Subgroups — C₂×D₄×C₉×A₄ #13164823

Order 1728.

1167 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉×A₄	C₂	1	2	yes	maximal, complemented
2	D₄×C₉×A₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₉×A₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₄×A₄	C₃	1	1	yes	maximal, characteristic
5	C₂³×D₄×C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₂²⋊C₉	C₃	1	2	yes	maximal, complemented
7	C₂²×C₉×A₄	—	2	4	no	—
8	C₂²×C₉×A₄	C₂²	1	1	yes	characteristic
9	C₂²×C₉×A₄	C₂²	1	4	yes	complemented
10	C₂×C₃×D₄×C₉	—	4	1	no	maximal
11	C₄×C₉×A₄	C₂²	1	2	yes	complemented
12	C₂³×C₃×A₄	C₂×C₃	1	2	yes	—
13	C₃×D₄×A₄	C₂×C₃	1	4	yes	—
14	C₂×C₃×C₄×A₄	C₂×C₃	1	1	yes	characteristic
15	C₂⁵×C₉	C₂×C₃	1	2	yes	complemented
16	C₂³×C₂²⋊C₉	C₂×C₃	1	4	yes	complemented
17	C₂²×D₄×C₉	—	3	1	no	—
18	C₂²×D₄×C₉	—	3	1	no	—
19	C₂²×D₄×C₉	—	3	2	no	—
20	C₂²×D₄×C₉	—	3	4	no	—
21	C₂²×D₄×C₉	C₂×C₃	1	4	yes	complemented
22	C₂³×C₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
23	D₄×C₂²⋊C₉	C₂×C₃	1	8	yes	complemented
24	C₂×C₄×C₂²⋊C₉	C₂×C₃	1	2	yes	complemented
25	C₂³×C₃×C₉	—	4	2	no	—
26	C₂×C₉×A₄	—	2	4	no	—
27	C₂×C₉×A₄	D₄	1	2	yes	direct product factor
28	C₂×C₉×A₄	C₂³	1	1	yes	characteristic
29	C₃×D₄×C₉	—	4	4	no	—
30	C₂×C₃×C₄×C₉	—	4	1	no	—
31	C₂³×C₃×D₄	C₃²	1	1	yes	characteristic
32	C₂×D₄×A₄	C₉	1	3	yes	direct product factor
33	C₂²×C₃×A₄	—	2	4	no	—
34	C₂²×C₃×A₄	C₂²×C₃	1	4	yes	—
35	C₂²×C₃×A₄	C₂²×C₃	1	1	yes	characteristic
36	C₂×C₃²×D₄	—	4	1	no	—
37	C₃×C₄×A₄	C₂²×C₃	1	2	yes	—
38	C₂⁴×C₉	—	2	4	no	—
39	C₂⁴×C₉	—	3	2	no	—
40	C₂⁴×C₉	—	3	4	no	—
41	C₂⁴×C₉	—	3	2	no	—
42	C₂⁴×C₉	—	6	4	no	—
43	C₂⁴×C₉	C₂²×C₃	1	1	yes	characteristic
44	C₂⁴×C₉	C₂²×C₃	1	4	yes	complemented
45	C₂²×C₂²⋊C₉	—	2	8	no	—
46	C₂²×C₂²⋊C₉	C₂²×C₃	1	2	yes	—
47	C₂²×C₂²⋊C₉	C₂²×C₃	1	8	yes	complemented
48	C₂×D₄×C₉	—	3	8	no	—
49	C₂×D₄×C₉	—	3	2	no	—
50	C₂×D₄×C₉	—	3	4	no	—
51	C₂×D₄×C₉	—	3	2	no	—
52	C₂×D₄×C₉	—	3	4	no	—
53	C₂×D₄×C₉	—	3	4	no	—
54	C₂×D₄×C₉	—	3	4	no	—
55	C₂×D₄×C₉	—	3	8	no	—
56	C₂×D₄×C₉	—	3	1	no	—
57	C₂×D₄×C₉	—	4	2	no	—
58	C₂×D₄×C₉	A₄	1	1	yes	characteristic, direct product factor
