Subgroups — C₉×#5635 #13152933

Order 1728.

758 conjugacy classes of subgroups.

The subgroup lattice has 502 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, complemented
2	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic
5	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#897	C₂	1	2	yes	maximal, complemented
7	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#889	C₂	1	2	yes	maximal, complemented
9	C₉×#888	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×#5635	C₃	1	1	yes	maximal, characteristic
13	C₉×#554	—	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	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
20	C₂×C₉×Dic₆	C₂²	1	2	yes	—
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₉×#217	C₂²	1	1	yes	characteristic
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
28	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
30	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
31	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#946	C₂×C₃	1	1	yes	characteristic
39	C₃×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic
40	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×#897	C₂×C₃	1	2	yes	—
43	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
44	C₃×#889	C₂×C₃	1	2	yes	—
45	C₃×#888	C₂×C₃	1	1	yes	characteristic
46	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
47	C₃×#878	C₂×C₃	1	2	yes	—
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#125	—	3	2	no	—
50	C₉×C₂²⋊Q₈	—	2	1	no	—
51	C₉×C₂²⋊Q₈	—	3	1	no	—
52	C₉×C₂²⋊Q₈	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	2	no	—
54	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×D₄×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	2	no	—
58	C₂×C₉×C₄⋊C₄	—	3	1	no	—
59	C₂×C₉×C₄⋊C₄	—	3	1	no	—
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
62	C₃×Q₈×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	—	2	2	no	—
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×#67	Q₈	1	4	yes	complemented
69	C₂×C₉×Dic₃	—	4	2	no	—
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₉×Dic₃	C₂³	1	2	yes	—
72	C₂×C₉×Dic₃	C₂³	1	2	yes	—
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
75	C₄×D₃×C₉	—	2	2	no	—
76	C₄×D₃×C₉	—	4	2	no	—
77	C₉×Dic₆	—	4	2	no	—
78	C₃×#554	—	3	1	no	—
79	#5635	C₉	1	1	yes	characteristic, direct product factor
80	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
84	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
86	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
87	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×#217	C₂²×C₃	1	1	yes	characteristic
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
96	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
102	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
103	C₂×Q₈×C₉	—	2	1	no	—
104	C₂×Q₈×C₉	—	3	2	no	—
105	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
106	C₂×D₄×C₉	—	3	1	no	—
107	C₂²×C₄×C₉	—	2	1	no	—
108	C₂²×C₄×C₉	—	3	2	no	—
109	C₂²×C₄×C₉	—	3	1	no	—
110	C₂²×C₄×C₉	—	3	2	no	—
111	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
112	C₉×C₄⋊C₄	—	2	1	no	—
113	C₉×C₄⋊C₄	—	2	2	no	—
114	C₉×C₄⋊C₄	—	3	1	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	—	3	1	no	—
118	C₉×C₄⋊C₄	—	3	1	no	—
119	C₉×C₄⋊C₄	—	3	2	no	—
120	C₉×C₄⋊C₄	—	3	2	no	—
121	C₉×C₄⋊C₄	—	3	2	no	—
122	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
123	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
124	C₉×C₂²⋊C₄	—	2	2	no	—
125	C₉×C₂²⋊C₄	—	3	1	no	—
126	C₉×C₂²⋊C₄	—	3	1	no	—
127	C₉×C₂²⋊C₄	—	3	2	no	—
128	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
129	C₄²×C₉	—	3	2	no	—
130	C₄²×C₉	—	3	1	no	—
131	C₂²×C₃×C₉	—	2	1	no	—
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
134	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
135	C₂×D₃×C₉	—	2	1	no	—
136	C₂×D₃×C₉	—	2	1	no	—
137	C₂×D₃×C₉	C₂×Q₈	1	2	yes	—
138	C₃×C₄×C₉	—	2	1	no	—
139	C₃×C₄×C₉	—	2	2	no	—
140	C₃×C₄×C₉	—	2	2	no	—
141	C₃×C₄×C₉	#41	1	2	yes	—
142	C₉×Dic₃	—	2	1	no	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	2	no	—
