Subgroups — C₄₁×#23562 #23799763

Order 10496.

1054 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3458	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#428	C₂	1	2	yes	maximal
3	C₄₁×#2317	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2061	C₂	1	4	yes	maximal, complemented
5	C₄₁×#2060	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1742	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1733	C₂	1	2	yes	maximal
8	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
9	C₄₁×#544	—	2	2	no	—
10	C₄₁×#544	—	2	2	no	—
11	C₄₁×#544	C₂²	1	2	yes	—
12	C₄₁×#544	C₂²	1	2	yes	—
13	C₄₁×#543	—	2	2	no	—
14	C₄₁×#533	—	2	4	no	—
15	C₄₁×#533	—	2	2	no	—
16	C₂×#117×C₄₁	C₂²	1	2	yes	—
17	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#428	—	2	4	no	—
21	C₄₁×#428	C₂²	1	8	yes	—
22	C₂×#107×C₄₁	—	2	2	no	—
23	C₂×#106×C₄₁	—	2	2	no	—
24	C₄₁×#389	—	2	2	no	—
25	C₄₁×#385	—	2	2	no	—
26	C₄₁×#384	C₂²	1	2	yes	—
27	C₄₁×#382	C₂²	1	2	yes	—
28	C₄₁×#343	C₂²	1	2	yes	—
29	C₄₁×#343	C₂²	1	2	yes	—
30	C₄₁×#339	C₂²	1	8	yes	—
31	C₂³×C₄×C₄₁	—	2	1	no	—
32	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₄₁	—	2	2	no	—
34	C₂×M₁₆×C₄₁	—	2	4	no	—
35	C₂×M₁₆×C₄₁	Q₈	1	8	yes	complemented
36	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
37	C₂²×C₈×C₄₁	—	2	2	no	—
38	C₄⋊Q₈×C₄₁	—	2	2	no	—
39	C₄⋊Q₈×C₄₁	—	2	2	no	—
40	C₄⋊Q₈×C₄₁	—	2	4	no	—
41	C₄⋊Q₈×C₄₁	—	2	4	no	—
42	#125×C₄₁	—	2	4	no	—
43	#125×C₄₁	—	2	4	no	—
44	#125×C₄₁	—	2	4	no	—
45	C₂²⋊Q₈×C₄₁	—	2	8	no	—
46	C₂²⋊Q₈×C₄₁	—	2	8	no	—
47	C₂²⋊Q₈×C₄₁	—	2	4	no	—
48	C₂²⋊Q₈×C₄₁	—	2	4	no	—
49	C₄×Q₈×C₄₁	—	2	4	no	—
50	C₄×Q₈×C₄₁	—	2	4	no	—
51	#117×C₄₁	—	2	2	no	—
52	#117×C₄₁	—	2	2	no	—
53	#117×C₄₁	—	2	2	no	—
54	#117×C₄₁	—	2	2	no	—
55	#117×C₄₁	—	2	2	no	—
56	#117×C₄₁	D₄	1	4	yes	—
57	#117×C₄₁	Q₈	1	4	yes	complemented
58	#117×C₄₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	D₄	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
75	#107×C₄₁	—	2	8	no	—
76	#106×C₄₁	—	2	8	no	—
77	#95×C₄₁	—	2	4	no	—
78	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₄₁	—	2	4	no	—
80	C₂×Q₈×C₄₁	—	2	4	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	2	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	4	2	no	—
86	C₂²×C₄×C₄₁	—	8	2	no	—
87	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₁	#41	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₄₁	—	2	8	no	—
97	M₁₆×C₄₁	—	2	4	no	—
98	M₁₆×C₄₁	C₂×Q₈	1	8	yes	—
99	C₂×C₈×C₄₁	—	2	8	no	—
100	C₂×C₈×C₄₁	—	2	4	no	—
101	C₄⋊C₄×C₄₁	—	2	8	no	—
102	C₄⋊C₄×C₄₁	—	2	8	no	—
103	C₄⋊C₄×C₄₁	—	2	4	no	—
104	C₄⋊C₄×C₄₁	—	2	4	no	—
105	C₄⋊C₄×C₄₁	—	2	2	no	—
106	C₄⋊C₄×C₄₁	—	2	2	no	—
107	C₄⋊C₄×C₄₁	—	2	4	no	—
108	C₄⋊C₄×C₄₁	—	2	2	no	—
109	C₄⋊C₄×C₄₁	—	2	2	no	—
110	C₄⋊C₄×C₄₁	—	2	4	no	—
111	C₄⋊C₄×C₄₁	—	4	1	no	—
112	C₄⋊C₄×C₄₁	—	4	1	no	—
113	C₄⋊C₄×C₄₁	—	8	4	no	—
114	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
115	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
116	C₂²⋊C₄×C₄₁	—	2	4	no	—
117	C₂²⋊C₄×C₄₁	—	2	4	no	—
118	C₂²⋊C₄×C₄₁	—	2	4	no	—
119	C₂²⋊C₄×C₄₁	—	2	4	no	—
120	C₄²×C₄₁	—	2	4	no	—
121	C₄²×C₄₁	—	2	2	no	—
122	C₄²×C₄₁	—	2	2	no	—
123	C₄²×C₄₁	—	2	4	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	C₂×Q₈	1	4	yes	—
126	C₂³×C₄₁	—	4	1	no	—
127	C₂³×C₄₁	—	4	1	no	—
128	C₂³×C₄₁	#120	1	2	yes	—
