Subgroups — C₉×#4956 #13142485

Order 1728.

990 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4956	C₃	1	1	yes	maximal, characteristic
9	C₉×#386	—	3	1	no	maximal
10	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
11	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×#67	—	2	2	no	—
15	C₂×C₉×#67	—	2	2	no	—
16	C₂×C₉×#67	C₄	1	4	yes	complemented
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	—	2	2	no	—
21	C₂×C₄×D₃×C₉	—	2	2	no	—
22	C₂×C₄×D₃×C₉	—	2	2	no	—
23	C₃×C₉×C₂²⋊C₄	—	2	2	no	—
24	C₉×#217	—	2	2	no	—
25	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
26	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
27	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₂²×D₄×C₉	—	3	1	no	—
32	C₂³×C₄×C₉	—	3	1	no	—
33	C₃×C₃⋊#95	C₂×C₃	1	1	yes	characteristic
34	C₃×C₃⋊#95	C₂×C₃	1	1	yes	characteristic
35	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
36	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
37	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
38	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
39	C₉×#95	—	3	1	no	—
40	C₉×#95	—	3	1	no	—
41	C₂³×C₃×C₉	—	2	1	no	—
42	C₂³×C₃×C₉	—	2	1	no	—
43	C₂³×C₃×C₉	—	2	1	no	—
44	C₂³×C₃×C₉	—	2	1	no	—
45	C₂³×C₃×C₉	—	2	1	no	—
46	C₂³×C₃×C₉	—	2	1	no	—
47	C₂³×C₃×C₉	C₂×C₄	1	2	yes	complemented
48	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
49	C₂²×D₃×C₉	—	2	1	no	—
50	C₂²×D₃×C₉	—	2	1	no	—
51	C₂²×D₃×C₉	—	2	1	no	—
52	C₂²×D₃×C₉	—	2	1	no	—
53	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
54	C₂²×D₃×C₉	D₄	1	2	yes	—
55	C₂²×D₃×C₉	D₄	1	2	yes	—
56	C₂×C₃×C₄×C₉	—	2	1	no	—
57	C₂×C₃×C₄×C₉	—	2	1	no	—
58	C₂×C₃×C₄×C₉	—	2	1	no	—
59	C₂×C₃×C₄×C₉	—	2	1	no	—
60	C₂×C₃×C₄×C₉	—	2	1	no	—
61	C₂×C₃×C₄×C₉	D₄	1	2	yes	complemented
62	C₉×#67	—	2	8	no	—
63	C₂×C₉×Dic₃	—	2	1	no	—
64	C₂×C₉×Dic₃	—	2	1	no	—
65	C₂×C₉×Dic₃	—	2	1	no	—
66	C₂×C₉×Dic₃	—	2	1	no	—
67	C₂×C₉×Dic₃	—	2	1	no	—
68	C₂×C₉×Dic₃	—	2	1	no	—
69	C₂×C₉×Dic₃	—	2	1	no	—
70	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	complemented
71	C₂×C₉×Dic₃	D₄	1	2	yes	complemented
72	C₄×D₃×C₉	—	2	8	no	—
73	C₃×#386	—	3	1	no	—
74	#4956	C₉	1	1	yes	characteristic, direct product factor
75	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
76	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×#67	—	2	2	no	—
80	C₂×C₃×#67	—	2	2	no	—
81	C₂×C₃×#67	C₃×C₄	1	4	yes	—
82	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄×D₃	—	2	2	no	—
86	C₂×C₃×C₄×D₃	—	2	2	no	—
87	C₂×C₃×C₄×D₃	—	2	2	no	—
88	C₂⁴×C₉	—	2	1	no	—
89	C₂⁴×C₉	—	3	1	no	—
90	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
91	C₃²×C₂²⋊C₄	—	2	2	no	—
92	C₃×#217	—	2	2	no	—
93	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
94	C₂×D₄×C₉	—	3	4	no	—
