Subgroups — C₉×#5622 #13152901

Order 1728.

740 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#924	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₉×#889	C₂	1	2	yes	maximal, complemented
7	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#887	C₂	1	2	yes	maximal, complemented
10	C₉×#878	C₂	1	2	yes	maximal
11	C₉×#877	C₂	1	2	yes	maximal
12	C₃×#5622	C₃	1	1	yes	maximal, characteristic
13	C₉×#533	—	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	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×Dic₆	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₉×#217	C₂²	1	2	yes	—
24	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
26	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
27	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
28	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
32	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
33	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	2	yes	—
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic
39	C₃×#944	C₂×C₃	1	1	yes	characteristic
40	C₃×#924	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×#889	C₂×C₃	1	2	yes	—
43	C₃×#888	C₂×C₃	1	1	yes	characteristic
44	C₃×#887	C₂×C₃	1	1	yes	characteristic
45	C₃×#887	C₂×C₃	1	2	yes	—
46	C₃×#878	C₂×C₃	1	2	yes	—
47	C₃×#877	C₂×C₃	1	2	yes	—
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×C₄⋊Q₈	—	3	1	no	—
50	C₉×#125	—	3	2	no	—
51	C₉×C₂²⋊Q₈	—	2	1	no	—
52	C₉×C₂²⋊Q₈	—	3	1	no	—
53	C₉×C₂²⋊Q₈	—	3	2	no	—
54	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×Q₈×C₉	—	3	1	no	—
57	C₄×Q₈×C₉	—	3	2	no	—
58	C₉×#117	—	3	2	no	—
59	C₂×C₄²×C₉	—	3	1	no	—
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₉×Dic₃	—	2	2	no	—
68	C₂×C₉×Dic₃	Q₈	1	4	yes	complemented
69	C₂×C₉×Dic₃	C₂³	1	2	yes	—
70	C₂×C₉×Dic₃	C₂³	1	2	yes	—
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
75	C₉×Dic₆	—	2	2	no	—
76	C₉×Dic₆	—	2	4	no	—
77	C₃×#533	—	3	1	no	—
78	#5622	C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
84	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃×#217	C₂²×C₃	1	2	yes	—
89	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
90	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
97	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
98	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₂×Q₈×C₉	—	2	1	no	—
103	C₂×Q₈×C₉	—	3	2	no	—
104	C₂×Q₈×C₉	—	3	1	no	—
105	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₄×C₉	—	2	1	no	—
107	C₂²×C₄×C₉	—	3	1	no	—
108	C₂²×C₄×C₉	—	3	1	no	—
109	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	—	2	2	no	—
112	C₉×C₄⋊C₄	—	3	2	no	—
113	C₉×C₄⋊C₄	—	3	2	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	—	3	2	no	—
118	C₉×C₄⋊C₄	—	3	1	no	—
119	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
120	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
121	C₉×C₂²⋊C₄	—	2	2	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
124	C₄²×C₉	—	3	1	no	—
125	C₄²×C₉	—	3	1	no	—
126	C₄²×C₉	—	3	1	no	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	—	3	2	no	—
129	C₄²×C₉	—	3	2	no	—
130	C₂²×C₃×C₉	—	2	1	no	—
131	C₂²×C₃×C₉	—	2	1	no	—
132	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
133	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	1	no	—
136	C₃×C₄×C₉	—	2	2	no	—
137	C₃×C₄×C₉	#41	1	2	yes	—
138	C₉×Dic₃	—	2	2	no	—
139	C₉×Dic₃	—	2	2	no	—
140	C₉×Dic₃	—	2	1	no	—
141	C₉×Dic₃	C₂×Q₈	1	2	yes	—
142	C₉×Dic₃	C₂×Q₈	1	2	yes	—
143	C₉×Dic₃	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	3	1	no	—
145	C₃×C₄⋊Q₈	—	3	1	no	—
