Subgroups — C₃×#36261 #10654868

Order 768.

2350 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#554	C₂	1	2	yes	maximal
2	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	2	yes	maximal, complemented
4	C₃×#2584	C₂	1	2	yes	maximal, complemented
5	C₃×#2583	C₂	1	4	yes	maximal, complemented
6	C₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2550	C₂	1	2	yes	maximal, complemented
9	C₃×#2549	C₂	1	4	yes	maximal, complemented
10	C₃×#2440	C₂	1	2	yes	maximal, complemented
11	C₃×#2440	C₂	1	2	yes	maximal, complemented
12	C₃×#2349	C₂	1	2	yes	maximal
13	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#389	C₂	1	2	yes	maximal, complemented
17	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
18	#36261	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#554	—	2	16	no	—
20	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₃×#125	C₂²	1	2	yes	—
24	C₂×C₃×#125	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
29	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
31	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄⋊C₄	C₂²	1	4	yes	—
35	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₃×C₄²	C₂²	1	2	yes	—
38	C₃×#398	C₂²	1	4	yes	—
39	C₃×#398	C₂²	1	4	yes	—
40	C₃×#398	C₂²	1	4	yes	—
41	C₃×#395	C₂²	1	4	yes	—
42	C₃×#395	C₂²	1	4	yes	—
43	C₃×#395	C₂²	1	4	yes	—
44	C₃×#391	C₂²	1	2	yes	—
45	C₃×#391	C₂²	1	4	yes	—
46	C₃×#389	C₂²	1	2	yes	—
47	C₃×#389	C₂²	1	2	yes	—
48	C₃×#389	C₂²	1	2	yes	—
49	C₃×#389	C₂²	1	1	yes	characteristic
50	C₃×#389	C₂²	1	4	yes	—
51	C₃×#389	C₂²	1	4	yes	—
52	C₃×#389	C₂²	1	2	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	2	yes	—
55	C₃×#389	C₂²	1	2	yes	—
56	C₃×#389	C₂²	1	2	yes	—
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	2	yes	—
59	C₃×#389	C₂²	1	1	yes	characteristic
60	C₃×#389	C₂²	1	2	yes	—
61	C₃×#389	C₂²	1	4	yes	—
62	C₃×#385	C₂²	1	4	yes	—
63	C₃×#385	C₂²	1	4	yes	—
64	C₃×#385	C₂²	1	4	yes	—
65	C₃×#385	C₂²	1	4	yes	—
66	C₃×#384	C₂²	1	1	yes	characteristic
67	C₃×#384	C₂²	1	2	yes	—
68	C₃×#384	C₂²	1	1	yes	characteristic
69	C₃×#384	C₂²	1	1	yes	characteristic
70	C₃×#382	C₂²	1	2	yes	—
71	C₃×#380	C₂²	1	2	yes	—
72	C₃×#380	C₂²	1	2	yes	—
73	C₃×#380	C₂²	1	4	yes	—
74	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
78	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₂×C₃×#95	C₂²	1	4	yes	—
84	C₃×C₄³	C₂²	1	1	yes	characteristic
85	C₂×#554	C₂×C₃	1	2	yes	—
86	#2859	C₂×C₃	1	1	yes	characteristic, complemented
87	#2857	C₂×C₃	1	2	yes	complemented
88	#2584	C₂×C₃	1	2	yes	complemented
89	#2583	C₂×C₃	1	4	yes	complemented
90	#2552	C₂×C₃	1	1	yes	characteristic, complemented
91	#2551	C₂×C₃	1	1	yes	characteristic, complemented
92	#2550	C₂×C₃	1	2	yes	complemented
93	#2549	C₂×C₃	1	4	yes	complemented
94	#2440	C₂×C₃	1	2	yes	complemented
95	#2440	C₂×C₃	1	2	yes	complemented
96	#2349	C₂×C₃	1	2	yes	—
97	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
98	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
99	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂×#389	C₂×C₃	1	2	yes	complemented
101	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
102	C₂²×C₃×Q₈	C₂³	1	2	yes	—
103	C₂²×C₃×Q₈	C₂³	1	4	yes	—
