Subgroups — C₉×#2974 #11767695

Order 1152.

696 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×#436	C₂	1	2	yes	maximal, complemented
3	C₉×#435	C₂	1	4	yes	maximal, complemented
4	C₈×D₄×C₉	C₂	1	2	yes	maximal, complemented
5	C₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#407	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₃×#2974	C₃	1	1	yes	maximal, characteristic
10	C₂²×D₄×C₉	C₄	1	1	yes	characteristic
11	C₂³×C₄×C₉	C₂²	1	2	yes	—
12	C₂×C₉×M₁₆	C₂²	1	4	yes	complemented
13	C₂²×C₈×C₉	C₂²	1	4	yes	complemented
14	C₄×D₄×C₉	C₄	1	2	yes	—
15	C₄×D₄×C₉	C₄	1	1	yes	characteristic
16	C₄×D₄×C₉	C₄	1	1	yes	characteristic
17	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
18	C₄×D₄×C₉	C₂²	1	2	yes	—
19	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₂×C₉×C₂²⋊C₄	C₄	1	2	yes	—
22	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
23	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
24	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
25	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
29	C₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
30	C₉×#97	C₂²	1	2	yes	complemented
31	C₄×C₈×C₉	C₂²	1	2	yes	complemented
32	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
33	C₃×#436	C₂×C₃	1	2	yes	—
34	C₃×#435	C₂×C₃	1	4	yes	—
35	C₃×C₈×D₄	C₂×C₃	1	2	yes	—
36	C₃×#432	C₂×C₃	1	1	yes	characteristic
37	C₃×#431	C₂×C₃	1	1	yes	characteristic
38	C₃×#407	C₂×C₃	1	2	yes	—
39	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	2	yes	—
40	C₂⁴×C₉	C₂×C₄	1	2	yes	—
41	C₂×D₄×C₉	—	2	4	no	—
42	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
43	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
44	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₉	—	4	4	no	—
46	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
49	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
50	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
51	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₉	C₂³	1	2	yes	—
54	C₉×M₁₆	—	4	4	no	—
55	C₂×C₈×C₉	—	4	4	no	—
56	C₂×C₈×C₉	C₂³	1	2	yes	—
57	C₂×C₈×C₉	C₂³	1	4	yes	—
58	C₂×C₈×C₉	C₂³	1	2	yes	—
59	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
67	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
68	C₄²×C₉	C₂³	1	1	yes	characteristic
69	C₄²×C₉	C₂³	1	1	yes	characteristic
70	#2974	C₉	1	1	yes	characteristic, direct product factor, Sylow
71	C₂²×C₃×D₄	C₃×C₄	1	1	yes	characteristic
72	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
74	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
75	C₃×C₄×D₄	C₃×C₄	1	2	yes	—
76	C₃×C₄×D₄	C₃×C₄	1	1	yes	characteristic
77	C₃×C₄×D₄	C₃×C₄	1	1	yes	characteristic
78	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
80	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
82	C₂×C₃×C₂²⋊C₄	C₃×C₄	1	2	yes	—
83	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
84	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
85	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
86	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
87	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
88	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
90	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
91	C₃×#97	C₂²×C₃	1	2	yes	—
92	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
93	C₂³×C₉	—	2	4	no	—
94	C₂³×C₉	—	2	4	no	—
95	C₂³×C₉	—	4	2	no	—
96	C₂³×C₉	C₂²×C₄	1	2	yes	—
97	C₂³×C₉	C₂²×C₄	1	2	yes	—
98	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
99	D₄×C₉	—	2	4	no	—
100	D₄×C₉	—	2	2	no	—
101	D₄×C₉	M₁₆	1	4	yes	complemented
102	C₂×C₄×C₉	—	2	2	no	—
103	C₂×C₄×C₉	—	2	2	no	—
104	C₂×C₄×C₉	—	2	4	no	—
105	C₂×C₄×C₉	—	2	4	no	—
106	C₂×C₄×C₉	—	2	2	no	—
107	C₂×C₄×C₉	—	4	2	no	—
108	C₂×C₄×C₉	—	4	2	no	—
109	C₂×C₄×C₉	—	4	2	no	—
110	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
115	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
116	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
118	C₈×C₉	—	2	2	no	—
119	C₈×C₉	—	2	4	no	—
120	C₈×C₉	—	2	2	no	—
121	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
122	#436	C₂×C₉	1	2	yes	complemented
123	#435	C₂×C₉	1	4	yes	complemented
124	C₈×D₄	C₂×C₉	1	2	yes	complemented
125	#432	C₂×C₉	1	1	yes	characteristic, complemented
126	#431	C₂×C₉	1	1	yes	characteristic, complemented
127	#407	C₂×C₉	1	2	yes	complemented
