Subgroups — C₉×#5585 #13152706

Order 1728.

778 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	2	yes	maximal, complemented
3	C₉×#894	C₂	1	4	yes	maximal, complemented
4	C₉×#893	C₂	1	2	yes	maximal, complemented
5	C₉×#875	C₂	1	2	yes	maximal, complemented
6	C₉×#874	C₂	1	1	yes	maximal, characteristic
7	C₄×C₉×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5585	C₃	1	1	yes	maximal, characteristic
10	C₉×#559	—	3	1	no	maximal
11	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×D₁₂	C₂²	1	2	yes	—
13	C₂×C₉×D₁₂	C₂²	1	2	yes	—
14	C₂×C₉×D₁₂	C₂²	1	2	yes	—
15	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
16	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
20	C₃×C₄²×C₉	C₂²	1	2	yes	—
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
24	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
26	C₄×C₉×Dic₃	C₂²	1	2	yes	—
27	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
28	C₃×#947	C₂×C₃	1	2	yes	—
29	C₃×#894	C₂×C₃	1	4	yes	—
30	C₃×#893	C₂×C₃	1	2	yes	—
31	C₃×#875	C₂×C₃	1	2	yes	—
32	C₃×#874	C₂×C₃	1	1	yes	characteristic
33	C₃×C₄×D₁₂	C₂×C₃	1	2	yes	—
34	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
35	C₉×#127	—	3	1	no	—
36	C₉×#124	—	3	2	no	—
37	C₉×#124	—	3	2	no	—
38	C₉×#123	—	3	4	no	—
39	C₄×Q₈×C₉	—	2	1	no	—
40	C₄×Q₈×C₉	—	3	1	no	—
41	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
42	C₄×D₄×C₉	—	3	2	no	—
43	C₄×D₄×C₉	—	3	2	no	—
44	C₂²×D₃×C₉	C₂³	1	4	yes	—
45	C₃×Q₈×C₉	—	2	2	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₉×Dic₃	C₂³	1	2	yes	—
52	C₂×C₉×Dic₃	C₂³	1	2	yes	—
53	C₉×D₁₂	—	2	4	no	—
54	C₉×D₁₂	—	2	4	no	—
55	C₉×D₁₂	—	4	2	no	—
56	C₄×D₃×C₉	—	4	4	no	—
57	C₉×Dic₆	—	2	2	no	—
58	C₃×#559	—	3	1	no	—
59	#5585	C₉	1	1	yes	characteristic, direct product factor
60	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
62	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
63	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
64	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
65	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
66	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
67	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
69	C₃²×C₄²	C₂²×C₃	1	2	yes	—
70	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
71	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
72	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
73	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
74	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
75	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
76	C₂×Q₈×C₉	—	2	1	no	—
77	C₂×Q₈×C₉	—	3	1	no	—
78	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
79	C₂×D₄×C₉	—	3	2	no	—
80	C₂×D₄×C₉	—	3	2	no	—
81	C₂×D₄×C₉	—	3	2	no	—
82	C₂²×C₄×C₉	—	3	4	no	—
83	C₉×C₄⋊C₄	—	2	1	no	—
84	C₉×C₄⋊C₄	—	2	2	no	—
85	C₉×C₄⋊C₄	—	3	1	no	—
86	C₉×C₄⋊C₄	—	3	2	no	—
87	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
89	C₉×C₂²⋊C₄	—	3	4	no	—
90	C₉×C₂²⋊C₄	—	3	4	no	—
91	C₉×C₂²⋊C₄	—	3	4	no	—
92	C₄²×C₉	—	2	2	no	—
93	C₄²×C₉	—	2	1	no	—
94	C₄²×C₉	—	3	2	no	—
95	C₄²×C₉	C₂×D₃	1	2	yes	—
96	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
97	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
98	C₂×D₃×C₉	—	2	4	no	—
99	C₂×D₃×C₉	—	2	4	no	—
100	C₂×D₃×C₉	—	2	4	no	—
101	C₃×C₄×C₉	—	2	2	no	—
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	—	2	1	no	—
104	C₃×C₄×C₉	#41	1	2	yes	—
105	C₃×C₄×C₉	#41	1	2	yes	—
106	C₉×Dic₃	—	2	2	no	—
107	C₉×Dic₃	—	2	2	no	—
108	C₃×#127	—	3	1	no	—
109	C₃×#124	—	3	2	no	—
110	C₃×#124	—	3	2	no	—
111	C₃×#123	—	3	4	no	—
112	C₃×C₄×Q₈	—	2	1	no	—
113	C₃×C₄×Q₈	—	3	1	no	—
114	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
115	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
116	C₃×C₄×D₄	—	3	2	no	—
117	C₃×C₄×D₄	—	3	2	no	—
118	#947	C₂×C₉	1	2	yes	complemented
119	#894	C₂×C₉	1	4	yes	complemented
120	#893	C₂×C₉	1	2	yes	complemented
121	#875	C₂×C₉	1	2	yes	complemented
122	#874	C₂×C₉	1	1	yes	characteristic
123	C₄×D₁₂	C₂×C₉	1	2	yes	complemented
