Subgroups — C₄₁×#23454 #23799655

Order 10496.

1482 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#418	C₂	1	2	yes	maximal
3	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2025	C₂	1	4	yes	maximal, complemented
5	C₄₁×#2023	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1736	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1728	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
10	C₄₁×#533	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
12	C₂×#125×C₄₁	C₂²	1	2	yes	complemented
13	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
14	C₂×C₄×Q₈×C₄₁	—	2	2	no	—
15	C₂×#117×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₄₁	—	2	2	no	—
18	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#418	—	2	8	no	—
20	C₂×#102×C₄₁	C₂²	1	8	yes	—
21	C₄₁×#390	—	2	2	no	—
22	C₄₁×#390	C₂²	1	2	yes	—
23	C₄₁×#390	C₂²	1	2	yes	—
24	C₄₁×#340	C₂²	1	8	yes	complemented
25	C₄₁×#336	C₂²	1	2	yes	complemented
26	C₄₁×#336	C₂²	1	2	yes	complemented
27	C₂⁵×C₄₁	—	2	1	no	—
28	C₂²×Q₈×C₄₁	—	2	2	no	—
29	C₂²×D₄×C₄₁	—	2	4	no	—
30	C₂²×D₄×C₄₁	—	2	1	no	—
31	C₂²×D₄×C₄₁	—	2	4	no	—
32	C₂²×D₄×C₄₁	—	2	2	no	—
33	C₂²×D₄×C₄₁	Q₈	1	4	yes	complemented
34	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₁	—	2	1	no	—
36	C₂³×C₄×C₄₁	D₄	1	2	yes	—
37	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₄₁	—	2	4	no	—
39	C₂×M₁₆×C₄₁	—	2	4	no	—
40	C₂×M₁₆×C₄₁	—	2	4	no	—
41	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
42	C₄⋊Q₈×C₄₁	—	2	8	no	—
43	#125×C₄₁	—	2	8	no	—
44	C₂²⋊Q₈×C₄₁	—	2	16	no	—
45	C₄×Q₈×C₄₁	—	2	16	no	—
46	#117×C₄₁	—	2	4	no	—
47	#117×C₄₁	D₄	1	8	yes	—
48	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	4	8	no	—
58	C₂×C₄²×C₄₁	—	2	4	no	—
59	C₂×C₄²×C₄₁	—	2	2	no	—
60	C₂×C₄²×C₄₁	D₄	1	2	yes	—
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
63	#102×C₄₁	—	2	16	no	—
64	C₂⁴×C₄₁	—	2	4	no	—
65	C₂⁴×C₄₁	—	2	2	no	—
66	C₂⁴×C₄₁	—	4	4	no	—
67	C₂⁴×C₄₁	—	4	4	no	—
68	C₂⁴×C₄₁	—	4	2	no	—
69	C₂⁴×C₄₁	—	4	2	no	—
70	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
71	C₂×Q₈×C₄₁	—	2	8	no	—
72	C₂×Q₈×C₄₁	—	4	4	no	—
73	C₂×Q₈×C₄₁	—	4	4	no	—
74	C₂×D₄×C₄₁	—	2	16	no	—
75	C₂×D₄×C₄₁	—	2	4	no	—
76	C₂×D₄×C₄₁	—	2	4	no	—
77	C₂×D₄×C₄₁	—	2	4	no	—
78	C₂×D₄×C₄₁	—	2	2	no	—
79	C₂×D₄×C₄₁	—	4	2	no	—
80	C₂×D₄×C₄₁	—	4	8	no	—
81	C₂×D₄×C₄₁	—	4	2	no	—
82	C₂×D₄×C₄₁	C₂×Q₈	1	4	yes	—
83	C₂²×C₄×C₄₁	—	2	4	no	—
84	C₂²×C₄×C₄₁	—	2	4	no	—
85	C₂²×C₄×C₄₁	—	2	4	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	4	2	no	—
88	C₂²×C₄×C₄₁	—	4	4	no	—
89	C₂²×C₄×C₄₁	—	4	2	no	—
90	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₁	#41	1	4	yes	—
96	C₂²×C₄×C₄₁	#41	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
98	M₁₆×C₄₁	—	4	8	no	—
99	C₂×C₈×C₄₁	—	2	4	no	—
100	C₂×C₈×C₄₁	—	2	4	no	—
101	C₂×C₈×C₄₁	—	2	4	no	—
102	C₄⋊C₄×C₄₁	—	2	16	no	—
103	C₄⋊C₄×C₄₁	—	2	8	no	—
104	C₄⋊C₄×C₄₁	—	2	4	no	—
105	C₄⋊C₄×C₄₁	—	2	4	no	—
106	C₄⋊C₄×C₄₁	—	4	2	no	—
107	C₄⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
108	C₂²⋊C₄×C₄₁	—	2	8	no	—
109	C₂²⋊C₄×C₄₁	—	4	8	no	—
110	C₂²⋊C₄×C₄₁	—	4	8	no	—
111	C₄²×C₄₁	—	2	4	no	—
112	C₄²×C₄₁	—	2	8	no	—
113	C₄²×C₄₁	—	2	2	no	—
114	C₄²×C₄₁	—	2	2	no	—
115	C₂³×C₄₁	—	2	2	no	—
116	C₂³×C₄₁	—	2	2	no	—
117	C₂³×C₄₁	—	2	4	no	—
118	C₂³×C₄₁	—	4	16	no	—
119	C₂³×C₄₁	—	4	2	no	—
120	C₂³×C₄₁	—	4	2	no	—
121	C₂³×C₄₁	—	4	4	no	—
122	C₂³×C₄₁	—	4	4	no	—
123	C₂³×C₄₁	—	4	8	no	—
124	C₂³×C₄₁	—	8	4	no	—
125	C₂³×C₄₁	—	8	4	no	—
126	C₂³×C₄₁	—	8	8	no	—
127	C₂³×C₄₁	#120	1	2	yes	—
128	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
129	C₂³×C₄₁	#124	1	2	yes	—
