Finite Group Databasebeta

← D9×D9⋊C9 #72243329

Subgroups — D9×D9⋊C9 #72243329

Order 2916.

259 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 259 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C9×D9⋊C9C211yesmaximal, characteristic, complemented
2#13090615C211yesmaximal, characteristic, complemented
3D9×C9⋊C9C211yesmaximal, characteristic, complemented
4D3×D9⋊C9—31nomaximal
5D3×C9×D9—31nomaximal
6C3×D92C311yesmaximal, characteristic
7C9×C9⋊C9C2211yescharacteristic, complemented, Sylow
8C3⋊(D9⋊C9)—31no—
9C3×C9⋊D9C2×C311yescharacteristic
10C9×C3⋊D9—31no—
11D3×C9⋊C9—31no—
12C3×D9⋊C9—21no—
13C3×D9⋊C9D311yescharacteristic
14D3×C92—31no—
15C3×C9×D9—21no—
16C3×C9×D9D311yescharacteristic
17C3×C9×D9C2×C311yescharacteristic
18C3×C9×D9C2×C311yescharacteristic
19#92158—61no—
20D32×C9—91no—
21C3×D3×D9—31no—
22C3×D3×D9—31no—
23C2×D9⋊C9—91no—
24C2×C9×D9—91no—
25D92C911yescharacteristic, complemented
26C3×C9⋊C9—21no—
27C3×C9⋊C9C2×D311yescharacteristic
28C3×C92—21no—
29C3×C92C2×D311yescharacteristic
30C3×C92C22×C311yescharacteristic
31#6855—21no—
32#6855—41no—
33C9×C3⋊D3—91no—
34C3×C3⋊D9—31no—
35C3×C3⋊D9—31no—
36C3×C3⋊D9—61no—
37C3×D3×C9—31no—
38C3×D3×C9—31no—
39C3×D3×C9—31no—
40C3×D3×C9—31no—
41C3×D3×C9—61no—
42C3×D3×C9—61no—
43C32×D9C3×D311yescharacteristic
44C32×D9C3×D311yescharacteristic
45C2×C9⋊C9—91no—
46C2×C92—91no—
47C9⋊D9C2×C911yescharacteristic, complemented
48D9⋊C9—23no—
49D9⋊C9—21no—
50D9⋊C9—91no—
51D9⋊C9—181no—
52D9⋊C9D911yescharacteristic, direct product factor
53C9×D9—21no—
54C9×D9—21no—
55C9×D9—31no—
56C9×D9—61no—
57C9×D9—91no—
58C9×D9—181no—
59C9×D9C2×C911yescharacteristic, complemented
60C9×D9C2×C911yescharacteristic, complemented
61C3×D32—91no—
62C2×D3×C9—271no—
63C2×D3×C9—271no—
64C2×C3×D9—91no—
65C2×C3×D9—91no—
66D3×D9—31no—
67D3×D9—31no—
68C32×C9—21no—
69C32×C9—21no—
70C32×C9—21no—
71C32×C9—41no—
72C32×C9D3211yescharacteristic
73C32×C9C2×C3×D311yescharacteristic
74C32×C9C2×C3×D311yescharacteristic
75C9⋊C9—23no—
76C9⋊C9—21no—
77C9⋊C9—21no—
78C9⋊C9—41no—
79C9⋊C9—43no—
80C9⋊C9C2×D911yescharacteristic, complemented
81C92—21no—
82C92—21no—
83C92—31no—
84C92—41no—
85C92—61no—
86C92—121no—
87C92—121no—
88C92C22×C911yescharacteristic, complemented
89C3×C3⋊D3—91no—
90C32×D3—31no—
91C32×D3—31no—
92C2×C3×C9—91no—
93C2×C3×C9—91no—
94C2×C3×C9—91no—
95C2×C3×C9—91no—
96C2×C3×C9—181no—
97C2×C3×C9—181no—
98C3⋊D9—31no—
99C3⋊D9—31no—
100C3⋊D9—61no—
101D3×C9—31no—
102D3×C9—31no—
103D3×C9—31no—
104D3×C9—61no—
105D3×C9—61no—
106D3×C9—61no—
107D3×C9—63no—
108D3×C9—181no—
109D3×C9—181no—
110D3×C9—271no—
111D3×C9—271no—
112D3×C9—541no—
113C3×D9—21no—
114C3×D9—21no—
115C3×D9—91no—
116C3×D9—91no—
117C3×D9—181no—
118C3×D9—181no—
119C3×D9—541no—
120C3×D9C3×D911yescharacteristic
121C3×D9D3×C911yescharacteristic
122C3×D9D3×C911yescharacteristic
123C3×D9AGL(1,ℤ/9)11yescharacteristic
