Finite Group Databasebeta

← C11×D15⋊D47 #44526669

Subgroups — C11×D15⋊D47 #44526669

Order 31020.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×D15×C47C211yesmaximal, characteristic, complemented
2C5×C11×D141C211yesmaximal, characteristic, complemented
3C3×C11×D235C211yesmaximal, characteristic, complemented
4D5×C11×D47—31nomaximal, Hall
5C3×C5×C11×C47C2211yescharacteristic, complemented, Hall
6D3×C11×D47—51nomaximal, Hall
7C11×D235D311yescharacteristic, complemented
8D5×C11×C47—31no—
9C5×C11×D47—31no—
10C11×D141D511yescharacteristic, complemented
11D3×C11×C47—51no—
12C3×C11×D47—51no—
13D15⋊D47C1111yesmaximal, characteristic, direct product factor, Hall
14C5×C11×C47C2×D311yescharacteristic, complemented, Hall
15C2×C11×D47—151noHall
16C3×C11×C47C2×D511yescharacteristic, complemented, Hall
17D15×C47C2×C1111yescharacteristic, complemented
18C5×D141C2×C1111yescharacteristic, complemented
19C3×D235C2×C1111yescharacteristic, complemented
20C2×C11×C47—151no—
21C11×D47—31no—
22C11×D47—51no—
23D5×D47—31noHall
24C3×C5×C47C22×C1111yescharacteristic, complemented, Hall
25D3×D5×C11—471nomaximal, Hall
26D3×D47—51noHall
27C11×C47D3×D511yescharacteristic, complemented, Hall
28D235D3×C1111yescharacteristic, complemented
29C5×D47—31no—
30D5×C47—31no—
31C11×D15D4711yescharacteristic, complemented
32C5×D3×C11—471no—
33C3×D5×C11—471no—
34D141D5×C1111yescharacteristic, complemented
35C3×D47—51no—
36D3×C47—51no—
37C5×C47C2×D3×C1111yescharacteristic, complemented, Hall
38C2×D5×C11—1411noHall
39C2×D47—151noHall
40C3×C5×C11C2×D4711yescharacteristic, complemented, Hall
41C3×C47C2×D5×C1111yescharacteristic, complemented, Hall
42C2×D3×C11—2351noHall
43C2×C5×C11—1411no—
44D5×C11—31no—
45D5×C11—471no—
46C2×C47—151no—
47D47—31no—
48D47—51no—
49C2×C3×C11—2351no—
50D3×C11—51no—
51D3×C11—471no—
52D3×D5—471noHall
53C5×C11D3×D4711yescharacteristic, complemented, Hall
54C47D3×D5×C1111yescharacteristic, complemented, Sylow
55C22×C11—7051noHall
56C3×C11D5×D4711yescharacteristic, complemented, Hall
57D15C11×D4711yescharacteristic, complemented
58C3×D5—471no—
59C5×D3—471no—
60C2×C11—151no—
61C2×C11—1411no—
62C2×C11—2351no—
63C2×D5—1411noHall
64C3×C5C2×C11×D4711yescharacteristic, complemented, Hall
65C2×D3—2351noHall
66C11D15⋊D4711yescharacteristic, direct product factor, Sylow
67C2×C5—1411no—
68D5—31no—
69D5—471no—
70C2×C3—2351no—
71D3—51no—
72D3—471no—
73C5D3×C11×D4711yescharacteristic, complemented, Sylow
74C22—7051noSylow
75C3D5×C11×D4711yescharacteristic, complemented, Sylow
76C2—151no—
77C2—1411no—
78C2—2351no—
subgroupG/H
center, hypercenterC11D15⋊D47
commutator, cosocle, hypocenterC3×C5×C47C22×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C47C22
LCSG ▷ C3×C5×C47
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D15×C47C2semidirect
2. C5×C11×D141C2semidirect
3. C3×C11×D235C2semidirect
5. C3×C5×C11×C47C22semidirect
7. C11×D235D3semidirect
10. C11×D141D5semidirect
13. D15⋊D47C11direct (N × H)
14. C5×C11×C47C2×D3semidirect
16. C3×C11×C47C2×D5semidirect
17. D15×C47C2×C11semidirect
18. C5×D141C2×C11semidirect
19. C3×D235C2×C11semidirect
24. C3×C5×C47C22×C11semidirect
27. C11×C47D3×D5semidirect
28. D235D3×C11semidirect
31. C11×D15D47semidirect
34. D141D5×C11semidirect
37. C5×C47C2×D3×C11semidirect
40. C3×C5×C11C2×D47semidirect
41. C3×C47C2×D5×C11semidirect
53. C5×C11D3×D47semidirect
54. C47D3×D5×C11semidirect
56. C3×C11D5×D47semidirect
57. D15C11×D47semidirect
64. C3×C5C2×C11×D47semidirect
66. C11D15⋊D47direct (N × H)
73. C5D3×C11×D47semidirect
75. C3D5×C11×D47semidirect

Maximal subgroups

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

subgroupindex
C11×D15×C472
C5×C11×D1412
C3×C11×D2352
D5×C11×D473
D3×C11×D475
D15⋊D4711
D3×D5×C1147