Subgroups — C₄₁×#23251 #23799452

Order 10496.

680 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	C₄₁×#2399	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1985	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1984	C₂	1	2	yes	maximal
4	C₄₁×#1984	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1940	C₂	1	2	yes	maximal
6	C₄₁×#1939	C₂	1	2	yes	maximal
7	C₄₁×#1771	C₂	1	2	yes	maximal
8	C₈×C₄⋊C₄×C₄₁	C₂	1	2	yes	maximal
9	C₄₁×#1768	C₂	1	2	yes	maximal
10	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
17	C₂×#97×C₄₁	C₂²	1	2	yes	—
18	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#398	C₄	1	2	yes	—
23	C₄₁×#398	C₄	1	1	yes	characteristic
24	C₄₁×#398	C₄	1	1	yes	characteristic
25	C₄₁×#395	C₄	1	1	yes	characteristic
26	C₄₁×#395	C₄	1	1	yes	characteristic
27	C₄₁×#395	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#376	C₂²	1	1	yes	characteristic
31	C₄₁×#336	C₂²	1	2	yes	—
32	C₄₁×#336	C₂²	1	2	yes	—
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₄₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
43	C₄×Q₈×C₄₁	—	4	1	no	—
44	C₄×Q₈×C₄₁	—	4	1	no	—
45	C₄×Q₈×C₄₁	—	4	1	no	—
46	C₄×Q₈×C₄₁	—	4	1	no	—
47	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
61	C₄⋊C₈×C₄₁	—	2	4	no	—
62	C₄⋊C₈×C₄₁	—	4	1	no	—
63	C₄⋊C₈×C₄₁	—	4	2	no	—
64	C₄⋊C₈×C₄₁	—	4	1	no	—
65	C₄⋊C₈×C₄₁	Q₈	1	8	yes	complemented
66	#97×C₄₁	—	2	4	no	—
67	#97×C₄₁	—	4	1	no	—
68	C₄×C₈×C₄₁	—	2	4	no	—
69	C₄×C₈×C₄₁	—	4	1	no	—
70	C₄×C₈×C₄₁	—	4	2	no	—
71	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
72	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
73	#95×C₄₁	C₂×C₄	1	2	yes	—
74	#95×C₄₁	C₂×C₄	1	2	yes	—
75	#95×C₄₁	C₂×C₄	1	2	yes	—
76	#95×C₄₁	C₂×C₄	1	2	yes	—
77	#95×C₄₁	C₂×C₄	1	2	yes	—
78	C₂×Q₈×C₄₁	—	2	4	no	—
79	C₂×Q₈×C₄₁	—	2	2	no	—
80	C₂×Q₈×C₄₁	—	4	1	no	—
81	C₂×Q₈×C₄₁	—	4	1	no	—
82	C₂×Q₈×C₄₁	—	4	1	no	—
83	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
94	C₂×C₈×C₄₁	—	2	2	no	—
95	C₂×C₈×C₄₁	—	2	2	no	—
96	C₂×C₈×C₄₁	—	2	2	no	—
97	C₂×C₈×C₄₁	—	2	2	no	—
98	C₂×C₈×C₄₁	—	2	2	no	—
99	C₂×C₈×C₄₁	—	2	2	no	—
100	C₂×C₈×C₄₁	—	2	2	no	—
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	C₂×Q₈	1	4	yes	—
105	C₂×C₈×C₄₁	C₂×Q₈	1	4	yes	—
106	C₄⋊C₄×C₄₁	—	2	4	no	—
107	C₄⋊C₄×C₄₁	—	2	4	no	—
108	C₄⋊C₄×C₄₁	—	2	4	no	—
109	C₄⋊C₄×C₄₁	—	4	2	no	—
110	C₄⋊C₄×C₄₁	—	4	1	no	—
111	C₄⋊C₄×C₄₁	—	4	2	no	—
112	C₄⋊C₄×C₄₁	—	4	1	no	—
113	C₄⋊C₄×C₄₁	—	4	1	no	—
114	C₄⋊C₄×C₄₁	—	4	1	no	—
115	C₄²×C₄₁	—	2	1	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	1	no	—
118	C₄²×C₄₁	—	2	1	no	—
119	C₄²×C₄₁	—	2	2	no	—
120	C₄²×C₄₁	—	2	1	no	—
121	C₄²×C₄₁	—	2	1	no	—
122	C₄²×C₄₁	—	2	1	no	—
123	C₄²×C₄₁	C₂×Q₈	1	4	yes	—
124	C₄²×C₄₁	#41	1	4	yes	—
125	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
126	Q₈×C₄₁	—	4	4	no	—
127	Q₈×C₄₁	—	4	4	no	—
