Subgroups — C₉×#4666 #13141289

Order 1728.

850 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄×C₉×Dic₃	C₂	1	2	yes	maximal, complemented
4	C₃×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4666	C₃	1	1	yes	maximal, characteristic
7	C₄×C₉×C₂²⋊C₄	—	3	1	no	maximal
8	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
11	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
12	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	—	2	4	no	—
14	C₂×C₄×D₃×C₉	C₄	1	4	yes	complemented
15	C₉×(C₂×D₃)⋊C₄	C₄	1	8	yes	complemented
16	C₄×C₉×Dic₃	—	2	4	no	—
17	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
19	C₂×C₃×C₄×Dic₃	C₂×C₃	1	2	yes	—
20	C₂³×C₄×C₉	—	3	1	no	—
21	C₃²×#95	C₂×C₃	1	1	yes	characteristic
22	C₃×C₃⋊#95	C₂×C₃	1	1	yes	characteristic
23	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
24	C₂×C₄²×C₉	—	3	2	no	—
25	C₉×#95	—	2	1	no	—
26	C₉×#95	—	3	1	no	—
27	C₉×#95	D₃	1	1	yes	characteristic, complemented
28	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
29	C₂²×D₃×C₉	—	2	2	no	—
30	C₂²×D₃×C₉	—	2	1	no	—
31	C₂²×D₃×C₉	—	2	1	no	—
32	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
33	C₂²×D₃×C₉	C₂×C₄	1	4	yes	—
34	C₂×C₃×C₄×C₉	—	2	2	no	—
35	C₂×C₃×C₄×C₉	—	2	2	no	—
36	C₂×C₃×C₄×C₉	—	2	2	no	—
37	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
39	C₂×C₉×Dic₃	—	2	2	no	—
40	C₂×C₉×Dic₃	—	2	2	no	—
41	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
42	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	complemented
43	C₂×C₉×Dic₃	D₄	1	4	yes	—
44	C₄×D₃×C₉	—	2	8	no	—
45	C₃×C₄×C₂²⋊C₄	—	3	1	no	—
46	#4666	C₉	1	1	yes	characteristic, direct product factor
47	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
49	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
51	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₃×C₄×D₃	—	2	4	no	—
53	C₂×C₃×C₄×D₃	C₃×C₄	1	4	yes	—
54	C₂⁴×C₉	—	3	1	no	—
55	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	8	yes	—
56	C₃×C₄×Dic₃	—	2	4	no	—
57	C₂²×C₄×C₉	—	2	1	no	—
58	C₂²×C₄×C₉	—	2	2	no	—
59	C₂²×C₄×C₉	—	3	1	no	—
60	C₂²×C₄×C₉	—	3	2	no	—
61	C₂²×C₄×C₉	—	3	4	no	—
62	C₂²×C₄×C₉	—	6	4	no	—
63	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
65	C₉×C₂²⋊C₄	—	3	8	no	—
66	C₄²×C₉	—	6	4	no	—
67	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
69	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
70	C₂²×C₃×C₉	#41	1	1	yes	characteristic
71	C₂²×C₃×C₉	#41	1	1	yes	characteristic
72	C₂×D₃×C₉	—	2	2	no	—
73	C₂×D₃×C₉	—	2	2	no	—
74	C₂×D₃×C₉	—	2	4	no	—
75	C₂×D₃×C₉	—	2	4	no	—
76	C₂×D₃×C₉	C₄²	1	4	yes	complemented
77	C₃×C₄×C₉	—	2	2	no	—
78	C₃×C₄×C₉	—	2	4	no	—
79	C₉×Dic₃	—	2	4	no	—
80	C₉×Dic₃	C₂²⋊C₄	1	4	yes	complemented
81	C₂³×C₃×C₄	—	3	1	no	—
82	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
84	C₂×C₃×C₄²	—	3	2	no	—
85	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	—
86	C₂×C₄×Dic₃	C₂×C₉	1	2	yes	complemented
87	C₃×#95	—	2	1	no	—
88	C₃×#95	—	3	1	no	—
89	C₃×#95	C₂×C₉	1	1	yes	characteristic, complemented
90	C₃×#95	C₃×D₃	1	1	yes	characteristic
91	C₃⋊#95	C₂×C₉	1	1	yes	characteristic, complemented
92	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
