Subgroups — C₉×#5724 #13153306

Order 1728.

878 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#896	C₂	1	4	yes	maximal, complemented
7	C₉×#894	C₂	1	4	yes	maximal, complemented
8	C₉×#875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5724	C₃	1	1	yes	maximal, characteristic
11	C₉×#536	—	3	1	no	maximal
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₉×#239	—	2	4	no	—
15	D₃×Q₈×C₉	—	2	4	no	—
16	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₉×D₁₂	C₂²	1	2	yes	—
18	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
19	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
20	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
22	C₂×C₉×Dic₆	C₂²	1	2	yes	—
23	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	—
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
28	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
29	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
30	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
33	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
34	C₃×#947	C₂×C₃	1	1	yes	characteristic
35	C₃×#944	C₂×C₃	1	1	yes	characteristic
36	C₃×#896	C₂×C₃	1	4	yes	—
37	C₃×#894	C₂×C₃	1	4	yes	—
38	C₃×#875	C₂×C₃	1	1	yes	characteristic
39	C₃×#872	C₂×C₃	1	1	yes	characteristic
40	C₂×C₉×#41	—	3	1	no	—
41	C₂²×Q₈×C₉	—	3	1	no	—
42	C₉×C₄⋊Q₈	—	2	1	no	—
43	C₉×C₄⋊Q₈	—	3	1	no	—
44	C₉×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
45	C₉×#124	—	3	1	no	—
46	C₉×#124	—	3	1	no	—
47	C₉×#123	—	3	4	no	—
48	C₉×C₂²⋊Q₈	—	3	4	no	—
49	C₉×#117	—	3	1	no	—
50	C₂²×D₃×C₉	C₂³	1	2	yes	—
51	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
52	C₃×Q₈×C₉	—	2	2	no	—
53	C₃×Q₈×C₉	—	2	2	no	—
54	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
55	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×C₉×Dic₃	C₂³	1	2	yes	—
59	C₂×C₉×Dic₃	C₂³	1	2	yes	—
60	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
61	C₉×D₁₂	—	2	4	no	—
62	C₉×D₁₂	—	2	2	no	—
63	C₄×D₃×C₉	—	2	4	no	—
64	C₄×D₃×C₉	—	2	4	no	—
65	C₄×D₃×C₉	D₄	1	4	yes	—
66	C₉×Dic₆	—	2	2	no	—
67	C₉×Dic₆	—	2	4	no	—
68	C₃×#536	—	3	1	no	—
69	#5724	C₉	1	1	yes	characteristic, direct product factor
70	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
72	C₃×#239	—	2	4	no	—
73	C₃×D₃×Q₈	—	2	4	no	—
74	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
75	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
78	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
80	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
81	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
82	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
85	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
86	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
87	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
89	C₉×#41	—	6	4	no	—
90	C₂×Q₈×C₉	—	2	1	no	—
91	C₂×Q₈×C₉	—	2	1	no	—
92	C₂×Q₈×C₉	—	3	2	no	—
93	C₂×Q₈×C₉	—	3	1	no	—
94	C₂×Q₈×C₉	—	6	4	no	—
95	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
96	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
97	C₂×D₄×C₉	—	3	2	no	—
98	C₂×D₄×C₉	—	3	1	no	—
99	C₂²×C₄×C₉	—	3	1	no	—
100	C₂²×C₄×C₉	—	3	2	no	—
101	C₂²×C₄×C₉	—	3	2	no	—
102	C₉×C₄⋊C₄	—	2	4	no	—
103	C₉×C₄⋊C₄	—	3	2	no	—
104	C₉×C₄⋊C₄	—	3	4	no	—
105	C₉×C₄⋊C₄	C₂×D₃	1	4	yes	—
106	C₉×C₂²⋊C₄	—	3	2	no	—
107	C₉×C₂²⋊C₄	—	3	4	no	—
108	C₉×C₂²⋊C₄	—	3	4	no	—
109	C₄²×C₉	—	2	1	no	—
110	C₄²×C₉	—	3	1	no	—
111	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
112	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
