Subgroups — C₉×#4957 #13142465

Order 1728.

906 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4957	C₃	1	1	yes	maximal, characteristic
9	C₉×#390	—	3	1	no	maximal
10	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
11	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×#67	—	2	2	no	—
15	C₂×C₉×#67	—	2	2	no	—
16	C₂×C₉×#67	C₄	1	4	yes	complemented
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₂²⋊C₄	—	2	2	no	—
21	C₉×#217	—	2	2	no	—
22	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
23	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
24	C₉×Dic₃⋊C₄	—	2	2	no	—
25	C₄×C₉×Dic₃	—	2	2	no	—
26	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
33	C₂²×D₄×C₉	—	3	1	no	—
34	C₂×C₉×C₄⋊C₄	—	3	1	no	—
35	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
36	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
37	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
38	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
39	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
40	C₂×C₄²×C₉	—	3	1	no	—
41	C₂³×C₃×C₉	—	2	1	no	—
42	C₂³×C₃×C₉	—	2	1	no	—
43	C₂³×C₃×C₉	—	2	1	no	—
44	C₂³×C₃×C₉	—	2	1	no	—
45	C₂³×C₃×C₉	—	2	1	no	—
46	C₂³×C₃×C₉	—	2	1	no	—
47	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
48	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
49	C₂²×D₃×C₉	—	2	1	no	—
50	C₂²×D₃×C₉	—	2	1	no	—
51	C₂²×D₃×C₉	—	2	1	no	—
52	C₂²×D₃×C₉	—	2	1	no	—
53	C₂²×D₃×C₉	—	2	1	no	—
54	C₂²×D₃×C₉	—	2	1	no	—
55	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₄×C₉	—	2	1	no	—
57	C₂×C₃×C₄×C₉	—	2	1	no	—
58	C₂×C₃×C₄×C₉	—	2	1	no	—
59	C₂×C₃×C₄×C₉	—	2	1	no	—
60	C₂×C₃×C₄×C₉	—	2	1	no	—
61	C₂×C₃×C₄×C₉	D₄	1	2	yes	complemented
62	C₉×#67	—	2	8	no	—
63	C₂×C₉×Dic₃	—	2	1	no	—
64	C₂×C₉×Dic₃	—	2	1	no	—
65	C₂×C₉×Dic₃	—	2	1	no	—
66	C₂×C₉×Dic₃	—	2	1	no	—
67	C₂×C₉×Dic₃	—	2	1	no	—
68	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
69	C₂×C₉×Dic₃	D₄	1	2	yes	—
70	C₂×C₉×Dic₃	D₄	1	2	yes	—
71	C₂×C₉×Dic₃	D₄	1	2	yes	complemented
72	C₃×#390	—	3	1	no	—
73	#4957	C₉	1	1	yes	characteristic, direct product factor
74	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
75	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×#67	—	2	2	no	—
79	C₂×C₃×#67	—	2	2	no	—
80	C₂×C₃×#67	C₃×C₄	1	4	yes	—
81	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
84	C₂⁴×C₉	—	2	1	no	—
85	C₂⁴×C₉	—	3	1	no	—
86	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
87	C₃²×C₂²⋊C₄	—	2	2	no	—
88	C₃×#217	—	2	2	no	—
89	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
90	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
91	C₃×Dic₃⋊C₄	—	2	2	no	—
92	C₃×C₄×Dic₃	—	2	2	no	—
93	C₂×D₄×C₉	—	3	4	no	—
94	C₂×D₄×C₉	—	6	2	no	—
95	C₂×D₄×C₉	—	6	2	no	—
96	C₂²×C₄×C₉	—	2	1	no	—
97	C₂²×C₄×C₉	—	2	1	no	—
98	C₂²×C₄×C₉	—	3	1	no	—
99	C₂²×C₄×C₉	—	3	1	no	—
100	C₂²×C₄×C₉	—	3	1	no	—
101	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
103	C₉×C₄⋊C₄	—	6	2	no	—
104	C₉×C₂²⋊C₄	—	2	4	no	—
105	C₉×C₂²⋊C₄	—	2	2	no	—
106	C₉×C₂²⋊C₄	—	6	2	no	—
107	C₉×C₂²⋊C₄	—	6	2	no	—
108	C₉×C₂²⋊C₄	—	6	2	no	—
109	C₄²×C₉	—	6	2	no	—
110	C₂²×C₃×C₉	—	2	2	no	—
