Subgroups — C₄₁×#24072 #23800273

Order 10496.

1002 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#485	C₂	1	2	yes	maximal
3	C₄₁×#2316	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2059	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2043	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1872	C₂	1	2	yes	maximal
7	C₄₁×#1865	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1863	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1818	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#541	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#126×C₄₁	—	2	2	no	—
13	C₂×#125×C₄₁	—	2	2	no	—
14	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#485	—	2	8	no	—
21	C₂×#107×C₄₁	C₂²	1	2	yes	—
22	C₂×#106×C₄₁	C₂²	1	2	yes	—
23	C₂×#103×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#103×C₄₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#389	—	2	2	no	—
29	C₄₁×#389	C₂²	1	2	yes	—
30	C₄₁×#389	C₂²	1	2	yes	—
31	C₄₁×#380	—	2	2	no	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₄₁×#336	C₂²	1	1	yes	characteristic
36	C₄₁×#336	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₁	—	2	1	no	—
39	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
42	C₄⋊Q₈×C₄₁	—	2	4	no	—
43	#126×C₄₁	—	2	16	no	—
44	#125×C₄₁	—	2	16	no	—
45	#125×C₄₁	—	2	4	no	—
46	C₂²⋊Q₈×C₄₁	—	2	4	no	—
47	C₂²⋊Q₈×C₄₁	D₄	1	8	yes	—
48	C₄×Q₈×C₄₁	—	2	4	no	—
49	C₄×Q₈×C₄₁	—	2	4	no	—
50	#117×C₄₁	—	2	4	no	—
51	#117×C₄₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
67	C₂×C₄²×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	1	no	—
69	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	#107×C₄₁	—	2	4	no	—
72	#106×C₄₁	—	2	4	no	—
73	#103×C₄₁	—	2	4	no	—
74	#103×C₄₁	—	2	4	no	—
75	#103×C₄₁	—	2	4	no	—
76	#103×C₄₁	—	2	4	no	—
77	C₂²⋊C₈×C₄₁	—	2	4	no	—
78	#95×C₄₁	—	2	2	no	—
79	#95×C₄₁	—	2	2	no	—
80	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	—	2	2	no	—
84	C₂×Q₈×C₄₁	—	2	2	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	1	no	—
89	C₂²×C₄×C₄₁	—	2	1	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	2	2	no	—
93	C₂²×C₄×C₄₁	—	2	4	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	—	8	2	no	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₄₁	—	2	2	no	—
102	C₂×C₈×C₄₁	—	2	2	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	2	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₄⋊C₄×C₄₁	—	2	4	no	—
108	C₄⋊C₄×C₄₁	—	2	8	no	—
109	C₄⋊C₄×C₄₁	—	2	8	no	—
110	C₄⋊C₄×C₄₁	—	2	8	no	—
111	C₄⋊C₄×C₄₁	—	2	8	no	—
112	C₄⋊C₄×C₄₁	—	2	4	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	8	2	no	—
118	C₄⋊C₄×C₄₁	—	8	2	no	—
119	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₄₁	#41	1	4	yes	—
121	C₂²⋊C₄×C₄₁	—	2	8	no	—
122	C₂²⋊C₄×C₄₁	—	2	4	no	—
123	C₂²⋊C₄×C₄₁	—	4	2	no	—
124	C₄²×C₄₁	—	2	8	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	—	2	2	no	—
127	C₄²×C₄₁	—	4	2	no	—
128	C₂³×C₄₁	—	2	1	no	—
129	C₂³×C₄₁	—	2	1	no	—
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	#120	1	2	yes	—
133	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₄₁	—	2	4	no	—
135	Q₈×C₄₁	—	2	4	no	—
136	Q₈×C₄₁	—	4	2	no	—
137	Q₈×C₄₁	—	4	2	no	—
138	C₂×C₄×C₄₁	—	2	1	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	4	no	—
141	C₂×C₄×C₄₁	—	2	4	no	—
142	C₂×C₄×C₄₁	—	2	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	2	4	no	—
146	C₂×C₄×C₄₁	—	2	4	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	8	4	no	—
161	C₂×C₄×C₄₁	#120	1	2	yes	—
162	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
164	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
166	C₈×C₄₁	—	4	2	no	—
167	C₈×C₄₁	—	4	2	no	—
168	#24072	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₄₁	—	2	2	no	—
170	C₂²×C₄₁	—	2	4	no	—
171	C₂²×C₄₁	—	4	1	no	—
172	C₂²×C₄₁	—	4	1	no	—
173	C₂²×C₄₁	—	4	2	no	—
174	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
175	C₂²×C₄₁	#525	1	1	yes	characteristic
176	C₂²×C₄₁	#536	1	1	yes	characteristic
177	C₂²×C₄₁	#577	1	2	yes	—
178	C₂²×C₄₁	#578	1	2	yes	—
179	C₄×C₄₁	—	2	2	no	—
180	C₄×C₄₁	—	4	4	no	—
181	C₄×C₄₁	—	4	4	no	—
182	C₄×C₄₁	—	4	2	no	—
183	C₄×C₄₁	—	4	2	no	—
184	C₄×C₄₁	—	4	4	no	—
185	C₄×C₄₁	—	8	2	no	—
