Finite Group Databasebeta

← C3⋊(C11⋊#11759817) #45689605

Subgroups — C3⋊(C11⋊#11759817) #45689605

Order 33462.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#92788C211yesmaximal, characteristic, complemented, Hall
2C13×D429C311yesmaximal, characteristic, complemented
3C11⋊#11759817—31nomaximal
4C11×#92788—21no—
5C11×#92788D311yescharacteristic, complemented
6C3×C11×C132C2×C311yescharacteristic, complemented
7C13×D143—31noHall
8C3⋊#11759817—111nomaximal, Hall
9C13⋊C3×D33—131nomaximal
10C3⋊(C11⋊(D13⋊C3))—131nomaximal
11C11×C132C3×D311yescharacteristic, complemented, Hall
12C3×#92788D1111yescharacteristic, complemented, Hall
13C3×C11×C13⋊C3—131no—
14C3×C11×C13⋊C3—131no—
15C3×C11×C13⋊C3—266no—
16C13×D39—111no—
17#11759817—331no—
18D429C13⋊C311yescharacteristic, complemented
19C13×D33—131no—
20C11⋊(D13⋊C3)—391no—
21D11×C13⋊C3—391no—
22C3×C132C3×D1111yescharacteristic, complemented
23#92788—21no—
24#92788D3311yescharacteristic, complemented
25C3×C11×C13—26no—
26C3×C11×C13D13⋊C311yescharacteristic, complemented
27C3×C11×C13C2×C13⋊C311yescharacteristic, complemented
28C11×C13⋊C3—131no—
29C11×C13⋊C3—131no—
30C11×C13⋊C3—2612no—
31C11×C13⋊C3—266no—
32C11×C13⋊C3—261no—
33C11×C13⋊C3—261no—
34C13×D13—331noHall
35D143—31no—
36C13×D11—391no—
37C3⋊(D13⋊C3)—1431no—
38D3×C13⋊C3—1431no—
39C3×D33—1691noHall
40C132C3×D3311yescharacteristic, complemented, Sylow
41C11×C13—26no—
42C11×C13D3×C13⋊C311yescharacteristic, complemented
43C11×C13C3⋊(D13⋊C3)11yescharacteristic, complemented
44C3×C13⋊C3—131no—
45C3×C13⋊C3—131no—
46C3×C13⋊C3—266no—
47C32×C11—1691noHall
48D39—111no—
49D3×C13—1431no—
50C2×C13⋊C3—4291no—
51D13⋊C3—4291no—
52D33—131no—
53C3×D11—5071no—
54C3×C13—26no—
55C3×C13D11×C13⋊C311yescharacteristic, complemented
56C3×C13C11⋊(D13⋊C3)11yescharacteristic, complemented
57C13⋊C3—131no—
58C13⋊C3—131no—
59C13⋊C3—2612no—
60C13⋊C3—261no—
61C13⋊C3—261no—
62C13⋊C3—266no—
63C3×C11—3381no—
64C3×C11—1691no—
65C3×C11#1175981711yescharacteristic, complemented
66C2×C13—4291no—
67D13—331no—
68D11—391noHall
69C3×D3—18591noHall
70C13—26no—
71C13C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented
72C13C13⋊C3×D3311yescharacteristic, complemented
73C11C3⋊#1175981711yescharacteristic, complemented, Sylow
74C32—1691noSylow
75C2×C3—55771no—
76D3—1431no—
77C3—3381no—
78C3—1691no—
79C3C11⋊#1175981711yescharacteristic, complemented
80C2—4291noSylow
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×#92788C2semidirect
2. C13×D429C3semidirect
5. C11×#92788D3semidirect
6. C3×C11×C132C2×C3semidirect
11. C11×C132C3×D3semidirect
12. C3×#92788D11semidirect
18. D429C13⋊C3semidirect
22. C3×C132C3×D11semidirect
24. #92788D33semidirect
26. C3×C11×C13D13⋊C3semidirect
27. C3×C11×C13C2×C13⋊C3semidirect
40. C132C3×D33semidirect
42. C11×C13D3×C13⋊C3semidirect
43. C11×C13C3⋊(D13⋊C3)semidirect
55. C3×C13D11×C13⋊C3semidirect
56. C3×C13C11⋊(D13⋊C3)semidirect
65. C3×C11#11759817semidirect
71. C13C3⋊(C11⋊(D13⋊C3))semidirect
72. C13C13⋊C3×D33semidirect
73. C11C3⋊#11759817semidirect
79. C3C11⋊#11759817semidirect

Maximal subgroups

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

subgroupindex
C3×C11×#927882
C13×D4293
C11⋊#117598173
C3⋊#1175981711
C13⋊C3×D3313
C3⋊(C11⋊(D13⋊C3))13