Subgroups — C₉×#5583 #13152704

Order 1728.

646 conjugacy classes of subgroups.

The subgroup lattice has 452 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×#946	C₂	1	1	yes	maximal, characteristic
3	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#898	C₂	1	2	yes	maximal
5	C₉×#897	C₂	1	1	yes	maximal, characteristic
6	C₉×#890	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#889	C₂	1	2	yes	maximal, complemented
8	C₉×#876	C₂	1	2	yes	maximal
9	C₉×#872	C₂	1	1	yes	maximal, characteristic
10	C₉×#870	C₂	1	2	yes	maximal, complemented
11	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5583	C₃	1	1	yes	maximal, characteristic
13	C₉×#541	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
20	C₃×C₄²×C₉	C₂²	1	2	yes	—
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
22	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
27	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
29	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	2	yes	—
36	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#946	C₂×C₃	1	1	yes	characteristic
39	C₃×#944	C₂×C₃	1	1	yes	characteristic
40	C₃×#898	C₂×C₃	1	2	yes	—
41	C₃×#897	C₂×C₃	1	1	yes	characteristic
42	C₃×#890	C₂×C₃	1	1	yes	characteristic
43	C₃×#889	C₂×C₃	1	2	yes	—
44	C₃×#876	C₂×C₃	1	2	yes	—
45	C₃×#872	C₂×C₃	1	1	yes	characteristic
46	C₃×#870	C₂×C₃	1	2	yes	—
47	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#126	—	3	2	no	—
50	C₉×#126	—	3	2	no	—
51	C₉×#125	—	3	2	no	—
52	C₉×#125	—	3	1	no	—
53	C₉×#125	—	3	2	no	—
54	C₉×C₂²⋊Q₈	—	3	1	no	—
55	C₉×C₂²⋊Q₈	—	3	1	no	—
56	C₄×Q₈×C₉	—	2	1	no	—
57	C₄×Q₈×C₉	—	3	1	no	—
58	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
59	C₉×#117	—	3	1	no	—
60	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
68	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	2	yes	—
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₄×D₃×C₉	—	2	2	no	—
73	C₉×Dic₆	—	2	2	no	—
74	C₃×#541	—	3	1	no	—
75	#5583	C₉	1	1	yes	characteristic, direct product factor
76	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
79	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₃²×C₄²	C₂²×C₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
88	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
89	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
90	C₃×Dic₃⋊C₄	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×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
98	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₂×Q₈×C₉	—	2	1	no	—
100	C₂×Q₈×C₉	—	3	1	no	—
101	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₄×C₉	—	3	1	no	—
103	C₉×C₄⋊C₄	—	2	1	no	—
104	C₉×C₄⋊C₄	—	2	2	no	—
105	C₉×C₄⋊C₄	—	3	1	no	—
106	C₉×C₄⋊C₄	—	3	1	no	—
107	C₉×C₄⋊C₄	—	3	1	no	—
108	C₉×C₄⋊C₄	—	3	2	no	—
109	C₉×C₄⋊C₄	—	3	2	no	—
110	C₉×C₄⋊C₄	—	3	2	no	—
111	C₉×C₄⋊C₄	—	3	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	C₂×D₃	1	1	yes	characteristic
116	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
117	C₉×C₂²⋊C₄	—	3	1	no	—
118	C₉×C₂²⋊C₄	—	3	1	no	—
119	C₉×C₂²⋊C₄	—	3	2	no	—
120	C₉×C₂²⋊C₄	—	3	2	no	—
121	C₄²×C₉	—	2	1	no	—
122	C₄²×C₉	—	2	2	no	—
123	C₄²×C₉	—	3	1	no	—
124	C₄²×C₉	—	3	2	no	—
125	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
126	C₄²×C₉	C₂×D₃	1	2	yes	—
127	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
128	C₂×D₃×C₉	—	2	1	no	—
129	C₂×D₃×C₉	—	2	1	no	—