111	C₂²×C₃×C₉	—	2	2	no	—
112	C₂²×C₃×C₉	—	2	2	no	—
113	C₂²×C₃×C₉	—	4	1	no	—
114	C₂²×C₃×C₉	—	4	1	no	—
115	C₂²×C₃×C₉	—	4	1	no	—
116	C₂²×C₃×C₉	—	4	1	no	—
117	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₃×C₉	#41	1	1	yes	characteristic
123	C₂²×C₃×C₉	#41	1	1	yes	characteristic
124	C₂×D₃×C₉	—	2	2	no	—
125	C₂×D₃×C₉	—	2	2	no	—
126	C₂×D₃×C₉	—	2	2	no	—
127	C₂×D₃×C₉	—	4	1	no	—
128	C₂×D₃×C₉	—	4	1	no	—
129	C₂×D₃×C₉	—	4	1	no	—
130	C₂×D₃×C₉	—	4	1	no	—
131	C₃×C₄×C₉	—	2	2	no	—
132	C₃×C₄×C₉	—	4	1	no	—
133	C₉×Dic₃	—	2	2	no	—
134	C₉×Dic₃	—	4	1	no	—
135	C₉×Dic₃	C₂²⋊C₄	1	4	yes	complemented
136	C₂²×C₃×D₄	—	3	1	no	—
137	C₂²×#67	C₂×C₉	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	—	3	1	no	—
139	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
140	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
141	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
143	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
144	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
145	C₂×C₃×C₄²	—	3	1	no	—
146	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
147	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
148	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
149	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
150	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
151	C₂³×C₃²	—	2	1	no	—
152	C₂³×C₃²	—	2	1	no	—
153	C₂³×C₃²	—	2	1	no	—
154	C₂³×C₃²	—	2	1	no	—
155	C₂³×C₃²	—	2	1	no	—
156	C₂³×C₃²	—	2	1	no	—
157	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
158	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×D₃	—	2	1	no	—
160	C₂²×C₃×D₃	—	2	1	no	—
161	C₂²×C₃×D₃	—	2	1	no	—
162	C₂²×C₃×D₃	—	2	1	no	—
163	C₂²×C₃×D₃	—	2	1	no	—
164	C₂²×C₃×D₃	—	2	1	no	—
165	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
166	C₂×C₃²×C₄	—	2	1	no	—
167	C₂×C₃²×C₄	—	2	1	no	—
168	C₂×C₃²×C₄	—	2	1	no	—
169	C₂×C₃²×C₄	—	2	1	no	—
170	C₂×C₃²×C₄	—	2	1	no	—
171	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
172	C₃×#67	—	2	8	no	—
173	C₂×C₃×Dic₃	—	2	1	no	—
174	C₂×C₃×Dic₃	—	2	1	no	—
175	C₂×C₃×Dic₃	—	2	1	no	—
176	C₂×C₃×Dic₃	—	2	1	no	—
177	C₂×C₃×Dic₃	—	2	1	no	—
178	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
179	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
180	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
181	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
182	C₂³×C₉	—	2	2	no	—
183	C₂³×C₉	—	2	2	no	—
184	C₂³×C₉	—	2	1	no	—
185	C₂³×C₉	—	2	1	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	1	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	2	1	no	—
190	C₂³×C₉	—	2	2	no	—
191	C₂³×C₉	—	2	1	no	—
192	C₂³×C₉	—	3	2	no	—
193	C₂³×C₉	—	4	1	no	—
194	C₂³×C₉	—	4	1	no	—
195	C₂³×C₉	—	4	1	no	—
196	C₂³×C₉	—	4	1	no	—
197	C₂³×C₉	—	6	1	no	—
198	C₂³×C₉	—	6	1	no	—
199	C₂³×C₉	—	6	1	no	—
200	C₂³×C₉	—	6	1	no	—
201	C₂³×C₉	—	6	1	no	—
202	C₂³×C₉	—	6	1	no	—
203	C₂³×C₉	C₄×D₃	1	2	yes	—
204	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
205	D₄×C₉	—	6	8	no	—
206	C₂×C₄×C₉	—	2	1	no	—
207	C₂×C₄×C₉	—	2	1	no	—
208	C₂×C₄×C₉	—	2	2	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	2	no	—
