Subgroups — C₉×#5648 #13153004

Order 1728.

888 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#896	C₂	1	2	yes	maximal, complemented
7	C₉×#888	C₂	1	2	yes	maximal, complemented
8	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#885	C₂	1	2	yes	maximal, complemented
10	C₉×#878	C₂	1	2	yes	maximal, complemented
11	C₉×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5648	C₃	1	1	yes	maximal, characteristic
13	C₉×#536	—	3	1	no	maximal
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×#67	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	1	yes	characteristic
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₉×#237	—	2	4	no	—
22	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
23	C₂×C₉×Dic₆	—	2	4	no	—
24	C₂×C₉×Dic₆	C₂²	1	2	yes	—
25	C₂×C₉×Dic₆	C₂²	1	2	yes	—
26	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₉×#217	C₂²	1	1	yes	characteristic
31	C₉×#217	C₂²	1	2	yes	—
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
35	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₄×C₉×Dic₃	C₂²	1	2	yes	—
39	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
40	C₂²×C₃×Dic₆	C₂×C₃	1	1	yes	characteristic
41	C₃²×#123	C₂×C₃	1	1	yes	characteristic
42	C₃×#935	C₂×C₃	1	1	yes	characteristic
43	C₃×#929	C₂×C₃	1	1	yes	characteristic
44	C₃×#896	C₂×C₃	1	2	yes	—
45	C₃×#888	C₂×C₃	1	2	yes	—
46	C₃×#886	C₂×C₃	1	1	yes	characteristic
47	C₃×#885	C₂×C₃	1	2	yes	—
48	C₃×#878	C₂×C₃	1	2	yes	—
49	C₃×#877	C₂×C₃	1	1	yes	characteristic
50	C₂×C₉×#41	—	3	1	no	—
51	C₂²×Q₈×C₉	—	3	1	no	—
52	C₉×C₄⋊Q₈	—	3	2	no	—
53	C₉×#124	—	3	2	no	—
54	C₉×#123	—	2	1	no	—
55	C₉×#123	—	3	1	no	—
56	C₉×#123	—	3	1	no	—
57	C₉×#123	—	3	1	no	—
58	C₉×#123	D₃	1	1	yes	characteristic, complemented
59	C₉×C₂²⋊Q₈	—	3	2	no	—
60	C₉×C₂²⋊Q₈	—	3	2	no	—
61	C₉×#117	—	3	1	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
65	C₃×D₄×C₉	—	2	2	no	—
66	C₂×C₃×C₄×C₉	—	2	2	no	—
67	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
70	C₉×#67	—	2	2	no	—
71	C₉×#67	—	2	2	no	—
72	C₂×C₉×Dic₃	—	2	2	no	—
73	C₂×C₉×Dic₃	—	2	2	no	—
74	C₂×C₉×Dic₃	D₄	1	4	yes	—
75	C₂×C₉×Dic₃	C₂³	1	2	yes	—
76	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₉×Dic₃	C₂³	1	2	yes	—
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
80	C₄×D₃×C₉	—	2	2	no	—
81	C₉×Dic₆	—	2	4	no	—
82	C₉×Dic₆	—	2	4	no	—
83	C₉×Dic₆	—	2	2	no	—
84	C₃×#536	—	3	1	no	—
85	#5648	C₉	1	1	yes	characteristic, direct product factor
86	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₃×#237	—	2	4	no	—
94	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×Dic₆	—	2	4	no	—
96	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
97	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
98	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
99	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₃×#217	C₂²×C₃	1	1	yes	characteristic
103	C₃×#217	C₂²×C₃	1	2	yes	—
104	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
105	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
107	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
108	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
109	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
110	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
111	C₉×#41	—	6	4	no	—
112	C₂×Q₈×C₉	—	3	2	no	—
113	C₂×Q₈×C₉	—	3	2	no	—
114	C₂×Q₈×C₉	—	3	1	no	—
115	C₂×Q₈×C₉	—	6	4	no	—
116	C₂×D₄×C₉	—	2	1	no	—
117	C₂×D₄×C₉	—	3	1	no	—
118	C₂×D₄×C₉	—	3	1	no	—
