Subgroups — C₉×#4529 #13135564

Order 1728.

434 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#4529	C₃	1	1	yes	maximal, characteristic
5	C₉×#340	—	3	1	no	maximal
6	C₂²×C₃×C₄×C₉	—	2	1	no	—
7	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₉×Dic₃	—	2	1	no	—
9	C₃×C₉×C₄⋊C₄	—	2	1	no	—
10	C₃×C₉×C₄⋊C₄	C₄	1	2	yes	complemented
11	C₉×C₄⋊Dic₃	—	2	1	no	—
12	C₉×C₄⋊Dic₃	C₄	1	2	yes	complemented
13	C₂×C₉×C₃⋊C₈	—	2	1	no	—
14	C₂×C₉×C₃⋊C₈	—	2	1	no	—
15	C₂×C₉×C₃⋊C₈	C₄	1	2	yes	complemented
16	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
17	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
18	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₈×C₉	—	3	1	no	—
20	C₂×C₉×C₄⋊C₄	—	2	1	no	—
21	C₂×C₉×C₄⋊C₄	—	3	1	no	—
22	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic
23	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
24	C₂×C₃×C₄×C₉	—	2	2	no	—
25	C₂×C₃×C₄×C₉	—	4	1	no	—
26	C₂×C₃×C₄×C₉	—	4	1	no	—
27	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
31	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
32	C₂×C₃×C₄×C₉	Q₈	1	1	yes	characteristic
33	C₂×C₉×Dic₃	—	2	2	no	—
34	C₂×C₉×Dic₃	—	4	1	no	—
35	C₂×C₉×Dic₃	—	4	1	no	—
36	C₉×C₃⋊C₈	—	2	2	no	—
37	C₃×#340	—	3	1	no	—
38	#4529	C₉	1	1	yes	characteristic, direct product factor
39	C₂²×C₃²×C₄	—	2	1	no	—
40	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	—	2	1	no	—
42	C₃²×C₄⋊C₄	—	2	1	no	—
43	C₃²×C₄⋊C₄	C₃×C₄	1	2	yes	—
44	C₃×C₄⋊Dic₃	—	2	1	no	—
45	C₃×C₄⋊Dic₃	C₃×C₄	1	2	yes	—
46	C₂×C₃×C₃⋊C₈	—	2	1	no	—
47	C₂×C₃×C₃⋊C₈	—	2	1	no	—
48	C₂×C₃×C₃⋊C₈	C₃×C₄	1	2	yes	—
49	C₂²×C₄×C₉	—	2	1	no	—
50	C₂²×C₄×C₉	—	2	2	no	—
51	C₂²×C₄×C₉	—	2	1	no	—
52	C₂²×C₄×C₉	—	6	1	no	—
53	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
54	C₂×C₈×C₉	—	3	2	no	—
55	C₂×C₈×C₉	—	6	1	no	—
56	C₂×C₈×C₉	—	6	1	no	—
57	C₉×C₄⋊C₄	—	2	2	no	—
58	C₉×C₄⋊C₄	—	2	2	no	—
59	C₉×C₄⋊C₄	—	2	1	no	—
60	C₉×C₄⋊C₄	—	3	2	no	—
61	C₉×C₄⋊C₄	—	6	1	no	—
62	C₉×C₄⋊C₄	Dic₃	1	2	yes	complemented
63	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₃×C₉	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₃×C₉	D₈	1	1	yes	characteristic
67	C₂²×C₃×C₉	SD₁₆	1	1	yes	characteristic
68	C₂²×C₃×C₉	SD₁₆	1	1	yes	characteristic
69	C₂²×C₃×C₉	Q₁₆	1	1	yes	characteristic
70	C₃×C₄×C₉	—	4	2	no	—
71	C₃×C₄×C₉	C₄²	1	1	yes	characteristic
72	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₃×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
74	C₃×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
75	C₉×Dic₃	—	4	2	no	—
76	C₂²×C₃×C₈	—	3	1	no	—
77	C₂×C₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₃×C₄⋊C₄	—	3	1	no	—
79	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
