Finite Group Databasebeta

← C3×C11×C5⋊AGL(1,𝔽11) #31827632

Subgroups — C3×C11×C5⋊AGL(1,𝔽11) #31827632

Order 18150.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C11×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C11×C5⋊AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
3C3×C11×D55C511yesmaximal, characteristic, complemented
4C3×C11×AGL(1,𝔽11)—51nomaximal
5C5×C11×C11⋊C5C2×C311yescharacteristic, complemented, Hall
6C3×C5×C112C2×C511yescharacteristic, complemented
7C3×C11×C11⋊C5—22no—
8C3×C11×C11⋊C5D511yescharacteristic, complemented
9C3×C5×D5×C11—111nomaximal
10C3×C5⋊AGL(1,𝔽11)C1111yesmaximal, characteristic, direct product factor
11C11×D55C3×C511yescharacteristic, complemented
12C11×AGL(1,𝔽11)—51no—
13C3×C52×C11—111no—
14C3×C5×C11⋊C5C2×C1111yescharacteristic, complemented
15C3×C11×D11—51noHall
16C5×C112C2×C3×C511yescharacteristic, complemented
17C11×C11⋊C5—22no—
18C11×C11⋊C5C3×D511yescharacteristic, complemented
19C5×D5×C11—111no—
20C5⋊AGL(1,𝔽11)C3×C1111yescharacteristic, direct product factor
21C3×C112C5×D511yescharacteristic, complemented, Hall
22C2×C3×C5×C11—551no—
23C3×D55C5×C1111yescharacteristic, complemented
24C3×D5×C11—111no—
25C3×AGL(1,𝔽11)—51no—
26C52×C11—111no—
27C5×C11⋊C5C2×C3×C1111yescharacteristic, complemented
28C11×D11—51noHall
29C3×C5×C11—101no—
30C3×C5×C11—111no—
31C3×C5×C11—222no—
32C3×C5×C11AGL(1,𝔽11)11yescharacteristic, complemented
33C3×C5×C11C2×C5×C1111yescharacteristic, complemented
34C3×C11⋊C5—22no—
35C3×C11⋊C5D5×C1111yescharacteristic, complemented
36C3×C5×D5—111noHall
37C112C3×C5×D511yescharacteristic, complemented, Sylow
38C2×C5×C11—551no—
39D55C3×C5×C1111yescharacteristic, complemented
40D5×C11—111no—
41AGL(1,𝔽11)—51no—
42C3×C52—111noHall
43C2×C3×C11—551no—
44C3×D11—51no—
45C5×C11—101no—
46C5×C11—111no—
47C5×C11—222no—
48C5×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
49C5×C11C2×C3×C5×C1111yescharacteristic, complemented
50C11⋊C5—22no—
51C11⋊C5C3×D5×C1111yescharacteristic, complemented
52C5×D5—111noHall
53C3×C11—101no—
54C3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
55C3×C11C5×D5×C1111yescharacteristic, complemented
56C2×C3×C5—551no—
57C3×D5—111no—
58C52—111noSylow
59C2×C11—551no—
60D11—51no—
61C3×C5—111no—
62C3×C5—222no—
63C3×C5C11×AGL(1,𝔽11)11yescharacteristic, complemented
64C11—101no—
65C11C3×C5⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
66C11C3×C5×D5×C1111yescharacteristic, complemented
67C2×C5—551no—
68D5—111no—
69C2×C3—551noHall
70C5—111no—
71C5—222no—
72C5C3×C11×AGL(1,𝔽11)11yescharacteristic, complemented
73C3C11×C5⋊AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
74C2—551noSylow
subgroupG/H
center, hypercenterC3×C11C5⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C11⋊C5C2semidirect
2. C11×C5⋊AGL(1,𝔽11)C3direct (N × H)
3. C3×C11×D55C5semidirect
5. C5×C11×C11⋊C5C2×C3semidirect
6. C3×C5×C112C2×C5semidirect
8. C3×C11×C11⋊C5D5semidirect
10. C3×C5⋊AGL(1,𝔽11)C11direct (N × H)
11. C11×D55C3×C5semidirect
14. C3×C5×C11⋊C5C2×C11semidirect
16. C5×C112C2×C3×C5semidirect
18. C11×C11⋊C5C3×D5semidirect
20. C5⋊AGL(1,𝔽11)C3×C11direct (N × H)
21. C3×C112C5×D5semidirect
23. C3×D55C5×C11semidirect
27. C5×C11⋊C5C2×C3×C11semidirect
32. C3×C5×C11AGL(1,𝔽11)semidirect
33. C3×C5×C11C2×C5×C11semidirect
35. C3×C11⋊C5D5×C11semidirect
37. C112C3×C5×D5semidirect
39. D55C3×C5×C11semidirect
48. C5×C11C3×AGL(1,𝔽11)semidirect
49. C5×C11C2×C3×C5×C11semidirect
51. C11⋊C5C3×D5×C11semidirect
54. C3×C11C5⋊AGL(1,𝔽11)direct (N × H)
55. C3×C11C5×D5×C11semidirect
63. C3×C5C11×AGL(1,𝔽11)semidirect
65. C11C3×C5⋊AGL(1,𝔽11)direct (N × H)
66. C11C3×C5×D5×C11semidirect
72. C5C3×C11×AGL(1,𝔽11)semidirect
73. C3C11×C5⋊AGL(1,𝔽11)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C11×C11⋊C52
C11×C5⋊AGL(1,𝔽11)3
C3×C11×D555
C3×C11×AGL(1,𝔽11)5
C3×C5×D5×C1111
C3×C5⋊AGL(1,𝔽11)11