Subgroups — C₄₁×#33027 #23809228

Order 10496.

854 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#477	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2862	C₂	1	1	yes	maximal, characteristic
4	C₄²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1987	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1981	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1928	C₂	1	4	yes	maximal
8	C₄₁×#1878	C₂	1	4	yes	maximal
9	C₄₁×#1831	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#477	—	2	4	no	—
16	C₄₁×#462	—	2	4	no	—
17	C₂×#107×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#103×C₄₁	C₂²	1	2	yes	—
21	C₂×#103×C₄₁	C₂²	1	4	yes	—
22	C₂×#103×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#391	—	2	2	no	—
24	C₄₁×#391	C₂²	1	4	yes	—
25	C₄₁×#382	—	2	1	no	—
26	C₄₁×#382	—	2	1	no	—
27	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄³×C₄₁	—	2	1	no	—
32	C₄³×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#340	C₂²	1	4	yes	—
34	C₄₁×#336	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₁	—	2	1	no	—
36	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
37	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₄₁	—	2	4	no	—
39	C₂×Q₁₆×C₄₁	—	2	8	no	—
40	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
42	C₄⋊Q₈×C₄₁	—	2	2	no	—
43	C₄⋊Q₈×C₄₁	—	2	2	no	—
44	C₄⋊Q₈×C₄₁	—	2	2	no	—
45	C₄⋊Q₈×C₄₁	—	2	2	no	—
46	C₄×Q₈×C₄₁	—	2	4	no	—
47	C₄×Q₈×C₄₁	—	2	4	no	—
48	C₄×Q₈×C₄₁	—	2	2	no	—
49	C₄×Q₈×C₄₁	D₄	1	4	yes	—
50	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₄₁	—	2	2	no	—
59	C₂×C₄²×C₄₁	—	2	1	no	—
60	C₂×C₄²×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	—	2	1	no	—
62	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₁	D₄	1	2	yes	—
64	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
67	#107×C₄₁	—	2	4	no	—
68	C₄⋊C₈×C₄₁	—	2	2	no	—
69	C₄⋊C₈×C₄₁	—	2	2	no	—
70	#103×C₄₁	—	2	4	no	—
71	#103×C₄₁	—	2	4	no	—
72	#103×C₄₁	—	2	8	no	—
73	#95×C₄₁	—	2	2	no	—
74	#95×C₄₁	—	2	1	no	—
75	#95×C₄₁	—	2	4	no	—
76	#95×C₄₁	—	2	4	no	—
77	C₂×Q₈×C₄₁	—	2	1	no	—
78	C₂×Q₈×C₄₁	—	2	2	no	—
79	C₂×Q₈×C₄₁	—	2	2	no	—
80	C₂×Q₈×C₄₁	—	2	4	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	2	4	no	—
83	C₂×Q₈×C₄₁	—	4	4	no	—
84	C₂×Q₈×C₄₁	—	4	2	no	—
85	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
86	C₂×Q₈×C₄₁	#41	1	4	yes	—
87	C₂²×C₄×C₄₁	—	2	1	no	—
88	C₂²×C₄×C₄₁	—	2	1	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
97	Q₁₆×C₄₁	—	4	8	no	—
98	C₂×C₈×C₄₁	—	2	2	no	—
99	C₂×C₈×C₄₁	—	2	2	no	—
100	C₂×C₈×C₄₁	—	2	4	no	—
101	C₂×C₈×C₄₁	—	2	4	no	—
102	C₄⋊C₄×C₄₁	—	2	8	no	—
103	C₄⋊C₄×C₄₁	—	2	4	no	—
104	C₄⋊C₄×C₄₁	—	2	1	no	—
105	C₄⋊C₄×C₄₁	—	2	2	no	—
106	C₄⋊C₄×C₄₁	—	2	2	no	—
107	C₄⋊C₄×C₄₁	—	2	2	no	—
108	C₄⋊C₄×C₄₁	—	4	2	no	—
109	C₄⋊C₄×C₄₁	—	4	2	no	—
110	C₄⋊C₄×C₄₁	—	4	2	no	—
111	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
112	C₄⋊C₄×C₄₁	#41	1	4	yes	—
113	C₄²×C₄₁	—	2	8	no	—
