Subgroups — C₄₁×#20822 #23797023

Order 10496.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2314	C₂	1	2	yes	maximal
3	C₄₁×#1847	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1809	C₂	1	2	yes	maximal
7	C₄₁×#1808	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1807	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1776	C₂	1	2	yes	maximal, complemented
10	C₄×#107×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#106×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#107×C₄₁	C₂²	1	2	yes	—
16	C₂×#107×C₄₁	C₂²	1	2	yes	—
17	C₂×#106×C₄₁	C₂²	1	2	yes	—
18	C₂×#106×C₄₁	C₂²	1	2	yes	—
19	C₄₁×#405	C₄	1	8	yes	complemented
20	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#388	—	2	2	no	—
25	C₄₁×#388	—	2	2	no	—
26	C₄₁×#387	—	2	2	no	—
27	C₄₁×#387	—	2	2	no	—
28	C₄₁×#384	C₂²	1	2	yes	—
29	C₄₁×#382	C₂²	1	2	yes	—
30	C₄₁×#380	C₂²	1	2	yes	—
31	C₄₁×#380	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
34	C₄₁×#340	C₂²	1	1	yes	characteristic
35	C₄₁×#340	C₂²	1	1	yes	characteristic
36	C₄₁×#340	C₂²	1	1	yes	characteristic
37	C₄₁×#340	C₂²	1	1	yes	characteristic
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₄₁	—	2	4	no	—
42	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₄₁	—	2	4	no	—
44	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
49	#117×C₄₁	C₂×C₄	1	4	yes	—
50	#117×C₄₁	Q₈	1	4	yes	—
51	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₁	—	2	2	no	—
64	C₂×C₄²×C₄₁	—	2	2	no	—
65	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
67	#107×C₄₁	—	2	4	no	—
68	#107×C₄₁	—	2	4	no	—
69	#106×C₄₁	—	2	4	no	—
70	#106×C₄₁	—	2	4	no	—
71	#97×C₄₁	C₂×C₄	1	4	yes	—
72	#97×C₄₁	C₂×C₄	1	4	yes	—
73	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	—
74	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	—
75	#95×C₄₁	—	2	2	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	2	no	—
78	#95×C₄₁	—	2	2	no	—
79	#95×C₄₁	—	2	2	no	—
80	#95×C₄₁	—	2	2	no	—
81	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	2	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₄₁	—	2	8	no	—
97	C₂×C₈×C₄₁	—	2	2	no	—
98	C₂×C₈×C₄₁	—	2	2	no	—
99	C₂×C₈×C₄₁	—	2	8	no	—
100	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₁	#41	1	4	yes	—
105	C₂×C₈×C₄₁	#41	1	4	yes	—
106	C₄⋊C₄×C₄₁	—	2	2	no	—
107	C₄⋊C₄×C₄₁	—	2	2	no	—
108	C₄⋊C₄×C₄₁	—	2	2	no	—
109	C₄⋊C₄×C₄₁	—	2	2	no	—
110	C₄⋊C₄×C₄₁	—	2	2	no	—
111	C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₄⋊C₄×C₄₁	—	2	2	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	8	2	no	—
115	C₄⋊C₄×C₄₁	—	8	2	no	—
116	C₄⋊C₄×C₄₁	C₄⋊C₄	1	4	yes	—
117	C₄⋊C₄×C₄₁	C₄⋊C₄	1	4	yes	—
118	C₂²⋊C₄×C₄₁	—	8	2	no	—
119	C₂²⋊C₄×C₄₁	—	8	2	no	—
120	C₂²⋊C₄×C₄₁	C₄⋊C₄	1	4	yes	—
121	C₂²⋊C₄×C₄₁	C₄⋊C₄	1	4	yes	—
122	C₄²×C₄₁	—	8	2	no	—
123	C₄²×C₄₁	—	8	2	no	—
124	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
125	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
127	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
128	C₂³×C₄₁	—	2	2	no	—
129	C₂³×C₄₁	—	2	1	no	—
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	2	1	no	—
132	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
133	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	1	no	—
136	C₂×C₄×C₄₁	—	2	1	no	—
137	C₂×C₄×C₄₁	—	2	2	no	—
138	C₂×C₄×C₄₁	—	2	2	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	2	2	no	—
143	C₂×C₄×C₄₁	—	2	4	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	4	2	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
164	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
165	C₈×C₄₁	—	2	2	no	—
166	C₈×C₄₁	—	2	2	no	—
167	C₈×C₄₁	#117	1	4	yes	—
168	C₈×C₄₁	#117	1	4	yes	—
169	#20822	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₁	—	2	2	no	—
171	C₂²×C₄₁	—	2	2	no	—
172	C₂²×C₄₁	—	2	2	no	—
173	C₂²×C₄₁	—	4	2	no	—
174	C₂²×C₄₁	—	4	2	no	—
175	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₁	#532	1	2	yes	—
177	C₂²×C₄₁	#576	1	1	yes	characteristic
178	C₂²×C₄₁	#577	1	2	yes	—
179	C₂²×C₄₁	#578	1	1	yes	characteristic
180	C₄×C₄₁	—	2	2	no	—
181	C₄×C₄₁	—	2	2	no	—
182	C₄×C₄₁	—	2	2	no	—
183	C₄×C₄₁	—	2	2	no	—
184	C₄×C₄₁	—	2	2	no	—
185	C₄×C₄₁	—	8	2	no	—
186	C₄×C₄₁	—	8	2	no	—
187	C₄×C₄₁	—	8	2	no	—
188	C₄×C₄₁	—	8	2	no	—
189	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
190	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
191	C₄×C₄₁	#533	1	2	yes	—
192	C₂×#405	C₂×C₄₁	1	1	yes	characteristic
193	#2314	C₂×C₄₁	1	2	yes	—
194	#1847	C₂×C₄₁	1	2	yes	complemented
195	#1835	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#1834	C₂×C₄₁	1	1	yes	characteristic, complemented
