Subgroups — C₄₁×#20571 #23796772

Order 10496.

826 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2295	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1771	C₂	1	2	yes	maximal
5	C₄₁×#1770	C₂	1	1	yes	maximal, characteristic
6	C₈×C₄⋊C₄×C₄₁	C₂	1	2	yes	maximal
7	C₈×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1768	C₂	1	2	yes	maximal
9	C₄×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#1746	C₂	1	2	yes	maximal
11	C₄₁×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#446	C₄	1	8	yes	complemented
14	C₈×Q₈×C₄₁	C₄	1	8	yes	complemented
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
19	C₂×#97×C₄₁	C₂²	1	2	yes	—
20	C₂×#97×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#391	C₄	1	2	yes	—
27	C₄₁×#389	C₄	1	2	yes	—
28	C₄₁×#387	C₄	1	4	yes	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#376	C₂²	1	2	yes	—
32	C₄³×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	1	yes	characteristic
35	C₄₁×#336	C₂²	1	1	yes	characteristic
36	C₄₁×#336	C₂²	1	2	yes	—
37	C₄₁×#336	C₂²	1	2	yes	—
38	C₄₁×#336	C₂²	1	1	yes	characteristic
39	C₄₁×#336	C₂²	1	1	yes	characteristic
40	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
48	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
50	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
60	C₄⋊C₈×C₄₁	C₂×C₄	1	4	yes	—
61	C₄⋊C₈×C₄₁	C₂×C₄	1	8	yes	—
62	C₄⋊C₈×C₄₁	C₂×C₄	1	4	yes	—
63	C₄⋊C₈×C₄₁	C₂×C₄	1	8	yes	—
64	#97×C₄₁	—	4	2	no	—
65	#97×C₄₁	C₂×C₄	1	8	yes	—
66	C₄×C₈×C₄₁	—	4	2	no	—
67	C₄×C₈×C₄₁	—	4	2	no	—
68	C₄×C₈×C₄₁	C₂×C₄	1	8	yes	—
69	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	—
70	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	—
71	#95×C₄₁	C₂×C₄	1	4	yes	—
72	#95×C₄₁	C₂×C₄	1	4	yes	—
73	#95×C₄₁	C₂×C₄	1	2	yes	—
74	#95×C₄₁	C₂×C₄	1	4	yes	—
75	C₂×Q₈×C₄₁	—	2	4	no	—
76	C₂×Q₈×C₄₁	C₄²	1	4	yes	—
77	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₄₁	—	2	2	no	—
86	C₂×C₈×C₄₁	—	2	1	no	—
87	C₂×C₈×C₄₁	—	2	2	no	—
88	C₂×C₈×C₄₁	—	2	1	no	—
89	C₂×C₈×C₄₁	—	2	1	no	—
90	C₂×C₈×C₄₁	—	2	1	no	—
91	C₂×C₈×C₄₁	—	2	1	no	—
92	C₂×C₈×C₄₁	—	2	1	no	—
93	C₂×C₈×C₄₁	—	2	2	no	—
94	C₂×C₈×C₄₁	—	2	1	no	—
95	C₂×C₈×C₄₁	—	2	2	no	—
96	C₂×C₈×C₄₁	—	2	1	no	—
97	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
103	C₄⋊C₄×C₄₁	—	2	8	no	—
104	C₄⋊C₄×C₄₁	—	2	4	no	—
105	C₄⋊C₄×C₄₁	C₄²	1	8	yes	—
106	C₄⋊C₄×C₄₁	C₄²	1	4	yes	—
107	C₄²×C₄₁	—	2	4	no	—
108	C₄²×C₄₁	—	2	4	no	—
109	C₄²×C₄₁	—	2	1	no	—
110	C₄²×C₄₁	—	2	2	no	—
111	C₄²×C₄₁	—	2	1	no	—
112	C₄²×C₄₁	—	2	1	no	—
113	C₄²×C₄₁	—	2	1	no	—
114	C₄²×C₄₁	—	2	2	no	—
115	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
116	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
119	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
120	Q₈×C₄₁	—	2	8	no	—
121	C₂×C₄×C₄₁	—	2	2	no	—
122	C₂×C₄×C₄₁	—	2	2	no	—
123	C₂×C₄×C₄₁	—	2	2	no	—
124	C₂×C₄×C₄₁	—	2	4	no	—
125	C₂×C₄×C₄₁	—	2	4	no	—
126	C₂×C₄×C₄₁	—	2	2	no	—
127	C₂×C₄×C₄₁	—	2	4	no	—
128	C₂×C₄×C₄₁	—	2	2	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	4	no	—
131	C₂×C₄×C₄₁	—	2	4	no	—
132	C₂×C₄×C₄₁	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
134	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
