Subgroups — C₄₁×#18179 #23794380

Order 10496.

1250 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3496	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3112	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1607	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1601	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1505	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(5,𝔽₂)×C₄₁	—	2	1	no	—
9	C₄₁×#547	—	2	2	no	—
10	C₄₁×#546	—	2	4	no	—
11	D₄²×C₄₁	—	2	2	no	—
12	C₄₁×#537	—	2	1	no	—
13	C₄₁×#534	C₂²	1	4	yes	—
14	C₄₁×#532	C₂²	1	2	yes	—
15	C₂×#121×C₄₁	—	2	2	no	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#480	C₂²	1	4	yes	complemented
19	C₄₁×#477	—	2	2	no	—
20	C₄₁×#460	—	2	2	no	—
21	C₄₁×#448	C₂²	1	4	yes	complemented
22	C₄₁×#440	—	2	4	no	—
23	C₄₁×#432	C₂²	1	2	yes	complemented
24	C₄₁×#400	—	2	1	no	—
25	C₄₁×#397	C₂²	1	2	yes	complemented
26	C₄₁×#394	—	2	1	no	—
27	C₄₁×#393	C₂²	1	2	yes	complemented
28	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
29	C₄₁×#376	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#327	C₂²	1	8	yes	complemented
31	C₄₁×#323	C₂²	1	4	yes	complemented
32	H(5,𝔽₂)×C₄₁	—	4	8	no	—
33	C₂×#41×C₄₁	—	2	4	no	—
34	C₂×#41×C₄₁	—	2	2	no	—
35	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₄₁	—	2	4	no	—
37	C₂²×D₄×C₄₁	—	2	4	no	—
38	C₂²×D₄×C₄₁	—	2	2	no	—
39	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₁	D₄	1	2	yes	—
41	C₂×SD₁₆×C₄₁	—	2	4	no	—
42	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
43	#127×C₄₁	D₄	1	2	yes	—
44	#124×C₄₁	—	2	2	no	—
45	#123×C₄₁	—	2	8	no	—
46	C₂²⋊Q₈×C₄₁	—	2	4	no	—
47	#121×C₄₁	—	2	4	no	—
48	#121×C₄₁	—	2	4	no	—
49	#121×C₄₁	—	2	4	no	—
50	#121×C₄₁	—	2	2	no	—
51	#121×C₄₁	—	2	4	no	—
52	#121×C₄₁	C₂³	1	4	yes	—
53	#120×C₄₁	—	2	8	no	—
54	C₄×Q₈×C₄₁	—	2	2	no	—
55	C₄×Q₈×C₄₁	—	2	2	no	—
56	C₄×D₄×C₄₁	—	2	2	no	—
57	C₄×D₄×C₄₁	—	2	2	no	—
58	C₄×D₄×C₄₁	—	2	2	no	—
59	C₄×D₄×C₄₁	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₁	—	2	1	no	—
69	C₂×C₄²×C₄₁	—	2	1	no	—
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	#107×C₄₁	—	2	4	no	—
72	C₄⋊C₈×C₄₁	—	2	2	no	—
73	#103×C₄₁	—	2	4	no	—
74	#102×C₄₁	—	2	4	no	—
75	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
76	#97×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	1	no	—
78	#95×C₄₁	—	2	2	no	—
79	#95×C₄₁	—	2	2	no	—
80	#95×C₄₁	C₂³	1	2	yes	—
81	C₂⁴×C₄₁	—	2	4	no	—
82	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
83	#41×C₄₁	—	4	8	no	—
84	#41×C₄₁	—	4	16	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	2	no	—
87	C₂×Q₈×C₄₁	—	4	2	no	—
88	C₂×D₄×C₄₁	—	2	4	no	—
89	C₂×D₄×C₄₁	—	2	8	no	—
90	C₂×D₄×C₄₁	—	2	4	no	—
91	C₂×D₄×C₄₁	—	2	4	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	2	2	no	—
94	C₂×D₄×C₄₁	—	2	2	no	—
95	C₂×D₄×C₄₁	—	4	16	no	—
96	C₂×D₄×C₄₁	—	4	8	no	—
97	C₂×D₄×C₄₁	—	4	8	no	—
98	C₂×D₄×C₄₁	—	8	4	no	—
99	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	1	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	4	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	4	4	no	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
112	SD₁₆×C₄₁	—	4	8	no	—
113	C₂×C₈×C₄₁	—	2	4	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	2	no	—
118	C₄⋊C₄×C₄₁	—	4	2	no	—
119	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
120	C₂²⋊C₄×C₄₁	—	2	8	no	—
121	C₂²⋊C₄×C₄₁	—	2	4	no	—
122	C₂²⋊C₄×C₄₁	—	2	4	no	—
123	C₂²⋊C₄×C₄₁	—	2	4	no	—
