Subgroups — C₉×#4987 #13142592

Order 1728.

794 conjugacy classes of subgroups.

The subgroup lattice has 446 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×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
4	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×C₃⋊#95	C₂	1	2	yes	maximal, complemented
6	C₃×#4987	C₃	1	1	yes	maximal, characteristic
7	C₉×#380	—	3	1	no	maximal
8	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
12	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	—	2	2	no	—
14	C₂×C₄×D₃×C₉	—	2	2	no	—
15	C₂×C₄×D₃×C₉	C₄	1	4	yes	complemented
16	C₃×C₉×C₄⋊C₄	—	2	2	no	—
17	C₉×(C₂×D₃)⋊C₄	—	2	4	no	—
18	C₉×C₄⋊Dic₃	—	2	2	no	—
19	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
22	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
23	C₂³×C₄×C₉	—	3	1	no	—
24	C₃×C₃⋊#95	C₂×C₃	1	2	yes	—
25	C₂×C₉×C₄⋊C₄	—	2	1	no	—
26	C₂×C₉×C₄⋊C₄	—	3	1	no	—
27	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
28	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
29	C₉×#95	—	3	2	no	—
30	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
31	C₂²×D₃×C₉	—	2	1	no	—
32	C₂²×D₃×C₉	—	2	1	no	—
33	C₂²×D₃×C₉	—	2	1	no	—
34	C₂²×D₃×C₉	—	2	1	no	—
35	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
36	C₂²×D₃×C₉	D₄	1	2	yes	—
37	C₂²×D₃×C₉	Q₈	1	2	yes	—
38	C₂×C₃×C₄×C₉	—	2	2	no	—
39	C₂×C₃×C₄×C₉	—	2	2	no	—
40	C₂×C₃×C₄×C₉	—	2	2	no	—
41	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
43	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
44	C₂×C₉×Dic₃	—	2	1	no	—
45	C₂×C₉×Dic₃	—	2	1	no	—
46	C₂×C₉×Dic₃	—	2	2	no	—
47	C₂×C₉×Dic₃	—	2	2	no	—
48	C₂×C₉×Dic₃	—	2	2	no	—
49	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
50	C₄×D₃×C₉	—	2	8	no	—
51	C₃×#380	—	3	1	no	—
52	#4987	C₉	1	1	yes	characteristic, direct product factor
53	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
55	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
56	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
57	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	—	2	2	no	—
59	C₂×C₃×C₄×D₃	—	2	2	no	—
60	C₂×C₃×C₄×D₃	C₃×C₄	1	4	yes	—
61	C₂⁴×C₉	—	3	1	no	—
62	C₃²×C₄⋊C₄	—	2	2	no	—
63	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₃×C₄⋊Dic₃	—	2	2	no	—
65	C₂²×C₄×C₉	—	2	1	no	—
66	C₂²×C₄×C₉	—	2	2	no	—
67	C₂²×C₄×C₉	—	3	1	no	—
68	C₂²×C₄×C₉	—	3	4	no	—
69	C₂²×C₄×C₉	—	3	2	no	—
70	C₂²×C₄×C₉	—	6	2	no	—
71	C₂²×C₄×C₉	—	6	2	no	—
72	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
73	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
74	C₉×C₄⋊C₄	—	2	4	no	—
75	C₉×C₄⋊C₄	—	2	2	no	—
76	C₉×C₄⋊C₄	—	6	2	no	—
77	C₉×C₂²⋊C₄	—	6	4	no	—
78	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₃×C₉	#41	1	1	yes	characteristic
84	C₂²×C₃×C₉	#41	1	1	yes	characteristic
85	C₂×D₃×C₉	—	2	2	no	—
86	C₂×D₃×C₉	—	2	2	no	—
87	C₂×D₃×C₉	—	2	2	no	—
88	C₂×D₃×C₉	—	2	2	no	—
89	C₂×D₃×C₉	—	2	2	no	—
90	C₂×D₃×C₉	—	2	2	no	—
91	C₂×D₃×C₉	C₄⋊C₄	1	4	yes	complemented
92	C₃×C₄×C₉	—	4	2	no	—
93	C₃×C₄×C₉	C₂²⋊C₄	1	4	yes	complemented
