Subgroups — C₄₁×#21339 #23797540

Order 10496.

814 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1984	C₂	1	2	yes	maximal
3	C₄₁×#1939	C₂	1	2	yes	maximal
4	C₄₁×#1916	C₂	1	4	yes	maximal
5	C₄×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄×C₄⋊C₈×C₄₁	C₂	1	2	yes	maximal
7	C₄₁×#1744	C₂	1	2	yes	maximal
8	C₄²×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₄₁	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₄₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	—
13	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₄₁	C₄	1	2	yes	—
20	C₄×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₁	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₄³×C₄₁	C₂²	1	1	yes	characteristic
26	C₄³×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#336	C₂²	1	2	yes	—
28	C₄₁×#336	C₂²	1	4	yes	—
29	C₄₁×#336	C₂²	1	4	yes	—
30	C₄₁×#336	C₂²	1	4	yes	—
31	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
33	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
35	C₄×Q₈×C₄₁	—	2	4	no	—
36	C₄×Q₈×C₄₁	—	2	4	no	—
37	C₄×Q₈×C₄₁	C₈	1	8	yes	complemented
38	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
53	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
55	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₄₁	—	2	8	no	—
58	C₄⋊C₈×C₄₁	—	2	4	no	—
59	C₄×C₈×C₄₁	—	2	4	no	—
60	C₄×C₈×C₄₁	—	2	4	no	—
61	C₄×C₈×C₄₁	—	2	2	no	—
62	C₄×C₈×C₄₁	—	2	4	no	—
63	C₄×C₈×C₄₁	Q₈	1	4	yes	complemented
64	#95×C₄₁	C₂×C₄	1	2	yes	—
65	#95×C₄₁	C₂×C₄	1	2	yes	—
66	#95×C₄₁	C₂×C₄	1	2	yes	—
67	C₂×Q₈×C₄₁	—	2	2	no	—
68	C₂×Q₈×C₄₁	—	2	2	no	—
69	C₂×Q₈×C₄₁	C₂×C₈	1	4	yes	—
70	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
71	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₄₁	—	2	2	no	—
82	C₂×C₈×C₄₁	—	2	2	no	—
83	C₂×C₈×C₄₁	—	2	2	no	—
84	C₂×C₈×C₄₁	—	2	2	no	—
85	C₂×C₈×C₄₁	—	2	4	no	—
86	C₂×C₈×C₄₁	—	2	4	no	—
87	C₂×C₈×C₄₁	—	2	4	no	—
88	C₂×C₈×C₄₁	C₂×Q₈	1	4	yes	—
89	C₂×C₈×C₄₁	#41	1	4	yes	—
90	C₄⋊C₄×C₄₁	—	2	4	no	—
91	C₄⋊C₄×C₄₁	—	2	2	no	—
92	C₄⋊C₄×C₄₁	—	2	4	no	—
93	C₄⋊C₄×C₄₁	—	2	2	no	—
94	C₄⋊C₄×C₄₁	C₂×C₈	1	8	yes	—
95	C₄⋊C₄×C₄₁	C₂×C₈	1	4	yes	—
96	C₄²×C₄₁	—	2	4	no	—
97	C₄²×C₄₁	—	2	2	no	—
98	C₄²×C₄₁	—	2	2	no	—
99	C₄²×C₄₁	—	2	4	no	—
100	C₄²×C₄₁	—	2	4	no	—
101	C₄²×C₄₁	—	2	2	no	—
102	C₄²×C₄₁	—	2	4	no	—
103	C₄²×C₄₁	—	2	4	no	—
104	C₄²×C₄₁	C₂×C₈	1	8	yes	—
105	C₄²×C₄₁	C₂×C₈	1	4	yes	—
106	C₄²×C₄₁	M₁₆	1	4	yes	—
107	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
108	C₄²×C₄₁	#41	1	4	yes	—
109	C₄²×C₄₁	#41	1	2	yes	—
110	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
111	Q₈×C₄₁	—	2	8	no	—
112	C₂×C₄×C₄₁	—	2	2	no	—
113	C₂×C₄×C₄₁	—	2	1	no	—
114	C₂×C₄×C₄₁	—	2	2	no	—
115	C₂×C₄×C₄₁	—	2	1	no	—
116	C₂×C₄×C₄₁	—	2	2	no	—
117	C₂×C₄×C₄₁	—	2	1	no	—
118	C₂×C₄×C₄₁	—	2	1	no	—
119	C₂×C₄×C₄₁	—	2	1	no	—
120	C₂×C₄×C₄₁	—	2	2	no	—
121	C₂×C₄×C₄₁	—	2	1	no	—
122	C₂×C₄×C₄₁	—	2	2	no	—
123	C₂×C₄×C₄₁	—	2	2	no	—
124	C₂×C₄×C₄₁	—	2	2	no	—
125	C₂×C₄×C₄₁	—	2	2	no	—
126	C₂×C₄×C₄₁	—	2	2	no	—
127	C₂×C₄×C₄₁	—	2	2	no	—
128	C₂×C₄×C₄₁	#117	1	2	yes	—
129	C₂×C₄×C₄₁	#117	1	2	yes	—
130	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
131	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₄₁	C₂²×C₈	1	4	yes	—
133	C₂×C₄×C₄₁	C₂²×C₈	1	2	yes	—
134	C₂×C₄×C₄₁	C₂²×C₈	1	4	yes	—
