Subgroups — C₉×#5596 #13152797

Order 1728.

1024 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#237	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#940	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#939	C₂	1	2	yes	maximal, complemented
5	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#885	C₂	1	2	yes	maximal, complemented
11	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#5596	C₃	1	1	yes	maximal, characteristic
13	C₉×#532	—	3	1	no	maximal
14	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂×C₉×#67	C₂²	1	2	yes	—
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
22	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
23	C₉×#237	—	2	8	no	—
24	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
26	C₂×C₉×Dic₆	C₂²	1	2	yes	—
27	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₉×#217	C₂²	1	2	yes	—
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
37	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₃×#237	C₂×C₃	1	2	yes	—
39	C₃²×#121	C₂×C₃	1	1	yes	characteristic
40	C₃×#940	C₂×C₃	1	1	yes	characteristic
41	C₃×#939	C₂×C₃	1	2	yes	—
42	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
43	C₃×#930	C₂×C₃	1	1	yes	characteristic
44	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
45	C₃×#893	C₂×C₃	1	1	yes	characteristic
46	C₃×#888	C₂×C₃	1	1	yes	characteristic
47	C₃×#885	C₂×C₃	1	2	yes	—
48	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
49	C₂×C₉×#41	—	3	2	no	—
50	C₉×C₄⋊Q₈	—	3	1	no	—
51	C₉×#127	—	3	1	no	—
52	C₉×#124	—	3	2	no	—
53	C₉×#121	—	2	1	no	—
54	C₉×#121	—	3	2	no	—
55	C₉×#121	—	3	1	no	—
56	C₉×#121	D₃	1	1	yes	characteristic, complemented
57	C₄×D₄×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	1	no	—
59	C₄×D₄×C₉	—	3	2	no	—
60	C₂×C₄²×C₉	—	3	1	no	—
61	C₂³×C₃×C₉	C₂³	1	2	yes	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	C₂³	1	2	yes	—
64	C₃×D₄×C₉	—	2	4	no	—
65	C₃×D₄×C₉	—	2	2	no	—
66	C₂×C₃×C₄×C₉	—	2	2	no	—
67	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×#67	—	2	4	no	—
71	C₉×#67	—	2	4	no	—
72	C₉×#67	—	2	4	no	—
73	C₂×C₉×Dic₃	—	2	4	no	—
74	C₂×C₉×Dic₃	—	2	2	no	—
75	C₂×C₉×Dic₃	D₄	1	4	yes	complemented
76	C₂×C₉×Dic₃	C₂³	1	2	yes	—
77	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
81	C₉×D₁₂	—	2	2	no	—
82	C₄×D₃×C₉	—	2	4	no	—
83	C₉×Dic₆	—	2	4	no	—
84	C₃×#532	—	3	1	no	—
85	#5596	C₉	1	1	yes	characteristic, direct product factor
86	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
88	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
90	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
91	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
92	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
93	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₃×#237	—	2	8	no	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
98	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
99	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₃×#217	C₂²×C₃	1	2	yes	—
102	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
