Finite Group Databasebeta

← C9×D9×C3⋊D3 #72228643

Subgroups — C9×D9×C3⋊D3 #72228643

Order 2916.

730 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C92×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C9×D9C211yesmaximal, characteristic, complemented
4D3×C9×C3⋊D3—31nomaximal
5C3×D9×C3⋊D3C311yesmaximal, characteristic
6D3×C9×D9—34nomaximal
7C32×C92C2211yescharacteristic, complemented, Sylow
8C9×C3⋊(C3⋊D3)—31no—
9C3×C3⋊(C3⋊D9)C2×C311yescharacteristic
10C3×C9×C3⋊D3—21no—
11C3×C9×C3⋊D3D311yescharacteristic
12C3×C9×C3⋊D3C2×C311yescharacteristic
13C32×D3×C9—31no—
14C33×D9C2×C311yescharacteristic
15C9×C3⋊D9—34no—
16C9×C3⋊D9—64no—
17D3×C92—34no—
18C3×C9×D9—24no—
19C3×C9×D9D314yescomplemented
20C3×D3×C3⋊D3—31no—
21C2×C9×C3⋊D3—91no—
22D9×C3⋊D3C911yescharacteristic, direct product factor
23D32×C9—94no—
24C3×D3×D9—34no—
25C2×C9×D9—91no—
26C33×C9—21no—
27C33×C9C2×D311yescharacteristic
28C33×C9C22×C311yescharacteristic
29C3×C92—24no—
30C3×C92—24no—
31C3×C92—44no—
32C3×C92C2×D314yescomplemented
33C3×C3⋊(C3⋊D3)—31no—
34C32×C3⋊D3C3×D311yescharacteristic
35C33×D3—31no—
36C2×C32×C9—91no—
37C3⋊(C3⋊D9)C2×C911yescharacteristic, complemented
38C9×C3⋊D3—23no—
39C9×C3⋊D3—21no—
40C9×C3⋊D3—21no—
41C9×C3⋊D3—91no—
42C9×C3⋊D3—94no—
43C9×C3⋊D3—184no—
44C9×C3⋊D3D911yescharacteristic, direct product factor
45C9×C3⋊D3C2×C911yescharacteristic, complemented
46C3×C3⋊D9—34no—
47C3×C3⋊D9—64no—
48C3×D3×C9—34no—
49C3×D3×C9—34no—
50C3×D3×C9—34no—
51C3×D3×C9—64no—
52C3×D3×C9—64no—
53C32×D9—24no—
54C32×D9C2×C911yescharacteristic, complemented
55C32×D9C3×D314yes—
56C2×C92—91no—
57C9×D9—24no—
58C9×D9—91no—
59C9×D9—184no—
60C9×D9C3⋊D311yescharacteristic, direct product factor
61C2×C3×C3⋊D3—91no—
62D3×C3⋊D3—31no—
63C3×D32—94no—
64C2×D3×C9—271no—
65C2×D3×C9—274no—
66C2×C3×D9—91no—
67D3×D9—34no—
68C34C2×C3×D311yescharacteristic
69C32×C9—23no—
70C32×C9—21no—
71C32×C9—21no—
72C32×C9—24no—
73C32×C9—24no—
74C32×C9—24no—
75C32×C9—24no—
76C32×C9—24no—
77C32×C9—44no—
78C32×C9—44no—
79C32×C9—412no—
80C32×C9—44no—
81C32×C9C2×D911yescharacteristic, complemented
82C32×C9C22×C911yescharacteristic, complemented
83C32×C9D3214yes—
84C32×C9C2×C3×D314yes—
85C92—24no—
86C92—24no—
87C92—44no—
88C92—412no—
89C92C2×C3⋊D311yescharacteristic, complemented
90C2×C33—91no—
91C3⋊(C3⋊D3)—31no—
92C3×C3⋊D3—21no—
93C3×C3⋊D3—91no—
94C3×C3⋊D3—94no—
95C3×C3⋊D3—184no—
96C3×C3⋊D3C3×D911yescharacteristic
97C3×C3⋊D3D3×C911yescharacteristic
98C32×D3—31no—
99C32×D3—34no—
100C32×D3—34no—
101C32×D3—64no—
102C2×C3×C9—94no—
103C2×C3×C9—91no—
104C2×C3×C9—91no—
105C2×C3×C9—181no—
106C2×C3×C9—184no—
107C3⋊D9—34no—
108C3⋊D9—64no—
109D3×C9—34no—
110D3×C9—34no—
111D3×C9—31no—
112D3×C9—64no—
113D3×C9—64no—
114D3×C9—64no—
115D3×C9—612no—
116D3×C9—274no—
117D3×C9—271no—
118D3×C9—544no—
119C3×D9—24no—
120C3×D9—91no—
121C3×D9—184no—
122C3×D9D3×C914yescomplemented
123C3×D9C3×C3⋊D311yescharacteristic
124C2×C3⋊D3—91no—
125C2×C3×D3—271no—
126C2×C3×D3—274no—
127D32—94no—
128C22×C9—811no—
129C2×D9—91no—
130C33—21no—
131C33—24no—
