Subgroups — C₄₁×#34481 #23810682

Order 10496.

2132 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2383	C₂	1	4	yes	maximal, complemented
3	C₄₁×#2367	C₂	1	2	yes	maximal
4	C₄₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2360	C₂	1	2	yes	maximal, complemented
6	Q₈×C₄⋊C₄×C₄₁	C₂	1	2	yes	maximal, complemented
7	Q₈×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#2347	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2334	C₂	1	4	yes	maximal, complemented
11	C₄₁×#2326	C₂	1	2	yes	maximal
12	C₄₁×#2323	C₂	1	2	yes	maximal, complemented
13	C₄₁×#2320	C₂	1	2	yes	maximal, complemented
14	C₄₁×#2317	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2293	C₂	1	1	yes	maximal, characteristic
18	C₄₁×#556	C₄	1	16	yes	complemented
19	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#126×C₄₁	C₂²	1	4	yes	—
21	C₂×#124×C₄₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₁	C₂²	1	2	yes	—
31	C₂×#117×C₄₁	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
33	C₄₁×#391	C₂²	1	1	yes	characteristic
34	C₄₁×#391	C₂²	1	1	yes	characteristic
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#391	C₂²	1	2	yes	—
37	C₄₁×#390	C₂²	1	1	yes	characteristic
38	C₄₁×#390	C₂²	1	1	yes	characteristic
39	C₄₁×#389	C₂²	1	1	yes	characteristic
40	C₄₁×#389	C₂²	1	1	yes	characteristic
41	C₄₁×#389	C₂²	1	1	yes	characteristic
42	C₄₁×#389	C₂²	1	1	yes	characteristic
43	C₄₁×#389	C₂²	1	2	yes	—
44	C₄₁×#389	C₂²	1	2	yes	—
45	C₄₁×#389	C₂²	1	2	yes	—
46	C₄₁×#389	C₂²	1	2	yes	—
47	C₄₁×#389	C₂²	1	2	yes	—
48	C₄₁×#389	C₂²	1	4	yes	—
49	C₄₁×#389	C₂²	1	4	yes	—
50	C₄₁×#389	C₂²	1	4	yes	—
51	C₄₁×#388	C₂²	1	2	yes	—
52	C₄₁×#388	C₂²	1	2	yes	—
53	C₄₁×#388	C₂²	1	4	yes	—
54	C₄₁×#388	C₂²	1	4	yes	—
55	C₄₁×#388	C₂²	1	4	yes	—
56	C₄₁×#388	C₂²	1	4	yes	—
57	C₄₁×#387	C₂²	1	2	yes	—
58	C₄₁×#387	C₂²	1	2	yes	—
59	C₄₁×#387	C₂²	1	4	yes	—
60	C₄₁×#387	C₂²	1	4	yes	—
61	C₄₁×#387	C₂²	1	4	yes	—
62	C₄₁×#385	C₂²	1	4	yes	—
63	C₄₁×#385	C₂²	1	4	yes	—
64	C₄₁×#385	C₂²	1	4	yes	—
65	C₄₁×#385	C₂²	1	4	yes	—
66	C₄₁×#384	C₂²	1	1	yes	characteristic
67	C₄₁×#384	C₂²	1	4	yes	—
68	C₄₁×#384	C₂²	1	2	yes	—
69	C₄₁×#383	C₂²	1	4	yes	—
70	C₄₁×#382	C₂²	1	4	yes	—
71	C₄₁×#380	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
80	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
82	C₄₁×#376	C₂²	1	2	yes	—
83	C₄³×C₄₁	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
89	C₄⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
90	#126×C₄₁	C₂×C₄	1	32	yes	complemented
91	#124×C₄₁	C₂×C₄	1	16	yes	—
92	C₂²⋊Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
93	C₄×Q₈×C₄₁	—	4	4	no	—
94	C₄×Q₈×C₄₁	—	4	4	no	—
95	C₄×Q₈×C₄₁	—	4	4	no	—
96	C₄×Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
97	C₄×Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
98	C₄×D₄×C₄₁	—	4	4	no	—
99	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	—
100	#117×C₄₁	—	4	4	no	—
101	#117×C₄₁	C₂×C₄	1	16	yes	complemented