103	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
104	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
105	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
108	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
109	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
110	C₉×#41	—	6	8	no	—
111	C₂×Q₈×C₉	—	3	2	no	—
112	C₂×D₄×C₉	—	2	1	no	—
113	C₂×D₄×C₉	—	2	2	no	—
114	C₂×D₄×C₉	—	3	2	no	—
115	C₂×D₄×C₉	—	3	2	no	—
116	C₂×D₄×C₉	—	3	2	no	—
117	C₂×D₄×C₉	—	3	1	no	—
118	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
119	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
120	C₂²×C₄×C₉	—	2	1	no	—
121	C₂²×C₄×C₉	—	3	1	no	—
122	C₂²×C₄×C₉	—	3	1	no	—
123	C₂²×C₄×C₉	—	3	2	no	—
124	C₂²×C₄×C₉	—	3	2	no	—
125	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
126	C₉×C₄⋊C₄	—	2	1	no	—
127	C₉×C₄⋊C₄	—	3	2	no	—
128	C₉×C₄⋊C₄	—	3	1	no	—
129	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
130	C₉×C₂²⋊C₄	—	2	2	no	—
131	C₉×C₂²⋊C₄	—	3	2	no	—
132	C₉×C₂²⋊C₄	—	3	2	no	—
133	C₉×C₂²⋊C₄	—	3	2	no	—
134	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
135	C₄²×C₉	—	3	1	no	—
136	C₄²×C₉	—	3	1	no	—
137	C₄²×C₉	—	3	1	no	—
138	C₄²×C₉	—	3	1	no	—
139	C₂²×C₃×C₉	—	2	1	no	—
140	C₂²×C₃×C₉	—	2	1	no	—
141	C₂²×C₃×C₉	—	2	2	no	—
142	C₂²×C₃×C₉	—	2	2	no	—
143	C₂²×C₃×C₉	—	2	2	no	—
144	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
145	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
146	C₂×D₃×C₉	—	2	2	no	—
147	C₂×D₃×C₉	—	2	2	no	—
148	C₂×D₃×C₉	—	2	2	no	—
149	C₃×C₄×C₉	—	2	2	no	—
150	C₃×C₄×C₉	—	2	1	no	—
151	C₃×C₄×C₉	#41	1	2	yes	complemented
152	C₉×Dic₃	—	2	2	no	—
153	C₉×Dic₃	—	2	1	no	—
154	C₉×Dic₃	C₂×D₄	1	2	yes	—
155	C₉×Dic₃	C₂×D₄	1	2	yes	—
156	C₉×Dic₃	#41	1	2	yes	complemented
157	C₂×C₃×#41	—	3	2	no	—
158	C₂×#237	C₂×C₉	1	2	yes	complemented
159	C₃×C₄⋊Q₈	—	3	1	no	—
160	C₃×#127	—	3	1	no	—
161	C₃×#124	—	3	2	no	—
162	C₃×#121	—	2	1	no	—
163	C₃×#121	—	3	2	no	—
164	C₃×#121	—	3	1	no	—
165	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
166	C₃×#121	C₃×D₃	1	1	yes	characteristic
167	C₃×C₄×D₄	—	3	1	no	—
168	C₃×C₄×D₄	—	3	1	no	—
169	C₃×C₄×D₄	—	3	2	no	—
170	C₂×C₃×C₄²	—	3	1	no	—
171	#940	C₂×C₉	1	1	yes	characteristic, complemented
172	#939	C₂×C₉	1	2	yes	complemented
173	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
174	#930	C₂×C₉	1	1	yes	characteristic, complemented
175	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
176	#893	C₂×C₉	1	1	yes	characteristic, complemented
177	#888	C₂×C₉	1	1	yes	characteristic, complemented
178	#885	C₂×C₉	1	2	yes	complemented
179	#67⋊C₄	C₂×C₉	1	2	yes	complemented
180	C₂³×C₃²	C₂³×C₃	1	2	yes	—
181	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
183	C₃²×D₄	—	2	4	no	—
184	C₃²×D₄	—	2	2	no	—
185	C₂×C₃²×C₄	—	2	2	no	—
186	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
188	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₃×#67	—	2	4	no	—
190	C₃×#67	—	2	4	no	—
191	C₃×#67	—	2	4	no	—
192	C₂×C₃×Dic₃	—	2	4	no	—
193	C₂×C₃×Dic₃	—	2	2	no	—
