Subgroups — C₉×#2993 #11767714

Order 1152.

531 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#436	C₂	1	2	yes	maximal, complemented
6	C₉×#435	C₂	1	2	yes	maximal, complemented
7	C₈×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#433	C₂	1	2	yes	maximal, complemented
9	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#424	C₂	1	2	yes	maximal, complemented
11	C₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2993	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×M₁₆	C₂²	1	2	yes	—
14	C₂×C₉×M₁₆	C₂²	1	2	yes	—
15	C₂²×C₈×C₉	C₂²	1	2	yes	—
16	C₉×#126	C₄	1	2	yes	—
17	C₉×#125	C₄	1	1	yes	characteristic
18	C₉×#124	C₄	1	1	yes	characteristic
19	C₉×#123	C₄	1	2	yes	—
20	C₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
21	C₉×#121	C₄	1	1	yes	characteristic
22	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
23	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
24	C₄×D₄×C₉	C₂²	1	2	yes	—
25	C₉×#117	C₂²	1	2	yes	—
26	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
27	C₉×C₄⋊C₈	C₂²	1	2	yes	—
28	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊C₈	C₂²	1	2	yes	—
32	C₉×C₄⋊C₈	C₂²	1	2	yes	—
33	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₉×#97	C₂²	1	2	yes	—
39	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
41	C₄×C₈×C₉	C₂²	1	2	yes	—
42	C₃×#529	C₂×C₃	1	1	yes	characteristic
43	C₃×#446	C₂×C₃	1	1	yes	characteristic
44	C₃×C₈×Q₈	C₂×C₃	1	1	yes	characteristic
45	C₃×#436	C₂×C₃	1	1	yes	characteristic
46	C₃×#436	C₂×C₃	1	2	yes	—
47	C₃×#435	C₂×C₃	1	2	yes	—
48	C₃×C₈×D₄	C₂×C₃	1	1	yes	characteristic
49	C₃×#433	C₂×C₃	1	2	yes	—
50	C₃×#431	C₂×C₃	1	1	yes	characteristic
51	C₃×#424	C₂×C₃	1	2	yes	—
52	C₃×#423	C₂×C₃	1	1	yes	characteristic
53	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
54	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
55	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
56	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	2	yes	—
60	C₉×M₁₆	—	4	2	no	—
61	C₉×M₁₆	—	4	2	no	—
62	C₂×C₈×C₉	—	4	2	no	—
63	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₈×C₉	C₂³	1	2	yes	—
65	C₂×C₈×C₉	C₂³	1	2	yes	—
66	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
69	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
70	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
71	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
73	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
75	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
81	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
82	C₄²×C₉	C₂³	1	1	yes	characteristic
83	C₄²×C₉	C₂³	1	1	yes	characteristic
84	C₄²×C₉	C₂³	1	2	yes	—
85	#2993	C₉	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
87	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
88	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
89	C₃×#126	C₃×C₄	1	2	yes	—
90	C₃×#125	C₃×C₄	1	1	yes	characteristic
91	C₃×#124	C₃×C₄	1	1	yes	characteristic
92	C₃×#123	C₃×C₄	1	2	yes	—
93	C₃×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
94	C₃×#121	C₃×C₄	1	1	yes	characteristic
95	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
96	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
97	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
98	C₃×#117	C₂²×C₃	1	2	yes	—
99	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
101	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
104	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
105	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
106	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
108	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
109	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
110	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
111	C₃×#97	C₂²×C₃	1	2	yes	—
112	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
114	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
115	C₂³×C₉	C₂²×C₄	1	2	yes	—
116	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
117	Q₈×C₉	—	2	2	no	—
118	D₄×C₉	—	2	2	no	—
119	D₄×C₉	—	4	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	2	no	—
125	C₂×C₄×C₉	—	4	1	no	—
126	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
131	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
132	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
133	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
135	C₈×C₉	—	2	1	no	—
136	C₈×C₉	—	2	2	no	—
137	C₈×C₉	—	2	2	no	—
138	C₈×C₉	—	2	1	no	—
139	C₈×C₉	—	2	1	no	—
140	C₈×C₉	—	2	1	no	—
141	#529	C₂×C₉	1	1	yes	characteristic
142	#446	C₂×C₉	1	1	yes	characteristic, complemented
143	C₈×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
144	#436	C₂×C₉	1	1	yes	characteristic, complemented
145	#436	C₂×C₉	1	2	yes	complemented
146	#435	C₂×C₉	1	2	yes	complemented
147	C₈×D₄	C₂×C₉	1	1	yes	characteristic, complemented
148	#433	C₂×C₉	1	2	yes	complemented
149	#431	C₂×C₉	1	1	yes	characteristic, complemented
150	#424	C₂×C₉	1	2	yes	complemented
151	#423	C₂×C₉	1	1	yes	characteristic, complemented
152	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
155	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
159	C₃×M₁₆	—	4	2	no	—
160	C₃×M₁₆	—	4	2	no	—
161	C₂×C₃×C₈	—	4	2	no	—
162	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
167	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
168	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
169	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
170	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
171	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
172	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
173	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
174	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
175	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
176	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
177	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
178	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
179	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
180	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
181	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
182	C₃×C₄²	C₂³×C₃	1	2	yes	—
183	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₉	—	2	2	no	—
185	C₂²×C₉	—	2	1	no	—
186	C₂²×C₉	—	2	1	no	—
187	C₂²×C₉	—	2	2	no	—
188	C₂²×C₉	—	2	1	no	—
189	C₂²×C₉	—	2	2	no	—
