Subgroups — C₉×#4668 #13141324

Order 1728.

778 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	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4668	C₃	1	1	yes	maximal, characteristic
9	C₉×#385	—	3	1	no	maximal
10	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×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	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	—	2	2	no	—
18	C₂×C₄×D₃×C₉	—	2	2	no	—
19	C₂×C₄×D₃×C₉	—	2	2	no	—
20	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
21	C₉×(C₂×D₃)⋊C₄	C₄	1	4	yes	complemented
22	C₉×C₄⋊Dic₃	—	2	2	no	—
23	C₉×Dic₃⋊C₄	—	2	2	no	—
24	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
29	C₂³×C₄×C₉	—	3	1	no	—
30	C₃²×#95	C₂×C₃	1	1	yes	characteristic
31	C₃×C₃⋊#95	C₂×C₃	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	—	3	1	no	—
33	C₂×C₉×C₄⋊C₄	—	3	1	no	—
34	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
35	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
36	C₉×#95	—	2	1	no	—
37	C₉×#95	—	3	1	no	—
38	C₉×#95	D₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
40	C₂²×D₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	2	1	no	—
42	C₂²×D₃×C₉	—	2	1	no	—
43	C₂²×D₃×C₉	—	2	1	no	—
44	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
45	C₂²×D₃×C₉	D₄	1	2	yes	—
46	C₂²×D₃×C₉	Q₈	1	2	yes	—
47	C₂×C₃×C₄×C₉	—	2	1	no	—
48	C₂×C₃×C₄×C₉	—	2	1	no	—
49	C₂×C₃×C₄×C₉	—	2	1	no	—
50	C₂×C₃×C₄×C₉	—	2	1	no	—
51	C₂×C₃×C₄×C₉	—	2	1	no	—
52	C₂×C₃×C₄×C₉	—	2	1	no	—
53	C₂×C₃×C₄×C₉	—	2	1	no	—
54	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	complemented
55	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
56	C₂×C₉×Dic₃	—	2	1	no	—
57	C₂×C₉×Dic₃	—	2	1	no	—
58	C₂×C₉×Dic₃	—	2	1	no	—
59	C₂×C₉×Dic₃	—	2	1	no	—
60	C₂×C₉×Dic₃	—	2	1	no	—
61	C₂×C₉×Dic₃	—	2	1	no	—
62	C₂×C₉×Dic₃	—	2	1	no	—
63	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	complemented
64	C₂×C₉×Dic₃	D₄	1	2	yes	—
65	C₄×D₃×C₉	—	2	8	no	—
66	C₃×#385	—	3	1	no	—
67	#4668	C₉	1	1	yes	characteristic, direct product factor
68	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃×C₄×D₃	—	2	2	no	—
76	C₂×C₃×C₄×D₃	—	2	2	no	—
77	C₂×C₃×C₄×D₃	—	2	2	no	—
78	C₂⁴×C₉	—	3	1	no	—
79	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	4	yes	—
81	C₃×C₄⋊Dic₃	—	2	2	no	—
82	C₃×Dic₃⋊C₄	—	2	2	no	—
83	C₂²×C₄×C₉	—	2	1	no	—
84	C₂²×C₄×C₉	—	2	1	no	—
85	C₂²×C₄×C₉	—	2	1	no	—
86	C₂²×C₄×C₉	—	3	1	no	—
87	C₂²×C₄×C₉	—	3	1	no	—
88	C₂²×C₄×C₉	—	3	1	no	—
89	C₂²×C₄×C₉	—	6	2	no	—
90	C₂²×C₄×C₉	—	6	2	no	—
91	C₂²×C₄×C₉	—	6	2	no	—
92	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
95	C₉×C₄⋊C₄	—	6	2	no	—
96	C₉×C₄⋊C₄	—	6	2	no	—
97	C₉×C₂²⋊C₄	—	3	4	no	—
98	C₉×C₂²⋊C₄	—	6	2	no	—
99	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₃×C₉	#41	1	1	yes	characteristic
