Subgroups — C₉×#5531 #13152476

Order 1728.

718 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#886	C₂	1	1	yes	maximal, characteristic
9	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#876	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5531	C₃	1	1	yes	maximal, characteristic
17	C₉×#552	—	3	1	no	maximal
18	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₉×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
23	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
29	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
30	C₉×#217	C₂²	1	1	yes	characteristic
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
38	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
39	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
53	C₃²×#117	C₂×C₃	1	1	yes	characteristic
54	C₃×#929	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
56	C₃×#898	C₂×C₃	1	1	yes	characteristic
57	C₃×#896	C₂×C₃	1	1	yes	characteristic
58	C₃×#889	C₂×C₃	1	1	yes	characteristic
59	C₃×#889	C₂×C₃	1	1	yes	characteristic
60	C₃×#886	C₂×C₃	1	1	yes	characteristic
61	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
62	C₃×#878	C₂×C₃	1	1	yes	characteristic
63	C₃×#877	C₂×C₃	1	1	yes	characteristic
64	C₃×#876	C₂×C₃	1	1	yes	characteristic
65	C₃×#872	C₂×C₃	1	1	yes	characteristic
66	C₃×#870	C₂×C₃	1	1	yes	characteristic
67	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
68	C₉×#126	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#125	—	3	1	no	—
71	C₉×#125	—	3	1	no	—
72	C₉×#125	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×#123	—	3	1	no	—
75	C₉×C₂²⋊Q₈	—	3	1	no	—
76	C₉×C₂²⋊Q₈	—	3	1	no	—
77	C₄×Q₈×C₉	—	3	1	no	—
78	C₄×D₄×C₉	—	3	1	no	—
79	C₉×#117	—	2	1	no	—
80	C₉×#117	—	3	1	no	—
81	C₉×#117	—	3	1	no	—
82	C₉×#117	D₃	1	1	yes	characteristic, complemented
83	C₂×C₉×C₄⋊C₄	—	3	1	no	—
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×C₉	—	2	2	no	—
87	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₉×#67	—	2	2	no	—
94	C₂×C₉×Dic₃	—	2	2	no	—
95	C₂×C₉×Dic₃	—	2	2	no	—
96	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
97	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
99	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
100	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
102	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
103	C₄×D₃×C₉	—	2	2	no	—
104	C₉×Dic₆	—	2	2	no	—
105	C₃×#552	—	3	1	no	—
106	#5531	C₉	1	1	yes	characteristic, direct product factor
107	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
113	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
118	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
119	C₃×#217	C₂²×C₃	1	1	yes	characteristic
120	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
126	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
127	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
128	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
140	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
141	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
142	C₂×Q₈×C₉	—	3	1	no	—
143	C₂×D₄×C₉	—	3	1	no	—
144	C₂²×C₄×C₉	—	2	1	no	—
145	C₂²×C₄×C₉	—	3	1	no	—
146	C₂²×C₄×C₉	—	3	1	no	—