119	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
120	C₂²×C₄×C₉	—	2	1	no	—
121	C₂²×C₄×C₉	—	3	1	no	—
122	C₂²×C₄×C₉	—	3	1	no	—
123	C₂²×C₄×C₉	—	3	1	no	—
124	C₂²×C₄×C₉	—	3	1	no	—
125	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
126	C₉×C₄⋊C₄	—	2	2	no	—
127	C₉×C₄⋊C₄	—	3	2	no	—
128	C₉×C₄⋊C₄	—	3	2	no	—
129	C₉×C₄⋊C₄	—	3	2	no	—
130	C₉×C₄⋊C₄	—	3	2	no	—
131	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
132	C₉×C₂²⋊C₄	—	2	1	no	—
133	C₉×C₂²⋊C₄	—	2	2	no	—
134	C₉×C₂²⋊C₄	—	3	1	no	—
135	C₉×C₂²⋊C₄	—	3	2	no	—
136	C₉×C₂²⋊C₄	—	3	2	no	—
137	C₉×C₂²⋊C₄	—	3	2	no	—
138	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
140	C₄²×C₉	—	3	2	no	—
141	C₂²×C₃×C₉	—	2	2	no	—
142	C₂²×C₃×C₉	—	2	1	no	—
143	C₂²×C₃×C₉	—	2	2	no	—
144	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
145	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
146	C₂×D₃×C₉	—	2	1	no	—
147	C₂×D₃×C₉	—	2	2	no	—
148	C₃×C₄×C₉	—	2	2	no	—
149	C₃×C₄×C₉	—	2	1	no	—
150	C₃×C₄×C₉	—	2	2	no	—
151	C₉×Dic₃	—	2	2	no	—
152	C₉×Dic₃	—	2	1	no	—
153	C₉×Dic₃	—	2	2	no	—
154	C₉×Dic₃	C₂×D₄	1	2	yes	—
155	C₉×Dic₃	C₂×D₄	1	2	yes	—
156	C₂×C₃×#41	—	3	1	no	—
157	C₂²×C₃×Q₈	—	3	1	no	—
158	C₂×#237	C₂×C₉	1	1	yes	characteristic
159	C₂²×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
160	C₃×C₄⋊Q₈	—	3	2	no	—
161	C₃×#124	—	3	2	no	—
162	C₃×#123	—	2	1	no	—
163	C₃×#123	—	3	1	no	—
164	C₃×#123	—	3	1	no	—
165	C₃×#123	—	3	1	no	—
166	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
167	C₃×#123	C₃×D₃	1	1	yes	characteristic
168	C₃×C₂²⋊Q₈	—	3	2	no	—
169	C₃×C₂²⋊Q₈	—	3	2	no	—
170	C₃×#117	—	3	1	no	—
171	#935	C₂×C₉	1	1	yes	characteristic, complemented
172	#929	C₂×C₉	1	1	yes	characteristic, complemented
173	#896	C₂×C₉	1	2	yes	complemented
174	#888	C₂×C₉	1	2	yes	complemented
175	#886	C₂×C₉	1	1	yes	characteristic, complemented
176	#885	C₂×C₉	1	2	yes	complemented
177	#878	C₂×C₉	1	2	yes	complemented
178	#877	C₂×C₉	1	1	yes	characteristic, complemented
179	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
180	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
182	C₃²×D₄	—	2	2	no	—
183	C₂×C₃²×C₄	—	2	2	no	—
184	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
187	C₃×#67	—	2	2	no	—
188	C₃×#67	—	2	2	no	—
189	C₂×C₃×Dic₃	—	2	2	no	—
190	C₂×C₃×Dic₃	—	2	2	no	—
191	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
192	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
193	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
195	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
197	C₃×C₄×D₃	—	2	2	no	—
198	C₃×Dic₆	—	2	4	no	—
199	C₃×Dic₆	—	2	4	no	—
200	C₃×Dic₆	—	2	2	no	—
201	C₂³×C₉	—	2	1	no	—
202	C₂³×C₉	—	2	1	no	—
203	C₂³×C₉	—	3	1	no	—
204	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
205	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
206	Q₈×C₉	—	6	4	no	—
207	Q₈×C₉	—	6	4	no	—
208	Q₈×C₉	—	6	2	no	—
209	D₄×C₉	—	2	2	no	—
210	D₄×C₉	—	4	2	no	—
211	D₄×C₉	—	6	2	no	—
212	D₄×C₉	—	6	2	no	—
213	C₂×C₄×C₉	—	2	2	no	—
214	C₂×C₄×C₉	—	2	2	no	—
215	C₂×C₄×C₉	—	2	2	no	—
216	C₂×C₄×C₉	—	2	1	no	—
217	C₂×C₄×C₉	—	3	4	no	—
218	C₂×C₄×C₉	—	3	1	no	—
219	C₂×C₄×C₉	—	3	1	no	—
220	C₂×C₄×C₉	—	3	2	no	—
221	C₂×C₄×C₉	—	3	2	no	—
222	C₂×C₄×C₉	—	3	1	no	—
223	C₂×C₄×C₉	—	4	2	no	—
224	C₂×C₄×C₉	—	6	2	no	—
225	C₂×C₄×C₉	—	6	2	no	—
226	C₂×C₄×C₉	—	6	2	no	—
227	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
228	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
