Finite Group Databasebeta

← C7×C11×C3⋊D39 #31825083

Subgroups — C7×C11×C3⋊D39 #31825083

Order 18018.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×C13C211yesmaximal, characteristic, complemented, Hall
2C7×C11×D39—34nomaximal
3C3×C7×C11×C13D314yescomplemented
4C11×C3⋊D39C711yesmaximal, characteristic, direct product factor, Hall
5C7×C11×D13—91noHall
6C7×C3⋊D39C1111yesmaximal, characteristic, direct product factor, Hall
7C7×C11×C3⋊D3—131nomaximal, Hall
8C32×C11×C13C2×C711yescharacteristic, complemented, Hall
9C7×C11×C13C3⋊D311yescharacteristic, complemented, Hall
10C11×D39—34no—
11C32×C7×C13C2×C1111yescharacteristic, complemented, Hall
12C32×C7×C11D1311yescharacteristic, complemented, Hall
13C7×D39—34no—
14D3×C7×C11—394no—
15C3×C11×C13D3×C714yescomplemented
16C11×D13—91noHall
17C3×C7×C13D3×C1114yescomplemented
18C3⋊D39C7×C1111yescharacteristic, direct product factor, Hall
19C3×C7×C11D3914yescomplemented
20C11×C3⋊D3—131noHall
21C7×D13—91noHall
22C2×C7×C11—1171noHall
23C11×C13C7×C3⋊D311yescharacteristic, complemented, Hall
24C7×C3⋊D3—131noHall
25C32×C13C2×C7×C1111yescharacteristic, complemented, Hall
26C32×C11C7×D1311yescharacteristic, complemented, Hall
27C7×C13C11×C3⋊D311yescharacteristic, complemented, Hall
28D39—34no—
29C7×C11C3⋊D3911yescharacteristic, direct product factor, Hall
30D3×C11—394no—
31C32×C7C11×D1311yescharacteristic, complemented, Hall
32D3×C7—394no—
33C3×C13D3×C7×C1114yescomplemented
34C3×C11C7×D3914yescomplemented
35D13—91noHall
36C2×C11—1171noHall
37C3×C7C11×D3914yescomplemented
38C3⋊D3—131noHall
39C2×C7—1171noHall
40C13C7×C11×C3⋊D311yescharacteristic, complemented, Sylow
41C11C7×C3⋊D3911yescharacteristic, direct product factor, Sylow
42C32C7×C11×D1311yescharacteristic, complemented, Sylow
43C7C11×C3⋊D3911yescharacteristic, direct product factor, Sylow
44D3—394no—
45C3C7×C11×D3914yescomplemented
46C2—1171noSylow
subgroupG/H
center, hypercenterC7×C11C3⋊D39
commutator, cosocle, hypocenterC32×C13C2×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C32×C13
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×C13C2semidirect
3. C3×C7×C11×C13D3semidirect
4. C11×C3⋊D39C7direct (N × H)
6. C7×C3⋊D39C11direct (N × H)
8. C32×C11×C13C2×C7semidirect
9. C7×C11×C13C3⋊D3semidirect
11. C32×C7×C13C2×C11semidirect
12. C32×C7×C11D13semidirect
15. C3×C11×C13D3×C7semidirect
17. C3×C7×C13D3×C11semidirect
18. C3⋊D39C7×C11direct (N × H)
19. C3×C7×C11D39semidirect
23. C11×C13C7×C3⋊D3semidirect
25. C32×C13C2×C7×C11semidirect
26. C32×C11C7×D13semidirect
27. C7×C13C11×C3⋊D3semidirect
29. C7×C11C3⋊D39direct (N × H)
31. C32×C7C11×D13semidirect
33. C3×C13D3×C7×C11semidirect
34. C3×C11C7×D39semidirect
37. C3×C7C11×D39semidirect
40. C13C7×C11×C3⋊D3semidirect
41. C11C7×C3⋊D39direct (N × H)
42. C32C7×C11×D13semidirect
43. C7C11×C3⋊D39direct (N × H)
45. C3C7×C11×D39semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×C132
C7×C11×D393
C11×C3⋊D397
C7×C3⋊D3911
C7×C11×C3⋊D313