Finite Group Databasebeta

← C3×D3×C9×D9 #72243333

Subgroups — C3×D3×C9×D9 #72243333

Order 2916.

793 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 793 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C32×C9×D9C211yesmaximal, characteristic, complemented
2C3×C9×C3⋊D9C211yesmaximal, characteristic, complemented
3C3×D3×C92C211yesmaximal, characteristic, complemented
4C3×D32×C9—31nomaximal
5C32×D3×D9C311yesmaximal, characteristic
6C2×C3×C9×D9—31nomaximal
7D3×C9×D9C313yesmaximal, direct product factor
8C32×C92C2211yescharacteristic, complemented, Sylow
9C3×C9×C3⋊D3—31no—
10C32×C3⋊D9C2×C311yescharacteristic
11C32×D3×C9—21no—
12C32×D3×C9—31no—
13C32×D3×C9D311yescharacteristic
14C32×D3×C9C2×C311yescharacteristic
15C33×D9C2×C311yescharacteristic
16C2×C3×C92—31no—
17C9×C3⋊D9C2×C313yescomplemented
18D3×C92—23no—
19D3×C92C2×C313yescomplemented
20C3×C9×D9—21no—
21C3×C9×D9—23no—
22C3×C9×D9—31no—
23C3×C9×D9—61no—
24C3×C9×D9D311yescharacteristic, direct product factor
25C3×C9×D9C2×C313yescomplemented
26C32×D32—31no—
27C2×C3×D3×C9—91no—
28C2×C3×D3×C9—91no—
29C2×C32×D9—31no—
30D32×C9—33no—
31C3×D3×D9C913yesdirect product factor
32C3×D3×D9C3211yescharacteristic
33C2×C9×D9—33no—
34C33×C9—21no—
35C33×C9C2×D311yescharacteristic
36C33×C9C22×C311yescharacteristic
37C3×C92—21no—
38C3×C92—21no—
39C3×C92—23no—
40C3×C92—23no—
41C3×C92—43no—
42C3×C92—41no—
43C3×C92C2×D311yescharacteristic, complemented
44C3×C92C22×C313yescomplemented
45C32×C3⋊D3—31no—
46C33×D3—31no—
47C33×D3C3×D311yescharacteristic
48C2×C32×C9—31no—
49C2×C32×C9—31no—
50C2×C32×C9—61no—
51C2×C32×C9—91no—
52C9×C3⋊D3—33no—
53C3×C3⋊D9C2×C913yescomplemented
54C3×C3⋊D9C2×C3211yescharacteristic
55C3×D3×C9—29no—
56C3×D3×C9—21no—
57C3×D3×C9—23no—
58C3×D3×C9—21no—
59C3×D3×C9—23no—
60C3×D3×C9—23no—
61C3×D3×C9—31no—
62C3×D3×C9—33no—
63C3×D3×C9—63no—
64C3×D3×C9—61no—
65C3×D3×C9—91no—
66C3×D3×C9—91no—
67C3×D3×C9—181no—
68C3×D3×C9D911yescharacteristic, direct product factor
69C3×D3×C9C2×C913yescomplemented
70C3×D3×C9C3×D313yes—
71C3×D3×C9C2×C3211yescharacteristic
72C32×D9—23no—
73C32×D9—21no—
74C32×D9—31no—
75C32×D9—61no—
76C32×D9C2×C913yescomplemented
77C32×D9C3×D311yescharacteristic
78C32×D9C2×C3211yescharacteristic
79C2×C92—33no—
80C2×C92—63no—
81C9×D9—23no—
82C9×D9—33no—
83C9×D9—63no—
84C9×D9C3×D313yesdirect product factor
85C2×C32×D3—91no—
86C2×C32×D3—91no—
87C3×D32—33no—
88C3×D32—31no—
89C22×C3×C9—271no—
90C2×D3×C9—93no—
91C2×D3×C9—93no—
92C2×C3×D9—33no—
93C2×C3×D9—31no—
94D3×D9C3×C911yescharacteristic, direct product factor
95C34C2×C3×D311yescharacteristic
96C32×C9—21no—
97C32×C9—29no—
98C32×C9—21no—
99C32×C9—23no—
100C32×C9—21no—
101C32×C9—21no—
102C32×C9—23no—
103C32×C9—21no—
104C32×C9—21no—
105C32×C9—23no—
106C32×C9—23no—
107C32×C9—23no—
108C32×C9—21no—
109C32×C9—43no—
110C32×C9—41no—
111C32×C9—43no—
112C32×C9—41no—
113C32×C9—43no—
114C32×C9—49no—
115C32×C9—41no—
116C32×C9C2×D911yescharacteristic, complemented
117C32×C9C22×C913yescomplemented
118C32×C9D3211yescharacteristic
119C32×C9C2×C3×D311yescharacteristic
120C32×C9C2×C3×D313yes—
121C32×C9C22×C3211yescharacteristic
122C92—23no—
123C92—23no—
124C92—23no—
125C92—43no—
126C92—43no—
127C92—46no—
128C92—43no—
129C92C2×C3×D313yescomplemented
130C2×C33—31no—
131C2×C33—91no—
132C3×C3⋊D3—33no—
133C3×C3⋊D3—31no—
134C32×D3—23no—
135C32×D3—21no—
136C32×D3—31no—
137C32×D3—33no—
138C32×D3—31no—
139C32×D3—61no—
140C32×D3—63no—
141C32×D3—91no—
142C32×D3—91no—
143C32×D3—181no—
144C32×D3C3×D911yescharacteristic
145C32×D3D3×C913yes—
146C32×D3C32×D311yescharacteristic
147C2×C3×C9—31no—
148C2×C3×C9—33no—
149C2×C3×C9—33no—
150C2×C3×C9—31no—
151C2×C3×C9—63no—
152C2×C3×C9—63no—
153C2×C3×C9—61no—
154C2×C3×C9—61no—
155C2×C3×C9—63no—
156C2×C3×C9—69no—
157C2×C3×C9—91no—
158C2×C3×C9—93no—
159C2×C3×C9—183no—
160C2×C3×C9—181no—
161C2×C3×C9—271no—