95	C₂×D₄×C₉	—	6	2	no	—
96	C₂×D₄×C₉	—	6	2	no	—
97	C₂²×C₄×C₉	—	2	1	no	—
98	C₂²×C₄×C₉	—	2	1	no	—
99	C₂²×C₄×C₉	—	3	1	no	—
100	C₂²×C₄×C₉	—	3	1	no	—
101	C₂²×C₄×C₉	—	3	1	no	—
102	C₂²×C₄×C₉	—	6	2	no	—
103	C₂²×C₄×C₉	—	6	2	no	—
104	C₂²×C₄×C₉	—	6	2	no	—
105	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
107	C₉×C₂²⋊C₄	—	2	4	no	—
108	C₉×C₂²⋊C₄	—	2	2	no	—
109	C₉×C₂²⋊C₄	—	6	2	no	—
110	C₉×C₂²⋊C₄	—	6	2	no	—
111	C₂²×C₃×C₉	—	2	2	no	—
112	C₂²×C₃×C₉	—	2	2	no	—
113	C₂²×C₃×C₉	—	2	2	no	—
114	C₂²×C₃×C₉	—	4	1	no	—
115	C₂²×C₃×C₉	—	4	1	no	—
116	C₂²×C₃×C₉	—	4	1	no	—
117	C₂²×C₃×C₉	—	4	1	no	—
118	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₃×C₉	#41	1	1	yes	characteristic
124	C₂²×C₃×C₉	#41	1	1	yes	characteristic
125	C₂×D₃×C₉	—	2	2	no	—
126	C₂×D₃×C₉	—	2	2	no	—
127	C₂×D₃×C₉	—	2	2	no	—
128	C₂×D₃×C₉	—	2	2	no	—
129	C₂×D₃×C₉	—	2	2	no	—
130	C₂×D₃×C₉	—	2	2	no	—
131	C₂×D₃×C₉	C₂²⋊C₄	1	4	yes	complemented
132	C₃×C₄×C₉	—	2	2	no	—
133	C₃×C₄×C₉	—	4	1	no	—
134	C₉×Dic₃	—	2	2	no	—
135	C₉×Dic₃	—	2	2	no	—
136	C₉×Dic₃	—	4	1	no	—
137	C₂²×C₃×D₄	—	3	1	no	—
138	C₂³×C₃×C₄	—	3	1	no	—
139	C₂²×#67	C₂×C₉	1	1	yes	characteristic
140	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
141	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
143	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
144	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
145	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
146	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
147	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
148	C₃×#95	—	3	1	no	—
149	C₃×#95	—	3	1	no	—
150	C₃⋊#95	C₂×C₉	1	1	yes	characteristic, complemented
151	C₃⋊#95	C₂×C₉	1	1	yes	characteristic, complemented
152	C₂³×C₃²	—	2	1	no	—
153	C₂³×C₃²	—	2	1	no	—
154	C₂³×C₃²	—	2	1	no	—
155	C₂³×C₃²	—	2	1	no	—
156	C₂³×C₃²	—	2	1	no	—
157	C₂³×C₃²	—	2	1	no	—
158	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
159	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₃×D₃	—	2	1	no	—
161	C₂²×C₃×D₃	—	2	1	no	—
162	C₂²×C₃×D₃	—	2	1	no	—
163	C₂²×C₃×D₃	—	2	1	no	—
164	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
165	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
166	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
167	C₂×C₃²×C₄	—	2	1	no	—
168	C₂×C₃²×C₄	—	2	1	no	—
169	C₂×C₃²×C₄	—	2	1	no	—
170	C₂×C₃²×C₄	—	2	1	no	—
171	C₂×C₃²×C₄	—	2	1	no	—
172	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
173	C₃×#67	—	2	8	no	—
174	C₂×C₃×Dic₃	—	2	1	no	—
175	C₂×C₃×Dic₃	—	2	1	no	—
176	C₂×C₃×Dic₃	—	2	1	no	—
177	C₂×C₃×Dic₃	—	2	1	no	—
178	C₂×C₃×Dic₃	—	2	1	no	—
179	C₂×C₃×Dic₃	—	2	1	no	—
180	C₂×C₃×Dic₃	—	2	1	no	—
181	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
