Subgroups — C₄₁×#9681 #23785882

Order 10496.

668 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2850	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#328	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#327	C₂	1	2	yes	maximal
5	C₄₁×#1434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#124×C₄₁	C₄	1	1	yes	characteristic, complemented
7	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₄₁	—	2	1	no	—
12	C₄₁×#391	C₄	1	1	yes	characteristic, complemented
13	C₄₁×#390	C₄	1	1	yes	characteristic, complemented
14	C₄₁×#388	—	2	1	no	—
15	C₄₁×#388	—	2	1	no	—
16	C₄₁×#386	—	2	1	no	—
17	C₄₁×#386	—	2	1	no	—
18	C₄₁×#382	C₄	1	1	yes	characteristic, complemented
19	C₂×#95×C₄₁	—	2	1	no	—
20	C₂×#95×C₄₁	—	2	1	no	—
21	C₂×#95×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#336	—	2	1	no	—
23	C₄₁×#328	—	2	4	no	—
24	C₄₁×#327	—	2	4	no	—
25	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₄₁	—	2	1	no	—
27	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₁	—	2	2	no	—
29	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₄₁	—	2	2	no	—
33	#124×C₄₁	—	4	2	no	—
34	C₂²⋊Q₈×C₄₁	—	2	2	no	—
35	C₂²⋊Q₈×C₄₁	—	2	2	no	—
36	#121×C₄₁	—	2	2	no	—
37	#121×C₄₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
39	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
47	C₂×C₄²×C₄₁	—	4	2	no	—
48	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
52	C₂²⋊C₈×C₄₁	—	2	2	no	—
53	C₂²⋊C₈×C₄₁	D₄	1	4	yes	—
54	C₄×C₈×C₄₁	—	4	2	no	—
55	#95×C₄₁	—	2	4	no	—
56	#95×C₄₁	—	2	1	no	—
57	#95×C₄₁	—	2	1	no	—
58	#95×C₄₁	—	2	1	no	—
59	#95×C₄₁	—	2	1	no	—
60	#95×C₄₁	—	2	2	no	—
61	#95×C₄₁	—	2	2	no	—
62	#95×C₄₁	—	4	2	no	—
63	C₂⁴×C₄₁	—	2	1	no	—
64	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
65	C₂×Q₈×C₄₁	—	2	2	no	—
66	C₂×Q₈×C₄₁	—	4	1	no	—
67	C₂×Q₈×C₄₁	—	4	1	no	—
68	C₂×D₄×C₄₁	—	2	2	no	—
69	C₂×D₄×C₄₁	—	4	1	no	—
70	C₂×D₄×C₄₁	—	4	1	no	—
71	C₂×D₄×C₄₁	—	4	1	no	—
72	C₂×D₄×C₄₁	—	4	1	no	—
73	C₂×D₄×C₄₁	—	4	2	no	—
74	C₂×D₄×C₄₁	—	4	2	no	—
75	C₂²×C₄×C₄₁	—	2	2	no	—
76	C₂²×C₄×C₄₁	—	2	2	no	—
77	C₂²×C₄×C₄₁	—	2	2	no	—
78	C₂²×C₄×C₄₁	—	2	2	no	—
79	C₂²×C₄×C₄₁	—	2	4	no	—
80	C₂²×C₄×C₄₁	—	2	1	no	—
81	C₂²×C₄×C₄₁	—	2	1	no	—
82	C₂²×C₄×C₄₁	—	2	1	no	—
83	C₂²×C₄×C₄₁	—	4	1	no	—
84	C₂²×C₄×C₄₁	—	4	1	no	—
85	C₂²×C₄×C₄₁	—	4	1	no	—
86	C₂²×C₄×C₄₁	—	4	1	no	—
87	C₂²×C₄×C₄₁	—	4	2	no	—
88	C₂²×C₄×C₄₁	—	4	2	no	—
89	C₂²×C₄×C₄₁	—	4	2	no	—
90	C₂²×C₄×C₄₁	—	4	2	no	—
91	C₂²×C₄×C₄₁	—	4	2	no	—
92	C₂²×C₄×C₄₁	—	4	2	no	—
93	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₁	#41	1	2	yes	—
101	C₂×C₈×C₄₁	—	2	4	no	—
102	C₂×C₈×C₄₁	—	4	2	no	—
103	C₂×C₈×C₄₁	—	4	2	no	—
104	C₄⋊C₄×C₄₁	—	2	2	no	—
105	C₄⋊C₄×C₄₁	—	2	2	no	—
106	C₄⋊C₄×C₄₁	—	4	2	no	—
107	C₂²⋊C₄×C₄₁	—	4	2	no	—
108	C₂²⋊C₄×C₄₁	—	4	2	no	—
109	C₂²⋊C₄×C₄₁	—	4	1	no	—
110	C₂²⋊C₄×C₄₁	—	4	1	no	—
111	C₂²⋊C₄×C₄₁	—	4	2	no	—
112	C₂²⋊C₄×C₄₁	—	4	2	no	—
113	C₂²⋊C₄×C₄₁	—	4	2	no	—
114	C₄²×C₄₁	—	2	2	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	4	1	no	—
117	C₄²×C₄₁	—	4	1	no	—
118	C₂³×C₄₁	—	2	1	no	—
119	C₂³×C₄₁	—	2	1	no	—
120	C₂³×C₄₁	—	2	1	no	—
121	C₂³×C₄₁	—	2	1	no	—
122	C₂³×C₄₁	—	4	1	no	—
123	C₂³×C₄₁	—	4	1	no	—
124	C₂³×C₄₁	—	4	1	no	—
125	C₂³×C₄₁	—	4	1	no	—
126	C₂³×C₄₁	—	4	1	no	—