194	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
195	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
197	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
200	C₃×D₁₂	—	2	2	no	—
201	C₃×C₄×D₃	—	2	4	no	—
202	C₃×Dic₆	—	2	4	no	—
203	C₂³×C₉	—	2	1	no	—
204	C₂³×C₉	—	2	2	no	—
205	C₂³×C₉	—	3	2	no	—
206	C₂³×C₉	C₂²×D₃	1	2	yes	—
207	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
208	Q₈×C₉	—	6	4	no	—
209	D₄×C₉	—	2	4	no	—
210	D₄×C₉	—	2	2	no	—
211	D₄×C₉	—	4	2	no	—
212	D₄×C₉	—	4	4	no	—
213	D₄×C₉	—	6	4	no	—
214	D₄×C₉	—	6	4	no	—
215	D₄×C₉	—	6	4	no	—
216	D₄×C₉	—	6	2	no	—
217	C₂×C₄×C₉	—	2	2	no	—
218	C₂×C₄×C₉	—	2	1	no	—
219	C₂×C₄×C₉	—	2	1	no	—
220	C₂×C₄×C₉	—	2	2	no	—
221	C₂×C₄×C₉	—	3	4	no	—
222	C₂×C₄×C₉	—	3	1	no	—
223	C₂×C₄×C₉	—	3	1	no	—
224	C₂×C₄×C₉	—	3	1	no	—
225	C₂×C₄×C₉	—	3	1	no	—
226	C₂×C₄×C₉	—	3	2	no	—
227	C₂×C₄×C₉	—	4	2	no	—
228	C₂×C₄×C₉	—	6	4	no	—
229	C₂×C₄×C₉	—	6	2	no	—
230	C₂×C₄×C₉	—	6	4	no	—
231	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
233	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
234	#532	—	3	1	no	Sylow
235	C₂×C₃×C₉	—	2	2	no	—
236	C₂×C₃×C₉	—	4	2	no	—
237	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
240	D₃×C₉	—	4	2	no	—
241	C₃×#41	—	6	8	no	—
242	C₂×C₃×Q₈	—	3	2	no	—
243	C₂×C₃×D₄	—	2	1	no	—
244	C₂×C₃×D₄	—	2	2	no	—
245	C₂×C₃×D₄	—	3	2	no	—
246	C₂×C₃×D₄	—	3	2	no	—
247	C₂×C₃×D₄	—	3	2	no	—
248	C₂×C₃×D₄	—	3	1	no	—
249	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
250	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
251	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
252	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
253	C₂²×C₃×C₄	—	2	1	no	—
254	C₂²×C₃×C₄	—	3	1	no	—
255	C₂²×C₃×C₄	—	3	1	no	—
256	C₂²×C₃×C₄	—	3	2	no	—
257	C₂²×C₃×C₄	—	3	2	no	—
258	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
260	C₂×#67	C₂²×C₉	1	2	yes	—
261	C₂×#67	C₂²×C₉	1	2	yes	—
262	C₂×#67	C₂²×C₉	1	2	yes	—
263	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
264	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
265	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
266	#237	—	2	8	no	—
267	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
268	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
269	C₂×Dic₆	C₂²×C₉	1	2	yes	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	3	2	no	—
272	C₃×C₄⋊C₄	—	3	1	no	—
273	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
275	C₃×C₂²⋊C₄	—	2	2	no	—
276	C₃×C₂²⋊C₄	—	3	2	no	—
277	C₃×C₂²⋊C₄	—	3	2	no	—
278	C₃×C₂²⋊C₄	—	3	2	no	—
279	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
280	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
281	C₃×C₄²	—	3	1	no	—
282	C₃×C₄²	—	3	1	no	—
283	C₃×C₄²	—	3	1	no	—
284	C₃×C₄²	—	3	1	no	—
285	#217	C₂²×C₉	1	2	yes	—
286	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
287	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
288	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
289	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
