Subgroups — C₄×C₉×#213 #13142731

Order 1728.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#213	C₂	1	1	yes	maximal, characteristic
3	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#832	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#807	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#213	C₃	1	1	yes	maximal, characteristic
9	C₄×C₉×D₈	—	3	1	no	maximal
10	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	—	2	1	no	—
12	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	—	2	1	no	—
14	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₉×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₉×#213	C₄	1	4	yes	direct product factor
18	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×#213	C₂×C₃	1	1	yes	characteristic
24	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
25	C₃×#832	C₂×C₃	1	1	yes	characteristic
26	C₃×#809	C₂×C₃	1	1	yes	characteristic
27	C₃×#807	C₂×C₃	1	1	yes	characteristic
28	C₃×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×D₈	—	3	1	no	—
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	—	3	1	no	—
32	C₄×D₄×C₉	D₃	1	1	yes	characteristic, complemented
33	C₉×#107	—	3	1	no	—
34	C₉×#102	—	3	1	no	—
35	C₉×#102	—	3	1	no	—
36	C₄×C₈×C₉	—	3	1	no	—
37	C₂³×C₃×C₉	—	2	1	no	—
38	C₂²×D₃×C₉	—	2	1	no	—
39	C₃×D₄×C₉	—	2	1	no	—
40	C₃×D₄×C₉	C₂×C₄	1	2	yes	complemented
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	—	4	2	no	—
43	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
44	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₉×D₁₂	—	2	1	no	—
48	C₉×D₁₂	C₂×C₄	1	2	yes	complemented
49	C₄×D₃×C₉	—	4	2	no	—
50	C₉×C₃⋊C₈	—	2	1	no	—
51	C₉×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
52	C₃×C₄×D₈	—	3	1	no	—
53	C₄×#213	C₉	1	1	yes	characteristic, direct product factor
54	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₃²×C₄	—	2	1	no	—
56	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₃×C₄×D₃	—	2	1	no	—
58	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
59	C₃²×C₂²⋊C₄	—	2	1	no	—
60	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
61	C₃×#213	C₃×C₄	1	4	yes	—
62	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
63	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂×D₄×C₉	—	2	1	no	—
67	C₂×D₄×C₉	—	3	1	no	—
68	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₄×C₉	—	2	2	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	—	6	1	no	—
72	C₉×D₈	—	3	4	no	—
73	C₂×C₈×C₉	—	3	1	no	—
74	C₂×C₈×C₉	—	3	1	no	—
75	C₉×C₄⋊C₄	—	2	1	no	—
76	C₉×C₄⋊C₄	—	3	1	no	—
77	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₉×C₂²⋊C₄	—	2	2	no	—
79	C₉×C₂²⋊C₄	—	2	1	no	—
80	C₉×C₂²⋊C₄	—	6	1	no	—
81	C₄²×C₉	—	2	1	no	—
82	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₃×C₉	—	2	2	no	—
84	C₂²×C₃×C₉	—	4	1	no	—
85	C₂²×C₃×C₉	—	4	1	no	—
86	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
87	C₂×D₃×C₉	—	2	2	no	—
88	C₂×D₃×C₉	—	4	1	no	—
89	C₂×D₃×C₉	—	4	1	no	—
90	C₃×C₄×C₉	—	2	1	no	—
91	C₃×C₄×C₉	—	4	1	no	—
92	C₃×C₄×C₉	D₈	1	2	yes	complemented
93	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
94	C₃×C₄×C₉	#41	1	1	yes	characteristic
95	C₉×Dic₃	—	4	1	no	—
96	C₂×C₃×D₈	—	3	1	no	—