102	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
133	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
141	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
145	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
147	#95×C₄₁	C₂³	1	2	yes	—
148	#95×C₄₁	C₂³	1	2	yes	—
149	#95×C₄₁	C₂³	1	2	yes	—
150	#95×C₄₁	C₂³	1	2	yes	—
151	#95×C₄₁	C₂³	1	2	yes	—
152	#95×C₄₁	C₂³	1	2	yes	—
153	#95×C₄₁	C₂³	1	4	yes	—
154	#95×C₄₁	C₂³	1	2	yes	—
155	#95×C₄₁	C₂³	1	4	yes	—
156	#95×C₄₁	C₂³	1	4	yes	—
157	#95×C₄₁	C₂³	1	4	yes	—
158	#95×C₄₁	C₂³	1	4	yes	—
159	#95×C₄₁	C₂³	1	4	yes	—
160	#95×C₄₁	C₂³	1	2	yes	—
161	#95×C₄₁	C₂³	1	2	yes	—
162	#95×C₄₁	C₂³	1	2	yes	—
163	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
164	C₂×Q₈×C₄₁	—	2	2	no	—
165	C₂×Q₈×C₄₁	—	2	4	no	—
166	C₂×Q₈×C₄₁	—	2	2	no	—
167	C₂×Q₈×C₄₁	—	2	4	no	—
168	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
169	C₂×Q₈×C₄₁	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₄₁	—	2	2	no	—
171	C₂×D₄×C₄₁	—	2	2	no	—
172	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₄₁	—	2	4	no	—
174	C₂²×C₄×C₄₁	—	2	4	no	—
175	C₂²×C₄×C₄₁	—	4	4	no	—
176	C₂²×C₄×C₄₁	—	4	4	no	—
177	C₂²×C₄×C₄₁	—	4	4	no	—
178	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
179	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
195	C₄⋊C₄×C₄₁	—	2	2	no	—
196	C₄⋊C₄×C₄₁	—	2	4	no	—
197	C₄⋊C₄×C₄₁	—	2	4	no	—
198	C₄⋊C₄×C₄₁	—	2	2	no	—
199	C₄⋊C₄×C₄₁	—	2	4	no	—
200	C₄⋊C₄×C₄₁	—	2	2	no	—
201	C₄⋊C₄×C₄₁	—	2	2	no	—
202	C₄⋊C₄×C₄₁	—	4	4	no	—
203	C₄⋊C₄×C₄₁	—	4	2	no	—
204	C₄⋊C₄×C₄₁	—	4	2	no	—
205	C₄⋊C₄×C₄₁	—	4	4	no	—
206	C₄⋊C₄×C₄₁	—	4	2	no	—
207	C₄⋊C₄×C₄₁	—	4	2	no	—
208	C₄⋊C₄×C₄₁	—	4	4	no	—
209	C₄⋊C₄×C₄₁	—	4	4	no	—
210	C₄⋊C₄×C₄₁	—	4	4	no	—
211	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
214	C₄⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
215	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
216	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
217	C₂²⋊C₄×C₄₁	—	2	4	no	—
218	C₂²⋊C₄×C₄₁	—	4	2	no	—
219	C₂²⋊C₄×C₄₁	—	4	2	no	—
220	C₂²⋊C₄×C₄₁	—	4	2	no	—
221	C₂²⋊C₄×C₄₁	—	4	4	no	—
222	C₂²⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
223	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
225	C₄²×C₄₁	—	2	2	no	—
226	C₄²×C₄₁	—	2	4	no	—
227	C₄²×C₄₁	—	2	4	no	—
228	C₄²×C₄₁	—	2	2	no	—
229	C₄²×C₄₁	—	2	2	no	—
230	C₄²×C₄₁	—	2	2	no	—
231	C₄²×C₄₁	—	2	2	no	—
232	C₄²×C₄₁	—	4	1	no	—
233	C₄²×C₄₁	—	4	4	no	—
234	C₄²×C₄₁	—	4	4	no	—
235	C₄²×C₄₁	—	4	4	no	—
236	C₄²×C₄₁	C₂²×C₄	1	16	yes	—
237	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
238	C₄²×C₄₁	C₂²×C₄	1	8	yes	—
239	C₂³×C₄₁	—	2	2	no	—
240	C₂³×C₄₁	—	2	2	no	—
241	C₂³×C₄₁	—	2	2	no	—
242	C₂³×C₄₁	—	2	2	no	—
243	C₂³×C₄₁	—	2	2	no	—
244	C₂³×C₄₁	—	2	2	no	—
245	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
246	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
247	Q₈×C₄₁	—	2	8	no	—
248	Q₈×C₄₁	—	2	16	no	—
