Subgroups — C₉×#4740 #13141647

Order 1728.

526 conjugacy classes of subgroups.

The subgroup lattice has 388 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	C₉×#877	C₂	1	2	yes	maximal, complemented
3	C₃×C₉×#99	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#834	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#806	C₂	1	2	yes	maximal, complemented
6	C₃×#4740	C₃	1	1	yes	maximal, characteristic
7	C₉×#410	—	3	1	no	maximal
8	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×#67	C₄	1	1	yes	characteristic, complemented
10	C₂×C₉×#67	C₂²	1	1	yes	characteristic
11	C₂²×C₉×Dic₃	C₄	1	1	yes	characteristic, complemented
12	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
13	C₉×#237	—	2	2	no	—
14	C₉×#237	—	2	2	no	—
15	C₂×C₄×D₃×C₉	C₄	1	1	yes	characteristic, complemented
16	C₂×C₉×Dic₆	C₄	1	1	yes	characteristic, complemented
17	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₉×#217	C₂²	1	2	yes	—
19	C₉×Dic₃⋊C₄	—	2	2	no	—
20	C₄×C₉×Dic₃	—	2	2	no	—
21	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
22	C₃×#877	C₂×C₃	1	2	yes	—
23	C₂×C₉×#41	—	3	1	no	—
24	C₃²×#99	C₂×C₃	1	1	yes	characteristic
25	C₃×#834	C₂×C₃	1	1	yes	characteristic
26	C₃×#806	C₂×C₃	1	2	yes	—
27	C₉×#117	—	3	2	no	—
28	C₉×#99	—	2	1	no	—
29	C₉×#99	—	3	1	no	—
30	C₉×#99	—	3	2	no	—
31	C₉×#99	D₃	1	1	yes	characteristic, complemented
32	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
34	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
35	C₃×D₄×C₉	—	2	2	no	—
36	C₂×C₃×C₄×C₉	—	2	2	no	—
37	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
38	C₉×#67	—	2	2	no	—
39	C₉×#67	—	2	2	no	—
40	C₂×C₉×Dic₃	—	2	1	no	—
41	C₂×C₉×Dic₃	—	2	1	no	—
42	C₂×C₉×Dic₃	—	2	2	no	—
43	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₉×Dic₃	D₄	1	2	yes	—
47	C₂×C₉×Dic₃	D₄	1	2	yes	—
48	C₄×D₃×C₉	—	2	1	no	—
49	C₄×D₃×C₉	—	2	1	no	—
50	C₉×Dic₆	—	2	2	no	—
51	C₃×#410	—	3	1	no	—
52	#4740	C₉	1	1	yes	characteristic, direct product factor
53	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₃×#67	C₃×C₄	1	1	yes	characteristic
55	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
56	C₂²×C₃×Dic₃	C₃×C₄	1	1	yes	characteristic
57	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
58	C₃×#237	—	2	2	no	—
59	C₃×#237	—	2	2	no	—
60	C₂×C₃×C₄×D₃	C₃×C₄	1	1	yes	characteristic
61	C₂×C₃×Dic₆	C₃×C₄	1	1	yes	characteristic
62	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
63	C₃×#217	C₂²×C₃	1	2	yes	—
64	C₃×Dic₃⋊C₄	—	2	2	no	—
65	C₃×C₄×Dic₃	—	2	2	no	—
66	C₉×#41	—	6	2	no	—
67	C₉×#41	—	6	2	no	—
68	C₂×Q₈×C₉	—	3	1	no	—
69	C₂×D₄×C₉	—	2	1	no	—
70	C₂×D₄×C₉	—	3	1	no	—
71	C₂×D₄×C₉	—	3	1	no	—
72	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₄×C₉	—	3	1	no	—
74	C₂²×C₄×C₉	—	3	1	no	—
75	C₂²×C₄×C₉	—	3	1	no	—
76	C₉×C₄⋊C₄	—	6	2	no	—
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₉×C₂²⋊C₄	—	3	2	no	—
79	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
80	C₄²×C₉	—	6	2	no	—
81	C₂²×C₃×C₉	—	2	1	no	—
82	C₂²×C₃×C₉	—	4	1	no	—
83	C₂²×C₃×C₉	—	4	1	no	—
84	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
86	C₂×D₃×C₉	—	2	1	no	—
87	C₂×D₃×C₉	—	4	1	no	—
88	C₃×C₄×C₉	—	2	1	no	—
89	C₃×C₄×C₉	—	4	2	no	—
90	C₉×Dic₃	—	2	1	no	—
91	C₉×Dic₃	—	4	2	no	—
92	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
93	C₉×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₉×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×#41	—	3	1	no	—
96	C₂×#237	C₂×C₉	1	1	yes	characteristic
97	C₃×#117	—	3	2	no	—
98	#877	C₂×C₉	1	2	yes	complemented
99	C₃×#99	—	2	1	no	—
100	C₃×#99	—	3	1	no	—
101	C₃×#99	—	3	2	no	—
102	C₃×#99	C₂×C₉	1	1	yes	characteristic, complemented
103	C₃×#99	C₃×D₃	1	1	yes	characteristic
104	#834	C₂×C₉	1	1	yes	characteristic, complemented
105	#806	C₂×C₉	1	2	yes	complemented
106	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
107	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
108	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
109	C₃²×D₄	—	2	2	no	—
110	C₂×C₃²×C₄	—	2	2	no	—
111	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
112	C₃×#67	—	2	2	no	—
113	C₃×#67	—	2	2	no	—
114	C₂×C₃×Dic₃	—	2	1	no	—
