Finite Group Databasebeta

← C3⋊(C11⋊((C13⋊C3)⋊D13)) #45689601

Subgroups — C3⋊(C11⋊((C13⋊C3)⋊D13)) #45689601

Order 33462.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×C13×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C11⋊(C13⋊D13))C311yesmaximal, characteristic, complemented
3C11⋊((C13⋊C3)⋊D13)—31nomaximal
4C11×C13×C13⋊C3—21no—
5C11×C13×C13⋊C3D311yescharacteristic, complemented
6C3×C11×C132C2×C311yescharacteristic, complemented
7C11⋊(C13⋊D13)—31noHall
8C3⋊((C13⋊C3)⋊D13)—111nomaximal, Hall
9C3×D429—131nomaximal
10C3⋊(C11⋊(D13⋊C3))—131nomaximal
11C11×C132C3×D311yescharacteristic, complemented, Hall
12C3×C13×C13⋊C3D1111yescharacteristic, complemented, Hall
13C32×C11×C13—131no—
14C3×C11×C13⋊C3D1311yescharacteristic, complemented
15C3⋊(C13⋊D13)—111no—
16(C13⋊C3)⋊D13—331no—
17D429—131no—
18D429—131no—
19D429—394no—
20C3×D143—391no—
21C11⋊(D13⋊C3)—391no—
22C3×C132C3×D1111yescharacteristic, complemented
23C13×C13⋊C3—21no—
24C13×C13⋊C3D3311yescharacteristic, complemented
25C3×C11×C13—34no—
26C3×C11×C13—131no—
27C3×C11×C13—261no—
28C3×C11×C13D13⋊C311yescharacteristic, complemented
29C3×C11×C13C3×D1311yescharacteristic, complemented
30C11×C13⋊C3—21no—
31C11×C13⋊C3D3911yescharacteristic, complemented
32C13⋊D13—331noHall
33D143—391no—
34D143—391no—
35D143—1174no—
36C3×D39—1431no—
37C3⋊(D13⋊C3)—1431no—
38C3×D33—1691noHall
39C132C3×D3311yescharacteristic, complemented, Sylow
40C11×C13—34no—
41C11×C13C3⋊(D13⋊C3)11yescharacteristic, complemented
42C11×C13C3×D3911yescharacteristic, complemented
43C32×C13—131no—
44C3×C13⋊C3D14311yescharacteristic, complemented
45C32×C11—131noHall
46D39—1431no—
47D39—1431no—
48D39—4294no—
49C3×D13—4291no—
50D13⋊C3—4291no—
51D33—1691no—
52C3×D11—5071no—
53C3×C13—34no—
54C3×C13—131no—
55C3×C13—261no—
56C3×C13C11⋊(D13⋊C3)11yescharacteristic, complemented
57C3×C13C3×D14311yescharacteristic, complemented
58C13⋊C3—21no—
59C13⋊C3D42911yescharacteristic, complemented
60C3×C11—131no—
61C3×C11—261no—
62C3×C11(C13⋊C3)⋊D1311yescharacteristic, complemented
63D13—12874no—
64D13—4291no—
65D13—4291no—
66D11—5071noHall
67C3×D3—18591noHall
68C13—34no—
69C13C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented
70C13C3×D42911yescharacteristic, complemented
71C11C3⋊((C13⋊C3)⋊D13)11yescharacteristic, complemented, Sylow
72C32—131noSylow
73C2×C3—55771no—
74D3—18591no—
75C3—131no—
76C3—261no—
77C3C11⋊((C13⋊C3)⋊D13)11yescharacteristic, complemented
78C2—55771noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C132C2×C3
LCSG ▷ C3×C11×C132
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C11×C13×C13⋊C3C2semidirect
2. C3⋊(C11⋊(C13⋊D13))C3semidirect
5. C11×C13×C13⋊C3D3semidirect
6. C3×C11×C132C2×C3semidirect
11. C11×C132C3×D3semidirect
12. C3×C13×C13⋊C3D11semidirect
14. C3×C11×C13⋊C3D13semidirect
22. C3×C132C3×D11semidirect
24. C13×C13⋊C3D33semidirect
28. C3×C11×C13D13⋊C3semidirect
29. C3×C11×C13C3×D13semidirect
31. C11×C13⋊C3D39semidirect
39. C132C3×D33semidirect
41. C11×C13C3⋊(D13⋊C3)semidirect
42. C11×C13C3×D39semidirect
44. C3×C13⋊C3D143semidirect
56. C3×C13C11⋊(D13⋊C3)semidirect
57. C3×C13C3×D143semidirect
59. C13⋊C3D429semidirect
62. C3×C11(C13⋊C3)⋊D13semidirect
69. C13C3⋊(C11⋊(D13⋊C3))semidirect
70. C13C3×D429semidirect
71. C11C3⋊((C13⋊C3)⋊D13)semidirect
77. C3C11⋊((C13⋊C3)⋊D13)semidirect

Maximal subgroups

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

subgroupindex
C3×C11×C13×C13⋊C32
C3⋊(C11⋊(C13⋊D13))3
C11⋊((C13⋊C3)⋊D13)3
C3⋊((C13⋊C3)⋊D13)11
C3×D42913
C3⋊(C11⋊(D13⋊C3))13