Subgroups — C₉×#5675 #13153100

Order 1728.

886 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic
3	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#883	C₂	1	4	yes	maximal, complemented
7	C₉×#878	C₂	1	4	yes	maximal, complemented
8	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5675	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×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×#67	C₂²	1	2	yes	—
15	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
16	D₃×Q₈×C₉	—	2	4	no	—
17	C₉×#237	—	2	4	no	—
18	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
19	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×Dic₆	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×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₉×#217	C₂²	1	4	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×C₄⋊Dic₃	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×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
33	C₃²×#124	C₂×C₃	1	1	yes	characteristic
34	C₃×#944	C₂×C₃	1	1	yes	characteristic
35	C₃×#936	C₂×C₃	1	1	yes	characteristic
36	C₃×#883	C₂×C₃	1	4	yes	—
37	C₃×#878	C₂×C₃	1	4	yes	—
38	C₃×#872	C₂×C₃	1	1	yes	characteristic
39	C₃×#869	C₂×C₃	1	1	yes	characteristic
40	C₂×C₉×#41	—	3	1	no	—
41	C₂²×Q₈×C₉	—	3	1	no	—
42	C₉×C₄⋊Q₈	—	3	1	no	—
43	C₉×C₄⋊Q₈	—	3	1	no	—
44	C₉×#124	—	2	1	no	—
45	C₉×#124	—	3	1	no	—
46	C₉×#124	D₃	1	1	yes	characteristic, complemented
47	C₉×#123	—	3	4	no	—
48	C₉×C₂²⋊Q₈	—	3	4	no	—
49	C₉×#117	—	3	1	no	—
50	C₂³×C₃×C₉	C₂³	1	2	yes	—
51	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
52	C₃×Q₈×C₉	—	2	2	no	—
53	C₃×D₄×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	1	yes	characteristic
57	C₉×#67	—	2	4	no	—
58	C₂×C₉×Dic₃	—	2	4	no	—
59	C₂×C₉×Dic₃	C₂³	1	2	yes	—
60	C₂×C₉×Dic₃	C₂³	1	2	yes	—
61	C₂×C₉×Dic₃	C₂³	1	2	yes	—
62	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
63	C₄×D₃×C₉	—	2	4	no	—
64	C₄×D₃×C₉	D₄	1	4	yes	—
65	C₉×Dic₆	—	2	2	no	—
66	C₉×Dic₆	—	2	2	no	—
67	C₉×Dic₆	—	2	4	no	—
68	C₃×#536	—	3	1	no	—
69	#5675	C₉	1	1	yes	characteristic, direct product factor
70	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
73	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
74	C₃×D₃×Q₈	—	2	4	no	—
75	C₃×#237	—	2	4	no	—
76	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
79	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
81	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
82	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
83	C₃×#217	C₂²×C₃	1	4	yes	—
84	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
86	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	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	—	3	2	no	—
92	C₂×Q₈×C₉	—	3	1	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×D₄×C₉	—	2	1	no	—
97	C₂×D₄×C₉	—	3	2	no	—
98	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
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	—	3	2	no	—
103	C₉×C₄⋊C₄	—	3	4	no	—
104	C₉×C₄⋊C₄	—	3	4	no	—
105	C₉×C₂²⋊C₄	—	2	4	no	—
106	C₉×C₂²⋊C₄	—	3	4	no	—
107	C₉×C₂²⋊C₄	—	3	2	no	—
108	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	—
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	—	2	2	no	—
113	C₂²×C₃×C₉	—	2	4	no	—
114	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
115	C₂×D₃×C₉	—	2	2	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	C₂×D₄	1	2	yes	—
120	C₉×Dic₃	—	2	2	no	—
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×D₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
127	C₂×#237	C₂×C₉	1	1	yes	characteristic
128	C₃×C₄⋊Q₈	—	3	1	no	—
129	C₃×C₄⋊Q₈	—	3	1	no	—
130	C₃×#124	—	2	1	no	—
131	C₃×#124	—	3	1	no	—
132	C₃×#124	C₂×C₉	1	1	yes	characteristic, complemented
133	C₃×#124	C₃×D₃	1	1	yes	characteristic
134	C₃×#123	—	3	4	no	—
135	C₃×C₂²⋊Q₈	—	3	4	no	—
136	C₃×#117	—	3	1	no	—
137	#944	C₂×C₉	1	1	yes	characteristic, complemented
138	#936	C₂×C₉	1	1	yes	characteristic, complemented
139	#883	C₂×C₉	1	4	yes	complemented
140	#878	C₂×C₉	1	4	yes	complemented
141	#872	C₂×C₉	1	1	yes	characteristic, complemented
142	#869	C₂×C₉	1	1	yes	characteristic, complemented
143	C₂³×C₃²	C₂³×C₃	1	2	yes	—
144	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
