Subgroups — C₄₁×#20626 #23796827

Order 10496.

2118 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#423	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#407	C₂	1	2	yes	maximal
4	C₄₁×#1797	C₂	1	8	yes	maximal, complemented
5	C₄₁×#1728	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₄₁	C₄	1	2	yes	—
7	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₁	C₂²	1	4	yes	—
9	C₂²×C₄²×C₄₁	—	2	8	no	—
10	C₂²×C₄²×C₄₁	C₄	1	2	yes	—
11	C₂²×C₄²×C₄₁	C₄	1	2	yes	—
12	C₂²×C₄²×C₄₁	C₄	1	2	yes	—
13	C₂²×C₄²×C₄₁	C₂²	1	4	yes	—
14	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#423	—	2	8	no	—
17	C₂×C₄⋊C₈×C₄₁	C₂²	1	8	yes	complemented
18	C₄₁×#407	—	2	8	no	—
19	C₂×C₂²⋊C₈×C₄₁	C₂²	1	8	yes	—
20	C₄₁×#336	C₂²	1	8	yes	complemented
21	C₂⁵×C₄₁	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₄₁	—	2	8	no	—
23	C₂³×C₄×C₄₁	—	2	16	no	—
24	C₂³×C₄×C₄₁	—	2	4	no	—
25	C₂³×C₄×C₄₁	—	2	4	no	—
26	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
28	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₄₁	D₄	1	4	yes	—
33	C₂³×C₄×C₄₁	Q₈	1	4	yes	—
34	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₁	—	2	8	no	—
37	C₂×M₁₆×C₄₁	—	2	8	no	—
38	C₂×M₁₆×C₄₁	—	2	8	no	—
39	C₂²×C₈×C₄₁	C₂³	1	8	yes	—
40	C₂×C₄²×C₄₁	—	2	8	no	—
41	C₂×C₄²×C₄₁	—	2	4	no	—
42	C₂×C₄²×C₄₁	—	2	8	no	—
43	C₂×C₄²×C₄₁	—	2	8	no	—
44	C₂×C₄²×C₄₁	—	2	16	no	—
45	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₁	D₄	1	8	yes	—
51	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
52	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
53	C₄⋊C₈×C₄₁	—	2	16	no	—
54	C₂²⋊C₈×C₄₁	—	2	16	no	—
55	C₂⁴×C₄₁	—	2	2	no	—
56	C₂⁴×C₄₁	—	2	2	no	—
57	C₂⁴×C₄₁	—	2	8	no	—
58	C₂⁴×C₄₁	C₄⋊C₄	1	4	yes	—
59	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
60	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
61	C₂²×C₄×C₄₁	—	2	64	no	—
62	C₂²×C₄×C₄₁	—	2	4	no	—
63	C₂²×C₄×C₄₁	—	2	2	no	—
64	C₂²×C₄×C₄₁	—	2	2	no	—
65	C₂²×C₄×C₄₁	—	2	8	no	—
66	C₂²×C₄×C₄₁	—	2	8	no	—
67	C₂²×C₄×C₄₁	—	2	4	no	—
68	C₂²×C₄×C₄₁	—	2	8	no	—
69	C₂²×C₄×C₄₁	—	2	4	no	—
70	C₂²×C₄×C₄₁	—	2	16	no	—
71	C₂²×C₄×C₄₁	—	2	16	no	—
72	C₂²×C₄×C₄₁	—	2	8	no	—
73	C₂²×C₄×C₄₁	—	2	8	no	—
74	C₂²×C₄×C₄₁	—	2	8	no	—
75	C₂²×C₄×C₄₁	—	2	8	no	—
76	C₂²×C₄×C₄₁	—	2	4	no	—
77	C₂²×C₄×C₄₁	—	2	4	no	—
78	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
79	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₄₁	C₄⋊C₄	1	8	yes	—
81	C₂²×C₄×C₄₁	M₁₆	1	16	yes	complemented
82	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
88	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₄₁	#41	1	4	yes	—
93	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₄₁	—	4	16	no	—
95	C₂×C₈×C₄₁	—	2	8	no	—
96	C₂×C₈×C₄₁	—	2	8	no	—
97	C₂×C₈×C₄₁	—	2	8	no	—
98	C₄²×C₄₁	—	2	8	no	—
99	C₄²×C₄₁	—	2	4	no	—
100	C₄²×C₄₁	—	2	8	no	—
101	C₄²×C₄₁	—	2	4	no	—
102	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
103	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
104	C₄²×C₄₁	C₂×D₄	1	8	yes	—
105	C₂³×C₄₁	—	2	16	no	—
106	C₂³×C₄₁	—	2	16	no	—
107	C₂³×C₄₁	—	2	2	no	—
108	C₂³×C₄₁	—	2	2	no	—
109	C₂³×C₄₁	—	2	4	no	—
110	C₂³×C₄₁	—	2	4	no	—
111	C₂³×C₄₁	—	2	8	no	—
112	C₂³×C₄₁	—	2	16	no	—
113	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
114	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
115	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
116	C₂³×C₄₁	#117	1	2	yes	—
117	C₂³×C₄₁	C₂×M₁₆	1	8	yes	—
118	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
119	C₂×C₄×C₄₁	—	2	32	no	—
120	C₂×C₄×C₄₁	—	2	16	no	—
121	C₂×C₄×C₄₁	—	2	4	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	8	no	—
127	C₂×C₄×C₄₁	—	2	8	no	—
128	C₂×C₄×C₄₁	—	2	8	no	—
129	C₂×C₄×C₄₁	—	2	16	no	—
130	C₂×C₄×C₄₁	—	2	16	no	—