105	C₂²×C₃×C₉	#41	1	1	yes	characteristic
106	C₂×D₃×C₉	—	2	2	no	—
107	C₂×D₃×C₉	—	2	2	no	—
108	C₂×D₃×C₉	—	2	2	no	—
109	C₂×D₃×C₉	—	2	2	no	—
110	C₂×D₃×C₉	—	2	2	no	—
111	C₂×D₃×C₉	—	2	2	no	—
112	C₂×D₃×C₉	C₄⋊C₄	1	4	yes	complemented
113	C₃×C₄×C₉	—	2	2	no	—
114	C₃×C₄×C₉	—	2	2	no	—
115	C₃×C₄×C₉	—	4	1	no	—
116	C₉×Dic₃	—	2	2	no	—
117	C₉×Dic₃	—	2	2	no	—
118	C₉×Dic₃	—	4	1	no	—
119	C₂³×C₃×C₄	—	3	1	no	—
120	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	—	3	1	no	—
122	C₂×C₃×C₄⋊C₄	—	3	1	no	—
123	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
124	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
125	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
126	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
127	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
128	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
129	C₃×#95	—	2	1	no	—
130	C₃×#95	—	3	1	no	—
131	C₃×#95	C₂×C₉	1	1	yes	characteristic, complemented
132	C₃×#95	C₃×D₃	1	1	yes	characteristic
133	C₃⋊#95	C₂×C₉	1	1	yes	characteristic, complemented
134	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
135	C₂²×C₃×D₃	—	2	1	no	—
136	C₂²×C₃×D₃	—	2	1	no	—
137	C₂²×C₃×D₃	—	2	1	no	—
138	C₂²×C₃×D₃	—	2	1	no	—
139	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
140	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
141	C₂²×C₃×D₃	C₃×Q₈	1	2	yes	—
142	C₂×C₃²×C₄	—	2	1	no	—
143	C₂×C₃²×C₄	—	2	1	no	—
144	C₂×C₃²×C₄	—	2	1	no	—
145	C₂×C₃²×C₄	—	2	1	no	—
146	C₂×C₃²×C₄	—	2	1	no	—
147	C₂×C₃²×C₄	—	2	1	no	—
148	C₂×C₃²×C₄	—	2	1	no	—
149	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
150	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
151	C₂×C₃×Dic₃	—	2	1	no	—
152	C₂×C₃×Dic₃	—	2	1	no	—
153	C₂×C₃×Dic₃	—	2	1	no	—
154	C₂×C₃×Dic₃	—	2	1	no	—
155	C₂×C₃×Dic₃	—	2	1	no	—
156	C₂×C₃×Dic₃	—	2	1	no	—
157	C₂×C₃×Dic₃	—	2	1	no	—
158	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
159	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
160	C₃×C₄×D₃	—	2	8	no	—
161	C₂³×C₉	—	2	1	no	—
162	C₂³×C₉	—	3	2	no	—
163	C₂³×C₉	—	3	2	no	—
164	C₂³×C₉	—	3	2	no	—
165	C₂³×C₉	—	6	1	no	—
166	C₂³×C₉	—	6	1	no	—
167	C₂³×C₉	—	6	1	no	—
168	C₂³×C₉	—	6	1	no	—
169	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
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	2	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	2	no	—
179	C₂×C₄×C₉	—	2	2	no	—
180	C₂×C₄×C₉	—	3	2	no	—
181	C₂×C₄×C₉	—	3	2	no	—
182	C₂×C₄×C₉	—	4	1	no	—
183	C₂×C₄×C₉	—	4	1	no	—
184	C₂×C₄×C₉	—	4	1	no	—
185	C₂×C₄×C₉	—	4	1	no	—
186	C₂×C₄×C₉	—	4	1	no	—
187	C₂×C₄×C₉	—	4	1	no	—
188	C₂×C₄×C₉	—	6	8	no	—
189	C₂×C₄×C₉	—	6	1	no	—
190	C₂×C₄×C₉	—	6	1	no	—
191	C₂×C₄×C₉	—	6	1	no	—
192	C₂×C₄×C₉	—	6	1	no	—
193	C₂×C₄×C₉	—	6	1	no	—
194	C₂×C₄×C₉	—	6	1	no	—
