Subgroups — C₄₁×#22497 #23798698

Order 10496.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#435	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2352	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₁×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#554	—	2	4	no	—
19	C₄₁×#554	C₄	1	8	yes	complemented
20	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#125×C₄₁	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₁	—	2	1	no	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#435	—	2	4	no	—
34	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#388	—	2	1	no	—
43	C₄₁×#387	—	2	1	no	—
44	C₄₁×#386	—	2	1	no	—
45	C₄₁×#382	C₂²	1	1	yes	characteristic
46	C₄₁×#380	C₂²	1	1	yes	characteristic
47	C₄₁×#380	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
50	C₄₁×#340	C₂²	1	1	yes	characteristic
51	C₄₁×#340	C₂²	1	1	yes	characteristic
52	C₄₁×#340	C₂²	1	1	yes	characteristic
53	C₄₁×#340	C₂²	1	1	yes	characteristic
54	C₄₁×#340	C₂²	1	1	yes	characteristic
55	C₄₁×#340	C₂²	1	1	yes	characteristic
56	C₄₁×#340	C₂²	1	1	yes	characteristic
57	C₄₁×#340	C₂²	1	1	yes	characteristic
58	C₄₁×#340	C₂²	1	1	yes	characteristic
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#340	C₂²	1	1	yes	characteristic
61	C₄₁×#340	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₄₁	—	2	1	no	—
63	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	—	2	1	no	—
66	C₂³×C₄×C₄₁	—	2	1	no	—
67	C₂³×C₄×C₄₁	—	2	1	no	—
68	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₄₁	—	2	2	no	—
71	C₂×M₁₆×C₄₁	—	2	2	no	—
72	C₂×M₁₆×C₄₁	—	4	1	no	—
73	C₂²×C₈×C₄₁	—	2	2	no	—
74	C₂²×C₈×C₄₁	—	2	2	no	—
75	C₂²×C₈×C₄₁	—	4	1	no	—
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₁	—	2	2	no	—
81	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
82	#125×C₄₁	—	2	8	no	—
83	C₂²⋊Q₈×C₄₁	—	2	2	no	—
84	C₂²⋊Q₈×C₄₁	—	2	2	no	—
85	C₂²⋊Q₈×C₄₁	—	2	8	no	—
86	C₂²⋊Q₈×C₄₁	—	2	8	no	—
87	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
88	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
89	C₄×Q₈×C₄₁	—	2	2	no	—
90	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
91	C₄×D₄×C₄₁	—	2	8	no	—
92	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
93	C₄×D₄×C₄₁	D₄	1	4	yes	—
94	#117×C₄₁	—	2	2	no	—
95	#117×C₄₁	—	4	1	no	—
96	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
105	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₄₁	—	4	1	no	—
107	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
108	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	complemented
109	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₄₁	—	2	1	no	—
125	C₂×C₄²×C₄₁	—	2	1	no	—
126	C₂×C₄²×C₄₁	—	2	1	no	—
127	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₄₁	—	2	2	no	—
129	#103×C₄₁	—	2	2	no	—
130	#103×C₄₁	—	2	2	no	—
131	#103×C₄₁	—	4	1	no	—
132	#103×C₄₁	—	4	1	no	—
133	C₂²⋊C₈×C₄₁	—	2	2	no	—
134	C₂²⋊C₈×C₄₁	—	2	2	no	—
135	#97×C₄₁	—	2	2	no	—
136	#95×C₄₁	—	2	1	no	—
137	#95×C₄₁	—	2	1	no	—
