Finite Group Databasebeta

← C31×C3⋊(C3⋊AGL(1,𝔽11)) #44501823

Subgroups — C31×C3⋊(C3⋊AGL(1,𝔽11)) #44501823

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C31×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C31×C3⋊AGL(1,𝔽11)—34nomaximal
3C31×C3⋊D33C511yesmaximal, characteristic, complemented, Hall
4C3×C31×C11⋊C5D314yescomplemented
5C31×AGL(1,𝔽11)—91noHall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C5×C3⋊D3×C31—111nomaximal, Hall
8C31×D33—34no—
9C31×C11⋊C5C3⋊D311yescharacteristic, complemented, Hall
10C32×C5×C31—111noHall
11C3×C11×C31C5×D314yescomplemented
12C3⋊(C3⋊AGL(1,𝔽11))C3111yesmaximal, characteristic, direct product factor, Hall
13C5×D3×C31—334no—
14D11×C31—91noHall
15C3⋊D3×C31—111noHall
16C32×C11⋊C5C2×C3111yescharacteristic, complemented, Hall
17C3×C5×C31—114no—
18C11×C31C5×C3⋊D311yescharacteristic, complemented, Hall
19C3⋊AGL(1,𝔽11)—34no—
20C2×C5×C31—991noHall
21C32×C31AGL(1,𝔽11)11yescharacteristic, complemented, Hall
22C3⋊D33C5×C3111yescharacteristic, complemented, Hall
23D3×C31—334no—
24C3×C11⋊C5D3×C3114yescomplemented
25C5×C31—111noHall
26AGL(1,𝔽11)—91noHall
27C32×C11C2×C5×C3111yescharacteristic, complemented, Hall
28C3×C31C3⋊AGL(1,𝔽11)14yescomplemented
29C5×C3⋊D3—111noHall
30D33—34no—
31C2×C31—991noHall
32C11⋊C5C3⋊D3×C3111yescharacteristic, complemented, Hall
33C32×C5—111noHall
34C3×C11C5×D3×C3114yescomplemented
35C31C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, direct product factor, Sylow
36C5×D3—334no—
37D11—91noHall
38C3⋊D3—111noHall
39C3×C5—114no—
40C11C5×C3⋊D3×C3111yescharacteristic, complemented, Sylow
41C2×C5—991noHall
42C32C31×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
43D3—334no—
44C5—111noSylow
45C3C31×C3⋊AGL(1,𝔽11)14yescomplemented
46C2—991noSylow
subgroupG/H
center, hypercenterC31C3⋊(C3⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC32×C11C2×C5×C31
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C31

Complements

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

NH ≅ G/Ntype
1. C32×C31×C11⋊C5C2semidirect
3. C31×C3⋊D33C5semidirect
4. C3×C31×C11⋊C5D3semidirect
6. C32×C11×C31C2×C5semidirect
9. C31×C11⋊C5C3⋊D3semidirect
11. C3×C11×C31C5×D3semidirect
12. C3⋊(C3⋊AGL(1,𝔽11))C31direct (N × H)
16. C32×C11⋊C5C2×C31semidirect
18. C11×C31C5×C3⋊D3semidirect
21. C32×C31AGL(1,𝔽11)semidirect
22. C3⋊D33C5×C31semidirect
24. C3×C11⋊C5D3×C31semidirect
27. C32×C11C2×C5×C31semidirect
28. C3×C31C3⋊AGL(1,𝔽11)semidirect
32. C11⋊C5C3⋊D3×C31semidirect
34. C3×C11C5×D3×C31semidirect
35. C31C3⋊(C3⋊AGL(1,𝔽11))direct (N × H)
40. C11C5×C3⋊D3×C31semidirect
42. C32C31×AGL(1,𝔽11)semidirect
45. C3C31×C3⋊AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
C32×C31×C11⋊C52
C31×C3⋊AGL(1,𝔽11)3
C31×C3⋊D335
C5×C3⋊D3×C3111
C3⋊(C3⋊AGL(1,𝔽11))31