Subgroups — C₄₁×#23939 #23800140

Order 10496.

1446 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#447	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2025	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2011	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1879	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1875	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1818	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₄₁	C₂²	1	4	yes	—
11	C₄₁×#540	—	2	8	no	—
12	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
13	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic, complemented
14	C₂×#123×C₄₁	—	2	2	no	—
15	C₂×#121×C₄₁	—	2	2	no	—
16	C₂×#121×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
18	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#447	—	2	8	no	—
21	C₂×#102×C₄₁	C₂²	1	4	yes	—
22	C₂×#102×C₄₁	C₂²	1	4	yes	complemented
23	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#390	—	2	2	no	—
25	C₄₁×#390	C₂²	1	2	yes	—
26	C₄₁×#390	C₂²	1	2	yes	—
27	C₄₁×#379	—	2	2	no	—
28	C₄₁×#340	C₂²	1	4	yes	complemented
29	C₄₁×#336	C₂²	1	2	yes	complemented
30	C₄₁×#336	C₂²	1	2	yes	complemented
31	C₂⁵×C₄₁	—	2	1	no	—
32	C₂²×D₄×C₄₁	—	2	2	no	—
33	C₂²×D₄×C₄₁	—	2	4	no	—
34	C₂²×D₄×C₄₁	—	2	1	no	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	4	no	—
37	C₂²×D₄×C₄₁	—	4	2	no	—
38	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
39	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₁	—	2	2	no	—
41	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
42	C₂×D₈×C₄₁	—	2	8	no	—
43	C₂×D₈×C₄₁	—	2	8	no	—
44	C₂×D₈×C₄₁	—	4	4	no	—
45	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
46	#127×C₄₁	—	2	4	no	—
47	#125×C₄₁	—	2	4	no	—
48	#123×C₄₁	—	2	16	no	—
49	#121×C₄₁	—	2	16	no	—
50	#121×C₄₁	—	2	4	no	—
51	#121×C₄₁	D₄	1	8	yes	—
52	C₄×D₄×C₄₁	—	2	4	no	—
53	C₄×D₄×C₄₁	—	2	4	no	—
54	#117×C₄₁	—	2	4	no	—
55	#117×C₄₁	—	4	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
66	C₂×C₄²×C₄₁	—	2	1	no	—
67	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	#102×C₄₁	—	2	8	no	—
70	#102×C₄₁	—	4	4	no	—
71	C₂²⋊C₈×C₄₁	—	2	4	no	—
72	C₂⁴×C₄₁	—	2	4	no	—
73	C₂⁴×C₄₁	—	2	2	no	—
74	C₂⁴×C₄₁	—	2	2	no	—
75	C₂⁴×C₄₁	—	4	2	no	—
76	C₂⁴×C₄₁	—	4	2	no	—
77	C₂⁴×C₄₁	—	8	4	no	—
78	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₄₁	—	2	4	no	—
80	C₂×D₄×C₄₁	—	2	8	no	—
81	C₂×D₄×C₄₁	—	2	8	no	—
82	C₂×D₄×C₄₁	—	2	4	no	—
83	C₂×D₄×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	2	4	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	4	no	—
87	C₂×D₄×C₄₁	—	2	4	no	—
88	C₂×D₄×C₄₁	—	4	16	no	—
89	C₂×D₄×C₄₁	—	4	2	no	—
90	C₂×D₄×C₄₁	—	4	2	no	—
91	C₂×D₄×C₄₁	—	8	4	no	—
92	C₂×D₄×C₄₁	—	8	4	no	—
93	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
94	C₂×D₄×C₄₁	#41	1	4	yes	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	8	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	8	4	no	—
101	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
106	D₈×C₄₁	—	4	16	no	—
107	C₂×C₈×C₄₁	—	2	4	no	—
108	C₂×C₈×C₄₁	—	2	4	no	—
109	C₂×C₈×C₄₁	—	2	4	no	—
110	C₄⋊C₄×C₄₁	—	2	8	no	—
111	C₄⋊C₄×C₄₁	—	2	4	no	—
112	C₄⋊C₄×C₄₁	—	2	2	no	—
113	C₄⋊C₄×C₄₁	—	2	4	no	—
114	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
115	C₂²⋊C₄×C₄₁	—	2	8	no	—
116	C₂²⋊C₄×C₄₁	—	2	4	no	—
117	C₂²⋊C₄×C₄₁	—	2	8	no	—
118	C₂²⋊C₄×C₄₁	—	4	2	no	—
119	C₂²⋊C₄×C₄₁	—	8	4	no	—
120	C₂²⋊C₄×C₄₁	—	8	4	no	—
121	C₄²×C₄₁	—	2	2	no	—
122	C₄²×C₄₁	—	2	2	no	—
123	C₄²×C₄₁	—	4	2	no	—
124	C₂³×C₄₁	—	2	1	no	—
125	C₂³×C₄₁	—	2	1	no	—
126	C₂³×C₄₁	—	2	4	no	—
127	C₂³×C₄₁	—	2	4	no	—
128	C₂³×C₄₁	—	2	4	no	—
