Subgroups — C₉×#2322 #11767043

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 435 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×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#389	C₂	1	2	yes	maximal, complemented
5	C₉×#388	C₂	1	2	yes	maximal, complemented
6	C₉×#387	C₂	1	2	yes	maximal, complemented
7	C₉×#386	C₂	1	1	yes	maximal, characteristic
8	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#385	C₂	1	2	yes	maximal, complemented
10	C₉×#381	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2322	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₉×#123	C₄	1	8	yes	complemented
19	C₄×D₄×C₉	—	2	4	no	—
20	C₂×C₉×C₄⋊C₄	—	2	4	no	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₉	C₂²	1	2	yes	—
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	C₉×#95	C₂²	1	2	yes	—
39	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
41	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
42	C₃×#389	C₂×C₃	1	2	yes	—
43	C₃×#388	C₂×C₃	1	2	yes	—
44	C₃×#387	C₂×C₃	1	2	yes	—
45	C₃×#386	C₂×C₃	1	1	yes	characteristic
46	C₃×#385	C₂×C₃	1	2	yes	—
47	C₃×#385	C₂×C₃	1	1	yes	characteristic
48	C₃×#381	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂⁴×C₉	C₂³	1	1	yes	characteristic
52	C₂×D₄×C₉	—	2	2	no	—
53	C₂×D₄×C₉	—	2	2	no	—
54	C₂×D₄×C₉	C₂×C₄	1	4	yes	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	—	2	2	no	—
57	C₂²×C₄×C₉	—	2	2	no	—
58	C₂²×C₄×C₉	—	2	2	no	—
59	C₂²×C₄×C₉	—	4	2	no	—
60	C₂²×C₄×C₉	—	4	2	no	—
61	C₂²×C₄×C₉	—	4	2	no	—
62	C₂²×C₄×C₉	C₂×C₄	1	4	yes	complemented
63	C₂²×C₄×C₉	D₄	1	4	yes	—
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₉	C₂³	1	2	yes	—
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	C₂³	1	2	yes	—
71	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₉×C₄⋊C₄	—	2	4	no	—
74	C₉×C₄⋊C₄	—	2	4	no	—
75	C₉×C₄⋊C₄	—	2	2	no	—
76	C₉×C₄⋊C₄	—	4	2	no	—
77	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
78	C₉×C₂²⋊C₄	—	2	2	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	—	2	2	no	—
81	C₉×C₂²⋊C₄	—	4	2	no	—
82	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
83	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
84	C₄²×C₉	—	2	2	no	—
85	C₄²×C₉	—	4	2	no	—
86	#2322	C₉	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₃×#123	C₃×C₄	1	8	yes	—
93	C₃×C₄×D₄	—	2	4	no	—
94	C₂×C₃×C₄⋊C₄	—	2	4	no	—
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
108	C₃×#95	C₂²×C₃	1	2	yes	—
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₃×#95	C₂²×C₃	1	2	yes	—
111	C₃×#95	C₂²×C₃	1	2	yes	—
112	C₃×#95	C₂²×C₃	1	2	yes	—
113	C₂³×C₉	—	2	2	no	—
114	C₂³×C₉	—	2	2	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	—	2	1	no	—
117	C₂³×C₉	—	2	2	no	—
118	C₂³×C₉	—	2	2	no	—
119	C₂³×C₉	C₂²×C₄	1	2	yes	—
120	C₂³×C₉	C₂²×C₄	1	2	yes	—
121	C₂³×C₉	C₂×D₄	1	2	yes	—
122	C₂³×C₉	#41	1	2	yes	—
123	C₂³×C₉	C₂⁴	1	1	yes	characteristic
124	D₄×C₉	—	2	8	no	—
125	C₂×C₄×C₉	—	2	8	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	2	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	2	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	4	4	no	—
145	C₂×C₄×C₉	—	4	4	no	—
146	C₂×C₄×C₉	—	4	4	no	—
147	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
148	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
149	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
150	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
151	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
152	C₂×#123	C₂×C₉	1	1	yes	characteristic
153	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
154	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
155	#389	C₂×C₉	1	2	yes	complemented
156	#388	C₂×C₉	1	2	yes	complemented
157	#387	C₂×C₉	1	2	yes	complemented
158	#386	C₂×C₉	1	1	yes	characteristic
159	#385	C₂×C₉	1	2	yes	complemented
