Subgroups — C₉×#5580 #13152701

Order 1728.

772 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#898	C₂	1	2	yes	maximal, complemented
5	C₉×#895	C₂	1	1	yes	maximal, characteristic
6	C₉×#894	C₂	1	2	yes	maximal, complemented
7	C₉×#890	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₉×D₁₂	C₂	1	2	yes	maximal, complemented
9	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#872	C₂	1	2	yes	maximal, complemented
11	C₄²×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5580	C₃	1	1	yes	maximal, characteristic
13	C₉×#529	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₉×D₁₂	C₂²	1	2	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	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×C₄²×C₉	C₂²	1	1	yes	characteristic
24	C₃×C₄²×C₉	C₂²	1	2	yes	—
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#947	C₂×C₃	1	1	yes	characteristic
39	C₃×#946	C₂×C₃	1	1	yes	characteristic
40	C₃×#898	C₂×C₃	1	2	yes	—
41	C₃×#895	C₂×C₃	1	1	yes	characteristic
42	C₃×#894	C₂×C₃	1	2	yes	—
43	C₃×#890	C₂×C₃	1	1	yes	characteristic
44	C₃×C₄×D₁₂	C₂×C₃	1	2	yes	—
45	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
46	C₃×#872	C₂×C₃	1	2	yes	—
47	C₃×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
48	C₉×#126	—	3	2	no	—
49	C₉×#125	—	3	1	no	—
50	C₉×#124	—	3	1	no	—
51	C₉×#123	—	3	2	no	—
52	C₉×C₂²⋊Q₈	—	3	1	no	—
53	C₉×#121	—	3	1	no	—
54	C₄×Q₈×C₉	—	2	1	no	—
55	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
56	C₄×D₄×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	2	no	—
58	C₉×#117	—	3	2	no	—
59	C₂×C₄²×C₉	—	3	1	no	—
60	C₂²×D₃×C₉	C₂³	1	2	yes	—
61	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
62	C₃×Q₈×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₉×Dic₃	C₂³	1	2	yes	—
72	C₉×D₁₂	—	2	4	no	—
73	C₉×D₁₂	—	2	2	no	—
74	C₄×D₃×C₉	—	2	2	no	—
75	C₄×D₃×C₉	—	2	2	no	—
76	C₄×D₃×C₉	—	2	2	no	—
77	C₄×D₃×C₉	—	2	4	no	—
78	C₃×#529	—	3	1	no	—
79	#5580	C₉	1	1	yes	characteristic, direct product factor
80	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
82	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃×C₄×D₃	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×C₄²	C₂²×C₃	1	1	yes	characteristic
90	C₃²×C₄²	C₂²×C₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
97	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
103	C₂×Q₈×C₉	—	2	1	no	—
104	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
105	C₂×D₄×C₉	—	3	2	no	—
106	C₂×D₄×C₉	—	3	1	no	—
107	C₂²×C₄×C₉	—	3	1	no	—
108	C₂²×C₄×C₉	—	3	1	no	—
109	C₂²×C₄×C₉	—	3	1	no	—
110	C₂²×C₄×C₉	—	3	2	no	—
111	C₉×C₄⋊C₄	—	2	1	no	—
112	C₉×C₄⋊C₄	—	2	2	no	—
113	C₉×C₄⋊C₄	—	3	2	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	1	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₂²⋊C₄	—	3	2	no	—
120	C₉×C₂²⋊C₄	—	3	2	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₄²×C₉	—	2	1	no	—
125	C₄²×C₉	—	2	2	no	—
126	C₄²×C₉	—	3	1	no	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	—	3	1	no	—
129	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
130	C₄²×C₉	C₂×D₃	1	2	yes	—
131	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
132	C₂×D₃×C₉	—	2	1	no	—
133	C₂×D₃×C₉	—	2	1	no	—
134	C₂×D₃×C₉	—	2	2	no	—
135	C₂×D₃×C₉	—	2	2	no	—
136	C₂×D₃×C₉	—	2	2	no	—
137	C₂×D₃×C₉	#41	1	2	yes	—
138	C₃×C₄×C₉	—	2	2	no	—
139	C₃×C₄×C₉	—	2	1	no	—
140	C₃×C₄×C₉	—	2	2	no	—
141	C₃×C₄×C₉	#41	1	2	yes	—
142	C₃×C₄×C₉	#41	1	2	yes	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	1	no	—
145	C₉×Dic₃	—	2	2	no	—
146	C₉×Dic₃	—	2	1	no	—
147	C₃×#126	—	3	2	no	—
148	C₃×#125	—	3	1	no	—
149	C₃×#124	—	3	1	no	—
150	C₃×#123	—	3	2	no	—
151	C₃×C₂²⋊Q₈	—	3	1	no	—
