Subgroups — C₉×#4944 #13142467

Order 1728.

702 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4944	C₃	1	1	yes	maximal, characteristic
9	C₉×#388	—	3	1	no	maximal
10	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₂²⋊C₄	—	2	2	no	—
18	C₉×#217	—	2	2	no	—
19	C₉×#217	C₄	1	4	yes	complemented
20	C₉×Dic₃⋊C₄	—	2	2	no	—
21	C₄×C₉×Dic₃	—	2	2	no	—
22	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
27	C₃×C₃⋊#95	C₂×C₃	1	1	yes	characteristic
28	C₃×C₃⋊#95	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	—	3	1	no	—
30	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
31	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
32	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
33	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic
34	C₂×C₄²×C₉	—	3	1	no	—
35	C₉×#95	—	3	1	no	—
36	C₉×#95	—	3	1	no	—
37	C₂³×C₃×C₉	—	2	1	no	—
38	C₂³×C₃×C₉	—	2	1	no	—
39	C₂³×C₃×C₉	—	2	1	no	—
40	C₂³×C₃×C₉	—	2	1	no	—
41	C₂³×C₃×C₉	—	2	1	no	—
42	C₂³×C₃×C₉	—	2	1	no	—
43	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
44	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	—	2	1	no	—
47	C₂×C₃×C₄×C₉	—	2	1	no	—
48	C₂×C₃×C₄×C₉	—	2	1	no	—
49	C₂×C₃×C₄×C₉	—	2	1	no	—
50	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
51	C₂×C₉×Dic₃	—	2	1	no	—
52	C₂×C₉×Dic₃	—	2	1	no	—
53	C₂×C₉×Dic₃	—	2	1	no	—
54	C₂×C₉×Dic₃	—	2	1	no	—
55	C₂×C₉×Dic₃	—	2	1	no	—
56	C₂×C₉×Dic₃	—	2	1	no	—
57	C₂×C₉×Dic₃	—	2	1	no	—
58	C₂×C₉×Dic₃	—	2	1	no	—
59	C₂×C₉×Dic₃	—	2	1	no	—
60	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
61	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
62	C₂×C₉×Dic₃	D₄	1	2	yes	—
63	C₃×#388	—	3	1	no	—
64	#4944	C₉	1	1	yes	characteristic, direct product factor
65	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₂⁴×C₉	—	2	1	no	—
73	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
74	C₃²×C₂²⋊C₄	—	2	2	no	—
75	C₃×#217	—	2	2	no	—
76	C₃×#217	C₃×C₄	1	4	yes	—
77	C₃×Dic₃⋊C₄	—	2	2	no	—
78	C₃×C₄×Dic₃	—	2	2	no	—
79	C₂²×C₄×C₉	—	2	1	no	—
80	C₂²×C₄×C₉	—	2	1	no	—
81	C₂²×C₄×C₉	—	3	1	no	—
82	C₂²×C₄×C₉	—	3	1	no	—
83	C₂²×C₄×C₉	—	3	1	no	—
84	C₂²×C₄×C₉	—	3	1	no	—
85	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
87	C₉×C₄⋊C₄	—	6	2	no	—
88	C₉×C₂²⋊C₄	—	2	4	no	—
89	C₉×C₂²⋊C₄	—	2	2	no	—
90	C₉×C₂²⋊C₄	—	3	4	no	—
91	C₉×C₂²⋊C₄	—	6	2	no	—
92	C₄²×C₉	—	6	2	no	—
93	C₂²×C₃×C₉	—	2	2	no	—
94	C₂²×C₃×C₉	—	2	2	no	—
95	C₂²×C₃×C₉	—	2	2	no	—
96	C₂²×C₃×C₉	—	4	1	no	—
97	C₂²×C₃×C₉	—	4	1	no	—
98	C₂²×C₃×C₉	—	4	1	no	—
99	C₂²×C₃×C₉	—	4	1	no	—
100	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₃×C₉	#41	1	1	yes	characteristic
104	C₂²×C₃×C₉	#41	1	1	yes	characteristic
105	C₂²×C₃×C₉	#41	1	1	yes	characteristic
106	C₂²×C₃×C₉	#41	1	1	yes	characteristic
107	C₃×C₄×C₉	—	2	2	no	—
108	C₃×C₄×C₉	—	4	1	no	—
109	C₉×Dic₃	—	2	2	no	—
110	C₉×Dic₃	—	2	2	no	—
111	C₉×Dic₃	—	2	2	no	—
112	C₉×Dic₃	—	4	1	no	—
113	C₂×C₃×C₄⋊C₄	—	3	1	no	—
114	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
116	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
117	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