80	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
81	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic
82	C₂²×C₃⋊C₈	C₂×C₉	1	1	yes	characteristic
83	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
84	C₂×C₃²×C₄	—	2	2	no	—
85	C₂×C₃²×C₄	—	4	1	no	—
86	C₂×C₃²×C₄	—	4	1	no	—
87	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
88	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
89	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
90	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
91	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
92	C₂×C₃²×C₄	C₃×Q₈	1	1	yes	characteristic
93	C₂×C₃×Dic₃	—	2	2	no	—
94	C₂×C₃×Dic₃	—	4	1	no	—
95	C₂×C₃×Dic₃	—	4	1	no	—
96	C₂³×C₉	—	2	1	no	—
97	C₂³×C₉	#67	1	1	yes	characteristic
98	C₃×C₃⋊C₈	—	2	2	no	—
99	C₂×C₄×C₉	—	2	4	no	—
100	C₂×C₄×C₉	—	2	2	no	—
101	C₂×C₄×C₉	—	2	1	no	—
102	C₂×C₄×C₉	—	2	1	no	—
103	C₂×C₄×C₉	—	2	1	no	—
104	C₂×C₄×C₉	—	2	1	no	—
105	C₂×C₄×C₉	—	2	1	no	—
106	C₂×C₄×C₉	—	2	1	no	—
107	C₂×C₄×C₉	—	4	2	no	—
108	C₂×C₄×C₉	—	4	2	no	—
109	C₂×C₄×C₉	—	4	1	no	—
110	C₂×C₄×C₉	—	4	1	no	—
111	C₂×C₄×C₉	—	6	2	no	—
112	C₂×C₄×C₉	—	12	1	no	—
113	C₂×C₄×C₉	—	12	1	no	—
114	C₂×C₄×C₉	Dic₆	1	1	yes	characteristic
115	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
116	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
117	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
118	C₂×C₄×C₉	C₂×Dic₃	1	1	yes	characteristic
119	C₂×C₄×C₉	#67	1	1	yes	characteristic
120	C₈×C₉	—	6	2	no	—
121	#340	—	3	1	no	Sylow
122	C₂×C₃×C₉	#95	1	1	yes	characteristic
123	C₂×C₃×C₉	#102	1	1	yes	characteristic
124	C₂×C₃×C₉	#102	1	1	yes	characteristic
125	C₂×C₃×C₉	#103	1	1	yes	characteristic
126	C₂×C₃×C₉	#103	1	1	yes	characteristic
127	C₂×C₃×C₉	#106	1	1	yes	characteristic
128	C₂×C₃×C₉	#107	1	1	yes	characteristic
129	C₂²×C₃×C₄	—	2	2	no	—
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	2	1	no	—
132	C₂²×C₃×C₄	—	2	1	no	—
133	C₂²×C₃×C₄	—	6	1	no	—
134	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
136	C₂²×Dic₃	—	2	1	no	—
137	C₂×C₃×C₈	—	3	2	no	—
138	C₂×C₃×C₈	—	6	1	no	—
139	C₂×C₃×C₈	—	6	1	no	—
140	C₃×C₄⋊C₄	—	2	2	no	—
141	C₃×C₄⋊C₄	—	2	1	no	—
142	C₃×C₄⋊C₄	—	2	1	no	—
143	C₃×C₄⋊C₄	—	2	2	no	—
144	C₃×C₄⋊C₄	—	3	2	no	—
145	C₃×C₄⋊C₄	—	6	1	no	—
146	C₃×C₄⋊C₄	C₄×C₉	1	2	yes	complemented
147	C₃×C₄⋊C₄	C₃×Dic₃	1	2	yes	—
148	C₄⋊Dic₃	—	2	1	no	—
149	C₄⋊Dic₃	C₄×C₉	1	2	yes	complemented
150	C₂×C₃⋊C₈	—	2	1	no	—
151	C₂×C₃⋊C₈	—	2	1	no	—
152	C₂×C₃⋊C₈	C₄×C₉	1	2	yes	complemented
153	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₃²	C₃×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×C₃²	C₃×D₈	1	1	yes	characteristic
