Finite Group Databasebeta

← C3×C11×#11759818 #45689574

Subgroups — C3×C11×#11759818 #45689574

Order 33462.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#92789C211yesmaximal, characteristic, complemented, Hall
2C3×C11×C13×D13C311yesmaximal, characteristic, complemented
3C11×#11759818C313yesmaximal, direct product factor
4C11×#92789C2×C313yescomplemented
5C3×C11×C132C2×C311yescharacteristic, complemented
6C11×C13×D13C3211yescharacteristic, complemented, Hall
7C3×#11759818C1111yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C11×C13⋊C3—131nomaximal
9C3×C11×D13⋊C3—131nomaximal
10C11×C132C2×C3211yescharacteristic, complemented, Hall
11C3×#92789C2×C1111yescharacteristic, complemented, Hall
12C3×C11×C13⋊C3—131no—
13C3×C11×C13⋊C3—131no—
14C3×C13×D13C3×C1111yescharacteristic, complemented
15#11759818C3×C1113yesdirect product factor
16C2×C3×C11×C13—131no—
17C3×C11×D13C13⋊C311yescharacteristic, complemented
18C2×C11×C13⋊C3—133no—
19C11×D13⋊C3—133no—
20C3×C132C2×C3×C1111yescharacteristic, complemented
21#92789C2×C3×C1113yescomplemented
22C3×C11×C13—62no—
23C3×C11×C13D13⋊C311yescharacteristic, complemented
24C3×C11×C13C2×C13⋊C311yescharacteristic, complemented
25C11×C13⋊C3—133no—
26C11×C13⋊C3—133no—
27C13×D13C32×C1111yescharacteristic, complemented, Hall
28C2×C11×C13—131no—
29C11×D13C3×C13⋊C311yescharacteristic, complemented
30C2×C3×C13⋊C3—131no—
31C3×D13⋊C3—131no—
32C2×C32×C11—1691noHall
33C132C2×C32×C1111yescharacteristic, complemented, Sylow
34C11×C13—62no—
35C11×C13C3×D13⋊C311yescharacteristic, complemented
36C11×C13C2×C3×C13⋊C311yescharacteristic, complemented
37C3×C13⋊C3—131no—
38C3×C13⋊C3—131no—
39C32×C11—1691noHall
40C2×C3×C13—131no—
41C3×D13C11×C13⋊C311yescharacteristic, complemented
42C2×C13⋊C3—133no—
43D13⋊C3—133no—
44C2×C3×C11—131no—
45C2×C3×C11—1693no—
46C3×C13—62no—
47C3×C13C11×D13⋊C311yescharacteristic, complemented
48C3×C13C2×C11×C13⋊C311yescharacteristic, complemented
49C13⋊C3—133no—
50C13⋊C3—133no—
51C3×C11—1693no—
52C3×C11#1175981811yescharacteristic, direct product factor
53C2×C13—131no—
54D13C3×C11×C13⋊C311yescharacteristic, complemented
55C2×C11—131noHall
56C2×C32—1691noHall
57C13—62no—
58C13C3×C11×D13⋊C311yescharacteristic, complemented
59C13C2×C3×C11×C13⋊C311yescharacteristic, complemented
60C11C3×#1175981811yescharacteristic, direct product factor, Sylow
61C32—1691noSylow
62C2×C3—131no—
63C2×C3—1693no—
64C3—1693no—
65C3C11×#1175981811yescharacteristic, direct product factor
66C2—131noSylow
subgroupG/H
center, hypercenterC3×C11#11759818
commutator, cosocle, hypocenterC132C2×C32×C11
FrattiniC1G
Fitting, socleC3×C11×C132C2×C3
LCSG ▷ C132
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×#92789C2semidirect
2. C3×C11×C13×D13C3semidirect
3. C11×#11759818C3direct (N × H)
4. C11×#92789C2×C3semidirect
5. C3×C11×C132C2×C3semidirect
6. C11×C13×D13C32semidirect
7. C3×#11759818C11direct (N × H)
10. C11×C132C2×C32semidirect
11. C3×#92789C2×C11semidirect
14. C3×C13×D13C3×C11semidirect
15. #11759818C3×C11direct (N × H)
17. C3×C11×D13C13⋊C3semidirect
20. C3×C132C2×C3×C11semidirect
21. #92789C2×C3×C11semidirect
23. C3×C11×C13D13⋊C3semidirect
24. C3×C11×C13C2×C13⋊C3semidirect
27. C13×D13C32×C11semidirect
29. C11×D13C3×C13⋊C3semidirect
33. C132C2×C32×C11semidirect
35. C11×C13C3×D13⋊C3semidirect
36. C11×C13C2×C3×C13⋊C3semidirect
41. C3×D13C11×C13⋊C3semidirect
47. C3×C13C11×D13⋊C3semidirect
48. C3×C13C2×C11×C13⋊C3semidirect
52. C3×C11#11759818direct (N × H)
54. D13C3×C11×C13⋊C3semidirect
58. C13C3×C11×D13⋊C3semidirect
59. C13C2×C3×C11×C13⋊C3semidirect
60. C11C3×#11759818direct (N × H)
65. C3C11×#11759818direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×#927892
C3×C11×C13×D133
C11×#117598183
C3×#1175981811
C2×C3×C11×C13⋊C313
C3×C11×D13⋊C313