Subgroups — C₉×#2976 #11767697

Order 1152.

618 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#525	C₂	1	1	yes	maximal, characteristic
2	C₉×#436	C₂	1	2	yes	maximal, complemented
3	C₉×#435	C₂	1	2	yes	maximal, complemented
4	C₉×#435	C₂	1	2	yes	maximal, complemented
5	C₈×D₄×C₉	C₂	1	2	yes	maximal, complemented
6	C₉×#433	C₂	1	2	yes	maximal, complemented
7	C₉×#408	C₂	1	2	yes	maximal, complemented
8	C₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2976	C₃	1	1	yes	maximal, characteristic
11	C₂×C₉×#41	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₉×M₁₆	C₂²	1	2	yes	complemented
16	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₉	C₂²	1	2	yes	complemented
19	C₉×#123	C₄	1	2	yes	—
20	C₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
21	C₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
22	C₉×#121	C₄	1	1	yes	characteristic
23	C₉×#121	C₄	1	1	yes	characteristic
24	C₉×#120	C₄	1	2	yes	—
25	C₄×D₄×C₉	C₂²	1	2	yes	—
26	C₄×D₄×C₉	C₂²	1	2	yes	—
27	C₉×#117	C₂²	1	1	yes	characteristic
28	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
29	C₉×C₄⋊C₈	C₂²	1	2	yes	complemented
30	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
35	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
36	C₉×#97	C₂²	1	2	yes	complemented
37	C₄×C₈×C₉	C₂²	1	2	yes	complemented
38	C₃×#525	C₂×C₃	1	1	yes	characteristic
39	C₃×#436	C₂×C₃	1	2	yes	—
40	C₃×#435	C₂×C₃	1	2	yes	—
41	C₃×#435	C₂×C₃	1	2	yes	—
42	C₃×C₈×D₄	C₂×C₃	1	2	yes	—
43	C₃×#433	C₂×C₃	1	2	yes	—
44	C₃×#408	C₂×C₃	1	2	yes	—
45	C₃×#407	C₂×C₃	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
47	C₂⁴×C₉	C₂×C₄	1	1	yes	characteristic
48	C₉×#41	—	4	1	no	—
49	C₉×#41	—	4	1	no	—
50	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
51	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
52	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
53	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
54	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₉	—	4	1	no	—
56	C₂²×C₄×C₉	—	4	1	no	—
57	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
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	C₉×M₁₆	—	4	1	no	—
65	C₉×M₁₆	—	4	1	no	—
66	C₉×M₁₆	—	4	2	no	—
67	C₂×C₈×C₉	—	4	1	no	—
68	C₂×C₈×C₉	—	4	1	no	—
69	C₂×C₈×C₉	—	4	2	no	—
70	C₂×C₈×C₉	C₂³	1	2	yes	—
71	C₂×C₈×C₉	C₂³	1	2	yes	—
72	C₂×C₈×C₉	C₂³	1	2	yes	—
73	C₂×C₈×C₉	C₂³	1	2	yes	—
74	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₉×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₉×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₉×C₄⋊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	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
82	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
83	C₄²×C₉	C₂³	1	2	yes	—
84	#2976	C₉	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
90	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
93	C₃×#123	C₃×C₄	1	2	yes	—
94	C₃×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
95	C₃×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
96	C₃×#121	C₃×C₄	1	1	yes	characteristic
97	C₃×#121	C₃×C₄	1	1	yes	characteristic
98	C₃×#120	C₃×C₄	1	2	yes	—
99	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
100	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
101	C₃×#117	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
103	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
104	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
105	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
107	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
108	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
109	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
110	C₃×#97	C₂²×C₃	1	2	yes	—
111	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
112	C₂³×C₉	—	2	2	no	—
113	C₂³×C₉	—	4	1	no	—
114	C₂³×C₉	—	4	1	no	—
115	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
117	C₂³×C₉	C₂²×C₄	1	2	yes	—
118	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
119	Q₈×C₉	—	4	1	no	—
120	D₄×C₉	—	2	4	no	—
121	D₄×C₉	—	4	2	no	—
122	D₄×C₉	—	4	1	no	—
123	D₄×C₉	—	4	2	no	—
124	C₂×C₄×C₉	—	2	1	no	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	4	1	no	—
133	C₂×C₄×C₉	—	4	1	no	—
134	C₂×C₄×C₉	—	4	1	no	—
135	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