186	C₄×C₄₁	#547	1	2	yes	—
187	C₄×C₄₁	#547	1	2	yes	—
188	C₂×#541	C₂×C₄₁	1	1	yes	characteristic
189	C₂×#485	C₂×C₄₁	1	2	yes	—
190	#2316	C₂×C₄₁	1	1	yes	characteristic
191	#2059	C₂×C₄₁	1	2	yes	complemented
192	#2043	C₂×C₄₁	1	2	yes	complemented
193	#1872	C₂×C₄₁	1	2	yes	—
194	#1865	C₂×C₄₁	1	2	yes	complemented
195	#1863	C₂×C₄₁	1	2	yes	complemented
196	#1818	C₂×C₄₁	1	1	yes	characteristic
197	C₂×C₄₁	—	4	2	no	—
198	C₂×C₄₁	#2406	1	1	yes	characteristic
199	C₂×C₄₁	#3013	1	2	yes	—
200	C₂×C₄₁	#3123	1	1	yes	characteristic
201	C₂×C₄₁	#3127	1	1	yes	characteristic
202	C₂×C₄₁	#3242	1	2	yes	—
203	#541	—	2	8	no	—
204	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
205	C₂×#126	—	2	2	no	—
206	C₂×#125	—	2	2	no	—
207	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
208	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
209	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
210	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
213	#485	—	2	8	no	—
214	C₂×#107	C₂²×C₄₁	1	2	yes	—
215	C₂×#106	C₂²×C₄₁	1	2	yes	—
216	C₂×#103	C₂²×C₄₁	1	2	yes	—
217	C₂×#103	C₂²×C₄₁	1	2	yes	—
218	C₂×#103	C₂²×C₄₁	1	2	yes	—
219	C₂×#103	C₂²×C₄₁	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
221	#389	—	2	2	no	—
222	#389	C₂²×C₄₁	1	2	yes	—
223	#389	C₂²×C₄₁	1	2	yes	—
224	#380	—	2	2	no	—
225	#340	C₂²×C₄₁	1	2	yes	—
226	#340	C₂²×C₄₁	1	2	yes	—
227	#336	C₂²×C₄₁	1	2	yes	—
228	#336	C₂²×C₄₁	1	1	yes	characteristic
229	#336	C₂²×C₄₁	1	1	yes	characteristic
230	C₄₁	#24072	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
235	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
236	C₄⋊Q₈	—	2	4	no	—
237	#126	—	2	16	no	—
238	#125	—	2	16	no	—
239	#125	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₂²⋊Q₈	D₄×C₄₁	1	8	yes	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	#117	—	2	4	no	—
245	#117	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
265	#107	—	2	4	no	—
266	#106	—	2	4	no	—
267	#103	—	2	4	no	—
268	#103	—	2	4	no	—
269	#103	—	2	4	no	—
270	#103	—	2	4	no	—
271	C₂²⋊C₈	—	2	4	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	8	2	no	—
290	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
294	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	8	2	no	—
312	C₄⋊C₄	—	8	2	no	—
313	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
314	C₄⋊C₄	#41×C₄₁	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	2	8	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	4	2	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	#120×C₄₁	1	2	yes	—
327	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
328	Q₈	—	2	4	no	—
329	Q₈	—	2	4	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	#120×C₄₁	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
357	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
358	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
359	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
360	C₈	—	4	2	no	—
361	C₈	—	4	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
368	C₂²	C₄₁×#525	1	1	yes	characteristic
369	C₂²	C₄₁×#536	1	1	yes	characteristic
370	C₂²	C₄₁×#577	1	2	yes	—
371	C₂²	C₄₁×#578	1	2	yes	—
372	C₄	—	2	2	no	—
373	C₄	—	4	4	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	8	2	no	—
379	C₄	C₄₁×#547	1	2	yes	—
380	C₄	C₄₁×#547	1	2	yes	—
381	C₂	—	4	2	no	—
382	C₂	C₄₁×#2406	1	1	yes	characteristic
383	C₂	C₄₁×#3013	1	2	yes	—
384	C₂	C₄₁×#3123	1	1	yes	characteristic
385	C₂	C₄₁×#3127	1	1	yes	characteristic
386	C₂	C₄₁×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
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
4. C₄₁×#2059	C₂	semidirect
5. C₄₁×#2043	C₂	semidirect
7. C₄₁×#1865	C₂	semidirect
8. C₄₁×#1863	C₂	semidirect
168. #24072	C₄₁	direct (N × H)
191. #2059	C₂×C₄₁	semidirect
192. #2043	C₂×C₄₁	semidirect
194. #1865	C₂×C₄₁	semidirect
195. #1863	C₂×C₄₁	semidirect
230. C₄₁	#24072	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×#541	2
C₂×C₄₁×#485	2
C₄₁×#2316	2
C₄₁×#2059	2
C₄₁×#2043	2
C₄₁×#1872	2
C₄₁×#1865	2
C₄₁×#1863	2
C₄₁×#1818	2
#24072	41

Subgroups — C41×#24072 #23800273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24072 #23800273