Subgroups — C₄₁×#21810 #23798011

Order 10496.

1990 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1982	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1961	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1786	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₄₁	—	2	1	no	—
8	C₂³×D₄×C₄₁	—	2	1	no	—
9	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
10	C₂×#127×C₄₁	—	2	1	no	—
11	C₂×#127×C₄₁	—	2	1	no	—
12	C₂×#127×C₄₁	—	2	4	no	—
13	C₂×#127×C₄₁	C₄	1	8	yes	complemented
14	C₂×#127×C₄₁	C₂²	1	2	yes	—
15	C₂×#127×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#432	—	2	4	no	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
19	C₂×#102×C₄₁	C₂²	1	16	yes	complemented
20	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
21	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
22	C₄₁×#383	—	2	1	no	—
23	C₄₁×#382	C₂²	1	2	yes	complemented
24	C₄₁×#381	—	2	1	no	—
25	C₄₁×#380	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
27	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
28	C₄₁×#376	—	2	1	no	—
29	C₂⁵×C₄₁	—	2	2	no	—
30	C₂²×D₄×C₄₁	—	2	8	no	—
31	C₂²×D₄×C₄₁	—	2	8	no	—
32	C₂²×D₄×C₄₁	—	2	2	no	—
33	C₂²×D₄×C₄₁	—	2	4	no	—
34	C₂²×D₄×C₄₁	—	2	2	no	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	—	2	2	no	—
38	C₂²×D₄×C₄₁	—	4	8	no	—
39	C₂²×D₄×C₄₁	—	4	8	no	—
40	C₂²×D₄×C₄₁	—	4	8	no	—
41	C₂²×D₄×C₄₁	C₂×C₄	1	8	yes	—
42	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
43	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
47	#127×C₄₁	—	2	8	no	—
48	#127×C₄₁	—	2	8	no	—
49	#127×C₄₁	—	2	4	no	—
50	#127×C₄₁	—	2	4	no	—
51	#127×C₄₁	C₂×C₄	1	8	yes	—
52	#127×C₄₁	C₂×C₄	1	8	yes	—
53	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄²×C₄₁	—	2	2	no	—
56	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₁	D₄	1	4	yes	—
60	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₄₁	—	2	4	no	—
63	#102×C₄₁	—	4	16	no	—
64	C₂²⋊C₈×C₄₁	—	2	4	no	—
65	#97×C₄₁	—	2	4	no	—
66	#95×C₄₁	—	2	2	no	—
67	#95×C₄₁	—	2	2	no	—
68	#95×C₄₁	—	2	2	no	—
69	#95×C₄₁	—	2	2	no	—
70	C₂⁴×C₄₁	—	2	8	no	—
71	C₂⁴×C₄₁	—	2	4	no	—
72	C₂⁴×C₄₁	—	4	8	no	—
73	C₂⁴×C₄₁	—	4	8	no	—
74	C₂⁴×C₄₁	—	4	8	no	—
75	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
76	C₂×D₄×C₄₁	—	2	8	no	—
77	C₂×D₄×C₄₁	—	2	8	no	—
78	C₂×D₄×C₄₁	—	2	8	no	—
79	C₂×D₄×C₄₁	—	2	8	no	—
80	C₂×D₄×C₄₁	—	2	8	no	—
81	C₂×D₄×C₄₁	—	2	4	no	—
82	C₂×D₄×C₄₁	—	2	16	no	—
83	C₂×D₄×C₄₁	—	4	16	no	—
84	C₂×D₄×C₄₁	—	4	8	no	—
85	C₂×D₄×C₄₁	—	4	8	no	—
86	C₂×D₄×C₄₁	—	4	8	no	—
87	C₂×D₄×C₄₁	—	4	8	no	—
88	C₂×D₄×C₄₁	—	4	32	no	—
89	C₂×D₄×C₄₁	—	4	16	no	—
90	C₂×D₄×C₄₁	—	4	32	no	—
91	C₂×D₄×C₄₁	—	4	8	no	—
92	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
93	C₂²×C₄×C₄₁	—	2	4	no	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	4	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₄₁	—	2	4	no	—
108	C₂×C₈×C₄₁	—	2	8	no	—
109	C₄⋊C₄×C₄₁	—	2	8	no	—
110	C₂²⋊C₄×C₄₁	—	4	4	no	—
111	C₄²×C₄₁	—	4	4	no	—
112	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
113	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
114	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
115	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
116	C₄²×C₄₁	C₂×D₄	1	2	yes	—
117	C₄²×C₄₁	C₂×D₄	1	2	yes	—
118	C₂³×C₄₁	—	2	2	no	—
119	C₂³×C₄₁	—	2	2	no	—
120	C₂³×C₄₁	—	2	8	no	—
121	C₂³×C₄₁	—	4	16	no	—
122	C₂³×C₄₁	—	4	16	no	—
123	C₂³×C₄₁	—	4	8	no	—
124	C₂³×C₄₁	—	4	8	no	—
125	C₂³×C₄₁	—	4	8	no	—
126	C₂³×C₄₁	—	4	16	no	—
127	C₂³×C₄₁	—	8	32	no	—
