Finite Group Databasebeta

← C3×(C67⋊C3)⋊Dic13 #44535656

Subgroups — C3×(C67⋊C3)⋊Dic13 #44535656

Order 31356.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×C67⋊C3C211yesmaximal, characteristic
2(C67⋊C3)⋊Dic13C313yesmaximal, direct product factor
3C3×Dic871C311yesmaximal, characteristic, complemented
4C3×C13×C67⋊C3C411yescharacteristic, complemented, Hall
5C2×C13×C67⋊C3C2×C313yes—
6C2×C3×C13×C67C2×C311yescharacteristic
7Dic871C3211yescharacteristic, complemented, Hall
8C3×C13×C67C3×C411yescharacteristic, complemented
9C13×C67⋊C3C3×C413yescomplemented
10C3×(C67⋊C3)⋊C4—131nomaximal, Hall
11C2×C13×C67C2×C3211yescharacteristic
12C2×C3×C67⋊C3D1311yescharacteristic
13C13×C67C32×C411yescharacteristic, complemented, Hall
14C3×Dic67—131no—
15(C67⋊C3)⋊C4—133no—
16C3×C67⋊C3Dic1311yescharacteristic, complemented, Hall
17C32×Dic13—671nomaximal, Hall
18C2×C3×C67C3×D1311yescharacteristic
19C2×C67⋊C3C3×D1313yes—
20Dic67—131noHall
21C2×C32×C13—671no—
22C3×C67C3×Dic1311yescharacteristic, complemented
23C67⋊C3C3×Dic1313yescomplemented
24C3×Dic13—673no—
25C3×Dic13—671no—
26C2×C67C32×D1311yescharacteristic
27C32×C13—671noHall
28C2×C3×C13—673no—
29C2×C3×C13D67⋊C311yescharacteristic
30C67C32×Dic1311yescharacteristic, complemented, Sylow
31Dic13—671noHall
32C3×C13—673no—
33C3×C13(C67⋊C3)⋊C411yescharacteristic, complemented
34C32×C4—8711noHall
35C2×C13C3×D67⋊C311yescharacteristic
36C2×C32—671no—
37C13C3×(C67⋊C3)⋊C411yescharacteristic, complemented, Sylow
38C3×C4—8713no—
39C3×C4—8711no—
40C32—671noSylow
41C2×C3—673no—
42C2×C3(C67⋊C3)⋊D1311yescharacteristic
43C4—8711noSylow
44C3—673no—
45C3(C67⋊C3)⋊Dic1311yescharacteristic, direct product factor
46C2C3×(C67⋊C3)⋊D1311yescharacteristic
subgroupG/H
center, hypercenterC2×C3(C67⋊C3)⋊D13
commutator, hypocenterC13×C67C32×C4
FrattiniC2C3×(C67⋊C3)⋊D13
Fitting, socleC2×C3×C13×C67C2×C3
prime radicalC2×C3×C13×C67⋊C3C2
cosocleC2×C13×C67C2×C32
LCSG ▷ C13×C67
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. (C67⋊C3)⋊Dic13C3direct (N × H)
3. C3×Dic871C3semidirect
4. C3×C13×C67⋊C3C4semidirect
7. Dic871C32semidirect
8. C3×C13×C67C3×C4semidirect
9. C13×C67⋊C3C3×C4semidirect
13. C13×C67C32×C4semidirect
16. C3×C67⋊C3Dic13semidirect
22. C3×C67C3×Dic13semidirect
23. C67⋊C3C3×Dic13semidirect
30. C67C32×Dic13semidirect
33. C3×C13(C67⋊C3)⋊C4semidirect
37. C13C3×(C67⋊C3)⋊C4semidirect
45. C3(C67⋊C3)⋊Dic13direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×C13×C67⋊C32
(C67⋊C3)⋊Dic133
C3×Dic8713
C3×(C67⋊C3)⋊C413
C32×Dic1367