Finite Group Databasebeta

← #17984639⋊C2 #22580242

Subgroups — #17984639⋊C2 #22580242

Order 8892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17984645C211yesmaximal, characteristic, complemented
2#17984641C211yesmaximal, characteristic, complemented
3#17984639C211yesmaximal, characteristic, complemented
4D13×D19⋊C3C311yesmaximal, characteristic
5#14555740C2211yescharacteristic, complemented, Hall
6(C19⋊C3)⋊D13C2×C311yescharacteristic
7D13×C19⋊C3C2×C311yescharacteristic
8C13×D19⋊C3C2×C311yescharacteristic
9D13×D19C911yescharacteristic, complemented, Hall
10C13×C19⋊C3C22×C311yescharacteristic
11C2×AGL(1,𝔽19)—131nomaximal, Hall
12D247C2×C911yescharacteristic, complemented
13C13×D19C2×C911yescharacteristic, complemented
14C19×D13C2×C911yescharacteristic, complemented
15C2×D13⋊C9—191nomaximal, Hall
16C2×#4296—131no—
17AGL(1,𝔽19)—131no—
18AGL(1,𝔽19)—131no—
19C13×C19C22×C911yescharacteristic, complemented, Hall
20C2×C13⋊C9—191no—
21D13⋊C9—191no—
22D13⋊C9—191no—
23C2×D19⋊C3—131no—
24#4296—131noHall
25C2×C3×D13—191no—
26C13⋊C9—191noHall
27C2×C19⋊C3—131no—
28D19⋊C3—131no—
29D19⋊C3D13⋊C311yescharacteristic
30C2×C3×C13—191no—
31C3×D13—191no—
32C3×D13—191no—
33C2×D19—131noHall
34C19⋊C3C2×D13⋊C311yescharacteristic
35C2×D13—191noHall
36C3×C13—191no—
37C2×C19—131no—
38D19—131no—
39D19D13⋊C911yescharacteristic, complemented
40C22×C9—2471noHall
41C2×C13—191no—
42D13—191no—
43D13AGL(1,𝔽19)11yescharacteristic, complemented
44C19C2×D13⋊C911yescharacteristic, complemented, Sylow
45C2×C9—2471no—
46C2×C9—2471no—
47C2×C9—2471no—
48C13C2×AGL(1,𝔽19)11yescharacteristic, complemented, Sylow
49C22×C3—2471no—
50C9—2471noSylow
51C2×C3—191no—
52C2×C3—2471no—
53C2×C3—2471no—
54C22—2471noSylow
55C3—191no—
56C2—131no—
57C2—191no—
58C2—2471no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C19C22×C9
LCSG ▷ C13×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. #17984645C2semidirect
2. #17984641C2semidirect
3. #17984639C2semidirect
5. #14555740C22semidirect
9. D13×D19C9semidirect
12. D247C2×C9semidirect
13. C13×D19C2×C9semidirect
14. C19×D13C2×C9semidirect
19. C13×C19C22×C9semidirect
39. D19D13⋊C9semidirect
43. D13AGL(1,𝔽19)semidirect
44. C19C2×D13⋊C9semidirect
48. C13C2×AGL(1,𝔽19)semidirect