59	C₂²×C₄×C₉	—	3	1	no	—
60	C₂²×C₄×C₉	—	3	1	no	—
61	C₂²×C₄×C₉	—	3	2	no	—
62	C₂²×C₄×C₉	C₂²×C₃	1	2	yes	complemented
63	C₄×C₂²⋊C₉	C₂²×C₃	1	4	yes	complemented
64	C₂²×C₃×C₉	—	4	1	no	—
65	C₂²×C₃×C₉	—	4	4	no	—
66	C₂²×C₃×C₉	—	8	4	no	—
67	C₉×A₄	C₂×D₄	1	1	yes	characteristic, direct product factor
68	C₃×C₄×C₉	—	4	2	no	—
69	C₂⁵×C₃	C₂×C₃²	1	2	yes	—
70	C₂³×A₄	C₂×C₉	1	6	yes	complemented
71	C₂²×C₃×D₄	—	3	1	no	—
72	C₂²×C₃×D₄	—	3	1	no	—
73	C₂²×C₃×D₄	—	3	2	no	—
74	C₂²×C₃×D₄	—	3	4	no	—
75	C₂²×C₃×D₄	C₂×C₃²	1	4	yes	—
76	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic
77	D₄×A₄	C₂×C₉	1	12	yes	direct product factor
78	C₂×C₄×A₄	C₂×C₉	1	3	yes	complemented
79	C₂³×C₃²	—	4	2	no	—
80	C₂×C₃×A₄	—	2	4	no	—
81	C₂×C₃×A₄	C₃×D₄	1	2	yes	—
82	C₂×C₃×A₄	C₂³×C₃	1	1	yes	characteristic
83	C₃²×D₄	—	4	4	no	—
84	C₂×C₃²×C₄	—	4	1	no	—
85	C₂³×C₉	—	2	4	no	—
86	C₂³×C₉	—	3	1	no	—
87	C₂³×C₉	—	3	2	no	—
88	C₂³×C₉	—	3	1	no	—
89	C₂³×C₉	—	3	4	no	—
90	C₂³×C₉	—	3	4	no	—
91	C₂³×C₉	—	3	2	no	—
92	C₂³×C₉	—	3	4	no	—
93	C₂³×C₉	—	3	4	no	—
94	C₂³×C₉	—	4	4	no	—
95	C₂³×C₉	—	6	4	no	—
96	C₂³×C₉	—	6	4	no	—
97	C₂³×C₉	—	6	4	no	—
98	C₂³×C₉	—	6	8	no	—
99	C₂³×C₉	—	6	4	no	—
100	C₂³×C₉	—	6	4	no	—
101	C₂³×C₉	—	6	8	no	—
102	C₂³×C₉	C₃×D₄	1	2	yes	complemented
103	C₂³×C₉	C₂×A₄	1	2	yes	complemented
104	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
105	C₂×C₂²⋊C₉	—	2	8	no	—
106	C₂×C₂²⋊C₉	C₃×D₄	1	4	yes	complemented
107	C₂×C₂²⋊C₉	C₂³×C₃	1	2	yes	—
108	D₄×C₉	—	3	8	no	—
109	D₄×C₉	—	3	8	no	—
110	D₄×C₉	—	3	4	no	—
111	D₄×C₉	—	4	8	no	—
112	D₄×C₉	C₂×A₄	1	4	yes	direct product factor
113	C₂×C₄×C₉	—	3	2	no	—
114	C₂×C₄×C₉	—	3	1	no	—
115	C₂×C₄×C₉	—	3	2	no	—
116	C₂×C₄×C₉	—	3	2	no	—
117	C₂×C₄×C₉	—	3	2	no	—
118	C₂×C₄×C₉	—	4	2	no	—
119	C₂×C₄×C₉	C₂×A₄	1	1	yes	characteristic, complemented
120	C₂³×D₄	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
121	C₂×C₃×C₉	—	4	2	no	—
122	C₂×C₃×C₉	—	4	1	no	—
123	C₂×C₃×C₉	—	8	4	no	—
124	C₂⁴×C₃	—	2	4	no	—
125	C₂⁴×C₃	—	3	4	no	—
126	C₂⁴×C₃	—	3	2	no	—
127	C₂⁴×C₃	—	3	2	no	—
128	C₂⁴×C₃	—	6	4	no	—
129	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
