Subgroups — C₉×#5632 #13152899

Order 1728.

914 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	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic
6	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#896	C₂	1	2	yes	maximal, complemented
8	C₉×#888	C₂	1	2	yes	maximal, complemented
9	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#67⋊C₄	C₂	1	2	yes	maximal
11	C₉×#878	C₂	1	2	yes	maximal, complemented
12	C₃×#5632	C₃	1	1	yes	maximal, characteristic
13	D₄×Q₈×C₉	—	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	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
18	D₃×Q₈×C₉	—	2	4	no	—
19	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
21	C₂×C₉×Dic₆	—	2	4	no	—
22	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
23	C₂×C₉×Dic₆	C₂²	1	2	yes	—
24	C₂×C₉×Dic₆	C₂²	1	2	yes	—
25	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₉×#217	C₂²	1	1	yes	characteristic
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	2	yes	—
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	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
38	C₄×C₉×Dic₃	C₂²	1	2	yes	—
39	C₂×C₃×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
40	C₂²×C₃×Dic₆	C₂×C₃	1	1	yes	characteristic
41	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
42	C₃×#944	C₂×C₃	1	1	yes	characteristic
43	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
44	C₃×#897	C₂×C₃	1	1	yes	characteristic
45	C₃×#896	C₂×C₃	1	2	yes	—
46	C₃×#888	C₂×C₃	1	2	yes	—
47	C₃×#887	C₂×C₃	1	1	yes	characteristic
48	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
49	C₃×#878	C₂×C₃	1	2	yes	—
50	C₂²×Q₈×C₉	—	3	1	no	—
51	C₂²×Q₈×C₉	—	3	1	no	—
52	C₉×C₄⋊Q₈	—	3	1	no	—
53	C₉×C₄⋊Q₈	—	3	2	no	—
54	C₉×C₂²⋊Q₈	—	2	1	no	—
55	C₉×C₂²⋊Q₈	—	3	2	no	—
56	C₉×C₂²⋊Q₈	—	3	1	no	—
57	C₉×C₂²⋊Q₈	—	3	2	no	—
58	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
59	C₄×Q₈×C₉	—	3	1	no	—
60	C₄×D₄×C₉	—	3	1	no	—
61	C₄×D₄×C₉	—	3	2	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
64	C₃×Q₈×C₉	—	2	2	no	—
65	C₂×C₃×C₄×C₉	—	2	2	no	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
68	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×#67	Q₈	1	4	yes	complemented
71	C₂×C₉×Dic₃	—	2	4	no	—
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
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	C₄×D₃×C₉	—	2	2	no	—
78	C₄×D₃×C₉	—	2	4	no	—
79	C₉×Dic₆	—	2	2	no	—
80	C₉×Dic₆	—	2	4	no	—
81	C₉×Dic₆	—	2	4	no	—
82	C₉×Dic₆	D₄	1	4	yes	complemented
83	C₃×D₄×Q₈	—	3	1	no	—
84	#5632	C₉	1	1	yes	characteristic, direct product factor
85	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
89	C₃×D₃×Q₈	—	2	4	no	—
90	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×Dic₆	—	2	4	no	—
93	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
94	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
95	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
97	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃×#217	C₂²×C₃	1	1	yes	characteristic
101	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
102	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
104	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
105	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
109	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
110	C₂×Q₈×C₉	—	2	1	no	—
111	C₂×Q₈×C₉	—	3	1	no	—
112	C₂×Q₈×C₉	—	3	2	no	—
113	C₂×Q₈×C₉	—	3	2	no	—
114	C₂×Q₈×C₉	—	3	1	no	—
115	C₂×Q₈×C₉	—	6	4	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	C₂²×C₄×C₉	—	2	1	no	—
120	C₂²×C₄×C₉	—	3	2	no	—
121	C₂²×C₄×C₉	—	3	2	no	—
