Subgroups — C₂×C₄₁×#2211 #23809779

Order 10496.

722 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SD₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2211	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#357	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₄₁	—	2	1	no	—
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₁	—	2	1	no	—
14	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
15	C₂×Q₃₂×C₄₁	—	2	4	no	—
16	C₂×Q₃₂×C₄₁	C₂²	1	4	yes	complemented
17	C₂×SD₃₂×C₄₁	—	2	4	no	—
18	C₂×SD₃₂×C₄₁	C₂²	1	4	yes	—
19	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#495	—	2	2	no	—
22	C₄₁×#495	C₂²	1	4	yes	—
23	C₄×Q₁₆×C₄₁	—	2	2	no	—
24	C₄×Q₁₆×C₄₁	C₂²	1	4	yes	complemented
25	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	—	2	1	no	—
27	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×C₄⋊C₁₆	C₂²	1	4	yes	complemented
29	C₄₁×#358	C₂²	1	4	yes	complemented
30	C₄₁×#357	C₂²	1	4	yes	—
31	C₂²×Q₈×C₄₁	—	2	1	no	—
32	C₂²×Q₈×C₄₁	—	2	1	no	—
33	C₂²×D₄×C₄₁	—	2	1	no	—
34	C₂×Q₁₆×C₄₁	—	2	1	no	—
35	C₂×Q₁₆×C₄₁	—	2	2	no	—
36	C₂×Q₁₆×C₄₁	—	2	1	no	—
37	C₂×Q₁₆×C₄₁	—	2	2	no	—
38	C₂×Q₁₆×C₄₁	—	2	2	no	—
39	C₂×Q₁₆×C₄₁	D₄	1	4	yes	—
40	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
41	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
42	C₂×SD₁₆×C₄₁	—	2	4	no	—
43	C₂×SD₁₆×C₄₁	—	4	4	no	—
44	C₂×D₈×C₄₁	—	2	2	no	—
45	C₂×D₈×C₄₁	—	2	1	no	—
46	C₂×D₈×C₄₁	—	2	2	no	—
47	C₂×D₈×C₄₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
50	#124×C₄₁	—	2	4	no	—
51	#124×C₄₁	—	4	2	no	—
52	C₄×Q₈×C₄₁	—	2	4	no	—
53	C₄×Q₈×C₄₁	—	4	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₁	—	4	1	no	—
56	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
58	C₂×C₄²×C₄₁	—	4	1	no	—
59	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
60	Q₃₂×C₄₁	—	2	8	no	—
61	SD₃₂×C₄₁	—	2	8	no	—
62	C₂×C₁₆×C₄₁	—	2	2	no	—
63	C₂×C₁₆×C₄₁	—	2	2	no	—
64	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
65	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
66	#107×C₄₁	—	2	1	no	—
67	#107×C₄₁	C₂³	1	2	yes	—
68	#103×C₄₁	—	2	4	no	—
69	C₄×C₈×C₄₁	D₄	1	2	yes	—
70	C₄×C₈×C₄₁	C₂³	1	2	yes	—
71	C₂⁴×C₄₁	—	4	1	no	—
72	C₂×Q₈×C₄₁	—	2	4	no	—
73	C₂×Q₈×C₄₁	—	2	2	no	—
74	C₂×Q₈×C₄₁	—	2	2	no	—
75	C₂×Q₈×C₄₁	—	4	1	no	—
76	C₂×Q₈×C₄₁	—	4	1	no	—
77	C₂×Q₈×C₄₁	—	4	2	no	—
78	C₂×Q₈×C₄₁	—	4	2	no	—
79	C₂×Q₈×C₄₁	—	4	2	no	—
80	C₂×D₄×C₄₁	—	2	2	no	—
81	C₂×D₄×C₄₁	—	4	2	no	—
82	C₂×D₄×C₄₁	—	4	1	no	—
83	C₂×D₄×C₄₁	—	4	2	no	—
84	C₂²×C₄×C₄₁	—	4	1	no	—
85	C₂²×C₄×C₄₁	—	4	1	no	—
86	C₂²×C₄×C₄₁	—	4	1	no	—
87	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
90	Q₁₆×C₄₁	—	2	4	no	—
91	Q₁₆×C₄₁	—	2	2	no	—
92	Q₁₆×C₄₁	—	2	2	no	—
93	Q₁₆×C₄₁	—	2	2	no	—
94	Q₁₆×C₄₁	—	4	2	no	—
95	Q₁₆×C₄₁	C₂×D₄	1	4	yes	—
96	SD₁₆×C₄₁	—	4	8	no	—
97	D₈×C₄₁	—	2	2	no	—
98	D₈×C₄₁	—	2	2	no	—