190	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
191	C₄×C₉	—	2	2	no	—
192	C₄×C₉	—	2	1	no	—
193	C₄×C₉	—	2	1	no	—
194	C₄×C₉	—	2	2	no	—
195	C₄×C₉	—	2	1	no	—
196	C₄×C₉	—	2	1	no	—
197	C₄×C₉	—	2	2	no	—
198	C₄×C₉	#131	1	2	yes	—
199	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×M₁₆	C₂²×C₉	1	2	yes	—
202	C₂×M₁₆	C₂²×C₉	1	2	yes	—
203	C₂²×C₈	C₂²×C₉	1	2	yes	—
204	#126	C₄×C₉	1	2	yes	—
205	#125	C₄×C₉	1	1	yes	characteristic
206	#124	C₄×C₉	1	1	yes	characteristic
207	#123	C₄×C₉	1	2	yes	—
208	C₂²⋊Q₈	C₄×C₉	1	1	yes	characteristic
209	#121	C₄×C₉	1	1	yes	characteristic
210	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
211	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
212	C₄×D₄	C₂²×C₉	1	2	yes	—
213	#117	C₂²×C₉	1	2	yes	—
214	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
215	C₄⋊C₈	C₂²×C₉	1	2	yes	—
216	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
217	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
218	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
219	C₄⋊C₈	C₂²×C₉	1	2	yes	—
220	C₄⋊C₈	C₂²×C₉	1	2	yes	—
221	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
222	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
223	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
224	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
225	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
226	#97	C₂²×C₉	1	2	yes	—
227	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
228	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
229	C₄×C₈	C₂²×C₉	1	2	yes	—
230	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
231	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
232	C₃×Q₈	—	2	2	no	—
233	C₃×D₄	—	2	2	no	—
234	C₃×D₄	—	4	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
246	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
247	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
248	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
250	C₃×C₈	—	2	1	no	—
251	C₃×C₈	—	2	2	no	—
252	C₃×C₈	—	2	1	no	—
253	C₃×C₈	—	2	2	no	—
254	C₃×C₈	—	2	1	no	—
255	C₃×C₈	—	2	1	no	—
256	C₂×C₉	—	4	1	no	—
257	C₂×C₉	—	4	2	no	—
258	C₂×C₉	#520	1	1	yes	characteristic
259	C₂×C₉	C₂×#131	1	1	yes	characteristic
260	C₂×C₉	#568	1	1	yes	characteristic
261	C₂×Q₈	C₂×C₄×C₉	1	1	yes	characteristic
262	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic
263	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
264	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
266	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
267	C₂²×C₄	C₂³×C₉	1	2	yes	—
268	M₁₆	—	4	2	no	—
269	M₁₆	—	4	2	no	—
270	C₂×C₈	—	4	2	no	—
271	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
272	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
273	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
274	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
275	C₂×C₈	C₂³×C₉	1	2	yes	—
276	C₂×C₈	C₂³×C₉	1	2	yes	—
277	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
278	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
279	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
280	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
281	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
282	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
283	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
284	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
285	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
286	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
287	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
288	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
289	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
290	C₄²	C₂³×C₉	1	1	yes	characteristic
291	C₄²	C₂³×C₉	1	2	yes	—
292	C₄²	C₂³×C₉	1	1	yes	characteristic
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	C₃×#131	1	2	yes	—
308	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
309	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
310	C₉	#2993	1	1	yes	characteristic, direct product factor, Sylow
311	C₂³	C₂²×C₄×C₉	1	2	yes	—
312	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
313	Q₈	—	2	2	no	—
314	D₄	—	2	2	no	—
315	D₄	—	4	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
323	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
325	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
327	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
328	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
329	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
330	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
331	C₈	—	2	1	no	—
332	C₈	—	2	2	no	—
333	C₈	—	2	1	no	—
334	C₈	—	2	2	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₂×C₃	—	4	1	no	—
338	C₂×C₃	—	4	2	no	—
339	C₂×C₃	C₃×#520	1	1	yes	characteristic
340	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
341	C₂×C₃	C₃×#568	1	1	yes	characteristic
342	C₂²	—	2	2	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	2	no	—
348	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	2	no	—
356	C₄	C₉×#131	1	2	yes	—
357	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
358	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
359	C₃	C₃×#2993	1	1	yes	characteristic
360	C₂	—	4	1	no	—
361	C₂	—	4	2	no	—
362	C₂	C₉×#520	1	1	yes	characteristic
363	C₂	C₂×C₉×#131	1	1	yes	characteristic
364	C₂	C₉×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₃×C₄
prime radical	C₃×#121	C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#446	C₂	semidirect
3. C₈×Q₈×C₉	C₂	semidirect
4. C₉×#436	C₂	semidirect
5. C₉×#436	C₂	semidirect
6. C₉×#435	C₂	semidirect
7. C₈×D₄×C₉	C₂	semidirect
8. C₉×#433	C₂	semidirect
9. C₉×#431	C₂	semidirect
10. C₉×#424	C₂	semidirect
11. C₉×#423	C₂	semidirect
85. #2993	C₉	direct (N × H)
142. #446	C₂×C₉	semidirect
143. C₈×Q₈	C₂×C₉	semidirect
144. #436	C₂×C₉	semidirect
145. #436	C₂×C₉	semidirect
146. #435	C₂×C₉	semidirect
147. C₈×D₄	C₂×C₉	semidirect
148. #433	C₂×C₉	semidirect
149. #431	C₂×C₉	semidirect
150. #424	C₂×C₉	semidirect
151. #423	C₂×C₉	semidirect
310. C₉	#2993	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×#529	2
C₉×#446	2
C₈×Q₈×C₉	2
C₉×#436	2
C₉×#435	2
C₈×D₄×C₉	2
C₉×#433	2
C₉×#431	2
C₉×#424	2
C₉×#423	2
C₃×#2993	3

Subgroups — C9×#2993 #11767714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2993 #11767714