Finite Group Databasebeta

← C3×C7×C3⋊(C11⋊D11) #29503908

Subgroups — C3×C7×C3⋊(C11⋊D11) #29503908

Order 15246.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C112C211yesmaximal, characteristic, complemented, Hall
2C7×C3⋊(C11⋊D11)C311yesmaximal, characteristic, direct product factor
3C3×C7×C11⋊D11—31nomaximal
4C3×C7×C112—21no—
5C3×C7×C112D311yescharacteristic, complemented
6C3×C7×C112C2×C311yescharacteristic, complemented
7C3×C3⋊(C11⋊D11)C711yesmaximal, characteristic, direct product factor, Hall
8C7×C11⋊D11—31noHall
9C3×C7×D33—1112nomaximal
10C32×C112C2×C711yescharacteristic, complemented, Hall
11C7×C112C3×D311yescharacteristic, complemented, Hall
12C3⋊(C11⋊D11)C3×C711yescharacteristic, direct product factor
13C3×C11⋊D11—31no—
14C32×C7×C11D11112yescomplemented
15C7×D33—1112no—
16C3×C7×D11—3312no—
17C3×C112—21no—
18C3×C112D3×C711yescharacteristic, complemented
19C3×C112C2×C3×C711yescharacteristic, complemented
20C11⋊D11—31noHall
21C3×C7×C11—212no—
22C3×C7×C11C3×D11112yescomplemented
23C3×C7×C11D33112yescomplemented
24C3×D33—1112no—
25C7×D11—3312no—
26C3×D3×C7—1211noHall
27C112C3×D3×C711yescharacteristic, complemented, Sylow
28C32×C11C7×D11112yescomplemented
29C7×C11C3×D33112yescomplemented
30D33—1112no—
31C3×D11—3312no—
32C32×C7C11⋊D1111yescharacteristic, complemented, Hall
33C2×C3×C7—3631no—
34D3×C7—1211no—
35C3×C11—212no—
36C3×C11C3×C7×D11112yescomplemented
37C3×C11C7×D33112yescomplemented
38D11—3312no—
39C3×C7—21no—
40C3×C7C3×C11⋊D1111yescharacteristic, complemented
41C3×C7C3⋊(C11⋊D11)11yescharacteristic, direct product factor
42C3×D3—1211noHall
43C2×C7—3631noHall
44C11C3×C7×D33112yescomplemented
45C32C7×C11⋊D1111yescharacteristic, complemented, Sylow
46C7C3×C3⋊(C11⋊D11)11yescharacteristic, direct product factor, Sylow
47C2×C3—3631no—
48D3—1211no—
49C3—21no—
50C3C3×C7×C11⋊D1111yescharacteristic, complemented
51C3C7×C3⋊(C11⋊D11)11yescharacteristic, direct product factor
52C2—3631noSylow
subgroupG/H
center, hypercenterC3×C7C3⋊(C11⋊D11)
commutator, cosocle, hypocenterC3×C112C2×C3×C7
FrattiniC1G
Fitting, socleC32×C7×C112C2
LCSG ▷ C3×C112
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C112C2semidirect
2. C7×C3⋊(C11⋊D11)C3direct (N × H)
5. C3×C7×C112D3semidirect
6. C3×C7×C112C2×C3semidirect
7. C3×C3⋊(C11⋊D11)C7direct (N × H)
10. C32×C112C2×C7semidirect
11. C7×C112C3×D3semidirect
12. C3⋊(C11⋊D11)C3×C7direct (N × H)
14. C32×C7×C11D11semidirect
18. C3×C112D3×C7semidirect
19. C3×C112C2×C3×C7semidirect
22. C3×C7×C11C3×D11semidirect
23. C3×C7×C11D33semidirect
27. C112C3×D3×C7semidirect
28. C32×C11C7×D11semidirect
29. C7×C11C3×D33semidirect
32. C32×C7C11⋊D11semidirect
36. C3×C11C3×C7×D11semidirect
37. C3×C11C7×D33semidirect
40. C3×C7C3×C11⋊D11semidirect
41. C3×C7C3⋊(C11⋊D11)direct (N × H)
44. C11C3×C7×D33semidirect
45. C32C7×C11⋊D11semidirect
46. C7C3×C3⋊(C11⋊D11)direct (N × H)
50. C3C3×C7×C11⋊D11semidirect
51. C3C7×C3⋊(C11⋊D11)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C1122
C7×C3⋊(C11⋊D11)3
C3×C7×C11⋊D113
C3×C3⋊(C11⋊D11)7
C3×C7×D3311