Finite Group Databasebeta

← C3×Dic741 #22580229

Subgroups — C3×Dic741 #22580229

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C13×C19C211yesmaximal, characteristic
2Dic741C311yesmaximal, characteristic, direct product factor
3C3×Dic247—31nomaximal
4C32×C13×C19C411yescharacteristic, complemented, Hall
5C2×C3×C13×C19—21no—
6C2×C3×C13×C19D311yescharacteristic
7C2×C3×C13×C19C2×C311yescharacteristic
8Dic247—31noHall
9C3×C13×C19—21no—
10C3×C13×C19Dic311yescharacteristic, complemented
11C3×C13×C19C3×C411yescharacteristic, complemented
12C3×Dic57—131nomaximal, Hall
13C2×C13×C19C3×D311yescharacteristic
14C3×Dic39—191nomaximal, Hall
15C2×C32×C19D1311yescharacteristic
16C13×C19C3×Dic311yescharacteristic, complemented, Hall
17C2×C32×C13D1911yescharacteristic
18Dic57—131no—
19C3×Dic19—391no—
20C32×C19Dic1311yescharacteristic, complemented, Hall
21Dic39—191no—
22C3×Dic13—571no—
23C32×C13Dic1911yescharacteristic, complemented, Hall
24C2×C3×C19—21no—
25C2×C3×C19C3×D1311yescharacteristic
26C2×C3×C19D3911yescharacteristic
27C2×C3×C13—21no—
28C2×C3×C13C3×D1911yescharacteristic
29C2×C3×C13D5711yescharacteristic
30Dic19—391noHall
31C3×C19—21no—
32C3×C19C3×Dic1311yescharacteristic, complemented
33C3×C19Dic3911yescharacteristic, complemented
34Dic13—571noHall
35C3×C13—21no—
36C3×C13C3×Dic1911yescharacteristic, complemented
37C3×C13Dic5711yescharacteristic, complemented
38C2×C19C3×D3911yescharacteristic
39C3×Dic3—2471noHall
40C2×C13C3×D5711yescharacteristic
41C19C3×Dic3911yescharacteristic, complemented, Sylow
42C2×C32D24711yescharacteristic
43C13C3×Dic5711yescharacteristic, complemented, Sylow
44C3×C4—7411no—
45Dic3—2471no—
46C32Dic24711yescharacteristic, complemented, Sylow
47C2×C3—21no—
48C2×C3C3×D24711yescharacteristic
49C2×C3D74111yescharacteristic
50C4—7411noSylow
51C3—21no—
52C3C3×Dic24711yescharacteristic, complemented
53C3Dic74111yescharacteristic, direct product factor
54C2C3×D74111yescharacteristic
subgroupG/H
center, hypercenterC2×C3D741
commutator, hypocenterC3×C13×C19C3×C4
FrattiniC2C3×D741
Fitting, socleC2×C32×C13×C19C2
LCSG ▷ C3×C13×C19
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. Dic741C3direct (N × H)
4. C32×C13×C19C4semidirect
10. C3×C13×C19Dic3semidirect
11. C3×C13×C19C3×C4semidirect
16. C13×C19C3×Dic3semidirect
20. C32×C19Dic13semidirect
23. C32×C13Dic19semidirect
32. C3×C19C3×Dic13semidirect
33. C3×C19Dic39semidirect
36. C3×C13C3×Dic19semidirect
37. C3×C13Dic57semidirect
41. C19C3×Dic39semidirect
43. C13C3×Dic57semidirect
46. C32Dic247semidirect
52. C3C3×Dic247semidirect
53. C3Dic741direct (N × H)