Subgroups — C₄₁×#21870 #23798071

Order 10496.

1086 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1993	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1960	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1873	C₂	1	4	yes	maximal
7	C₄₁×#1803	C₂	1	4	yes	maximal, complemented
8	C₄₁×#533	—	2	4	no	—
9	C₄₁×#533	C₄	1	8	yes	complemented
10	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#125×C₄₁	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×#117×C₄₁	—	2	1	no	—
18	C₂×#117×C₄₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#432	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
22	C₂×#103×C₄₁	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×#97×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#384	C₂²	1	2	yes	—
26	C₄₁×#382	C₂²	1	2	yes	—
27	C₄₁×#380	—	2	1	no	—
28	C₄₁×#380	—	2	1	no	—
29	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
30	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
31	C₄₁×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₄₁	—	2	1	no	—
33	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
38	C₄⋊Q₈×C₄₁	—	2	2	no	—
39	C₄⋊Q₈×C₄₁	—	2	2	no	—
40	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
41	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
42	#125×C₄₁	—	2	8	no	—
43	C₂²⋊Q₈×C₄₁	—	2	8	no	—
44	C₂²⋊Q₈×C₄₁	—	2	4	no	—
45	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	—
46	C₄×Q₈×C₄₁	—	2	8	no	—
47	C₄×Q₈×C₄₁	—	2	4	no	—
48	C₄×Q₈×C₄₁	C₂×C₄	1	8	yes	—
49	#117×C₄₁	—	2	8	no	—
50	#117×C₄₁	—	4	4	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	—	2	2	no	—
64	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₁	D₄	1	4	yes	—
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₁	—	2	4	no	—
71	#103×C₄₁	—	4	8	no	—
72	C₂²⋊C₈×C₄₁	—	2	4	no	—
73	#97×C₄₁	—	2	4	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₄₁	—	2	4	no	—
78	C₂×Q₈×C₄₁	—	2	2	no	—
79	C₂×Q₈×C₄₁	—	2	4	no	—
80	C₂×Q₈×C₄₁	—	2	4	no	—
81	C₂×Q₈×C₄₁	—	4	4	no	—
82	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₄₁	—	2	4	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	—	2	4	no	—
89	C₂²×C₄×C₄₁	—	4	2	no	—
90	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₄₁	—	2	4	no	—
101	C₂×C₈×C₄₁	—	2	4	no	—
102	C₂×C₈×C₄₁	—	2	4	no	—
103	C₄⋊C₄×C₄₁	—	2	4	no	—
104	C₄⋊C₄×C₄₁	—	2	4	no	—
105	C₄⋊C₄×C₄₁	—	2	4	no	—
106	C₄⋊C₄×C₄₁	—	2	8	no	—
107	C₄⋊C₄×C₄₁	—	2	8	no	—
108	C₄⋊C₄×C₄₁	—	2	2	no	—
109	C₄⋊C₄×C₄₁	—	2	8	no	—
110	C₄⋊C₄×C₄₁	—	4	4	no	—
111	C₄⋊C₄×C₄₁	—	4	4	no	—
112	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
113	C₂²⋊C₄×C₄₁	—	2	8	no	—
114	C₂²⋊C₄×C₄₁	—	4	4	no	—
115	C₄²×C₄₁	—	2	8	no	—
116	C₄²×C₄₁	—	4	4	no	—
117	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
121	C₄²×C₄₁	C₂×D₄	1	2	yes	—
122	C₄²×C₄₁	C₂×D₄	1	2	yes	—
123	C₂³×C₄₁	—	2	1	no	—
124	C₂³×C₄₁	—	2	1	no	—
125	C₂³×C₄₁	—	2	2	no	—
126	C₂³×C₄₁	—	2	2	no	—
127	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
128	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₄₁	—	2	8	no	—
130	Q₈×C₄₁	—	4	8	no	—
131	Q₈×C₄₁	—	4	4	no	—
132	C₂×C₄×C₄₁	—	2	1	no	—
133	C₂×C₄×C₄₁	—	2	1	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	2	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	4	no	—
139	C₂×C₄×C₄₁	—	2	8	no	—
140	C₂×C₄×C₄₁	—	2	4	no	—
141	C₂×C₄×C₄₁	—	2	4	no	—
142	C₂×C₄×C₄₁	—	4	4	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	4	4	no	—
146	C₂×C₄×C₄₁	—	4	4	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₁	#137	1	4	yes	—
155	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
158	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
159	C₈×C₄₁	—	4	4	no	—
160	#21870	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₄₁	—	2	2	no	—
162	C₂²×C₄₁	—	2	2	no	—
163	C₂²×C₄₁	—	2	2	no	—
164	C₂²×C₄₁	—	4	2	no	—
165	C₂²×C₄₁	—	4	2	no	—
166	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄₁	#535	1	1	yes	characteristic
168	C₂²×C₄₁	#536	1	1	yes	characteristic
169	C₂²×C₄₁	C₂×#137	1	2	yes	—
170	C₂²×C₄₁	#575	1	2	yes	—
171	C₄×C₄₁	—	2	2	no	—
172	C₄×C₄₁	—	2	2	no	—
173	C₄×C₄₁	—	2	2	no	—
174	C₄×C₄₁	—	2	2	no	—
175	C₄×C₄₁	—	4	4	no	—
176	C₄×C₄₁	—	4	4	no	—
177	C₄×C₄₁	—	8	4	no	—
178	C₄×C₄₁	#419	1	4	yes	—
179	C₄×C₄₁	#520	1	2	yes	—
180	C₄×C₄₁	#537	1	2	yes	—
181	C₂×#533	C₂×C₄₁	1	1	yes	characteristic
182	C₂×#432	C₂×C₄₁	1	1	yes	characteristic
