Subgroups — C₃×#10589757 #13153014

Order 1728.

954 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3699	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3697	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×Dic₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63458	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄⋊C₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#63445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#611⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#611⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#63440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5655	—	3	1	no	maximal
17	#10589757	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	C₂×C₃×#611	C₂²	1	1	yes	characteristic
21	C₂×C₃×#611	C₂²	1	1	yes	characteristic
22	C₂×C₃×#611	C₂²	1	1	yes	characteristic
23	C₂×C₃×#611	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
25	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
26	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
27	C₃×#3699	—	2	4	no	—
28	C₃×#3697	—	2	4	no	—
29	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
34	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
36	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×#3676	C₂²	1	1	yes	characteristic
42	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
47	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
48	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
50	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
53	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
54	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
55	C₂×C₃×#237	—	3	1	no	—
56	C₂×C₃×#235	—	3	1	no	—
57	C₃²×#123	D₃	1	1	yes	characteristic
58	C₃×#939	—	3	1	no	—
59	C₂×C₃×Dic₃⋊C₄	—	3	1	no	—
60	C₃×#896	—	3	1	no	—
61	C₃×#894	—	3	1	no	—
62	C₃×D₃×C₄⋊C₄	—	3	1	no	—
63	C₃×#888	—	3	1	no	—
64	C₃×#886	—	3	1	no	—
65	C₃×#884	—	3	1	no	—
66	C₃×#883	—	3	1	no	—
67	C₃×#67⋊C₄	—	3	1	no	—
68	C₃×#67⋊C₄	—	3	1	no	—
69	C₃×#878	—	3	1	no	—
70	C₂×#3699	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂×#3697	C₂×C₃	1	1	yes	characteristic, complemented
72	C₉×#123	—	2	1	no	—
73	C₉×#123	C₂×C₃	1	1	yes	characteristic, complemented
74	#63501	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×Dic₉⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	#63458	C₂×C₃	1	1	yes	characteristic, complemented
77	#63456	C₂×C₃	1	1	yes	characteristic, complemented
78	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
79	#63450	C₂×C₃	1	1	yes	characteristic, complemented
80	#63448	C₂×C₃	1	1	yes	characteristic, complemented
81	#63446	C₂×C₃	1	1	yes	characteristic, complemented
82	#63445	C₂×C₃	1	1	yes	characteristic, complemented
83	#611⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
84	#611⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
85	#63440	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
88	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
