Subgroups — C₄₁×#19989 #23796190

Order 10496.

620 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3303	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1710	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1683	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1675	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1646	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1635	C₂	1	2	yes	maximal, complemented
10	C₈×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#555	C₂²	1	2	yes	—
13	C₄₁×#547	C₂²	1	2	yes	—
14	C₄₁×#500	C₂²	1	1	yes	characteristic
15	C₄₁×#500	C₂²	1	1	yes	characteristic
16	C₄₁×#487	C₂²	1	2	yes	—
17	C₄₁×#487	C₂²	1	2	yes	—
18	C₄₁×#485	—	2	2	no	—
19	C₄₁×#482	—	2	2	no	—
20	C₄₁×#480	—	2	2	no	—
21	C₄₁×#476	C₂²	1	2	yes	—
22	C₄₁×#476	C₂²	1	2	yes	—
23	C₄₁×#474	C₂²	1	2	yes	—
24	C₄₁×#466	—	2	1	no	—
25	C₄₁×#466	—	2	1	no	—
26	C₄₁×#465	—	2	2	no	—
27	C₄₁×#461	C₂²	1	2	yes	—
28	C₄₁×#449	—	2	2	no	—
29	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₈×D₄×C₄₁	C₂²	1	2	yes	—
32	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#427	—	2	1	no	—
35	C₂×#107×C₄₁	—	2	1	no	—
36	C₄₁×#416	—	2	2	no	—
37	C₄₁×#335	C₂²	1	1	yes	characteristic
38	C₄₁×#335	C₂²	1	1	yes	characteristic
39	C₄₁×#333	C₂²	1	2	yes	—
40	C₄₁×#332	C₂²	1	2	yes	—
41	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
43	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×SD₁₆×C₄₁	—	2	2	no	—
47	C₂×D₈×C₄₁	D₄	1	1	yes	characteristic
48	C₂×D₈×C₄₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₄₁	—	2	1	no	—
50	C₂²×C₈×C₄₁	—	2	1	no	—
51	C₂²×C₈×C₄₁	—	2	2	no	—
52	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
54	#124×C₄₁	—	4	2	no	—
55	#123×C₄₁	—	4	2	no	—
56	C₂²⋊Q₈×C₄₁	—	2	2	no	—
57	#121×C₄₁	—	2	2	no	—
58	#121×C₄₁	—	2	2	no	—
59	#121×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₄₁	C₂³	1	2	yes	—
62	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
63	#117×C₄₁	—	2	2	no	—
64	#117×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	#107×C₄₁	—	2	1	no	—
67	#107×C₄₁	—	2	1	no	—
68	#107×C₄₁	—	2	1	no	—
69	#107×C₄₁	—	2	1	no	—
70	#107×C₄₁	—	2	2	no	—
71	#107×C₄₁	D₄	1	1	yes	characteristic
72	#107×C₄₁	D₄	1	1	yes	characteristic
73	#106×C₄₁	—	2	2	no	—
74	#106×C₄₁	—	2	2	no	—
75	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
77	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
78	#103×C₄₁	—	2	2	no	—
79	#103×C₄₁	—	2	2	no	—
80	#103×C₄₁	—	2	2	no	—
81	#103×C₄₁	—	4	2	no	—
82	#102×C₄₁	—	2	2	no	—
83	#102×C₄₁	—	2	2	no	—
84	#102×C₄₁	—	2	2	no	—
85	#102×C₄₁	D₄	1	1	yes	characteristic
86	#102×C₄₁	D₄	1	1	yes	characteristic
87	#102×C₄₁	D₄	1	2	yes	—
88	C₂²⋊C₈×C₄₁	—	2	2	no	—
89	C₂²⋊C₈×C₄₁	—	2	1	no	—
90	C₂²⋊C₈×C₄₁	—	2	1	no	—
91	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
94	#41×C₄₁	—	4	4	no	—
95	#41×C₄₁	—	8	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	1	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	4	2	no	—
107	SD₁₆×C₄₁	—	8	2	no	—
108	D₈×C₄₁	—	2	2	no	—
109	D₈×C₄₁	—	2	2	no	—
110	C₂×C₈×C₄₁	—	2	1	no	—
111	C₂×C₈×C₄₁	—	2	1	no	—
112	C₂×C₈×C₄₁	—	2	2	no	—
113	C₂×C₈×C₄₁	—	2	1	no	—
114	C₂×C₈×C₄₁	—	4	2	no	—
115	C₂×C₈×C₄₁	—	4	2	no	—
116	C₂×C₈×C₄₁	—	8	2	no	—
117	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₄⋊C₄×C₄₁	—	2	2	no	—
122	C₄⋊C₄×C₄₁	—	2	2	no	—
123	C₄⋊C₄×C₄₁	—	2	2	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	4	2	no	—
126	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₄₁	—	2	1	no	—
130	C₂²⋊C₄×C₄₁	—	2	2	no	—
131	C₂²⋊C₄×C₄₁	—	2	1	no	—
132	C₂²⋊C₄×C₄₁	—	4	2	no	—
133	C₂²⋊C₄×C₄₁	—	4	2	no	—
