Finite Group Databasebeta

← D9×#67 #88667

Subgroups — D9×#67 #88667

Order 432.

178 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C22×C3×D9C211yesmaximal, characteristic, complemented
2C2×D3×D9C211yesmaximal, characteristic, complemented
3#6233C211yesmaximal, characteristic, complemented
4C9×#67C211yesmaximal, characteristic, complemented
5#6194C211yesmaximal, characteristic, complemented
6#6192C211yesmaximal, characteristic, complemented
7Dic3×D9C211yesmaximal, characteristic, complemented
8D3×#67—31nomaximal
9D4×D9—31nomaximal
10C22×C3×C9C2211yescharacteristic, complemented
11C2×C3⋊D9C2211yescharacteristic, complemented
12C2×D3×C9C2211yescharacteristic, complemented
13C2×C3×D9—22no—
14C2×C3×D9C2211yescharacteristic
15C2×C3×D9C2211yescharacteristic, complemented
16D3×D9—22no—
17C3⋊Dic9C2211yescharacteristic, complemented
18C9×Dic3C2211yescharacteristic, complemented
19C22×C3×D3—31no—
20C2×D32—31no—
21#638—31no—
22C3×#67D311yescharacteristic
23#626—31no—
24#625—31no—
25D3×Dic3—31no—
26C22×D9—31no—
27C22×D9D311yescharacteristic, complemented
28D4×C9—31no—
29#611—31no—
30#611—31no—
31#611—61no—
32D36—31no—
33C4×D9—31no—
34C2×C3×C9—21no—
35C2×C3×C9C2311yescharacteristic
36C3⋊D9—21no—
37D3×C9—21no—
38C3×D9—21no—
39C3×D9D412yescomplemented
40C2×#67—91no—
41D3×D4—91no—
42C22×C32C2×D311yescharacteristic
43C2×C3⋊D3—31no—
44C2×C3×D3—31no—
45C2×C3×D3—31no—
46C2×C3×D3—62no—
47C2×C3×D3C2×D311yescharacteristic
48D32—62no—
49C3⋊Dic3—31no—
50C3×Dic3C2×D311yescharacteristic
51C22×C9—21no—
52C22×C9—31no—
53C22×C9C2×D311yescharacteristic, complemented
54C2×D9—22no—
55C2×D9—31no—
56C2×D9—61no—
57C2×D9—62no—
58C2×D9C2×D311yescharacteristic
59C2×D9C2×D311yescharacteristic, complemented
60C4×C9—31no—
61Dic9—31no—
62Dic9—61no—
63C3×C9C2×D411yescharacteristic, complemented, Sylow
64C23×C3—91no—
65C22×D3—31no—
66C22×D3—91no—
67C22×D3—91no—
68C3×D4—31no—
69#67—91no—
70#67—91no—
71#67—91no—
72#67—91no—
73#67—91no—
74#67—181no—
75#67D911yescharacteristic, direct product factor
76C2×Dic3—91no—
77D12—91no—
78C4×D3—91no—
79C2×C32—21no—
80C2×C32C22×D311yescharacteristic
81C3⋊D3—61no—
82C3×D3—21no—
83C3×D3—32no—
84C3×D3—61no—
85C2×C9—21no—
86C2×C9—21no—
87C2×C9—41no—
88C2×C9—61no—
89C2×C9C22×D311yescharacteristic
90D9—21no—
91D9—61no—
92D9—121no—
93D9#6712yesdirect product factor
94C2×D4—271noSylow
95C22×C3—21no—
96C22×C3—31no—
97C22×C3—91no—
98C22×C3—91no—
99C22×C3—182no—
100C22×C3C2×D911yescharacteristic, complemented
101C22×C3D3211yescharacteristic
102C2×D3—31no—
103C2×D3—31no—
104C2×D3—62no—
105C2×D3—91no—
106C2×D3—91no—
107C2×D3—181no—
108C2×D3—182no—
109C2×D3—182no—
110C2×D3C2×D911yescharacteristic, complemented
111C3×C4—31no—
112Dic3—91no—
113Dic3—91no—
114Dic3—181no—
115Dic3C2×D911yescharacteristic, complemented
116C32D3×D411yescharacteristic
117C9—21no—
118C9C2×#6711yescharacteristic, complemented
119C23—91no—
120C23—271no—
121D4—31no—
122D4—271no—
123D4—271no—
124D4—271no—
125C2×C4—271no—
126C2×C3—21no—
127C2×C3—21no—
128C2×C3—21no—
129C2×C3—41no—
130C2×C3—61no—
131C2×C3—92no—
132C2×C3—181no—
133C2×C3C22×D911yescharacteristic
134C2×C3C2×D3211yescharacteristic
135D3—21no—
136D3—32no—
137D3—61no—
138D3—181no—
139D3—181no—
140D3—361no—
141C22—31no—
142C22—91no—
143C22—91no—
144C22—182no—
145C22—271no—
146C22—542no—
147C22D3×D911yescharacteristic, complemented
148C4—31no—
149C4—271no—
150C3—21no—
151C3D4×D911yescharacteristic, complemented
152C3D3×#6711yescharacteristic
153C2—21no—
154C2—61no—
155C2—92no—
156C2—181no—
157C2—541no—
158C2C2×D3×D911yescharacteristic
subgroupG/H
centerC2C2×D3×D9
commutator, cosocleC2×C3×C9C23
FrattiniC2×C3C2×D32
FittingC22×C3×C9C22
socleC2×C32C22×D3
hypercenterC22D3×D9
hypocenterC3×C9C2×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×D9C2semidirect
2. C2×D3×D9C2semidirect
3. #6233C2semidirect
4. C9×#67C2semidirect
5. #6194C2semidirect
6. #6192C2semidirect
7. Dic3×D9C2semidirect
10. C22×C3×C9C22semidirect
11. C2×C3⋊D9C22semidirect
12. C2×D3×C9C22semidirect
15. C2×C3×D9C22semidirect
17. C3⋊Dic9C22semidirect
18. C9×Dic3C22semidirect
27. C22×D9D3semidirect
39. C3×D9D4semidirect
53. C22×C9C2×D3semidirect
59. C2×D9C2×D3semidirect
63. C3×C9C2×D4semidirect
75. #67D9direct (N × H)
93. D9#67direct (N × H)
100. C22×C3C2×D9semidirect
110. C2×D3C2×D9semidirect
115. Dic3C2×D9semidirect
118. C9C2×#67semidirect
147. C22D3×D9semidirect
151. C3D4×D9semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D92
C2×D3×D92
#62332
C9×#672
#61942
#61922
Dic3×D92
D3×#673
D4×D93