Subgroups — C₉×#2498 #11767219

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#123	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#388	C₂	1	2	yes	maximal, complemented
8	C₉×#387	C₂	1	2	yes	maximal, complemented
9	C₉×#386	C₂	1	2	yes	maximal
10	C₉×#380	C₂	1	2	yes	maximal, complemented
11	C₂×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2498	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	2	yes	—
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₉×#123	—	2	4	no	—
17	C₉×#117	—	2	4	no	—
18	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₄²×C₉	C₂²	1	2	yes	—
31	C₉×#95	C₂²	1	2	yes	—
32	C₉×#95	C₂²	1	1	yes	characteristic
33	C₉×#95	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
40	C₃×#400	C₂×C₃	1	1	yes	characteristic
41	C₃×#399	C₂×C₃	1	1	yes	characteristic
42	C₃×#398	C₂×C₃	1	1	yes	characteristic
43	C₃×#397	C₂×C₃	1	1	yes	characteristic
44	C₃×#388	C₂×C₃	1	2	yes	—
45	C₃×#387	C₂×C₃	1	2	yes	—
46	C₃×#386	C₂×C₃	1	2	yes	—
47	C₃×#380	C₂×C₃	1	2	yes	—
48	C₂×C₃×#95	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×D₄×C₉	—	2	2	no	—
52	C₂×D₄×C₉	—	2	4	no	—
53	C₂²×C₄×C₉	—	2	4	no	—
54	C₂²×C₄×C₉	—	2	4	no	—
55	C₂²×C₄×C₉	—	2	4	no	—
56	C₂²×C₄×C₉	—	4	2	no	—
57	C₂²×C₄×C₉	D₄	1	4	yes	—
58	C₂²×C₄×C₉	C₂³	1	2	yes	—
59	C₂²×C₄×C₉	C₂³	1	2	yes	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	C₂³	1	2	yes	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	2	yes	—
67	C₉×C₄⋊C₄	—	2	2	no	—
68	C₉×C₄⋊C₄	—	2	2	no	—
69	C₉×C₄⋊C₄	—	2	2	no	—
70	C₉×C₄⋊C₄	—	2	2	no	—
71	C₉×C₄⋊C₄	—	2	4	no	—
72	C₉×C₄⋊C₄	—	4	2	no	—
73	C₉×C₂²⋊C₄	—	2	4	no	—
74	C₉×C₂²⋊C₄	—	2	2	no	—
75	C₉×C₂²⋊C₄	—	2	2	no	—
76	C₉×C₂²⋊C₄	—	2	2	no	—
77	C₉×C₂²⋊C₄	—	2	4	no	—
78	C₉×C₂²⋊C₄	—	4	2	no	—
79	C₄²×C₉	—	2	4	no	—
80	#2498	C₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
83	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
84	C₃×#123	—	2	4	no	—
85	C₃×#117	—	2	4	no	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
99	C₃×#95	C₂²×C₃	1	2	yes	—
100	C₃×#95	C₂²×C₃	1	1	yes	characteristic
101	C₃×#95	C₂²×C₃	1	1	yes	characteristic
102	C₃×#95	C₂²×C₃	1	2	yes	—
103	C₃×#95	C₂²×C₃	1	2	yes	—
104	C₃×#95	C₂²×C₃	1	2	yes	—
105	C₃×#95	C₂²×C₃	1	2	yes	—
106	C₂³×C₉	—	2	2	no	—
107	C₂³×C₉	—	2	1	no	—
108	C₂³×C₉	—	2	1	no	—
109	C₂³×C₉	—	2	1	no	—
110	C₂³×C₉	—	2	2	no	—
111	C₂³×C₉	—	2	2	no	—
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	C₂×D₄	1	2	yes	—
115	C₂³×C₉	#41	1	4	yes	—
116	C₂³×C₉	C₂⁴	1	1	yes	characteristic
117	D₄×C₉	—	4	4	no	—
118	C₂×C₄×C₉	—	2	8	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	2	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	2	2	no	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	4	8	no	—
140	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
141	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
142	C₂×C₄×C₉	#41	1	4	yes	—
143	C₂×#123	C₂×C₉	1	1	yes	characteristic
144	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
145	#400	C₂×C₉	1	1	yes	characteristic, complemented