130	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₄₁	—	4	16	no	—
132	D₄×C₄₁	—	2	8	no	—
133	D₄×C₄₁	—	4	4	no	—
134	D₄×C₄₁	—	4	8	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	8	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	4	8	no	—
142	C₂×C₄×C₄₁	—	4	4	no	—
143	C₂×C₄×C₄₁	—	4	4	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	4	4	no	—
146	C₂×C₄×C₄₁	—	8	4	no	—
147	C₂×C₄×C₄₁	#120	1	2	yes	—
148	C₂×C₄×C₄₁	C₂²⋊Q₈	1	8	yes	—
149	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₄₁	#124	1	8	yes	—
151	C₂×C₄×C₄₁	#124	1	2	yes	—
152	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
153	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
157	C₈×C₄₁	—	4	4	no	—
158	#23454	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₄₁	—	2	4	no	—
160	C₂²×C₄₁	—	2	2	no	—
161	C₂²×C₄₁	—	2	2	no	—
162	C₂²×C₄₁	—	2	4	no	—
163	C₂²×C₄₁	—	4	8	no	—
164	C₂²×C₄₁	—	4	4	no	—
165	C₂²×C₄₁	—	8	16	no	—
166	C₂²×C₄₁	—	8	2	no	—
167	C₂²×C₄₁	—	8	2	no	—
168	C₂²×C₄₁	—	8	4	no	—
169	C₂²×C₄₁	#393	1	4	yes	—
170	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
171	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
172	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
173	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
174	C₂²×C₄₁	#575	1	2	yes	—
175	C₄×C₄₁	—	2	4	no	—
176	C₄×C₄₁	—	4	2	no	—
177	C₄×C₄₁	—	4	8	no	—
178	C₄×C₄₁	—	8	2	no	—
179	C₄×C₄₁	#393	1	4	yes	—
180	C₄×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
181	C₄×C₄₁	C₂×#124	1	2	yes	—
182	C₂×#533	C₂×C₄₁	1	1	yes	characteristic, complemented
183	C₂×#418	C₂×C₄₁	1	2	yes	—
184	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
185	#2025	C₂×C₄₁	1	4	yes	complemented
186	#2023	C₂×C₄₁	1	4	yes	complemented
187	#1736	C₂×C₄₁	1	2	yes	complemented
188	#1728	C₂×C₄₁	1	1	yes	characteristic, complemented
189	C₂×C₄₁	—	2	4	no	—
190	C₂×C₄₁	—	8	4	no	—
191	C₂×C₄₁	C₂×#393	1	1	yes	characteristic
192	C₂×C₄₁	#3006	1	2	yes	—
193	C₂×C₄₁	#3077	1	2	yes	—
194	C₂×C₄₁	#3138	1	1	yes	characteristic
195	C₂×C₄₁	#3140	1	1	yes	characteristic
196	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
197	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
198	#533	—	2	8	no	—
199	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
200	C₂×#125	C₂²×C₄₁	1	2	yes	complemented
201	C₂×C₂²⋊Q₈	—	2	2	no	—
202	C₂×C₄×Q₈	—	2	2	no	—
203	C₂×#117	C₂²×C₄₁	1	2	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
205	C₂²×C₂²⋊C₄	—	2	2	no	—
206	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
207	#418	—	2	8	no	—
208	C₂×#102	C₂²×C₄₁	1	8	yes	—
209	#390	—	2	2	no	—
210	#390	C₂²×C₄₁	1	2	yes	—
211	#390	C₂²×C₄₁	1	2	yes	—
212	#340	C₂²×C₄₁	1	8	yes	complemented
213	#336	C₂²×C₄₁	1	2	yes	complemented
214	#336	C₂²×C₄₁	1	2	yes	complemented
215	C₄₁	#23454	1	1	yes	characteristic, direct product factor, Sylow
216	C₂⁵	—	2	1	no	—
217	C₂²×Q₈	—	2	2	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	Q₈×C₄₁	1	4	yes	complemented
223	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	D₄×C₄₁	1	2	yes	—
226	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
227	C₂×M₁₆	—	2	4	no	—
228	C₂×M₁₆	—	2	4	no	—
229	C₂×M₁₆	—	2	4	no	—
230	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
231	C₄⋊Q₈	—	2	8	no	—
232	#125	—	2	8	no	—
233	C₂²⋊Q₈	—	2	16	no	—
234	C₄×Q₈	—	2	16	no	—
235	#117	—	2	4	no	—
236	#117	D₄×C₄₁	1	8	yes	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₂²⋊C₄	—	4	8	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	4	no	—
249	C₂×C₄²	D₄×C₄₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
252	#102	—	2	16	no	—