229	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
230	#536	—	3	1	no	Sylow
231	C₂×C₃×C₉	—	2	2	no	—
232	C₂×C₃×C₉	—	4	1	no	—
233	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₃×C₉	2₋¹⁺⁴	1	2	yes	—
235	D₃×C₉	—	4	1	no	—
236	C₃×#41	—	6	4	no	—
237	C₂×C₃×Q₈	—	3	2	no	—
238	C₂×C₃×Q₈	—	3	2	no	—
239	C₂×C₃×Q₈	—	3	1	no	—
240	C₂×C₃×Q₈	—	6	4	no	—
241	C₂×C₃×D₄	—	2	1	no	—
242	C₂×C₃×D₄	—	3	1	no	—
243	C₂×C₃×D₄	—	3	1	no	—
244	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
245	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	—	3	1	no	—
248	C₂²×C₃×C₄	—	3	1	no	—
249	C₂²×C₃×C₄	—	3	1	no	—
250	C₂²×C₃×C₄	—	3	1	no	—
251	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
253	C₂×#67	C₂²×C₉	1	1	yes	characteristic
254	C₂×#67	C₂²×C₉	1	1	yes	characteristic
255	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
256	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
257	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
258	#237	—	2	4	no	—
259	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
260	C₂×Dic₆	—	2	4	no	—
261	C₂×Dic₆	C₂²×C₉	1	2	yes	—
262	C₂×Dic₆	C₂²×C₉	1	2	yes	—
263	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
264	C₃×C₄⋊C₄	—	2	2	no	—
265	C₃×C₄⋊C₄	—	3	2	no	—
266	C₃×C₄⋊C₄	—	3	2	no	—
267	C₃×C₄⋊C₄	—	3	2	no	—
268	C₃×C₄⋊C₄	—	3	2	no	—
269	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
270	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
271	C₃×C₂²⋊C₄	—	2	1	no	—
272	C₃×C₂²⋊C₄	—	2	2	no	—
273	C₃×C₂²⋊C₄	—	3	1	no	—
274	C₃×C₂²⋊C₄	—	3	2	no	—
275	C₃×C₂²⋊C₄	—	3	2	no	—
276	C₃×C₂²⋊C₄	—	3	2	no	—
277	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
278	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
279	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
281	C₃×C₄²	—	3	2	no	—
282	#217	C₂²×C₉	1	1	yes	characteristic
283	#217	C₂²×C₉	1	2	yes	—
284	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
285	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
286	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
287	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
288	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
289	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
290	C₄×Dic₃	C₂²×C₉	1	2	yes	—
291	C₂²×C₃²	—	2	2	no	—
292	C₂²×C₃²	—	2	1	no	—
293	C₂²×C₃²	—	2	2	no	—
294	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
295	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
296	C₂×C₃×D₃	—	2	1	no	—
297	C₂×C₃×D₃	—	2	2	no	—
298	C₃²×C₄	—	2	2	no	—
299	C₃²×C₄	—	2	1	no	—
300	C₃²×C₄	—	2	2	no	—
301	C₃×Dic₃	—	2	2	no	—
302	C₃×Dic₃	—	2	1	no	—
303	C₃×Dic₃	—	2	2	no	—
304	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
305	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
306	C₂²×C₉	—	2	2	no	—
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	2	no	—
309	C₂²×C₉	—	2	1	no	—
310	C₂²×C₉	—	2	2	no	—
311	C₂²×C₉	—	4	2	no	—
312	C₂²×C₉	—	4	1	no	—
313	C₂²×C₉	—	4	2	no	—
314	C₂²×C₉	—	6	1	no	—
315	C₂²×C₉	—	6	2	no	—
316	C₂²×C₉	D₃×D₄	1	2	yes	—
317	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
318	C₄×C₉	—	2	2	no	—
319	C₄×C₉	—	2	1	no	—
320	C₄×C₉	—	2	2	no	—
321	C₄×C₉	—	3	2	no	—
322	C₄×C₉	—	3	2	no	—
323	C₄×C₉	—	4	2	no	—
324	C₄×C₉	—	4	2	no	—
325	C₄×C₉	—	4	1	no	—
326	C₄×C₉	—	6	1	no	—
327	C₄×C₉	—	6	2	no	—
328	C₄×C₉	—	6	2	no	—
329	C₂×#41	—	3	1	no	—
330	C₂²×Q₈	—	3	1	no	—
331	C₄⋊Q₈	—	3	2	no	—
332	#124	—	3	2	no	—
333	#123	—	3	1	no	—
334	#123	—	3	1	no	—
335	#123	—	3	1	no	—