130	C₂⁴×C₃	C₂²×C₃²	1	4	yes	—
131	C₂²×A₄	—	2	12	no	—
132	C₂²×A₄	C₂²×C₉	1	3	yes	—
133	C₂²×A₄	C₂²×C₉	1	12	yes	complemented
134	C₂×C₃×D₄	—	3	8	no	—
135	C₂×C₃×D₄	—	3	2	no	—
136	C₂×C₃×D₄	—	3	4	no	—
137	C₂×C₃×D₄	—	3	2	no	—
138	C₂×C₃×D₄	—	3	4	no	—
139	C₂×C₃×D₄	—	3	4	no	—
140	C₂×C₃×D₄	—	3	4	no	—
141	C₂×C₃×D₄	—	3	8	no	—
142	C₂×C₃×D₄	—	3	1	no	—
143	C₂×C₃×D₄	—	4	3	no	—
144	C₂×C₃×D₄	C₃×A₄	1	1	yes	characteristic
145	C₂²×C₃×C₄	—	3	1	no	—
146	C₂²×C₃×C₄	—	3	1	no	—
147	C₂²×C₃×C₄	—	3	2	no	—
148	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
149	C₄×A₄	C₂²×C₉	1	6	yes	complemented
150	C₂²×C₃²	—	4	1	no	—
151	C₂²×C₃²	—	4	4	no	—
152	C₂²×C₃²	—	8	4	no	—
153	C₃×A₄	C₂×C₃×D₄	1	1	yes	characteristic
154	C₃²×C₄	—	4	2	no	—
155	C₂²×C₉	—	2	4	no	—
156	C₂²×C₉	—	3	2	no	—
157	C₂²×C₉	—	3	1	no	—
158	C₂²×C₉	—	3	2	no	—
159	C₂²×C₉	—	3	2	no	—
160	C₂²×C₉	—	3	2	no	—
161	C₂²×C₉	—	3	1	no	—
162	C₂²×C₉	—	3	1	no	—
163	C₂²×C₉	—	3	4	no	—
164	C₂²×C₉	—	4	2	no	—
165	C₂²×C₉	—	4	8	no	—
166	C₂²×C₉	—	6	4	no	—
167	C₂²×C₉	—	6	8	no	—
168	C₂²×C₉	—	6	4	no	—
169	C₂²×C₉	—	6	4	no	—
170	C₂²×C₉	—	6	4	no	—
171	C₂²×C₉	—	6	8	no	—
172	C₂²×C₉	—	6	4	no	—
173	C₂²×C₉	—	8	8	no	—
174	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic, complemented
175	C₂²×C₉	C₂²×A₄	1	1	yes	characteristic
176	C₂²×C₉	C₂²×A₄	1	4	yes	complemented
177	C₂²⋊C₉	C₂×C₃×D₄	1	2	yes	complemented
178	C₄×C₉	—	3	2	no	—
179	C₄×C₉	—	4	4	no	—
180	C₄×C₉	C₂²×A₄	1	2	yes	complemented
181	C₂⁵	C₂×C₃×C₉	1	2	yes	complemented
182	C₂²×D₄	—	3	1	no	—
183	C₂²×D₄	—	3	1	no	—
184	C₂²×D₄	—	3	2	no	—
185	C₂²×D₄	—	3	4	no	—
186	C₂²×D₄	C₂×C₃×C₉	1	4	yes	complemented
187	C₂³×C₄	C₂×C₃×C₉	1	1	yes	characteristic, complemented
188	C₃×C₉	—	4	1	no	Sylow
189	C₂³×C₃	—	2	4	no	—
190	C₂³×C₃	—	3	1	no	—
191	C₂³×C₃	—	3	2	no	—
192	C₂³×C₃	—	3	1	no	—
193	C₂³×C₃	—	3	4	no	—
194	C₂³×C₃	—	3	4	no	—
195	C₂³×C₃	—	3	2	no	—
196	C₂³×C₃	—	3	4	no	—
197	C₂³×C₃	—	3	4	no	—
198	C₂³×C₃	—	4	6	no	—
199	C₂³×C₃	—	6	4	no	—
200	C₂³×C₃	—	6	4	no	—
201	C₂³×C₃	—	6	4	no	—
202	C₂³×C₃	—	6	8	no	—
203	C₂³×C₃	—	6	4	no	—
204	C₂³×C₃	—	6	4	no	—