89	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
90	C₃×D₄×C₉	—	2	2	no	—
91	C₂×C₃×C₄×C₉	—	2	2	no	—
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₃×#611	—	2	2	no	—
98	C₃×#611	—	2	2	no	—
99	C₃×#611	—	2	2	no	—
100	C₃×#611	D₄	1	4	yes	complemented
101	C₂×C₃×Dic₉	—	2	2	no	—
102	C₂×C₃×Dic₉	—	2	2	no	—
103	C₂×C₃×Dic₉	—	2	2	no	—
104	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
105	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
106	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
107	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
108	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
109	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
110	C₃×D₃₆	—	2	2	no	—
111	C₃×C₄×D₉	—	2	2	no	—
112	C₃×C₄×D₉	—	2	2	no	—
113	C₃×C₄×D₉	—	2	2	no	—
114	C₃×C₄×D₉	—	2	2	no	—
115	C₃×Dic₁₈	—	2	2	no	—
116	C₃×Dic₁₈	—	2	2	no	—
117	C₃×#547	—	9	1	no	—
118	#5655	—	3	1	no	—
119	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
120	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
121	C₂×C₃×#67	—	3	1	no	—
122	C₂×C₃×#67	—	3	1	no	—
123	C₂×C₃×#67	—	3	1	no	—
124	C₂×C₃×#67	—	3	1	no	—
125	C₂²×C₃×Dic₃	—	3	1	no	—
126	C₂²×C₃×Dic₃	—	3	1	no	—
127	C₂²×C₃×Dic₃	—	3	1	no	—
128	C₃×#237	—	6	4	no	—
129	C₃×#235	—	6	4	no	—
130	C₂×C₃×D₁₂	—	3	1	no	—
131	C₂×C₃×C₄×D₃	—	3	1	no	—
132	C₂×C₃×C₄×D₃	—	3	1	no	—
133	C₂×C₃×C₄×D₃	—	3	1	no	—
134	C₂×C₃×C₄×D₃	—	3	1	no	—
135	C₂×C₃×Dic₆	—	3	1	no	—
136	C₂×C₃×Dic₆	—	3	1	no	—
137	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
138	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
140	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
141	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
142	C₃×#217	—	3	1	no	—
143	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
144	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
145	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
146	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
147	C₃×C₄⋊Dic₃	—	3	1	no	—
148	C₃×C₄⋊Dic₃	—	3	1	no	—
149	C₃×Dic₃⋊C₄	—	3	1	no	—
150	C₃×Dic₃⋊C₄	—	3	1	no	—
151	C₃×Dic₃⋊C₄	—	3	1	no	—
152	C₃×Dic₃⋊C₄	—	3	1	no	—
153	C₃×Dic₃⋊C₄	—	3	1	no	—
154	C₃×Dic₃⋊C₄	—	3	1	no	—
155	C₃×C₄×Dic₃	—	3	1	no	—
156	C₂×D₄×C₉	—	2	1	no	—
157	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
158	C₂²×C₄×C₉	—	2	1	no	—
159	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
160	C₂×#611	C₂²×C₃	1	1	yes	characteristic
161	C₂×#611	C₂²×C₃	1	1	yes	characteristic
162	C₂×#611	C₂²×C₃	1	1	yes	characteristic
163	C₂×#611	C₂²×C₃	1	1	yes	characteristic
164	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
165	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
166	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
167	#3699	—	2	4	no	—
168	#3697	—	2	4	no	—
169	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
174	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
175	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
176	C₉×C₄⋊C₄	—	2	1	no	—
177	C₉×C₄⋊C₄	—	2	1	no	—