147	C₂²×C₄×C₉	—	3	1	no	—
148	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
149	C₉×C₄⋊C₄	—	2	1	no	—
150	C₉×C₄⋊C₄	—	2	1	no	—
151	C₉×C₄⋊C₄	—	3	1	no	—
152	C₉×C₄⋊C₄	—	3	1	no	—
153	C₉×C₄⋊C₄	—	3	1	no	—
154	C₉×C₄⋊C₄	—	3	1	no	—
155	C₉×C₄⋊C₄	—	3	1	no	—
156	C₉×C₄⋊C₄	—	3	1	no	—
157	C₉×C₄⋊C₄	—	3	1	no	—
158	C₉×C₄⋊C₄	—	3	1	no	—
159	C₉×C₄⋊C₄	—	3	1	no	—
160	C₉×C₄⋊C₄	—	3	1	no	—
161	C₉×C₄⋊C₄	—	3	1	no	—
162	C₉×C₄⋊C₄	—	3	1	no	—
163	C₉×C₄⋊C₄	—	3	1	no	—
164	C₉×C₄⋊C₄	—	3	1	no	—
165	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
166	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
167	C₉×C₂²⋊C₄	—	2	1	no	—
168	C₉×C₂²⋊C₄	—	2	1	no	—
169	C₉×C₂²⋊C₄	—	3	1	no	—
170	C₉×C₂²⋊C₄	—	3	1	no	—
171	C₉×C₂²⋊C₄	—	3	1	no	—
172	C₉×C₂²⋊C₄	—	3	1	no	—
173	C₉×C₂²⋊C₄	—	3	1	no	—
174	C₉×C₂²⋊C₄	—	3	1	no	—
175	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
176	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
177	C₄²×C₉	—	2	1	no	—
178	C₄²×C₉	—	2	1	no	—
179	C₄²×C₉	—	3	1	no	—
180	C₄²×C₉	—	3	1	no	—
181	C₄²×C₉	—	3	1	no	—
182	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
183	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₉	—	2	1	no	—
185	C₂²×C₃×C₉	—	2	1	no	—
186	C₂²×C₃×C₉	#41	1	2	yes	—
187	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
188	C₂×D₃×C₉	—	2	1	no	—
189	C₂×D₃×C₉	—	2	1	no	—
190	C₂×D₃×C₉	—	2	1	no	—
191	C₃×C₄×C₉	—	2	1	no	—
192	C₃×C₄×C₉	—	2	1	no	—
193	C₃×C₄×C₉	—	2	1	no	—
194	C₃×C₄×C₉	—	2	1	no	—
195	C₃×C₄×C₉	—	2	1	no	—
196	C₃×C₄×C₉	—	2	1	no	—
197	C₉×Dic₃	—	2	1	no	—
198	C₉×Dic₃	—	2	1	no	—
199	C₉×Dic₃	—	2	1	no	—
200	C₉×Dic₃	—	2	1	no	—
201	C₉×Dic₃	—	2	1	no	—
202	C₉×Dic₃	—	2	1	no	—
203	C₉×Dic₃	#41	1	2	yes	—
204	C₃×#126	—	3	1	no	—
205	C₃×#126	—	3	1	no	—
206	C₃×#125	—	3	1	no	—
207	C₃×#125	—	3	1	no	—
208	C₃×#125	—	3	1	no	—
209	C₃×#123	—	3	1	no	—
210	C₃×#123	—	3	1	no	—
211	C₃×C₂²⋊Q₈	—	3	1	no	—
212	C₃×C₂²⋊Q₈	—	3	1	no	—
213	C₃×C₄×Q₈	—	3	1	no	—
214	C₃×C₄×D₄	—	3	1	no	—
215	C₃×#117	—	2	1	no	—
216	C₃×#117	—	3	1	no	—
217	C₃×#117	—	3	1	no	—
218	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
219	C₃×#117	C₃×D₃	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	—	3	1	no	—
221	#929	C₂×C₉	1	1	yes	characteristic
222	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
223	#898	C₂×C₉	1	1	yes	characteristic, complemented
224	#896	C₂×C₉	1	1	yes	characteristic, complemented
225	#889	C₂×C₉	1	1	yes	characteristic, complemented
226	#889	C₂×C₉	1	1	yes	characteristic, complemented
227	#886	C₂×C₉	1	1	yes	characteristic
228	#67⋊C₄	C₂×C₉	1	1	yes	characteristic
229	#878	C₂×C₉	1	1	yes	characteristic, complemented
230	#877	C₂×C₉	1	1	yes	characteristic, complemented
231	#876	C₂×C₉	1	1	yes	characteristic, complemented
232	#872	C₂×C₉	1	1	yes	characteristic, complemented
233	#870	C₂×C₉	1	1	yes	characteristic, complemented
234	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
235	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₃²×C₄	—	2	2	no	—
238	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
240	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
244	C₃×#67	—	2	2	no	—
245	C₂×C₃×Dic₃	—	2	2	no	—
246	C₂×C₃×Dic₃	—	2	2	no	—
