Subgroups — C₄₁×#10771 #23786972

Order 10496.

1164 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#413	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#344	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1742	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
7	C₄₁×#568	—	2	4	no	—
8	C₄₁×#568	—	2	4	no	—
9	C₂×#131×C₄₁	—	2	2	no	—
10	C₂×#131×C₄₁	—	2	2	no	—
11	C₂²×M₁₆×C₄₁	C₄	1	4	yes	complemented
12	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#413	—	2	2	no	—
17	C₄₁×#413	—	2	2	no	—
18	C₂×#101×C₄₁	C₄	1	2	yes	complemented
19	C₂×#100×C₄₁	C₄	1	2	yes	complemented
20	C₄₁×#410	—	2	2	no	—
21	C₄₁×#410	—	2	2	no	—
22	C₂×#99×C₄₁	C₄	1	4	yes	—
23	C₄₁×#344	—	2	4	no	—
24	C₄₁×#343	—	2	4	no	—
25	C₂×#41×C₄₁	—	2	2	no	—
26	C₂×#41×C₄₁	—	2	2	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	—	2	2	no	—
29	C₂×#41×C₄₁	D₄	1	2	yes	—
30	C₂×#41×C₄₁	D₄	1	2	yes	—
31	C₂×#41×C₄₁	D₄	1	2	yes	—
32	C₂×#41×C₄₁	Q₈	1	2	yes	—
33	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
38	#131×C₄₁	—	2	16	no	—
39	#131×C₄₁	—	2	16	no	—
40	C₂×M₁₆×C₄₁	—	2	4	no	—
41	C₂×M₁₆×C₄₁	—	2	1	no	—
42	C₂×M₁₆×C₄₁	—	2	1	no	—
43	C₂×M₁₆×C₄₁	—	2	2	no	—
44	C₂×M₁₆×C₄₁	—	2	2	no	—
45	C₂×M₁₆×C₄₁	—	2	8	no	—
46	C₂×M₁₆×C₄₁	—	2	8	no	—
47	C₂×M₁₆×C₄₁	—	2	2	no	—
48	C₂×M₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂×M₁₆×C₄₁	—	2	2	no	—
52	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	—
53	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
54	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
55	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
56	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
57	C₂²×C₈×C₄₁	—	2	4	no	—
58	C₂²×C₈×C₄₁	—	2	1	no	—
59	C₂²×C₈×C₄₁	—	2	1	no	—
60	C₂²×C₈×C₄₁	—	2	2	no	—
61	#117×C₄₁	—	2	2	no	—
62	#117×C₄₁	—	2	2	no	—
63	#117×C₄₁	—	2	2	no	—
64	#117×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₄₁	—	2	2	no	—
68	#101×C₄₁	—	2	4	no	—
69	#100×C₄₁	—	2	4	no	—
70	#99×C₄₁	—	2	8	no	—
71	C₂⁴×C₄₁	C₄²	1	2	yes	—
72	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
73	#41×C₄₁	—	2	4	no	—
74	#41×C₄₁	—	2	4	no	—
75	#41×C₄₁	—	2	4	no	—
76	#41×C₄₁	—	2	4	no	—
77	#41×C₄₁	—	2	4	no	—
78	#41×C₄₁	—	2	4	no	—
79	#41×C₄₁	—	2	4	no	—
80	#41×C₄₁	—	2	4	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
84	C₂×Q₈×C₄₁	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₄₁	—	2	4	no	—
86	C₂×D₄×C₄₁	—	2	4	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
90	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
91	C₂×D₄×C₄₁	C₄⋊C₄	1	4	yes	—
92	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	4	no	—
98	C₂²×C₄×C₄₁	C₄²	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
101	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	#41	1	2	yes	—
110	C₂²×C₄×C₄₁	#41	1	2	yes	—
111	M₁₆×C₄₁	—	2	16	no	—
112	M₁₆×C₄₁	—	2	2	no	—
113	M₁₆×C₄₁	—	2	2	no	—
114	M₁₆×C₄₁	—	2	4	no	—
115	M₁₆×C₄₁	—	2	4	no	—
116	M₁₆×C₄₁	—	2	4	no	—
117	M₁₆×C₄₁	—	2	4	no	—
118	M₁₆×C₄₁	—	4	2	no	—
119	M₁₆×C₄₁	—	4	2	no	—
120	M₁₆×C₄₁	C₂²⋊C₄	1	4	yes	—
121	M₁₆×C₄₁	C₂²⋊C₄	1	4	yes	—
122	C₂×C₈×C₄₁	—	2	16	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	4	no	—
126	C₂×C₈×C₄₁	—	2	4	no	—
127	C₂×C₈×C₄₁	—	2	4	no	—
128	C₂×C₈×C₄₁	—	4	2	no	—
129	C₂×C₈×C₄₁	—	4	2	no	—
130	C₄⋊C₄×C₄₁	—	4	2	no	—
131	C₄⋊C₄×C₄₁	—	4	2	no	—
132	C₂²⋊C₄×C₄₁	—	2	4	no	—
133	C₂²⋊C₄×C₄₁	—	2	4	no	—
134	C₄²×C₄₁	—	4	2	no	—
135	C₄²×C₄₁	—	4	2	no	—
136	C₂³×C₄₁	—	2	2	no	—
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	8	1	no	—
139	C₂³×C₄₁	—	8	2	no	—