160	#385	C₂×C₉	1	1	yes	characteristic, complemented
161	#381	C₂×C₉	1	1	yes	characteristic, complemented
162	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
163	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
164	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₃×D₄	—	2	2	no	—
166	C₂×C₃×D₄	—	2	2	no	—
167	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
168	C₂²×C₃×C₄	—	2	2	no	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	2	2	no	—
171	C₂²×C₃×C₄	—	2	2	no	—
172	C₂²×C₃×C₄	—	4	2	no	—
173	C₂²×C₃×C₄	—	4	2	no	—
174	C₂²×C₃×C₄	—	4	2	no	—
175	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
176	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₃×C₄⋊C₄	—	2	4	no	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	—	4	2	no	—
190	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
191	C₃×C₂²⋊C₄	—	2	2	no	—
192	C₃×C₂²⋊C₄	—	2	2	no	—
193	C₃×C₂²⋊C₄	—	2	2	no	—
194	C₃×C₂²⋊C₄	—	4	2	no	—
195	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
196	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
197	C₃×C₄²	—	2	2	no	—
198	C₃×C₄²	—	4	2	no	—
199	C₂²×C₉	—	2	4	no	—
200	C₂²×C₉	—	2	2	no	—
201	C₂²×C₉	—	2	2	no	—
202	C₂²×C₉	—	2	4	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	4	no	—
205	C₂²×C₉	—	4	1	no	—
206	C₂²×C₉	—	4	1	no	—
207	C₂²×C₉	—	4	2	no	—
208	C₂²×C₉	C₄×D₄	1	4	yes	—
209	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
210	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
211	C₂²×C₉	C₂×#41	1	1	yes	characteristic
212	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
213	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
214	C₄×C₉	—	2	4	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	4	no	—
217	C₄×C₉	—	2	2	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	4	1	no	—
220	C₄×C₉	—	4	2	no	—
221	C₄×C₉	—	4	1	no	—
222	C₄×C₉	—	4	2	no	—
223	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
224	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
225	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
226	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
227	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
228	#123	C₄×C₉	1	8	yes	complemented
229	C₄×D₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
233	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
242	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²×C₉	1	2	yes	—
244	#95	C₂²×C₉	1	2	yes	—
245	#95	C₂²×C₉	1	2	yes	—
246	#95	C₂²×C₉	1	2	yes	—
247	#95	C₂²×C₉	1	2	yes	—
248	#95	C₂²×C₉	1	2	yes	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	2	2	no	—
254	C₂³×C₃	—	2	2	no	—
255	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
256	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
257	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
258	C₂³×C₃	C₃×#41	1	2	yes	—
259	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
260	C₃×D₄	—	2	8	no	—
261	C₂×C₃×C₄	—	2	8	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	4	4	no	—
281	C₂×C₃×C₄	—	4	4	no	—
282	C₂×C₃×C₄	—	4	4	no	—
283	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
284	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
285	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
288	C₂×C₉	—	2	4	no	—
289	C₂×C₉	—	4	2	no	—
290	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×C₉	#520	1	2	yes	—
292	C₂×C₉	#534	1	1	yes	characteristic
293	C₂×C₉	#536	1	1	yes	characteristic
294	C₂×C₉	#539	1	2	yes	—
295	C₂⁴	C₂³×C₉	1	1	yes	characteristic
296	C₂⁴	C₂³×C₉	1	1	yes	characteristic
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	C₂×C₄×C₉	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	C₂×C₄×C₉	1	4	yes	complemented
308	C₂²×C₄	D₄×C₉	1	4	yes	—
309	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
