Finite Group Databasebeta

← C11×C22⋊#63271 #26046576

Subgroups — C11×C22⋊#63271 #26046576

Order 12012.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C11×C13C311yesmaximal, characteristic, complemented, Hall
2C11×#63271—41nomaximal, Hall
3C2×C7×C11×C13—31no—
4C11×C22⋊(C13⋊C3)—71nomaximal, Hall
5C22⋊#63271C1111yesmaximal, characteristic, direct product factor, Hall
6C7×C11×C13A411yescharacteristic, complemented, Hall
7C11×C22⋊ΓL(1,𝔽8)—131nomaximal, Hall
8C22×C11×C13ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
9C11×C13⋊C3—281noHall
10C22×C7×C13C3×C1111yescharacteristic, complemented, Hall
11C22×C7×C11C13⋊C311yescharacteristic, complemented, Hall
12C2×C11×C13—31no—
13#63271—41noHall
14C11×ΓL(1,𝔽8)—521noHall
15C2×C7×C13—31no—
16C22⋊(C13⋊C3)—71noHall
17C2×C7×C11—31no—
18C11×C13C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
19C11×A4—911noHall
20C7×C13C11×A411yescharacteristic, complemented, Hall
21C22⋊ΓL(1,𝔽8)—131noHall
22C7×C11C22⋊(C13⋊C3)11yescharacteristic, complemented, Hall
23C22×C13C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
24C22×C11#6327111yescharacteristic, complemented, Hall
25C13⋊C3—281noHall
26C3×C11—3641noHall
27C22×C7C11×C13⋊C311yescharacteristic, complemented, Hall
28C2×C13—31no—
29C2×C11—31no—
30ΓL(1,𝔽8)—521noHall
31C2×C7—31no—
32C13C11×C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
33A4—911noHall
34C11C22⋊#6327111yescharacteristic, direct product factor, Sylow
35C7C11×C22⋊(C13⋊C3)11yescharacteristic, complemented, Sylow
36C22C11×#6327111yescharacteristic, complemented, Sylow
37C3—3641noSylow
38C2—31no—
subgroupG/H
center, hypercenterC11C22⋊#63271
commutator, cosocle, hypocenterC22×C7×C13C3×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C3
LCSG ▷ C22×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C22×C7×C11×C13C3semidirect
5. C22⋊#63271C11direct (N × H)
6. C7×C11×C13A4semidirect
8. C22×C11×C13ΓL(1,𝔽8)semidirect
10. C22×C7×C13C3×C11semidirect
11. C22×C7×C11C13⋊C3semidirect
18. C11×C13C22⋊ΓL(1,𝔽8)semidirect
20. C7×C13C11×A4semidirect
22. C7×C11C22⋊(C13⋊C3)semidirect
23. C22×C13C11×ΓL(1,𝔽8)semidirect
24. C22×C11#63271semidirect
27. C22×C7C11×C13⋊C3semidirect
32. C13C11×C22⋊ΓL(1,𝔽8)semidirect
34. C11C22⋊#63271direct (N × H)
35. C7C11×C22⋊(C13⋊C3)semidirect
36. C22C11×#63271semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C11×C133
C11×#632714
C11×C22⋊(C13⋊C3)7
C22⋊#6327111
C11×C22⋊ΓL(1,𝔽8)13