178	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₉×C₂²⋊C₄	—	2	1	no	—
181	C₉×C₂²⋊C₄	—	2	1	no	—
182	C₉×C₂²⋊C₄	—	2	1	no	—
183	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
185	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	#3676	C₂²×C₃	1	1	yes	characteristic
187	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
189	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
190	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
191	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
192	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
193	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
194	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
195	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
196	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
197	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
198	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
199	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
200	C₂²×C₃×C₉	—	2	1	no	—
201	C₂²×C₃×C₉	—	2	1	no	—
202	C₂²×C₃×C₉	—	2	1	no	—
203	C₂²×C₃×C₉	—	2	1	no	—
204	C₂²×C₃×C₉	—	2	1	no	—
205	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
206	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
207	C₂×C₃×D₉	—	2	1	no	—
208	C₂×C₃×D₉	—	2	1	no	—
209	C₂×C₃×D₉	—	2	1	no	—
210	C₂×C₃×D₉	—	2	1	no	—
211	C₂×C₃×D₉	—	2	1	no	—
212	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
213	C₃×C₄×C₉	—	2	1	no	—
214	C₃×C₄×C₉	—	2	1	no	—
215	C₃×C₄×C₉	—	2	1	no	—
216	C₃×C₄×C₉	—	2	1	no	—
217	C₃×C₄×C₉	—	2	1	no	—
218	C₃×Dic₉	—	2	1	no	—
219	C₃×Dic₉	—	2	1	no	—
220	C₃×Dic₉	—	2	1	no	—
221	C₃×Dic₉	—	2	1	no	—
222	C₃×Dic₉	C₂×D₄	1	2	yes	—
223	C₃×Dic₉	#41	1	2	yes	complemented
224	C₂×C₃×#41	—	9	1	no	—
225	C₂×C₃×#41	—	9	1	no	—
226	C₂×#237	—	3	1	no	—
227	C₂×#235	—	3	1	no	—
228	C₃×C₄⋊Q₈	—	9	1	no	—
229	C₃×#123	—	2	1	no	—
230	C₃×#123	—	9	1	no	—
231	C₃×#123	—	9	1	no	—
232	C₃×#123	—	9	1	no	—
233	C₃×#123	D₉	1	1	yes	characteristic, complemented
234	C₃×#123	C₃×D₃	1	1	yes	characteristic
235	C₃×C₂²⋊Q₈	—	9	1	no	—
236	C₃×C₂²⋊Q₈	—	9	1	no	—
237	C₃×#121	—	9	1	no	—
238	C₃×#121	—	9	1	no	—
239	C₃×C₄×D₄	—	9	1	no	—
240	C₃×C₄×D₄	—	9	1	no	—
241	C₂×C₃×C₄⋊C₄	—	9	1	no	—
242	C₂×C₃×C₄⋊C₄	—	9	1	no	—
243	#939	—	3	1	no	—
244	C₂×Dic₃⋊C₄	—	3	1	no	—
245	#896	—	3	1	no	—
246	#894	—	3	1	no	—
247	D₃×C₄⋊C₄	—	3	1	no	—
248	#888	—	3	1	no	—
249	#886	—	3	1	no	—
250	#884	—	3	1	no	—
251	#883	—	3	1	no	—
252	#67⋊C₄	—	3	1	no	—
253	#67⋊C₄	—	3	1	no	—
254	#878	—	3	1	no	—
255	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
256	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
257	C₂²×C₃×D₃	—	3	1	no	—
258	C₂²×C₃×D₃	—	3	1	no	—
259	C₃²×D₄	—	2	2	no	—
260	C₂×C₃²×C₄	—	2	2	no	—
261	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
262	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
264	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
266	C₃×#67	—	3	4	no	—
267	C₃×#67	—	6	2	no	—
268	C₃×#67	—	6	2	no	—
269	C₃×#67	—	6	2	no	—
270	C₂×C₃×Dic₃	—	3	1	no	—
271	C₂×C₃×Dic₃	—	3	1	no	—
