Finite Group Databasebeta

← C2×C13⋊(C42⋊C3) #11928750

Subgroups — C2×C13⋊(C42⋊C3) #11928750

Order 1248.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13⋊(C42⋊C3)C211yesmaximal, characteristic, direct product factor
2C2×C42×C13C311yesmaximal, characteristic, complemented, Hall
3C2×C22⋊(C13⋊C3)—41nomaximal
4C22×C4×C13—31no—
5C42×C13—31no—
6C42×C13C2×C311yescharacteristic, complemented
7C22⋊(C13⋊C3)—41no—
8C23×C13A411yescharacteristic
9C2×C4×C13—32no—
10C2×C4×C13—32no—
11C2×C4×C13—31no—
12C2×C4×C13—31no—
13C2×C42⋊C3—131nomaximal, Hall
14C2×C13⋊C3—161no—
15C22×C13—31no—
16C22×C13—31no—
17C22×C13C2×A411yescharacteristic
18C4×C13—32no—
19C4×C13—32no—
20C42⋊C3—131no—
21C13⋊C3—161noHall
22C2×C42C13⋊C311yescharacteristic, complemented, Sylow
23C2×C13—31no—
24C2×C13—31no—
25C2×C13C42⋊C311yescharacteristic, complemented
26C2×A4—521no—
27C22×C4—31no—
28C42—31no—
29C42C2×C13⋊C311yescharacteristic, complemented
30C13C2×C42⋊C311yescharacteristic, complemented, Sylow
31A4—521no—
32C23C22⋊(C13⋊C3)11yescharacteristic
33C2×C4—32no—
34C2×C4—32no—
35C2×C4—31no—
36C2×C4—31no—
37C2×C3—2081no—
38C22—31no—
39C22—31no—
40C22C2×C22⋊(C13⋊C3)11yescharacteristic
41C4—32no—
42C4—32no—
43C3—2081noSylow
44C2—31no—
45C2—31no—
46C2C13⋊(C42⋊C3)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C13⋊(C42⋊C3)
commutator, cosocle, hypocenterC42×C13C2×C3
FrattiniC22C2×C22⋊(C13⋊C3)
FittingC2×C42×C13C3
socleC23×C13A4
LCSG ▷ C42×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C13⋊(C42⋊C3)C2direct (N × H)
2. C2×C42×C13C3semidirect
6. C42×C13C2×C3semidirect
22. C2×C42C13⋊C3semidirect
25. C2×C13C42⋊C3semidirect
29. C42C2×C13⋊C3semidirect
30. C13C2×C42⋊C3semidirect
46. C2C13⋊(C42⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C13⋊(C42⋊C3)2
C2×C42×C133
C2×C22⋊(C13⋊C3)4
C2×C42⋊C313