Subgroups — C₃×#10589752 #13152999

Order 1728.

720 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic
2	C₃×#63497	C₂	1	1	yes	maximal, characteristic
3	C₃×D₄×Dic₉	C₂	1	1	yes	maximal, characteristic
4	C₃×#63488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×Dic₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63449	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63441	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#63440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#63440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#63439	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#63439	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5650	—	3	1	no	maximal
17	#10589752	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
23	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×#3676	C₂²	1	1	yes	characteristic
30	C₃×#3676	C₂²	1	1	yes	characteristic
31	C₃×#3676	C₂²	1	1	yes	characteristic
32	C₃×#3676	C₂²	1	1	yes	characteristic
33	C₃×#3676	C₂²	1	1	yes	characteristic
34	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
36	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
37	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
38	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
47	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
50	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
51	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
52	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
53	C₃²×#123	D₃	1	1	yes	characteristic
54	C₃×#935	—	3	1	no	—
55	C₃×D₄×Dic₃	—	3	1	no	—
56	C₃×#926	—	3	1	no	—
57	C₂×C₃×Dic₃⋊C₄	—	3	1	no	—
58	C₃×#890	—	3	1	no	—
59	C₃×#889	—	3	1	no	—
60	C₃×#889	—	3	1	no	—
61	C₃×#887	—	3	1	no	—
62	C₃×#879	—	3	1	no	—
63	C₃×#879	—	3	1	no	—
64	C₃×#878	—	3	1	no	—
65	C₃×#878	—	3	1	no	—
66	C₃×#877	—	3	1	no	—
67	C₃×#877	—	3	1	no	—
68	C₉×#123	—	2	1	no	—
69	C₉×#123	C₂×C₃	1	1	yes	characteristic
70	#63497	C₂×C₃	1	1	yes	characteristic
71	D₄×Dic₉	C₂×C₃	1	1	yes	characteristic
72	#63488	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×Dic₉⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
74	#63452	C₂×C₃	1	1	yes	characteristic, complemented
75	#63451	C₂×C₃	1	1	yes	characteristic, complemented
76	#63451	C₂×C₃	1	1	yes	characteristic, complemented
77	#63449	C₂×C₃	1	1	yes	characteristic, complemented
78	#63441	C₂×C₃	1	1	yes	characteristic, complemented
79	#63441	C₂×C₃	1	1	yes	characteristic, complemented
80	#63440	C₂×C₃	1	1	yes	characteristic, complemented
81	#63440	C₂×C₃	1	1	yes	characteristic, complemented
82	#63439	C₂×C₃	1	1	yes	characteristic, complemented
83	#63439	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
86	C₃×D₄×C₉	—	2	2	no	—
87	C₂×C₃×C₄×C₉	—	2	2	no	—
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₉	—	2	2	no	—
94	C₂×C₃×Dic₉	—	2	2	no	—
95	C₂×C₃×Dic₉	—	2	2	no	—