129	C₂³×C₄₁	—	4	8	no	—
130	C₂³×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	4	2	no	—
132	C₂³×C₄₁	—	4	2	no	—
133	C₂³×C₄₁	—	4	2	no	—
134	C₂³×C₄₁	—	4	4	no	—
135	C₂³×C₄₁	—	4	4	no	—
136	C₂³×C₄₁	—	4	4	no	—
137	C₂³×C₄₁	—	4	4	no	—
138	C₂³×C₄₁	—	8	8	no	—
139	C₂³×C₄₁	—	8	8	no	—
140	C₂³×C₄₁	—	8	8	no	—
141	C₂³×C₄₁	#120	1	2	yes	—
142	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
143	D₄×C₄₁	—	2	8	no	—
144	D₄×C₄₁	—	2	8	no	—
145	D₄×C₄₁	—	4	8	no	—
146	D₄×C₄₁	—	4	4	no	—
147	D₄×C₄₁	—	4	4	no	—
148	D₄×C₄₁	—	8	8	no	—
149	D₄×C₄₁	—	8	8	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	8	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	—	2	4	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	4	4	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	8	8	no	—
162	C₂×C₄×C₄₁	#120	1	2	yes	—
163	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
165	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
166	C₈×C₄₁	—	4	4	no	—
167	#23939	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₄₁	—	2	2	no	—
169	C₂²×C₄₁	—	2	4	no	—
170	C₂²×C₄₁	—	4	2	no	—
171	C₂²×C₄₁	—	4	2	no	—
172	C₂²×C₄₁	—	4	8	no	—
173	C₂²×C₄₁	—	4	4	no	—
174	C₂²×C₄₁	—	4	4	no	—
175	C₂²×C₄₁	—	4	4	no	—
176	C₂²×C₄₁	—	4	4	no	—
177	C₂²×C₄₁	—	8	16	no	—
178	C₂²×C₄₁	—	8	4	no	—
179	C₂²×C₄₁	—	8	4	no	—
180	C₂²×C₄₁	—	8	2	no	—
181	C₂²×C₄₁	—	8	2	no	—
182	C₂²×C₄₁	—	8	4	no	—
183	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
184	C₂²×C₄₁	#525	1	1	yes	characteristic
185	C₂²×C₄₁	#535	1	1	yes	characteristic
186	C₂²×C₄₁	#576	1	4	yes	—
187	C₄×C₄₁	—	2	2	no	—
188	C₄×C₄₁	—	4	2	no	—
189	C₄×C₄₁	—	4	2	no	—
190	C₄×C₄₁	—	4	4	no	—
191	C₄×C₄₁	—	8	2	no	—
192	C₄×C₄₁	#546	1	4	yes	—
193	C₂×#540	C₂×C₄₁	1	1	yes	characteristic, complemented
194	C₂×#447	C₂×C₄₁	1	2	yes	complemented
195	#2309	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#2025	C₂×C₄₁	1	2	yes	complemented
197	#2011	C₂×C₄₁	1	2	yes	complemented
198	#1879	C₂×C₄₁	1	4	yes	complemented
199	#1875	C₂×C₄₁	1	2	yes	complemented
200	#1818	C₂×C₄₁	1	1	yes	characteristic, complemented
201	C₂×C₄₁	—	4	2	no	—
202	C₂×C₄₁	—	8	4	no	—
203	C₂×C₄₁	—	8	4	no	—
204	C₂×C₄₁	#2404	1	1	yes	characteristic
205	C₂×C₄₁	#3008	1	2	yes	—
206	C₂×C₄₁	#3122	1	2	yes	—
207	C₂×C₄₁	#3220	1	2	yes	—
208	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
209	C₂²×D₈	C₂²×C₄₁	1	4	yes	—
210	#540	—	2	8	no	—
211	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
212	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic, complemented
213	C₂×#123	—	2	2	no	—
214	C₂×#121	—	2	2	no	—
215	C₂×#121	C₂²×C₄₁	1	2	yes	—
216	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
217	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
219	#447	—	2	8	no	—
220	C₂×#102	C₂²×C₄₁	1	4	yes	—
221	C₂×#102	C₂²×C₄₁	1	4	yes	complemented
222	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
223	#390	—	2	2	no	—
224	#390	C₂²×C₄₁	1	2	yes	—
225	#390	C₂²×C₄₁	1	2	yes	—
226	#379	—	2	2	no	—
227	#340	C₂²×C₄₁	1	4	yes	complemented
228	#336	C₂²×C₄₁	1	2	yes	complemented
229	#336	C₂²×C₄₁	1	2	yes	complemented
230	C₄₁	#23939	1	1	yes	characteristic, direct product factor, Sylow
231	C₂⁵	—	2	1	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	—	2	4	no	—
237	C₂²×D₄	—	4	2	no	—
238	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
239	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
240	C₂³×C₄	—	2	2	no	—
241	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
242	C₂×D₈	—	2	8	no	—
243	C₂×D₈	—	2	8	no	—
244	C₂×D₈	—	4	4	no	—
245	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
246	#127	—	2	4	no	—