152	C₃×#121	—	3	1	no	—
153	C₃×C₄×Q₈	—	2	1	no	—
154	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
155	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
156	C₃×C₄×D₄	—	3	1	no	—
157	C₃×C₄×D₄	—	3	2	no	—
158	C₃×#117	—	3	2	no	—
159	C₂×C₃×C₄²	—	3	1	no	—
160	#947	C₂×C₉	1	1	yes	characteristic, complemented
161	#946	C₂×C₉	1	1	yes	characteristic, complemented
162	#898	C₂×C₉	1	2	yes	complemented
163	#895	C₂×C₉	1	1	yes	characteristic
164	#894	C₂×C₉	1	2	yes	complemented
165	#890	C₂×C₉	1	1	yes	characteristic, complemented
166	C₄×D₁₂	C₂×C₉	1	2	yes	complemented
167	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
168	#872	C₂×C₉	1	2	yes	complemented
169	C₄²×D₃	C₂×C₉	1	1	yes	characteristic, complemented
170	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
171	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
172	C₃²×Q₈	—	2	2	no	—
173	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
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	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
182	C₃×D₁₂	—	2	4	no	—
183	C₃×D₁₂	—	2	2	no	—
184	C₃×C₄×D₃	—	2	2	no	—
185	C₃×C₄×D₃	—	2	2	no	—
186	C₃×C₄×D₃	—	2	2	no	—
187	C₃×C₄×D₃	—	2	4	no	—
188	C₂³×C₉	—	3	1	no	—
189	C₂³×C₉	—	3	2	no	—
190	Q₈×C₉	—	2	4	no	—
191	Q₈×C₉	—	2	2	no	—
192	D₄×C₉	—	6	4	no	—
193	D₄×C₉	—	6	2	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	2	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	2	no	—
199	C₂×C₄×C₉	—	3	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	—	6	2	no	—
204	C₂×C₄×C₉	—	6	2	no	—
205	C₂×C₄×C₉	—	6	2	no	—
206	C₂×C₄×C₉	—	6	4	no	—
207	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
208	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
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	1	yes	characteristic
212	#529	—	3	1	no	Sylow
213	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
216	D₃×C₉	—	2	2	no	—
217	D₃×C₉	—	4	2	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
220	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
221	C₂×C₃×D₄	—	3	2	no	—
222	C₂×C₃×D₄	—	3	1	no	—
223	C₂²×C₃×C₄	—	3	1	no	—
224	C₂²×C₃×C₄	—	3	1	no	—
225	C₂²×C₃×C₄	—	3	1	no	—
226	C₂²×C₃×C₄	—	3	2	no	—
227	C₂×D₁₂	C₂²×C₉	1	2	yes	—
228	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
229	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
230	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
231	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
232	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	3	2	no	—
236	C₃×C₄⋊C₄	—	3	2	no	—
237	C₃×C₄⋊C₄	—	3	1	no	—
238	C₃×C₄⋊C₄	—	3	2	no	—
239	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
241	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
242	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
243	C₃×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₂²⋊C₄	—	3	2	no	—
245	C₃×C₂²⋊C₄	—	3	2	no	—
246	C₃×C₂²⋊C₄	—	3	2	no	—
247	C₃×C₂²⋊C₄	—	3	2	no	—
248	C₃×C₄²	—	2	1	no	—
249	C₃×C₄²	—	2	2	no	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	3	1	no	—
252	C₃×C₄²	—	3	1	no	—
253	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
254	C₃×C₄²	C₂²×C₉	1	2	yes	—
255	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
256	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
257	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
258	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
259	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
260	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
261	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
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	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