135	C₂×C₄×C₄₁	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₄₁	#131	1	4	yes	—
137	C₂×C₄×C₄₁	#131	1	4	yes	—
138	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
142	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
144	C₈×C₄₁	—	2	2	no	—
145	C₈×C₄₁	—	2	2	no	—
146	C₈×C₄₁	—	2	4	no	—
147	C₈×C₄₁	—	2	2	no	—
148	C₈×C₄₁	—	2	4	no	—
149	C₈×C₄₁	—	2	2	no	—
150	#20571	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂²×C₄₁	C₂²×C₄²	1	1	yes	characteristic
152	C₂²×C₄₁	#519	1	1	yes	characteristic
153	C₂²×C₄₁	#520	1	1	yes	characteristic
154	C₂²×C₄₁	C₂×#131	1	2	yes	—
155	C₂²×C₄₁	C₂×#131	1	2	yes	—
156	C₄×C₄₁	—	2	4	no	—
157	C₄×C₄₁	—	2	2	no	—
158	C₄×C₄₁	—	2	4	no	—
159	C₄×C₄₁	—	2	4	no	—
160	C₄×C₄₁	—	4	2	no	—
161	C₄×C₄₁	—	4	4	no	—
162	C₄×C₄₁	#405	1	4	yes	—
163	C₄×C₄₁	#519	1	1	yes	characteristic
164	C₄×C₄₁	#519	1	1	yes	characteristic
165	C₄×C₄₁	#520	1	1	yes	characteristic
166	C₄×C₄₁	#520	1	1	yes	characteristic
167	C₂×#446	C₂×C₄₁	1	1	yes	characteristic
168	C₂×C₈×Q₈	C₂×C₄₁	1	1	yes	characteristic
169	#2295	C₂×C₄₁	1	1	yes	characteristic
170	#1771	C₂×C₄₁	1	2	yes	—
171	#1770	C₂×C₄₁	1	1	yes	characteristic
172	C₈×C₄⋊C₄	C₂×C₄₁	1	2	yes	—
173	C₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
174	#1768	C₂×C₄₁	1	2	yes	—
175	C₄×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic
176	#1746	C₂×C₄₁	1	2	yes	—
177	#1744	C₂×C₄₁	1	1	yes	characteristic
178	C₂×C₄₁	#2276	1	1	yes	characteristic
179	C₂×C₄₁	C₂×#405	1	1	yes	characteristic
180	C₂×C₄₁	C₄×#131	1	1	yes	characteristic
181	C₂×C₄₁	#2986	1	2	yes	—
182	C₂×C₄₁	#2994	1	2	yes	—
183	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
184	#446	C₄×C₄₁	1	8	yes	complemented
185	C₈×Q₈	C₄×C₄₁	1	8	yes	complemented
186	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
190	C₂×#97	C₂²×C₄₁	1	2	yes	—
191	C₂×#97	C₂²×C₄₁	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
197	#391	C₄×C₄₁	1	2	yes	—
198	#389	C₄×C₄₁	1	2	yes	—
199	#387	C₄×C₄₁	1	4	yes	—
200	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
201	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
202	#376	C₂²×C₄₁	1	2	yes	—
203	C₄³	C₂²×C₄₁	1	1	yes	characteristic
204	#336	C₂²×C₄₁	1	1	yes	characteristic
205	#336	C₂²×C₄₁	1	1	yes	characteristic
206	#336	C₂²×C₄₁	1	1	yes	characteristic
207	#336	C₂²×C₄₁	1	1	yes	characteristic
208	#336	C₂²×C₄₁	1	2	yes	—
209	#336	C₂²×C₄₁	1	2	yes	—
210	#336	C₂²×C₄₁	1	2	yes	—
211	C₄₁	#20571	1	1	yes	characteristic, direct product factor, Sylow
212	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
217	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
218	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
219	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
220	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
222	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
227	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
230	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
232	C₄⋊C₈	C₂×C₄×C₄₁	1	4	yes	—
233	C₄⋊C₈	C₂×C₄×C₄₁	1	8	yes	—
234	C₄⋊C₈	C₂×C₄×C₄₁	1	4	yes	—
235	C₄⋊C₈	C₂×C₄×C₄₁	1	8	yes	—
236	#97	—	4	2	no	—
237	#97	C₂×C₄×C₄₁	1	8	yes	—
238	C₄×C₈	—	4	2	no	—
239	C₄×C₈	—	4	2	no	—
240	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	—