124	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
125	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
126	C₃²×Q₈	—	2	2	no	—
127	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
129	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
130	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
132	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
133	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
134	C₃×D₁₂	—	2	4	no	—
135	C₃×D₁₂	—	2	4	no	—
136	C₃×D₁₂	—	4	2	no	—
137	C₃×C₄×D₃	—	4	4	no	—
138	C₃×Dic₆	—	2	2	no	—
139	C₂³×C₉	—	3	4	no	—
140	Q₈×C₉	—	2	4	no	—
141	Q₈×C₉	—	2	2	no	—
142	Q₈×C₉	—	6	2	no	—
143	D₄×C₉	—	6	4	no	—
144	D₄×C₉	—	6	4	no	—
145	D₄×C₉	—	12	2	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	3	2	no	—
152	C₂×C₄×C₉	—	3	2	no	—
153	C₂×C₄×C₉	—	12	4	no	—
154	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
155	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
156	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
158	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
159	#559	—	3	1	no	Sylow
160	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
163	D₃×C₉	—	4	4	no	—
164	C₂×C₃×Q₈	—	2	1	no	—
165	C₂×C₃×Q₈	—	3	1	no	—
166	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
167	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
168	C₂×C₃×D₄	—	3	2	no	—
169	C₂×C₃×D₄	—	3	2	no	—
170	C₂×C₃×D₄	—	3	2	no	—
171	C₂²×C₃×C₄	—	3	4	no	—
172	C₂×D₁₂	C₂²×C₉	1	2	yes	—
173	C₂×D₁₂	C₂²×C₉	1	2	yes	—
174	C₂×D₁₂	C₂²×C₉	1	2	yes	—
175	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
176	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	2	no	—
179	C₃×C₄⋊C₄	—	3	2	no	—
180	C₃×C₄⋊C₄	—	3	1	no	—
181	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
183	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
185	C₃×C₂²⋊C₄	—	3	4	no	—
186	C₃×C₂²⋊C₄	—	3	4	no	—
187	C₃×C₂²⋊C₄	—	3	4	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	—	3	2	no	—
191	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
192	C₃×C₄²	C₂²×C₉	1	2	yes	—
193	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
194	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
195	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
196	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
197	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
198	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
199	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
200	C₄×Dic₃	C₂²×C₉	1	2	yes	—
201	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
202	C₂×C₃×D₃	—	2	4	no	—
203	C₂×C₃×D₃	—	2	4	no	—
204	C₂×C₃×D₃	—	2	4	no	—
205	C₃²×C₄	—	2	2	no	—
206	C₃²×C₄	—	2	2	no	—
207	C₃²×C₄	—	2	1	no	—
208	C₃²×C₄	C₃×#41	1	2	yes	—
209	C₃²×C₄	C₃×#41	1	2	yes	—
210	C₃×Dic₃	—	2	2	no	—
211	C₃×Dic₃	—	2	2	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	6	4	no	—
214	C₂²×C₉	—	6	4	no	—
215	C₂²×C₉	—	6	4	no	—
216	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
217	C₄×C₉	—	2	4	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	2	2	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	2	2	no	—
222	C₄×C₉	—	2	2	no	—
223	C₄×C₉	—	4	2	no	—
224	C₄×C₉	—	4	1	no	—
225	C₄×C₉	—	6	2	no	—
226	C₄×C₉	—	6	2	no	—
227	C₄×C₉	#235	1	2	yes	—
228	C₄×C₉	#239	1	2	yes	—
229	#127	—	3	1	no	—
230	#124	—	3	2	no	—
231	#124	—	3	2	no	—
232	#123	—	3	4	no	—
233	C₄×Q₈	—	3	1	no	—
234	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
235	C₄×D₄	—	3	2	no	—
236	C₄×D₄	—	3	2	no	—
237	C₃×C₉	#559	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₃	—	3	4	no	—
239	C₂²×D₃	C₂³×C₉	1	4	yes	—
240	C₃×Q₈	—	2	4	no	—
241	C₃×Q₈	—	2	2	no	—
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	6	2	no	—
244	C₃×D₄	—	6	4	no	—
245	C₃×D₄	—	6	4	no	—
246	C₃×D₄	—	12	2	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	3	2	no	—
253	C₂×C₃×C₄	—	3	2	no	—
254	C₂×C₃×C₄	—	12	4	no	—
255	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
257	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