99	D₈×C₄₁	—	4	2	no	—
100	C₂×C₈×C₄₁	—	2	2	no	—
101	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₄₁	#41	1	2	yes	—
105	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₄₁	—	2	2	no	—
107	C₄⋊C₄×C₄₁	—	4	1	no	—
108	C₄⋊C₄×C₄₁	—	4	4	no	—
109	C₂²⋊C₄×C₄₁	—	4	4	no	—
110	C₂²⋊C₄×C₄₁	—	4	4	no	—
111	C₄²×C₄₁	—	4	4	no	—
112	C₄²×C₄₁	D₈	1	2	yes	—
113	C₄²×C₄₁	C₂×D₄	1	2	yes	—
114	C₁₆×C₄₁	—	2	2	no	—
115	C₁₆×C₄₁	—	2	2	no	—
116	C₂³×C₄₁	—	4	2	no	—
117	C₂³×C₄₁	—	8	2	no	—
118	C₂³×C₄₁	—	8	2	no	—
119	C₂³×C₄₁	—	8	2	no	—
120	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
121	Q₈×C₄₁	—	2	4	no	—
122	Q₈×C₄₁	—	4	2	no	—
123	Q₈×C₄₁	—	4	4	no	—
124	Q₈×C₄₁	—	4	2	no	—
125	Q₈×C₄₁	—	4	2	no	—
126	Q₈×C₄₁	—	8	2	no	—
127	D₄×C₄₁	—	4	2	no	—
128	D₄×C₄₁	—	4	2	no	—
129	D₄×C₄₁	—	8	2	no	—
130	C₂×C₄×C₄₁	—	2	2	no	—
131	C₂×C₄×C₄₁	—	2	2	no	—
132	C₂×C₄×C₄₁	—	4	2	no	—
133	C₂×C₄×C₄₁	—	4	4	no	—
134	C₂×C₄×C₄₁	—	4	2	no	—
135	C₂×C₄×C₄₁	—	4	2	no	—
136	C₂×C₄×C₄₁	—	8	2	no	—
137	C₂×C₄×C₄₁	—	8	2	no	—
138	C₂×C₄×C₄₁	#121	1	2	yes	—
139	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
140	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
141	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
142	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
143	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
144	C₈×C₄₁	—	2	2	no	—
145	C₈×C₄₁	#121	1	2	yes	—
146	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
147	C₈×C₄₁	C₂×#41	1	1	yes	characteristic
148	C₂×#2211	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂²×C₄₁	—	8	2	no	—
150	C₂²×C₄₁	—	8	2	no	—
151	C₂²×C₄₁	—	8	2	no	—
152	C₂²×C₄₁	—	16	4	no	—
153	C₂²×C₄₁	#459	1	2	yes	—
154	C₂²×C₄₁	#508	1	2	yes	—
155	C₂²×C₄₁	#510	1	2	yes	—
156	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
157	C₄×C₄₁	—	2	2	no	—
158	C₄×C₄₁	—	2	2	no	—
159	C₄×C₄₁	—	4	4	no	—
160	C₄×C₄₁	—	8	2	no	—
161	C₄×C₄₁	—	8	2	no	—
162	C₄×C₄₁	#459	1	2	yes	—
163	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
164	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂²×Q₃₂	C₂×C₄₁	1	1	yes	characteristic, complemented
166	C₂²×SD₃₂	C₂×C₄₁	1	1	yes	characteristic
167	C₂×#495	C₂×C₄₁	1	1	yes	characteristic
168	C₂×C₄×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
169	#2211	C₂×C₄₁	1	8	yes	direct product factor
170	C₂×C₄⋊C₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
171	C₂×#358	C₂×C₄₁	1	1	yes	characteristic, complemented
172	C₂×#357	C₂×C₄₁	1	1	yes	characteristic
173	C₂×C₄₁	—	16	2	no	—
174	C₂×C₄₁	#2211	1	4	yes	direct product factor
175	C₂×C₄₁	C₂×#459	1	1	yes	characteristic
176	C₂×C₄₁	C₂×#508	1	1	yes	characteristic
177	C₂×C₄₁	C₂×#510	1	1	yes	characteristic
178	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
179	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
180	C₂²×SD₁₆	—	2	1	no	—