97	C₃×C₄×D₄	—	2	1	no	—
98	C₃×C₄×D₄	—	3	1	no	—
99	C₃×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
100	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
101	C₂×#213	C₂×C₉	1	1	yes	characteristic
102	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
103	C₃×#107	—	3	1	no	—
104	C₃×#102	—	3	1	no	—
105	C₃×#102	—	3	1	no	—
106	C₃×C₄×C₈	—	3	1	no	—
107	#832	C₂×C₉	1	1	yes	characteristic, complemented
108	#809	C₂×C₉	1	1	yes	characteristic, complemented
109	#807	C₂×C₉	1	1	yes	characteristic, complemented
110	C₄×C₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
111	C₂³×C₃²	—	2	1	no	—
112	C₂²×C₃×D₃	—	2	1	no	—
113	C₃²×D₄	—	2	1	no	—
114	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	4	2	no	—
117	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₃×Dic₃	—	2	1	no	—
121	C₃×D₁₂	—	2	1	no	—
122	C₃×D₁₂	C₂×C₃×C₄	1	2	yes	—
123	C₃×C₄×D₃	—	4	2	no	—
124	C₂³×C₉	—	2	2	no	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	—	6	1	no	—
127	C₃×C₃⋊C₈	—	2	1	no	—
128	C₃×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
129	D₄×C₉	—	2	2	no	—
130	D₄×C₉	—	2	1	no	—
131	D₄×C₉	—	2	2	no	—
132	D₄×C₉	—	3	2	no	—
133	D₄×C₉	—	6	1	no	—
134	D₄×C₉	C₄×D₃	1	2	yes	complemented
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	4	4	no	—
141	C₂×C₄×C₉	—	4	2	no	—
142	C₂×C₄×C₉	—	6	1	no	—
143	C₂×C₄×C₉	—	12	2	no	—
144	C₂×C₄×C₉	#67	1	1	yes	characteristic
145	C₂×C₄×C₉	#67	1	1	yes	characteristic
146	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
147	C₈×C₉	—	3	2	no	—
148	C₈×C₉	—	6	1	no	—
149	C₄×D₈	—	3	1	no	Sylow
150	C₂×C₃×C₉	—	4	2	no	—
151	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₃×C₉	C₂×D₈	1	1	yes	characteristic
153	C₂×C₃×C₉	#135	1	1	yes	characteristic
154	D₃×C₉	—	4	2	no	—
155	C₂×C₃×D₄	—	2	1	no	—
156	C₂×C₃×D₄	—	3	1	no	—
157	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
158	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	2	1	no	—
162	C₂²×C₃×C₄	—	6	1	no	—
163	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
164	C₂×C₄×D₃	—	2	1	no	—
165	C₃×D₈	—	3	4	no	—
166	C₂×C₃×C₈	—	3	1	no	—
167	C₂×C₃×C₈	—	3	1	no	—
168	C₃×C₄⋊C₄	—	2	1	no	—
169	C₃×C₄⋊C₄	—	3	1	no	—
170	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
171	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
172	C₃×C₂²⋊C₄	—	2	2	no	—
173	C₃×C₂²⋊C₄	—	2	1	no	—
174	C₃×C₂²⋊C₄	—	2	1	no	—
175	C₃×C₂²⋊C₄	—	6	1	no	—
176	C₃×C₄²	—	2	1	no	—
177	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
178	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
179	#213	C₄×C₉	1	4	yes	direct product factor
180	(C₂×D₃)⋊C₄	—	2	1	no	—
181	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
182	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
183	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
184	C₂²×C₃²	—	2	2	no	—
185	C₂²×C₃²	—	4	1	no	—
186	C₂²×C₃²	—	4	1	no	—
187	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
188	C₂×C₃×D₃	—	2	2	no	—
189	C₂×C₃×D₃	—	4	1	no	—
190	C₂×C₃×D₃	—	4	1	no	—
191	C₃²×C₄	—	2	1	no	—
192	C₃²×C₄	—	4	1	no	—
193	C₃²×C₄	C₃×D₈	1	2	yes	—
194	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
195	C₃²×C₄	C₃×#41	1	1	yes	characteristic
196	C₃×Dic₃	—	4	1	no	—