249	D₄×C₄₁	—	2	8	no	—
250	C₂×C₄×C₄₁	—	2	1	no	—
251	C₂×C₄×C₄₁	—	2	2	no	—
252	C₂×C₄×C₄₁	—	2	4	no	—
253	C₂×C₄×C₄₁	—	2	2	no	—
254	C₂×C₄×C₄₁	—	2	1	no	—
255	C₂×C₄×C₄₁	—	2	1	no	—
256	C₂×C₄×C₄₁	—	2	2	no	—
257	C₂×C₄×C₄₁	—	2	2	no	—
258	C₂×C₄×C₄₁	—	2	4	no	—
259	C₂×C₄×C₄₁	—	2	2	no	—
260	C₂×C₄×C₄₁	—	2	1	no	—
261	C₂×C₄×C₄₁	—	2	2	no	—
262	C₂×C₄×C₄₁	—	2	16	no	—
263	C₂×C₄×C₄₁	—	2	2	no	—
264	C₂×C₄×C₄₁	—	2	2	no	—
265	C₂×C₄×C₄₁	—	2	1	no	—
266	C₂×C₄×C₄₁	—	2	1	no	—
267	C₂×C₄×C₄₁	—	2	2	no	—
268	C₂×C₄×C₄₁	—	2	1	no	—
269	C₂×C₄×C₄₁	—	2	2	no	—
270	C₂×C₄×C₄₁	—	2	2	no	—
271	C₂×C₄×C₄₁	—	2	4	no	—
272	C₂×C₄×C₄₁	—	2	4	no	—
273	C₂×C₄×C₄₁	—	2	2	no	—
274	C₂×C₄×C₄₁	—	2	1	no	—
275	C₂×C₄×C₄₁	—	2	1	no	—
276	C₂×C₄×C₄₁	—	2	1	no	—
277	C₂×C₄×C₄₁	—	2	1	no	—
278	C₂×C₄×C₄₁	—	2	2	no	—
279	C₂×C₄×C₄₁	—	2	2	no	—
280	C₂×C₄×C₄₁	—	2	2	no	—
281	C₂×C₄×C₄₁	—	2	2	no	—
282	C₂×C₄×C₄₁	—	2	1	no	—
283	C₂×C₄×C₄₁	—	2	1	no	—
284	C₂×C₄×C₄₁	—	2	2	no	—
285	C₂×C₄×C₄₁	—	2	4	no	—
286	C₂×C₄×C₄₁	—	2	2	no	—
287	C₂×C₄×C₄₁	—	8	8	no	—
288	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
289	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
290	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₄₁	C₂³×C₄	1	8	yes	—
292	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
296	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
297	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
298	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
299	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
300	#34481	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂²×C₄₁	—	2	4	no	—
302	C₂²×C₄₁	—	2	4	no	—
303	C₂²×C₄₁	—	2	4	no	—
304	C₂²×C₄₁	—	4	2	no	—
305	C₂²×C₄₁	—	4	2	no	—
306	C₂²×C₄₁	—	4	2	no	—
307	C₂²×C₄₁	—	4	2	no	—
308	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
309	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
312	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
313	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂²×C₄₁	#585	1	1	yes	characteristic
315	C₄×C₄₁	—	2	4	no	—
316	C₄×C₄₁	—	2	4	no	—
317	C₄×C₄₁	—	2	8	no	—
318	C₄×C₄₁	—	2	2	no	—
319	C₄×C₄₁	—	2	4	no	—
320	C₄×C₄₁	—	2	2	no	—
321	C₄×C₄₁	—	4	1	no	—
322	C₄×C₄₁	—	4	2	no	—
323	C₄×C₄₁	—	4	4	no	—
324	C₄×C₄₁	—	4	2	no	—
325	C₄×C₄₁	—	4	2	no	—
326	C₄×C₄₁	—	4	1	no	—
327	C₄×C₄₁	—	4	2	no	—
328	C₄×C₄₁	—	4	1	no	—
329	C₄×C₄₁	#520	1	4	yes	—
330	C₄×C₄₁	#520	1	4	yes	—
331	C₂×#556	C₂×C₄₁	1	1	yes	characteristic
332	#2383	C₂×C₄₁	1	4	yes	complemented
333	#2367	C₂×C₄₁	1	2	yes	—
334	#2365	C₂×C₄₁	1	1	yes	characteristic, complemented
335	#2360	C₂×C₄₁	1	2	yes	complemented
336	Q₈×C₄⋊C₄	C₂×C₄₁	1	2	yes	complemented
337	Q₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
338	D₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
339	#2347	C₂×C₄₁	1	2	yes	complemented
340	#2334	C₂×C₄₁	1	4	yes	complemented
341	#2326	C₂×C₄₁	1	2	yes	—
342	#2323	C₂×C₄₁	1	2	yes	complemented
343	#2320	C₂×C₄₁	1	2	yes	complemented