197	#1809	C₂×C₄₁	1	2	yes	—
198	#1808	C₂×C₄₁	1	1	yes	characteristic
199	#1807	C₂×C₄₁	1	1	yes	characteristic
200	#1776	C₂×C₄₁	1	2	yes	complemented
201	C₄×#107	C₂×C₄₁	1	1	yes	characteristic, complemented
202	C₄×#106	C₂×C₄₁	1	1	yes	characteristic, complemented
203	C₂×C₄₁	—	4	2	no	—
204	C₂×C₄₁	#2285	1	1	yes	characteristic
205	C₂×C₄₁	#2912	1	1	yes	characteristic
206	C₂×C₄₁	#2913	1	1	yes	characteristic
207	C₂×C₄₁	#3178	1	2	yes	—
208	C₂×C₄₁	#3179	1	2	yes	—
209	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
212	C₂×#107	C₂²×C₄₁	1	2	yes	—
213	C₂×#107	C₂²×C₄₁	1	2	yes	—
214	C₂×#106	C₂²×C₄₁	1	2	yes	—
215	C₂×#106	C₂²×C₄₁	1	2	yes	—
216	#405	C₄×C₄₁	1	8	yes	complemented
217	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
221	#388	—	2	2	no	—
222	#388	—	2	2	no	—
223	#387	—	2	2	no	—
224	#387	—	2	2	no	—
225	#384	C₂²×C₄₁	1	2	yes	—
226	#382	C₂²×C₄₁	1	2	yes	—
227	#380	C₂²×C₄₁	1	2	yes	—
228	#380	C₂²×C₄₁	1	2	yes	—
229	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
231	#340	C₂²×C₄₁	1	1	yes	characteristic
232	#340	C₂²×C₄₁	1	1	yes	characteristic
233	#340	C₂²×C₄₁	1	1	yes	characteristic
234	#340	C₂²×C₄₁	1	1	yes	characteristic
235	#340	C₂²×C₄₁	1	2	yes	—
236	#340	C₂²×C₄₁	1	2	yes	—
237	C₄₁	#20822	1	1	yes	characteristic, direct product factor, Sylow
238	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
243	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
247	#117	C₂×C₄×C₄₁	1	4	yes	—
248	#117	Q₈×C₄₁	1	4	yes	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
252	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
265	#107	—	2	4	no	—
266	#107	—	2	4	no	—
267	#106	—	2	4	no	—
268	#106	—	2	4	no	—
269	#97	C₂×C₄×C₄₁	1	4	yes	—
270	#97	C₂×C₄×C₄₁	1	4	yes	—
271	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	—
272	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
294	M₁₆	—	2	8	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	8	no	—
298	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
299	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
300	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
301	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
302	C₂×C₈	#41×C₄₁	1	4	yes	—
303	C₂×C₈	#41×C₄₁	1	4	yes	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	8	2	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₄⋊C₄	C₄⋊C₄×C₄₁	1	4	yes	—
315	C₄⋊C₄	C₄⋊C₄×C₄₁	1	4	yes	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	C₄⋊C₄×C₄₁	1	4	yes	—
319	C₂²⋊C₄	C₄⋊C₄×C₄₁	1	4	yes	—
320	C₄²	—	8	2	no	—
321	C₄²	—	8	2	no	—
322	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
323	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
324	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
325	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
331	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
355	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
356	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
357	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
358	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
359	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
362	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	#117×C₄₁	1	4	yes	—
366	C₈	#117×C₄₁	1	4	yes	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
373	C₂²	C₄₁×#532	1	2	yes	—
374	C₂²	C₄₁×#576	1	1	yes	characteristic
375	C₂²	C₄₁×#577	1	2	yes	—
376	C₂²	C₄₁×#578	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
387	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
388	C₄	C₄₁×#533	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	C₄₁×#2285	1	1	yes	characteristic
391	C₂	C₄₁×#2912	1	1	yes	characteristic
392	C₂	C₄₁×#2913	1	1	yes	characteristic
393	C₂	C₄₁×#3178	1	2	yes	—
394	C₂	C₄₁×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1847	C₂	semidirect
4. C₄₁×#1835	C₂	semidirect
5. C₄₁×#1834	C₂	semidirect
9. C₄₁×#1776	C₂	semidirect
10. C₄×#107×C₄₁	C₂	semidirect
11. C₄×#106×C₄₁	C₂	semidirect
19. C₄₁×#405	C₄	semidirect
169. #20822	C₄₁	direct (N × H)
194. #1847	C₂×C₄₁	semidirect
195. #1835	C₂×C₄₁	semidirect
196. #1834	C₂×C₄₁	semidirect
200. #1776	C₂×C₄₁	semidirect
201. C₄×#107	C₂×C₄₁	semidirect
202. C₄×#106	C₂×C₄₁	semidirect
216. #405	C₄×C₄₁	semidirect
237. C₄₁	#20822	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×#405	2
C₄₁×#2314	2
C₄₁×#1847	2
C₄₁×#1835	2
C₄₁×#1834	2
C₄₁×#1809	2
C₄₁×#1808	2
C₄₁×#1807	2
C₄₁×#1776	2
C₄×#107×C₄₁	2
C₄×#106×C₄₁	2
#20822	41

Subgroups — C41×#20822 #23797023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20822 #23797023