140	C₂³×C₄₁	#95	1	4	yes	—
141	C₂³×C₄₁	C₂×C₄²	1	1	yes	characteristic
142	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₁	C₄×D₄	1	2	yes	—
145	C₂³×C₄₁	C₄×D₄	1	2	yes	—
146	Q₈×C₄₁	—	2	4	no	—
147	Q₈×C₄₁	—	2	4	no	—
148	D₄×C₄₁	—	2	8	no	—
149	D₄×C₄₁	—	2	8	no	—
150	D₄×C₄₁	—	2	4	no	—
151	D₄×C₄₁	—	2	4	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	4	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	4	4	no	—
159	C₂×C₄×C₄₁	—	8	4	no	—
160	C₂×C₄×C₄₁	#95	1	4	yes	—
161	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
168	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₁	#120	1	2	yes	—
172	C₂×C₄×C₄₁	#120	1	2	yes	—
173	C₂×C₄×C₄₁	#121	1	2	yes	—
174	C₂×C₄×C₄₁	#121	1	2	yes	—
175	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₄₁	#123	1	2	yes	—
178	C₂×C₄×C₄₁	#123	1	2	yes	—
179	C₈×C₄₁	—	2	4	no	—
180	C₈×C₄₁	—	2	4	no	—
181	C₈×C₄₁	—	4	4	no	—
182	#10771	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₁	—	2	4	no	—
184	C₂²×C₄₁	—	4	2	no	—
185	C₂²×C₄₁	—	4	1	no	—
186	C₂²×C₄₁	—	4	1	no	—
187	C₂²×C₄₁	—	4	1	no	—
188	C₂²×C₄₁	—	4	2	no	—
189	C₂²×C₄₁	—	4	4	no	—
190	C₂²×C₄₁	—	8	2	no	—
191	C₂²×C₄₁	—	8	2	no	—
192	C₂²×C₄₁	C₂×#95	1	1	yes	characteristic
193	C₂²×C₄₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₁	#385	1	2	yes	—
196	C₂²×C₄₁	#386	1	2	yes	—
197	C₄×C₄₁	—	2	4	no	—
198	C₄×C₄₁	—	8	4	no	—
199	C₄×C₄₁	#379	1	1	yes	characteristic
200	C₄×C₄₁	#380	1	1	yes	characteristic
201	C₄×C₄₁	#380	1	1	yes	characteristic
202	C₄×C₄₁	#381	1	1	yes	characteristic
203	C₄×C₄₁	#385	1	2	yes	—
204	C₄×C₄₁	#386	1	2	yes	—
205	C₂×#568	C₂×C₄₁	1	1	yes	characteristic
206	C₂×#413	C₂×C₄₁	1	1	yes	characteristic
207	C₂×#410	C₂×C₄₁	1	1	yes	characteristic
208	C₂×#344	C₂×C₄₁	1	2	yes	complemented
209	#1742	C₂×C₄₁	1	2	yes	complemented
210	C₂×C₄₁	—	2	2	no	—
211	C₂×C₄₁	—	2	1	no	—
212	C₂×C₄₁	—	2	1	no	—
213	C₂×C₄₁	—	2	1	no	—
214	C₂×C₄₁	—	2	2	no	—
215	C₂×C₄₁	—	4	4	no	—
216	C₂×C₄₁	C₂²⋊#95	1	1	yes	characteristic
217	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
218	#568	—	2	4	no	—
219	#568	—	2	4	no	—
220	C₂×#131	—	2	2	no	—
221	C₂×#131	—	2	2	no	—
222	C₂²×M₁₆	C₄×C₄₁	1	4	yes	complemented
223	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
224	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#117	C₂²×C₄₁	1	2	yes	—
227	#413	—	2	2	no	—
228	#413	—	2	2	no	—
229	C₂×#101	C₄×C₄₁	1	2	yes	complemented
230	C₂×#100	C₄×C₄₁	1	2	yes	complemented
231	#410	—	2	2	no	—
232	#410	—	2	2	no	—
233	C₂×#99	C₄×C₄₁	1	4	yes	—
234	#344	—	2	4	no	—
235	#343	—	2	4	no	—
236	C₄₁	#10771	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	D₄×C₄₁	1	2	yes	—
242	C₂×#41	D₄×C₄₁	1	2	yes	—
243	C₂×#41	D₄×C₄₁	1	2	yes	—
244	C₂×#41	Q₈×C₄₁	1	2	yes	—
245	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
246	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
247	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
248	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
249	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
250	#131	—	2	16	no	—
251	#131	—	2	16	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	8	no	—
258	C₂×M₁₆	—	2	8	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	—
265	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
266	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
267	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
268	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
269	C₂²×C₈	—	2	4	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	2	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
