Subgroups — C₄₁×#23807 #23800008

Order 10496.

1006 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×#441	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₁×#440	C₂	1	2	yes	maximal
3	C₄×C₄⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#124×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2097	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2095	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2094	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2015	C₂	1	2	yes	maximal
10	C₄₁×#2013	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#441	—	2	8	no	—
20	C₄₁×#440	—	2	8	no	—
21	C₂×#107×C₄₁	C₂²	1	2	yes	—
22	C₂×#106×C₄₁	C₂²	1	2	yes	—
23	C₂×#103×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
27	C₂×#97×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#391	C₂²	1	2	yes	—
29	C₄₁×#391	C₂²	1	1	yes	characteristic
30	C₄₁×#390	C₂²	1	1	yes	characteristic
31	C₄₁×#389	—	2	2	no	—
32	C₄₁×#388	—	2	2	no	—
33	C₄₁×#384	C₂²	1	1	yes	characteristic
34	C₄₁×#382	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
36	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
37	C₄³×C₄₁	C₂²	1	1	yes	characteristic
38	C₄₁×#336	C₂²	1	1	yes	characteristic
39	C₄₁×#336	C₂²	1	2	yes	—
40	C₄₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂×Q₁₆×C₄₁	—	2	4	no	—
46	C₂×Q₁₆×C₄₁	—	2	4	no	—
47	C₂×Q₁₆×C₄₁	—	2	4	no	—
48	C₂×SD₁₆×C₄₁	—	2	4	no	—
49	C₂×SD₁₆×C₄₁	—	2	4	no	—
50	C₂×SD₁₆×C₄₁	—	2	4	no	—
51	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₄₁	—	2	4	no	—
54	#124×C₄₁	—	2	2	no	—
55	#124×C₄₁	—	2	2	no	—
56	C₄×Q₈×C₄₁	—	2	4	no	—
57	C₄×Q₈×C₄₁	—	2	4	no	—
58	C₄×Q₈×C₄₁	—	2	4	no	—
59	C₄×D₄×C₄₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₄²×C₄₁	—	2	1	no	—
71	C₂×C₄²×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	D₄	1	2	yes	—
73	C₂×C₄²×C₄₁	D₄	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
77	#107×C₄₁	—	2	4	no	—
78	#106×C₄₁	—	2	4	no	—
79	#103×C₄₁	—	2	4	no	—
80	#103×C₄₁	—	2	4	no	—
81	#103×C₄₁	—	2	4	no	—
82	#102×C₄₁	—	2	4	no	—
83	#97×C₄₁	D₄	1	8	yes	—
84	#95×C₄₁	—	2	2	no	—
85	#95×C₄₁	—	2	2	no	—
86	#95×C₄₁	—	2	4	no	—
87	C₂⁴×C₄₁	—	2	1	no	—
88	C₂×Q₈×C₄₁	—	2	1	no	—
89	C₂×Q₈×C₄₁	—	2	2	no	—
90	C₂×Q₈×C₄₁	—	2	2	no	—
91	C₂×Q₈×C₄₁	—	2	2	no	—
92	C₂×Q₈×C₄₁	—	2	2	no	—
93	C₂×Q₈×C₄₁	—	2	2	no	—
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	#41	1	2	yes	—
97	C₂×Q₈×C₄₁	#41	1	4	yes	—
98	C₂×D₄×C₄₁	—	2	2	no	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	1	no	—
101	C₂×D₄×C₄₁	#41	1	2	yes	—
102	C₂²×C₄×C₄₁	—	2	1	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	1	no	—
105	C₂²×C₄×C₄₁	—	2	1	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	4	4	no	—
108	C₂²×C₄×C₄₁	—	4	2	no	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₄₁	—	2	16	no	—
115	SD₁₆×C₄₁	—	2	16	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	2	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
122	C₄⋊C₄×C₄₁	—	2	8	no	—
123	C₄⋊C₄×C₄₁	—	2	2	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	2	no	—
127	C₄⋊C₄×C₄₁	—	4	4	no	—
128	C₄⋊C₄×C₄₁	—	4	2	no	—
129	C₄⋊C₄×C₄₁	—	4	4	no	—
130	C₂²⋊C₄×C₄₁	—	2	8	no	—
131	C₂²⋊C₄×C₄₁	—	4	2	no	—
132	C₂²⋊C₄×C₄₁	—	4	4	no	—
