Finite Group Databasebeta

← C7×C112×C3⋊D3 #29503904

Subgroups — C7×C112×C3⋊D3 #29503904

Order 15246.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C112C211yesmaximal, characteristic, complemented, Hall
2D3×C7×C112—34nomaximal
3C3×C7×C112D314yescomplemented
4C112×C3⋊D3C711yesmaximal, characteristic, direct product factor, Hall
5C2×C7×C112—91noHall
6C7×C11×C3⋊D3C11112yesmaximal, direct product factor
7C32×C112C2×C711yescharacteristic, complemented, Hall
8C7×C112C3⋊D311yescharacteristic, direct product factor, Hall
9D3×C112—34no—
10C32×C7×C11C2×C11112yescomplemented
11D3×C7×C11—348no—
12C3×C112D3×C714yescomplemented
13C2×C112—91noHall
14C3×C7×C11D3×C11148yescomplemented
15C11×C3⋊D3C7×C11112yesdirect product factor
16C2×C7×C11—912no—
17C7×C3⋊D3C11211yescharacteristic, direct product factor, Hall
18C112C7×C3⋊D311yescharacteristic, direct product factor, Sylow
19C32×C11C2×C7×C11112yescomplemented
20C7×C11C11×C3⋊D3112yesdirect product factor
21D3×C11—348no—
22C32×C7C2×C11211yescharacteristic, complemented, Hall
23D3×C7—34no—
24C3×C11D3×C7×C11148yescomplemented
25C2×C11—912no—
26C3×C7D3×C11214yescomplemented
27C3⋊D3C7×C11211yescharacteristic, direct product factor, Hall
28C2×C7—91noHall
29C11C7×C11×C3⋊D3112yesdirect product factor
30C32C2×C7×C11211yescharacteristic, complemented, Sylow
31C7C112×C3⋊D311yescharacteristic, direct product factor, Sylow
32D3—34no—
33C3D3×C7×C11214yescomplemented
34C2—91noSylow
subgroupG/H
center, hypercenterC7×C112C3⋊D3
commutator, cosocle, hypocenterC32C2×C7×C112
FrattiniC1G
Fitting, socleC32×C7×C112C2
LCSG ▷ C32
UCSC1 ◁ C7×C112

Complements

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

NH ≅ G/Ntype
1. C32×C7×C112C2semidirect
3. C3×C7×C112D3semidirect
4. C112×C3⋊D3C7direct (N × H)
6. C7×C11×C3⋊D3C11direct (N × H)
7. C32×C112C2×C7semidirect
8. C7×C112C3⋊D3direct (N × H)
10. C32×C7×C11C2×C11semidirect
12. C3×C112D3×C7semidirect
14. C3×C7×C11D3×C11semidirect
15. C11×C3⋊D3C7×C11direct (N × H)
17. C7×C3⋊D3C112direct (N × H)
18. C112C7×C3⋊D3direct (N × H)
19. C32×C11C2×C7×C11semidirect
20. C7×C11C11×C3⋊D3direct (N × H)
22. C32×C7C2×C112semidirect
24. C3×C11D3×C7×C11semidirect
26. C3×C7D3×C112semidirect
27. C3⋊D3C7×C112direct (N × H)
29. C11C7×C11×C3⋊D3direct (N × H)
30. C32C2×C7×C112semidirect
31. C7C112×C3⋊D3direct (N × H)
33. C3D3×C7×C112semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C1122
D3×C7×C1123
C112×C3⋊D37
C7×C11×C3⋊D311