205	C₂³×C₃	—	6	8	no	—
206	C₂³×C₃	C₃²×D₄	1	2	yes	—
207	C₂³×C₃	C₂×C₃×A₄	1	2	yes	—
208	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
209	C₂×A₄	—	2	12	no	—
210	C₂×A₄	D₄×C₉	1	6	yes	direct product factor
211	C₂×A₄	C₂³×C₉	1	3	yes	—
212	C₃×D₄	—	3	8	no	—
213	C₃×D₄	—	3	8	no	—
214	C₃×D₄	—	3	4	no	—
215	C₃×D₄	—	4	12	no	—
216	C₃×D₄	C₂×C₃×A₄	1	4	yes	—
217	C₂×C₃×C₄	—	3	2	no	—
218	C₂×C₃×C₄	—	3	1	no	—
219	C₂×C₃×C₄	—	3	2	no	—
220	C₂×C₃×C₄	—	3	2	no	—
221	C₂×C₃×C₄	—	3	2	no	—
222	C₂×C₃×C₄	—	4	3	no	—
223	C₂×C₃×C₄	C₂×C₃×A₄	1	1	yes	characteristic
224	C₂×C₃²	—	4	2	no	—
225	C₂×C₃²	—	4	1	no	—
226	C₂×C₃²	—	8	4	no	—
227	C₂×C₉	—	2	4	no	—
228	C₂×C₉	—	3	2	no	—
229	C₂×C₉	—	3	1	no	—
230	C₂×C₉	—	3	1	no	—
231	C₂×C₉	—	4	4	no	—
232	C₂×C₉	—	4	2	no	—
233	C₂×C₉	—	6	4	no	—
234	C₂×C₉	—	8	8	no	—
235	C₂×C₉	D₄×A₄	1	2	yes	direct product factor
236	C₂×C₉	C₂³×A₄	1	1	yes	characteristic
237	C₂⁴	—	2	4	no	—
238	C₂⁴	—	3	4	no	—
239	C₂⁴	—	3	2	no	—
240	C₂⁴	—	3	2	no	—
241	C₂⁴	—	6	4	no	—
242	C₂⁴	C₂²×C₃×C₉	1	1	yes	characteristic
243	C₂⁴	C₂²×C₃×C₉	1	4	yes	complemented
244	C₂×D₄	—	3	8	no	—
245	C₂×D₄	—	3	2	no	—
246	C₂×D₄	—	3	4	no	—
247	C₂×D₄	—	3	2	no	—
248	C₂×D₄	—	3	4	no	—
249	C₂×D₄	—	3	4	no	—
250	C₂×D₄	—	3	4	no	—
251	C₂×D₄	—	3	8	no	—
252	C₂×D₄	—	3	1	no	—
253	C₂×D₄	C₉×A₄	1	1	yes	characteristic, direct product factor
254	C₂²×C₄	—	3	1	no	—
255	C₂²×C₄	—	3	1	no	—
256	C₂²×C₄	—	3	2	no	—
257	C₂²×C₄	C₂²×C₃×C₉	1	2	yes	complemented
258	C₂²×C₃	—	2	4	no	—
259	C₂²×C₃	—	3	2	no	—
260	C₂²×C₃	—	3	1	no	—
261	C₂²×C₃	—	3	2	no	—
262	C₂²×C₃	—	3	2	no	—
263	C₂²×C₃	—	3	2	no	—
264	C₂²×C₃	—	3	1	no	—
265	C₂²×C₃	—	3	1	no	—
266	C₂²×C₃	—	3	4	no	—
267	C₂²×C₃	—	4	3	no	—
268	C₂²×C₃	—	4	12	no	—
269	C₂²×C₃	—	6	4	no	—
270	C₂²×C₃	—	6	8	no	—
271	C₂²×C₃	—	6	4	no	—
272	C₂²×C₃	—	6	4	no	—
273	C₂²×C₃	—	6	4	no	—
274	C₂²×C₃	—	6	8	no	—
275	C₂²×C₃	—	6	4	no	—
276	C₂²×C₃	—	8	12	no	—
277	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
278	C₂²×C₃	C₂²×C₃×A₄	1	1	yes	characteristic
279	C₂²×C₃	C₂²×C₃×A₄	1	4	yes	—
280	A₄	C₂×D₄×C₉	1	3	yes	direct product factor
281	C₃×C₄	—	3	2	no	—