96	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
97	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
98	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
99	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
101	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
102	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
103	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
104	C₃×Dic₁₈	—	2	2	no	—
105	C₃×#552	—	9	1	no	—
106	#5650	—	3	1	no	—
107	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
109	C₂²×C₃×Dic₃	—	3	1	no	—
110	C₂²×C₃×Dic₃	—	3	1	no	—
111	C₂²×C₃×Dic₃	—	3	1	no	—
112	C₂×C₃×Dic₆	—	3	1	no	—
113	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
114	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
115	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
116	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
117	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₃×#217	—	3	1	no	—
119	C₃×#217	—	3	1	no	—
120	C₃×#217	—	3	1	no	—
121	C₃×#217	—	3	1	no	—
122	C₃×#217	—	3	1	no	—
123	C₃×C₄⋊Dic₃	—	3	1	no	—
124	C₃×C₄⋊Dic₃	—	3	1	no	—
125	C₃×C₄⋊Dic₃	—	3	1	no	—
126	C₃×C₄⋊Dic₃	—	3	1	no	—
127	C₃×Dic₃⋊C₄	—	3	1	no	—
128	C₃×Dic₃⋊C₄	—	3	1	no	—
129	C₃×Dic₃⋊C₄	—	3	1	no	—
130	C₃×Dic₃⋊C₄	—	3	1	no	—
131	C₃×Dic₃⋊C₄	—	3	1	no	—
132	C₃×Dic₃⋊C₄	—	3	1	no	—
133	C₃×Dic₃⋊C₄	—	3	1	no	—
134	C₃×Dic₃⋊C₄	—	3	1	no	—
135	C₃×Dic₃⋊C₄	—	3	1	no	—
136	C₃×Dic₃⋊C₄	—	3	1	no	—
137	C₃×C₄×Dic₃	—	3	1	no	—
138	C₃×C₄×Dic₃	—	3	1	no	—
139	C₃×C₄×Dic₃	—	3	1	no	—
140	C₃×C₄×Dic₃	—	3	1	no	—
141	C₃×C₄×Dic₃	—	3	1	no	—
142	C₂×D₄×C₉	—	2	1	no	—
143	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₄×C₉	—	2	1	no	—
145	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
146	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
147	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
148	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
149	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
150	C₉×C₄⋊C₄	—	2	1	no	—
151	C₉×C₄⋊C₄	—	2	1	no	—
152	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₉×C₂²⋊C₄	—	2	1	no	—
155	C₉×C₂²⋊C₄	—	2	1	no	—
156	C₉×C₂²⋊C₄	—	2	1	no	—
157	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	#3676	C₂²×C₃	1	1	yes	characteristic
161	#3676	C₂²×C₃	1	1	yes	characteristic
162	#3676	C₂²×C₃	1	1	yes	characteristic
163	#3676	C₂²×C₃	1	1	yes	characteristic
164	#3676	C₂²×C₃	1	1	yes	characteristic
165	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
166	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
167	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
168	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
169	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
180	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
181	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
182	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
