Subgroups — C₂×C₉×#386 #11767008

Order 1152.

2364 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₉×#386	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₉×#95	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#386	C₃	1	1	yes	maximal, characteristic
8	C₂⁵×C₉	C₂²	1	1	yes	characteristic
9	C₂⁵×C₉	C₂²	1	1	yes	characteristic
10	C₂²×D₄×C₉	—	2	4	no	—
11	C₂²×D₄×C₉	—	2	4	no	—
12	C₂²×D₄×C₉	C₄	1	8	yes	complemented
13	C₂²×D₄×C₉	C₂²	1	4	yes	—
14	C₂³×C₄×C₉	—	2	4	no	—
15	C₂³×C₄×C₉	—	2	8	no	—
16	C₂³×C₄×C₉	C₂²	1	2	yes	—
17	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₉	C₂²	1	2	yes	—
19	C₂³×C₄×C₉	C₂²	1	4	yes	complemented
20	C₂×C₉×C₂²⋊C₄	—	2	4	no	—
21	C₂×C₉×C₂²⋊C₄	—	2	8	no	—
22	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
23	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
24	C₉×#95	C₂²	1	8	yes	complemented
25	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
26	C₂⁴×C₃×C₄	C₂×C₃	1	1	yes	characteristic
27	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
28	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
29	C₃×#386	C₂×C₃	1	8	yes	—
30	C₂×C₃×#95	C₂×C₃	1	2	yes	—
31	C₂⁴×C₉	—	2	4	no	—
32	C₂⁴×C₉	—	2	4	no	—
33	C₂⁴×C₉	—	2	4	no	—
34	C₂⁴×C₉	—	2	2	no	—
35	C₂⁴×C₉	—	2	2	no	—
36	C₂⁴×C₉	—	2	4	no	—
37	C₂⁴×C₉	C₂×C₄	1	4	yes	—
38	C₂⁴×C₉	C₂×C₄	1	4	yes	complemented
39	C₂⁴×C₉	D₄	1	4	yes	—
40	C₂⁴×C₉	D₄	1	4	yes	—
41	C₂⁴×C₉	C₂³	1	2	yes	—
42	C₂⁴×C₉	C₂³	1	2	yes	—
43	C₂⁴×C₉	C₂³	1	1	yes	characteristic
44	C₂×D₄×C₉	—	2	32	no	—
45	C₂×D₄×C₉	—	2	8	no	—
46	C₂×D₄×C₉	—	2	8	no	—
47	C₂×D₄×C₉	C₂×C₄	1	16	yes	complemented
48	C₂²×C₄×C₉	—	2	32	no	—
49	C₂²×C₄×C₉	—	2	4	no	—
50	C₂²×C₄×C₉	—	2	4	no	—
51	C₂²×C₄×C₉	—	2	8	no	—
52	C₂²×C₄×C₉	—	2	2	no	—
53	C₂²×C₄×C₉	—	2	2	no	—
54	C₂²×C₄×C₉	—	2	16	no	—
55	C₂²×C₄×C₉	—	2	4	no	—
56	C₂²×C₄×C₉	—	2	4	no	—
57	C₂²×C₄×C₉	—	2	4	no	—
58	C₂²×C₄×C₉	C₂×C₄	1	4	yes	complemented
59	C₂²×C₄×C₉	D₄	1	8	yes	complemented
60	C₂²×C₄×C₉	C₂³	1	4	yes	—
61	C₂²×C₄×C₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₉	C₂³	1	4	yes	—
63	C₉×C₂²⋊C₄	—	2	8	no	—
64	C₉×C₂²⋊C₄	—	2	16	no	—
65	C₂×#386	C₉	1	1	yes	characteristic, direct product factor, Sylow
66	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
67	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃×D₄	—	2	4	no	—
69	C₂²×C₃×D₄	—	2	4	no	—
70	C₂²×C₃×D₄	C₃×C₄	1	8	yes	—
71	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
72	C₂³×C₃×C₄	—	2	4	no	—
73	C₂³×C₃×C₄	—	2	8	no	—
74	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
75	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
77	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
78	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
