Subgroups — D₃×C₉×#123 #13153023

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic
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×#935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#894	C₂	1	2	yes	maximal, complemented
7	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#883	C₂	1	2	yes	maximal, complemented
10	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	D₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₃×#123	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#123	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
15	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₉×#67	C₂²	1	1	yes	characteristic
19	C₂×C₉×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
21	D₃×D₄×C₉	—	2	4	no	—
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₃×C₉	—	2	4	no	—
24	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
27	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
28	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₉×#217	C₂²	1	1	yes	characteristic, complemented
32	C₉×#217	C₂²	1	2	yes	complemented
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₃×D₃×D₄	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×#935	C₂×C₃	1	1	yes	characteristic
43	C₃×#929	C₂×C₃	1	1	yes	characteristic
44	C₃×#894	C₂×C₃	1	2	yes	—
45	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
46	C₃×#886	C₂×C₃	1	1	yes	characteristic
47	C₃×#883	C₂×C₃	1	2	yes	—
48	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
49	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂²×D₄×C₉	—	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	—	3	1	no	—
55	C₉×#123	—	3	2	no	—
56	C₉×#123	—	3	2	no	—
57	C₉×#123	—	3	1	no	—
58	C₉×#123	D₃	1	1	yes	characteristic, direct product factor
59	C₂×C₉×C₄⋊C₄	—	3	2	no	—
60	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
61	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	—	2	4	no	—
65	C₂²×D₃×C₉	—	2	2	no	—
66	C₂²×D₃×C₉	—	2	4	no	—
67	C₂²×D₃×C₉	D₄	1	4	yes	—
68	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
69	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
70	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
71	C₃×D₄×C₉	—	2	2	no	—
72	C₂×C₃×C₄×C₉	—	2	2	no	—
73	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
74	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
76	C₉×#67	—	2	2	no	—
77	C₉×#67	—	2	2	no	—
78	C₂×C₉×Dic₃	—	2	2	no	—
79	C₂×C₉×Dic₃	C₂³	1	2	yes	—
80	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₉×Dic₃	C₂³	1	2	yes	—
82	C₉×D₁₂	—	2	2	no	—
83	C₄×D₃×C₉	—	2	4	no	—
84	C₄×D₃×C₉	—	2	4	no	—
85	C₄×D₃×C₉	—	2	2	no	—
86	C₄×D₃×C₉	—	2	4	no	—
87	C₂×C₃×#123	—	3	1	no	—
88	D₃×#123	C₉	1	1	yes	characteristic, direct product factor
89	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
90	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
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	C₃×D₃×D₄	—	2	4	no	—
97	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄×D₃	—	2	4	no	—
99	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
103	C₂⁴×C₉	—	3	1	no	—
104	C₂⁴×C₉	—	3	1	no	—
105	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₃×#217	C₂²×C₃	1	2	yes	—
109	C₃×#217	C₂²×C₃	1	1	yes	characteristic
110	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
