Subgroups — C₉×#2370 #11767091

Order 1152.

696 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₉×#389	C₂	1	1	yes	maximal, characteristic
3	C₉×#389	C₂	1	1	yes	maximal, characteristic
4	C₉×#389	C₂	1	2	yes	maximal
5	C₉×#387	C₂	1	2	yes	maximal
6	C₉×#387	C₂	1	2	yes	maximal
7	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₄×C₉×C₄⋊C₄	C₂	1	2	yes	maximal
9	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₃×#2370	C₃	1	1	yes	maximal, characteristic
13	C₉×#125	C₄	1	8	yes	complemented
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	2	yes	—
18	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₉	C₂²	1	2	yes	—
25	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₉	C₂²	1	2	yes	—
28	C₂×C₄²×C₉	C₂²	1	2	yes	—
29	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
30	C₉×#95	C₂²	1	1	yes	characteristic
31	C₉×#95	C₂²	1	1	yes	characteristic
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	C₉×#95	C₂²	1	2	yes	—
37	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
38	C₃×#389	C₂×C₃	1	1	yes	characteristic
39	C₃×#389	C₂×C₃	1	2	yes	—
40	C₃×#389	C₂×C₃	1	1	yes	characteristic
41	C₃×#387	C₂×C₃	1	2	yes	—
42	C₃×#387	C₂×C₃	1	2	yes	—
43	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
44	C₃×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	—
45	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₉	C₂³	1	2	yes	—
50	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₉	C₂³	1	2	yes	—
55	C₂²×C₄×C₉	C₂³	1	2	yes	—
56	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₉×C₄⋊C₄	—	2	2	no	—
60	C₉×C₄⋊C₄	—	2	4	no	—
61	C₉×C₄⋊C₄	—	2	2	no	—
62	C₉×C₄⋊C₄	—	2	2	no	—
63	C₉×C₄⋊C₄	—	4	2	no	—
64	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
65	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
66	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
67	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
68	C₉×C₄⋊C₄	Q₈	1	4	yes	—
69	C₄²×C₉	—	2	4	no	—
70	C₄²×C₉	—	2	2	no	—
71	C₄²×C₉	—	2	2	no	—
72	C₄²×C₉	—	4	2	no	—
73	C₄²×C₉	—	4	2	no	—
74	C₄²×C₉	C₂×C₄	1	4	yes	—
75	#2370	C₉	1	1	yes	characteristic, direct product factor, Sylow
76	C₃×#125	C₃×C₄	1	8	yes	—
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×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
93	C₃×#95	C₂²×C₃	1	1	yes	characteristic
94	C₃×#95	C₂²×C₃	1	1	yes	characteristic
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	C₃×#95	C₂²×C₃	1	2	yes	—
99	C₃×#95	C₂²×C₃	1	2	yes	—
100	C₂³×C₉	C₂⁴	1	1	yes	characteristic
101	C₂×C₄×C₉	—	2	2	no	—
102	C₂×C₄×C₉	—	2	1	no	—
103	C₂×C₄×C₉	—	2	1	no	—
104	C₂×C₄×C₉	—	2	2	no	—
105	C₂×C₄×C₉	—	2	1	no	—
106	C₂×C₄×C₉	—	2	2	no	—
107	C₂×C₄×C₉	—	2	1	no	—
108	C₂×C₄×C₉	—	2	1	no	—
109	C₂×C₄×C₉	—	2	1	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	1	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	1	no	—
117	C₂×C₄×C₉	—	2	1	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	1	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	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
126	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
127	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
128	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
129	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
130	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
131	C₂×C₄×C₉	#41	1	2	yes	—
132	C₂×C₄×C₉	#41	1	2	yes	—
133	C₂×C₄×C₉	#41	1	2	yes	—
134	C₂×#125	C₂×C₉	1	1	yes	characteristic
135	#389	C₂×C₉	1	1	yes	characteristic
136	#389	C₂×C₉	1	2	yes	—
137	#389	C₂×C₉	1	1	yes	characteristic
138	#387	C₂×C₉	1	2	yes	—
139	#387	C₂×C₉	1	2	yes	—
140	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
141	C₄×C₄⋊C₄	C₂×C₉	1	2	yes	—
142	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
143	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
144	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
148	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
150	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
152	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
153	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₃×C₄⋊C₄	—	2	2	no	—
157	C₃×C₄⋊C₄	—	2	4	no	—
158	C₃×C₄⋊C₄	—	2	2	no	—
159	C₃×C₄⋊C₄	—	2	2	no	—
160	C₃×C₄⋊C₄	—	4	2	no	—
161	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
162	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
163	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
164	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
165	C₃×C₄⋊C₄	C₃×Q₈	1	4	yes	—
166	C₃×C₄²	—	2	4	no	—
167	C₃×C₄²	—	2	2	no	—
168	C₃×C₄²	—	2	2	no	—
169	C₃×C₄²	—	4	2	no	—
170	C₃×C₄²	—	4	2	no	—
171	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
172	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
173	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
174	C₂²×C₉	C₂×#41	1	1	yes	characteristic
175	C₂²×C₉	C₂×#41	1	1	yes	characteristic
176	C₂²×C₉	C₂×#41	1	1	yes	characteristic
177	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
179	C₄×C₉	—	2	4	no	—
180	C₄×C₉	—	2	2	no	—
181	C₄×C₉	—	2	2	no	—
182	C₄×C₉	—	2	4	no	—
183	C₄×C₉	—	2	2	no	—
184	C₄×C₉	—	2	2	no	—
185	C₄×C₉	—	2	4	no	—
186	C₄×C₉	—	4	1	no	—
187	C₄×C₉	—	4	1	no	—
188	C₄×C₉	—	4	2	no	—
189	C₄×C₉	C₄×Q₈	1	4	yes	—
