Subgroups — C₉×#2462 #11767183

Order 1152.

678 conjugacy classes of subgroups.

The subgroup lattice has 504 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	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×#398	C₂	1	1	yes	maximal, characteristic
4	C₉×#398	C₂	1	1	yes	maximal, characteristic
5	C₉×#395	C₂	1	1	yes	maximal, characteristic
6	C₉×#395	C₂	1	1	yes	maximal, characteristic
7	C₉×#389	C₂	1	1	yes	maximal, characteristic
8	C₉×#389	C₂	1	1	yes	maximal, characteristic
9	C₉×#387	C₂	1	1	yes	maximal, characteristic
10	C₉×#387	C₂	1	1	yes	maximal, characteristic
11	C₉×#387	C₂	1	1	yes	maximal, characteristic
12	C₉×#387	C₂	1	1	yes	maximal, characteristic
13	C₉×#387	C₂	1	1	yes	maximal, characteristic
14	C₉×#387	C₂	1	1	yes	maximal, characteristic
15	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₃×#2462	C₃	1	1	yes	maximal, characteristic
17	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
18	C₉×#125	—	2	4	no	—
19	C₄×Q₈×C₉	—	2	4	no	—
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	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
37	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
39	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
40	C₉×#95	C₂²	1	1	yes	characteristic
41	C₉×#95	C₂²	1	1	yes	characteristic
42	C₉×#95	C₂²	1	1	yes	characteristic
43	C₉×#95	C₂²	1	1	yes	characteristic
44	C₉×#95	C₂²	1	1	yes	characteristic
45	C₉×#95	C₂²	1	1	yes	characteristic
46	C₉×#95	C₂²	1	1	yes	characteristic
47	C₉×#95	C₂²	1	1	yes	characteristic
48	C₉×#95	C₂²	1	1	yes	characteristic
49	C₉×#95	C₂²	1	1	yes	characteristic
50	C₉×#95	C₂²	1	1	yes	characteristic
51	C₉×#95	C₂²	1	1	yes	characteristic
52	C₉×#95	C₂²	1	1	yes	characteristic
53	C₉×#95	C₂²	1	1	yes	characteristic
54	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
56	C₃×#398	C₂×C₃	1	1	yes	characteristic
57	C₃×#398	C₂×C₃	1	1	yes	characteristic
58	C₃×#395	C₂×C₃	1	1	yes	characteristic
59	C₃×#395	C₂×C₃	1	1	yes	characteristic
60	C₃×#389	C₂×C₃	1	1	yes	characteristic
61	C₃×#389	C₂×C₃	1	1	yes	characteristic
62	C₃×#387	C₂×C₃	1	1	yes	characteristic
63	C₃×#387	C₂×C₃	1	1	yes	characteristic
64	C₃×#387	C₂×C₃	1	1	yes	characteristic
65	C₃×#387	C₂×C₃	1	1	yes	characteristic
66	C₃×#387	C₂×C₃	1	1	yes	characteristic
67	C₃×#387	C₂×C₃	1	1	yes	characteristic
68	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
69	C₂×Q₈×C₉	—	2	2	no	—
70	C₂×Q₈×C₉	—	2	2	no	—
71	C₂×Q₈×C₉	—	2	2	no	—
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₉×C₄⋊C₄	—	2	2	no	—
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	2	2	no	—
90	C₉×C₄⋊C₄	—	2	2	no	—
91	C₉×C₄⋊C₄	—	2	2	no	—
92	C₉×C₄⋊C₄	—	2	2	no	—
93	C₉×C₄⋊C₄	—	2	2	no	—
94	C₉×C₄⋊C₄	—	2	2	no	—
95	C₉×C₄⋊C₄	—	2	2	no	—
96	C₉×C₄⋊C₄	—	2	2	no	—
97	C₉×C₄⋊C₄	—	2	2	no	—
98	C₉×C₄⋊C₄	—	2	2	no	—
99	C₉×C₄⋊C₄	—	2	2	no	—
100	C₉×C₄⋊C₄	D₄	1	4	yes	—
101	C₉×C₄⋊C₄	Q₈	1	4	yes	complemented
102	C₄²×C₉	—	2	2	no	—
103	C₄²×C₉	—	2	2	no	—
104	C₄²×C₉	—	2	2	no	—
105	C₄²×C₉	—	2	2	no	—
106	C₄²×C₉	—	2	2	no	—
107	#2462	C₉	1	1	yes	characteristic, direct product factor, Sylow
108	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
109	C₃×#125	—	2	4	no	—
110	C₃×C₄×Q₈	—	2	4	no	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
131	C₃×#95	C₂²×C₃	1	1	yes	characteristic
132	C₃×#95	C₂²×C₃	1	1	yes	characteristic
133	C₃×#95	C₂²×C₃	1	1	yes	characteristic
134	C₃×#95	C₂²×C₃	1	1	yes	characteristic
135	C₃×#95	C₂²×C₃	1	1	yes	characteristic
136	C₃×#95	C₂²×C₃	1	1	yes	characteristic
137	C₃×#95	C₂²×C₃	1	1	yes	characteristic
138	C₃×#95	C₂²×C₃	1	1	yes	characteristic
139	C₃×#95	C₂²×C₃	1	1	yes	characteristic
140	C₃×#95	C₂²×C₃	1	1	yes	characteristic
141	C₃×#95	C₂²×C₃	1	1	yes	characteristic
142	C₃×#95	C₂²×C₃	1	1	yes	characteristic
143	C₃×#95	C₂²×C₃	1	1	yes	characteristic
144	C₃×#95	C₂²×C₃	1	1	yes	characteristic
145	C₂³×C₉	C₂⁴	1	1	yes	characteristic
146	Q₈×C₉	—	2	8	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	2	1	no	—
162	C₂×C₄×C₉	—	2	1	no	—
163	C₂×C₄×C₉	—	2	1	no	—
