Subgroups — C₄₁×#23195 #23799396

Order 10496.

1126 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1968	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1776	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₁	—	2	1	no	—
24	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#496	C₄	1	8	yes	complemented
28	C₄₁×#440	—	2	4	no	—
29	C₄×D₈×C₄₁	—	2	4	no	—
30	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
44	C₄₁×#391	C₂²	1	1	yes	characteristic
45	C₄₁×#390	—	2	1	no	—
46	C₄₁×#390	C₂²	1	1	yes	characteristic
47	C₄₁×#390	C₂²	1	1	yes	characteristic
48	C₄₁×#390	C₂²	1	1	yes	characteristic
49	C₄₁×#388	—	2	1	no	—
50	C₄₁×#388	—	2	1	no	—
51	C₄₁×#386	—	2	1	no	—
52	C₄₁×#386	—	2	1	no	—
53	C₄₁×#385	—	2	1	no	—
54	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
58	C₄₁×#340	C₂²	1	1	yes	characteristic
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#336	C₂²	1	1	yes	characteristic
61	C₄₁×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₄₁	—	2	1	no	—
64	C₂²×D₄×C₄₁	—	2	1	no	—
65	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	—	2	1	no	—
69	C₂³×C₄×C₄₁	—	2	1	no	—
70	C₂³×C₄×C₄₁	—	2	1	no	—
71	C₂×SD₁₆×C₄₁	—	2	2	no	—
72	C₂×SD₁₆×C₄₁	—	2	2	no	—
73	C₂×SD₁₆×C₄₁	—	4	1	no	—
74	C₂×SD₁₆×C₄₁	—	4	1	no	—
75	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
76	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
77	C₂×D₈×C₄₁	—	2	2	no	—
78	C₂×D₈×C₄₁	—	2	2	no	—
79	C₂×D₈×C₄₁	—	4	1	no	—
80	C₂×D₈×C₄₁	—	4	1	no	—
81	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	complemented
82	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	complemented
83	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
87	#127×C₄₁	—	2	2	no	—
88	#127×C₄₁	C₂×C₄	1	4	yes	complemented
89	#124×C₄₁	—	2	2	no	—
90	#124×C₄₁	C₂×C₄	1	4	yes	complemented
91	C₄×Q₈×C₄₁	—	2	2	no	—
92	C₄×Q₈×C₄₁	—	4	1	no	—
93	C₄×D₄×C₄₁	—	2	2	no	—
94	C₄×D₄×C₄₁	—	2	2	no	—
95	C₄×D₄×C₄₁	—	2	2	no	—
96	C₄×D₄×C₄₁	—	4	1	no	—
97	C₄×D₄×C₄₁	—	4	1	no	—
98	C₄×D₄×C₄₁	—	4	1	no	—
99	C₄×D₄×C₄₁	—	4	4	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₄²×C₄₁	—	2	1	no	—
119	C₂×C₄²×C₄₁	—	2	1	no	—
120	C₂×C₄²×C₄₁	—	2	1	no	—
121	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
124	#107×C₄₁	D₄	1	4	yes	complemented
125	#106×C₄₁	—	2	2	no	—
126	C₄⋊C₈×C₄₁	—	2	2	no	—
127	#103×C₄₁	—	2	2	no	—
128	#103×C₄₁	—	4	1	no	—
129	#102×C₄₁	—	2	2	no	—
130	#102×C₄₁	—	2	2	no	—
131	#102×C₄₁	—	2	2	no	—
132	#102×C₄₁	—	4	1	no	—
133	#102×C₄₁	—	4	1	no	—
134	#102×C₄₁	—	4	1	no	—
135	#97×C₄₁	—	2	2	no	—
136	#97×C₄₁	C₂×C₄	1	4	yes	complemented
137	C₄×C₈×C₄₁	—	2	2	no	—
138	#95×C₄₁	—	2	1	no	—
139	#95×C₄₁	—	2	1	no	—
140	#95×C₄₁	—	2	1	no	—
141	#95×C₄₁	—	2	1	no	—
142	#95×C₄₁	D₄	1	1	yes	characteristic
143	#95×C₄₁	D₄	1	1	yes	characteristic
144	C₂⁴×C₄₁	—	2	1	no	—
145	C₂⁴×C₄₁	—	2	1	no	—
146	C₂⁴×C₄₁	—	2	1	no	—
147	C₂×Q₈×C₄₁	—	2	1	no	—
148	C₂×Q₈×C₄₁	—	2	1	no	—
149	C₂×Q₈×C₄₁	—	2	1	no	—
150	C₂×Q₈×C₄₁	—	2	1	no	—
151	C₂×Q₈×C₄₁	—	2	1	no	—
152	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
153	C₂×D₄×C₄₁	—	2	4	no	—
154	C₂×D₄×C₄₁	—	2	4	no	—