130	C₂×D₃×C₉	—	2	1	no	—
131	C₃×C₄×C₉	—	2	2	no	—
132	C₃×C₄×C₉	—	2	1	no	—
133	C₃×C₄×C₉	—	2	1	no	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	#41	1	2	yes	—
136	C₉×Dic₃	—	2	2	no	—
137	C₉×Dic₃	—	2	1	no	—
138	C₉×Dic₃	—	2	2	no	—
139	C₉×Dic₃	—	2	1	no	—
140	C₉×Dic₃	—	2	1	no	—
141	C₃×C₄⋊Q₈	—	3	1	no	—
142	C₃×#126	—	3	2	no	—
143	C₃×#126	—	3	2	no	—
144	C₃×#125	—	3	2	no	—
145	C₃×#125	—	3	1	no	—
146	C₃×#125	—	3	2	no	—
147	C₃×C₂²⋊Q₈	—	3	1	no	—
148	C₃×C₂²⋊Q₈	—	3	1	no	—
149	C₃×C₄×Q₈	—	2	1	no	—
150	C₃×C₄×Q₈	—	3	1	no	—
151	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
152	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
153	C₃×#117	—	3	1	no	—
154	#946	C₂×C₉	1	1	yes	characteristic
155	#944	C₂×C₉	1	1	yes	characteristic, complemented
156	#898	C₂×C₉	1	2	yes	—
157	#897	C₂×C₉	1	1	yes	characteristic
158	#890	C₂×C₉	1	1	yes	characteristic, complemented
159	#889	C₂×C₉	1	2	yes	complemented
160	#876	C₂×C₉	1	2	yes	—
161	#872	C₂×C₉	1	1	yes	characteristic
162	#870	C₂×C₉	1	2	yes	complemented
163	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
164	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
165	C₃²×Q₈	—	2	2	no	—
166	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
169	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
170	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
173	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
175	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
176	C₃×C₄×D₃	—	2	2	no	—
177	C₃×Dic₆	—	2	2	no	—
178	C₂³×C₉	—	3	1	no	—
179	Q₈×C₉	—	2	4	no	—
180	Q₈×C₉	—	2	2	no	—
181	Q₈×C₉	—	6	2	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	2	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	2	no	—
187	C₂×C₄×C₉	—	3	1	no	—
188	C₂×C₄×C₉	—	3	2	no	—
189	C₂×C₄×C₉	—	3	1	no	—
190	C₂×C₄×C₉	—	3	2	no	—
191	C₂×C₄×C₉	—	3	1	no	—
192	C₂×C₄×C₉	—	6	2	no	—
193	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
196	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
197	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
198	#541	—	3	1	no	Sylow
199	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
202	D₃×C₉	—	4	1	no	—
203	C₂×C₃×Q₈	—	2	1	no	—
204	C₂×C₃×Q₈	—	3	1	no	—
205	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
206	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
207	C₂²×C₃×C₄	—	3	1	no	—
208	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
209	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
210	C₃×C₄⋊C₄	—	2	1	no	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	3	1	no	—
213	C₃×C₄⋊C₄	—	3	1	no	—
214	C₃×C₄⋊C₄	—	3	2	no	—
215	C₃×C₄⋊C₄	—	3	2	no	—
216	C₃×C₄⋊C₄	—	3	2	no	—
217	C₃×C₄⋊C₄	—	3	2	no	—
218	C₃×C₄⋊C₄	—	3	2	no	—
219	C₃×C₄⋊C₄	—	3	1	no	—
220	C₃×C₄⋊C₄	—	3	2	no	—
221	C₃×C₄⋊C₄	—	3	2	no	—
222	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
223	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
224	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
225	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
226	C₃×C₂²⋊C₄	—	3	1	no	—
227	C₃×C₂²⋊C₄	—	3	1	no	—
228	C₃×C₂²⋊C₄	—	3	2	no	—
229	C₃×C₂²⋊C₄	—	3	2	no	—
230	C₃×C₄²	—	2	1	no	—
231	C₃×C₄²	—	2	2	no	—
232	C₃×C₄²	—	3	1	no	—
233	C₃×C₄²	—	3	2	no	—
234	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
235	C₃×C₄²	C₂²×C₉	1	2	yes	—
236	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
