Subgroups — C₉×#5210 #13143519

Order 1728.

938 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₉×C₃⋊#95	C₂	1	2	yes	maximal, complemented
6	C₃×#5210	C₃	1	1	yes	maximal, characteristic
7	C₉×#385	—	3	1	no	maximal
8	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×C₉	—	2	2	no	—
10	C₂²×C₃×C₄×C₉	—	2	4	no	—
11	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
12	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
15	C₉×#217	—	2	2	no	—
16	C₉×#217	C₄	1	4	yes	complemented
17	C₉×Dic₃⋊C₄	—	2	4	no	—
18	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	2	yes	—
22	C₂³×C₄×C₉	—	2	1	no	—
23	C₂³×C₄×C₉	D₃	1	1	yes	characteristic
24	C₃×C₃⋊#95	C₂×C₃	1	2	yes	—
25	C₂×C₉×C₄⋊C₄	—	3	2	no	—
26	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
27	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
28	C₉×#95	—	3	2	no	—
29	C₂³×C₃×C₉	—	2	2	no	—
30	C₂³×C₃×C₉	—	2	2	no	—
31	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
32	C₂³×C₃×C₉	D₄	1	2	yes	—
33	C₂³×C₃×C₉	Q₈	1	2	yes	—
34	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₄×C₉	—	2	8	no	—
36	C₂×C₃×C₄×C₉	—	2	2	no	—
37	C₂×C₃×C₄×C₉	—	2	2	no	—
38	C₂×C₃×C₄×C₉	D₄	1	4	yes	—
39	C₂×C₉×Dic₃	—	2	2	no	—
40	C₂×C₉×Dic₃	—	2	2	no	—
41	C₂×C₉×Dic₃	—	2	2	no	—
42	C₂×C₉×Dic₃	—	2	1	no	—
43	C₂×C₉×Dic₃	—	2	1	no	—
44	C₂×C₉×Dic₃	—	2	2	no	—
45	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	complemented
46	C₃×#385	—	3	1	no	—
47	#5210	C₉	1	1	yes	characteristic, direct product factor
48	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₃²×C₄	—	2	2	no	—
50	C₂²×C₃²×C₄	—	2	4	no	—
51	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
52	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
55	C₂⁴×C₉	—	2	1	no	—
56	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
57	C₃×#217	—	2	2	no	—
58	C₃×#217	C₃×C₄	1	4	yes	—
59	C₃×Dic₃⋊C₄	—	2	4	no	—
60	C₂²×C₄×C₉	—	2	4	no	—
61	C₂²×C₄×C₉	—	2	8	no	—
62	C₂²×C₄×C₉	—	2	2	no	—
63	C₂²×C₄×C₉	—	2	2	no	—
64	C₂²×C₄×C₉	—	2	4	no	—
65	C₂²×C₄×C₉	—	3	2	no	—
66	C₂²×C₄×C₉	—	3	1	no	—
67	C₂²×C₄×C₉	—	3	1	no	—
68	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
69	C₉×C₄⋊C₄	—	6	4	no	—
70	C₉×C₂²⋊C₄	—	3	4	no	—
71	C₉×C₂²⋊C₄	—	6	2	no	—
72	C₂²×C₃×C₉	—	2	4	no	—
73	C₂²×C₃×C₉	—	2	2	no	—
74	C₂²×C₃×C₉	—	2	4	no	—
75	C₂²×C₃×C₉	—	2	2	no	—
76	C₂²×C₃×C₉	C₄⋊C₄	1	4	yes	complemented
77	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
80	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₃×C₉	#41	1	2	yes	—
82	C₃×C₄×C₉	—	2	4	no	—
83	C₉×Dic₃	—	2	4	no	—
84	C₉×Dic₃	—	4	1	no	—
85	C₉×Dic₃	—	4	1	no	—
86	C₂³×C₃×C₄	—	2	1	no	—
87	C₂³×C₃×C₄	C₂×C₉	1	1	yes	characteristic
88	C₂³×C₃×C₄	C₃×D₃	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	—	3	2	no	—
90	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
91	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
92	C₂×#217	C₂×C₉	1	1	yes	characteristic
93	C₂×#217	C₂×C₉	1	1	yes	characteristic
94	C₂×Dic₃⋊C₄	C₂×C₉	1	2	yes	complemented
95	C₃×#95	—	3	2	no	—
96	C₃⋊#95	C₂×C₉	1	2	yes	complemented
97	C₂³×C₃²	—	2	2	no	—
98	C₂³×C₃²	—	2	2	no	—