155	C₂×D₄×C₄₁	—	2	1	no	—
156	C₂×D₄×C₄₁	—	2	1	no	—
157	C₂×D₄×C₄₁	—	2	1	no	—
158	C₂×D₄×C₄₁	—	2	1	no	—
159	C₂×D₄×C₄₁	—	2	1	no	—
160	C₂×D₄×C₄₁	—	2	1	no	—
161	C₂×D₄×C₄₁	—	2	1	no	—
162	C₂×D₄×C₄₁	—	2	1	no	—
163	C₂×D₄×C₄₁	—	2	1	no	—
164	C₂×D₄×C₄₁	—	2	1	no	—
165	C₂×D₄×C₄₁	—	2	1	no	—
166	C₂×D₄×C₄₁	—	2	1	no	—
167	C₂×D₄×C₄₁	—	2	1	no	—
168	C₂×D₄×C₄₁	—	2	1	no	—
169	C₂×D₄×C₄₁	—	2	1	no	—
170	C₂×D₄×C₄₁	—	4	2	no	—
171	C₂×D₄×C₄₁	—	4	2	no	—
172	C₂×D₄×C₄₁	—	8	1	no	—
173	C₂×D₄×C₄₁	—	8	1	no	—
174	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
175	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
176	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₄₁	—	2	1	no	—
178	C₂²×C₄×C₄₁	—	2	1	no	—
179	C₂²×C₄×C₄₁	—	2	1	no	—
180	C₂²×C₄×C₄₁	—	2	1	no	—
181	C₂²×C₄×C₄₁	—	2	1	no	—
182	C₂²×C₄×C₄₁	—	4	2	no	—
183	C₂²×C₄×C₄₁	—	4	2	no	—
184	C₂²×C₄×C₄₁	—	4	2	no	—
185	C₂²×C₄×C₄₁	—	4	2	no	—
186	C₂²×C₄×C₄₁	—	4	2	no	—
187	C₂²×C₄×C₄₁	—	4	2	no	—
188	C₂²×C₄×C₄₁	—	8	1	no	—
189	C₂²×C₄×C₄₁	—	8	1	no	—
190	C₂²×C₄×C₄₁	—	8	1	no	—
191	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₄₁	—	2	8	no	—
199	SD₁₆×C₄₁	—	4	4	no	—
200	D₈×C₄₁	—	2	8	no	—
201	D₈×C₄₁	—	4	4	no	—
202	C₂×C₈×C₄₁	—	2	1	no	—
203	C₂×C₈×C₄₁	—	2	1	no	—
204	C₂×C₈×C₄₁	—	2	1	no	—
205	C₂×C₈×C₄₁	—	2	1	no	—
206	C₂×C₈×C₄₁	—	2	1	no	—
207	C₂×C₈×C₄₁	—	2	1	no	—
208	C₂×C₈×C₄₁	—	2	1	no	—
209	C₂×C₈×C₄₁	—	2	1	no	—
210	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
211	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₄₁	#41	1	2	yes	—
214	C₄⋊C₄×C₄₁	—	2	2	no	—
215	C₄⋊C₄×C₄₁	—	2	1	no	—
216	C₄⋊C₄×C₄₁	—	2	1	no	—
217	C₄⋊C₄×C₄₁	—	2	1	no	—
218	C₄⋊C₄×C₄₁	—	2	1	no	—
219	C₄⋊C₄×C₄₁	—	2	1	no	—
220	C₄⋊C₄×C₄₁	—	2	1	no	—
221	C₄⋊C₄×C₄₁	—	4	1	no	—
222	C₄⋊C₄×C₄₁	—	4	2	no	—
223	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
224	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
225	C₂²⋊C₄×C₄₁	—	2	4	no	—
226	C₂²⋊C₄×C₄₁	—	2	4	no	—
227	C₂²⋊C₄×C₄₁	—	4	2	no	—
228	C₂²⋊C₄×C₄₁	—	4	2	no	—
229	C₂²⋊C₄×C₄₁	—	4	2	no	—
230	C₂²⋊C₄×C₄₁	—	4	2	no	—
231	C₂²⋊C₄×C₄₁	—	4	2	no	—
232	C₂²⋊C₄×C₄₁	—	4	2	no	—
233	C₂²⋊C₄×C₄₁	—	8	1	no	—
234	C₂²⋊C₄×C₄₁	—	8	1	no	—
235	C₂²⋊C₄×C₄₁	—	8	1	no	—
236	C₄²×C₄₁	—	2	1	no	—
237	C₄²×C₄₁	—	2	1	no	—
238	C₄²×C₄₁	—	2	1	no	—
239	C₄²×C₄₁	—	2	1	no	—
240	C₄²×C₄₁	—	4	2	no	—
241	C₄²×C₄₁	—	4	2	no	—
242	C₄²×C₄₁	—	8	1	no	—
243	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
244	C₄²×C₄₁	#41	1	2	yes	—
245	C₂³×C₄₁	—	2	2	no	—
246	C₂³×C₄₁	—	2	2	no	—
247	C₂³×C₄₁	—	2	2	no	—
248	C₂³×C₄₁	—	4	1	no	—
249	C₂³×C₄₁	—	4	1	no	—
250	C₂³×C₄₁	—	4	1	no	—
251	C₂³×C₄₁	—	4	1	no	—
252	C₂³×C₄₁	—	4	1	no	—
253	C₂³×C₄₁	—	4	1	no	—
254	C₂³×C₄₁	—	4	1	no	—
255	C₂³×C₄₁	—	4	1	no	—
256	C₂³×C₄₁	—	4	1	no	—
257	C₂³×C₄₁	—	4	1	no	—
258	C₂³×C₄₁	—	4	1	no	—
259	C₂³×C₄₁	—	4	1	no	—
260	C₂³×C₄₁	—	4	1	no	—
261	C₂³×C₄₁	—	4	1	no	—
262	C₂³×C₄₁	—	4	1	no	—
263	C₂³×C₄₁	—	4	1	no	—
264	C₂³×C₄₁	—	4	1	no	—
265	C₂³×C₄₁	—	4	1	no	—
266	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₄₁	—	2	2	no	—
268	Q₈×C₄₁	—	2	2	no	—
269	Q₈×C₄₁	—	4	1	no	—
270	Q₈×C₄₁	—	4	1	no	—