157	C₂²×C₃²	C₃×SD₁₆	1	1	yes	characteristic
158	C₂²×C₃²	C₃×SD₁₆	1	1	yes	characteristic
159	C₂²×C₃²	C₃×Q₁₆	1	1	yes	characteristic
160	C₃²×C₄	—	4	2	no	—
161	C₃²×C₄	C₃×C₄²	1	1	yes	characteristic
162	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
163	C₃²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
164	C₃²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
165	C₃×Dic₃	—	4	2	no	—
166	C₂²×C₉	—	2	1	no	—
167	C₂²×C₉	—	2	1	no	—
168	C₂²×C₉	—	2	1	no	—
169	C₂²×C₉	—	2	1	no	—
170	C₂²×C₉	—	2	1	no	—
171	C₂²×C₉	—	2	1	no	—
172	C₂²×C₉	—	2	1	no	—
173	C₂²×C₉	Dic₃⋊C₄	1	1	yes	characteristic
174	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
175	C₂²×C₉	#213	1	1	yes	characteristic
176	C₂²×C₉	#214	1	1	yes	characteristic
177	C₂²×C₉	#215	1	1	yes	characteristic
178	C₂²×C₉	#216	1	1	yes	characteristic
179	C₂²×C₉	#217	1	1	yes	characteristic
180	C₄×C₉	—	2	1	no	—
181	C₄×C₉	—	2	1	no	—
182	C₄×C₉	—	2	1	no	—
183	C₄×C₉	—	2	1	no	—
184	C₄×C₉	—	4	4	no	—
185	C₄×C₉	—	4	2	no	—
186	C₄×C₉	—	12	2	no	—
187	C₄×C₉	C₄×Dic₃	1	1	yes	characteristic
188	C₄×C₉	Dic₃⋊C₄	1	1	yes	characteristic
189	C₄×C₉	C₄⋊Dic₃	1	1	yes	characteristic
190	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
191	C₂²×C₈	—	3	1	no	—
192	C₂×C₄⋊C₄	—	3	1	no	—
193	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic
194	C₃×C₉	#340	1	1	yes	characteristic, complemented, Sylow
195	C₂³×C₃	—	2	1	no	—
196	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
197	C₂³×C₃	C₃×#67	1	1	yes	characteristic
198	C₂×C₃×C₄	—	2	4	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	2	2	no	—
201	C₂×C₃×C₄	—	2	1	no	—
202	C₂×C₃×C₄	—	2	1	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	2	1	no	—
205	C₂×C₃×C₄	—	2	1	no	—
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	4	2	no	—
208	C₂×C₃×C₄	—	4	2	no	—
209	C₂×C₃×C₄	—	4	1	no	—
210	C₂×C₃×C₄	—	4	1	no	—
211	C₂×C₃×C₄	—	4	1	no	—
212	C₂×C₃×C₄	—	4	1	no	—
213	C₂×C₃×C₄	—	6	2	no	—
214	C₂×C₃×C₄	—	12	1	no	—
215	C₂×C₃×C₄	—	12	1	no	—
216	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
219	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
220	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
221	C₂×C₃×C₄	Q₈×C₉	1	1	yes	characteristic
222	C₂×C₃×C₄	C₃×Dic₆	1	1	yes	characteristic
223	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
224	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
225	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
227	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
228	C₂×Dic₃	—	2	2	no	—
229	C₂×Dic₃	—	4	1	no	—
230	C₂×Dic₃	—	4	1	no	—
231	C₃×C₈	—	6	2	no	—
232	C₃⋊C₈	—	2	2	no	—
233	C₂×C₃²	C₃×#95	1	1	yes	characteristic
