Subgroups — C₉×#5656 #13153003

Order 1728.

1068 conjugacy classes of subgroups.

The subgroup lattice has 574 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#896	C₂	1	2	yes	maximal, complemented
7	C₉×#893	C₂	1	2	yes	maximal, complemented
8	C₉×#884	C₂	1	2	yes	maximal, complemented
9	C₉×#882	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₉×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5656	C₃	1	1	yes	maximal, characteristic
13	C₉×#525	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₉×#237	—	2	4	no	—
23	C₂×C₉×D₁₂	C₂²	1	2	yes	—
24	C₂×C₄×D₃×C₉	—	2	4	no	—
25	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
26	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
27	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₉×#217	C₂²	1	1	yes	characteristic
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
39	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
40	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
41	C₃²×#123	C₂×C₃	1	1	yes	characteristic
42	C₃×#937	C₂×C₃	1	1	yes	characteristic
43	C₃×#929	C₂×C₃	1	1	yes	characteristic
44	C₃×#896	C₂×C₃	1	2	yes	—
45	C₃×#893	C₂×C₃	1	2	yes	—
46	C₃×#884	C₂×C₃	1	2	yes	—
47	C₃×#882	C₂×C₃	1	1	yes	characteristic
48	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
49	C₃×#877	C₂×C₃	1	1	yes	characteristic
50	C₂×C₉×#41	—	3	1	no	—
51	C₂³×C₄×C₉	—	3	1	no	—
52	C₉×#123	—	2	1	no	—
53	C₉×#123	—	3	1	no	—
54	C₉×#123	D₃	1	1	yes	characteristic, complemented
55	C₉×C₂²⋊Q₈	—	3	2	no	—
56	C₉×#121	—	3	2	no	—
57	C₉×#120	—	3	1	no	—
58	C₉×#120	—	3	1	no	—
59	C₄×D₄×C₉	—	3	2	no	—
60	C₄×D₄×C₉	—	3	2	no	—
61	C₉×#117	—	3	1	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	—	2	2	no	—
65	C₂²×D₃×C₉	—	2	4	no	—
66	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
67	C₂²×D₃×C₉	C₂³	1	2	yes	—
68	C₃×D₄×C₉	—	2	2	no	—
69	C₂×C₃×C₄×C₉	—	2	2	no	—
70	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
72	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
73	C₉×#67	—	2	2	no	—
74	C₉×#67	—	2	4	no	—
75	C₉×#67	—	2	2	no	—
76	C₂×C₉×Dic₃	—	2	2	no	—
77	C₂×C₉×Dic₃	D₄	1	4	yes	complemented
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₉×Dic₃	C₂³	1	2	yes	—
80	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
82	C₉×D₁₂	—	2	4	no	—
83	C₄×D₃×C₉	—	2	4	no	—
84	C₄×D₃×C₉	—	2	4	no	—
85	C₄×D₃×C₉	—	2	2	no	—
86	C₉×Dic₆	—	2	2	no	—
87	C₃×#525	—	3	1	no	—
88	#5656	C₉	1	1	yes	characteristic, direct product factor
89	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
93	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
96	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
97	C₃×#237	—	2	4	no	—
98	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
99	C₂×C₃×C₄×D₃	—	2	4	no	—
100	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
104	C₂⁴×C₉	—	3	1	no	—
105	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₃×#217	C₂²×C₃	1	1	yes	characteristic
109	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
110	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
114	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
115	C₉×#41	—	6	4	no	—
