Finite Group Databasebeta

← C3⋊(C3⋊((C11⋊C5)⋊D31)) #44501832

Subgroups — C3⋊(C3⋊((C11⋊C5)⋊D31)) #44501832

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C31×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C3⋊((C11⋊C5)⋊D31)—34nomaximal
3C3⋊D1023C511yesmaximal, characteristic, complemented, Hall
4C3×C31×C11⋊C5D314yescomplemented
5(C11⋊C5)⋊D31—91noHall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C5×C3⋊D93—111nomaximal, Hall
8D1023—34no—
9C31×C11⋊C5C3⋊D311yescharacteristic, complemented, Hall
10C32×C5×C31—111noHall
11C3×C11×C31C5×D314yescomplemented
12C3⋊(C3⋊AGL(1,𝔽11))—311nomaximal, Hall
13C5×D93—334no—
14D341—91noHall
15C3⋊D93—111noHall
16C32×C11⋊C5D3111yescharacteristic, complemented, Hall
17C3×C5×C31—114no—
18C11×C31C5×C3⋊D311yescharacteristic, complemented, Hall
19C3⋊AGL(1,𝔽11)—934no—
20C5×D31—991noHall
21C32×C31AGL(1,𝔽11)11yescharacteristic, complemented, Hall
22C3⋊D33—311noHall
23D93—334no—
24C3×C11⋊C5D9314yescomplemented
25C5×C31—111noHall
26AGL(1,𝔽11)—2791noHall
27C32×C11C5×D3111yescharacteristic, complemented, Hall
28C3×C31C3⋊AGL(1,𝔽11)14yescomplemented
29C5×C3⋊D3—3411noHall
30D33—934no—
31D31—991noHall
32C11⋊C5C3⋊D9311yescharacteristic, complemented, Hall
33C32×C5—111noHall
34C3×C11C5×D9314yescomplemented
35C31C3⋊(C3⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
36C5×D3—10234no—
37D11—2791noHall
38C3⋊D3—3411noHall
39C3×C5—114no—
40C11C5×C3⋊D9311yescharacteristic, complemented, Sylow
41C2×C5—30691noHall
42C32(C11⋊C5)⋊D3111yescharacteristic, complemented, Sylow
43D3—10234no—
44C5—111noSylow
45C3C3⋊((C11⋊C5)⋊D31)14yescomplemented
46C2—30691noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C31C2×C5
LCSG ▷ C32×C11×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C31×C11⋊C5C2semidirect
3. C3⋊D1023C5semidirect
4. C3×C31×C11⋊C5D3semidirect
6. C32×C11×C31C2×C5semidirect
9. C31×C11⋊C5C3⋊D3semidirect
11. C3×C11×C31C5×D3semidirect
16. C32×C11⋊C5D31semidirect
18. C11×C31C5×C3⋊D3semidirect
21. C32×C31AGL(1,𝔽11)semidirect
24. C3×C11⋊C5D93semidirect
27. C32×C11C5×D31semidirect
28. C3×C31C3⋊AGL(1,𝔽11)semidirect
32. C11⋊C5C3⋊D93semidirect
34. C3×C11C5×D93semidirect
35. C31C3⋊(C3⋊AGL(1,𝔽11))semidirect
40. C11C5×C3⋊D93semidirect
42. C32(C11⋊C5)⋊D31semidirect
45. C3C3⋊((C11⋊C5)⋊D31)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
C3⋊((C11⋊C5)⋊D31)3
C3⋊D10235
C5×C3⋊D9311
C3⋊(C3⋊AGL(1,𝔽11))31