247	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
251	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
252	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
254	C₃×C₄×D₃	—	2	2	no	—
255	C₃×Dic₆	—	2	2	no	—
256	C₂³×C₉	—	2	1	no	—
257	C₂³×C₉	—	3	1	no	—
258	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
259	Q₈×C₉	—	6	2	no	—
260	D₄×C₉	—	6	2	no	—
261	C₂×C₄×C₉	—	2	4	no	—
262	C₂×C₄×C₉	—	2	2	no	—
263	C₂×C₄×C₉	—	2	1	no	—
264	C₂×C₄×C₉	—	2	1	no	—
265	C₂×C₄×C₉	—	2	1	no	—
266	C₂×C₄×C₉	—	2	1	no	—
267	C₂×C₄×C₉	—	2	1	no	—
268	C₂×C₄×C₉	—	2	1	no	—
269	C₂×C₄×C₉	—	3	1	no	—
270	C₂×C₄×C₉	—	3	1	no	—
271	C₂×C₄×C₉	—	3	1	no	—
272	C₂×C₄×C₉	—	3	1	no	—
273	C₂×C₄×C₉	—	3	1	no	—
274	C₂×C₄×C₉	—	3	1	no	—
275	C₂×C₄×C₉	—	3	1	no	—
276	C₂×C₄×C₉	—	6	2	no	—
277	C₂×C₄×C₉	—	6	2	no	—
278	C₂×C₄×C₉	—	6	2	no	—
279	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
280	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
281	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
282	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
285	#552	—	3	1	no	Sylow
286	C₂×C₃×C₉	—	2	2	no	—
287	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
290	D₃×C₉	—	4	1	no	—
291	C₂×C₃×Q₈	—	3	1	no	—
292	C₂×C₃×D₄	—	3	1	no	—
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	—	3	1	no	—
295	C₂²×C₃×C₄	—	3	1	no	—
296	C₂²×C₃×C₄	—	3	1	no	—
297	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
298	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
299	C₂×#67	C₂²×C₉	1	1	yes	characteristic
300	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
301	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
302	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
303	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
304	C₃×C₄⋊C₄	—	2	1	no	—
305	C₃×C₄⋊C₄	—	2	1	no	—
306	C₃×C₄⋊C₄	—	3	1	no	—
307	C₃×C₄⋊C₄	—	3	1	no	—
308	C₃×C₄⋊C₄	—	3	1	no	—
309	C₃×C₄⋊C₄	—	3	1	no	—
310	C₃×C₄⋊C₄	—	3	1	no	—
311	C₃×C₄⋊C₄	—	3	1	no	—
312	C₃×C₄⋊C₄	—	3	1	no	—
313	C₃×C₄⋊C₄	—	3	1	no	—
314	C₃×C₄⋊C₄	—	3	1	no	—
315	C₃×C₄⋊C₄	—	3	1	no	—
316	C₃×C₄⋊C₄	—	3	1	no	—
317	C₃×C₄⋊C₄	—	3	1	no	—
318	C₃×C₄⋊C₄	—	3	1	no	—
319	C₃×C₄⋊C₄	—	3	1	no	—
320	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
321	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
322	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
323	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
324	C₃×C₂²⋊C₄	—	2	1	no	—
325	C₃×C₂²⋊C₄	—	2	1	no	—
326	C₃×C₂²⋊C₄	—	3	1	no	—
327	C₃×C₂²⋊C₄	—	3	1	no	—
328	C₃×C₂²⋊C₄	—	3	1	no	—
329	C₃×C₂²⋊C₄	—	3	1	no	—
330	C₃×C₂²⋊C₄	—	3	1	no	—
331	C₃×C₂²⋊C₄	—	3	1	no	—
332	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
333	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
334	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
335	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
336	C₃×C₄²	—	2	1	no	—
337	C₃×C₄²	—	2	1	no	—
338	C₃×C₄²	—	3	1	no	—
339	C₃×C₄²	—	3	1	no	—
340	C₃×C₄²	—	3	1	no	—
341	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
342	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
343	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
344	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