146	C₃×#125	—	3	2	no	—
147	C₃×C₂²⋊Q₈	—	2	1	no	—
148	C₃×C₂²⋊Q₈	—	3	1	no	—
149	C₃×C₂²⋊Q₈	—	3	2	no	—
150	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
151	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
152	C₃×C₄×Q₈	—	3	1	no	—
153	C₃×C₄×Q₈	—	3	1	no	—
154	C₃×C₄×Q₈	—	3	2	no	—
155	C₃×#117	—	3	2	no	—
156	C₂×C₃×C₄²	—	3	1	no	—
157	Q₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
158	#944	C₂×C₉	1	1	yes	characteristic, complemented
159	#924	C₂×C₉	1	1	yes	characteristic
160	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic
161	#889	C₂×C₉	1	2	yes	complemented
162	#888	C₂×C₉	1	1	yes	characteristic, complemented
163	#887	C₂×C₉	1	1	yes	characteristic, complemented
164	#887	C₂×C₉	1	2	yes	complemented
165	#878	C₂×C₉	1	2	yes	—
166	#877	C₂×C₉	1	2	yes	—
167	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
168	C₃²×Q₈	—	2	2	no	—
169	C₂×C₃²×C₄	—	2	2	no	—
170	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
172	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
173	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃×Dic₃	—	2	2	no	—
175	C₂×C₃×Dic₃	C₃×Q₈	1	4	yes	—
176	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
178	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
179	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
182	C₃×Dic₆	—	2	2	no	—
183	C₃×Dic₆	—	2	4	no	—
184	C₂³×C₉	—	2	1	no	—
185	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
186	Q₈×C₉	—	2	2	no	—
187	Q₈×C₉	—	4	2	no	—
188	Q₈×C₉	—	6	4	no	—
189	Q₈×C₉	—	6	2	no	—
190	C₂×C₄×C₉	—	2	2	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	2	2	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	3	4	no	—
196	C₂×C₄×C₉	—	3	1	no	—
197	C₂×C₄×C₉	—	3	1	no	—
198	C₂×C₄×C₉	—	3	1	no	—
199	C₂×C₄×C₉	—	3	1	no	—
200	C₂×C₄×C₉	—	3	2	no	—
201	C₂×C₄×C₉	—	3	2	no	—
202	C₂×C₄×C₉	—	4	2	no	—
203	C₂×C₄×C₉	—	6	2	no	—
204	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
206	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
207	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
208	#533	—	3	1	no	Sylow
209	C₂×C₃×C₉	—	2	2	no	—
210	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₃×Q₈	—	2	1	no	—
214	C₂×C₃×Q₈	—	3	2	no	—
215	C₂×C₃×Q₈	—	3	1	no	—
216	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	—	2	1	no	—
219	C₂²×C₃×C₄	—	3	1	no	—
220	C₂²×C₃×C₄	—	3	1	no	—
221	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
224	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
225	C₂×Dic₆	C₂²×C₉	1	2	yes	—
226	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	1	no	—
229	C₃×C₄⋊C₄	—	3	2	no	—
230	C₃×C₄⋊C₄	—	3	2	no	—
231	C₃×C₄⋊C₄	—	3	2	no	—
232	C₃×C₄⋊C₄	—	3	2	no	—
233	C₃×C₄⋊C₄	—	3	2	no	—
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₄⋊C₄	—	3	1	no	—
236	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
240	C₃×C₂²⋊C₄	—	2	2	no	—
241	C₃×C₂²⋊C₄	—	3	2	no	—
242	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
243	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
244	C₃×C₄²	—	3	1	no	—
245	C₃×C₄²	—	3	1	no	—
246	C₃×C₄²	—	3	1	no	—
247	C₃×C₄²	—	3	1	no	—
248	C₃×C₄²	—	3	2	no	—
249	C₃×C₄²	—	3	2	no	—
250	#217	C₂²×C₉	1	2	yes	—
251	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
252	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
253	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
254	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
255	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
256	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
257	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
