Subgroups — C₉×#4928 #13142395

Order 1728.

618 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₉×C₃⋊#95	C₂	1	2	yes	maximal
6	C₃×#4928	C₃	1	1	yes	maximal, characteristic
7	C₉×#389	—	3	1	no	maximal
8	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
12	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
13	C₃×C₄²×C₉	—	2	2	no	—
14	C₉×C₄⋊Dic₃	—	2	2	no	—
15	C₉×C₄⋊Dic₃	C₄	1	4	yes	complemented
16	C₉×Dic₃⋊C₄	—	2	4	no	—
17	C₂×C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	2	yes	—
21	C₃×C₃⋊#95	C₂×C₃	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	—	3	1	no	—
23	C₂×C₉×C₄⋊C₄	—	3	2	no	—
24	C₂×C₉×C₄⋊C₄	—	3	1	no	—
25	C₂×C₄²×C₉	—	2	1	no	—
26	C₂×C₄²×C₉	D₃	1	1	yes	characteristic
27	C₉×#95	—	3	2	no	—
28	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
29	C₂×C₃×C₄×C₉	—	2	1	no	—
30	C₂×C₃×C₄×C₉	—	2	1	no	—
31	C₂×C₃×C₄×C₉	—	2	1	no	—
32	C₂×C₃×C₄×C₉	—	2	1	no	—
33	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
35	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
36	C₂×C₃×C₄×C₉	Q₈	1	2	yes	—
37	C₂×C₃×C₄×C₉	Q₈	1	2	yes	—
38	C₂×C₉×Dic₃	—	2	2	no	—
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	2	no	—
43	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	—
44	C₃×#389	—	3	1	no	—
45	#4928	C₉	1	1	yes	characteristic, direct product factor
46	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
47	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
50	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
51	C₃²×C₄²	—	2	2	no	—
52	C₃×C₄⋊Dic₃	—	2	2	no	—
53	C₃×C₄⋊Dic₃	C₃×C₄	1	4	yes	—
54	C₃×Dic₃⋊C₄	—	2	4	no	—
55	C₂²×C₄×C₉	—	2	1	no	—
56	C₂²×C₄×C₉	—	2	1	no	—
57	C₂²×C₄×C₉	—	2	1	no	—
58	C₂²×C₄×C₉	—	3	2	no	—
59	C₂²×C₄×C₉	—	3	2	no	—
60	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
63	C₉×C₄⋊C₄	—	3	4	no	—
64	C₉×C₄⋊C₄	—	6	4	no	—
65	C₉×C₄⋊C₄	—	6	2	no	—
66	C₄²×C₉	—	2	4	no	—
67	C₄²×C₉	—	2	2	no	—
68	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₃×C₉	#41	1	1	yes	characteristic
74	C₂²×C₃×C₉	#41	1	1	yes	characteristic
75	C₃×C₄×C₉	—	2	2	no	—
76	C₃×C₄×C₉	—	2	2	no	—
77	C₃×C₄×C₉	C₄⋊C₄	1	4	yes	complemented
78	C₉×Dic₃	—	2	4	no	—
79	C₉×Dic₃	—	4	2	no	—
80	C₂×C₃×C₄⋊C₄	—	3	1	no	—
81	C₂×C₃×C₄⋊C₄	—	3	2	no	—
82	C₂×C₃×C₄⋊C₄	—	3	1	no	—
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	C₂×C₉	1	1	yes	characteristic
85	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
86	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic
87	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic
88	C₂×Dic₃⋊C₄	C₂×C₉	1	2	yes	—
89	C₃×#95	—	3	2	no	—
90	C₃⋊#95	C₂×C₉	1	2	yes	—
91	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
92	C₂×C₃²×C₄	—	2	1	no	—
93	C₂×C₃²×C₄	—	2	1	no	—
94	C₂×C₃²×C₄	—	2	1	no	—
95	C₂×C₃²×C₄	—	2	1	no	—
96	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
97	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
98	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
99	C₂×C₃²×C₄	C₃×Q₈	1	2	yes	—
100	C₂×C₃²×C₄	C₃×Q₈	1	2	yes	—
