Finite Group Databasebeta

← C4×D3×D9 #88643

Subgroups — C4×D3×D9 #88643

Order 432.

178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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×D3×D9C211yesmaximal, characteristic
2C4×C3⋊D9C211yesmaximal, characteristic, complemented
3C4×D3×C9C211yesmaximal, characteristic, complemented
4C3×C4×D9C211yesmaximal, characteristic, complemented
5D3×Dic9C211yesmaximal, characteristic, complemented
6(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
7Dic3×D9C211yesmaximal, characteristic, complemented
8C4×D32—31nomaximal
9C2×C4×D9—31nomaximal
10C2×C3⋊D9C2211yescharacteristic
11C2×D3×C9C2211yescharacteristic
12C2×C3×D9C2211yescharacteristic
13D3×D9C414yesdirect product factor
14C3×C4×C9C2211yescharacteristic, complemented
15C3⋊Dic9C2211yescharacteristic, complemented
16C9×Dic3C2211yescharacteristic, complemented
17C3×Dic9C2211yescharacteristic, complemented
18C2×D32—31no—
19C4×C3⋊D3—31no—
20C3×C4×D3—31no—
21C3×C4×D3D311yescharacteristic
22#624—31no—
23D3×Dic3—31no—
24D3×Dic3—31no—
25C22×D9—31no—
26C2×C4×C9—31no—
27C2×Dic9—31no—
28C4×D9—31no—
29C4×D9—31no—
30C4×D9—31no—
31C4×D9—61no—
32C4×D9D311yescharacteristic, direct product factor
33C2×C3×C9C2311yescharacteristic
34C3⋊D9C2×C412yescomplemented
35D3×C9C2×C412yescomplemented
36C3×D9C2×C412yescomplemented
37C2×C4×D3—91no—
38C2×C4×D3—91no—
39C2×C3⋊D3—31no—
40C2×C3×D3—31no—
41C2×C3×D3C2×D311yescharacteristic
42D32—34no—
43C32×C4C2×D311yescharacteristic
44C3⋊Dic3—31no—
45C3×Dic3—31no—
46C3×Dic3C2×D311yescharacteristic
47C22×C9—31no—
48C2×D9—31no—
49C2×D9—34no—
50C2×D9—61no—
51C2×D9C2×D311yescharacteristic
52C4×C9—21no—
53C4×C9—31no—
54C4×C9C2×D311yescharacteristic, complemented
55Dic9—31no—
56Dic9—61no—
57Dic9C2×D311yescharacteristic, complemented
58C3×C9C22×C411yescharacteristic, complemented, Sylow
59C22×D3—91no—
60C22×D3—91no—
61C2×C3×C4—31no—
62C2×C3×C4—91no—
63C2×Dic3—91no—
64C2×Dic3—91no—
65C4×D3—31no—
66C4×D3—91no—
67C4×D3—91no—
68C4×D3—91no—
69C4×D3—91no—
70C4×D3—91no—
71C4×D3—91no—
72C4×D3—181no—
73C4×D3D911yescharacteristic, direct product factor
74C2×C32C22×D311yescharacteristic
75C3⋊D3—32no—
76C3×D3—32no—
77C3×D3C4×D312yes—
78C2×C9—21no—
79C2×C9—32no—
80C2×C9C22×D311yescharacteristic
81D9—32no—
82D9—62no—
83D9C4×D312yesdirect product factor
84C22×C4—271noSylow
85C22×C3—31no—
86C22×C3—91no—
87C2×D3—31no—
88C2×D3—94no—
89C2×D3—91no—
90C2×D3—91no—
91C2×D3—94no—
92C2×D3—181no—
93C2×D3C2×D911yescharacteristic
94C3×C4—21no—
95C3×C4—31no—
96C3×C4—91no—
97C3×C4C2×D911yescharacteristic, complemented
98C3×C4D3211yescharacteristic
99Dic3—31no—
100Dic3—91no—
101Dic3—91no—
102Dic3—181no—
103Dic3C2×D911yescharacteristic, complemented
104C32C2×C4×D311yescharacteristic
105C9—21no—
106C9C2×C4×D311yescharacteristic, complemented
107C23—271no—
108C2×C4—31no—
109C2×C4—91no—
110C2×C4—271no—
111C2×C4—271no—
112C2×C4—271no—
113C2×C4—271no—
114C2×C3—21no—
115C2×C3—32no—
116C2×C3—92no—
117C2×C3C22×D911yescharacteristic
118C2×C3C2×D3211yescharacteristic
119D3—32no—
120D3—92no—
121D3—92no—
122D3—182no—
123D3C4×D912yesdirect product factor
124C22—31no—
125C22—91no—
126C22—274no—
127C22—271no—
128C4—31no—
129C4—91no—
130C4—271no—
131C4D3×D911yescharacteristic, direct product factor
132C3—21no—
133C3C2×C4×D911yescharacteristic, complemented
134C3C4×D3211yescharacteristic
135C2—32no—
136C2—92no—
137C2—272no—
138C2C2×D3×D911yescharacteristic
subgroupG/H
center, hypercenterC4D3×D9
commutator, hypocenterC3×C9C22×C4
FrattiniC2×C3C2×D32
FittingC3×C4×C9C22
socleC2×C32C22×D3
prime radicalC2×D3×D9C2
cosocleC2×C3×C9C23
LCSG ▷ C3×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C3⋊D9C2semidirect
3. C4×D3×C9C2semidirect
4. C3×C4×D9C2semidirect
5. D3×Dic9C2semidirect
6. (C3⋊D9)⋊C4C2semidirect
7. Dic3×D9C2semidirect
13. D3×D9C4direct (N × H)
14. C3×C4×C9C22semidirect
15. C3⋊Dic9C22semidirect
16. C9×Dic3C22semidirect
17. C3×Dic9C22semidirect
32. C4×D9D3direct (N × H)
34. C3⋊D9C2×C4semidirect
35. D3×C9C2×C4semidirect
36. C3×D9C2×C4semidirect
54. C4×C9C2×D3semidirect
57. Dic9C2×D3semidirect
58. C3×C9C22×C4semidirect
73. C4×D3D9direct (N × H)
83. D9C4×D3direct (N × H)
97. C3×C4C2×D9semidirect
103. Dic3C2×D9semidirect
106. C9C2×C4×D3semidirect
123. D3C4×D9direct (N × H)
131. C4D3×D9direct (N × H)
133. C3C2×C4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D92
C4×C3⋊D92
C4×D3×C92
C3×C4×D92
D3×Dic92
(C3⋊D9)⋊C42
Dic3×D92
C4×D323
C2×C4×D93