116	C₂×Q₈×C₉	—	3	1	no	—
117	C₂×D₄×C₉	—	2	1	no	—
118	C₂×D₄×C₉	—	3	2	no	—
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	3	1	no	—
121	C₂×D₄×C₉	—	3	2	no	—
122	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
123	C₂²×C₄×C₉	—	2	1	no	—
124	C₂²×C₄×C₉	—	3	1	no	—
125	C₂²×C₄×C₉	—	3	1	no	—
126	C₂²×C₄×C₉	—	3	2	no	—
127	C₂²×C₄×C₉	—	3	1	no	—
128	C₂²×C₄×C₉	—	3	2	no	—
129	C₂²×C₄×C₉	—	6	4	no	—
130	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
131	C₉×C₄⋊C₄	—	2	2	no	—
132	C₉×C₄⋊C₄	—	3	2	no	—
133	C₉×C₄⋊C₄	—	3	2	no	—
134	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
135	C₉×C₂²⋊C₄	—	2	1	no	—
136	C₉×C₂²⋊C₄	—	2	2	no	—
137	C₉×C₂²⋊C₄	—	3	1	no	—
138	C₉×C₂²⋊C₄	—	3	2	no	—
139	C₉×C₂²⋊C₄	—	3	2	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
142	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
143	C₄²×C₉	—	3	2	no	—
144	C₂²×C₃×C₉	—	2	2	no	—
145	C₂²×C₃×C₉	—	2	1	no	—
146	C₂²×C₃×C₉	—	2	2	no	—
147	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
148	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
149	C₂×D₃×C₉	—	2	8	no	—
150	C₂×D₃×C₉	—	2	2	no	—
151	C₂×D₃×C₉	—	2	2	no	—
152	C₂×D₃×C₉	—	2	1	no	—
153	C₂×D₃×C₉	—	2	2	no	—
154	C₂×D₃×C₉	#41	1	4	yes	complemented
155	C₃×C₄×C₉	—	2	1	no	—
156	C₃×C₄×C₉	—	2	2	no	—
157	C₃×C₄×C₉	—	2	2	no	—
158	C₉×Dic₃	—	2	1	no	—
159	C₉×Dic₃	—	2	2	no	—
160	C₉×Dic₃	C₂×D₄	1	2	yes	—
161	C₉×Dic₃	C₂×D₄	1	2	yes	—
162	C₂×C₃×#41	—	3	1	no	—
163	C₂³×C₃×C₄	—	3	1	no	—
164	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
165	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
166	C₃×#123	—	2	1	no	—
167	C₃×#123	—	3	1	no	—
168	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
169	C₃×#123	C₃×D₃	1	1	yes	characteristic
170	C₃×C₂²⋊Q₈	—	3	2	no	—
171	C₃×#121	—	3	2	no	—
172	C₃×#120	—	3	1	no	—
173	C₃×#120	—	3	1	no	—
174	C₃×C₄×D₄	—	3	2	no	—
175	C₃×C₄×D₄	—	3	2	no	—
176	C₃×#117	—	3	1	no	—
177	#937	C₂×C₉	1	1	yes	characteristic, complemented
178	#929	C₂×C₉	1	1	yes	characteristic, complemented
179	#896	C₂×C₉	1	2	yes	complemented
180	#893	C₂×C₉	1	2	yes	complemented
181	#884	C₂×C₉	1	2	yes	complemented
182	#882	C₂×C₉	1	1	yes	characteristic, complemented
183	#67⋊C₄	C₂×C₉	1	2	yes	complemented
184	#877	C₂×C₉	1	1	yes	characteristic, complemented
185	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
186	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
187	C₂²×C₃×D₃	—	2	2	no	—
188	C₂²×C₃×D₃	—	2	4	no	—
189	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
191	C₃²×D₄	—	2	2	no	—
192	C₂×C₃²×C₄	—	2	2	no	—
193	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
194	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
195	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₃×#67	—	2	2	no	—
197	C₃×#67	—	2	4	no	—
198	C₃×#67	—	2	2	no	—
199	C₂×C₃×Dic₃	—	2	2	no	—
200	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
201	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
202	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
205	C₃×D₁₂	—	2	4	no	—
206	C₃×C₄×D₃	—	2	4	no	—
207	C₃×C₄×D₃	—	2	4	no	—
208	C₃×C₄×D₃	—	2	2	no	—
209	C₃×Dic₆	—	2	2	no	—