138	#95×C₄₁	—	2	1	no	—
139	#95×C₄₁	—	2	1	no	—
140	#95×C₄₁	—	2	1	no	—
141	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₄₁	—	2	4	no	—
144	C₂×Q₈×C₄₁	—	2	1	no	—
145	C₂×Q₈×C₄₁	—	2	1	no	—
146	C₂×Q₈×C₄₁	—	2	1	no	—
147	C₂×Q₈×C₄₁	—	2	1	no	—
148	C₂×Q₈×C₄₁	—	2	1	no	—
149	C₂×Q₈×C₄₁	—	8	1	no	—
150	C₂×Q₈×C₄₁	—	8	1	no	—
151	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
152	C₂×D₄×C₄₁	—	2	2	no	—
153	C₂×D₄×C₄₁	—	2	2	no	—
154	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
155	C₂²×C₄×C₄₁	—	2	1	no	—
156	C₂²×C₄×C₄₁	—	2	1	no	—
157	C₂²×C₄×C₄₁	—	2	1	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	1	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	2	1	no	—
162	C₂²×C₄×C₄₁	—	2	1	no	—
163	C₂²×C₄×C₄₁	—	2	1	no	—
164	C₂²×C₄×C₄₁	—	2	1	no	—
165	C₂²×C₄×C₄₁	—	2	1	no	—
166	C₂²×C₄×C₄₁	—	2	1	no	—
167	C₂²×C₄×C₄₁	—	2	1	no	—
168	C₂²×C₄×C₄₁	—	2	4	no	—
169	C₂²×C₄×C₄₁	—	2	4	no	—
170	C₂²×C₄×C₄₁	—	2	1	no	—
171	C₂²×C₄×C₄₁	—	2	1	no	—
172	C₂²×C₄×C₄₁	—	2	1	no	—
173	C₂²×C₄×C₄₁	—	4	2	no	—
174	C₂²×C₄×C₄₁	—	4	2	no	—
175	C₂²×C₄×C₄₁	—	8	1	no	—
176	C₂²×C₄×C₄₁	—	8	1	no	—
177	C₂²×C₄×C₄₁	—	8	1	no	—
178	C₂²×C₄×C₄₁	—	8	1	no	—
179	C₂²×C₄×C₄₁	—	8	1	no	—
180	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
181	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
189	M₁₆×C₄₁	—	4	4	no	—
190	C₂×C₈×C₄₁	—	2	1	no	—
191	C₂×C₈×C₄₁	—	2	1	no	—
192	C₂×C₈×C₄₁	—	2	1	no	—
193	C₂×C₈×C₄₁	—	2	1	no	—
194	C₂×C₈×C₄₁	—	2	1	no	—
195	C₂×C₈×C₄₁	—	2	1	no	—
196	C₂×C₈×C₄₁	—	2	1	no	—
197	C₂×C₈×C₄₁	—	2	1	no	—
198	C₂×C₈×C₄₁	—	2	1	no	—
199	C₂×C₈×C₄₁	—	2	1	no	—
200	C₂×C₈×C₄₁	—	2	1	no	—
201	C₂×C₈×C₄₁	—	4	4	no	—
202	C₂×C₈×C₄₁	#41	1	2	yes	—
203	C₄⋊C₄×C₄₁	—	2	4	no	—
204	C₄⋊C₄×C₄₁	—	2	4	no	—
205	C₄⋊C₄×C₄₁	—	2	4	no	—
206	C₄⋊C₄×C₄₁	—	2	4	no	—
207	C₄⋊C₄×C₄₁	—	2	4	no	—
208	C₄⋊C₄×C₄₁	—	2	4	no	—
209	C₄⋊C₄×C₄₁	—	2	1	no	—
210	C₄⋊C₄×C₄₁	—	2	1	no	—
211	C₄⋊C₄×C₄₁	—	2	1	no	—
212	C₄⋊C₄×C₄₁	—	2	1	no	—
213	C₄⋊C₄×C₄₁	—	2	1	no	—
214	C₄⋊C₄×C₄₁	—	2	1	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	—	4	2	no	—
220	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
221	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
224	C₄⋊C₄×C₄₁	#41	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	—	8	1	no	—
230	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
231	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
232	C₄²×C₄₁	—	2	4	no	—
233	C₄²×C₄₁	—	4	2	no	—
234	C₄²×C₄₁	—	8	1	no	—
235	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
236	C₄²×C₄₁	C₂×D₄	1	2	yes	—
237	C₂³×C₄₁	—	2	1	no	—
238	C₂³×C₄₁	—	2	1	no	—
239	C₂³×C₄₁	—	2	1	no	—
240	C₂³×C₄₁	—	2	1	no	—
241	C₂³×C₄₁	—	2	1	no	—
242	C₂³×C₄₁	—	2	1	no	—
243	C₂³×C₄₁	—	2	1	no	—
244	C₂³×C₄₁	—	2	1	no	—
245	C₂³×C₄₁	—	2	1	no	—
246	C₂³×C₄₁	—	2	1	no	—
247	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂³×C₄₁	#137	1	2	yes	—
250	C₂³×C₄₁	#137	1	2	yes	—
251	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₄₁	—	2	2	no	—
253	Q₈×C₄₁	—	2	2	no	—
254	Q₈×C₄₁	—	4	1	no	—