183	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
184	C₂²×C₃×C₉	—	2	1	no	—
185	C₂²×C₃×C₉	—	2	1	no	—
186	C₂²×C₃×C₉	—	2	1	no	—
187	C₂²×C₃×C₉	—	2	1	no	—
188	C₂²×C₃×C₉	—	2	1	no	—
189	C₂²×C₃×C₉	#41	1	2	yes	—
190	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
191	C₃×C₄×C₉	—	2	1	no	—
192	C₃×C₄×C₉	—	2	1	no	—
193	C₃×C₄×C₉	—	2	1	no	—
194	C₃×C₄×C₉	—	2	1	no	—
195	C₃×C₄×C₉	—	2	1	no	—
196	C₃×Dic₉	—	2	1	no	—
197	C₃×Dic₉	—	2	1	no	—
198	C₃×Dic₉	—	2	1	no	—
199	C₃×Dic₉	—	2	1	no	—
200	C₃×Dic₉	—	2	1	no	—
201	C₃×Dic₉	—	2	1	no	—
202	C₃×Dic₉	—	2	1	no	—
203	C₃×Dic₉	#41	1	2	yes	—
204	C₃×#126	—	9	1	no	—
205	C₃×#126	—	9	1	no	—
206	C₃×#125	—	9	1	no	—
207	C₃×#125	—	9	1	no	—
208	C₃×#125	—	9	1	no	—
209	C₃×#123	—	2	1	no	—
210	C₃×#123	—	9	1	no	—
211	C₃×#123	D₉	1	1	yes	characteristic
212	C₃×#123	C₃×D₃	1	1	yes	characteristic
213	C₃×C₂²⋊Q₈	—	9	1	no	—
214	C₃×C₂²⋊Q₈	—	9	1	no	—
215	C₃×C₄×Q₈	—	9	1	no	—
216	C₃×C₄×D₄	—	9	1	no	—
217	C₃×#117	—	9	1	no	—
218	C₃×#117	—	9	1	no	—
219	C₃×#117	—	9	1	no	—
220	C₂×C₃×C₄⋊C₄	—	9	1	no	—
221	#935	—	3	1	no	—
222	D₄×Dic₃	—	3	1	no	—
223	#926	—	3	1	no	—
224	C₂×Dic₃⋊C₄	—	3	1	no	—
225	#890	—	3	1	no	—
226	#889	—	3	1	no	—
227	#889	—	3	1	no	—
228	#887	—	3	1	no	—
229	#879	—	3	1	no	—
230	#879	—	3	1	no	—
231	#878	—	3	1	no	—
232	#878	—	3	1	no	—
233	#877	—	3	1	no	—
234	#877	—	3	1	no	—
235	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
236	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
237	C₃²×D₄	—	2	2	no	—
238	C₂×C₃²×C₄	—	2	2	no	—
239	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
240	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
241	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
242	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
244	C₂×C₃×Dic₃	—	3	1	no	—
245	C₂×C₃×Dic₃	—	3	1	no	—
246	C₂×C₃×Dic₃	—	3	1	no	—
247	C₂×C₃×Dic₃	—	3	1	no	—
248	C₂×C₃×Dic₃	—	3	1	no	—
249	C₂×C₃×Dic₃	—	3	1	no	—
250	C₂×C₃×Dic₃	—	3	1	no	—
251	C₂×C₃×Dic₃	—	3	1	no	—
252	C₂×C₃×Dic₃	—	6	2	no	—
253	C₂×C₃×Dic₃	—	6	2	no	—
254	C₂×C₃×Dic₃	—	6	2	no	—
255	C₃×Dic₆	—	6	2	no	—
256	C₂³×C₉	—	2	1	no	—
257	C₂³×C₉	—	2	1	no	—
258	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
259	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
260	D₄×C₉	—	2	2	no	—
261	D₄×C₉	—	4	2	no	—
262	C₂×C₄×C₉	—	2	2	no	—
263	C₂×C₄×C₉	—	2	1	no	—
264	C₂×C₄×C₉	—	2	1	no	—
265	C₂×C₄×C₉	—	2	1	no	—
266	C₂×C₄×C₉	—	2	1	no	—
267	C₂×C₄×C₉	—	2	1	no	—
268	C₂×C₄×C₉	—	4	2	no	—
269	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
271	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
274	C₂×Dic₉	—	2	2	no	—
275	C₂×Dic₉	—	2	2	no	—
276	C₂×Dic₉	—	2	2	no	—
277	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
278	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
279	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
280	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
281	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
