Finite Group Databasebeta

← C9×#16811785 #44501679

Subgroups — C9×#16811785 #44501679

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#13133722C211yesmaximal, characteristic, complemented, Hall
2C3×#16811785C311yesmaximal, characteristic
3C9×D341C511yesmaximal, characteristic, complemented, Hall
4C3×#13133722C2×C311yescharacteristic
5#16811785C911yescharacteristic, direct product factor, Hall
6C9×C11×C31C2×C511yescharacteristic, complemented, Hall
7C9×D31⋊C5—111nomaximal, Hall
8C3×D341C3×C511yescharacteristic
9#13133722C2×C911yescharacteristic, complemented, Hall
10C9×ΓL(1,𝔽32)—111noHall
11C3×C11×C31C2×C3×C511yescharacteristic
12C9×AGL(1,𝔽11)—311nomaximal, Hall
13C3×D31⋊C5—111no—
14D341C5×C911yescharacteristic, complemented, Hall
15C9×D31—111noHall
16C9×C11⋊C5—311noHall
17C3×ΓL(1,𝔽32)—111no—
18C11×C31C2×C5×C911yescharacteristic, complemented, Hall
19C3×AGL(1,𝔽11)—311no—
20D31⋊C5—111noHall
21C9×C31AGL(1,𝔽11)11yescharacteristic, complemented, Hall
22C9×D11—311noHall
23C3×D31—111no—
24C3×C11⋊C5—311no—
25ΓL(1,𝔽32)—111noHall
26AGL(1,𝔽11)—311noHall
27C9×C11D31⋊C511yescharacteristic, complemented, Hall
28C3×C31C3×AGL(1,𝔽11)11yescharacteristic
29C2×C5×C9—3411noHall
30C3×D11—311no—
31D31—111noHall
32C11⋊C5—311noHall
33C5×C9—3411noHall
34C3×C11C3×D31⋊C511yescharacteristic
35C31C9×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
36C2×C3×C5—3411no—
37D11—311noHall
38C2×C9—3411noHall
39C3×C5—3411no—
40C11C9×D31⋊C511yescharacteristic, complemented, Sylow
41C2×C5—3411noHall
42C9#1681178511yescharacteristic, direct product factor, Sylow
43C2×C3—3411no—
44C5—3411noSylow
45C3C3×#1681178511yescharacteristic
46C2—3411noSylow
subgroupG/H
center, hypercenterC9#16811785
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C3×#16811785
FittingC9×C11×C31C2×C5
socle, cosocleC3×C11×C31C2×C3×C5
prime radicalC3×#16811785C3
LCSG ▷ C11×C31
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C9×#13133722C2semidirect
3. C9×D341C5semidirect
5. #16811785C9direct (N × H)
6. C9×C11×C31C2×C5semidirect
9. #13133722C2×C9semidirect
14. D341C5×C9semidirect
18. C11×C31C2×C5×C9semidirect
21. C9×C31AGL(1,𝔽11)semidirect
27. C9×C11D31⋊C5semidirect
35. C31C9×AGL(1,𝔽11)semidirect
40. C11C9×D31⋊C5semidirect
42. C9#16811785direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#131337222
C3×#168117853
C9×D3415
C9×D31⋊C511
C9×AGL(1,𝔽11)31