255	Q₈×C₄₁	—	4	1	no	—
256	Q₈×C₄₁	—	8	4	no	—
257	D₄×C₄₁	—	2	8	no	—
258	C₂×C₄×C₄₁	—	2	1	no	—
259	C₂×C₄×C₄₁	—	2	1	no	—
260	C₂×C₄×C₄₁	—	2	1	no	—
261	C₂×C₄×C₄₁	—	2	1	no	—
262	C₂×C₄×C₄₁	—	2	1	no	—
263	C₂×C₄×C₄₁	—	2	1	no	—
264	C₂×C₄×C₄₁	—	2	1	no	—
265	C₂×C₄×C₄₁	—	2	1	no	—
266	C₂×C₄×C₄₁	—	2	2	no	—
267	C₂×C₄×C₄₁	—	2	2	no	—
268	C₂×C₄×C₄₁	—	2	2	no	—
269	C₂×C₄×C₄₁	—	2	2	no	—
270	C₂×C₄×C₄₁	—	2	2	no	—
271	C₂×C₄×C₄₁	—	2	2	no	—
272	C₂×C₄×C₄₁	—	2	2	no	—
273	C₂×C₄×C₄₁	—	2	2	no	—
274	C₂×C₄×C₄₁	—	2	2	no	—
275	C₂×C₄×C₄₁	—	2	2	no	—
276	C₂×C₄×C₄₁	—	2	2	no	—
277	C₂×C₄×C₄₁	—	2	2	no	—
278	C₂×C₄×C₄₁	—	2	2	no	—
279	C₂×C₄×C₄₁	—	4	1	no	—
280	C₂×C₄×C₄₁	—	4	1	no	—
281	C₂×C₄×C₄₁	—	4	1	no	—
282	C₂×C₄×C₄₁	—	4	1	no	—
283	C₂×C₄×C₄₁	—	4	1	no	—
284	C₂×C₄×C₄₁	—	4	1	no	—
285	C₂×C₄×C₄₁	—	4	1	no	—
286	C₂×C₄×C₄₁	—	4	1	no	—
287	C₂×C₄×C₄₁	—	4	1	no	—
288	C₂×C₄×C₄₁	—	4	1	no	—
289	C₂×C₄×C₄₁	—	4	1	no	—
290	C₂×C₄×C₄₁	—	4	1	no	—
291	C₂×C₄×C₄₁	—	4	1	no	—
292	C₂×C₄×C₄₁	—	4	1	no	—
293	C₂×C₄×C₄₁	—	4	1	no	—
294	C₂×C₄×C₄₁	—	4	1	no	—
295	C₂×C₄×C₄₁	—	4	1	no	—
296	C₂×C₄×C₄₁	—	4	1	no	—
297	C₂×C₄×C₄₁	—	4	1	no	—
298	C₂×C₄×C₄₁	—	8	4	no	—
299	C₂×C₄×C₄₁	—	8	4	no	—
300	C₂×C₄×C₄₁	—	8	4	no	—
301	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
311	C₈×C₄₁	—	2	2	no	—
312	C₈×C₄₁	—	4	1	no	—
313	C₈×C₄₁	—	4	1	no	—
314	C₈×C₄₁	—	4	1	no	—
315	#22497	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂²×C₄₁	—	2	2	no	—
317	C₂²×C₄₁	—	2	2	no	—
318	C₂²×C₄₁	—	2	2	no	—
319	C₂²×C₄₁	—	2	2	no	—
320	C₂²×C₄₁	—	2	2	no	—
321	C₂²×C₄₁	—	2	2	no	—
322	C₂²×C₄₁	—	2	2	no	—
323	C₂²×C₄₁	—	2	2	no	—
324	C₂²×C₄₁	—	2	2	no	—
325	C₂²×C₄₁	—	4	1	no	—
326	C₂²×C₄₁	—	4	1	no	—
327	C₂²×C₄₁	—	4	1	no	—
328	C₂²×C₄₁	—	4	1	no	—
329	C₂²×C₄₁	#419	1	4	yes	—
330	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
331	C₂²×C₄₁	#546	1	1	yes	characteristic
332	C₂²×C₄₁	#547	1	1	yes	characteristic
333	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
334	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
335	C₂²×C₄₁	#576	1	1	yes	characteristic
336	C₂²×C₄₁	#577	1	1	yes	characteristic
337	C₄×C₄₁	—	2	2	no	—
338	C₄×C₄₁	—	2	2	no	—
339	C₄×C₄₁	—	2	2	no	—
340	C₄×C₄₁	—	2	2	no	—
341	C₄×C₄₁	—	4	2	no	—
342	C₄×C₄₁	—	4	2	no	—
343	C₄×C₄₁	—	4	2	no	—
344	C₄×C₄₁	—	4	2	no	—
345	C₄×C₄₁	—	4	2	no	—
346	C₄×C₄₁	—	8	1	no	—
347	C₄×C₄₁	—	8	1	no	—
348	C₄×C₄₁	—	8	1	no	—
349	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
350	C₄×C₄₁	#520	1	1	yes	characteristic
351	C₄×C₄₁	#546	1	1	yes	characteristic
352	C₄×C₄₁	#547	1	1	yes	characteristic
353	C₂×#554	C₂×C₄₁	1	1	yes	characteristic
354	C₂×#435	C₂×C₄₁	1	1	yes	characteristic
355	#2352	C₂×C₄₁	1	1	yes	characteristic
356	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
357	#1988	C₂×C₄₁	1	1	yes	characteristic, complemented
358	#1894	C₂×C₄₁	1	1	yes	characteristic, complemented
359	#1892	C₂×C₄₁	1	1	yes	characteristic, complemented
360	#1873	C₂×C₄₁	1	1	yes	characteristic, complemented