104	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂³	1	4	yes	—
106	C₂³×C₃×C₄	C₂³	1	2	yes	—
107	C₂³×C₃×C₄	C₂³	1	4	yes	—
108	C₂³×C₃×C₄	C₂³	1	2	yes	—
109	C₂³×C₃×C₄	C₂³	1	2	yes	—
110	C₃×C₄⋊Q₈	—	2	8	no	—
111	C₃×C₄⋊Q₈	—	2	4	no	—
112	C₃×C₄⋊Q₈	—	4	4	no	—
113	C₃×#125	—	2	8	no	—
114	C₃×#125	—	2	8	no	—
115	C₃×C₂²⋊Q₈	—	2	16	no	—
116	C₃×C₂²⋊Q₈	—	2	16	no	—
117	C₃×C₂²⋊Q₈	—	2	16	no	—
118	C₃×C₄×Q₈	—	2	8	no	—
119	C₃×C₄×D₄	—	2	8	no	—
120	C₃×C₄×D₄	—	2	8	no	—
121	C₃×C₄×D₄	D₄	1	8	yes	—
122	C₃×C₄×D₄	Q₈	1	8	yes	complemented
123	C₃×C₄×D₄	Q₈	1	8	yes	complemented
124	C₂×C₃×C₄⋊C₄	—	2	16	no	—
125	C₂×C₃×C₄⋊C₄	—	2	8	no	—
126	C₂×C₃×C₄⋊C₄	—	4	4	no	—
127	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄²	—	4	4	no	—
160	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄²	C₂³	1	2	yes	—
163	C₂×C₃×C₄²	C₂³	1	2	yes	—
164	C₂×C₃×C₄²	C₂³	1	2	yes	—
165	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂³	1	2	yes	—
168	C₂×C₃×C₄²	C₂³	1	2	yes	—
169	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
172	C₃×#95	C₂³	1	2	yes	—
173	C₃×#95	C₂³	1	4	yes	—
174	C₃×#95	C₂³	1	4	yes	—
175	C₃×#95	C₂³	1	4	yes	—
176	C₃×#95	C₂³	1	2	yes	—
177	C₃×#95	C₂³	1	2	yes	—
178	C₃×#95	C₂³	1	2	yes	—
179	C₃×#95	C₂³	1	2	yes	—
180	C₃×#95	C₂³	1	2	yes	—
181	C₃×#95	C₂³	1	2	yes	—
182	C₃×#95	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	4	yes	—
184	C₃×#95	C₂³	1	4	yes	—
185	#554	—	2	16	no	—
186	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
187	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
188	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
189	C₂×#125	C₂²×C₃	1	2	yes	—
190	C₂×#125	C₂²×C₃	1	2	yes	—
191	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
192	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
193	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
194	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
195	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
196	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
197	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
198	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
199	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
203	C₂²×C₄²	C₂²×C₃	1	2	yes	—
204	#398	C₂²×C₃	1	4	yes	—
205	#398	C₂²×C₃	1	4	yes	—
206	#398	C₂²×C₃	1	4	yes	—
207	#395	C₂²×C₃	1	4	yes	—
208	#395	C₂²×C₃	1	4	yes	—
209	#395	C₂²×C₃	1	4	yes	—
210	#391	C₂²×C₃	1	2	yes	—
211	#391	C₂²×C₃	1	4	yes	—
212	#389	C₂²×C₃	1	2	yes	—
213	#389	C₂²×C₃	1	1	yes	characteristic
214	#389	C₂²×C₃	1	1	yes	characteristic
215	#389	C₂²×C₃	1	2	yes	—
216	#389	C₂²×C₃	1	4	yes	—
217	#389	C₂²×C₃	1	4	yes	—
218	#389	C₂²×C₃	1	2	yes	—
219	#389	C₂²×C₃	1	2	yes	—
220	#389	C₂²×C₃	1	2	yes	—
221	#389	C₂²×C₃	1	2	yes	—
222	#389	C₂²×C₃	1	2	yes	—
223	#389	C₂²×C₃	1	2	yes	—
224	#389	C₂²×C₃	1	2	yes	—
225	#389	C₂²×C₃	1	2	yes	—
226	#389	C₂²×C₃	1	2	yes	—
227	#389	C₂²×C₃	1	4	yes	—
228	#385	C₂²×C₃	1	4	yes	—
229	#385	C₂²×C₃	1	4	yes	—
230	#385	C₂²×C₃	1	4	yes	—
231	#385	C₂²×C₃	1	4	yes	—
232	#384	C₂²×C₃	1	1	yes	characteristic
233	#384	C₂²×C₃	1	2	yes	—
234	#384	C₂²×C₃	1	1	yes	characteristic
235	#384	C₂²×C₃	1	1	yes	characteristic
236	#382	C₂²×C₃	1	2	yes	—
237	#380	C₂²×C₃	1	2	yes	—
238	#380	C₂²×C₃	1	2	yes	—
