Finite Group Databasebeta

← C2×C3⋊(C7⋊(C11⋊D11)) #23779078

Subgroups — C2×C3⋊(C7⋊(C11⋊D11)) #23779078

Order 10164.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C7⋊(C11⋊D11))C212yesmaximal, direct product factor
2C2×C3×C7×C112C211yesmaximal, characteristic, complemented
3C2×C7⋊(C11⋊D11)—31nomaximal, Hall
4C3×C7×C112C2211yescharacteristic, complemented, Hall
5C2×C7×C112D311yescharacteristic, complemented
6C7⋊(C11⋊D11)—32no—
7C2×C3⋊(C11⋊D11)—71nomaximal, Hall
8C2×D231—1112nomaximal
9C7×C112C2×D311yescharacteristic, complemented, Hall
10C2×C3×C112D711yescharacteristic, complemented
11C3⋊(C11⋊D11)—72no—
12C2×C11⋊D11—211noHall
13C2×C3×C7×C11D11112yescomplemented
14D231—1124no—
15C3×C112C2×D711yescharacteristic, complemented, Hall
16C2×D77—3312no—
17C2×C112D2111yescharacteristic, complemented
18C11⋊D11—212no—
19C3×C7×C11C2×D11112yescomplemented
20C2×C7×C11D33112yescomplemented
21D77—3324no—
22C2×D33—7712no—
23C112C2×D2111yescharacteristic, complemented, Sylow
24C2×D21—1211noHall
25C7×C11C2×D33112yescomplemented
26C2×C3×C11D77112yescomplemented
27D33—7724no—
28C2×D11—23112no—
29C2×C3×C7C11⋊D1111yescharacteristic, complemented
30D21—1212no—
31C3×C11C2×D77112yescomplemented
32C2×D7—3631noHall
33C2×C11D231112yescomplemented
34D11—23124no—
35C3×C7C2×C11⋊D1111yescharacteristic, complemented, Hall
36C2×C7C3⋊(C11⋊D11)11yescharacteristic, complemented
37D7—3632no—
38C2×D3—8471noHall
39C11C2×D231112yescomplemented
40C7C2×C3⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
41C2×C3C7⋊(C11⋊D11)11yescharacteristic, complemented
42D3—8472no—
43C22—25411noSylow
44C3C2×C7⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
45C2—25412no—
46C2C3⋊(C7⋊(C11⋊D11))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C7⋊(C11⋊D11))
commutator, cosocle, hypocenterC3×C7×C112C22
FrattiniC1G
Fitting, socleC2×C3×C7×C112C2
LCSG ▷ C3×C7×C112
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊(C7⋊(C11⋊D11))C2direct (N × H)
2. C2×C3×C7×C112C2semidirect
4. C3×C7×C112C22semidirect
5. C2×C7×C112D3semidirect
9. C7×C112C2×D3semidirect
10. C2×C3×C112D7semidirect
13. C2×C3×C7×C11D11semidirect
15. C3×C112C2×D7semidirect
17. C2×C112D21semidirect
19. C3×C7×C11C2×D11semidirect
20. C2×C7×C11D33semidirect
23. C112C2×D21semidirect
25. C7×C11C2×D33semidirect
26. C2×C3×C11D77semidirect
29. C2×C3×C7C11⋊D11semidirect
31. C3×C11C2×D77semidirect
33. C2×C11D231semidirect
35. C3×C7C2×C11⋊D11semidirect
36. C2×C7C3⋊(C11⋊D11)semidirect
39. C11C2×D231semidirect
40. C7C2×C3⋊(C11⋊D11)semidirect
41. C2×C3C7⋊(C11⋊D11)semidirect
44. C3C2×C7⋊(C11⋊D11)semidirect
46. C2C3⋊(C7⋊(C11⋊D11))direct (N × H)