Finite Group Databasebeta

← C22×C11×#63270 #26046580

Subgroups — C22×C11×#63270 #26046580

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#63270C213yesmaximal, direct product factor
2C22×C7×C11×C13C311yesmaximal, characteristic, complemented, Hall
3C11×#63270C2211yescharacteristic, direct product factor, Hall
4C2×C7×C11×C13C2×C313yescomplemented
5C22×C11×C13⋊C3—71nomaximal, Hall
6C22×#63270C1111yesmaximal, characteristic, direct product factor, Hall
7C7×C11×C13C22×C311yescharacteristic, complemented, Hall
8C22×C11×ΓL(1,𝔽8)—131nomaximal, Hall
9C2×C11×C13⋊C3—73no—
10C22×C11×C13ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
11C2×#63270C2×C1113yesdirect product factor
12C2×C11×ΓL(1,𝔽8)—133no—
13C11×C13⋊C3—71noHall
14C22×C7×C13C3×C1111yescharacteristic, complemented, Hall
15C22×C7×C11C13⋊C311yescharacteristic, complemented, Hall
16C2×C11×C13C2×ΓL(1,𝔽8)13yescomplemented
17#63270C22×C1111yescharacteristic, direct product factor, Hall
18C11×ΓL(1,𝔽8)—131noHall
19C2×C7×C13C2×C3×C1113yescomplemented
20C22×C13⋊C3—71noHall
21C2×C7×C11C2×C13⋊C313yescomplemented
22C11×C13C22×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
23C22×C3×C11—911noHall
24C7×C13C22×C3×C1111yescharacteristic, complemented, Hall
25C22×ΓL(1,𝔽8)—131noHall
26C2×C13⋊C3—73no—
27C7×C11C22×C13⋊C311yescharacteristic, complemented, Hall
28C2×C3×C11—913no—
29C22×C13C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
30C22×C11#6327011yescharacteristic, direct product factor, Hall
31C2×ΓL(1,𝔽8)—133no—
32C13⋊C3—71noHall
33C3×C11—911noHall
34C22×C7C11×C13⋊C311yescharacteristic, complemented, Hall
35C2×C13C2×C11×ΓL(1,𝔽8)13yescomplemented
36C2×C11C2×#6327013yesdirect product factor
37ΓL(1,𝔽8)—131noHall
38C2×C7C2×C11×C13⋊C313yescomplemented
39C13C22×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
40C22×C3—911noHall
41C11C22×#6327011yescharacteristic, direct product factor, Sylow
42C7C22×C11×C13⋊C311yescharacteristic, complemented, Sylow
43C2×C3—913no—
44C22C11×#6327011yescharacteristic, direct product factor, Sylow
45C3—911noSylow
46C2C2×C11×#6327013yesdirect product factor
subgroupG/H
center, hypercenterC22×C11#63270
commutator, cosocle, hypocenterC7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C22×C11

Complements

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

NH ≅ G/Ntype
1. C2×C11×#63270C2direct (N × H)
2. C22×C7×C11×C13C3semidirect
3. C11×#63270C22direct (N × H)
4. C2×C7×C11×C13C2×C3semidirect
6. C22×#63270C11direct (N × H)
7. C7×C11×C13C22×C3semidirect
10. C22×C11×C13ΓL(1,𝔽8)semidirect
11. C2×#63270C2×C11direct (N × H)
14. C22×C7×C13C3×C11semidirect
15. C22×C7×C11C13⋊C3semidirect
16. C2×C11×C13C2×ΓL(1,𝔽8)semidirect
17. #63270C22×C11direct (N × H)
19. C2×C7×C13C2×C3×C11semidirect
21. C2×C7×C11C2×C13⋊C3semidirect
22. C11×C13C22×ΓL(1,𝔽8)semidirect
24. C7×C13C22×C3×C11semidirect
27. C7×C11C22×C13⋊C3semidirect
29. C22×C13C11×ΓL(1,𝔽8)semidirect
30. C22×C11#63270direct (N × H)
34. C22×C7C11×C13⋊C3semidirect
35. C2×C13C2×C11×ΓL(1,𝔽8)semidirect
36. C2×C11C2×#63270direct (N × H)
38. C2×C7C2×C11×C13⋊C3semidirect
39. C13C22×C11×ΓL(1,𝔽8)semidirect
41. C11C22×#63270direct (N × H)
42. C7C22×C11×C13⋊C3semidirect
44. C22C11×#63270direct (N × H)
46. C2C2×C11×#63270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#632702
C22×C7×C11×C133
C22×C11×C13⋊C37
C22×#6327011
C22×C11×ΓL(1,𝔽8)13