115	C₂×C₃×Dic₃	—	2	1	no	—
116	C₂×C₃×Dic₃	—	2	2	no	—
117	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
121	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
122	C₃×C₄×D₃	—	2	1	no	—
123	C₃×C₄×D₃	—	2	1	no	—
124	C₃×Dic₆	—	2	2	no	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	—	3	1	no	—
128	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
129	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
130	Q₈×C₉	—	6	2	no	—
131	D₄×C₉	—	2	2	no	—
132	D₄×C₉	—	4	2	no	—
133	D₄×C₉	—	6	2	no	—
134	D₄×C₉	—	6	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	3	1	no	—
138	C₂×C₄×C₉	—	3	1	no	—
139	C₂×C₄×C₉	—	3	2	no	—
140	C₂×C₄×C₉	—	3	2	no	—
141	C₂×C₄×C₉	—	3	1	no	—
142	C₂×C₄×C₉	—	4	2	no	—
143	C₂×C₄×C₉	—	6	1	no	—
144	C₂×C₄×C₉	—	6	1	no	—
145	C₂×C₄×C₉	—	6	1	no	—
146	C₂×C₄×C₉	—	6	1	no	—
147	C₂×C₄×C₉	—	6	2	no	—
148	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
149	#410	—	3	1	no	Sylow
150	C₂×C₃×C₉	—	2	2	no	—
151	C₂×C₃×C₉	—	2	1	no	—
152	C₂×C₃×C₉	—	4	1	no	—
153	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	D₃×C₉	—	4	1	no	—
155	C₃×#41	—	6	2	no	—
156	C₃×#41	—	6	2	no	—
157	C₂×C₃×Q₈	—	3	1	no	—
158	C₂×C₃×D₄	—	2	1	no	—
159	C₂×C₃×D₄	—	3	1	no	—
160	C₂×C₃×D₄	—	3	1	no	—
161	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
162	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
163	C₂²×C₃×C₄	—	3	1	no	—
164	C₂²×C₃×C₄	—	3	1	no	—
165	C₂²×C₃×C₄	—	3	1	no	—
166	C₂×#67	C₄×C₉	1	1	yes	characteristic, complemented
167	C₂×#67	C₂²×C₉	1	1	yes	characteristic
168	C₂²×Dic₃	C₄×C₉	1	1	yes	characteristic, complemented
169	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
170	#237	—	2	2	no	—
171	#237	—	2	2	no	—
172	C₂×C₄×D₃	C₄×C₉	1	1	yes	characteristic, complemented
173	C₂×Dic₆	C₄×C₉	1	1	yes	characteristic, complemented
174	C₃×C₄⋊C₄	—	6	2	no	—
175	C₃×C₂²⋊C₄	—	2	2	no	—
176	C₃×C₂²⋊C₄	—	3	2	no	—
177	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
178	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
179	C₃×C₄²	—	6	2	no	—
180	#217	C₂²×C₉	1	2	yes	—
181	Dic₃⋊C₄	—	2	2	no	—
182	C₄×Dic₃	—	2	2	no	—
183	C₂²×C₃²	—	2	1	no	—
184	C₂²×C₃²	—	4	1	no	—
185	C₂²×C₃²	—	4	1	no	—
186	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
187	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
188	C₂×C₃×D₃	—	2	1	no	—
189	C₂×C₃×D₃	—	4	1	no	—
190	C₃²×C₄	—	2	1	no	—
191	C₃²×C₄	—	4	2	no	—
192	C₃×Dic₃	—	2	1	no	—
193	C₃×Dic₃	—	4	2	no	—
194	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
195	C₃×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
196	C₃×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₉	—	2	1	no	—
198	C₂²×C₉	—	2	1	no	—
199	C₂²×C₉	—	2	2	no	—
200	C₂²×C₉	—	4	1	no	—
201	C₂²×C₉	—	4	1	no	—
202	C₂²×C₉	—	4	1	no	—
203	C₂²×C₉	—	6	1	no	—
204	C₂²×C₉	—	8	1	no	—
205	C₂²×C₉	—	8	1	no	—
206	C₂²×C₉	—	12	1	no	—
207	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
208	C₂²×C₉	D₃×D₄	1	2	yes	—
209	C₄×C₉	—	2	1	no	—
210	C₄×C₉	—	3	1	no	—
211	C₄×C₉	—	3	1	no	—
212	C₄×C₉	—	3	2	no	—
213	C₄×C₉	—	4	1	no	—
214	C₄×C₉	—	4	2	no	—
215	C₄×C₉	—	6	1	no	—
216	C₄×C₉	—	8	2	no	—
217	C₄×C₉	—	12	2	no	—
218	C₂×#41	—	3	1	no	—
219	#117	—	3	2	no	—
220	#99	—	3	1	no	—
221	#99	—	3	2	no	—
222	#99	D₃×C₉	1	1	yes	characteristic, complemented
223	C₃×C₉	#410	1	1	yes	characteristic, complemented, Sylow
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	2	1	no	—
226	C₂³×C₃	—	3	1	no	—
227	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic
228	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
229	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
230	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
231	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
232	C₃×Q₈	—	6	2	no	—
233	C₃×D₄	—	2	2	no	—
234	C₃×D₄	—	2	2	no	—
235	C₃×D₄	—	4	2	no	—
236	C₃×D₄	—	6	2	no	—
237	C₃×D₄	—	6	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	3	1	no	—
242	C₂×C₃×C₄	—	3	1	no	—
243	C₂×C₃×C₄	—	3	2	no	—
244	C₂×C₃×C₄	—	3	2	no	—
245	C₂×C₃×C₄	—	3	1	no	—
246	C₂×C₃×C₄	—	4	2	no	—
247	C₂×C₃×C₄	—	6	1	no	—
248	C₂×C₃×C₄	—	6	1	no	—
249	C₂×C₃×C₄	—	6	1	no	—
250	C₂×C₃×C₄	—	6	1	no	—
251	C₂×C₃×C₄	—	6	2	no	—
