Subgroups — C₉×#5628 #13152927

Order 1728.

884 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic
3	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#894	C₂	1	2	yes	maximal, complemented
8	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#888	C₂	1	2	yes	maximal, complemented
10	C₉×#885	C₂	1	2	yes	maximal, complemented
11	C₉×#883	C₂	1	2	yes	maximal, complemented
12	C₃×#5628	C₃	1	1	yes	maximal, characteristic
13	C₉×#536	—	3	1	no	maximal
14	C₂×C₃×Q₈×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	D₃×Q₈×C₉	—	2	4	no	—
19	C₉×#235	—	2	4	no	—
20	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
23	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
24	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
25	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
26	C₂×C₉×Dic₆	C₂²	1	2	yes	—
27	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₉×#217	C₂²	1	2	yes	—
31	C₉×(C₂×D₃)⋊C₄	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	1	yes	characteristic
35	C₉×C₄⋊Dic₃	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×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
41	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
42	C₃×#946	C₂×C₃	1	1	yes	characteristic
43	C₃×#924	C₂×C₃	1	1	yes	characteristic
44	C₃×#897	C₂×C₃	1	1	yes	characteristic
45	C₃×#894	C₂×C₃	1	2	yes	—
46	C₃×#892	C₂×C₃	1	1	yes	characteristic
47	C₃×#888	C₂×C₃	1	2	yes	—
48	C₃×#885	C₂×C₃	1	2	yes	—
49	C₃×#883	C₂×C₃	1	2	yes	—
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	—	3	2	no	—
55	C₉×#123	—	3	2	no	—
56	C₉×C₂²⋊Q₈	—	2	1	no	—
57	C₉×C₂²⋊Q₈	—	3	1	no	—
58	C₉×C₂²⋊Q₈	—	3	1	no	—
59	C₉×C₂²⋊Q₈	—	3	1	no	—
60	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
61	C₉×#117	—	3	1	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
65	C₃×Q₈×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	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₉×#67	—	2	2	no	—
72	C₉×#67	—	2	2	no	—
73	C₂×C₉×Dic₃	C₂³	1	2	yes	—
74	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₉×Dic₃	C₂³	1	2	yes	—
76	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
77	C₉×D₁₂	—	2	2	no	—
78	C₄×D₃×C₉	—	2	4	no	—
79	C₄×D₃×C₉	—	2	2	no	—
80	C₄×D₃×C₉	D₄	1	4	yes	—
81	C₉×Dic₆	—	2	2	no	—
82	C₉×Dic₆	—	2	2	no	—
83	C₉×Dic₆	—	2	4	no	—
84	C₃×#536	—	3	1	no	—
85	#5628	C₉	1	1	yes	characteristic, direct product factor
86	C₂×C₃²×Q₈	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	C₃×D₃×Q₈	—	2	4	no	—
91	C₃×#235	—	2	4	no	—
92	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
94	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
97	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
99	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₃×#217	C₂²×C₃	1	2	yes	—
103	C₃×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
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	—	2	1	no	—
113	C₂×Q₈×C₉	—	3	1	no	—
114	C₂×Q₈×C₉	—	3	2	no	—
115	C₂×Q₈×C₉	—	3	1	no	—
116	C₂×Q₈×C₉	—	6	4	no	—
117	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
118	C₂×D₄×C₉	—	3	1	no	—
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	3	1	no	—
121	C₂²×C₄×C₉	—	2	1	no	—
122	C₂²×C₄×C₉	—	3	1	no	—
123	C₂²×C₄×C₉	—	3	1	no	—
124	C₂²×C₄×C₉	—	3	2	no	—
125	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
126	C₉×C₄⋊C₄	—	2	1	no	—
127	C₉×C₄⋊C₄	—	2	2	no	—
128	C₉×C₄⋊C₄	—	3	1	no	—
129	C₉×C₄⋊C₄	—	3	2	no	—