361	#1872	C₂×C₄₁	1	1	yes	characteristic, complemented
362	#1824	C₂×C₄₁	1	1	yes	characteristic, complemented
363	#1823	C₂×C₄₁	1	1	yes	characteristic, complemented
364	#1805	C₂×C₄₁	1	1	yes	characteristic, complemented
365	#1763	C₂×C₄₁	1	1	yes	characteristic, complemented
366	#1736	C₂×C₄₁	1	1	yes	characteristic, complemented
367	C₂×#340	C₂×C₄₁	1	1	yes	characteristic, complemented
368	C₂×C₄₁	—	2	4	no	—
369	C₂×C₄₁	—	4	2	no	—
370	C₂×C₄₁	#2339	1	1	yes	characteristic
371	C₂×C₄₁	C₂×#419	1	1	yes	characteristic
372	C₂×C₄₁	#2897	1	1	yes	characteristic
373	C₂×C₄₁	#3314	1	1	yes	characteristic
374	C₂×C₄₁	#3316	1	1	yes	characteristic
375	C₂×C₄₁	#3344	1	1	yes	characteristic
376	C₂×C₄₁	#3346	1	1	yes	characteristic
377	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
378	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
379	#554	—	2	4	no	—
380	#554	C₄×C₄₁	1	8	yes	complemented
381	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
382	C₂×#125	—	2	1	no	—
383	C₂×C₂²⋊Q₈	—	2	1	no	—
384	C₂×C₂²⋊Q₈	—	2	1	no	—
385	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
386	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
387	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
388	C₂×C₄×D₄	—	2	1	no	—
389	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
390	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
391	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
394	#435	—	2	4	no	—
395	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
396	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
397	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
398	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
399	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
400	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
401	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
402	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
403	#388	—	2	1	no	—
404	#387	—	2	1	no	—
405	#386	—	2	1	no	—
406	#382	C₂²×C₄₁	1	1	yes	characteristic
407	#380	C₂²×C₄₁	1	1	yes	characteristic
408	#380	C₂²×C₄₁	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	—	2	1	no	—
411	#340	C₂²×C₄₁	1	1	yes	characteristic
412	#340	C₂²×C₄₁	1	1	yes	characteristic
413	#340	C₂²×C₄₁	1	1	yes	characteristic
414	#340	C₂²×C₄₁	1	1	yes	characteristic
415	#340	C₂²×C₄₁	1	1	yes	characteristic
416	#340	C₂²×C₄₁	1	1	yes	characteristic
417	#340	C₂²×C₄₁	1	1	yes	characteristic
418	#340	C₂²×C₄₁	1	1	yes	characteristic
419	#340	C₂²×C₄₁	1	1	yes	characteristic
420	#340	C₂²×C₄₁	1	1	yes	characteristic
421	#340	C₂²×C₄₁	1	1	yes	characteristic
422	#340	C₂²×C₄₁	1	1	yes	characteristic
423	C₄₁	#22497	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
426	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	—	2	1	no	—
429	C₂³×C₄	—	2	1	no	—
430	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
432	C₂×M₁₆	—	2	2	no	—
433	C₂×M₁₆	—	2	2	no	—
434	C₂×M₁₆	—	4	1	no	—
435	C₂²×C₈	—	2	2	no	—
436	C₂²×C₈	—	2	2	no	—