258	C₄×Dic₃	C₂²×C₉	1	2	yes	—
259	C₄×Dic₃	C₂²×C₉	1	2	yes	—
260	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
261	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
262	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
263	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
264	C₂²×C₃²	—	2	1	no	—
265	C₂²×C₃²	—	2	1	no	—
266	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
267	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	2	1	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	C₃×#41	1	2	yes	—
272	C₃×Dic₃	—	2	2	no	—
273	C₃×Dic₃	—	2	2	no	—
274	C₃×Dic₃	—	2	1	no	—
275	C₃×Dic₃	C₂×C₃×Q₈	1	2	yes	—
276	C₃×Dic₃	C₂×C₃×Q₈	1	2	yes	—
277	C₃×Dic₃	C₃×#41	1	2	yes	—
278	C₂²×C₉	—	2	1	no	—
279	C₂²×C₉	—	2	1	no	—
280	C₂²×C₉	—	2	1	no	—
281	C₂²×C₉	—	2	2	no	—
282	C₂²×C₉	—	4	1	no	—
283	C₂²×C₉	—	4	1	no	—
284	C₂²×C₉	D₃×Q₈	1	2	yes	—
285	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
286	C₄×C₉	—	2	1	no	—
287	C₄×C₉	—	2	2	no	—
288	C₄×C₉	—	2	2	no	—
289	C₄×C₉	—	2	2	no	—
290	C₄×C₉	—	3	2	no	—
291	C₄×C₉	—	3	2	no	—
292	C₄×C₉	—	3	2	no	—
293	C₄×C₉	—	4	2	no	—
294	C₄×C₉	—	4	1	no	—
295	C₄×C₉	—	4	2	no	—
296	C₄×C₉	—	6	2	no	—
297	C₄×C₉	—	6	1	no	—
298	C₄×C₉	—	6	2	no	—
299	C₄×C₉	#237	1	2	yes	—
300	C₄⋊Q₈	—	3	1	no	—
301	C₄⋊Q₈	—	3	1	no	—
302	#125	—	3	2	no	—
303	C₂²⋊Q₈	—	3	1	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	—	3	1	no	—
308	C₄×Q₈	—	3	2	no	—
309	#117	—	3	2	no	—
310	C₂×C₄²	—	3	1	no	—
311	C₃×C₉	#533	1	1	yes	characteristic, complemented, Sylow
312	C₂³×C₃	—	2	1	no	—
313	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
314	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	4	2	no	—
318	C₃×Q₈	—	6	4	no	—
319	C₃×Q₈	—	6	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	3	1	no	—
327	C₂×C₃×C₄	—	3	1	no	—
328	C₂×C₃×C₄	—	3	1	no	—
329	C₂×C₃×C₄	—	3	4	no	—
330	C₂×C₃×C₄	—	3	1	no	—
331	C₂×C₃×C₄	—	3	2	no	—
332	C₂×C₃×C₄	—	3	2	no	—
333	C₂×C₃×C₄	—	4	2	no	—
334	C₂×C₃×C₄	—	6	2	no	—
335	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
337	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
338	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
341	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
342	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
343	C₂×Dic₃	—	2	2	no	—
344	C₂×Dic₃	Q₈×C₉	1	4	yes	complemented
345	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
346	C₂×Dic₃	C₂³×C₉	1	2	yes	—
347	C₂×Dic₃	C₂³×C₉	1	2	yes	—
348	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
349	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
350	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
351	Dic₆	—	2	2	no	—
352	Dic₆	—	2	4	no	—
353	C₂×C₃²	—	2	2	no	—
354	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
355	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
356	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
357	C₂×C₉	—	2	2	no	—
358	C₂×C₉	—	2	1	no	—
359	C₂×C₉	—	2	1	no	—
360	C₂×C₉	—	2	1	no	—
361	C₂×C₉	—	4	2	no	—
362	C₂×C₉	C₂×#237	1	1	yes	characteristic
363	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
364	C₂×C₉	D₃×#41	1	1	yes	characteristic
365	C₂×Q₈	—	3	2	no	—
366	C₂×Q₈	—	3	1	no	—
367	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
368	C₂²×C₄	—	3	1	no	—
369	C₂²×C₄	—	3	1	no	—
370	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	—	3	2	no	—
373	C₄⋊C₄	—	3	2	no	—
374	C₄⋊C₄	—	3	2	no	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	—	3	1	no	—
378	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