267	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
268	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
269	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
270	C₂×C₃×D₃	—	2	1	no	—
271	C₂×C₃×D₃	—	2	1	no	—
272	C₂×C₃×D₃	—	2	2	no	—
273	C₂×C₃×D₃	—	2	2	no	—
274	C₂×C₃×D₃	—	2	2	no	—
275	C₂×C₃×D₃	C₃×#41	1	2	yes	—
276	C₃²×C₄	—	2	2	no	—
277	C₃²×C₄	—	2	1	no	—
278	C₃²×C₄	—	2	2	no	—
279	C₃²×C₄	C₃×#41	1	2	yes	—
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	1	no	—
285	C₂²×C₉	—	2	1	no	—
286	C₂²×C₉	—	3	2	no	—
287	C₂²×C₉	—	6	1	no	—
288	C₂²×C₉	—	6	1	no	—
289	C₂²×C₉	—	6	2	no	—
290	C₂²×C₉	—	6	2	no	—
291	C₂²×C₉	—	6	2	no	—
292	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
293	C₄×C₉	—	2	4	no	—
294	C₄×C₉	—	2	2	no	—
295	C₄×C₉	—	2	1	no	—
296	C₄×C₉	—	2	2	no	—
297	C₄×C₉	—	2	2	no	—
298	C₄×C₉	—	2	2	no	—
299	C₄×C₉	—	4	1	no	—
300	C₄×C₉	—	4	2	no	—
301	C₄×C₉	—	6	1	no	—
302	C₄×C₉	—	6	1	no	—
303	C₄×C₉	—	6	2	no	—
304	C₄×C₉	—	6	1	no	—
305	C₄×C₉	#235	1	2	yes	—
306	C₄×C₉	#239	1	2	yes	—
307	#126	—	3	2	no	—
308	#125	—	3	1	no	—
309	#124	—	3	1	no	—
310	#123	—	3	2	no	—
311	C₂²⋊Q₈	—	3	1	no	—
312	#121	—	3	1	no	—
313	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	2	no	—
316	#117	—	3	2	no	—
317	C₂×C₄²	—	3	1	no	—
318	C₃×C₉	#529	1	1	yes	characteristic, complemented, Sylow
319	C₂³×C₃	—	3	1	no	—
320	C₂³×C₃	—	3	2	no	—
321	C₂²×D₃	C₂³×C₉	1	2	yes	—
322	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
323	C₃×Q₈	—	2	4	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×D₄	—	6	4	no	—
327	C₃×D₄	—	6	2	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	3	1	no	—
334	C₂×C₃×C₄	—	3	1	no	—
335	C₂×C₃×C₄	—	3	1	no	—
336	C₂×C₃×C₄	—	3	2	no	—
337	C₂×C₃×C₄	—	6	2	no	—
338	C₂×C₃×C₄	—	6	2	no	—
339	C₂×C₃×C₄	—	6	2	no	—
340	C₂×C₃×C₄	—	6	4	no	—
341	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
343	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
344	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
348	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
351	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
352	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
353	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
354	C₂×Dic₃	C₂³×C₉	1	2	yes	—
355	D₁₂	—	2	4	no	—
356	D₁₂	—	2	2	no	—
357	C₄×D₃	—	2	2	no	—
358	C₄×D₃	—	2	2	no	—
359	C₄×D₃	—	2	2	no	—
360	C₄×D₃	—	2	4	no	—
361	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
362	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
363	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
364	C₃×D₃	—	2	2	no	—
365	C₃×D₃	—	4	2	no	—
366	C₂×C₉	—	2	1	no	—
367	C₂×C₉	—	2	1	no	—
368	C₂×C₉	—	2	1	no	—
369	C₂×C₉	—	6	2	no	—
370	C₂×C₉	—	12	2	no	—
371	C₂×C₉	C₂×#235	1	1	yes	characteristic
372	C₂×C₉	C₂×#239	1	1	yes	characteristic
373	C₂×C₉	D₃×#41	1	1	yes	characteristic
374	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
375	C₂×D₄	—	3	2	no	—
376	C₂×D₄	—	3	1	no	—
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	3	1	no	—
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	2	no	—
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	—	3	2	no	—
383	C₄⋊C₄	—	3	1	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
386	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
387	C₂²⋊C₄	—	3	2	no	—
388	C₂²⋊C₄	—	3	2	no	—
389	C₂²⋊C₄	—	3	2	no	—
390	C₂²⋊C₄	—	3	2	no	—
391	C₂²⋊C₄	—	3	2	no	—
392	C₄²	—	3	1	no	—
393	C₄²	—	3	1	no	—
394	C₄²	—	3	1	no	—
395	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
396	C₄²	C₂×D₃×C₉	1	2	yes	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	3	2	no	—