118	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
119	C₂×C₃×C₄²	—	3	1	no	—
120	C₂×#217	C₂×C₉	1	1	yes	characteristic
121	C₂×#217	C₂×C₉	1	1	yes	characteristic
122	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
123	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
124	C₃×#95	—	3	1	no	—
125	C₃×#95	—	3	1	no	—
126	C₃⋊#95	C₂×C₉	1	1	yes	characteristic, complemented
127	C₃⋊#95	C₂×C₉	1	1	yes	characteristic, complemented
128	C₂³×C₃²	—	2	1	no	—
129	C₂³×C₃²	—	2	1	no	—
130	C₂³×C₃²	—	2	1	no	—
131	C₂³×C₃²	—	2	1	no	—
132	C₂³×C₃²	—	2	1	no	—
133	C₂³×C₃²	—	2	1	no	—
134	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
135	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₃²×C₄	—	2	1	no	—
137	C₂×C₃²×C₄	—	2	1	no	—
138	C₂×C₃²×C₄	—	2	1	no	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	—	2	1	no	—
141	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
142	C₂×C₃×Dic₃	—	2	1	no	—
143	C₂×C₃×Dic₃	—	2	1	no	—
144	C₂×C₃×Dic₃	—	2	1	no	—
145	C₂×C₃×Dic₃	—	2	1	no	—
146	C₂×C₃×Dic₃	—	2	1	no	—
147	C₂×C₃×Dic₃	—	2	1	no	—
148	C₂×C₃×Dic₃	—	2	1	no	—
149	C₂×C₃×Dic₃	—	2	1	no	—
150	C₂×C₃×Dic₃	—	2	1	no	—
151	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
153	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
154	C₂³×C₉	—	2	2	no	—
155	C₂³×C₉	—	2	2	no	—
156	C₂³×C₉	—	2	1	no	—
157	C₂³×C₉	—	2	1	no	—
158	C₂³×C₉	—	2	1	no	—
159	C₂³×C₉	—	2	1	no	—
160	C₂³×C₉	—	2	1	no	—
161	C₂³×C₉	—	2	1	no	—
162	C₂³×C₉	—	2	2	no	—
163	C₂³×C₉	—	2	1	no	—
164	C₂³×C₉	—	4	1	no	—
165	C₂³×C₉	—	4	1	no	—
166	C₂³×C₉	—	4	1	no	—
167	C₂³×C₉	—	4	1	no	—
168	C₂³×C₉	C₄×D₃	1	2	yes	—
169	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	2	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	2	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	—	4	1	no	—
181	C₂×C₄×C₉	—	4	1	no	—
182	C₂×C₄×C₉	—	4	1	no	—
183	C₂×C₄×C₉	—	4	1	no	—
184	C₂×C₄×C₉	—	6	1	no	—
185	C₂×C₄×C₉	—	6	1	no	—
186	C₂×C₄×C₉	—	6	1	no	—
187	C₂×C₄×C₉	—	6	1	no	—
188	C₂×C₄×C₉	—	6	1	no	—
189	C₂×C₄×C₉	—	6	1	no	—
190	C₂×C₄×C₉	—	6	1	no	—
191	C₂×C₄×C₉	—	6	1	no	—
192	C₂×C₄×C₉	—	6	1	no	—
193	C₂×C₄×C₉	#67	1	2	yes	—
194	#388	—	3	1	no	Sylow
195	C₂×C₃×C₉	—	4	2	no	—
196	C₂×C₃×C₉	#117	1	1	yes	characteristic
197	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
198	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
199	C₂×C₃×C₉	#121	1	1	yes	characteristic
200	C₂×C₃×C₉	#123	1	1	yes	characteristic
201	C₂×C₃×C₉	#124	1	1	yes	characteristic
202	C₂×C₃×C₉	#126	1	1	yes	characteristic
203	C₂⁴×C₃	—	2	1	no	—
204	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
205	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	3	1	no	—
210	C₂²×C₃×C₄	—	3	1	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
216	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
217	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
218	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
219	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
220	C₃×C₄⋊C₄	—	6	2	no	—
221	C₃×C₂²⋊C₄	—	2	4	no	—
222	C₃×C₂²⋊C₄	—	2	2	no	—
223	C₃×C₂²⋊C₄	—	2	2	no	—
