Finite Group Databasebeta

← C11×C13⋊C3×D39 #45689591

Subgroups — C11×C13⋊C3×D39 #45689591

Order 33462.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×C13×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11×C13×D39C311yesmaximal, characteristic, complemented
3C11×D13×C13⋊C3—31nomaximal
4C11×C13×C13⋊C3—21no—
5C11×C13×C13⋊C3D311yescharacteristic, complemented
6C3×C11×C132C2×C311yescharacteristic, complemented
7C11×C13×D13—31noHall
8C13⋊C3×D39C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C11×D39—131nomaximal
10D3×C11×C13⋊C3—131nomaximal
11C11×C132C3×D311yescharacteristic, complemented, Hall
12C3×C13×C13⋊C3C2×C1111yescharacteristic, complemented, Hall
13C32×C11×C13—131no—
14C3×C11×C13⋊C3D1311yescharacteristic, complemented
15C13×D39C3×C1111yescharacteristic, complemented
16D13×C13⋊C3—31no—
17C11×D39C13⋊C311yescharacteristic, direct product factor
18D3×C11×C13—131no—
19C3×C11×D13—391no—
20C2×C11×C13⋊C3—391no—
21C3×C132C2×C3×C1111yescharacteristic, complemented
22C13×C13⋊C3—21no—
23C13×C13⋊C3D3×C1111yescharacteristic, complemented
24C3×C11×C13—62no—
25C3×C11×C13—131no—
26C3×C11×C13—261no—
27C3×C11×C13C2×C13⋊C311yescharacteristic, complemented
28C3×C11×C13C3×D1311yescharacteristic, complemented
29C11×C13⋊C3—21no—
30C11×C13⋊C3D3911yescharacteristic, direct product factor
31C13×D13—31noHall
32C2×C11×C13—391no—
33C11×D13—31no—
34C3×D39—131no—
35D3×C13⋊C3—131no—
36C3×D3×C11—1691noHall
37C132C3×D3×C1111yescharacteristic, complemented, Sylow
38C11×C13—62no—
39C11×C13D3×C13⋊C311yescharacteristic, complemented
40C11×C13C3×D3911yescharacteristic, complemented
41C32×C13—131no—
42C3×C13⋊C3C11×D1311yescharacteristic, complemented
43C32×C11—131noHall
44D39C11×C13⋊C311yescharacteristic, direct product factor
45C3×D13—391no—
46D3×C13—131no—
47C2×C13⋊C3—391no—
48C2×C3×C11—5071no—
49D3×C11—131no—
50C3×C13—62no—
51C3×C13—131no—
52C3×C13—261no—
53C3×C13C2×C11×C13⋊C311yescharacteristic, complemented
54C3×C13C3×C11×D1311yescharacteristic, complemented
55C13⋊C3—21no—
56C13⋊C3C11×D3911yescharacteristic, direct product factor
57C3×C11—131no—
58C3×C11—261no—
59C3×C11D13×C13⋊C311yescharacteristic, complemented
60C2×C13—391no—
61D13—31no—
62C2×C11—391noHall
63C3×D3—1691noHall
64C13—62no—
65C13D3×C11×C13⋊C311yescharacteristic, complemented
66C13C3×C11×D3911yescharacteristic, complemented
67C11C13⋊C3×D3911yescharacteristic, direct product factor, Sylow
68C32—131noSylow
69C2×C3—5071no—
70D3—131no—
71C3—131no—
72C3—261no—
73C3C11×D13×C13⋊C311yescharacteristic, complemented
74C2—391noSylow
subgroupG/H
center, hypercenterC11C13⋊C3×D39
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×C13×C13⋊C3C2semidirect
2. C11×C13×D39C3semidirect
5. C11×C13×C13⋊C3D3semidirect
6. C3×C11×C132C2×C3semidirect
8. C13⋊C3×D39C11direct (N × H)
11. C11×C132C3×D3semidirect
12. C3×C13×C13⋊C3C2×C11semidirect
14. C3×C11×C13⋊C3D13semidirect
15. C13×D39C3×C11semidirect
17. C11×D39C13⋊C3direct (N × H)
21. C3×C132C2×C3×C11semidirect
23. C13×C13⋊C3D3×C11semidirect
27. C3×C11×C13C2×C13⋊C3semidirect
28. C3×C11×C13C3×D13semidirect
30. C11×C13⋊C3D39direct (N × H)
37. C132C3×D3×C11semidirect
39. C11×C13D3×C13⋊C3semidirect
40. C11×C13C3×D39semidirect
42. C3×C13⋊C3C11×D13semidirect
44. D39C11×C13⋊C3direct (N × H)
53. C3×C13C2×C11×C13⋊C3semidirect
54. C3×C13C3×C11×D13semidirect
56. C13⋊C3C11×D39direct (N × H)
59. C3×C11D13×C13⋊C3semidirect
65. C13D3×C11×C13⋊C3semidirect
66. C13C3×C11×D39semidirect
67. C11C13⋊C3×D39direct (N × H)
73. C3C11×D13×C13⋊C3semidirect

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
C11×C13×D393
C11×D13×C13⋊C33
C13⋊C3×D3911
C3×C11×D3913
D3×C11×C13⋊C313