145	C₉×Dic₃	—	2	2	no	—
146	C₉×Dic₃	C₂×Q₈	1	2	yes	—
147	C₃×C₄⋊Q₈	—	3	1	no	—
148	C₃×#125	—	3	2	no	—
149	C₃×C₂²⋊Q₈	—	2	1	no	—
150	C₃×C₂²⋊Q₈	—	3	1	no	—
151	C₃×C₂²⋊Q₈	—	3	2	no	—
152	C₃×C₂²⋊Q₈	—	3	2	no	—
153	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
154	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
155	C₃×C₄×Q₈	—	3	1	no	—
156	C₃×C₄×D₄	—	3	1	no	—
157	C₃×C₄×D₄	—	3	2	no	—
158	C₂×C₃×C₄⋊C₄	—	3	1	no	—
159	C₂×C₃×C₄⋊C₄	—	3	1	no	—
160	#946	C₂×C₉	1	1	yes	characteristic, complemented
161	Q₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
162	C₄×#67	C₂×C₉	1	1	yes	characteristic
163	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
164	#897	C₂×C₉	1	2	yes	complemented
165	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
166	#889	C₂×C₉	1	2	yes	complemented
167	#888	C₂×C₉	1	1	yes	characteristic, complemented
168	#67⋊C₄	C₂×C₉	1	2	yes	—
169	#878	C₂×C₉	1	2	yes	complemented
170	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
172	C₃²×Q₈	—	2	2	no	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
175	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
176	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₃×#67	C₃×Q₈	1	4	yes	—
179	C₂×C₃×Dic₃	—	4	2	no	—
180	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
181	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
184	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
185	C₃×C₄×D₃	—	2	2	no	—
186	C₃×C₄×D₃	—	4	2	no	—
187	C₃×Dic₆	—	4	2	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	3	1	no	—
190	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
191	Q₈×C₉	—	2	2	no	—
192	Q₈×C₉	—	4	2	no	—
193	Q₈×C₉	—	12	2	no	—
194	D₄×C₉	—	3	4	no	—
195	C₂×C₄×C₉	—	2	2	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	2	2	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	3	1	no	—
201	C₂×C₄×C₉	—	3	1	no	—
202	C₂×C₄×C₉	—	3	2	no	—
203	C₂×C₄×C₉	—	3	1	no	—
204	C₂×C₄×C₉	—	3	2	no	—
205	C₂×C₄×C₉	—	4	2	no	—
206	C₂×C₄×C₉	—	6	2	no	—
207	C₂×C₄×C₉	—	12	2	no	—
208	C₂×C₄×C₉	—	12	2	no	—
209	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
210	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
211	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
212	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
213	#554	—	3	1	no	Sylow
214	C₂×C₃×C₉	—	2	2	no	—
215	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
218	D₃×C₉	—	2	2	no	—
219	C₂×C₃×Q₈	—	2	1	no	—
220	C₂×C₃×Q₈	—	3	2	no	—
221	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
222	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂×C₃×D₄	—	3	1	no	—
224	C₂²×C₃×C₄	—	2	1	no	—
225	C₂²×C₃×C₄	—	3	2	no	—
226	C₂²×C₃×C₄	—	3	1	no	—
227	C₂²×C₃×C₄	—	3	2	no	—
228	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
230	C₂×#67	C₂²×C₉	1	1	yes	characteristic
231	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
232	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
233	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
234	C₂×Dic₆	C₂²×C₉	1	2	yes	—
235	C₃×C₄⋊C₄	—	2	1	no	—
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	3	2	no	—
238	C₃×C₄⋊C₄	—	3	1	no	—
239	C₃×C₄⋊C₄	—	3	2	no	—
240	C₃×C₄⋊C₄	—	3	2	no	—
241	C₃×C₄⋊C₄	—	3	1	no	—
242	C₃×C₄⋊C₄	—	3	2	no	—
243	C₃×C₄⋊C₄	—	3	1	no	—
244	C₃×C₄⋊C₄	—	3	2	no	—
245	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
246	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
247	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
248	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
249	C₃×C₂²⋊C₄	—	2	2	no	—
250	C₃×C₂²⋊C₄	—	3	1	no	—
251	C₃×C₂²⋊C₄	—	3	1	no	—
252	C₃×C₂²⋊C₄	—	3	2	no	—
253	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
254	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
255	C₃×C₄²	—	3	2	no	—
256	C₃×C₄²	—	3	1	no	—
257	#217	C₂²×C₉	1	1	yes	characteristic
258	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
259	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
260	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