133	C₄²×C₄₁	—	2	4	no	—
134	C₄²×C₄₁	—	2	1	no	—
135	C₄²×C₄₁	—	2	1	no	—
136	C₄²×C₄₁	—	2	2	no	—
137	C₄²×C₄₁	—	4	2	no	—
138	C₄²×C₄₁	—	4	4	no	—
139	C₄²×C₄₁	—	4	2	no	—
140	C₄²×C₄₁	C₂×D₄	1	4	yes	—
141	C₂³×C₄₁	—	2	2	no	—
142	C₂³×C₄₁	—	4	1	no	—
143	C₂³×C₄₁	—	4	1	no	—
144	C₂³×C₄₁	—	4	2	no	—
145	C₂³×C₄₁	—	4	2	no	—
146	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₁	—	2	4	no	—
148	Q₈×C₄₁	—	2	4	no	—
149	Q₈×C₄₁	—	2	4	no	—
150	Q₈×C₄₁	—	4	2	no	—
151	Q₈×C₄₁	—	4	2	no	—
152	Q₈×C₄₁	—	4	2	no	—
153	D₄×C₄₁	—	2	4	no	—
154	D₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	4	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	1	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	1	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	4	1	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	4	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	8	4	no	—
175	C₂×C₄×C₄₁	#127	1	2	yes	—
176	C₂×C₄×C₄₁	#127	1	2	yes	—
177	C₂×C₄×C₄₁	#137	1	4	yes	—
178	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
180	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
182	C₈×C₄₁	—	2	4	no	—
183	C₈×C₄₁	—	2	4	no	—
184	#23807	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₁	—	4	4	no	—
186	C₂²×C₄₁	—	4	2	no	—
187	C₂²×C₄₁	—	8	2	no	—
188	C₂²×C₄₁	—	8	1	no	—
189	C₂²×C₄₁	—	8	1	no	—
190	C₂²×C₄₁	#525	1	1	yes	characteristic
191	C₂²×C₄₁	#525	1	1	yes	characteristic
192	C₂²×C₄₁	C₂×#127	1	1	yes	characteristic
193	C₂²×C₄₁	C₂×#137	1	2	yes	—
194	C₂²×C₄₁	#575	1	2	yes	—
195	C₄×C₄₁	—	2	4	no	—
196	C₄×C₄₁	—	2	2	no	—
197	C₄×C₄₁	—	2	2	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	—	4	2	no	—
200	C₄×C₄₁	—	4	4	no	—
201	C₄×C₄₁	—	8	1	no	—
202	C₄×C₄₁	—	8	2	no	—
203	C₄×C₄₁	—	8	1	no	—
204	C₄×C₄₁	#525	1	2	yes	—
205	C₄×C₄₁	#525	1	2	yes	—
206	C₂×#441	C₂×C₄₁	1	2	yes	complemented
207	C₂×#440	C₂×C₄₁	1	2	yes	—
208	C₄×C₄⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
209	C₄×#124	C₂×C₄₁	1	1	yes	characteristic
210	#2097	C₂×C₄₁	1	2	yes	complemented
211	#2095	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#2094	C₂×C₄₁	1	1	yes	characteristic
213	#2016	C₂×C₄₁	1	1	yes	characteristic, complemented
214	#2015	C₂×C₄₁	1	2	yes	—
215	#2013	C₂×C₄₁	1	1	yes	characteristic
216	#1745	C₂×C₄₁	1	1	yes	characteristic, complemented
217	C₂×C₄₁	—	8	2	no	—
218	C₂×C₄₁	#2397	1	1	yes	characteristic
219	C₂×C₄₁	#3116	1	2	yes	—
220	C₂×C₄₁	#3117	1	2	yes	—
221	C₂×C₄₁	#3152	1	1	yes	characteristic
222	C₂×C₄₁	#3153	1	1	yes	characteristic
223	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
224	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
225	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
230	#441	—	2	8	no	—
231	#440	—	2	8	no	—
232	C₂×#107	C₂²×C₄₁	1	2	yes	—
233	C₂×#106	C₂²×C₄₁	1	2	yes	—
234	C₂×#103	C₂²×C₄₁	1	2	yes	—
235	C₂×#103	C₂²×C₄₁	1	2	yes	—
236	C₂×#103	C₂²×C₄₁	1	2	yes	—
237	C₂×#102	C₂²×C₄₁	1	2	yes	—
238	C₂×#97	C₂²×C₄₁	1	2	yes	—
239	#391	C₂²×C₄₁	1	2	yes	—
240	#391	C₂²×C₄₁	1	1	yes	characteristic
241	#390	C₂²×C₄₁	1	1	yes	characteristic
242	#389	—	2	2	no	—
243	#388	—	2	2	no	—
244	#384	C₂²×C₄₁	1	1	yes	characteristic
245	#382	C₂²×C₄₁	1	1	yes	characteristic