247	#125	—	2	4	no	—
248	#123	—	2	16	no	—
249	#121	—	2	16	no	—
250	#121	—	2	4	no	—
251	#121	D₄×C₄₁	1	8	yes	—
252	C₄×D₄	—	2	4	no	—
253	C₄×D₄	—	2	4	no	—
254	#117	—	2	4	no	—
255	#117	—	4	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
269	#102	—	2	8	no	—
270	#102	—	4	4	no	—
271	C₂²⋊C₈	—	2	4	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	2	2	no	—
275	C₂⁴	—	4	2	no	—
276	C₂⁴	—	4	2	no	—
277	C₂⁴	—	8	4	no	—
278	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	4	16	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	8	4	no	—
292	C₂×D₄	—	8	4	no	—
293	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
294	C₂×D₄	#41×C₄₁	1	4	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	8	4	no	—
301	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
306	D₈	—	4	16	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	8	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	8	4	no	—
320	C₂²⋊C₄	—	8	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	4	2	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	4	8	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	8	8	no	—
339	C₂³	—	8	8	no	—
340	C₂³	—	8	8	no	—
341	C₂³	#120×C₄₁	1	2	yes	—
342	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
343	D₄	—	2	8	no	—
344	D₄	—	2	8	no	—
345	D₄	—	4	8	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	8	8	no	—
349	D₄	—	8	8	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	8	8	no	—
362	C₂×C₄	#120×C₄₁	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
364	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
365	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
366	C₈	—	4	4	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	8	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	8	16	no	—
377	C₂²	—	8	4	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	4	no	—
381	C₂²	—	8	4	no	—
382	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
383	C₂²	C₄₁×#525	1	1	yes	characteristic
384	C₂²	C₄₁×#535	1	1	yes	characteristic
385	C₂²	C₄₁×#576	1	4	yes	—
386	C₄	—	2	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	8	2	no	—
391	C₄	C₄₁×#546	1	4	yes	—
392	C₂	—	4	2	no	—
393	C₂	—	8	4	no	—
394	C₂	—	8	4	no	—
395	C₂	C₄₁×#2404	1	1	yes	characteristic
396	C₂	C₄₁×#3008	1	2	yes	—
397	C₂	C₄₁×#3122	1	2	yes	—
398	C₂	C₄₁×#3220	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#540	C₂	semidirect
2. C₂×C₄₁×#447	C₂	semidirect
3. C₄₁×#2309	C₂	semidirect
4. C₄₁×#2025	C₂	semidirect
5. C₄₁×#2011	C₂	semidirect
6. C₄₁×#1879	C₂	semidirect
7. C₄₁×#1875	C₂	semidirect
8. C₄₁×#1818	C₂	semidirect
12. C₂×#127×C₄₁	C₂²	semidirect
13. C₂×#125×C₄₁	C₂²	semidirect
17. C₂×C₄×D₄×C₄₁	C₂²	semidirect
22. C₂×#102×C₄₁	C₂²	semidirect
28. C₄₁×#340	C₂²	semidirect
29. C₄₁×#336	C₂²	semidirect
30. C₄₁×#336	C₂²	semidirect
167. #23939	C₄₁	direct (N × H)
193. C₂×#540	C₂×C₄₁	semidirect
194. C₂×#447	C₂×C₄₁	semidirect
195. #2309	C₂×C₄₁	semidirect
196. #2025	C₂×C₄₁	semidirect
197. #2011	C₂×C₄₁	semidirect
198. #1879	C₂×C₄₁	semidirect
199. #1875	C₂×C₄₁	semidirect
200. #1818	C₂×C₄₁	semidirect
211. C₂×#127	C₂²×C₄₁	semidirect
212. C₂×#125	C₂²×C₄₁	semidirect
216. C₂×C₄×D₄	C₂²×C₄₁	semidirect
221. C₂×#102	C₂²×C₄₁	semidirect
227. #340	C₂²×C₄₁	semidirect
228. #336	C₂²×C₄₁	semidirect
229. #336	C₂²×C₄₁	semidirect
230. C₄₁	#23939	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#540	2
C₂×C₄₁×#447	2
C₄₁×#2309	2
C₄₁×#2025	2
C₄₁×#2011	2
C₄₁×#1879	2
C₄₁×#1875	2
C₄₁×#1818	2
#23939	41

Subgroups — C41×#23939 #23800140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23939 #23800140