237	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
238	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
239	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
240	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
241	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
242	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
243	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
244	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
245	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
246	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
247	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
248	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
249	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
250	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
251	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
252	C₄×Dic₃	C₂²×C₉	1	2	yes	—
253	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
254	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
255	C₂×C₃×D₃	—	2	1	no	—
256	C₂×C₃×D₃	—	2	1	no	—
257	C₂×C₃×D₃	—	2	1	no	—
258	C₃²×C₄	—	2	2	no	—
259	C₃²×C₄	—	2	1	no	—
260	C₃²×C₄	—	2	1	no	—
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	C₃×#41	1	2	yes	—
263	C₃×Dic₃	—	2	2	no	—
264	C₃×Dic₃	—	2	1	no	—
265	C₃×Dic₃	—	2	2	no	—
266	C₃×Dic₃	—	2	1	no	—
267	C₃×Dic₃	—	2	1	no	—
268	C₂²×C₉	—	2	1	no	—
269	C₂²×C₉	—	6	1	no	—
270	C₂²×C₉	—	6	1	no	—
271	C₂²×C₉	—	6	1	no	—
272	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
273	C₄×C₉	—	2	2	no	—
274	C₄×C₉	—	2	4	no	—
275	C₄×C₉	—	2	2	no	—
276	C₄×C₉	—	2	1	no	—
277	C₄×C₉	—	2	1	no	—
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	4	1	no	—
281	C₄×C₉	—	4	2	no	—
282	C₄×C₉	—	6	1	no	—
283	C₄×C₉	—	6	2	no	—
284	C₄×C₉	—	6	1	no	—
285	C₄×C₉	—	6	2	no	—
286	C₄×C₉	—	6	1	no	—
287	C₄×C₉	#235	1	2	yes	—
288	C₄⋊Q₈	—	3	1	no	—
289	#126	—	3	2	no	—
290	#126	—	3	2	no	—
291	#125	—	3	2	no	—
292	#125	—	3	1	no	—
293	#125	—	3	2	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₄×Q₈	—	3	1	no	—
297	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
298	#117	—	3	1	no	—
299	C₃×C₉	#541	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	3	1	no	—
301	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
302	C₃×Q₈	—	2	4	no	—
303	C₃×Q₈	—	2	2	no	—
304	C₃×Q₈	—	2	2	no	—
305	C₃×Q₈	—	6	2	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	3	1	no	—
312	C₂×C₃×C₄	—	3	2	no	—
313	C₂×C₃×C₄	—	3	1	no	—
314	C₂×C₃×C₄	—	3	2	no	—
315	C₂×C₃×C₄	—	3	1	no	—
316	C₂×C₃×C₄	—	6	2	no	—
317	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
320	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
321	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
328	C₂×Dic₃	C₂³×C₉	1	2	yes	—
329	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
330	C₂×Dic₃	C₂³×C₉	1	2	yes	—
331	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
332	C₄×D₃	—	2	2	no	—
333	Dic₆	—	2	2	no	—
334	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
335	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
336	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
337	C₃×D₃	—	4	1	no	—
338	C₂×C₉	—	2	1	no	—
339	C₂×C₉	—	2	1	no	—
340	C₂×C₉	—	2	1	no	—
341	C₂×C₉	—	12	1	no	—
342	C₂×C₉	C₂×#235	1	1	yes	characteristic
343	C₂×C₉	#1007	1	1	yes	characteristic
344	C₂×C₉	#1010	1	1	yes	characteristic
345	C₂×Q₈	—	3	1	no	—
346	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