261	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
262	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
263	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
264	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
265	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
266	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
267	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
268	C₄×Dic₃	C₂²×C₉	1	2	yes	—
269	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
270	C₂²×C₃²	—	2	1	no	—
271	C₂²×C₃²	—	2	1	no	—
272	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
273	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
274	C₂×C₃×D₃	—	2	1	no	—
275	C₂×C₃×D₃	—	2	1	no	—
276	C₂×C₃×D₃	C₂×C₃×Q₈	1	2	yes	—
277	C₃²×C₄	—	2	1	no	—
278	C₃²×C₄	—	2	2	no	—
279	C₃²×C₄	—	2	2	no	—
280	C₃²×C₄	C₃×#41	1	2	yes	—
281	C₃×Dic₃	—	2	1	no	—
282	C₃×Dic₃	—	2	1	no	—
283	C₃×Dic₃	—	2	2	no	—
284	C₃×Dic₃	—	2	2	no	—
285	C₃×Dic₃	C₂×C₃×Q₈	1	2	yes	—
286	C₂²×C₉	—	2	1	no	—
287	C₂²×C₉	—	2	1	no	—
288	C₂²×C₉	—	2	1	no	—
289	C₂²×C₉	—	2	2	no	—
290	C₂²×C₉	—	3	2	no	—
291	C₂²×C₉	—	4	1	no	—
292	C₂²×C₉	—	4	1	no	—
293	C₂²×C₉	—	6	1	no	—
294	C₂²×C₉	—	6	1	no	—
295	C₂²×C₉	D₃×Q₈	1	2	yes	—
296	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
297	C₄×C₉	—	2	1	no	—
298	C₄×C₉	—	2	2	no	—
299	C₄×C₉	—	2	2	no	—
300	C₄×C₉	—	2	2	no	—
301	C₄×C₉	—	3	2	no	—
302	C₄×C₉	—	4	2	no	—
303	C₄×C₉	—	4	1	no	—
304	C₄×C₉	—	4	2	no	—
305	C₄×C₉	—	6	1	no	—
306	C₄×C₉	—	6	2	no	—
307	C₄×C₉	—	6	2	no	—
308	C₄×C₉	—	6	1	no	—
309	C₄×C₉	#237	1	2	yes	—
310	C₄⋊Q₈	—	3	1	no	—
311	#125	—	3	2	no	—
312	C₂²⋊Q₈	—	3	1	no	—
313	C₂²⋊Q₈	—	3	2	no	—
314	C₂²⋊Q₈	—	3	2	no	—
315	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
316	C₄×Q₈	—	3	1	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	3	2	no	—
319	C₂×C₄⋊C₄	—	3	1	no	—
320	C₂×C₄⋊C₄	—	3	1	no	—
321	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
322	C₂³×C₃	—	2	1	no	—
323	C₂³×C₃	—	3	1	no	—
324	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
325	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
326	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
327	C₃×Q₈	—	2	2	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	—	4	2	no	—
330	C₃×Q₈	—	12	2	no	—
331	C₃×D₄	—	3	4	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	3	1	no	—
339	C₂×C₃×C₄	—	3	1	no	—
340	C₂×C₃×C₄	—	3	2	no	—
341	C₂×C₃×C₄	—	3	1	no	—
342	C₂×C₃×C₄	—	3	2	no	—
343	C₂×C₃×C₄	—	4	2	no	—
344	C₂×C₃×C₄	—	6	2	no	—
345	C₂×C₃×C₄	—	12	2	no	—
346	C₂×C₃×C₄	—	12	2	no	—
347	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
348	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
349	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
352	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
354	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
355	#67	Q₈×C₉	1	4	yes	complemented
356	C₂×Dic₃	—	4	2	no	—
357	C₂×Dic₃	C₂³×C₉	1	2	yes	—
358	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
359	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
360	C₂×Dic₃	C₂³×C₉	1	2	yes	—
361	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
362	C₄×D₃	—	2	2	no	—
363	C₄×D₃	—	4	2	no	—
364	Dic₆	—	4	2	no	—
365	C₂×C₃²	—	2	2	no	—
366	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
367	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
368	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
369	C₃×D₃	—	2	2	no	—
370	C₂×C₉	—	2	2	no	—
371	C₂×C₉	—	2	1	no	—
372	C₂×C₉	—	2	1	no	—
373	C₂×C₉	—	2	1	no	—
374	C₂×C₉	—	4	2	no	—
375	C₂×C₉	—	6	2	no	—
376	C₂×C₉	C₂×#237	1	1	yes	characteristic
377	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
378	C₂×C₉	#1009	1	1	yes	characteristic
379	C₂×Q₈	—	3	2	no	—
380	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
381	C₂×D₄	—	3	1	no	—
382	C₂²×C₄	—	3	2	no	—
383	C₂²×C₄	—	3	1	no	—
384	C₂²×C₄	—	3	2	no	—
385	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
386	C₄⋊C₄	—	3	1	no	—
387	C₄⋊C₄	—	3	2	no	—
388	C₄⋊C₄	—	3	2	no	—
389	C₄⋊C₄	—	3	1	no	—
390	C₄⋊C₄	—	3	1	no	—