136	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
137	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
140	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
142	C₈×C₉	—	2	2	no	—
143	C₈×C₉	—	2	2	no	—
144	C₈×C₉	—	2	2	no	—
145	C₈×C₉	—	2	2	no	—
146	#525	C₂×C₉	1	1	yes	characteristic
147	#436	C₂×C₉	1	2	yes	complemented
148	#435	C₂×C₉	1	2	yes	complemented
149	#435	C₂×C₉	1	2	yes	complemented
150	C₈×D₄	C₂×C₉	1	2	yes	complemented
151	#433	C₂×C₉	1	2	yes	complemented
152	#408	C₂×C₉	1	2	yes	complemented
153	#407	C₂×C₉	1	1	yes	characteristic, complemented
154	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
155	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
156	C₃×#41	—	4	1	no	—
157	C₃×#41	—	4	1	no	—
158	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
160	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
161	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
162	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
163	C₂²×C₃×C₄	—	4	1	no	—
164	C₂²×C₃×C₄	—	4	1	no	—
165	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂×C₃×C₄	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	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
172	C₃×M₁₆	—	4	1	no	—
173	C₃×M₁₆	—	4	1	no	—
174	C₃×M₁₆	—	4	2	no	—
175	C₂×C₃×C₈	—	4	1	no	—
176	C₂×C₃×C₈	—	4	1	no	—
177	C₂×C₃×C₈	—	4	2	no	—
178	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
179	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
180	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
181	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
182	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
185	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
186	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
188	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
191	C₃×C₄²	C₂³×C₃	1	2	yes	—
192	C₂²×C₉	—	2	1	no	—
193	C₂²×C₉	—	2	1	no	—
194	C₂²×C₉	—	2	1	no	—
195	C₂²×C₉	—	2	1	no	—
196	C₂²×C₉	—	2	2	no	—
197	C₂²×C₉	—	2	2	no	—
198	C₂²×C₉	—	2	1	no	—
199	C₂²×C₉	—	2	1	no	—
200	C₂²×C₉	—	2	1	no	—
201	C₂²×C₉	—	2	2	no	—
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	—	4	4	no	—
204	C₂²×C₉	#131	1	2	yes	—
205	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
206	C₄×C₉	—	2	1	no	—
207	C₄×C₉	—	2	1	no	—
208	C₄×C₉	—	2	1	no	—
209	C₄×C₉	—	2	2	no	—
210	C₄×C₉	—	2	2	no	—
211	C₄×C₉	—	2	2	no	—
212	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
213	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×#41	C₂²×C₉	1	1	yes	characteristic
215	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
216	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
217	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
218	C₂×M₁₆	C₂²×C₉	1	2	yes	complemented
219	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
220	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
221	C₂²×C₈	C₂²×C₉	1	2	yes	complemented
222	#123	C₄×C₉	1	2	yes	—
223	C₂²⋊Q₈	C₄×C₉	1	1	yes	characteristic
224	C₂²⋊Q₈	C₄×C₉	1	1	yes	characteristic
225	#121	C₄×C₉	1	1	yes	characteristic
226	#121	C₄×C₉	1	1	yes	characteristic
227	#120	C₄×C₉	1	2	yes	—
228	C₄×D₄	C₂²×C₉	1	2	yes	—
229	C₄×D₄	C₂²×C₉	1	2	yes	—
230	#117	C₂²×C₉	1	1	yes	characteristic
231	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
232	C₄⋊C₈	C₂²×C₉	1	2	yes	complemented
233	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
234	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
235	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
236	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
237	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
238	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
239	#97	C₂²×C₉	1	2	yes	complemented
240	C₄×C₈	C₂²×C₉	1	2	yes	complemented
241	C₂³×C₃	—	2	2	no	—
242	C₂³×C₃	—	4	1	no	—
243	C₂³×C₃	—	4	1	no	—
244	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
246	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
247	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
248	C₃×Q₈	—	4	1	no	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	4	2	no	—
251	C₃×D₄	—	4	1	no	—
252	C₃×D₄	—	4	2	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	4	1	no	—
262	C₂×C₃×C₄	—	4	1	no	—
263	C₂×C₃×C₄	—	4	1	no	—
264	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
265	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