113	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
114	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
115	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
116	C₂×D₄×C₉	—	2	1	no	—
117	C₂×D₄×C₉	—	3	1	no	—
118	C₂×D₄×C₉	—	3	1	no	—
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	6	4	no	—
121	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
122	C₂²×C₄×C₉	—	2	1	no	—
123	C₂²×C₄×C₉	—	3	1	no	—
124	C₂²×C₄×C₉	—	3	2	no	—
125	C₂²×C₄×C₉	—	3	2	no	—
126	C₂²×C₄×C₉	—	3	1	no	—
127	C₂²×C₄×C₉	—	3	2	no	—
128	C₂²×C₄×C₉	—	6	4	no	—
129	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
130	C₉×C₄⋊C₄	—	2	2	no	—
131	C₉×C₄⋊C₄	—	3	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	—	3	2	no	—
142	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
143	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
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	2	no	—
150	C₂×D₃×C₉	—	2	8	no	—
151	C₂×D₃×C₉	—	2	1	no	—
152	C₂×D₃×C₉	—	2	2	no	—
153	C₂×D₃×C₉	—	4	4	no	—
154	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
155	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
156	C₂×D₃×C₉	#41	1	4	yes	—
157	C₃×C₄×C₉	—	2	2	no	—
158	C₃×C₄×C₉	—	2	1	no	—
159	C₃×C₄×C₉	—	2	2	no	—
160	C₉×Dic₃	—	2	2	no	—
161	C₉×Dic₃	—	2	1	no	—
162	C₉×Dic₃	—	2	2	no	—
163	C₂²×C₃×D₄	—	3	1	no	—
164	C₂³×C₃×C₄	—	3	1	no	—
165	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic
166	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
167	C₃×#123	—	2	1	no	—
168	C₃×#123	—	3	1	no	—
169	C₃×#123	—	3	1	no	—
170	C₃×#123	—	3	2	no	—
171	C₃×#123	—	3	2	no	—
172	C₃×#123	—	3	1	no	—
173	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
174	C₃×#123	C₃×D₃	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	—	3	2	no	—
176	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
177	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
178	#935	C₂×C₉	1	1	yes	characteristic, complemented
179	#929	C₂×C₉	1	1	yes	characteristic, complemented
180	#894	C₂×C₉	1	2	yes	complemented
181	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
182	#886	C₂×C₉	1	1	yes	characteristic, complemented
183	#883	C₂×C₉	1	2	yes	complemented
184	D₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
185	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
186	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
187	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₃×D₃	—	2	4	no	—
189	C₂²×C₃×D₃	—	2	2	no	—
190	C₂²×C₃×D₃	—	2	4	no	—
191	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
192	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
195	C₃²×D₄	—	2	2	no	—
196	C₂×C₃²×C₄	—	2	2	no	—
197	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
199	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
200	C₃×#67	—	2	2	no	—
201	C₃×#67	—	2	2	no	—
202	C₂×C₃×Dic₃	—	2	2	no	—
203	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
205	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
206	C₃×D₁₂	—	2	2	no	—
207	C₃×C₄×D₃	—	2	4	no	—
208	C₃×C₄×D₃	—	2	4	no	—
209	C₃×C₄×D₃	—	2	2	no	—
210	C₃×C₄×D₃	—	2	4	no	—
211	C₂³×C₉	—	2	1	no	—
212	C₂³×C₉	—	2	1	no	—
213	C₂³×C₉	—	3	1	no	—
214	C₂³×C₉	—	3	4	no	—
215	C₂³×C₉	—	3	1	no	—
216	C₂³×C₉	—	3	1	no	—
217	C₂³×C₉	—	6	4	no	—