114	C₄²×C₄₁	—	2	4	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	2	no	—
118	C₄²×C₄₁	—	4	2	no	—
119	C₄²×C₄₁	—	4	4	no	—
120	C₄²×C₄₁	—	4	2	no	—
121	C₄²×C₄₁	Q₁₆	1	4	yes	complemented
122	C₄²×C₄₁	C₂×D₄	1	2	yes	—
123	C₄²×C₄₁	#41	1	2	yes	—
124	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₄₁	—	2	4	no	—
126	Q₈×C₄₁	—	2	2	no	—
127	Q₈×C₄₁	—	4	2	no	—
128	Q₈×C₄₁	—	4	4	no	—
129	Q₈×C₄₁	—	4	2	no	—
130	Q₈×C₄₁	—	8	4	no	—
131	Q₈×C₄₁	#124	1	4	yes	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	2	no	—
134	C₂×C₄×C₄₁	—	2	4	no	—
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	2	no	—
137	C₂×C₄×C₄₁	—	2	2	no	—
138	C₂×C₄×C₄₁	—	2	2	no	—
139	C₂×C₄×C₄₁	—	2	4	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	#121	1	2	yes	—
150	C₂×C₄×C₄₁	#121	1	2	yes	—
151	C₂×C₄×C₄₁	C₂×Q₁₆	1	4	yes	—
152	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
153	C₂×C₄×C₄₁	#137	1	2	yes	—
154	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
158	C₈×C₄₁	—	4	2	no	—
159	C₈×C₄₁	—	4	2	no	—
160	#33027	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
162	C₂²×C₄₁	#525	1	2	yes	—
163	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
164	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
165	C₂²×C₄₁	#575	1	2	yes	—
166	C₄×C₄₁	—	2	4	no	—
167	C₄×C₄₁	—	2	4	no	—
168	C₄×C₄₁	—	2	2	no	—
169	C₄×C₄₁	—	4	2	no	—
170	C₄×C₄₁	—	4	4	no	—
171	C₄×C₄₁	—	4	2	no	—
172	C₄×C₄₁	—	8	2	no	—
173	C₄×C₄₁	—	8	2	no	—
174	C₄×C₄₁	#462	1	4	yes	—
175	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
176	C₄×C₄₁	#529	1	2	yes	—
177	C₄×C₄₁	#532	1	1	yes	characteristic
178	C₂×#477	C₂×C₄₁	1	1	yes	characteristic
179	C₂×#462	C₂×C₄₁	1	1	yes	characteristic
180	#2862	C₂×C₄₁	1	1	yes	characteristic
181	C₄²×Q₈	C₂×C₄₁	1	1	yes	characteristic
182	#1987	C₂×C₄₁	1	1	yes	characteristic
183	#1981	C₂×C₄₁	1	1	yes	characteristic
184	#1928	C₂×C₄₁	1	4	yes	—
185	#1878	C₂×C₄₁	1	4	yes	—
186	#1831	C₂×C₄₁	1	1	yes	characteristic
187	C₂×C₄₁	#2850	1	1	yes	characteristic
188	C₂×C₄₁	C₂×#462	1	1	yes	characteristic
189	C₂×C₄₁	#3040	1	1	yes	characteristic
190	C₂×C₄₁	#3104	1	2	yes	—
191	C₂×C₄₁	#3116	1	2	yes	—
192	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
196	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
197	#477	—	2	4	no	—
198	#462	—	2	4	no	—
199	C₂×#107	C₂²×C₄₁	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
202	C₂×#103	C₂²×C₄₁	1	2	yes	—
203	C₂×#103	C₂²×C₄₁	1	4	yes	—
204	C₂×#103	C₂²×C₄₁	1	2	yes	—
205	#391	—	2	2	no	—
206	#391	C₂²×C₄₁	1	4	yes	—
207	#382	—	2	1	no	—
208	#382	—	2	1	no	—
209	C₄×C₄⋊C₄	—	2	1	no	—
210	C₄×C₄⋊C₄	—	2	2	no	—
211	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
213	C₄³	—	2	1	no	—
214	C₄³	C₂²×C₄₁	1	1	yes	characteristic
215	#340	C₂²×C₄₁	1	4	yes	—
216	#336	C₂²×C₄₁	1	4	yes	—
217	C₄₁	#33027	1	1	yes	characteristic, direct product factor, Sylow
218	C₂²×Q₈	—	2	1	no	—
219	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
220	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