266	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
269	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
271	C₃×C₈	—	2	2	no	—
272	C₃×C₈	—	2	2	no	—
273	C₃×C₈	—	2	2	no	—
274	C₃×C₈	—	2	2	no	—
275	C₂×C₉	—	2	2	no	—
276	C₂×C₉	—	4	2	no	—
277	C₂×C₉	—	4	1	no	—
278	C₂×C₉	—	4	1	no	—
279	C₂×C₉	#518	1	1	yes	characteristic
280	C₂×C₉	C₂×#131	1	1	yes	characteristic
281	C₂×C₉	#568	1	1	yes	characteristic
282	C₂⁴	C₂×C₄×C₉	1	1	yes	characteristic
283	#41	—	4	1	no	—
284	#41	—	4	1	no	—
285	C₂×Q₈	C₂×C₄×C₉	1	1	yes	characteristic
286	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
287	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
288	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
289	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₉	1	2	yes	—
299	M₁₆	—	4	1	no	—
300	M₁₆	—	4	1	no	—
301	M₁₆	—	4	2	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	C₂³×C₉	1	2	yes	—
306	C₂×C₈	C₂³×C₉	1	2	yes	—
307	C₂×C₈	C₂³×C₉	1	2	yes	—
308	C₂×C₈	C₂³×C₉	1	2	yes	—
309	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
310	C₄⋊C₄	C₂×C₄×C₉	1	1	yes	characteristic
311	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
312	C₄⋊C₄	C₂×C₄×C₉	1	2	yes	—
313	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
314	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
315	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
316	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
317	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
318	C₄²	C₂³×C₉	1	2	yes	—
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	2	no	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	4	4	no	—
331	C₂²×C₃	C₃×#131	1	2	yes	—
332	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
340	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
341	C₉	#2976	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
346	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
347	C₂³	C₂²×C₄×C₉	1	2	yes	—
348	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
366	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
367	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
370	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
371	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	2	2	no	—
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	4	1	no	—
378	C₂×C₃	—	4	1	no	—
379	C₂×C₃	—	4	2	no	—
380	C₂×C₃	C₃×#518	1	1	yes	characteristic
381	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
382	C₂×C₃	C₃×#568	1	1	yes	characteristic
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	C₉×#131	1	2	yes	—
396	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	2	no	—
403	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
404	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
405	C₃	C₃×#2976	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	1	no	—
408	C₂	—	4	1	no	—
409	C₂	—	4	2	no	—
410	C₂	C₉×#518	1	1	yes	characteristic
411	C₂	C₂×C₉×#131	1	1	yes	characteristic
412	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×#525	C₂×C₃
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×#436	C₂	semidirect
3. C₉×#435	C₂	semidirect
4. C₉×#435	C₂	semidirect
5. C₈×D₄×C₉	C₂	semidirect
6. C₉×#433	C₂	semidirect
7. C₉×#408	C₂	semidirect
8. C₉×#407	C₂	semidirect
9. C₂×C₉×C₂²⋊C₈	C₂	semidirect
15. C₂×C₉×M₁₆	C₂²	semidirect
18. C₂²×C₈×C₉	C₂²	semidirect
28. C₉×C₄⋊C₈	C₂²	semidirect
29. C₉×C₄⋊C₈	C₂²	semidirect
34. C₉×C₂²⋊C₈	C₂²	semidirect
35. C₉×C₂²⋊C₈	C₂²	semidirect
36. C₉×#97	C₂²	semidirect
37. C₄×C₈×C₉	C₂²	semidirect
84. #2976	C₉	direct (N × H)
147. #436	C₂×C₉	semidirect
148. #435	C₂×C₉	semidirect
149. #435	C₂×C₉	semidirect
150. C₈×D₄	C₂×C₉	semidirect
151. #433	C₂×C₉	semidirect
152. #408	C₂×C₉	semidirect
153. #407	C₂×C₉	semidirect
154. C₂×C₂²⋊C₈	C₂×C₉	semidirect
218. C₂×M₁₆	C₂²×C₉	semidirect
221. C₂²×C₈	C₂²×C₉	semidirect
231. C₄⋊C₈	C₂²×C₉	semidirect
232. C₄⋊C₈	C₂²×C₉	semidirect
237. C₂²⋊C₈	C₂²×C₉	semidirect
238. C₂²⋊C₈	C₂²×C₉	semidirect
239. #97	C₂²×C₉	semidirect
240. C₄×C₈	C₂²×C₉	semidirect
341. C₉	#2976	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×#525	2
C₉×#436	2
C₉×#435	2
C₈×D₄×C₉	2
C₉×#433	2
C₉×#408	2
C₉×#407	2
C₂×C₉×C₂²⋊C₈	2
C₃×#2976	3

Subgroups — C9×#2976 #11767697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2976 #11767697