145	C₃²×Q₈	—	2	2	no	—
146	C₃²×D₄	—	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	1	yes	characteristic
150	C₃×#67	—	2	4	no	—
151	C₂×C₃×Dic₃	—	2	4	no	—
152	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
153	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
154	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
155	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
156	C₃×C₄×D₃	—	2	4	no	—
157	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
158	C₃×Dic₆	—	2	2	no	—
159	C₃×Dic₆	—	2	2	no	—
160	C₃×Dic₆	—	2	4	no	—
161	C₂³×C₉	—	2	2	no	—
162	C₂³×C₉	—	3	1	no	—
163	C₂³×C₉	C₂²×D₃	1	2	yes	—
164	Q₈×C₉	—	2	2	no	—
165	Q₈×C₉	—	4	2	no	—
166	Q₈×C₉	—	6	4	no	—
167	Q₈×C₉	—	6	2	no	—
168	Q₈×C₉	—	6	2	no	—
169	D₄×C₉	—	2	2	no	—
170	D₄×C₉	—	4	2	no	—
171	D₄×C₉	—	6	4	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	—	3	2	no	—
180	C₂×C₄×C₉	—	6	4	no	—
181	C₂×C₄×C₉	—	6	4	no	—
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	—	4	2	no	—
187	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₃×C₉	2₋¹⁺⁴	1	2	yes	—
189	D₃×C₉	—	2	2	no	—
190	C₃×#41	—	6	4	no	—
191	C₂×C₃×Q₈	—	2	1	no	—
192	C₂×C₃×Q₈	—	3	2	no	—
193	C₂×C₃×Q₈	—	3	1	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	C₂×C₃×D₃	1	1	yes	characteristic
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	—	3	2	no	—
200	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
201	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
202	C₂²×C₃×C₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	3	2	no	—
204	C₂²×C₃×C₄	—	3	2	no	—
205	C₂×#67	C₂²×C₉	1	2	yes	—
206	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
207	D₃×Q₈	—	2	4	no	—
208	#237	—	2	4	no	—
209	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
210	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
211	C₂×Dic₆	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	—	3	2	no	—
215	C₃×C₄⋊C₄	—	3	4	no	—
216	C₃×C₄⋊C₄	—	3	4	no	—
217	C₃×C₂²⋊C₄	—	2	4	no	—
218	C₃×C₂²⋊C₄	—	3	4	no	—
219	C₃×C₂²⋊C₄	—	3	2	no	—
220	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
221	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
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	#217	C₂²×C₉	1	4	yes	—
227	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
228	C₄⋊Dic₃	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	—	2	2	no	—
233	C₂²×C₃²	—	2	4	no	—
234	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
235	C₂×C₃×D₃	—	2	2	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	C₂×C₃×D₄	1	2	yes	—
240	C₃×Dic₃	—	2	2	no	—
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	2	no	—
245	C₂²×C₉	—	2	4	no	—
246	C₂²×C₉	—	2	1	no	—
247	C₂²×C₉	—	3	2	no	—
248	C₂²×C₉	—	4	2	no	—
249	C₂²×C₉	—	4	4	no	—
250	C₂²×C₉	—	6	2	no	—
251	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
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	—	6	2	no	—
261	C₄×C₉	D₃×D₄	1	2	yes	—
262	C₂×#41	—	3	1	no	—
263	C₂²×Q₈	—	3	1	no	—
264	C₄⋊Q₈	—	3	1	no	—
265	C₄⋊Q₈	—	3	1	no	—
266	#124	—	3	1	no	—
267	#124	D₃×C₉	1	1	yes	characteristic, complemented
268	#123	—	3	4	no	—
269	C₂²⋊Q₈	—	3	4	no	—
270	#117	—	3	1	no	—
271	C₃×C₉	#536	1	1	yes	characteristic, complemented, Sylow
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	3	1	no	—
274	C₂³×C₃	C₂³×C₉	1	2	yes	—
275	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
276	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
277	C₃×Q₈	—	2	2	no	—
278	C₃×Q₈	—	2	2	no	—
279	C₃×Q₈	—	4	2	no	—
280	C₃×Q₈	—	6	4	no	—
281	C₃×Q₈	—	6	2	no	—
282	C₃×Q₈	—	6	2	no	—
283	C₃×D₄	—	2	2	no	—
284	C₃×D₄	—	2	2	no	—
285	C₃×D₄	—	4	2	no	—
286	C₃×D₄	—	6	4	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	3	1	no	—
291	C₂×C₃×C₄	—	3	4	no	—
292	C₂×C₃×C₄	—	3	2	no	—
293	C₂×C₃×C₄	—	3	2	no	—
294	C₂×C₃×C₄	—	3	2	no	—
295	C₂×C₃×C₄	—	6	4	no	—
296	C₂×C₃×C₄	—	6	4	no	—
297	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
298	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
299	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
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	#67	—	2	4	no	—
304	C₂×Dic₃	—	2	4	no	—
305	C₂×Dic₃	C₂³×C₉	1	2	yes	—
306	C₂×Dic₃	C₂³×C₉	1	2	yes	—
307	C₂×Dic₃	C₂³×C₉	1	2	yes	—
