Subgroups — C₉×#2495 #11767216

Order 1152.

618 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#400	C₂	1	2	yes	maximal, complemented
2	C₉×#397	C₂	1	2	yes	maximal
3	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#388	C₂	1	2	yes	maximal
6	C₉×#383	C₂	1	2	yes	maximal, complemented
7	C₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#380	C₂	1	1	yes	maximal, characteristic
9	C₉×#380	C₂	1	1	yes	maximal, characteristic
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₃×#2495	C₃	1	1	yes	maximal, characteristic
13	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₉	C₂²	1	2	yes	—
27	C₉×#95	C₂²	1	1	yes	characteristic
28	C₉×#95	C₂²	1	1	yes	characteristic
29	C₉×#95	C₂²	1	2	yes	—
30	C₉×#95	C₂²	1	2	yes	—
31	C₉×#95	C₂²	1	2	yes	—
32	C₉×#95	C₂²	1	2	yes	—
33	C₉×#95	C₂²	1	2	yes	—
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₃×#400	C₂×C₃	1	2	yes	—
37	C₃×#397	C₂×C₃	1	2	yes	—
38	C₃×#389	C₂×C₃	1	1	yes	characteristic
39	C₃×#389	C₂×C₃	1	1	yes	characteristic
40	C₃×#388	C₂×C₃	1	2	yes	—
41	C₃×#383	C₂×C₃	1	2	yes	—
42	C₃×#382	C₂×C₃	1	1	yes	characteristic
43	C₃×#380	C₂×C₃	1	1	yes	characteristic
44	C₃×#380	C₂×C₃	1	1	yes	characteristic
45	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₂⁴×C₉	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₉	—	2	2	no	—
49	C₂²×C₄×C₉	—	2	2	no	—
50	C₂²×C₄×C₉	—	2	2	no	—
51	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₉	C₂³	1	2	yes	—
54	C₂²×C₄×C₉	C₂³	1	2	yes	—
55	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂³	1	2	yes	—
57	C₂²×C₄×C₉	C₂³	1	2	yes	—
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₉×C₄⋊C₄	—	2	2	no	—
62	C₉×C₄⋊C₄	—	2	2	no	—
63	C₉×C₄⋊C₄	—	2	2	no	—
64	C₉×C₄⋊C₄	—	2	2	no	—
65	C₉×C₄⋊C₄	—	4	2	no	—
66	C₉×C₄⋊C₄	—	4	2	no	—
67	C₉×C₂²⋊C₄	—	2	2	no	—
68	C₉×C₂²⋊C₄	—	2	4	no	—
69	C₉×C₂²⋊C₄	—	2	2	no	—
70	C₉×C₂²⋊C₄	—	4	2	no	—
71	C₄²×C₉	—	2	2	no	—
72	C₄²×C₉	—	2	4	no	—
73	C₄²×C₉	—	2	2	no	—
74	#2495	C₉	1	1	yes	characteristic, direct product factor, Sylow
75	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
89	C₃×#95	C₂²×C₃	1	1	yes	characteristic
90	C₃×#95	C₂²×C₃	1	1	yes	characteristic
91	C₃×#95	C₂²×C₃	1	2	yes	—
92	C₃×#95	C₂²×C₃	1	2	yes	—
93	C₃×#95	C₂²×C₃	1	2	yes	—
94	C₃×#95	C₂²×C₃	1	2	yes	—
95	C₃×#95	C₂²×C₃	1	2	yes	—
96	C₃×#95	C₂²×C₃	1	2	yes	—
97	C₃×#95	C₂²×C₃	1	2	yes	—
98	C₂³×C₉	—	2	1	no	—
99	C₂³×C₉	—	2	1	no	—
100	C₂³×C₉	—	2	1	no	—
101	C₂³×C₉	—	2	1	no	—
102	C₂³×C₉	—	2	1	no	—
103	C₂³×C₉	—	2	1	no	—
104	C₂³×C₉	#41	1	2	yes	—
105	C₂³×C₉	C₂⁴	1	1	yes	characteristic
106	C₂×C₄×C₉	—	2	1	no	—
107	C₂×C₄×C₉	—	2	1	no	—
108	C₂×C₄×C₉	—	2	2	no	—
109	C₂×C₄×C₉	—	2	1	no	—
110	C₂×C₄×C₉	—	2	1	no	—
111	C₂×C₄×C₉	—	2	1	no	—
112	C₂×C₄×C₉	—	2	2	no	—
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	1	no	—
115	C₂×C₄×C₉	—	2	1	no	—
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	1	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	—	2	1	no	—
123	C₂×C₄×C₉	—	2	1	no	—
