Subgroups — C₄₁×#21653 #23797854

Order 10496.

770 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	C₂×C₄₁×#491	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2330	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2327	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1991	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1956	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1935	C₂	1	2	yes	maximal
7	C₄₁×#1933	C₂	1	2	yes	maximal
8	C₄₁×#1836	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1763	C₂	1	2	yes	maximal
10	C₄×#103×C₄₁	C₂	1	2	yes	maximal
11	C₄₁×#1726	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#491	C₄	1	8	yes	complemented
16	C₂×#103×C₄₁	C₂²	1	2	yes	—
17	C₂×#103×C₄₁	C₂²	1	2	yes	—
18	C₂×#103×C₄₁	C₂²	1	2	yes	—
19	C₂×#103×C₄₁	C₂²	1	2	yes	—
20	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#391	C₂²	1	2	yes	—
27	C₄₁×#389	—	2	2	no	—
28	C₄₁×#389	C₂²	1	2	yes	—
29	C₄₁×#387	—	2	2	no	—
30	C₄₁×#387	—	2	2	no	—
31	C₄₁×#387	—	2	2	no	—
32	C₄₁×#384	C₂²	1	1	yes	characteristic
33	C₄₁×#382	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
35	C₄₁×#376	C₂²	1	1	yes	characteristic
36	C₄₁×#340	C₂²	1	2	yes	—
37	C₄₁×#340	C₂²	1	2	yes	—
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₄⋊Q₈×C₄₁	—	2	2	no	—
46	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
47	#125×C₄₁	—	2	2	no	—
48	#125×C₄₁	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₄₁	—	2	4	no	—
50	C₄×Q₈×C₄₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	2	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	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₄²×C₄₁	—	2	2	no	—
60	C₂×C₄²×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
64	#103×C₄₁	—	2	4	no	—
65	#103×C₄₁	—	2	4	no	—
66	#103×C₄₁	C₂×C₄	1	8	yes	—
67	#103×C₄₁	C₂×C₄	1	8	yes	—
68	#97×C₄₁	—	2	2	no	—
69	#97×C₄₁	—	2	2	no	—
70	#97×C₄₁	C₂×C₄	1	4	yes	—
71	C₄×C₈×C₄₁	—	2	2	no	—
72	C₄×C₈×C₄₁	—	2	2	no	—
73	C₄×C₈×C₄₁	—	2	2	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	2	no	—
78	#95×C₄₁	—	2	2	no	—
79	#95×C₄₁	D₄	1	2	yes	—
80	#95×C₄₁	D₄	1	2	yes	—
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	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₄₁	—	2	1	no	—
97	C₂×C₈×C₄₁	—	2	1	no	—
98	C₂×C₈×C₄₁	—	2	1	no	—
99	C₂×C₈×C₄₁	—	2	1	no	—
100	C₂×C₈×C₄₁	—	2	1	no	—
101	C₂×C₈×C₄₁	—	2	1	no	—
102	C₂×C₈×C₄₁	—	2	1	no	—
103	C₂×C₈×C₄₁	—	2	1	no	—
104	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₁	#41	1	2	yes	—
107	C₂×C₈×C₄₁	#41	1	2	yes	—
108	C₄⋊C₄×C₄₁	—	2	8	no	—
109	C₄⋊C₄×C₄₁	—	2	8	no	—
110	C₄⋊C₄×C₄₁	—	2	2	no	—
111	C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₄⋊C₄×C₄₁	—	2	2	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	4	4	no	—
116	C₄⋊C₄×C₄₁	—	8	2	no	—
117	C₄⋊C₄×C₄₁	—	8	2	no	—
118	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
119	C₄²×C₄₁	—	2	1	no	—
120	C₄²×C₄₁	—	2	1	no	—
121	C₄²×C₄₁	—	4	4	no	—
122	C₄²×C₄₁	—	8	2	no	—
123	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₁	#41	1	2	yes	—
125	C₄²×C₄₁	#41	1	2	yes	—
126	C₄²×C₄₁	#41	1	2	yes	—
127	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₄₁	—	2	4	no	—
129	Q₈×C₄₁	—	2	4	no	—
130	Q₈×C₄₁	—	4	2	no	—
131	Q₈×C₄₁	—	4	2	no	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	2	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	1	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	4	2	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
153	C₂×C₄×C₄₁	#124	1	4	yes	—
154	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
160	C₈×C₄₁	—	2	2	no	—
161	C₈×C₄₁	—	2	2	no	—
162	C₈×C₄₁	—	2	2	no	—
163	C₈×C₄₁	—	2	2	no	—
164	#21653	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
167	C₂²×C₄₁	#532	1	1	yes	characteristic
168	C₂²×C₄₁	#577	1	2	yes	—
169	C₂²×C₄₁	#578	1	2	yes	—
170	C₄×C₄₁	—	2	4	no	—
171	C₄×C₄₁	—	2	4	no	—
172	C₄×C₄₁	—	4	1	no	—
173	C₄×C₄₁	—	4	1	no	—
174	C₄×C₄₁	—	4	4	no	—
175	C₄×C₄₁	—	4	4	no	—
176	C₄×C₄₁	—	8	2	no	—
177	C₄×C₄₁	—	8	2	no	—