132C33—24no—
133C33—44no—
134C33C2×C3×D911yescharacteristic
135C33C2×D3×C911yescharacteristic
136C33C3×D3214yes—
137C3×C9—24no—
138C3×C9—24no—
139C3×C9—21no—
140C3×C9—212no—
141C3×C9—24no—
142C3×C9—24no—
143C3×C9—24no—
144C3×C9—24no—
145C3×C9—24no—
146C3×C9—24no—
147C3×C9—44no—
148C3×C9—44no—
149C3×C9—412no—
150C3×C9—412no—
151C3×C9—412no—
152C3×C9—412no—
153C3×C9—424no—
154C3×C9—44no—
155C3×C9—44no—
156C3×C9—44no—
157C3×C9D3×D914yescomplemented
158C3×C9C2×D3×C914yescomplemented
159C3×C9D3×C3⋊D311yescharacteristic
160C3×C9C2×C3×C3⋊D311yescharacteristic
161C2×C32—91no—
162C2×C32—94no—
163C2×C32—91no—
164C2×C32—184no—
165C3⋊D3—91no—
166C3⋊D3—94no—
167C3⋊D3—184no—
168C3⋊D3C9×D911yescharacteristic, direct product factor
169C3×D3—34no—
170C3×D3—34no—
171C3×D3—34no—
172C3×D3—31no—
173C3×D3—64no—
174C3×D3—64no—
175C3×D3—274no—
176C3×D3—271no—
177C3×D3—544no—
178C2×C9—91no—
179C2×C9—91no—
180C2×C9—91no—
181C2×C9—181no—
182C2×C9—181no—
183C2×C9—184no—
184C2×C9—183no—
185C2×C9—811no—
186D9—91no—
187D9—184no—
188D9C9×C3⋊D311yescharacteristic, direct product factor
189C22×C3—811no—
190C2×D3—271no—
191C2×D3—274no—
192C32—24no—
193C32—24no—
194C32—24no—
195C32—24no—
196C32—24no—
197C32—44no—
198C32—412no—
199C32—44no—
200C32C2×C9×D911yescharacteristic, complemented
201C32C3×D3×D914yes—
202C32D32×C914yes—
203C32C3×D3×C3⋊D311yescharacteristic
204C9—23no—
205C9—24no—
206C9—21no—
207C9—24no—
208C9—21no—
209C9—412no—
210C9—44no—
211C9—44no—
212C9D9×C3⋊D311yescharacteristic, direct product factor
213C9C2×C9×C3⋊D311yescharacteristic, complemented
214C2×C3—94no—
215C2×C3—91no—
216C2×C3—91no—
217C2×C3—91no—
218C2×C3—181no—
219C2×C3—184no—
220C2×C3—811no—
221D3—34no—
222D3—31no—
223D3—274no—
224D3—271no—
225D3—544no—
226C22—811noSylow
227C3—24no—
228C3—21no—
229C3—24no—
230C3—44no—
231C3D3×C9×D914yescomplemented
232C3C3×D9×C3⋊D311yescharacteristic
233C3D3×C9×C3⋊D311yescharacteristic
234C2—91no—
235C2—91no—
236C2—811no—
subgroupG/H
center, hypercenterC9D9×C3⋊D3
commutator, hypocenterC32×C9C22×C9
FrattiniC32C3×D3×C3⋊D3
FittingC32×C92C22
socleC34C2×C3×D3
prime radicalC3×D9×C3⋊D3C3
cosocleC33×C9C22×C3
LCSG ▷ C32×C9
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C9×C3⋊(C3⋊D9)C2semidirect
2. C92×C3⋊D3C2semidirect
3. C32×C9×D9C2semidirect
7. C32×C92C22semidirect
19. C3×C9×D9D3semidirect
22. D9×C3⋊D3C9direct (N × H)
32. C3×C92C2×D3semidirect
37. C3⋊(C3⋊D9)C2×C9semidirect
44. C9×C3⋊D3D9direct (N × H)
45. C9×C3⋊D3C2×C9semidirect
54. C32×D9C2×C9semidirect
60. C9×D9C3⋊D3direct (N × H)
81. C32×C9C2×D9semidirect
82. C32×C9C22×C9semidirect
89. C92C2×C3⋊D3semidirect
122. C3×D9D3×C9semidirect
157. C3×C9D3×D9semidirect
158. C3×C9C2×D3×C9semidirect
168. C3⋊D3C9×D9direct (N × H)
188. D9C9×C3⋊D3direct (N × H)
200. C32C2×C9×D9semidirect
212. C9D9×C3⋊D3direct (N × H)
213. C9C2×C9×C3⋊D3semidirect
231. C3D3×C9×D9semidirect

Maximal subgroups

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

subgroupindex
C9×C3⋊(C3⋊D9)2
C92×C3⋊D32
C32×C9×D92
D3×C9×C3⋊D33
C3×D9×C3⋊D33
D3×C9×D93