Finite Group Databasebeta

← C3⋊(C11⋊((C13⋊C3)⋊D7)) #31825071

Subgroups — C3⋊(C11⋊((C13⋊C3)⋊D7)) #31825071

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C11×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11⋊((C13⋊C3)⋊D7)—31nomaximal
3D3003C311yesmaximal, characteristic, complemented
4C7×C11×C13⋊C3—21no—
5C7×C11×C13⋊C3D311yescharacteristic, complemented
6C3×C7×C11×C13C2×C311yescharacteristic, complemented
7C3⋊(C11⋊(D13⋊C3))—71nomaximal, Hall
8D1001—31noHall
9C3⋊((C13⋊C3)⋊D7)—111nomaximal, Hall
10C3×D231—131nomaximal, Hall
11C3×C11×C13⋊C3D711yescharacteristic, complemented, Hall
12C7×C11×C13C3×D311yescharacteristic, complemented, Hall
13D429—71no—
14C11⋊(D13⋊C3)—211no—
15C3×C7×C13⋊C3D1111yescharacteristic, complemented, Hall
16C32×C7×C11—261noHall
17D273—111no—
18(C13⋊C3)⋊D7—331no—
19D231—131no—
20C3×D77—391no—
21C3×C11×C13C3×D711yescharacteristic, complemented
22C11×C13⋊C3—21no—
23C11×C13⋊C3D2111yescharacteristic, complemented
24D143—211noHall
25C3×C7×C13C3×D1111yescharacteristic, complemented
26C7×C13⋊C3—21no—
27C7×C13⋊C3D3311yescharacteristic, complemented
28C3⋊(D13⋊C3)—771noHall
29C3×C7×C11—261no—
30C3×C7×C11—261no—
31C3×C7×C11D13⋊C311yescharacteristic, complemented
32C3×D33—911noHall
33D91—331noHall
34D77—391noHall
35C11×C13C3×D2111yescharacteristic, complemented, Hall
36C3×D21—1431noHall
37C3×C13⋊C3D7711yescharacteristic, complemented, Hall
38C32×C11—261noHall
39C7×C13C3×D3311yescharacteristic, complemented, Hall
40D39—771no—
41D13⋊C3—2311no—
42C7×C11C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
43D33—911no—
44C3×D11—2731no—
45C32×C7—261noHall
46D21—1431no—
47C3×D7—4291no—
48C3×C13C3×D7711yescharacteristic, complemented
49C13⋊C3—21no—
50C13⋊C3D23111yescharacteristic, complemented
51C3×C11—261no—
52C3×C11—261no—
53C3×C11(C13⋊C3)⋊D711yescharacteristic, complemented
54D13—2311noHall
55D11—2731noHall
56C3×C7—261no—
57C3×C7—261no—
58C3×C7C11⋊(D13⋊C3)11yescharacteristic, complemented
59C3×D3—10011noHall
60D7—4291noHall
61C13C3×D23111yescharacteristic, complemented, Sylow
62C11C3⋊((C13⋊C3)⋊D7)11yescharacteristic, complemented, Sylow
63C32—261noSylow
64C7C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented, Sylow
65C2×C3—30031no—
66D3—10011no—
67C3—261no—
68C3—261no—
69C3C11⋊((C13⋊C3)⋊D7)11yescharacteristic, complemented
70C2—30031noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×C13⋊C3C2semidirect
3. D3003C3semidirect
5. C7×C11×C13⋊C3D3semidirect
6. C3×C7×C11×C13C2×C3semidirect
11. C3×C11×C13⋊C3D7semidirect
12. C7×C11×C13C3×D3semidirect
15. C3×C7×C13⋊C3D11semidirect
21. C3×C11×C13C3×D7semidirect
23. C11×C13⋊C3D21semidirect
25. C3×C7×C13C3×D11semidirect
27. C7×C13⋊C3D33semidirect
31. C3×C7×C11D13⋊C3semidirect
35. C11×C13C3×D21semidirect
37. C3×C13⋊C3D77semidirect
39. C7×C13C3×D33semidirect
42. C7×C11C3⋊(D13⋊C3)semidirect
48. C3×C13C3×D77semidirect
50. C13⋊C3D231semidirect
53. C3×C11(C13⋊C3)⋊D7semidirect
58. C3×C7C11⋊(D13⋊C3)semidirect
61. C13C3×D231semidirect
62. C11C3⋊((C13⋊C3)⋊D7)semidirect
64. C7C3⋊(C11⋊(D13⋊C3))semidirect
69. C3C11⋊((C13⋊C3)⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C11×C13⋊C32
C11⋊((C13⋊C3)⋊D7)3
D30033
C3⋊(C11⋊(D13⋊C3))7
C3⋊((C13⋊C3)⋊D7)11
C3×D23113