146	#399	C₂×C₉	1	1	yes	characteristic, complemented
147	#398	C₂×C₉	1	1	yes	characteristic, complemented
148	#397	C₂×C₉	1	1	yes	characteristic, complemented
149	#388	C₂×C₉	1	2	yes	complemented
150	#387	C₂×C₉	1	2	yes	complemented
151	#386	C₂×C₉	1	2	yes	—
152	#380	C₂×C₉	1	2	yes	complemented
153	C₂×#95	C₂×C₉	1	1	yes	characteristic, complemented
154	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
155	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₃×D₄	—	2	2	no	—
157	C₂×C₃×D₄	—	2	4	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	—	2	4	no	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	4	2	no	—
162	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
163	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
164	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
166	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	—	2	4	no	—
177	C₃×C₄⋊C₄	—	4	2	no	—
178	C₃×C₂²⋊C₄	—	2	4	no	—
179	C₃×C₂²⋊C₄	—	2	2	no	—
180	C₃×C₂²⋊C₄	—	2	2	no	—
181	C₃×C₂²⋊C₄	—	2	2	no	—
182	C₃×C₂²⋊C₄	—	2	4	no	—
183	C₃×C₂²⋊C₄	—	4	2	no	—
184	C₃×C₄²	—	2	4	no	—
185	C₂²×C₉	—	2	2	no	—
186	C₂²×C₉	—	2	2	no	—
187	C₂²×C₉	—	2	4	no	—
188	C₂²×C₉	—	2	4	no	—
189	C₂²×C₉	—	4	1	no	—
190	C₂²×C₉	—	4	1	no	—
191	C₂²×C₉	—	4	1	no	—
192	C₂²×C₉	—	4	2	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	#123	1	4	yes	—
195	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
196	C₂²×C₉	C₂×#41	1	2	yes	—
197	C₂²×C₉	C₂×#41	1	2	yes	—
198	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
200	C₄×C₉	—	2	2	no	—
201	C₄×C₉	—	2	2	no	—
202	C₄×C₉	—	2	4	no	—
203	C₄×C₉	—	4	1	no	—
204	C₄×C₉	—	4	2	no	—
205	C₄×C₉	—	4	1	no	—
206	C₄×C₉	—	4	2	no	—
207	C₄×C₉	—	4	1	no	—
208	C₄×C₉	—	4	2	no	—
209	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
210	C₂³×C₄	C₂²×C₉	1	2	yes	—
211	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
212	#123	—	2	4	no	—
213	#117	—	2	4	no	—
214	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
219	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
221	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
226	C₂×C₄²	C₂²×C₉	1	2	yes	—
227	#95	C₂²×C₉	1	2	yes	—
228	#95	C₂²×C₉	1	1	yes	characteristic
229	#95	C₂²×C₉	1	1	yes	characteristic
230	#95	C₂²×C₉	1	2	yes	—
231	#95	C₂²×C₉	1	2	yes	—
232	#95	C₂²×C₉	1	2	yes	—
233	#95	C₂²×C₉	1	2	yes	—
234	C₂³×C₃	—	2	2	no	—
235	C₂³×C₃	—	2	1	no	—
236	C₂³×C₃	—	2	1	no	—
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	2	2	no	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
243	C₂³×C₃	C₃×#41	1	4	yes	—
244	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
245	C₃×D₄	—	4	4	no	—
246	C₂×C₃×C₄	—	2	8	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	4	8	no	—
268	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
269	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₃×#41	1	4	yes	—
271	C₂×C₉	—	2	4	no	—
272	C₂×C₉	—	8	1	no	—
273	C₂×C₉	C₂×#123	1	1	yes	characteristic
274	C₂×C₉	#532	1	1	yes	characteristic
275	C₂×C₉	#537	1	1	yes	characteristic
276	C₂×C₉	#551	1	2	yes	—
277	C₂×C₉	#552	1	2	yes	—
