Subgroups — C₉×#2966 #11767687

Order 1152.

570 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#435	C₂	1	2	yes	maximal, complemented
6	C₈×D₄×C₉	C₂	1	2	yes	maximal, complemented
7	C₈×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#433	C₂	1	2	yes	maximal, complemented
9	C₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#405	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2966	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₉	C₂²	1	2	yes	—
17	C₉×#126	C₄	1	2	yes	—
18	C₉×#125	C₄	1	1	yes	characteristic
19	C₉×#124	C₄	1	1	yes	characteristic
20	C₉×#123	C₄	1	2	yes	—
21	C₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
22	C₉×#121	C₄	1	1	yes	characteristic
23	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
24	C₄×D₄×C₉	C₂²	1	2	yes	—
25	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
26	C₉×#117	C₂²	1	2	yes	—
27	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊C₈	C₂²	1	2	yes	—
31	C₉×C₄⋊C₈	C₂²	1	2	yes	—
32	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₉×#97	C₂²	1	2	yes	—
36	C₉×#97	C₂²	1	2	yes	—
37	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
38	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
39	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
41	C₄×C₈×C₉	C₂²	1	2	yes	—
42	C₃×#529	C₂×C₃	1	1	yes	characteristic
43	C₃×#446	C₂×C₃	1	1	yes	characteristic
44	C₃×C₈×Q₈	C₂×C₃	1	1	yes	characteristic
45	C₃×#436	C₂×C₃	1	1	yes	characteristic
46	C₃×#435	C₂×C₃	1	2	yes	—
47	C₃×C₈×D₄	C₂×C₃	1	1	yes	characteristic
48	C₃×C₈×D₄	C₂×C₃	1	2	yes	—
49	C₃×#433	C₂×C₃	1	2	yes	—
50	C₃×#432	C₂×C₃	1	1	yes	characteristic
51	C₃×#405	C₂×C₃	1	2	yes	—
52	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
53	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
54	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
55	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	2	yes	—
60	C₉×M₁₆	—	2	4	no	—
61	C₂×C₈×C₉	—	2	2	no	—
62	C₂×C₈×C₉	—	2	4	no	—
63	C₂×C₈×C₉	—	2	2	no	—
64	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₈×C₉	C₂³	1	2	yes	—
67	C₂×C₈×C₉	C₂³	1	2	yes	—
68	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
70	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
71	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
82	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
83	C₄²×C₉	C₂³	1	1	yes	characteristic
84	C₄²×C₉	C₂³	1	1	yes	characteristic
85	C₄²×C₉	C₂³	1	2	yes	—
86	#2966	C₉	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
88	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
91	C₃×#126	C₃×C₄	1	2	yes	—
92	C₃×#125	C₃×C₄	1	1	yes	characteristic
93	C₃×#124	C₃×C₄	1	1	yes	characteristic
94	C₃×#123	C₃×C₄	1	2	yes	—
95	C₃×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
96	C₃×#121	C₃×C₄	1	1	yes	characteristic
97	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
99	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
100	C₃×#117	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
104	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
105	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
106	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
107	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
108	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
109	C₃×#97	C₂²×C₃	1	2	yes	—
110	C₃×#97	C₂²×C₃	1	2	yes	—
111	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
112	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
114	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
115	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
116	C₂³×C₉	C₂²×C₄	1	2	yes	—
117	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
118	Q₈×C₉	—	2	2	no	—
119	D₄×C₉	—	2	4	no	—
120	D₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	2	no	—
123	C₂×C₄×C₉	—	2	1	no	—
124	C₂×C₄×C₉	—	2	1	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
132	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
133	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
134	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
136	C₈×C₉	—	2	1	no	—
137	C₈×C₉	—	2	1	no	—
138	C₈×C₉	—	2	2	no	—
139	C₈×C₉	—	2	2	no	—
140	C₈×C₉	#41	1	2	yes	—
141	C₈×C₉	#41	1	2	yes	—
142	#529	C₂×C₉	1	1	yes	characteristic
143	#446	C₂×C₉	1	1	yes	characteristic, complemented
144	C₈×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
145	#436	C₂×C₉	1	1	yes	characteristic, complemented
146	#435	C₂×C₉	1	2	yes	complemented
147	C₈×D₄	C₂×C₉	1	1	yes	characteristic, complemented
148	C₈×D₄	C₂×C₉	1	2	yes	complemented
149	#433	C₂×C₉	1	2	yes	complemented
150	#432	C₂×C₉	1	1	yes	characteristic, complemented
151	#405	C₂×C₉	1	2	yes	complemented
152	C₂×C₄×C₈	C₂×C₉	1	1	yes	characteristic, complemented
153	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
155	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
160	C₃×M₁₆	—	2	4	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	4	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
167	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
168	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
170	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
171	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
172	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
173	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
174	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
176	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
177	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
178	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
179	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
180	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
181	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
182	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
183	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
184	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
185	C₃×C₄²	C₂³×C₃	1	2	yes	—
186	C₂²×C₉	—	2	1	no	—
187	C₂²×C₉	—	2	1	no	—
188	C₂²×C₉	—	2	2	no	—
189	C₂²×C₉	—	2	2	no	—
190	C₂²×C₉	—	2	2	no	—
191	C₂²×C₉	#131	1	2	yes	—
192	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
193	C₄×C₉	—	2	1	no	—