135	C₂×C₄×C₄₁	C₂²×C₈	1	2	yes	—
136	C₂×C₄×C₄₁	C₂²×C₈	1	2	yes	—
137	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
140	C₂×C₄×C₄₁	#131	1	2	yes	—
141	C₂×C₄×C₄₁	#131	1	2	yes	—
142	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
145	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
146	C₈×C₄₁	—	2	4	no	—
147	C₈×C₄₁	—	2	4	no	—
148	C₈×C₄₁	—	4	4	no	—
149	#21339	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
151	C₂²×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
152	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
153	C₂²×C₄₁	C₂³×C₈	1	1	yes	characteristic
154	C₂²×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
155	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
156	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
157	C₄×C₄₁	—	2	4	no	—
158	C₄×C₄₁	—	2	2	no	—
159	C₄×C₄₁	—	2	2	no	—
160	C₄×C₄₁	—	2	4	no	—
161	C₄×C₄₁	—	2	2	no	—
162	C₄×C₄₁	—	4	2	no	—
163	C₄×C₄₁	—	4	2	no	—
164	C₄×C₄₁	#431	1	4	yes	—
165	C₄×C₄₁	C₈×Q₈	1	4	yes	—
166	C₄×C₄₁	#446	1	4	yes	—
167	C₄×C₄₁	#529	1	2	yes	—
168	C₄×C₄₁	#533	1	2	yes	—
169	C₄²×Q₈	C₂×C₄₁	1	1	yes	characteristic
170	#1984	C₂×C₄₁	1	2	yes	—
171	#1939	C₂×C₄₁	1	2	yes	—
172	#1916	C₂×C₄₁	1	4	yes	—
173	C₄×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic
174	C₄×C₄⋊C₈	C₂×C₄₁	1	2	yes	—
175	#1744	C₂×C₄₁	1	2	yes	—
176	C₄²×C₈	C₂×C₄₁	1	1	yes	characteristic
177	C₂×C₄₁	#2295	1	1	yes	characteristic
178	C₂×C₄₁	C₂×#431	1	1	yes	characteristic
179	C₂×C₄₁	#2922	1	1	yes	characteristic
180	C₂×C₄₁	C₂×C₈×Q₈	1	1	yes	characteristic
181	C₂×C₄₁	C₂×#446	1	1	yes	characteristic
182	C₂×C₄₁	C₈×#41	1	1	yes	characteristic
183	C₂×C₄₁	#2965	1	1	yes	characteristic
184	C₂×C₄×Q₈	C₄×C₄₁	1	1	yes	characteristic
185	C₂×C₄×Q₈	C₄×C₄₁	1	1	yes	characteristic
186	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	—
188	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
190	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
194	C₄×C₄⋊C₄	C₄×C₄₁	1	2	yes	—
195	C₄×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
196	C₄×C₄⋊C₄	C₄×C₄₁	1	2	yes	—
197	C₄×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
199	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
200	C₄³	C₂²×C₄₁	1	1	yes	characteristic
201	C₄³	C₂²×C₄₁	1	2	yes	—
202	#336	C₂²×C₄₁	1	2	yes	—
203	#336	C₂²×C₄₁	1	4	yes	—
204	#336	C₂²×C₄₁	1	4	yes	—
205	#336	C₂²×C₄₁	1	4	yes	—
206	C₄₁	#21339	1	1	yes	characteristic, direct product factor, Sylow
207	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
209	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
210	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
211	C₄×Q₈	—	2	4	no	—
212	C₄×Q₈	—	2	4	no	—
213	C₄×Q₈	C₈×C₄₁	1	8	yes	complemented
214	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
221	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
227	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
229	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
231	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
233	C₄⋊C₈	—	2	8	no	—
234	C₄⋊C₈	—	2	4	no	—
235	C₄×C₈	—	2	4	no	—
236	C₄×C₈	—	2	4	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	—	2	4	no	—
239	C₄×C₈	Q₈×C₄₁	1	4	yes	complemented
240	#95	C₂×C₄×C₄₁	1	2	yes	—
241	#95	C₂×C₄×C₄₁	1	2	yes	—