210	C₂³×C₉	—	2	1	no	—
211	C₂³×C₉	—	2	1	no	—
212	C₂³×C₉	—	3	2	no	—
213	C₂³×C₉	—	3	1	no	—
214	C₂³×C₉	—	6	4	no	—
215	C₂³×C₉	—	6	2	no	—
216	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
217	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
218	Q₈×C₉	—	6	2	no	—
219	D₄×C₉	—	2	2	no	—
220	D₄×C₉	—	4	2	no	—
221	D₄×C₉	—	6	4	no	—
222	D₄×C₉	—	6	2	no	—
223	D₄×C₉	—	6	4	no	—
224	D₄×C₉	—	6	2	no	—
225	C₂×C₄×C₉	—	2	2	no	—
226	C₂×C₄×C₉	—	2	2	no	—
227	C₂×C₄×C₉	—	2	2	no	—
228	C₂×C₄×C₉	—	2	1	no	—
229	C₂×C₄×C₉	—	3	4	no	—
230	C₂×C₄×C₉	—	3	1	no	—
231	C₂×C₄×C₉	—	3	1	no	—
232	C₂×C₄×C₉	—	3	2	no	—
233	C₂×C₄×C₉	—	3	1	no	—
234	C₂×C₄×C₉	—	4	2	no	—
235	C₂×C₄×C₉	—	6	4	no	—
236	C₂×C₄×C₉	—	6	4	no	—
237	C₂×C₄×C₉	—	6	2	no	—
238	C₂×C₄×C₉	—	6	2	no	—
239	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
240	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
241	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
242	#525	—	3	1	no	Sylow
243	C₂×C₃×C₉	—	2	2	no	—
244	C₂×C₃×C₉	—	4	1	no	—
245	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₃×C₉	C₂×#41	1	2	yes	—
247	D₃×C₉	—	2	4	no	—
248	D₃×C₉	—	4	1	no	—
249	C₂⁴×C₃	—	3	1	no	—
250	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
251	C₃×#41	—	6	4	no	—
252	C₂×C₃×Q₈	—	3	1	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×C₃×D₄	—	3	2	no	—
255	C₂×C₃×D₄	—	3	1	no	—
256	C₂×C₃×D₄	—	3	1	no	—
257	C₂×C₃×D₄	—	3	2	no	—
258	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
259	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
260	C₂²×C₃×C₄	—	2	1	no	—
261	C₂²×C₃×C₄	—	3	1	no	—
262	C₂²×C₃×C₄	—	3	1	no	—
263	C₂²×C₃×C₄	—	3	2	no	—
264	C₂²×C₃×C₄	—	3	1	no	—
265	C₂²×C₃×C₄	—	3	2	no	—
266	C₂²×C₃×C₄	—	6	4	no	—
267	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
269	C₂×#67	C₂²×C₉	1	2	yes	—
270	C₂×#67	C₂²×C₉	1	1	yes	characteristic
271	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
272	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
273	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
274	#237	—	2	4	no	—
275	C₂×D₁₂	C₂²×C₉	1	2	yes	—
276	C₂×C₄×D₃	—	2	4	no	—
277	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
278	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
279	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
280	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	—	3	2	no	—
283	C₃×C₄⋊C₄	—	3	2	no	—
284	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
285	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
286	C₃×C₂²⋊C₄	—	2	1	no	—
287	C₃×C₂²⋊C₄	—	2	2	no	—
288	C₃×C₂²⋊C₄	—	3	1	no	—
289	C₃×C₂²⋊C₄	—	3	2	no	—
290	C₃×C₂²⋊C₄	—	3	2	no	—
291	C₃×C₂²⋊C₄	—	3	2	no	—
292	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
293	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
294	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
295	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
296	C₃×C₄²	—	3	2	no	—
297	#217	C₂²×C₉	1	1	yes	characteristic
298	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
299	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
300	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