130	C₉×C₄⋊C₄	—	3	2	no	—
131	C₉×C₄⋊C₄	—	3	2	no	—
132	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
134	C₉×C₂²⋊C₄	—	2	2	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	—	3	2	no	—
139	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
140	C₄²×C₉	—	3	2	no	—
141	C₂²×C₃×C₉	—	2	1	no	—
142	C₂²×C₃×C₉	—	2	1	no	—
143	C₂²×C₃×C₉	—	2	1	no	—
144	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
145	C₂×D₃×C₉	—	2	1	no	—
146	C₂×D₃×C₉	—	2	1	no	—
147	C₂×D₃×C₉	—	2	1	no	—
148	C₂×D₃×C₉	—	2	1	no	—
149	C₂×D₃×C₉	—	2	1	no	—
150	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
151	C₃×C₄×C₉	—	2	2	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	C₂×D₄	1	2	yes	—
159	C₂×C₃×#41	—	3	1	no	—
160	C₂²×C₃×Q₈	—	3	1	no	—
161	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
162	C₂×#235	C₂×C₉	1	1	yes	characteristic
163	C₃×C₄⋊Q₈	—	3	2	no	—
164	C₃×#124	—	3	2	no	—
165	C₃×#123	—	3	2	no	—
166	C₃×#123	—	3	2	no	—
167	C₃×C₂²⋊Q₈	—	2	1	no	—
168	C₃×C₂²⋊Q₈	—	3	1	no	—
169	C₃×C₂²⋊Q₈	—	3	1	no	—
170	C₃×C₂²⋊Q₈	—	3	1	no	—
171	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
172	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
173	C₃×#117	—	3	1	no	—
174	#946	C₂×C₉	1	1	yes	characteristic, complemented
175	#924	C₂×C₉	1	1	yes	characteristic, complemented
176	#897	C₂×C₉	1	1	yes	characteristic, complemented
177	#894	C₂×C₉	1	2	yes	complemented
178	#892	C₂×C₉	1	1	yes	characteristic, complemented
179	#888	C₂×C₉	1	2	yes	complemented
180	#885	C₂×C₉	1	2	yes	complemented
181	#883	C₂×C₉	1	2	yes	complemented
182	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
185	C₃²×Q₈	—	2	2	no	—
186	C₂×C₃²×C₄	—	2	2	no	—
187	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
188	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
190	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
191	C₃×#67	—	2	2	no	—
192	C₃×#67	—	2	2	no	—
193	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
194	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
196	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
197	C₃×D₁₂	—	2	2	no	—
198	C₃×C₄×D₃	—	2	4	no	—
199	C₃×C₄×D₃	—	2	2	no	—
200	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
201	C₃×Dic₆	—	2	2	no	—
202	C₃×Dic₆	—	2	2	no	—
203	C₃×Dic₆	—	2	4	no	—
204	C₂³×C₉	—	2	1	no	—
205	C₂³×C₉	—	3	1	no	—
206	C₂³×C₉	—	3	1	no	—
207	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
208	Q₈×C₉	—	2	2	no	—
209	Q₈×C₉	—	4	2	no	—
210	Q₈×C₉	—	6	4	no	—
211	Q₈×C₉	—	6	2	no	—
212	Q₈×C₉	—	6	2	no	—
213	D₄×C₉	—	6	2	no	—
214	D₄×C₉	—	6	2	no	—
215	D₄×C₉	—	6	2	no	—
216	C₂×C₄×C₉	—	2	2	no	—
217	C₂×C₄×C₉	—	2	1	no	—
218	C₂×C₄×C₉	—	2	2	no	—
219	C₂×C₄×C₉	—	2	2	no	—
220	C₂×C₄×C₉	—	2	1	no	—
221	C₂×C₄×C₉	—	3	1	no	—
222	C₂×C₄×C₉	—	3	4	no	—
223	C₂×C₄×C₉	—	3	2	no	—
224	C₂×C₄×C₉	—	3	2	no	—
225	C₂×C₄×C₉	—	3	1	no	—
226	C₂×C₄×C₉	—	4	2	no	—
227	C₂×C₄×C₉	—	6	4	no	—
228	C₂×C₄×C₉	—	6	2	no	—
229	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
230	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
231	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
233	#536	—	3	1	no	Sylow
234	C₂×C₃×C₉	—	4	1	no	—
235	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
238	D₃×C₉	—	2	2	no	—
239	D₃×C₉	—	4	1	no	—
240	C₃×#41	—	6	4	no	—
241	C₂×C₃×Q₈	—	2	1	no	—
242	C₂×C₃×Q₈	—	3	1	no	—
243	C₂×C₃×Q₈	—	3	2	no	—
244	C₂×C₃×Q₈	—	3	1	no	—
245	C₂×C₃×Q₈	—	6	4	no	—