282	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
283	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
284	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
285	Dic₁₈	—	2	2	no	—
286	#552	—	9	1	no	Sylow
287	C₂×C₃×C₉	—	2	2	no	—
288	C₂×C₃×C₉	—	4	1	no	—
289	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
291	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
292	C₂×C₃×Q₈	—	9	1	no	—
293	C₂×C₃×D₄	—	2	1	no	—
294	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
295	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
296	C₂²×C₃×C₄	—	2	1	no	—
297	C₂²×C₃×C₄	—	9	1	no	—
298	C₂²×C₃×C₄	—	9	1	no	—
299	C₂²×C₃×C₄	—	9	1	no	—
300	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
301	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
302	C₂²×Dic₃	—	3	1	no	—
303	C₂²×Dic₃	—	3	1	no	—
304	C₂²×Dic₃	—	3	1	no	—
305	C₂×Dic₆	—	3	1	no	—
306	C₃×C₄⋊C₄	—	2	1	no	—
307	C₃×C₄⋊C₄	—	2	1	no	—
308	C₃×C₄⋊C₄	—	9	1	no	—
309	C₃×C₄⋊C₄	—	9	1	no	—
310	C₃×C₄⋊C₄	—	9	1	no	—
311	C₃×C₄⋊C₄	—	9	1	no	—
312	C₃×C₄⋊C₄	—	9	1	no	—
313	C₃×C₄⋊C₄	—	9	1	no	—
314	C₃×C₄⋊C₄	—	9	1	no	—
315	C₃×C₄⋊C₄	—	9	1	no	—
316	C₃×C₄⋊C₄	—	9	1	no	—
317	C₃×C₄⋊C₄	—	9	1	no	—
318	C₃×C₄⋊C₄	—	9	1	no	—
319	C₃×C₄⋊C₄	—	9	1	no	—
320	C₃×C₄⋊C₄	—	9	1	no	—
321	C₃×C₄⋊C₄	—	9	1	no	—
322	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
323	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
324	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
325	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
326	C₃×C₂²⋊C₄	—	2	1	no	—
327	C₃×C₂²⋊C₄	—	2	1	no	—
328	C₃×C₂²⋊C₄	—	2	1	no	—
329	C₃×C₂²⋊C₄	—	9	1	no	—
330	C₃×C₂²⋊C₄	—	9	1	no	—
331	C₃×C₂²⋊C₄	—	9	1	no	—
332	C₃×C₂²⋊C₄	—	9	1	no	—
333	C₃×C₂²⋊C₄	—	9	1	no	—
334	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
335	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
336	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
337	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
338	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
339	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
340	C₃×C₄²	—	9	1	no	—
341	C₃×C₄²	—	9	1	no	—
342	C₃×C₄²	—	9	1	no	—
343	C₃×C₄²	—	9	1	no	—
344	C₃×C₄²	—	9	1	no	—
345	#217	—	3	1	no	—
346	#217	—	3	1	no	—
347	#217	—	3	1	no	—
348	#217	—	3	1	no	—
349	#217	—	3	1	no	—
350	C₄⋊Dic₃	—	3	1	no	—
351	C₄⋊Dic₃	—	3	1	no	—
352	C₄⋊Dic₃	—	3	1	no	—
353	C₄⋊Dic₃	—	3	1	no	—
354	Dic₃⋊C₄	—	3	1	no	—
355	Dic₃⋊C₄	—	3	1	no	—
356	Dic₃⋊C₄	—	3	1	no	—
357	Dic₃⋊C₄	—	3	1	no	—
358	Dic₃⋊C₄	—	3	1	no	—
359	Dic₃⋊C₄	—	3	1	no	—
360	Dic₃⋊C₄	—	3	1	no	—
361	Dic₃⋊C₄	—	3	1	no	—
362	Dic₃⋊C₄	—	3	1	no	—
363	Dic₃⋊C₄	—	3	1	no	—
364	C₄×Dic₃	—	3	1	no	—
365	C₄×Dic₃	—	3	1	no	—
366	C₄×Dic₃	—	3	1	no	—
367	C₄×Dic₃	—	3	1	no	—
368	C₄×Dic₃	—	3	1	no	—
369	C₂²×C₃²	—	2	1	no	—
370	C₂²×C₃²	—	2	1	no	—
371	C₂²×C₃²	—	2	1	no	—
372	C₂²×C₃²	—	2	1	no	—
373	C₂²×C₃²	—	2	1	no	—
374	C₂²×C₃²	#237	1	2	yes	—