437	C₂²×C₈	—	4	1	no	—
438	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
444	#125	—	2	8	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	8	no	—
448	C₂²⋊Q₈	—	2	8	no	—
449	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
450	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
453	C₄×D₄	—	2	8	no	—
454	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
455	C₄×D₄	D₄×C₄₁	1	4	yes	—
456	#117	—	2	2	no	—
457	#117	—	4	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	2	no	—
461	C₂×C₄⋊C₄	—	2	2	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	2	1	no	—
466	C₂×C₄⋊C₄	—	2	2	no	—
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄⋊C₄	—	4	1	no	—
469	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
470	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	complemented
471	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
486	C₂×C₄²	—	2	1	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
490	C₄⋊C₈	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	2	2	no	—
493	#103	—	4	1	no	—
494	#103	—	4	1	no	—
495	C₂²⋊C₈	—	2	2	no	—
496	C₂²⋊C₈	—	2	2	no	—
497	#97	—	2	2	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
504	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	8	1	no	—
512	C₂×Q₈	—	8	1	no	—
513	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	8	1	no	—
538	C₂²×C₄	—	8	1	no	—
539	C₂²×C₄	—	8	1	no	—
540	C₂²×C₄	—	8	1	no	—
541	C₂²×C₄	—	8	1	no	—
542	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
543	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
544	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
549	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
551	M₁₆	—	4	4	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	4	4	no	—
564	C₂×C₈	#41×C₄₁	1	2	yes	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
583	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
584	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
585	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
586	C₄⋊C₄	#41×C₄₁	1	2	yes	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	2	no	—
591	C₂²⋊C₄	—	8	1	no	—
592	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
593	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
594	C₄²	—	2	4	no	—
595	C₄²	—	4	2	no	—
596	C₄²	—	8	1	no	—
597	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
598	C₄²	C₂×D₄×C₄₁	1	2	yes	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
610	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
611	C₂³	#137×C₄₁	1	2	yes	—
612	C₂³	#137×C₄₁	1	2	yes	—
613	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
614	Q₈	—	2	2	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	8	4	no	—
619	D₄	—	2	8	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	8	4	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	—	8	4	no	—
663	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
664	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
