Finite Group Databasebeta

← C2×#13064104⋊C11 #44526229

Subgroups — C2×#13064104⋊C11 #44526229

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13064104⋊C11C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C67⋊C11C311yesmaximal, characteristic, complemented, Hall
3C7×C67⋊C11C2×C311yescharacteristic, complemented, Hall
4C2×(C67⋊C3)⋊C11—71nomaximal, Hall
5C2×#13064104C1111yesmaximal, characteristic, complemented, Hall
6(C67⋊C3)⋊C11—71noHall
7C2×C67⋊C11ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
8#13064104C2×C1111yescharacteristic, complemented, Hall
9C2×C7×C67C3×C1111yescharacteristic, complemented, Hall
10C67⋊C11C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
11C7×C67C2×C3×C1111yescharacteristic, complemented, Hall
12C2×C11×ΓL(1,𝔽8)—671nomaximal, Hall
13C2×C67⋊C3—71noHall
14C11×ΓL(1,𝔽8)—671noHall
15C67⋊C3—71noHall
16C2×C7×C11—671noHall
17C2×C67C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
18C7×C11—671noHall
19C67C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
20C2×C3×C11—4691noHall
21C2×ΓL(1,𝔽8)—671noHall
22C3×C11—4691noHall
23C2×C11—671noHall
24ΓL(1,𝔽8)—671noHall
25C2×C7(C67⋊C3)⋊C1111yescharacteristic, complemented, Hall
26C11—671noSylow
27C7C2×(C67⋊C3)⋊C1111yescharacteristic, complemented, Sylow
28C2×C3—4691noHall
29C3—4691noSylow
30C2#13064104⋊C1111yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2#13064104⋊C11
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C67C3×C11
LCSG ▷ C7×C67
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #13064104⋊C11C2direct (N × H)
2. C2×C7×C67⋊C11C3semidirect
3. C7×C67⋊C11C2×C3semidirect
5. C2×#13064104C11semidirect
7. C2×C67⋊C11ΓL(1,𝔽8)semidirect
8. #13064104C2×C11semidirect
9. C2×C7×C67C3×C11semidirect
10. C67⋊C11C2×ΓL(1,𝔽8)semidirect
11. C7×C67C2×C3×C11semidirect
17. C2×C67C11×ΓL(1,𝔽8)semidirect
19. C67C2×C11×ΓL(1,𝔽8)semidirect
25. C2×C7(C67⋊C3)⋊C11semidirect
27. C7C2×(C67⋊C3)⋊C11semidirect
30. C2#13064104⋊C11direct (N × H)

Maximal subgroups

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

subgroupindex
#13064104⋊C112
C2×C7×C67⋊C113
C2×(C67⋊C3)⋊C117
C2×#1306410411
C2×C11×ΓL(1,𝔽8)67