344	#2317	C₂×C₄₁	1	2	yes	complemented
345	C₄×C₄⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
346	#2295	C₂×C₄₁	1	1	yes	characteristic, complemented
347	#2293	C₂×C₄₁	1	1	yes	characteristic
348	C₂×C₄₁	—	4	4	no	—
349	C₂×C₄₁	C₂×#520	1	1	yes	characteristic
350	C₂×C₄₁	C₂×#520	1	1	yes	characteristic
351	C₂×C₄₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
352	C₂×C₄₁	#3546	1	1	yes	characteristic
353	C₂×C₄₁	#3550	1	1	yes	characteristic
354	C₂×C₄₁	#3552	1	1	yes	characteristic
355	C₂×C₄₁	#3555	1	1	yes	characteristic
356	#556	C₄×C₄₁	1	16	yes	complemented
357	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
358	C₂×#126	C₂²×C₄₁	1	4	yes	—
359	C₂×#124	C₂²×C₄₁	1	2	yes	—
360	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
361	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
362	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
363	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
364	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
365	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
366	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
368	C₂×#117	C₂²×C₄₁	1	2	yes	—
369	C₂×#117	C₂²×C₄₁	1	2	yes	—
370	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
371	#391	C₂²×C₄₁	1	2	yes	—
372	#391	C₂²×C₄₁	1	2	yes	—
373	#391	C₂²×C₄₁	1	1	yes	characteristic
374	#391	C₂²×C₄₁	1	1	yes	characteristic
375	#390	C₂²×C₄₁	1	1	yes	characteristic
376	#390	C₂²×C₄₁	1	1	yes	characteristic
377	#389	C₂²×C₄₁	1	2	yes	—
378	#389	C₂²×C₄₁	1	2	yes	—
379	#389	C₂²×C₄₁	1	1	yes	characteristic
380	#389	C₂²×C₄₁	1	2	yes	—
381	#389	C₂²×C₄₁	1	2	yes	—
382	#389	C₂²×C₄₁	1	1	yes	characteristic
383	#389	C₂²×C₄₁	1	2	yes	—
384	#389	C₂²×C₄₁	1	4	yes	—
385	#389	C₂²×C₄₁	1	4	yes	—
386	#389	C₂²×C₄₁	1	4	yes	—
387	#389	C₂²×C₄₁	1	1	yes	characteristic
388	#389	C₂²×C₄₁	1	1	yes	characteristic
389	#388	C₂²×C₄₁	1	4	yes	—
390	#388	C₂²×C₄₁	1	4	yes	—
391	#388	C₂²×C₄₁	1	4	yes	—
392	#388	C₂²×C₄₁	1	2	yes	—
393	#388	C₂²×C₄₁	1	4	yes	—
394	#388	C₂²×C₄₁	1	2	yes	—
395	#387	C₂²×C₄₁	1	4	yes	—
396	#387	C₂²×C₄₁	1	4	yes	—
397	#387	C₂²×C₄₁	1	2	yes	—
398	#387	C₂²×C₄₁	1	4	yes	—
399	#387	C₂²×C₄₁	1	2	yes	—
400	#385	C₂²×C₄₁	1	4	yes	—
401	#385	C₂²×C₄₁	1	4	yes	—
402	#385	C₂²×C₄₁	1	4	yes	—
403	#385	C₂²×C₄₁	1	4	yes	—
404	#384	C₂²×C₄₁	1	1	yes	characteristic
405	#384	C₂²×C₄₁	1	4	yes	—
406	#384	C₂²×C₄₁	1	2	yes	—
407	#383	C₂²×C₄₁	1	4	yes	—
408	#382	C₂²×C₄₁	1	4	yes	—
409	#380	C₂²×C₄₁	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
415	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
416	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
420	#376	C₂²×C₄₁	1	2	yes	—
421	C₄³	C₂²×C₄₁	1	1	yes	characteristic
422	C₄₁	#34481	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
424	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
425	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
427	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