99	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
100	C₂³×C₃²	C₃×D₄	1	2	yes	—
101	C₂³×C₃²	C₃×Q₈	1	2	yes	—
102	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
103	C₂×C₃²×C₄	—	2	8	no	—
104	C₂×C₃²×C₄	—	2	2	no	—
105	C₂×C₃²×C₄	—	2	2	no	—
106	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
107	C₂×C₃×Dic₃	—	2	2	no	—
108	C₂×C₃×Dic₃	—	2	2	no	—
109	C₂×C₃×Dic₃	—	2	2	no	—
110	C₂×C₃×Dic₃	—	2	1	no	—
111	C₂×C₃×Dic₃	—	2	1	no	—
112	C₂×C₃×Dic₃	—	2	2	no	—
113	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
114	C₂³×C₉	—	2	4	no	—
115	C₂³×C₉	—	2	4	no	—
116	C₂³×C₉	—	2	2	no	—
117	C₂³×C₉	—	2	2	no	—
118	C₂³×C₉	—	2	2	no	—
119	C₂³×C₉	—	2	2	no	—
120	C₂³×C₉	—	2	2	no	—
121	C₂³×C₉	—	2	1	no	—
122	C₂³×C₉	Dic₆	1	2	yes	—
123	C₂³×C₉	C₄×D₃	1	2	yes	—
124	C₂³×C₉	#67	1	2	yes	—
125	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
126	C₂×C₄×C₉	—	2	16	no	—
127	C₂×C₄×C₉	—	2	8	no	—
128	C₂×C₄×C₉	—	2	4	no	—
129	C₂×C₄×C₉	—	2	4	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	4	no	—
133	C₂×C₄×C₉	—	3	4	no	—
134	C₂×C₄×C₉	—	6	2	no	—
135	C₂×C₄×C₉	—	6	2	no	—
136	C₂×C₄×C₉	—	6	2	no	—
137	C₂×C₄×C₉	—	6	1	no	—
138	C₂×C₄×C₉	—	6	1	no	—
139	C₂×C₄×C₉	—	6	2	no	—
140	C₂×C₄×C₉	#67	1	4	yes	—
141	#385	—	3	1	no	Sylow
142	C₂×C₃×C₉	—	2	4	no	—
143	C₂×C₃×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₃×C₉	C₄×D₄	1	2	yes	—
145	C₂×C₃×C₉	#120	1	1	yes	characteristic
146	C₂×C₃×C₉	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₃×C₉	#123	1	1	yes	characteristic
148	C₂⁴×C₃	—	2	1	no	—
149	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
150	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	8	no	—
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	3	2	no	—
159	C₂²×C₃×C₄	—	3	1	no	—
160	C₂²×C₃×C₄	—	3	1	no	—
161	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
162	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
163	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
164	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
165	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
166	C₃×C₄⋊C₄	—	6	4	no	—
167	C₃×C₂²⋊C₄	—	3	4	no	—
168	C₃×C₂²⋊C₄	—	6	2	no	—
169	#217	—	2	2	no	—
170	#217	C₄×C₉	1	4	yes	complemented
171	Dic₃⋊C₄	—	2	4	no	—
172	C₂²×C₃²	—	2	4	no	—
173	C₂²×C₃²	—	2	2	no	—
174	C₂²×C₃²	—	2	4	no	—
175	C₂²×C₃²	—	2	2	no	—
176	C₂²×C₃²	C₃×C₄⋊C₄	1	4	yes	—
177	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
178	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
179	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
180	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
181	C₂²×C₃²	C₃×#41	1	2	yes	—
182	C₃²×C₄	—	2	4	no	—
183	C₃×Dic₃	—	2	4	no	—
184	C₃×Dic₃	—	4	1	no	—
185	C₃×Dic₃	—	4	1	no	—
186	C₂²×C₉	—	2	4	no	—
187	C₂²×C₉	—	2	8	no	—
188	C₂²×C₉	—	2	8	no	—
189	C₂²×C₉	—	2	4	no	—
190	C₂²×C₉	—	2	4	no	—
191	C₂²×C₉	—	2	4	no	—
192	C₂²×C₉	—	2	2	no	—
193	C₂²×C₉	—	2	2	no	—
194	C₂²×C₉	—	2	4	no	—
195	C₂²×C₉	—	2	1	no	—
196	C₂²×C₉	—	2	1	no	—
197	C₂²×C₉	—	2	2	no	—
198	C₂²×C₉	—	2	1	no	—
199	C₂²×C₉	—	2	2	no	—
200	C₂²×C₉	Dic₃⋊C₄	1	4	yes	complemented
201	C₂²×C₉	C₂×Dic₆	1	1	yes	characteristic