272	C₂×C₃×Dic₃	—	3	1	no	—
273	C₂×C₃×Dic₃	—	3	1	no	—
274	C₂×C₃×Dic₃	—	3	1	no	—
275	C₂×C₃×Dic₃	—	3	1	no	—
276	C₂×C₃×Dic₃	—	6	2	no	—
277	C₂×C₃×Dic₃	—	6	2	no	—
278	C₂×C₃×Dic₃	—	6	2	no	—
279	C₃×D₁₂	—	6	2	no	—
280	C₃×C₄×D₃	—	6	2	no	—
281	C₃×C₄×D₃	—	6	2	no	—
282	C₃×C₄×D₃	—	6	2	no	—
283	C₃×C₄×D₃	—	6	2	no	—
284	C₃×Dic₆	—	6	2	no	—
285	C₃×Dic₆	—	6	2	no	—
286	C₂³×C₉	—	2	1	no	—
287	C₂³×C₉	—	2	1	no	—
288	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
289	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
290	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
291	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
292	D₄×C₉	—	2	2	no	—
293	D₄×C₉	—	4	2	no	—
294	C₂×C₄×C₉	—	2	2	no	—
295	C₂×C₄×C₉	—	2	1	no	—
296	C₂×C₄×C₉	—	2	1	no	—
297	C₂×C₄×C₉	—	2	1	no	—
298	C₂×C₄×C₉	—	2	1	no	—
299	C₂×C₄×C₉	—	2	1	no	—
300	C₂×C₄×C₉	—	4	2	no	—
301	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
306	#611	—	2	2	no	—
307	#611	—	2	2	no	—
308	#611	—	2	2	no	—
309	#611	C₃×D₄	1	4	yes	complemented
310	C₂×Dic₉	—	2	2	no	—
311	C₂×Dic₉	—	2	2	no	—
312	C₂×Dic₉	—	2	2	no	—
313	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
314	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
315	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
316	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
317	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
318	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
319	D₃₆	—	2	2	no	—
320	C₄×D₉	—	2	2	no	—
321	C₄×D₉	—	2	2	no	—
322	C₄×D₉	—	2	2	no	—
323	C₄×D₉	—	2	2	no	—
324	Dic₁₈	—	2	2	no	—
325	Dic₁₈	—	2	2	no	—
326	#547	—	9	1	no	Sylow
327	C₂×C₃×C₉	—	2	2	no	—
328	C₂×C₃×C₉	—	4	1	no	—
329	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
331	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
332	C₃×D₉	—	2	2	no	—
333	C₃×D₉	—	4	1	no	—
334	C₃×#41	—	18	4	no	—
335	C₃×#41	—	18	4	no	—
336	C₂×C₃×Q₈	—	9	1	no	—
337	C₂×C₃×Q₈	—	9	1	no	—
338	C₂×C₃×D₄	—	2	1	no	—
339	C₂×C₃×D₄	—	9	1	no	—
340	C₂×C₃×D₄	—	9	1	no	—
341	C₂×C₃×D₄	—	9	1	no	—
342	C₂×C₃×D₄	—	9	1	no	—
343	C₂×C₃×D₄	—	9	1	no	—
344	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
345	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
346	C₂²×C₃×C₄	—	2	1	no	—
347	C₂²×C₃×C₄	—	9	1	no	—
348	C₂²×C₃×C₄	—	9	1	no	—
349	C₂²×C₃×C₄	—	9	1	no	—
350	C₂²×C₃×C₄	—	9	1	no	—
351	C₂²×C₃×C₄	—	9	1	no	—
352	C₂²×C₃×C₄	—	9	1	no	—
353	C₂²×C₃×C₄	—	9	1	no	—
354	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
355	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
356	C₂×#67	—	3	1	no	—
357	C₂×#67	—	3	1	no	—
358	C₂×#67	—	3	1	no	—
359	C₂×#67	—	3	1	no	—
360	C₂²×Dic₃	—	3	1	no	—
361	C₂²×Dic₃	—	3	1	no	—
362	C₂²×Dic₃	—	3	1	no	—
363	#237	—	6	4	no	—
364	#235	—	6	4	no	—
365	C₂×D₁₂	—	3	1	no	—
366	C₂×C₄×D₃	—	3	1	no	—
367	C₂×C₄×D₃	—	3	1	no	—
368	C₂×C₄×D₃	—	3	1	no	—
369	C₂×C₄×D₃	—	3	1	no	—
370	C₂×Dic₆	—	3	1	no	—
371	C₂×Dic₆	—	3	1	no	—
372	C₃×C₄⋊C₄	—	2	1	no	—
373	C₃×C₄⋊C₄	—	2	1	no	—
374	C₃×C₄⋊C₄	—	9	1	no	—
375	C₃×C₄⋊C₄	—	9	1	no	—