79	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
80	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
81	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
82	C₃×#95	C₂²×C₃	1	8	yes	—
83	C₂³×C₉	—	2	16	no	—
84	C₂³×C₉	—	2	8	no	—
85	C₂³×C₉	—	2	16	no	—
86	C₂³×C₉	—	2	8	no	—
87	C₂³×C₉	—	2	4	no	—
88	C₂³×C₉	—	2	4	no	—
89	C₂³×C₉	—	2	8	no	—
90	C₂³×C₉	—	2	16	no	—
91	C₂³×C₉	—	2	4	no	—
92	C₂³×C₉	—	2	2	no	—
93	C₂³×C₉	—	2	2	no	—
94	C₂³×C₉	—	2	4	no	—
95	C₂³×C₉	—	4	4	no	—
96	C₂³×C₉	—	4	8	no	—
97	C₂³×C₉	—	4	4	no	—
98	C₂³×C₉	C₂²⋊C₄	1	16	yes	complemented
99	C₂³×C₉	C₂²×C₄	1	4	yes	—
100	C₂³×C₉	C₂²×C₄	1	2	yes	—
101	C₂³×C₉	C₂²×C₄	1	4	yes	complemented
102	C₂³×C₉	C₂×D₄	1	4	yes	—
103	C₂³×C₉	C₂×D₄	1	4	yes	—
104	C₂³×C₉	C₂×D₄	1	2	yes	—
105	C₂³×C₉	C₂×D₄	1	2	yes	—
106	C₂³×C₉	C₂×D₄	1	4	yes	—
107	C₂³×C₉	#41	1	4	yes	—
108	C₂³×C₉	C₂⁴	1	1	yes	characteristic
109	D₄×C₉	—	2	32	no	—
110	C₂×C₄×C₉	—	2	32	no	—
111	C₂×C₄×C₉	—	2	8	no	—
112	C₂×C₄×C₉	—	2	16	no	—
113	C₂×C₄×C₉	—	2	4	no	—
114	C₂×C₄×C₉	—	2	4	no	—
115	C₂×C₄×C₉	—	2	2	no	—
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	4	no	—
118	C₂×C₄×C₉	—	2	4	no	—
119	C₂×C₄×C₉	—	2	4	no	—
120	C₂×C₄×C₉	—	4	8	no	—
121	C₂×C₄×C₉	C₂²×C₄	1	4	yes	complemented
122	C₂×C₄×C₉	C₂×D₄	1	8	yes	complemented
123	C₂³×D₄	C₂×C₉	1	1	yes	characteristic
124	C₂⁴×C₄	C₂×C₉	1	1	yes	characteristic, complemented
125	C₂²×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
126	C₂²×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
127	#386	C₂×C₉	1	8	yes	direct product factor
128	C₂×#95	C₂×C₉	1	2	yes	complemented
129	C₂⁴×C₃	—	2	4	no	—
130	C₂⁴×C₃	—	2	4	no	—
131	C₂⁴×C₃	—	2	4	no	—
132	C₂⁴×C₃	—	2	2	no	—
133	C₂⁴×C₃	—	2	2	no	—
134	C₂⁴×C₃	—	2	4	no	—
135	C₂⁴×C₃	C₂×C₃×C₄	1	4	yes	—
136	C₂⁴×C₃	C₂×C₃×C₄	1	4	yes	—
137	C₂⁴×C₃	C₃×D₄	1	4	yes	—
138	C₂⁴×C₃	C₃×D₄	1	4	yes	—
139	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
140	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
141	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₃×D₄	—	2	32	no	—
143	C₂×C₃×D₄	—	2	8	no	—
144	C₂×C₃×D₄	—	2	8	no	—
145	C₂×C₃×D₄	C₂×C₃×C₄	1	16	yes	—
146	C₂²×C₃×C₄	—	2	32	no	—
147	C₂²×C₃×C₄	—	2	4	no	—
148	C₂²×C₃×C₄	—	2	4	no	—
149	C₂²×C₃×C₄	—	2	8	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	—	2	16	no	—
153	C₂²×C₃×C₄	—	2	4	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
157	C₂²×C₃×C₄	C₃×D₄	1	8	yes	—
158	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
161	C₃×C₂²⋊C₄	—	2	8	no	—
162	C₃×C₂²⋊C₄	—	2	16	no	—
163	C₂²×C₉	—	2	8	no	—
164	C₂²×C₉	—	2	4	no	—
165	C₂²×C₉	—	2	8	no	—
166	C₂²×C₉	—	2	4	no	—
167	C₂²×C₉	—	2	32	no	—
168	C₂²×C₉	—	2	4	no	—
169	C₂²×C₉	—	2	8	no	—
170	C₂²×C₉	—	4	2	no	—
171	C₂²×C₉	—	4	4	no	—
172	C₂²×C₉	—	4	2	no	—
