Subgroups — C₄₁×#8569 #23784770

Order 10496.

548 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2293	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×D₄⋊C₈	C₂	1	2	yes	maximal
5	C₄₁×#1279	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×#117×C₄₁	—	2	1	no	—
8	C₂×C₄⋊C₈×C₄₁	—	2	1	no	—
9	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
11	C₄₁×#390	C₄	1	1	yes	characteristic
12	C₄₁×#390	C₄	1	1	yes	characteristic
13	C₄₁×#389	C₄	1	1	yes	characteristic
14	C₄₁×#389	C₄	1	1	yes	characteristic
15	C₄₁×#388	—	2	1	no	—
16	C₄₁×#388	—	2	1	no	—
17	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
19	C₄³×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#336	—	2	1	no	—
21	C₄₁×#336	—	2	1	no	—
22	C₄₁×#336	—	2	1	no	—
23	C₄₁×D₄⋊C₈	—	2	4	no	—
24	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₄₁	—	2	1	no	—
26	C₂²×C₈×C₄₁	—	2	2	no	—
27	C₂²×C₈×C₄₁	—	2	2	no	—
28	C₄×D₄×C₄₁	—	2	1	no	—
29	C₄×D₄×C₄₁	—	2	1	no	—
30	C₄×D₄×C₄₁	D₄	1	2	yes	—
31	C₄×D₄×C₄₁	Q₈	1	2	yes	—
32	#117×C₄₁	—	4	4	no	—
33	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
34	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
35	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
43	C₂×C₄²×C₄₁	—	2	1	no	—
44	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
51	C₄⋊C₈×C₄₁	—	2	4	no	—
52	C₄⋊C₈×C₄₁	—	2	2	no	—
53	C₄⋊C₈×C₄₁	—	2	2	no	—
54	C₄×C₈×C₄₁	—	2	2	no	—
55	C₄×C₈×C₄₁	—	2	2	no	—
56	#95×C₄₁	—	2	1	no	—
57	#95×C₄₁	—	2	1	no	—
58	#95×C₄₁	—	2	1	no	—
59	C₂⁴×C₄₁	—	2	1	no	—
60	C₂×D₄×C₄₁	—	2	1	no	—
61	C₂×D₄×C₄₁	—	2	2	no	—
62	C₂×D₄×C₄₁	—	2	2	no	—
63	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₄₁	—	2	1	no	—
65	C₂²×C₄×C₄₁	—	2	2	no	—
66	C₂²×C₄×C₄₁	—	2	2	no	—
67	C₂²×C₄×C₄₁	—	2	1	no	—
68	C₂²×C₄×C₄₁	—	2	1	no	—
69	C₂²×C₄×C₄₁	—	4	2	no	—
70	C₂²×C₄×C₄₁	—	4	2	no	—
71	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₄₁	—	2	4	no	—
79	C₂×C₈×C₄₁	—	4	2	no	—
80	C₂×C₈×C₄₁	—	4	2	no	—
81	C₂×C₈×C₄₁	—	4	2	no	—
82	C₂×C₈×C₄₁	—	4	2	no	—
83	C₂×C₈×C₄₁	—	4	2	no	—
84	C₄⋊C₄×C₄₁	—	2	1	no	—
85	C₄⋊C₄×C₄₁	—	2	2	no	—
86	C₄⋊C₄×C₄₁	—	2	2	no	—
87	C₄⋊C₄×C₄₁	—	4	2	no	—
88	C₄⋊C₄×C₄₁	—	4	2	no	—
89	C₄⋊C₄×C₄₁	C₄⋊C₄	1	2	yes	—
90	C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂²⋊C₄×C₄₁	—	4	2	no	—
93	C₂²⋊C₄×C₄₁	—	4	2	no	—
94	C₂²⋊C₄×C₄₁	—	4	2	no	—
95	C₂²⋊C₄×C₄₁	—	4	2	no	—
96	C₄²×C₄₁	—	2	2	no	—
97	C₄²×C₄₁	—	2	2	no	—
98	C₄²×C₄₁	—	2	2	no	—
99	C₄²×C₄₁	—	2	2	no	—
100	C₄²×C₄₁	—	2	2	no	—
101	C₄²×C₄₁	—	4	1	no	—
102	C₄²×C₄₁	—	4	2	no	—
103	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₄₁	C₂×Q₈	1	1	yes	characteristic
105	C₄²×C₄₁	#41	1	1	yes	characteristic
106	C₄²×C₄₁	#41	1	1	yes	characteristic
107	C₂³×C₄₁	—	2	2	no	—
108	C₂³×C₄₁	—	4	1	no	—
109	C₂³×C₄₁	—	4	1	no	—
110	C₂³×C₄₁	—	4	1	no	—
111	C₂³×C₄₁	—	4	1	no	—
112	C₂³×C₄₁	—	4	1	no	—
113	C₂³×C₄₁	—	4	1	no	—
114	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	D₄×C₄₁	—	2	4	no	—
116	D₄×C₄₁	—	4	2	no	—
117	C₂×C₄×C₄₁	—	2	1	no	—
118	C₂×C₄×C₄₁	—	2	1	no	—
119	C₂×C₄×C₄₁	—	2	1	no	—
120	C₂×C₄×C₄₁	—	2	1	no	—
121	C₂×C₄×C₄₁	—	2	2	no	—
122	C₂×C₄×C₄₁	—	2	1	no	—