124	C₂×C₄×C₉	—	2	1	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	4	4	no	—
133	C₂×C₄×C₉	#41	1	2	yes	—
134	C₂×C₄×C₉	#41	1	2	yes	—
135	C₂×C₄×C₉	#41	1	2	yes	—
136	C₂×C₄×C₉	#41	1	2	yes	—
137	#400	C₂×C₉	1	2	yes	complemented
138	#397	C₂×C₉	1	2	yes	—
139	#389	C₂×C₉	1	1	yes	characteristic, complemented
140	#389	C₂×C₉	1	1	yes	characteristic, complemented
141	#388	C₂×C₉	1	2	yes	—
142	#383	C₂×C₉	1	2	yes	complemented
143	#382	C₂×C₉	1	1	yes	characteristic, complemented
144	#380	C₂×C₉	1	1	yes	characteristic
145	#380	C₂×C₉	1	1	yes	characteristic
146	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
147	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
148	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₃×C₄	—	2	2	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
155	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₃×C₄⋊C₄	—	2	2	no	—
163	C₃×C₄⋊C₄	—	2	2	no	—
164	C₃×C₄⋊C₄	—	2	2	no	—
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	—	4	2	no	—
167	C₃×C₄⋊C₄	—	4	2	no	—
168	C₃×C₂²⋊C₄	—	2	2	no	—
169	C₃×C₂²⋊C₄	—	2	4	no	—
170	C₃×C₂²⋊C₄	—	2	2	no	—
171	C₃×C₂²⋊C₄	—	4	2	no	—
172	C₃×C₄²	—	2	2	no	—
173	C₃×C₄²	—	2	4	no	—
174	C₃×C₄²	—	2	2	no	—
175	C₂²×C₉	—	2	2	no	—
176	C₂²×C₉	—	2	2	no	—
177	C₂²×C₉	—	2	2	no	—
178	C₂²×C₉	—	4	1	no	—
179	C₂²×C₉	—	4	1	no	—
180	C₂²×C₉	—	4	1	no	—
181	C₂²×C₉	—	4	1	no	—
182	C₂²×C₉	C₂×#41	1	1	yes	characteristic
183	C₂²×C₉	C₂×#41	1	1	yes	characteristic
184	C₂²×C₉	C₂×#41	1	1	yes	characteristic
185	C₂²×C₉	C₂×#41	1	1	yes	characteristic
186	C₂²×C₉	C₂×#41	1	1	yes	characteristic
187	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₄×C₉	—	2	2	no	—
190	C₄×C₉	—	4	1	no	—
191	C₄×C₉	—	4	2	no	—
192	C₄×C₉	—	4	2	no	—
193	C₄×C₉	—	4	1	no	—
194	C₄×C₉	—	4	1	no	—
195	C₄×C₉	—	4	2	no	—
196	C₄×C₉	—	4	1	no	—
197	C₄×C₉	—	4	2	no	—
198	C₄×C₉	#126	1	4	yes	—
199	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
205	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
206	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
208	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
210	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
211	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
212	C₂×C₄²	C₂²×C₉	1	2	yes	—
213	#95	C₂²×C₉	1	1	yes	characteristic
214	#95	C₂²×C₉	1	1	yes	characteristic
215	#95	C₂²×C₉	1	2	yes	—
216	#95	C₂²×C₉	1	2	yes	—
217	#95	C₂²×C₉	1	2	yes	—
218	#95	C₂²×C₉	1	2	yes	—
219	#95	C₂²×C₉	1	2	yes	—
220	#95	C₂²×C₉	1	2	yes	—
221	#95	C₂²×C₉	1	2	yes	—
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	2	1	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	2	1	no	—
226	C₂³×C₃	—	2	1	no	—
227	C₂³×C₃	—	2	1	no	—
228	C₂³×C₃	C₃×#41	1	2	yes	—
229	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	4	4	no	—
257	C₂×C₃×C₄	C₃×#41	1	2	yes	—
258	C₂×C₃×C₄	C₃×#41	1	2	yes	—
259	C₂×C₃×C₄	C₃×#41	1	2	yes	—
260	C₂×C₃×C₄	C₃×#41	1	2	yes	—
261	C₂×C₉	—	4	2	no	—
262	C₂×C₉	C₂×#126	1	1	yes	characteristic
263	C₂×C₉	#529	1	1	yes	characteristic