218	C₂³×C₉	—	6	2	no	—
219	C₂³×C₉	—	6	4	no	—
220	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
221	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
222	D₄×C₉	—	2	2	no	—
223	D₄×C₉	—	4	2	no	—
224	D₄×C₉	—	6	2	no	—
225	D₄×C₉	—	6	2	no	—
226	D₄×C₉	—	6	2	no	—
227	C₂×C₄×C₉	—	2	2	no	—
228	C₂×C₄×C₉	—	2	2	no	—
229	C₂×C₄×C₉	—	2	2	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	3	2	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	4	no	—
238	C₂×C₄×C₉	—	6	2	no	—
239	C₂×C₄×C₉	—	6	2	no	—
240	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
241	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
242	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
243	C₂×#123	—	3	1	no	Sylow
244	C₂×C₃×C₉	—	2	2	no	—
245	C₂×C₃×C₉	—	4	1	no	—
246	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₃×C₉	C₂×#41	1	2	yes	—
248	D₃×C₉	—	2	2	no	—
249	D₃×C₉	—	4	1	no	—
250	D₃×C₉	#123	1	4	yes	direct product factor
251	C₂⁴×C₃	—	3	1	no	—
252	C₂⁴×C₃	—	3	1	no	—
253	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
254	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
255	C₂×C₃×D₄	—	2	1	no	—
256	C₂×C₃×D₄	—	3	1	no	—
257	C₂×C₃×D₄	—	3	1	no	—
258	C₂×C₃×D₄	—	3	1	no	—
259	C₂×C₃×D₄	—	6	4	no	—
260	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
261	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	—	3	1	no	—
264	C₂²×C₃×C₄	—	3	2	no	—
265	C₂²×C₃×C₄	—	3	2	no	—
266	C₂²×C₃×C₄	—	3	1	no	—
267	C₂²×C₃×C₄	—	3	2	no	—
268	C₂²×C₃×C₄	—	6	4	no	—
269	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
270	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
271	C₂×#67	C₂²×C₉	1	1	yes	characteristic
272	C₂×#67	C₂²×C₉	1	1	yes	characteristic
273	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
274	D₃×D₄	—	2	4	no	—
275	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
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
280	C₂×C₄×D₃	C₂²×C₉	1	2	yes	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	—	3	2	no	—
285	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
286	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₂²⋊C₄	—	2	2	no	—
289	C₃×C₂²⋊C₄	—	3	1	no	—
290	C₃×C₂²⋊C₄	—	3	2	no	—
291	C₃×C₂²⋊C₄	—	3	2	no	—
292	C₃×C₂²⋊C₄	—	3	2	no	—
293	C₃×C₂²⋊C₄	—	3	2	no	—
294	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
295	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
296	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
297	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
298	#217	C₂²×C₉	1	2	yes	complemented
299	#217	C₂²×C₉	1	1	yes	characteristic, complemented
300	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
301	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
302	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
303	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
304	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
305	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
306	C₂²×C₃²	—	2	2	no	—
307	C₂²×C₃²	—	2	1	no	—
308	C₂²×C₃²	—	2	2	no	—
309	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
310	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
311	C₂×C₃×D₃	—	2	2	no	—
312	C₂×C₃×D₃	—	2	8	no	—
313	C₂×C₃×D₃	—	2	1	no	—
314	C₂×C₃×D₃	—	2	2	no	—
315	C₂×C₃×D₃	—	4	4	no	—