234	C₂×C₃²	C₃×#102	1	1	yes	characteristic
235	C₂×C₃²	C₃×#102	1	1	yes	characteristic
236	C₂×C₃²	C₃×#103	1	1	yes	characteristic
237	C₂×C₃²	C₃×#103	1	1	yes	characteristic
238	C₂×C₃²	C₃×#106	1	1	yes	characteristic
239	C₂×C₃²	C₃×#107	1	1	yes	characteristic
240	C₂×C₉	—	2	1	no	—
241	C₂×C₉	—	2	1	no	—
242	C₂×C₉	—	2	1	no	—
243	C₂×C₉	—	2	1	no	—
244	C₂×C₉	—	2	1	no	—
245	C₂×C₉	—	2	1	no	—
246	C₂×C₉	—	2	1	no	—
247	C₂×C₉	#807	1	1	yes	characteristic
248	C₂×C₉	#808	1	1	yes	characteristic
249	C₂×C₉	#809	1	1	yes	characteristic
250	C₂×C₉	#810	1	1	yes	characteristic
251	C₂×C₉	C₃⋊#95	1	1	yes	characteristic
252	C₂×C₉	#832	1	1	yes	characteristic
253	C₂×C₉	#835	1	1	yes	characteristic
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	6	1	no	—
256	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
257	C₂×C₈	—	3	2	no	—
258	C₂×C₈	—	6	1	no	—
259	C₂×C₈	—	6	1	no	—
260	C₄⋊C₄	—	2	1	no	—
261	C₄⋊C₄	—	3	2	no	—
262	C₄⋊C₄	—	6	1	no	—
263	C₄⋊C₄	C₉×Dic₃	1	2	yes	complemented
264	C₂²×C₃	—	2	1	no	—
265	C₂²×C₃	—	2	1	no	—
266	C₂²×C₃	—	2	1	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₃	C₉×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₃	C₉×D₈	1	1	yes	characteristic
275	C₂²×C₃	C₉×SD₁₆	1	1	yes	characteristic
276	C₂²×C₃	C₉×SD₁₆	1	1	yes	characteristic
277	C₂²×C₃	C₉×Q₁₆	1	1	yes	characteristic
278	C₂²×C₃	C₃×Dic₃⋊C₄	1	1	yes	characteristic
279	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
280	C₂²×C₃	C₃×#213	1	1	yes	characteristic
281	C₂²×C₃	C₃×#214	1	1	yes	characteristic
282	C₂²×C₃	C₃×#215	1	1	yes	characteristic
283	C₂²×C₃	C₃×#216	1	1	yes	characteristic
284	C₂²×C₃	C₃×#217	1	1	yes	characteristic
285	C₃×C₄	—	2	1	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	4	4	no	—
290	C₃×C₄	—	4	2	no	—
291	C₃×C₄	—	4	2	no	—
292	C₃×C₄	—	12	2	no	—
293	C₃×C₄	C₄²×C₉	1	1	yes	characteristic
294	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
295	C₃×C₄	C₉×C₄⋊C₄	1	1	yes	characteristic
296	C₃×C₄	C₉×C₄⋊C₄	1	1	yes	characteristic
297	C₃×C₄	C₃×C₄×Dic₃	1	1	yes	characteristic
298	C₃×C₄	C₃×Dic₃⋊C₄	1	1	yes	characteristic
299	C₃×C₄	C₃×C₄⋊Dic₃	1	1	yes	characteristic
300	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
301	Dic₃	—	4	2	no	—
302	C₃²	C₃×#340	1	1	yes	characteristic
303	C₉	—	2	1	no	—
304	C₉	#4529	1	1	yes	characteristic, direct product factor
305	C₂³	C₉×#67	1	1	yes	characteristic
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	6	2	no	—
310	C₂×C₄	—	12	1	no	—
311	C₂×C₄	—	12	1	no	—
312	C₂×C₄	C₉×Dic₆	1	1	yes	characteristic
313	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
314	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
315	C₂×C₄	C₉×D₁₂	1	1	yes	characteristic
