Finite Group Databasebeta

← C3×C11⋊C5×#3861 #37564689

Subgroups — C3×C11⋊C5×#3861 #37564689

Order 24255.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C72×C11⋊C5C311yesmaximal, characteristic, complemented
2C11⋊C5×#3861C313yesmaximal, direct product factor
3C3×C11×#3861C511yesmaximal, characteristic, complemented, Hall
4C3×ΓL(1,𝔽8)×C11⋊C5—78nomaximal
5C72×C11⋊C5C3211yescharacteristic, complemented, Hall
6C3×C5×#3861—111nomaximal, Hall
7C3×C72×C11C3×C511yescharacteristic, complemented
8C11×#3861C3×C513yescomplemented
9C3×C7×C11⋊C5ΓL(1,𝔽8)18yescomplemented
10ΓL(1,𝔽8)×C11⋊C5—724no—
11C3×C5×C72—111no—
12C5×#3861—113no—
13C3×C11×ΓL(1,𝔽8)—78no—
14C72×C11C32×C511yescharacteristic, complemented, Hall
15C32×C11⋊C5—491noHall
16C3×#3861C11⋊C511yescharacteristic, direct product factor, Hall
17C7×C11⋊C5C3×ΓL(1,𝔽8)18yescomplemented
18C3×C5×ΓL(1,𝔽8)—778no—
19C5×C72—111noHall
20C3×C7×C11C5×ΓL(1,𝔽8)18yescomplemented
21C11×ΓL(1,𝔽8)—724no—
22C3×C11⋊C5—493no—
23C3×C11⋊C5#386111yescharacteristic, direct product factor
24C3×C72C3×C11⋊C511yescharacteristic, complemented
25#3861C3×C11⋊C513yesdirect product factor
26C3×C5×C7—118no—
27C5×ΓL(1,𝔽8)—7724no—
28C32×C11—491noHall
29C7×C11C3×C5×ΓL(1,𝔽8)18yescomplemented
30C3×ΓL(1,𝔽8)—78no—
31C11⋊C5C3×#386111yescharacteristic, direct product factor, Hall
32C72C32×C11⋊C511yescharacteristic, complemented, Sylow
33C32×C5—5391noHall
34C5×C7—118no—
35C3×C11—493no—
36C3×C11C5×#386111yescharacteristic, complemented
37C3×C7ΓL(1,𝔽8)×C11⋊C518yescomplemented
38ΓL(1,𝔽8)—724no—
39C3×C5—111no—
40C3×C5—5393no—
41C11C3×C5×#386111yescharacteristic, complemented, Sylow
42C32—491noSylow
43C7C3×ΓL(1,𝔽8)×C11⋊C518yescomplemented
44C5—111noSylow
45C3—493no—
46C3C11⋊C5×#386111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC3C11⋊C5×#3861
commutator, cosocle, hypocenterC72×C11C32×C5
FrattiniC1G
Fitting, socleC3×C72×C11C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C72×C11⋊C5C3semidirect
2. C11⋊C5×#3861C3direct (N × H)
3. C3×C11×#3861C5semidirect
5. C72×C11⋊C5C32semidirect
7. C3×C72×C11C3×C5semidirect
8. C11×#3861C3×C5semidirect
9. C3×C7×C11⋊C5ΓL(1,𝔽8)semidirect
14. C72×C11C32×C5semidirect
16. C3×#3861C11⋊C5direct (N × H)
17. C7×C11⋊C5C3×ΓL(1,𝔽8)semidirect
20. C3×C7×C11C5×ΓL(1,𝔽8)semidirect
23. C3×C11⋊C5#3861direct (N × H)
24. C3×C72C3×C11⋊C5semidirect
25. #3861C3×C11⋊C5direct (N × H)
29. C7×C11C3×C5×ΓL(1,𝔽8)semidirect
31. C11⋊C5C3×#3861direct (N × H)
32. C72C32×C11⋊C5semidirect
36. C3×C11C5×#3861semidirect
37. C3×C7ΓL(1,𝔽8)×C11⋊C5semidirect
41. C11C3×C5×#3861semidirect
43. C7C3×ΓL(1,𝔽8)×C11⋊C5semidirect
46. C3C11⋊C5×#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C72×C11⋊C53
C11⋊C5×#38613
C3×C11×#38615
C3×ΓL(1,𝔽8)×C11⋊C57
C3×C5×#386111