Finite Group Databasebeta

← C2×C32×#13133723 #44501865

Subgroups — C2×C32×#13133723 #44501865

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#13133723C211yesmaximal, characteristic, direct product factor, Hall
2C2×C3×#13133723C314yesmaximal, direct product factor
3C2×C32×C11×C31C511yesmaximal, characteristic, complemented, Hall
4C3×#13133723C2×C314yesdirect product factor
5C2×#13133723C3211yescharacteristic, direct product factor, Hall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C2×C32×ΓL(1,𝔽32)—111nomaximal, Hall
8C2×C3×C11×C31C3×C514yescomplemented
9#13133723C2×C3211yescharacteristic, direct product factor, Hall
10C32×ΓL(1,𝔽32)—111noHall
11C3×C11×C31C2×C3×C514yescomplemented
12C2×C32×C11⋊C5—311nomaximal, Hall
13C2×C3×ΓL(1,𝔽32)—114no—
14C2×C11×C31C32×C511yescharacteristic, complemented, Hall
15C2×C32×C31C11⋊C511yescharacteristic, complemented, Hall
16C32×C11⋊C5—311noHall
17C3×ΓL(1,𝔽32)—114no—
18C11×C31C2×C32×C511yescharacteristic, complemented, Hall
19C2×C3×C11⋊C5—314no—
20C2×ΓL(1,𝔽32)—111noHall
21C32×C31C2×C11⋊C511yescharacteristic, complemented, Hall
22C2×C32×C11ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
23C2×C3×C31C3×C11⋊C514yescomplemented
24C3×C11⋊C5—314no—
25ΓL(1,𝔽32)—111noHall
26C2×C11⋊C5—311noHall
27C32×C11C2×ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
28C3×C31C2×C3×C11⋊C514yescomplemented
29C2×C32×C5—3411noHall
30C2×C3×C11C3×ΓL(1,𝔽32)14yescomplemented
31C2×C31C32×C11⋊C511yescharacteristic, complemented, Hall
32C11⋊C5—311noHall
33C32×C5—3411noHall
34C3×C11C2×C3×ΓL(1,𝔽32)14yescomplemented
35C31C2×C32×C11⋊C511yescharacteristic, complemented, Sylow
36C2×C3×C5—3414no—
37C2×C11C32×ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
38C2×C32#1313372311yescharacteristic, direct product factor, Hall
39C3×C5—3414no—
40C11C2×C32×ΓL(1,𝔽32)11yescharacteristic, complemented, Sylow
41C2×C5—3411noHall
42C32C2×#1313372311yescharacteristic, direct product factor, Sylow
43C2×C3C3×#1313372314yesdirect product factor
44C5—3411noSylow
45C3C2×C3×#1313372314yesdirect product factor
46C2C32×#1313372311yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C32#13133723
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C11×C31C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C32

Complements

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

NH ≅ G/Ntype
1. C32×#13133723C2direct (N × H)
2. C2×C3×#13133723C3direct (N × H)
3. C2×C32×C11×C31C5semidirect
4. C3×#13133723C2×C3direct (N × H)
5. C2×#13133723C32direct (N × H)
6. C32×C11×C31C2×C5semidirect
8. C2×C3×C11×C31C3×C5semidirect
9. #13133723C2×C32direct (N × H)
11. C3×C11×C31C2×C3×C5semidirect
14. C2×C11×C31C32×C5semidirect
15. C2×C32×C31C11⋊C5semidirect
18. C11×C31C2×C32×C5semidirect
21. C32×C31C2×C11⋊C5semidirect
22. C2×C32×C11ΓL(1,𝔽32)semidirect
23. C2×C3×C31C3×C11⋊C5semidirect
27. C32×C11C2×ΓL(1,𝔽32)semidirect
28. C3×C31C2×C3×C11⋊C5semidirect
30. C2×C3×C11C3×ΓL(1,𝔽32)semidirect
31. C2×C31C32×C11⋊C5semidirect
34. C3×C11C2×C3×ΓL(1,𝔽32)semidirect
35. C31C2×C32×C11⋊C5semidirect
37. C2×C11C32×ΓL(1,𝔽32)semidirect
38. C2×C32#13133723direct (N × H)
40. C11C2×C32×ΓL(1,𝔽32)semidirect
42. C32C2×#13133723direct (N × H)
43. C2×C3C3×#13133723direct (N × H)
45. C3C2×C3×#13133723direct (N × H)
46. C2C32×#13133723direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#131337232
C2×C3×#131337233
C2×C32×C11×C315
C2×C32×ΓL(1,𝔽32)11
C2×C32×C11⋊C531