Finite Group Databasebeta

← C2×C3⋊(C17⋊AGL(1,𝔽11)) #26014366

Subgroups — C2×C3⋊(C17⋊AGL(1,𝔽11)) #26014366

Order 11220.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C17⋊AGL(1,𝔽11))C212yesmaximal, direct product factor
2C2×C3×C17×C11⋊C5C211yesmaximal, characteristic, complemented
3C2×C17⋊AGL(1,𝔽11)—31nomaximal, Hall
4C3×C17×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×D561C511yesmaximal, characteristic, complemented, Hall
6C2×C17×C11⋊C5D311yescharacteristic, complemented
7C17⋊AGL(1,𝔽11)—32no—
8C2×C3×C11×C17C2×C511yescharacteristic, complemented
9D561C2×C512yescomplemented
10C2×C5×D51—111nomaximal, Hall
11C17×C11⋊C5C2×D311yescharacteristic, complemented, Hall
12C2×D187—31noHall
13C2×C3⋊AGL(1,𝔽11)—171nomaximal, Hall
14C3×C11×C17C22×C511yescharacteristic, complemented, Hall
15C2×C3×C5×C17—111no—
16C5×D51—112no—
17C2×C11×C17C5×D311yescharacteristic, complemented
18D187—32no—
19C2×C5×D17—331noHall
20C2×C3×C11⋊C5D1711yescharacteristic, complemented
21C3⋊AGL(1,𝔽11)—172no—
22C3×C5×C17—111noHall
23C2×AGL(1,𝔽11)—511noHall
24C2×D51—111noHall
25C11×C17C2×C5×D311yescharacteristic, complemented, Hall
26C2×C5×C17—111no—
27C5×D17—332no—
28C3×C11⋊C5C2×D1711yescharacteristic, complemented, Hall
29C2×D33—171noHall
30C2×C11⋊C5D5111yescharacteristic, complemented
31AGL(1,𝔽11)—512no—
32C2×C3×C17AGL(1,𝔽11)11yescharacteristic, complemented
33D51—112no—
34C5×C17—111noHall
35C2×D17—331noHall
36C2×C3×C11C5×D1711yescharacteristic, complemented
37D33—172no—
38C2×C5×D3—1871noHall
39C11⋊C5C2×D5111yescharacteristic, complemented, Hall
40C3×C17C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
41C2×D11—511noHall
42C2×C17C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
43D17—332no—
44C3×C11C2×C5×D1711yescharacteristic, complemented, Hall
45C2×C3×C5—111no—
46C5×D3—1872no—
47C2×C11C5×D5111yescharacteristic, complemented
48D11—512no—
49C22×C5—5611noHall
50C17C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
51C3×C5—111noHall
52C2×D3—1871noHall
53C11C2×C5×D5111yescharacteristic, complemented, Sylow
54C2×C5—111no—
55C2×C5—5612no—
56C2×C3C17⋊AGL(1,𝔽11)11yescharacteristic, complemented
57D3—1872no—
58C5—111noSylow
59C22—5611noSylow
60C3C2×C17⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
61C2—5612no—
62C2C3⋊(C17⋊AGL(1,𝔽11))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C17⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C17C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C17C2×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊(C17⋊AGL(1,𝔽11))C2direct (N × H)
2. C2×C3×C17×C11⋊C5C2semidirect
4. C3×C17×C11⋊C5C22semidirect
5. C2×D561C5semidirect
6. C2×C17×C11⋊C5D3semidirect
8. C2×C3×C11×C17C2×C5semidirect
9. D561C2×C5semidirect
11. C17×C11⋊C5C2×D3semidirect
14. C3×C11×C17C22×C5semidirect
17. C2×C11×C17C5×D3semidirect
20. C2×C3×C11⋊C5D17semidirect
25. C11×C17C2×C5×D3semidirect
28. C3×C11⋊C5C2×D17semidirect
30. C2×C11⋊C5D51semidirect
32. C2×C3×C17AGL(1,𝔽11)semidirect
36. C2×C3×C11C5×D17semidirect
39. C11⋊C5C2×D51semidirect
40. C3×C17C2×AGL(1,𝔽11)semidirect
42. C2×C17C3⋊AGL(1,𝔽11)semidirect
44. C3×C11C2×C5×D17semidirect
47. C2×C11C5×D51semidirect
50. C17C2×C3⋊AGL(1,𝔽11)semidirect
53. C11C2×C5×D51semidirect
56. C2×C3C17⋊AGL(1,𝔽11)semidirect
60. C3C2×C17⋊AGL(1,𝔽11)semidirect
62. C2C3⋊(C17⋊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⋊(C17⋊AGL(1,𝔽11))2
C2×C3×C17×C11⋊C52
C2×C17⋊AGL(1,𝔽11)3
C2×D5615
C2×C5×D5111
C2×C3⋊AGL(1,𝔽11)17