Subgroups — C₉×#4772 #13141755

Order 1728.

524 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#816	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4772	C₃	1	1	yes	maximal, characteristic
9	C₉×#416	—	3	1	no	maximal
10	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×#67	—	2	1	no	—
12	C₂²×C₉×Dic₃	—	2	1	no	—
13	C₉×#237	—	2	2	no	—
14	C₉×#237	C₄	1	4	yes	complemented
15	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
20	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₄×C₉×Dic₃	—	2	1	no	—
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	D₃×C₈×C₉	—	2	2	no	—
24	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
26	C₃×#892	C₂×C₃	1	1	yes	characteristic
27	C₂×C₉×#41	—	3	1	no	—
28	C₃²×#102	C₂×C₃	1	1	yes	characteristic
29	C₃×#832	C₂×C₃	1	1	yes	characteristic
30	C₃×#816	C₂×C₃	1	1	yes	characteristic
31	C₃×#810	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₈×C₉	—	3	1	no	—
33	C₉×#117	—	3	1	no	—
34	C₉×#103	—	3	1	no	—
35	C₉×#103	—	3	1	no	—
36	C₉×#102	—	2	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₉×#102	D₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×C₉	—	2	1	no	—
40	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
41	C₃×D₄×C₉	—	2	1	no	—
42	C₃×D₄×C₉	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₉×#67	—	2	4	no	—
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₂×C₉×Dic₃	—	2	4	no	—
48	C₂×C₉×Dic₃	—	2	1	no	—
49	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
50	C₄×D₃×C₉	C₂×C₄	1	2	yes	—
51	C₄×D₃×C₉	D₄	1	2	yes	—
52	C₉×Dic₆	—	2	1	no	—
53	C₉×Dic₆	C₂×C₄	1	2	yes	—
54	C₃×C₈×C₉	—	2	1	no	—
55	C₉×C₃⋊C₈	—	2	1	no	—
56	C₃×#416	—	3	1	no	—
57	#4772	C₉	1	1	yes	characteristic, direct product factor
58	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×#67	—	2	1	no	—
60	C₂²×C₃×Dic₃	—	2	1	no	—
61	C₃×#237	—	2	2	no	—
62	C₃×#237	C₃×C₄	1	4	yes	—
63	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
66	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
67	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
68	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
69	C₃×C₄×Dic₃	—	2	1	no	—
70	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
71	C₃×D₃×C₈	—	2	2	no	—
72	C₉×#41	—	3	4	no	—
73	C₉×#41	—	6	2	no	—
74	C₂×Q₈×C₉	—	3	1	no	—
75	C₂×D₄×C₉	—	2	1	no	—
76	C₂×D₄×C₉	—	6	1	no	—
77	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₄×C₉	—	3	1	no	—
79	C₂²×C₄×C₉	—	6	1	no	—
80	C₂×C₈×C₉	—	2	1	no	—
81	C₂×C₈×C₉	—	3	1	no	—
82	C₂×C₈×C₉	—	6	2	no	—
83	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	—	3	1	no	—
86	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₉×C₂²⋊C₄	—	6	1	no	—
88	C₄²×C₉	—	6	1	no	—
89	C₂²×C₃×C₉	—	2	2	no	—
90	C₂²×C₃×C₉	—	4	1	no	—
91	C₂²×C₃×C₉	—	4	1	no	—
92	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
93	C₂×D₃×C₉	—	2	1	no	—
94	C₂×D₃×C₉	—	2	1	no	—
95	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
96	C₃×C₄×C₉	—	4	1	no	—
97	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
98	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
99	C₉×Dic₃	—	2	2	no	—
100	C₉×Dic₃	—	4	1	no	—
101	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
102	C₂×C₃×#41	—	3	1	no	—
103	C₂×#237	C₂×C₉	1	1	yes	characteristic