182	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
183	C₃×C₄×D₃	—	2	8	no	—
184	C₂³×C₉	—	2	2	no	—
185	C₂³×C₉	—	2	2	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	1	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	2	1	no	—
190	C₂³×C₉	—	2	1	no	—
191	C₂³×C₉	—	2	1	no	—
192	C₂³×C₉	—	2	2	no	—
193	C₂³×C₉	—	2	1	no	—
194	C₂³×C₉	—	3	2	no	—
195	C₂³×C₉	—	3	2	no	—
196	C₂³×C₉	—	3	2	no	—
197	C₂³×C₉	—	4	1	no	—
198	C₂³×C₉	—	4	1	no	—
199	C₂³×C₉	—	4	1	no	—
200	C₂³×C₉	—	4	1	no	—
201	C₂³×C₉	—	6	1	no	—
202	C₂³×C₉	—	6	1	no	—
203	C₂³×C₉	—	6	1	no	—
204	C₂³×C₉	—	6	1	no	—
205	C₂³×C₉	C₄×D₃	1	2	yes	complemented
206	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
207	D₄×C₉	—	6	8	no	—
208	C₂×C₄×C₉	—	2	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	2	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	2	2	no	—
215	C₂×C₄×C₉	—	3	2	no	—
216	C₂×C₄×C₉	—	3	2	no	—
217	C₂×C₄×C₉	—	4	1	no	—
218	C₂×C₄×C₉	—	4	1	no	—
219	C₂×C₄×C₉	—	4	1	no	—
220	C₂×C₄×C₉	—	4	1	no	—
221	C₂×C₄×C₉	—	6	8	no	—
222	C₂×C₄×C₉	—	6	1	no	—
223	C₂×C₄×C₉	—	6	1	no	—
224	C₂×C₄×C₉	—	6	1	no	—
225	C₂×C₄×C₉	—	6	1	no	—
226	C₂×C₄×C₉	—	6	1	no	—
227	C₂×C₄×C₉	—	6	1	no	—
228	C₂×C₄×C₉	—	6	1	no	—
229	C₂×C₄×C₉	#67	1	2	yes	complemented
230	#386	—	3	1	no	Sylow
231	C₂×C₃×C₉	—	4	2	no	—
232	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
234	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
235	C₂×C₃×C₉	#120	1	1	yes	characteristic
236	C₂×C₃×C₉	#121	1	1	yes	characteristic
237	C₂×C₃×C₉	#121	1	1	yes	characteristic
238	C₂×C₃×C₉	#123	1	1	yes	characteristic
239	D₃×C₉	—	2	4	no	—
240	C₂⁴×C₃	—	2	1	no	—
241	C₂⁴×C₃	—	3	1	no	—
242	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
243	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
244	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
245	C₂×C₃×D₄	—	3	4	no	—
246	C₂×C₃×D₄	—	6	2	no	—
247	C₂×C₃×D₄	—	6	2	no	—
248	C₂²×C₃×C₄	—	2	1	no	—
249	C₂²×C₃×C₄	—	2	1	no	—
250	C₂²×C₃×C₄	—	3	1	no	—
251	C₂²×C₃×C₄	—	3	1	no	—
252	C₂²×C₃×C₄	—	3	1	no	—
253	C₂²×C₃×C₄	—	6	2	no	—
254	C₂²×C₃×C₄	—	6	2	no	—
255	C₂²×C₃×C₄	—	6	2	no	—
256	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
260	C₂×#67	—	2	2	no	—
261	C₂×#67	—	2	2	no	—
262	C₂×#67	C₄×C₉	1	4	yes	complemented
263	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
264	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
265	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
266	C₂×C₄×D₃	—	2	2	no	—
267	C₂×C₄×D₃	—	2	2	no	—
268	C₂×C₄×D₃	—	2	2	no	—
269	C₃×C₂²⋊C₄	—	2	4	no	—
270	C₃×C₂²⋊C₄	—	2	2	no	—
271	C₃×C₂²⋊C₄	—	2	2	no	—
272	C₃×C₂²⋊C₄	—	6	2	no	—
273	C₃×C₂²⋊C₄	—	6	2	no	—
274	#217	—	2	2	no	—
275	(C₂×D₃)⋊C₄	—	2	2	no	—
276	C₂²×C₃²	—	2	2	no	—
277	C₂²×C₃²	—	2	2	no	—