202	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
203	C₂²×C₉	#235	1	2	yes	—
204	C₂²×C₉	C₂×#67	1	1	yes	characteristic
205	C₂²×C₉	C₂×#67	1	2	yes	—
206	C₄×C₉	—	2	8	no	—
207	C₄×C₉	—	2	4	no	—
208	C₄×C₉	—	6	4	no	—
209	C₄×C₉	—	12	1	no	—
210	C₄×C₉	—	12	1	no	—
211	C₂³×C₄	D₃×C₉	1	1	yes	characteristic
212	C₂×C₄⋊C₄	—	3	2	no	—
213	C₂×C₂²⋊C₄	—	3	1	no	—
214	C₂×C₂²⋊C₄	—	3	1	no	—
215	#95	—	3	2	no	—
216	C₃×C₉	#385	1	1	yes	characteristic, complemented, Sylow
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	2	no	—
220	C₂³×C₃	—	2	2	no	—
221	C₂³×C₃	—	2	2	no	—
222	C₂³×C₃	—	2	2	no	—
223	C₂³×C₃	—	2	2	no	—
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	—	2	1	no	—
227	C₂³×C₃	C₂×C₄×C₉	1	2	yes	—
228	C₂³×C₃	D₄×C₉	1	2	yes	—
229	C₂³×C₃	Q₈×C₉	1	2	yes	—
230	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
231	C₂³×C₃	C₃×Dic₆	1	2	yes	—
232	C₂³×C₃	C₃×C₄×D₃	1	2	yes	—
233	C₂³×C₃	C₃×#67	1	2	yes	—
234	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	2	16	no	—
237	C₂×C₃×C₄	—	2	8	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	3	4	no	—
246	C₂×C₃×C₄	—	6	2	no	—
247	C₂×C₃×C₄	—	6	2	no	—
248	C₂×C₃×C₄	—	6	2	no	—
249	C₂×C₃×C₄	—	6	1	no	—
250	C₂×C₃×C₄	—	6	1	no	—
251	C₂×C₃×C₄	—	6	2	no	—
252	C₂×C₃×C₄	D₄×C₉	1	4	yes	—
253	C₂×C₃×C₄	C₃×#67	1	4	yes	—
254	C₂×Dic₃	—	2	2	no	—
255	C₂×Dic₃	—	2	2	no	—
256	C₂×Dic₃	—	2	2	no	—
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	—	2	1	no	—
259	C₂×Dic₃	—	2	2	no	—
260	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	complemented
261	C₂×C₃²	—	2	4	no	—
262	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
263	C₂×C₃²	C₃×C₄×D₄	1	2	yes	—
264	C₂×C₃²	C₃×#120	1	1	yes	characteristic
265	C₂×C₃²	C₃×C₂²⋊Q₈	1	2	yes	—
266	C₂×C₃²	C₃×#123	1	1	yes	characteristic
267	C₂×C₉	—	2	8	no	—
268	C₂×C₉	—	2	4	no	—
269	C₂×C₉	—	2	1	no	—
270	C₂×C₉	—	2	2	no	—
271	C₂×C₉	—	2	2	no	—
272	C₂×C₉	—	2	1	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	C₂×Dic₃⋊C₄	1	1	yes	characteristic
275	C₂×C₉	#924	1	2	yes	—
276	C₂×C₉	C₄×#67	1	2	yes	—
277	C₂×C₉	#929	1	1	yes	characteristic
278	C₂×C₉	#953	1	1	yes	characteristic
279	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	3	2	no	—
283	C₂²×C₄	—	3	1	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
286	C₄⋊C₄	—	6	4	no	—
287	C₂²⋊C₄	—	3	4	no	—
288	C₂²⋊C₄	—	6	2	no	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	2	8	no	—
291	C₂²×C₃	—	2	8	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	4	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	4	no	—
298	C₂²×C₃	—	2	4	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	4	no	—
307	C₂²×C₃	C₉×C₄⋊C₄	1	4	yes	complemented
308	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
309	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
310	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
311	C₂²×C₃	C₂×Q₈×C₉	1	1	yes	characteristic
312	C₂²×C₃	C₉×#41	1	2	yes	—
313	C₂²×C₃	C₃×Dic₃⋊C₄	1	4	yes	—
314	C₂²×C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
316	C₂²×C₃	C₃×#235	1	2	yes	—
317	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
319	C₃×C₄	—	2	8	no	—