301	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
302	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
303	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
304	C₂²×C₃²	—	2	2	no	—
305	C₂²×C₃²	—	2	1	no	—
306	C₂²×C₃²	—	2	2	no	—
307	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
308	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
309	C₂×C₃×D₃	—	2	8	no	—
310	C₂×C₃×D₃	—	2	2	no	—
311	C₂×C₃×D₃	—	2	2	no	—
312	C₂×C₃×D₃	—	2	1	no	—
313	C₂×C₃×D₃	—	2	2	no	—
314	C₂×C₃×D₃	C₃×#41	1	4	yes	—
315	C₃²×C₄	—	2	1	no	—
316	C₃²×C₄	—	2	2	no	—
317	C₃²×C₄	—	2	2	no	—
318	C₃×Dic₃	—	2	1	no	—
319	C₃×Dic₃	—	2	2	no	—
320	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
321	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
322	C₂²×C₉	—	2	2	no	—
323	C₂²×C₉	—	2	1	no	—
324	C₂²×C₉	—	2	2	no	—
325	C₂²×C₉	—	2	1	no	—
326	C₂²×C₉	—	2	2	no	—
327	C₂²×C₉	—	3	4	no	—
328	C₂²×C₉	—	4	2	no	—
329	C₂²×C₉	—	4	1	no	—
330	C₂²×C₉	—	4	2	no	—
331	C₂²×C₉	—	6	8	no	—
332	C₂²×C₉	—	6	2	no	—
333	C₂²×C₉	—	6	2	no	—
334	C₂²×C₉	—	6	1	no	—
335	C₂²×C₉	—	6	2	no	—
336	C₂²×C₉	D₃×D₄	1	2	yes	—
337	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
338	C₄×C₉	—	2	2	no	—
339	C₄×C₉	—	2	1	no	—
340	C₄×C₉	—	2	2	no	—
341	C₄×C₉	—	3	2	no	—
342	C₄×C₉	—	3	2	no	—
343	C₄×C₉	—	4	2	no	—
344	C₄×C₉	—	4	2	no	—
345	C₄×C₉	—	4	1	no	—
346	C₄×C₉	—	6	1	no	—
347	C₄×C₉	—	6	2	no	—
348	C₂×#41	—	3	1	no	—
349	C₂³×C₄	—	3	1	no	—
350	#123	—	3	1	no	—
351	#123	D₃×C₉	1	1	yes	characteristic, complemented
352	C₂²⋊Q₈	—	3	2	no	—
353	#121	—	3	2	no	—
354	#120	—	3	1	no	—
355	#120	—	3	1	no	—
356	C₄×D₄	—	3	2	no	—
357	C₄×D₄	—	3	2	no	—
358	#117	—	3	1	no	—
359	C₃×C₉	#525	1	1	yes	characteristic, complemented, Sylow
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	3	2	no	—
363	C₂³×C₃	—	3	1	no	—
364	C₂³×C₃	—	6	4	no	—
365	C₂³×C₃	—	6	2	no	—
366	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
367	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
368	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
369	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
370	C₂²×D₃	—	2	2	no	—
371	C₂²×D₃	—	2	4	no	—
372	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
373	C₂²×D₃	C₂³×C₉	1	2	yes	—
374	C₃×Q₈	—	6	2	no	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	4	2	no	—
378	C₃×D₄	—	6	4	no	—
379	C₃×D₄	—	6	2	no	—
380	C₃×D₄	—	6	4	no	—
381	C₃×D₄	—	6	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	3	1	no	—
388	C₂×C₃×C₄	—	3	1	no	—
389	C₂×C₃×C₄	—	3	4	no	—
390	C₂×C₃×C₄	—	3	2	no	—
391	C₂×C₃×C₄	—	3	1	no	—
392	C₂×C₃×C₄	—	4	2	no	—
393	C₂×C₃×C₄	—	6	4	no	—
394	C₂×C₃×C₄	—	6	4	no	—
395	C₂×C₃×C₄	—	6	2	no	—
396	C₂×C₃×C₄	—	6	2	no	—
397	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
398	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
399	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
401	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
403	#67	—	2	2	no	—
404	#67	—	2	4	no	—
405	#67	—	2	2	no	—
406	C₂×Dic₃	—	2	2	no	—
407	C₂×Dic₃	D₄×C₉	1	4	yes	complemented
408	C₂×Dic₃	C₂³×C₉	1	2	yes	—