271	D₄×C₄₁	—	2	2	no	—
272	D₄×C₄₁	—	2	2	no	—
273	D₄×C₄₁	—	2	2	no	—
274	D₄×C₄₁	—	2	2	no	—
275	D₄×C₄₁	—	2	2	no	—
276	D₄×C₄₁	—	2	2	no	—
277	D₄×C₄₁	—	4	8	no	—
278	D₄×C₄₁	—	4	1	no	—
279	D₄×C₄₁	—	4	1	no	—
280	D₄×C₄₁	—	4	1	no	—
281	D₄×C₄₁	—	4	1	no	—
282	D₄×C₄₁	—	4	1	no	—
283	D₄×C₄₁	—	4	1	no	—
284	D₄×C₄₁	—	8	4	no	—
285	C₂×C₄×C₄₁	—	2	1	no	—
286	C₂×C₄×C₄₁	—	2	1	no	—
287	C₂×C₄×C₄₁	—	2	1	no	—
288	C₂×C₄×C₄₁	—	2	1	no	—
289	C₂×C₄×C₄₁	—	2	1	no	—
290	C₂×C₄×C₄₁	—	2	1	no	—
291	C₂×C₄×C₄₁	—	2	2	no	—
292	C₂×C₄×C₄₁	—	2	1	no	—
293	C₂×C₄×C₄₁	—	2	1	no	—
294	C₂×C₄×C₄₁	—	2	1	no	—
295	C₂×C₄×C₄₁	—	2	2	no	—
296	C₂×C₄×C₄₁	—	2	2	no	—
297	C₂×C₄×C₄₁	—	2	1	no	—
298	C₂×C₄×C₄₁	—	2	1	no	—
299	C₂×C₄×C₄₁	—	2	1	no	—
300	C₂×C₄×C₄₁	—	2	1	no	—
301	C₂×C₄×C₄₁	—	2	1	no	—
302	C₂×C₄×C₄₁	—	2	1	no	—
303	C₂×C₄×C₄₁	—	4	1	no	—
304	C₂×C₄×C₄₁	—	4	1	no	—
305	C₂×C₄×C₄₁	—	4	1	no	—
306	C₂×C₄×C₄₁	—	4	1	no	—
307	C₂×C₄×C₄₁	—	4	1	no	—
308	C₂×C₄×C₄₁	—	4	1	no	—
309	C₂×C₄×C₄₁	—	4	1	no	—
310	C₂×C₄×C₄₁	—	4	1	no	—
311	C₂×C₄×C₄₁	—	4	1	no	—
312	C₂×C₄×C₄₁	—	4	1	no	—
313	C₂×C₄×C₄₁	—	4	1	no	—
314	C₂×C₄×C₄₁	—	4	1	no	—
315	C₂×C₄×C₄₁	—	8	4	no	—
316	C₂×C₄×C₄₁	—	8	4	no	—
317	C₂×C₄×C₄₁	—	8	4	no	—
318	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
320	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
321	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
327	C₈×C₄₁	—	2	2	no	—
328	C₈×C₄₁	—	4	1	no	—
329	C₈×C₄₁	—	4	1	no	—
330	C₈×C₄₁	C₄×D₄	1	4	yes	complemented
331	#23195	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂²×C₄₁	—	4	2	no	—
333	C₂²×C₄₁	—	4	2	no	—
334	C₂²×C₄₁	—	4	2	no	—
335	C₂²×C₄₁	—	4	2	no	—
336	C₂²×C₄₁	—	4	2	no	—
337	C₂²×C₄₁	—	4	2	no	—
338	C₂²×C₄₁	—	4	2	no	—
339	C₂²×C₄₁	—	4	2	no	—
340	C₂²×C₄₁	—	4	2	no	—
341	C₂²×C₄₁	—	8	1	no	—
342	C₂²×C₄₁	—	8	1	no	—
343	C₂²×C₄₁	—	8	1	no	—
344	C₂²×C₄₁	—	8	1	no	—
345	C₂²×C₄₁	—	8	1	no	—
346	C₂²×C₄₁	—	8	1	no	—
347	C₂²×C₄₁	—	8	1	no	—
348	C₂²×C₄₁	—	8	1	no	—
349	C₂²×C₄₁	—	8	1	no	—
350	C₂²×C₄₁	—	8	1	no	—
351	C₂²×C₄₁	—	8	1	no	—
352	C₂²×C₄₁	—	8	1	no	—
353	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
354	C₂²×C₄₁	D₄²	1	1	yes	characteristic
355	C₂²×C₄₁	#550	1	1	yes	characteristic
356	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂²×C₄₁	#575	1	1	yes	characteristic
358	C₂²×C₄₁	#576	1	1	yes	characteristic
359	C₂²×C₄₁	#577	1	1	yes	characteristic
360	C₄×C₄₁	—	2	2	no	—
361	C₄×C₄₁	—	2	2	no	—
362	C₄×C₄₁	—	2	2	no	—
363	C₄×C₄₁	—	4	2	no	—
364	C₄×C₄₁	—	4	1	no	—
365	C₄×C₄₁	—	4	2	no	—
366	C₄×C₄₁	—	4	2	no	—
367	C₄×C₄₁	—	4	1	no	—
368	C₄×C₄₁	—	4	1	no	—
369	C₄×C₄₁	—	8	1	no	—
370	C₄×C₄₁	—	8	1	no	—
371	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
372	C₄×C₄₁	#518	1	1	yes	characteristic
373	C₄×C₄₁	#550	1	1	yes	characteristic
374	C₄×C₄₁	#559	1	1	yes	characteristic
375	C₂×#496	C₂×C₄₁	1	1	yes	characteristic
376	C₂×#440	C₂×C₄₁	1	1	yes	characteristic, complemented
377	C₂×C₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
378	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
379	#2366	C₂×C₄₁	1	1	yes	characteristic, complemented