173	C₂²×C₉	—	4	16	no	—
174	C₂²×C₉	C₂×C₂²⋊C₄	1	4	yes	—
175	C₂²×C₉	C₂×C₂²⋊C₄	1	8	yes	complemented
176	C₂²×C₉	C₄×D₄	1	8	yes	—
177	C₂²×C₉	#120	1	4	yes	—
178	C₂²×C₉	#121	1	8	yes	—
179	C₂²×C₉	#123	1	4	yes	—
180	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
181	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
183	C₂²×C₉	C₂²×D₄	1	2	yes	—
184	C₂²×C₉	C₂×#41	1	2	yes	—
185	C₄×C₉	—	2	4	no	—
186	C₄×C₉	—	2	8	no	—
187	C₄×C₉	—	4	4	no	—
188	C₂⁵	C₂²×C₉	1	1	yes	characteristic
189	C₂⁵	C₂²×C₉	1	1	yes	characteristic
190	C₂²×D₄	—	2	4	no	—
191	C₂²×D₄	—	2	4	no	—
192	C₂²×D₄	C₄×C₉	1	8	yes	complemented
193	C₂²×D₄	C₂²×C₉	1	4	yes	—
194	C₂³×C₄	—	2	4	no	—
195	C₂³×C₄	—	2	8	no	—
196	C₂³×C₄	C₂²×C₉	1	2	yes	—
197	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
198	C₂³×C₄	C₂²×C₉	1	2	yes	—
199	C₂³×C₄	C₂²×C₉	1	4	yes	complemented
200	C₂×C₂²⋊C₄	—	2	4	no	—
201	C₂×C₂²⋊C₄	—	2	8	no	—
202	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
203	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
204	#95	C₂²×C₉	1	8	yes	complemented
205	C₂³×C₃	—	2	16	no	—
206	C₂³×C₃	—	2	8	no	—
207	C₂³×C₃	—	2	16	no	—
208	C₂³×C₃	—	2	8	no	—
209	C₂³×C₃	—	2	4	no	—
210	C₂³×C₃	—	2	4	no	—
211	C₂³×C₃	—	2	8	no	—
212	C₂³×C₃	—	2	16	no	—
213	C₂³×C₃	—	2	4	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	4	4	no	—
218	C₂³×C₃	—	4	8	no	—
219	C₂³×C₃	—	4	4	no	—
220	C₂³×C₃	C₃×C₂²⋊C₄	1	16	yes	—
221	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
222	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
223	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
224	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
225	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
226	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
227	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
228	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
229	C₂³×C₃	C₃×#41	1	4	yes	—
230	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
231	C₃×D₄	—	2	32	no	—
232	C₂×C₃×C₄	—	2	32	no	—
233	C₂×C₃×C₄	—	2	8	no	—
234	C₂×C₃×C₄	—	2	16	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	4	8	no	—
243	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
244	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
245	C₂×C₉	—	2	8	no	—
246	C₂×C₉	—	4	4	no	—
247	C₂×C₉	#386	1	8	yes	direct product factor
248	C₂×C₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₉	C₂×C₄×D₄	1	2	yes	—
250	C₂×C₉	C₂×#120	1	1	yes	characteristic
251	C₂×C₉	C₂×#121	1	2	yes	—
252	C₂×C₉	C₂×#123	1	1	yes	characteristic
253	C₂⁴	—	2	4	no	—
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	2	no	—
257	C₂⁴	—	2	2	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	C₂×C₄×C₉	1	4	yes	—