213	C₂×C₄×C₉	—	3	2	no	—
214	C₂×C₄×C₉	—	3	2	no	—
215	C₂×C₄×C₉	—	3	2	no	—
216	C₂×C₄×C₉	—	3	2	no	—
217	C₂×C₄×C₉	—	4	1	no	—
218	C₂×C₄×C₉	—	4	1	no	—
219	C₂×C₄×C₉	—	4	1	no	—
220	C₂×C₄×C₉	—	4	1	no	—
221	C₂×C₄×C₉	—	6	1	no	—
222	C₂×C₄×C₉	—	6	1	no	—
223	C₂×C₄×C₉	—	6	1	no	—
224	C₂×C₄×C₉	—	6	1	no	—
225	C₂×C₄×C₉	—	6	1	no	—
226	C₂×C₄×C₉	#67	1	2	yes	complemented
227	#390	—	3	1	no	Sylow
228	C₂×C₃×C₉	—	4	2	no	—
229	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₃×C₉	#121	1	1	yes	characteristic
233	C₂×C₃×C₉	#121	1	1	yes	characteristic
234	C₂×C₃×C₉	#124	1	1	yes	characteristic
235	C₂×C₃×C₉	#127	1	1	yes	characteristic
236	D₃×C₉	—	4	2	no	—
237	C₂⁴×C₃	—	2	1	no	—
238	C₂⁴×C₃	—	3	1	no	—
239	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
240	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
241	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₃×D₄	—	3	4	no	—
243	C₂×C₃×D₄	—	6	2	no	—
244	C₂×C₃×D₄	—	6	2	no	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	—	3	1	no	—
248	C₂²×C₃×C₄	—	3	1	no	—
249	C₂²×C₃×C₄	—	3	1	no	—
250	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
254	C₂×#67	—	2	2	no	—
255	C₂×#67	—	2	2	no	—
256	C₂×#67	C₄×C₉	1	4	yes	complemented
257	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
258	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
259	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
260	C₃×C₄⋊C₄	—	6	2	no	—
261	C₃×C₂²⋊C₄	—	2	4	no	—
262	C₃×C₂²⋊C₄	—	2	2	no	—
263	C₃×C₂²⋊C₄	—	2	2	no	—
264	C₃×C₂²⋊C₄	—	6	2	no	—
265	C₃×C₂²⋊C₄	—	6	2	no	—
266	C₃×C₂²⋊C₄	—	6	2	no	—
267	C₃×C₄²	—	6	2	no	—
268	#217	—	2	2	no	—
269	(C₂×D₃)⋊C₄	—	2	2	no	—
270	(C₂×D₃)⋊C₄	—	2	2	no	—
271	Dic₃⋊C₄	—	2	2	no	—
272	C₄×Dic₃	—	2	2	no	—
273	C₂²×C₃²	—	2	2	no	—
274	C₂²×C₃²	—	2	2	no	—
275	C₂²×C₃²	—	2	2	no	—
276	C₂²×C₃²	—	4	1	no	—
277	C₂²×C₃²	—	4	1	no	—
278	C₂²×C₃²	—	4	1	no	—
279	C₂²×C₃²	—	4	1	no	—
280	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
281	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
286	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
287	C₂×C₃×D₃	—	2	2	no	—
288	C₂×C₃×D₃	—	2	2	no	—
289	C₂×C₃×D₃	—	2	2	no	—
290	C₂×C₃×D₃	—	4	1	no	—
291	C₂×C₃×D₃	—	4	1	no	—
292	C₂×C₃×D₃	—	4	1	no	—
293	C₂×C₃×D₃	—	4	1	no	—
294	C₃²×C₄	—	2	2	no	—
295	C₃²×C₄	—	4	1	no	—
296	C₃×Dic₃	—	2	2	no	—
297	C₃×Dic₃	—	4	1	no	—
298	C₃×Dic₃	C₃×C₂²⋊C₄	1	4	yes	—
299	C₂²×C₉	—	2	4	no	—
300	C₂²×C₉	—	2	2	no	—
301	C₂²×C₉	—	2	2	no	—
302	C₂²×C₉	—	2	2	no	—
303	C₂²×C₉	—	2	1	no	—
304	C₂²×C₉	—	2	1	no	—
305	C₂²×C₉	—	2	1	no	—
306	C₂²×C₉	—	2	1	no	—
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	1	no	—
309	C₂²×C₉	—	2	1	no	—
310	C₂²×C₉	—	4	2	no	—
311	C₂²×C₉	—	4	2	no	—
312	C₂²×C₉	—	4	2	no	—
313	C₂²×C₉	—	4	2	no	—
314	C₂²×C₉	—	4	2	no	—
315	C₂²×C₉	—	4	2	no	—
316	C₂²×C₉	—	4	1	no	—
317	C₂²×C₉	—	4	1	no	—
318	C₂²×C₉	—	4	1	no	—
319	C₂²×C₉	—	4	1	no	—
320	C₂²×C₉	—	6	2	no	—
321	C₂²×C₉	—	6	2	no	—
322	C₂²×C₉	—	6	2	no	—
323	C₂²×C₉	—	12	1	no	—
324	C₂²×C₉	—	12	1	no	—
325	C₂²×C₉	—	12	1	no	—
326	C₂²×C₉	—	12	1	no	—
327	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
