Subgroups — C₄×C₉×#214 #13142735

Order 1728.

460 conjugacy classes of subgroups.

The subgroup lattice has 356 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
2	C₂×C₉×#214	C₂	1	1	yes	maximal, characteristic
3	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#832	C₂	1	1	yes	maximal, characteristic
5	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#808	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#214	C₃	1	1	yes	maximal, characteristic
9	C₄×C₉×SD₁₆	—	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×Dic₆	C₂²	1	1	yes	characteristic
13	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₃×C₉×C₂²⋊C₄	—	2	1	no	—
15	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
16	C₉×#214	C₄	1	4	yes	direct product factor
17	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₉×Dic₃⋊C₄	—	2	1	no	—
19	C₄×C₉×Dic₃	—	2	1	no	—
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×#214	C₂×C₃	1	1	yes	characteristic
24	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
25	C₃×#832	C₂×C₃	1	1	yes	characteristic
26	C₃×#810	C₂×C₃	1	1	yes	characteristic
27	C₃×#808	C₂×C₃	1	1	yes	characteristic
28	C₃×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×SD₁₆	—	3	1	no	—
30	C₄×Q₈×C₉	—	3	1	no	—
31	C₄×D₄×C₉	—	2	1	no	—
32	C₄×D₄×C₉	D₃	1	1	yes	characteristic
33	C₉×#106	—	3	1	no	—
34	C₉×#103	—	3	1	no	—
35	C₉×#102	—	3	1	no	—
36	C₄×C₈×C₉	—	3	1	no	—
37	C₂³×C₃×C₉	—	2	1	no	—
38	C₃×D₄×C₉	—	2	1	no	—
39	C₃×D₄×C₉	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	4	2	no	—
42	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
44	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₂×C₉×Dic₃	—	2	1	no	—
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₉×Dic₆	—	2	1	no	—
48	C₉×Dic₆	C₂×C₄	1	2	yes	complemented
49	C₉×C₃⋊C₈	—	2	1	no	—
50	C₉×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
51	C₃×C₄×SD₁₆	—	3	1	no	—
52	C₄×#214	C₉	1	1	yes	characteristic, direct product factor
53	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₃²×C₄	—	2	1	no	—
55	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
56	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
57	C₃²×C₂²⋊C₄	—	2	1	no	—
58	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
59	C₃×#214	C₃×C₄	1	4	yes	—
60	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
61	C₃×Dic₃⋊C₄	—	2	1	no	—
62	C₃×C₄×Dic₃	—	2	1	no	—
63	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×Q₈×C₉	—	3	1	no	—
66	C₂×D₄×C₉	—	2	1	no	—
67	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
68	C₂²×C₄×C₉	—	2	2	no	—
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₉×SD₁₆	—	3	4	no	—
71	C₂×C₈×C₉	—	3	1	no	—
72	C₂×C₈×C₉	—	3	1	no	—
73	C₉×C₄⋊C₄	—	2	1	no	—
74	C₉×C₄⋊C₄	—	3	1	no	—
75	C₉×C₄⋊C₄	—	6	1	no	—
76	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
77	C₉×C₂²⋊C₄	—	2	2	no	—
78	C₉×C₂²⋊C₄	—	2	1	no	—
79	C₄²×C₉	—	2	1	no	—
80	C₄²×C₉	—	6	1	no	—
81	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃×C₉	—	2	2	no	—
83	C₂²×C₃×C₉	—	4	1	no	—
84	C₂²×C₃×C₉	—	4	1	no	—
85	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