278	C₂²×C₃²	—	2	2	no	—
279	C₂²×C₃²	—	4	1	no	—
280	C₂²×C₃²	—	4	1	no	—
281	C₂²×C₃²	—	4	1	no	—
282	C₂²×C₃²	—	4	1	no	—
283	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
284	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
289	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
290	C₂×C₃×D₃	—	2	2	no	—
291	C₂×C₃×D₃	—	2	2	no	—
292	C₂×C₃×D₃	—	2	2	no	—
293	C₂×C₃×D₃	—	2	2	no	—
294	C₂×C₃×D₃	—	2	2	no	—
295	C₂×C₃×D₃	—	2	2	no	—
296	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	4	yes	—
297	C₃²×C₄	—	2	2	no	—
298	C₃²×C₄	—	4	1	no	—
299	C₃×Dic₃	—	2	2	no	—
300	C₃×Dic₃	—	2	2	no	—
301	C₃×Dic₃	—	4	1	no	—
302	C₂²×C₉	—	2	4	no	—
303	C₂²×C₉	—	2	2	no	—
304	C₂²×C₉	—	2	2	no	—
305	C₂²×C₉	—	2	2	no	—
306	C₂²×C₉	—	2	1	no	—
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	1	no	—
309	C₂²×C₉	—	2	1	no	—
310	C₂²×C₉	—	2	1	no	—
311	C₂²×C₉	—	2	1	no	—
312	C₂²×C₉	—	2	1	no	—
313	C₂²×C₉	—	3	4	no	—
314	C₂²×C₉	—	4	2	no	—
315	C₂²×C₉	—	4	2	no	—
316	C₂²×C₉	—	4	2	no	—
317	C₂²×C₉	—	4	2	no	—
318	C₂²×C₉	—	4	2	no	—
319	C₂²×C₉	—	4	2	no	—
320	C₂²×C₉	—	4	1	no	—
321	C₂²×C₉	—	4	1	no	—
322	C₂²×C₉	—	4	1	no	—
323	C₂²×C₉	—	4	1	no	—
324	C₂²×C₉	—	6	2	no	—
325	C₂²×C₉	—	6	2	no	—
326	C₂²×C₉	—	6	2	no	—
327	C₂²×C₉	—	6	2	no	—
328	C₂²×C₉	—	6	2	no	—
329	C₂²×C₉	—	6	2	no	—
330	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂²×C₉	#235	1	1	yes	characteristic
332	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
333	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
334	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
335	C₂²×C₉	#237	1	1	yes	characteristic
336	C₂²×C₉	C₂×#67	1	1	yes	characteristic
337	C₄×C₉	—	2	2	no	—
338	C₄×C₉	—	4	2	no	—
339	C₄×C₉	—	4	2	no	—
340	C₄×C₉	—	4	1	no	—
341	C₄×C₉	—	6	2	no	—
342	C₄×C₉	—	6	2	no	—
343	C₄×C₉	—	12	1	no	—
344	C₂²×D₄	—	3	1	no	—
345	C₂³×C₄	—	3	1	no	—
346	C₂×C₂²⋊C₄	—	3	1	no	—
347	C₂×C₂²⋊C₄	—	3	1	no	—
348	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
349	#95	—	3	1	no	—
350	#95	—	3	1	no	—
351	C₃×C₉	#386	1	1	yes	characteristic, complemented, Sylow
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	1	no	—
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	—	2	2	no	—
367	C₂³×C₃	—	2	1	no	—
368	C₂³×C₃	—	3	2	no	—
369	C₂³×C₃	—	3	2	no	—
370	C₂³×C₃	—	3	2	no	—
371	C₂³×C₃	—	4	1	no	—
372	C₂³×C₃	—	4	1	no	—
373	C₂³×C₃	—	4	1	no	—
374	C₂³×C₃	—	4	1	no	—
375	C₂³×C₃	—	6	1	no	—
376	C₂³×C₃	—	6	1	no	—
377	C₂³×C₃	—	6	1	no	—
378	C₂³×C₃	—	6	1	no	—
379	C₂³×C₃	C₂×C₄×C₉	1	2	yes	complemented
380	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
381	C₂³×C₃	C₃×C₄×D₃	1	2	yes	—
382	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
383	C₂²×D₃	—	2	1	no	—
384	C₂²×D₃	—	2	1	no	—
385	C₂²×D₃	—	2	1	no	—
386	C₂²×D₃	—	2	1	no	—