409	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
410	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
411	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
412	D₁₂	—	2	4	no	—
413	C₄×D₃	—	2	4	no	—
414	C₄×D₃	—	2	4	no	—
415	C₄×D₃	—	2	2	no	—
416	Dic₆	—	2	2	no	—
417	C₂×C₃²	—	2	2	no	—
418	C₂×C₃²	—	4	1	no	—
419	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
420	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
421	C₃×D₃	—	2	4	no	—
422	C₃×D₃	—	4	1	no	—
423	C₂×C₉	—	2	2	no	—
424	C₂×C₉	—	2	1	no	—
425	C₂×C₉	—	2	2	no	—
426	C₂×C₉	—	4	2	no	—
427	C₂×C₉	—	4	1	no	—
428	C₂×C₉	—	6	4	no	—
429	C₂×C₉	—	8	1	no	—
430	C₂×C₉	—	12	1	no	—
431	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
432	C₂×C₉	D₃×#41	1	2	yes	—
433	C₂⁴	—	3	1	no	—
434	#41	—	6	4	no	—
435	C₂×Q₈	—	3	1	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	3	1	no	—
438	C₂×D₄	—	3	1	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	6	4	no	—
447	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
451	C₂²⋊C₄	—	3	1	no	—
452	C₂²⋊C₄	—	3	2	no	—
453	C₂²⋊C₄	—	3	2	no	—
454	C₂²⋊C₄	—	3	2	no	—
455	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
456	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
457	C₄²	—	3	2	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	3	4	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	—	4	1	no	—
469	C₂²×C₃	—	4	2	no	—
470	C₂²×C₃	—	6	8	no	—
471	C₂²×C₃	—	6	2	no	—
472	C₂²×C₃	—	6	2	no	—
473	C₂²×C₃	—	6	1	no	—
474	C₂²×C₃	—	6	2	no	—
475	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
476	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
477	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
478	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
479	C₂×D₃	—	2	8	no	—
480	C₂×D₃	—	2	2	no	—
481	C₂×D₃	—	2	2	no	—
482	C₂×D₃	—	2	1	no	—
483	C₂×D₃	—	2	2	no	—
484	C₂×D₃	C₉×#41	1	4	yes	complemented
485	C₃×C₄	—	2	2	no	—
486	C₃×C₄	—	2	1	no	—
487	C₃×C₄	—	2	2	no	—
488	C₃×C₄	—	2	1	no	—
489	C₃×C₄	—	2	2	no	—
490	C₃×C₄	—	2	2	no	—
491	C₃×C₄	—	3	2	no	—
492	C₃×C₄	—	3	2	no	—
493	C₃×C₄	—	4	2	no	—
494	C₃×C₄	—	4	1	no	—
495	C₃×C₄	—	4	2	no	—
496	C₃×C₄	—	6	1	no	—
497	C₃×C₄	—	6	2	no	—
498	Dic₃	—	2	1	no	—
499	Dic₃	—	2	2	no	—
500	Dic₃	C₂×D₄×C₉	1	2	yes	—
501	Dic₃	C₂×D₄×C₉	1	2	yes	—
502	C₃²	C₃×#525	1	1	yes	characteristic
503	C₉	—	2	1	no	—
504	C₉	#5656	1	1	yes	characteristic, direct product factor
505	C₂³	—	3	2	no	—
506	C₂³	—	3	1	no	—
507	C₂³	—	6	4	no	—
508	C₂³	—	6	2	no	—
509	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
510	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
511	Q₈	—	6	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	6	4	no	—
514	D₄	—	6	2	no	—
515	D₄	—	6	4	no	—
516	D₄	—	6	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	3	1	no	—
519	C₂×C₄	—	3	1	no	—
520	C₂×C₄	—	3	4	no	—
521	C₂×C₄	—	3	2	no	—
522	C₂×C₄	—	3	1	no	—
523	C₂×C₄	—	6	4	no	—
524	C₂×C₄	—	6	4	no	—
525	C₂×C₄	—	6	2	no	—
526	C₂×C₄	—	6	2	no	—
527	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
528	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
530	C₂×C₃	—	2	2	no	—
531	C₂×C₃	—	2	2	no	—