101	C₂×C₃×Dic₃	—	2	2	no	—
102	C₂×C₃×Dic₃	—	2	2	no	—
103	C₂×C₃×Dic₃	—	2	2	no	—
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₂×C₃×Dic₃	—	2	2	no	—
106	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
107	C₂³×C₉	—	2	1	no	—
108	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
109	C₂×C₄×C₉	—	2	2	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	2	no	—
113	C₂×C₄×C₉	—	2	1	no	—
114	C₂×C₄×C₉	—	2	1	no	—
115	C₂×C₄×C₉	—	2	1	no	—
116	C₂×C₄×C₉	—	2	1	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	3	4	no	—
123	C₂×C₄×C₉	—	6	2	no	—
124	C₂×C₄×C₉	—	6	2	no	—
125	C₂×C₄×C₉	—	6	2	no	—
126	C₂×C₄×C₉	—	6	2	no	—
127	C₂×C₄×C₉	—	6	2	no	—
128	C₂×C₄×C₉	Dic₆	1	2	yes	—
129	C₂×C₄×C₉	Dic₆	1	2	yes	—
130	C₂×C₄×C₉	C₄×D₃	1	2	yes	—
131	C₂×C₄×C₉	D₁₂	1	2	yes	—
132	C₂×C₄×C₉	#67	1	2	yes	—
133	#389	—	3	1	no	Sylow
134	C₂×C₃×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₃×C₉	C₄×Q₈	1	1	yes	characteristic
137	C₂×C₃×C₉	#121	1	1	yes	characteristic
138	C₂×C₃×C₉	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₃×C₉	#125	1	1	yes	characteristic
140	C₂×C₃×C₉	C₄⋊Q₈	1	1	yes	characteristic
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	3	2	no	—
145	C₂²×C₃×C₄	—	3	2	no	—
146	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
152	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
153	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
154	C₃×C₄⋊C₄	—	3	4	no	—
155	C₃×C₄⋊C₄	—	6	4	no	—
156	C₃×C₄⋊C₄	—	6	2	no	—
157	C₃×C₄²	—	2	4	no	—
158	C₃×C₄²	—	2	2	no	—
159	C₃×C₄²	—	2	2	no	—
160	C₄⋊Dic₃	—	2	2	no	—
161	C₄⋊Dic₃	C₄×C₉	1	4	yes	complemented
162	Dic₃⋊C₄	—	2	4	no	—
163	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
164	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
165	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
166	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
167	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
168	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
169	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
170	C₃²×C₄	—	2	2	no	—
171	C₃²×C₄	—	2	2	no	—
172	C₃²×C₄	C₃×C₄⋊C₄	1	4	yes	—
173	C₃×Dic₃	—	2	4	no	—
174	C₃×Dic₃	—	4	2	no	—
175	C₂²×C₉	—	2	1	no	—
176	C₂²×C₉	—	2	1	no	—
177	C₂²×C₉	—	2	1	no	—
178	C₂²×C₉	—	2	1	no	—
179	C₂²×C₉	—	2	1	no	—
180	C₂²×C₉	—	2	1	no	—
181	C₂²×C₉	—	2	1	no	—
182	C₂²×C₉	C₂×Dic₆	1	1	yes	characteristic
183	C₂²×C₉	C₂×Dic₆	1	1	yes	characteristic
184	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
185	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
186	C₂²×C₉	#235	1	1	yes	characteristic
187	C₂²×C₉	#235	1	1	yes	characteristic
188	C₂²×C₉	C₂×#67	1	1	yes	characteristic
189	C₄×C₉	—	2	4	no	—
190	C₄×C₉	—	2	4	no	—
191	C₄×C₉	—	2	2	no	—
192	C₄×C₉	—	2	2	no	—
193	C₄×C₉	—	2	4	no	—
194	C₄×C₉	—	6	4	no	—
195	C₄×C₉	—	12	2	no	—
196	C₄×C₉	Dic₃⋊C₄	1	4	yes	complemented
197	C₂×C₄⋊C₄	—	3	1	no	—
198	C₂×C₄⋊C₄	—	3	2	no	—
199	C₂×C₄⋊C₄	—	3	1	no	—
200	C₂×C₄²	D₃×C₉	1	1	yes	characteristic