86	C₃×C₄×C₉	—	2	1	no	—
87	C₃×C₄×C₉	—	4	1	no	—
88	C₃×C₄×C₉	SD₁₆	1	2	yes	complemented
89	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
90	C₃×C₄×C₉	#41	1	1	yes	characteristic
91	C₉×Dic₃	—	2	2	no	—
92	C₉×Dic₃	—	4	1	no	—
93	C₂×C₃×SD₁₆	—	3	1	no	—
94	C₃×C₄×Q₈	—	3	1	no	—
95	C₃×C₄×D₄	—	2	1	no	—
96	C₃×C₄×D₄	C₂×C₉	1	1	yes	characteristic
97	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
98	C₂×#214	C₂×C₉	1	1	yes	characteristic
99	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
100	C₃×#106	—	3	1	no	—
101	C₃×#103	—	3	1	no	—
102	C₃×#102	—	3	1	no	—
103	C₃×C₄×C₈	—	3	1	no	—
104	#832	C₂×C₉	1	1	yes	characteristic
105	#810	C₂×C₉	1	1	yes	characteristic, complemented
106	#808	C₂×C₉	1	1	yes	characteristic, complemented
107	C₄×C₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
108	C₂³×C₃²	—	2	1	no	—
109	C₃²×D₄	—	2	1	no	—
110	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
111	C₂×C₃²×C₄	—	2	1	no	—
112	C₂×C₃²×C₄	—	4	2	no	—
113	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
116	C₂×C₃×Dic₃	—	2	1	no	—
117	C₂×C₃×Dic₃	—	2	1	no	—
118	C₃×Dic₆	—	2	1	no	—
119	C₃×Dic₆	C₂×C₃×C₄	1	2	yes	—
120	C₂³×C₉	—	2	2	no	—
121	C₂³×C₉	—	2	1	no	—
122	C₃×C₃⋊C₈	—	2	1	no	—
123	C₃×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
124	Q₈×C₉	—	3	2	no	—
125	Q₈×C₉	—	6	1	no	—
126	D₄×C₉	—	2	2	no	—
127	D₄×C₉	—	2	1	no	—
128	D₄×C₉	—	2	2	no	—
129	D₄×C₉	C₄×D₃	1	2	yes	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	4	4	no	—
136	C₂×C₄×C₉	—	4	2	no	—
137	C₂×C₄×C₉	—	6	1	no	—
138	C₂×C₄×C₉	—	6	1	no	—
139	C₂×C₄×C₉	#67	1	1	yes	characteristic
140	C₂×C₄×C₉	#67	1	1	yes	characteristic
141	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
142	C₈×C₉	—	3	2	no	—
143	C₈×C₉	—	6	1	no	—
144	C₄×SD₁₆	—	3	1	no	Sylow
145	C₂×C₃×C₉	—	4	2	no	—
146	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
148	C₂×C₃×C₉	#135	1	1	yes	characteristic
149	C₂×C₃×Q₈	—	3	1	no	—
150	C₂×C₃×D₄	—	2	1	no	—
151	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	2	1	no	—
156	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
157	C₃×SD₁₆	—	3	4	no	—
158	C₂×C₃×C₈	—	3	1	no	—
159	C₂×C₃×C₈	—	3	1	no	—
160	C₃×C₄⋊C₄	—	2	1	no	—
161	C₃×C₄⋊C₄	—	3	1	no	—
162	C₃×C₄⋊C₄	—	6	1	no	—
163	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
164	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
165	C₃×C₂²⋊C₄	—	2	2	no	—
166	C₃×C₂²⋊C₄	—	2	1	no	—
167	C₃×C₂²⋊C₄	—	2	1	no	—
168	C₃×C₄²	—	2	1	no	—
169	C₃×C₄²	—	6	1	no	—
170	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
171	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
172	#214	C₄×C₉	1	4	yes	direct product factor
173	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
174	Dic₃⋊C₄	—	2	1	no	—
175	C₄×Dic₃	—	2	1	no	—
176	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
177	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
178	C₂²×C₃²	—	2	2	no	—
179	C₂²×C₃²	—	4	1	no	—
180	C₂²×C₃²	—	4	1	no	—
181	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
182	C₃²×C₄	—	2	1	no	—
183	C₃²×C₄	—	4	1	no	—
184	C₃²×C₄	C₃×SD₁₆	1	2	yes	—
