Finite Group Databasebeta

← ΓL(1,𝔽8)×D11×C67 #44526257

Subgroups — ΓL(1,𝔽8)×D11×C67 #44526257

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×ΓL(1,𝔽8)×C67C211yesmaximal, characteristic, complemented, Hall
2C7×D11×C67C311yesmaximal, characteristic, complemented, Hall
3C7×C11×C67C2×C311yescharacteristic, complemented, Hall
4C3×D11×C67—71nomaximal, Hall
5C2×ΓL(1,𝔽8)×C67—111nomaximal, Hall
6C3×C11×C67—71noHall
7D11×C67ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
8ΓL(1,𝔽8)×C67D1111yescharacteristic, direct product factor, Hall
9C2×C7×C67—111noHall
10C11×C67C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
11C7×C67C3×D1111yescharacteristic, complemented, Hall
12ΓL(1,𝔽8)×D11C6711yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C67—771noHall
14C11×ΓL(1,𝔽8)C2×C6711yescharacteristic, complemented, Hall
15C3×C67—71noHall
16C7×D11C3×C6711yescharacteristic, complemented, Hall
17C2×C67—111noHall
18C7×C11C2×C3×C6711yescharacteristic, complemented, Hall
19C67ΓL(1,𝔽8)×D1111yescharacteristic, direct product factor, Sylow
20C3×D11—71noHall
21C2×ΓL(1,𝔽8)—111noHall
22C3×C11—71noHall
23D11ΓL(1,𝔽8)×C6711yescharacteristic, direct product factor, Hall
24ΓL(1,𝔽8)D11×C6711yescharacteristic, direct product factor, Hall
25C2×C7—111noHall
26C11C2×ΓL(1,𝔽8)×C6711yescharacteristic, complemented, Sylow
27C7C3×D11×C6711yescharacteristic, complemented, Sylow
28C2×C3—771noHall
29C3—71noSylow
30C2—111noSylow
subgroupG/H
center, hypercenterC67ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C2×C3×C67
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C67

Complements

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

NH ≅ G/Ntype
1. C11×ΓL(1,𝔽8)×C67C2semidirect
2. C7×D11×C67C3semidirect
3. C7×C11×C67C2×C3semidirect
7. D11×C67ΓL(1,𝔽8)direct (N × H)
8. ΓL(1,𝔽8)×C67D11direct (N × H)
10. C11×C67C2×ΓL(1,𝔽8)semidirect
11. C7×C67C3×D11semidirect
12. ΓL(1,𝔽8)×D11C67direct (N × H)
14. C11×ΓL(1,𝔽8)C2×C67semidirect
16. C7×D11C3×C67semidirect
18. C7×C11C2×C3×C67semidirect
19. C67ΓL(1,𝔽8)×D11direct (N × H)
23. D11ΓL(1,𝔽8)×C67direct (N × H)
24. ΓL(1,𝔽8)D11×C67direct (N × H)
26. C11C2×ΓL(1,𝔽8)×C67semidirect
27. C7C3×D11×C67semidirect

Maximal subgroups

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

subgroupindex
C11×ΓL(1,𝔽8)×C672
C7×D11×C673
C3×D11×C677
C2×ΓL(1,𝔽8)×C6711
ΓL(1,𝔽8)×D1167