239	#380	C₂²×C₃	1	4	yes	—
240	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
242	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
243	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
244	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
245	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
247	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
248	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
249	C₂×#95	C₂²×C₃	1	4	yes	—
250	C₄³	C₂²×C₃	1	1	yes	characteristic
251	C₂⁴×C₃	C₂⁴	1	2	yes	—
252	C₂×C₃×Q₈	—	2	4	no	—
253	C₂×C₃×Q₈	—	2	8	no	—
254	C₂×C₃×Q₈	—	2	4	no	—
255	C₂×C₃×Q₈	—	4	2	no	—
256	C₂×C₃×Q₈	—	4	4	no	—
257	C₂×C₃×Q₈	—	4	4	no	—
258	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
259	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
260	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
261	C₂²×C₃×C₄	—	2	4	no	—
262	C₂²×C₃×C₄	—	2	4	no	—
263	C₂²×C₃×C₄	—	2	8	no	—
264	C₂²×C₃×C₄	—	2	8	no	—
265	C₂²×C₃×C₄	—	2	8	no	—
266	C₂²×C₃×C₄	—	4	2	no	—
267	C₂²×C₃×C₄	—	4	2	no	—
268	C₂²×C₃×C₄	—	4	2	no	—
269	C₂²×C₃×C₄	—	4	2	no	—
270	C₂²×C₃×C₄	—	4	4	no	—
271	C₂²×C₃×C₄	—	4	4	no	—
272	C₂²×C₃×C₄	—	4	4	no	—
273	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
274	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
275	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
276	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
277	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
278	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
279	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
280	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
281	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
288	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
289	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
290	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
292	C₃×C₄⋊C₄	—	2	4	no	—
293	C₃×C₄⋊C₄	—	2	8	no	—
294	C₃×C₄⋊C₄	—	2	8	no	—
295	C₃×C₄⋊C₄	—	2	8	no	—
296	C₃×C₄⋊C₄	—	2	4	no	—
297	C₃×C₄⋊C₄	—	2	4	no	—
298	C₃×C₄⋊C₄	—	2	4	no	—
299	C₃×C₄⋊C₄	—	2	4	no	—
300	C₃×C₄⋊C₄	—	2	8	no	—
301	C₃×C₄⋊C₄	—	2	8	no	—
302	C₃×C₄⋊C₄	—	2	8	no	—
303	C₃×C₄⋊C₄	—	2	4	no	—
304	C₃×C₄⋊C₄	—	2	4	no	—
305	C₃×C₄⋊C₄	—	2	2	no	—
306	C₃×C₄⋊C₄	—	2	2	no	—
307	C₃×C₄⋊C₄	—	2	4	no	—
308	C₃×C₄⋊C₄	—	2	2	no	—
309	C₃×C₄⋊C₄	—	4	4	no	—
310	C₃×C₄⋊C₄	—	4	2	no	—
311	C₃×C₄⋊C₄	—	4	2	no	—
312	C₃×C₄⋊C₄	—	4	2	no	—
313	C₃×C₄⋊C₄	—	4	4	no	—
314	C₃×C₄⋊C₄	—	4	4	no	—
315	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
316	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
317	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
318	C₃×C₄⋊C₄	#41	1	4	yes	—
319	C₃×C₂²⋊C₄	—	2	8	no	—
320	C₃×C₂²⋊C₄	—	2	8	no	—
321	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
322	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
323	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
324	C₃×C₄²	—	2	4	no	—
325	C₃×C₄²	—	2	4	no	—
326	C₃×C₄²	—	2	2	no	—
327	C₃×C₄²	—	2	2	no	—
328	C₃×C₄²	—	2	4	no	—
329	C₃×C₄²	—	4	2	no	—
330	C₃×C₄²	—	4	2	no	—
331	C₃×C₄²	—	4	1	no	—
332	C₃×C₄²	—	4	1	no	—
333	C₃×C₄²	C₂×D₄	1	4	yes	—
334	C₃×C₄²	C₂×Q₈	1	4	yes	—
335	C₃×C₄²	C₂×Q₈	1	4	yes	—
336	C₂²×Q₈	C₂³×C₃	1	2	yes	—