252	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
253	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
254	#67	—	2	2	no	—
255	#67	—	2	2	no	—
256	C₂×Dic₃	—	2	1	no	—
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	—	2	2	no	—
259	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
260	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
261	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
262	C₂×Dic₃	D₄×C₉	1	2	yes	—
263	C₂×Dic₃	D₄×C₉	1	2	yes	—
264	C₄×D₃	—	2	1	no	—
265	C₄×D₃	—	2	1	no	—
266	Dic₆	—	2	2	no	—
267	C₂×C₃²	—	2	2	no	—
268	C₂×C₃²	—	2	1	no	—
269	C₂×C₃²	—	4	1	no	—
270	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
271	C₃×D₃	—	4	1	no	—
272	C₂×C₉	—	2	2	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	4	2	no	—
276	C₂×C₉	—	4	1	no	—
277	C₂×C₉	—	4	1	no	—
278	C₂×C₉	—	8	1	no	—
279	C₂×C₉	—	12	1	no	—
280	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
281	#41	—	6	2	no	—
282	#41	—	6	2	no	—
283	C₂×Q₈	—	3	1	no	—
284	C₂×D₄	—	3	1	no	—
285	C₂×D₄	—	3	1	no	—
286	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
287	C₂²×C₄	—	3	1	no	—
288	C₂²×C₄	—	3	1	no	—
289	C₂²×C₄	—	3	1	no	—
290	C₄⋊C₄	—	6	2	no	—
291	C₂²⋊C₄	—	3	2	no	—
292	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
293	C₄²	—	6	2	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	4	1	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	—	6	1	no	—
304	C₂²×C₃	—	8	1	no	—
305	C₂²×C₃	—	8	1	no	—
306	C₂²×C₃	—	12	1	no	—
307	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
308	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
309	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
310	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
311	C₂×D₃	—	2	1	no	—
312	C₂×D₃	—	4	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	3	1	no	—
316	C₃×C₄	—	3	1	no	—
317	C₃×C₄	—	3	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	4	2	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	—	6	1	no	—
322	C₃×C₄	—	8	2	no	—
323	C₃×C₄	—	12	2	no	—
324	Dic₃	—	2	1	no	—
325	Dic₃	—	4	2	no	—
326	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
327	Dic₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
328	Dic₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
329	C₃²	C₃×#410	1	1	yes	characteristic
330	C₉	—	2	1	no	—
331	C₉	#4740	1	1	yes	characteristic, direct product factor
332	C₂³	—	3	1	no	—
333	C₂³	C₄×D₃×C₉	1	1	yes	characteristic
334	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
335	Q₈	—	6	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	6	2	no	—
338	D₄	—	6	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	3	1	no	—
341	C₂×C₄	—	3	1	no	—
342	C₂×C₄	—	3	2	no	—
343	C₂×C₄	—	3	2	no	—
344	C₂×C₄	—	3	1	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	6	1	no	—
347	C₂×C₄	—	6	1	no	—
348	C₂×C₄	—	6	1	no	—
349	C₂×C₄	—	6	2	no	—
350	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
351	C₂×C₃	—	2	2	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	2	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	1	no	—
356	C₂×C₃	—	4	2	no	—
357	C₂×C₃	—	4	1	no	—
358	C₂×C₃	—	4	1	no	—
359	C₂×C₃	—	4	1	no	—
360	C₂×C₃	—	8	1	no	—
361	C₂×C₃	—	12	1	no	—
362	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
364	D₃	—	4	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	6	1	no	—
369	C₂²	—	12	1	no	—
370	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
371	C₂²	D₃×D₄×C₉	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	3	1	no	—
374	C₄	—	3	1	no	—
375	C₄	—	3	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	6	1	no	—
378	C₄	—	12	2	no	—
379	C₃	—	2	1	no	—
380	C₃	C₉×#410	1	1	yes	characteristic, complemented
381	C₃	C₃×#4740	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	2	1	no	—
384	C₂	—	4	1	no	—
385	C₂	—	12	1	no	—
386	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	D₃×C₂²⋊C₄
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₃×C₉×#99	C₂
socle	C₂×C₃²	C₂×C₃×C₂²⋊C₄
prime radical	C₂×C₃×#237	C₂×C₃
cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₉×#99	D₃
hypocenter	C₃	C₉×#410
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂³×C₉ ◁ C₉×#99