127	C₂³×C₄₁	—	4	1	no	—
128	C₂³×C₄₁	—	4	1	no	—
129	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₁	#124	1	1	yes	characteristic
131	C₂³×C₄₁	#127	1	1	yes	characteristic
132	C₂³×C₄₁	#135	1	2	yes	—
133	C₂³×C₄₁	#135	1	2	yes	—
134	Q₈×C₄₁	—	8	2	no	—
135	D₄×C₄₁	—	8	2	no	—
136	D₄×C₄₁	—	8	2	no	—
137	D₄×C₄₁	—	8	2	no	—
138	C₂×C₄×C₄₁	—	2	1	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	1	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	1	no	—
144	C₂×C₄×C₄₁	—	2	1	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	1	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	1	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	4	no	—
155	C₂×C₄×C₄₁	—	4	4	no	—
156	C₂×C₄×C₄₁	—	4	4	no	—
157	C₂×C₄×C₄₁	—	4	4	no	—
158	C₂×C₄×C₄₁	—	4	4	no	—
159	C₂×C₄×C₄₁	—	4	1	no	—
160	C₂×C₄×C₄₁	—	4	1	no	—
161	C₂×C₄×C₄₁	—	4	1	no	—
162	C₂×C₄×C₄₁	—	4	1	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	—	4	1	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	1	no	—
167	C₂×C₄×C₄₁	—	4	1	no	—
168	C₂×C₄×C₄₁	—	8	2	no	—
169	C₂×C₄×C₄₁	—	8	2	no	—
170	C₂×C₄×C₄₁	—	8	2	no	—
171	C₂×C₄×C₄₁	—	8	2	no	—
172	C₂×C₄×C₄₁	#99	1	2	yes	—
173	C₂×C₄×C₄₁	#104	1	2	yes	—
174	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₁	#121	1	2	yes	—
176	C₈×C₄₁	—	4	4	no	—
177	#9681	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₄₁	—	2	1	no	—
179	C₂²×C₄₁	—	2	1	no	—
180	C₂²×C₄₁	—	2	1	no	—
181	C₂²×C₄₁	—	2	1	no	—
182	C₂²×C₄₁	—	2	2	no	—
183	C₂²×C₄₁	—	2	2	no	—
184	C₂²×C₄₁	—	2	2	no	—
185	C₂²×C₄₁	—	2	2	no	—
186	C₂²×C₄₁	—	8	1	no	—
187	C₂²×C₄₁	—	8	1	no	—
188	C₂²×C₄₁	—	8	1	no	—
189	C₂²×C₄₁	—	8	1	no	—
190	C₂²×C₄₁	—	8	1	no	—
191	C₂²×C₄₁	—	8	1	no	—
192	C₂²×C₄₁	—	8	1	no	—
193	C₂²×C₄₁	#390	1	1	yes	characteristic
194	C₂²×C₄₁	C₂×#99	1	1	yes	characteristic
195	C₂²×C₄₁	#410	1	1	yes	characteristic
196	C₂²×C₄₁	#416	1	1	yes	characteristic
197	C₂²×C₄₁	#416	1	1	yes	characteristic
198	C₂²×C₄₁	C₂×#104	1	1	yes	characteristic
199	C₂²×C₄₁	#421	1	1	yes	characteristic
200	C₂²×C₄₁	#488	1	2	yes	—
201	C₂²×C₄₁	#495	1	2	yes	—
202	C₄×C₄₁	—	2	2	no	—
203	C₄×C₄₁	—	2	2	no	—
204	C₄×C₄₁	—	2	2	no	—
205	C₄×C₄₁	—	2	2	no	—
206	C₄×C₄₁	—	4	1	no	—
207	C₄×C₄₁	—	4	1	no	—
208	C₄×C₄₁	—	8	4	no	—
209	C₄×C₄₁	—	8	1	no	—
210	C₄×C₄₁	—	8	1	no	—
211	C₄×C₄₁	—	8	1	no	—
212	#2850	C₂×C₄₁	1	1	yes	characteristic
213	C₄×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
214	C₂×#328	C₂×C₄₁	1	2	yes	complemented
215	C₂×#327	C₂×C₄₁	1	2	yes	—
216	#1434	C₂×C₄₁	1	1	yes	characteristic, complemented
217	C₂×C₄₁	—	2	2	no	—
218	C₂×C₄₁	—	2	2	no	—
219	C₂×C₄₁	—	16	1	no	—
220	C₂×C₄₁	#1500	1	1	yes	characteristic
221	C₂×C₄₁	#1501	1	1	yes	characteristic
222	C₂×C₄₁	#1516	1	1	yes	characteristic
223	C₂×C₄₁	#1521	1	1	yes	characteristic
224	C₂×C₄₁	#1958	1	1	yes	characteristic
225	C₂×C₄₁	#1964	1	1	yes	characteristic
226	C₂×C₄₁	#1980	1	1	yes	characteristic
227	C₂×#124	C₄×C₄₁	1	1	yes	characteristic, complemented
228	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
230	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
232	C₂×C₄×C₈	—	2	1	no	—
233	#391	C₄×C₄₁	1	1	yes	characteristic, complemented
234	#390	C₄×C₄₁	1	1	yes	characteristic, complemented
235	#388	—	2	1	no	—