316	C₂×C₄	C₂×C₉×Dic₃	1	1	yes	characteristic
317	C₂×C₄	C₉×#67	1	1	yes	characteristic
318	C₈	—	6	2	no	—
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	—	2	1	no	—
322	C₂×C₃	—	2	1	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	2	1	no	—
326	C₂×C₃	C₉×#95	1	1	yes	characteristic
327	C₂×C₃	C₉×#102	1	1	yes	characteristic
328	C₂×C₃	C₉×#102	1	1	yes	characteristic
329	C₂×C₃	C₉×#103	1	1	yes	characteristic
330	C₂×C₃	C₉×#103	1	1	yes	characteristic
331	C₂×C₃	C₉×#106	1	1	yes	characteristic
332	C₂×C₃	C₉×#107	1	1	yes	characteristic
333	C₂×C₃	C₃×#807	1	1	yes	characteristic
334	C₂×C₃	C₃×#808	1	1	yes	characteristic
335	C₂×C₃	C₃×#809	1	1	yes	characteristic
336	C₂×C₃	C₃×#810	1	1	yes	characteristic
337	C₂×C₃	C₃×C₃⋊#95	1	1	yes	characteristic
338	C₂×C₃	C₃×#832	1	1	yes	characteristic
339	C₂×C₃	C₃×#835	1	1	yes	characteristic
340	C₂²	C₉×Dic₃⋊C₄	1	1	yes	characteristic
341	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
342	C₂²	C₉×#213	1	1	yes	characteristic
343	C₂²	C₉×#214	1	1	yes	characteristic
344	C₂²	C₉×#215	1	1	yes	characteristic
345	C₂²	C₉×#216	1	1	yes	characteristic
346	C₂²	C₉×#217	1	1	yes	characteristic
347	C₄	—	4	2	no	—
348	C₄	—	12	2	no	—
349	C₄	C₄×C₉×Dic₃	1	1	yes	characteristic
350	C₄	C₉×Dic₃⋊C₄	1	1	yes	characteristic
351	C₄	C₉×C₄⋊Dic₃	1	1	yes	characteristic
352	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
353	C₃	—	2	1	no	—
354	C₃	C₉×#340	1	1	yes	characteristic, complemented
355	C₃	C₃×#4529	1	1	yes	characteristic
356	C₂	C₉×#807	1	1	yes	characteristic
357	C₂	C₉×#808	1	1	yes	characteristic
358	C₂	C₉×#809	1	1	yes	characteristic
359	C₂	C₉×#810	1	1	yes	characteristic
360	C₂	C₉×C₃⋊#95	1	1	yes	characteristic
361	C₂	C₉×#832	1	1	yes	characteristic
362	C₂	C₉×#835	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	#67
commutator	C₃×C₄	C₄²×C₉
Frattini	C₂²×C₃×C₄	C₂×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃²	C₃×D₄
cosocle	C₂²×C₃²×C₄	C₂²×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₉×#340
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂²×C₄×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
10. C₃×C₉×C₄⋊C₄	C₄	semidirect
12. C₉×C₄⋊Dic₃	C₄	semidirect
15. C₂×C₉×C₃⋊C₈	C₄	semidirect
38. #4529	C₉	direct (N × H)
62. C₉×C₄⋊C₄	Dic₃	semidirect
146. C₃×C₄⋊C₄	C₄×C₉	semidirect
149. C₄⋊Dic₃	C₄×C₉	semidirect
152. C₂×C₃⋊C₈	C₄×C₉	semidirect
194. C₃×C₉	#340	semidirect
263. C₄⋊C₄	C₉×Dic₃	semidirect
304. C₉	#4529	direct (N × H)
354. C₃	C₉×#340	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂²×C₉×C₃⋊C₈	2
C₃×#4529	3
C₉×#340	3

Subgroups — C9×#4529 #13135564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4529 #13135564