195	C₂×C₄×C₉	—	6	1	no	—
196	C₂×C₄×C₉	C₄×D₃	1	2	yes	complemented
197	C₂×C₄×C₉	D₁₂	1	2	yes	—
198	#385	—	3	1	no	Sylow
199	C₂×C₃×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
202	C₂×C₃×C₉	#120	1	1	yes	characteristic
203	C₂×C₃×C₉	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₃×C₉	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₃×C₉	#123	1	1	yes	characteristic
206	D₃×C₉	—	2	4	no	—
207	C₂⁴×C₃	—	3	1	no	—
208	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	—	3	1	no	—
213	C₂²×C₃×C₄	—	3	1	no	—
214	C₂²×C₃×C₄	—	3	1	no	—
215	C₂²×C₃×C₄	—	6	2	no	—
216	C₂²×C₃×C₄	—	6	2	no	—
217	C₂²×C₃×C₄	—	6	2	no	—
218	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
224	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
225	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
226	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
227	C₂×C₄×D₃	—	2	2	no	—
228	C₂×C₄×D₃	—	2	2	no	—
229	C₂×C₄×D₃	—	2	2	no	—
230	C₃×C₄⋊C₄	—	6	2	no	—
231	C₃×C₄⋊C₄	—	6	2	no	—
232	C₃×C₂²⋊C₄	—	3	4	no	—
233	C₃×C₂²⋊C₄	—	6	2	no	—
234	(C₂×D₃)⋊C₄	—	2	2	no	—
235	(C₂×D₃)⋊C₄	C₄×C₉	1	4	yes	complemented
236	C₄⋊Dic₃	—	2	2	no	—
237	Dic₃⋊C₄	—	2	2	no	—
238	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
243	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
244	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
245	C₂×C₃×D₃	—	2	2	no	—
246	C₂×C₃×D₃	—	2	2	no	—
247	C₂×C₃×D₃	—	2	2	no	—
248	C₂×C₃×D₃	—	2	2	no	—
249	C₂×C₃×D₃	—	2	2	no	—
250	C₂×C₃×D₃	—	2	2	no	—
251	C₂×C₃×D₃	C₃×C₄⋊C₄	1	4	yes	—
252	C₃²×C₄	—	2	2	no	—
253	C₃²×C₄	—	2	2	no	—
254	C₃²×C₄	—	4	1	no	—
255	C₃×Dic₃	—	2	2	no	—
256	C₃×Dic₃	—	2	2	no	—
257	C₃×Dic₃	—	4	1	no	—
258	C₂²×C₉	—	2	1	no	—
259	C₂²×C₉	—	2	1	no	—
260	C₂²×C₉	—	2	1	no	—
261	C₂²×C₉	—	2	1	no	—
262	C₂²×C₉	—	2	1	no	—
263	C₂²×C₉	—	2	1	no	—
264	C₂²×C₉	—	2	1	no	—
265	C₂²×C₉	—	3	4	no	—
266	C₂²×C₉	—	6	2	no	—
267	C₂²×C₉	—	6	2	no	—
268	C₂²×C₉	—	6	2	no	—
269	C₂²×C₉	—	6	2	no	—
270	C₂²×C₉	—	6	2	no	—
271	C₂²×C₉	—	6	2	no	—
272	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
273	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
274	C₂²×C₉	#235	1	1	yes	characteristic
275	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
276	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
277	C₂²×C₉	#237	1	1	yes	characteristic
278	C₂²×C₉	D₃×Q₈	1	1	yes	characteristic
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	2	no	—
281	C₄×C₉	—	4	2	no	—
282	C₄×C₉	—	4	2	no	—
283	C₄×C₉	—	4	2	no	—
284	C₄×C₉	—	4	1	no	—
285	C₄×C₉	—	6	2	no	—
286	C₄×C₉	—	6	2	no	—
287	C₄×C₉	—	12	1	no	—
288	C₂³×C₄	—	3	1	no	—
289	C₂×C₄⋊C₄	—	3	1	no	—
290	C₂×C₄⋊C₄	—	3	1	no	—
291	C₂×C₂²⋊C₄	—	3	1	no	—
292	C₂×C₂²⋊C₄	—	3	1	no	—
293	#95	—	3	1	no	—
294	#95	D₃×C₉	1	1	yes	characteristic, complemented