93	C₂²×C₃×D₃	—	2	2	no	—
94	C₂²×C₃×D₃	—	2	1	no	—
95	C₂²×C₃×D₃	—	2	1	no	—
96	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
97	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
98	C₂×C₃²×C₄	—	2	2	no	—
99	C₂×C₃²×C₄	—	2	2	no	—
100	C₂×C₃²×C₄	—	2	2	no	—
101	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
102	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
103	C₂×C₃×Dic₃	—	2	2	no	—
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
106	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
107	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
108	C₃×C₄×D₃	—	2	8	no	—
109	C₂³×C₉	—	2	1	no	—
110	C₂³×C₉	—	3	4	no	—
111	C₂³×C₉	—	3	2	no	—
112	C₂³×C₉	—	6	2	no	—
113	C₂³×C₉	—	6	1	no	—
114	C₂³×C₉	—	6	1	no	—
115	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	4	no	—
121	C₂×C₄×C₉	—	3	2	no	—
122	C₂×C₄×C₉	—	3	4	no	—
123	C₂×C₄×C₉	—	3	4	no	—
124	C₂×C₄×C₉	—	4	2	no	—
125	C₂×C₄×C₉	—	4	2	no	—
126	C₂×C₄×C₉	—	4	2	no	—
127	C₂×C₄×C₉	—	6	8	no	—
128	C₂×C₄×C₉	—	6	2	no	—
129	C₂×C₄×C₉	—	6	2	no	—
130	C₂×C₄×C₉	C₄×D₃	1	2	yes	—
131	C₂×C₄×C₉	C₄×D₃	1	4	yes	complemented
132	C₄×C₂²⋊C₄	—	3	1	no	Sylow
133	C₂×C₃×C₉	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₃×C₉	#117	1	1	yes	characteristic
136	C₂×C₃×C₉	C₄×D₄	1	2	yes	—
137	C₂×C₃×C₉	C₄×D₄	1	2	yes	—
138	D₃×C₉	—	2	4	no	—
139	C₂⁴×C₃	—	3	1	no	—
140	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	3	1	no	—
144	C₂²×C₃×C₄	—	3	2	no	—
145	C₂²×C₃×C₄	—	3	4	no	—
146	C₂²×C₃×C₄	—	6	4	no	—
147	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
149	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
151	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
152	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
153	C₂×C₄×D₃	—	2	4	no	—
154	C₂×C₄×D₃	C₄×C₉	1	4	yes	complemented
155	C₃×C₂²⋊C₄	—	3	8	no	—
156	C₃×C₄²	—	6	4	no	—
157	(C₂×D₃)⋊C₄	C₄×C₉	1	8	yes	complemented
158	C₄×Dic₃	—	2	4	no	—
159	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
160	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
161	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
162	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
163	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
164	C₂×C₃×D₃	—	2	2	no	—
165	C₂×C₃×D₃	—	2	2	no	—
166	C₂×C₃×D₃	—	2	4	no	—
167	C₂×C₃×D₃	—	2	4	no	—
168	C₂×C₃×D₃	C₃×C₄²	1	4	yes	—
169	C₃²×C₄	—	2	2	no	—
170	C₃²×C₄	—	2	4	no	—
171	C₃×Dic₃	—	2	4	no	—
172	C₃×Dic₃	C₃×C₂²⋊C₄	1	4	yes	—
173	C₂²×C₉	—	2	1	no	—
174	C₂²×C₉	—	2	2	no	—
175	C₂²×C₉	—	2	2	no	—
176	C₂²×C₉	—	2	1	no	—
177	C₂²×C₉	—	2	1	no	—
178	C₂²×C₉	—	3	4	no	—
179	C₂²×C₉	—	6	2	no	—
180	C₂²×C₉	—	6	4	no	—
181	C₂²×C₉	—	6	2	no	—
182	C₂²×C₉	—	6	4	no	—
183	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
184	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
185	C₂²×C₉	D₃×D₄	1	2	yes	—
186	C₂²×C₉	#237	1	1	yes	characteristic
187	C₂²×C₉	#239	1	1	yes	characteristic
188	C₄×C₉	—	2	2	no	—
189	C₄×C₉	—	2	4	no	—
190	C₄×C₉	—	3	4	no	—
191	C₄×C₉	—	4	2	no	—
192	C₄×C₉	—	4	4	no	—
193	C₄×C₉	—	6	4	no	—
194	C₂³×C₄	—	3	1	no	—
195	C₂×C₂²⋊C₄	—	3	2	no	—
196	C₂×C₄²	—	3	2	no	—
197	#95	—	3	1	no	—