246	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
247	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
248	C₂×C₃×D₄	—	3	1	no	—
249	C₂×C₃×D₄	—	3	1	no	—
250	C₂×C₃×D₄	—	3	1	no	—
251	C₂²×C₃×C₄	—	2	1	no	—
252	C₂²×C₃×C₄	—	3	1	no	—
253	C₂²×C₃×C₄	—	3	1	no	—
254	C₂²×C₃×C₄	—	3	2	no	—
255	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
257	C₂×#67	C₂²×C₉	1	1	yes	characteristic
258	C₂×#67	C₂²×C₉	1	1	yes	characteristic
259	D₃×Q₈	—	2	4	no	—
260	#235	—	2	4	no	—
261	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
262	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
263	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
264	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
265	C₂×Dic₆	C₂²×C₉	1	2	yes	—
266	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
267	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
268	C₃×C₄⋊C₄	—	2	1	no	—
269	C₃×C₄⋊C₄	—	2	2	no	—
270	C₃×C₄⋊C₄	—	3	2	no	—
271	C₃×C₄⋊C₄	—	3	2	no	—
272	C₃×C₄⋊C₄	—	3	1	no	—
273	C₃×C₄⋊C₄	—	3	2	no	—
274	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
275	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
278	C₃×C₂²⋊C₄	—	2	2	no	—
279	C₃×C₂²⋊C₄	—	3	2	no	—
280	C₃×C₂²⋊C₄	—	3	2	no	—
281	C₃×C₂²⋊C₄	—	3	2	no	—
282	C₃×C₂²⋊C₄	—	3	2	no	—
283	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
284	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
285	C₃×C₄²	—	3	2	no	—
286	#217	C₂²×C₉	1	2	yes	—
287	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
288	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
289	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
290	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
291	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
292	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
293	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
294	C₄×Dic₃	C₂²×C₉	1	2	yes	—
295	C₂²×C₃²	—	2	1	no	—
296	C₂²×C₃²	—	2	1	no	—
297	C₂²×C₃²	—	2	1	no	—
298	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
299	C₂×C₃×D₃	—	2	1	no	—
300	C₂×C₃×D₃	—	2	1	no	—
301	C₂×C₃×D₃	—	2	1	no	—
302	C₂×C₃×D₃	—	2	1	no	—
303	C₂×C₃×D₃	—	2	1	no	—
304	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
305	C₃²×C₄	—	2	2	no	—
306	C₃²×C₄	—	2	1	no	—
307	C₃²×C₄	—	2	2	no	—
308	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
309	C₃×Dic₃	—	2	2	no	—
310	C₃×Dic₃	—	2	1	no	—
311	C₃×Dic₃	—	2	2	no	—
312	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
313	C₂²×C₉	—	2	2	no	—
314	C₂²×C₉	—	2	1	no	—
315	C₂²×C₉	—	2	1	no	—
316	C₂²×C₉	—	2	1	no	—
317	C₂²×C₉	—	2	1	no	—
318	C₂²×C₉	—	3	2	no	—
319	C₂²×C₉	—	4	1	no	—
320	C₂²×C₉	—	4	1	no	—
321	C₂²×C₉	—	6	1	no	—
322	C₂²×C₉	—	6	1	no	—
323	C₂²×C₉	—	6	1	no	—
324	C₂²×C₉	—	6	1	no	—
325	C₂²×C₉	—	6	1	no	—
326	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
327	C₄×C₉	—	2	1	no	—
328	C₄×C₉	—	2	2	no	—
329	C₄×C₉	—	2	2	no	—
330	C₄×C₉	—	2	2	no	—
331	C₄×C₉	—	3	2	no	—
332	C₄×C₉	—	4	2	no	—
333	C₄×C₉	—	4	1	no	—
334	C₄×C₉	—	4	2	no	—
335	C₄×C₉	—	6	1	no	—
336	C₄×C₉	—	6	2	no	—
337	C₄×C₉	—	6	2	no	—
338	C₄×C₉	D₃×D₄	1	2	yes	—
339	C₂×#41	—	3	1	no	—
340	C₂²×Q₈	—	3	1	no	—
341	C₄⋊Q₈	—	3	2	no	—
342	#124	—	3	2	no	—
343	#123	—	3	2	no	—
344	#123	—	3	2	no	—
345	C₂²⋊Q₈	—	3	1	no	—
346	C₂²⋊Q₈	—	3	1	no	—
347	C₂²⋊Q₈	—	3	1	no	—
348	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
349	#117	—	3	1	no	—
350	C₃×C₉	#536	1	1	yes	characteristic, complemented, Sylow