337	C₂²×Q₈	C₂³×C₃	1	4	yes	—
338	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₃	1	4	yes	—
340	C₂³×C₄	C₂³×C₃	1	2	yes	—
341	C₂³×C₄	C₂³×C₃	1	4	yes	—
342	C₂³×C₄	C₂³×C₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₃	1	2	yes	—
344	C₄⋊Q₈	—	2	8	no	—
345	C₄⋊Q₈	—	2	4	no	—
346	C₄⋊Q₈	—	4	4	no	—
347	#125	—	2	8	no	—
348	#125	—	2	8	no	—
349	C₂²⋊Q₈	—	2	16	no	—
350	C₂²⋊Q₈	—	2	16	no	—
351	C₂²⋊Q₈	—	2	16	no	—
352	C₄×Q₈	—	2	8	no	—
353	C₄×D₄	—	2	8	no	—
354	C₄×D₄	—	2	8	no	—
355	C₄×D₄	C₃×D₄	1	8	yes	—
356	C₄×D₄	C₃×Q₈	1	8	yes	complemented
357	C₄×D₄	C₃×Q₈	1	8	yes	complemented
358	C₂×C₄⋊C₄	—	2	16	no	—
359	C₂×C₄⋊C₄	—	2	8	no	—
360	C₂×C₄⋊C₄	—	4	4	no	—
361	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
393	C₂×C₄²	—	4	4	no	—
394	C₂×C₄²	C₂³×C₃	1	2	yes	—
395	C₂×C₄²	C₂³×C₃	1	2	yes	—
396	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₃	1	2	yes	—
398	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₃	1	2	yes	—
403	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
406	#95	C₂³×C₃	1	2	yes	—
407	#95	C₂³×C₃	1	4	yes	—
408	#95	C₂³×C₃	1	4	yes	—
409	#95	C₂³×C₃	1	4	yes	—
410	#95	C₂³×C₃	1	2	yes	—
411	#95	C₂³×C₃	1	2	yes	—
412	#95	C₂³×C₃	1	2	yes	—
413	#95	C₂³×C₃	1	2	yes	—
414	#95	C₂³×C₃	1	2	yes	—
415	#95	C₂³×C₃	1	2	yes	—
416	#95	C₂³×C₃	1	4	yes	—
417	#95	C₂³×C₃	1	4	yes	—
418	#95	C₂³×C₃	1	4	yes	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	2	2	no	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	C₂²×D₄	1	4	yes	—
424	C₂³×C₃	C₂²×Q₈	1	4	yes	—
425	C₂³×C₃	C₂²×Q₈	1	4	yes	—
426	C₂³×C₃	C₂⁵	1	1	yes	characteristic
427	C₃×Q₈	—	4	8	no	—
428	C₃×Q₈	—	8	8	no	—
429	C₃×D₄	C₄⋊Q₈	1	16	yes	complemented
430	C₂×C₃×C₄	—	2	2	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	2	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	2	2	no	—
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	2	16	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	4	no	—
453	C₂×C₃×C₄	—	2	4	no	—
454	C₂×C₃×C₄	—	2	4	no	—
455	C₂×C₃×C₄	—	2	2	no	—
456	C₂×C₃×C₄	—	2	2	no	—
457	C₂×C₃×C₄	—	2	4	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	2	4	no	—
460	C₂×C₃×C₄	—	2	2	no	—
461	C₂×C₃×C₄	—	2	2	no	—
462	C₂×C₃×C₄	—	2	4	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	4	8	no	—
465	C₂×C₃×C₄	—	4	8	no	—
466	C₂×C₃×C₄	—	4	16	no	—
467	C₂×C₃×C₄	—	8	8	no	—
468	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
469	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
470	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
471	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
472	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
473	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
474	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
475	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
476	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
477	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
478	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
479	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
480	C₂×C₃×C₄	C₂×#41	1	4	yes	—
481	C₂×C₃×C₄	C₂×#41	1	2	yes	—
482	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
483	C₂⁴	C₂⁴×C₃	1	2	yes	—