387	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
388	C₂²×D₃	D₄×C₉	1	2	yes	—
389	C₂²×D₃	D₄×C₉	1	2	yes	—
390	C₃×D₄	—	6	8	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	3	2	no	—
404	C₂×C₃×C₄	—	3	2	no	—
405	C₂×C₃×C₄	—	4	1	no	—
406	C₂×C₃×C₄	—	4	1	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	—	4	1	no	—
409	C₂×C₃×C₄	—	6	8	no	—
410	C₂×C₃×C₄	—	6	1	no	—
411	C₂×C₃×C₄	—	6	1	no	—
412	C₂×C₃×C₄	—	6	1	no	—
413	C₂×C₃×C₄	—	6	1	no	—
414	C₂×C₃×C₄	—	6	1	no	—
415	C₂×C₃×C₄	—	6	1	no	—
416	C₂×C₃×C₄	—	6	1	no	—
417	C₂×C₃×C₄	D₄×C₉	1	2	yes	complemented
418	C₂×C₃×C₄	C₃×#67	1	2	yes	—
419	#67	—	2	8	no	—
420	C₂×Dic₃	—	2	1	no	—
421	C₂×Dic₃	—	2	1	no	—
422	C₂×Dic₃	—	2	1	no	—
423	C₂×Dic₃	—	2	1	no	—
424	C₂×Dic₃	—	2	1	no	—
425	C₂×Dic₃	—	2	1	no	—
426	C₂×Dic₃	—	2	1	no	—
427	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	complemented
428	C₂×Dic₃	D₄×C₉	1	2	yes	complemented
429	C₄×D₃	—	2	8	no	—
430	C₂×C₃²	—	4	2	no	—
431	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
433	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
434	C₂×C₃²	C₃×#120	1	1	yes	characteristic
435	C₂×C₃²	C₃×#121	1	1	yes	characteristic
436	C₂×C₃²	C₃×#121	1	1	yes	characteristic
437	C₂×C₃²	C₃×#123	1	1	yes	characteristic
438	C₃×D₃	—	2	4	no	—
439	C₂×C₉	—	2	1	no	—
440	C₂×C₉	—	2	1	no	—
441	C₂×C₉	—	2	1	no	—
442	C₂×C₉	—	2	1	no	—
443	C₂×C₉	—	2	1	no	—
444	C₂×C₉	—	2	1	no	—
445	C₂×C₉	—	2	1	no	—
446	C₂×C₉	—	4	4	no	—
447	C₂×C₉	—	4	2	no	—
448	C₂×C₉	—	6	4	no	—
449	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
450	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
451	C₂×C₉	#883	1	1	yes	characteristic
452	C₂×C₉	#884	1	1	yes	characteristic
453	C₂×C₉	C₄×#67	1	1	yes	characteristic
454	C₂×C₉	#937	1	1	yes	characteristic
455	C₂×C₉	#938	1	1	yes	characteristic
456	C₂⁴	—	3	1	no	—
457	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
458	C₂×D₄	—	3	4	no	—
459	C₂×D₄	—	6	2	no	—
460	C₂×D₄	—	6	2	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	1	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	6	2	no	—
465	C₂²×C₄	—	6	2	no	—
466	C₂²×C₄	—	6	2	no	—
467	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	6	2	no	—
471	C₂²⋊C₄	—	6	2	no	—
472	C₂²×C₃	—	2	4	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	2	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	3	4	no	—
487	C₂²×C₃	—	4	2	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	4	2	no	—
490	C₂²×C₃	—	4	2	no	—
491	C₂²×C₃	—	4	2	no	—
492	C₂²×C₃	—	4	2	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	1	no	—
496	C₂²×C₃	—	4	1	no	—
497	C₂²×C₃	—	4	1	no	—
498	C₂²×C₃	—	4	1	no	—
499	C₂²×C₃	—	4	1	no	—
500	C₂²×C₃	—	4	1	no	—
501	C₂²×C₃	—	6	2	no	—
502	C₂²×C₃	—	6	2	no	—