94	C₉×Dic₃	—	2	2	no	—
95	C₉×Dic₃	—	4	2	no	—
96	C₂³×C₃×C₄	—	3	1	no	—
97	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic
98	C₂×C₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₃×C₄⋊C₄	—	3	1	no	—
100	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
101	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
102	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
103	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	—
104	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
105	C₃×#95	—	3	2	no	—
106	C₃⋊#95	C₂×C₉	1	2	yes	complemented
107	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
108	C₂²×C₃×D₃	—	2	1	no	—
109	C₂²×C₃×D₃	—	2	1	no	—
110	C₂²×C₃×D₃	—	2	1	no	—
111	C₂²×C₃×D₃	—	2	1	no	—
112	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
113	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
114	C₂²×C₃×D₃	C₃×Q₈	1	2	yes	—
115	C₂×C₃²×C₄	—	2	2	no	—
116	C₂×C₃²×C₄	—	2	2	no	—
117	C₂×C₃²×C₄	—	2	2	no	—
118	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
119	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
120	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
121	C₂×C₃×Dic₃	—	2	1	no	—
122	C₂×C₃×Dic₃	—	2	1	no	—
123	C₂×C₃×Dic₃	—	2	2	no	—
124	C₂×C₃×Dic₃	—	2	2	no	—
125	C₂×C₃×Dic₃	—	2	2	no	—
126	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
127	C₃×C₄×D₃	—	2	8	no	—
128	C₂³×C₉	—	2	1	no	—
129	C₂³×C₉	—	3	2	no	—
130	C₂³×C₉	—	3	2	no	—
131	C₂³×C₉	—	3	2	no	—
132	C₂³×C₉	—	6	1	no	—
133	C₂³×C₉	—	6	1	no	—
134	C₂³×C₉	—	6	1	no	—
135	C₂³×C₉	—	6	1	no	—
136	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
137	C₂×C₄×C₉	—	2	4	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	3	2	no	—
145	C₂×C₄×C₉	—	4	2	no	—
146	C₂×C₄×C₉	—	4	2	no	—
147	C₂×C₄×C₉	—	6	1	no	—
148	C₂×C₄×C₉	—	6	1	no	—
149	C₂×C₄×C₉	—	6	8	no	—
150	C₂×C₄×C₉	—	6	2	no	—
151	C₂×C₄×C₉	—	6	2	no	—
152	C₂×C₄×C₉	—	6	2	no	—
153	C₂×C₄×C₉	C₄×D₃	1	2	yes	—
154	C₂×C₄×C₉	D₁₂	1	2	yes	—
155	C₂×C₄×C₉	#67	1	2	yes	—
156	#380	—	3	1	no	Sylow
157	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₃×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₃×C₉	#117	1	1	yes	characteristic
160	C₂×C₃×C₉	#121	1	1	yes	characteristic
161	C₂×C₃×C₉	#121	1	1	yes	characteristic
162	C₂×C₃×C₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₃×C₉	C₂²⋊Q₈	1	1	yes	characteristic
164	D₃×C₉	—	2	4	no	—
165	C₂⁴×C₃	—	3	1	no	—
166	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	2	2	no	—
169	C₂²×C₃×C₄	—	3	1	no	—
170	C₂²×C₃×C₄	—	3	4	no	—
171	C₂²×C₃×C₄	—	3	2	no	—
172	C₂²×C₃×C₄	—	6	2	no	—
173	C₂²×C₃×C₄	—	6	2	no	—
174	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
175	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
177	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
178	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
179	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
180	C₂×C₄×D₃	—	2	2	no	—
181	C₂×C₄×D₃	—	2	2	no	—
182	C₂×C₄×D₃	C₄×C₉	1	4	yes	complemented