128	C₂×C₂²⋊C₈	C₂×C₉	1	2	yes	complemented
129	C₂⁴×C₃	C₂×C₃×C₄	1	2	yes	—
130	C₂×C₃×D₄	—	2	4	no	—
131	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
132	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	—	4	4	no	—
135	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
138	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
139	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
140	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
142	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
143	C₃×M₁₆	—	4	4	no	—
144	C₂×C₃×C₈	—	4	4	no	—
145	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
146	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
147	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
148	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
149	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
150	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
151	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
152	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
153	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
154	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
155	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
156	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
157	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
158	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₉	—	2	1	no	—
160	C₂²×C₉	—	2	2	no	—
161	C₂²×C₉	—	2	1	no	—
162	C₂²×C₉	—	2	2	no	—
163	C₂²×C₉	—	2	2	no	—
164	C₂²×C₉	—	2	2	no	—
165	C₂²×C₉	—	2	2	no	—
166	C₂²×C₉	—	4	8	no	—
167	C₂²×C₉	C₂×M₁₆	1	4	yes	—
168	C₂²×C₉	#131	1	2	yes	—
169	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
170	C₄×C₉	—	2	1	no	—
171	C₄×C₉	—	2	2	no	—
172	C₄×C₉	—	2	2	no	—
173	C₄×C₉	—	2	1	no	—
174	C₄×C₉	—	2	1	no	—
175	C₄×C₉	—	2	1	no	—
176	C₄×C₉	C₂×M₁₆	1	2	yes	—
177	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
178	C₂²×D₄	C₄×C₉	1	1	yes	characteristic
179	C₂³×C₄	C₂²×C₉	1	2	yes	—
180	C₂×M₁₆	C₂²×C₉	1	4	yes	complemented
181	C₂²×C₈	C₂²×C₉	1	4	yes	complemented
182	C₄×D₄	C₄×C₉	1	2	yes	—
183	C₄×D₄	C₄×C₉	1	1	yes	characteristic
184	C₄×D₄	C₄×C₉	1	1	yes	characteristic
185	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
186	C₄×D₄	C₂²×C₉	1	2	yes	—
187	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
188	C₂×C₄⋊C₄	C₄×C₉	1	1	yes	characteristic
189	C₂×C₂²⋊C₄	C₄×C₉	1	2	yes	—
190	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
191	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
192	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
193	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
194	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
195	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
196	C₂²⋊C₈	C₂²×C₉	1	4	yes	complemented
197	C₂²⋊C₈	C₂²×C₉	1	4	yes	complemented
198	#97	C₂²×C₉	1	2	yes	complemented
199	C₄×C₈	C₂²×C₉	1	2	yes	complemented
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	—	2	4	no	—
202	C₂³×C₃	—	4	2	no	—
203	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
204	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
205	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
206	C₃×D₄	—	2	4	no	—
207	C₃×D₄	—	2	2	no	—
208	C₃×D₄	C₃×M₁₆	1	4	yes	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	4	2	no	—
215	C₂×C₃×C₄	—	4	2	no	—
216	C₂×C₃×C₄	—	4	2	no	—
217	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
219	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
222	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
223	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
225	C₃×C₈	—	2	2	no	—
226	C₃×C₈	—	2	4	no	—
227	C₃×C₈	—	2	2	no	—
228	C₂×C₉	—	2	2	no	—
229	C₂×C₉	—	2	4	no	—
230	C₂×C₉	—	4	2	no	—
231	C₂×C₉	#518	1	1	yes	characteristic
232	C₂×C₉	C₂²×M₁₆	1	1	yes	characteristic
233	C₂×C₉	C₂×#131	1	1	yes	characteristic
234	C₂⁴	C₂×C₄×C₉	1	2	yes	—
235	C₂×D₄	—	2	4	no	—
236	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
237	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic
238	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic
239	C₂²×C₄	—	4	4	no	—
240	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
243	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
244	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
245	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