197	C₂²×C₉	—	2	4	no	—
198	C₂²×C₉	—	2	2	no	—
199	C₂²×C₉	—	2	1	no	—
200	C₂²×C₉	—	4	2	no	—
201	C₂²×C₉	—	4	2	no	—
202	C₂²×C₉	—	4	1	no	—
203	C₂²×C₉	—	4	1	no	—
204	C₂²×C₉	—	6	2	no	—
205	C₂²×C₉	—	12	1	no	—
206	C₂²×C₉	—	12	1	no	—
207	C₂²×C₉	C₂×#67	1	1	yes	characteristic
208	C₄×C₉	—	2	1	no	—
209	C₄×C₉	—	2	2	no	—
210	C₄×C₉	—	2	1	no	—
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	4	1	no	—
213	C₄×C₉	—	4	2	no	—
214	C₄×C₉	—	4	1	no	—
215	C₄×C₉	—	12	1	no	—
216	C₄×C₉	#213	1	2	yes	direct product factor
217	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
218	C₄×C₉	#235	1	1	yes	characteristic
219	C₂×D₈	—	3	1	no	—
220	C₄×D₄	—	3	1	no	—
221	C₄×D₄	D₃×C₉	1	1	yes	characteristic, complemented
222	#107	—	3	1	no	—
223	#102	—	3	1	no	—
224	#102	—	3	1	no	—
225	C₄×C₈	—	3	1	no	—
226	C₃×C₉	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
227	C₂³×C₃	—	2	2	no	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	6	1	no	—
231	C₂²×D₃	—	2	1	no	—
232	C₃×D₄	—	2	2	no	—
233	C₃×D₄	—	2	1	no	—
234	C₃×D₄	—	2	1	no	—
235	C₃×D₄	—	2	2	no	—
236	C₃×D₄	—	3	2	no	—
237	C₃×D₄	—	6	1	no	—
238	C₃×D₄	C₂×C₄×C₉	1	2	yes	complemented
239	C₃×D₄	C₃×C₄×D₃	1	2	yes	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	4	4	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	—	4	2	no	—
249	C₂×C₃×C₄	—	6	1	no	—
250	C₂×C₃×C₄	—	12	2	no	—
251	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
252	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
254	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
255	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
257	C₂×Dic₃	—	2	1	no	—
258	D₁₂	—	2	1	no	—
259	D₁₂	C₂×C₄×C₉	1	2	yes	complemented
260	C₄×D₃	—	4	2	no	—
261	C₃×C₈	—	3	2	no	—
262	C₃×C₈	—	6	1	no	—
263	C₃⋊C₈	—	2	1	no	—
264	C₃⋊C₈	C₂×C₄×C₉	1	2	yes	complemented
265	C₂×C₃²	—	4	2	no	—
266	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
267	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
268	C₂×C₃²	C₃×#135	1	1	yes	characteristic
269	C₃×D₃	—	4	2	no	—
270	C₂×C₉	—	2	1	no	—
271	C₂×C₉	—	2	1	no	—
272	C₂×C₉	—	2	1	no	—
273	C₂×C₉	—	4	4	no	—
274	C₂×C₉	—	4	2	no	—
275	C₂×C₉	—	12	2	no	—
276	C₂×C₉	C₄×#67	1	1	yes	characteristic
277	C₂×C₉	C₂×#213	1	1	yes	characteristic
278	C₂×C₉	#950	1	1	yes	characteristic
279	C₂×D₄	—	3	1	no	—
280	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	6	1	no	—
283	D₈	—	3	4	no	—
284	C₂×C₈	—	3	1	no	—
285	C₂×C₈	—	3	1	no	—
286	C₄⋊C₄	—	3	1	no	—
287	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	6	1	no	—
290	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	—	4	1	no	—
298	C₂²×C₃	—	4	1	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	6	2	no	—
302	C₂²×C₃	—	12	1	no	—
303	C₂²×C₃	—	12	1	no	—
304	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
306	C₂×D₃	—	2	2	no	—
307	C₂×D₃	—	4	1	no	—
308	C₂×D₃	—	4	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	—	4	2	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	—	4	1	no	—
318	C₃×C₄	—	12	1	no	—
319	C₃×C₄	C₉×D₈	1	2	yes	complemented
320	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
321	C₃×C₄	C₉×#41	1	1	yes	characteristic
322	C₃×C₄	C₃×#213	1	2	yes	—
