Finite Group Databasebeta

← C4×D3×C3⋊D9 #13048649

Subgroups — C4×D3×C3⋊D9 #13048649

Order 1296.

660 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 134 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×C3⋊D9C211yesmaximal, characteristic
2C4×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
3C3×C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C3×C4×D3×C9C211yesmaximal, characteristic, complemented
5D3×C3⋊Dic9C211yesmaximal, characteristic, complemented
6#10619872C211yesmaximal, characteristic, complemented
7Dic3×C3⋊D9C211yesmaximal, characteristic, complemented
8C4×D3×C3⋊D3—31nomaximal
9C2×C4×C3⋊D9—31nomaximal
10C4×D3×D9—33nomaximal
11C2×C3⋊(C3⋊D9)C2211yescharacteristic
12C2×C3×C3⋊D9C2211yescharacteristic
13C2×C3×D3×C9C2211yescharacteristic
14D3×C3⋊D9C414yesdirect product factor
15C32×C4×C9C2211yescharacteristic, complemented
16C3⋊(C3⋊Dic9)C2211yescharacteristic, complemented
17C3×C3⋊Dic9C2211yescharacteristic, complemented
18C3×C9×Dic3C2211yescharacteristic, complemented
19C2×D3×C3⋊D3—31no—
20C4×C3⋊(C3⋊D3)—31no—
21C3×C4×C3⋊D3—31no—
22C32×C4×D3D311yescharacteristic
23#6289—31no—
24Dic3×C3⋊D3—31no—
25D3×C3⋊Dic3—31no—
26C22×C3⋊D9—31no—
27C2×D3×D9—33no—
28C2×C3×C4×C9—31no—
29C2×C3⋊Dic9—31no—
30C4×C3⋊D9—31no—
31C4×C3⋊D9—31no—
32C4×C3⋊D9—33no—
33C4×C3⋊D9—31no—
34C4×C3⋊D9—63no—
35C4×C3⋊D9—61no—
36C4×C3⋊D9D311yescharacteristic, direct product factor
37C4×D3×C9D313yescomplemented
38C3×C4×D9—33no—
39D3×Dic9—33no—
40(C3⋊D9)⋊C4—33no—
41Dic3×D9—33no—
42C2×C32×C9C2311yescharacteristic
43C3⋊(C3⋊D9)C2×C412yescomplemented
44C3×C3⋊D9C2×C412yescomplemented
45C3×D3×C9C2×C412yescomplemented
46C2×C4×C3⋊D3—91no—
47C4×D32—93no—
48C4×D32—91no—
49C2×C4×D9—93no—
50C2×C3⋊(C3⋊D3)—31no—
51C2×C3×C3⋊D3—31no—
52C2×C32×D3C2×D311yescharacteristic
53D3×C3⋊D3—34no—
54C33×C4C2×D311yescharacteristic
55C3⋊(C3⋊Dic3)—31no—
56C3×C3⋊Dic3—31no—
57C32×Dic3C2×D311yescharacteristic
58C22×C3×C9—31no—
59C2×C3⋊D9—31no—
60C2×C3⋊D9—33no—
61C2×C3⋊D9—34no—
62C2×C3⋊D9—63no—
63C2×C3⋊D9—61no—
64C2×C3⋊D9C2×D311yescharacteristic
65C2×D3×C9C2×D313yes—
66C2×C3×D9—33no—
67D3×D9—312no—
68C3×C4×C9—21no—
69C3×C4×C9—23no—
70C3×C4×C9—31no—
71C3×C4×C9C2×D313yescomplemented
72C3×C4×C9C2×D311yescharacteristic, complemented
73C3⋊Dic9—31no—
74C3⋊Dic9—33no—
75C3⋊Dic9—63no—
76C3⋊Dic9—61no—
77C3⋊Dic9C2×D311yescharacteristic, complemented
78C9×Dic3C2×D313yescomplemented
79C3×Dic9—33no—
80C32×C9C22×C411yescharacteristic, complemented, Sylow
81C22×C3⋊D3—91no—
82C2×D32—93no—
83C2×D32—91no—
84C2×C32×C4—31no—
85C2×C3⋊Dic3—91no—
86C4×C3⋊D3—31no—
87C4×C3⋊D3—91no—
88C4×C3⋊D3—91no—
89C4×C3⋊D3—91no—
90C4×C3⋊D3—93no—
91C4×C3⋊D3—91no—
92C4×C3⋊D3—181no—
93C4×C3⋊D3—183no—
94C3×C4×D3—93no—
95C3×C4×D3—91no—
96C3×C4×D3D913yescomplemented
97C3×C4×D3C3⋊D311yescharacteristic
