Subgroups — C₉×#5824 #13153707

Order 1728.

1040 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#939	C₂	1	2	yes	maximal, complemented
6	C₉×#935	C₂	1	2	yes	maximal, complemented
7	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#929	C₂	1	2	yes	maximal, complemented
9	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₉×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#5824	C₃	1	1	yes	maximal, characteristic
13	C₉×#547	—	3	1	no	maximal
14	C₃×C₉×#41	—	2	4	no	—
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
17	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
19	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×#67	C₂²	1	2	yes	—
21	C₂×C₉×#67	C₂²	1	1	yes	characteristic
22	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
23	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
24	C₉×#237	—	2	4	no	—
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
27	C₉×#217	C₂²	1	2	yes	—
28	C₉×#217	C₂²	1	1	yes	characteristic
29	C₉×#217	C₂²	1	2	yes	—
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×Dic₃⋊C₄	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	1	yes	characteristic
39	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
41	C₃×#946	C₂×C₃	1	1	yes	characteristic
42	C₃×#944	C₂×C₃	1	1	yes	characteristic
43	C₃×#939	C₂×C₃	1	2	yes	—
44	C₃×#935	C₂×C₃	1	2	yes	—
45	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
46	C₃×#929	C₂×C₃	1	2	yes	—
47	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
48	C₃×#924	C₂×C₃	1	1	yes	characteristic
49	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	2	1	no	—
51	C₂×C₉×#41	—	3	1	no	—
52	C₂×C₉×#41	D₃	1	1	yes	characteristic, complemented
53	C₉×C₄⋊Q₈	—	3	1	no	—
54	C₉×#123	—	3	2	no	—
55	C₉×#123	—	3	2	no	—
56	C₉×C₂²⋊Q₈	—	3	1	no	—
57	C₉×C₂²⋊Q₈	—	3	1	no	—
58	C₉×#121	—	3	2	no	—
59	C₄×D₄×C₉	—	3	1	no	—
60	C₄×D₄×C₉	—	3	1	no	—
61	C₂×C₉×C₄⋊C₄	—	3	2	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂³×C₃×C₉	C₂³	1	2	yes	—
64	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
65	C₃×Q₈×C₉	—	2	2	no	—
66	C₃×D₄×C₉	—	2	4	no	—
67	C₃×D₄×C₉	D₄	1	4	yes	complemented
68	C₂×C₃×C₄×C₉	—	2	4	no	—
69	C₂×C₃×C₄×C₉	—	2	2	no	—
70	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
72	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₉×#67	—	2	4	no	—
74	C₉×#67	—	2	2	no	—
75	C₂×C₉×Dic₃	—	2	4	no	—
76	C₂×C₉×Dic₃	—	2	4	no	—
77	C₂×C₉×Dic₃	C₂³	1	2	yes	—
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₉×Dic₃	C₂³	1	2	yes	—
80	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
82	C₄×D₃×C₉	—	2	2	no	—
83	C₉×Dic₆	—	2	2	no	—
84	C₃×#547	—	3	1	no	—
85	#5824	C₉	1	1	yes	characteristic, direct product factor
86	C₃²×#41	—	2	4	no	—
87	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
89	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
91	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
95	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
96	C₃×#237	—	2	4	no	—
97	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
99	C₃×#217	C₂²×C₃	1	2	yes	—
100	C₃×#217	C₂²×C₃	1	1	yes	characteristic
