Finite Group Databasebeta

← C2×C3×(C11⋊C5)⋊D11 #20300056

Subgroups — C2×C3×(C11⋊C5)⋊D11 #20300056

Order 7260.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C11×C11⋊C5C211yesmaximal, characteristic, complemented
2C3×(C11⋊C5)⋊D11C212yesmaximal, direct product factor
3C2×(C11⋊C5)⋊D11C311yesmaximal, characteristic, direct product factor, Hall
4C3×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C3×C11⋊D11C511yesmaximal, characteristic, complemented, Hall
6C2×C11×C11⋊C5C2×C311yescharacteristic, complemented
7(C11⋊C5)⋊D11C2×C312yesdirect product factor
8C2×C3×C112C2×C511yescharacteristic, complemented
9C3×C11⋊D11C2×C512yescomplemented
10C2×C3×C5×D11—111nomaximal
11C2×C3×AGL(1,𝔽11)—111nomaximal
12C11×C11⋊C5C22×C311yescharacteristic, complemented, Hall
13C2×C11⋊D11C3×C511yescharacteristic, complemented, Hall
14C3×C112C22×C511yescharacteristic, complemented, Hall
15C2×C3×C5×C11—111no—
16C3×C5×D11—112no—
17C2×C3×C11⋊C5D1111yescharacteristic, complemented
18C3×AGL(1,𝔽11)—112no—
19C2×C112C2×C3×C511yescharacteristic, complemented
20C11⋊D11C2×C3×C512yescomplemented
21C2×C5×D11—111no—
22C2×AGL(1,𝔽11)—111no—
23C3×C5×C11—111no—
24C3×C11⋊C5C2×D1111yescharacteristic, complemented
25C2×C3×D11—111no—
26C2×C3×D11—111no—
27C2×C3×D11—552no—
28C112C22×C3×C511yescharacteristic, complemented, Sylow
29C2×C5×C11—111no—
30C5×D11—112no—
31C2×C11⋊C5C3×D1111yescharacteristic, complemented
32AGL(1,𝔽11)—112no—
33C2×C3×C11—52no—
34C2×C3×C11AGL(1,𝔽11)11yescharacteristic, complemented
35C2×C3×C11C5×D1111yescharacteristic, complemented
36C3×D11—112no—
37C3×D11—112no—
38C3×D11—554no—
39C22×C3×C5—1211noHall
40C5×C11—111no—
41C11⋊C5C2×C3×D1111yescharacteristic, complemented
42C2×D11—111no—
43C2×D11—111no—
44C2×D11—552no—
45C3×C11—52no—
46C3×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
47C3×C11C2×C5×D1111yescharacteristic, complemented
48C2×C3×C5—111no—
49C2×C3×C5—1212no—
50C2×C11—52no—
51C2×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
52C2×C11C3×C5×D1111yescharacteristic, complemented
53D11—112no—
54D11—112no—
55D11—554no—
56C22×C5—1211noHall
57C3×C5—111noHall
58C22×C3—1211noHall
59C11—52no—
60C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
61C11C2×C3×C5×D1111yescharacteristic, complemented
62C2×C5—111no—
63C2×C5—1212no—
64C2×C3—1212no—
65C2×C3(C11⋊C5)⋊D1111yescharacteristic, direct product factor
66C5—111noSylow
67C22—1211noSylow
68C3C2×(C11⋊C5)⋊D1111yescharacteristic, direct product factor, Sylow
69C2—1212no—
70C2C3×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3(C11⋊C5)⋊D11
commutator, hypocenterC112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C11×C11⋊C5C2semidirect
2. C3×(C11⋊C5)⋊D11C2direct (N × H)
3. C2×(C11⋊C5)⋊D11C3direct (N × H)
4. C3×C11×C11⋊C5C22semidirect
5. C2×C3×C11⋊D11C5semidirect
6. C2×C11×C11⋊C5C2×C3semidirect
7. (C11⋊C5)⋊D11C2×C3direct (N × H)
8. C2×C3×C112C2×C5semidirect
9. C3×C11⋊D11C2×C5semidirect
12. C11×C11⋊C5C22×C3semidirect
13. C2×C11⋊D11C3×C5semidirect
14. C3×C112C22×C5semidirect
17. C2×C3×C11⋊C5D11semidirect
19. C2×C112C2×C3×C5semidirect
20. C11⋊D11C2×C3×C5semidirect
24. C3×C11⋊C5C2×D11semidirect
28. C112C22×C3×C5semidirect
31. C2×C11⋊C5C3×D11semidirect
34. C2×C3×C11AGL(1,𝔽11)semidirect
35. C2×C3×C11C5×D11semidirect
41. C11⋊C5C2×C3×D11semidirect
46. C3×C11C2×AGL(1,𝔽11)semidirect
47. C3×C11C2×C5×D11semidirect
51. C2×C11C3×AGL(1,𝔽11)semidirect
52. C2×C11C3×C5×D11semidirect
60. C11C2×C3×AGL(1,𝔽11)semidirect
61. C11C2×C3×C5×D11semidirect
65. C2×C3(C11⋊C5)⋊D11direct (N × H)
68. C3C2×(C11⋊C5)⋊D11direct (N × H)
70. C2C3×(C11⋊C5)⋊D11direct (N × H)