Finite Group Databasebeta

← C7×C3⋊D3×C11⋊C5 #20294167

Subgroups — C7×C3⋊D3×C11⋊C5 #20294167

Order 6930.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2D3×C7×C11⋊C5—34nomaximal
3C7×C11×C3⋊D3C511yesmaximal, characteristic, complemented, Hall
4C3×C7×C11⋊C5D314yescomplemented
5C3⋊D3×C11⋊C5C711yesmaximal, characteristic, direct product factor, Hall
6C2×C7×C11⋊C5—91noHall
7C32×C7×C11C2×C511yescharacteristic, complemented, Hall
8C5×C7×C3⋊D3—111nomaximal, Hall
9C32×C11⋊C5C2×C711yescharacteristic, complemented, Hall
10D3×C7×C11—34no—
11C7×C11⋊C5C3⋊D311yescharacteristic, direct product factor, Hall
12D3×C11⋊C5—34no—
13C32×C5×C7—111noHall
14C3×C7×C11C5×D314yescomplemented
15C5×D3×C7—334no—
16C11×C3⋊D3C5×C711yescharacteristic, complemented, Hall
17C3×C11⋊C5D3×C714yescomplemented
18C2×C7×C11—91noHall
19C7×C3⋊D3C11⋊C511yescharacteristic, direct product factor, Hall
20C2×C11⋊C5—91noHall
21C3×C5×C7—114no—
22C32×C11C2×C5×C711yescharacteristic, complemented, Hall
23C5×C3⋊D3—111noHall
24C7×C11C5×C3⋊D311yescharacteristic, complemented, Hall
25C2×C5×C7—991noHall
26D3×C11—34no—
27C32×C7C2×C11⋊C511yescharacteristic, complemented, Hall
28C11⋊C5C7×C3⋊D311yescharacteristic, direct product factor, Hall
29C32×C5—111noHall
30D3×C7—34no—
31C5×C7—111noHall
32C3×C11C5×D3×C714yescomplemented
33C5×D3—334no—
34C2×C11—91noHall
35C3×C7D3×C11⋊C514yescomplemented
36C3⋊D3C7×C11⋊C511yescharacteristic, direct product factor, Hall
37C3×C5—114no—
38C2×C7—91noHall
39C11C5×C7×C3⋊D311yescharacteristic, complemented, Sylow
40C2×C5—991noHall
41C32C2×C7×C11⋊C511yescharacteristic, complemented, Sylow
42C7C3⋊D3×C11⋊C511yescharacteristic, direct product factor, Sylow
43D3—34no—
44C5—111noSylow
45C3D3×C7×C11⋊C514yescomplemented
46C2—91noSylow
subgroupG/H
center, hypercenterC7C3⋊D3×C11⋊C5
commutator, hypocenterC32×C11C2×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C11C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11⋊C5C2semidirect
3. C7×C11×C3⋊D3C5semidirect
4. C3×C7×C11⋊C5D3semidirect
5. C3⋊D3×C11⋊C5C7direct (N × H)
7. C32×C7×C11C2×C5semidirect
9. C32×C11⋊C5C2×C7semidirect
11. C7×C11⋊C5C3⋊D3direct (N × H)
14. C3×C7×C11C5×D3semidirect
16. C11×C3⋊D3C5×C7semidirect
17. C3×C11⋊C5D3×C7semidirect
19. C7×C3⋊D3C11⋊C5direct (N × H)
22. C32×C11C2×C5×C7semidirect
24. C7×C11C5×C3⋊D3semidirect
27. C32×C7C2×C11⋊C5semidirect
28. C11⋊C5C7×C3⋊D3direct (N × H)
32. C3×C11C5×D3×C7semidirect
35. C3×C7D3×C11⋊C5semidirect
36. C3⋊D3C7×C11⋊C5direct (N × H)
39. C11C5×C7×C3⋊D3semidirect
41. C32C2×C7×C11⋊C5semidirect
42. C7C3⋊D3×C11⋊C5direct (N × H)
45. C3D3×C7×C11⋊C5semidirect