131	C₂×C₄×C₄₁	—	2	32	no	—
132	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
133	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
136	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₄₁	#117	1	2	yes	—
138	C₂×C₄×C₄₁	#121	1	8	yes	—
139	C₂×C₄×C₄₁	C₂²⋊Q₈	1	8	yes	—
140	C₂×C₄×C₄₁	C₂×M₁₆	1	8	yes	—
141	C₂×C₄×C₄₁	C₂×M₁₆	1	8	yes	—
142	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
146	C₈×C₄₁	—	4	8	no	—
147	#20626	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂²×C₄₁	—	2	32	no	—
149	C₂²×C₄₁	—	2	4	no	—
150	C₂²×C₄₁	—	2	8	no	—
151	C₂²×C₄₁	—	2	4	no	—
152	C₂²×C₄₁	—	2	4	no	—
153	C₂²×C₄₁	—	2	4	no	—
154	C₂²×C₄₁	—	2	8	no	—
155	C₂²×C₄₁	—	2	4	no	—
156	C₂²×C₄₁	#380	1	4	yes	—
157	C₂²×C₄₁	#423	1	8	yes	complemented
158	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
161	C₂²×C₄₁	C₂²×M₁₆	1	4	yes	—
162	C₄×C₄₁	—	2	4	no	—
163	C₄×C₄₁	—	2	8	no	—
164	C₄×C₄₁	—	2	4	no	—
165	C₄×C₄₁	#380	1	4	yes	—
166	C₄×C₄₁	#407	1	8	yes	complemented
167	C₄×C₄₁	C₂×#121	1	2	yes	—
168	C₄×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
169	C₂³×C₄²	C₂×C₄₁	1	1	yes	characteristic
170	C₂×#423	C₂×C₄₁	1	2	yes	complemented
171	C₂×#407	C₂×C₄₁	1	2	yes	—
172	#1797	C₂×C₄₁	1	8	yes	complemented
173	#1728	C₂×C₄₁	1	2	yes	complemented
174	C₂×C₄₁	—	2	4	no	—
175	C₂×C₄₁	—	2	8	no	—
176	C₂×C₄₁	C₂×#380	1	1	yes	characteristic
177	C₂×C₄₁	C₂×#407	1	2	yes	—
178	C₂×C₄₁	C₂×#423	1	2	yes	—
179	C₂×C₄₁	#2920	1	2	yes	—
180	C₂⁴×C₄	C₄×C₄₁	1	2	yes	—
181	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
182	C₂²×M₁₆	C₂²×C₄₁	1	4	yes	—
183	C₂²×C₄²	—	2	8	no	—
184	C₂²×C₄²	C₄×C₄₁	1	2	yes	—
185	C₂²×C₄²	C₄×C₄₁	1	2	yes	—
186	C₂²×C₄²	C₄×C₄₁	1	2	yes	—
187	C₂²×C₄²	C₂²×C₄₁	1	4	yes	—
188	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
189	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
190	#423	—	2	8	no	—
191	C₂×C₄⋊C₈	C₂²×C₄₁	1	8	yes	complemented
192	#407	—	2	8	no	—
193	C₂×C₂²⋊C₈	C₂²×C₄₁	1	8	yes	—
194	#336	C₂²×C₄₁	1	8	yes	complemented
195	C₄₁	#20626	1	1	yes	characteristic, direct product factor, Sylow
196	C₂⁵	C₂×C₄×C₄₁	1	1	yes	characteristic
197	C₂³×C₄	—	2	8	no	—
198	C₂³×C₄	—	2	16	no	—
199	C₂³×C₄	—	2	4	no	—
200	C₂³×C₄	—	2	4	no	—
201	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
202	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
203	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
204	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
205	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
206	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
207	C₂³×C₄	D₄×C₄₁	1	4	yes	—
208	C₂³×C₄	Q₈×C₄₁	1	4	yes	—
209	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
210	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
211	C₂×M₁₆	—	2	8	no	—
212	C₂×M₁₆	—	2	8	no	—
213	C₂×M₁₆	—	2	8	no	—
214	C₂²×C₈	C₂³×C₄₁	1	8	yes	—
215	C₂×C₄²	—	2	8	no	—
216	C₂×C₄²	—	2	4	no	—
217	C₂×C₄²	—	2	8	no	—
218	C₂×C₄²	—	2	8	no	—
219	C₂×C₄²	—	2	16	no	—
220	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
221	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
222	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
225	C₂×C₄²	D₄×C₄₁	1	8	yes	—
226	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
227	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
228	C₄⋊C₈	—	2	16	no	—
229	C₂²⋊C₈	—	2	16	no	—
230	C₂⁴	—	2	2	no	—
231	C₂⁴	—	2	2	no	—
232	C₂⁴	—	2	8	no	—
233	C₂⁴	C₄⋊C₄×C₄₁	1	4	yes	—
234	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
235	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
236	C₂²×C₄	—	2	64	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	8	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	16	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