347	C₂²×C₄	—	3	1	no	—
348	C₄⋊C₄	—	3	1	no	—
349	C₄⋊C₄	—	3	1	no	—
350	C₄⋊C₄	—	3	1	no	—
351	C₄⋊C₄	—	3	2	no	—
352	C₄⋊C₄	—	3	2	no	—
353	C₄⋊C₄	—	3	2	no	—
354	C₄⋊C₄	—	3	2	no	—
355	C₄⋊C₄	—	3	2	no	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
360	C₂²⋊C₄	—	3	1	no	—
361	C₂²⋊C₄	—	3	1	no	—
362	C₂²⋊C₄	—	3	2	no	—
363	C₂²⋊C₄	—	3	2	no	—
364	C₄²	—	3	1	no	—
365	C₄²	—	3	2	no	—
366	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
367	C₄²	C₂×D₃×C₉	1	2	yes	—
368	C₂²×C₃	—	2	1	no	—
369	C₂²×C₃	—	6	1	no	—
370	C₂²×C₃	—	6	1	no	—
371	C₂²×C₃	—	6	1	no	—
372	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
373	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
374	C₂×D₃	—	2	1	no	—
375	C₂×D₃	—	2	1	no	—
376	C₂×D₃	—	2	1	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	4	1	no	—
389	C₃×C₄	—	4	2	no	—
390	C₃×C₄	—	6	1	no	—
391	C₃×C₄	—	6	2	no	—
392	C₃×C₄	—	6	1	no	—
393	C₃×C₄	—	6	2	no	—
394	C₃×C₄	—	6	1	no	—
395	C₃×C₄	C₉×#41	1	2	yes	—
396	C₃×C₄	C₃×#235	1	2	yes	—
397	Dic₃	—	2	2	no	—
398	Dic₃	—	2	1	no	—
399	Dic₃	—	2	2	no	—
400	Dic₃	—	2	1	no	—
401	Dic₃	—	2	1	no	—
402	C₃²	C₃×#541	1	1	yes	characteristic
403	C₉	—	2	1	no	—
404	C₉	#5583	1	1	yes	characteristic, direct product factor
405	C₂³	—	3	1	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	6	2	no	—
408	C₂×C₄	—	3	1	no	—
409	C₂×C₄	—	3	2	no	—
410	C₂×C₄	—	3	1	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	3	1	no	—
413	C₂×C₄	—	6	2	no	—
414	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
417	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
418	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	12	1	no	—
423	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
424	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
425	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
427	C₂×C₃	C₃×#1007	1	1	yes	characteristic
428	C₂×C₃	C₃×#1010	1	1	yes	characteristic
429	D₃	—	4	1	no	—
430	C₂²	—	6	1	no	—
431	C₂²	—	6	1	no	—
432	C₂²	—	6	1	no	—
433	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	6	1	no	—
439	C₄	—	6	2	no	—
440	C₄	—	6	1	no	—
441	C₄	—	6	2	no	—
442	C₄	—	6	1	no	—
443	C₄	C₉×#235	1	2	yes	—
444	C₃	—	2	1	no	—
445	C₃	C₉×#541	1	1	yes	characteristic, complemented
446	C₃	C₃×#5583	1	1	yes	characteristic
447	C₂	—	12	1	no	—
448	C₂	C₂×C₉×#235	1	1	yes	characteristic
449	C₂	C₉×#1007	1	1	yes	characteristic
450	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×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂²×C₃×D₃	C₂³×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×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
3. C₉×#944	C₂	semidirect
6. C₉×#890	C₂	semidirect
7. C₉×#889	C₂	semidirect
10. C₉×#870	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
58. C₄×Q₈×C₉	D₃	semidirect
75. #5583	C₉	direct (N × H)
151. C₃×C₄×Q₈	C₂×C₉	semidirect
155. #944	C₂×C₉	semidirect
158. #890	C₂×C₉	semidirect
159. #889	C₂×C₉	semidirect
162. #870	C₂×C₉	semidirect
163. C₄×Dic₆	C₂×C₉	semidirect
297. C₄×Q₈	D₃×C₉	semidirect
299. C₃×C₉	#541	semidirect
404. C₉	#5583	direct (N × H)
445. C₃	C₉×#541	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×#946	2
C₉×#944	2
C₉×#898	2
C₉×#897	2
C₉×#890	2
C₉×#889	2
C₉×#876	2
C₉×#872	2
C₉×#870	2
C₄×C₉×Dic₆	2
C₃×#5583	3
C₉×#541	3

Subgroups — C9×#5583 #13152704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5583 #13152704