376	C₃×C₄⋊C₄	—	9	1	no	—
377	C₃×C₄⋊C₄	—	9	1	no	—
378	C₃×C₄⋊C₄	—	9	1	no	—
379	C₃×C₄⋊C₄	—	9	1	no	—
380	C₃×C₄⋊C₄	—	9	1	no	—
381	C₃×C₄⋊C₄	—	9	1	no	—
382	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
383	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
384	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
385	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
386	C₃×C₂²⋊C₄	—	2	1	no	—
387	C₃×C₂²⋊C₄	—	2	1	no	—
388	C₃×C₂²⋊C₄	—	2	1	no	—
389	C₃×C₂²⋊C₄	—	9	1	no	—
390	C₃×C₂²⋊C₄	—	9	1	no	—
391	C₃×C₂²⋊C₄	—	9	1	no	—
392	C₃×C₂²⋊C₄	—	9	1	no	—
393	C₃×C₂²⋊C₄	—	9	1	no	—
394	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
395	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
396	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
397	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
398	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
399	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
400	C₃×C₄²	—	9	1	no	—
401	#217	—	3	1	no	—
402	(C₂×D₃)⋊C₄	—	3	1	no	—
403	(C₂×D₃)⋊C₄	—	3	1	no	—
404	(C₂×D₃)⋊C₄	—	3	1	no	—
405	(C₂×D₃)⋊C₄	—	3	1	no	—
406	C₄⋊Dic₃	—	3	1	no	—
407	C₄⋊Dic₃	—	3	1	no	—
408	Dic₃⋊C₄	—	3	1	no	—
409	Dic₃⋊C₄	—	3	1	no	—
410	Dic₃⋊C₄	—	3	1	no	—
411	Dic₃⋊C₄	—	3	1	no	—
412	Dic₃⋊C₄	—	3	1	no	—
413	Dic₃⋊C₄	—	3	1	no	—
414	C₄×Dic₃	—	3	1	no	—
415	C₂²×C₃²	—	2	1	no	—
416	C₂²×C₃²	—	2	1	no	—
417	C₂²×C₃²	—	2	1	no	—
418	C₂²×C₃²	—	2	1	no	—
419	C₂²×C₃²	—	2	1	no	—
420	C₂²×C₃²	D₃×D₄	1	2	yes	—
421	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
422	C₂×C₃×D₃	—	3	2	no	—
423	C₂×C₃×D₃	—	6	1	no	—
424	C₂×C₃×D₃	—	6	1	no	—
425	C₂×C₃×D₃	—	6	1	no	—
426	C₂×C₃×D₃	—	6	1	no	—
427	C₂×C₃×D₃	—	6	1	no	—
428	C₃²×C₄	—	2	1	no	—
429	C₃²×C₄	—	2	1	no	—
430	C₃²×C₄	—	2	1	no	—
431	C₃²×C₄	—	2	1	no	—
432	C₃²×C₄	—	2	1	no	—
433	C₃×Dic₃	—	3	2	no	—
434	C₃×Dic₃	—	3	2	no	—
435	C₃×Dic₃	—	6	1	no	—
436	C₃×Dic₃	—	6	1	no	—
437	C₃×Dic₃	—	6	1	no	—
438	C₃×Dic₃	—	6	1	no	—
439	C₂²×C₉	—	2	1	no	—
440	C₂²×C₉	—	2	1	no	—
441	C₂²×C₉	—	2	1	no	—
442	C₂²×C₉	—	2	1	no	—
443	C₂²×C₉	—	2	1	no	—
444	C₂²×C₉	—	2	1	no	—
445	C₂²×C₉	—	2	2	no	—
446	C₂²×C₉	—	4	1	no	—
447	C₂²×C₉	—	4	1	no	—
448	C₂²×C₉	—	4	1	no	—
449	C₂²×C₉	—	4	1	no	—
450	C₂²×C₉	—	4	1	no	—
451	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
452	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
453	C₂×D₉	—	2	1	no	—
454	C₂×D₉	—	2	1	no	—
455	C₂×D₉	—	2	1	no	—
456	C₂×D₉	—	2	1	no	—
457	C₂×D₉	—	2	1	no	—
458	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
459	C₄×C₉	—	2	1	no	—
460	C₄×C₉	—	2	1	no	—
461	C₄×C₉	—	2	1	no	—
462	C₄×C₉	—	2	1	no	—
463	C₄×C₉	—	2	1	no	—
464	C₄×C₉	—	4	1	no	—
465	C₄×C₉	—	4	1	no	—
466	C₄×C₉	—	4	1	no	—
467	C₄×C₉	—	4	1	no	—
468	C₄×C₉	—	4	1	no	—
469	Dic₉	—	2	1	no	—
470	Dic₉	—	2	1	no	—
471	Dic₉	—	2	1	no	—
472	Dic₉	—	2	1	no	—
473	Dic₉	C₂×C₃×D₄	1	2	yes	—
474	Dic₉	C₃×#41	1	2	yes	complemented
475	C₂×#41	—	9	1	no	—
476	C₂×#41	—	9	1	no	—
477	C₄⋊Q₈	—	9	1	no	—
478	#123	—	9	1	no	—
479	#123	—	9	1	no	—
480	#123	—	9	1	no	—
481	#123	C₃×D₉	1	1	yes	characteristic, complemented