101	C₃×#217	C₂²×C₃	1	2	yes	—
102	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
104	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
105	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₃×Dic₃⋊C₄	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	1	yes	characteristic
111	C₉×#41	—	2	8	no	—
112	C₉×#41	—	2	4	no	—
113	C₉×#41	—	6	4	no	—
114	C₂×Q₈×C₉	—	2	1	no	—
115	C₂×Q₈×C₉	—	3	1	no	—
116	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
117	C₂×D₄×C₉	—	2	2	no	—
118	C₂×D₄×C₉	—	2	1	no	—
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	3	2	no	—
121	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
122	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
123	C₂²×C₄×C₉	—	2	2	no	—
124	C₂²×C₄×C₉	—	2	1	no	—
125	C₂²×C₄×C₉	—	3	2	no	—
126	C₂²×C₄×C₉	—	3	2	no	—
127	C₂²×C₄×C₉	—	3	1	no	—
128	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
129	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
130	C₉×C₄⋊C₄	—	3	1	no	—
131	C₉×C₄⋊C₄	—	3	2	no	—
132	C₉×C₄⋊C₄	—	3	2	no	—
133	C₉×C₄⋊C₄	—	3	2	no	—
134	C₉×C₄⋊C₄	—	3	1	no	—
135	C₉×C₄⋊C₄	—	3	2	no	—
136	C₉×C₂²⋊C₄	—	3	2	no	—
137	C₉×C₂²⋊C₄	—	3	1	no	—
138	C₉×C₂²⋊C₄	—	3	2	no	—
139	C₉×C₂²⋊C₄	—	3	1	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₄²×C₉	—	3	1	no	—
142	C₂²×C₃×C₉	—	2	2	no	—
143	C₂²×C₃×C₉	—	2	2	no	—
144	C₂²×C₃×C₉	—	2	1	no	—
145	C₂²×C₃×C₉	—	2	1	no	—
146	C₂²×C₃×C₉	—	2	1	no	—
147	C₂²×C₃×C₉	C₂×D₄	1	4	yes	—
148	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
149	C₂×D₃×C₉	—	2	1	no	—
150	C₂×D₃×C₉	—	2	1	no	—
151	C₂×D₃×C₉	—	2	1	no	—
152	C₃×C₄×C₉	—	2	1	no	—
153	C₃×C₄×C₉	—	2	2	no	—
154	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
155	C₉×Dic₃	—	2	2	no	—
156	C₉×Dic₃	—	2	1	no	—
157	C₉×Dic₃	—	2	2	no	—
158	C₉×Dic₃	—	2	1	no	—
159	C₉×Dic₃	#41	1	2	yes	complemented
160	C₂×C₃×#41	—	2	1	no	—
161	C₂×C₃×#41	—	3	1	no	—
162	C₂×C₃×#41	C₂×C₉	1	1	yes	characteristic, complemented
163	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
164	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
165	C₃×C₄⋊Q₈	—	3	1	no	—
166	C₃×#123	—	3	2	no	—
167	C₃×#123	—	3	2	no	—
168	C₃×C₂²⋊Q₈	—	3	1	no	—
169	C₃×C₂²⋊Q₈	—	3	1	no	—
170	C₃×#121	—	3	2	no	—
171	C₃×C₄×D₄	—	3	1	no	—
172	C₃×C₄×D₄	—	3	1	no	—
173	C₂×C₃×C₄⋊C₄	—	3	2	no	—
174	#946	C₂×C₉	1	1	yes	characteristic, complemented
175	#944	C₂×C₉	1	1	yes	characteristic, complemented
176	#939	C₂×C₉	1	2	yes	complemented
177	#935	C₂×C₉	1	2	yes	complemented
178	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
179	#929	C₂×C₉	1	2	yes	complemented
180	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
181	#924	C₂×C₉	1	1	yes	characteristic, complemented
182	C₂×Dic₃⋊C₄	C₂×C₉	1	2	yes	complemented
183	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
184	C₂³×C₃²	C₂³×C₃	1	2	yes	—
185	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
186	C₃²×Q₈	—	2	2	no	—
187	C₃²×D₄	—	2	4	no	—
188	C₃²×D₄	C₃×D₄	1	4	yes	—
189	C₂×C₃²×C₄	—	2	4	no	—
190	C₂×C₃²×C₄	—	2	2	no	—
191	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