113	C₂×D₃×C₉	—	2	2	no	—
114	C₂×D₃×C₉	—	2	2	no	—
115	C₂×D₃×C₉	—	2	4	no	—
116	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
117	C₃×C₄×C₉	—	2	2	no	—
118	C₃×C₄×C₉	—	2	2	no	—
119	C₃×C₄×C₉	—	2	2	no	—
120	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
121	C₉×Dic₃	—	2	2	no	—
122	C₉×Dic₃	—	2	2	no	—
123	C₉×Dic₃	C₂×D₄	1	2	yes	—
124	C₂×C₃×#41	—	3	1	no	—
125	C₂²×C₃×Q₈	—	3	1	no	—
126	C₂×#239	C₂×C₉	1	1	yes	characteristic
127	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
128	C₃×C₄⋊Q₈	—	2	1	no	—
129	C₃×C₄⋊Q₈	—	3	1	no	—
130	C₃×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
131	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
132	C₃×#124	—	3	1	no	—
133	C₃×#124	—	3	1	no	—
134	C₃×#123	—	3	4	no	—
135	C₃×C₂²⋊Q₈	—	3	4	no	—
136	C₃×#117	—	3	1	no	—
137	#947	C₂×C₉	1	1	yes	characteristic, complemented
138	#944	C₂×C₉	1	1	yes	characteristic, complemented
139	#896	C₂×C₉	1	4	yes	complemented
140	#894	C₂×C₉	1	4	yes	complemented
141	#875	C₂×C₉	1	1	yes	characteristic, complemented
142	#872	C₂×C₉	1	1	yes	characteristic, complemented
143	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
144	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
145	C₃²×Q₈	—	2	2	no	—
146	C₃²×Q₈	—	2	2	no	—
147	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
148	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
149	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
152	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
153	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
154	C₃×D₁₂	—	2	4	no	—
155	C₃×D₁₂	—	2	2	no	—
156	C₃×C₄×D₃	—	2	4	no	—
157	C₃×C₄×D₃	—	2	4	no	—
158	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
159	C₃×Dic₆	—	2	2	no	—
160	C₃×Dic₆	—	2	4	no	—
161	C₂³×C₉	—	3	1	no	—
162	C₂³×C₉	—	3	2	no	—
163	Q₈×C₉	—	2	2	no	—
164	Q₈×C₉	—	2	2	no	—
165	Q₈×C₉	—	4	2	no	—
166	Q₈×C₉	—	4	2	no	—
167	Q₈×C₉	—	6	4	no	—
168	Q₈×C₉	—	6	2	no	—
169	D₄×C₉	—	6	4	no	—
170	D₄×C₉	—	6	2	no	—
171	C₂×C₄×C₉	—	2	2	no	—
172	C₂×C₄×C₉	—	2	1	no	—
173	C₂×C₄×C₉	—	2	2	no	—
174	C₂×C₄×C₉	—	2	2	no	—
175	C₂×C₄×C₉	—	3	1	no	—
176	C₂×C₄×C₉	—	3	4	no	—
177	C₂×C₄×C₉	—	3	2	no	—
178	C₂×C₄×C₉	—	3	2	no	—
179	C₂×C₄×C₉	—	6	4	no	—
180	C₂×C₄×C₉	—	6	4	no	—
181	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
182	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
183	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
184	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
185	#536	—	3	1	no	Sylow
186	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₃×C₉	2₋¹⁺⁴	1	2	yes	—
188	D₃×C₉	—	2	2	no	—
189	D₃×C₉	—	4	2	no	—
190	C₃×#41	—	6	4	no	—
191	C₂×C₃×Q₈	—	2	1	no	—
192	C₂×C₃×Q₈	—	2	1	no	—
193	C₂×C₃×Q₈	—	3	2	no	—
194	C₂×C₃×Q₈	—	3	1	no	—
195	C₂×C₃×Q₈	—	6	4	no	—
196	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
197	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
198	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
199	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
200	C₂×C₃×D₄	—	3	2	no	—
201	C₂×C₃×D₄	—	3	1	no	—
202	C₂²×C₃×C₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	3	2	no	—
204	C₂²×C₃×C₄	—	3	2	no	—
205	#239	—	2	4	no	—
206	D₃×Q₈	—	2	4	no	—
207	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
208	C₂×D₁₂	C₂²×C₉	1	2	yes	—
209	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
210	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
211	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
212	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