122	C₂²×C₄×C₉	—	3	1	no	—
123	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
124	C₉×C₄⋊C₄	—	2	1	no	—
125	C₉×C₄⋊C₄	—	2	2	no	—
126	C₉×C₄⋊C₄	—	3	1	no	—
127	C₉×C₄⋊C₄	—	3	2	no	—
128	C₉×C₄⋊C₄	—	3	2	no	—
129	C₉×C₄⋊C₄	—	3	2	no	—
130	C₉×C₄⋊C₄	—	3	2	no	—
131	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
133	C₉×C₂²⋊C₄	—	2	2	no	—
134	C₉×C₂²⋊C₄	—	3	1	no	—
135	C₉×C₂²⋊C₄	—	3	1	no	—
136	C₉×C₂²⋊C₄	—	3	2	no	—
137	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
138	C₄²×C₉	—	3	2	no	—
139	C₄²×C₉	—	3	1	no	—
140	C₂²×C₃×C₉	—	2	1	no	—
141	C₂²×C₃×C₉	—	2	1	no	—
142	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	complemented
143	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
144	C₂×D₃×C₉	—	2	1	no	—
145	C₂×D₃×C₉	—	2	1	no	—
146	C₂×D₃×C₉	C₂×Q₈	1	2	yes	complemented
147	C₃×C₄×C₉	—	2	1	no	—
148	C₃×C₄×C₉	—	2	2	no	—
149	C₃×C₄×C₉	—	2	2	no	—
150	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
151	C₉×Dic₃	—	2	1	no	—
152	C₉×Dic₃	—	2	2	no	—
153	C₉×Dic₃	—	2	1	no	—
154	C₉×Dic₃	C₂×D₄	1	4	yes	—
155	C₉×Dic₃	C₂×Q₈	1	2	yes	complemented
156	C₂²×C₃×Q₈	—	3	1	no	—
157	C₂²×C₃×Q₈	—	3	1	no	—
158	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
159	C₂²×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
160	C₃×C₄⋊Q₈	—	3	1	no	—
161	C₃×C₄⋊Q₈	—	3	2	no	—
162	C₃×C₂²⋊Q₈	—	2	1	no	—
163	C₃×C₂²⋊Q₈	—	3	2	no	—
164	C₃×C₂²⋊Q₈	—	3	1	no	—
165	C₃×C₂²⋊Q₈	—	3	2	no	—
166	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
167	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
168	C₃×C₄×Q₈	—	3	1	no	—
169	C₃×C₄×D₄	—	3	1	no	—
170	C₃×C₄×D₄	—	3	2	no	—
171	#944	C₂×C₉	1	1	yes	characteristic, complemented
172	C₄×#67	C₂×C₉	1	1	yes	characteristic
173	#897	C₂×C₉	1	1	yes	characteristic, complemented
174	#896	C₂×C₉	1	2	yes	complemented
175	#888	C₂×C₉	1	2	yes	complemented
176	#887	C₂×C₉	1	1	yes	characteristic, complemented
177	#67⋊C₄	C₂×C₉	1	2	yes	—
178	#878	C₂×C₉	1	2	yes	complemented
179	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
181	C₃²×Q₈	—	2	2	no	—
182	C₂×C₃²×C₄	—	2	2	no	—
183	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
184	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₃×#67	C₃×Q₈	1	4	yes	—
188	C₂×C₃×Dic₃	—	2	4	no	—
189	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
191	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
193	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
194	C₃×C₄×D₃	—	2	2	no	—
195	C₃×C₄×D₃	—	2	4	no	—
196	C₃×Dic₆	—	2	2	no	—
197	C₃×Dic₆	—	2	4	no	—
198	C₃×Dic₆	—	2	4	no	—
199	C₃×Dic₆	C₃×D₄	1	4	yes	—
200	C₂³×C₉	—	2	1	no	—
201	C₂³×C₉	—	3	1	no	—
202	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
203	Q₈×C₉	—	2	2	no	—
204	Q₈×C₉	—	3	4	no	—
205	Q₈×C₉	—	4	2	no	—
206	Q₈×C₉	—	6	4	no	—
207	Q₈×C₉	—	6	4	no	—
208	Q₈×C₉	—	6	2	no	—
209	D₄×C₉	—	3	4	no	—
210	C₂×C₄×C₉	—	2	2	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	2	no	—
213	C₂×C₄×C₉	—	2	2	no	—
214	C₂×C₄×C₉	—	2	1	no	—
215	C₂×C₄×C₉	—	3	1	no	—
216	C₂×C₄×C₉	—	3	2	no	—
217	C₂×C₄×C₉	—	3	1	no	—
218	C₂×C₄×C₉	—	3	1	no	—
219	C₂×C₄×C₉	—	3	2	no	—
220	C₂×C₄×C₉	—	4	2	no	—
221	C₂×C₄×C₉	—	6	4	no	—
222	C₂×C₄×C₉	—	6	4	no	—
223	C₂×C₄×C₉	—	6	2	no	—
224	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
225	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
226	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
227	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
228	D₄×Q₈	—	3	1	no	Sylow
229	C₂×C₃×C₉	—	2	2	no	—
230	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
233	D₃×C₉	—	2	2	no	—
234	C₂×C₃×Q₈	—	2	1	no	—