532	C₂×C₃	—	2	1	no	—
533	C₂×C₃	—	2	2	no	—
534	C₂×C₃	—	4	2	no	—
535	C₂×C₃	—	4	1	no	—
536	C₂×C₃	—	4	1	no	—
537	C₂×C₃	—	6	4	no	—
538	C₂×C₃	—	8	1	no	—
539	C₂×C₃	—	12	1	no	—
540	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
541	C₂×C₃	C₂×C₉×#41	1	2	yes	—
542	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
543	C₂×C₃	C₃×D₃×#41	1	2	yes	—
544	D₃	—	2	4	no	—
545	D₃	—	4	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	3	4	no	—
550	C₂²	—	6	8	no	—
551	C₂²	—	6	2	no	—
552	C₂²	—	6	2	no	—
553	C₂²	—	6	1	no	—
554	C₂²	—	6	2	no	—
555	C₂²	D₃×D₄×C₉	1	2	yes	—
556	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	2	no	—
560	C₄	—	3	2	no	—
561	C₄	—	3	2	no	—
562	C₄	—	6	1	no	—
563	C₄	—	6	2	no	—
564	C₃	—	2	1	no	—
565	C₃	C₉×#525	1	1	yes	characteristic, complemented
566	C₃	C₃×#5656	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	6	4	no	—
570	C₂	—	12	1	no	—
571	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
572	C₂	D₃×C₉×#41	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×#123	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5656	C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#237	C₂	semidirect
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₉×#937	C₂	semidirect
5. C₉×#929	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#893	C₂	semidirect
8. C₉×#884	C₂	semidirect
9. C₉×#882	C₂	semidirect
10. C₉×#67⋊C₄	C₂	semidirect
11. C₉×#877	C₂	semidirect
19. C₂×C₉×#67	C₂²	semidirect
21. C₂²×C₉×Dic₃	C₂²	semidirect
27. C₂×C₄×D₃×C₉	C₂²	semidirect
28. C₂×C₉×Dic₆	C₂²	semidirect
29. C₃×C₉×C₄⋊C₄	C₂²	semidirect
31. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×Dic₃⋊C₄	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
54. C₉×#123	D₃	semidirect
77. C₂×C₉×Dic₃	D₄	semidirect
88. #5656	C₉	direct (N × H)
134. C₉×C₄⋊C₄	C₂×D₃	semidirect
142. C₉×C₂²⋊C₄	C₂×D₃	semidirect
154. C₂×D₃×C₉	#41	semidirect
164. C₂×#237	C₂×C₉	semidirect
165. C₂²×C₄×D₃	C₂×C₉	semidirect
168. C₃×#123	C₂×C₉	semidirect
177. #937	C₂×C₉	semidirect
178. #929	C₂×C₉	semidirect
179. #896	C₂×C₉	semidirect
180. #893	C₂×C₉	semidirect
181. #884	C₂×C₉	semidirect
182. #882	C₂×C₉	semidirect
183. #67⋊C₄	C₂×C₉	semidirect
184. #877	C₂×C₉	semidirect
271. C₂×#67	C₂²×C₉	semidirect
273. C₂²×Dic₃	C₂²×C₉	semidirect
279. C₂×C₄×D₃	C₂²×C₉	semidirect
280. C₂×Dic₆	C₂²×C₉	semidirect
284. C₃×C₄⋊C₄	C₂²×C₉	semidirect
293. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
300. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
301. Dic₃⋊C₄	C₂²×C₉	semidirect
302. Dic₃⋊C₄	C₂²×C₉	semidirect
303. C₄×Dic₃	C₂²×C₉	semidirect
351. #123	D₃×C₉	semidirect
359. C₃×C₉	#525	semidirect
407. C₂×Dic₃	D₄×C₉	semidirect
450. C₄⋊C₄	C₂×D₃×C₉	semidirect
456. C₂²⋊C₄	C₂×D₃×C₉	semidirect
484. C₂×D₃	C₉×#41	semidirect
504. C₉	#5656	direct (N × H)
565. C₃	C₉×#525	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
C₂²×C₄×D₃×C₉	2
C₃×C₉×#123	2
C₉×#937	2
C₉×#929	2
C₉×#896	2
C₉×#893	2
C₉×#884	2
C₉×#882	2
C₉×#67⋊C₄	2
C₉×#877	2
C₃×#5656	3
C₉×#525	3

Subgroups — C9×#5656 #13153003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5656 #13153003