183	#2285	C₂×C₄₁	1	1	yes	characteristic
184	#1993	C₂×C₄₁	1	2	yes	complemented
185	#1960	C₂×C₄₁	1	2	yes	complemented
186	#1873	C₂×C₄₁	1	4	yes	—
187	#1803	C₂×C₄₁	1	4	yes	complemented
188	C₂×C₄₁	—	4	2	no	—
189	C₂×C₄₁	#2311	1	1	yes	characteristic
190	C₂×C₄₁	C₂×#419	1	1	yes	characteristic
191	C₂×C₄₁	#2896	1	1	yes	characteristic
192	C₂×C₄₁	#3216	1	2	yes	—
193	C₂×C₄₁	#3237	1	2	yes	—
194	#533	—	2	4	no	—
195	#533	C₄×C₄₁	1	8	yes	complemented
196	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
198	C₂×#125	—	2	1	no	—
199	C₂×C₂²⋊Q₈	—	2	1	no	—
200	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
201	C₂×C₄×Q₈	—	2	1	no	—
202	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
203	C₂×#117	—	2	1	no	—
204	C₂×#117	C₂²×C₄₁	1	2	yes	—
205	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
206	#432	—	2	4	no	—
207	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
208	C₂×#103	C₂²×C₄₁	1	8	yes	—
209	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
210	C₂×#97	C₂²×C₄₁	1	2	yes	—
211	#384	C₂²×C₄₁	1	2	yes	—
212	#382	C₂²×C₄₁	1	2	yes	—
213	#380	—	2	1	no	—
214	#380	—	2	1	no	—
215	C₄×C₄⋊C₄	—	2	1	no	—
216	C₄×C₄⋊C₄	—	2	1	no	—
217	#340	C₂²×C₄₁	1	8	yes	—
218	C₄₁	#21870	1	1	yes	characteristic, direct product factor, Sylow
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
221	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
228	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
229	#125	—	2	8	no	—
230	C₂²⋊Q₈	—	2	8	no	—
231	C₂²⋊Q₈	—	2	4	no	—
232	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	—
233	C₄×Q₈	—	2	8	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	C₂×C₄×C₄₁	1	8	yes	—
236	#117	—	2	8	no	—
237	#117	—	4	4	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
246	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
252	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
254	C₂×C₄²	D₄×C₄₁	1	4	yes	—
255	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
257	C₄⋊C₈	—	2	4	no	—
258	#103	—	4	8	no	—
259	C₂²⋊C₈	—	2	4	no	—
260	#97	—	2	4	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	4	4	no	—
269	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
278	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
279	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
300	C₂²⋊C₄	—	2	8	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₄²	—	2	8	no	—
303	C₄²	—	4	4	no	—
304	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
305	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
306	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
307	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
308	C₄²	C₂×D₄×C₄₁	1	2	yes	—
309	C₄²	C₂×D₄×C₄₁	1	2	yes	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
315	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
316	Q₈	—	2	8	no	—
317	Q₈	—	4	8	no	—
318	Q₈	—	4	4	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
341	C₂×C₄	#137×C₄₁	1	4	yes	—
342	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
344	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
345	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
346	C₈	—	4	4	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
353	C₂²	C₄₁×#535	1	1	yes	characteristic
354	C₂²	C₄₁×#536	1	1	yes	characteristic
355	C₂²	C₂×#137×C₄₁	1	2	yes	—
356	C₂²	C₄₁×#575	1	2	yes	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	4	no	—
362	C₄	—	4	4	no	—
363	C₄	—	8	4	no	—
364	C₄	C₄₁×#419	1	4	yes	—
365	C₄	C₄₁×#520	1	2	yes	—
366	C₄	C₄₁×#537	1	2	yes	—
367	C₂	—	4	2	no	—
368	C₂	C₄₁×#2311	1	1	yes	characteristic
369	C₂	C₂×C₄₁×#419	1	1	yes	characteristic
370	C₂	C₄₁×#2896	1	1	yes	characteristic
371	C₂	C₄₁×#3216	1	2	yes	—
372	C₂	C₄₁×#3237	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 ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#1993	C₂	semidirect
5. C₄₁×#1960	C₂	semidirect
7. C₄₁×#1803	C₂	semidirect
9. C₄₁×#533	C₄	semidirect
160. #21870	C₄₁	direct (N × H)
184. #1993	C₂×C₄₁	semidirect
185. #1960	C₂×C₄₁	semidirect
187. #1803	C₂×C₄₁	semidirect
195. #533	C₄×C₄₁	semidirect
218. C₄₁	#21870	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×#533	2
C₂×C₄₁×#432	2
C₄₁×#2285	2
C₄₁×#1993	2
C₄₁×#1960	2
C₄₁×#1873	2
C₄₁×#1803	2
#21870	41

Subgroups — C41×#21870 #23798071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21870 #23798071