183	C₃×C₄⋊C₄	—	2	4	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	—	6	2	no	—
187	C₃×C₂²⋊C₄	—	6	4	no	—
188	(C₂×D₃)⋊C₄	—	2	4	no	—
189	C₄⋊Dic₃	—	2	2	no	—
190	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
191	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
193	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
195	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
196	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
197	C₂×C₃×D₃	—	2	2	no	—
198	C₂×C₃×D₃	—	2	2	no	—
199	C₂×C₃×D₃	—	2	2	no	—
200	C₂×C₃×D₃	—	2	2	no	—
201	C₂×C₃×D₃	—	2	2	no	—
202	C₂×C₃×D₃	—	2	2	no	—
203	C₂×C₃×D₃	C₃×C₄⋊C₄	1	4	yes	—
204	C₃²×C₄	—	4	2	no	—
205	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
206	C₃×Dic₃	—	2	2	no	—
207	C₃×Dic₃	—	4	2	no	—
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	2	1	no	—
211	C₂²×C₉	—	2	1	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	2	1	no	—
214	C₂²×C₉	—	2	1	no	—
215	C₂²×C₉	—	3	4	no	—
216	C₂²×C₉	—	6	2	no	—
217	C₂²×C₉	—	6	2	no	—
218	C₂²×C₉	—	6	2	no	—
219	C₂²×C₉	—	6	2	no	—
220	C₂²×C₉	—	6	2	no	—
221	C₂²×C₉	—	6	2	no	—
222	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
223	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
224	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
225	C₂²×C₉	#237	1	1	yes	characteristic
226	C₂²×C₉	D₃×Q₈	1	1	yes	characteristic
227	C₂²×C₉	#239	1	1	yes	characteristic
228	C₂²×C₉	C₂×#67	1	1	yes	characteristic
229	C₄×C₉	—	2	4	no	—
230	C₄×C₉	—	4	4	no	—
231	C₄×C₉	—	4	2	no	—
232	C₄×C₉	—	6	2	no	—
233	C₄×C₉	—	12	2	no	—
234	C₄×C₉	(C₂×D₃)⋊C₄	1	4	yes	complemented
235	C₂³×C₄	—	3	1	no	—
236	C₂×C₄⋊C₄	—	3	1	no	—
237	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
238	C₂×C₂²⋊C₄	—	3	2	no	—
239	#95	—	3	2	no	—
240	C₃×C₉	#380	1	1	yes	characteristic, complemented, Sylow
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	—	3	2	no	—
243	C₂³×C₃	—	3	2	no	—
244	C₂³×C₃	—	3	2	no	—
245	C₂³×C₃	—	6	1	no	—
246	C₂³×C₃	—	6	1	no	—
247	C₂³×C₃	—	6	1	no	—
248	C₂³×C₃	—	6	1	no	—
249	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
250	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
251	C₂²×D₃	—	2	1	no	—
252	C₂²×D₃	—	2	1	no	—
253	C₂²×D₃	—	2	1	no	—
254	C₂²×D₃	—	2	1	no	—
255	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
256	C₂²×D₃	D₄×C₉	1	2	yes	—
257	C₂²×D₃	Q₈×C₉	1	2	yes	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	3	2	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	2	no	—
271	C₂×C₃×C₄	—	6	1	no	—
272	C₂×C₃×C₄	—	6	1	no	—
273	C₂×C₃×C₄	—	6	8	no	—
274	C₂×C₃×C₄	—	6	2	no	—
275	C₂×C₃×C₄	—	6	2	no	—
276	C₂×C₃×C₄	—	6	2	no	—
277	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
278	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
279	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
280	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
281	C₂×C₃×C₄	C₃×D₁₂	1	2	yes	—
282	C₂×C₃×C₄	C₃×#67	1	2	yes	—
283	C₂×Dic₃	—	2	1	no	—
284	C₂×Dic₃	—	2	1	no	—
285	C₂×Dic₃	—	2	2	no	—
286	C₂×Dic₃	—	2	2	no	—