380	#1983	C₂×C₄₁	1	1	yes	characteristic, complemented
381	#1982	C₂×C₄₁	1	1	yes	characteristic, complemented
382	#1972	C₂×C₄₁	1	1	yes	characteristic, complemented
383	#1968	C₂×C₄₁	1	1	yes	characteristic, complemented
384	#1880	C₂×C₄₁	1	1	yes	characteristic, complemented
385	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
386	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
387	#1877	C₂×C₄₁	1	1	yes	characteristic, complemented
388	#1776	C₂×C₄₁	1	1	yes	characteristic, complemented
389	#1771	C₂×C₄₁	1	1	yes	characteristic, complemented
390	C₂×C₄₁	—	8	2	no	—
391	C₂×C₄₁	—	8	2	no	—
392	C₂×C₄₁	—	8	2	no	—
393	C₂×C₄₁	#2366	1	1	yes	characteristic
394	C₂×C₄₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₂×C₄₁	#2946	1	1	yes	characteristic
396	C₂×C₄₁	#3264	1	1	yes	characteristic
397	C₂×C₄₁	#3271	1	1	yes	characteristic
398	C₂×C₄₁	#3397	1	1	yes	characteristic
399	C₂×C₄₁	#3403	1	1	yes	characteristic
400	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
401	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
402	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
403	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
404	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
405	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
407	C₂×C₄×D₄	—	2	1	no	—
408	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
411	#496	C₄×C₄₁	1	8	yes	complemented
412	#440	—	2	4	no	—
413	C₄×D₈	—	2	4	no	—
414	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
415	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
416	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
417	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
418	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
419	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
420	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
421	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
422	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
423	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
424	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
425	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
426	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
427	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
428	#391	C₂²×C₄₁	1	1	yes	characteristic
429	#390	—	2	1	no	—
430	#390	C₂²×C₄₁	1	1	yes	characteristic
431	#390	C₂²×C₄₁	1	1	yes	characteristic
432	#390	C₂²×C₄₁	1	1	yes	characteristic
433	#388	—	2	1	no	—
434	#388	—	2	1	no	—
435	#386	—	2	1	no	—
436	#386	—	2	1	no	—
437	#385	—	2	1	no	—
438	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	—	2	1	no	—
442	#340	C₂²×C₄₁	1	1	yes	characteristic
443	#340	C₂²×C₄₁	1	1	yes	characteristic
444	#336	C₂²×C₄₁	1	1	yes	characteristic
445	#336	C₂²×C₄₁	1	1	yes	characteristic
446	C₄₁	#23195	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
448	C₂²×D₄	—	2	1	no	—
449	C₂²×D₄	—	2	1	no	—
450	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
453	C₂³×C₄	—	2	1	no	—
454	C₂³×C₄	—	2	1	no	—
455	C₂³×C₄	—	2	1	no	—