295	C₃×C₉	#385	1	1	yes	characteristic, complemented, Sylow
296	C₂³×C₃	—	2	1	no	—
297	C₂³×C₃	—	3	2	no	—
298	C₂³×C₃	—	3	2	no	—
299	C₂³×C₃	—	3	2	no	—
300	C₂³×C₃	—	6	1	no	—
301	C₂³×C₃	—	6	1	no	—
302	C₂³×C₃	—	6	1	no	—
303	C₂³×C₃	—	6	1	no	—
304	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
305	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
306	C₂²×D₃	—	2	1	no	—
307	C₂²×D₃	—	2	1	no	—
308	C₂²×D₃	—	2	1	no	—
309	C₂²×D₃	—	2	1	no	—
310	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
311	C₂²×D₃	D₄×C₉	1	2	yes	—
312	C₂²×D₃	Q₈×C₉	1	2	yes	—
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	2	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	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	3	2	no	—
331	C₂×C₃×C₄	—	3	2	no	—
332	C₂×C₃×C₄	—	4	1	no	—
333	C₂×C₃×C₄	—	4	1	no	—
334	C₂×C₃×C₄	—	4	1	no	—
335	C₂×C₃×C₄	—	4	1	no	—
336	C₂×C₃×C₄	—	4	1	no	—
337	C₂×C₃×C₄	—	4	1	no	—
338	C₂×C₃×C₄	—	6	8	no	—
339	C₂×C₃×C₄	—	6	1	no	—
340	C₂×C₃×C₄	—	6	1	no	—
341	C₂×C₃×C₄	—	6	1	no	—
342	C₂×C₃×C₄	—	6	1	no	—
343	C₂×C₃×C₄	—	6	1	no	—
344	C₂×C₃×C₄	—	6	1	no	—
345	C₂×C₃×C₄	—	6	1	no	—
346	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	complemented
347	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
348	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
349	C₂×C₃×C₄	C₃×D₁₂	1	2	yes	—
350	C₂×Dic₃	—	2	1	no	—
351	C₂×Dic₃	—	2	1	no	—
352	C₂×Dic₃	—	2	1	no	—
353	C₂×Dic₃	—	2	1	no	—
354	C₂×Dic₃	—	2	1	no	—
355	C₂×Dic₃	—	2	1	no	—
356	C₂×Dic₃	—	2	1	no	—
357	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	complemented
358	C₂×Dic₃	D₄×C₉	1	2	yes	—
359	C₄×D₃	—	2	8	no	—
360	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
361	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
362	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
363	C₂×C₃²	C₃×#120	1	1	yes	characteristic
364	C₂×C₃²	C₃×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃²	C₃×C₂²⋊Q₈	1	1	yes	characteristic
366	C₂×C₃²	C₃×#123	1	1	yes	characteristic
367	C₃×D₃	—	2	4	no	—
368	C₂×C₉	—	2	1	no	—
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	2	1	no	—
371	C₂×C₉	—	2	1	no	—
372	C₂×C₉	—	2	1	no	—
373	C₂×C₉	—	2	1	no	—
374	C₂×C₉	—	2	1	no	—
375	C₂×C₉	—	6	4	no	—
376	C₂×C₉	C₄×D₁₂	1	1	yes	characteristic
377	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
378	C₂×C₉	#882	1	1	yes	characteristic
379	C₂×C₉	#883	1	1	yes	characteristic
380	C₂×C₉	D₃×C₄⋊C₄	1	1	yes	characteristic
381	C₂×C₉	#896	1	1	yes	characteristic
382	C₂×C₉	#897	1	1	yes	characteristic
383	C₂⁴	—	3	1	no	—
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	3	1	no	—
386	C₂²×C₄	—	3	1	no	—
387	C₂²×C₄	—	6	2	no	—
388	C₂²×C₄	—	6	2	no	—
389	C₂²×C₄	—	6	2	no	—
390	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