164	C₂×C₄×C₉	—	2	1	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	1	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	1	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	2	1	no	—
178	C₂×C₄×C₉	—	2	1	no	—
179	C₂×C₄×C₉	—	2	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
184	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
185	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
186	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
187	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
188	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
189	C₂×C₄×C₉	#41	1	2	yes	—
190	C₂×C₄×C₉	#41	1	2	yes	—
191	C₂×C₄×C₉	#41	1	2	yes	—
192	C₂×#125	C₂×C₉	1	1	yes	characteristic
193	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic
194	#398	C₂×C₉	1	1	yes	characteristic
195	#398	C₂×C₉	1	1	yes	characteristic
196	#395	C₂×C₉	1	1	yes	characteristic
197	#395	C₂×C₉	1	1	yes	characteristic
198	#389	C₂×C₉	1	1	yes	characteristic
199	#389	C₂×C₉	1	1	yes	characteristic
200	#387	C₂×C₉	1	1	yes	characteristic
201	#387	C₂×C₉	1	1	yes	characteristic
202	#387	C₂×C₉	1	1	yes	characteristic
203	#387	C₂×C₉	1	1	yes	characteristic
204	#387	C₂×C₉	1	1	yes	characteristic
205	#387	C₂×C₉	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
207	C₂×C₃×Q₈	—	2	2	no	—
208	C₂×C₃×Q₈	—	2	2	no	—
209	C₂×C₃×Q₈	—	2	2	no	—
210	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
225	C₃×C₄⋊C₄	—	2	2	no	—
226	C₃×C₄⋊C₄	—	2	2	no	—
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	2	no	—
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₄⋊C₄	—	2	2	no	—
231	C₃×C₄⋊C₄	—	2	2	no	—
232	C₃×C₄⋊C₄	—	2	2	no	—
233	C₃×C₄⋊C₄	—	2	2	no	—
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	2	2	no	—
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	2	2	no	—
238	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
239	C₃×C₄⋊C₄	C₃×Q₈	1	4	yes	—
240	C₃×C₄²	—	2	2	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	2	2	no	—
243	C₃×C₄²	—	2	2	no	—
244	C₃×C₄²	—	2	2	no	—
245	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
246	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
247	C₂²×C₉	C₂×#41	1	1	yes	characteristic
248	C₂²×C₉	C₂×#41	1	1	yes	characteristic
249	C₂²×C₉	C₂×#41	1	1	yes	characteristic
250	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
251	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
252	C₄×C₉	—	2	2	no	—
253	C₄×C₉	—	2	2	no	—
254	C₄×C₉	—	2	2	no	—
255	C₄×C₉	—	2	2	no	—
256	C₄×C₉	—	2	2	no	—
257	C₄×C₉	—	2	2	no	—
258	C₄×C₉	—	2	2	no	—
259	C₄×C₉	—	2	2	no	—
260	C₄×C₉	—	2	2	no	—
261	C₄×C₉	—	4	1	no	—
262	C₄×C₉	—	4	1	no	—
263	C₄×C₉	—	4	1	no	—
264	C₄×C₉	—	4	1	no	—
265	C₄×C₉	—	4	1	no	—
266	C₄×C₉	—	4	1	no	—
267	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
268	#125	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
285	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
286	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
287	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
288	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
289	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
290	#95	C₂²×C₉	1	1	yes	characteristic
291	#95	C₂²×C₉	1	1	yes	characteristic
292	#95	C₂²×C₉	1	1	yes	characteristic
293	#95	C₂²×C₉	1	1	yes	characteristic
294	#95	C₂²×C₉	1	1	yes	characteristic
295	#95	C₂²×C₉	1	1	yes	characteristic
296	#95	C₂²×C₉	1	1	yes	characteristic
297	#95	C₂²×C₉	1	1	yes	characteristic
298	#95	C₂²×C₉	1	1	yes	characteristic
299	#95	C₂²×C₉	1	1	yes	characteristic
300	#95	C₂²×C₉	1	1	yes	characteristic
301	#95	C₂²×C₉	1	1	yes	characteristic
302	#95	C₂²×C₉	1	1	yes	characteristic
303	#95	C₂²×C₉	1	1	yes	characteristic
304	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
305	C₃×Q₈	—	2	8	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	1	no	—
312	C₂×C₃×C₄	—	2	1	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
344	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