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	2	4	no	—
322	C₃×C₄	—	6	4	no	—
323	C₃×C₄	—	12	1	no	—
324	C₃×C₄	—	12	1	no	—
325	Dic₃	—	2	4	no	—
326	Dic₃	—	4	1	no	—
327	Dic₃	—	4	1	no	—
328	C₃²	C₃×#385	1	1	yes	characteristic
329	C₉	—	2	1	no	—
330	C₉	#5210	1	1	yes	characteristic, direct product factor
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	C₉×Dic₆	1	2	yes	—
334	C₂³	C₄×D₃×C₉	1	2	yes	—
335	C₂³	C₉×#67	1	2	yes	—
336	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	3	4	no	—
341	C₂×C₄	—	6	2	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	—	6	2	no	—
344	C₂×C₄	—	6	1	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	6	2	no	—
347	C₂×C₄	C₉×#67	1	4	yes	—
348	C₂×C₃	—	2	8	no	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	—	2	4	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	2	2	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	1	no	—
356	C₂×C₃	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₃	C₄×D₄×C₉	1	2	yes	—
358	C₂×C₃	C₉×#120	1	1	yes	characteristic
359	C₂×C₃	C₉×C₂²⋊Q₈	1	2	yes	—
360	C₂×C₃	C₉×#123	1	1	yes	characteristic
361	C₂×C₃	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
362	C₂×C₃	C₃×#924	1	2	yes	—
363	C₂×C₃	C₃×C₄×#67	1	2	yes	—
364	C₂×C₃	C₃×#929	1	1	yes	characteristic
365	C₂×C₃	C₃×#953	1	1	yes	characteristic
366	C₂²	—	2	4	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	C₉×Dic₃⋊C₄	1	4	yes	complemented
371	C₂²	C₂×C₉×Dic₆	1	1	yes	characteristic
372	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
373	C₂²	C₉×#235	1	2	yes	—
374	C₂²	C₂×C₉×#67	1	1	yes	characteristic
375	C₂²	C₂×C₉×#67	1	2	yes	—
376	C₄	—	2	4	no	—
377	C₄	—	6	4	no	—
378	C₄	—	12	1	no	—
379	C₄	—	12	1	no	—
380	C₃	—	2	1	no	—
381	C₃	C₉×#385	1	1	yes	characteristic, complemented
382	C₃	C₃×#5210	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	C₂×C₉×Dic₃⋊C₄	1	1	yes	characteristic
385	C₂	C₉×#924	1	2	yes	—
386	C₂	C₄×C₉×#67	1	2	yes	—
387	C₂	C₉×#929	1	1	yes	characteristic
388	C₂	C₉×#953	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂³×C₃×C₄×C₉	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂⁴×C₃²	C₂²×C₃
hypercenter	C₂³×C₄×C₉	D₃
hypocenter	C₃	C₉×#385
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂³×C₄×C₉

Complements

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

N	H ≅ G/N	type
4. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
5. C₉×C₃⋊#95	C₂	semidirect
16. C₉×#217	C₄	semidirect
45. C₂×C₉×Dic₃	C₂×C₄	semidirect
47. #5210	C₉	direct (N × H)
76. C₂²×C₃×C₉	C₄⋊C₄	semidirect
94. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
96. C₃⋊#95	C₂×C₉	semidirect
170. #217	C₄×C₉	semidirect
200. C₂²×C₉	Dic₃⋊C₄	semidirect
216. C₃×C₉	#385	semidirect
260. C₂×Dic₃	C₂×C₄×C₉	semidirect
307. C₂²×C₃	C₉×C₄⋊C₄	semidirect
330. C₉	#5210	direct (N × H)
370. C₂²	C₉×Dic₃⋊C₄	semidirect
381. C₃	C₉×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×C₉	2
C₂×C₉×#217	2
C₂×C₉×Dic₃⋊C₄	2
C₉×C₃⋊#95	2
C₃×#5210	3
C₉×#385	3

Subgroups — C9×#5210 #13143519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5210 #13143519