Finite Group Databasebeta

← C2×C7×(C67⋊C3)⋊C11 #44526226

Subgroups — C2×C7×(C67⋊C3)⋊C11 #44526226

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×(C67⋊C3)⋊C11C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C67⋊C11C311yesmaximal, characteristic, complemented, Hall
3C7×C67⋊C11C2×C311yescharacteristic, complemented, Hall
4C2×(C67⋊C3)⋊C11C711yesmaximal, characteristic, direct product factor, Hall
5C2×C7×C67⋊C3C1111yesmaximal, characteristic, complemented, Hall
6(C67⋊C3)⋊C11C2×C711yescharacteristic, direct product factor, Hall
7C2×C67⋊C11C3×C711yescharacteristic, complemented, Hall
8C7×C67⋊C3C2×C1111yescharacteristic, complemented, Hall
9C2×C7×C67C3×C1111yescharacteristic, complemented, Hall
10C67⋊C11C2×C3×C711yescharacteristic, complemented, Hall
11C7×C67C2×C3×C1111yescharacteristic, complemented, Hall
12C2×C3×C7×C11—671nomaximal, Hall
13C2×C67⋊C3C7×C1111yescharacteristic, complemented, Hall
14C3×C7×C11—671noHall
15C67⋊C3C2×C7×C1111yescharacteristic, complemented, Hall
16C2×C7×C11—671noHall
17C2×C67C3×C7×C1111yescharacteristic, complemented, Hall
18C7×C11—671noHall
19C67C2×C3×C7×C1111yescharacteristic, complemented, Sylow
20C2×C3×C11—671noHall
21C2×C3×C7—671noHall
22C3×C11—671noHall
23C2×C11—671noHall
24C3×C7—671noHall
25C2×C7(C67⋊C3)⋊C1111yescharacteristic, direct product factor, Hall
26C11—671noSylow
27C7C2×(C67⋊C3)⋊C1111yescharacteristic, direct product factor, Sylow
28C2×C3—671noHall
29C3—671noSylow
30C2C7×(C67⋊C3)⋊C1111yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C7(C67⋊C3)⋊C11
commutator, cosocle, hypocenterC67C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C67C3×C11
LCSG ▷ C67
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×(C67⋊C3)⋊C11C2direct (N × H)
2. C2×C7×C67⋊C11C3semidirect
3. C7×C67⋊C11C2×C3semidirect
4. C2×(C67⋊C3)⋊C11C7direct (N × H)
5. C2×C7×C67⋊C3C11semidirect
6. (C67⋊C3)⋊C11C2×C7direct (N × H)
7. C2×C67⋊C11C3×C7semidirect
8. C7×C67⋊C3C2×C11semidirect
9. C2×C7×C67C3×C11semidirect
10. C67⋊C11C2×C3×C7semidirect
11. C7×C67C2×C3×C11semidirect
13. C2×C67⋊C3C7×C11semidirect
15. C67⋊C3C2×C7×C11semidirect
17. C2×C67C3×C7×C11semidirect
19. C67C2×C3×C7×C11semidirect
25. C2×C7(C67⋊C3)⋊C11direct (N × H)
27. C7C2×(C67⋊C3)⋊C11direct (N × H)
30. C2C7×(C67⋊C3)⋊C11direct (N × H)

Maximal subgroups

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

subgroupindex
C7×(C67⋊C3)⋊C112
C2×C7×C67⋊C113
C2×(C67⋊C3)⋊C117
C2×C7×C67⋊C311
C2×C3×C7×C1167