Finite Group Databasebeta

← C2×ΓL(1,𝔽8)×C23⋊C11 #24922296

Subgroups — C2×ΓL(1,𝔽8)×C23⋊C11 #24922296

Order 10626.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1ΓL(1,𝔽8)×C23⋊C11C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C23⋊C11C311yesmaximal, characteristic, complemented, Hall
3C7×C23⋊C11C2×C311yescharacteristic, complemented, Hall
4C2×C3×C23⋊C11—71nomaximal, Hall
5C2×ΓL(1,𝔽8)×C23C1111yesmaximal, characteristic, complemented, Hall
6C3×C23⋊C11—71noHall
7C2×C23⋊C11ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
8ΓL(1,𝔽8)×C23C2×C1111yescharacteristic, complemented, Hall
9C2×C11×ΓL(1,𝔽8)—231nomaximal, Hall
10C2×C7×C23C3×C1111yescharacteristic, complemented, Hall
11C23⋊C11C2×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
12C11×ΓL(1,𝔽8)—231noHall
13C7×C23C2×C3×C1111yescharacteristic, complemented, Hall
14C2×C7×C11—231noHall
15C2×C3×C23—71noHall
16C7×C11—231noHall
17C3×C23—71noHall
18C2×C3×C11—1611noHall
19C2×C23C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
20C2×ΓL(1,𝔽8)C23⋊C1111yescharacteristic, direct product factor, Hall
21C3×C11—1611noHall
22C23C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
23C2×C11—231noHall
24ΓL(1,𝔽8)C2×C23⋊C1111yescharacteristic, direct product factor, Hall
25C2×C7C3×C23⋊C1111yescharacteristic, complemented, Hall
26C11—231noSylow
27C7C2×C3×C23⋊C1111yescharacteristic, complemented, Sylow
28C2×C3—71noHall
29C3—71noSylow
30C2ΓL(1,𝔽8)×C23⋊C1111yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×C23⋊C11
commutator, cosocle, hypocenterC7×C23C2×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C23C3×C11
LCSG ▷ C7×C23
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. ΓL(1,𝔽8)×C23⋊C11C2direct (N × H)
2. C2×C7×C23⋊C11C3semidirect
3. C7×C23⋊C11C2×C3semidirect
5. C2×ΓL(1,𝔽8)×C23C11semidirect
7. C2×C23⋊C11ΓL(1,𝔽8)direct (N × H)
8. ΓL(1,𝔽8)×C23C2×C11semidirect
10. C2×C7×C23C3×C11semidirect
11. C23⋊C11C2×ΓL(1,𝔽8)direct (N × H)
13. C7×C23C2×C3×C11semidirect
19. C2×C23C11×ΓL(1,𝔽8)semidirect
20. C2×ΓL(1,𝔽8)C23⋊C11direct (N × H)
22. C23C2×C11×ΓL(1,𝔽8)semidirect
24. ΓL(1,𝔽8)C2×C23⋊C11direct (N × H)
25. C2×C7C3×C23⋊C11semidirect
27. C7C2×C3×C23⋊C11semidirect
30. C2ΓL(1,𝔽8)×C23⋊C11direct (N × H)