134	C₂²⋊C₄×C₄₁	—	4	2	no	—
135	C₄²×C₄₁	—	4	2	no	—
136	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
137	C₂³×C₄₁	—	2	1	no	—
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	2	1	no	—
140	Q₈×C₄₁	—	4	2	no	—
141	Q₈×C₄₁	—	4	2	no	—
142	Q₈×C₄₁	—	8	2	no	—
143	D₄×C₄₁	—	2	1	no	—
144	D₄×C₄₁	—	2	2	no	—
145	D₄×C₄₁	—	2	1	no	—
146	D₄×C₄₁	—	2	1	no	—
147	D₄×C₄₁	—	2	2	no	—
148	D₄×C₄₁	—	8	4	no	—
149	D₄×C₄₁	—	16	2	no	—
150	D₄×C₄₁	#135	1	2	yes	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	4	1	no	—
155	C₂×C₄×C₄₁	—	4	1	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	4	1	no	—
159	C₂×C₄×C₄₁	—	4	1	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	8	4	no	—
163	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₈×C₄₁	—	2	1	no	—
167	C₈×C₄₁	—	2	1	no	—
168	C₈×C₄₁	—	2	1	no	—
169	C₈×C₄₁	—	4	1	no	—
170	C₈×C₄₁	—	4	1	no	—
171	C₈×C₄₁	—	4	1	no	—
172	C₈×C₄₁	—	4	2	no	—
173	C₈×C₄₁	#135	1	2	yes	—
174	#19989	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₁	—	2	2	no	—
176	C₂²×C₄₁	—	4	1	no	—
177	C₂²×C₄₁	—	4	1	no	—
178	C₂²×C₄₁	—	4	2	no	—
179	C₂²×C₄₁	—	4	1	no	—
180	C₂²×C₄₁	—	4	1	no	—
181	C₂²×C₄₁	—	4	2	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	—	4	2	no	—
184	C₂²×C₄₁	D₄²	1	1	yes	characteristic
185	C₄×C₄₁	—	2	1	no	—
186	C₄×C₄₁	—	4	2	no	—
187	C₄×C₄₁	—	4	1	no	—
188	C₄×C₄₁	—	4	1	no	—
189	C₄×C₄₁	—	8	2	no	—
190	C₄×C₄₁	—	8	2	no	—
191	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
192	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
193	C₄×C₄₁	#576	1	1	yes	characteristic
194	C₄×C₄₁	#578	1	1	yes	characteristic
195	#3341	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#3334	C₂×C₄₁	1	1	yes	characteristic, complemented
197	#3303	C₂×C₄₁	1	2	yes	complemented
198	#1710	C₂×C₄₁	1	1	yes	characteristic, complemented
199	#1683	C₂×C₄₁	1	2	yes	complemented
200	#1675	C₂×C₄₁	1	1	yes	characteristic, complemented
201	#1673	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#1646	C₂×C₄₁	1	2	yes	complemented
203	#1635	C₂×C₄₁	1	2	yes	complemented
204	C₈×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
205	C₈×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
206	C₂×C₄₁	—	4	2	no	—
207	C₂×C₄₁	—	8	2	no	—
208	C₂×C₄₁	—	8	1	no	—
209	C₂×C₄₁	#3280	1	1	yes	characteristic
210	C₂×C₄₁	#3283	1	1	yes	characteristic
211	C₂×C₄₁	#3290	1	1	yes	characteristic
212	#555	C₂²×C₄₁	1	2	yes	—
213	#547	C₂²×C₄₁	1	2	yes	—
214	#500	C₂²×C₄₁	1	1	yes	characteristic
215	#500	C₂²×C₄₁	1	1	yes	characteristic
216	#487	C₂²×C₄₁	1	2	yes	—
217	#487	C₂²×C₄₁	1	2	yes	—
218	#485	—	2	2	no	—
219	#482	—	2	2	no	—
220	#480	—	2	2	no	—
221	#476	C₂²×C₄₁	1	2	yes	—
222	#476	C₂²×C₄₁	1	2	yes	—
223	#474	C₂²×C₄₁	1	2	yes	—
224	#466	—	2	1	no	—
225	#466	—	2	1	no	—
226	#465	—	2	2	no	—
227	#461	C₂²×C₄₁	1	2	yes	—
228	#449	—	2	2	no	—
229	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
230	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
231	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
232	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
233	C₈×D₄	C₂²×C₄₁	1	2	yes	—
234	#427	—	2	1	no	—
235	C₂×#107	—	2	1	no	—
236	#416	—	2	2	no	—
237	#335	C₂²×C₄₁	1	1	yes	characteristic
238	#335	C₂²×C₄₁	1	1	yes	characteristic
239	#333	C₂²×C₄₁	1	2	yes	—
240	#332	C₂²×C₄₁	1	2	yes	—
241	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
242	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
243	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
244	C₈²	C₂²×C₄₁	1	1	yes	characteristic
245	C₄₁	#19989	1	1	yes	characteristic, direct product factor, Sylow