193	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₃×#67	—	2	4	no	—
195	C₃×#67	—	2	2	no	—
196	C₂×C₃×Dic₃	—	2	4	no	—
197	C₂×C₃×Dic₃	—	2	4	no	—
198	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
200	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
202	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
203	C₃×C₄×D₃	—	2	2	no	—
204	C₃×Dic₆	—	2	2	no	—
205	C₂³×C₉	—	2	1	no	—
206	C₂³×C₉	—	2	2	no	—
207	C₂³×C₉	—	3	1	no	—
208	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
209	C₂³×C₉	C₂²×D₃	1	2	yes	—
210	Q₈×C₉	—	2	4	no	—
211	Q₈×C₉	—	2	2	no	—
212	Q₈×C₉	—	6	2	no	—
213	D₄×C₉	—	2	8	no	—
214	D₄×C₉	—	2	4	no	—
215	D₄×C₉	—	2	4	no	—
216	D₄×C₉	—	6	2	no	—
217	D₄×C₉	—	6	4	no	—
218	D₄×C₉	#67	1	4	yes	complemented
219	C₂×C₄×C₉	—	2	8	no	—
220	C₂×C₄×C₉	—	2	4	no	—
221	C₂×C₄×C₉	—	2	4	no	—
222	C₂×C₄×C₉	—	2	2	no	—
223	C₂×C₄×C₉	—	2	1	no	—
224	C₂×C₄×C₉	—	2	2	no	—
225	C₂×C₄×C₉	—	2	1	no	—
226	C₂×C₄×C₉	—	3	1	no	—
227	C₂×C₄×C₉	—	3	1	no	—
228	C₂×C₄×C₉	—	3	2	no	—
229	C₂×C₄×C₉	—	3	1	no	—
230	C₂×C₄×C₉	—	3	2	no	—
231	C₂×C₄×C₉	—	6	4	no	—
232	C₂×C₄×C₉	—	6	4	no	—
233	C₂×C₄×C₉	—	6	2	no	—
234	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
235	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
236	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
237	#547	—	3	1	no	Sylow
238	C₂×C₃×C₉	—	2	4	no	—
239	C₂×C₃×C₉	—	4	1	no	—
240	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
242	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
243	D₃×C₉	—	4	1	no	—
244	C₃×#41	—	2	8	no	—
245	C₃×#41	—	2	4	no	—
246	C₃×#41	—	2	4	no	—
247	C₃×#41	—	6	4	no	—
248	C₂×C₃×Q₈	—	2	1	no	—
249	C₂×C₃×Q₈	—	3	1	no	—
250	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
251	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
252	C₂×C₃×D₄	—	2	2	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×C₃×D₄	—	3	1	no	—
255	C₂×C₃×D₄	—	3	2	no	—
256	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
257	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
258	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
259	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
260	C₂²×C₃×C₄	—	2	2	no	—
261	C₂²×C₃×C₄	—	2	1	no	—
262	C₂²×C₃×C₄	—	3	2	no	—
263	C₂²×C₃×C₄	—	3	2	no	—
264	C₂²×C₃×C₄	—	3	1	no	—
265	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
266	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
268	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
269	C₂×#67	C₂²×C₉	1	1	yes	characteristic
270	C₂×#67	C₂²×C₉	1	2	yes	—
271	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
272	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
273	#237	—	2	4	no	—
274	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
275	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
276	C₃×C₄⋊C₄	—	3	1	no	—
277	C₃×C₄⋊C₄	—	3	2	no	—
278	C₃×C₄⋊C₄	—	3	2	no	—
279	C₃×C₄⋊C₄	—	3	2	no	—
280	C₃×C₄⋊C₄	—	3	2	no	—
281	C₃×C₄⋊C₄	—	3	1	no	—
282	C₃×C₂²⋊C₄	—	3	2	no	—
283	C₃×C₂²⋊C₄	—	3	1	no	—
284	C₃×C₂²⋊C₄	—	3	2	no	—
285	C₃×C₂²⋊C₄	—	3	1	no	—
286	C₃×C₂²⋊C₄	—	3	2	no	—
287	C₃×C₄²	—	3	1	no	—
288	#217	C₂²×C₉	1	2	yes	—