484	C₂×Q₈	—	2	4	no	—
485	C₂×Q₈	—	2	8	no	—
486	C₂×Q₈	—	2	4	no	—
487	C₂×Q₈	—	4	2	no	—
488	C₂×Q₈	—	4	4	no	—
489	C₂×Q₈	—	4	4	no	—
490	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
491	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
492	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	8	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	4	no	—
503	C₂²×C₄	—	4	4	no	—
504	C₂²×C₄	—	4	4	no	—
505	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
506	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
507	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
508	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	8	no	—
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	2	8	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	8	no	—
533	C₄⋊C₄	—	2	8	no	—
534	C₄⋊C₄	—	2	8	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	4	no	—
547	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
548	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
549	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
550	C₄⋊C₄	C₃×#41	1	4	yes	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
554	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
555	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	2	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	4	2	no	—
562	C₄²	—	4	2	no	—
563	C₄²	—	4	1	no	—
564	C₄²	—	4	1	no	—
565	C₄²	C₂×C₃×D₄	1	4	yes	—
566	C₄²	C₂×C₃×Q₈	1	4	yes	—
567	C₄²	C₂×C₃×Q₈	1	4	yes	—
568	C₂²×C₃	—	2	4	no	—
569	C₂²×C₃	—	2	4	no	—
570	C₂²×C₃	—	2	4	no	—
571	C₂²×C₃	—	2	4	no	—
572	C₂²×C₃	—	2	4	no	—
573	C₂²×C₃	—	2	4	no	—
574	C₂²×C₃	C₂×C₄⋊Q₈	1	8	yes	—
575	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
576	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
577	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
578	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
579	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂²×C₃	#585	1	1	yes	characteristic
581	C₂²×C₃	#585	1	1	yes	characteristic
582	C₃×C₄	—	2	4	no	—
583	C₃×C₄	—	2	2	no	—
584	C₃×C₄	—	2	4	no	—
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	2	no	—
587	C₃×C₄	—	2	4	no	—
588	C₃×C₄	—	2	2	no	—
589	C₃×C₄	—	2	4	no	—
590	C₃×C₄	—	2	2	no	—
591	C₃×C₄	—	4	4	no	—
592	C₃×C₄	—	4	2	no	—
593	C₃×C₄	—	4	2	no	—
594	C₃×C₄	—	4	4	no	—
595	C₃×C₄	—	4	2	no	—
596	C₃×C₄	C₂×C₄⋊Q₈	1	4	yes	—
597	C₃×C₄	#554	1	4	yes	complemented
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	C₂²×C₃×D₄	1	4	yes	—
603	C₂³	C₂²×C₃×Q₈	1	4	yes	—
604	C₂³	C₂²×C₃×Q₈	1	4	yes	—
605	C₂³	C₂⁵×C₃	1	1	yes	characteristic
606	Q₈	—	4	8	no	—
607	Q₈	—	8	8	no	—
608	D₄	C₃×C₄⋊Q₈	1	16	yes	complemented
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	16	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	16	no	—
646	C₂×C₄	—	8	8	no	—
647	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
648	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
649	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
650	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
651	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
652	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
653	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