124	C₂²⋊C₄×C₄₁	—	4	4	no	—
125	C₂²⋊C₄×C₄₁	—	4	4	no	—
126	C₄²×C₄₁	—	4	2	no	—
127	C₄²×C₄₁	—	4	1	no	—
128	C₄²×C₄₁	—	4	1	no	—
129	C₄²×C₄₁	C₂×D₄	1	2	yes	—
130	C₄²×C₄₁	C₂×D₄	1	2	yes	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	2	no	—
133	C₂³×C₄₁	—	2	4	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	—	4	2	no	—
136	C₂³×C₄₁	—	4	8	no	—
137	C₂³×C₄₁	—	8	4	no	—
138	C₂³×C₄₁	—	8	4	no	—
139	C₂³×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
140	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₄₁	—	2	4	no	—
142	Q₈×C₄₁	—	4	2	no	—
143	Q₈×C₄₁	—	4	4	no	—
144	D₄×C₄₁	—	2	8	no	—
145	D₄×C₄₁	—	4	4	no	—
146	D₄×C₄₁	—	4	4	no	—
147	D₄×C₄₁	—	4	16	no	—
148	D₄×C₄₁	—	4	8	no	—
149	D₄×C₄₁	—	4	4	no	—
150	D₄×C₄₁	—	8	4	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	4	1	no	—
157	C₂×C₄×C₄₁	—	4	8	no	—
158	C₂×C₄×C₄₁	—	4	8	no	—
159	C₂×C₄×C₄₁	—	4	1	no	—
160	C₂×C₄×C₄₁	—	4	1	no	—
161	C₂×C₄×C₄₁	—	4	4	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	8	2	no	—
169	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#120	1	2	yes	—
171	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
173	C₈×C₄₁	—	4	4	no	—
174	#18179	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₁	—	2	1	no	—
176	C₂²×C₄₁	—	2	1	no	—
177	C₂²×C₄₁	—	2	4	no	—
178	C₂²×C₄₁	—	4	4	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	4	2	no	—
181	C₂²×C₄₁	—	4	4	no	—
182	C₂²×C₄₁	—	4	4	no	—
183	C₂²×C₄₁	—	4	4	no	—
184	C₂²×C₄₁	—	8	2	no	—
185	C₂²×C₄₁	—	16	8	no	—
186	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
187	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
188	C₄×C₄₁	—	2	2	no	—
189	C₄×C₄₁	—	2	1	no	—
190	C₄×C₄₁	—	2	2	no	—
191	C₄×C₄₁	—	4	4	no	—
192	C₄×C₄₁	—	4	2	no	—
193	C₄×C₄₁	—	4	2	no	—
194	C₄×C₄₁	—	8	2	no	—
195	C₄×C₄₁	—	8	1	no	—
196	C₄×C₄₁	#455	1	2	yes	—
197	#3496	C₂×C₄₁	1	1	yes	characteristic
198	#3112	C₂×C₄₁	1	2	yes	complemented
199	#2398	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1607	C₂×C₄₁	1	4	yes	complemented
201	#1601	C₂×C₄₁	1	4	yes	complemented
202	#1505	C₂×C₄₁	1	2	yes	complemented
203	#1466	C₂×C₄₁	1	1	yes	characteristic, complemented
204	C₂×C₄₁	—	2	2	no	—
205	C₂×C₄₁	—	4	4	no	—
206	C₂×C₄₁	—	8	4	no	—
207	C₂×C₄₁	#3003	1	1	yes	characteristic
208	C₂×C₄₁	C₂×#455	1	1	yes	characteristic
209	C₂×C₄₁	#3025	1	1	yes	characteristic
210	C₂×H(5,𝔽₂)	—	2	1	no	—
211	#547	—	2	2	no	—
212	#546	—	2	4	no	—
213	D₄²	—	2	2	no	—
214	#537	—	2	1	no	—
215	#534	C₂²×C₄₁	1	4	yes	—
216	#532	C₂²×C₄₁	1	2	yes	—
217	C₂×#121	—	2	2	no	—
218	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
219	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
220	#480	C₂²×C₄₁	1	4	yes	complemented
221	#477	—	2	2	no	—
222	#460	—	2	2	no	—
223	#448	C₂²×C₄₁	1	4	yes	complemented
224	#440	—	2	4	no	—
225	#432	C₂²×C₄₁	1	2	yes	complemented
226	#400	—	2	1	no	—
227	#397	C₂²×C₄₁	1	2	yes	complemented
228	#394	—	2	1	no	—
229	#393	C₂²×C₄₁	1	2	yes	complemented
230	C₄×C₂²⋊C₄	—	2	2	no	—
231	#376	C₂²×C₄₁	1	1	yes	characteristic, complemented
232	#327	C₂²×C₄₁	1	8	yes	complemented
233	#323	C₂²×C₄₁	1	4	yes	complemented
234	C₄₁	#18179	1	1	yes	characteristic, direct product factor, Sylow
235	H(5,𝔽₂)	—	4	8	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	2	no	—
238	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
243	C₂³×C₄	D₄×C₄₁	1	2	yes	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
