Subgroups — C₉×#1871 #11766592

Order 1152.

564 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#525	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#104	C₂	1	2	yes	maximal, complemented
4	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#339	C₂	1	2	yes	maximal, complemented
6	C₃×#1871	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×#41	C₂²	1	1	yes	characteristic
8	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×M₁₆	—	2	1	no	—
10	C₂×C₉×M₁₆	—	2	4	no	—
11	C₂×C₉×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₈×C₉	—	2	1	no	—
13	C₉×#123	—	2	1	no	—
14	C₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
15	C₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
16	C₉×#121	C₄	1	1	yes	characteristic, complemented
17	C₉×#121	C₄	1	1	yes	characteristic, complemented
18	C₉×#120	—	2	1	no	—
19	C₄×D₄×C₉	—	2	1	no	—
20	C₄×D₄×C₉	—	2	1	no	—
21	C₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
23	C₂×C₄²×C₉	C₂²	1	2	yes	—
24	C₉×#104	—	2	4	no	—
25	C₉×#95	—	2	1	no	—
26	C₂²×C₃×M₁₆	C₂×C₃	1	1	yes	characteristic
27	C₃×#525	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×#104	C₂×C₃	1	2	yes	—
29	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₃×#339	C₂×C₃	1	2	yes	—
31	C₂⁴×C₉	D₄	1	1	yes	characteristic
32	C₉×#41	—	2	2	no	—
33	C₉×#41	—	2	2	no	—
34	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
35	C₂×D₄×C₉	—	2	1	no	—
36	C₂×D₄×C₉	—	2	1	no	—
37	C₂×D₄×C₉	—	2	1	no	—
38	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₉	—	2	2	no	—
40	C₂²×C₄×C₉	—	2	2	no	—
41	C₂²×C₄×C₉	—	2	2	no	—
42	C₂²×C₄×C₉	—	2	1	no	—
43	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
46	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
47	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
48	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₉×M₁₆	—	2	4	no	—
50	C₉×M₁₆	—	2	2	no	—
51	C₉×M₁₆	D₄	1	4	yes	complemented
52	C₂×C₈×C₉	—	2	4	no	—
53	C₂×C₈×C₉	—	2	2	no	—
54	C₉×C₄⋊C₄	—	2	1	no	—
55	C₉×C₄⋊C₄	—	2	1	no	—
56	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₉×C₂²⋊C₄	—	2	4	no	—
59	C₉×C₂²⋊C₄	—	2	1	no	—
60	C₉×C₂²⋊C₄	—	2	1	no	—
61	C₉×C₂²⋊C₄	—	2	1	no	—
62	C₉×C₂²⋊C₄	—	2	1	no	—
63	C₉×C₂²⋊C₄	—	2	1	no	—
64	C₄²×C₉	—	2	1	no	—
65	C₄²×C₉	—	2	2	no	—
66	C₄²×C₉	—	2	2	no	—
67	#1871	C₉	1	1	yes	characteristic, direct product factor, Sylow
68	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
69	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×M₁₆	—	2	1	no	—
71	C₂×C₃×M₁₆	—	2	4	no	—
72	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
73	C₂²×C₃×C₈	—	2	1	no	—
74	C₃×#123	—	2	1	no	—
75	C₃×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
76	C₃×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
77	C₃×#121	C₃×C₄	1	1	yes	characteristic
78	C₃×#121	C₃×C₄	1	1	yes	characteristic
79	C₃×#120	—	2	1	no	—
80	C₃×C₄×D₄	—	2	1	no	—
81	C₃×C₄×D₄	—	2	1	no	—
82	C₃×#117	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
85	C₃×#104	—	2	4	no	—
86	C₃×#95	—	2	1	no	—
87	C₂³×C₉	—	2	2	no	—
88	C₂³×C₉	—	2	2	no	—
89	C₂³×C₉	—	2	1	no	—
90	C₂³×C₉	—	4	1	no	—
91	C₂³×C₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂³×C₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
94	Q₈×C₉	—	2	2	no	—
95	D₄×C₉	—	2	2	no	—
96	D₄×C₉	—	4	2	no	—
97	D₄×C₉	—	4	2	no	—
98	D₄×C₉	—	4	2	no	—
99	C₂×C₄×C₉	—	2	2	no	—
100	C₂×C₄×C₉	—	2	2	no	—
101	C₂×C₄×C₉	—	2	2	no	—
102	C₂×C₄×C₉	—	2	1	no	—
103	C₂×C₄×C₉	—	2	1	no	—
104	C₂×C₄×C₉	—	2	1	no	—
105	C₂×C₄×C₉	—	2	1	no	—
106	C₂×C₄×C₉	—	2	4	no	—
107	C₂×C₄×C₉	—	2	1	no	—
108	C₂×C₄×C₉	—	2	1	no	—
109	C₂×C₄×C₉	—	2	1	no	—
110	C₂×C₄×C₉	—	4	2	no	—
