Finite Group Databasebeta

← C3⋊(C11⋊#11759818) #45689606

Subgroups — C3⋊(C11⋊#11759818) #45689606

Order 33462.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#92789C211yesmaximal, characteristic, complemented, Hall
2C13×D429C311yesmaximal, characteristic, complemented
3C11⋊#11759818—31nomaximal
4C11×#92789—21no—
5C11×#92789D311yescharacteristic, complemented
6C3×C11×C132C2×C311yescharacteristic, complemented
7C13×D143—31noHall
8C3⋊#11759818—111nomaximal, Hall
9C13⋊C3×D33—131nomaximal
10C3⋊(C11⋊(D13⋊C3))—131nomaximal
11C11×C132C3×D311yescharacteristic, complemented, Hall
12C3×#92789D1111yescharacteristic, complemented, Hall
13C3×C11×C13⋊C3—131no—
14C3×C11×C13⋊C3—131no—
15C13×D39—111no—
16#11759818—331no—
17D429C13⋊C311yescharacteristic, complemented
18C13×D33—131no—
19C11⋊(D13⋊C3)—391no—
20D11×C13⋊C3—391no—
21C3×C132C3×D1111yescharacteristic, complemented
22#92789—21no—
23#92789D3311yescharacteristic, complemented
24C3×C11×C13—62no—
25C3×C11×C13D13⋊C311yescharacteristic, complemented
26C3×C11×C13C2×C13⋊C311yescharacteristic, complemented
27C11×C13⋊C3—131no—
28C11×C13⋊C3—131no—
29C11×C13⋊C3—261no—
30C11×C13⋊C3—261no—
31C13×D13—331noHall
32D143—31no—
33C13×D11—391no—
34C3⋊(D13⋊C3)—1431no—
35D3×C13⋊C3—1431no—
36C3×D33—1691noHall
37C132C3×D3311yescharacteristic, complemented, Sylow
38C11×C13—62no—
39C11×C13D3×C13⋊C311yescharacteristic, complemented
40C11×C13C3⋊(D13⋊C3)11yescharacteristic, complemented
41C3×C13⋊C3—131no—
42C3×C13⋊C3—131no—
43C32×C11—1691noHall
44D39—111no—
45D3×C13—1431no—
46C2×C13⋊C3—4291no—
47D13⋊C3—4291no—
48D33—131no—
49C3×D11—5071no—
50C3×C13—62no—
51C3×C13D11×C13⋊C311yescharacteristic, complemented
52C3×C13C11⋊(D13⋊C3)11yescharacteristic, complemented
53C13⋊C3—131no—
54C13⋊C3—131no—
55C13⋊C3—261no—
56C13⋊C3—261no—
57C3×C11—3381no—
58C3×C11—1691no—
59C3×C11#1175981811yescharacteristic, complemented
60C2×C13—4291no—
61D13—331no—
62D11—391noHall
63C3×D3—18591noHall
64C13—62no—
65C13C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented
66C13C13⋊C3×D3311yescharacteristic, complemented
67C11C3⋊#1175981811yescharacteristic, complemented, Sylow
68C32—1691noSylow
69C2×C3—55771no—
70D3—1431no—
71C3—3381no—
72C3—1691no—
73C3C11⋊#1175981811yescharacteristic, complemented
74C2—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×#92789C2semidirect
2. C13×D429C3semidirect
5. C11×#92789D3semidirect
6. C3×C11×C132C2×C3semidirect
11. C11×C132C3×D3semidirect
12. C3×#92789D11semidirect
17. D429C13⋊C3semidirect
21. C3×C132C3×D11semidirect
23. #92789D33semidirect
25. C3×C11×C13D13⋊C3semidirect
26. C3×C11×C13C2×C13⋊C3semidirect
37. C132C3×D33semidirect
39. C11×C13D3×C13⋊C3semidirect
40. C11×C13C3⋊(D13⋊C3)semidirect
51. C3×C13D11×C13⋊C3semidirect
52. C3×C13C11⋊(D13⋊C3)semidirect
59. C3×C11#11759818semidirect
65. C13C3⋊(C11⋊(D13⋊C3))semidirect
66. C13C13⋊C3×D33semidirect
67. C11C3⋊#11759818semidirect
73. C3C11⋊#11759818semidirect

Maximal subgroups

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

subgroupindex
C3×C11×#927892
C13×D4293
C11⋊#117598183
C3⋊#1175981811
C13⋊C3×D3313
C3⋊(C11⋊(D13⋊C3))13