Finite Group Databasebeta

← C2×D3×C22⋊C9 #88894

Subgroups — C2×D3×C22⋊C9 #88894

Order 432.

148 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C22⋊C9C211yesmaximal, characteristic, complemented
2D3×C22⋊C9C212yesmaximal, direct product factor
3C23×C3×D3C311yesmaximal, characteristic
4C22×C22⋊C9—31nomaximal
5C2×D3×C9—41nomaximal
6C3×C22⋊C9C2211yescharacteristic, complemented
7C23×C32C2×C311yescharacteristic
8C22×C3×D3—31no—
9C22×C3×D3—31no—
10C22×C3×D3—32no—
11C22×C3×D3C2×C312yes—
12C2×C22⋊C9—21no—
13C2×C22⋊C9—32no—
14C2×C22⋊C9D311yescharacteristic, direct product factor
15C2×C3×C9—41no—
16D3×C9—42no—
17C24×C3—31no—
18C23×D3C911yescharacteristic, complemented
19C22×C32—31no—
20C22×C32—31no—
21C22×C32C22×C311yescharacteristic
22C2×C3×D3—32no—
23C2×C3×D3—31no—
24C2×C3×D3—32no—
25C2×C3×D3—32no—
26C2×C3×D3—32no—
27C2×C3×D3A411yescharacteristic
28C22×C9—121no—
29C22⋊C9—21no—
30C22⋊C9C2×D311yescharacteristic, direct product factor
31C3×C9—41noSylow
32C23×C3—21no—
33C23×C3—32no—
34C23×C3—91no—
35C23×C3—92no—
36C23×C3—91no—
37C23×C3C2×C911yescharacteristic, complemented
38C23×C3C3×D311yescharacteristic
39C22×D3—31no—
40C22×D3—31no—
41C22×D3—32no—
42C22×D3C2×C912yescomplemented
43C2×C32—31no—
44C2×C32—31no—
45C2×C32C2×A411yescharacteristic
46C3×D3—32no—
47C3×D3C2×A412yes—
48C2×C9—41no—
49C2×C9—81no—
50C2×C9—122no—
51C24—31noSylow
52C22×C3—21no—
53C22×C3—31no—
54C22×C3—31no—
55C22×C3—31no—
56C22×C3—31no—
57C22×C3—31no—
58C22×C3—61no—
59C22×C3—61no—
60C22×C3—92no—
61C22×C3—92no—
62C22×C3—92no—
63C22×C3—92no—
64C22×C3—91no—
65C22×C3C22×C911yescharacteristic, complemented
66C22×C3C2×C3×D311yescharacteristic
67C2×D3—32no—
68C2×D3—31no—
69C2×D3—32no—
70C2×D3—32no—
71C2×D3—32no—
72C2×D3C22⋊C911yescharacteristic, direct product factor
73C32C22×A411yescharacteristic
74C9—41no—
75C9—81no—
76C23—32no—
77C23—91no—
78C23—92no—
79C23—91no—
80C23D3×C911yescharacteristic, complemented
81C2×C3—21no—
82C2×C3—31no—
83C2×C3—31no—
84C2×C3—32no—
85C2×C3—31no—
86C2×C3—31no—
87C2×C3—61no—
88C2×C3—61no—
89C2×C3—92no—
90C2×C3C2×C22⋊C911yescharacteristic, complemented
91C2×C3D3×A411yescharacteristic
92D3—32no—
93D3C2×C22⋊C912yesdirect product factor
94C22—31no—
95C22—31no—
96C22—31no—
97C22—92no—
98C22—92no—
99C22—92no—
100C22—92no—
101C22—91no—
102C22C2×D3×C911yescharacteristic, complemented
103C3—21no—
104C3C22×C22⋊C911yescharacteristic, complemented
105C3C2×D3×A411yescharacteristic
106C2—31no—
107C2—31no—
108C2—32no—
109C2—92no—
110C2D3×C22⋊C911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D3×A4
commutator, hypocenterC22×C3C22×C9
FrattiniC3C2×D3×A4
Fitting, socleC23×C32C2×C3
prime radicalC23×C3×D3C3
cosocleC22×C32C22×C3
LCSG ▷ C22×C3
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C22⋊C9C2semidirect
2. D3×C22⋊C9C2direct (N × H)
6. C3×C22⋊C9C22semidirect
14. C2×C22⋊C9D3direct (N × H)
18. C23×D3C9semidirect
30. C22⋊C9C2×D3direct (N × H)
37. C23×C3C2×C9semidirect
42. C22×D3C2×C9semidirect
65. C22×C3C22×C9semidirect
72. C2×D3C22⋊C9direct (N × H)
80. C23D3×C9semidirect
90. C2×C3C2×C22⋊C9semidirect
93. D3C2×C22⋊C9direct (N × H)
102. C22C2×D3×C9semidirect
104. C3C22×C22⋊C9semidirect
110. C2D3×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊C92
D3×C22⋊C92
C23×C3×D33
C22×C22⋊C93
C2×D3×C94