128	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
129	C₂³×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
130	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
131	D₄×C₄₁	—	2	16	no	—
132	D₄×C₄₁	—	4	16	no	—
133	D₄×C₄₁	—	4	16	no	—
134	D₄×C₄₁	—	4	16	no	—
135	D₄×C₄₁	—	4	16	no	—
136	D₄×C₄₁	—	4	8	no	—
137	D₄×C₄₁	—	4	16	no	—
138	C₂×C₄×C₄₁	—	2	2	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	2	8	no	—
143	C₂×C₄×C₄₁	—	2	4	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	2	8	no	—
146	C₂×C₄×C₄₁	—	4	4	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
155	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
158	C₈×C₄₁	—	4	4	no	—
159	#21810	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂²×C₄₁	—	2	2	no	—
161	C₂²×C₄₁	—	2	2	no	—
162	C₂²×C₄₁	—	2	8	no	—
163	C₂²×C₄₁	—	4	8	no	—
164	C₂²×C₄₁	—	4	8	no	—
165	C₂²×C₄₁	—	4	8	no	—
166	C₂²×C₄₁	—	8	32	no	—
167	C₂²×C₄₁	—	8	16	no	—
168	C₂²×C₄₁	#418	1	4	yes	—
169	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄₁	#535	1	2	yes	—
171	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
172	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
173	C₄×C₄₁	—	2	2	no	—
174	C₄×C₄₁	—	2	2	no	—
175	C₄×C₄₁	—	2	2	no	—
176	C₄×C₄₁	—	2	2	no	—
177	C₄×C₄₁	—	8	4	no	—
178	C₄×C₄₁	#418	1	4	yes	—
179	C₄×C₄₁	#518	1	2	yes	—
180	C₄×C₄₁	#535	1	2	yes	—
181	C₂²×#127	C₂×C₄₁	1	1	yes	characteristic
182	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
183	#2283	C₂×C₄₁	1	1	yes	characteristic, complemented
184	#1982	C₂×C₄₁	1	4	yes	complemented
185	#1961	C₂×C₄₁	1	4	yes	complemented
186	#1786	C₂×C₄₁	1	4	yes	complemented
187	C₂×C₄₁	—	2	4	no	—
188	C₂×C₄₁	—	8	8	no	—
189	C₂×C₄₁	#2309	1	1	yes	characteristic
190	C₂×C₄₁	C₂×#418	1	1	yes	characteristic
191	C₂×C₄₁	C₂×#418	1	1	yes	characteristic
192	C₂×C₄₁	#3217	1	4	yes	—
193	C₂³×D₄	—	2	1	no	—
194	C₂³×D₄	—	2	1	no	—
195	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
196	C₂×#127	—	2	1	no	—
197	C₂×#127	—	2	1	no	—
198	C₂×#127	—	2	4	no	—
199	C₂×#127	C₄×C₄₁	1	8	yes	complemented
200	C₂×#127	C₂²×C₄₁	1	2	yes	—
201	C₂×#127	C₂²×C₄₁	1	2	yes	—
202	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
203	#432	—	2	4	no	—
204	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
205	C₂×#102	C₂²×C₄₁	1	16	yes	complemented
206	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
207	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
208	#383	—	2	1	no	—
209	#382	C₂²×C₄₁	1	2	yes	complemented
210	#381	—	2	1	no	—
211	#380	C₂²×C₄₁	1	2	yes	—
212	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
213	C₄×C₂²⋊C₄	—	2	1	no	—
214	#376	—	2	1	no	—
215	C₄₁	#21810	1	1	yes	characteristic, direct product factor, Sylow
216	C₂⁵	—	2	2	no	—
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	2	8	no	—
219	C₂²×D₄	—	2	2	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	2	2	no	—
225	C₂²×D₄	—	4	8	no	—
226	C₂²×D₄	—	4	8	no	—
227	C₂²×D₄	—	4	8	no	—
228	C₂²×D₄	C₂×C₄×C₄₁	1	8	yes	—
229	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
230	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
231	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
234	#127	—	2	8	no	—
235	#127	—	2	8	no	—
236	#127	—	2	4	no	—
237	#127	—	2	4	no	—
238	#127	C₂×C₄×C₄₁	1	8	yes	—
239	#127	C₂×C₄×C₄₁	1	8	yes	—
240	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
244	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₄₁	1	4	yes	—
247	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