375	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
376	C₃²×C₄	—	2	1	no	—
377	C₃²×C₄	—	2	1	no	—
378	C₃²×C₄	—	2	1	no	—
379	C₃²×C₄	—	2	1	no	—
380	C₃²×C₄	—	2	1	no	—
381	C₃×Dic₃	—	3	2	no	—
382	C₃×Dic₃	—	6	1	no	—
383	C₃×Dic₃	—	6	1	no	—
384	C₃×Dic₃	—	6	1	no	—
385	C₃×Dic₃	—	6	1	no	—
386	C₃×Dic₃	—	6	1	no	—
387	C₃×Dic₃	—	6	1	no	—
388	C₃×Dic₃	—	6	1	no	—
389	C₂²×C₉	—	2	1	no	—
390	C₂²×C₉	—	2	1	no	—
391	C₂²×C₉	—	2	1	no	—
392	C₂²×C₉	—	2	1	no	—
393	C₂²×C₉	—	2	1	no	—
394	C₂²×C₉	—	2	1	no	—
395	C₂²×C₉	—	2	2	no	—
396	C₂²×C₉	—	4	1	no	—
397	C₂²×C₉	—	4	1	no	—
398	C₂²×C₉	—	4	1	no	—
399	C₂²×C₉	—	4	1	no	—
400	C₂²×C₉	—	4	1	no	—
401	C₂²×C₉	C₃×#41	1	2	yes	—
402	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
403	C₄×C₉	—	2	1	no	—
404	C₄×C₉	—	2	1	no	—
405	C₄×C₉	—	2	1	no	—
406	C₄×C₉	—	2	1	no	—
407	C₄×C₉	—	2	1	no	—
408	C₄×C₉	—	4	1	no	—
409	C₄×C₉	—	4	1	no	—
410	C₄×C₉	—	4	1	no	—
411	C₄×C₉	—	4	1	no	—
412	C₄×C₉	—	4	1	no	—
413	Dic₉	—	2	1	no	—
414	Dic₉	—	2	1	no	—
415	Dic₉	—	2	1	no	—
416	Dic₉	—	2	1	no	—
417	Dic₉	—	2	1	no	—
418	Dic₉	—	2	1	no	—
419	Dic₉	—	2	1	no	—
420	Dic₉	C₃×#41	1	2	yes	—
421	#126	—	9	1	no	—
422	#126	—	9	1	no	—
423	#125	—	9	1	no	—
424	#125	—	9	1	no	—
425	#125	—	9	1	no	—
426	#123	—	9	1	no	—
427	#123	C₃×D₉	1	1	yes	characteristic
428	C₂²⋊Q₈	—	9	1	no	—
429	C₂²⋊Q₈	—	9	1	no	—
430	C₄×Q₈	—	9	1	no	—
431	C₄×D₄	—	9	1	no	—
432	#117	—	9	1	no	—
433	#117	—	9	1	no	—
434	#117	—	9	1	no	—
435	C₂×C₄⋊C₄	—	9	1	no	—
436	C₃×C₉	#552	1	1	yes	characteristic, complemented, Sylow
437	C₂³×C₃	—	2	1	no	—
438	C₂³×C₃	—	2	1	no	—
439	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
440	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
441	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
442	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
443	C₃×Q₈	—	18	2	no	—
444	C₃×D₄	—	2	2	no	—
445	C₃×D₄	—	2	2	no	—
446	C₃×D₄	—	4	2	no	—
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	2	2	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	4	2	no	—
455	C₂×C₃×C₄	—	9	1	no	—
456	C₂×C₃×C₄	—	9	1	no	—
457	C₂×C₃×C₄	—	9	1	no	—
458	C₂×C₃×C₄	—	9	1	no	—
459	C₂×C₃×C₄	—	9	1	no	—
460	C₂×C₃×C₄	—	9	1	no	—
461	C₂×C₃×C₄	—	9	1	no	—
462	C₂×C₃×C₄	—	9	1	no	—
463	C₂×C₃×C₄	—	18	2	no	—
464	C₂×C₃×C₄	—	18	2	no	—
465	C₂×C₃×C₄	—	18	2	no	—
466	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
468	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
471	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
472	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
473	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
474	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
475	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
476	C₂×Dic₃	—	3	1	no	—
477	C₂×Dic₃	—	3	1	no	—
478	C₂×Dic₃	—	3	1	no	—
479	C₂×Dic₃	—	3	1	no	—
480	C₂×Dic₃	—	3	1	no	—
481	C₂×Dic₃	—	3	1	no	—
482	C₂×Dic₃	—	3	1	no	—
483	C₂×Dic₃	—	3	1	no	—