503	C₂²×C₃	—	6	2	no	—
504	C₂²×C₃	—	6	2	no	—
505	C₂²×C₃	—	6	2	no	—
506	C₂²×C₃	—	6	2	no	—
507	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
508	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
509	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
510	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
511	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
512	C₂²×C₃	C₉×#41	1	1	yes	characteristic
513	C₂²×C₃	C₉×#41	1	1	yes	characteristic
514	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
515	C₂²×C₃	C₃×#235	1	1	yes	characteristic
516	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
517	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
518	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
519	C₂²×C₃	C₃×#237	1	1	yes	characteristic
520	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	2	2	no	—
523	C₂×D₃	—	2	2	no	—
524	C₂×D₃	—	2	2	no	—
525	C₂×D₃	—	2	2	no	—
526	C₂×D₃	—	2	2	no	—
527	C₂×D₃	C₉×C₂²⋊C₄	1	4	yes	complemented
528	C₃×C₄	—	2	2	no	—
529	C₃×C₄	—	2	2	no	—
530	C₃×C₄	—	4	2	no	—
531	C₃×C₄	—	4	2	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	4	1	no	—
534	C₃×C₄	—	6	2	no	—
535	C₃×C₄	—	6	2	no	—
536	C₃×C₄	—	12	1	no	—
537	Dic₃	—	2	2	no	—
538	Dic₃	—	2	2	no	—
539	Dic₃	—	4	1	no	—
540	C₃²	C₃×#386	1	1	yes	characteristic
541	C₉	—	2	1	no	—
542	C₉	#4956	1	1	yes	characteristic, direct product factor
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	3	2	no	—
550	C₂³	—	3	2	no	—
551	C₂³	—	3	2	no	—
552	C₂³	—	6	1	no	—
553	C₂³	—	6	1	no	—
554	C₂³	—	6	1	no	—
555	C₂³	—	6	1	no	—
556	C₂³	C₄×D₃×C₉	1	2	yes	complemented
557	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
558	D₄	—	6	8	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	3	2	no	—
565	C₂×C₄	—	3	2	no	—
566	C₂×C₄	—	6	8	no	—
567	C₂×C₄	—	6	1	no	—
568	C₂×C₄	—	6	1	no	—
569	C₂×C₄	—	6	1	no	—
570	C₂×C₄	—	6	1	no	—
571	C₂×C₄	—	6	1	no	—
572	C₂×C₄	—	6	1	no	—
573	C₂×C₄	—	6	1	no	—
574	C₂×C₄	C₉×#67	1	2	yes	complemented
575	C₂×C₃	—	2	1	no	—
576	C₂×C₃	—	2	1	no	—
577	C₂×C₃	—	2	1	no	—
578	C₂×C₃	—	2	1	no	—
579	C₂×C₃	—	2	1	no	—
580	C₂×C₃	—	2	1	no	—
581	C₂×C₃	—	2	1	no	—
582	C₂×C₃	—	4	4	no	—
583	C₂×C₃	—	4	2	no	—
584	C₂×C₃	—	4	2	no	—
585	C₂×C₃	—	6	4	no	—
586	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
587	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
588	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
589	C₂×C₃	C₉×#120	1	1	yes	characteristic
590	C₂×C₃	C₉×#121	1	1	yes	characteristic
591	C₂×C₃	C₉×#121	1	1	yes	characteristic
592	C₂×C₃	C₉×#123	1	1	yes	characteristic
593	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
594	C₂×C₃	C₃×#67⋊C₄	1	1	yes	characteristic
595	C₂×C₃	C₃×#883	1	1	yes	characteristic