128	C₂×C₄×C₄₁	—	2	1	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	2	no	—
131	C₂×C₄×C₄₁	—	2	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	1	no	—
136	C₂×C₄×C₄₁	—	2	1	no	—
137	C₂×C₄×C₄₁	—	2	1	no	—
138	C₂×C₄×C₄₁	—	2	2	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	1	no	—
142	C₂×C₄×C₄₁	—	2	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	C₄×Q₈	1	4	yes	—
152	C₂×C₄×C₄₁	C₄×Q₈	1	4	yes	—
153	C₂×C₄×C₄₁	#131	1	2	yes	—
154	C₂×C₄×C₄₁	#131	1	4	yes	—
155	C₂×C₄×C₄₁	C₂²×Q₈	1	2	yes	—
156	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
157	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
159	C₈×C₄₁	—	2	4	no	—
160	C₈×C₄₁	—	2	4	no	—
161	C₈×C₄₁	—	4	2	no	—
162	C₈×C₄₁	—	4	2	no	—
163	#23251	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₄₁	C₂×C₄×Q₈	1	2	yes	—
165	C₂²×C₄₁	#518	1	1	yes	characteristic
166	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
167	C₂²×C₄₁	C₂×#131	1	2	yes	—
168	C₂²×C₄₁	#568	1	1	yes	characteristic
169	C₄×C₄₁	—	2	4	no	—
170	C₄×C₄₁	—	2	4	no	—
171	C₄×C₄₁	—	2	2	no	—
172	C₄×C₄₁	—	2	4	no	—
173	C₄×C₄₁	—	4	2	no	—
174	C₄×C₄₁	—	4	1	no	—
175	C₄×C₄₁	—	4	1	no	—
176	C₄×C₄₁	—	4	1	no	—
177	C₄×C₄₁	—	4	1	no	—
178	C₄×C₄₁	—	4	1	no	—
179	C₄×C₄₁	#554	1	2	yes	—
180	C₄×C₄₁	#555	1	1	yes	characteristic
181	C₄×C₄₁	Q₈²	1	1	yes	characteristic
182	#2399	C₂×C₄₁	1	1	yes	characteristic
183	#1985	C₂×C₄₁	1	1	yes	characteristic
184	#1984	C₂×C₄₁	1	2	yes	—
185	#1984	C₂×C₄₁	1	1	yes	characteristic
186	#1940	C₂×C₄₁	1	2	yes	—
187	#1939	C₂×C₄₁	1	2	yes	—
188	#1771	C₂×C₄₁	1	2	yes	—
189	C₈×C₄⋊C₄	C₂×C₄₁	1	2	yes	—
190	#1768	C₂×C₄₁	1	2	yes	—
191	C₂×C₄₁	#2369	1	1	yes	characteristic
192	C₂×C₄₁	#2960	1	2	yes	—
193	C₂×C₄₁	#2962	1	2	yes	—
194	C₂×C₄₁	#2976	1	1	yes	characteristic
195	C₂×C₄₁	#2977	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
199	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
203	C₂×#97	C₂²×C₄₁	1	2	yes	—
204	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
206	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
208	#398	C₄×C₄₁	1	1	yes	characteristic
209	#398	C₄×C₄₁	1	2	yes	—
210	#398	C₄×C₄₁	1	1	yes	characteristic
211	#395	C₄×C₄₁	1	1	yes	characteristic
212	#395	C₄×C₄₁	1	1	yes	characteristic
213	#395	C₄×C₄₁	1	2	yes	—
214	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
215	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
216	#376	C₂²×C₄₁	1	1	yes	characteristic
217	#336	C₂²×C₄₁	1	2	yes	—
218	#336	C₂²×C₄₁	1	2	yes	—
219	#336	C₂²×C₄₁	1	2	yes	—
220	#336	C₂²×C₄₁	1	2	yes	—
221	#336	C₂²×C₄₁	1	2	yes	—
222	#336	C₂²×C₄₁	1	2	yes	—
223	C₄₁	#23251	1	1	yes	characteristic, direct product factor, Sylow
224	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
225	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
227	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