316	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
317	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
318	C₂×C₃×D₃	C₃×#41	1	4	yes	—
319	C₃²×C₄	—	2	2	no	—
320	C₃²×C₄	—	2	1	no	—
321	C₃²×C₄	—	2	2	no	—
322	C₃×Dic₃	—	2	2	no	—
323	C₃×Dic₃	—	2	1	no	—
324	C₃×Dic₃	—	2	2	no	—
325	C₂²×C₉	—	2	2	no	—
326	C₂²×C₉	—	2	1	no	—
327	C₂²×C₉	—	2	2	no	—
328	C₂²×C₉	—	2	1	no	—
329	C₂²×C₉	—	2	2	no	—
330	C₂²×C₉	—	3	2	no	—
331	C₂²×C₉	—	3	4	no	—
332	C₂²×C₉	—	3	2	no	—
333	C₂²×C₉	—	4	2	no	—
334	C₂²×C₉	—	4	1	no	—
335	C₂²×C₉	—	4	2	no	—
336	C₂²×C₉	—	6	8	no	—
337	C₂²×C₉	—	6	2	no	—
338	C₂²×C₉	—	6	1	no	—
339	C₂²×C₉	—	6	2	no	—
340	C₂²×C₉	—	12	4	no	—
341	C₂²×C₉	D₃×D₄	1	2	yes	—
342	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
343	C₄×C₉	—	2	2	no	—
344	C₄×C₉	—	2	1	no	—
345	C₄×C₉	—	2	2	no	—
346	C₄×C₉	—	4	2	no	—
347	C₄×C₉	—	4	2	no	—
348	C₄×C₉	—	4	1	no	—
349	C₄×C₉	—	6	2	no	—
350	C₄×C₉	—	6	1	no	—
351	C₄×C₉	—	6	2	no	—
352	C₂²×D₄	—	3	1	no	—
353	C₂³×C₄	—	3	1	no	—
354	#123	—	3	1	no	—
355	#123	—	3	1	no	—
356	#123	—	3	2	no	—
357	#123	—	3	2	no	—
358	#123	—	3	1	no	—
359	#123	D₃×C₉	1	1	yes	characteristic, direct product factor
360	C₂×C₄⋊C₄	—	3	2	no	—
361	C₂×C₂²⋊C₄	—	3	1	no	—
362	C₂×C₂²⋊C₄	—	3	2	no	—
363	C₃×C₉	C₂×#123	1	1	yes	characteristic, complemented, Sylow
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	—	3	1	no	—
367	C₂³×C₃	—	3	1	no	—
368	C₂³×C₃	—	3	4	no	—
369	C₂³×C₃	—	3	1	no	—
370	C₂³×C₃	—	6	4	no	—
371	C₂³×C₃	—	6	2	no	—
372	C₂³×C₃	—	6	4	no	—
373	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
374	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
375	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
376	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
377	C₂²×D₃	—	2	4	no	—
378	C₂²×D₃	—	2	2	no	—
379	C₂²×D₃	—	2	4	no	—
380	C₂²×D₃	D₄×C₉	1	4	yes	—
381	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
382	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
383	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
384	C₃×D₄	—	2	2	no	—
385	C₃×D₄	—	2	2	no	—
386	C₃×D₄	—	4	2	no	—
387	C₃×D₄	—	6	2	no	—
388	C₃×D₄	—	6	2	no	—
389	C₃×D₄	—	6	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	3	2	no	—
396	C₂×C₃×C₄	—	3	2	no	—
397	C₂×C₃×C₄	—	3	1	no	—
398	C₂×C₃×C₄	—	4	2	no	—
399	C₂×C₃×C₄	—	6	4	no	—
400	C₂×C₃×C₄	—	6	4	no	—
401	C₂×C₃×C₄	—	6	4	no	—
402	C₂×C₃×C₄	—	6	2	no	—
403	C₂×C₃×C₄	—	6	2	no	—
404	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
406	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
407	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
408	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
409	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
410	#67	—	2	2	no	—
411	#67	—	2	2	no	—
412	C₂×Dic₃	—	2	2	no	—
413	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
414	C₂×Dic₃	C₂³×C₉	1	2	yes	—
415	C₂×Dic₃	C₂³×C₉	1	2	yes	—
416	D₁₂	—	2	2	no	—
417	C₄×D₃	—	2	4	no	—
418	C₄×D₃	—	2	4	no	—
419	C₄×D₃	—	2	2	no	—
420	C₄×D₃	—	2	4	no	—
421	C₂×C₃²	—	2	2	no	—
422	C₂×C₃²	—	4	1	no	—
423	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
424	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
425	C₃×D₃	—	2	2	no	—
426	C₃×D₃	—	4	1	no	—
427	C₃×D₃	C₃×#123	1	4	yes	—
428	C₂×C₉	—	2	2	no	—
429	C₂×C₉	—	2	1	no	—
430	C₂×C₉	—	2	2	no	—