123	C₂×C₄×C₄₁	—	2	1	no	—
124	C₂×C₄×C₄₁	—	2	1	no	—
125	C₂×C₄×C₄₁	—	2	1	no	—
126	C₂×C₄×C₄₁	—	2	1	no	—
127	C₂×C₄×C₄₁	—	2	1	no	—
128	C₂×C₄×C₄₁	—	2	1	no	—
129	C₂×C₄×C₄₁	—	2	1	no	—
130	C₂×C₄×C₄₁	—	2	1	no	—
131	C₂×C₄×C₄₁	—	4	1	no	—
132	C₂×C₄×C₄₁	—	4	1	no	—
133	C₂×C₄×C₄₁	—	4	4	no	—
134	C₂×C₄×C₄₁	—	4	4	no	—
135	C₂×C₄×C₄₁	—	4	1	no	—
136	C₂×C₄×C₄₁	—	4	1	no	—
137	C₂×C₄×C₄₁	—	4	1	no	—
138	C₂×C₄×C₄₁	—	4	1	no	—
139	C₂×C₄×C₄₁	—	4	1	no	—
140	C₂×C₄×C₄₁	—	4	1	no	—
141	C₂×C₄×C₄₁	#104	1	2	yes	—
142	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
144	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
145	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
146	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₁	#131	1	2	yes	—
149	C₂×C₄×C₄₁	#131	1	2	yes	—
150	C₂×C₄×C₄₁	#135	1	2	yes	—
151	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
152	C₈×C₄₁	—	4	4	no	—
153	C₈×C₄₁	—	8	2	no	—
154	#8569	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₄₁	—	4	2	no	—
156	C₂²×C₄₁	—	4	2	no	—
157	C₂²×C₄₁	—	4	2	no	—
158	C₂²×C₄₁	—	8	1	no	—
159	C₂²×C₄₁	—	8	1	no	—
160	C₂²×C₄₁	—	8	1	no	—
161	C₂²×C₄₁	—	8	1	no	—
162	C₂²×C₄₁	#380	1	1	yes	characteristic
163	C₂²×C₄₁	#408	1	1	yes	characteristic
164	C₂²×C₄₁	#408	1	1	yes	characteristic
165	C₂²×C₄₁	#416	1	1	yes	characteristic
166	C₂²×C₄₁	#418	1	1	yes	characteristic
167	C₂²×C₄₁	C₂×#104	1	1	yes	characteristic
168	C₂²×C₄₁	#421	1	1	yes	characteristic
169	C₄×C₄₁	—	2	1	no	—
170	C₄×C₄₁	—	2	1	no	—
171	C₄×C₄₁	—	2	2	no	—
172	C₄×C₄₁	—	4	2	no	—
173	C₄×C₄₁	—	4	1	no	—
174	C₄×C₄₁	—	4	1	no	—
175	C₄×C₄₁	—	4	1	no	—
176	C₄×C₄₁	—	8	1	no	—
177	C₄×C₄₁	—	8	1	no	—
178	C₄×C₄₁	#424	1	2	yes	—
179	C₄×C₄₁	#433	1	2	yes	—
180	C₄×C₄₁	#463	1	2	yes	—
181	C₄×C₄₁	#478	1	2	yes	—
182	#2293	C₂×C₄₁	1	1	yes	characteristic
183	#1831	C₂×C₄₁	1	1	yes	characteristic, complemented
184	C₄×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
185	C₂×D₄⋊C₈	C₂×C₄₁	1	2	yes	—
186	#1279	C₂×C₄₁	1	2	yes	complemented
187	C₂×C₄₁	—	8	2	no	—
188	C₂×C₄₁	#1482	1	1	yes	characteristic
189	C₂×C₄₁	#1484	1	1	yes	characteristic
190	C₂×C₄₁	#1494	1	1	yes	characteristic
191	C₂×C₄₁	#1496	1	1	yes	characteristic
192	C₂×C₄₁	#1798	1	1	yes	characteristic
193	C₂×C₄₁	#1804	1	1	yes	characteristic
194	C₂×C₄₁	#1806	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
196	C₂×#117	—	2	1	no	—
197	C₂×C₄⋊C₈	—	2	1	no	—
198	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
200	#390	C₄×C₄₁	1	1	yes	characteristic
201	#390	C₄×C₄₁	1	1	yes	characteristic
202	#389	C₄×C₄₁	1	1	yes	characteristic
203	#389	C₄×C₄₁	1	1	yes	characteristic
204	#388	—	2	1	no	—
205	#388	—	2	1	no	—
206	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
207	C₄×C₂²⋊C₄	—	2	1	no	—
208	C₄³	C₂²×C₄₁	1	1	yes	characteristic
209	#336	—	2	1	no	—
210	#336	—	2	1	no	—
211	#336	—	2	1	no	—
212	D₄⋊C₈	—	2	4	no	—
213	C₄₁	#8569	1	1	yes	characteristic, direct product factor, Sylow
214	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
215	C₂³×C₄	—	2	1	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	D₄×C₄₁	1	2	yes	—
221	C₄×D₄	Q₈×C₄₁	1	2	yes	—