246	C₂×#41	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×D₈	D₄×C₄₁	1	1	yes	characteristic
249	C₂×D₈	D₄×C₄₁	1	1	yes	characteristic
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
254	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
255	#124	—	4	2	no	—
256	#123	—	4	2	no	—
257	C₂²⋊Q₈	—	2	2	no	—
258	#121	—	2	2	no	—
259	#121	—	2	2	no	—
260	#121	—	2	2	no	—
261	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
262	C₄×D₄	C₂³×C₄₁	1	2	yes	—
263	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	#107	—	2	1	no	—
268	#107	—	2	1	no	—
269	#107	—	2	1	no	—
270	#107	—	2	1	no	—
271	#107	—	2	2	no	—
272	#107	D₄×C₄₁	1	1	yes	characteristic
273	#107	D₄×C₄₁	1	1	yes	characteristic
274	#106	—	2	2	no	—
275	#106	—	2	2	no	—
276	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
277	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
278	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#103	—	4	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	D₄×C₄₁	1	1	yes	characteristic
287	#102	D₄×C₄₁	1	1	yes	characteristic
288	#102	D₄×C₄₁	1	2	yes	—
289	C₂²⋊C₈	—	2	2	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
295	#41	—	4	4	no	—
296	#41	—	8	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
302	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
303	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	SD₁₆	—	8	2	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	8	2	no	—
318	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
328	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
329	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	4	2	no	—
337	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
338	C₂³	—	2	1	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	1	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	8	2	no	—
344	D₄	—	2	1	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	2	no	—
349	D₄	—	8	4	no	—
350	D₄	—	16	2	no	—
351	D₄	#135×C₄₁	1	2	yes	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
366	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	2	no	—
374	C₈	#135×C₄₁	1	2	yes	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	D₄²×C₄₁	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
392	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
393	C₄	C₄₁×#576	1	1	yes	characteristic
394	C₄	C₄₁×#578	1	1	yes	characteristic
395	C₂	—	4	2	no	—
396	C₂	—	8	2	no	—
397	C₂	—	8	1	no	—
398	C₂	C₄₁×#3280	1	1	yes	characteristic
399	C₂	C₄₁×#3283	1	1	yes	characteristic
400	C₂	C₄₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3341	C₂	semidirect
2. C₄₁×#3334	C₂	semidirect
3. C₄₁×#3303	C₂	semidirect
4. C₄₁×#1710	C₂	semidirect
5. C₄₁×#1683	C₂	semidirect
6. C₄₁×#1675	C₂	semidirect
7. C₄₁×#1673	C₂	semidirect
8. C₄₁×#1646	C₂	semidirect
9. C₄₁×#1635	C₂	semidirect
10. C₈×D₈×C₄₁	C₂	semidirect
11. C₈×D₈×C₄₁	C₂	semidirect
174. #19989	C₄₁	direct (N × H)
195. #3341	C₂×C₄₁	semidirect
196. #3334	C₂×C₄₁	semidirect
197. #3303	C₂×C₄₁	semidirect
198. #1710	C₂×C₄₁	semidirect
199. #1683	C₂×C₄₁	semidirect
200. #1675	C₂×C₄₁	semidirect
201. #1673	C₂×C₄₁	semidirect
202. #1646	C₂×C₄₁	semidirect
203. #1635	C₂×C₄₁	semidirect
204. C₈×D₈	C₂×C₄₁	semidirect
205. C₈×D₈	C₂×C₄₁	semidirect
245. C₄₁	#19989	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×#3341	2
C₄₁×#3334	2
C₄₁×#3303	2
C₄₁×#1710	2
C₄₁×#1683	2
C₄₁×#1675	2
C₄₁×#1673	2
C₄₁×#1646	2
C₄₁×#1635	2
C₈×D₈×C₄₁	2
#19989	41

Subgroups — C41×#19989 #23796190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19989 #23796190