393	C₄⋊C₄	—	6	2	no	—
394	C₄⋊C₄	—	6	2	no	—
395	C₂²⋊C₄	—	3	4	no	—
396	C₂²⋊C₄	—	6	2	no	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	2	1	no	—
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	3	4	no	—
405	C₂²×C₃	—	6	2	no	—
406	C₂²×C₃	—	6	2	no	—
407	C₂²×C₃	—	6	2	no	—
408	C₂²×C₃	—	6	2	no	—
409	C₂²×C₃	—	6	2	no	—
410	C₂²×C₃	—	6	2	no	—
411	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
412	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
413	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
414	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
415	C₂²×C₃	C₂×Q₈×C₉	1	1	yes	characteristic
416	C₂²×C₃	C₉×#41	1	1	yes	characteristic
417	C₂²×C₃	C₉×#41	1	1	yes	characteristic
418	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
419	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
420	C₂²×C₃	C₃×#235	1	1	yes	characteristic
421	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
422	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
423	C₂²×C₃	C₃×#237	1	1	yes	characteristic
424	C₂²×C₃	C₃×D₃×Q₈	1	1	yes	characteristic
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	2	2	no	—
427	C₂×D₃	—	2	2	no	—
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	—	2	2	no	—
430	C₂×D₃	—	2	2	no	—
431	C₂×D₃	C₉×C₄⋊C₄	1	4	yes	complemented
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	4	2	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	—	4	2	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	6	2	no	—
442	C₃×C₄	—	6	2	no	—
443	C₃×C₄	—	12	1	no	—
444	Dic₃	—	2	2	no	—
445	Dic₃	—	2	2	no	—
446	Dic₃	—	4	1	no	—
447	C₃²	C₃×#385	1	1	yes	characteristic
448	C₉	—	2	1	no	—
449	C₉	#4668	1	1	yes	characteristic, direct product factor
450	C₂³	—	3	2	no	—
451	C₂³	—	3	2	no	—
452	C₂³	—	3	2	no	—
453	C₂³	—	6	1	no	—
454	C₂³	—	6	1	no	—
455	C₂³	—	6	1	no	—
456	C₂³	—	6	1	no	—
457	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	3	2	no	—
466	C₂×C₄	—	3	2	no	—
467	C₂×C₄	—	6	8	no	—
468	C₂×C₄	—	6	1	no	—
469	C₂×C₄	—	6	1	no	—
470	C₂×C₄	—	6	1	no	—
471	C₂×C₄	—	6	1	no	—
472	C₂×C₄	—	6	1	no	—
473	C₂×C₄	—	6	1	no	—
474	C₂×C₄	—	6	1	no	—
475	C₂×C₄	C₄×D₃×C₉	1	2	yes	complemented
476	C₂×C₄	C₉×D₁₂	1	2	yes	—
477	C₂×C₃	—	2	1	no	—
478	C₂×C₃	—	2	1	no	—
479	C₂×C₃	—	2	1	no	—
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	2	1	no	—
482	C₂×C₃	—	2	1	no	—
483	C₂×C₃	—	2	1	no	—
484	C₂×C₃	—	6	4	no	—
485	C₂×C₃	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
486	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
487	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
488	C₂×C₃	C₉×#120	1	1	yes	characteristic
489	C₂×C₃	C₉×C₂²⋊Q₈	1	1	yes	characteristic
490	C₂×C₃	C₉×C₂²⋊Q₈	1	1	yes	characteristic
491	C₂×C₃	C₉×#123	1	1	yes	characteristic