111	C₂×C₄×C₉	—	4	2	no	—
112	C₂×C₄×C₉	—	4	1	no	—
113	C₂×C₄×C₉	—	4	1	no	—
114	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
118	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₉	#41	1	2	yes	—
120	C₈×C₉	—	2	4	no	—
121	C₂²×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
122	#525	C₂×C₉	1	1	yes	characteristic
123	C₂×#104	C₂×C₉	1	2	yes	complemented
124	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
125	#339	C₂×C₉	1	2	yes	complemented
126	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
127	C₃×#41	—	2	2	no	—
128	C₃×#41	—	2	2	no	—
129	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂×C₃×D₄	—	2	1	no	—
131	C₂×C₃×D₄	—	2	1	no	—
132	C₂×C₃×D₄	—	2	1	no	—
133	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	—	2	2	no	—
135	C₂²×C₃×C₄	—	2	2	no	—
136	C₂²×C₃×C₄	—	2	2	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
143	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₃×M₁₆	—	2	4	no	—
145	C₃×M₁₆	—	2	2	no	—
146	C₃×M₁₆	C₃×D₄	1	4	yes	—
147	C₂×C₃×C₈	—	2	4	no	—
148	C₂×C₃×C₈	—	2	2	no	—
149	C₃×C₄⋊C₄	—	2	1	no	—
150	C₃×C₄⋊C₄	—	2	1	no	—
151	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
152	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
153	C₃×C₂²⋊C₄	—	2	4	no	—
154	C₃×C₂²⋊C₄	—	2	1	no	—
155	C₃×C₂²⋊C₄	—	2	1	no	—
156	C₃×C₂²⋊C₄	—	2	1	no	—
157	C₃×C₂²⋊C₄	—	2	1	no	—
158	C₃×C₂²⋊C₄	—	2	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	—	2	2	no	—
161	C₃×C₄²	—	2	2	no	—
162	C₂²×C₉	—	2	1	no	—
163	C₂²×C₉	—	2	1	no	—
164	C₂²×C₉	—	2	1	no	—
165	C₂²×C₉	—	2	1	no	—
166	C₂²×C₉	—	2	1	no	—
167	C₂²×C₉	—	2	1	no	—
168	C₂²×C₉	—	2	1	no	—
169	C₂²×C₉	—	4	4	no	—
170	C₂²×C₉	—	4	1	no	—
171	C₂²×C₉	—	4	1	no	—
172	C₂²×C₉	—	4	1	no	—
173	C₂²×C₉	#104	1	2	yes	complemented
174	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₉	#121	1	2	yes	—
176	C₄×C₉	—	2	1	no	—
177	C₄×C₉	—	2	1	no	—
178	C₄×C₉	—	4	4	no	—
179	C₄×C₉	—	4	1	no	—
180	C₄×C₉	—	4	1	no	—
181	C₄×C₉	—	4	1	no	—
182	C₄×C₉	C₄×D₄	1	2	yes	—
183	C₄×C₉	#120	1	1	yes	characteristic
184	C₄×C₉	#123	1	1	yes	characteristic
185	C₂×#41	C₂²×C₉	1	1	yes	characteristic
186	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
187	C₂×M₁₆	—	2	1	no	—
188	C₂×M₁₆	—	2	4	no	—
189	C₂×M₁₆	C₂²×C₉	1	2	yes	—
190	C₂²×C₈	—	2	1	no	—
191	#123	—	2	1	no	—
192	C₂²⋊Q₈	C₄×C₉	1	1	yes	characteristic, complemented
193	C₂²⋊Q₈	C₄×C₉	1	1	yes	characteristic, complemented
194	#121	C₄×C₉	1	1	yes	characteristic, complemented
195	#121	C₄×C₉	1	1	yes	characteristic, complemented
196	#120	—	2	1	no	—
197	C₄×D₄	—	2	1	no	—
198	C₄×D₄	—	2	1	no	—
199	#117	C₂²×C₉	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₄²	C₂²×C₉	1	2	yes	—
202	#104	—	2	4	no	—
203	#95	—	2	1	no	—
204	C₂³×C₃	—	2	2	no	—
205	C₂³×C₃	—	2	2	no	—
206	C₂³×C₃	—	2	1	no	—
207	C₂³×C₃	—	4	1	no	—
208	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
210	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
211	C₃×Q₈	—	2	2	no	—
212	C₃×D₄	—	2	2	no	—
213	C₃×D₄	—	4	2	no	—
214	C₃×D₄	—	4	2	no	—
215	C₃×D₄	—	4	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	4	2	no	—
228	C₂×C₃×C₄	—	4	2	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	4	1	no	—
231	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₃×#41	1	2	yes	—
237	C₃×C₈	—	2	4	no	—
238	C₂×C₉	—	2	2	no	—
239	C₂×C₉	—	2	2	no	—
240	C₂×C₉	—	4	1	no	—
241	C₂×C₉	—	8	1	no	—
242	C₂×C₉	#386	1	1	yes	characteristic
243	C₂×C₉	C₂×#104	1	1	yes	characteristic
244	C₂×C₉	#421	1	1	yes	characteristic
245	C₂⁴	D₄×C₉	1	1	yes	characteristic
246	#41	—	2	2	no	—
247	#41	—	2	2	no	—
248	C₂×Q₈	C₂×C₄×C₉	1	1	yes	characteristic