228	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
229	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
230	C₄×Q₈	—	4	1	no	—
231	C₄×Q₈	—	4	1	no	—
232	C₄×Q₈	—	4	1	no	—
233	C₄×Q₈	—	4	1	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
243	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
245	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
248	C₄⋊C₈	—	2	4	no	—
249	C₄⋊C₈	—	4	1	no	—
250	C₄⋊C₈	—	4	2	no	—
251	C₄⋊C₈	—	4	1	no	—
252	C₄⋊C₈	Q₈×C₄₁	1	8	yes	complemented
253	#97	—	2	4	no	—
254	#97	—	4	1	no	—
255	C₄×C₈	—	2	4	no	—
256	C₄×C₈	—	4	1	no	—
257	C₄×C₈	—	4	2	no	—
258	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
259	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
260	#95	C₂×C₄×C₄₁	1	2	yes	—
261	#95	C₂×C₄×C₄₁	1	2	yes	—
262	#95	C₂×C₄×C₄₁	1	2	yes	—
263	#95	C₂×C₄×C₄₁	1	2	yes	—
264	#95	C₂×C₄×C₄₁	1	2	yes	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
277	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
280	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	C₂×Q₈×C₄₁	1	4	yes	—
292	C₂×C₈	C₂×Q₈×C₄₁	1	4	yes	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	1	no	—
310	C₄²	C₂×Q₈×C₄₁	1	4	yes	—
311	C₄²	#41×C₄₁	1	4	yes	—
312	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
313	Q₈	—	4	4	no	—
314	Q₈	—	4	4	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	C₄×Q₈×C₄₁	1	4	yes	—
339	C₂×C₄	C₄×Q₈×C₄₁	1	4	yes	—
340	C₂×C₄	#131×C₄₁	1	2	yes	—
341	C₂×C₄	#131×C₄₁	1	4	yes	—
342	C₂×C₄	C₂²×Q₈×C₄₁	1	2	yes	—
343	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
344	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
345	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
346	C₈	—	2	4	no	—
347	C₈	—	2	4	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₂²	C₂×C₄×Q₈×C₄₁	1	2	yes	—
351	C₂²	C₄₁×#518	1	1	yes	characteristic
352	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
353	C₂²	C₂×#131×C₄₁	1	2	yes	—
354	C₂²	C₄₁×#568	1	1	yes	characteristic
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	4	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	C₄₁×#554	1	2	yes	—
366	C₄	C₄₁×#555	1	1	yes	characteristic
367	C₄	Q₈²×C₄₁	1	1	yes	characteristic
368	C₂	C₄₁×#2369	1	1	yes	characteristic
369	C₂	C₄₁×#2960	1	2	yes	—
370	C₂	C₄₁×#2962	1	2	yes	—
371	C₂	C₄₁×#2976	1	1	yes	characteristic
372	C₂	C₄₁×#2977	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
65. C₄⋊C₈×C₄₁	Q₈	semidirect
163. #23251	C₄₁	direct (N × H)
223. C₄₁	#23251	direct (N × H)
252. C₄⋊C₈	Q₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#2399	2
C₄₁×#1985	2
C₄₁×#1984	2
C₄₁×#1940	2
C₄₁×#1939	2
C₄₁×#1771	2
C₈×C₄⋊C₄×C₄₁	2
C₄₁×#1768	2
#23251	41

Subgroups — C41×#23251 #23799452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23251 #23799452