336	#123	D₃×C₉	1	1	yes	characteristic, complemented
337	C₂²⋊Q₈	—	3	2	no	—
338	C₂²⋊Q₈	—	3	2	no	—
339	#117	—	3	1	no	—
340	C₃×C₉	#536	1	1	yes	characteristic, complemented, Sylow
341	C₂³×C₃	—	2	1	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	3	1	no	—
344	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
345	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
346	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
347	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
348	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
349	C₃×Q₈	—	6	4	no	—
350	C₃×Q₈	—	6	4	no	—
351	C₃×Q₈	—	6	2	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	2	2	no	—
354	C₃×D₄	—	4	2	no	—
355	C₃×D₄	—	6	2	no	—
356	C₃×D₄	—	6	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	3	1	no	—
363	C₂×C₃×C₄	—	3	1	no	—
364	C₂×C₃×C₄	—	3	4	no	—
365	C₂×C₃×C₄	—	3	2	no	—
366	C₂×C₃×C₄	—	3	2	no	—
367	C₂×C₃×C₄	—	3	1	no	—
368	C₂×C₃×C₄	—	4	2	no	—
369	C₂×C₃×C₄	—	6	2	no	—
370	C₂×C₃×C₄	—	6	2	no	—
371	C₂×C₃×C₄	—	6	2	no	—
372	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
373	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
375	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
376	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
377	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
378	#67	—	2	2	no	—
379	#67	—	2	2	no	—
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	—	2	2	no	—
382	C₂×Dic₃	D₄×C₉	1	4	yes	—
383	C₂×Dic₃	C₂³×C₉	1	2	yes	—
384	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
385	C₂×Dic₃	C₂³×C₉	1	2	yes	—
386	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
387	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
388	C₄×D₃	—	2	2	no	—
389	Dic₆	—	2	4	no	—
390	Dic₆	—	2	4	no	—
391	Dic₆	—	2	2	no	—
392	C₂×C₃²	—	2	2	no	—
393	C₂×C₃²	—	4	1	no	—
394	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
395	C₂×C₃²	C₃×2₋¹⁺⁴	1	2	yes	—
396	C₃×D₃	—	4	1	no	—
397	C₂×C₉	—	2	2	no	—
398	C₂×C₉	—	2	1	no	—
399	C₂×C₉	—	2	2	no	—
400	C₂×C₉	—	4	2	no	—
401	C₂×C₉	—	4	1	no	—
402	C₂×C₉	—	8	1	no	—
403	C₂×C₉	—	12	1	no	—
404	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
405	C₂×C₉	#1010	1	2	yes	—
406	#41	—	6	4	no	—
407	C₂×Q₈	—	3	2	no	—
408	C₂×Q₈	—	3	2	no	—
409	C₂×Q₈	—	3	1	no	—
410	C₂×Q₈	—	6	4	no	—
411	C₂×D₄	—	3	1	no	—
412	C₂×D₄	—	3	1	no	—
413	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
414	C₂²×C₄	—	3	1	no	—
415	C₂²×C₄	—	3	1	no	—
416	C₂²×C₄	—	3	1	no	—
417	C₂²×C₄	—	3	1	no	—
418	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
419	C₄⋊C₄	—	3	2	no	—
420	C₄⋊C₄	—	3	2	no	—
421	C₄⋊C₄	—	3	2	no	—
422	C₄⋊C₄	—	3	2	no	—
423	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
424	C₂²⋊C₄	—	3	1	no	—
425	C₂²⋊C₄	—	3	2	no	—
426	C₂²⋊C₄	—	3	2	no	—
427	C₂²⋊C₄	—	3	2	no	—
428	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
429	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
430	C₄²	—	3	2	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	1	no	—
434	C₂²×C₃	—	2	2	no	—
435	C₂²×C₃	—	2	1	no	—
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	2	1	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	—	4	1	no	—
441	C₂²×C₃	—	4	2	no	—
442	C₂²×C₃	—	6	1	no	—
443	C₂²×C₃	—	6	2	no	—
444	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
445	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
446	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
447	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