181	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
182	C₂×#124	—	2	1	no	—
183	C₂×C₄×Q₈	—	2	1	no	—
184	C₂×Q₃₂	—	2	4	no	—
185	C₂×Q₃₂	C₂²×C₄₁	1	4	yes	complemented
186	C₂×SD₃₂	—	2	4	no	—
187	C₂×SD₃₂	C₂²×C₄₁	1	4	yes	—
188	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
189	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
190	#495	—	2	2	no	—
191	#495	C₂²×C₄₁	1	4	yes	—
192	C₄×Q₁₆	—	2	2	no	—
193	C₄×Q₁₆	C₂²×C₄₁	1	4	yes	complemented
194	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
195	C₂×#103	—	2	1	no	—
196	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
197	C₄⋊C₁₆	C₂²×C₄₁	1	4	yes	complemented
198	#358	C₂²×C₄₁	1	4	yes	complemented
199	#357	C₂²×C₄₁	1	4	yes	—
200	C₄₁	C₂×#2211	1	1	yes	characteristic, direct product factor, Sylow
201	C₂²×Q₈	—	2	1	no	—
202	C₂²×Q₈	—	2	1	no	—
203	C₂²×D₄	—	2	1	no	—
204	C₂×Q₁₆	—	2	1	no	—
205	C₂×Q₁₆	—	2	2	no	—
206	C₂×Q₁₆	—	2	1	no	—
207	C₂×Q₁₆	—	2	2	no	—
208	C₂×Q₁₆	—	2	2	no	—
209	C₂×Q₁₆	D₄×C₄₁	1	4	yes	—
210	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
211	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
212	C₂×SD₁₆	—	2	4	no	—
213	C₂×SD₁₆	—	4	4	no	—
214	C₂×D₈	—	2	2	no	—
215	C₂×D₈	—	2	1	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	C₂³×C₄₁	1	2	yes	—
218	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
220	#124	—	2	4	no	—
221	#124	—	4	2	no	—
222	C₄×Q₈	—	2	4	no	—
223	C₄×Q₈	—	4	2	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	4	1	no	—
226	C₂×C₂²⋊C₄	—	4	1	no	—
227	C₂×C₂²⋊C₄	—	4	1	no	—
228	C₂×C₄²	—	4	1	no	—
229	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
230	Q₃₂	—	2	8	no	—
231	SD₃₂	—	2	8	no	—
232	C₂×C₁₆	—	2	2	no	—
233	C₂×C₁₆	—	2	2	no	—
234	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
235	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
236	#107	—	2	1	no	—
237	#107	C₂³×C₄₁	1	2	yes	—
238	#103	—	2	4	no	—
239	C₄×C₈	D₄×C₄₁	1	2	yes	—
240	C₄×C₈	C₂³×C₄₁	1	2	yes	—
241	C₂⁴	—	4	1	no	—
242	C₂×Q₈	—	2	4	no	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	2	2	no	—
245	C₂×Q₈	—	4	1	no	—
246	C₂×Q₈	—	4	1	no	—
247	C₂×Q₈	—	4	2	no	—
248	C₂×Q₈	—	4	2	no	—
249	C₂×Q₈	—	4	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂×D₄	—	4	1	no	—
253	C₂×D₄	—	4	2	no	—
254	C₂²×C₄	—	4	1	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
258	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
260	Q₁₆	—	2	4	no	—
261	Q₁₆	—	2	2	no	—
262	Q₁₆	—	2	2	no	—
263	Q₁₆	—	2	2	no	—
264	Q₁₆	—	4	2	no	—
265	Q₁₆	C₂×D₄×C₄₁	1	4	yes	—
266	SD₁₆	—	4	8	no	—
267	D₈	—	2	2	no	—
268	D₈	—	2	2	no	—
269	D₈	—	4	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
272	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
273	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
274	C₂×C₈	#41×C₄₁	1	2	yes	—