492	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
493	C₂×C₃	C₃×#67⋊C₄	1	1	yes	characteristic
494	C₂×C₃	C₃×#882	1	1	yes	characteristic
495	C₂×C₃	C₃×#883	1	1	yes	characteristic
496	C₂×C₃	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
497	C₂×C₃	C₃×#896	1	1	yes	characteristic
498	C₂×C₃	C₃×#897	1	1	yes	characteristic
499	D₃	—	2	4	no	—
500	C₂²	—	3	4	no	—
501	C₂²	—	6	2	no	—
502	C₂²	—	6	2	no	—
503	C₂²	—	6	2	no	—
504	C₂²	—	6	2	no	—
505	C₂²	—	6	2	no	—
506	C₂²	—	6	2	no	—
507	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
508	C₂²	C₂×C₉×D₁₂	1	1	yes	characteristic
509	C₂²	C₉×#235	1	1	yes	characteristic
510	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
511	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
512	C₂²	C₉×#237	1	1	yes	characteristic
513	C₂²	D₃×Q₈×C₉	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	6	2	no	—
518	C₄	—	6	2	no	—
519	C₄	—	12	1	no	—
520	C₃	—	2	1	no	—
521	C₃	C₉×#385	1	1	yes	characteristic, complemented
522	C₃	C₃×#4668	1	1	yes	characteristic
523	C₂	—	6	4	no	—
524	C₂	C₄×C₉×D₁₂	1	1	yes	characteristic
525	C₂	C₉×#67⋊C₄	1	1	yes	characteristic
526	C₂	C₉×#882	1	1	yes	characteristic
527	C₂	C₉×#883	1	1	yes	characteristic
528	C₂	D₃×C₉×C₄⋊C₄	1	1	yes	characteristic
529	C₂	C₉×#896	1	1	yes	characteristic
530	C₂	C₉×#897	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	C₃×C₉×#95	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
hypercenter	C₉×#95	D₃
hypocenter	C₃	C₉×#385
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₉×#95

Complements

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

N	H ≅ G/N	type
4. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
5. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
6. C₃×C₉×#95	C₂	semidirect
7. C₉×C₃⋊#95	C₂	semidirect
21. C₉×(C₂×D₃)⋊C₄	C₄	semidirect
38. C₉×#95	D₃	semidirect
54. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
63. C₂×C₉×Dic₃	C₂×C₄	semidirect
67. #4668	C₉	direct (N × H)
112. C₂×D₃×C₉	C₄⋊C₄	semidirect
127. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
128. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
131. C₃×#95	C₂×C₉	semidirect
133. C₃⋊#95	C₂×C₉	semidirect
196. C₂×C₄×C₉	C₄×D₃	semidirect
235. (C₂×D₃)⋊C₄	C₄×C₉	semidirect
294. #95	D₃×C₉	semidirect
295. C₃×C₉	#385	semidirect
346. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
357. C₂×Dic₃	C₂×C₄×C₉	semidirect
431. C₂×D₃	C₉×C₄⋊C₄	semidirect
449. C₉	#4668	direct (N × H)
475. C₂×C₄	C₄×D₃×C₉	semidirect
521. C₃	C₉×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃×C₉	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₉×Dic₃⋊C₄	2
C₃×C₉×#95	2
C₉×C₃⋊#95	2
C₃×#4668	3
C₉×#385	3

Subgroups — C9×#4668 #13141324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4668 #13141324