287	C₂×Dic₃	—	2	2	no	—
288	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
289	C₄×D₃	—	2	8	no	—
290	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
292	C₂×C₃²	C₃×#117	1	1	yes	characteristic
293	C₂×C₃²	C₃×#121	1	1	yes	characteristic
294	C₂×C₃²	C₃×#121	1	1	yes	characteristic
295	C₂×C₃²	C₃×C₂²⋊Q₈	1	1	yes	characteristic
296	C₂×C₃²	C₃×C₂²⋊Q₈	1	1	yes	characteristic
297	C₃×D₃	—	2	4	no	—
298	C₂×C₉	—	2	1	no	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	2	1	no	—
301	C₂×C₉	—	2	1	no	—
302	C₂×C₉	—	2	1	no	—
303	C₂×C₉	—	2	1	no	—
304	C₂×C₉	—	2	1	no	—
305	C₂×C₉	—	6	4	no	—
306	C₂×C₉	D₃×C₄⋊C₄	1	1	yes	characteristic
307	C₂×C₉	#892	1	1	yes	characteristic
308	C₂×C₉	#895	1	1	yes	characteristic
309	C₂×C₉	#897	1	1	yes	characteristic
310	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
311	C₂×C₉	#938	1	1	yes	characteristic
312	C₂×C₉	#946	1	1	yes	characteristic
313	C₂⁴	—	3	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	3	4	no	—
316	C₂²×C₄	—	3	2	no	—
317	C₂²×C₄	—	6	2	no	—
318	C₂²×C₄	—	6	2	no	—
319	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
320	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	6	2	no	—
323	C₂²⋊C₄	—	6	4	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	3	4	no	—
332	C₂²×C₃	—	6	2	no	—
333	C₂²×C₃	—	6	2	no	—
334	C₂²×C₃	—	6	2	no	—
335	C₂²×C₃	—	6	2	no	—
336	C₂²×C₃	—	6	2	no	—
337	C₂²×C₃	—	6	2	no	—
338	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
339	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
340	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
341	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
342	C₂²×C₃	C₂×Q₈×C₉	1	1	yes	characteristic
343	C₂²×C₃	C₉×#41	1	1	yes	characteristic
344	C₂²×C₃	C₉×#41	1	1	yes	characteristic
345	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
346	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
347	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
348	C₂²×C₃	C₃×#237	1	1	yes	characteristic
349	C₂²×C₃	C₃×D₃×Q₈	1	1	yes	characteristic
350	C₂²×C₃	C₃×#239	1	1	yes	characteristic
351	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
352	C₂×D₃	—	2	2	no	—
353	C₂×D₃	—	2	2	no	—
354	C₂×D₃	—	2	2	no	—
355	C₂×D₃	—	2	2	no	—
356	C₂×D₃	—	2	2	no	—
357	C₂×D₃	—	2	2	no	—
358	C₂×D₃	C₉×C₄⋊C₄	1	4	yes	complemented
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	4	4	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	6	2	no	—
364	C₃×C₄	—	12	2	no	—
365	C₃×C₄	C₉×C₂²⋊C₄	1	4	yes	complemented
366	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
367	Dic₃	—	2	2	no	—
368	Dic₃	—	4	2	no	—
369	C₃²	C₃×#380	1	1	yes	characteristic
370	C₉	—	2	1	no	—
371	C₉	#4987	1	1	yes	characteristic, direct product factor
372	C₂³	—	3	2	no	—
373	C₂³	—	3	2	no	—
374	C₂³	—	3	2	no	—
375	C₂³	—	6	1	no	—
376	C₂³	—	6	1	no	—
377	C₂³	—	6	1	no	—
378	C₂³	—	6	1	no	—
379	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	3	2	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	—	6	1	no	—
386	C₂×C₄	—	6	8	no	—