198	#95	D₃×C₉	1	1	yes	characteristic, complemented
199	C₃×C₉	C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
200	C₂³×C₃	—	2	1	no	—
201	C₂³×C₃	—	3	4	no	—
202	C₂³×C₃	—	3	2	no	—
203	C₂³×C₃	—	6	2	no	—
204	C₂³×C₃	—	6	1	no	—
205	C₂³×C₃	—	6	1	no	—
206	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
207	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
208	C₂²×D₃	—	2	2	no	—
209	C₂²×D₃	—	2	1	no	—
210	C₂²×D₃	—	2	1	no	—
211	C₂²×D₃	C₂×C₄×C₉	1	4	yes	—
212	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	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	2	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	3	2	no	—
222	C₂×C₃×C₄	—	3	4	no	—
223	C₂×C₃×C₄	—	3	4	no	—
224	C₂×C₃×C₄	—	4	2	no	—
225	C₂×C₃×C₄	—	4	2	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	—	6	8	no	—
228	C₂×C₃×C₄	—	6	2	no	—
229	C₂×C₃×C₄	—	6	2	no	—
230	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
232	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
233	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
234	C₂×Dic₃	—	2	2	no	—
235	C₂×Dic₃	—	2	2	no	—
236	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
237	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	complemented
238	C₂×Dic₃	D₄×C₉	1	4	yes	—
239	C₄×D₃	—	2	8	no	—
240	C₂×C₃²	C₂×C₃×C₄²	1	1	yes	characteristic
241	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₃²	C₃×#117	1	1	yes	characteristic
243	C₂×C₃²	C₃×C₄×D₄	1	2	yes	—
244	C₂×C₃²	C₃×C₄×D₄	1	2	yes	—
245	C₃×D₃	—	2	4	no	—
246	C₂×C₉	—	2	1	no	—
247	C₂×C₉	—	2	2	no	—
248	C₂×C₉	—	2	1	no	—
249	C₂×C₉	—	2	2	no	—
250	C₂×C₉	—	2	1	no	—
251	C₂×C₉	—	6	4	no	—
252	C₂×C₉	C₄²×D₃	1	1	yes	characteristic
253	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₉	#67⋊C₄	1	2	yes	—
255	C₂×C₉	#892	1	1	yes	characteristic
256	C₂×C₉	#893	1	2	yes	—
257	C₂⁴	—	3	1	no	—
258	C₂²×C₄	—	3	1	no	—
259	C₂²×C₄	—	3	2	no	—
260	C₂²×C₄	—	3	4	no	—
261	C₂²×C₄	—	6	4	no	—
262	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
264	C₂²⋊C₄	—	3	8	no	—
265	C₄²	—	6	4	no	—
266	C₂²×C₃	—	2	1	no	—
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	3	4	no	—
272	C₂²×C₃	—	6	2	no	—
273	C₂²×C₃	—	6	4	no	—
274	C₂²×C₃	—	6	2	no	—
275	C₂²×C₃	—	6	4	no	—
276	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
277	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
278	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
279	C₂²×C₃	C₉×#41	1	1	yes	characteristic
280	C₂²×C₃	C₉×#41	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
282	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
283	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
284	C₂²×C₃	C₃×#237	1	1	yes	characteristic
285	C₂²×C₃	C₃×#239	1	1	yes	characteristic
286	C₂×D₃	—	2	2	no	—
287	C₂×D₃	—	2	2	no	—
288	C₂×D₃	—	2	4	no	—
289	C₂×D₃	—	2	4	no	—
290	C₂×D₃	C₄²×C₉	1	4	yes	complemented
291	C₃×C₄	—	2	2	no	—
292	C₃×C₄	—	2	4	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	3	4	no	—
296	C₃×C₄	—	4	2	no	—
297	C₃×C₄	—	4	4	no	—
298	C₃×C₄	—	6	4	no	—
299	Dic₃	—	2	4	no	—
300	Dic₃	C₉×C₂²⋊C₄	1	4	yes	complemented
301	C₃²	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
302	C₉	—	2	1	no	—