482	C₂²⋊Q₈	—	9	1	no	—
483	C₂²⋊Q₈	—	9	1	no	—
484	#121	—	9	1	no	—
485	#121	—	9	1	no	—
486	C₄×D₄	—	9	1	no	—
487	C₄×D₄	—	9	1	no	—
488	C₂×C₄⋊C₄	—	9	1	no	—
489	C₂×C₄⋊C₄	—	9	1	no	—
490	C₃×C₉	#547	1	1	yes	characteristic, complemented, Sylow
491	C₂³×C₃	—	2	1	no	—
492	C₂³×C₃	—	2	1	no	—
493	C₂³×C₃	—	9	1	no	—
494	C₂³×C₃	—	9	1	no	—
495	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
496	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
497	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
498	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
499	C₂²×D₃	—	3	1	no	—
500	C₂²×D₃	—	3	1	no	—
501	C₃×Q₈	—	18	2	no	—
502	C₃×Q₈	—	18	2	no	—
503	C₃×D₄	—	2	2	no	—
504	C₃×D₄	—	2	2	no	—
505	C₃×D₄	—	4	2	no	—
506	C₃×D₄	—	9	4	no	—
507	C₃×D₄	—	18	2	no	—
508	C₃×D₄	—	18	2	no	—
509	C₃×D₄	—	18	2	no	—
510	C₃×D₄	—	18	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	4	2	no	—
519	C₂×C₃×C₄	—	9	1	no	—
520	C₂×C₃×C₄	—	9	1	no	—
521	C₂×C₃×C₄	—	9	1	no	—
522	C₂×C₃×C₄	—	9	1	no	—
523	C₂×C₃×C₄	—	9	1	no	—
524	C₂×C₃×C₄	—	9	1	no	—
525	C₂×C₃×C₄	—	18	2	no	—
526	C₂×C₃×C₄	—	18	2	no	—
527	C₂×C₃×C₄	—	18	2	no	—
528	C₂×C₃×C₄	—	18	2	no	—
529	C₂×C₃×C₄	—	18	2	no	—
530	C₂×C₃×C₄	—	18	2	no	—
531	C₂×C₃×C₄	—	18	2	no	—
532	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
537	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
538	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
542	#67	—	3	4	no	—
543	#67	—	6	2	no	—
544	#67	—	6	2	no	—
545	#67	—	6	2	no	—
546	C₂×Dic₃	—	3	1	no	—
547	C₂×Dic₃	—	3	1	no	—
548	C₂×Dic₃	—	3	1	no	—
549	C₂×Dic₃	—	3	1	no	—
550	C₂×Dic₃	—	3	1	no	—
551	C₂×Dic₃	—	3	1	no	—
552	C₂×Dic₃	—	6	2	no	—
553	C₂×Dic₃	—	6	2	no	—
554	C₂×Dic₃	—	6	2	no	—
555	D₁₂	—	6	2	no	—
556	C₄×D₃	—	6	2	no	—
557	C₄×D₃	—	6	2	no	—
558	C₄×D₃	—	6	2	no	—
559	C₄×D₃	—	6	2	no	—
560	Dic₆	—	6	2	no	—
561	Dic₆	—	6	2	no	—
562	C₂×C₃²	—	2	2	no	—
563	C₂×C₃²	—	4	1	no	—
564	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
565	C₂×C₃²	D₃×#41	1	1	yes	characteristic
566	C₂×C₃²	#1010	1	1	yes	characteristic
567	C₃×D₃	—	6	2	no	—
568	C₃×D₃	—	12	1	no	—
569	C₂×C₉	—	2	2	no	—
570	C₂×C₉	—	2	1	no	—
571	C₂×C₉	—	2	1	no	—
572	C₂×C₉	—	2	1	no	—
573	C₂×C₉	—	4	2	no	—
574	C₂×C₉	—	4	1	no	—
575	C₂×C₉	—	8	1	no	—
576	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
577	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
578	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
579	D₉	—	2	2	no	—
580	D₉	—	4	1	no	—
581	#41	—	18	4	no	—
582	#41	—	18	4	no	—
583	C₂×Q₈	—	9	1	no	—
584	C₂×Q₈	—	9	1	no	—
585	C₂×D₄	—	9	1	no	—
586	C₂×D₄	—	9	1	no	—
587	C₂×D₄	—	9	1	no	—
588	C₂×D₄	—	9	1	no	—
589	C₂×D₄	—	9	1	no	—
590	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
591	C₂²×C₄	—	9	1	no	—
592	C₂²×C₄	—	9	1	no	—
593	C₂²×C₄	—	9	1	no	—
594	C₂²×C₄	—	9	1	no	—
595	C₂²×C₄	—	9	1	no	—
596	C₂²×C₄	—	9	1	no	—
597	C₂²×C₄	—	9	1	no	—
598	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
599	C₄⋊C₄	—	9	1	no	—
600	C₄⋊C₄	—	9	1	no	—
601	C₄⋊C₄	—	9	1	no	—