345	#217	C₂²×C₉	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
347	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
348	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
349	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
350	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
351	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
352	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
353	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
354	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
355	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
356	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
365	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
366	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
367	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
368	C₂²×C₃²	—	2	1	no	—
369	C₂²×C₃²	—	2	1	no	—
370	C₂²×C₃²	C₃×#41	1	2	yes	—
371	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
372	C₂×C₃×D₃	—	2	1	no	—
373	C₂×C₃×D₃	—	2	1	no	—
374	C₂×C₃×D₃	—	2	1	no	—
375	C₃²×C₄	—	2	1	no	—
376	C₃²×C₄	—	2	1	no	—
377	C₃²×C₄	—	2	1	no	—
378	C₃²×C₄	—	2	1	no	—
379	C₃²×C₄	—	2	1	no	—
380	C₃²×C₄	—	2	1	no	—
381	C₃×Dic₃	—	2	1	no	—
382	C₃×Dic₃	—	2	1	no	—
383	C₃×Dic₃	—	2	1	no	—
384	C₃×Dic₃	—	2	1	no	—
385	C₃×Dic₃	—	2	1	no	—
386	C₃×Dic₃	—	2	1	no	—
387	C₃×Dic₃	C₃×#41	1	2	yes	—
388	C₂²×C₉	—	2	1	no	—
389	C₂²×C₉	—	2	1	no	—
390	C₂²×C₉	—	2	1	no	—
391	C₂²×C₉	—	2	2	no	—
392	C₂²×C₉	—	4	1	no	—
393	C₂²×C₉	—	4	1	no	—
394	C₂²×C₉	—	6	1	no	—
395	C₂²×C₉	—	6	1	no	—
396	C₂²×C₉	—	6	1	no	—
397	C₂²×C₉	#235	1	2	yes	—
398	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
399	C₄×C₉	—	2	2	no	—
400	C₄×C₉	—	2	2	no	—
401	C₄×C₉	—	2	1	no	—
402	C₄×C₉	—	2	1	no	—
403	C₄×C₉	—	2	1	no	—
404	C₄×C₉	—	2	1	no	—
405	C₄×C₉	—	2	1	no	—
406	C₄×C₉	—	2	1	no	—
407	C₄×C₉	—	3	2	no	—
408	C₄×C₉	—	4	1	no	—
409	C₄×C₉	—	4	1	no	—
410	C₄×C₉	—	4	1	no	—
411	C₄×C₉	—	4	1	no	—
412	C₄×C₉	—	6	1	no	—
413	C₄×C₉	—	6	1	no	—
414	C₄×C₉	—	6	1	no	—
415	C₄×C₉	—	6	1	no	—
416	C₄×C₉	—	6	1	no	—
417	C₄×C₉	—	6	1	no	—
418	#126	—	3	1	no	—
419	#126	—	3	1	no	—
420	#125	—	3	1	no	—
421	#125	—	3	1	no	—
422	#125	—	3	1	no	—
423	#123	—	3	1	no	—
424	#123	—	3	1	no	—
425	C₂²⋊Q₈	—	3	1	no	—
426	C₂²⋊Q₈	—	3	1	no	—
427	C₄×Q₈	—	3	1	no	—
428	C₄×D₄	—	3	1	no	—
429	#117	—	3	1	no	—
430	#117	—	3	1	no	—
431	#117	D₃×C₉	1	1	yes	characteristic, complemented
432	C₂×C₄⋊C₄	—	3	1	no	—
433	C₃×C₉	#552	1	1	yes	characteristic, complemented, Sylow
434	C₂³×C₃	—	2	1	no	—
435	C₂³×C₃	—	3	1	no	—
436	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
437	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
438	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
439	C₃×Q₈	—	6	2	no	—
440	C₃×D₄	—	6	2	no	—
441	C₂×C₃×C₄	—	2	4	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	3	1	no	—
451	C₂×C₃×C₄	—	3	1	no	—
452	C₂×C₃×C₄	—	3	1	no	—
453	C₂×C₃×C₄	—	3	1	no	—
454	C₂×C₃×C₄	—	3	1	no	—
455	C₂×C₃×C₄	—	3	1	no	—
456	C₂×C₃×C₄	—	3	1	no	—
457	C₂×C₃×C₄	—	6	2	no	—
458	C₂×C₃×C₄	—	6	2	no	—
459	C₂×C₃×C₄	—	6	2	no	—
460	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
461	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