275	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	4	1	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₂²⋊C₄	—	4	4	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₄²	—	4	4	no	—
282	C₄²	D₈×C₄₁	1	2	yes	—
283	C₄²	C₂×D₄×C₄₁	1	2	yes	—
284	C₁₆	—	2	2	no	—
285	C₁₆	—	2	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	—	8	2	no	—
288	C₂³	—	8	2	no	—
289	C₂³	—	8	2	no	—
290	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
291	Q₈	—	2	4	no	—
292	Q₈	—	4	2	no	—
293	Q₈	—	4	4	no	—
294	Q₈	—	4	2	no	—
295	Q₈	—	4	2	no	—
296	Q₈	—	8	2	no	—
297	D₄	—	4	2	no	—
298	D₄	—	4	2	no	—
299	D₄	—	8	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	8	2	no	—
307	C₂×C₄	—	8	2	no	—
308	C₂×C₄	#121×C₄₁	1	2	yes	—
309	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
310	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
311	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
312	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
313	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
314	C₈	—	2	2	no	—
315	C₈	#121×C₄₁	1	2	yes	—
316	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
317	C₈	C₂×#41×C₄₁	1	1	yes	characteristic
318	C₂²	—	8	2	no	—
319	C₂²	—	8	2	no	—
320	C₂²	—	8	2	no	—
321	C₂²	—	16	4	no	—
322	C₂²	C₄₁×#459	1	2	yes	—
323	C₂²	C₄₁×#508	1	2	yes	—
324	C₂²	C₄₁×#510	1	2	yes	—
325	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	4	4	no	—
329	C₄	—	8	2	no	—
330	C₄	—	8	2	no	—
331	C₄	C₄₁×#459	1	2	yes	—
332	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
333	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
334	C₂	—	16	2	no	—
335	C₂	C₄₁×#2211	1	4	yes	direct product factor
336	C₂	C₂×C₄₁×#459	1	1	yes	characteristic
337	C₂	C₂×C₄₁×#508	1	1	yes	characteristic
338	C₂	C₂×C₄₁×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ C₂×C₄×C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₃₂×C₄₁	C₂	semidirect
4. C₂×C₄×Q₁₆×C₄₁	C₂	semidirect
5. C₄₁×#2211	C₂	direct (N × H)
6. C₂×C₄₁×C₄⋊C₁₆	C₂	semidirect
7. C₂×C₄₁×#358	C₂	semidirect
16. C₂×Q₃₂×C₄₁	C₂²	semidirect
24. C₄×Q₁₆×C₄₁	C₂²	semidirect
28. C₄₁×C₄⋊C₁₆	C₂²	semidirect
29. C₄₁×#358	C₂²	semidirect
148. C₂×#2211	C₄₁	direct (N × H)
165. C₂²×Q₃₂	C₂×C₄₁	semidirect
168. C₂×C₄×Q₁₆	C₂×C₄₁	semidirect
169. #2211	C₂×C₄₁	direct (N × H)
170. C₂×C₄⋊C₁₆	C₂×C₄₁	semidirect
171. C₂×#358	C₂×C₄₁	semidirect
174. C₂×C₄₁	#2211	direct (N × H)
185. C₂×Q₃₂	C₂²×C₄₁	semidirect
193. C₄×Q₁₆	C₂²×C₄₁	semidirect
197. C₄⋊C₁₆	C₂²×C₄₁	semidirect
198. #358	C₂²×C₄₁	semidirect
200. C₄₁	C₂×#2211	direct (N × H)
335. C₂	C₄₁×#2211	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Q₃₂×C₄₁	2
C₂²×SD₃₂×C₄₁	2
C₂×C₄₁×#495	2
C₂×C₄×Q₁₆×C₄₁	2
C₄₁×#2211	2
C₂×C₄₁×C₄⋊C₁₆	2
C₂×C₄₁×#358	2
C₂×C₄₁×#357	2
C₂×#2211	41

Subgroups — C2×C41×#2211 #23809779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2211 #23809779