596	C₂×C₃	C₃×#884	1	1	yes	characteristic
597	C₂×C₃	C₃×C₄×#67	1	1	yes	characteristic
598	C₂×C₃	C₃×#937	1	1	yes	characteristic
599	C₂×C₃	C₃×#938	1	1	yes	characteristic
600	D₃	—	2	4	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	3	4	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	6	2	no	—
610	C₂²	—	6	2	no	—
611	C₂²	—	6	2	no	—
612	C₂²	—	6	2	no	—
613	C₂²	—	6	2	no	—
614	C₂²	—	6	2	no	—
615	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
616	C₂²	C₉×#235	1	1	yes	characteristic
617	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
618	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
619	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
620	C₂²	C₉×#237	1	1	yes	characteristic
621	C₂²	C₂×C₉×#67	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	6	2	no	—
625	C₄	—	6	2	no	—
626	C₄	—	12	1	no	—
627	C₃	—	2	1	no	—
628	C₃	C₉×#386	1	1	yes	characteristic, complemented
629	C₃	C₃×#4956	1	1	yes	characteristic
630	C₂	—	4	2	no	—
631	C₂	—	6	4	no	—
632	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
633	C₂	C₉×#67⋊C₄	1	1	yes	characteristic
634	C₂	C₉×#883	1	1	yes	characteristic
635	C₂	C₉×#884	1	1	yes	characteristic
636	C₂	C₄×C₉×#67	1	1	yes	characteristic
637	C₂	C₉×#937	1	1	yes	characteristic
638	C₂	C₉×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×#67	C₂×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₉×#386
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
4. C₂×C₉×#217	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₉×C₃⋊#95	C₂	semidirect
7. C₉×C₃⋊#95	C₂	semidirect
16. C₂×C₉×#67	C₄	semidirect
38. C₂×C₉×C₂²⋊C₄	D₃	semidirect
47. C₂³×C₃×C₉	C₂×C₄	semidirect
61. C₂×C₃×C₄×C₉	D₄	semidirect
70. C₂×C₉×Dic₃	C₂×C₄	semidirect
71. C₂×C₉×Dic₃	D₄	semidirect
74. #4956	C₉	direct (N × H)
131. C₂×D₃×C₉	C₂²⋊C₄	semidirect
140. C₂²×C₄×D₃	C₂×C₉	semidirect
144. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
146. C₂×#217	C₂×C₉	semidirect
147. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
150. C₃⋊#95	C₂×C₉	semidirect
151. C₃⋊#95	C₂×C₉	semidirect
205. C₂³×C₉	C₄×D₃	semidirect
229. C₂×C₄×C₉	#67	semidirect
262. C₂×#67	C₄×C₉	semidirect
348. C₂×C₂²⋊C₄	D₃×C₉	semidirect
351. C₃×C₉	#386	semidirect
379. C₂³×C₃	C₂×C₄×C₉	semidirect
417. C₂×C₃×C₄	D₄×C₉	semidirect
427. C₂×Dic₃	C₂×C₄×C₉	semidirect
428. C₂×Dic₃	D₄×C₉	semidirect
527. C₂×D₃	C₉×C₂²⋊C₄	semidirect
542. C₉	#4956	direct (N × H)
556. C₂³	C₄×D₃×C₉	semidirect
574. C₂×C₄	C₉×#67	semidirect
628. C₃	C₉×#386	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×#67	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×C₃⋊#95	2
C₃×#4956	3
C₉×#386	3

Subgroups — C9×#4956 #13142485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4956 #13142485