462	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
463	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
464	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
468	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
471	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
472	#67	—	2	2	no	—
473	C₂×Dic₃	—	2	2	no	—
474	C₂×Dic₃	—	2	2	no	—
475	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
476	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
477	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
478	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
479	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
480	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
481	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
482	C₄×D₃	—	2	2	no	—
483	Dic₆	—	2	2	no	—
484	C₂×C₃²	—	2	2	no	—
485	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
486	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
487	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
488	C₃×D₃	—	4	1	no	—
489	C₂×C₉	—	2	2	no	—
490	C₂×C₉	—	2	1	no	—
491	C₂×C₉	—	2	1	no	—
492	C₂×C₉	—	2	1	no	—
493	C₂×C₉	—	4	2	no	—
494	C₂×C₉	—	12	1	no	—
495	C₂×C₉	C₂×#235	1	1	yes	characteristic
496	C₂×C₉	D₃×#41	1	1	yes	characteristic
497	C₂×C₉	#1010	1	1	yes	characteristic
498	C₂×Q₈	—	3	1	no	—
499	C₂×D₄	—	3	1	no	—
500	C₂²×C₄	—	3	1	no	—
501	C₂²×C₄	—	3	1	no	—
502	C₂²×C₄	—	3	1	no	—
503	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
504	C₄⋊C₄	—	3	1	no	—
505	C₄⋊C₄	—	3	1	no	—
506	C₄⋊C₄	—	3	1	no	—
507	C₄⋊C₄	—	3	1	no	—
508	C₄⋊C₄	—	3	1	no	—
509	C₄⋊C₄	—	3	1	no	—
510	C₄⋊C₄	—	3	1	no	—
511	C₄⋊C₄	—	3	1	no	—
512	C₄⋊C₄	—	3	1	no	—
513	C₄⋊C₄	—	3	1	no	—
514	C₄⋊C₄	—	3	1	no	—
515	C₄⋊C₄	—	3	1	no	—
516	C₄⋊C₄	—	3	1	no	—
517	C₄⋊C₄	—	3	1	no	—
518	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
520	C₂²⋊C₄	—	3	1	no	—
521	C₂²⋊C₄	—	3	1	no	—
522	C₂²⋊C₄	—	3	1	no	—
523	C₂²⋊C₄	—	3	1	no	—
524	C₂²⋊C₄	—	3	1	no	—
525	C₂²⋊C₄	—	3	1	no	—
526	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
527	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
528	C₄²	—	3	1	no	—
529	C₄²	—	3	1	no	—
530	C₄²	—	3	1	no	—
531	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
532	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
533	C₂²×C₃	—	2	1	no	—
534	C₂²×C₃	—	2	1	no	—
535	C₂²×C₃	—	2	1	no	—
536	C₂²×C₃	—	2	1	no	—
537	C₂²×C₃	—	2	1	no	—
538	C₂²×C₃	—	2	2	no	—
539	C₂²×C₃	—	4	1	no	—
540	C₂²×C₃	—	4	1	no	—
541	C₂²×C₃	—	6	1	no	—
542	C₂²×C₃	—	6	1	no	—
543	C₂²×C₃	—	6	1	no	—
544	C₂²×C₃	C₉×#41	1	2	yes	—
545	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
546	C₂²×C₃	C₃×#235	1	2	yes	—
547	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
548	C₂×D₃	—	2	1	no	—
549	C₂×D₃	—	2	1	no	—
550	C₂×D₃	—	2	1	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	2	no	—
553	C₃×C₄	—	2	1	no	—
554	C₃×C₄	—	2	1	no	—
555	C₃×C₄	—	2	1	no	—
556	C₃×C₄	—	2	1	no	—
557	C₃×C₄	—	2	1	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	3	2	no	—
566	C₃×C₄	—	4	1	no	—
567	C₃×C₄	—	4	1	no	—
568	C₃×C₄	—	4	1	no	—
569	C₃×C₄	—	4	1	no	—
570	C₃×C₄	—	6	1	no	—
571	C₃×C₄	—	6	1	no	—
572	C₃×C₄	—	6	1	no	—
573	C₃×C₄	—	6	1	no	—
574	C₃×C₄	—	6	1	no	—