290	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
291	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
292	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
293	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
294	C₂²×C₃²	—	2	1	no	—
295	C₂²×C₃²	—	2	1	no	—
296	C₂²×C₃²	—	2	2	no	—
297	C₂²×C₃²	—	2	2	no	—
298	C₂²×C₃²	—	2	2	no	—
299	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
300	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
301	C₂×C₃×D₃	—	2	2	no	—
302	C₂×C₃×D₃	—	2	2	no	—
303	C₂×C₃×D₃	—	2	2	no	—
304	C₃²×C₄	—	2	2	no	—
305	C₃²×C₄	—	2	1	no	—
306	C₃²×C₄	C₃×#41	1	2	yes	—
307	C₃×Dic₃	—	2	2	no	—
308	C₃×Dic₃	—	2	1	no	—
309	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
310	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
311	C₃×Dic₃	C₃×#41	1	2	yes	—
312	C₂²×C₉	—	2	1	no	—
313	C₂²×C₉	—	2	1	no	—
314	C₂²×C₉	—	2	2	no	—
315	C₂²×C₉	—	2	2	no	—
316	C₂²×C₉	—	2	2	no	—
317	C₂²×C₉	—	2	1	no	—
318	C₂²×C₉	—	2	2	no	—
319	C₂²×C₉	—	4	1	no	—
320	C₂²×C₉	—	4	1	no	—
321	C₂²×C₉	—	4	2	no	—
322	C₂²×C₉	—	4	2	no	—
323	C₂²×C₉	—	4	2	no	—
324	C₂²×C₉	—	6	2	no	—
325	C₂²×C₉	—	6	2	no	—
326	C₂²×C₉	—	6	2	no	—
327	C₂²×C₉	D₃×D₄	1	2	yes	—
328	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
329	C₄×C₉	—	2	2	no	—
330	C₄×C₉	—	2	1	no	—
331	C₄×C₉	—	2	2	no	—
332	C₄×C₉	—	3	2	no	—
333	C₄×C₉	—	3	2	no	—
334	C₄×C₉	—	3	2	no	—
335	C₄×C₉	—	4	1	no	—
336	C₄×C₉	—	4	2	no	—
337	C₄×C₉	—	6	2	no	—
338	C₄×C₉	—	6	1	no	—
339	C₄×C₉	#237	1	2	yes	complemented
340	C₂×#41	—	3	2	no	—
341	C₄⋊Q₈	—	3	1	no	—
342	#127	—	3	1	no	—
343	#124	—	3	2	no	—
344	#121	—	3	2	no	—
345	#121	—	3	1	no	—
346	#121	D₃×C₉	1	1	yes	characteristic, complemented
347	C₄×D₄	—	3	1	no	—
348	C₄×D₄	—	3	1	no	—
349	C₄×D₄	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₃×C₉	#532	1	1	yes	characteristic, complemented, Sylow
352	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	3	2	no	—
355	C₂³×C₃	C₂³×C₉	1	2	yes	—
356	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
357	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
358	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
359	C₂²×D₃	C₂³×C₉	1	2	yes	—
360	C₃×Q₈	—	6	4	no	—
361	C₃×D₄	—	2	4	no	—
362	C₃×D₄	—	2	4	no	—
363	C₃×D₄	—	2	2	no	—
364	C₃×D₄	—	2	2	no	—
365	C₃×D₄	—	4	2	no	—
366	C₃×D₄	—	4	4	no	—
367	C₃×D₄	—	6	4	no	—
368	C₃×D₄	—	6	4	no	—
369	C₃×D₄	—	6	4	no	—
370	C₃×D₄	—	6	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	3	1	no	—
377	C₂×C₃×C₄	—	3	1	no	—
378	C₂×C₃×C₄	—	3	1	no	—
379	C₂×C₃×C₄	—	3	4	no	—
380	C₂×C₃×C₄	—	3	1	no	—
381	C₂×C₃×C₄	—	3	2	no	—
382	C₂×C₃×C₄	—	4	2	no	—
383	C₂×C₃×C₄	—	6	4	no	—
384	C₂×C₃×C₄	—	6	2	no	—
385	C₂×C₃×C₄	—	6	4	no	—
386	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
388	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
391	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
392	#67	—	2	4	no	—
393	#67	—	2	4	no	—
394	#67	—	2	4	no	—
395	C₂×Dic₃	—	2	4	no	—
396	C₂×Dic₃	—	2	2	no	—
397	C₂×Dic₃	D₄×C₉	1	4	yes	complemented
398	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