308	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
309	C₄×D₃	—	2	4	no	—
310	C₄×D₃	D₄×C₉	1	4	yes	—
311	Dic₆	—	2	2	no	—
312	Dic₆	—	2	2	no	—
313	Dic₆	—	2	4	no	—
314	C₂×C₃²	—	4	2	no	—
315	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
316	C₂×C₃²	C₃×2₋¹⁺⁴	1	2	yes	—
317	C₃×D₃	—	2	2	no	—
318	C₂×C₉	—	2	1	no	—
319	C₂×C₉	—	2	2	no	—
320	C₂×C₉	—	4	2	no	—
321	C₂×C₉	—	6	2	no	—
322	C₂×C₉	—	8	2	no	—
323	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
324	C₂×C₉	#1010	1	2	yes	—
325	#41	—	6	4	no	—
326	C₂×Q₈	—	3	2	no	—
327	C₂×Q₈	—	3	1	no	—
328	C₂×Q₈	—	3	1	no	—
329	C₂×Q₈	—	6	4	no	—
330	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
331	C₂×D₄	—	3	2	no	—
332	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	3	2	no	—
335	C₂²×C₄	—	3	2	no	—
336	C₄⋊C₄	—	3	2	no	—
337	C₄⋊C₄	—	3	4	no	—
338	C₄⋊C₄	—	3	4	no	—
339	C₂²⋊C₄	—	3	4	no	—
340	C₂²⋊C₄	—	3	2	no	—
341	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	—
342	C₄²	—	3	1	no	—
343	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	4	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	3	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	4	no	—
352	C₂²×C₃	—	6	2	no	—
353	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
354	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
355	C₂×D₃	—	2	2	no	—
356	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
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	—	2	2	no	—
362	C₃×C₄	—	3	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	6	2	no	—
366	C₃×C₄	—	6	2	no	—
367	C₃×C₄	—	6	2	no	—
368	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
369	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
370	Dic₃	—	2	2	no	—
371	Dic₃	—	2	2	no	—
372	Dic₃	—	2	2	no	—
373	Dic₃	C₂×D₄×C₉	1	2	yes	—
374	C₃²	C₃×#536	1	1	yes	characteristic
375	C₉	—	2	1	no	—
376	C₉	#5675	1	1	yes	characteristic, direct product factor
377	C₂³	—	3	1	no	—
378	C₂³	C₂²×D₃×C₉	1	2	yes	—
379	Q₈	—	2	2	no	—
380	Q₈	—	6	4	no	—
381	Q₈	—	6	2	no	—
382	Q₈	—	6	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	6	4	no	—
385	C₂×C₄	—	3	1	no	—
386	C₂×C₄	—	3	4	no	—
387	C₂×C₄	—	3	2	no	—
388	C₂×C₄	—	3	2	no	—
389	C₂×C₄	—	3	2	no	—
390	C₂×C₄	—	6	4	no	—
391	C₂×C₄	—	6	4	no	—
392	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
393	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
394	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	2	no	—
397	C₂×C₃	—	4	2	no	—
398	C₂×C₃	—	4	2	no	—
399	C₂×C₃	—	6	2	no	—
400	C₂×C₃	—	8	2	no	—
401	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
402	C₂×C₃	C₉×2₋¹⁺⁴	1	2	yes	—
403	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
404	C₂×C₃	C₃×#1010	1	2	yes	—
405	D₃	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	3	2	no	—
409	C₂²	—	6	2	no	—
410	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	3	2	no	—
414	C₄	—	6	2	no	—
415	C₄	—	6	2	no	—
416	C₄	—	6	2	no	—
417	C₄	D₃×D₄×C₉	1	2	yes	—
418	C₃	—	2	1	no	—
419	C₃	C₉×#536	1	1	yes	characteristic, complemented
420	C₃	C₃×#5675	1	1	yes	characteristic
421	C₂	—	4	2	no	—
422	C₂	—	6	2	no	—
423	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
424	C₂	C₉×#1010	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×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#237	C₂×C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×Q₈×C₉	C₂	semidirect
3. C₃×C₉×#124	C₂	semidirect
4. C₉×#944	C₂	semidirect
5. C₉×#936	C₂	semidirect
6. C₉×#883	C₂	semidirect
7. C₉×#878	C₂	semidirect
8. C₉×#872	C₂	semidirect
9. C₉×#869	C₂	semidirect
46. C₉×#124	D₃	semidirect
69. #5675	C₉	direct (N × H)
126. C₂×D₃×Q₈	C₂×C₉	semidirect
132. C₃×#124	C₂×C₉	semidirect
137. #944	C₂×C₉	semidirect
138. #936	C₂×C₉	semidirect
139. #883	C₂×C₉	semidirect
140. #878	C₂×C₉	semidirect
141. #872	C₂×C₉	semidirect
142. #869	C₂×C₉	semidirect
267. #124	D₃×C₉	semidirect
271. C₃×C₉	#536	semidirect
376. C₉	#5675	direct (N × H)
419. 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×D₃×Q₈×C₉	2
C₂×C₉×#237	2
C₃×C₉×#124	2
C₉×#944	2
C₉×#936	2
C₉×#883	2
C₉×#878	2
C₉×#872	2
C₉×#869	2
C₃×#5675	3
C₉×#536	3

Subgroups — C9×#5675 #13153100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5675 #13153100