249	C₄⋊C₈	—	2	4	no	—
250	#102	—	4	16	no	—
251	C₂²⋊C₈	—	2	4	no	—
252	#97	—	2	4	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	4	8	no	—
260	C₂⁴	—	4	8	no	—
261	C₂⁴	—	4	8	no	—
262	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
263	C₂×D₄	—	2	8	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	4	16	no	—
271	C₂×D₄	—	4	8	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	32	no	—
276	C₂×D₄	—	4	16	no	—
277	C₂×D₄	—	4	32	no	—
278	C₂×D₄	—	4	8	no	—
279	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
286	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	8	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₄²	—	4	4	no	—
299	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
300	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
301	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
302	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
303	C₄²	C₂×D₄×C₄₁	1	2	yes	—
304	C₄²	C₂×D₄×C₄₁	1	2	yes	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	8	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	16	no	—
314	C₂³	—	8	32	no	—
315	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
316	C₂³	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
317	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
318	D₄	—	2	16	no	—
319	D₄	—	4	16	no	—
320	D₄	—	4	16	no	—
321	D₄	—	4	16	no	—
322	D₄	—	4	16	no	—
323	D₄	—	4	8	no	—
324	D₄	—	4	16	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
341	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
342	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
344	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
345	C₈	—	4	4	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	8	32	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₄₁×#418	1	4	yes	—
355	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
356	C₂²	C₄₁×#535	1	2	yes	—
357	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
358	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	8	4	no	—
364	C₄	C₄₁×#418	1	4	yes	—
365	C₄	C₄₁×#518	1	2	yes	—
366	C₄	C₄₁×#535	1	2	yes	—
367	C₂	—	2	4	no	—
368	C₂	—	8	8	no	—
369	C₂	C₄₁×#2309	1	1	yes	characteristic
370	C₂	C₂×C₄₁×#418	1	1	yes	characteristic
371	C₂	C₂×C₄₁×#418	1	1	yes	characteristic
372	C₂	C₄₁×#3217	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#127×C₄₁	C₂
LCS	G ▷ C₂×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
2. C₂×C₄₁×#432	C₂	semidirect
3. C₄₁×#2283	C₂	semidirect
4. C₄₁×#1982	C₂	semidirect
5. C₄₁×#1961	C₂	semidirect
6. C₄₁×#1786	C₂	semidirect
13. C₂×#127×C₄₁	C₄	semidirect
18. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
19. C₂×#102×C₄₁	C₂²	semidirect
21. C₂×#97×C₄₁	C₂²	semidirect
23. C₄₁×#382	C₂²	semidirect
26. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
159. #21810	C₄₁	direct (N × H)
182. C₂×#432	C₂×C₄₁	semidirect
183. #2283	C₂×C₄₁	semidirect
184. #1982	C₂×C₄₁	semidirect
185. #1961	C₂×C₄₁	semidirect
186. #1786	C₂×C₄₁	semidirect
199. C₂×#127	C₄×C₄₁	semidirect
204. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
205. C₂×#102	C₂²×C₄₁	semidirect
207. C₂×#97	C₂²×C₄₁	semidirect
209. #382	C₂²×C₄₁	semidirect
212. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
215. C₄₁	#21810	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#127×C₄₁	2
C₂×C₄₁×#432	2
C₄₁×#2283	2
C₄₁×#1982	2
C₄₁×#1961	2
C₄₁×#1786	2
#21810	41

Subgroups — C41×#21810 #23798011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21810 #23798011