Complements

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

N	H ≅ G/N	type
2. C₉×#877	C₂	semidirect
3. C₃×C₉×#99	C₂	semidirect
4. C₉×#834	C₂	semidirect
5. C₉×#806	C₂	semidirect
9. C₂×C₉×#67	C₄	semidirect
11. C₂²×C₉×Dic₃	C₄	semidirect
15. C₂×C₄×D₃×C₉	C₄	semidirect
16. C₂×C₉×Dic₆	C₄	semidirect
31. C₉×#99	D₃	semidirect
52. #4740	C₉	direct (N × H)
98. #877	C₂×C₉	semidirect
102. C₃×#99	C₂×C₉	semidirect
104. #834	C₂×C₉	semidirect
105. #806	C₂×C₉	semidirect
166. C₂×#67	C₄×C₉	semidirect
168. C₂²×Dic₃	C₄×C₉	semidirect
172. C₂×C₄×D₃	C₄×C₉	semidirect
173. C₂×Dic₆	C₄×C₉	semidirect
222. #99	D₃×C₉	semidirect
223. C₃×C₉	#410	semidirect
331. C₉	#4740	direct (N × H)
380. C₃	C₉×#410	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
C₉×#877	2
C₃×C₉×#99	2
C₉×#834	2
C₉×#806	2
C₃×#4740	3
C₉×#410	3

Subgroups — C9×#4740 #13141647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4740 #13141647