129	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
130	C₂³×C₄₁	C₄⋊Q₈	1	2	yes	—
131	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₄₁	—	8	4	no	—
133	Q₈×C₄₁	—	8	4	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	4	no	—
139	C₂×C₄×C₄₁	—	4	2	no	—
140	C₂×C₄×C₄₁	—	4	2	no	—
141	C₂×C₄×C₄₁	—	4	2	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	4	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	8	2	no	—
146	C₂×C₄×C₄₁	—	8	2	no	—
147	C₂×C₄×C₄₁	—	8	4	no	—
148	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
149	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
150	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
152	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
153	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
154	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
155	C₂×C₄×C₄₁	C₄⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₄₁	C₂²×Q₈	1	2	yes	—
158	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
160	C₈×C₄₁	—	2	8	no	—
161	#23562	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂²×C₄₁	—	2	1	no	—
163	C₂²×C₄₁	—	2	2	no	—
164	C₂²×C₄₁	—	2	1	no	—
165	C₂²×C₄₁	—	2	2	no	—
166	C₂²×C₄₁	—	4	2	no	—
167	C₂²×C₄₁	—	4	2	no	—
168	C₂²×C₄₁	#395	1	4	yes	—
169	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
170	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
171	C₂²×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
172	C₄×C₄₁	—	4	4	no	—
173	C₄×C₄₁	—	4	2	no	—
174	C₄×C₄₁	—	4	4	no	—
175	C₄×C₄₁	—	4	2	no	—
176	C₄×C₄₁	—	4	4	no	—
177	C₄×C₄₁	—	8	2	no	—
178	C₄×C₄₁	#395	1	2	yes	—
179	C₄×C₄₁	#395	1	2	yes	—
180	C₄×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
181	C₄×C₄₁	C₂×C₄⋊Q₈	1	2	yes	—
182	#3458	C₂×C₄₁	1	1	yes	characteristic
183	C₂×#428	C₂×C₄₁	1	2	yes	—
184	#2317	C₂×C₄₁	1	1	yes	characteristic
185	#2061	C₂×C₄₁	1	4	yes	complemented
186	#2060	C₂×C₄₁	1	4	yes	complemented
187	#1742	C₂×C₄₁	1	1	yes	characteristic
188	#1733	C₂×C₄₁	1	2	yes	—
189	C₂×C₄₁	—	2	1	no	—
190	C₂×C₄₁	—	2	1	no	—
191	C₂×C₄₁	—	2	4	no	—
192	C₂×C₄₁	C₂×#395	1	1	yes	characteristic
193	C₂×C₄₁	#3021	1	1	yes	characteristic
194	C₂×C₄₁	#3022	1	1	yes	characteristic
195	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
196	#544	—	2	2	no	—
197	#544	—	2	2	no	—
198	#544	C₂²×C₄₁	1	2	yes	—
199	#544	C₂²×C₄₁	1	2	yes	—
200	#543	—	2	2	no	—
201	#533	—	2	4	no	—
202	#533	—	2	2	no	—
203	C₂×#117	C₂²×C₄₁	1	2	yes	—
204	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
205	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
207	#428	—	2	4	no	—
208	#428	C₂²×C₄₁	1	8	yes	—
209	C₂×#107	—	2	2	no	—
210	C₂×#106	—	2	2	no	—
211	#389	—	2	2	no	—
212	#385	—	2	2	no	—
213	#384	C₂²×C₄₁	1	2	yes	—
214	#382	C₂²×C₄₁	1	2	yes	—
215	#343	C₂²×C₄₁	1	2	yes	—
216	#343	C₂²×C₄₁	1	2	yes	—
217	#339	C₂²×C₄₁	1	8	yes	—
218	C₄₁	#23562	1	1	yes	characteristic, direct product factor, Sylow
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	4	no	—
223	C₂×M₁₆	Q₈×C₄₁	1	8	yes	complemented
224	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
225	C₂²×C₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	—	2	4	no	—
229	C₄⋊Q₈	—	2	4	no	—
230	#125	—	2	4	no	—
231	#125	—	2	4	no	—
232	#125	—	2	4	no	—
233	C₂²⋊Q₈	—	2	8	no	—