253	C₂⁴	—	2	4	no	—
254	C₂⁴	—	2	2	no	—
255	C₂⁴	—	4	4	no	—
256	C₂⁴	—	4	4	no	—
257	C₂⁴	—	4	2	no	—
258	C₂⁴	—	4	2	no	—
259	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	4	4	no	—
262	C₂×Q₈	—	4	4	no	—
263	C₂×D₄	—	2	16	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	8	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	C₂×Q₈×C₄₁	1	4	yes	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
283	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
284	C₂²×C₄	#41×C₄₁	1	4	yes	—
285	C₂²×C₄	#41×C₄₁	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
287	M₁₆	—	4	8	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
297	C₂²⋊C₄	—	2	8	no	—
298	C₂²⋊C₄	—	4	8	no	—
299	C₂²⋊C₄	—	4	8	no	—
300	C₄²	—	2	4	no	—
301	C₄²	—	2	8	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	4	16	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	4	no	—
311	C₂³	—	4	4	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	8	4	no	—
314	C₂³	—	8	4	no	—
315	C₂³	—	8	8	no	—
316	C₂³	#120×C₄₁	1	2	yes	—
317	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
318	C₂³	#124×C₄₁	1	2	yes	—
319	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
320	Q₈	—	4	16	no	—
321	D₄	—	2	8	no	—
322	D₄	—	4	4	no	—
323	D₄	—	4	8	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	8	4	no	—
336	C₂×C₄	#120×C₄₁	1	2	yes	—
337	C₂×C₄	C₂²⋊Q₈×C₄₁	1	8	yes	—
338	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
339	C₂×C₄	#124×C₄₁	1	8	yes	—
340	C₂×C₄	#124×C₄₁	1	2	yes	—
341	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
342	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
343	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
345	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	8	16	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	4	no	—
357	C₂²	C₄₁×#393	1	4	yes	—
358	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
359	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
360	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
361	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
362	C₂²	C₄₁×#575	1	2	yes	—
363	C₄	—	2	4	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	8	no	—
366	C₄	—	8	2	no	—
367	C₄	C₄₁×#393	1	4	yes	—
368	C₄	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
369	C₄	C₂×#124×C₄₁	1	2	yes	—
370	C₂	—	2	4	no	—
371	C₂	—	8	4	no	—
372	C₂	C₂×C₄₁×#393	1	1	yes	characteristic
373	C₂	C₄₁×#3006	1	2	yes	—
374	C₂	C₄₁×#3077	1	2	yes	—
375	C₂	C₄₁×#3138	1	1	yes	characteristic
376	C₂	C₄₁×#3140	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#533	C₂	semidirect
4. C₄₁×#2025	C₂	semidirect
5. C₄₁×#2023	C₂	semidirect
6. C₄₁×#1736	C₂	semidirect
7. C₄₁×#1728	C₂	semidirect
11. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
12. C₂×#125×C₄₁	C₂²	semidirect
24. C₄₁×#340	C₂²	semidirect
25. C₄₁×#336	C₂²	semidirect
26. C₄₁×#336	C₂²	semidirect
33. C₂²×D₄×C₄₁	Q₈	semidirect
158. #23454	C₄₁	direct (N × H)
182. C₂×#533	C₂×C₄₁	semidirect
185. #2025	C₂×C₄₁	semidirect
186. #2023	C₂×C₄₁	semidirect
187. #1736	C₂×C₄₁	semidirect
188. #1728	C₂×C₄₁	semidirect
199. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
200. C₂×#125	C₂²×C₄₁	semidirect
212. #340	C₂²×C₄₁	semidirect
213. #336	C₂²×C₄₁	semidirect
214. #336	C₂²×C₄₁	semidirect
215. C₄₁	#23454	direct (N × H)
222. C₂²×D₄	Q₈×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×#533	2
C₂×C₄₁×#418	2
C₂×C₄₁×#390	2
C₄₁×#2025	2
C₄₁×#2023	2
C₄₁×#1736	2
C₄₁×#1728	2
#23454	41

Subgroups — C41×#23454 #23799655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23454 #23799655