Finite Group Databasebeta

← C11×AGL(1,𝔽7)×C67 #44526265

Subgroups — C11×AGL(1,𝔽7)×C67 #44526265

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×ΓL(1,𝔽8)×C67C211yesmaximal, characteristic, complemented, Hall
2C11×D7×C67C311yesmaximal, characteristic, complemented, Hall
3C7×C11×C67C2×C311yescharacteristic, complemented, Hall
4C2×C3×C11×C67—71nomaximal, Hall
5AGL(1,𝔽7)×C67C1111yesmaximal, characteristic, direct product factor, Hall
6C3×C11×C67—71noHall
7C2×C11×C67—71noHall
8ΓL(1,𝔽8)×C67C2×C1111yescharacteristic, complemented, Hall
9D7×C67C3×C1111yescharacteristic, complemented, Hall
10C11×C67AGL(1,𝔽7)11yescharacteristic, direct product factor, Hall
11C7×C67C2×C3×C1111yescharacteristic, complemented, Hall
12C11×AGL(1,𝔽7)C6711yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C67—71noHall
14C11×ΓL(1,𝔽8)C2×C6711yescharacteristic, complemented, Hall
15C3×C67—71noHall
16C11×D7C3×C6711yescharacteristic, complemented, Hall
17C2×C67—71noHall
18C7×C11C2×C3×C6711yescharacteristic, complemented, Hall
19C67C11×AGL(1,𝔽7)11yescharacteristic, direct product factor, Sylow
20C2×C3×C11—71noHall
21AGL(1,𝔽7)C11×C6711yescharacteristic, direct product factor, Hall
22C3×C11—71noHall
23C2×C11—71noHall
24ΓL(1,𝔽8)C2×C11×C6711yescharacteristic, complemented, Hall
25D7C3×C11×C6711yescharacteristic, complemented, Hall
26C11AGL(1,𝔽7)×C6711yescharacteristic, direct product factor, Sylow
27C7C2×C3×C11×C6711yescharacteristic, complemented, Sylow
28C2×C3—71noHall
29C3—71noSylow
30C2—71noSylow
subgroupG/H
center, hypercenterC11×C67AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C11×C67
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C7
UCSC1 ◁ C11×C67

Complements

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

NH ≅ G/Ntype
1. C11×ΓL(1,𝔽8)×C67C2semidirect
2. C11×D7×C67C3semidirect
3. C7×C11×C67C2×C3semidirect
5. AGL(1,𝔽7)×C67C11direct (N × H)
8. ΓL(1,𝔽8)×C67C2×C11semidirect
9. D7×C67C3×C11semidirect
10. C11×C67AGL(1,𝔽7)direct (N × H)
11. C7×C67C2×C3×C11semidirect
12. C11×AGL(1,𝔽7)C67direct (N × H)
14. C11×ΓL(1,𝔽8)C2×C67semidirect
16. C11×D7C3×C67semidirect
18. C7×C11C2×C3×C67semidirect
19. C67C11×AGL(1,𝔽7)direct (N × H)
21. AGL(1,𝔽7)C11×C67direct (N × H)
24. ΓL(1,𝔽8)C2×C11×C67semidirect
25. D7C3×C11×C67semidirect
26. C11AGL(1,𝔽7)×C67direct (N × H)
27. C7C2×C3×C11×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
C11×D7×C673
C2×C3×C11×C677
AGL(1,𝔽7)×C6711
C11×AGL(1,𝔽7)67