431	C₂×C₉	—	3	4	no	—
432	C₂×C₉	—	4	2	no	—
433	C₂×C₉	—	4	1	no	—
434	C₂×C₉	—	6	2	no	—
435	C₂×C₉	—	8	1	no	—
436	C₂×C₉	—	12	1	no	—
437	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
438	C₂×C₉	D₃×#41	1	2	yes	—
439	C₂⁴	—	3	1	no	—
440	C₂⁴	—	3	1	no	—
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	3	1	no	—
443	C₂×D₄	—	3	1	no	—
444	C₂×D₄	—	6	4	no	—
445	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	6	4	no	—
452	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
453	C₄⋊C₄	—	3	2	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
457	C₂²⋊C₄	—	3	1	no	—
458	C₂²⋊C₄	—	3	2	no	—
459	C₂²⋊C₄	—	3	2	no	—
460	C₂²⋊C₄	—	3	2	no	—
461	C₂²⋊C₄	—	3	2	no	—
462	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
463	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	1	no	—
467	C₂²×C₃	—	2	2	no	—
468	C₂²×C₃	—	2	1	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	3	2	no	—
473	C₂²×C₃	—	3	4	no	—
474	C₂²×C₃	—	3	2	no	—
475	C₂²×C₃	—	4	2	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	2	no	—
478	C₂²×C₃	—	6	8	no	—
479	C₂²×C₃	—	6	2	no	—
480	C₂²×C₃	—	6	1	no	—
481	C₂²×C₃	—	6	2	no	—
482	C₂²×C₃	—	12	4	no	—
483	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
484	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
485	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
486	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
487	C₂×D₃	—	2	2	no	—
488	C₂×D₃	—	2	8	no	—
489	C₂×D₃	—	2	1	no	—
490	C₂×D₃	—	2	2	no	—
491	C₂×D₃	—	4	4	no	—
492	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
493	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
494	C₂×D₃	C₉×#41	1	4	yes	—
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	2	no	—
498	C₃×C₄	—	2	2	no	—
499	C₃×C₄	—	2	1	no	—
500	C₃×C₄	—	2	2	no	—
501	C₃×C₄	—	4	2	no	—
502	C₃×C₄	—	4	1	no	—
503	C₃×C₄	—	4	2	no	—
504	C₃×C₄	—	6	2	no	—
505	C₃×C₄	—	6	1	no	—
506	C₃×C₄	—	6	2	no	—
507	Dic₃	—	2	2	no	—
508	Dic₃	—	2	1	no	—
509	Dic₃	—	2	2	no	—
510	C₃²	C₂×C₃×#123	1	1	yes	characteristic
511	C₉	—	2	1	no	—
512	C₉	D₃×#123	1	1	yes	characteristic, direct product factor
513	C₂³	—	3	1	no	—
514	C₂³	—	3	1	no	—
515	C₂³	—	3	4	no	—
516	C₂³	—	3	1	no	—
517	C₂³	—	6	4	no	—
518	C₂³	—	6	2	no	—
519	C₂³	—	6	4	no	—
520	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
521	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
522	D₄	—	2	2	no	—
523	D₄	—	6	2	no	—
524	D₄	—	6	2	no	—
525	D₄	—	6	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	3	2	no	—
528	C₂×C₄	—	3	2	no	—
529	C₂×C₄	—	3	1	no	—
530	C₂×C₄	—	6	4	no	—
531	C₂×C₄	—	6	4	no	—
532	C₂×C₄	—	6	2	no	—
533	C₂×C₄	—	6	4	no	—
534	C₂×C₄	—	6	2	no	—
535	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
536	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
537	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
538	C₂×C₃	—	2	2	no	—
539	C₂×C₃	—	2	2	no	—
540	C₂×C₃	—	2	1	no	—
541	C₂×C₃	—	2	2	no	—
542	C₂×C₃	—	3	4	no	—
543	C₂×C₃	—	4	2	no	—
544	C₂×C₃	—	4	1	no	—
545	C₂×C₃	—	4	1	no	—
546	C₂×C₃	—	6	2	no	—
547	C₂×C₃	—	8	1	no	—
548	C₂×C₃	—	12	1	no	—
549	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
550	C₂×C₃	C₂×C₉×#41	1	2	yes	—
551	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
552	C₂×C₃	C₃×D₃×#41	1	2	yes	—
553	D₃	—	2	2	no	—
554	D₃	—	4	1	no	—