602	C₄⋊C₄	—	9	1	no	—
603	C₄⋊C₄	—	9	1	no	—
604	C₄⋊C₄	—	9	1	no	—
605	C₄⋊C₄	—	9	1	no	—
606	C₄⋊C₄	—	9	1	no	—
607	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
608	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
609	C₂²⋊C₄	—	9	1	no	—
610	C₂²⋊C₄	—	9	1	no	—
611	C₂²⋊C₄	—	9	1	no	—
612	C₂²⋊C₄	—	9	1	no	—
613	C₂²⋊C₄	—	9	1	no	—
614	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
615	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
616	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
617	C₄²	—	9	1	no	—
618	C₂²×C₃	—	2	1	no	—
619	C₂²×C₃	—	2	1	no	—
620	C₂²×C₃	—	2	1	no	—
621	C₂²×C₃	—	2	1	no	—
622	C₂²×C₃	—	2	1	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	2	1	no	—
625	C₂²×C₃	—	2	1	no	—
626	C₂²×C₃	—	2	1	no	—
627	C₂²×C₃	—	2	1	no	—
628	C₂²×C₃	—	2	1	no	—
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	4	1	no	—
631	C₂²×C₃	—	4	1	no	—
632	C₂²×C₃	—	4	1	no	—
633	C₂²×C₃	—	4	1	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	—	9	2	no	—
636	C₂²×C₃	—	18	1	no	—
637	C₂²×C₃	—	18	1	no	—
638	C₂²×C₃	—	18	1	no	—
639	C₂²×C₃	—	18	1	no	—
640	C₂²×C₃	—	18	1	no	—
641	C₂²×C₃	D₄×D₉	1	2	yes	—
642	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
643	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
644	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
645	C₂×D₃	—	3	2	no	—
646	C₂×D₃	—	6	1	no	—
647	C₂×D₃	—	6	1	no	—
648	C₂×D₃	—	6	1	no	—
649	C₂×D₃	—	6	1	no	—
650	C₂×D₃	—	6	1	no	—
651	C₃×C₄	—	2	1	no	—
652	C₃×C₄	—	2	1	no	—
653	C₃×C₄	—	2	1	no	—
654	C₃×C₄	—	2	1	no	—
655	C₃×C₄	—	2	1	no	—
656	C₃×C₄	—	2	1	no	—
657	C₃×C₄	—	2	1	no	—
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	2	1	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	4	1	no	—
662	C₃×C₄	—	4	1	no	—
663	C₃×C₄	—	4	1	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	4	1	no	—
666	C₃×C₄	—	9	2	no	—
667	C₃×C₄	—	9	2	no	—
668	C₃×C₄	—	18	1	no	—
669	C₃×C₄	—	18	1	no	—
670	C₃×C₄	—	18	1	no	—
671	C₃×C₄	—	18	1	no	—
672	Dic₃	—	3	2	no	—
673	Dic₃	—	3	2	no	—
674	Dic₃	—	6	1	no	—
675	Dic₃	—	6	1	no	—
676	Dic₃	—	6	1	no	—
677	Dic₃	—	6	1	no	—
678	C₃²	#5655	1	1	yes	characteristic
679	C₉	—	2	1	no	—
680	C₉	C₃×#547	1	1	yes	characteristic, complemented
681	C₂³	—	9	1	no	—
682	C₂³	—	9	1	no	—
683	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
684	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
685	Q₈	—	18	2	no	—
686	Q₈	—	18	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	9	4	no	—
689	D₄	—	18	2	no	—
690	D₄	—	18	2	no	—
691	D₄	—	18	2	no	—
692	D₄	—	18	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	9	1	no	—
695	C₂×C₄	—	9	1	no	—
696	C₂×C₄	—	9	1	no	—
697	C₂×C₄	—	9	1	no	—
698	C₂×C₄	—	9	1	no	—
699	C₂×C₄	—	9	1	no	—
700	C₂×C₄	—	18	2	no	—
701	C₂×C₄	—	18	2	no	—
702	C₂×C₄	—	18	2	no	—
703	C₂×C₄	—	18	2	no	—
704	C₂×C₄	—	18	2	no	—
705	C₂×C₄	—	18	2	no	—
706	C₂×C₄	—	18	2	no	—
707	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
708	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
709	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