235	C₂×C₃×Q₈	—	3	1	no	—
236	C₂×C₃×Q₈	—	3	2	no	—
237	C₂×C₃×Q₈	—	3	2	no	—
238	C₂×C₃×Q₈	—	3	1	no	—
239	C₂×C₃×Q₈	—	6	4	no	—
240	C₂×C₃×Q₈	—	6	4	no	—
241	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
243	C₂×C₃×D₄	—	3	1	no	—
244	C₂²×C₃×C₄	—	2	1	no	—
245	C₂²×C₃×C₄	—	3	2	no	—
246	C₂²×C₃×C₄	—	3	2	no	—
247	C₂²×C₃×C₄	—	3	1	no	—
248	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
250	C₂×#67	C₂²×C₉	1	1	yes	characteristic
251	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
252	D₃×Q₈	—	2	4	no	—
253	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
254	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
255	C₂×Dic₆	—	2	4	no	—
256	C₂×Dic₆	C₂²×C₉	1	2	yes	—
257	C₂×Dic₆	C₂²×C₉	1	2	yes	—
258	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
259	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
260	C₃×C₄⋊C₄	—	2	1	no	—
261	C₃×C₄⋊C₄	—	2	2	no	—
262	C₃×C₄⋊C₄	—	3	1	no	—
263	C₃×C₄⋊C₄	—	3	2	no	—
264	C₃×C₄⋊C₄	—	3	2	no	—
265	C₃×C₄⋊C₄	—	3	2	no	—
266	C₃×C₄⋊C₄	—	3	2	no	—
267	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
268	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
269	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
270	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
271	C₃×C₂²⋊C₄	—	2	2	no	—
272	C₃×C₂²⋊C₄	—	3	1	no	—
273	C₃×C₂²⋊C₄	—	3	1	no	—
274	C₃×C₂²⋊C₄	—	3	2	no	—
275	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
276	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
277	C₃×C₄²	—	3	2	no	—
278	C₃×C₄²	—	3	1	no	—
279	#217	C₂²×C₉	1	1	yes	characteristic
280	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
281	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
282	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
283	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
284	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
285	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
286	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
287	C₄×Dic₃	C₂²×C₉	1	2	yes	—
288	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
289	C₂²×C₃²	—	2	1	no	—
290	C₂²×C₃²	—	2	1	no	—
291	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
292	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
293	C₂×C₃×D₃	—	2	1	no	—
294	C₂×C₃×D₃	—	2	1	no	—
295	C₂×C₃×D₃	C₂×C₃×Q₈	1	2	yes	—
296	C₃²×C₄	—	2	1	no	—
297	C₃²×C₄	—	2	2	no	—
298	C₃²×C₄	—	2	2	no	—
299	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
300	C₃×Dic₃	—	2	1	no	—
301	C₃×Dic₃	—	2	2	no	—
302	C₃×Dic₃	—	2	1	no	—
303	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
304	C₃×Dic₃	C₂×C₃×Q₈	1	2	yes	—
305	C₂²×C₉	—	2	1	no	—
306	C₂²×C₉	—	2	1	no	—
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	2	no	—
309	C₂²×C₉	—	3	2	no	—
310	C₂²×C₉	—	4	1	no	—
311	C₂²×C₉	—	4	1	no	—
312	C₂²×C₉	—	6	1	no	—
313	C₂²×C₉	—	6	1	no	—
314	C₂²×C₉	D₃×Q₈	1	2	yes	complemented
315	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
316	C₄×C₉	—	2	1	no	—
317	C₄×C₉	—	2	2	no	—
318	C₄×C₉	—	2	2	no	—
319	C₄×C₉	—	2	2	no	—
320	C₄×C₉	—	3	4	no	—
321	C₄×C₉	—	3	2	no	—
322	C₄×C₉	—	4	2	no	—
323	C₄×C₉	—	4	1	no	—
324	C₄×C₉	—	4	2	no	—
325	C₄×C₉	—	6	1	no	—
326	C₄×C₉	—	6	2	no	—
327	C₄×C₉	—	6	1	no	—
328	C₄×C₉	D₃×D₄	1	2	yes	—
329	C₂²×Q₈	—	3	1	no	—
330	C₂²×Q₈	—	3	1	no	—
331	C₄⋊Q₈	—	3	1	no	—
332	C₄⋊Q₈	—	3	2	no	—
333	C₂²⋊Q₈	—	3	2	no	—
334	C₂²⋊Q₈	—	3	1	no	—
335	C₂²⋊Q₈	—	3	2	no	—
336	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
337	C₄×Q₈	—	3	1	no	—
338	C₄×D₄	—	3	1	no	—
339	C₄×D₄	—	3	2	no	—
340	C₃×C₉	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