162C3⋊D9C2×C3×C911yescharacteristic, complemented
163D3×C9—29no—
164D3×C9—23no—
165D3×C9—23no—
166D3×C9—21no—
167D3×C9—33no—
168D3×C9—63no—
169D3×C9—93no—
170D3×C9—93no—
171D3×C9—183no—
172D3×C9C3×D913yesdirect product factor
173D3×C9C2×C3×C911yescharacteristic, complemented
174C3×D9—23no—
175C3×D9—21no—
176C3×D9—33no—
177C3×D9—31no—
178C3×D9—61no—
179C3×D9—63no—
180C3×D9D3×C913yesdirect product factor
181C3×D9C2×C3×C911yescharacteristic, complemented
182C3×D9C32×D311yescharacteristic
183C22×C32—271no—
184C2×C3×D3—91no—
185C2×C3×D3—93no—
186C2×C3×D3—93no—
187C2×C3×D3—91no—
188D32—31no—
189C22×C9—273no—
190C2×D9—31no—
191C33—23no—
192C33—21no—
193C33—23no—
194C33—21no—
195C33—21no—
196C33—43no—
197C33—41no—
198C33C2×C3×D911yescharacteristic
199C33C2×D3×C913yes—
200C33C3×D3211yescharacteristic
201C33C2×C32×D311yescharacteristic
202C3×C9—29no—
203C3×C9—21no—
204C3×C9—21no—
205C3×C9—23no—
206C3×C9—21no—
207C3×C9—23no—
208C3×C9—23no—
209C3×C9—23no—
210C3×C9—29no—
211C3×C9—23no—
212C3×C9—23no—
213C3×C9—23no—
214C3×C9—21no—
215C3×C9—21no—
216C3×C9—23no—
217C3×C9—23no—
218C3×C9—23no—
219C3×C9—21no—
220C3×C9—43no—
221C3×C9—43no—
222C3×C9—41no—
223C3×C9—46no—
224C3×C9—43no—
225C3×C9—43no—
226C3×C9—46no—
227C3×C9—43no—
228C3×C9—43no—
229C3×C9—49no—
230C3×C9—427no—
231C3×C9—49no—
232C3×C9—41no—
233C3×C9—43no—
234C3×C9—43no—
235C3×C9—41no—
236C3×C9—43no—
237C3×C9D3×D911yescharacteristic, direct product factor
238C3×C9C2×C3×D913yescomplemented
239C3×C9C2×D3×C913yescomplemented
240C3×C9C22×C3×C911yescharacteristic, complemented
241C3×C9C3×D3213yes—
242C3×C9C2×C32×D311yescharacteristic
243C2×C32—31no—
244C2×C32—33no—
245C2×C32—31no—
246C2×C32—63no—
247C2×C32—61no—
248C2×C32—91no—
249C2×C32—93no—
250C2×C32—91no—
251C2×C32—181no—
252C2×C32—183no—
253C2×C32—271no—
254C3⋊D3—31no—
255C3×D3—21no—
256C3×D3—23no—
257C3×D3—33no—
258C3×D3—31no—
259C3×D3—31no—
260C3×D3—63no—
261C3×D3—61no—
262C3×D3—93no—
263C3×D3—93no—
264C3×D3—91no—
265C3×D3—91no—
266C3×D3—181no—
267C3×D3—183no—
268C3×D3C9×D913yesdirect product factor
269C3×D3C32×D911yescharacteristic
270C3×D3C3×D3×C911yescharacteristic
271C2×C9—33no—
272C2×C9—31no—
273C2×C9—63no—
274C2×C9—63no—
275C2×C9—61no—
276C2×C9—69no—
277C2×C9—93no—
278C2×C9—183no—
279C2×C9—273no—
280D9—31no—
281D9—61no—
282D9C3×D3×C911yescharacteristic, direct product factor
283C22×C3—271no—
284C22×C3—273no—
285C2×D3—91no—
286C2×D3—91no—
287C32—23no—
288C32—23no—
289C32—21no—
290C32—21no—
291C32—21no—
292C32—23no—
293C32—23no—
294C32—21no—
295C32—23no—
296C32—21no—
297C32—41no—
298C32—43no—
299C32—43no—
300C32—46no—
301C32—43no—
302C32—43no—
303C32—41no—
304C32C2×C9×D913yescomplemented
305C32C3×D3×D911yescharacteristic
306C32D32×C913yes—
307C32C2×C32×D911yescharacteristic
308C32C2×C3×D3×C911yescharacteristic
309C32C32×D3211yescharacteristic
310C9—29no—
311C9—23no—
312C9—23no—
313C9—21no—
314C9—23no—
315C9—21no—
316C9—49no—
317C9—43no—
318C9—43no—
319C9—41no—
320C9C3×D3×D913yesdirect product factor
321C9C2×C3×D3×C911yescharacteristic, complemented
322C2×C3—33no—
323C2×C3—31no—
324C2×C3—31no—
325C2×C3—61no—
326C2×C3—63no—
327C2×C3—91no—
328C2×C3—93no—
329C2×C3—91no—
330C2×C3—183no—
331C2×C3—181no—
332C2×C3—273no—
333C2×C3—271no—
334D3—31no—
335D3—91no—
336D3—91no—
337D3—181no—
338D3C3×C9×D911yescharacteristic, direct product factor
339C22—271noSylow
340C3—21no—
341C3—21no—
342C3—23no—
343C3—23no—
344C3—21no—
345C3—41no—
346C3—43no—
347C3D3×C9×D913yesdirect product factor
348C3C2×C3×C9×D911yescharacteristic, complemented
349C3C32×D3×D911yescharacteristic
350C3C3×D32×C911yescharacteristic
351C2—31no—
352C2—91no—
353C2—271no—
subgroupG/H
center, hypercenterC3×C9D3×D9
commutator, hypocenterC3×C9C22×C3×C9
FrattiniC32C32×D32
FittingC32×C92C22
socleC34C2×C3×D3
prime radicalC32×D3×D9C3
cosocleC32×C9C22×C32
LCSG ▷ C3×C9
UCSC1 ◁ C3×C9

