Finite Group Databasebeta

← Dic3×#10625202 #22580214

Subgroups — Dic3×#10625202 #22580214

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#10625202C211yesmaximal, characteristic
2Dic3×C13×C19C311yesmaximal, characteristic, complemented
3C4×#10625202—31nomaximal
4C3×#10625202C411yescharacteristic, complemented, Hall
5C2×C3×C13×C19C2×C311yescharacteristic
6C2×#10625202—21no—
7C2×#10625202D311yescharacteristic
8C4×C13×C19—31noHall
9C3×C13×C19C3×C411yescharacteristic, complemented
10#10625202—21no—
11#10625202Dic311yescharacteristic, direct product factor
12Dic3×C19⋊C3—131nomaximal, Hall
13C2×C13×C19C3×D311yescharacteristic
14Dic3×C13⋊C3—191nomaximal, Hall
15C2×C3×C19⋊C3—131no—
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C2×C3×C13⋊C3—191no—
18Dic3×C19C13⋊C311yescharacteristic, complemented
19C4×C19⋊C3—391no—
20C3×C19⋊C3—131noHall
21Dic3×C13C19⋊C311yescharacteristic, complemented
22C4×C13⋊C3—571no—
23C3×C13⋊C3—191noHall
24C2×C3×C19C2×C13⋊C311yescharacteristic
25C2×C19⋊C3—131no—
26C2×C19⋊C3—261no—
27C2×C3×C13C2×C19⋊C311yescharacteristic
28C2×C13⋊C3—191no—
29C2×C13⋊C3—381no—
30C4×C19—31noHall
31C3×C19C4×C13⋊C311yescharacteristic, complemented
32C19⋊C3—131no—
33C19⋊C3—261no—
34C4×C13—31noHall
35C3×C13C4×C19⋊C311yescharacteristic, complemented
36C13⋊C3—191no—
37C13⋊C3—381no—
38C2×C19D3×C13⋊C311yescharacteristic
39C3×Dic3—2471noHall
40C2×C13D3×C19⋊C311yescharacteristic
41C19Dic3×C13⋊C311yescharacteristic, complemented, Sylow
42C2×C32—2471no—
43C13Dic3×C19⋊C311yescharacteristic, complemented, Sylow
44C3×C4—7411no—
45Dic3#1062520211yescharacteristic, direct product factor
46C32—2471noSylow
47C2×C3—4941no—
48C2×C3—2471no—
49C2×C3C2×#1062520211yescharacteristic
50C4—31noSylow
51C3—4941no—
52C3—2471no—
53C3C4×#1062520211yescharacteristic, complemented
54C2D3×#1062520211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×#10625202
commutator, hypocenterC3×C13×C19C3×C4
Fitting, socleC2×C3×C13×C19C2×C3
LCSG ▷ C3×C13×C19
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic3×C13×C19C3semidirect
4. C3×#10625202C4semidirect
9. C3×C13×C19C3×C4semidirect
11. #10625202Dic3direct (N × H)
16. C13×C19C3×Dic3semidirect
18. Dic3×C19C13⋊C3semidirect
21. Dic3×C13C19⋊C3semidirect
31. C3×C19C4×C13⋊C3semidirect
35. C3×C13C4×C19⋊C3semidirect
41. C19Dic3×C13⋊C3semidirect
43. C13Dic3×C19⋊C3semidirect
45. Dic3#10625202direct (N × H)
53. C3C4×#10625202semidirect