104	C₂²×C₃×C₈	—	3	1	no	—
105	C₃×#117	—	3	1	no	—
106	C₂×D₃×C₈	C₂×C₉	1	1	yes	characteristic, complemented
107	#892	C₂×C₉	1	1	yes	characteristic, complemented
108	C₃×#103	—	3	1	no	—
109	C₃×#103	—	3	1	no	—
110	C₃×#102	—	2	1	no	—
111	C₃×#102	—	3	1	no	—
112	C₃×#102	C₂×C₉	1	1	yes	characteristic, complemented
113	C₃×#102	C₃×D₃	1	1	yes	characteristic
114	#832	C₂×C₉	1	1	yes	characteristic, complemented
115	#816	C₂×C₉	1	1	yes	characteristic, complemented
116	#810	C₂×C₉	1	1	yes	characteristic, complemented
117	C₂³×C₃²	—	2	1	no	—
118	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
119	C₃²×D₄	—	2	1	no	—
120	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
121	C₂×C₃²×C₄	—	2	1	no	—
122	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
123	C₃×#67	—	2	4	no	—
124	C₂×C₃×Dic₃	—	2	1	no	—
125	C₂×C₃×Dic₃	—	2	4	no	—
126	C₂×C₃×Dic₃	—	2	1	no	—
127	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
128	C₃×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
129	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
130	C₃×Dic₆	—	2	1	no	—
131	C₃×Dic₆	C₂×C₃×C₄	1	2	yes	—
132	C₂³×C₉	—	2	1	no	—
133	C₂³×C₉	—	3	1	no	—
134	C₂³×C₉	—	4	1	no	—
135	C₃²×C₈	—	2	1	no	—
136	C₃×C₃⋊C₈	—	2	1	no	—
137	Q₈×C₉	—	3	2	no	—
138	Q₈×C₉	—	6	1	no	—
139	D₄×C₉	—	2	1	no	—
140	D₄×C₉	—	2	2	no	—
141	D₄×C₉	—	4	1	no	—
142	D₄×C₉	—	6	4	no	—
143	D₄×C₉	C₄×D₃	1	2	yes	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	3	1	no	—
147	C₂×C₄×C₉	—	3	2	no	—
148	C₂×C₄×C₉	—	3	2	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	—	6	4	no	—
151	C₂×C₄×C₉	—	6	1	no	—
152	C₂×C₄×C₉	—	6	1	no	—
153	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
154	C₈×C₉	—	2	1	no	—
155	C₈×C₉	—	4	1	no	—
156	C₈×C₉	—	6	1	no	—
157	#416	—	3	1	no	Sylow
158	C₂×C₃×C₉	—	4	2	no	—
159	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₃×C₉	#135	1	1	yes	characteristic
161	C₂×C₃×C₉	#135	1	1	yes	characteristic
162	D₃×C₉	—	2	2	no	—
163	C₃×#41	—	3	4	no	—
164	C₃×#41	—	6	2	no	—
165	C₂×C₃×Q₈	—	3	1	no	—
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	—	6	1	no	—
168	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
169	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
170	C₂²×C₃×C₄	—	3	1	no	—
171	C₂²×C₃×C₄	—	6	1	no	—
172	C₂×#67	—	2	1	no	—
173	C₂²×Dic₃	—	2	1	no	—
174	#237	—	2	2	no	—
175	#237	C₄×C₉	1	4	yes	complemented
176	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
177	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	3	1	no	—
180	C₂×C₃×C₈	—	6	2	no	—
181	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	3	1	no	—
185	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
187	C₃×C₂²⋊C₄	—	6	1	no	—
188	C₃×C₄²	—	6	1	no	—
189	(C₂×D₃)⋊C₄	—	2	1	no	—
190	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
191	C₄×Dic₃	—	2	1	no	—
192	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
193	D₃×C₈	—	2	2	no	—
194	C₂²×C₃²	—	2	2	no	—
195	C₂²×C₃²	—	4	1	no	—
196	C₂²×C₃²	—	4	1	no	—
197	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
198	C₂×C₃×D₃	—	2	1	no	—
199	C₂×C₃×D₃	—	2	1	no	—
200	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
201	C₃²×C₄	—	4	1	no	—
202	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