213	C₂×Dic₆	C₂²×C₉	1	2	yes	—
214	C₃×C₄⋊C₄	—	2	4	no	—
215	C₃×C₄⋊C₄	—	3	2	no	—
216	C₃×C₄⋊C₄	—	3	4	no	—
217	C₃×C₄⋊C₄	C₂²×C₉	1	4	yes	—
218	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
219	C₃×C₂²⋊C₄	—	3	2	no	—
220	C₃×C₂²⋊C₄	—	3	4	no	—
221	C₃×C₂²⋊C₄	—	3	4	no	—
222	C₃×C₄²	—	2	1	no	—
223	C₃×C₄²	—	3	1	no	—
224	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
225	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
226	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
228	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
229	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
230	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
231	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
232	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
233	C₂×C₃×D₃	—	2	2	no	—
234	C₂×C₃×D₃	—	2	2	no	—
235	C₂×C₃×D₃	—	2	4	no	—
236	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
237	C₃²×C₄	—	2	2	no	—
238	C₃²×C₄	—	2	2	no	—
239	C₃²×C₄	—	2	2	no	—
240	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
241	C₃×Dic₃	—	2	2	no	—
242	C₃×Dic₃	—	2	2	no	—
243	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
244	C₂²×C₉	—	2	1	no	—
245	C₂²×C₉	—	3	2	no	—
246	C₂²×C₉	—	6	2	no	—
247	C₂²×C₉	—	6	2	no	—
248	C₂²×C₉	—	6	4	no	—
249	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
250	C₄×C₉	—	2	4	no	—
251	C₄×C₉	—	2	2	no	—
252	C₄×C₉	—	2	2	no	—
253	C₄×C₉	—	2	2	no	—
254	C₄×C₉	—	2	2	no	—
255	C₄×C₉	—	3	2	no	—
256	C₄×C₉	—	4	2	no	—
257	C₄×C₉	—	4	2	no	—
258	C₄×C₉	—	6	2	no	—
259	C₄×C₉	—	6	2	no	—
260	C₄×C₉	D₃×D₄	1	2	yes	—
261	C₂×#41	—	3	1	no	—
262	C₂²×Q₈	—	3	1	no	—
263	C₄⋊Q₈	—	3	1	no	—
264	C₄⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
265	#124	—	3	1	no	—
266	#124	—	3	1	no	—
267	#123	—	3	4	no	—
268	C₂²⋊Q₈	—	3	4	no	—
269	#117	—	3	1	no	—
270	C₃×C₉	#536	1	1	yes	characteristic, complemented, Sylow
271	C₂³×C₃	—	3	1	no	—
272	C₂³×C₃	—	3	2	no	—
273	C₂²×D₃	C₂³×C₉	1	2	yes	—
274	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
275	C₃×Q₈	—	2	2	no	—
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	2	2	no	—
278	C₃×Q₈	—	2	2	no	—
279	C₃×Q₈	—	4	2	no	—
280	C₃×Q₈	—	4	2	no	—
281	C₃×Q₈	—	6	4	no	—
282	C₃×Q₈	—	6	2	no	—
283	C₃×D₄	—	6	4	no	—
284	C₃×D₄	—	6	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	3	1	no	—
290	C₂×C₃×C₄	—	3	4	no	—
291	C₂×C₃×C₄	—	3	2	no	—
292	C₂×C₃×C₄	—	3	2	no	—
293	C₂×C₃×C₄	—	6	4	no	—
294	C₂×C₃×C₄	—	6	4	no	—
295	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
296	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
297	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
298	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
300	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
301	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
302	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₂×Dic₃	C₂³×C₉	1	2	yes	—
304	C₂×Dic₃	C₂³×C₉	1	2	yes	—
305	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
306	D₁₂	—	2	4	no	—
307	D₁₂	—	2	2	no	—
308	C₄×D₃	—	2	4	no	—
309	C₄×D₃	—	2	4	no	—
310	C₄×D₃	D₄×C₉	1	4	yes	—
311	Dic₆	—	2	2	no	—
312	Dic₆	—	2	4	no	—
313	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
314	C₂×C₃²	C₃×2₋¹⁺⁴	1	2	yes	—
315	C₃×D₃	—	2	2	no	—
316	C₃×D₃	—	4	2	no	—
317	C₂×C₉	—	2	1	no	—
318	C₂×C₉	—	2	2	no	—
319	C₂×C₉	—	6	2	no	—
320	C₂×C₉	—	12	2	no	—
321	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
322	C₂×C₉	#1007	1	2	yes	—
323	#41	—	6	4	no	—
324	C₂×Q₈	—	3	2	no	—