Complements

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

NH ≅ G/Ntype
1. C32×C9×D9C2semidirect
2. C3×C9×C3⋊D9C2semidirect
3. C3×D3×C92C2semidirect
7. D3×C9×D9C3direct (N × H)
8. C32×C92C22semidirect
17. C9×C3⋊D9C2×C3semidirect
19. D3×C92C2×C3semidirect
24. C3×C9×D9D3direct (N × H)
25. C3×C9×D9C2×C3semidirect
31. C3×D3×D9C9direct (N × H)
43. C3×C92C2×D3semidirect
44. C3×C92C22×C3semidirect
53. C3×C3⋊D9C2×C9semidirect
68. C3×D3×C9D9direct (N × H)
69. C3×D3×C9C2×C9semidirect
76. C32×D9C2×C9semidirect
84. C9×D9C3×D3direct (N × H)
94. D3×D9C3×C9direct (N × H)
116. C32×C9C2×D9semidirect
117. C32×C9C22×C9semidirect
129. C92C2×C3×D3semidirect
162. C3⋊D9C2×C3×C9semidirect
172. D3×C9C3×D9direct (N × H)
173. D3×C9C2×C3×C9semidirect
180. C3×D9D3×C9direct (N × H)
181. C3×D9C2×C3×C9semidirect
237. C3×C9D3×D9direct (N × H)
238. C3×C9C2×C3×D9semidirect
239. C3×C9C2×D3×C9semidirect
240. C3×C9C22×C3×C9semidirect
268. C3×D3C9×D9direct (N × H)
282. D9C3×D3×C9direct (N × H)
304. C32C2×C9×D9semidirect
320. C9C3×D3×D9direct (N × H)
321. C9C2×C3×D3×C9semidirect
338. D3C3×C9×D9direct (N × H)
347. C3D3×C9×D9direct (N × H)
348. C3C2×C3×C9×D9semidirect

Maximal subgroups

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

subgroupindex
C32×C9×D92
C3×C9×C3⋊D92
C3×D3×C922
C3×D32×C93
C32×D3×D93
C2×C3×C9×D93
D3×C9×D93