264	C₂×C₉	#542	1	1	yes	characteristic
265	C₂×C₉	#552	1	1	yes	characteristic
266	C₂×C₉	#552	1	1	yes	characteristic
267	C₂×C₉	#553	1	1	yes	characteristic
268	C₂×C₉	#555	1	1	yes	characteristic
269	C₂⁴	C₂³×C₉	1	1	yes	characteristic
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
275	C₂²×C₄	C₂³×C₉	1	2	yes	—
276	C₂²×C₄	C₂³×C₉	1	2	yes	—
277	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₉	1	2	yes	—
280	C₂²×C₄	C₂³×C₉	1	2	yes	—
281	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₂²⋊C₄	—	2	4	no	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	4	no	—
295	C₄²	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
304	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
307	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
308	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	4	1	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	2	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	—	4	1	no	—
318	C₃×C₄	—	4	2	no	—
319	C₃×C₄	C₃×#126	1	4	yes	—
320	C₉	#2495	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	C₉×#41	1	2	yes	—
328	C₂³	C₂⁴×C₉	1	1	yes	characteristic
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	C₉×#41	1	2	yes	—
357	C₂×C₄	C₉×#41	1	2	yes	—
358	C₂×C₄	C₉×#41	1	2	yes	—
359	C₂×C₄	C₉×#41	1	2	yes	—
360	C₂×C₃	—	4	2	no	—
361	C₂×C₃	C₂×C₃×#126	1	1	yes	characteristic
362	C₂×C₃	C₃×#529	1	1	yes	characteristic
363	C₂×C₃	C₃×#542	1	1	yes	characteristic
364	C₂×C₃	C₃×#552	1	1	yes	characteristic
365	C₂×C₃	C₃×#552	1	1	yes	characteristic
366	C₂×C₃	C₃×#553	1	1	yes	characteristic
367	C₂×C₃	C₃×#555	1	1	yes	characteristic
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	C₂×C₉×#41	1	1	yes	characteristic
376	C₂²	C₂×C₉×#41	1	1	yes	characteristic
377	C₂²	C₂×C₉×#41	1	1	yes	characteristic
378	C₂²	C₂×C₉×#41	1	1	yes	characteristic
379	C₂²	C₂×C₉×#41	1	1	yes	characteristic
380	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	2	no	—
391	C₄	C₉×#126	1	4	yes	—
392	C₃	C₃×#2495	1	1	yes	characteristic
393	C₂	—	4	2	no	—
394	C₂	C₂×C₉×#126	1	1	yes	characteristic
395	C₂	C₉×#529	1	1	yes	characteristic
396	C₂	C₉×#542	1	1	yes	characteristic
397	C₂	C₉×#552	1	1	yes	characteristic
398	C₂	C₉×#552	1	1	yes	characteristic
399	C₂	C₉×#553	1	1	yes	characteristic
400	C₂	C₉×#555	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₉×#400	C₂	semidirect
3. C₉×#389	C₂	semidirect
4. C₉×#389	C₂	semidirect
6. C₉×#383	C₂	semidirect
7. C₉×#382	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
74. #2495	C₉	direct (N × H)
137. #400	C₂×C₉	semidirect
139. #389	C₂×C₉	semidirect
140. #389	C₂×C₉	semidirect
142. #383	C₂×C₉	semidirect
143. #382	C₂×C₉	semidirect
146. C₄×C₄⋊C₄	C₂×C₉	semidirect
320. C₉	#2495	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#400	2
C₉×#397	2
C₉×#389	2
C₉×#388	2
C₉×#383	2
C₉×#382	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2495	3

Subgroups — C9×#2495 #11767216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2495 #11767216