201	#95	—	3	2	no	—
202	C₃×C₉	#389	1	1	yes	characteristic, complemented, Sylow
203	C₂³×C₃	—	2	1	no	—
204	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
205	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
206	C₂×C₃×C₄	—	2	2	no	—
207	C₂×C₃×C₄	—	2	2	no	—
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	2	1	no	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	3	4	no	—
224	C₂×C₃×C₄	—	6	2	no	—
225	C₂×C₃×C₄	—	6	2	no	—
226	C₂×C₃×C₄	—	6	2	no	—
227	C₂×C₃×C₄	—	6	2	no	—
228	C₂×C₃×C₄	—	6	2	no	—
229	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
230	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
231	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
232	C₂×C₃×C₄	Q₈×C₉	1	2	yes	—
233	C₂×C₃×C₄	Q₈×C₉	1	2	yes	—
234	C₂×C₃×C₄	C₃×Dic₆	1	2	yes	—
235	C₂×C₃×C₄	C₃×Dic₆	1	2	yes	—
236	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
237	C₂×C₃×C₄	C₃×D₁₂	1	2	yes	—
238	C₂×C₃×C₄	C₃×#67	1	2	yes	—
239	C₂×Dic₃	—	2	2	no	—
240	C₂×Dic₃	—	2	2	no	—
241	C₂×Dic₃	—	2	2	no	—
242	C₂×Dic₃	—	2	2	no	—
243	C₂×Dic₃	—	2	2	no	—
244	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	—
245	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
246	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
247	C₂×C₃²	C₃×C₄×Q₈	1	1	yes	characteristic
248	C₂×C₃²	C₃×#121	1	1	yes	characteristic
249	C₂×C₃²	C₃×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₃²	C₃×#125	1	1	yes	characteristic
251	C₂×C₃²	C₃×C₄⋊Q₈	1	1	yes	characteristic
252	C₂×C₉	—	2	1	no	—
253	C₂×C₉	—	2	1	no	—
254	C₂×C₉	—	2	1	no	—
255	C₂×C₉	—	2	1	no	—
256	C₂×C₉	—	2	1	no	—
257	C₂×C₉	—	2	1	no	—
258	C₂×C₉	—	2	1	no	—
259	C₂×C₉	C₄×Dic₆	1	1	yes	characteristic
260	C₂×C₉	#869	1	1	yes	characteristic
261	C₂×C₉	#870	1	1	yes	characteristic
262	C₂×C₉	C₄×D₁₂	1	1	yes	characteristic
263	C₂×C₉	C₂×Dic₃⋊C₄	1	1	yes	characteristic
264	C₂×C₉	#924	1	1	yes	characteristic
265	C₂×C₉	#930	1	1	yes	characteristic
266	C₂²×C₄	—	3	2	no	—
267	C₂²×C₄	—	3	2	no	—
268	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
271	C₄⋊C₄	—	3	4	no	—
272	C₄⋊C₄	—	6	4	no	—
273	C₄⋊C₄	—	6	2	no	—
274	C₄²	—	2	2	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
283	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
284	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
285	C₂²×C₃	C₂×Q₈×C₉	1	1	yes	characteristic
286	C₂²×C₃	C₂×Q₈×C₉	1	1	yes	characteristic
287	C₂²×C₃	C₉×#41	1	1	yes	characteristic
288	C₂²×C₃	C₉×#41	1	1	yes	characteristic
289	C₂²×C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
290	C₂²×C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
291	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
292	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
293	C₂²×C₃	C₃×#235	1	1	yes	characteristic
294	C₂²×C₃	C₃×#235	1	1	yes	characteristic
295	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	2	no	—
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	6	4	no	—
304	C₃×C₄	—	12	2	no	—
305	C₃×C₄	C₉×C₄⋊C₄	1	4	yes	complemented