328	C₂²×C₉	#235	1	1	yes	characteristic
329	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
330	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
331	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
332	C₂²×C₉	#237	1	1	yes	characteristic
333	C₂²×C₉	C₂×#67	1	1	yes	characteristic
334	C₄×C₉	—	2	2	no	—
335	C₄×C₉	—	3	4	no	—
336	C₄×C₉	—	4	2	no	—
337	C₄×C₉	—	4	2	no	—
338	C₄×C₉	—	4	1	no	—
339	C₄×C₉	—	6	2	no	—
340	C₄×C₉	—	12	1	no	—
341	C₂²×D₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₂²⋊C₄	—	3	1	no	—
344	C₂×C₂²⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	1	no	—
346	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
347	C₂×C₄²	—	3	1	no	—
348	C₃×C₉	#390	1	1	yes	characteristic, complemented, Sylow
349	C₂³×C₃	—	2	2	no	—
350	C₂³×C₃	—	2	2	no	—
351	C₂³×C₃	—	2	1	no	—
352	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	1	no	—
363	C₂³×C₃	—	2	2	no	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	3	2	no	—
366	C₂³×C₃	—	4	1	no	—
367	C₂³×C₃	—	4	1	no	—
368	C₂³×C₃	—	4	1	no	—
369	C₂³×C₃	—	4	1	no	—
370	C₂³×C₃	—	6	1	no	—
371	C₂³×C₃	—	6	1	no	—
372	C₂³×C₃	—	6	1	no	—
373	C₂³×C₃	—	6	1	no	—
374	C₂³×C₃	—	6	1	no	—
375	C₂³×C₃	—	6	1	no	—
376	C₂³×C₃	C₂×C₄×C₉	1	2	yes	—
377	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
378	C₂³×C₃	C₃×C₄×D₃	1	2	yes	—
379	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
380	C₂²×D₃	—	2	1	no	—
381	C₂²×D₃	—	2	1	no	—
382	C₂²×D₃	—	2	1	no	—
383	C₂²×D₃	—	2	1	no	—
384	C₂²×D₃	—	2	1	no	—
385	C₂²×D₃	—	2	1	no	—
386	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
387	C₃×D₄	—	6	8	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	3	2	no	—
401	C₂×C₃×C₄	—	3	2	no	—
402	C₂×C₃×C₄	—	3	2	no	—
403	C₂×C₃×C₄	—	3	2	no	—
404	C₂×C₃×C₄	—	4	1	no	—
405	C₂×C₃×C₄	—	4	1	no	—
406	C₂×C₃×C₄	—	4	1	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	—	6	1	no	—
409	C₂×C₃×C₄	—	6	1	no	—
410	C₂×C₃×C₄	—	6	1	no	—
411	C₂×C₃×C₄	—	6	1	no	—
412	C₂×C₃×C₄	—	6	1	no	—
413	C₂×C₃×C₄	D₄×C₉	1	2	yes	complemented
414	C₂×C₃×C₄	C₃×#67	1	2	yes	—
415	#67	—	2	8	no	—
416	C₂×Dic₃	—	2	1	no	—
417	C₂×Dic₃	—	2	1	no	—
418	C₂×Dic₃	—	2	1	no	—
419	C₂×Dic₃	—	2	1	no	—
420	C₂×Dic₃	—	2	1	no	—
421	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
422	C₂×Dic₃	D₄×C₉	1	2	yes	—
423	C₂×Dic₃	D₄×C₉	1	2	yes	—
424	C₂×Dic₃	D₄×C₉	1	2	yes	complemented
425	C₂×C₃²	—	4	2	no	—
426	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
427	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
428	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
429	C₂×C₃²	C₃×#121	1	1	yes	characteristic
430	C₂×C₃²	C₃×#121	1	1	yes	characteristic
431	C₂×C₃²	C₃×#124	1	1	yes	characteristic
432	C₂×C₃²	C₃×#127	1	1	yes	characteristic
433	C₃×D₃	—	4	2	no	—
434	C₂×C₉	—	2	1	no	—
435	C₂×C₉	—	2	1	no	—
436	C₂×C₉	—	2	1	no	—
437	C₂×C₉	—	2	1	no	—
438	C₂×C₉	—	2	1	no	—
439	C₂×C₉	—	2	1	no	—
440	C₂×C₉	—	2	1	no	—
441	C₂×C₉	—	4	4	no	—
442	C₂×C₉	—	4	2	no	—
443	C₂×C₉	—	12	2	no	—
444	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
445	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
446	C₂×C₉	#884	1	1	yes	characteristic