203	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
204	C₃×Dic₃	—	2	2	no	—
205	C₃×Dic₃	—	4	1	no	—
206	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	3	2	no	—
210	C₂²×C₉	—	4	2	no	—
211	C₂²×C₉	—	4	1	no	—
212	C₂²×C₉	—	4	1	no	—
213	C₂²×C₉	—	6	1	no	—
214	C₂²×C₉	—	6	1	no	—
215	C₂²×C₉	—	8	1	no	—
216	C₂²×C₉	—	8	1	no	—
217	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
218	C₄×C₉	—	2	1	no	—
219	C₄×C₉	—	2	1	no	—
220	C₄×C₉	—	3	2	no	—
221	C₄×C₉	—	4	1	no	—
222	C₄×C₉	—	6	2	no	—
223	C₄×C₉	—	8	1	no	—
224	C₄×C₉	—	12	1	no	—
225	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
226	C₄×C₉	D₃×D₄	1	1	yes	characteristic
227	C₂×#41	—	3	1	no	—
228	C₂²×C₈	—	3	1	no	—
229	#117	—	3	1	no	—
230	#103	—	3	1	no	—
231	#103	—	3	1	no	—
232	#102	—	3	1	no	—
233	#102	D₃×C₉	1	1	yes	characteristic, complemented
234	C₃×C₉	#416	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	2	1	no	—
236	C₂³×C₃	—	2	1	no	—
237	C₂³×C₃	—	3	1	no	—
238	C₂³×C₃	—	4	1	no	—
239	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
240	C₃×Q₈	—	3	2	no	—
241	C₃×Q₈	—	6	1	no	—
242	C₃×D₄	—	2	1	no	—
243	C₃×D₄	—	2	1	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	4	1	no	—
246	C₃×D₄	—	6	4	no	—
247	C₃×D₄	C₂×C₄×C₉	1	2	yes	—
248	C₃×D₄	C₃×C₄×D₃	1	2	yes	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	3	1	no	—
253	C₂×C₃×C₄	—	3	2	no	—
254	C₂×C₃×C₄	—	3	2	no	—
255	C₂×C₃×C₄	—	4	1	no	—
256	C₂×C₃×C₄	—	6	4	no	—
257	C₂×C₃×C₄	—	6	1	no	—
258	C₂×C₃×C₄	—	6	1	no	—
259	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
261	#67	—	2	4	no	—
262	C₂×Dic₃	—	2	1	no	—
263	C₂×Dic₃	—	2	4	no	—
264	C₂×Dic₃	—	2	1	no	—
265	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
266	C₄×D₃	C₂×C₄×C₉	1	2	yes	—
267	C₄×D₃	D₄×C₉	1	2	yes	—
268	Dic₆	—	2	1	no	—
269	Dic₆	C₂×C₄×C₉	1	2	yes	—
270	C₃×C₈	—	2	1	no	—
271	C₃×C₈	—	2	1	no	—
272	C₃×C₈	—	4	1	no	—
273	C₃×C₈	—	6	1	no	—
274	C₃⋊C₈	—	2	1	no	—
275	C₂×C₃²	—	4	2	no	—
276	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₃²	C₃×#135	1	1	yes	characteristic
278	C₂×C₃²	C₃×#135	1	1	yes	characteristic
279	C₃×D₃	—	2	2	no	—
280	C₂×C₉	—	2	1	no	—
281	C₂×C₉	—	2	1	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	—	4	2	no	—
284	C₂×C₉	—	6	2	no	—
285	C₂×C₉	—	8	2	no	—
286	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₉	#912	1	1	yes	characteristic
288	C₂×C₉	#916	1	1	yes	characteristic
289	#41	—	3	4	no	—
290	#41	—	6	2	no	—
291	C₂×Q₈	—	3	1	no	—
292	C₂×D₄	—	6	1	no	—
293	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
294	C₂²×C₄	—	3	1	no	—
295	C₂²×C₄	—	6	1	no	—
296	C₂×C₈	—	3	1	no	—
297	C₂×C₈	—	6	2	no	—
298	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
299	C₄⋊C₄	—	3	1	no	—
300	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
301	C₂²⋊C₄	—	6	1	no	—
302	C₄²	—	6	1	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	3	2	no	—
307	C₂²×C₃	—	4	2	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	1	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	—	6	1	no	—
313	C₂²×C₃	—	6	1	no	—
314	C₂²×C₃	—	8	1	no	—
315	C₂²×C₃	—	8	1	no	—
316	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
317	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
318	C₂×D₃	—	2	1	no	—
319	C₂×D₃	—	2	1	no	—