241	C₄×C₈	C₂×C₄×C₄₁	1	8	yes	—
242	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	—
243	#95	C₂×C₄×C₄₁	1	4	yes	—
244	#95	C₂×C₄×C₄₁	1	4	yes	—
245	#95	C₂×C₄×C₄₁	1	2	yes	—
246	#95	C₂×C₄×C₄₁	1	4	yes	—
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	C₄²×C₄₁	1	4	yes	—
249	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
251	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
256	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
270	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
271	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
272	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
273	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
274	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	C₄²×C₄₁	1	8	yes	—
278	C₄⋊C₄	C₄²×C₄₁	1	4	yes	—
279	C₄²	—	2	4	no	—
280	C₄²	—	2	4	no	—
281	C₄²	—	2	1	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	2	1	no	—
286	C₄²	—	2	2	no	—
287	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
288	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
289	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
290	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
291	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
292	Q₈	—	2	8	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	C₂×C₄²×C₄₁	1	2	yes	—
305	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
306	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
307	C₂×C₄	C₂×C₄²×C₄₁	1	2	yes	—
308	C₂×C₄	#131×C₄₁	1	4	yes	—
309	C₂×C₄	#131×C₄₁	1	4	yes	—
310	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
311	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
312	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
313	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
314	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
315	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
316	C₈	—	2	2	no	—
317	C₈	—	2	2	no	—
318	C₈	—	2	4	no	—
319	C₈	—	2	2	no	—
320	C₈	—	2	4	no	—
321	C₈	—	2	2	no	—
322	C₂²	C₂²×C₄²×C₄₁	1	1	yes	characteristic
323	C₂²	C₄₁×#519	1	1	yes	characteristic
324	C₂²	C₄₁×#520	1	1	yes	characteristic
325	C₂²	C₂×#131×C₄₁	1	2	yes	—
326	C₂²	C₂×#131×C₄₁	1	2	yes	—
327	C₄	—	2	4	no	—
328	C₄	—	2	2	no	—
329	C₄	—	2	4	no	—
330	C₄	—	2	4	no	—
331	C₄	—	4	2	no	—
332	C₄	—	4	4	no	—
333	C₄	C₄₁×#405	1	4	yes	—
334	C₄	C₄₁×#519	1	1	yes	characteristic
335	C₄	C₄₁×#519	1	1	yes	characteristic
336	C₄	C₄₁×#520	1	1	yes	characteristic
337	C₄	C₄₁×#520	1	1	yes	characteristic
338	C₂	C₄₁×#2276	1	1	yes	characteristic
339	C₂	C₂×C₄₁×#405	1	1	yes	characteristic
340	C₂	C₄×#131×C₄₁	1	1	yes	characteristic
341	C₂	C₄₁×#2986	1	2	yes	—
342	C₂	C₄₁×#2994	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
13. C₄₁×#446	C₄	semidirect
14. C₈×Q₈×C₄₁	C₄	semidirect
150. #20571	C₄₁	direct (N × H)
184. #446	C₄×C₄₁	semidirect
185. C₈×Q₈	C₄×C₄₁	semidirect
211. C₄₁	#20571	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×C₄₁×#446	2
C₂×C₈×Q₈×C₄₁	2
C₄₁×#2295	2
C₄₁×#1771	2
C₄₁×#1770	2
C₈×C₄⋊C₄×C₄₁	2
C₄₁×#1768	2
C₄×C₄⋊C₈×C₄₁	2
C₄₁×#1746	2
C₄₁×#1744	2
#20571	41

Subgroups — C41×#20571 #23796772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20571 #23796772