391	C₄⋊C₄	—	3	2	no	—
392	C₄⋊C₄	—	3	2	no	—
393	C₄⋊C₄	—	3	2	no	—
394	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
395	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
396	C₂²⋊C₄	—	3	1	no	—
397	C₂²⋊C₄	—	3	1	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
400	C₄²	—	3	2	no	—
401	C₄²	—	3	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	3	2	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	—	4	1	no	—
411	C₂²×C₃	—	6	1	no	—
412	C₂²×C₃	—	6	1	no	—
413	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	—
414	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
415	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
416	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
417	C₂×D₃	—	2	1	no	—
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	C₂×Q₈×C₉	1	2	yes	—
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	3	2	no	—
428	C₃×C₄	—	4	1	no	—
429	C₃×C₄	—	4	2	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	—	6	1	no	—
432	C₃×C₄	—	6	2	no	—
433	C₃×C₄	—	6	2	no	—
434	C₃×C₄	—	6	1	no	—
435	C₃×C₄	C₉×#41	1	2	yes	—
436	C₃×C₄	C₃×#237	1	2	yes	—
437	Dic₃	—	2	1	no	—
438	Dic₃	—	2	1	no	—
439	Dic₃	—	2	2	no	—
440	Dic₃	—	2	2	no	—
441	Dic₃	C₂×Q₈×C₉	1	2	yes	—
442	C₃²	C₃×#554	1	1	yes	characteristic
443	C₉	—	2	1	no	—
444	C₉	#5635	1	1	yes	characteristic, direct product factor
445	C₂³	—	3	1	no	—
446	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
447	Q₈	—	2	2	no	—
448	Q₈	—	12	2	no	—
449	D₄	—	3	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	—	12	2	no	—
458	C₂×C₄	—	12	2	no	—
459	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
460	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
462	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
463	C₂×C₃	—	2	2	no	—
464	C₂×C₃	—	2	2	no	—
465	C₂×C₃	—	2	1	no	—
466	C₂×C₃	—	2	1	no	—
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	4	2	no	—
469	C₂×C₃	—	6	2	no	—
470	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
471	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
472	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
474	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
475	C₂×C₃	C₃×#1009	1	1	yes	characteristic
476	D₃	—	2	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	3	2	no	—
480	C₂²	—	6	1	no	—
481	C₂²	—	6	1	no	—
482	C₂²	D₃×Q₈×C₉	1	2	yes	—
483	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	3	2	no	—
488	C₄	—	6	1	no	—
489	C₄	—	6	2	no	—
490	C₄	—	6	2	no	—
491	C₄	—	6	1	no	—
492	C₄	C₉×#237	1	2	yes	—
493	C₃	—	2	1	no	—
494	C₃	C₉×#554	1	1	yes	characteristic, complemented
495	C₃	C₃×#5635	1	1	yes	characteristic
496	C₂	—	2	2	no	—
497	C₂	—	6	2	no	—
498	C₂	C₂×C₉×#237	1	1	yes	characteristic
499	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
500	C₂	C₉×#1009	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	C₉×#554
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. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
2. C₉×#946	C₂	semidirect
3. Q₈×C₉×Dic₃	C₂	semidirect
5. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
6. C₉×#897	C₂	semidirect
7. D₃×C₉×C₄⋊C₄	C₂	semidirect
8. C₉×#889	C₂	semidirect
9. C₉×#888	C₂	semidirect
11. C₉×#878	C₂	semidirect
54. C₉×C₂²⋊Q₈	D₃	semidirect
68. C₉×#67	Q₈	semidirect
79. #5635	C₉	direct (N × H)
153. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
160. #946	C₂×C₉	semidirect
161. Q₈×Dic₃	C₂×C₉	semidirect
163. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
164. #897	C₂×C₉	semidirect
165. D₃×C₄⋊C₄	C₂×C₉	semidirect
166. #889	C₂×C₉	semidirect
167. #888	C₂×C₉	semidirect
169. #878	C₂×C₉	semidirect
315. C₂²⋊Q₈	D₃×C₉	semidirect
321. C₃×C₉	#554	semidirect
355. #67	Q₈×C₉	semidirect
444. C₉	#5635	direct (N × H)
494. C₃	C₉×#554	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
C₉×#946	2
Q₈×C₉×Dic₃	2
C₄×C₉×#67	2
C₂×C₉×C₄⋊Dic₃	2
C₉×#897	2
D₃×C₉×C₄⋊C₄	2
C₉×#889	2
C₉×#888	2
C₉×#67⋊C₄	2
C₉×#878	2
C₃×#5635	3
C₉×#554	3

Subgroups — C9×#5635 #13152933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5635 #13152933