124C2×C3×D3—271no—
125C2×C3×D3—271no—
126D32—91no—
127C22×C9—811no—
128C2×D9—91no—
129C2×D9—91no—
130C33C3×D3211yescharacteristic
131C3×C9—21no—
132C3×C9—21no—
133C3×C9—21no—
134C3×C9—21no—
135C3×C9—21no—
136C3×C9—21no—
137C3×C9—21no—
138C3×C9—21no—
139C3×C9—23no—
140C3×C9—21no—
141C3×C9—41no—
142C3×C9—41no—
143C3×C9—43no—
144C3×C9—41no—
145C3×C9—41no—
146C3×C9—61no—
147C3×C9—61no—
148C3×C9—61no—
149C3×C9—61no—
150C3×C9—121no—
151C3×C9—121no—
152C3×C9—121no—
153C3×C9—121no—
154C3×C9—121no—
155C3×C9—121no—
156C3×C9—121no—
157C3×C9D3×D911yescharacteristic
158C3×C9C2×C3×D911yescharacteristic
159C3×C9C2×D3×C911yescharacteristic
160C3×C9C2×D3×C911yescharacteristic
161C3×C9C2×AGL(1,ℤ/9)11yescharacteristic
162C2×C32—91no—
163C2×C32—91no—
164C3⋊D3—91no—
165C3×D3—31no—
166C3×D3—31no—
167C3×D3—31no—
168C3×D3—31no—
169C3×D3—61no—
170C3×D3—61no—
171C3×D3—271no—
172C3×D3—271no—
173C3×D3—541no—
174C2×C9—91no—
175C2×C9—91no—
176C2×C9—91no—
177C2×C9—181no—
178C2×C9—181no—
179C2×C9—181no—
180C2×C9—183no—
181C2×C9—541no—
182C2×C9—541no—
183C2×C9—811no—
184D9—91no—
185D9—91no—
186D9—181no—
187D9—181no—
188D9—541no—
189D9C9×D911yescharacteristic, complemented
190D9D9⋊C911yescharacteristic, direct product factor
191C22×C3—811no—
192C2×D3—271no—
193C2×D3—271no—
194C32—21no—
195C32—21no—
196C32—21no—
197C32—41no—
198C32C3×D3×D911yescharacteristic
199C32D32×C911yescharacteristic
200C32D3×AGL(1,ℤ/9)11yescharacteristic
201C9—21no—
202C9—21no—
203C9—21no—
204C9—21no—
205C9—41no—
206C9—41no—
207C9—61no—
208C9—61no—
209C9—61no—
210C9—123no—
211C9—121no—
212C9—121no—
213C9—123no—
214C9—121no—
215C9C2×C9×D911yescharacteristic, complemented
216C9C2×D9⋊C911yescharacteristic, complemented
217C2×C3—91no—
218C2×C3—91no—
219C2×C3—91no—
220C2×C3—91no—
221C2×C3—181no—
222C2×C3—181no—
223C2×C3—811no—
224D3—31no—
225D3—31no—
226D3—271no—
227D3—271no—
228D3—541no—
229C22—811noSylow
230C3—21no—
231C3—21no—
232C3—21no—
233C3—41no—
234C3D3×C9×D911yescharacteristic
235C3D3×D9⋊C911yescharacteristic
236C3D9×AGL(1,ℤ/9)11yescharacteristic
237C2—91no—
238C2—91no—
239C2—811no—
subgroupG/H
center, hypercenterC3D9×AGL(1,ℤ/9)
commutator, hypocenterC92C22×C9
Frattini, socleC33C3×D32
FittingC9×C9⋊C9C22
prime radicalC3×D92C3
cosocleC3×C92C22×C3
LCSG ▷ C92
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C9×D9⋊C9C2semidirect
2. #13090615C2semidirect
3. D9×C9⋊C9C2semidirect
7. C9×C9⋊C9C22semidirect
25. D92C9semidirect
47. C9⋊D9C2×C9semidirect
52. D9⋊C9D9direct (N × H)
59. C9×D9C2×C9semidirect
60. C9×D9C2×C9semidirect
80. C9⋊C9C2×D9semidirect
88. C92C22×C9semidirect
189. D9C9×D9semidirect
190. D9D9⋊C9direct (N × H)
215. C9C2×C9×D9semidirect
216. C9C2×D9⋊C9semidirect

Maximal subgroups

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

subgroupindex
C9×D9⋊C92
#130906152
D9×C9⋊C92
D3×D9⋊C93
D3×C9×D93
C3×D923