190	#125	C₄×C₉	1	8	yes	complemented
191	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
192	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
193	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
195	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
196	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
197	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
200	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
201	C₂×C₄²	C₂²×C₉	1	2	yes	—
202	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
203	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
204	C₂×C₄²	C₂²×C₉	1	2	yes	—
205	C₂×C₄²	C₂²×C₉	1	2	yes	—
206	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
207	#95	C₂²×C₉	1	1	yes	characteristic
208	#95	C₂²×C₉	1	1	yes	characteristic
209	#95	C₂²×C₉	1	2	yes	—
210	#95	C₂²×C₉	1	2	yes	—
211	#95	C₂²×C₉	1	2	yes	—
212	#95	C₂²×C₉	1	2	yes	—
213	#95	C₂²×C₉	1	2	yes	—
214	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
215	C₂×C₃×C₄	—	2	2	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	1	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
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	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
239	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
240	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
241	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
242	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
243	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
244	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
245	C₂×C₃×C₄	C₃×#41	1	2	yes	—
246	C₂×C₃×C₄	C₃×#41	1	2	yes	—
247	C₂×C₃×C₄	C₃×#41	1	2	yes	—
248	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
249	C₂×C₉	C₄×#41	1	1	yes	characteristic
250	C₂×C₉	#520	1	1	yes	characteristic
251	C₂×C₉	#552	1	1	yes	characteristic
252	C₂×C₉	#553	1	1	yes	characteristic
253	C₂×C₉	#554	1	1	yes	characteristic
254	C₂×C₉	#557	1	1	yes	characteristic
255	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
257	C₂²×C₄	C₂³×C₉	1	2	yes	—
258	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
259	C₂²×C₄	C₂³×C₉	1	2	yes	—
260	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₉	1	2	yes	—
262	C₂²×C₄	C₂³×C₉	1	2	yes	—
263	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	4	2	no	—
271	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
272	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
273	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
274	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
275	C₄⋊C₄	Q₈×C₉	1	4	yes	—
276	C₄²	—	2	4	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	4	2	no	—
280	C₄²	—	4	2	no	—
281	C₄²	C₂×C₄×C₉	1	4	yes	—
282	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
283	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
284	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
285	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
286	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
287	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	2	no	—
292	C₃×C₄	—	2	4	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	4	1	no	—
297	C₃×C₄	—	4	1	no	—
298	C₃×C₄	—	4	2	no	—
299	C₃×C₄	C₃×C₄×Q₈	1	4	yes	—
300	C₉	#2370	1	1	yes	characteristic, direct product factor, Sylow
301	C₂³	C₂⁴×C₉	1	1	yes	characteristic
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
326	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
327	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
328	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
329	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
330	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
331	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
332	C₂×C₄	C₉×#41	1	2	yes	—
333	C₂×C₄	C₉×#41	1	2	yes	—
334	C₂×C₄	C₉×#41	1	2	yes	—
335	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
336	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
337	C₂×C₃	C₃×#520	1	1	yes	characteristic
338	C₂×C₃	C₃×#552	1	1	yes	characteristic
339	C₂×C₃	C₃×#553	1	1	yes	characteristic
340	C₂×C₃	C₃×#554	1	1	yes	characteristic
341	C₂×C₃	C₃×#557	1	1	yes	characteristic
342	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
343	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
344	C₂²	C₂×C₉×#41	1	1	yes	characteristic
345	C₂²	C₂×C₉×#41	1	1	yes	characteristic
346	C₂²	C₂×C₉×#41	1	1	yes	characteristic
347	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	2	no	—
359	C₄	C₄×Q₈×C₉	1	4	yes	—
360	C₃	C₃×#2370	1	1	yes	characteristic
361	C₂	C₂×C₄×Q₈×C₉	1	1	yes	characteristic
362	C₂	C₄×C₉×#41	1	1	yes	characteristic
363	C₂	C₉×#520	1	1	yes	characteristic
364	C₂	C₉×#552	1	1	yes	characteristic
365	C₂	C₉×#553	1	1	yes	characteristic
366	C₂	C₉×#554	1	1	yes	characteristic
367	C₂	C₉×#557	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂⁴×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
13. C₉×#125	C₄	semidirect
75. #2370	C₉	direct (N × H)
190. #125	C₄×C₉	semidirect
300. C₉	#2370	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×#125	2
C₉×#389	2
C₉×#387	2
C₄×C₉×C₄⋊C₄	2
C₃×#2370	3

Subgroups — C9×#2370 #11767091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2370 #11767091