Finite Group Databasebeta

← C3×#16811771⋊C2 #35205702

Subgroups — C3×#16811771⋊C2 #35205702

Order 20460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#16811783C211yesmaximal, characteristic, complemented
2C3×#16811777C211yesmaximal, characteristic, complemented
3C3×#16811771C211yesmaximal, characteristic, complemented
4#16811771⋊C2C311yesmaximal, characteristic, direct product factor, Hall
5C3×#13133721C2211yescharacteristic, complemented, Hall
6C3×D11×D31C511yesmaximal, characteristic, complemented, Hall
7#16811783C2×C311yescharacteristic, complemented
8#16811777C2×C311yescharacteristic, complemented
9#16811771C2×C311yescharacteristic, complemented
10C3×D341C2×C511yescharacteristic, complemented
11C3×D11×C31C2×C511yescharacteristic, complemented
12C3×C11×D31C2×C511yescharacteristic, complemented
13C2×C3×D31⋊C5—111nomaximal, Hall
14#13133721C22×C311yescharacteristic, complemented, Hall
15D11×D31C3×C511yescharacteristic, complemented, Hall
16C3×C11×C31C22×C511yescharacteristic, complemented, Hall
17C2×C3×ΓL(1,𝔽32)—111no—
18C3×D31⋊C5—111no—
19C3×D31⋊C5—111no—
20D341C2×C3×C511yescharacteristic, complemented
21C11×D31C2×C3×C511yescharacteristic, complemented
22D11×C31C2×C3×C511yescharacteristic, complemented
23C2×C3×AGL(1,𝔽11)—311nomaximal, Hall
24C2×D31⋊C5—111noHall
25C3×ΓL(1,𝔽32)—111noHall
26C2×C3×D31—551noHall
27C11×C31C22×C3×C511yescharacteristic, complemented, Hall
28C2×C3×C11⋊C5—311no—
29C3×AGL(1,𝔽11)—311no—
30C3×AGL(1,𝔽11)—311no—
31C2×ΓL(1,𝔽32)—111no—
32D31⋊C5—111no—
33D31⋊C5—111no—
34C2×AGL(1,𝔽11)—311noHall
35C2×C3×C31—551no—
36C3×D31—551no—
37C3×D31AGL(1,𝔽11)11yescharacteristic, complemented
38C3×C11⋊C5—311noHall
39ΓL(1,𝔽32)—111noHall
40C2×C3×D11—1551noHall
41C2×D31—551noHall
42C2×C11⋊C5—311no—
43AGL(1,𝔽11)—311no—
44AGL(1,𝔽11)—311no—
45C3×C31C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
46C2×C3×C11—1551no—
47C3×D11—1551no—
48C3×D11D31⋊C511yescharacteristic, complemented
49C2×C31—551no—
50D31—551no—
51D31C3×AGL(1,𝔽11)11yescharacteristic, complemented
52C22×C3×C5—3411noHall
53C11⋊C5—311noHall
54C2×D11—1551noHall
55C3×C11C2×D31⋊C511yescharacteristic, complemented, Hall
56C31C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
57C2×C3×C5—3411no—
58C2×C3×C5—3411no—
59C2×C3×C5—3411no—
60C2×C11—1551no—
61D11—1551no—
62D11C3×D31⋊C511yescharacteristic, complemented
63C22×C5—3411noHall
64C3×C5—3411noHall
65C22×C3—17051noHall
66C11C2×C3×D31⋊C511yescharacteristic, complemented, Sylow
67C2×C5—3411no—
68C2×C5—3411no—
69C2×C5—3411no—
70C2×C3—551no—
71C2×C3—1551no—
72C2×C3—17051no—
73C5—3411noSylow
74C22—17051noSylow
75C3#16811771⋊C211yescharacteristic, direct product factor, Sylow
76C2—551no—
77C2—1551no—
78C2—17051no—
subgroupG/H
center, hypercenterC3#16811771⋊C2
commutator, cosocle, hypocenterC11×C31C22×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C31C22×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#16811783C2semidirect
2. C3×#16811777C2semidirect
3. C3×#16811771C2semidirect
4. #16811771⋊C2C3direct (N × H)
5. C3×#13133721C22semidirect
6. C3×D11×D31C5semidirect
7. #16811783C2×C3semidirect
8. #16811777C2×C3semidirect
9. #16811771C2×C3semidirect
10. C3×D341C2×C5semidirect
11. C3×D11×C31C2×C5semidirect
12. C3×C11×D31C2×C5semidirect
14. #13133721C22×C3semidirect
15. D11×D31C3×C5semidirect
16. C3×C11×C31C22×C5semidirect
20. D341C2×C3×C5semidirect
21. C11×D31C2×C3×C5semidirect
22. D11×C31C2×C3×C5semidirect
27. C11×C31C22×C3×C5semidirect
37. C3×D31AGL(1,𝔽11)semidirect
45. C3×C31C2×AGL(1,𝔽11)semidirect
48. C3×D11D31⋊C5semidirect
51. D31C3×AGL(1,𝔽11)semidirect
55. C3×C11C2×D31⋊C5semidirect
56. C31C2×C3×AGL(1,𝔽11)semidirect
62. D11C3×D31⋊C5semidirect
66. C11C2×C3×D31⋊C5semidirect
75. C3#16811771⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#168117832
C3×#168117772
C3×#168117712
#16811771⋊C23
C3×D11×D315
C2×C3×D31⋊C511
C2×C3×AGL(1,𝔽11)31