246	C₄×C₄⋊C₄	—	2	2	no	—
247	C₄×C₂²⋊C₄	—	2	2	no	—
248	C₄³	C₂²×C₄₁	1	1	yes	characteristic
249	#336	C₂²×C₄₁	1	1	yes	characteristic
250	#336	C₂²×C₄₁	1	1	yes	characteristic
251	#336	C₂²×C₄₁	1	2	yes	—
252	C₄₁	#23807	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
255	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂×Q₁₆	—	2	4	no	—
258	C₂×Q₁₆	—	2	4	no	—
259	C₂×Q₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	2	4	no	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
264	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
265	C₄⋊Q₈	—	2	4	no	—
266	#124	—	2	2	no	—
267	#124	—	2	2	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	D₄×C₄₁	1	2	yes	—
285	C₂×C₄²	D₄×C₄₁	1	2	yes	—
286	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
289	#107	—	2	4	no	—
290	#106	—	2	4	no	—
291	#103	—	2	4	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	#102	—	2	4	no	—
295	#97	D₄×C₄₁	1	8	yes	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	4	no	—
299	C₂⁴	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	#41×C₄₁	1	2	yes	—
309	C₂×Q₈	#41×C₄₁	1	4	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	#41×C₄₁	1	2	yes	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
326	Q₁₆	—	2	16	no	—
327	SD₁₆	—	2	16	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
333	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	4	no	—
351	C₄²	—	4	2	no	—
352	C₄²	C₂×D₄×C₄₁	1	4	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	Q₈	—	2	4	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	4	no	—
387	C₂×C₄	#127×C₄₁	1	2	yes	—
388	C₂×C₄	#127×C₄₁	1	2	yes	—
389	C₂×C₄	#137×C₄₁	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
391	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
392	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
394	C₈	—	2	4	no	—
395	C₈	—	2	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₄₁×#525	1	1	yes	characteristic
402	C₂²	C₄₁×#525	1	1	yes	characteristic
403	C₂²	C₂×#127×C₄₁	1	1	yes	characteristic
404	C₂²	C₂×#137×C₄₁	1	2	yes	—
405	C₂²	C₄₁×#575	1	2	yes	—
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	1	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	2	no	—
415	C₄	C₄₁×#525	1	2	yes	—
416	C₄	C₄₁×#525	1	2	yes	—
417	C₂	—	8	2	no	—
418	C₂	C₄₁×#2397	1	1	yes	characteristic
419	C₂	C₄₁×#3116	1	2	yes	—
420	C₂	C₄₁×#3117	1	2	yes	—
421	C₂	C₄₁×#3152	1	1	yes	characteristic
422	C₂	C₄₁×#3153	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#441	C₂	semidirect
3. C₄×C₄⋊Q₈×C₄₁	C₂	semidirect
5. C₄₁×#2097	C₂	semidirect
6. C₄₁×#2095	C₂	semidirect
8. C₄₁×#2016	C₂	semidirect
11. C₄₁×#1745	C₂	semidirect
184. #23807	C₄₁	direct (N × H)
206. C₂×#441	C₂×C₄₁	semidirect
208. C₄×C₄⋊Q₈	C₂×C₄₁	semidirect
210. #2097	C₂×C₄₁	semidirect
211. #2095	C₂×C₄₁	semidirect
213. #2016	C₂×C₄₁	semidirect
216. #1745	C₂×C₄₁	semidirect
252. C₄₁	#23807	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×#441	2
C₂×C₄₁×#440	2
C₄×C₄⋊Q₈×C₄₁	2
C₄×#124×C₄₁	2
C₄₁×#2097	2
C₄₁×#2095	2
C₄₁×#2094	2
C₄₁×#2016	2
C₄₁×#2015	2
C₄₁×#2013	2
C₄₁×#1745	2
#23807	41

Subgroups — C41×#23807 #23800008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23807 #23800008