282	C₃×C₄	—	4	6	no	—
283	C₃×C₄	C₂²×C₃×A₄	1	2	yes	—
284	C₃²	—	4	1	no	—
285	C₉	—	4	2	no	—
286	C₉	C₂×D₄×A₄	1	1	yes	characteristic, direct product factor
287	C₂³	—	2	4	no	—
288	C₂³	—	3	1	no	—
289	C₂³	—	3	2	no	—
290	C₂³	—	3	1	no	—
291	C₂³	—	3	4	no	—
292	C₂³	—	3	4	no	—
293	C₂³	—	3	2	no	—
294	C₂³	—	3	4	no	—
295	C₂³	—	3	4	no	—
296	C₂³	—	6	4	no	—
297	C₂³	—	6	4	no	—
298	C₂³	—	6	4	no	—
299	C₂³	—	6	8	no	—
300	C₂³	—	6	4	no	—
301	C₂³	—	6	4	no	—
302	C₂³	—	6	8	no	—
303	C₂³	C₃×D₄×C₉	1	2	yes	complemented
304	C₂³	C₂×C₉×A₄	1	2	yes	complemented
305	C₂³	C₂³×C₃×C₉	1	1	yes	characteristic
306	D₄	—	3	8	no	—
307	D₄	—	3	8	no	—
308	D₄	—	3	4	no	—
309	D₄	C₂×C₉×A₄	1	4	yes	direct product factor
310	C₂×C₄	—	3	2	no	—
311	C₂×C₄	—	3	1	no	—
312	C₂×C₄	—	3	2	no	—
313	C₂×C₄	—	3	2	no	—
314	C₂×C₄	—	3	2	no	—
315	C₂×C₄	C₂×C₉×A₄	1	1	yes	characteristic, complemented
316	C₂×C₃	—	2	4	no	—
317	C₂×C₃	—	3	1	no	—
318	C₂×C₃	—	3	2	no	—
319	C₂×C₃	—	3	1	no	—
320	C₂×C₃	—	4	3	no	—
321	C₂×C₃	—	4	6	no	—
322	C₂×C₃	—	6	4	no	—
323	C₂×C₃	—	8	12	no	—
324	C₂×C₃	C₃×D₄×A₄	1	2	yes	—
325	C₂×C₃	C₂³×C₃×A₄	1	1	yes	characteristic
326	C₂²	—	2	4	no	—
327	C₂²	—	3	2	no	—
328	C₂²	—	3	1	no	—
329	C₂²	—	3	2	no	—
330	C₂²	—	3	1	no	—
331	C₂²	—	3	1	no	—
332	C₂²	—	3	2	no	—
333	C₂²	—	3	2	no	—
334	C₂²	—	3	4	no	—
335	C₂²	—	6	4	no	—
336	C₂²	—	6	4	no	—
337	C₂²	—	6	8	no	—
338	C₂²	—	6	4	no	—
339	C₂²	—	6	4	no	—
340	C₂²	—	6	8	no	—
341	C₂²	—	6	4	no	—
342	C₂²	C₂×C₃×D₄×C₉	1	1	yes	characteristic, complemented
343	C₂²	C₂²×C₉×A₄	1	1	yes	characteristic
344	C₂²	C₂²×C₉×A₄	1	4	yes	complemented
345	C₄	—	3	2	no	—
346	C₄	C₂²×C₉×A₄	1	2	yes	complemented
347	C₃	—	4	3	no	—
348	C₃	C₂×C₃×D₄×A₄	1	1	yes	characteristic
349	C₂	—	2	4	no	—
350	C₂	—	3	1	no	—
351	C₂	—	3	2	no	—
352	C₂	—	3	1	no	—
353	C₂	—	6	4	no	—
354	C₂	D₄×C₉×A₄	1	2	yes	direct product factor
355	C₂	C₂³×C₉×A₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×A₄
commutator	C₂³	C₂³×C₃×C₉
Frattini	C₂×C₃	C₂³×C₃×A₄
Fitting	C₂³×D₄×C₉	C₃
socle	C₂⁴×C₃	C₂²×C₃²
prime radical	C₂×C₃×D₄×A₄	C₃
cosocle	C₂³×C₃	C₂³×C₃²
hypercenter	C₂×D₄×C₉	A₄