185	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
186	C₃²×C₄	C₃×#41	1	1	yes	characteristic
187	C₃×Dic₃	—	2	2	no	—
188	C₃×Dic₃	—	4	1	no	—
189	C₂²×C₉	—	2	4	no	—
190	C₂²×C₉	—	2	2	no	—
191	C₂²×C₉	—	2	1	no	—
192	C₂²×C₉	—	4	2	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	—	4	1	no	—
195	C₂²×C₉	—	4	1	no	—
196	C₂²×C₉	C₂×#67	1	1	yes	characteristic
197	C₄×C₉	—	2	1	no	—
198	C₄×C₉	—	2	2	no	—
199	C₄×C₉	—	2	1	no	—
200	C₄×C₉	—	2	1	no	—
201	C₄×C₉	—	4	1	no	—
202	C₄×C₉	—	4	2	no	—
203	C₄×C₉	—	4	1	no	—
204	C₄×C₉	—	6	2	no	—
205	C₄×C₉	—	12	1	no	—
206	C₄×C₉	#214	1	2	yes	direct product factor
207	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
208	C₄×C₉	#235	1	1	yes	characteristic
209	C₂×SD₁₆	—	3	1	no	—
210	C₄×Q₈	—	3	1	no	—
211	C₄×D₄	D₃×C₉	1	1	yes	characteristic
212	#106	—	3	1	no	—
213	#103	—	3	1	no	—
214	#102	—	3	1	no	—
215	C₄×C₈	—	3	1	no	—
216	C₃×C₉	C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₃×Q₈	—	3	2	no	—
221	C₃×Q₈	—	6	1	no	—
222	C₃×D₄	—	2	2	no	—
223	C₃×D₄	—	2	1	no	—
224	C₃×D₄	—	2	1	no	—
225	C₃×D₄	—	2	2	no	—
226	C₃×D₄	C₂×C₄×C₉	1	2	yes	—
227	C₃×D₄	C₃×C₄×D₃	1	2	yes	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	4	4	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	—	4	2	no	—
237	C₂×C₃×C₄	—	6	1	no	—
238	C₂×C₃×C₄	—	6	1	no	—
239	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
240	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
242	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
243	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
245	C₂×Dic₃	—	2	1	no	—
246	C₂×Dic₃	—	2	1	no	—
247	Dic₆	—	2	1	no	—
248	Dic₆	C₂×C₄×C₉	1	2	yes	complemented
249	C₃×C₈	—	3	2	no	—
250	C₃×C₈	—	6	1	no	—
251	C₃⋊C₈	—	2	1	no	—
252	C₃⋊C₈	C₂×C₄×C₉	1	2	yes	complemented
253	C₂×C₃²	—	4	2	no	—
254	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
255	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
256	C₂×C₃²	C₃×#135	1	1	yes	characteristic
257	C₂×C₉	—	2	1	no	—
258	C₂×C₉	—	2	1	no	—
259	C₂×C₉	—	2	1	no	—
260	C₂×C₉	—	4	4	no	—
261	C₂×C₉	—	4	2	no	—
262	C₂×C₉	C₄×#67	1	1	yes	characteristic
263	C₂×C₉	C₂×#214	1	1	yes	characteristic
264	C₂×C₉	#950	1	1	yes	characteristic
265	C₂×Q₈	—	3	1	no	—
266	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
267	C₂²×C₄	—	2	1	no	—
268	SD₁₆	—	3	4	no	—
269	C₂×C₈	—	3	1	no	—
270	C₂×C₈	—	3	1	no	—
271	C₄⋊C₄	—	3	1	no	—
272	C₄⋊C₄	—	6	1	no	—
273	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
274	C₂²⋊C₄	—	2	1	no	—
275	C₄²	—	6	1	no	—
276	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
277	C₂²×C₃	—	2	4	no	—
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	2	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	4	2	no	—
282	C₂²×C₃	—	4	2	no	—
283	C₂²×C₃	—	4	1	no	—
284	C₂²×C₃	—	4	1	no	—
285	C₂²×C₃	—	4	1	no	—
286	C₂²×C₃	—	4	1	no	—
287	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
288	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
289	C₃×C₄	—	2	1	no	—
290	C₃×C₄	—	2	1	no	—
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	1	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	4	1	no	—