289	#217	C₂²×C₉	1	1	yes	characteristic
290	#217	C₂²×C₉	1	2	yes	—
291	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
292	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
293	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
294	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
295	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
296	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
297	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
298	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
299	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
300	C₂²×C₃²	—	2	1	no	—
301	C₂²×C₃²	—	2	2	no	—
302	C₂²×C₃²	—	2	2	no	—
303	C₂²×C₃²	—	2	1	no	—
304	C₂²×C₃²	—	2	1	no	—
305	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
306	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
307	C₂×C₃×D₃	—	2	1	no	—
308	C₂×C₃×D₃	—	2	1	no	—
309	C₂×C₃×D₃	—	2	1	no	—
310	C₃²×C₄	—	2	1	no	—
311	C₃²×C₄	—	2	2	no	—
312	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
313	C₃×Dic₃	—	2	2	no	—
314	C₃×Dic₃	—	2	1	no	—
315	C₃×Dic₃	—	2	2	no	—
316	C₃×Dic₃	—	2	1	no	—
317	C₃×Dic₃	C₃×#41	1	2	yes	—
318	C₂²×C₉	—	2	2	no	—
319	C₂²×C₉	—	2	2	no	—
320	C₂²×C₉	—	2	2	no	—
321	C₂²×C₉	—	2	1	no	—
322	C₂²×C₉	—	2	1	no	—
323	C₂²×C₉	—	2	1	no	—
324	C₂²×C₉	—	2	1	no	—
325	C₂²×C₉	—	2	4	no	—
326	C₂²×C₉	—	4	2	no	—
327	C₂²×C₉	—	4	2	no	—
328	C₂²×C₉	—	4	1	no	—
329	C₂²×C₉	—	4	1	no	—
330	C₂²×C₉	—	6	1	no	—
331	C₂²×C₉	—	6	1	no	—
332	C₂²×C₉	—	6	1	no	—
333	C₂²×C₉	C₂×#67	1	4	yes	—
334	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
335	C₄×C₉	—	2	2	no	—
336	C₄×C₉	—	2	4	no	—
337	C₄×C₉	—	2	1	no	—
338	C₄×C₉	—	2	2	no	—
339	C₄×C₉	—	2	2	no	—
340	C₄×C₉	—	3	2	no	—
341	C₄×C₉	—	6	2	no	—
342	C₄×C₉	—	6	1	no	—
343	C₄×C₉	—	6	1	no	—
344	C₄×C₉	—	6	2	no	—
345	C₄×C₉	C₂×#67	1	2	yes	—
346	C₂×#41	—	3	1	no	—
347	C₂×#41	D₃×C₉	1	1	yes	characteristic, complemented
348	C₄⋊Q₈	—	3	1	no	—
349	#123	—	3	2	no	—
350	#123	—	3	2	no	—
351	C₂²⋊Q₈	—	3	1	no	—
352	C₂²⋊Q₈	—	3	1	no	—
353	#121	—	3	2	no	—
354	C₄×D₄	—	3	1	no	—
355	C₄×D₄	—	3	1	no	—
356	C₂×C₄⋊C₄	—	3	2	no	—
357	C₃×C₉	#547	1	1	yes	characteristic, complemented, Sylow
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	2	no	—
360	C₂³×C₃	—	3	1	no	—
361	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
362	C₂³×C₃	C₂³×C₉	1	2	yes	—
363	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
364	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
365	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
366	C₃×Q₈	—	2	4	no	—
367	C₃×Q₈	—	2	2	no	—
368	C₃×Q₈	—	2	2	no	—
369	C₃×Q₈	—	6	2	no	—
370	C₃×D₄	—	2	8	no	—
371	C₃×D₄	—	2	4	no	—
372	C₃×D₄	—	2	4	no	—
373	C₃×D₄	—	2	4	no	—
374	C₃×D₄	—	6	2	no	—
375	C₃×D₄	—	6	4	no	—
376	C₃×D₄	D₄×C₉	1	4	yes	complemented
377	C₃×D₄	C₃×#67	1	4	yes	—
378	C₂×C₃×C₄	—	2	8	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	2	4	no	—
381	C₂×C₃×C₄	—	2	4	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	3	1	no	—
388	C₂×C₃×C₄	—	3	1	no	—
389	C₂×C₃×C₄	—	3	2	no	—
390	C₂×C₃×C₄	—	3	1	no	—
391	C₂×C₃×C₄	—	3	2	no	—
392	C₂×C₃×C₄	—	6	4	no	—