260	C₂⁴	C₂×C₄×C₉	1	4	yes	complemented
261	C₂⁴	D₄×C₉	1	4	yes	—
262	C₂⁴	D₄×C₉	1	4	yes	—
263	C₂⁴	C₂³×C₉	1	2	yes	—
264	C₂⁴	C₂³×C₉	1	2	yes	—
265	C₂⁴	C₂³×C₉	1	1	yes	characteristic
266	C₂×D₄	—	2	32	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	8	no	—
269	C₂×D₄	C₂×C₄×C₉	1	16	yes	complemented
270	C₂²×C₄	—	2	32	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	16	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	C₂×C₄×C₉	1	4	yes	complemented
281	C₂²×C₄	D₄×C₉	1	8	yes	complemented
282	C₂²×C₄	C₂³×C₉	1	4	yes	—
283	C₂²×C₄	C₂³×C₉	1	2	yes	—
284	C₂²×C₄	C₂³×C₉	1	4	yes	—
285	C₂²⋊C₄	—	2	8	no	—
286	C₂²⋊C₄	—	2	16	no	—
287	C₂²×C₃	—	2	32	no	—
288	C₂²×C₃	—	2	8	no	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	2	8	no	—
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	8	no	—
294	C₂²×C₃	—	4	16	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	—	4	2	no	—
298	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	4	yes	—
299	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	8	yes	—
300	C₂²×C₃	C₃×C₄×D₄	1	8	yes	—
301	C₂²×C₃	C₃×#120	1	4	yes	—
302	C₂²×C₃	C₃×#121	1	8	yes	—
303	C₂²×C₃	C₃×#123	1	4	yes	—
304	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
305	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
306	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
307	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
308	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	2	8	no	—
311	C₃×C₄	—	4	4	no	—
312	C₉	C₂×#386	1	1	yes	characteristic, direct product factor, Sylow
313	C₂³	—	2	16	no	—
314	C₂³	—	2	8	no	—
315	C₂³	—	2	16	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	8	no	—
320	C₂³	—	2	16	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	4	4	no	—
328	C₂³	C₉×C₂²⋊C₄	1	16	yes	complemented
329	C₂³	C₂²×C₄×C₉	1	4	yes	—
330	C₂³	C₂²×C₄×C₉	1	2	yes	—
331	C₂³	C₂²×C₄×C₉	1	4	yes	complemented
332	C₂³	C₂×D₄×C₉	1	4	yes	—
333	C₂³	C₂×D₄×C₉	1	4	yes	—
334	C₂³	C₂×D₄×C₉	1	2	yes	—
335	C₂³	C₂×D₄×C₉	1	2	yes	—
336	C₂³	C₂×D₄×C₉	1	4	yes	—
337	C₂³	C₉×#41	1	4	yes	—
338	C₂³	C₂⁴×C₉	1	1	yes	characteristic
339	D₄	—	2	32	no	—
340	C₂×C₄	—	2	32	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	16	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	C₂²×C₄×C₉	1	4	yes	complemented
352	C₂×C₄	C₂×D₄×C₉	1	8	yes	complemented
353	C₂×C₃	—	2	8	no	—
354	C₂×C₃	—	4	4	no	—
355	C₂×C₃	C₃×#386	1	8	yes	—
356	C₂×C₃	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
357	C₂×C₃	C₂×C₃×C₄×D₄	1	2	yes	—
358	C₂×C₃	C₂×C₃×#120	1	1	yes	characteristic
359	C₂×C₃	C₂×C₃×#121	1	2	yes	—
360	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
361	C₂²	—	2	4	no	—
362	C₂²	—	2	8	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	32	no	—