351	C₂³×C₃	—	2	1	no	—
352	C₂³×C₃	—	3	1	no	—
353	C₂³×C₃	—	3	1	no	—
354	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
355	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
356	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
357	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
358	C₃×Q₈	—	2	2	no	—
359	C₃×Q₈	—	2	2	no	—
360	C₃×Q₈	—	4	2	no	—
361	C₃×Q₈	—	6	4	no	—
362	C₃×Q₈	—	6	2	no	—
363	C₃×Q₈	—	6	2	no	—
364	C₃×D₄	—	6	2	no	—
365	C₃×D₄	—	6	2	no	—
366	C₃×D₄	—	6	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	3	1	no	—
374	C₂×C₃×C₄	—	3	4	no	—
375	C₂×C₃×C₄	—	3	2	no	—
376	C₂×C₃×C₄	—	3	2	no	—
377	C₂×C₃×C₄	—	3	1	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	6	4	no	—
380	C₂×C₃×C₄	—	6	2	no	—
381	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
382	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
384	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
386	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
387	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
389	#67	—	2	2	no	—
390	#67	—	2	2	no	—
391	C₂×Dic₃	C₂³×C₉	1	2	yes	—
392	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
393	C₂×Dic₃	C₂³×C₉	1	2	yes	—
394	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
395	D₁₂	—	2	2	no	—
396	C₄×D₃	—	2	4	no	—
397	C₄×D₃	—	2	2	no	—
398	C₄×D₃	D₄×C₉	1	4	yes	—
399	Dic₆	—	2	2	no	—
400	Dic₆	—	2	2	no	—
401	Dic₆	—	2	4	no	—
402	C₂×C₃²	—	4	1	no	—
403	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
404	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
406	C₃×D₃	—	2	2	no	—
407	C₃×D₃	—	4	1	no	—
408	C₂×C₉	—	2	1	no	—
409	C₂×C₉	—	2	1	no	—
410	C₂×C₉	—	2	1	no	—
411	C₂×C₉	—	4	2	no	—
412	C₂×C₉	—	4	1	no	—
413	C₂×C₉	—	6	2	no	—
414	C₂×C₉	—	12	1	no	—
415	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
416	C₂×C₉	#1007	1	1	yes	characteristic
417	C₂×C₉	#1010	1	1	yes	characteristic
418	#41	—	6	4	no	—
419	C₂×Q₈	—	3	1	no	—
420	C₂×Q₈	—	3	2	no	—
421	C₂×Q₈	—	3	1	no	—
422	C₂×Q₈	—	6	4	no	—
423	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
424	C₂×D₄	—	3	1	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	1	no	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
431	C₄⋊C₄	—	3	1	no	—
432	C₄⋊C₄	—	3	2	no	—
433	C₄⋊C₄	—	3	2	no	—
434	C₄⋊C₄	—	3	2	no	—
435	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
436	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
437	C₂²⋊C₄	—	3	2	no	—
438	C₂²⋊C₄	—	3	2	no	—
439	C₂²⋊C₄	—	3	2	no	—
440	C₂²⋊C₄	—	3	2	no	—
441	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
442	C₄²	—	3	2	no	—
443	C₂²×C₃	—	2	2	no	—
444	C₂²×C₃	—	2	1	no	—
445	C₂²×C₃	—	2	1	no	—
446	C₂²×C₃	—	2	1	no	—
447	C₂²×C₃	—	2	1	no	—
448	C₂²×C₃	—	2	1	no	—
449	C₂²×C₃	—	2	1	no	—
450	C₂²×C₃	—	2	1	no	—
451	C₂²×C₃	—	3	2	no	—
452	C₂²×C₃	—	4	1	no	—
453	C₂²×C₃	—	4	1	no	—
454	C₂²×C₃	—	6	1	no	—
455	C₂²×C₃	—	6	1	no	—
456	C₂²×C₃	—	6	1	no	—
457	C₂²×C₃	—	6	1	no	—
458	C₂²×C₃	—	6	1	no	—
459	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
460	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
461	C₂×D₃	—	2	1	no	—
462	C₂×D₃	—	2	1	no	—
463	C₂×D₃	—	2	1	no	—
464	C₂×D₃	—	2	1	no	—
465	C₂×D₃	—	2	1	no	—
466	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
467	C₃×C₄	—	2	1	no	—
468	C₃×C₄	—	2	2	no	—
469	C₃×C₄	—	2	2	no	—
470	C₃×C₄	—	2	2	no	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	2	no	—
473	C₃×C₄	—	2	2	no	—