447	C₂×C₉	#885	1	1	yes	characteristic
448	C₂×C₉	C₄×#67	1	1	yes	characteristic
449	C₂×C₉	#939	1	1	yes	characteristic
450	C₂×C₉	#940	1	1	yes	characteristic
451	C₂⁴	—	3	1	no	—
452	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
453	C₂×D₄	—	3	4	no	—
454	C₂×D₄	—	6	2	no	—
455	C₂×D₄	—	6	2	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
461	C₄⋊C₄	—	6	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	6	2	no	—
464	C₂²⋊C₄	—	6	2	no	—
465	C₂²⋊C₄	—	6	2	no	—
466	C₄²	—	6	2	no	—
467	C₂²×C₃	—	2	4	no	—
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	4	2	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	4	2	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	—	4	2	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	4	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	6	2	no	—
496	C₂²×C₃	—	6	2	no	—
497	C₂²×C₃	—	6	2	no	—
498	C₂²×C₃	—	12	1	no	—
499	C₂²×C₃	—	12	1	no	—
500	C₂²×C₃	—	12	1	no	—
501	C₂²×C₃	—	12	1	no	—
502	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
503	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
504	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
505	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
506	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
507	C₂²×C₃	C₉×#41	1	1	yes	characteristic
508	C₂²×C₃	C₉×#41	1	1	yes	characteristic
509	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
510	C₂²×C₃	C₃×#235	1	1	yes	characteristic
511	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
512	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
513	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
514	C₂²×C₃	C₃×#237	1	1	yes	characteristic
515	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
516	C₂×D₃	—	2	2	no	—
517	C₂×D₃	—	2	2	no	—
518	C₂×D₃	—	2	2	no	—
519	C₂×D₃	—	4	1	no	—
520	C₂×D₃	—	4	1	no	—
521	C₂×D₃	—	4	1	no	—
522	C₂×D₃	—	4	1	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	3	4	no	—
526	C₃×C₄	—	4	2	no	—
527	C₃×C₄	—	4	2	no	—
528	C₃×C₄	—	4	1	no	—
529	C₃×C₄	—	4	1	no	—
530	C₃×C₄	—	6	2	no	—
531	C₃×C₄	—	12	1	no	—
532	Dic₃	—	2	2	no	—
533	Dic₃	—	4	1	no	—
534	Dic₃	C₉×C₂²⋊C₄	1	4	yes	complemented
535	C₃²	C₃×#390	1	1	yes	characteristic
536	C₉	—	2	1	no	—
537	C₉	#4957	1	1	yes	characteristic, direct product factor
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	3	2	no	—
545	C₂³	—	6	1	no	—
546	C₂³	—	6	1	no	—
547	C₂³	—	6	1	no	—
548	C₂³	—	6	1	no	—
549	C₂³	—	6	1	no	—
550	C₂³	—	6	1	no	—
551	C₂³	C₄×D₃×C₉	1	2	yes	—
552	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
553	D₄	—	6	8	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	3	2	no	—
560	C₂×C₄	—	3	2	no	—
561	C₂×C₄	—	3	2	no	—
562	C₂×C₄	—	3	2	no	—
563	C₂×C₄	—	6	1	no	—
564	C₂×C₄	—	6	1	no	—
565	C₂×C₄	—	6	1	no	—
566	C₂×C₄	—	6	1	no	—
567	C₂×C₄	—	6	1	no	—
568	C₂×C₄	C₉×#67	1	2	yes	complemented
569	C₂×C₃	—	2	1	no	—
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	2	1	no	—
572	C₂×C₃	—	2	1	no	—
573	C₂×C₃	—	2	1	no	—
574	C₂×C₃	—	2	1	no	—
575	C₂×C₃	—	2	1	no	—
576	C₂×C₃	—	4	4	no	—
577	C₂×C₃	—	4	2	no	—
578	C₂×C₃	—	4	2	no	—