456	C₂×SD₁₆	—	2	2	no	—
457	C₂×SD₁₆	—	2	2	no	—
458	C₂×SD₁₆	—	4	1	no	—
459	C₂×SD₁₆	—	4	1	no	—
460	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
461	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
462	C₂×D₈	—	2	2	no	—
463	C₂×D₈	—	2	2	no	—
464	C₂×D₈	—	4	1	no	—
465	C₂×D₈	—	4	1	no	—
466	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	complemented
467	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	complemented
468	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
472	#127	—	2	2	no	—
473	#127	C₂×C₄×C₄₁	1	4	yes	complemented
474	#124	—	2	2	no	—
475	#124	C₂×C₄×C₄₁	1	4	yes	complemented
476	C₄×Q₈	—	2	2	no	—
477	C₄×Q₈	—	4	1	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	4	1	no	—
482	C₄×D₄	—	4	1	no	—
483	C₄×D₄	—	4	1	no	—
484	C₄×D₄	—	4	4	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
487	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
509	#107	D₄×C₄₁	1	4	yes	complemented
510	#106	—	2	2	no	—
511	C₄⋊C₈	—	2	2	no	—
512	#103	—	2	2	no	—
513	#103	—	4	1	no	—
514	#102	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	—	4	1	no	—
518	#102	—	4	1	no	—
519	#102	—	4	1	no	—
520	#97	—	2	2	no	—
521	#97	C₂×C₄×C₄₁	1	4	yes	complemented
522	C₄×C₈	—	2	2	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	—	2	1	no	—
527	#95	D₄×C₄₁	1	1	yes	characteristic
528	#95	D₄×C₄₁	1	1	yes	characteristic
529	C₂⁴	—	2	1	no	—
530	C₂⁴	—	2	1	no	—
531	C₂⁴	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	8	1	no	—
558	C₂×D₄	—	8	1	no	—
559	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
560	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
561	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	8	1	no	—
574	C₂²×C₄	—	8	1	no	—
575	C₂²×C₄	—	8	1	no	—
576	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	4	4	no	—
585	D₈	—	2	8	no	—
586	D₈	—	4	4	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
596	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
597	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
598	C₂×C₈	#41×C₄₁	1	2	yes	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	4	1	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
609	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	8	1	no	—
619	C₂²⋊C₄	—	8	1	no	—
620	C₂²⋊C₄	—	8	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	4	2	no	—
626	C₄²	—	4	2	no	—
627	C₄²	—	8	1	no	—
628	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
629	C₄²	#41×C₄₁	1	2	yes	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	D₄	—	2	2	no	—
657	D₄	—	2	2	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	8	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	8	4	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
704	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
705	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
708	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
709	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
710	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