234	C₂²⋊Q₈	—	2	8	no	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	D₄×C₄₁	1	4	yes	—
245	#117	Q₈×C₄₁	1	4	yes	complemented
246	#117	C₂³×C₄₁	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
253	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	D₄×C₄₁	1	2	yes	—
262	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
263	#107	—	2	8	no	—
264	#106	—	2	8	no	—
265	#95	—	2	4	no	—
266	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	8	2	no	—
275	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
280	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
281	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
282	C₂²×C₄	#41×C₄₁	1	2	yes	—
283	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
284	M₁₆	—	2	8	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	C₂×Q₈×C₄₁	1	8	yes	—
287	C₂×C₈	—	2	8	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	8	4	no	—
302	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
303	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₄²	—	2	4	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂×Q₈×C₄₁	1	4	yes	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	#120×C₄₁	1	2	yes	—
317	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
318	C₂³	C₄⋊Q₈×C₄₁	1	2	yes	—
319	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
320	Q₈	—	8	4	no	—
321	Q₈	—	8	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	4	no	—
336	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
337	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
338	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
339	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
340	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
341	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
342	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
343	C₂×C₄	C₄⋊Q₈×C₄₁	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
345	C₂×C₄	C₂²×Q₈×C₄₁	1	2	yes	—
346	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
348	C₈	—	2	8	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	C₄₁×#395	1	4	yes	—
356	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
357	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
358	C₂²	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
359	C₄	—	4	4	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	4	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	4	no	—
364	C₄	—	8	2	no	—
365	C₄	C₄₁×#395	1	2	yes	—
366	C₄	C₄₁×#395	1	2	yes	—
367	C₄	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
368	C₄	C₂×C₄⋊Q₈×C₄₁	1	2	yes	—
369	C₂	—	2	1	no	—
370	C₂	—	2	1	no	—
371	C₂	—	2	4	no	—
372	C₂	C₂×C₄₁×#395	1	1	yes	characteristic
373	C₂	C₄₁×#3021	1	1	yes	characteristic
374	C₂	C₄₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#2061	C₂	semidirect
5. C₄₁×#2060	C₂	semidirect
35. C₂×M₁₆×C₄₁	Q₈	semidirect
57. #117×C₄₁	Q₈	semidirect
161. #23562	C₄₁	direct (N × H)
185. #2061	C₂×C₄₁	semidirect
186. #2060	C₂×C₄₁	semidirect
218. C₄₁	#23562	direct (N × H)
223. C₂×M₁₆	Q₈×C₄₁	semidirect
245. #117	Q₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3458	2
C₂×C₄₁×#428	2
C₄₁×#2317	2
C₄₁×#2061	2
C₄₁×#2060	2
C₄₁×#1742	2
C₄₁×#1733	2
#23562	41

Subgroups — C41×#23562 #23799763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23562 #23799763