242	#95	C₂×C₄×C₄₁	1	2	yes	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	2	2	no	—
245	C₂×Q₈	C₂×C₈×C₄₁	1	4	yes	—
246	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
256	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	C₂×Q₈×C₄₁	1	4	yes	—
265	C₂×C₈	#41×C₄₁	1	4	yes	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	C₂×C₈×C₄₁	1	8	yes	—
271	C₄⋊C₄	C₂×C₈×C₄₁	1	4	yes	—
272	C₄²	—	2	4	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	4	no	—
276	C₄²	—	2	4	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	4	no	—
280	C₄²	C₂×C₈×C₄₁	1	8	yes	—
281	C₄²	C₂×C₈×C₄₁	1	4	yes	—
282	C₄²	M₁₆×C₄₁	1	4	yes	—
283	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
284	C₄²	#41×C₄₁	1	4	yes	—
285	C₄²	#41×C₄₁	1	2	yes	—
286	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
287	Q₈	—	2	8	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	#117×C₄₁	1	2	yes	—
305	C₂×C₄	#117×C₄₁	1	2	yes	—
306	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
307	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
308	C₂×C₄	C₂²×C₈×C₄₁	1	4	yes	—
309	C₂×C₄	C₂²×C₈×C₄₁	1	2	yes	—
310	C₂×C₄	C₂²×C₈×C₄₁	1	4	yes	—
311	C₂×C₄	C₂²×C₈×C₄₁	1	2	yes	—
312	C₂×C₄	C₂²×C₈×C₄₁	1	2	yes	—
313	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
314	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
315	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
316	C₂×C₄	#131×C₄₁	1	2	yes	—
317	C₂×C₄	#131×C₄₁	1	2	yes	—
318	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
319	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
321	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
322	C₈	—	2	4	no	—
323	C₈	—	2	4	no	—
324	C₈	—	4	4	no	—
325	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
326	C₂²	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
327	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
328	C₂²	C₂³×C₈×C₄₁	1	1	yes	characteristic
329	C₂²	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
330	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
331	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	4	no	—
336	C₄	—	2	2	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	2	no	—
339	C₄	C₄₁×#431	1	4	yes	—
340	C₄	C₈×Q₈×C₄₁	1	4	yes	—
341	C₄	C₄₁×#446	1	4	yes	—
342	C₄	C₄₁×#529	1	2	yes	—
343	C₄	C₄₁×#533	1	2	yes	—
344	C₂	C₄₁×#2295	1	1	yes	characteristic
345	C₂	C₂×C₄₁×#431	1	1	yes	characteristic
346	C₂	C₄₁×#2922	1	1	yes	characteristic
347	C₂	C₂×C₈×Q₈×C₄₁	1	1	yes	characteristic
348	C₂	C₂×C₄₁×#446	1	1	yes	characteristic
349	C₂	C₈×#41×C₄₁	1	1	yes	characteristic
350	C₂	C₄₁×#2965	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₄₁	C₂³
commutator	C₂²	C₂³×C₈×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle, prime radical	C₂³×C₄₁	C₂³×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
37. C₄×Q₈×C₄₁	C₈	semidirect
63. C₄×C₈×C₄₁	Q₈	semidirect
149. #21339	C₄₁	direct (N × H)
206. C₄₁	#21339	direct (N × H)
213. C₄×Q₈	C₈×C₄₁	semidirect
239. 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
C₄²×Q₈×C₄₁	2
C₄₁×#1984	2
C₄₁×#1939	2
C₄₁×#1916	2
C₄×C₄⋊C₈×C₄₁	2
C₄₁×#1744	2
C₄²×C₈×C₄₁	2
#21339	41

Subgroups — C41×#21339 #23797540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21339 #23797540