Subgroups — C₂×C₉×#892 #13152414

Order 1728.

1082 conjugacy classes of subgroups.

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

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#117
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
4. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
5. C₂×C₄×C₉×Dic₃	C₂	semidirect
6. C₉×#892	C₂	direct (N × H)
14. C₂×C₄×D₃×C₉	C₄	semidirect
16. C₃×C₉×C₄⋊C₄	C₂²	semidirect
18. C₉×C₄⋊Dic₃	C₂²	semidirect
19. C₄×C₉×Dic₃	C₂²	semidirect
30. C₂×C₉×C₄⋊C₄	D₃	semidirect
46. C₄×D₃×C₉	C₂×C₄	semidirect
48. C₂×#892	C₉	direct (N × H)
71. C₉×C₄⋊C₄	C₂×D₃	semidirect
91. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
96. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
97. C₂×C₄×Dic₃	C₂×C₉	semidirect
98. #892	C₂×C₉	direct (N × H)
133. C₂×C₃×C₉	#117	semidirect
152. C₂×C₄×D₃	C₄×C₉	semidirect
156. C₃×C₄⋊C₄	C₂²×C₉	semidirect
161. C₄⋊Dic₃	C₂²×C₉	semidirect
162. C₄×Dic₃	C₂²×C₉	semidirect
196. C₂×C₄⋊C₄	D₃×C₉	semidirect
199. C₃×C₉	C₂×#117	semidirect
232. C₄×D₃	C₂×C₄×C₉	semidirect
243. C₂×C₉	#892	direct (N × H)
255. C₄⋊C₄	C₂×D₃×C₉	semidirect
290. C₉	C₂×#892	direct (N × H)
310. C₂×C₃	C₉×#117	semidirect
332. C₃	C₂×C₉×#117	semidirect
335. C₂	C₉×#892	direct (N × H)

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×C₃×C₉×C₄⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₄×C₉×Dic₃	2
C₉×#892	2
C₂×C₃×#892	3
C₂×C₉×#117	3

Subgroups — C2×C9×#892 #13152414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#892 #13152414