399	C₂×Dic₃	C₂³×C₉	1	2	yes	—
400	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
401	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
402	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
403	D₁₂	—	2	2	no	—
404	C₄×D₃	—	2	4	no	—
405	Dic₆	—	2	4	no	—
406	C₂×C₃²	—	2	2	no	—
407	C₂×C₃²	—	4	2	no	—
408	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
409	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
410	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
411	C₃×D₃	—	4	2	no	—
412	C₂×C₉	—	2	2	no	—
413	C₂×C₉	—	2	1	no	—
414	C₂×C₉	—	2	1	no	—
415	C₂×C₉	—	2	1	no	—
416	C₂×C₉	—	4	2	no	—
417	C₂×C₉	—	4	2	no	—
418	C₂×C₉	—	8	2	no	—
419	C₂×C₉	—	12	2	no	—
420	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
421	C₂×C₉	C₂×#237	1	1	yes	characteristic
422	C₂×C₉	D₃×#41	1	1	yes	characteristic
423	#41	—	6	8	no	—
424	C₂×Q₈	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
430	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
436	C₄⋊C₄	—	3	2	no	—
437	C₄⋊C₄	—	3	1	no	—
438	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
439	C₂²⋊C₄	—	3	2	no	—
440	C₂²⋊C₄	—	3	2	no	—
441	C₂²⋊C₄	—	3	2	no	—
442	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
443	C₄²	—	3	1	no	—
444	C₄²	—	3	1	no	—
445	C₄²	—	3	1	no	—
446	C₄²	—	3	1	no	—
447	C₂²×C₃	—	2	1	no	—
448	C₂²×C₃	—	2	1	no	—
449	C₂²×C₃	—	2	1	no	—
450	C₂²×C₃	—	2	1	no	—
451	C₂²×C₃	—	2	2	no	—
452	C₂²×C₃	—	2	2	no	—
453	C₂²×C₃	—	2	2	no	—
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	2	1	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	4	1	no	—
460	C₂²×C₃	—	4	1	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	—	4	2	no	—
463	C₂²×C₃	—	4	2	no	—
464	C₂²×C₃	—	6	2	no	—
465	C₂²×C₃	—	6	2	no	—
466	C₂²×C₃	—	6	2	no	—
467	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
468	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
469	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
470	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
471	C₂×D₃	—	2	2	no	—
472	C₂×D₃	—	2	2	no	—
473	C₂×D₃	—	2	2	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	1	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	2	1	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	3	2	no	—
480	C₃×C₄	—	3	2	no	—
481	C₃×C₄	—	3	2	no	—
482	C₃×C₄	—	4	1	no	—
483	C₃×C₄	—	4	2	no	—
484	C₃×C₄	—	6	2	no	—
485	C₃×C₄	—	6	1	no	—
486	C₃×C₄	C₉×#41	1	2	yes	complemented
487	C₃×C₄	C₃×#237	1	2	yes	—
488	Dic₃	—	2	2	no	—
489	Dic₃	—	2	1	no	—
490	Dic₃	C₂×D₄×C₉	1	2	yes	—
491	Dic₃	C₂×D₄×C₉	1	2	yes	—
492	Dic₃	C₉×#41	1	2	yes	complemented
493	C₃²	C₃×#532	1	1	yes	characteristic
494	C₉	—	2	1	no	—
495	C₉	#5596	1	1	yes	characteristic, direct product factor
496	C₂³	—	3	2	no	—
497	C₂³	C₂²×D₃×C₉	1	2	yes	—
498	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
499	Q₈	—	6	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	2	2	no	—
502	D₄	—	6	4	no	—
503	D₄	—	6	4	no	—
504	D₄	—	6	4	no	—
505	D₄	—	6	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	3	1	no	—
508	C₂×C₄	—	3	1	no	—