303	C₉	#4666	1	1	yes	characteristic, direct product factor
304	C₂³	—	3	4	no	—
305	C₂³	—	3	2	no	—
306	C₂³	—	6	2	no	—
307	C₂³	—	6	1	no	—
308	C₂³	—	6	1	no	—
309	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	3	2	no	—
314	C₂×C₄	—	3	4	no	—
315	C₂×C₄	—	3	4	no	—
316	C₂×C₄	—	6	8	no	—
317	C₂×C₄	—	6	2	no	—
318	C₂×C₄	—	6	2	no	—
319	C₂×C₄	C₄×D₃×C₉	1	2	yes	—
320	C₂×C₄	C₄×D₃×C₉	1	4	yes	complemented
321	C₂×C₃	—	2	1	no	—
322	C₂×C₃	—	2	1	no	—
323	C₂×C₃	—	2	2	no	—
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	2	2	no	—
326	C₂×C₃	—	6	4	no	—
327	C₂×C₃	C₂×C₄²×C₉	1	1	yes	characteristic
328	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
329	C₂×C₃	C₉×#117	1	1	yes	characteristic
330	C₂×C₃	C₄×D₄×C₉	1	2	yes	—
331	C₂×C₃	C₄×D₄×C₉	1	2	yes	—
332	C₂×C₃	C₃×C₄²×D₃	1	1	yes	characteristic
333	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₃	C₃×#67⋊C₄	1	2	yes	—
335	C₂×C₃	C₃×#892	1	1	yes	characteristic
336	C₂×C₃	C₃×#893	1	2	yes	—
337	D₃	—	2	4	no	—
338	C₂²	—	3	4	no	—
339	C₂²	—	6	2	no	—
340	C₂²	—	6	4	no	—
341	C₂²	—	6	2	no	—
342	C₂²	—	6	4	no	—
343	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
344	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
345	C₂²	D₃×D₄×C₉	1	2	yes	—
346	C₂²	C₉×#237	1	1	yes	characteristic
347	C₂²	C₉×#239	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	3	4	no	—
351	C₄	—	6	4	no	—
352	C₃	—	2	1	no	—
353	C₃	C₄×C₉×C₂²⋊C₄	1	1	yes	characteristic, complemented
354	C₃	C₃×#4666	1	1	yes	characteristic
355	C₂	—	6	4	no	—
356	C₂	C₄²×D₃×C₉	1	1	yes	characteristic
357	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
358	C₂	C₉×#67⋊C₄	1	2	yes	—
359	C₂	C₉×#892	1	1	yes	characteristic
360	C₂	C₉×#893	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂×C₃	C₂×C₄²×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₃×C₉×#95	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
hypercenter	C₉×#95	D₃
hypocenter	C₃	C₄×C₉×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₉×#95

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₉×Dic₃	C₂	semidirect
4. C₃×C₉×#95	C₂	semidirect
5. C₉×C₃⋊#95	C₂	semidirect
14. C₂×C₄×D₃×C₉	C₄	semidirect
15. C₉×(C₂×D₃)⋊C₄	C₄	semidirect
27. C₉×#95	D₃	semidirect
38. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
42. C₂×C₉×Dic₃	C₂×C₄	semidirect
46. #4666	C₉	direct (N × H)
76. C₂×D₃×C₉	C₄²	semidirect
80. C₉×Dic₃	C₂²⋊C₄	semidirect
86. C₂×C₄×Dic₃	C₂×C₉	semidirect
89. C₃×#95	C₂×C₉	semidirect
91. C₃⋊#95	C₂×C₉	semidirect
131. C₂×C₄×C₉	C₄×D₃	semidirect
154. C₂×C₄×D₃	C₄×C₉	semidirect
157. (C₂×D₃)⋊C₄	C₄×C₉	semidirect
198. #95	D₃×C₉	semidirect
199. C₃×C₉	C₄×C₂²⋊C₄	semidirect
231. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
237. C₂×Dic₃	C₂×C₄×C₉	semidirect
290. C₂×D₃	C₄²×C₉	semidirect
300. Dic₃	C₉×C₂²⋊C₄	semidirect
303. C₉	#4666	direct (N × H)
320. C₂×C₄	C₄×D₃×C₉	semidirect
353. C₃	C₄×C₉×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃×C₉	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₄×C₉×Dic₃	2
C₃×C₉×#95	2
C₉×C₃⋊#95	2
C₃×#4666	3
C₄×C₉×C₂²⋊C₄	3

Subgroups — C9×#4666 #13141289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4666 #13141289