Finite Group Databasebeta

← C3×(C43⋊C3)⋊Dic7 #24925513

Subgroups — C3×(C43⋊C3)⋊Dic7 #24925513

Order 10836.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C7×C43⋊C3C211yesmaximal, characteristic
2C3×Dic301C311yesmaximal, characteristic, complemented
3(C43⋊C3)⋊Dic7C313yesmaximal, direct product factor
4C3×C7×C43⋊C3C411yescharacteristic, complemented, Hall
5C2×C3×C7×C43C2×C311yescharacteristic
6C2×C7×C43⋊C3C2×C313yes—
7C3×(C43⋊C3)⋊C4—71nomaximal, Hall
8Dic301C3211yescharacteristic, complemented, Hall
9C3×C7×C43C3×C411yescharacteristic, complemented
10C7×C43⋊C3C3×C413yescomplemented
11C2×C3×C43⋊C3D711yescharacteristic
12C2×C7×C43C2×C3211yescharacteristic
13C3×Dic43—71no—
14(C43⋊C3)⋊C4—73no—
15C3×C43⋊C3Dic711yescharacteristic, complemented, Hall
16C7×C43C32×C411yescharacteristic, complemented, Hall
17C2×C3×C43C3×D711yescharacteristic
18C2×C43⋊C3C3×D713yes—
19C32×Dic7—431nomaximal, Hall
20Dic43—71noHall
21C3×C43C3×Dic711yescharacteristic, complemented
22C43⋊C3C3×Dic713yescomplemented
23C2×C32×C7—431no—
24C2×C43C32×D711yescharacteristic
25C3×Dic7—433no—
26C3×Dic7—431no—
27C32×C7—431noHall
28C43C32×Dic711yescharacteristic, complemented, Sylow
29C2×C3×C7—433no—
30C2×C3×C7D43⋊C311yescharacteristic
31C32×C4—3011noHall
32Dic7—431noHall
33C3×C7—433no—
34C3×C7(C43⋊C3)⋊C411yescharacteristic, complemented
35C2×C32—431no—
36C2×C7C3×D43⋊C311yescharacteristic
37C3×C4—3013no—
38C3×C4—3011no—
39C32—431noSylow
40C7C3×(C43⋊C3)⋊C411yescharacteristic, complemented, Sylow
41C2×C3—433no—
42C2×C3(C43⋊C3)⋊D711yescharacteristic
43C4—3011noSylow
44C3—433no—
45C3(C43⋊C3)⋊Dic711yescharacteristic, direct product factor
46C2C3×(C43⋊C3)⋊D711yescharacteristic
subgroupG/H
center, hypercenterC2×C3(C43⋊C3)⋊D7
commutator, hypocenterC7×C43C32×C4
FrattiniC2C3×(C43⋊C3)⋊D7
Fitting, socleC2×C3×C7×C43C2×C3
prime radicalC2×C3×C7×C43⋊C3C2
cosocleC2×C7×C43C2×C32
LCSG ▷ C7×C43
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×Dic301C3semidirect
3. (C43⋊C3)⋊Dic7C3direct (N × H)
4. C3×C7×C43⋊C3C4semidirect
8. Dic301C32semidirect
9. C3×C7×C43C3×C4semidirect
10. C7×C43⋊C3C3×C4semidirect
15. C3×C43⋊C3Dic7semidirect
16. C7×C43C32×C4semidirect
21. C3×C43C3×Dic7semidirect
22. C43⋊C3C3×Dic7semidirect
28. C43C32×Dic7semidirect
34. C3×C7(C43⋊C3)⋊C4semidirect
40. C7C3×(C43⋊C3)⋊C4semidirect
45. C3(C43⋊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×C43⋊C32
C3×Dic3013
(C43⋊C3)⋊Dic73
C3×(C43⋊C3)⋊C47
C32×Dic743