Finite Group Databasebeta

← C9×#67 #6221

Subgroups — C9×#67 #6221

Order 216.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C9C211yesmaximal, characteristic, complemented
2C2×D3×C9C211yesmaximal, characteristic, complemented
3C9×Dic3C211yesmaximal, characteristic, complemented
4C3×#67C311yesmaximal, characteristic
5D4×C9—31nomaximal
6C2×C3×C9—21no—
7C2×C3×C9C2211yescharacteristic
8D3×C9—21no—
9C22×C32C2×C311yescharacteristic
10C2×C3×D3C2×C311yescharacteristic
11C3×Dic3C2×C311yescharacteristic
12C22×C9—21no—
13C22×C9—31no—
14C22×C9D311yescharacteristic, complemented
15C4×C9—31no—
16C3×C9D411yescharacteristic, complemented, Sylow
17C3×D4—31no—
18#67C911yescharacteristic, direct product factor
19C2×C32—21no—
20C2×C32C22×C311yescharacteristic
21C3×D3—21no—
22C2×C9—22no—
23C2×C9—21no—
24C2×C9—21no—
25C2×C9—61no—
26C2×C9C2×D311yescharacteristic
27C22×C3—21no—
28C22×C3—31no—
29C22×C3C2×C911yescharacteristic, complemented
30C22×C3C3×D311yescharacteristic
31C2×D3C2×C911yescharacteristic, complemented
32C3×C4—31no—
33Dic3C2×C911yescharacteristic, complemented
34C32C3×D411yescharacteristic
35C9—21no—
36C9#6711yescharacteristic, direct product factor
37D4—31noSylow
38C2×C3—22no—
39C2×C3—21no—
40C2×C3—21no—
41C2×C3—21no—
42C2×C3—61no—
43C2×C3C22×C911yescharacteristic
44C2×C3C2×C3×D311yescharacteristic
45D3—21no—
46C22—31no—
47C22D3×C911yescharacteristic, complemented
48C4—31no—
49C3—21no—
50C3D4×C911yescharacteristic, complemented
51C3C3×#6711yescharacteristic
52C2—21no—
53C2—61no—
54C2C2×D3×C911yescharacteristic
subgroupG/H
centerC2×C9C2×D3
commutatorC2×C3C22×C9
FrattiniC2×C3C2×C3×D3
FittingC22×C3×C9C2
socle, cosocleC2×C32C22×C3
prime radicalC3×#67C3
hypercenterC22×C9D3
hypocenterC3D4×C9
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C9 ◁ C22×C9

Complements

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

NH ≅ G/Ntype
1. C22×C3×C9C2semidirect
2. C2×D3×C9C2semidirect
3. C9×Dic3C2semidirect
14. C22×C9D3semidirect
16. C3×C9D4semidirect
18. #67C9direct (N × H)
29. C22×C3C2×C9semidirect
31. C2×D3C2×C9semidirect
33. Dic3C2×C9semidirect
36. C9#67direct (N × H)
47. C22D3×C9semidirect
50. C3D4×C9semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C92
C2×D3×C92
C9×Dic32
C3×#673
D4×C93