474	C₃×C₄	—	3	2	no	—
475	C₃×C₄	—	4	1	no	—
476	C₃×C₄	—	4	2	no	—
477	C₃×C₄	—	4	2	no	—
478	C₃×C₄	—	6	1	no	—
479	C₃×C₄	—	6	2	no	—
480	C₃×C₄	—	6	2	no	—
481	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
482	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
483	Dic₃	—	2	2	no	—
484	Dic₃	—	2	1	no	—
485	Dic₃	—	2	2	no	—
486	Dic₃	C₂×D₄×C₉	1	2	yes	—
487	C₃²	C₃×#536	1	1	yes	characteristic
488	C₉	—	2	1	no	—
489	C₉	#5628	1	1	yes	characteristic, direct product factor
490	C₂³	—	3	1	no	—
491	C₂³	—	3	1	no	—
492	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
493	Q₈	—	2	2	no	—
494	Q₈	—	6	4	no	—
495	Q₈	—	6	2	no	—
496	Q₈	—	6	2	no	—
497	D₄	—	6	2	no	—
498	D₄	—	6	2	no	—
499	D₄	—	6	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	3	1	no	—
502	C₂×C₄	—	3	4	no	—
503	C₂×C₄	—	3	2	no	—
504	C₂×C₄	—	3	2	no	—
505	C₂×C₄	—	3	1	no	—
506	C₂×C₄	—	6	4	no	—
507	C₂×C₄	—	6	2	no	—
508	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
509	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
510	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
512	C₂×C₃	—	2	1	no	—
513	C₂×C₃	—	2	1	no	—
514	C₂×C₃	—	2	1	no	—
515	C₂×C₃	—	4	2	no	—
516	C₂×C₃	—	4	1	no	—
517	C₂×C₃	—	4	1	no	—
518	C₂×C₃	—	6	2	no	—
519	C₂×C₃	—	12	1	no	—
520	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
521	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
523	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
524	C₂×C₃	C₃×#1007	1	1	yes	characteristic
525	C₂×C₃	C₃×#1010	1	1	yes	characteristic
526	D₃	—	2	2	no	—
527	D₃	—	4	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	3	2	no	—
532	C₂²	—	6	1	no	—
533	C₂²	—	6	1	no	—
534	C₂²	—	6	1	no	—
535	C₂²	—	6	1	no	—
536	C₂²	—	6	1	no	—
537	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	3	2	no	—
542	C₄	—	6	1	no	—
543	C₄	—	6	2	no	—
544	C₄	—	6	2	no	—
545	C₄	D₃×D₄×C₉	1	2	yes	—
546	C₃	—	2	1	no	—
547	C₃	C₉×#536	1	1	yes	characteristic, complemented
548	C₃	C₃×#5628	1	1	yes	characteristic
549	C₂	—	4	1	no	—
550	C₂	—	6	2	no	—
551	C₂	—	12	1	no	—
552	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
553	C₂	C₉×#1007	1	1	yes	characteristic
554	C₂	C₉×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₂²⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#235	C₂×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×Q₈×C₉	C₂	semidirect
3. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₉×#946	C₂	semidirect
5. C₉×#924	C₂	semidirect
6. C₉×#897	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. C₉×#892	C₂	semidirect
9. C₉×#888	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#883	C₂	semidirect
60. C₉×C₂²⋊Q₈	D₃	semidirect
85. #5628	C₉	direct (N × H)
161. C₂×D₃×Q₈	C₂×C₉	semidirect
171. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
174. #946	C₂×C₉	semidirect
175. #924	C₂×C₉	semidirect
176. #897	C₂×C₉	semidirect
177. #894	C₂×C₉	semidirect
178. #892	C₂×C₉	semidirect
179. #888	C₂×C₉	semidirect
180. #885	C₂×C₉	semidirect
181. #883	C₂×C₉	semidirect
348. C₂²⋊Q₈	D₃×C₉	semidirect
350. C₃×C₉	#536	semidirect
489. C₉	#5628	direct (N × H)
547. 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×D₃×Q₈×C₉	2
C₂×C₉×#235	2
C₃×C₉×C₂²⋊Q₈	2
C₉×#946	2
C₉×#924	2
C₉×#897	2
C₉×#894	2
C₉×#892	2
C₉×#888	2
C₉×#885	2
C₉×#883	2
C₃×#5628	3
C₉×#536	3

Subgroups — C9×#5628 #13152927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5628 #13152927