320	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	3	2	no	—
324	C₃×C₄	—	4	1	no	—
325	C₃×C₄	—	4	1	no	—
326	C₃×C₄	—	6	2	no	—
327	C₃×C₄	—	8	1	no	—
328	C₃×C₄	—	12	1	no	—
329	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
330	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
331	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
332	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
333	Dic₃	—	2	2	no	—
334	Dic₃	—	4	1	no	—
335	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
336	C₃²	C₃×#416	1	1	yes	characteristic
337	C₉	—	2	1	no	—
338	C₉	#4772	1	1	yes	characteristic, direct product factor
339	C₂³	—	2	1	no	—
340	C₂³	—	3	1	no	—
341	Q₈	—	3	2	no	—
342	Q₈	—	6	1	no	—
343	D₄	—	2	1	no	—
344	D₄	—	6	4	no	—
345	D₄	C₄×D₃×C₉	1	2	yes	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	3	1	no	—
348	C₂×C₄	—	3	2	no	—
349	C₂×C₄	—	3	2	no	—
350	C₂×C₄	—	6	4	no	—
351	C₂×C₄	—	6	1	no	—
352	C₂×C₄	—	6	1	no	—
353	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	6	1	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	4	2	no	—
360	C₂×C₃	—	4	2	no	—
361	C₂×C₃	—	6	2	no	—
362	C₂×C₃	—	8	2	no	—
363	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₃	C₉×#135	1	1	yes	characteristic
365	C₂×C₃	C₉×#135	1	1	yes	characteristic
366	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
367	C₂×C₃	C₃×#912	1	1	yes	characteristic
368	C₂×C₃	C₃×#916	1	1	yes	characteristic
369	D₃	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	3	2	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	6	1	no	—
375	C₂²	—	6	1	no	—
376	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
377	C₄	—	3	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	6	2	no	—
380	C₄	—	12	1	no	—
381	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
382	C₄	D₃×D₄×C₉	1	1	yes	characteristic
383	C₃	—	2	1	no	—
384	C₃	C₉×#416	1	1	yes	characteristic, complemented
385	C₃	C₃×#4772	1	1	yes	characteristic
386	C₂	—	4	2	no	—
387	C₂	—	6	2	no	—
388	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
389	C₂	C₉×#912	1	1	yes	characteristic
390	C₂	C₉×#916	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#102	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#237	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#102	D₃
hypocenter	C₃	C₉×#416
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#102

Complements

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

N	H ≅ G/N	type
2. C₂×D₃×C₈×C₉	C₂	semidirect
3. C₉×#892	C₂	semidirect
4. C₃×C₉×#102	C₂	semidirect
5. C₉×#832	C₂	semidirect
6. C₉×#816	C₂	semidirect
7. C₉×#810	C₂	semidirect
14. C₉×#237	C₄	semidirect
38. C₉×#102	D₃	semidirect
57. #4772	C₉	direct (N × H)
106. C₂×D₃×C₈	C₂×C₉	semidirect
107. #892	C₂×C₉	semidirect
112. C₃×#102	C₂×C₉	semidirect
114. #832	C₂×C₉	semidirect
115. #816	C₂×C₉	semidirect
116. #810	C₂×C₉	semidirect
175. #237	C₄×C₉	semidirect
233. #102	D₃×C₉	semidirect
234. C₃×C₉	#416	semidirect
338. C₉	#4772	direct (N × H)
384. C₃	C₉×#416	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#237	2
C₂×D₃×C₈×C₉	2
C₉×#892	2
C₃×C₉×#102	2
C₉×#832	2
C₉×#816	2
C₉×#810	2
C₃×#4772	3
C₉×#416	3

Subgroups — C9×#4772 #13141755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4772 #13141755