Finite Group Databasebeta

← C2×C11×#13064105 #44526224

Subgroups — C2×C11×#13064105 #44526224

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#13064105C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C11×C67C311yesmaximal, characteristic, complemented, Hall
3C7×C11×C67C2×C311yescharacteristic, complemented, Hall
4C2×C11×C67⋊C3—71nomaximal, Hall
5C2×#13064105C1111yesmaximal, characteristic, direct product factor, Hall
6C11×C67⋊C3—71noHall
7C2×C11×C67ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
8#13064105C2×C1111yescharacteristic, direct product factor, Hall
9C2×C7×C67C3×C1111yescharacteristic, complemented, Hall
10C11×C67C2×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×C11C67⋊C311yescharacteristic, complemented, Hall
17C2×C67C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
18C7×C11C2×C67⋊C311yescharacteristic, complemented, Hall
19C67C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
20C2×C3×C11—4691noHall
21C2×ΓL(1,𝔽8)—671noHall
22C3×C11—4691noHall
23C2×C11#1306410511yescharacteristic, direct product factor, Hall
24ΓL(1,𝔽8)—671noHall
25C2×C7C11×C67⋊C311yescharacteristic, complemented, Hall
26C11C2×#1306410511yescharacteristic, direct product factor, Sylow
27C7C2×C11×C67⋊C311yescharacteristic, complemented, Sylow
28C2×C3—4691noHall
29C3—4691noSylow
30C2C11×#1306410511yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C11#13064105
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C67C3
LCSG ▷ C7×C67
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
1. C11×#13064105C2direct (N × H)
2. C2×C7×C11×C67C3semidirect
3. C7×C11×C67C2×C3semidirect
5. C2×#13064105C11direct (N × H)
7. C2×C11×C67ΓL(1,𝔽8)semidirect
8. #13064105C2×C11direct (N × H)
9. C2×C7×C67C3×C11semidirect
10. C11×C67C2×ΓL(1,𝔽8)semidirect
11. C7×C67C2×C3×C11semidirect
16. C2×C7×C11C67⋊C3semidirect
17. C2×C67C11×ΓL(1,𝔽8)semidirect
18. C7×C11C2×C67⋊C3semidirect
19. C67C2×C11×ΓL(1,𝔽8)semidirect
23. C2×C11#13064105direct (N × H)
25. C2×C7C11×C67⋊C3semidirect
26. C11C2×#13064105direct (N × H)
27. C7C2×C11×C67⋊C3semidirect
30. C2C11×#13064105direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#130641052
C2×C7×C11×C673
C2×C11×C67⋊C37
C2×#1306410511
C2×C11×ΓL(1,𝔽8)67