHall
19C3×C11×C19C2×C3×C711yescharacteristic, complemented
20C11×C19⋊C3—21no—
21C11×C19⋊C3D3×C711yescharacteristic, complemented
22C7×D33—191no—
23C3×C7×D11—571no—
24D209—31noHall
25C3×C7×C19C3×D1111yescharacteristic, complemented
26C7×C19⋊C3—21no—
27C7×C19⋊C3D3311yescharacteristic, complemented
28C3⋊(D19⋊C3)—111noHall
29C7×D19—331noHall
30C3×C7×C11—191no—
31C3×C7×C11—381no—
32C3×C7×C11D19⋊C311yescharacteristic, complemented
33C11×C19C3×D3×C711yescharacteristic, complemented, Hall
34C3×D33—191noHall
35C3×C19⋊C3C7×D1111yescharacteristic, complemented, Hall
36C7×D11—571noHall
37C7×C19C3×D3311yescharacteristic, complemented, Hall
38C3×D3×C7—2091noHall
39D57—111no—
40D19⋊C3—331no—
41C32×C11—191noHall
42C7×C11C3⋊(D19⋊C3)11yescharacteristic, complemented, Hall
43D33—191no—
44C3×D11—571no—
45C32×C7—191noHall
46C3×C19C3×C7×D1111yescharacteristic, complemented
47C19⋊C3—21no—
48C19⋊C3C7×D3311yescharacteristic, complemented
49C2×C3×C7—6271no—
50D3×C7—2091no—
51D19—331noHall
52C3×C11—191no—
53C3×C11—381no—
54C3×C11C7×D19⋊C311yescharacteristic, complemented
55D11—571noHall
56C3×C7—191no—
57C3×C7—381no—
58C3×C7C11⋊(D19⋊C3)11yescharacteristic, complemented
59C19C3×C7×D3311yescharacteristic, complemented, Sylow
60C3×D3—2091noHall
61C2×C7—6271noHall
62C11C7×C3⋊(D19⋊C3)11yescharacteristic, complemented, Sylow
63C32—191noSylow
64C7C3⋊(C11⋊(D19⋊C3))11yescharacteristic, direct product factor, Sylow
65C2×C3—6271no—
66D3—2091no—
67C3—191no—
68C3—381no—
69C3C7×C11⋊(D19⋊C3)11yescharacteristic, complemented
70C2—6271noSylow
subgroupG/H
center, hypercenterC7C3⋊(C11⋊(D19⋊C3))
commutator, cosocle, hypocenterC3×C11×C19C2×C3×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2×C3
LCSG ▷ C3×C11×C19
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×C19⋊C3C2semidirect
3. C7×D627C3semidirect
5. C7×C11×C19⋊C3D3semidirect
6. C3×C7×C11×C19C2×C3semidirect
7. C3⋊(C11⋊(D19⋊C3))C7direct (N × H)
10. C3×C11×C19⋊C3C2×C7semidirect
11. C7×C11×C19C3×D3semidirect
13. D627C3×C7semidirect
15. C3×C7×C19⋊C3D11semidirect
19. C3×C11×C19C2×C3×C7semidirect
21. C11×C19⋊C3D3×C7semidirect
25. C3×C7×C19C3×D11semidirect
27. C7×C19⋊C3D33semidirect
32. C3×C7×C11D19⋊C3semidirect
33. C11×C19C3×D3×C7semidirect
35. C3×C19⋊C3C7×D11semidirect
37. C7×C19C3×D33semidirect
42. C7×C11C3⋊(D19⋊C3)semidirect
46. C3×C19C3×C7×D11semidirect
48. C19⋊C3C7×D33semidirect
54. C3×C11C7×D19⋊C3semidirect
58. C3×C7C11⋊(D19⋊C3)semidirect
59. C19C3×C7×D33semidirect
62. C11C7×C3⋊(D19⋊C3)semidirect
64. C7C3⋊(C11⋊(D19⋊C3))direct (N × H)
69. C3C7×C11⋊(D19⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C11×C19⋊C32
C7×C11⋊(D19⋊C3)3
C7×D6273
C3⋊(C11⋊(D19⋊C3))7
C7×C3⋊(D19⋊C3)11
C3×C7×D3319