323	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
324	C₃×C₄	C₃×#235	1	1	yes	characteristic
325	Dic₃	—	4	1	no	—
326	C₃²	C₃×C₄×D₈	1	1	yes	characteristic
327	C₉	—	2	1	no	—
328	C₉	C₄×#213	1	1	yes	characteristic, direct product factor
329	C₂³	—	2	1	no	—
330	C₂³	—	6	1	no	—
331	D₄	—	2	1	no	—
332	D₄	—	3	2	no	—
333	D₄	—	6	1	no	—
334	D₄	C₄×D₃×C₉	1	2	yes	complemented
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	6	1	no	—
338	C₂×C₄	—	12	2	no	—
339	C₂×C₄	C₉×#67	1	1	yes	characteristic
340	C₂×C₄	C₉×#67	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
342	C₈	—	3	2	no	—
343	C₈	—	6	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	4	4	no	—
348	C₂×C₃	—	4	2	no	—
349	C₂×C₃	—	4	2	no	—
350	C₂×C₃	—	12	2	no	—
351	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
352	C₂×C₃	C₂×C₉×D₈	1	1	yes	characteristic
353	C₂×C₃	C₉×#135	1	1	yes	characteristic
354	C₂×C₃	C₃×C₄×#67	1	1	yes	characteristic
355	C₂×C₃	C₂×C₃×#213	1	1	yes	characteristic
356	C₂×C₃	C₃×#950	1	1	yes	characteristic
357	D₃	—	4	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	6	2	no	—
362	C₂²	—	12	1	no	—
363	C₂²	—	12	1	no	—
364	C₂²	C₂×C₉×#67	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	12	1	no	—
368	C₄	C₉×#213	1	2	yes	direct product factor
369	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
370	C₄	C₉×#235	1	1	yes	characteristic
371	C₃	—	2	1	no	—
372	C₃	C₄×C₉×D₈	1	1	yes	characteristic, complemented
373	C₃	C₃×C₄×#213	1	1	yes	characteristic
374	C₂	—	4	2	no	—
375	C₂	—	12	2	no	—
376	C₂	C₄×C₉×#67	1	1	yes	characteristic
377	C₂	C₂×C₉×#213	1	1	yes	characteristic
378	C₂	C₉×#950	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	#67
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₄×D₄×C₉	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#213	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₄×D₄×C₉	D₃
hypocenter	C₃	C₄×C₉×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₄²×C₉ ◁ C₄×D₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×D₄×C₉	C₂	semidirect
3. C₄×C₉×D₁₂	C₂	semidirect
4. C₉×#832	C₂	semidirect
5. C₉×#809	C₂	semidirect
6. C₉×#807	C₂	semidirect
7. C₄×C₉×C₃⋊C₈	C₂	semidirect
17. C₉×#213	C₄	direct (N × H)
32. C₄×D₄×C₉	D₃	semidirect
40. C₃×D₄×C₉	C₂×C₄	semidirect
48. C₉×D₁₂	C₂×C₄	semidirect
51. C₉×C₃⋊C₈	C₂×C₄	semidirect
53. C₄×#213	C₉	direct (N × H)
92. C₃×C₄×C₉	D₈	semidirect
99. C₃×C₄×D₄	C₂×C₉	semidirect
102. C₄×D₁₂	C₂×C₉	semidirect
107. #832	C₂×C₉	semidirect
108. #809	C₂×C₉	semidirect
109. #807	C₂×C₉	semidirect
110. C₄×C₃⋊C₈	C₂×C₉	semidirect
134. D₄×C₉	C₄×D₃	semidirect
179. #213	C₄×C₉	direct (N × H)
216. C₄×C₉	#213	direct (N × H)
221. C₄×D₄	D₃×C₉	semidirect
226. C₃×C₉	C₄×D₈	semidirect
238. C₃×D₄	C₂×C₄×C₉	semidirect
259. D₁₂	C₂×C₄×C₉	semidirect
264. C₃⋊C₈	C₂×C₄×C₉	semidirect
319. C₃×C₄	C₉×D₈	semidirect
328. C₉	C₄×#213	direct (N × H)
334. D₄	C₄×D₃×C₉	semidirect
368. C₄	C₉×#213	direct (N × H)
372. C₃	C₄×C₉×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₄×C₉	2
C₂×C₉×#213	2
C₄×C₉×D₁₂	2
C₉×#832	2
C₉×#809	2
C₉×#807	2
C₄×C₉×C₃⋊C₈	2
C₃×C₄×#213	3
C₄×C₉×D₈	3

Subgroups — C4×C9×#213 #13142731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×#213 #13142731