575	C₃×C₄	—	6	1	no	—
576	Dic₃	—	2	1	no	—
577	Dic₃	—	2	1	no	—
578	Dic₃	—	2	1	no	—
579	Dic₃	—	2	1	no	—
580	Dic₃	—	2	1	no	—
581	Dic₃	—	2	1	no	—
582	Dic₃	C₉×#41	1	2	yes	—
583	C₃²	C₃×#552	1	1	yes	characteristic
584	C₉	—	2	1	no	—
585	C₉	#5531	1	1	yes	characteristic, direct product factor
586	C₂³	—	3	1	no	—
587	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
588	Q₈	—	6	2	no	—
589	D₄	—	6	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	1	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	3	1	no	—
598	C₂×C₄	—	6	2	no	—
599	C₂×C₄	—	6	2	no	—
600	C₂×C₄	—	6	2	no	—
601	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
607	C₂×C₃	—	2	2	no	—
608	C₂×C₃	—	2	2	no	—
609	C₂×C₃	—	2	1	no	—
610	C₂×C₃	—	2	1	no	—
611	C₂×C₃	—	2	1	no	—
612	C₂×C₃	—	4	2	no	—
613	C₂×C₃	—	12	1	no	—
614	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
615	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
616	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
617	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
618	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
619	C₂×C₃	C₃×#1010	1	1	yes	characteristic
620	D₃	—	4	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	6	1	no	—
624	C₂²	—	6	1	no	—
625	C₂²	—	6	1	no	—
626	C₂²	C₉×#235	1	2	yes	—
627	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	3	2	no	—
635	C₄	—	6	1	no	—
636	C₄	—	6	1	no	—
637	C₄	—	6	1	no	—
638	C₄	—	6	1	no	—
639	C₄	—	6	1	no	—
640	C₄	—	6	1	no	—
641	C₃	—	2	1	no	—
642	C₃	C₉×#552	1	1	yes	characteristic, complemented
643	C₃	C₃×#5531	1	1	yes	characteristic
644	C₂	—	2	2	no	—
645	C₂	—	12	1	no	—
646	C₂	C₂×C₉×#235	1	1	yes	characteristic
647	C₂	D₃×C₉×#41	1	1	yes	characteristic
648	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×#117	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#67	C₂²×C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₉×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#117	C₂	semidirect
3. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
4. C₉×#898	C₂	semidirect
5. C₉×#896	C₂	semidirect
6. C₉×#889	C₂	semidirect
7. C₉×#889	C₂	semidirect
10. C₉×#878	C₂	semidirect
11. C₉×#877	C₂	semidirect
12. C₉×#876	C₂	semidirect
13. C₉×#872	C₂	semidirect
14. C₉×#870	C₂	semidirect
15. C₄×C₉×Dic₆	C₂	semidirect
82. C₉×#117	D₃	semidirect
106. #5531	C₉	direct (N × H)
218. C₃×#117	C₂×C₉	semidirect
222. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
223. #898	C₂×C₉	semidirect
224. #896	C₂×C₉	semidirect
225. #889	C₂×C₉	semidirect
226. #889	C₂×C₉	semidirect
229. #878	C₂×C₉	semidirect
230. #877	C₂×C₉	semidirect
231. #876	C₂×C₉	semidirect
232. #872	C₂×C₉	semidirect
233. #870	C₂×C₉	semidirect
234. C₄×Dic₆	C₂×C₉	semidirect
431. #117	D₃×C₉	semidirect
433. C₃×C₉	#552	semidirect
585. C₉	#5531	direct (N × H)
642. C₃	C₉×#552	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#117	2
C₉×#929	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#898	2
C₉×#896	2
C₉×#889	2
C₉×#886	2
C₉×#67⋊C₄	2
C₉×#878	2
C₉×#877	2
C₉×#876	2
C₉×#872	2
C₉×#870	2
C₄×C₉×Dic₆	2
C₃×#5531	3
C₉×#552	3

Subgroups — C9×#5531 #13152476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5531 #13152476