Finite Group Databasebeta

← AGL(1,𝔽7)×C67⋊C11 #44526285

Subgroups — AGL(1,𝔽7)×C67⋊C11 #44526285

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1ΓL(1,𝔽8)×C67⋊C11C211yesmaximal, characteristic, complemented, Hall
2D7×C67⋊C11C311yesmaximal, characteristic, complemented, Hall
3C7×C67⋊C11C2×C311yescharacteristic, complemented, Hall
4C2×C3×C67⋊C11—71nomaximal, Hall
5AGL(1,𝔽7)×C67C1111yesmaximal, characteristic, complemented, Hall
6C3×C67⋊C11—71noHall
7C2×C67⋊C11—71noHall
8ΓL(1,𝔽8)×C67C2×C1111yescharacteristic, complemented, Hall
9D7×C67C3×C1111yescharacteristic, complemented, Hall
10C67⋊C11AGL(1,𝔽7)11yescharacteristic, direct product factor, Hall
11C7×C67C2×C3×C1111yescharacteristic, complemented, Hall
12C11×AGL(1,𝔽7)—671nomaximal, Hall
13C2×C3×C67—71noHall
14C11×ΓL(1,𝔽8)—671noHall
15C3×C67—71noHall
16C11×D7—671noHall
17C2×C67—71noHall
18C7×C11—671noHall
19C67C11×AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
20C2×C3×C11—4691noHall
21AGL(1,𝔽7)C67⋊C1111yescharacteristic, direct product factor, Hall
22C3×C11—4691noHall
23C2×C11—4691noHall
24ΓL(1,𝔽8)C2×C67⋊C1111yescharacteristic, complemented, Hall
25D7C3×C67⋊C1111yescharacteristic, complemented, Hall
26C11—671noSylow
27C7C2×C3×C67⋊C1111yescharacteristic, complemented, Sylow
28C2×C3—71noHall
29C3—71noSylow
30C2—71noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C67C2×C3×C11
LCSG ▷ C7×C67
UCSC1

Complements

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

NH ≅ G/Ntype
1. ΓL(1,𝔽8)×C67⋊C11C2semidirect
2. D7×C67⋊C11C3semidirect
3. C7×C67⋊C11C2×C3semidirect
5. AGL(1,𝔽7)×C67C11semidirect
8. ΓL(1,𝔽8)×C67C2×C11semidirect
9. D7×C67C3×C11semidirect
10. C67⋊C11AGL(1,𝔽7)direct (N × H)
11. C7×C67C2×C3×C11semidirect
19. C67C11×AGL(1,𝔽7)semidirect
21. AGL(1,𝔽7)C67⋊C11direct (N × H)
24. ΓL(1,𝔽8)C2×C67⋊C11semidirect
25. D7C3×C67⋊C11semidirect
27. C7C2×C3×C67⋊C11semidirect

Maximal subgroups

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

subgroupindex
ΓL(1,𝔽8)×C67⋊C112
D7×C67⋊C113
C2×C3×C67⋊C117
AGL(1,𝔽7)×C6711
C11×AGL(1,𝔽7)67