341	C₂³×C₃	—	2	1	no	—
342	C₂³×C₃	—	3	1	no	—
343	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
344	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
345	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
346	C₃×Q₈	—	2	2	no	—
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	3	4	no	—
349	C₃×Q₈	—	4	2	no	—
350	C₃×Q₈	—	6	4	no	—
351	C₃×Q₈	—	6	4	no	—
352	C₃×Q₈	—	6	2	no	—
353	C₃×D₄	—	3	4	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	3	1	no	—
361	C₂×C₃×C₄	—	3	2	no	—
362	C₂×C₃×C₄	—	3	1	no	—
363	C₂×C₃×C₄	—	3	2	no	—
364	C₂×C₃×C₄	—	3	1	no	—
365	C₂×C₃×C₄	—	4	2	no	—
366	C₂×C₃×C₄	—	6	4	no	—
367	C₂×C₃×C₄	—	6	4	no	—
368	C₂×C₃×C₄	—	6	2	no	—
369	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
370	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
371	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
374	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
376	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
377	#67	Q₈×C₉	1	4	yes	complemented
378	C₂×Dic₃	—	2	4	no	—
379	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
380	C₂×Dic₃	C₂³×C₉	1	2	yes	—
381	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
382	C₂×Dic₃	C₂³×C₉	1	2	yes	—
383	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
384	C₄×D₃	—	2	2	no	—
385	C₄×D₃	—	2	4	no	—
386	Dic₆	—	2	2	no	—
387	Dic₆	—	2	4	no	—
388	Dic₆	—	2	4	no	—
389	Dic₆	D₄×C₉	1	4	yes	complemented
390	C₂×C₃²	—	2	2	no	—
391	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
392	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
393	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
394	C₃×D₃	—	2	2	no	—
395	C₂×C₉	—	2	2	no	—
396	C₂×C₉	—	2	1	no	—
397	C₂×C₉	—	2	1	no	—
398	C₂×C₉	—	2	1	no	—
399	C₂×C₉	—	4	2	no	—
400	C₂×C₉	—	6	2	no	—
401	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
402	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
403	C₂×C₉	#1010	1	1	yes	characteristic
404	C₂×Q₈	—	3	1	no	—
405	C₂×Q₈	—	3	2	no	—
406	C₂×Q₈	—	3	2	no	—
407	C₂×Q₈	—	3	1	no	—
408	C₂×Q₈	—	6	4	no	—
409	C₂×Q₈	—	6	4	no	—
410	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
411	C₂×D₄	—	3	1	no	—
412	C₂²×C₄	—	3	2	no	—
413	C₂²×C₄	—	3	2	no	—
414	C₂²×C₄	—	3	1	no	—
415	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
416	C₄⋊C₄	—	3	1	no	—
417	C₄⋊C₄	—	3	2	no	—
418	C₄⋊C₄	—	3	2	no	—
419	C₄⋊C₄	—	3	2	no	—
420	C₄⋊C₄	—	3	2	no	—
421	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
422	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
423	C₂²⋊C₄	—	3	1	no	—
424	C₂²⋊C₄	—	3	1	no	—
425	C₂²⋊C₄	—	3	2	no	—
426	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
427	C₄²	—	3	2	no	—
428	C₄²	—	3	1	no	—
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	1	no	—
431	C₂²×C₃	—	2	1	no	—
432	C₂²×C₃	—	2	1	no	—
433	C₂²×C₃	—	2	1	no	—
434	C₂²×C₃	—	2	2	no	—
435	C₂²×C₃	—	3	2	no	—
436	C₂²×C₃	—	4	1	no	—
437	C₂²×C₃	—	4	1	no	—
438	C₂²×C₃	—	6	1	no	—
439	C₂²×C₃	—	6	1	no	—
440	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	complemented
441	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
442	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
443	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
444	C₂×D₃	—	2	1	no	—
445	C₂×D₃	—	2	1	no	—
446	C₂×D₃	C₂×Q₈×C₉	1	2	yes	complemented
447	C₃×C₄	—	2	1	no	—
448	C₃×C₄	—	2	2	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	1	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	3	4	no	—
455	C₃×C₄	—	3	2	no	—
456	C₃×C₄	—	4	1	no	—
457	C₃×C₄	—	4	2	no	—
458	C₃×C₄	—	4	2	no	—
459	C₃×C₄	—	6	2	no	—
