Finite Group Databasebeta

← C3×((C127⋊C3)⋊C4)⋊C7 #44544701

Subgroups — C3×((C127⋊C3)⋊C4)⋊C7 #44544701

Order 32004.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C127⋊C3)⋊C7C211yesmaximal, characteristic
2((C127⋊C3)⋊C4)⋊C7C313yesmaximal, direct product factor
3C3×Dic127⋊C7C311yesmaximal, characteristic, complemented
4C3×(C127⋊C3)⋊C7C411yescharacteristic, complemented, Hall
5C2×(C127⋊C3)⋊C7C2×C313yes—
6C2×C3×C127⋊C7C2×C311yescharacteristic
7C3×(C127⋊C3)⋊C4C711yesmaximal, characteristic, complemented, Hall
8Dic127⋊C7C3211yescharacteristic, complemented, Hall
9C3×C127⋊C7C3×C411yescharacteristic, complemented
10(C127⋊C3)⋊C7C3×C413yescomplemented
11C2×C3×C127⋊C3C2×C711yescharacteristic
12C2×C127⋊C7C2×C3211yescharacteristic
13C3×Dic127C3×C711yescharacteristic, complemented
14(C127⋊C3)⋊C4C3×C713yescomplemented
15C3×C127⋊C3C4×C711yescharacteristic, complemented, Hall
16C127⋊C7C32×C411yescharacteristic, complemented, Hall
17C2×C3×C127C2×C3×C711yescharacteristic
18C2×C127⋊C3C2×C3×C713yes—
19Dic127C32×C711yescharacteristic, complemented, Hall
20C3×C127C3×C4×C711yescharacteristic, complemented
21C127⋊C3C3×C4×C713yescomplemented
22C2×C127C2×C32×C711yescharacteristic
23C32×C4×C7—1271nomaximal, Hall
24C127C32×C4×C711yescharacteristic, complemented, Sylow
25C2×C32×C7—1271no—
26C3×C4×C7—1271no—
27C3×C4×C7—1273no—
28C32×C7—1271noHall
29C2×C3×C7—1273no—
30C2×C3×C7—1271no—
31C32×C4—1271noHall
32C4×C7—1271noHall
33C3×C7—1273no—
34C3×C7—1271no—
35C2×C32—1271no—
36C2×C7—1271no—
37C3×C4—1273no—
38C3×C4—1271no—
39C32—1271noSylow
40C7—1271noSylow
41C2×C3—1273no—
42C2×C3(D127⋊C3)⋊C711yescharacteristic
43C4—1271noSylow
44C3—1273no—
45C3((C127⋊C3)⋊C4)⋊C711yescharacteristic, direct product factor
46C2C3×(D127⋊C3)⋊C711yescharacteristic
subgroupG/H
center, hypercenterC2×C3(D127⋊C3)⋊C7
commutator, hypocenterC127C32×C4×C7
FrattiniC2C3×(D127⋊C3)⋊C7
Fitting, socleC2×C3×C127C2×C3×C7
prime radicalC2×C3×(C127⋊C3)⋊C7C2
cosocleC2×C127C2×C32×C7
LCSG ▷ C127
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. ((C127⋊C3)⋊C4)⋊C7C3direct (N × H)
3. C3×Dic127⋊C7C3semidirect
4. C3×(C127⋊C3)⋊C7C4semidirect
7. C3×(C127⋊C3)⋊C4C7semidirect
8. Dic127⋊C7C32semidirect
9. C3×C127⋊C7C3×C4semidirect
10. (C127⋊C3)⋊C7C3×C4semidirect
13. C3×Dic127C3×C7semidirect
14. (C127⋊C3)⋊C4C3×C7semidirect
15. C3×C127⋊C3C4×C7semidirect
16. C127⋊C7C32×C4semidirect
19. Dic127C32×C7semidirect
20. C3×C127C3×C4×C7semidirect
21. C127⋊C3C3×C4×C7semidirect
24. C127C32×C4×C7semidirect
45. C3((C127⋊C3)⋊C4)⋊C7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×(C127⋊C3)⋊C72
((C127⋊C3)⋊C4)⋊C73
C3×Dic127⋊C73
C3×(C127⋊C3)⋊C47
C32×C4×C7127