310	C₂²×C₄	C₂³×C₉	1	2	yes	—
311	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
312	C₂²×C₄	C₂³×C₉	1	2	yes	—
313	C₂²×C₄	C₂³×C₉	1	2	yes	—
314	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₉	1	2	yes	—
316	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
328	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
329	C₄²	—	2	2	no	—
330	C₄²	—	4	2	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	2	2	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	2	4	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	4	no	—
337	C₂²×C₃	—	4	1	no	—
338	C₂²×C₃	—	4	1	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	C₃×C₄×D₄	1	4	yes	—
341	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
342	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
344	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
345	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
346	C₃×C₄	—	2	4	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	4	1	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	—	4	2	no	—
355	C₉	#2322	1	1	yes	characteristic, direct product factor, Sylow
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	C₂²×C₄×C₉	1	2	yes	—
363	C₂³	C₂²×C₄×C₉	1	2	yes	—
364	C₂³	C₂×D₄×C₉	1	2	yes	—
365	C₂³	C₉×#41	1	2	yes	—
366	C₂³	C₂⁴×C₉	1	1	yes	characteristic
367	D₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
391	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
392	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
393	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
394	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
395	C₂×C₃	—	2	4	no	—
396	C₂×C₃	—	4	2	no	—
397	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
398	C₂×C₃	C₃×#520	1	2	yes	—
399	C₂×C₃	C₃×#534	1	1	yes	characteristic
400	C₂×C₃	C₃×#536	1	1	yes	characteristic
401	C₂×C₃	C₃×#539	1	2	yes	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₄×D₄×C₉	1	4	yes	—
412	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
413	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
414	C₂²	C₂×C₉×#41	1	1	yes	characteristic
415	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
416	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
417	C₄	—	2	4	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	4	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	2	no	—
426	C₃	C₃×#2322	1	1	yes	characteristic
427	C₂	—	2	4	no	—
428	C₂	—	4	2	no	—
429	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
430	C₂	C₉×#520	1	2	yes	—
431	C₂	C₉×#534	1	1	yes	characteristic
432	C₂	C₉×#536	1	1	yes	characteristic
433	C₂	C₉×#539	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂²×C₉×C₄⋊C₄	C₂	semidirect
4. C₉×#389	C₂	semidirect
5. C₉×#388	C₂	semidirect
6. C₉×#387	C₂	semidirect
8. C₉×#385	C₂	semidirect
9. C₉×#385	C₂	semidirect
10. C₉×#381	C₂	semidirect
11. C₄×C₉×C₂²⋊C₄	C₂	semidirect
18. C₉×#123	C₄	semidirect
62. C₂²×C₄×C₉	C₂×C₄	semidirect
77. C₉×C₄⋊C₄	C₂×C₄	semidirect
82. C₉×C₂²⋊C₄	C₂×C₄	semidirect
83. C₉×C₂²⋊C₄	C₂×C₄	semidirect
86. #2322	C₉	direct (N × H)
154. C₂²×C₄⋊C₄	C₂×C₉	semidirect
155. #389	C₂×C₉	semidirect
156. #388	C₂×C₉	semidirect
157. #387	C₂×C₉	semidirect
159. #385	C₂×C₉	semidirect
160. #385	C₂×C₉	semidirect
161. #381	C₂×C₉	semidirect
162. C₄×C₂²⋊C₄	C₂×C₉	semidirect
228. #123	C₄×C₉	semidirect
307. C₂²×C₄	C₂×C₄×C₉	semidirect
322. C₄⋊C₄	C₂×C₄×C₉	semidirect
327. C₂²⋊C₄	C₂×C₄×C₉	semidirect
328. C₂²⋊C₄	C₂×C₄×C₉	semidirect
355. C₉	#2322	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×C₄×D₄×C₉	2
C₂²×C₉×C₄⋊C₄	2
C₉×#389	2
C₉×#388	2
C₉×#387	2
C₉×#386	2
C₉×#385	2
C₉×#381	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2322	3

Subgroups — C9×#2322 #11767043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2322 #11767043