665	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
666	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
667	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
668	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
669	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
670	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
671	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
672	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	C₄₁×#419	1	4	yes	—
691	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
692	C₂²	C₄₁×#546	1	1	yes	characteristic
693	C₂²	C₄₁×#547	1	1	yes	characteristic
694	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
695	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
696	C₂²	C₄₁×#576	1	1	yes	characteristic
697	C₂²	C₄₁×#577	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
711	C₄	C₄₁×#520	1	1	yes	characteristic
712	C₄	C₄₁×#546	1	1	yes	characteristic
713	C₄	C₄₁×#547	1	1	yes	characteristic
714	C₂	—	2	4	no	—
715	C₂	—	4	2	no	—
716	C₂	C₄₁×#2339	1	1	yes	characteristic
717	C₂	C₂×C₄₁×#419	1	1	yes	characteristic
718	C₂	C₄₁×#2897	1	1	yes	characteristic
719	C₂	C₄₁×#3314	1	1	yes	characteristic
720	C₂	C₄₁×#3316	1	1	yes	characteristic
721	C₂	C₄₁×#3344	1	1	yes	characteristic
722	C₂	C₄₁×#3346	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	C₂²×D₄×C₄₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#1993	C₂	semidirect
5. C₄₁×#1988	C₂	semidirect
6. C₄₁×#1894	C₂	semidirect
7. C₄₁×#1892	C₂	semidirect
8. C₄₁×#1873	C₂	semidirect
9. C₄₁×#1872	C₂	semidirect
10. C₄₁×#1824	C₂	semidirect
11. C₄₁×#1823	C₂	semidirect
12. C₄₁×#1805	C₂	semidirect
13. C₄₁×#1763	C₂	semidirect
14. C₄₁×#1736	C₂	semidirect
15. C₂×C₄₁×#340	C₂	semidirect
19. C₄₁×#554	C₄	semidirect
81. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
88. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
90. C₄×Q₈×C₄₁	C₂×C₄	semidirect
108. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
315. #22497	C₄₁	direct (N × H)
356. #1993	C₂×C₄₁	semidirect
357. #1988	C₂×C₄₁	semidirect
358. #1894	C₂×C₄₁	semidirect
359. #1892	C₂×C₄₁	semidirect
360. #1873	C₂×C₄₁	semidirect
361. #1872	C₂×C₄₁	semidirect
362. #1824	C₂×C₄₁	semidirect
363. #1823	C₂×C₄₁	semidirect
364. #1805	C₂×C₄₁	semidirect
365. #1763	C₂×C₄₁	semidirect
366. #1736	C₂×C₄₁	semidirect
367. C₂×#340	C₂×C₄₁	semidirect
380. #554	C₄×C₄₁	semidirect
423. C₄₁	#22497	direct (N × H)
443. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
450. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
452. C₄×Q₈	C₂×C₄×C₄₁	semidirect
470. C₂×C₄⋊C₄	C₂×C₄×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×#554	2
C₂×C₄₁×#435	2
C₄₁×#2352	2
C₄₁×#1993	2
C₄₁×#1988	2
C₄₁×#1894	2
C₄₁×#1892	2
C₄₁×#1873	2
C₄₁×#1872	2
C₄₁×#1824	2
C₄₁×#1823	2
C₄₁×#1805	2
C₄₁×#1763	2
C₄₁×#1736	2
C₂×C₄₁×#340	2
#22497	41

Subgroups — C41×#22497 #23798698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22497 #23798698