Finite Group Databasebeta

← C32×#16811771 #44501790

Subgroups — C32×#16811771 #44501790

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#13133721C211yesmaximal, characteristic, complemented, Hall
2C3×#16811771C314yesmaximal, direct product factor
3C32×C11×D31C511yesmaximal, characteristic, complemented, Hall
4C3×#13133721C2×C314yescomplemented
5#16811771C3211yescharacteristic, direct product factor, Hall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C32×D31⋊C5—111nomaximal, Hall
8C3×C11×D31C3×C514yescomplemented
9#13133721C2×C3211yescharacteristic, complemented, Hall
10C32×ΓL(1,𝔽32)—111noHall
11C3×C11×C31C2×C3×C514yescomplemented
12C2×C32×C11⋊C5—311nomaximal, Hall
13C3×D31⋊C5—114no—
14C11×D31C32×C511yescharacteristic, complemented, Hall
15C32×D31C11⋊C511yescharacteristic, complemented, Hall
16C32×C11⋊C5—311noHall
17C3×ΓL(1,𝔽32)—114no—
18C11×C31C2×C32×C511yescharacteristic, complemented, Hall
19C2×C3×C11⋊C5—314no—
20D31⋊C5—111noHall
21C32×C31C2×C11⋊C511yescharacteristic, complemented, Hall
22C2×C32×C11—311noHall
23C3×D31C3×C11⋊C514yescomplemented
24C3×C11⋊C5—314no—
25ΓL(1,𝔽32)—111noHall
26C2×C11⋊C5—311noHall
27C32×C11D31⋊C511yescharacteristic, complemented, Hall
28C3×C31C2×C3×C11⋊C514yescomplemented
29C2×C32×C5—3411noHall
30C2×C3×C11—314no—
31D31C32×C11⋊C511yescharacteristic, complemented, Hall
32C11⋊C5—311noHall
33C32×C5—3411noHall
34C3×C11C3×D31⋊C514yescomplemented
35C31C2×C32×C11⋊C511yescharacteristic, complemented, Sylow
36C2×C3×C5—3414no—
37C2×C11—311noHall
38C2×C32—311noHall
39C3×C5—3414no—
40C11C32×D31⋊C511yescharacteristic, complemented, Sylow
41C2×C5—3411noHall
42C32#1681177111yescharacteristic, direct product factor, Sylow
43C2×C3—314no—
44C5—3411noSylow
45C3C3×#1681177114yesdirect product factor
46C2—311noSylow
subgroupG/H
center, hypercenterC32#16811771
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×#13133721C2semidirect
2. C3×#16811771C3direct (N × H)
3. C32×C11×D31C5semidirect
4. C3×#13133721C2×C3semidirect
5. #16811771C32direct (N × H)
6. C32×C11×C31C2×C5semidirect
8. C3×C11×D31C3×C5semidirect
9. #13133721C2×C32semidirect
11. C3×C11×C31C2×C3×C5semidirect
14. C11×D31C32×C5semidirect
15. C32×D31C11⋊C5semidirect
18. C11×C31C2×C32×C5semidirect
21. C32×C31C2×C11⋊C5semidirect
23. C3×D31C3×C11⋊C5semidirect
27. C32×C11D31⋊C5semidirect
28. C3×C31C2×C3×C11⋊C5semidirect
31. D31C32×C11⋊C5semidirect
34. C3×C11C3×D31⋊C5semidirect
35. C31C2×C32×C11⋊C5semidirect
40. C11C32×D31⋊C5semidirect
42. C32#16811771direct (N × H)
45. C3C3×#16811771direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#131337212
C3×#168117713
C32×C11×D315
C32×D31⋊C511
C2×C32×C11⋊C531