Subgroups — C₄₁×#23175 #23799376

Order 10496.

1116 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#435	C₂	1	4	yes	maximal, complemented
2	C₄×#127×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1955	C₂	1	4	yes	maximal, complemented
4	C₄₁×#1870	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1869	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1767	C₂	1	2	yes	maximal, complemented
7	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
9	C₂×#127×C₄₁	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
11	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#435	—	2	16	no	—
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
17	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
18	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
20	C₂×#97×C₄₁	C₂²	1	4	yes	—
21	C₄₁×#390	C₄	1	1	yes	characteristic
22	C₄₁×#390	C₄	1	1	yes	characteristic
23	C₄₁×#390	C₄	1	4	yes	—
24	C₄₁×#384	C₄	1	1	yes	characteristic
25	C₄³×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#336	C₂²	1	4	yes	—
27	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
28	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
32	C₂×M₁₆×C₄₁	—	2	8	no	—
33	C₂×M₁₆×C₄₁	—	4	2	no	—
34	C₂²×C₈×C₄₁	—	2	8	no	—
35	C₂²×C₈×C₄₁	—	4	2	no	—
36	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
37	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
38	#127×C₄₁	—	2	4	no	—
39	C₄×D₄×C₄₁	—	2	8	no	—
40	C₄×D₄×C₄₁	—	2	8	no	—
41	C₄×D₄×C₄₁	—	4	1	no	—
42	C₄×D₄×C₄₁	—	4	1	no	—
43	C₄×D₄×C₄₁	—	4	1	no	—
44	C₄×D₄×C₄₁	—	4	1	no	—
45	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
50	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
57	C₄⋊C₈×C₄₁	—	2	4	no	—
58	C₄⋊C₈×C₄₁	D₄	1	8	yes	complemented
59	C₂²⋊C₈×C₄₁	—	2	8	no	—
60	C₂²⋊C₈×C₄₁	—	2	8	no	—
61	C₂²⋊C₈×C₄₁	—	4	2	no	—
62	C₂²⋊C₈×C₄₁	—	4	2	no	—
63	#97×C₄₁	—	2	8	no	—
64	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
65	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
66	C₂×D₄×C₄₁	—	2	8	no	—
67	C₂×D₄×C₄₁	—	2	8	no	—
68	C₂×D₄×C₄₁	—	2	2	no	—
69	C₂×D₄×C₄₁	—	4	1	no	—
70	C₂×D₄×C₄₁	—	4	1	no	—
71	C₂×D₄×C₄₁	—	4	1	no	—
72	C₂×D₄×C₄₁	—	4	4	no	—
73	C₂×D₄×C₄₁	—	4	1	no	—
74	C₂×D₄×C₄₁	M₁₆	1	4	yes	complemented
75	C₂²×C₄×C₄₁	—	2	4	no	—
76	C₂²×C₄×C₄₁	—	2	4	no	—
77	C₂²×C₄×C₄₁	—	2	4	no	—
78	C₂²×C₄×C₄₁	—	2	4	no	—
79	C₂²×C₄×C₄₁	—	2	2	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
90	M₁₆×C₄₁	—	4	8	no	—
91	C₂×C₈×C₄₁	—	2	4	no	—
92	C₂×C₈×C₄₁	—	2	4	no	—
93	C₂×C₈×C₄₁	—	2	4	no	—
94	C₂×C₈×C₄₁	—	2	4	no	—
95	C₂×C₈×C₄₁	—	2	4	no	—
96	C₂×C₈×C₄₁	—	4	8	no	—
97	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	—
98	C₄⋊C₄×C₄₁	—	2	8	no	—
99	C₄⋊C₄×C₄₁	—	4	1	no	—
100	C₄⋊C₄×C₄₁	—	4	1	no	—
101	C₂²⋊C₄×C₄₁	—	2	8	no	—
102	C₂²⋊C₄×C₄₁	—	2	8	no	—
103	C₂²⋊C₄×C₄₁	—	4	2	no	—
104	C₂²⋊C₄×C₄₁	—	4	2	no	—
105	C₄²×C₄₁	—	2	2	no	—
106	C₄²×C₄₁	—	2	1	no	—
107	C₄²×C₄₁	—	2	1	no	—
108	C₄²×C₄₁	—	4	1	no	—
109	C₄²×C₄₁	—	4	2	no	—
110	C₄²×C₄₁	C₂×D₄	1	4	yes	—
111	C₄²×C₄₁	#41	1	4	yes	—
112	C₂³×C₄₁	—	2	4	no	—
113	C₂³×C₄₁	—	2	2	no	—
114	C₂³×C₄₁	—	2	4	no	—
115	C₂³×C₄₁	—	2	2	no	—
116	C₂³×C₄₁	—	2	4	no	—
117	C₂³×C₄₁	—	2	2	no	—
118	C₂³×C₄₁	—	2	2	no	—
119	C₂³×C₄₁	—	2	2	no	—
120	C₂³×C₄₁	—	2	4	no	—
121	C₂³×C₄₁	C₂×M₁₆	1	4	yes	—
122	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