379	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
380	C₂²⋊C₄	—	3	2	no	—
381	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
382	C₄²	—	3	1	no	—
383	C₄²	—	3	1	no	—
384	C₄²	—	3	1	no	—
385	C₄²	—	3	1	no	—
386	C₄²	—	3	2	no	—
387	C₄²	—	3	2	no	—
388	C₂²×C₃	—	2	1	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	2	2	no	—
394	C₂²×C₃	—	4	1	no	—
395	C₂²×C₃	—	4	1	no	—
396	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	—
397	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
398	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
399	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	3	2	no	—
408	C₃×C₄	—	3	2	no	—
409	C₃×C₄	—	3	2	no	—
410	C₃×C₄	—	4	1	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	—	6	2	no	—
414	C₃×C₄	—	6	1	no	—
415	C₃×C₄	—	6	2	no	—
416	C₃×C₄	C₉×#41	1	2	yes	—
417	C₃×C₄	C₃×#237	1	2	yes	—
418	Dic₃	—	2	2	no	—
419	Dic₃	—	2	2	no	—
420	Dic₃	—	2	1	no	—
421	Dic₃	C₂×Q₈×C₉	1	2	yes	—
422	Dic₃	C₂×Q₈×C₉	1	2	yes	—
423	Dic₃	C₉×#41	1	2	yes	—
424	C₃²	C₃×#533	1	1	yes	characteristic
425	C₉	—	2	1	no	—
426	C₉	#5622	1	1	yes	characteristic, direct product factor
427	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
428	Q₈	—	2	2	no	—
429	Q₈	—	6	4	no	—
430	Q₈	—	6	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	3	1	no	—
434	C₂×C₄	—	3	1	no	—
435	C₂×C₄	—	3	4	no	—
436	C₂×C₄	—	3	1	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	6	2	no	—
440	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
441	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
442	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
443	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
444	C₂×C₃	—	2	2	no	—
445	C₂×C₃	—	2	2	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	4	2	no	—
450	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
451	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
452	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
453	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
454	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
455	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	D₃×Q₈×C₉	1	2	yes	—
459	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	3	2	no	—
464	C₄	—	3	2	no	—
465	C₄	—	3	2	no	—
466	C₄	—	6	2	no	—
467	C₄	—	6	1	no	—
468	C₄	—	6	2	no	—
469	C₄	C₉×#237	1	2	yes	—
470	C₃	—	2	1	no	—
471	C₃	C₉×#533	1	1	yes	characteristic, complemented
472	C₃	C₃×#5622	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	C₂×C₉×#237	1	1	yes	characteristic
475	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
476	C₂	D₃×C₉×#41	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	C₂³×C₃²	C₂³×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#533
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
2. Q₈×C₉×Dic₃	C₂	semidirect
3. C₉×#944	C₂	semidirect
6. C₉×#889	C₂	semidirect
7. C₉×#888	C₂	semidirect
8. C₉×#887	C₂	semidirect
9. C₉×#887	C₂	semidirect
68. C₂×C₉×Dic₃	Q₈	semidirect
78. #5622	C₉	direct (N × H)
157. Q₈×Dic₃	C₂×C₉	semidirect
158. #944	C₂×C₉	semidirect
161. #889	C₂×C₉	semidirect
162. #888	C₂×C₉	semidirect
163. #887	C₂×C₉	semidirect
164. #887	C₂×C₉	semidirect
311. C₃×C₉	#533	semidirect
344. C₂×Dic₃	Q₈×C₉	semidirect
426. C₉	#5622	direct (N × H)
471. C₃	C₉×#533	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₂²⋊Q₈	2
Q₈×C₉×Dic₃	2
C₉×#944	2
C₉×#924	2
C₂×C₄×C₉×Dic₃	2
C₉×#889	2
C₉×#888	2
C₉×#887	2
C₉×#878	2
C₉×#877	2
C₃×#5622	3
C₉×#533	3

Subgroups — C9×#5622 #13152901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5622 #13152901