393	C₂×C₃×C₄	—	6	4	no	—
394	C₂×C₃×C₄	—	6	2	no	—
395	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
397	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
400	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
401	#67	—	2	4	no	—
402	#67	—	2	2	no	—
403	C₂×Dic₃	—	2	4	no	—
404	C₂×Dic₃	—	2	4	no	—
405	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
406	C₂×Dic₃	C₂³×C₉	1	2	yes	—
407	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
408	C₂×Dic₃	C₂³×C₉	1	2	yes	—
409	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
410	C₄×D₃	—	2	2	no	—
411	Dic₆	—	2	2	no	—
412	C₂×C₃²	—	2	4	no	—
413	C₂×C₃²	—	4	1	no	—
414	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
415	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
416	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
417	C₃×D₃	—	4	1	no	—
418	C₂×C₉	—	2	4	no	—
419	C₂×C₉	—	2	1	no	—
420	C₂×C₉	—	2	1	no	—
421	C₂×C₉	—	2	1	no	—
422	C₂×C₉	—	4	4	no	—
423	C₂×C₉	—	4	2	no	—
424	C₂×C₉	—	4	1	no	—
425	C₂×C₉	—	12	1	no	—
426	C₂×C₉	D₃×#41	1	1	yes	characteristic
427	C₂×C₉	#1010	1	1	yes	characteristic
428	C₂×C₉	C₂²×#67	1	1	yes	characteristic
429	#41	—	2	4	no	—
430	#41	—	6	4	no	—
431	C₂×Q₈	—	3	1	no	—
432	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
433	C₂×D₄	—	3	1	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
436	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
441	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
442	C₄⋊C₄	—	3	1	no	—
443	C₄⋊C₄	—	3	2	no	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	3	2	no	—
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₂²⋊C₄	—	3	2	no	—
449	C₂²⋊C₄	—	3	1	no	—
450	C₂²⋊C₄	—	3	2	no	—
451	C₂²⋊C₄	—	3	1	no	—
452	C₂²⋊C₄	—	3	2	no	—
453	C₄²	—	3	1	no	—
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	1	no	—
466	C₂²×C₃	—	2	4	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	—	4	2	no	—
469	C₂²×C₃	—	4	1	no	—
470	C₂²×C₃	—	4	1	no	—
471	C₂²×C₃	—	6	1	no	—
472	C₂²×C₃	—	6	1	no	—
473	C₂²×C₃	—	6	1	no	—
474	C₂²×C₃	C₂×D₄×C₉	1	4	yes	—
475	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
476	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
477	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
478	C₂×D₃	—	2	1	no	—
479	C₂×D₃	—	2	1	no	—
480	C₂×D₃	—	2	1	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	2	4	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	2	2	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	—	2	2	no	—
487	C₃×C₄	—	2	2	no	—
488	C₃×C₄	—	3	2	no	—
489	C₃×C₄	—	6	2	no	—
490	C₃×C₄	—	6	1	no	—
491	C₃×C₄	—	6	1	no	—
492	C₃×C₄	—	6	2	no	—
493	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
494	C₃×C₄	C₂×C₃×#67	1	2	yes	—
495	Dic₃	—	2	2	no	—
496	Dic₃	—	2	1	no	—
497	Dic₃	—	2	2	no	—
498	Dic₃	—	2	1	no	—
499	Dic₃	C₉×#41	1	2	yes	complemented
500	C₃²	C₃×#547	1	1	yes	characteristic
501	C₉	—	2	1	no	—
502	C₉	#5824	1	1	yes	characteristic, direct product factor
503	C₂³	—	3	1	no	—
504	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
505	C₂³	C₂²×D₃×C₉	1	2	yes	—
506	Q₈	—	2	2	no	—
507	Q₈	—	6	2	no	—
