Finite Group Databasebeta

← C2×C4×D3×D9 #11722469

Subgroups — C2×C4×D3×D9 #11722469

Order 864.

762 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 215 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×D3×D9C211yesmaximal, characteristic
2C2×C4×C3⋊D9C211yesmaximal, characteristic, complemented
3C2×C4×D3×C9C211yesmaximal, characteristic, complemented
4C2×C3×C4×D9C211yesmaximal, characteristic, complemented
5C2×D3×Dic9C211yesmaximal, characteristic, complemented
6C2×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
7C2×Dic3×D9C211yesmaximal, characteristic, complemented
8C4×D3×D9C218yesmaximal, direct product factor
9C2×C4×D32—31nomaximal
10C22×C4×D9—31nomaximal
11C22×C3⋊D9C2211yescharacteristic
12C22×D3×C9C2211yescharacteristic
13C22×C3×D9C2211yescharacteristic
14C2×D3×D9C418yesdirect product factor
15C2×D3×D9C2214yes—
16C2×C3×C4×C9C2211yescharacteristic, complemented
17C2×C3⋊Dic9C2211yescharacteristic, complemented
18C4×C3⋊D9C2214yescomplemented
19C2×C9×Dic3C2211yescharacteristic, complemented
20C2×C3×Dic9C2211yescharacteristic, complemented
21C4×D3×C9C2214yescomplemented
22C3×C4×D9C2214yescomplemented
23D3×Dic9C2214yescomplemented
24(C3⋊D9)⋊C4C2214yescomplemented
25Dic3×D9C2214yescomplemented
26C22×D32—31no—
27C2×C4×C3⋊D3—31no—
28C2×C3×C4×D3—31no—
29C2×C3×C4×D3D311yescharacteristic
30C2×#624—31no—
31C2×D3×Dic3—31no—
32C2×D3×Dic3—31no—
33C4×D32—38no—
34C23×D9—31no—
35C22×C4×C9—31no—
36C22×Dic9—31no—
37C2×C4×D9—31no—
38C2×C4×D9—31no—
39C2×C4×D9—31no—
40C2×C4×D9—38no—
41C2×C4×D9—61no—
42C2×C4×D9D311yescharacteristic, direct product factor
43C22×C3×C9C2311yescharacteristic
44C2×C3⋊D9C2×C414yescomplemented
45C2×C3⋊D9C2312yes—
46C2×D3×C9C2×C414yescomplemented
47C2×D3×C9C2312yes—
48C2×C3×D9C2×C414yescomplemented
49C2×C3×D9C2312yes—
50D3×D9C2×C4116yesdirect product factor
51C3×C4×C9C2312yescomplemented
52C3⋊Dic9C2312yescomplemented
53C9×Dic3C2312yescomplemented
54C3×Dic9C2312yescomplemented
55C22×C4×D3—91no—
56C22×C4×D3—91no—
57C22×C3⋊D3—31no—
58C22×C3×D3—31no—
59C22×C3×D3C2×D311yescharacteristic
60C2×D32—38no—
61C2×D32—34no—
62C2×C32×C4C2×D311yescharacteristic
63C2×C3⋊Dic3—31no—
64C4×C3⋊D3—34no—
65C2×C3×Dic3—31no—
66C2×C3×Dic3C2×D311yescharacteristic
67C3×C4×D3—34no—
68C3×C4×D3C2×D314yes—
69#624—34no—
70D3×Dic3—34no—
71D3×Dic3—34no—
72C23×C9—31no—
73C22×D9—31no—
74C22×D9—38no—
75C22×D9—34no—
76C22×D9—61no—
77C22×D9C2×D311yescharacteristic
78C2×C4×C9—21no—
79C2×C4×C9—31no—
80C2×C4×C9—34no—
81C2×C4×C9C2×D311yescharacteristic, complemented
82C2×Dic9—31no—
83C2×Dic9—34no—
84C2×Dic9—61no—
85C2×Dic9C2×D311yescharacteristic, complemented
86C4×D9—34no—
87C4×D9—34no—
88C4×D9—34no—
89C4×D9—64no—
90C4×D9C2×D314yesdirect product factor
91C2×C3×C9C22×C412yescomplemented
92C2×C3×C9C2411yescharacteristic
93C3⋊D9C22×C414yescomplemented
94D3×C9C22×C414yescomplemented