254	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
255	C₂²×C₄	C₄⋊C₄×C₄₁	1	8	yes	—
256	C₂²×C₄	M₁₆×C₄₁	1	16	yes	complemented
257	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
260	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
264	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
265	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
266	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
267	C₂²×C₄	#41×C₄₁	1	4	yes	—
268	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
269	M₁₆	—	4	16	no	—
270	C₂×C₈	—	2	8	no	—
271	C₂×C₈	—	2	8	no	—
272	C₂×C₈	—	2	8	no	—
273	C₄²	—	2	8	no	—
274	C₄²	—	2	4	no	—
275	C₄²	—	2	8	no	—
276	C₄²	—	2	4	no	—
277	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
278	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
279	C₄²	C₂×D₄×C₄₁	1	8	yes	—
280	C₂³	—	2	16	no	—
281	C₂³	—	2	16	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	4	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	2	16	no	—
288	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
289	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
290	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
291	C₂³	#117×C₄₁	1	2	yes	—
292	C₂³	C₂×M₁₆×C₄₁	1	8	yes	—
293	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
294	C₂×C₄	—	2	32	no	—
295	C₂×C₄	—	2	16	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	16	no	—
305	C₂×C₄	—	2	16	no	—
306	C₂×C₄	—	2	32	no	—
307	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
308	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
310	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
311	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
312	C₂×C₄	#117×C₄₁	1	2	yes	—
313	C₂×C₄	#121×C₄₁	1	8	yes	—
314	C₂×C₄	C₂²⋊Q₈×C₄₁	1	8	yes	—
315	C₂×C₄	C₂×M₁₆×C₄₁	1	8	yes	—
316	C₂×C₄	C₂×M₁₆×C₄₁	1	8	yes	—
317	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
318	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
319	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
321	C₈	—	4	8	no	—
322	C₂²	—	2	32	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	8	no	—
330	C₂²	C₄₁×#380	1	4	yes	—
331	C₂²	C₄₁×#423	1	8	yes	complemented
332	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
333	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
334	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
335	C₂²	C₂²×M₁₆×C₄₁	1	4	yes	—
336	C₄	—	2	4	no	—
337	C₄	—	2	4	no	—
338	C₄	—	2	8	no	—
339	C₄	C₄₁×#380	1	4	yes	—
340	C₄	C₄₁×#407	1	8	yes	complemented
341	C₄	C₂×#121×C₄₁	1	2	yes	—
342	C₄	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
343	C₂	—	2	4	no	—
344	C₂	—	2	8	no	—
345	C₂	C₂×C₄₁×#380	1	1	yes	characteristic
346	C₂	C₂×C₄₁×#407	1	2	yes	—
347	C₂	C₂×C₄₁×#423	1	2	yes	—
348	C₂	C₄₁×#2920	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₂⁵×C₄₁	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#423	C₂	semidirect
4. C₄₁×#1797	C₂	semidirect
5. C₄₁×#1728	C₂	semidirect
17. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
20. C₄₁×#336	C₂²	semidirect
81. C₂²×C₄×C₄₁	M₁₆	semidirect
147. #20626	C₄₁	direct (N × H)
157. C₂²×C₄₁	#423	semidirect
166. C₄×C₄₁	#407	semidirect
170. C₂×#423	C₂×C₄₁	semidirect
172. #1797	C₂×C₄₁	semidirect
173. #1728	C₂×C₄₁	semidirect
191. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
194. #336	C₂²×C₄₁	semidirect
195. C₄₁	#20626	direct (N × H)
256. C₂²×C₄	M₁₆×C₄₁	semidirect
331. C₂²	C₄₁×#423	semidirect
340. C₄	C₄₁×#407	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₄₁	2
C₂×C₄₁×#423	2
C₂×C₄₁×#407	2
C₄₁×#1797	2
C₄₁×#1728	2
#20626	41

Subgroups — C41×#20626 #23796827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20626 #23796827