508	D₄	—	2	4	no	—
509	D₄	—	6	2	no	—
510	D₄	—	6	4	no	—
511	D₄	C₉×#67	1	4	yes	complemented
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	3	1	no	—
516	C₂×C₄	—	3	2	no	—
517	C₂×C₄	—	3	1	no	—
518	C₂×C₄	—	3	2	no	—
519	C₂×C₄	—	6	4	no	—
520	C₂×C₄	—	6	4	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
524	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
525	C₂×C₃	—	2	4	no	—
526	C₂×C₃	—	2	4	no	—
527	C₂×C₃	—	2	1	no	—
528	C₂×C₃	—	2	1	no	—
529	C₂×C₃	—	2	1	no	—
530	C₂×C₃	—	4	4	no	—
531	C₂×C₃	—	4	2	no	—
532	C₂×C₃	—	4	1	no	—
533	C₂×C₃	—	4	1	no	—
534	C₂×C₃	—	12	1	no	—
535	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
536	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
537	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
538	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
539	C₂×C₃	C₃×#1010	1	1	yes	characteristic
540	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
541	D₃	—	4	1	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	6	1	no	—
548	C₂²	—	6	1	no	—
549	C₂²	—	6	1	no	—
550	C₂²	C₂×C₉×#67	1	4	yes	—
551	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
552	C₄	—	2	1	no	—
553	C₄	—	2	2	no	—
554	C₄	—	3	2	no	—
555	C₄	—	6	2	no	—
556	C₄	—	6	1	no	—
557	C₄	—	6	1	no	—
558	C₄	—	6	2	no	—
559	C₄	C₂×C₉×#67	1	2	yes	—
560	C₃	—	2	1	no	—
561	C₃	C₉×#547	1	1	yes	characteristic, complemented
562	C₃	C₃×#5824	1	1	yes	characteristic
563	C₂	—	2	4	no	—
564	C₂	—	4	1	no	—
565	C₂	—	12	1	no	—
566	C₂	D₃×C₉×#41	1	1	yes	characteristic
567	C₂	C₉×#1010	1	1	yes	characteristic
568	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×#41	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5824	C₃
hypercenter	C₂×C₉×#41	D₃
hypocenter	C₃	C₉×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂×C₉×#237	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₉×#944	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#935	C₂	semidirect
7. D₄×C₉×Dic₃	C₂	semidirect
8. C₉×#929	C₂	semidirect
9. C₄×C₉×#67	C₂	semidirect
10. C₉×#924	C₂	semidirect
11. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
52. C₂×C₉×#41	D₃	semidirect
67. C₃×D₄×C₉	D₄	semidirect
85. #5824	C₉	direct (N × H)
159. C₉×Dic₃	#41	semidirect
162. C₂×C₃×#41	C₂×C₉	semidirect
164. C₂×#237	C₂×C₉	semidirect
174. #946	C₂×C₉	semidirect
175. #944	C₂×C₉	semidirect
176. #939	C₂×C₉	semidirect
177. #935	C₂×C₉	semidirect
178. D₄×Dic₃	C₂×C₉	semidirect
179. #929	C₂×C₉	semidirect
180. C₄×#67	C₂×C₉	semidirect
181. #924	C₂×C₉	semidirect
182. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
218. D₄×C₉	#67	semidirect
347. C₂×#41	D₃×C₉	semidirect
357. C₃×C₉	#547	semidirect
376. C₃×D₄	D₄×C₉	semidirect
499. Dic₃	C₉×#41	semidirect
502. C₉	#5824	direct (N × H)
511. D₄	C₉×#67	semidirect
561. C₃	C₉×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×#41	2
C₂×C₉×#237	2
C₉×#946	2
C₉×#944	2
C₉×#939	2
C₉×#935	2
D₄×C₉×Dic₃	2
C₉×#929	2
C₄×C₉×#67	2
C₉×#924	2
C₂×C₉×Dic₃⋊C₄	2
C₃×#5824	3
C₉×#547	3

Subgroups — C9×#5824 #13153707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5824 #13153707