224	C₃×C₂²⋊C₄	—	3	4	no	—
225	C₃×C₂²⋊C₄	—	6	2	no	—
226	C₃×C₄²	—	6	2	no	—
227	#217	—	2	2	no	—
228	#217	C₄×C₉	1	4	yes	complemented
229	Dic₃⋊C₄	—	2	2	no	—
230	C₄×Dic₃	—	2	2	no	—
231	C₂²×C₃²	—	2	2	no	—
232	C₂²×C₃²	—	2	2	no	—
233	C₂²×C₃²	—	2	2	no	—
234	C₂²×C₃²	—	4	1	no	—
235	C₂²×C₃²	—	4	1	no	—
236	C₂²×C₃²	—	4	1	no	—
237	C₂²×C₃²	—	4	1	no	—
238	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
242	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
243	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
244	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
245	C₃²×C₄	—	2	2	no	—
246	C₃²×C₄	—	4	1	no	—
247	C₃×Dic₃	—	2	2	no	—
248	C₃×Dic₃	—	2	2	no	—
249	C₃×Dic₃	—	2	2	no	—
250	C₃×Dic₃	—	4	1	no	—
251	C₂²×C₉	—	2	4	no	—
252	C₂²×C₉	—	2	2	no	—
253	C₂²×C₉	—	2	2	no	—
254	C₂²×C₉	—	2	2	no	—
255	C₂²×C₉	—	2	1	no	—
256	C₂²×C₉	—	2	1	no	—
257	C₂²×C₉	—	2	1	no	—
258	C₂²×C₉	—	2	1	no	—
259	C₂²×C₉	—	2	1	no	—
260	C₂²×C₉	—	2	1	no	—
261	C₂²×C₉	—	2	1	no	—
262	C₂²×C₉	—	4	2	no	—
263	C₂²×C₉	—	4	2	no	—
264	C₂²×C₉	—	4	2	no	—
265	C₂²×C₉	—	4	2	no	—
266	C₂²×C₉	—	4	2	no	—
267	C₂²×C₉	—	4	2	no	—
268	C₂²×C₉	—	4	1	no	—
269	C₂²×C₉	—	4	1	no	—
270	C₂²×C₉	—	4	1	no	—
271	C₂²×C₉	—	4	1	no	—
272	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
273	C₂²×C₉	#235	1	1	yes	characteristic
274	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
275	C₂²×C₉	#237	1	1	yes	characteristic
276	C₂²×C₉	#237	1	1	yes	characteristic
277	C₂²×C₉	#237	1	1	yes	characteristic
278	C₂²×C₉	C₂×#67	1	1	yes	characteristic
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	4	2	no	—
281	C₄×C₉	—	4	2	no	—
282	C₄×C₉	—	4	1	no	—
283	C₄×C₉	—	6	2	no	—
284	C₄×C₉	—	6	2	no	—
285	C₄×C₉	—	6	2	no	—
286	C₄×C₉	—	12	1	no	—
287	C₂×C₄⋊C₄	—	3	1	no	—
288	C₂×C₂²⋊C₄	—	3	1	no	—
289	C₂×C₂²⋊C₄	—	3	1	no	—
290	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic
291	C₂×C₄²	—	3	1	no	—
292	#95	—	3	1	no	—
293	#95	—	3	1	no	—
294	C₃×C₉	#388	1	1	yes	characteristic, complemented, Sylow
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	2	1	no	—
298	C₂³×C₃	—	2	1	no	—
299	C₂³×C₃	—	2	1	no	—
300	C₂³×C₃	—	2	1	no	—
301	C₂³×C₃	—	2	1	no	—
302	C₂³×C₃	—	2	1	no	—
303	C₂³×C₃	—	2	1	no	—
304	C₂³×C₃	—	2	1	no	—
305	C₂³×C₃	—	2	1	no	—
306	C₂³×C₃	—	2	1	no	—
307	C₂³×C₃	—	2	1	no	—
308	C₂³×C₃	—	2	1	no	—
309	C₂³×C₃	—	2	2	no	—
310	C₂³×C₃	—	2	1	no	—
311	C₂³×C₃	—	4	1	no	—
312	C₂³×C₃	—	4	1	no	—
313	C₂³×C₃	—	4	1	no	—
314	C₂³×C₃	—	4	1	no	—
315	C₂³×C₃	C₂×C₄×C₉	1	2	yes	—
316	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
317	C₂³×C₃	C₃×C₄×D₃	1	2	yes	—
318	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	3	2	no	—
332	C₂×C₃×C₄	—	3	2	no	—
333	C₂×C₃×C₄	—	3	2	no	—
334	C₂×C₃×C₄	—	4	1	no	—
335	C₂×C₃×C₄	—	4	1	no	—
336	C₂×C₃×C₄	—	4	1	no	—
337	C₂×C₃×C₄	—	4	1	no	—
338	C₂×C₃×C₄	—	6	1	no	—
339	C₂×C₃×C₄	—	6	1	no	—
340	C₂×C₃×C₄	—	6	1	no	—
341	C₂×C₃×C₄	—	6	1	no	—
342	C₂×C₃×C₄	—	6	1	no	—
343	C₂×C₃×C₄	—	6	1	no	—
344	C₂×C₃×C₄	—	6	1	no	—
345	C₂×C₃×C₄	—	6	1	no	—
346	C₂×C₃×C₄	—	6	1	no	—
347	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
348	C₂×C₃×C₄	C₃×#67	1	2	yes	—
