Finite Group Databasebeta

← D3×(C67⋊C3)⋊C11 #27210708

Subgroups — D3×(C67⋊C3)⋊C11 #27210708

Order 13266.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×(C67⋊C3)⋊C11C211yesmaximal, characteristic, complemented, Hall
2D3×C67⋊C11C311yesmaximal, characteristic, complemented
3C2×(C67⋊C3)⋊C11—31nomaximal
4C3×C67⋊C11C2×C311yescharacteristic, complemented
5(C67⋊C3)⋊C11—21no—
6(C67⋊C3)⋊C11D311yescharacteristic, direct product factor
7C2×C67⋊C11—31noHall
8D3×C67⋊C3C1111yesmaximal, characteristic, complemented, Hall
9C67⋊C11C3×D311yescharacteristic, complemented, Hall
10C3×C67⋊C3C2×C1111yescharacteristic, complemented, Hall
11D3×C67C3×C1111yescharacteristic, complemented
12C2×C67⋊C3—31no—
13C3×C67C2×C3×C1111yescharacteristic, complemented
14C67⋊C3—21no—
15C67⋊C3D3×C1111yescharacteristic, complemented
16C3×D3×C11—671nomaximal, Hall
17C2×C67—31noHall
18C32×C11—671noHall
19C67C3×D3×C1111yescharacteristic, complemented, Sylow
20C2×C3×C11—2011no—
21D3×C11—671no—
22C3×C11—671no—
23C3×C11—671no—
24C3×C11—1341no—
25C2×C11—2011noHall
26C3×D3—671noHall
27C11—671noSylow
28C32—671noSylow
29C2×C3—2011no—
30D3(C67⋊C3)⋊C1111yescharacteristic, direct product factor
31C3—671no—
32C3—1341no—
33C3C2×(C67⋊C3)⋊C1111yescharacteristic, complemented
34C2—31noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C67C2×C3×C11
LCSG ▷ C3×C67
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×(C67⋊C3)⋊C11C2semidirect
2. D3×C67⋊C11C3semidirect
4. C3×C67⋊C11C2×C3semidirect
6. (C67⋊C3)⋊C11D3direct (N × H)
8. D3×C67⋊C3C11semidirect
9. C67⋊C11C3×D3semidirect
10. C3×C67⋊C3C2×C11semidirect
11. D3×C67C3×C11semidirect
13. C3×C67C2×C3×C11semidirect
15. C67⋊C3D3×C11semidirect
19. C67C3×D3×C11semidirect
30. D3(C67⋊C3)⋊C11direct (N × H)
33. C3C2×(C67⋊C3)⋊C11semidirect

Maximal subgroups

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

subgroupindex
C3×(C67⋊C3)⋊C112
D3×C67⋊C113
C2×(C67⋊C3)⋊C113
D3×C67⋊C311
C3×D3×C1167