579	C₂×C₃	—	12	2	no	—
580	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
581	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
582	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
583	C₂×C₃	C₉×#121	1	1	yes	characteristic
584	C₂×C₃	C₉×#121	1	1	yes	characteristic
585	C₂×C₃	C₉×#124	1	1	yes	characteristic
586	C₂×C₃	C₉×#127	1	1	yes	characteristic
587	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
588	C₂×C₃	C₃×#67⋊C₄	1	1	yes	characteristic
589	C₂×C₃	C₃×#884	1	1	yes	characteristic
590	C₂×C₃	C₃×#885	1	1	yes	characteristic
591	C₂×C₃	C₃×C₄×#67	1	1	yes	characteristic
592	C₂×C₃	C₃×#939	1	1	yes	characteristic
593	C₂×C₃	C₃×#940	1	1	yes	characteristic
594	D₃	—	4	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	6	2	no	—
603	C₂²	—	6	2	no	—
604	C₂²	—	6	2	no	—
605	C₂²	—	12	1	no	—
606	C₂²	—	12	1	no	—
607	C₂²	—	12	1	no	—
608	C₂²	—	12	1	no	—
609	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
610	C₂²	C₉×#235	1	1	yes	characteristic
611	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
612	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
613	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
614	C₂²	C₉×#237	1	1	yes	characteristic
615	C₂²	C₂×C₉×#67	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	3	4	no	—
618	C₄	—	4	1	no	—
619	C₄	—	6	2	no	—
620	C₄	—	12	1	no	—
621	C₃	—	2	1	no	—
622	C₃	C₉×#390	1	1	yes	characteristic, complemented
623	C₃	C₃×#4957	1	1	yes	characteristic
624	C₂	—	4	2	no	—
625	C₂	—	12	2	no	—
626	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
627	C₂	C₉×#67⋊C₄	1	1	yes	characteristic
628	C₂	C₉×#884	1	1	yes	characteristic
629	C₂	C₉×#885	1	1	yes	characteristic
630	C₂	C₄×C₉×#67	1	1	yes	characteristic
631	C₂	C₉×#939	1	1	yes	characteristic
632	C₂	C₉×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×#67	C₂×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₉×#390
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
3. C₂×C₉×#217	C₂	semidirect
4. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
7. C₂×C₄×C₉×Dic₃	C₂	semidirect
16. C₂×C₉×#67	C₄	semidirect
39. C₂×C₉×C₂²⋊C₄	D₃	semidirect
61. C₂×C₃×C₄×C₉	D₄	semidirect
71. C₂×C₉×Dic₃	D₄	semidirect
73. #4957	C₉	direct (N × H)
135. C₉×Dic₃	C₂²⋊C₄	semidirect
143. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
146. C₂×#217	C₂×C₉	semidirect
147. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
148. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
149. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
150. C₂×C₄×Dic₃	C₂×C₉	semidirect
226. C₂×C₄×C₉	#67	semidirect
256. C₂×#67	C₄×C₉	semidirect
346. C₂×C₂²⋊C₄	D₃×C₉	semidirect
348. C₃×C₉	#390	semidirect
413. C₂×C₃×C₄	D₄×C₉	semidirect
424. C₂×Dic₃	D₄×C₉	semidirect
534. Dic₃	C₉×C₂²⋊C₄	semidirect
537. C₉	#4957	direct (N × H)
568. C₂×C₄	C₉×#67	semidirect
622. C₃	C₉×#390	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×#67	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×Dic₃⋊C₄	2
C₂×C₄×C₉×Dic₃	2
C₃×#4957	3
C₉×#390	3

Subgroups — C9×#4957 #13142465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4957 #13142465