222	#117	—	4	4	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
241	C₄⋊C₈	—	2	4	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	—	2	2	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	C₂⁴	—	2	1	no	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	4	2	no	—
270	C₂×C₈	—	4	2	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	—	4	2	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₄⋊C₄	C₄⋊C₄×C₄₁	1	2	yes	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₂²⋊C₄	—	4	2	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	4	1	no	—
292	C₄²	—	4	2	no	—
293	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
294	C₄²	C₂×Q₈×C₄₁	1	1	yes	characteristic
295	C₄²	#41×C₄₁	1	1	yes	characteristic
296	C₄²	#41×C₄₁	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	4	1	no	—
299	C₂³	—	4	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	—	4	1	no	—
302	C₂³	—	4	1	no	—
303	C₂³	—	4	1	no	—
304	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
305	D₄	—	2	4	no	—
306	D₄	—	4	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	#104×C₄₁	1	2	yes	—
332	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
333	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
334	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
335	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
336	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
337	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
338	C₂×C₄	#131×C₄₁	1	2	yes	—
339	C₂×C₄	#131×C₄₁	1	2	yes	—
340	C₂×C₄	#135×C₄₁	1	2	yes	—
341	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
342	C₈	—	4	4	no	—
343	C₈	—	8	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	1	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	1	no	—
351	C₂²	C₄₁×#380	1	1	yes	characteristic
352	C₂²	C₄₁×#408	1	1	yes	characteristic
353	C₂²	C₄₁×#408	1	1	yes	characteristic
354	C₂²	C₄₁×#416	1	1	yes	characteristic
355	C₂²	C₄₁×#418	1	1	yes	characteristic
356	C₂²	C₂×#104×C₄₁	1	1	yes	characteristic
357	C₂²	C₄₁×#421	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	C₄₁×#424	1	2	yes	—
368	C₄	C₄₁×#433	1	2	yes	—
369	C₄	C₄₁×#463	1	2	yes	—
370	C₄	C₄₁×#478	1	2	yes	—
371	C₂	—	8	2	no	—
372	C₂	C₄₁×#1482	1	1	yes	characteristic
373	C₂	C₄₁×#1484	1	1	yes	characteristic
374	C₂	C₄₁×#1494	1	1	yes	characteristic
375	C₂	C₄₁×#1496	1	1	yes	characteristic
376	C₂	C₄₁×#1798	1	1	yes	characteristic
377	C₂	C₄₁×#1804	1	1	yes	characteristic
378	C₂	C₄₁×#1806	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
socle	C₂³×C₄₁	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₄₁	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#1831	C₂	semidirect
3. C₄×C₄⋊C₈×C₄₁	C₂	semidirect
5. C₄₁×#1279	C₂	semidirect
154. #8569	C₄₁	direct (N × H)
183. #1831	C₂×C₄₁	semidirect
184. C₄×C₄⋊C₈	C₂×C₄₁	semidirect
186. #1279	C₂×C₄₁	semidirect
213. C₄₁	#8569	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2293	2
C₄₁×#1831	2
C₄×C₄⋊C₈×C₄₁	2
C₂×C₄₁×D₄⋊C₈	2
C₄₁×#1279	2
#8569	41

Subgroups — C41×#8569 #23784770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#8569 #23784770