279	C₂×C₄²	—	2	2	no	—
280	#101	—	2	4	no	—
281	#100	—	2	4	no	—
282	#99	—	2	8	no	—
283	C₂⁴	C₄²×C₄₁	1	2	yes	—
284	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
296	C₂×Q₈	C₄⋊C₄×C₄₁	1	2	yes	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
302	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
303	C₂×D₄	C₄⋊C₄×C₄₁	1	4	yes	—
304	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	C₄²×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
312	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
313	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
320	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
321	C₂²×C₄	#41×C₄₁	1	2	yes	—
322	C₂²×C₄	#41×C₄₁	1	2	yes	—
323	M₁₆	—	2	16	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	2	4	no	—
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	4	2	no	—
331	M₁₆	—	4	2	no	—
332	M₁₆	C₂²⋊C₄×C₄₁	1	4	yes	—
333	M₁₆	C₂²⋊C₄×C₄₁	1	4	yes	—
334	C₂×C₈	—	2	16	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	2	no	—
352	C₂³	#95×C₄₁	1	4	yes	—
353	C₂³	C₂×C₄²×C₄₁	1	1	yes	characteristic
354	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
355	C₂³	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
356	C₂³	C₄×D₄×C₄₁	1	2	yes	—
357	C₂³	C₄×D₄×C₄₁	1	2	yes	—
358	Q₈	—	2	4	no	—
359	Q₈	—	2	4	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	8	4	no	—
372	C₂×C₄	#95×C₄₁	1	4	yes	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
379	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
380	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
381	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
382	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
383	C₂×C₄	#120×C₄₁	1	2	yes	—
384	C₂×C₄	#120×C₄₁	1	2	yes	—
385	C₂×C₄	#121×C₄₁	1	2	yes	—
386	C₂×C₄	#121×C₄₁	1	2	yes	—
387	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
388	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
389	C₂×C₄	#123×C₄₁	1	2	yes	—
390	C₂×C₄	#123×C₄₁	1	2	yes	—
391	C₈	—	2	4	no	—
392	C₈	—	2	4	no	—
393	C₈	—	4	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	C₂×#95×C₄₁	1	1	yes	characteristic
404	C₂²	C₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
405	C₂²	C₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
406	C₂²	C₄₁×#385	1	2	yes	—
407	C₂²	C₄₁×#386	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	8	4	no	—
410	C₄	C₄₁×#379	1	1	yes	characteristic
411	C₄	C₄₁×#380	1	1	yes	characteristic
412	C₄	C₄₁×#380	1	1	yes	characteristic
413	C₄	C₄₁×#381	1	1	yes	characteristic
414	C₄	C₄₁×#385	1	2	yes	—
415	C₄	C₄₁×#386	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	2	no	—
421	C₂	—	4	4	no	—
422	C₂	C₄₁×C₂²⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	#381
commutator	C₂³	C₂×C₄²×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂×C₄₁	C₂²⋊#95
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₁×#344	C₂	semidirect
5. C₄₁×#1742	C₂	semidirect
11. C₂²×M₁₆×C₄₁	C₄	semidirect
18. C₂×#101×C₄₁	C₄	semidirect
19. C₂×#100×C₄₁	C₄	semidirect
182. #10771	C₄₁	direct (N × H)
208. C₂×#344	C₂×C₄₁	semidirect
209. #1742	C₂×C₄₁	semidirect
222. C₂²×M₁₆	C₄×C₄₁	semidirect
229. C₂×#101	C₄×C₄₁	semidirect
230. C₂×#100	C₄×C₄₁	semidirect
236. C₄₁	#10771	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#568	2
C₂×C₄₁×#413	2
C₂×C₄₁×#410	2
C₂×C₄₁×#344	2
C₄₁×#1742	2
#10771	41

Subgroups — C41×#10771 #23786972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#10771 #23786972