Finite Group Databasebeta

← C11×ΓL(1,𝔽8)×D67 #44526253

Subgroups — C11×ΓL(1,𝔽8)×D67 #44526253

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×ΓL(1,𝔽8)×C67C211yesmaximal, characteristic, complemented, Hall
2C7×C11×D67C311yesmaximal, characteristic, complemented, Hall
3C7×C11×C67C2×C311yescharacteristic, complemented, Hall
4C3×C11×D67—71nomaximal, Hall
5ΓL(1,𝔽8)×D67C1111yesmaximal, characteristic, direct product factor, Hall
6C3×C11×C67—71noHall
7C11×D67ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
8ΓL(1,𝔽8)×C67C2×C1111yescharacteristic, complemented, Hall
9C7×D67C3×C1111yescharacteristic, complemented, Hall
10C11×C67C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
11C7×C67C2×C3×C1111yescharacteristic, complemented, Hall
12C2×C11×ΓL(1,𝔽8)—671nomaximal, Hall
13C3×D67—71noHall
14C11×ΓL(1,𝔽8)D6711yescharacteristic, direct product factor, Hall
15C3×C67—71noHall
16C2×C7×C11—671noHall
17D67C11×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
18C7×C11C3×D6711yescharacteristic, complemented, Hall
19C67C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
20C2×C3×C11—4691noHall
21C2×ΓL(1,𝔽8)—671noHall
22C3×C11—71noHall
23C2×C11—671noHall
24ΓL(1,𝔽8)C11×D6711yescharacteristic, direct product factor, Hall
25C2×C7—671noHall
26C11ΓL(1,𝔽8)×D6711yescharacteristic, direct product factor, Sylow
27C7C3×C11×D6711yescharacteristic, complemented, Sylow
28C2×C3—4691noHall
29C3—71noSylow
30C2—671noSylow
subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×D67
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C7×C67
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×ΓL(1,𝔽8)×C67C2semidirect
2. C7×C11×D67C3semidirect
3. C7×C11×C67C2×C3semidirect
5. ΓL(1,𝔽8)×D67C11direct (N × H)
7. C11×D67ΓL(1,𝔽8)direct (N × H)
8. ΓL(1,𝔽8)×C67C2×C11semidirect
9. C7×D67C3×C11semidirect
10. C11×C67C2×ΓL(1,𝔽8)semidirect
11. C7×C67C2×C3×C11semidirect
14. C11×ΓL(1,𝔽8)D67direct (N × H)
17. D67C11×ΓL(1,𝔽8)direct (N × H)
18. C7×C11C3×D67semidirect
19. C67C2×C11×ΓL(1,𝔽8)semidirect
24. ΓL(1,𝔽8)C11×D67direct (N × H)
26. C11ΓL(1,𝔽8)×D67direct (N × H)
27. C7C3×C11×D67semidirect

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×C11×D673
C3×C11×D677
ΓL(1,𝔽8)×D6711
C2×C11×ΓL(1,𝔽8)67