278	C₂⁴	C₂³×C₉	1	1	yes	characteristic
279	C₂⁴	C₂³×C₉	1	1	yes	characteristic
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	D₄×C₉	1	4	yes	—
287	C₂²×C₄	C₂³×C₉	1	2	yes	—
288	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₉	1	2	yes	—
290	C₂²×C₄	C₂³×C₉	1	2	yes	—
291	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₉	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₄²	—	2	4	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	—	4	1	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	—	4	2	no	—
317	C₂²×C₃	—	4	2	no	—
318	C₂²×C₃	C₃×#123	1	4	yes	—
319	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
320	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
321	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
322	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	2	4	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	4	2	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	4	2	no	—
331	C₃×C₄	—	4	1	no	—
332	C₃×C₄	—	4	2	no	—
333	C₉	#2498	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³	—	2	2	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	C₂×D₄×C₉	1	2	yes	—
343	C₂³	C₉×#41	1	4	yes	—
344	C₂³	C₂⁴×C₉	1	1	yes	characteristic
345	D₄	—	4	4	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
369	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
370	C₂×C₄	C₉×#41	1	4	yes	—
371	C₂×C₃	—	2	4	no	—
372	C₂×C₃	—	8	1	no	—
373	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
374	C₂×C₃	C₃×#532	1	1	yes	characteristic
375	C₂×C₃	C₃×#537	1	1	yes	characteristic
376	C₂×C₃	C₃×#551	1	2	yes	—
377	C₂×C₃	C₃×#552	1	2	yes	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	C₉×#123	1	4	yes	—
388	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
389	C₂²	C₂×C₉×#41	1	2	yes	—
390	C₂²	C₂×C₉×#41	1	2	yes	—
391	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	2	no	—
402	C₃	C₃×#2498	1	1	yes	characteristic
403	C₂	—	2	4	no	—
404	C₂	—	8	1	no	—
405	C₂	C₂×C₉×#123	1	1	yes	characteristic
406	C₂	C₉×#532	1	1	yes	characteristic
407	C₂	C₉×#537	1	1	yes	characteristic
408	C₂	C₉×#551	1	2	yes	—
409	C₂	C₉×#552	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×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
2. C₂×C₉×#117	C₂	semidirect
3. C₉×#400	C₂	semidirect
4. C₉×#399	C₂	semidirect
5. C₉×#398	C₂	semidirect
6. C₉×#397	C₂	semidirect
7. C₉×#388	C₂	semidirect
8. C₉×#387	C₂	semidirect
10. C₉×#380	C₂	semidirect
11. C₂×C₉×#95	C₂	semidirect
80. #2498	C₉	direct (N × H)
144. C₂×#117	C₂×C₉	semidirect
145. #400	C₂×C₉	semidirect
146. #399	C₂×C₉	semidirect
147. #398	C₂×C₉	semidirect
148. #397	C₂×C₉	semidirect
149. #388	C₂×C₉	semidirect
150. #387	C₂×C₉	semidirect
152. #380	C₂×C₉	semidirect
153. C₂×#95	C₂×C₉	semidirect
333. C₉	#2498	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#123	2
C₂×C₉×#117	2
C₉×#400	2
C₉×#399	2
C₉×#398	2
C₉×#397	2
C₉×#388	2
C₉×#387	2
C₉×#386	2
C₉×#380	2
C₂×C₉×#95	2
C₃×#2498	3

Subgroups — C9×#2498 #11767219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2498 #11767219