123	D₄×C₄₁	—	4	4	no	—
124	D₄×C₄₁	—	4	16	no	—
125	D₄×C₄₁	—	4	4	no	—
126	C₂×C₄×C₄₁	—	2	1	no	—
127	C₂×C₄×C₄₁	—	2	2	no	—
128	C₂×C₄×C₄₁	—	2	2	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	2	no	—
131	C₂×C₄×C₄₁	—	2	1	no	—
132	C₂×C₄×C₄₁	—	2	4	no	—
133	C₂×C₄×C₄₁	—	2	4	no	—
134	C₂×C₄×C₄₁	—	2	1	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	—	4	2	no	—
139	C₂×C₄×C₄₁	—	4	2	no	—
140	C₂×C₄×C₄₁	—	4	4	no	—
141	C₂×C₄×C₄₁	—	4	4	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
145	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
147	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
149	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
151	C₈×C₄₁	—	2	8	no	—
152	C₈×C₄₁	—	4	4	no	—
153	#23175	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂²×C₄₁	—	2	8	no	—
155	C₂²×C₄₁	—	2	4	no	—
156	C₂²×C₄₁	—	4	2	no	—
157	C₂²×C₄₁	—	4	4	no	—
158	C₂²×C₄₁	—	4	2	no	—
159	C₂²×C₄₁	—	4	2	no	—
160	C₂²×C₄₁	—	4	4	no	—
161	C₂²×C₄₁	—	4	4	no	—
162	C₂²×C₄₁	—	4	2	no	—
163	C₂²×C₄₁	—	4	2	no	—
164	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
165	C₂²×C₄₁	#518	1	1	yes	characteristic
166	C₂²×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
167	C₂²×C₄₁	#568	1	1	yes	characteristic
168	C₂²×C₄₁	#568	1	2	yes	—
169	C₄×C₄₁	—	2	4	no	—
170	C₄×C₄₁	—	2	4	no	—
171	C₄×C₄₁	—	2	2	no	—
172	C₄×C₄₁	—	4	2	no	—
173	C₄×C₄₁	—	4	2	no	—
174	C₄×C₄₁	—	4	1	no	—
175	C₄×C₄₁	D₄²	1	1	yes	characteristic
176	C₄×C₄₁	#550	1	2	yes	—
177	C₄×C₄₁	#559	1	1	yes	characteristic
178	C₂×#435	C₂×C₄₁	1	4	yes	complemented
179	C₄×#127	C₂×C₄₁	1	1	yes	characteristic
180	#1955	C₂×C₄₁	1	4	yes	complemented
181	#1870	C₂×C₄₁	1	2	yes	complemented
182	#1869	C₂×C₄₁	1	2	yes	complemented
183	#1767	C₂×C₄₁	1	2	yes	complemented
184	C₂×C₄₁	—	4	4	no	—
185	C₂×C₄₁	—	8	2	no	—
186	C₂×C₄₁	#2366	1	1	yes	characteristic
187	C₂×C₄₁	#2932	1	2	yes	—
188	C₂×C₄₁	D₄×M₁₆	1	2	yes	—
189	C₂×C₄₁	#2973	1	1	yes	characteristic
190	C₂×C₄₁	#2980	1	1	yes	characteristic
191	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
192	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
193	C₂×#127	C₄×C₄₁	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
195	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
196	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
197	#435	—	2	16	no	—
198	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
199	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
200	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
202	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
204	C₂×#97	C₂²×C₄₁	1	4	yes	—
205	#390	C₄×C₄₁	1	1	yes	characteristic
206	#390	C₄×C₄₁	1	1	yes	characteristic
207	#390	C₄×C₄₁	1	4	yes	—
208	#384	C₄×C₄₁	1	1	yes	characteristic
209	C₄³	C₂²×C₄₁	1	1	yes	characteristic
210	#336	C₂²×C₄₁	1	4	yes	—
211	C₄₁	#23175	1	1	yes	characteristic, direct product factor, Sylow
212	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
213	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
214	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
216	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
217	C₂×M₁₆	—	2	8	no	—
218	C₂×M₁₆	—	4	2	no	—
219	C₂²×C₈	—	2	8	no	—
220	C₂²×C₈	—	4	2	no	—
221	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
222	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