460	C₃×C₄	—	6	1	no	—
461	C₃×C₄	—	6	1	no	—
462	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
463	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
464	Dic₃	—	2	1	no	—
465	Dic₃	—	2	2	no	—
466	Dic₃	—	2	1	no	—
467	Dic₃	C₂×D₄×C₉	1	4	yes	—
468	Dic₃	C₂×Q₈×C₉	1	2	yes	complemented
469	C₃²	C₃×D₄×Q₈	1	1	yes	characteristic
470	C₉	—	2	1	no	—
471	C₉	#5632	1	1	yes	characteristic, direct product factor
472	C₂³	—	3	1	no	—
473	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	3	4	no	—
476	Q₈	—	6	4	no	—
477	Q₈	—	6	4	no	—
478	Q₈	—	6	2	no	—
479	D₄	—	3	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	3	1	no	—
482	C₂×C₄	—	3	2	no	—
483	C₂×C₄	—	3	1	no	—
484	C₂×C₄	—	3	1	no	—
485	C₂×C₄	—	3	2	no	—
486	C₂×C₄	—	6	4	no	—
487	C₂×C₄	—	6	4	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
490	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
492	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
493	C₂×C₃	—	2	2	no	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	2	1	no	—
497	C₂×C₃	—	2	1	no	—
498	C₂×C₃	—	4	2	no	—
499	C₂×C₃	—	6	2	no	—
500	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
501	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
502	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
503	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
504	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
505	C₂×C₃	C₃×#1010	1	1	yes	characteristic
506	D₃	—	2	2	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	3	2	no	—
510	C₂²	—	6	1	no	—
511	C₂²	—	6	1	no	—
512	C₂²	D₃×Q₈×C₉	1	2	yes	complemented
513	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	3	4	no	—
518	C₄	—	3	2	no	—
519	C₄	—	6	2	no	—
520	C₄	—	6	1	no	—
521	C₄	—	6	1	no	—
522	C₄	D₃×D₄×C₉	1	2	yes	—
523	C₃	—	2	1	no	—
524	C₃	D₄×Q₈×C₉	1	1	yes	characteristic, complemented
525	C₃	C₃×#5632	1	1	yes	characteristic
526	C₂	—	2	2	no	—
527	C₂	—	6	2	no	—
528	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
529	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
530	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×#67	C₂²×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	D₄×Q₈×C₉
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
2. C₂²×C₉×Dic₆	C₂	semidirect
3. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₉×#944	C₂	semidirect
6. C₉×#897	C₂	semidirect
7. C₉×#896	C₂	semidirect
8. C₉×#888	C₂	semidirect
9. C₉×#887	C₂	semidirect
11. C₉×#878	C₂	semidirect
58. C₉×C₂²⋊Q₈	D₃	semidirect
70. C₉×#67	Q₈	semidirect
82. C₉×Dic₆	D₄	semidirect
84. #5632	C₉	direct (N × H)
142. C₂²×C₃×C₉	C₂×Q₈	semidirect
146. C₂×D₃×C₉	C₂×Q₈	semidirect
155. C₉×Dic₃	C₂×Q₈	semidirect
158. C₂×D₃×Q₈	C₂×C₉	semidirect
159. C₂²×Dic₆	C₂×C₉	semidirect
166. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
171. #944	C₂×C₉	semidirect
173. #897	C₂×C₉	semidirect
174. #896	C₂×C₉	semidirect
175. #888	C₂×C₉	semidirect
176. #887	C₂×C₉	semidirect
178. #878	C₂×C₉	semidirect
314. C₂²×C₉	D₃×Q₈	semidirect
336. C₂²⋊Q₈	D₃×C₉	semidirect
340. C₃×C₉	D₄×Q₈	semidirect
377. #67	Q₈×C₉	semidirect
389. Dic₆	D₄×C₉	semidirect
440. C₂²×C₃	C₂×Q₈×C₉	semidirect
446. C₂×D₃	C₂×Q₈×C₉	semidirect
468. Dic₃	C₂×Q₈×C₉	semidirect
471. C₉	#5632	direct (N × H)
512. C₂²	D₃×Q₈×C₉	semidirect
524. C₃	D₄×Q₈×C₉	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
C₂²×C₉×Dic₆	2
C₃×C₉×C₂²⋊Q₈	2
C₉×#944	2
C₄×C₉×#67	2
C₉×#897	2
C₉×#896	2
C₉×#888	2
C₉×#887	2
C₉×#67⋊C₄	2
C₉×#878	2
C₃×#5632	3
D₄×Q₈×C₉	3

Subgroups — C9×#5632 #13152899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5632 #13152899