249	C₂×D₄	—	2	1	no	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	1	no	—
252	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
259	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
260	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
261	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
263	M₁₆	—	2	4	no	—
264	M₁₆	—	2	2	no	—
265	M₁₆	D₄×C₉	1	4	yes	complemented
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	2	no	—
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
271	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
272	C₂²⋊C₄	—	2	4	no	—
273	C₂²⋊C₄	—	2	1	no	—
274	C₂²⋊C₄	—	2	1	no	—
275	C₂²⋊C₄	—	2	1	no	—
276	C₂²⋊C₄	—	2	1	no	—
277	C₂²⋊C₄	—	2	1	no	—
278	C₄²	—	2	1	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	2	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	4	4	no	—
289	C₂²×C₃	—	4	1	no	—
290	C₂²×C₃	—	4	1	no	—
291	C₂²×C₃	—	4	1	no	—
292	C₂²×C₃	C₃×#104	1	2	yes	—
293	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₃	C₃×#121	1	2	yes	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	4	4	no	—
298	C₃×C₄	—	4	1	no	—
299	C₃×C₄	—	4	1	no	—
300	C₃×C₄	—	4	1	no	—
301	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
302	C₃×C₄	C₃×#120	1	1	yes	characteristic
303	C₃×C₄	C₃×#123	1	1	yes	characteristic
304	C₉	#1871	1	1	yes	characteristic, direct product factor, Sylow
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	C₉×C₂²⋊C₄	1	1	yes	characteristic
310	C₂³	C₉×C₂²⋊C₄	1	1	yes	characteristic
311	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	D₄	—	2	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
335	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
336	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
337	C₂×C₄	C₉×#41	1	2	yes	—
338	C₈	—	2	4	no	—
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	4	1	no	—
342	C₂×C₃	—	8	1	no	—
343	C₂×C₃	C₃×#386	1	1	yes	characteristic
344	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
345	C₂×C₃	C₃×#421	1	1	yes	characteristic
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	C₉×#104	1	2	yes	complemented
358	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
359	C₂²	C₉×#121	1	2	yes	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	4	4	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	C₄×D₄×C₉	1	2	yes	—
367	C₄	C₉×#120	1	1	yes	characteristic
368	C₄	C₉×#123	1	1	yes	characteristic
369	C₃	C₃×#1871	1	1	yes	characteristic
370	C₂	—	2	2	no	—
371	C₂	—	2	2	no	—
372	C₂	—	4	1	no	—
373	C₂	—	8	1	no	—
374	C₂	C₉×#386	1	1	yes	characteristic
375	C₂	C₂×C₉×#104	1	1	yes	characteristic
376	C₂	C₉×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×C₂²⋊C₄
prime radical	C₃×#525	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×M₁₆	C₂	semidirect
3. C₂×C₉×#104	C₂	semidirect
4. C₄×C₉×C₂²⋊C₄	C₂	semidirect
5. C₉×#339	C₂	semidirect
14. C₉×C₂²⋊Q₈	C₄	semidirect
15. C₉×C₂²⋊Q₈	C₄	semidirect
16. C₉×#121	C₄	semidirect
17. C₉×#121	C₄	semidirect
51. C₉×M₁₆	D₄	semidirect
67. #1871	C₉	direct (N × H)
121. C₂²×M₁₆	C₂×C₉	semidirect
123. C₂×#104	C₂×C₉	semidirect
124. C₄×C₂²⋊C₄	C₂×C₉	semidirect
125. #339	C₂×C₉	semidirect
173. C₂²×C₉	#104	semidirect
192. C₂²⋊Q₈	C₄×C₉	semidirect
193. C₂²⋊Q₈	C₄×C₉	semidirect
194. #121	C₄×C₉	semidirect
195. #121	C₄×C₉	semidirect
265. M₁₆	D₄×C₉	semidirect
304. C₉	#1871	direct (N × H)
357. C₂²	C₉×#104	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×M₁₆	2
C₉×#525	2
C₂×C₉×#104	2
C₄×C₉×C₂²⋊C₄	2
C₉×#339	2
C₃×#1871	3

Subgroups — C9×#1871 #11766592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1871 #11766592