246	#127	D₄×C₄₁	1	2	yes	—
247	#124	—	2	2	no	—
248	#123	—	2	8	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	#121	—	2	4	no	—
251	#121	—	2	4	no	—
252	#121	—	2	4	no	—
253	#121	—	2	2	no	—
254	#121	—	2	4	no	—
255	#121	C₂³×C₄₁	1	4	yes	—
256	#120	—	2	8	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	D₄×C₄₁	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
274	#107	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	#103	—	2	4	no	—
277	#102	—	2	4	no	—
278	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
279	#97	—	2	2	no	—
280	#95	—	2	1	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	C₂³×C₄₁	1	2	yes	—
284	C₂⁴	—	2	4	no	—
285	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
286	#41	—	4	8	no	—
287	#41	—	4	16	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	16	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	8	4	no	—
302	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
315	SD₁₆	—	4	8	no	—
316	C₂×C₈	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₄²	—	4	2	no	—
330	C₄²	—	4	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	C₂×D₄×C₄₁	1	2	yes	—
333	C₄²	C₂×D₄×C₄₁	1	2	yes	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	8	no	—
340	C₂³	—	8	4	no	—
341	C₂³	—	8	4	no	—
342	C₂³	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
343	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	4	no	—
347	D₄	—	2	8	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	16	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	4	no	—
353	D₄	—	8	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
373	C₂×C₄	#120×C₄₁	1	2	yes	—
374	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
376	C₈	—	4	4	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	16	8	no	—
388	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
389	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	C₄₁×#455	1	2	yes	—
399	C₂	—	2	2	no	—
400	C₂	—	4	4	no	—
401	C₂	—	8	4	no	—
402	C₂	C₄₁×#3003	1	1	yes	characteristic
403	C₂	C₂×C₄₁×#455	1	1	yes	characteristic
404	C₂	C₄₁×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#3496	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#3112	C₂	semidirect
3. C₄₁×#2398	C₂	semidirect
4. C₄₁×#1607	C₂	semidirect
5. C₄₁×#1601	C₂	semidirect
6. C₄₁×#1505	C₂	semidirect
7. C₄₁×#1466	C₂	semidirect
16. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
18. C₄₁×#480	C₂²	semidirect
21. C₄₁×#448	C₂²	semidirect
23. C₄₁×#432	C₂²	semidirect
25. C₄₁×#397	C₂²	semidirect
27. C₄₁×#393	C₂²	semidirect
29. C₄₁×#376	C₂²	semidirect
30. C₄₁×#327	C₂²	semidirect
31. C₄₁×#323	C₂²	semidirect
174. #18179	C₄₁	direct (N × H)
198. #3112	C₂×C₄₁	semidirect
199. #2398	C₂×C₄₁	semidirect
200. #1607	C₂×C₄₁	semidirect
201. #1601	C₂×C₄₁	semidirect
202. #1505	C₂×C₄₁	semidirect
203. #1466	C₂×C₄₁	semidirect
218. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
220. #480	C₂²×C₄₁	semidirect
223. #448	C₂²×C₄₁	semidirect
225. #432	C₂²×C₄₁	semidirect
227. #397	C₂²×C₄₁	semidirect
229. #393	C₂²×C₄₁	semidirect
231. #376	C₂²×C₄₁	semidirect
232. #327	C₂²×C₄₁	semidirect
233. #323	C₂²×C₄₁	semidirect
234. C₄₁	#18179	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3496	2
C₄₁×#3112	2
C₄₁×#2398	2
C₄₁×#1607	2
C₄₁×#1601	2
C₄₁×#1505	2
C₄₁×#1466	2
#18179	41

Subgroups — C41×#18179 #23794380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18179 #23794380