Finite Group Databasebeta

← C11×C3⋊#11759818 #45689595

Subgroups — C11×C3⋊#11759818 #45689595

Order 33462.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#92789C211yesmaximal, characteristic, complemented, Hall
2C11×C13×D39C311yesmaximal, characteristic, complemented
3C11×#11759818—31nomaximal
4C11×#92789—21no—
5C11×#92789D311yescharacteristic, complemented
6C3×C11×C132C2×C311yescharacteristic, complemented
7C11×C13×D13—31noHall
8C3⋊#11759818C1111yesmaximal, characteristic, direct product factor, Hall
9D3×C11×C13⋊C3—131nomaximal
10C11×C3⋊(D13⋊C3)—131nomaximal
11C11×C132C3×D311yescharacteristic, complemented, Hall
12C3×#92789C2×C1111yescharacteristic, complemented, Hall
13C3×C11×C13⋊C3—131no—
14C3×C11×C13⋊C3—131no—
15C13×D39C3×C1111yescharacteristic, complemented
16#11759818—31no—
17C11×D39C13⋊C311yescharacteristic, complemented
18D3×C11×C13—131no—
19C2×C11×C13⋊C3—391no—
20C11×D13⋊C3—391no—
21C3×C132C2×C3×C1111yescharacteristic, complemented
22#92789—21no—
23#92789D3×C1111yescharacteristic, 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—31noHall
32C2×C11×C13—391no—
33C11×D13—31no—
34C3⋊(D13⋊C3)—131no—
35D3×C13⋊C3—131no—
36C3×D3×C11—1691noHall
37C132C3×D3×C1111yescharacteristic, 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
44D39C11×C13⋊C311yescharacteristic, complemented
45D3×C13—131no—
46C2×C13⋊C3—391no—
47D13⋊C3—391no—
48C2×C3×C11—5071no—
49D3×C11—131no—
50C3×C13—62no—
51C3×C13C11×D13⋊C311yescharacteristic, complemented
52C3×C13C2×C11×C13⋊C311yescharacteristic, 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—391no—
61D13—31no—
62C2×C11—391noHall
63C3×D3—1691noHall
64C13—62no—
65C13C11×C3⋊(D13⋊C3)11yescharacteristic, complemented
66C13D3×C11×C13⋊C311yescharacteristic, complemented
67C11C3⋊#1175981811yescharacteristic, direct product factor, Sylow
68C32—1691noSylow
69C2×C3—5071no—
70D3—131no—
71C3—3381no—
72C3—1691no—
73C3C11×#1175981811yescharacteristic, complemented
74C2—391noSylow
subgroupG/H
center, hypercenterC11C3⋊#11759818
commutator, cosocle, hypocenterC3×C132C2×C3×C11
FrattiniC1G
Fitting, socleC3×C11×C132C2×C3
LCSG ▷ C3×C132
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×#92789C2semidirect
2. C11×C13×D39C3semidirect
5. C11×#92789D3semidirect
6. C3×C11×C132C2×C3semidirect
8. C3⋊#11759818C11direct (N × H)
11. C11×C132C3×D3semidirect
12. C3×#92789C2×C11semidirect
15. C13×D39C3×C11semidirect
17. C11×D39C13⋊C3semidirect
21. C3×C132C2×C3×C11semidirect
23. #92789D3×C11semidirect
25. C3×C11×C13D13⋊C3semidirect
26. C3×C11×C13C2×C13⋊C3semidirect
37. C132C3×D3×C11semidirect
39. C11×C13D3×C13⋊C3semidirect
40. C11×C13C3⋊(D13⋊C3)semidirect
44. D39C11×C13⋊C3semidirect
51. C3×C13C11×D13⋊C3semidirect
52. C3×C13C2×C11×C13⋊C3semidirect
59. C3×C11#11759818semidirect
65. C13C11×C3⋊(D13⋊C3)semidirect
66. C13D3×C11×C13⋊C3semidirect
67. C11C3⋊#11759818direct (N × H)
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
C11×C13×D393
C11×#117598183
C3⋊#1175981811
D3×C11×C13⋊C313
C11×C3⋊(D13⋊C3)13