Finite Group Databasebeta

← D11×#4294⋊C2 #21418970

Subgroups — D11×#4294⋊C2 #21418970

Order 7524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊(#4294⋊C2)C211yesmaximal, characteristic, complemented
2D11×#4294C211yesmaximal, characteristic, complemented
3C11×#4294⋊C2C211yesmaximal, characteristic, complemented
4C3×D11×D19C311yesmaximal, characteristic
5C11×#4294C2211yescharacteristic, complemented, Hall
6C3×D209C2×C311yescharacteristic
7C3×C19×D11C2×C311yescharacteristic
8C3×C11×D19C2×C311yescharacteristic
9D11×D19C911yescharacteristic, complemented, Hall
10C2×#4294⋊C2—111nomaximal, Hall
11C3×C11×C19C22×C311yescharacteristic
12D209C2×C911yescharacteristic, complemented
13C11×D19C2×C911yescharacteristic, complemented
14C19×D11C2×C911yescharacteristic, complemented
15C2×C9×D11—191nomaximal, Hall
16C2×#4294—111no—
17#4294⋊C2—111no—
18#4294⋊C2D1111yescharacteristic, direct product factor
19C2×C3×D19—111no—
20C11×C19C22×C911yescharacteristic, complemented, Hall
21C2×C9×C11—191no—
22C9×D11—191no—
23C9×D11—191no—
24#4294C2×D1111yescharacteristic, complemented, Hall
25C2×C3×D11—191no—
26C2×C3×C19—111no—
27C3×D19—111no—
28C3×D19C3×D1111yescharacteristic
29C9×C11—191noHall
30C2×D19—111noHall
31C2×C3×C11—191no—
32C3×D11—191no—
33C3×D11D19⋊C311yescharacteristic
34C3×C19C2×C3×D1111yescharacteristic
35C2×D11—191noHall
36C2×C19—111no—
37D19—111no—
38D19C9×D1111yescharacteristic, complemented
39C22×C9—2091noHall
40C3×C11C2×D19⋊C311yescharacteristic
41C2×C11—191no—
42D11—191no—
43D11#4294⋊C211yescharacteristic, direct product factor
44C19C2×C9×D1111yescharacteristic, complemented, Sylow
45C2×C9—191no—
46C2×C9—2091no—
47C2×C9—2091no—
48C22×C3—2091no—
49C11C2×#4294⋊C211yescharacteristic, complemented, Sylow
50C9—191noSylow
51C2×C3—111no—
52C2×C3—191no—
53C2×C3—2091no—
54C22—2091noSylow
55C3D11×D19⋊C311yescharacteristic
56C2—111no—
57C2—191no—
58C2—2091no—
subgroupG/H
center, Frattini, hypercenterC3D11×D19⋊C3
commutator, hypocenterC11×C19C22×C9
Fitting, socleC3×C11×C19C22×C3
LCSG ▷ C11×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C11⋊(#4294⋊C2)C2semidirect
2. D11×#4294C2semidirect
3. C11×#4294⋊C2C2semidirect
5. C11×#4294C22semidirect
9. D11×D19C9semidirect
12. D209C2×C9semidirect
13. C11×D19C2×C9semidirect
14. C19×D11C2×C9semidirect
18. #4294⋊C2D11direct (N × H)
20. C11×C19C22×C9semidirect
24. #4294C2×D11semidirect
38. D19C9×D11semidirect
43. D11#4294⋊C2direct (N × H)
44. C19C2×C9×D11semidirect
49. C11C2×#4294⋊C2semidirect