484	C₂×Dic₃	—	6	2	no	—
485	C₂×Dic₃	—	6	2	no	—
486	C₂×Dic₃	—	6	2	no	—
487	Dic₆	—	6	2	no	—
488	C₂×C₃²	—	2	2	no	—
489	C₂×C₃²	—	4	1	no	—
490	C₂×C₃²	C₂×#237	1	1	yes	characteristic
491	C₂×C₃²	D₃×#41	1	1	yes	characteristic
492	C₂×C₃²	#1010	1	1	yes	characteristic
493	C₂×C₉	—	2	2	no	—
494	C₂×C₉	—	2	1	no	—
495	C₂×C₉	—	2	1	no	—
496	C₂×C₉	—	2	1	no	—
497	C₂×C₉	—	4	2	no	—
498	C₂×C₉	—	4	1	no	—
499	C₂×C₉	—	8	1	no	—
500	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
501	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
502	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
503	C₂×Q₈	—	9	1	no	—
504	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
505	C₂²×C₄	—	9	1	no	—
506	C₂²×C₄	—	9	1	no	—
507	C₂²×C₄	—	9	1	no	—
508	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
509	C₄⋊C₄	—	9	1	no	—
510	C₄⋊C₄	—	9	1	no	—
511	C₄⋊C₄	—	9	1	no	—
512	C₄⋊C₄	—	9	1	no	—
513	C₄⋊C₄	—	9	1	no	—
514	C₄⋊C₄	—	9	1	no	—
515	C₄⋊C₄	—	9	1	no	—
516	C₄⋊C₄	—	9	1	no	—
517	C₄⋊C₄	—	9	1	no	—
518	C₄⋊C₄	—	9	1	no	—
519	C₄⋊C₄	—	9	1	no	—
520	C₄⋊C₄	—	9	1	no	—
521	C₄⋊C₄	—	9	1	no	—
522	C₄⋊C₄	—	9	1	no	—
523	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
525	C₂²⋊C₄	—	9	1	no	—
526	C₂²⋊C₄	—	9	1	no	—
527	C₂²⋊C₄	—	9	1	no	—
528	C₂²⋊C₄	—	9	1	no	—
529	C₂²⋊C₄	—	9	1	no	—
530	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
531	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
532	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
533	C₄²	—	9	1	no	—
534	C₄²	—	9	1	no	—
535	C₄²	—	9	1	no	—
536	C₄²	—	9	1	no	—
537	C₄²	—	9	1	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	2	1	no	—
540	C₂²×C₃	—	2	1	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	1	no	—
544	C₂²×C₃	—	2	1	no	—
545	C₂²×C₃	—	2	1	no	—
546	C₂²×C₃	—	2	1	no	—
547	C₂²×C₃	—	2	1	no	—
548	C₂²×C₃	—	2	1	no	—
549	C₂²×C₃	—	2	2	no	—
550	C₂²×C₃	—	4	1	no	—
551	C₂²×C₃	—	4	1	no	—
552	C₂²×C₃	—	4	1	no	—
553	C₂²×C₃	—	4	1	no	—
554	C₂²×C₃	—	4	1	no	—
555	C₂²×C₃	#3699	1	2	yes	—
556	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
557	C₂²×C₃	C₃×#237	1	2	yes	—
558	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	2	1	no	—
569	C₃×C₄	—	4	1	no	—
570	C₃×C₄	—	4	1	no	—
571	C₃×C₄	—	4	1	no	—
572	C₃×C₄	—	4	1	no	—
573	C₃×C₄	—	4	1	no	—
574	C₃×C₄	—	9	2	no	—
575	C₃×C₄	—	18	1	no	—
576	C₃×C₄	—	18	1	no	—
577	C₃×C₄	—	18	1	no	—
578	C₃×C₄	—	18	1	no	—
579	C₃×C₄	—	18	1	no	—
580	C₃×C₄	—	18	1	no	—
581	C₃×C₄	—	18	1	no	—
582	Dic₃	—	3	2	no	—
583	Dic₃	—	6	1	no	—
584	Dic₃	—	6	1	no	—
585	Dic₃	—	6	1	no	—
586	Dic₃	—	6	1	no	—
587	Dic₃	—	6	1	no	—
588	Dic₃	—	6	1	no	—
589	Dic₃	—	6	1	no	—
590	C₃²	#5650	1	1	yes	characteristic
591	C₉	—	2	1	no	—
592	C₉	C₃×#552	1	1	yes	characteristic, complemented
593	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
594	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
595	Q₈	—	18	2	no	—
596	D₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	9	1	no	—