509	C₂×C₄	—	3	1	no	—
510	C₂×C₄	—	3	4	no	—
511	C₂×C₄	—	3	1	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	6	4	no	—
514	C₂×C₄	—	6	4	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
518	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
519	C₂×C₃	—	2	2	no	—
520	C₂×C₃	—	2	2	no	—
521	C₂×C₃	—	2	1	no	—
522	C₂×C₃	—	2	1	no	—
523	C₂×C₃	—	2	1	no	—
524	C₂×C₃	—	4	2	no	—
525	C₂×C₃	—	4	2	no	—
526	C₂×C₃	—	4	2	no	—
527	C₂×C₃	—	8	2	no	—
528	C₂×C₃	—	12	2	no	—
529	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
530	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
531	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
532	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
533	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
534	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
535	D₃	—	4	2	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	6	2	no	—
542	C₂²	—	6	2	no	—
543	C₂²	—	6	2	no	—
544	C₂²	D₃×D₄×C₉	1	2	yes	—
545	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	1	no	—
548	C₄	—	3	2	no	—
549	C₄	—	3	2	no	—
550	C₄	—	3	2	no	—
551	C₄	—	6	2	no	—
552	C₄	—	6	1	no	—
553	C₄	C₉×#237	1	2	yes	complemented
554	C₃	—	2	1	no	—
555	C₃	C₉×#532	1	1	yes	characteristic, complemented
556	C₃	C₃×#5596	1	1	yes	characteristic
557	C₂	—	2	2	no	—
558	C₂	—	4	2	no	—
559	C₂	—	12	2	no	—
560	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
561	C₂	C₂×C₉×#237	1	1	yes	characteristic
562	C₂	D₃×C₉×#41	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×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5596	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#532
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#237	C₂	semidirect
2. C₃×C₉×#121	C₂	semidirect
3. C₉×#940	C₂	semidirect
4. C₉×#939	C₂	semidirect
5. D₄×C₉×Dic₃	C₂	semidirect
6. C₉×#930	C₂	semidirect
7. C₂×C₄×C₉×Dic₃	C₂	semidirect
8. C₉×#893	C₂	semidirect
9. C₉×#888	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#67⋊C₄	C₂	semidirect
56. C₉×#121	D₃	semidirect
75. C₂×C₉×Dic₃	D₄	semidirect
85. #5596	C₉	direct (N × H)
151. C₃×C₄×C₉	#41	semidirect
156. C₉×Dic₃	#41	semidirect
158. C₂×#237	C₂×C₉	semidirect
165. C₃×#121	C₂×C₉	semidirect
171. #940	C₂×C₉	semidirect
172. #939	C₂×C₉	semidirect
173. D₄×Dic₃	C₂×C₉	semidirect
174. #930	C₂×C₉	semidirect
175. C₂×C₄×Dic₃	C₂×C₉	semidirect
176. #893	C₂×C₉	semidirect
177. #888	C₂×C₉	semidirect
178. #885	C₂×C₉	semidirect
179. #67⋊C₄	C₂×C₉	semidirect
339. C₄×C₉	#237	semidirect
346. #121	D₃×C₉	semidirect
351. C₃×C₉	#532	semidirect
397. C₂×Dic₃	D₄×C₉	semidirect
486. C₃×C₄	C₉×#41	semidirect
492. Dic₃	C₉×#41	semidirect
495. C₉	#5596	direct (N × H)
553. C₄	C₉×#237	semidirect
555. C₃	C₉×#532	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#237	2
C₃×C₉×#121	2
C₉×#940	2
C₉×#939	2
D₄×C₉×Dic₃	2
C₉×#930	2
C₂×C₄×C₉×Dic₃	2
C₉×#893	2
C₉×#888	2
C₉×#885	2
C₉×#67⋊C₄	2
C₃×#5596	3
C₉×#532	3

Subgroups — C9×#5596 #13152797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5596 #13152797