Finite Group Databasebeta

← C7×C3⋊(C3⋊(C11⋊D11)) #29503902

Subgroups — C7×C3⋊(C3⋊(C11⋊D11)) #29503902

Order 15246.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C112C211yesmaximal, characteristic, complemented, Hall
2C7×C3⋊(C11⋊D11)—34nomaximal
3C3×C7×C112D314yescomplemented
4C3⋊(C3⋊(C11⋊D11))C711yesmaximal, characteristic, direct product factor, Hall
5C7×C11⋊D11—91noHall
6C7×C3⋊D33—1112nomaximal
7C32×C112C2×C711yescharacteristic, complemented, Hall
8C7×C112C3⋊D311yescharacteristic, complemented, Hall
9C3⋊(C11⋊D11)—34no—
10C32×C7×C11D11112yescomplemented
11C7×D33—3348no—
12C3×C112D3×C714yescomplemented
13C11⋊D11—91noHall
14C3×C7×C11D33148yescomplemented
15C3⋊D33—1112no—
16C7×D11—9912no—
17C7×C3⋊D3—1211noHall
18C112C7×C3⋊D311yescharacteristic, complemented, Sylow
19C32×C11C7×D11112yescomplemented
20C7×C11C3⋊D33112yescomplemented
21D33—3348no—
22C32×C7C11⋊D1111yescharacteristic, complemented, Hall
23D3×C7—3634no—
24C3×C11C7×D33148yescomplemented
25D11—9912no—
26C3×C7C3⋊(C11⋊D11)14yescomplemented
27C3⋊D3—1211noHall
28C2×C7—10891noHall
29C11C7×C3⋊D33112yescomplemented
30C32C7×C11⋊D1111yescharacteristic, complemented, Sylow
31C7C3⋊(C3⋊(C11⋊D11))11yescharacteristic, direct product factor, Sylow
32D3—3634no—
33C3C7×C3⋊(C11⋊D11)14yescomplemented
34C2—10891noSylow
subgroupG/H
center, hypercenterC7C3⋊(C3⋊(C11⋊D11))
commutator, cosocle, hypocenterC32×C112C2×C7
FrattiniC1G
Fitting, socleC32×C7×C112C2
LCSG ▷ C32×C112
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C112C2semidirect
3. C3×C7×C112D3semidirect
4. C3⋊(C3⋊(C11⋊D11))C7direct (N × H)
7. C32×C112C2×C7semidirect
8. C7×C112C3⋊D3semidirect
10. C32×C7×C11D11semidirect
12. C3×C112D3×C7semidirect
14. C3×C7×C11D33semidirect
18. C112C7×C3⋊D3semidirect
19. C32×C11C7×D11semidirect
20. C7×C11C3⋊D33semidirect
22. C32×C7C11⋊D11semidirect
24. C3×C11C7×D33semidirect
26. C3×C7C3⋊(C11⋊D11)semidirect
29. C11C7×C3⋊D33semidirect
30. C32C7×C11⋊D11semidirect
31. C7C3⋊(C3⋊(C11⋊D11))direct (N × H)
33. C3C7×C3⋊(C11⋊D11)semidirect

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⋊(C3⋊(C11⋊D11))7
C7×C3⋊D3311