98#624—93no—
99#624—91no—
100D3×Dic3—93no—
101D3×Dic3—91no—
102D3×Dic3—93no—
103D3×Dic3—91no—
104C22×D9—93no—
105C2×C4×C9—33no—
106C2×Dic9—93no—
107C4×D9—33no—
108C4×D9—93no—
109C4×D9—93no—
110C4×D9—93no—
111C4×D9—183no—
112C2×C33C22×D311yescharacteristic
113C3⋊(C3⋊D3)—32no—
114C3×C3⋊D3—32no—
115C32×D3C4×D312yes—
116C2×C3×C9—21no—
117C2×C3×C9—23no—
118C2×C3×C9—32no—
119C2×C3×C9C22×D313yes—
120C2×C3×C9C22×D311yescharacteristic
121C3⋊D9—32no—
122C3⋊D9—36no—
123C3⋊D9—66no—
124C3⋊D9—62no—
125C3⋊D9C4×D312yesdirect product factor
126D3×C9C4×D316yescomplemented
127C3×D9—36no—
128C2×C4×D3—271no—
129C2×C4×D3—273no—
130C2×C4×D3—271no—
131C22×C32—31no—
132C2×C3⋊D3—31no—
133C2×C3⋊D3—94no—
134C2×C3⋊D3—91no—
135C2×C3⋊D3—93no—
136C2×C3⋊D3—91no—
137C2×C3⋊D3—181no—
138C2×C3⋊D3—183no—
139C2×C3×D3—93no—
140C2×C3×D3—91no—
141C2×C3×D3C2×D913yes—
142C2×C3×D3C2×C3⋊D311yescharacteristic
143D32—912no—
144D32—94no—
145C32×C4—23no—
146C32×C4—21no—
147C32×C4—31no—
148C32×C4C2×D913yescomplemented
149C32×C4D3211yescharacteristic
150C32×C4C2×C3⋊D311yescharacteristic
151C3⋊Dic3—31no—
152C3⋊Dic3—91no—
153C3⋊Dic3—93no—
154C3⋊Dic3—91no—
155C3⋊Dic3—181no—
156C3⋊Dic3—183no—
157C3×Dic3—93no—
158C3×Dic3—91no—
159C3×Dic3C2×D913yescomplemented
160C3×Dic3C2×C3⋊D311yescharacteristic
161C22×C9—33no—
162C2×D9—33no—
163C2×D9—912no—
164C2×D9—93no—
165C2×D9—183no—
166C4×C9—23no—
167C4×C9—33no—
168C4×C9D3213yescomplemented
169Dic9—33no—
170Dic9—93no—
171Dic9—183no—
172C33C2×C4×D311yescharacteristic
173C3×C9—21no—
174C3×C9—23no—
175C3×C9C2×C4×D313yescomplemented
176C3×C9C2×C4×D311yescharacteristic, complemented
177C22×D3—271no—
178C22×D3—273no—
179C22×D3—271no—
180C2×C3×C4—33no—
181C2×C3×C4—31no—
182C2×C3×C4—271no—
183C2×Dic3—271no—
184C2×Dic3—273no—
185C2×Dic3—271no—
186C4×D3—93no—
187C4×D3—91no—
188C4×D3—271no—
189C4×D3—273no—
190C4×D3—271no—
191C4×D3—273no—
192C4×D3—271no—
193C4×D3—273no—
194C4×D3—271no—
195C4×D3—271no—
196C4×D3—271no—
197C4×D3—543no—
198C4×D3—541no—
199C4×D3C3⋊D911yescharacteristic, direct product factor
200C2×C32—23no—
201C2×C32—21no—
202C2×C32—32no—
203C2×C32C22×D913yes—
204C2×C32C2×D3211yescharacteristic
205C2×C32C22×C3⋊D311yescharacteristic
206C3⋊D3—32no—
207C3⋊D3—92no—
208C3⋊D3—96no—
209C3⋊D3—92no—
210C3⋊D3—182no—
211C3⋊D3—186no—
212C3×D3—96no—
213C3×D3—92no—
214C3×D3C4×D916yescomplemented
215C3×D3C4×C3⋊D312yes—
216C2×C9—23no—
217C2×C9—36no—
218C2×C9C2×D3213yes—
219D9—36no—
220D9—96no—
221D9—186no—
222C22×C4—811noSylow
223C22×C3—33no—
224C22×C3—31no—
225C22×C3—271no—
226C2×D3—93no—
227C2×D3—91no—
228C2×D3—274no—
229C2×D3—2712no—
230C2×D3—273no—
231C2×D3—271no—
232C2×D3—271no—
233C2×D3—274no—
234C2×D3—543no—
235C2×D3—541no—
236C2×D3C2×C3⋊D911yescharacteristic
237C3×C4—23no—
238C3×C4—21no—
239C3×C4—33no—
240C3×C4—31no—