345	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
346	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
347	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
348	C₂×C₃×C₄	C₃×#41	1	2	yes	—
349	C₂×C₃×C₄	C₃×#41	1	2	yes	—
350	C₂×C₃×C₄	C₃×#41	1	2	yes	—
351	C₂×C₉	#525	1	1	yes	characteristic
352	C₂×C₉	#533	1	1	yes	characteristic
353	C₂×C₉	#541	1	1	yes	characteristic
354	C₂×C₉	#547	1	1	yes	characteristic
355	C₂×C₉	D₄×Q₈	1	1	yes	characteristic
356	C₂×C₉	#552	1	1	yes	characteristic
357	C₂×C₉	#557	1	1	yes	characteristic
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
362	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
364	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
365	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
366	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
367	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
368	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
369	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
370	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
371	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
372	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
373	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
374	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
375	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	D₄×C₉	1	4	yes	—
390	C₄⋊C₄	Q₈×C₉	1	4	yes	complemented
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
397	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
398	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
399	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
400	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
401	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
402	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	—	2	2	no	—
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	4	1	no	—
413	C₃×C₄	—	4	1	no	—
414	C₃×C₄	—	4	1	no	—
415	C₃×C₄	—	4	1	no	—
416	C₃×C₄	—	4	1	no	—
417	C₃×C₄	—	4	1	no	—
418	C₉	#2462	1	1	yes	characteristic, direct product factor, Sylow
419	C₂³	C₂⁴×C₉	1	1	yes	characteristic
420	Q₈	—	2	8	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
458	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
459	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
460	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
461	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
462	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
463	C₂×C₄	C₉×#41	1	2	yes	—
464	C₂×C₄	C₉×#41	1	2	yes	—
465	C₂×C₄	C₉×#41	1	2	yes	—
466	C₂×C₃	C₃×#525	1	1	yes	characteristic
467	C₂×C₃	C₃×#533	1	1	yes	characteristic
468	C₂×C₃	C₃×#541	1	1	yes	characteristic
469	C₂×C₃	C₃×#547	1	1	yes	characteristic
470	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
471	C₂×C₃	C₃×#552	1	1	yes	characteristic
472	C₂×C₃	C₃×#557	1	1	yes	characteristic
473	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
474	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
475	C₂²	C₂×C₉×#41	1	1	yes	characteristic
476	C₂²	C₂×C₉×#41	1	1	yes	characteristic
477	C₂²	C₂×C₉×#41	1	1	yes	characteristic
478	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
479	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₃	C₃×#2462	1	1	yes	characteristic
496	C₂	C₉×#525	1	1	yes	characteristic
497	C₂	C₉×#533	1	1	yes	characteristic
498	C₂	C₉×#541	1	1	yes	characteristic
499	C₂	C₉×#547	1	1	yes	characteristic
500	C₂	D₄×Q₈×C₉	1	1	yes	characteristic
501	C₂	C₉×#552	1	1	yes	characteristic
502	C₂	C₉×#557	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂⁴×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
101. C₉×C₄⋊C₄	Q₈	semidirect
107. #2462	C₉	direct (N × H)
390. C₄⋊C₄	Q₈×C₉	semidirect
418. C₉	#2462	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
C₂×C₄×Q₈×C₉	2
C₉×#398	2
C₉×#395	2
C₉×#389	2
C₉×#387	2
C₄×C₉×C₄⋊C₄	2
C₃×#2462	3

Subgroups — C9×#2462 #11767183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2462 #11767183