Finite Group Databasebeta

← C3×C22⋊AGL(1,𝔽11) #13050323

Subgroups — C3×C22⋊AGL(1,𝔽11) #13050323

Order 1320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C11⋊C5C211yesmaximal, characteristic, complemented
2C2×C3×AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
3C3×Dic11⋊C5C211yesmaximal, characteristic, complemented
4C22⋊AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C11⋊C5—21no—
6C2×C3×C11⋊C5C2211yescharacteristic
7C3×AGL(1,𝔽11)—21no—
8C3×C22⋊D11C511yesmaximal, characteristic, complemented, Hall
9C22×C11⋊C5C2×C311yescharacteristic, complemented
10C2×AGL(1,𝔽11)C2×C311yescharacteristic, complemented
11Dic11⋊C5C2×C311yescharacteristic, complemented
12C3×C11⋊C5D411yescharacteristic, complemented, Hall
13C22×C3×C11C2×C511yescharacteristic, complemented
14C2×C3×D11C2×C511yescharacteristic, complemented
15C3×Dic11C2×C511yescharacteristic, complemented
16C3×C5×D4—111nomaximal, Hall
17C2×C11⋊C5—21no—
18C2×C11⋊C5C22×C311yescharacteristic
19AGL(1,𝔽11)—21no—
20C22⋊D11C3×C511yescharacteristic, complemented, Hall
21C2×C3×C11—21no—
22C2×C3×C11C22×C511yescharacteristic
23C3×D11—21no—
24C22×C3×C5—111no—
25C22×C3×C5—111no—
26C3×C4×C5—111no—
27C11⋊C5C3×D411yescharacteristic, complemented, Hall
28C22×C11C2×C3×C511yescharacteristic, complemented
29C2×D11C2×C3×C511yescharacteristic, complemented
30Dic11C2×C3×C511yescharacteristic, complemented
31C5×D4—111noHall
32C3×C11C5×D411yescharacteristic, complemented, Hall
33C2×C3×C5—111no—
34C2×C3×C5—221no—
35C2×C3×C5—221no—
36C3×D4—111noHall
37C2×C11—21no—
38C2×C11C22×C3×C511yescharacteristic
39D11—21no—
40C22×C5—111no—
41C22×C5—111no—
42C4×C5—111no—
43C3×C5—111noHall
44C22×C3—111no—
45C22×C3AGL(1,𝔽11)11yescharacteristic, complemented
46C3×C4—111no—
47C11C3×C5×D411yescharacteristic, complemented, Sylow
48C2×C5—111no—
49C2×C5—221no—
50C2×C5—221no—
51D4—111noSylow
52C2×C3—21no—
53C2×C3—221no—
54C2×C3C2×AGL(1,𝔽11)11yescharacteristic
55C5—111noSylow
56C22—111no—
57C22C3×AGL(1,𝔽11)11yescharacteristic, complemented
58C4—111no—
59C3C22⋊AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
60C2—21no—
61C2—221no—
62C2C2×C3×AGL(1,𝔽11)11yescharacteristic
subgroupG/H
centerC2×C3C2×AGL(1,𝔽11)
commutator, cosocleC2×C11C22×C3×C5
FrattiniC2C2×C3×AGL(1,𝔽11)
FittingC22×C3×C11C2×C5
socleC2×C3×C11C22×C5
hypercenterC22×C3AGL(1,𝔽11)
hypocenterC11C3×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C11⋊C5C2semidirect
2. C2×C3×AGL(1,𝔽11)C2semidirect
3. C3×Dic11⋊C5C2semidirect
4. C22⋊AGL(1,𝔽11)C3direct (N × H)
8. C3×C22⋊D11C5semidirect
9. C22×C11⋊C5C2×C3semidirect
10. C2×AGL(1,𝔽11)C2×C3semidirect
11. Dic11⋊C5C2×C3semidirect
12. C3×C11⋊C5D4semidirect
13. C22×C3×C11C2×C5semidirect
14. C2×C3×D11C2×C5semidirect
15. C3×Dic11C2×C5semidirect
20. C22⋊D11C3×C5semidirect
27. C11⋊C5C3×D4semidirect
28. C22×C11C2×C3×C5semidirect
29. C2×D11C2×C3×C5semidirect
30. Dic11C2×C3×C5semidirect
32. C3×C11C5×D4semidirect
45. C22×C3AGL(1,𝔽11)semidirect
47. C11C3×C5×D4semidirect
57. C22C3×AGL(1,𝔽11)semidirect
59. C3C22⋊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
C22×C3×C11⋊C52
C2×C3×AGL(1,𝔽11)2
C3×Dic11⋊C52
C22⋊AGL(1,𝔽11)3
C3×C22⋊D115
C3×C5×D411