241C3×C4—271no—
242C3×C4D3×D913yescomplemented
243C3×C4C2×C3⋊D911yescharacteristic, complemented
244C3×C4D3×C3⋊D311yescharacteristic
245Dic3—93no—
246Dic3—91no—
247Dic3—273no—
248Dic3—271no—
249Dic3—271no—
250Dic3—543no—
251Dic3—541no—
252Dic3C2×C3⋊D911yescharacteristic, complemented
253C32—23no—
254C32—21no—
255C32C2×C4×D913yescomplemented
256C32C4×D3211yescharacteristic
257C32C2×C4×C3⋊D311yescharacteristic
258C9—23no—
259C9C4×D3213yescomplemented
260C23—811no—
261C2×C4—31no—
262C2×C4—271no—
263C2×C4—811no—
264C2×C4—811no—
265C2×C4—811no—
266C2×C4—811no—
267C2×C3—23no—
268C2×C3—21no—
269C2×C3—36no—
270C2×C3—32no—
271C2×C3—272no—
272C2×C3C2×D3×D913yes—
273C2×C3C22×C3⋊D911yescharacteristic
274C2×C3C2×D3×C3⋊D311yescharacteristic
275D3—96no—
276D3—92no—
277D3—276no—
278D3—272no—
279D3—272no—
280D3—546no—
281D3—542no—
282D3C4×C3⋊D912yesdirect product factor
283C22—31no—
284C22—271no—
285C22—814no—
286C22—811no—
287C4—31no—
288C4—271no—
289C4—811no—
290C4D3×C3⋊D911yescharacteristic, direct product factor
291C3—23no—
292C3—21no—
293C3C4×D3×D913yescomplemented
294C3C2×C4×C3⋊D911yescharacteristic, complemented
295C3C4×D3×C3⋊D311yescharacteristic
296C2—32no—
297C2—272no—
298C2—812no—
299C2C2×D3×C3⋊D911yescharacteristic
subgroupG/H
center, hypercenterC4D3×C3⋊D9
commutator, hypocenterC32×C9C22×C4
FrattiniC2×C3C2×D3×C3⋊D3
FittingC32×C4×C9C22
socleC2×C33C22×D3
prime radicalC2×D3×C3⋊D9C2
cosocleC2×C32×C9C23
LCSG ▷ C32×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C3⋊(C3⋊D9)C2semidirect
3. C3×C4×C3⋊D9C2semidirect
4. C3×C4×D3×C9C2semidirect
5. D3×C3⋊Dic9C2semidirect
6. #10619872C2semidirect
7. Dic3×C3⋊D9C2semidirect
14. D3×C3⋊D9C4direct (N × H)
15. C32×C4×C9C22semidirect
16. C3⋊(C3⋊Dic9)C22semidirect
17. C3×C3⋊Dic9C22semidirect
18. C3×C9×Dic3C22semidirect
36. C4×C3⋊D9D3direct (N × H)
37. C4×D3×C9D3semidirect
43. C3⋊(C3⋊D9)C2×C4semidirect
44. C3×C3⋊D9C2×C4semidirect
45. C3×D3×C9C2×C4semidirect
71. C3×C4×C9C2×D3semidirect
72. C3×C4×C9C2×D3semidirect
77. C3⋊Dic9C2×D3semidirect
78. C9×Dic3C2×D3semidirect
80. C32×C9C22×C4semidirect
96. C3×C4×D3D9semidirect
125. C3⋊D9C4×D3direct (N × H)
126. D3×C9C4×D3semidirect
148. C32×C4C2×D9semidirect
159. C3×Dic3C2×D9semidirect
168. C4×C9D32semidirect
175. C3×C9C2×C4×D3semidirect
176. C3×C9C2×C4×D3semidirect
199. C4×D3C3⋊D9direct (N × H)
214. C3×D3C4×D9semidirect
242. C3×C4D3×D9semidirect
243. C3×C4C2×C3⋊D9semidirect
252. Dic3C2×C3⋊D9semidirect
255. C32C2×C4×D9semidirect
259. C9C4×D32semidirect
282. D3C4×C3⋊D9direct (N × H)
290. C4D3×C3⋊D9direct (N × H)
293. C3C4×D3×D9semidirect
294. C3C2×C4×C3⋊D9semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊D92
C4×C3⋊(C3⋊D9)2
C3×C4×C3⋊D92
C3×C4×D3×C92
D3×C3⋊Dic92
#106198722
Dic3×C3⋊D92
C4×D3×C3⋊D33
C2×C4×C3⋊D93
C4×D3×D93