365	C₂²	—	2	8	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	8	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	16	no	—
372	C₂²	C₂×C₉×C₂²⋊C₄	1	4	yes	—
373	C₂²	C₂×C₉×C₂²⋊C₄	1	8	yes	complemented
374	C₂²	C₄×D₄×C₉	1	8	yes	—
375	C₂²	C₉×#120	1	4	yes	—
376	C₂²	C₉×#121	1	8	yes	—
377	C₂²	C₉×#123	1	4	yes	—
378	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
379	C₂²	C₂²×D₄×C₉	1	2	yes	—
380	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
381	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
382	C₂²	C₂×C₉×#41	1	2	yes	—
383	C₄	—	2	8	no	—
384	C₄	—	2	4	no	—
385	C₄	—	4	4	no	—
386	C₃	C₂×C₃×#386	1	1	yes	characteristic
387	C₂	—	2	8	no	—
388	C₂	—	4	4	no	—
389	C₂	C₉×#386	1	8	yes	direct product factor
390	C₂	C₂²×C₉×C₂²⋊C₄	1	1	yes	characteristic
391	C₂	C₂×C₄×D₄×C₉	1	2	yes	—
392	C₂	C₂×C₉×#120	1	1	yes	characteristic
393	C₂	C₂×C₉×#121	1	2	yes	—
394	C₂	C₂×C₉×#123	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃
socle	C₂⁴×C₃	C₂³×C₃
prime radical	C₂³×C₃×D₄	C₂×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₄×C₉	C₂	semidirect
3. C₂²×C₉×C₂²⋊C₄	C₂	semidirect
4. C₂²×C₉×C₂²⋊C₄	C₂	semidirect
5. C₉×#386	C₂	direct (N × H)
6. C₂×C₉×#95	C₂	semidirect
12. C₂²×D₄×C₉	C₄	semidirect
19. C₂³×C₄×C₉	C₂²	semidirect
22. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
23. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
24. C₉×#95	C₂²	semidirect
38. C₂⁴×C₉	C₂×C₄	semidirect
47. C₂×D₄×C₉	C₂×C₄	semidirect
58. C₂²×C₄×C₉	C₂×C₄	semidirect
59. C₂²×C₄×C₉	D₄	semidirect
65. C₂×#386	C₉	direct (N × H)
98. C₂³×C₉	C₂²⋊C₄	semidirect
101. C₂³×C₉	C₂²×C₄	semidirect
121. C₂×C₄×C₉	C₂²×C₄	semidirect
122. C₂×C₄×C₉	C₂×D₄	semidirect
124. C₂⁴×C₄	C₂×C₉	semidirect
125. C₂²×C₂²⋊C₄	C₂×C₉	semidirect
126. C₂²×C₂²⋊C₄	C₂×C₉	semidirect
127. #386	C₂×C₉	direct (N × H)
128. C₂×#95	C₂×C₉	semidirect
175. C₂²×C₉	C₂×C₂²⋊C₄	semidirect
192. C₂²×D₄	C₄×C₉	semidirect
199. C₂³×C₄	C₂²×C₉	semidirect
202. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
203. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
204. #95	C₂²×C₉	semidirect
247. C₂×C₉	#386	direct (N × H)
260. C₂⁴	C₂×C₄×C₉	semidirect
269. C₂×D₄	C₂×C₄×C₉	semidirect
280. C₂²×C₄	C₂×C₄×C₉	semidirect
281. C₂²×C₄	D₄×C₉	semidirect
312. C₉	C₂×#386	direct (N × H)
328. C₂³	C₉×C₂²⋊C₄	semidirect
331. C₂³	C₂²×C₄×C₉	semidirect
351. C₂×C₄	C₂²×C₄×C₉	semidirect
352. C₂×C₄	C₂×D₄×C₉	semidirect
373. C₂²	C₂×C₉×C₂²⋊C₄	semidirect
389. C₂	C₉×#386	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×C₉	2
C₂⁴×C₄×C₉	2
C₂²×C₉×C₂²⋊C₄	2
C₉×#386	2
C₂×C₉×#95	2
C₂×C₃×#386	3

Subgroups — C2×C9×#386 #11767008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#386 #11767008