178	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
179	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
180	C₄×C₄₁	#529	1	1	yes	characteristic
181	C₄×C₄₁	#529	1	1	yes	characteristic
182	C₂×#491	C₂×C₄₁	1	1	yes	characteristic
183	#2330	C₂×C₄₁	1	1	yes	characteristic
184	#2327	C₂×C₄₁	1	1	yes	characteristic
185	#1991	C₂×C₄₁	1	1	yes	characteristic
186	#1956	C₂×C₄₁	1	1	yes	characteristic
187	#1935	C₂×C₄₁	1	2	yes	—
188	#1933	C₂×C₄₁	1	2	yes	—
189	#1836	C₂×C₄₁	1	1	yes	characteristic
190	#1763	C₂×C₄₁	1	2	yes	—
191	C₄×#103	C₂×C₄₁	1	2	yes	—
192	#1726	C₂×C₄₁	1	1	yes	characteristic
193	C₂×C₄₁	C₄×#124	1	1	yes	characteristic
194	C₂×C₄₁	#2947	1	2	yes	—
195	C₂×C₄₁	#3137	1	2	yes	—
196	C₂×C₄₁	#3174	1	1	yes	characteristic
197	C₂×C₄₁	#3177	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
199	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
200	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
201	#491	C₄×C₄₁	1	8	yes	complemented
202	C₂×#103	C₂²×C₄₁	1	2	yes	—
203	C₂×#103	C₂²×C₄₁	1	2	yes	—
204	C₂×#103	C₂²×C₄₁	1	2	yes	—
205	C₂×#103	C₂²×C₄₁	1	2	yes	—
206	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
207	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
208	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
212	#391	C₂²×C₄₁	1	2	yes	—
213	#389	—	2	2	no	—
214	#389	C₂²×C₄₁	1	2	yes	—
215	#387	—	2	2	no	—
216	#387	—	2	2	no	—
217	#387	—	2	2	no	—
218	#384	C₂²×C₄₁	1	1	yes	characteristic
219	#382	C₂²×C₄₁	1	1	yes	characteristic
220	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
221	#376	C₂²×C₄₁	1	1	yes	characteristic
222	#340	C₂²×C₄₁	1	2	yes	—
223	#340	C₂²×C₄₁	1	2	yes	—
224	#340	C₂²×C₄₁	1	2	yes	—
225	#340	C₂²×C₄₁	1	2	yes	—
226	C₄₁	#21653	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
228	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
234	#125	—	2	2	no	—
235	#125	C₂×C₄×C₄₁	1	4	yes	—
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
251	#103	—	2	4	no	—
252	#103	—	2	4	no	—
253	#103	C₂×C₄×C₄₁	1	8	yes	—
254	#103	C₂×C₄×C₄₁	1	8	yes	—
255	#97	—	2	2	no	—
256	#97	—	2	2	no	—
257	#97	C₂×C₄×C₄₁	1	4	yes	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	D₄×C₄₁	1	2	yes	—
267	#95	D₄×C₄₁	1	2	yes	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
292	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
293	C₂×C₈	#41×C₄₁	1	2	yes	—
294	C₂×C₈	#41×C₄₁	1	2	yes	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	8	2	no	—
304	C₄⋊C₄	—	8	2	no	—
305	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	4	4	no	—
309	C₄²	—	8	2	no	—
310	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
311	C₄²	#41×C₄₁	1	2	yes	—
312	C₄²	#41×C₄₁	1	2	yes	—
313	C₄²	#41×C₄₁	1	2	yes	—
314	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
340	C₂×C₄	#124×C₄₁	1	4	yes	—
341	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
352	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
353	C₂²	C₄₁×#532	1	1	yes	characteristic
354	C₂²	C₄₁×#577	1	2	yes	—
355	C₂²	C₄₁×#578	1	2	yes	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	4	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	2	no	—
364	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
365	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
366	C₄	C₄₁×#529	1	1	yes	characteristic
367	C₄	C₄₁×#529	1	1	yes	characteristic
368	C₂	C₄×#124×C₄₁	1	1	yes	characteristic
369	C₂	C₄₁×#2947	1	2	yes	—
370	C₂	C₄₁×#3137	1	2	yes	—
371	C₂	C₄₁×#3174	1	1	yes	characteristic
372	C₂	C₄₁×#3177	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
15. C₄₁×#491	C₄	semidirect
164. #21653	C₄₁	direct (N × H)
201. #491	C₄×C₄₁	semidirect
226. C₄₁	#21653	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×#491	2
C₄₁×#2330	2
C₄₁×#2327	2
C₄₁×#1991	2
C₄₁×#1956	2
C₄₁×#1935	2
C₄₁×#1933	2
C₄₁×#1836	2
C₄₁×#1763	2
C₄×#103×C₄₁	2
C₄₁×#1726	2
#21653	41

Subgroups — C41×#21653 #23797854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21653 #23797854