221	C₂×Q₁₆	—	2	4	no	—
222	C₂×Q₁₆	—	2	8	no	—
223	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
224	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄×Q₈	—	2	4	no	—
230	C₄×Q₈	—	2	4	no	—
231	C₄×Q₈	—	2	2	no	—
232	C₄×Q₈	D₄×C₄₁	1	4	yes	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₄₁	1	2	yes	—
247	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
250	#107	—	2	4	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	2	2	no	—
253	#103	—	2	4	no	—
254	#103	—	2	4	no	—
255	#103	—	2	8	no	—
256	#95	—	2	2	no	—
257	#95	—	2	1	no	—
258	#95	—	2	4	no	—
259	#95	—	2	4	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	4	4	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
269	C₂×Q₈	#41×C₄₁	1	4	yes	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
280	Q₁₆	—	4	8	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
295	C₄⋊C₄	#41×C₄₁	1	4	yes	—
296	C₄²	—	2	8	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	4	2	no	—
302	C₄²	—	4	4	no	—
303	C₄²	—	4	2	no	—
304	C₄²	Q₁₆×C₄₁	1	4	yes	complemented
305	C₄²	C₂×D₄×C₄₁	1	2	yes	—
306	C₄²	#41×C₄₁	1	2	yes	—
307	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
308	Q₈	—	2	4	no	—
309	Q₈	—	2	2	no	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	4	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	8	4	no	—
314	Q₈	#124×C₄₁	1	4	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	#121×C₄₁	1	2	yes	—
333	C₂×C₄	#121×C₄₁	1	2	yes	—
334	C₂×C₄	C₂×Q₁₆×C₄₁	1	4	yes	—
335	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
336	C₂×C₄	#137×C₄₁	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
338	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
339	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
341	C₈	—	4	2	no	—
342	C₈	—	4	2	no	—
343	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
344	C₂²	C₄₁×#525	1	2	yes	—
345	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
346	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
347	C₂²	C₄₁×#575	1	2	yes	—
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	2	4	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	4	no	—
354	C₄	—	8	2	no	—
355	C₄	—	8	2	no	—
356	C₄	C₄₁×#462	1	4	yes	—
357	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
358	C₄	C₄₁×#529	1	2	yes	—
359	C₄	C₄₁×#532	1	1	yes	characteristic
360	C₂	C₄₁×#2850	1	1	yes	characteristic
361	C₂	C₂×C₄₁×#462	1	1	yes	characteristic
362	C₂	C₄₁×#3040	1	1	yes	characteristic
363	C₂	C₄₁×#3104	1	2	yes	—
364	C₂	C₄₁×#3116	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
121. C₄²×C₄₁	Q₁₆	semidirect
160. #33027	C₄₁	direct (N × H)
217. C₄₁	#33027	direct (N × H)
304. C₄²	Q₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#477	2
C₂×C₄₁×#462	2
C₄₁×#2862	2
C₄²×Q₈×C₄₁	2
C₄₁×#1987	2
C₄₁×#1981	2
C₄₁×#1928	2
C₄₁×#1878	2
C₄₁×#1831	2
#33027	41

Subgroups — C41×#33027 #23809228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33027 #23809228