Finite Group Databasebeta

← C7×C3⋊(D67⋊C11) #44526249

Subgroups — C7×C3⋊(D67⋊C11) #44526249

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C67⋊C11C211yesmaximal, characteristic, complemented, Hall
2C7×D67⋊C11—31nomaximal, Hall
3C7×C67⋊C11D311yescharacteristic, complemented, Hall
4C3⋊(D67⋊C11)C711yesmaximal, characteristic, direct product factor, Hall
5C7×D201C1111yesmaximal, characteristic, complemented, Hall
6C3×C67⋊C11C2×C711yescharacteristic, complemented, Hall
7D67⋊C11—31noHall
8C3×C7×C67C2×C1111yescharacteristic, complemented, Hall
9C7×D67—31noHall
10C67⋊C11D3×C711yescharacteristic, complemented, Hall
11C7×C67D3×C1111yescharacteristic, complemented, Hall
12D3×C7×C11—671nomaximal, Hall
13D201C7×C1111yescharacteristic, complemented, Hall
14C3×C7×C11—671noHall
15C3×C67C2×C7×C1111yescharacteristic, complemented, Hall
16C2×C7×C11—2011noHall
17D67—31noHall
18C7×C11—671noHall
19C67D3×C7×C1111yescharacteristic, complemented, Sylow
20D3×C11—671noHall
21D3×C7—671noHall
22C3×C11—671noHall
23C2×C11—2011noHall
24C3×C7D67⋊C1111yescharacteristic, complemented, Hall
25C2×C7—2011noHall
26C11—671noSylow
27C7C3⋊(D67⋊C11)11yescharacteristic, direct product factor, Sylow
28D3—671noHall
29C3C7×D67⋊C1111yescharacteristic, complemented, Sylow
30C2—2011noSylow
subgroupG/H
center, hypercenterC7C3⋊(D67⋊C11)
commutator, cosocle, hypocenterC3×C67C2×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C67C2×C11
LCSG ▷ C3×C67
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C67⋊C11C2semidirect
3. C7×C67⋊C11D3semidirect
4. C3⋊(D67⋊C11)C7direct (N × H)
5. C7×D201C11semidirect
6. C3×C67⋊C11C2×C7semidirect
8. C3×C7×C67C2×C11semidirect
10. C67⋊C11D3×C7semidirect
11. C7×C67D3×C11semidirect
13. D201C7×C11semidirect
15. C3×C67C2×C7×C11semidirect
19. C67D3×C7×C11semidirect
24. C3×C7D67⋊C11semidirect
27. C7C3⋊(D67⋊C11)direct (N × H)
29. C3C7×D67⋊C11semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C67⋊C112
C7×D67⋊C113
C3⋊(D67⋊C11)7
C7×D20111
D3×C7×C1167