295	C₃×C₄	—	4	2	no	—
296	C₃×C₄	—	4	1	no	—
297	C₃×C₄	—	4	1	no	—
298	C₃×C₄	—	6	2	no	—
299	C₃×C₄	—	12	1	no	—
300	C₃×C₄	C₉×SD₁₆	1	2	yes	complemented
301	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
302	C₃×C₄	C₉×#41	1	1	yes	characteristic
303	C₃×C₄	C₃×#214	1	2	yes	—
304	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
305	C₃×C₄	C₃×#235	1	1	yes	characteristic
306	Dic₃	—	2	2	no	—
307	Dic₃	—	4	1	no	—
308	C₃²	C₃×C₄×SD₁₆	1	1	yes	characteristic
309	C₉	—	2	1	no	—
310	C₉	C₄×#214	1	1	yes	characteristic, direct product factor
311	C₂³	—	2	1	no	—
312	Q₈	—	3	2	no	—
313	Q₈	—	6	1	no	—
314	D₄	—	2	1	no	—
315	D₄	C₄×D₃×C₉	1	2	yes	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	6	1	no	—
319	C₂×C₄	—	6	1	no	—
320	C₂×C₄	C₉×#67	1	1	yes	characteristic
321	C₂×C₄	C₉×#67	1	1	yes	characteristic
322	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
323	C₈	—	3	2	no	—
324	C₈	—	6	1	no	—
325	C₂×C₃	—	2	1	no	—
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	—	2	1	no	—
328	C₂×C₃	—	4	4	no	—
329	C₂×C₃	—	4	2	no	—
330	C₂×C₃	—	4	2	no	—
331	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
332	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
333	C₂×C₃	C₉×#135	1	1	yes	characteristic
334	C₂×C₃	C₃×C₄×#67	1	1	yes	characteristic
335	C₂×C₃	C₂×C₃×#214	1	1	yes	characteristic
336	C₂×C₃	C₃×#950	1	1	yes	characteristic
337	C₂²	—	2	2	no	—
338	C₂²	—	4	1	no	—
339	C₂²	—	4	1	no	—
340	C₂²	C₂×C₉×#67	1	1	yes	characteristic
341	C₄	—	2	1	no	—
342	C₄	—	4	1	no	—
343	C₄	—	6	2	no	—
344	C₄	—	12	1	no	—
345	C₄	C₉×#214	1	2	yes	direct product factor
346	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
347	C₄	C₉×#235	1	1	yes	characteristic
348	C₃	—	2	1	no	—
349	C₃	C₄×C₉×SD₁₆	1	1	yes	characteristic, complemented
350	C₃	C₃×C₄×#214	1	1	yes	characteristic
351	C₂	—	4	2	no	—
352	C₂	C₄×C₉×#67	1	1	yes	characteristic
353	C₂	C₂×C₉×#214	1	1	yes	characteristic
354	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×C₃²×D₄	C₂²×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₄×D₄×C₉	D₃
hypocenter	C₃	C₄×C₉×SD₁₆
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
3. C₄×C₉×Dic₆	C₂	semidirect
5. C₉×#810	C₂	semidirect
6. C₉×#808	C₂	semidirect
7. C₄×C₉×C₃⋊C₈	C₂	semidirect
16. C₉×#214	C₄	direct (N × H)
48. C₉×Dic₆	C₂×C₄	semidirect
50. C₉×C₃⋊C₈	C₂×C₄	semidirect
52. C₄×#214	C₉	direct (N × H)
88. C₃×C₄×C₉	SD₁₆	semidirect
99. C₄×Dic₆	C₂×C₉	semidirect
105. #810	C₂×C₉	semidirect
106. #808	C₂×C₉	semidirect
107. C₄×C₃⋊C₈	C₂×C₉	semidirect
172. #214	C₄×C₉	direct (N × H)
206. C₄×C₉	#214	direct (N × H)
216. C₃×C₉	C₄×SD₁₆	semidirect
248. Dic₆	C₂×C₄×C₉	semidirect
252. C₃⋊C₈	C₂×C₄×C₉	semidirect
300. C₃×C₄	C₉×SD₁₆	semidirect
310. C₉	C₄×#214	direct (N × H)
345. C₄	C₉×#214	direct (N × H)
349. C₃	C₄×C₉×SD₁₆	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×#214	2
C₄×C₉×Dic₆	2
C₉×#832	2
C₉×#810	2
C₉×#808	2
C₄×C₉×C₃⋊C₈	2
C₃×C₄×#214	3
C₄×C₉×SD₁₆	3

Subgroups — C4×C9×#214 #13142735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×#214 #13142735