Finite Group Databasebeta

← #88417

Subgroups — #88417

Order 432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C3×D36C211yesmaximal, characteristic, complemented
3C9×C3⋊C8C211yesmaximal, characteristic, complemented
4#3714—31nomaximal
5D72—31nomaximal
6C2×C3⋊D9—21no—
7C2×C3×D9—21no—
8C3×C4×C9C2211yescharacteristic
9C4⋊(C3⋊D3)—31no—
10C3×D12—31no—
11C3×C3⋊C8D311yescharacteristic
12D36—31no—
13D36—61no—
14D36D311yescharacteristic, complemented
15C8×C9—31no—
16C2×C3×C9D411yescharacteristic
17C3⋊D9—41no—
18C3×D9—41no—
19#213—91no—
20D24—91no—
21C2×C3⋊D3—61no—
22C2×C3×D3—61no—
23C32×C4C2×D311yescharacteristic
24C2×D9—21no—
25C2×D9—62no—
26C2×D9—61no—
27C4×C9—21no—
28C4×C9C2×D311yescharacteristic
29C3×C9D811yescharacteristic, complemented, Sylow
30C3×D4—91no—
31D12—31no—
32D12—91no—
33D12—91no—
34D12—181no—
35C3×C8—31no—
36C3⋊C8D911yescharacteristic, complemented
37C2×C32D1211yescharacteristic
38C3⋊D3—121no—
39C3×D3—121no—
40C2×C9—21no—
41C2×C9#6711yescharacteristic
42D9—41no—
43D9—122no—
44D9—121no—
45D8—271noSylow
46C22×C3—181no—
47C2×D3—61no—
48C2×D3—182no—
49C2×D3—181no—
50C2×D3—181no—
51C3×C4—21no—
52C3×C4C2×D911yescharacteristic
53C3×C4D3211yescharacteristic
54C32D2411yescharacteristic
55C9—21no—
56C9#21311yescharacteristic, complemented
57D4—91no—
58D4—271no—
59C8—31no—
60C2×C3—21no—
61C2×C3—361no—
62C2×C3D3611yescharacteristic
63C2×C3#62611yescharacteristic
64D3—121no—
65D3—362no—
66D3—361no—
67D3—361no—
68C22—181no—
69C22—541no—
70C4D3×D911yescharacteristic
71C3—21no—
72C3D7211yescharacteristic, complemented
73C3#371411yescharacteristic
74C2—361no—
75C2—1081no—
76C2#619211yescharacteristic
subgroupG/H
centerC2#6192
commutator, Fitting, cosocleC3×C4×C9C22
FrattiniC3×C4D32
socleC2×C32D12
hypercenterC4D3×D9
hypocenterC3×C9D8
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C4⋊(C3⋊D9)C2semidirect
2. C3×D36C2semidirect
3. C9×C3⋊C8C2semidirect
14. D36D3semidirect
29. C3×C9D8semidirect
36. C3⋊C8D9semidirect
56. C9#213semidirect
72. C3D72semidirect

Maximal subgroups

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

subgroupindex
C4⋊(C3⋊D9)2
C3×D362
C9×C3⋊C82
#37143
D723