448	C₂×D₃	—	2	1	no	—
449	C₂×D₃	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	2	1	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	2	2	no	—
456	C₃×C₄	—	3	2	no	—
457	C₃×C₄	—	3	2	no	—
458	C₃×C₄	—	4	2	no	—
459	C₃×C₄	—	4	1	no	—
460	C₃×C₄	—	4	2	no	—
461	C₃×C₄	—	6	1	no	—
462	C₃×C₄	—	6	2	no	—
463	C₃×C₄	—	6	2	no	—
464	Dic₃	—	2	2	no	—
465	Dic₃	—	2	1	no	—
466	Dic₃	—	2	2	no	—
467	Dic₃	C₂×D₄×C₉	1	2	yes	—
468	Dic₃	C₂×D₄×C₉	1	2	yes	—
469	C₃²	C₃×#536	1	1	yes	characteristic
470	C₉	—	2	1	no	—
471	C₉	#5648	1	1	yes	characteristic, direct product factor
472	C₂³	—	3	1	no	—
473	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
474	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
475	Q₈	—	6	4	no	—
476	Q₈	—	6	4	no	—
477	Q₈	—	6	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	6	2	no	—
480	D₄	—	6	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	3	1	no	—
483	C₂×C₄	—	3	1	no	—
484	C₂×C₄	—	3	4	no	—
485	C₂×C₄	—	3	2	no	—
486	C₂×C₄	—	3	2	no	—
487	C₂×C₄	—	3	1	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	—	6	2	no	—
491	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
492	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
493	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	2	2	no	—
496	C₂×C₃	—	2	1	no	—
497	C₂×C₃	—	2	2	no	—
498	C₂×C₃	—	4	2	no	—
499	C₂×C₃	—	4	1	no	—
500	C₂×C₃	—	4	1	no	—
501	C₂×C₃	—	8	1	no	—
502	C₂×C₃	—	12	1	no	—
503	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
504	C₂×C₃	C₉×2₋¹⁺⁴	1	2	yes	—
505	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
506	C₂×C₃	C₃×#1010	1	2	yes	—
507	D₃	—	4	1	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	6	1	no	—
512	C₂²	—	6	2	no	—
513	C₂²	D₃×D₄×C₉	1	2	yes	—
514	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	2	no	—
518	C₄	—	3	2	no	—
519	C₄	—	3	2	no	—
520	C₄	—	6	1	no	—
521	C₄	—	6	2	no	—
522	C₄	—	6	2	no	—
523	C₃	—	2	1	no	—
524	C₃	C₉×#536	1	1	yes	characteristic, complemented
525	C₃	C₃×#5648	1	1	yes	characteristic
526	C₂	—	2	2	no	—
527	C₂	—	4	1	no	—
528	C₂	—	12	1	no	—
529	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
530	C₂	C₉×#1010	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#123	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#237	C₂×C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#123

Complements

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

N	H ≅ G/N	type
2. C₂²×C₉×Dic₆	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₉×#935	C₂	semidirect
5. C₉×#929	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#888	C₂	semidirect
8. C₉×#886	C₂	semidirect
9. C₉×#885	C₂	semidirect
10. C₉×#878	C₂	semidirect
11. C₉×#877	C₂	semidirect
58. C₉×#123	D₃	semidirect
85. #5648	C₉	direct (N × H)
159. C₂²×Dic₆	C₂×C₉	semidirect
166. C₃×#123	C₂×C₉	semidirect
171. #935	C₂×C₉	semidirect
172. #929	C₂×C₉	semidirect
173. #896	C₂×C₉	semidirect
174. #888	C₂×C₉	semidirect
175. #886	C₂×C₉	semidirect
176. #885	C₂×C₉	semidirect
177. #878	C₂×C₉	semidirect
178. #877	C₂×C₉	semidirect
336. #123	D₃×C₉	semidirect
340. C₃×C₉	#536	semidirect
471. C₉	#5648	direct (N × H)
524. C₃	C₉×#536	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×#237	2
C₂²×C₉×Dic₆	2
C₃×C₉×#123	2
C₉×#935	2
C₉×#929	2
C₉×#896	2
C₉×#888	2
C₉×#886	2
C₉×#885	2
C₉×#878	2
C₉×#877	2
C₃×#5648	3
C₉×#536	3

Subgroups — C9×#5648 #13153004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5648 #13153004