Finite Group Databasebeta

← C3×(C127⋊C3)⋊Dic7 #44544737

Subgroups — C3×(C127⋊C3)⋊Dic7 #44544737

Order 32004.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C7×C127⋊C3C211yesmaximal, characteristic
2(C127⋊C3)⋊Dic7C313yesmaximal, direct product factor
3C3×Dic889C311yesmaximal, characteristic, complemented
4C3×C7×C127⋊C3C411yescharacteristic, complemented, Hall
5C2×C7×C127⋊C3C2×C313yes—
6C2×C3×C7×C127C2×C311yescharacteristic
7C3×(C127⋊C3)⋊C4—71nomaximal, Hall
8Dic889C3211yescharacteristic, complemented, Hall
9C3×C7×C127C3×C411yescharacteristic, complemented
10C7×C127⋊C3C3×C413yescomplemented
11C2×C3×C127⋊C3D711yescharacteristic
12C2×C7×C127C2×C3211yescharacteristic
13C3×Dic127—71no—
14(C127⋊C3)⋊C4—73no—
15C3×C127⋊C3Dic711yescharacteristic, complemented, Hall
16C7×C127C32×C411yescharacteristic, complemented, Hall
17C2×C3×C127C3×D711yescharacteristic
18C2×C127⋊C3C3×D713yes—
19Dic127—71noHall
20C3×C127C3×Dic711yescharacteristic, complemented
21C127⋊C3C3×Dic713yescomplemented
22C2×C127C32×D711yescharacteristic
23C32×Dic7—1271nomaximal, Hall
24C127C32×Dic711yescharacteristic, complemented, Sylow
25C2×C32×C7—1271no—
26C3×Dic7—1273no—
27C3×Dic7—1271no—
28C32×C7—1271noHall
29C2×C3×C7—1273no—
30C2×C3×C7D127⋊C311yescharacteristic
31C32×C4—8891noHall
32Dic7—1271noHall
33C3×C7—1273no—
34C3×C7(C127⋊C3)⋊C411yescharacteristic, complemented
35C2×C32—1271no—
36C2×C7C3×D127⋊C311yescharacteristic
37C3×C4—8893no—
38C3×C4—8891no—
39C32—1271noSylow
40C7C3×(C127⋊C3)⋊C411yescharacteristic, complemented, Sylow
41C2×C3—1273no—
42C2×C3(C127⋊C3)⋊D711yescharacteristic
43C4—8891noSylow
44C3—1273no—
45C3(C127⋊C3)⋊Dic711yescharacteristic, direct product factor
46C2C3×(C127⋊C3)⋊D711yescharacteristic
subgroupG/H
center, hypercenterC2×C3(C127⋊C3)⋊D7
commutator, hypocenterC7×C127C32×C4
FrattiniC2C3×(C127⋊C3)⋊D7
Fitting, socleC2×C3×C7×C127C2×C3
prime radicalC2×C3×C7×C127⋊C3C2
cosocleC2×C7×C127C2×C32
LCSG ▷ C7×C127
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. (C127⋊C3)⋊Dic7C3direct (N × H)
3. C3×Dic889C3semidirect
4. C3×C7×C127⋊C3C4semidirect
8. Dic889C32semidirect
9. C3×C7×C127C3×C4semidirect
10. C7×C127⋊C3C3×C4semidirect
15. C3×C127⋊C3Dic7semidirect
16. C7×C127C32×C4semidirect
20. C3×C127C3×Dic7semidirect
21. C127⋊C3C3×Dic7semidirect
24. C127C32×Dic7semidirect
34. C3×C7(C127⋊C3)⋊C4semidirect
40. C7C3×(C127⋊C3)⋊C4semidirect
45. C3(C127⋊C3)⋊Dic7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C7×C127⋊C32
(C127⋊C3)⋊Dic73
C3×Dic8893
C3×(C127⋊C3)⋊C47
C32×Dic7127