Finite Group Databasebeta

← C2×C3⋊(C29⋊AGL(1,𝔽11)) #34062349

Subgroups — C2×C3⋊(C29⋊AGL(1,𝔽11)) #34062349

Order 19140.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C29⋊AGL(1,𝔽11))C212yesmaximal, direct product factor
2C2×C3×C29×C11⋊C5C211yesmaximal, characteristic, complemented
3C2×C29⋊AGL(1,𝔽11)—31nomaximal, Hall
4C3×C29×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×D957C511yesmaximal, characteristic, complemented, Hall
6C29⋊AGL(1,𝔽11)—32no—
7C2×C29×C11⋊C5D311yescharacteristic, complemented
8C2×C3×C11×C29C2×C511yescharacteristic, complemented
9D957C2×C512yescomplemented
10C2×C5×D87—111nomaximal, Hall
11C29×C11⋊C5C2×D311yescharacteristic, complemented, Hall
12C2×D319—31noHall
13C3×C11×C29C22×C511yescharacteristic, complemented, Hall
14C2×C3×C5×C29—111no—
15C5×D87—112no—
16C2×C3⋊AGL(1,𝔽11)—291nomaximal, Hall
17C2×C11×C29C5×D311yescharacteristic, complemented
18D319—32no—
19C2×C5×D29—331noHall
20C3×C5×C29—111noHall
21C2×D87—111noHall
22C2×C3×C11⋊C5D2911yescharacteristic, complemented
23C3⋊AGL(1,𝔽11)—292no—
24C11×C29C2×C5×D311yescharacteristic, complemented, Hall
25C2×C5×C29—111no—
26C5×D29—332no—
27C2×AGL(1,𝔽11)—871noHall
28C2×C3×C29AGL(1,𝔽11)11yescharacteristic, complemented
29D87—112no—
30C3×C11⋊C5C2×D2911yescharacteristic, complemented, Hall
31C5×C29—111noHall
32C2×D33—291noHall
33C2×D29—331noHall
34C2×C11⋊C5D8711yescharacteristic, complemented
35AGL(1,𝔽11)—872no—
36C3×C29C2×AGL(1,𝔽11)11yescharacteristic, complemented, Hall
37C2×C3×C11C5×D2911yescharacteristic, complemented
38D33—292no—
39C2×C5×D3—3191noHall
40C2×C29C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
41D29—332no—
42C11⋊C5C2×D8711yescharacteristic, complemented, Hall
43C2×D11—871noHall
44C3×C11C2×C5×D2911yescharacteristic, complemented, Hall
45C2×C3×C5—111no—
46C5×D3—3192no—
47C29C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
48C2×C11C5×D8711yescharacteristic, complemented
49D11—872no—
50C22×C5—9571noHall
51C3×C5—111noHall
52C2×D3—3191noHall
53C11C2×C5×D8711yescharacteristic, complemented, Sylow
54C2×C5—111no—
55C2×C5—9572no—
56C2×C3C29⋊AGL(1,𝔽11)11yescharacteristic, complemented
57D3—3192no—
58C5—111noSylow
59C22—9571noSylow
60C3C2×C29⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
61C2—9572no—
62C2C3⋊(C29⋊AGL(1,𝔽11))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C29⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C29C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C29C2×C5
LCSG ▷ C3×C11×C29
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊(C29⋊AGL(1,𝔽11))C2direct (N × H)
2. C2×C3×C29×C11⋊C5C2semidirect
4. C3×C29×C11⋊C5C22semidirect
5. C2×D957C5semidirect
7. C2×C29×C11⋊C5D3semidirect
8. C2×C3×C11×C29C2×C5semidirect
9. D957C2×C5semidirect
11. C29×C11⋊C5C2×D3semidirect
13. C3×C11×C29C22×C5semidirect
17. C2×C11×C29C5×D3semidirect
22. C2×C3×C11⋊C5D29semidirect
24. C11×C29C2×C5×D3semidirect
28. C2×C3×C29AGL(1,𝔽11)semidirect
30. C3×C11⋊C5C2×D29semidirect
34. C2×C11⋊C5D87semidirect
36. C3×C29C2×AGL(1,𝔽11)semidirect
37. C2×C3×C11C5×D29semidirect
40. C2×C29C3⋊AGL(1,𝔽11)semidirect
42. C11⋊C5C2×D87semidirect
44. C3×C11C2×C5×D29semidirect
47. C29C2×C3⋊AGL(1,𝔽11)semidirect
48. C2×C11C5×D87semidirect
53. C11C2×C5×D87semidirect
56. C2×C3C29⋊AGL(1,𝔽11)semidirect
60. C3C2×C29⋊AGL(1,𝔽11)semidirect
62. C2C3⋊(C29⋊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⋊(C29⋊AGL(1,𝔽11))2
C2×C3×C29×C11⋊C52
C2×C29⋊AGL(1,𝔽11)3
C2×D9575
C2×C5×D8711
C2×C3⋊AGL(1,𝔽11)29