555	D₃	C₉×#123	1	4	yes	direct product factor
556	C₂²	—	2	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	3	2	no	—
560	C₂²	—	3	4	no	—
561	C₂²	—	3	2	no	—
562	C₂²	—	6	8	no	—
563	C₂²	—	6	2	no	—
564	C₂²	—	6	1	no	—
565	C₂²	—	6	2	no	—
566	C₂²	—	12	4	no	—
567	C₂²	D₃×D₄×C₉	1	2	yes	—
568	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	6	2	no	—
573	C₄	—	6	1	no	—
574	C₄	—	6	2	no	—
575	C₃	—	2	1	no	—
576	C₃	C₂×C₉×#123	1	1	yes	characteristic, complemented
577	C₃	C₃×D₃×#123	1	1	yes	characteristic
578	C₂	—	2	2	no	—
579	C₂	—	3	4	no	—
580	C₂	—	4	1	no	—
581	C₂	—	6	2	no	—
582	C₂	—	12	1	no	—
583	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
584	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	C₂×C₃×D₃×D₄	C₂×C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₂×C₉×#123
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
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₉×#935	C₂	semidirect
5. C₉×#929	C₂	semidirect
6. C₉×#894	C₂	semidirect
7. D₃×C₉×C₄⋊C₄	C₂	semidirect
8. C₉×#886	C₂	semidirect
9. C₉×#883	C₂	semidirect
10. D₃×C₉×C₂²⋊C₄	C₂	semidirect
11. D₃×C₉×C₂²⋊C₄	C₂	semidirect
17. C₂²×C₃×C₄×C₉	C₂²	semidirect
20. C₂²×C₉×Dic₃	C₂²	semidirect
27. C₂×C₄×D₃×C₉	C₂²	semidirect
28. C₃×C₉×C₄⋊C₄	C₂²	semidirect
29. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
30. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
31. C₉×#217	C₂²	semidirect
32. C₉×#217	C₂²	semidirect
33. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×C₄⋊Dic₃	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₉×Dic₃⋊C₄	C₂²	semidirect
58. C₉×#123	D₃	direct (N × H)
88. D₃×#123	C₉	direct (N × H)
129. C₂²×C₄×C₉	C₂×D₃	semidirect
134. C₉×C₄⋊C₄	C₂×D₃	semidirect
142. C₉×C₂²⋊C₄	C₂×D₃	semidirect
143. C₉×C₂²⋊C₄	C₂×D₃	semidirect
166. C₂²×C₄×D₃	C₂×C₉	semidirect
173. C₃×#123	C₂×C₉	semidirect
178. #935	C₂×C₉	semidirect
179. #929	C₂×C₉	semidirect
180. #894	C₂×C₉	semidirect
181. D₃×C₄⋊C₄	C₂×C₉	semidirect
182. #886	C₂×C₉	semidirect
183. #883	C₂×C₉	semidirect
184. D₃×C₂²⋊C₄	C₂×C₉	semidirect
185. D₃×C₂²⋊C₄	C₂×C₉	semidirect
250. D₃×C₉	#123	direct (N × H)
269. C₂²×C₃×C₄	C₂²×C₉	semidirect
273. C₂²×Dic₃	C₂²×C₉	semidirect
280. C₂×C₄×D₃	C₂²×C₉	semidirect
285. C₃×C₄⋊C₄	C₂²×C₉	semidirect
294. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
295. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
298. #217	C₂²×C₉	semidirect
299. #217	C₂²×C₉	semidirect
300. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
301. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
302. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
303. C₄⋊Dic₃	C₂²×C₉	semidirect
304. Dic₃⋊C₄	C₂²×C₉	semidirect
305. Dic₃⋊C₄	C₂²×C₉	semidirect
359. #123	D₃×C₉	direct (N × H)
363. C₃×C₉	C₂×#123	semidirect
452. C₂²×C₄	C₂×D₃×C₉	semidirect
456. C₄⋊C₄	C₂×D₃×C₉	semidirect
462. C₂²⋊C₄	C₂×D₃×C₉	semidirect
463. C₂²⋊C₄	C₂×D₃×C₉	semidirect
512. C₉	D₃×#123	direct (N × H)
555. D₃	C₉×#123	direct (N × H)
576. C₃	C₂×C₉×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
C₂²×C₄×D₃×C₉	2
C₃×C₉×#123	2
C₉×#935	2
C₉×#929	2
C₉×#894	2
D₃×C₉×C₄⋊C₄	2
C₉×#886	2
C₉×#883	2
D₃×C₉×C₂²⋊C₄	2
C₃×D₃×#123	3
C₂×C₉×#123	3

Subgroups — D3×C9×#123 #13153023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#123 #13153023