Finite Group Databasebeta

← C9×#213 #88503

Subgroups — C9×#213 #88503

Order 432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×C9C211yesmaximal, characteristic, complemented
2C9×D12C211yesmaximal, characteristic, complemented
3C9×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#213C311yesmaximal, characteristic
5C9×D8—31nomaximal
6C22×C3×C9—21no—
7C2×D3×C9—21no—
8C3×C4×C9C2211yescharacteristic
9C32×D4C2×C311yescharacteristic
10C3×D12C2×C311yescharacteristic
11C3×C3⋊C8C2×C311yescharacteristic
12D4×C9—21no—
13D4×C9—31no—
14D4×C9D311yescharacteristic, complemented
15C8×C9—31no—
16C2×C3×C9—41no—
17C2×C3×C9D411yescharacteristic
18D3×C9—41no—
19C3×D8—31no—
20#213C911yescharacteristic, direct product factor
21C22×C32—21no—
22C2×C3×D3—21no—
23C32×C4C22×C311yescharacteristic
24C22×C9—22no—
25C22×C9—21no—
26C22×C9—61no—
27C4×C9—21no—
28C4×C9C2×D311yescharacteristic
29C3×C9D811yescharacteristic, complemented, Sylow
30C3×D4—21no—
31C3×D4—31no—
32C3×D4C2×C911yescharacteristic, complemented
33C3×D4C3×D311yescharacteristic
34D12C2×C911yescharacteristic, complemented
35C3×C8—31no—
36C3⋊C8C2×C911yescharacteristic, complemented
37C2×C32—41no—
38C2×C32C3×D411yescharacteristic
39C3×D3—41no—
40C2×C9—21no—
41C2×C9—42no—
42C2×C9—41no—
43C2×C9—121no—
44C2×C9#6711yescharacteristic
45D8—31noSylow
46C22×C3—22no—
47C22×C3—21no—
48C22×C3—21no—
49C22×C3—61no—
50C2×D3—21no—
51C3×C4—21no—
52C3×C4C22×C911yescharacteristic
53C3×C4C2×C3×D311yescharacteristic
54C32C3×D811yescharacteristic
55C9—21no—
56C9#21311yescharacteristic, direct product factor
57D4—31no—
58D4D3×C911yescharacteristic, complemented
59C8—31no—
60C2×C3—21no—
61C2×C3—42no—
62C2×C3—41no—
63C2×C3—41no—
64C2×C3—121no—
65C2×C3D4×C911yescharacteristic
66C2×C3C3×#6711yescharacteristic
67D3—41no—
68C22—21no—
69C22—61no—
70C4C2×D3×C911yescharacteristic
71C3—21no—
72C3C9×D811yescharacteristic, complemented
73C3C3×#21311yescharacteristic
74C2—41no—
75C2—121no—
76C2C9×#6711yescharacteristic
subgroupG/H
centerC2×C9#67
commutatorC3×C4C22×C9
FrattiniC3×C4C2×C3×D3
FittingC3×D4×C9C2
socleC2×C32C3×D4
prime radicalC3×#213C3
cosocleC32×C4C22×C3
hypercenterD4×C9D3
hypocenterC3C9×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ D4×C9

Complements

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

NH ≅ G/Ntype
1. C3×D4×C9C2semidirect
2. C9×D12C2semidirect
3. C9×C3⋊C8C2semidirect
14. D4×C9D3semidirect
20. #213C9direct (N × H)
29. C3×C9D8semidirect
32. C3×D4C2×C9semidirect
34. D12C2×C9semidirect
36. C3⋊C8C2×C9semidirect
56. C9#213direct (N × H)
58. D4D3×C9semidirect
72. C3C9×D8semidirect

Maximal subgroups

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

subgroupindex
C3×D4×C92
C9×D122
C9×C3⋊C82
C3×#2133
C9×D83