349	C₂×Dic₃	—	2	1	no	—
350	C₂×Dic₃	—	2	1	no	—
351	C₂×Dic₃	—	2	1	no	—
352	C₂×Dic₃	—	2	1	no	—
353	C₂×Dic₃	—	2	1	no	—
354	C₂×Dic₃	—	2	1	no	—
355	C₂×Dic₃	—	2	1	no	—
356	C₂×Dic₃	—	2	1	no	—
357	C₂×Dic₃	—	2	1	no	—
358	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
359	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
360	C₂×Dic₃	D₄×C₉	1	2	yes	—
361	C₂×C₃²	—	4	2	no	—
362	C₂×C₃²	C₃×#117	1	1	yes	characteristic
363	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
364	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
365	C₂×C₃²	C₃×#121	1	1	yes	characteristic
366	C₂×C₃²	C₃×#123	1	1	yes	characteristic
367	C₂×C₃²	C₃×#124	1	1	yes	characteristic
368	C₂×C₃²	C₃×#126	1	1	yes	characteristic
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	2	1	no	—
371	C₂×C₉	—	2	1	no	—
372	C₂×C₉	—	2	1	no	—
373	C₂×C₉	—	2	1	no	—
374	C₂×C₉	—	2	1	no	—
375	C₂×C₉	—	2	1	no	—
376	C₂×C₉	—	4	4	no	—
377	C₂×C₉	—	4	2	no	—
378	C₂×C₉	#877	1	1	yes	characteristic
379	C₂×C₉	#879	1	1	yes	characteristic
380	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
381	C₂×C₉	#885	1	1	yes	characteristic
382	C₂×C₉	C₄×#67	1	1	yes	characteristic
383	C₂×C₉	#935	1	1	yes	characteristic
384	C₂×C₉	#938	1	1	yes	characteristic
385	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
386	C₂²×C₄	—	3	1	no	—
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	3	1	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
392	C₄⋊C₄	—	6	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	3	4	no	—
395	C₂²⋊C₄	—	6	2	no	—
396	C₄²	—	6	2	no	—
397	C₂²×C₃	—	2	4	no	—
398	C₂²×C₃	—	2	2	no	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	2	2	no	—
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	2	2	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	1	no	—
411	C₂²×C₃	—	4	2	no	—
412	C₂²×C₃	—	4	2	no	—
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	—	4	2	no	—
415	C₂²×C₃	—	4	2	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	—	4	1	no	—
418	C₂²×C₃	—	4	1	no	—
419	C₂²×C₃	—	4	1	no	—
420	C₂²×C₃	—	4	1	no	—
421	C₂²×C₃	—	4	1	no	—
422	C₂²×C₃	—	4	1	no	—
423	C₂²×C₃	—	4	1	no	—
424	C₂²×C₃	—	4	1	no	—
425	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
426	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
427	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
428	C₂²×C₃	C₉×#41	1	1	yes	characteristic
429	C₂²×C₃	C₉×#41	1	1	yes	characteristic
430	C₂²×C₃	C₉×#41	1	1	yes	characteristic
431	C₂²×C₃	C₉×#41	1	1	yes	characteristic
432	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
433	C₂²×C₃	C₃×#235	1	1	yes	characteristic
434	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
435	C₂²×C₃	C₃×#237	1	1	yes	characteristic
436	C₂²×C₃	C₃×#237	1	1	yes	characteristic
437	C₂²×C₃	C₃×#237	1	1	yes	characteristic
438	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	2	2	no	—
441	C₃×C₄	—	4	2	no	—
442	C₃×C₄	—	4	2	no	—
443	C₃×C₄	—	4	1	no	—
444	C₃×C₄	—	4	1	no	—
445	C₃×C₄	—	6	2	no	—
446	C₃×C₄	—	6	2	no	—
447	C₃×C₄	—	6	2	no	—
448	C₃×C₄	—	12	1	no	—
449	Dic₃	—	2	2	no	—
450	Dic₃	—	2	2	no	—