399	C₂²×C₃	—	6	1	no	—
400	C₂²×C₃	—	6	1	no	—
401	C₂²×C₃	—	6	2	no	—
402	C₂²×C₃	—	6	2	no	—
403	C₂²×C₃	—	6	2	no	—
404	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
405	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
406	C₂×D₃	—	2	1	no	—
407	C₂×D₃	—	2	1	no	—
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	2	2	no	—
410	C₂×D₃	—	2	2	no	—
411	C₂×D₃	C₉×#41	1	2	yes	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	2	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	2	2	no	—
421	C₃×C₄	—	4	1	no	—
422	C₃×C₄	—	4	2	no	—
423	C₃×C₄	—	6	1	no	—
424	C₃×C₄	—	6	1	no	—
425	C₃×C₄	—	6	2	no	—
426	C₃×C₄	—	6	1	no	—
427	C₃×C₄	C₉×#41	1	2	yes	—
428	C₃×C₄	C₉×#41	1	2	yes	—
429	C₃×C₄	C₃×#235	1	2	yes	—
430	C₃×C₄	C₃×#239	1	2	yes	—
431	Dic₃	—	2	1	no	—
432	Dic₃	—	2	1	no	—
433	Dic₃	—	2	2	no	—
434	Dic₃	—	2	1	no	—
435	C₃²	C₃×#529	1	1	yes	characteristic
436	C₉	—	2	1	no	—
437	C₉	#5580	1	1	yes	characteristic, direct product factor
438	C₂³	—	3	1	no	—
439	C₂³	—	3	2	no	—
440	Q₈	—	2	2	no	—
441	D₄	—	6	4	no	—
442	D₄	—	6	2	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	3	1	no	—
445	C₂×C₄	—	3	1	no	—
446	C₂×C₄	—	3	2	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	—	6	4	no	—
451	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
453	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
454	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
456	C₂×C₃	—	2	1	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	2	1	no	—
459	C₂×C₃	—	6	2	no	—
460	C₂×C₃	—	12	2	no	—
461	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
462	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
463	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
464	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
465	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
466	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
467	D₃	—	2	2	no	—
468	D₃	—	4	2	no	—
469	C₂²	—	3	2	no	—
470	C₂²	—	6	1	no	—
471	C₂²	—	6	1	no	—
472	C₂²	—	6	2	no	—
473	C₂²	—	6	2	no	—
474	C₂²	—	6	2	no	—
475	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	6	1	no	—
480	C₄	—	6	1	no	—
481	C₄	—	6	2	no	—
482	C₄	—	6	1	no	—
483	C₄	C₉×#235	1	2	yes	—
484	C₄	C₉×#239	1	2	yes	—
485	C₃	—	2	1	no	—
486	C₃	C₉×#529	1	1	yes	characteristic, complemented
487	C₃	C₃×#5580	1	1	yes	characteristic
488	C₂	—	6	2	no	—
489	C₂	—	12	2	no	—
490	C₂	C₂×C₉×#235	1	1	yes	characteristic
491	C₂	C₂×C₉×#239	1	1	yes	characteristic
492	C₂	D₃×C₉×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#895	C₂×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₄×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
2. C₉×#947	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₉×#898	C₂	semidirect
6. C₉×#894	C₂	semidirect
7. C₉×#890	C₂	semidirect
8. C₄×C₉×D₁₂	C₂	semidirect
9. C₄×C₉×D₁₂	C₂	semidirect
10. C₉×#872	C₂	semidirect
11. C₄²×D₃×C₉	C₂	semidirect
55. C₄×Q₈×C₉	D₃	semidirect
79. #5580	C₉	direct (N × H)
154. C₃×C₄×Q₈	C₂×C₉	semidirect
160. #947	C₂×C₉	semidirect
161. #946	C₂×C₉	semidirect
162. #898	C₂×C₉	semidirect
164. #894	C₂×C₉	semidirect
165. #890	C₂×C₉	semidirect
166. C₄×D₁₂	C₂×C₉	semidirect
167. C₄×D₁₂	C₂×C₉	semidirect
168. #872	C₂×C₉	semidirect
169. C₄²×D₃	C₂×C₉	semidirect
313. C₄×Q₈	D₃×C₉	semidirect
318. C₃×C₉	#529	semidirect
437. C₉	#5580	direct (N × H)
486. C₃	C₉×#529	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈×C₉	2
C₉×#947	2
C₉×#946	2
C₉×#898	2
C₉×#895	2
C₉×#894	2
C₉×#890	2
C₄×C₉×D₁₂	2
C₉×#872	2
C₄²×D₃×C₉	2
C₃×#5580	3
C₉×#529	3

Subgroups — C9×#5580 #13152701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5580 #13152701