428	C₄⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
429	#126	C₂×C₄×C₄₁	1	32	yes	complemented
430	#124	C₂×C₄×C₄₁	1	16	yes	—
431	C₂²⋊Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
432	C₄×Q₈	—	4	4	no	—
433	C₄×Q₈	—	4	4	no	—
434	C₄×Q₈	—	4	4	no	—
435	C₄×Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
436	C₄×Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
437	C₄×D₄	—	4	4	no	—
438	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	—
439	#117	—	4	4	no	—
440	#117	C₂×C₄×C₄₁	1	16	yes	complemented
441	C₂×C₄⋊C₄	—	4	4	no	—
442	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
472	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
474	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
475	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
480	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
481	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
482	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
484	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
486	#95	C₂³×C₄₁	1	2	yes	—
487	#95	C₂³×C₄₁	1	2	yes	—
488	#95	C₂³×C₄₁	1	2	yes	—
489	#95	C₂³×C₄₁	1	2	yes	—
490	#95	C₂³×C₄₁	1	2	yes	—
491	#95	C₂³×C₄₁	1	2	yes	—
492	#95	C₂³×C₄₁	1	4	yes	—
493	#95	C₂³×C₄₁	1	2	yes	—
494	#95	C₂³×C₄₁	1	4	yes	—
495	#95	C₂³×C₄₁	1	4	yes	—
496	#95	C₂³×C₄₁	1	4	yes	—
497	#95	C₂³×C₄₁	1	4	yes	—
498	#95	C₂³×C₄₁	1	4	yes	—
499	#95	C₂³×C₄₁	1	2	yes	—
500	#95	C₂³×C₄₁	1	2	yes	—
501	#95	C₂³×C₄₁	1	2	yes	—
502	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
503	C₂×Q₈	—	2	2	no	—
504	C₂×Q₈	—	2	4	no	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	4	no	—
507	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
508	C₂×Q₈	C₂²×C₄×C₄₁	1	8	yes	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
518	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	4	no	—
545	C₄⋊C₄	—	4	4	no	—
546	C₄⋊C₄	—	4	4	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	4	no	—
550	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
552	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
553	C₄⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
554	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
564	C₄²	—	2	2	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	4	4	no	—
572	C₄²	—	4	4	no	—
573	C₄²	—	4	4	no	—
574	C₄²	—	4	1	no	—
575	C₄²	C₂²×C₄×C₄₁	1	16	yes	—
576	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
577	C₄²	C₂²×C₄×C₄₁	1	8	yes	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
585	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
586	Q₈	—	2	8	no	—
587	Q₈	—	2	16	no	—
588	D₄	—	2	8	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	16	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	8	8	no	—
627	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
629	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₄₁	1	8	yes	—