223	#127	—	2	4	no	—
224	C₄×D₄	—	2	8	no	—
225	C₄×D₄	—	2	8	no	—
226	C₄×D₄	—	4	1	no	—
227	C₄×D₄	—	4	1	no	—
228	C₄×D₄	—	4	1	no	—
229	C₄×D₄	—	4	1	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
237	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
239	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
242	C₄⋊C₈	—	2	4	no	—
243	C₄⋊C₈	D₄×C₄₁	1	8	yes	complemented
244	C₂²⋊C₈	—	2	8	no	—
245	C₂²⋊C₈	—	2	8	no	—
246	C₂²⋊C₈	—	4	2	no	—
247	C₂²⋊C₈	—	4	2	no	—
248	#97	—	2	8	no	—
249	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
250	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	—	4	1	no	—
256	C₂×D₄	—	4	1	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	M₁₆×C₄₁	1	4	yes	complemented
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
275	M₁₆	—	4	8	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	8	no	—
282	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	—
283	C₄⋊C₄	—	2	8	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	2	8	no	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	4	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	4	1	no	—
294	C₄²	—	4	2	no	—
295	C₄²	C₂×D₄×C₄₁	1	4	yes	—
296	C₄²	#41×C₄₁	1	4	yes	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	4	no	—
306	C₂³	C₂×M₁₆×C₄₁	1	4	yes	—
307	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
308	D₄	—	4	4	no	—
309	D₄	—	4	16	no	—
310	D₄	—	4	4	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
330	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
331	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
332	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
333	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
334	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
335	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
336	C₈	—	2	8	no	—
337	C₈	—	4	4	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
349	C₂²	C₄₁×#518	1	1	yes	characteristic
350	C₂²	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
351	C₂²	C₄₁×#568	1	1	yes	characteristic
352	C₂²	C₄₁×#568	1	2	yes	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	1	no	—
359	C₄	D₄²×C₄₁	1	1	yes	characteristic
360	C₄	C₄₁×#550	1	2	yes	—
361	C₄	C₄₁×#559	1	1	yes	characteristic
362	C₂	—	4	4	no	—
363	C₂	—	8	2	no	—
364	C₂	C₄₁×#2366	1	1	yes	characteristic
365	C₂	C₄₁×#2932	1	2	yes	—
366	C₂	D₄×M₁₆×C₄₁	1	2	yes	—
367	C₂	C₄₁×#2973	1	1	yes	characteristic
368	C₂	C₄₁×#2980	1	1	yes	characteristic

	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	C₂×#127×C₄₁	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
1. C₂×C₄₁×#435	C₂	semidirect
3. C₄₁×#1955	C₂	semidirect
4. C₄₁×#1870	C₂	semidirect
5. C₄₁×#1869	C₂	semidirect
6. C₄₁×#1767	C₂	semidirect
58. C₄⋊C₈×C₄₁	D₄	semidirect
74. C₂×D₄×C₄₁	M₁₆	semidirect
153. #23175	C₄₁	direct (N × H)
178. C₂×#435	C₂×C₄₁	semidirect
180. #1955	C₂×C₄₁	semidirect
181. #1870	C₂×C₄₁	semidirect
182. #1869	C₂×C₄₁	semidirect
183. #1767	C₂×C₄₁	semidirect
211. C₄₁	#23175	direct (N × H)
243. C₄⋊C₈	D₄×C₄₁	semidirect
259. C₂×D₄	M₁₆×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×#435	2
C₄×#127×C₄₁	2
C₄₁×#1955	2
C₄₁×#1870	2
C₄₁×#1869	2
C₄₁×#1767	2
#23175	41

Subgroups — C41×#23175 #23799376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23175 #23799376