246	C₂²×C₄	C₂³×C₉	1	2	yes	—
247	C₂²×C₄	C₂³×C₉	1	2	yes	—
248	M₁₆	—	4	4	no	—
249	C₂×C₈	—	4	4	no	—
250	C₂×C₈	C₂³×C₉	1	2	yes	—
251	C₂×C₈	C₂³×C₉	1	2	yes	—
252	C₂×C₈	C₂³×C₉	1	4	yes	—
253	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
254	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
255	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
256	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
257	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
258	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
259	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
260	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
261	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
262	C₄²	C₂³×C₉	1	1	yes	characteristic
263	C₄²	C₂³×C₉	1	1	yes	characteristic
264	C₂²×C₃	—	2	1	no	—
265	C₂²×C₃	—	2	2	no	—
266	C₂²×C₃	—	2	1	no	—
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	4	8	no	—
272	C₂²×C₃	C₂×C₃×M₁₆	1	4	yes	—
273	C₂²×C₃	C₃×#131	1	2	yes	—
274	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
275	C₃×C₄	—	2	1	no	—
276	C₃×C₄	—	2	1	no	—
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	1	no	—
279	C₃×C₄	—	2	2	no	—
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	C₂×C₃×M₁₆	1	2	yes	—
282	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
283	C₉	#2974	1	1	yes	characteristic, direct product factor, Sylow
284	C₂³	—	2	4	no	—
285	C₂³	—	2	4	no	—
286	C₂³	—	4	2	no	—
287	C₂³	C₂²×C₄×C₉	1	2	yes	—
288	C₂³	C₂²×C₄×C₉	1	2	yes	—
289	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
290	D₄	—	2	4	no	—
291	D₄	—	2	2	no	—
292	D₄	C₉×M₁₆	1	4	yes	complemented
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
302	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
303	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
304	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
305	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
306	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
307	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
308	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
309	C₈	—	2	2	no	—
310	C₈	—	2	4	no	—
311	C₈	—	2	2	no	—
312	C₂×C₃	—	2	2	no	—
313	C₂×C₃	—	2	4	no	—
314	C₂×C₃	—	4	2	no	—
315	C₂×C₃	C₃×#518	1	1	yes	characteristic
316	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
317	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
318	C₂²	—	2	1	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	8	no	—
326	C₂²	C₂×C₉×M₁₆	1	4	yes	—
327	C₂²	C₉×#131	1	2	yes	—
328	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
329	C₄	—	2	1	no	—
330	C₄	—	2	1	no	—
331	C₄	—	2	1	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	2	no	—
335	C₄	C₂×C₉×M₁₆	1	2	yes	—
336	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
337	C₃	C₃×#2974	1	1	yes	characteristic
338	C₂	—	2	2	no	—
339	C₂	—	2	4	no	—
340	C₂	—	4	2	no	—
341	C₂	C₉×#518	1	1	yes	characteristic
342	C₂	C₂²×C₉×M₁₆	1	1	yes	characteristic
343	C₂	C₂×C₉×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₃×C₄
prime radical	C₂²×C₃×D₄	C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#436	C₂	semidirect
3. C₉×#435	C₂	semidirect
4. C₈×D₄×C₉	C₂	semidirect
5. C₉×#432	C₂	semidirect
6. C₉×#431	C₂	semidirect
7. C₉×#407	C₂	semidirect
8. C₂×C₉×C₂²⋊C₈	C₂	semidirect
12. C₂×C₉×M₁₆	C₂²	semidirect
13. C₂²×C₈×C₉	C₂²	semidirect
23. C₉×C₄⋊C₈	C₂²	semidirect
24. C₉×C₄⋊C₈	C₂²	semidirect
28. C₉×C₂²⋊C₈	C₂²	semidirect
29. C₉×C₂²⋊C₈	C₂²	semidirect
30. C₉×#97	C₂²	semidirect
31. C₄×C₈×C₉	C₂²	semidirect
70. #2974	C₉	direct (N × H)
101. D₄×C₉	M₁₆	semidirect
122. #436	C₂×C₉	semidirect
123. #435	C₂×C₉	semidirect
124. C₈×D₄	C₂×C₉	semidirect
125. #432	C₂×C₉	semidirect
126. #431	C₂×C₉	semidirect
127. #407	C₂×C₉	semidirect
128. C₂×C₂²⋊C₈	C₂×C₉	semidirect
180. C₂×M₁₆	C₂²×C₉	semidirect
181. C₂²×C₈	C₂²×C₉	semidirect
191. C₄⋊C₈	C₂²×C₉	semidirect
192. C₄⋊C₈	C₂²×C₉	semidirect
196. C₂²⋊C₈	C₂²×C₉	semidirect
197. C₂²⋊C₈	C₂²×C₉	semidirect
198. #97	C₂²×C₉	semidirect
199. C₄×C₈	C₂²×C₉	semidirect
283. C₉	#2974	direct (N × H)
292. D₄	C₉×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄×C₉	2
C₉×#436	2
C₉×#435	2
C₈×D₄×C₉	2
C₉×#432	2
C₉×#431	2
C₉×#407	2
C₂×C₉×C₂²⋊C₈	2
C₃×#2974	3

Subgroups — C9×#2974 #11767695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2974 #11767695