387	C₂×C₄	—	6	2	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	—	6	2	no	—
390	C₂×C₄	C₄×D₃×C₉	1	2	yes	—
391	C₂×C₄	C₉×D₁₂	1	2	yes	—
392	C₂×C₄	C₉×#67	1	2	yes	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	6	4	no	—
401	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
402	C₂×C₃	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
403	C₂×C₃	C₉×#117	1	1	yes	characteristic
404	C₂×C₃	C₉×#121	1	1	yes	characteristic
405	C₂×C₃	C₉×#121	1	1	yes	characteristic
406	C₂×C₃	C₉×C₂²⋊Q₈	1	1	yes	characteristic
407	C₂×C₃	C₉×C₂²⋊Q₈	1	1	yes	characteristic
408	C₂×C₃	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
409	C₂×C₃	C₃×#892	1	1	yes	characteristic
410	C₂×C₃	C₃×#895	1	1	yes	characteristic
411	C₂×C₃	C₃×#897	1	1	yes	characteristic
412	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
413	C₂×C₃	C₃×#938	1	1	yes	characteristic
414	C₂×C₃	C₃×#946	1	1	yes	characteristic
415	D₃	—	2	4	no	—
416	C₂²	—	3	4	no	—
417	C₂²	—	6	2	no	—
418	C₂²	—	6	2	no	—
419	C₂²	—	6	2	no	—
420	C₂²	—	6	2	no	—
421	C₂²	—	6	2	no	—
422	C₂²	—	6	2	no	—
423	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
424	C₂²	C₂×C₉×D₁₂	1	1	yes	characteristic
425	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
426	C₂²	C₉×#237	1	1	yes	characteristic
427	C₂²	D₃×Q₈×C₉	1	1	yes	characteristic
428	C₂²	C₉×#239	1	1	yes	characteristic
429	C₂²	C₂×C₉×#67	1	1	yes	characteristic
430	C₄	—	4	2	no	—
431	C₄	—	6	2	no	—
432	C₄	—	12	2	no	—
433	C₄	C₉×(C₂×D₃)⋊C₄	1	4	yes	complemented
434	C₃	—	2	1	no	—
435	C₃	C₉×#380	1	1	yes	characteristic, complemented
436	C₃	C₃×#4987	1	1	yes	characteristic
437	C₂	—	6	4	no	—
438	C₂	D₃×C₉×C₄⋊C₄	1	1	yes	characteristic
439	C₂	C₉×#892	1	1	yes	characteristic
440	C₂	C₉×#895	1	1	yes	characteristic
441	C₂	C₉×#897	1	1	yes	characteristic
442	C₂	C₂×C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
443	C₂	C₉×#938	1	1	yes	characteristic
444	C₂	C₉×#946	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×C₄⋊C₄	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₉×#380
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
4. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
5. C₉×C₃⋊#95	C₂	semidirect
15. C₂×C₄×D₃×C₉	C₄	semidirect
27. C₂×C₉×C₄⋊C₄	D₃	semidirect
52. #4987	C₉	direct (N × H)
91. C₂×D₃×C₉	C₄⋊C₄	semidirect
93. C₃×C₄×C₉	C₂²⋊C₄	semidirect
100. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
104. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
106. C₃⋊#95	C₂×C₉	semidirect
182. C₂×C₄×D₃	C₄×C₉	semidirect
234. C₄×C₉	(C₂×D₃)⋊C₄	semidirect
237. C₂×C₄⋊C₄	D₃×C₉	semidirect
240. C₃×C₉	#380	semidirect
358. C₂×D₃	C₉×C₄⋊C₄	semidirect
365. C₃×C₄	C₉×C₂²⋊C₄	semidirect
371. C₉	#4987	direct (N × H)
433. C₄	C₉×(C₂×D₃)⋊C₄	semidirect
435. C₃	C₉×#380	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×C₃×C₉×C₄⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₉×C₃⋊#95	2
C₃×#4987	3
C₉×#380	3

Subgroups — C9×#4987 #13142592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4987 #13142592