95C3×D9C22×C414yescomplemented
96C23×D3—91no—
97C23×D3—91no—
98C22×C3×C4—31no—
99C22×C3×C4—91no—
100C22×Dic3—91no—
101C22×Dic3—91no—
102C2×C4×D3—31no—
103C2×C4×D3—98no—
104C2×C4×D3—91no—
105C2×C4×D3—91no—
106C2×C4×D3—91no—
107C2×C4×D3—91no—
108C2×C4×D3—91no—
109C2×C4×D3—91no—
110C2×C4×D3—98no—
111C2×C4×D3—181no—
112C2×C4×D3D911yescharacteristic, direct product factor
113C22×C32C22×D311yescharacteristic
114C2×C3⋊D3—34no—
115C2×C3⋊D3—32no—
116C2×C3×D3—34no—
117C2×C3×D3—32no—
118C2×C3×D3C4×D314yes—
119C2×C3×D3C22×D312yes—
120D32—316no—
121C32×C4C22×D312yes—
122C3⋊Dic3—32no—
123C3×Dic3—32no—
124C3×Dic3C22×D312yes—
125C22×C9—21no—
126C22×C9—34no—
127C22×C9—32no—
128C22×C9C22×D311yescharacteristic
129C2×D9—34no—
130C2×D9—32no—
131C2×D9—316no—
132C2×D9—64no—
133C2×D9—62no—
134C2×D9C4×D314yesdirect product factor
135C2×D9C22×D312yes—
136C4×C9—22no—
137C4×C9—32no—
138C4×C9C22×D312yescomplemented
139Dic9—32no—
140Dic9—62no—
141Dic9C22×D312yescomplemented
142C23×C4—271noSylow
143C3×C9C23×C411yescharacteristic, complemented, Sylow
144C23×C3—31no—
145C23×C3—91no—
146C22×D3—31no—
147C22×D3—94no—
148C22×D3—98no—
149C22×D3—91no—
150C22×D3—91no—
151C22×D3—98no—
152C22×D3—94no—
153C22×D3—181no—
154C22×D3C2×D911yescharacteristic
155C2×C3×C4—21no—
156C2×C3×C4—31no—
157C2×C3×C4—34no—
158C2×C3×C4—91no—
159C2×C3×C4—94no—
160C2×C3×C4C2×D911yescharacteristic, complemented
161C2×C3×C4D3211yescharacteristic
162C2×Dic3—31no—
163C2×Dic3—94no—
164C2×Dic3—91no—
165C2×Dic3—91no—
166C2×Dic3—94no—
167C2×Dic3—181no—
168C2×Dic3C2×D911yescharacteristic, complemented
169C4×D3—34no—
170C4×D3—94no—
171C4×D3—94no—
172C4×D3—94no—
173C4×D3—94no—
174C4×D3—94no—
175C4×D3—94no—
176C4×D3—184no—
177C4×D3C2×D914yesdirect product factor
178C2×C32C2×C4×D312yes—
179C2×C32C23×D311yescharacteristic
180C3⋊D3—34no—
181C3×D3—34no—
182C3×D3C2×C4×D314yes—
183C2×C9—21no—
184C2×C9—22no—
185C2×C9—34no—
186C2×C9C2×C4×D312yescomplemented
187C2×C9C23×D311yescharacteristic
188D9—34no—
189D9—64no—
190D9C2×C4×D314yesdirect product factor
191C24—271no—
192C22×C4—31no—
193C22×C4—91no—
194C22×C4—271no—
195C22×C4—278no—
196C22×C4—271no—
197C22×C4—271no—
198C22×C4—271no—
199C22×C3—21no—
200C22×C3—32no—
201C22×C3—34no—
202C22×C3—94no—
203C22×C3—92no—
204C22×C3C22×D911yescharacteristic
205C22×C3C2×D3211yescharacteristic
206C2×D3—32no—
207C2×D3—34no—
208C2×D3—916no—
209C2×D3—92no—
210C2×D3—94no—
211C2×D3—92no—
212C2×D3—94no—
213C2×D3—916no—
214C2×D3—182no—
215C2×D3—184no—
216C2×D3C4×D914yesdirect product factor
217C2×D3C22×D912yes—
218C3×C4—22no—
219C3×C4—32no—
220C3×C4—92no—
221C3×C4C22×D912yescomplemented
222C3×C4C2×D3212yes—
223Dic3—32no—
224Dic3—92no—
225Dic3—92no—
226Dic3—182no—
227Dic3C22×D912yescomplemented
228C32C22×C4×D311yescharacteristic
229C9—21no—
230C9C22×C4×D311yescharacteristic, complemented
231C23—31no—
232C23—91no—