194	C₄×C₉	—	2	2	no	—
195	C₄×C₉	—	2	1	no	—
196	C₄×C₉	—	2	1	no	—
197	C₄×C₉	—	2	1	no	—
198	C₄×C₉	—	2	2	no	—
199	C₄×C₉	—	2	2	no	—
200	C₄×C₉	#131	1	2	yes	—
201	C₄×C₉	C₂×#41	1	1	yes	characteristic
202	C₄×C₉	C₂×#41	1	1	yes	characteristic
203	C₂×M₁₆	C₂²×C₉	1	2	yes	—
204	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
205	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
206	C₂²×C₈	C₂²×C₉	1	2	yes	—
207	#126	C₄×C₉	1	2	yes	—
208	#125	C₄×C₉	1	1	yes	characteristic
209	#124	C₄×C₉	1	1	yes	characteristic
210	#123	C₄×C₉	1	2	yes	—
211	C₂²⋊Q₈	C₄×C₉	1	1	yes	characteristic
212	#121	C₄×C₉	1	1	yes	characteristic
213	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
214	C₄×D₄	C₂²×C₉	1	2	yes	—
215	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
216	#117	C₂²×C₉	1	2	yes	—
217	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
218	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
219	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
220	C₄⋊C₈	C₂²×C₉	1	2	yes	—
221	C₄⋊C₈	C₂²×C₉	1	2	yes	—
222	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
223	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
224	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
225	#97	C₂²×C₉	1	2	yes	—
226	#97	C₂²×C₉	1	2	yes	—
227	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
228	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
229	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
230	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
231	C₄×C₈	C₂²×C₉	1	2	yes	—
232	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
233	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₃×Q₈	—	2	2	no	—
235	C₃×D₄	—	2	4	no	—
236	C₃×D₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
248	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
249	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
250	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
252	C₃×C₈	—	2	1	no	—
253	C₃×C₈	—	2	1	no	—
254	C₃×C₈	—	2	2	no	—
255	C₃×C₈	—	2	2	no	—
256	C₃×C₈	C₃×#41	1	2	yes	—
257	C₃×C₈	C₃×#41	1	2	yes	—
258	C₂×C₉	—	2	2	no	—
259	C₂×C₉	—	4	2	no	—
260	C₂×C₉	C₄×#41	1	1	yes	characteristic
261	C₂×C₉	C₂×#131	1	1	yes	characteristic
262	C₂×C₉	C₂×#131	1	1	yes	characteristic
263	C₂×Q₈	C₂×C₄×C₉	1	1	yes	characteristic
264	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
265	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
268	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
269	C₂²×C₄	C₂³×C₉	1	2	yes	—
270	M₁₆	—	2	4	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
275	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
276	C₂×C₈	C₂³×C₉	1	2	yes	—
277	C₂×C₈	C₂³×C₉	1	2	yes	—
278	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
279	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
280	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
281	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
282	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
283	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
284	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
285	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
286	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
287	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
288	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
289	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
290	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
291	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
292	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
293	C₄²	C₂³×C₉	1	1	yes	characteristic
294	C₄²	C₂³×C₉	1	1	yes	characteristic
295	C₄²	C₂³×C₉	1	2	yes	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	C₃×#131	1	2	yes	—
302	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	C₃×#131	1	2	yes	—
311	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
312	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
313	C₉	#2966	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	C₂²×C₄×C₉	1	2	yes	—
315	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
316	Q₈	—	2	2	no	—
317	D₄	—	2	4	no	—
318	D₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
327	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
330	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
331	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
332	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
333	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	C₉×#41	1	2	yes	—
339	C₈	C₉×#41	1	2	yes	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	4	2	no	—
342	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
343	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
344	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	C₉×#131	1	2	yes	—
351	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	2	no	—
359	C₄	C₉×#131	1	2	yes	—
360	C₄	C₂×C₉×#41	1	1	yes	characteristic
361	C₄	C₂×C₉×#41	1	1	yes	characteristic
362	C₃	C₃×#2966	1	1	yes	characteristic
363	C₂	—	2	2	no	—
364	C₂	—	4	2	no	—
365	C₂	C₄×C₉×#41	1	1	yes	characteristic
366	C₂	C₂×C₉×#131	1	1	yes	characteristic
367	C₂	C₂×C₉×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₃×C₄
prime radical	C₃×#121	C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#446	C₂	semidirect
3. C₈×Q₈×C₉	C₂	semidirect
4. C₉×#436	C₂	semidirect
5. C₉×#435	C₂	semidirect
6. C₈×D₄×C₉	C₂	semidirect
7. C₈×D₄×C₉	C₂	semidirect
8. C₉×#433	C₂	semidirect
9. C₉×#432	C₂	semidirect
10. C₉×#405	C₂	semidirect
11. C₂×C₄×C₈×C₉	C₂	semidirect
86. #2966	C₉	direct (N × H)
143. #446	C₂×C₉	semidirect
144. C₈×Q₈	C₂×C₉	semidirect
145. #436	C₂×C₉	semidirect
146. #435	C₂×C₉	semidirect
147. C₈×D₄	C₂×C₉	semidirect
148. C₈×D₄	C₂×C₉	semidirect
149. #433	C₂×C₉	semidirect
150. #432	C₂×C₉	semidirect
151. #405	C₂×C₉	semidirect
152. C₂×C₄×C₈	C₂×C₉	semidirect
313. C₉	#2966	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#529	2
C₉×#446	2
C₈×Q₈×C₉	2
C₉×#436	2
C₉×#435	2
C₈×D₄×C₉	2
C₉×#433	2
C₉×#432	2
C₉×#405	2
C₂×C₄×C₈×C₉	2
C₃×#2966	3

Subgroups — C9×#2966 #11767687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2966 #11767687