654	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
655	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
656	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
657	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
658	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
659	C₂×C₄	C₂×C₃×#41	1	4	yes	—
660	C₂×C₄	C₂×C₃×#41	1	2	yes	—
661	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
662	C₂×C₃	—	2	8	no	—
663	C₂×C₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
664	C₂×C₃	D₄×#41	1	1	yes	characteristic
665	C₂×C₃	C₂×#554	1	1	yes	characteristic
666	C₂×C₃	Q₈×#41	1	1	yes	characteristic
667	C₂×C₃	#3496	1	1	yes	characteristic
668	C₂×C₃	#3501	1	1	yes	characteristic
669	C₂×C₃	#3504	1	1	yes	characteristic
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	2	4	no	—
676	C₂²	C₂×C₃×C₄⋊Q₈	1	8	yes	—
677	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
678	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
679	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
680	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
681	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂²	C₃×#585	1	1	yes	characteristic
683	C₂²	C₃×#585	1	1	yes	characteristic
684	C₄	—	2	4	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	4	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	4	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	2	no	—
698	C₄	C₂×C₃×C₄⋊Q₈	1	4	yes	—
699	C₄	C₃×#554	1	4	yes	complemented
700	C₃	#36261	1	1	yes	characteristic, direct product factor, Sylow
701	C₂	—	2	8	no	—
702	C₂	C₂²×C₃×C₄⋊Q₈	1	1	yes	characteristic
703	C₂	C₃×D₄×#41	1	1	yes	characteristic
704	C₂	C₂×C₃×#554	1	1	yes	characteristic
705	C₂	C₃×Q₈×#41	1	1	yes	characteristic
706	C₂	C₃×#3496	1	1	yes	characteristic
707	C₂	C₃×#3501	1	1	yes	characteristic
708	C₂	C₃×#3504	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2859	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2584	C₂	semidirect
5. C₃×#2583	C₂	semidirect
6. C₃×#2552	C₂	semidirect
7. C₃×#2551	C₂	semidirect
8. C₃×#2550	C₂	semidirect
9. C₃×#2549	C₂	semidirect
10. C₃×#2440	C₂	semidirect
11. C₃×#2440	C₂	semidirect
15. C₃×C₄×C₄⋊Q₈	C₂	semidirect
16. C₂×C₃×#389	C₂	semidirect
18. #36261	C₃	direct (N × H)
86. #2859	C₂×C₃	semidirect
87. #2857	C₂×C₃	semidirect
88. #2584	C₂×C₃	semidirect
89. #2583	C₂×C₃	semidirect
90. #2552	C₂×C₃	semidirect
91. #2551	C₂×C₃	semidirect
92. #2550	C₂×C₃	semidirect
93. #2549	C₂×C₃	semidirect
94. #2440	C₂×C₃	semidirect
95. #2440	C₂×C₃	semidirect
99. C₄×C₄⋊Q₈	C₂×C₃	semidirect
100. C₂×#389	C₂×C₃	semidirect
122. C₃×C₄×D₄	Q₈	semidirect
123. C₃×C₄×D₄	Q₈	semidirect
356. C₄×D₄	C₃×Q₈	semidirect
357. C₄×D₄	C₃×Q₈	semidirect
429. C₃×D₄	C₄⋊Q₈	semidirect
597. C₃×C₄	#554	semidirect
608. D₄	C₃×C₄⋊Q₈	semidirect
699. C₄	C₃×#554	semidirect
700. C₃	#36261	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×#554	2
C₃×#2859	2
C₃×#2857	2
C₃×#2584	2
C₃×#2583	2
C₃×#2552	2
C₃×#2551	2
C₃×#2550	2
C₃×#2549	2
C₃×#2440	2
C₃×#2349	2
C₃×D₄×C₄⋊C₄	2
C₃×C₄×C₄⋊Q₈	2
C₂×C₃×#389	2
C₃×C₄²×D₄	2
#36261	3

Subgroups — C3×#36261 #10654868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36261 #10654868