451	Dic₃	—	2	2	no	—
452	Dic₃	—	4	1	no	—
453	C₃²	C₃×#388	1	1	yes	characteristic
454	C₉	—	2	1	no	—
455	C₉	#4944	1	1	yes	characteristic, direct product factor
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	C₄×D₃×C₉	1	2	yes	—
463	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	3	2	no	—
470	C₂×C₄	—	3	2	no	—
471	C₂×C₄	—	3	2	no	—
472	C₂×C₄	—	6	1	no	—
473	C₂×C₄	—	6	1	no	—
474	C₂×C₄	—	6	1	no	—
475	C₂×C₄	—	6	1	no	—
476	C₂×C₄	—	6	1	no	—
477	C₂×C₄	—	6	1	no	—
478	C₂×C₄	—	6	1	no	—
479	C₂×C₄	—	6	1	no	—
480	C₂×C₄	—	6	1	no	—
481	C₂×C₄	C₉×#67	1	2	yes	—
482	C₂×C₃	—	2	1	no	—
483	C₂×C₃	—	2	1	no	—
484	C₂×C₃	—	2	1	no	—
485	C₂×C₃	—	2	1	no	—
486	C₂×C₃	—	2	1	no	—
487	C₂×C₃	—	2	1	no	—
488	C₂×C₃	—	2	1	no	—
489	C₂×C₃	—	4	4	no	—
490	C₂×C₃	—	4	2	no	—
491	C₂×C₃	—	4	2	no	—
492	C₂×C₃	C₉×#117	1	1	yes	characteristic
493	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
494	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
495	C₂×C₃	C₉×#121	1	1	yes	characteristic
496	C₂×C₃	C₉×#123	1	1	yes	characteristic
497	C₂×C₃	C₉×#124	1	1	yes	characteristic
498	C₂×C₃	C₉×#126	1	1	yes	characteristic
499	C₂×C₃	C₃×#877	1	1	yes	characteristic
500	C₂×C₃	C₃×#879	1	1	yes	characteristic
501	C₂×C₃	C₃×#67⋊C₄	1	1	yes	characteristic
502	C₂×C₃	C₃×#885	1	1	yes	characteristic
503	C₂×C₃	C₃×C₄×#67	1	1	yes	characteristic
504	C₂×C₃	C₃×#935	1	1	yes	characteristic
505	C₂×C₃	C₃×#938	1	1	yes	characteristic
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
514	C₂²	C₉×#235	1	1	yes	characteristic
515	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
516	C₂²	C₉×#237	1	1	yes	characteristic
517	C₂²	C₉×#237	1	1	yes	characteristic
518	C₂²	C₉×#237	1	1	yes	characteristic
519	C₂²	C₂×C₉×#67	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	6	2	no	—
523	C₄	—	6	2	no	—
524	C₄	—	6	2	no	—
525	C₄	—	12	1	no	—
526	C₃	—	2	1	no	—
527	C₃	C₉×#388	1	1	yes	characteristic, complemented
528	C₃	C₃×#4944	1	1	yes	characteristic
529	C₂	—	4	2	no	—
530	C₂	C₉×#877	1	1	yes	characteristic
531	C₂	C₉×#879	1	1	yes	characteristic
532	C₂	C₉×#67⋊C₄	1	1	yes	characteristic
533	C₂	C₉×#885	1	1	yes	characteristic
534	C₂	C₄×C₉×#67	1	1	yes	characteristic
535	C₂	C₉×#935	1	1	yes	characteristic
536	C₂	C₉×#938	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	C₂⁴×C₃²	C₂²×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₉×#388
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
4. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
5. C₂×C₄×C₉×Dic₃	C₂	semidirect
6. C₉×C₃⋊#95	C₂	semidirect
7. C₉×C₃⋊#95	C₂	semidirect
19. C₉×#217	C₄	semidirect
64. #4944	C₉	direct (N × H)
122. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
123. C₂×C₄×Dic₃	C₂×C₉	semidirect
126. C₃⋊#95	C₂×C₉	semidirect
127. C₃⋊#95	C₂×C₉	semidirect
228. #217	C₄×C₉	semidirect
294. C₃×C₉	#388	semidirect
455. C₉	#4944	direct (N × H)
527. C₃	C₉×#388	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₂×C₉×Dic₃⋊C₄	2
C₂×C₄×C₉×Dic₃	2
C₉×C₃⋊#95	2
C₃×#4944	3
C₉×#388	3

Subgroups — C9×#4944 #13142467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4944 #13142467