631	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
634	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
635	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
636	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
637	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
638	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
647	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
648	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
649	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
650	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
651	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
652	C₂²	C₄₁×#585	1	1	yes	characteristic
653	C₄	—	2	2	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	8	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	C₄₁×#520	1	4	yes	—
668	C₄	C₄₁×#520	1	4	yes	—
669	C₂	—	4	4	no	—
670	C₂	C₂×C₄₁×#520	1	1	yes	characteristic
671	C₂	C₂×C₄₁×#520	1	1	yes	characteristic
672	C₂	C₄×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
673	C₂	C₄₁×#3546	1	1	yes	characteristic
674	C₂	C₄₁×#3550	1	1	yes	characteristic
675	C₂	C₄₁×#3552	1	1	yes	characteristic
676	C₂	C₄₁×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2383	C₂	semidirect
4. C₄₁×#2365	C₂	semidirect
5. C₄₁×#2360	C₂	semidirect
6. Q₈×C₄⋊C₄×C₄₁	C₂	semidirect
7. Q₈×C₄⋊C₄×C₄₁	C₂	semidirect
9. C₄₁×#2347	C₂	semidirect
10. C₄₁×#2334	C₂	semidirect
12. C₄₁×#2323	C₂	semidirect
13. C₄₁×#2320	C₂	semidirect
14. C₄₁×#2317	C₂	semidirect
15. C₄×C₄⋊Q₈×C₄₁	C₂	semidirect
16. C₄₁×#2295	C₂	semidirect
18. C₄₁×#556	C₄	semidirect
89. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
90. #126×C₄₁	C₂×C₄	semidirect
92. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
96. C₄×Q₈×C₄₁	C₂×C₄	semidirect
97. C₄×Q₈×C₄₁	C₂×C₄	semidirect
101. #117×C₄₁	C₂×C₄	semidirect
300. #34481	C₄₁	direct (N × H)
332. #2383	C₂×C₄₁	semidirect
334. #2365	C₂×C₄₁	semidirect
335. #2360	C₂×C₄₁	semidirect
336. Q₈×C₄⋊C₄	C₂×C₄₁	semidirect
337. Q₈×C₄⋊C₄	C₂×C₄₁	semidirect
339. #2347	C₂×C₄₁	semidirect
340. #2334	C₂×C₄₁	semidirect
342. #2323	C₂×C₄₁	semidirect
343. #2320	C₂×C₄₁	semidirect
344. #2317	C₂×C₄₁	semidirect
345. C₄×C₄⋊Q₈	C₂×C₄₁	semidirect
346. #2295	C₂×C₄₁	semidirect
356. #556	C₄×C₄₁	semidirect
422. C₄₁	#34481	direct (N × H)
428. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
429. #126	C₂×C₄×C₄₁	semidirect
431. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
435. C₄×Q₈	C₂×C₄×C₄₁	semidirect
436. C₄×Q₈	C₂×C₄×C₄₁	semidirect
440. #117	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×#556	2
C₄₁×#2383	2
C₄₁×#2367	2
C₄₁×#2365	2
C₄₁×#2360	2
Q₈×C₄⋊C₄×C₄₁	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#2347	2
C₄₁×#2334	2
C₄₁×#2326	2
C₄₁×#2323	2
C₄₁×#2320	2
C₄₁×#2317	2
C₄×C₄⋊Q₈×C₄₁	2
C₄₁×#2295	2
C₄₁×#2293	2
#34481	41

Subgroups — C41×#34481 #23810682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34481 #23810682