306	C₃×C₄	C₃×Dic₃⋊C₄	1	4	yes	—
307	Dic₃	—	2	4	no	—
308	Dic₃	—	4	2	no	—
309	C₃²	C₃×#389	1	1	yes	characteristic
310	C₉	—	2	1	no	—
311	C₉	#4928	1	1	yes	characteristic, direct product factor
312	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	3	4	no	—
318	C₂×C₄	—	6	2	no	—
319	C₂×C₄	—	6	2	no	—
320	C₂×C₄	—	6	2	no	—
321	C₂×C₄	—	6	2	no	—
322	C₂×C₄	—	6	2	no	—
323	C₂×C₄	C₉×Dic₆	1	2	yes	—
324	C₂×C₄	C₉×Dic₆	1	2	yes	—
325	C₂×C₄	C₄×D₃×C₉	1	2	yes	—
326	C₂×C₄	C₉×D₁₂	1	2	yes	—
327	C₂×C₄	C₉×#67	1	2	yes	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	—	2	1	no	—
331	C₂×C₃	—	2	1	no	—
332	C₂×C₃	—	2	1	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
336	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
337	C₂×C₃	C₄×Q₈×C₉	1	1	yes	characteristic
338	C₂×C₃	C₉×#121	1	1	yes	characteristic
339	C₂×C₃	C₉×C₂²⋊Q₈	1	1	yes	characteristic
340	C₂×C₃	C₉×#125	1	1	yes	characteristic
341	C₂×C₃	C₉×C₄⋊Q₈	1	1	yes	characteristic
342	C₂×C₃	C₃×C₄×Dic₆	1	1	yes	characteristic
343	C₂×C₃	C₃×#869	1	1	yes	characteristic
344	C₂×C₃	C₃×#870	1	1	yes	characteristic
345	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
346	C₂×C₃	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
347	C₂×C₃	C₃×#924	1	1	yes	characteristic
348	C₂×C₃	C₃×#930	1	1	yes	characteristic
349	C₂²	C₂×C₉×Dic₆	1	1	yes	characteristic
350	C₂²	C₂×C₉×Dic₆	1	1	yes	characteristic
351	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
352	C₂²	C₂×C₉×D₁₂	1	1	yes	characteristic
353	C₂²	C₉×#235	1	1	yes	characteristic
354	C₂²	C₉×#235	1	1	yes	characteristic
355	C₂²	C₂×C₉×#67	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	6	4	no	—
359	C₄	—	12	2	no	—
360	C₄	C₉×Dic₃⋊C₄	1	4	yes	complemented
361	C₃	—	2	1	no	—
362	C₃	C₉×#389	1	1	yes	characteristic, complemented
363	C₃	C₃×#4928	1	1	yes	characteristic
364	C₂	C₄×C₉×Dic₆	1	1	yes	characteristic
365	C₂	C₉×#869	1	1	yes	characteristic
366	C₂	C₉×#870	1	1	yes	characteristic
367	C₂	C₄×C₉×D₁₂	1	1	yes	characteristic
368	C₂	C₂×C₉×Dic₃⋊C₄	1	1	yes	characteristic
369	C₂	C₉×#924	1	1	yes	characteristic
370	C₂	C₉×#930	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	C₂×C₃×C₄²×C₉	C₂
socle, prime radical, cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₂×C₄²×C₉	D₃
hypocenter	C₃	C₉×#389
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₄²×C₉

Complements

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

N	H ≅ G/N	type
15. C₉×C₄⋊Dic₃	C₄	semidirect
45. #4928	C₉	direct (N × H)
77. C₃×C₄×C₉	C₄⋊C₄	semidirect
161. C₄⋊Dic₃	C₄×C₉	semidirect
196. C₄×C₉	Dic₃⋊C₄	semidirect
202. C₃×C₉	#389	semidirect
305. C₃×C₄	C₉×C₄⋊C₄	semidirect
311. C₉	#4928	direct (N × H)
360. C₄	C₉×Dic₃⋊C₄	semidirect
362. C₃	C₉×#389	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×C₉	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₉×Dic₃⋊C₄	2
C₉×C₃⋊#95	2
C₃×#4928	3
C₉×#389	3

Subgroups — C9×#4928 #13142395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4928 #13142395