Finite Group Databasebeta

← C11×C3⋊((C13⋊C3)⋊D7) #31825069

Subgroups — C11×C3⋊((C13⋊C3)⋊D7) #31825069

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
3C11×D273C311yesmaximal, characteristic, complemented
4C7×C11×C13⋊C3—21no—
5C7×C11×C13⋊C3D311yescharacteristic, complemented
6C3×C7×C11×C13C2×C311yescharacteristic, complemented
7C11×C3⋊(D13⋊C3)—71nomaximal, Hall
8C11×D91—31noHall
9C3⋊((C13⋊C3)⋊D7)C1111yesmaximal, characteristic, direct product factor, Hall
10C3×C11×D21—131nomaximal, Hall
11C3×C11×C13⋊C3D711yescharacteristic, complemented, Hall
12C7×C11×C13C3×D311yescharacteristic, complemented, Hall
13C11×D39—71no—
14C11×D13⋊C3—211no—
15C3×C7×C13⋊C3C2×C1111yescharacteristic, complemented, Hall
16C32×C7×C11—131noHall
17D273C3×C1111yescharacteristic, complemented
18(C13⋊C3)⋊D7—31no—
19C11×D21—131no—
20C3×C11×D7—391no—
21C3×C11×C13C3×D711yescharacteristic, complemented
22C11×C13⋊C3—21no—
23C11×C13⋊C3D2111yescharacteristic, complemented
24C11×D13—211noHall
25C3×C7×C13C2×C3×C1111yescharacteristic, complemented
26C7×C13⋊C3—21no—
27C7×C13⋊C3D3×C1111yescharacteristic, complemented
28C3⋊(D13⋊C3)—71noHall
29C3×C7×C11—131no—
30C3×C7×C11—261no—
31C3×C7×C11D13⋊C311yescharacteristic, complemented
32C3×D3×C11—911noHall
33D91—31noHall
34C11×D7—391noHall
35C11×C13C3×D2111yescharacteristic, complemented, Hall
36C3×D21—131noHall
37C3×C13⋊C3C11×D711yescharacteristic, complemented, Hall
38C32×C11—131noHall
39C7×C13C3×D3×C1111yescharacteristic, complemented, Hall
40D39—71no—
41D13⋊C3—211no—
42C7×C11C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
43C2×C3×C11—2731no—
44D3×C11—911no—
45C32×C7—131noHall
46D21—131no—
47C3×D7—391no—
48C3×C13C3×C11×D711yescharacteristic, complemented
49C13⋊C3—21no—
50C13⋊C3C11×D2111yescharacteristic, complemented
51C3×C11—131no—
52C3×C11—261no—
53C3×C11(C13⋊C3)⋊D711yescharacteristic, complemented
54D13—211noHall
55C2×C11—2731noHall
56C3×C7—131no—
57C3×C7—261no—
58C3×C7C11×D13⋊C311yescharacteristic, complemented
59C3×D3—911noHall
60D7—391noHall
61C13C3×C11×D2111yescharacteristic, complemented, Sylow
62C11C3⋊((C13⋊C3)⋊D7)11yescharacteristic, direct product factor, Sylow
63C32—131noSylow
64C7C11×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
65C2×C3—2731no—
66D3—911no—
67C3—131no—
68C3—261no—
69C3C11×(C13⋊C3)⋊D711yescharacteristic, complemented
70C2—2731noSylow
subgroupG/H
center, hypercenterC11C3⋊((C13⋊C3)⋊D7)
commutator, cosocle, hypocenterC3×C7×C13C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×C13⋊C3C2semidirect
3. C11×D273C3semidirect
5. C7×C11×C13⋊C3D3semidirect
6. C3×C7×C11×C13C2×C3semidirect
9. C3⋊((C13⋊C3)⋊D7)C11direct (N × H)
11. C3×C11×C13⋊C3D7semidirect
12. C7×C11×C13C3×D3semidirect
15. C3×C7×C13⋊C3C2×C11semidirect
17. D273C3×C11semidirect
21. C3×C11×C13C3×D7semidirect
23. C11×C13⋊C3D21semidirect
25. C3×C7×C13C2×C3×C11semidirect
27. C7×C13⋊C3D3×C11semidirect
31. C3×C7×C11D13⋊C3semidirect
35. C11×C13C3×D21semidirect
37. C3×C13⋊C3C11×D7semidirect
39. C7×C13C3×D3×C11semidirect
42. C7×C11C3⋊(D13⋊C3)semidirect
48. C3×C13C3×C11×D7semidirect
50. C13⋊C3C11×D21semidirect
53. C3×C11(C13⋊C3)⋊D7semidirect
58. C3×C7C11×D13⋊C3semidirect
61. C13C3×C11×D21semidirect
62. C11C3⋊((C13⋊C3)⋊D7)direct (N × H)
64. C7C11×C3⋊(D13⋊C3)semidirect
69. C3C11×(C13⋊C3)⋊D7semidirect

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)⋊D73
C11×D2733
C11×C3⋊(D13⋊C3)7
C3⋊((C13⋊C3)⋊D7)11
C3×C11×D2113