Finite Group Databasebeta

← C3⋊(C3⋊(Dic127⋊C7)) #44544720

Subgroups — C3⋊(C3⋊(Dic127⋊C7)) #44544720

Order 32004.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C127⋊C7C211yesmaximal, characteristic
2C3⋊(Dic127⋊C7)—34nomaximal
3C32×C127⋊C7C411yescharacteristic, complemented, Hall
4C2×C3×C127⋊C7D314yes—
5C3⋊Dic381C711yesmaximal, characteristic, complemented, Hall
6Dic127⋊C7—91noHall
7C3×C127⋊C7Dic314yescomplemented
8C2×C32×C127C2×C711yescharacteristic
9C2×C127⋊C7C3⋊D311yescharacteristic
10Dic381—34no—
11C32×C127C4×C711yescharacteristic, complemented, Hall
12C127⋊C7C3⋊Dic311yescharacteristic, complemented, Hall
13C2×C3×C127D3×C714yes—
14Dic127—91noHall
15C3×C127C7×Dic314yescomplemented
16C2×C127C7×C3⋊D311yescharacteristic
17C7×C3⋊Dic3—1271nomaximal, Hall
18C127C7×C3⋊Dic311yescharacteristic, complemented, Sylow
19C2×C32×C7—1271no—
20C7×Dic3—3814no—
21C32×C7—1271noHall
22C2×C3×C7—1274no—
23C3⋊Dic3—1271noHall
24C4×C7—11431noHall
25C3×C7—1274no—
26C2×C32D127⋊C711yescharacteristic
27C2×C7—1271no—
28Dic3—3814no—
29C32Dic127⋊C711yescharacteristic, complemented, Sylow
30C7—1271noSylow
31C2×C3C3⋊(D127⋊C7)14yes—
32C4—11431noSylow
33C3C3⋊(Dic127⋊C7)14yescomplemented
34C2C3⋊(C3⋊(D127⋊C7))11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊(C3⋊(D127⋊C7))
commutator, hypocenterC32×C127C4×C7
Fitting, socle, cosocleC2×C32×C127C2×C7
prime radicalC2×C32×C127⋊C7C2
LCSG ▷ C32×C127
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C32×C127⋊C7C4semidirect
5. C3⋊Dic381C7semidirect
7. C3×C127⋊C7Dic3semidirect
11. C32×C127C4×C7semidirect
12. C127⋊C7C3⋊Dic3semidirect
15. C3×C127C7×Dic3semidirect
18. C127C7×C3⋊Dic3semidirect
29. C32Dic127⋊C7semidirect
33. C3C3⋊(Dic127⋊C7)semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C127⋊C72
C3⋊(Dic127⋊C7)3
C3⋊Dic3817
C7×C3⋊Dic3127