258	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
261	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
265	C₂×Dic₃	C₂³×C₉	1	2	yes	—
266	C₂×Dic₃	C₂³×C₉	1	2	yes	—
267	D₁₂	—	2	4	no	—
268	D₁₂	—	2	4	no	—
269	D₁₂	—	4	2	no	—
270	C₄×D₃	—	4	4	no	—
271	Dic₆	—	2	2	no	—
272	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
273	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
274	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
275	C₃×D₃	—	4	4	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	—	2	1	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	—	12	4	no	—
280	C₂×C₉	C₂×#235	1	1	yes	characteristic
281	C₂×C₉	C₂×#239	1	1	yes	characteristic
282	C₂×C₉	#1009	1	1	yes	characteristic
283	C₂×Q₈	—	3	1	no	—
284	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
285	C₂×D₄	—	3	2	no	—
286	C₂×D₄	—	3	2	no	—
287	C₂×D₄	—	3	2	no	—
288	C₂²×C₄	—	3	4	no	—
289	C₄⋊C₄	—	3	1	no	—
290	C₄⋊C₄	—	3	2	no	—
291	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
292	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
293	C₂²⋊C₄	—	3	4	no	—
294	C₂²⋊C₄	—	3	4	no	—
295	C₂²⋊C₄	—	3	4	no	—
296	C₄²	—	3	2	no	—
297	C₄²	C₂×D₃×C₉	1	2	yes	—
298	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	6	4	no	—
301	C₂²×C₃	—	6	4	no	—
302	C₂²×C₃	—	6	4	no	—
303	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
304	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
305	C₂×D₃	—	2	4	no	—
306	C₂×D₃	—	2	4	no	—
307	C₂×D₃	—	2	4	no	—
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	6	2	no	—
320	C₃×C₄	—	6	2	no	—
321	C₃×C₄	C₉×#41	1	2	yes	—
322	C₃×C₄	C₉×#41	1	2	yes	—
323	C₃×C₄	C₃×#235	1	2	yes	—
324	C₃×C₄	C₃×#239	1	2	yes	—
325	Dic₃	—	2	2	no	—
326	Dic₃	—	2	2	no	—
327	C₃²	C₃×#559	1	1	yes	characteristic
328	C₉	—	2	1	no	—
329	C₉	#5585	1	1	yes	characteristic, direct product factor
330	C₂³	—	3	4	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	6	2	no	—
333	D₄	—	6	4	no	—
334	D₄	—	6	4	no	—
335	D₄	—	12	2	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	3	2	no	—
338	C₂×C₄	—	12	4	no	—
339	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
340	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
341	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	12	4	no	—
348	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
349	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
350	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
352	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
353	C₂×C₃	C₃×#1009	1	1	yes	characteristic
354	D₃	—	4	4	no	—
355	C₂²	—	6	4	no	—
356	C₂²	—	6	4	no	—
357	C₂²	—	6	4	no	—
358	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	1	no	—
362	C₄	—	6	2	no	—
363	C₄	—	6	2	no	—
364	C₄	C₉×#235	1	2	yes	—
365	C₄	C₉×#239	1	2	yes	—
366	C₃	—	2	1	no	—
367	C₃	C₉×#559	1	1	yes	characteristic, complemented
368	C₃	C₃×#5585	1	1	yes	characteristic
369	C₂	—	12	4	no	—
370	C₂	C₂×C₉×#235	1	1	yes	characteristic
371	C₂	C₂×C₉×#239	1	1	yes	characteristic
372	C₂	C₉×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#874	C₂×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#559
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
2. C₉×#947	C₂	semidirect
3. C₉×#894	C₂	semidirect
4. C₉×#893	C₂	semidirect
5. C₉×#875	C₂	semidirect
7. C₄×C₉×D₁₂	C₂	semidirect
8. C₄×C₉×Dic₆	C₂	semidirect
41. C₄×Q₈×C₉	D₃	semidirect
59. #5585	C₉	direct (N × H)
114. C₃×C₄×Q₈	C₂×C₉	semidirect
118. #947	C₂×C₉	semidirect
119. #894	C₂×C₉	semidirect
120. #893	C₂×C₉	semidirect
121. #875	C₂×C₉	semidirect
123. C₄×D₁₂	C₂×C₉	semidirect
124. C₄×Dic₆	C₂×C₉	semidirect
234. C₄×Q₈	D₃×C₉	semidirect
237. C₃×C₉	#559	semidirect
329. C₉	#5585	direct (N × H)
367. C₃	C₉×#559	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈×C₉	2
C₉×#947	2
C₉×#894	2
C₉×#893	2
C₉×#875	2
C₉×#874	2
C₄×C₉×D₁₂	2
C₄×C₉×Dic₆	2
C₃×#5585	3
C₉×#559	3

Subgroups — C9×#5585 #13152706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5585 #13152706