236	#388	—	2	1	no	—
237	#386	—	2	1	no	—
238	#386	—	2	1	no	—
239	#382	C₄×C₄₁	1	1	yes	characteristic, complemented
240	C₂×#95	—	2	1	no	—
241	C₂×#95	—	2	1	no	—
242	C₂×#95	C₂²×C₄₁	1	2	yes	—
243	#336	—	2	1	no	—
244	#328	—	2	4	no	—
245	#327	—	2	4	no	—
246	C₄₁	#9681	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
252	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
254	C₂²×C₈	—	2	2	no	—
255	#124	—	4	2	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	—	2	2	no	—
258	#121	—	2	2	no	—
259	#121	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₄²	—	4	2	no	—
270	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
271	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
272	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	D₄×C₄₁	1	4	yes	—
276	C₄×C₈	—	4	2	no	—
277	#95	—	2	4	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	#95	—	2	1	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	4	2	no	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
316	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
318	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
322	C₂²×C₄	#41×C₄₁	1	2	yes	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
352	C₂³	#124×C₄₁	1	1	yes	characteristic
353	C₂³	#127×C₄₁	1	1	yes	characteristic
354	C₂³	#135×C₄₁	1	2	yes	—
355	C₂³	#135×C₄₁	1	2	yes	—
356	Q₈	—	8	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	8	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	#99×C₄₁	1	2	yes	—
395	C₂×C₄	#104×C₄₁	1	2	yes	—
396	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
397	C₂×C₄	#121×C₄₁	1	2	yes	—
398	C₈	—	4	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	C₄₁×#390	1	1	yes	characteristic
415	C₂²	C₂×#99×C₄₁	1	1	yes	characteristic
416	C₂²	C₄₁×#410	1	1	yes	characteristic
417	C₂²	C₄₁×#416	1	1	yes	characteristic
418	C₂²	C₄₁×#416	1	1	yes	characteristic
419	C₂²	C₂×#104×C₄₁	1	1	yes	characteristic
420	C₂²	C₄₁×#421	1	1	yes	characteristic
421	C₂²	C₄₁×#488	1	2	yes	—
422	C₂²	C₄₁×#495	1	2	yes	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	4	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₂	—	2	2	no	—
434	C₂	—	2	2	no	—
435	C₂	—	16	1	no	—
436	C₂	C₄₁×#1500	1	1	yes	characteristic
437	C₂	C₄₁×#1501	1	1	yes	characteristic
438	C₂	C₄₁×#1516	1	1	yes	characteristic
439	C₂	C₄₁×#1521	1	1	yes	characteristic
440	C₂	C₄₁×#1958	1	1	yes	characteristic
441	C₂	C₄₁×#1964	1	1	yes	characteristic
442	C₂	C₄₁×#1980	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂²⋊C₈×C₄₁	C₂	semidirect
3. C₂×C₄₁×#328	C₂	semidirect
5. C₄₁×#1434	C₂	semidirect
6. C₂×#124×C₄₁	C₄	semidirect
12. C₄₁×#391	C₄	semidirect
13. C₄₁×#390	C₄	semidirect
18. C₄₁×#382	C₄	semidirect
177. #9681	C₄₁	direct (N × H)
213. C₄×C₂²⋊C₈	C₂×C₄₁	semidirect
214. C₂×#328	C₂×C₄₁	semidirect
216. #1434	C₂×C₄₁	semidirect
227. C₂×#124	C₄×C₄₁	semidirect
233. #391	C₄×C₄₁	semidirect
234. #390	C₄×C₄₁	semidirect
239. #382	C₄×C₄₁	semidirect
246. C₄₁	#9681	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2850	2
C₄×C₂²⋊C₈×C₄₁	2
C₂×C₄₁×#328	2
C₂×C₄₁×#327	2
C₄₁×#1434	2
#9681	41

Subgroups — C41×#9681 #23785882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#9681 #23785882