hypocenter	C₂²	C₂×C₃×D₄×C₉
LCS	G ▷ C₂³ ▷ C₂²
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×D₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₂³×C₉×A₄	C₂	semidirect
2. D₄×C₉×A₄	C₂	direct (N × H)
3. C₂×C₄×C₉×A₄	C₂	semidirect
5. C₂³×D₄×C₉	C₃	semidirect
6. C₂×D₄×C₂²⋊C₉	C₃	semidirect
9. C₂²×C₉×A₄	C₂²	semidirect
11. C₄×C₉×A₄	C₂²	semidirect
15. C₂⁵×C₉	C₂×C₃	semidirect
16. C₂³×C₂²⋊C₉	C₂×C₃	semidirect
21. C₂²×D₄×C₉	C₂×C₃	semidirect
22. C₂³×C₄×C₉	C₂×C₃	semidirect
23. D₄×C₂²⋊C₉	C₂×C₃	semidirect
24. C₂×C₄×C₂²⋊C₉	C₂×C₃	semidirect
27. C₂×C₉×A₄	D₄	direct (N × H)
32. C₂×D₄×A₄	C₉	direct (N × H)
44. C₂⁴×C₉	C₂²×C₃	semidirect
47. C₂²×C₂²⋊C₉	C₂²×C₃	semidirect
58. C₂×D₄×C₉	A₄	direct (N × H)
62. C₂²×C₄×C₉	C₂²×C₃	semidirect
63. C₄×C₂²⋊C₉	C₂²×C₃	semidirect
67. C₉×A₄	C₂×D₄	direct (N × H)
70. C₂³×A₄	C₂×C₉	semidirect
77. D₄×A₄	C₂×C₉	direct (N × H)
78. C₂×C₄×A₄	C₂×C₉	semidirect
102. C₂³×C₉	C₃×D₄	semidirect
103. C₂³×C₉	C₂×A₄	semidirect
106. C₂×C₂²⋊C₉	C₃×D₄	semidirect
112. D₄×C₉	C₂×A₄	direct (N × H)
119. C₂×C₄×C₉	C₂×A₄	semidirect
120. C₂³×D₄	C₃×C₉	semidirect
133. C₂²×A₄	C₂²×C₉	semidirect
149. C₄×A₄	C₂²×C₉	semidirect
174. C₂²×C₉	C₂×C₃×D₄	semidirect
176. C₂²×C₉	C₂²×A₄	semidirect
177. C₂²⋊C₉	C₂×C₃×D₄	semidirect
180. C₄×C₉	C₂²×A₄	semidirect
181. C₂⁵	C₂×C₃×C₉	semidirect
186. C₂²×D₄	C₂×C₃×C₉	semidirect
187. C₂³×C₄	C₂×C₃×C₉	semidirect
210. C₂×A₄	D₄×C₉	direct (N × H)
235. C₂×C₉	D₄×A₄	direct (N × H)
243. C₂⁴	C₂²×C₃×C₉	semidirect
253. C₂×D₄	C₉×A₄	direct (N × H)
257. C₂²×C₄	C₂²×C₃×C₉	semidirect
280. A₄	C₂×D₄×C₉	direct (N × H)
286. C₉	C₂×D₄×A₄	direct (N × H)
303. C₂³	C₃×D₄×C₉	semidirect
304. C₂³	C₂×C₉×A₄	semidirect
309. D₄	C₂×C₉×A₄	direct (N × H)
315. C₂×C₄	C₂×C₉×A₄	semidirect
342. C₂²	C₂×C₃×D₄×C₉	semidirect
344. C₂²	C₂²×C₉×A₄	semidirect
346. C₄	C₂²×C₉×A₄	semidirect
354. C₂	D₄×C₉×A₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₉×A₄	2
D₄×C₉×A₄	2
C₂×C₄×C₉×A₄	2
C₂×C₃×D₄×A₄	3
C₂³×D₄×C₉	3
C₂×D₄×C₂²⋊C₉	3
C₂×C₃×D₄×C₉	4

Subgroups — C2×D4×C9×A4 #13164823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₉×A₄ #13164823