325	C₂×Q₈	—	3	1	no	—
326	C₂×Q₈	—	6	4	no	—
327	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
328	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
329	C₂×D₄	—	3	2	no	—
330	C₂×D₄	—	3	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	2	no	—
333	C₂²×C₄	—	3	2	no	—
334	C₄⋊C₄	—	3	2	no	—
335	C₄⋊C₄	—	3	4	no	—
336	C₄⋊C₄	C₂×D₃×C₉	1	4	yes	—
337	C₂²⋊C₄	—	3	2	no	—
338	C₂²⋊C₄	—	3	4	no	—
339	C₂²⋊C₄	—	3	4	no	—
340	C₄²	—	3	1	no	—
341	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	3	2	no	—
344	C₂²×C₃	—	6	2	no	—
345	C₂²×C₃	—	6	2	no	—
346	C₂²×C₃	—	6	4	no	—
347	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
348	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
349	C₂×D₃	—	2	2	no	—
350	C₂×D₃	—	2	2	no	—
351	C₂×D₃	—	2	4	no	—
352	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	3	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	6	2	no	—
365	C₃×C₄	—	6	2	no	—
366	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
367	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
368	Dic₃	—	2	2	no	—
369	Dic₃	—	2	2	no	—
370	Dic₃	C₂×D₄×C₉	1	2	yes	—
371	C₃²	C₃×#536	1	1	yes	characteristic
372	C₉	—	2	1	no	—
373	C₉	#5724	1	1	yes	characteristic, direct product factor
374	C₂³	—	3	1	no	—
375	C₂³	—	3	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	2	2	no	—
378	Q₈	—	6	4	no	—
379	Q₈	—	6	2	no	—
380	D₄	—	6	4	no	—
381	D₄	—	6	2	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	3	4	no	—
384	C₂×C₄	—	3	2	no	—
385	C₂×C₄	—	3	2	no	—
386	C₂×C₄	—	6	4	no	—
387	C₂×C₄	—	6	4	no	—
388	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
389	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
390	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
391	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	2	2	no	—
394	C₂×C₃	—	6	2	no	—
395	C₂×C₃	—	12	2	no	—
396	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
397	C₂×C₃	C₉×2₋¹⁺⁴	1	2	yes	—
398	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
399	C₂×C₃	C₃×#1007	1	2	yes	—
400	D₃	—	2	2	no	—
401	D₃	—	4	2	no	—
402	C₂²	—	3	2	no	—
403	C₂²	—	6	2	no	—
404	C₂²	—	6	2	no	—
405	C₂²	—	6	4	no	—
406	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	3	2	no	—
411	C₄	—	6	2	no	—
412	C₄	—	6	2	no	—
413	C₄	D₃×D₄×C₉	1	2	yes	—
414	C₃	—	2	1	no	—
415	C₃	C₉×#536	1	1	yes	characteristic, complemented
416	C₃	C₃×#5724	1	1	yes	characteristic
417	C₂	—	6	2	no	—
418	C₂	—	12	2	no	—
419	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
420	C₂	C₉×#1007	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#239	C₂×C₃
hypercenter	C₉×C₄⋊Q₈	D₃
hypocenter	C₃	C₉×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×D₃×Q₈×C₉	C₂	semidirect
3. C₃×C₉×C₄⋊Q₈	C₂	semidirect
4. C₉×#947	C₂	semidirect
5. C₉×#944	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. C₉×#875	C₂	semidirect
9. C₉×#872	C₂	semidirect
44. C₉×C₄⋊Q₈	D₃	semidirect
69. #5724	C₉	direct (N × H)
127. C₂×D₃×Q₈	C₂×C₉	semidirect
130. C₃×C₄⋊Q₈	C₂×C₉	semidirect
137. #947	C₂×C₉	semidirect
138. #944	C₂×C₉	semidirect
139. #896	C₂×C₉	semidirect
140. #894	C₂×C₉	semidirect
141. #875	C₂×C₉	semidirect
142. #872	C₂×C₉	semidirect
264. C₄⋊Q₈	D₃×C₉	semidirect
270. C₃×C₉	#536	semidirect
373. C₉	#5724	direct (N × H)
415. C₃	C₉×#536	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₂×D₃×Q₈×C₉	2
C₃×C₉×C₄⋊Q₈	2
C₉×#947	2
C₉×#944	2
C₉×#896	2
C₉×#894	2
C₉×#875	2
C₉×#872	2
C₃×#5724	3
C₉×#536	3

Subgroups — C9×#5724 #13153306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5724 #13153306