711	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	C₄×D₄×C₄₁	1	4	yes	complemented
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	8	1	no	—
726	C₂²	—	8	1	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
738	C₂²	D₄²×C₄₁	1	1	yes	characteristic
739	C₂²	C₄₁×#550	1	1	yes	characteristic
740	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
741	C₂²	C₄₁×#575	1	1	yes	characteristic
742	C₂²	C₄₁×#576	1	1	yes	characteristic
743	C₂²	C₄₁×#577	1	1	yes	characteristic
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	8	1	no	—
754	C₄	—	8	1	no	—
755	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
756	C₄	C₄₁×#518	1	1	yes	characteristic
757	C₄	C₄₁×#550	1	1	yes	characteristic
758	C₄	C₄₁×#559	1	1	yes	characteristic
759	C₂	—	8	2	no	—
760	C₂	—	8	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₄₁×#2366	1	1	yes	characteristic
763	C₂	C₄×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
764	C₂	C₄₁×#2946	1	1	yes	characteristic
765	C₂	C₄₁×#3264	1	1	yes	characteristic
766	C₂	C₄₁×#3271	1	1	yes	characteristic
767	C₂	C₄₁×#3397	1	1	yes	characteristic
768	C₂	C₄₁×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#440	C₂	semidirect
3. C₂×C₄×D₈×C₄₁	C₂	semidirect
4. C₄₁×#2367	C₂	semidirect
5. C₄₁×#2366	C₂	semidirect
6. C₄₁×#1983	C₂	semidirect
7. C₄₁×#1982	C₂	semidirect
8. C₄₁×#1972	C₂	semidirect
9. C₄₁×#1968	C₂	semidirect
10. C₄₁×#1880	C₂	semidirect
11. C₄₁×#1879	C₂	semidirect
12. C₄₁×#1879	C₂	semidirect
13. C₄₁×#1877	C₂	semidirect
14. C₄₁×#1776	C₂	semidirect
15. C₄₁×#1771	C₂	semidirect
27. C₄₁×#496	C₄	semidirect
75. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
76. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
81. C₂×D₈×C₄₁	C₂×C₄	semidirect
82. C₂×D₈×C₄₁	C₂×C₄	semidirect
88. #127×C₄₁	C₂×C₄	semidirect
90. #124×C₄₁	C₂×C₄	semidirect
124. #107×C₄₁	D₄	semidirect
136. #97×C₄₁	C₂×C₄	semidirect
330. C₈×C₄₁	C₄×D₄	semidirect
331. #23195	C₄₁	direct (N × H)
376. C₂×#440	C₂×C₄₁	semidirect
377. C₂×C₄×D₈	C₂×C₄₁	semidirect
378. #2367	C₂×C₄₁	semidirect
379. #2366	C₂×C₄₁	semidirect
380. #1983	C₂×C₄₁	semidirect
381. #1982	C₂×C₄₁	semidirect
382. #1972	C₂×C₄₁	semidirect
383. #1968	C₂×C₄₁	semidirect
384. #1880	C₂×C₄₁	semidirect
385. #1879	C₂×C₄₁	semidirect
386. #1879	C₂×C₄₁	semidirect
387. #1877	C₂×C₄₁	semidirect
388. #1776	C₂×C₄₁	semidirect
389. #1771	C₂×C₄₁	semidirect
411. #496	C₄×C₄₁	semidirect
446. C₄₁	#23195	direct (N × H)
460. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
461. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
466. C₂×D₈	C₂×C₄×C₄₁	semidirect
467. C₂×D₈	C₂×C₄×C₄₁	semidirect
473. #127	C₂×C₄×C₄₁	semidirect
475. #124	C₂×C₄×C₄₁	semidirect
509. #107	D₄×C₄₁	semidirect
521. #97	C₂×C₄×C₄₁	semidirect
715. C₈	C₄×D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#496	2
C₂×C₄₁×#440	2
C₂×C₄×D₈×C₄₁	2
C₄₁×#2367	2
C₄₁×#2366	2
C₄₁×#1983	2
C₄₁×#1982	2
C₄₁×#1972	2
C₄₁×#1968	2
C₄₁×#1880	2
C₄₁×#1879	2
C₄₁×#1877	2
C₄₁×#1776	2
C₄₁×#1771	2
#23195	41

Subgroups — C41×#23195 #23799396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23195 #23799396