233C23—274no—
234C23—278no—
235C23—271no—
236C2×C4—31no—
237C2×C4—34no—
238C2×C4—91no—
239C2×C4—94no—
240C2×C4—274no—
241C2×C4—274no—
242C2×C4—274no—
243C2×C4—271no—
244C2×C4—274no—
245C2×C4D3×D911yescharacteristic, direct product factor
246C2×C3—21no—
247C2×C3—22no—
248C2×C3—34no—
249C2×C3—94no—
250C2×C3C2×C4×D912yescomplemented
251C2×C3C23×D911yescharacteristic
252C2×C3C4×D3212yes—
253C2×C3C22×D3211yescharacteristic
254D3—34no—
255D3—94no—
256D3—94no—
257D3—184no—
258D3C2×C4×D914yesdirect product factor
259C22—32no—
260C22—34no—
261C22—92no—
262C22—94no—
263C22—2716no—
264C22—272no—
265C22—274no—
266C22C2×D3×D911yescharacteristic
267C4—32no—
268C4—92no—
269C4—272no—
270C4C2×D3×D912yesdirect product factor
271C3—21no—
272C3C22×C4×D911yescharacteristic, complemented
273C3C2×C4×D3211yescharacteristic
274C2—34no—
275C2—94no—
276C2—274no—
277C2C4×D3×D912yesdirect product factor
278C2C22×D3×D911yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×D9
commutator, hypocenterC3×C9C23×C4
FrattiniC2×C3C22×D32
FittingC2×C3×C4×C9C22
socleC22×C32C22×D3
prime radicalC22×D3×D9C2
cosocleC2×C3×C9C24
LCSG ▷ C3×C9
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊D9C2semidirect
3. C2×C4×D3×C9C2semidirect
4. C2×C3×C4×D9C2semidirect
5. C2×D3×Dic9C2semidirect
6. C2×(C3⋊D9)⋊C4C2semidirect
7. C2×Dic3×D9C2semidirect
8. C4×D3×D9C2direct (N × H)
14. C2×D3×D9C4direct (N × H)
16. C2×C3×C4×C9C22semidirect
17. C2×C3⋊Dic9C22semidirect
18. C4×C3⋊D9C22semidirect
19. C2×C9×Dic3C22semidirect
20. C2×C3×Dic9C22semidirect
21. C4×D3×C9C22semidirect
22. C3×C4×D9C22semidirect
23. D3×Dic9C22semidirect
24. (C3⋊D9)⋊C4C22semidirect
25. Dic3×D9C22semidirect
42. C2×C4×D9D3direct (N × H)
44. C2×C3⋊D9C2×C4semidirect
46. C2×D3×C9C2×C4semidirect
48. C2×C3×D9C2×C4semidirect
50. D3×D9C2×C4direct (N × H)
51. C3×C4×C9C23semidirect
52. C3⋊Dic9C23semidirect
53. C9×Dic3C23semidirect
54. C3×Dic9C23semidirect
81. C2×C4×C9C2×D3semidirect
85. C2×Dic9C2×D3semidirect
90. C4×D9C2×D3direct (N × H)
91. C2×C3×C9C22×C4semidirect
93. C3⋊D9C22×C4semidirect
94. D3×C9C22×C4semidirect
95. C3×D9C22×C4semidirect
112. C2×C4×D3D9direct (N × H)
134. C2×D9C4×D3direct (N × H)
138. C4×C9C22×D3semidirect
141. Dic9C22×D3semidirect
143. C3×C9C23×C4semidirect
160. C2×C3×C4C2×D9semidirect
168. C2×Dic3C2×D9semidirect
177. C4×D3C2×D9direct (N × H)
186. C2×C9C2×C4×D3semidirect
190. D9C2×C4×D3direct (N × H)
216. C2×D3C4×D9direct (N × H)
221. C3×C4C22×D9semidirect
227. Dic3C22×D9semidirect
230. C9C22×C4×D3semidirect
245. C2×C4D3×D9direct (N × H)
250. C2×C3C2×C4×D9semidirect
258. D3C2×C4×D9direct (N × H)
270. C4C2×D3×D9direct (N × H)
272. C3C22×C4×D9semidirect
277. C2C4×D3×D9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D92
C2×C4×C3⋊D92
C2×C4×D3×C92
C2×C3×C4×D92
C2×D3×Dic92
C2×(C3⋊D9)⋊C42
C2×Dic3×D92
C4×D3×D92
C2×C4×D323
C22×C4×D93