711	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
712	C₂×C₃	—	2	2	no	—
713	C₂×C₃	—	2	2	no	—
714	C₂×C₃	—	2	1	no	—
715	C₂×C₃	—	2	1	no	—
716	C₂×C₃	—	2	1	no	—
717	C₂×C₃	—	4	2	no	—
718	C₂×C₃	—	4	1	no	—
719	C₂×C₃	—	4	1	no	—
720	C₂×C₃	—	8	1	no	—
721	C₂×C₃	—	18	2	no	—
722	C₂×C₃	—	36	1	no	—
723	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
724	C₂×C₃	#41×D₉	1	1	yes	characteristic
725	C₂×C₃	#63716	1	1	yes	characteristic
726	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
727	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
728	C₂×C₃	C₃×#1010	1	1	yes	characteristic
729	D₃	—	6	2	no	—
730	D₃	—	12	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	9	2	no	—
737	C₂²	—	18	1	no	—
738	C₂²	—	18	1	no	—
739	C₂²	—	18	1	no	—
740	C₂²	—	18	1	no	—
741	C₂²	—	18	1	no	—
742	C₂²	C₃×D₄×D₉	1	2	yes	—
743	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	9	2	no	—
750	C₄	—	9	2	no	—
751	C₄	—	18	1	no	—
752	C₄	—	18	1	no	—
753	C₄	—	18	1	no	—
754	C₄	—	18	1	no	—
755	C₃	—	2	1	no	—
756	C₃	#10589757	1	1	yes	characteristic, direct product factor
757	C₃	C₃×#5655	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	4	1	no	—
760	C₂	—	18	2	no	—
761	C₂	—	36	1	no	—
762	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
763	C₂	C₃×#41×D₉	1	1	yes	characteristic
764	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
hypercenter	C₃×#123	D₉
hypocenter	C₉	C₃×#547
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
1. C₂×C₃×#3699	C₂	semidirect
2. C₂×C₃×#3697	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₃×#63501	C₂	semidirect
5. C₂×C₃×Dic₉⋊C₄	C₂	semidirect
6. C₃×#63458	C₂	semidirect
7. C₃×#63456	C₂	semidirect
8. C₃×C₄⋊C₄×D₉	C₂	semidirect
9. C₃×#63450	C₂	semidirect
10. C₃×#63448	C₂	semidirect
11. C₃×#63446	C₂	semidirect
12. C₃×#63445	C₂	semidirect
13. C₃×#611⋊C₄	C₂	semidirect
14. C₃×#611⋊C₄	C₂	semidirect
15. C₃×#63440	C₂	semidirect
17. #10589757	C₃	direct (N × H)
70. C₂×#3699	C₂×C₃	semidirect
71. C₂×#3697	C₂×C₃	semidirect
73. C₉×#123	C₂×C₃	semidirect
74. #63501	C₂×C₃	semidirect
75. C₂×Dic₉⋊C₄	C₂×C₃	semidirect
76. #63458	C₂×C₃	semidirect
77. #63456	C₂×C₃	semidirect
78. C₄⋊C₄×D₉	C₂×C₃	semidirect
79. #63450	C₂×C₃	semidirect
80. #63448	C₂×C₃	semidirect
81. #63446	C₂×C₃	semidirect
82. #63445	C₂×C₃	semidirect
83. #611⋊C₄	C₂×C₃	semidirect
84. #611⋊C₄	C₂×C₃	semidirect
85. #63440	C₂×C₃	semidirect
100. C₃×#611	D₄	semidirect
223. C₃×Dic₉	#41	semidirect
233. C₃×#123	D₉	semidirect
309. #611	C₃×D₄	semidirect
474. Dic₉	C₃×#41	semidirect
481. #123	C₃×D₉	semidirect
490. C₃×C₉	#547	semidirect
680. C₉	C₃×#547	semidirect
756. C₃	#10589757	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3699	2
C₂×C₃×#3697	2
C₃×C₉×#123	2
C₃×#63501	2
C₂×C₃×Dic₉⋊C₄	2
C₃×#63458	2
C₃×#63456	2
C₃×C₄⋊C₄×D₉	2
C₃×#63450	2
C₃×#63448	2
C₃×#63446	2
C₃×#63445	2
C₃×#611⋊C₄	2
C₃×#63440	2
C₃×#5655	3
#10589757	3

Subgroups — C3×#10589757 #13153014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589757 #13153014