Finite Group Databasebeta

← C3⋊(#16811772⋊C3) #44501764

Subgroups — C3⋊(#16811772⋊C3) #44501764

Order 30690.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#13133723⋊C3C211yesmaximal, characteristic, complemented, Hall
2#16811772⋊C3—31nomaximal
3C3⋊#16811772C311yesmaximal, characteristic, complemented
4C11×C3⋊(D31⋊C3)C511yesmaximal, characteristic, complemented, Hall
5#13133723⋊C3—21no—
6#13133723⋊C3D311yescharacteristic, complemented
7C3×#13133723C2×C311yescharacteristic, complemented
8#16811772—31noHall
9C3×C11×C31⋊C3C2×C511yescharacteristic, complemented, Hall
10C3⋊AGL(1,𝔽31)—111nomaximal, Hall
11C11×D31⋊C3—31no—
12C11×D93C3×C511yescharacteristic, complemented
13#13133723C3×D311yescharacteristic, complemented, Hall
14C3×(C31⋊C3)⋊C5—111noHall
15C3×C11×C31C2×C3×C511yescharacteristic, complemented
16C11×C31⋊C3—21no—
17C11×C31⋊C3C5×D311yescharacteristic, complemented
18C3×D3×C11⋊C5—311nomaximal, Hall
19C3⋊(D31⋊C5)—111no—
20AGL(1,𝔽31)—331no—
21C11×D31—31noHall
22C3⋊(D31⋊C3)C11⋊C511yescharacteristic, complemented, Hall
23C32×C11⋊C5—311noHall
24C3×ΓL(1,𝔽32)—111no—
25(C31⋊C3)⋊C5—111no—
26(C31⋊C3)⋊C5—221no—
27C11×C31C3×C5×D311yescharacteristic, complemented, Hall
28C2×C3×C11⋊C5—931no—
29D3×C11⋊C5—311no—
30D31⋊C5—331noHall
31C3×C31⋊C3C2×C11⋊C511yescharacteristic, complemented, Hall
32C3×D3×C11—311noHall
33D93C3×C11⋊C511yescharacteristic, complemented
34D31⋊C3—31no—
35C3×C11⋊C5—311no—
36C3×C11⋊C5—311no—
37C3×C11⋊C5—621no—
38ΓL(1,𝔽32)—111noHall
39C2×C11⋊C5—931noHall
40C32×C11—311noHall
41C3×C31C2×C3×C11⋊C511yescharacteristic, complemented
42C31⋊C3—21no—
43C31⋊C3D3×C11⋊C511yescharacteristic, complemented
44C3×C5×D3—3411noHall
45C2×C3×C11—931no—
46D3×C11—311no—
47D31—31noHall
48C11⋊C5—311noHall
49C32×C5—3411noHall
50C3×C11—311no—
51C3×C11—621no—
52C3×C11AGL(1,𝔽31)11yescharacteristic, complemented
53C31C3×D3×C11⋊C511yescharacteristic, complemented, Sylow
54C2×C3×C5—10231no—
55C5×D3—3411no—
56C2×C11—931noHall
57C3×D3—311noHall
58C3×C5—3411no—
59C3×C5—3411no—
60C3×C5—6821no—
61C11C3⋊AGL(1,𝔽31)11yescharacteristic, complemented, Sylow
62C2×C5—10231noHall
63C32—311noSylow
64C2×C3—931no—
65D3—311no—
66C5—3411noSylow
67C3—311no—
68C3—621no—
69C3#16811772⋊C311yescharacteristic, complemented
70C2—931noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C31C2×C3×C5
LCSG ▷ C3×C11×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#13133723⋊C3C2semidirect
3. C3⋊#16811772C3semidirect
4. C11×C3⋊(D31⋊C3)C5semidirect
6. #13133723⋊C3D3semidirect
7. C3×#13133723C2×C3semidirect
9. C3×C11×C31⋊C3C2×C5semidirect
12. C11×D93C3×C5semidirect
13. #13133723C3×D3semidirect
15. C3×C11×C31C2×C3×C5semidirect
17. C11×C31⋊C3C5×D3semidirect
22. C3⋊(D31⋊C3)C11⋊C5semidirect
27. C11×C31C3×C5×D3semidirect
31. C3×C31⋊C3C2×C11⋊C5semidirect
33. D93C3×C11⋊C5semidirect
41. C3×C31C2×C3×C11⋊C5semidirect
43. C31⋊C3D3×C11⋊C5semidirect
52. C3×C11AGL(1,𝔽31)semidirect
53. C31C3×D3×C11⋊C5semidirect
61. C11C3⋊AGL(1,𝔽31)semidirect
69. C3#16811772⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#13133723⋊C32
#16811772⋊C33
C3⋊#168117723
C11×C3⋊(D31⋊C3)5
C3⋊AGL(1,𝔽31)11
C3×D3×C11⋊C531