599	C₂×C₄	—	9	1	no	—
600	C₂×C₄	—	9	1	no	—
601	C₂×C₄	—	9	1	no	—
602	C₂×C₄	—	9	1	no	—
603	C₂×C₄	—	9	1	no	—
604	C₂×C₄	—	9	1	no	—
605	C₂×C₄	—	9	1	no	—
606	C₂×C₄	—	18	2	no	—
607	C₂×C₄	—	18	2	no	—
608	C₂×C₄	—	18	2	no	—
609	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
610	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
611	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
612	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
613	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
614	C₂×C₃	—	2	2	no	—
615	C₂×C₃	—	2	2	no	—
616	C₂×C₃	—	2	1	no	—
617	C₂×C₃	—	2	1	no	—
618	C₂×C₃	—	2	1	no	—
619	C₂×C₃	—	4	2	no	—
620	C₂×C₃	—	4	1	no	—
621	C₂×C₃	—	4	1	no	—
622	C₂×C₃	—	8	1	no	—
623	C₂×C₃	C₂×#3699	1	1	yes	characteristic
624	C₂×C₃	#41×D₉	1	1	yes	characteristic
625	C₂×C₃	#63716	1	1	yes	characteristic
626	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
627	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
628	C₂×C₃	C₃×#1010	1	1	yes	characteristic
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	C₃×#3699	1	2	yes	—
635	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	9	2	no	—
642	C₄	—	18	1	no	—
643	C₄	—	18	1	no	—
644	C₄	—	18	1	no	—
645	C₄	—	18	1	no	—
646	C₄	—	18	1	no	—
647	C₄	—	18	1	no	—
648	C₄	—	18	1	no	—
649	C₃	—	2	1	no	—
650	C₃	#10589752	1	1	yes	characteristic, direct product factor
651	C₃	C₃×#5650	1	1	yes	characteristic
652	C₂	—	2	2	no	—
653	C₂	—	4	1	no	—
654	C₂	C₂×C₃×#3699	1	1	yes	characteristic
655	C₂	C₃×#41×D₉	1	1	yes	characteristic
656	C₂	C₃×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#123	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃²×D₄	C₂×D₃
hypercenter	C₃×#123	D₉
hypocenter	C₉	C₃×#552
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
4. C₃×#63488	C₂	semidirect
5. C₂×C₃×Dic₉⋊C₄	C₂	semidirect
6. C₃×#63452	C₂	semidirect
7. C₃×#63451	C₂	semidirect
8. C₃×#63451	C₂	semidirect
9. C₃×#63449	C₂	semidirect
10. C₃×#63441	C₂	semidirect
11. C₃×#63441	C₂	semidirect
12. C₃×#63440	C₂	semidirect
13. C₃×#63440	C₂	semidirect
14. C₃×#63439	C₂	semidirect
15. C₃×#63439	C₂	semidirect
17. #10589752	C₃	direct (N × H)
72. #63488	C₂×C₃	semidirect
73. C₂×Dic₉⋊C₄	C₂×C₃	semidirect
74. #63452	C₂×C₃	semidirect
75. #63451	C₂×C₃	semidirect
76. #63451	C₂×C₃	semidirect
77. #63449	C₂×C₃	semidirect
78. #63441	C₂×C₃	semidirect
79. #63441	C₂×C₃	semidirect
80. #63440	C₂×C₃	semidirect
81. #63440	C₂×C₃	semidirect
82. #63439	C₂×C₃	semidirect
83. #63439	C₂×C₃	semidirect
436. C₃×C₉	#552	semidirect
592. C₉	C₃×#552	semidirect
650. C₃	#10589752	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₉×#123	2
C₃×#63497	2
C₃×D₄×Dic₉	2
C₃×#63488	2
C₂×C₃×Dic₉⋊C₄	2
C₃×#63452	2
C₃×#63451	2
C₃×#63449	2
C₃×#63441	2
C₃×#63440	2
C₃×#63439	2
C₃×#5650	3
#10589752	3

Subgroups — C3×#10589752 #13152999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589752 #13152999