Subgroups — C₄₁×#21026 #23797227

Order 10496.

906 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1917	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1916	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1728	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×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×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#424	—	2	4	no	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	—
19	C₄₁×#405	—	2	4	no	—
20	C₂×#97×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#384	C₄	1	2	yes	—
23	C₄₁×#382	C₄	1	2	yes	—
24	C₄₁×#380	C₄	1	4	yes	—
25	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
26	C₄₁×#336	C₂²	1	2	yes	—
27	C₄₁×#336	C₂²	1	2	yes	—
28	C₄₁×#336	C₂²	1	4	yes	—
29	C₄₁×#336	C₂²	1	4	yes	—
30	C₄₁×#336	C₂²	1	2	yes	—
31	C₄₁×#336	C₂²	1	2	yes	—
32	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₄₁	—	2	2	no	—
35	C₂×M₁₆×C₄₁	—	2	2	no	—
36	C₂×M₁₆×C₄₁	—	2	2	no	—
37	C₂×M₁₆×C₄₁	—	2	2	no	—
38	C₂×M₁₆×C₄₁	—	2	2	no	—
39	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
40	C₂²×C₈×C₄₁	—	2	2	no	—
41	C₂²×C₈×C₄₁	—	2	2	no	—
42	C₂²×C₈×C₄₁	—	2	2	no	—
43	C₂²×C₈×C₄₁	—	2	2	no	—
44	C₂²×C₈×C₄₁	—	2	2	no	—
45	C₂²×C₈×C₄₁	Q₈	1	4	yes	—
46	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
51	#117×C₄₁	—	2	2	no	—
52	#117×C₄₁	—	2	2	no	—
53	#117×C₄₁	—	2	2	no	—
54	#117×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
67	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
68	C₄⋊C₈×C₄₁	—	2	8	no	—
69	#97×C₄₁	—	2	4	no	—
70	C₄×C₈×C₄₁	—	2	4	no	—
71	#95×C₄₁	C₂×C₄	1	8	yes	—
72	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₁	—	2	4	no	—
74	C₂²×C₄×C₄₁	—	2	4	no	—
75	C₂²×C₄×C₄₁	—	4	2	no	—
76	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₄₁	#41	1	2	yes	—
84	C₂²×C₄×C₄₁	#41	1	2	yes	—
85	C₂²×C₄×C₄₁	#41	1	2	yes	—
86	C₂²×C₄×C₄₁	#41	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
88	M₁₆×C₄₁	—	2	8	no	—
89	M₁₆×C₄₁	—	4	4	no	—
90	C₂×C₈×C₄₁	—	2	8	no	—
91	C₂×C₈×C₄₁	—	2	1	no	—
92	C₂×C₈×C₄₁	—	2	1	no	—
93	C₂×C₈×C₄₁	—	2	1	no	—
94	C₂×C₈×C₄₁	—	2	1	no	—
95	C₂×C₈×C₄₁	—	2	2	no	—
96	C₂×C₈×C₄₁	—	2	2	no	—
97	C₂×C₈×C₄₁	—	2	2	no	—
98	C₂×C₈×C₄₁	—	2	2	no	—
99	C₂×C₈×C₄₁	—	2	2	no	—
100	C₂×C₈×C₄₁	—	2	2	no	—
101	C₂×C₈×C₄₁	—	2	2	no	—
102	C₂×C₈×C₄₁	—	2	2	no	—
103	C₂×C₈×C₄₁	—	4	4	no	—
104	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₄₁	C₂×Q₈	1	2	yes	—
106	C₂×C₈×C₄₁	C₂×Q₈	1	2	yes	—
107	C₄⋊C₄×C₄₁	—	2	4	no	—
108	C₄⋊C₄×C₄₁	—	2	4	no	—
109	C₄⋊C₄×C₄₁	—	2	8	no	—
110	C₄⋊C₄×C₄₁	—	4	4	no	—
111	C₂²⋊C₄×C₄₁	—	2	4	no	—
112	C₂²⋊C₄×C₄₁	—	2	4	no	—
113	C₄²×C₄₁	—	2	2	no	—
114	C₄²×C₄₁	—	2	2	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	2	no	—
118	C₄²×C₄₁	—	2	2	no	—
119	C₄²×C₄₁	—	2	2	no	—
120	C₄²×C₄₁	—	2	2	no	—
121	C₂³×C₄₁	—	2	2	no	—
122	C₂³×C₄₁	—	2	2	no	—
123	C₂³×C₄₁	#117	1	2	yes	—
124	C₂³×C₄₁	C₄×D₄	1	2	yes	—
125	C₂³×C₄₁	C₄×Q₈	1	2	yes	—
126	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₄₁	—	2	2	no	—
128	C₂×C₄×C₄₁	—	2	2	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	4	no	—
131	C₂×C₄×C₄₁	—	2	4	no	—
132	C₂×C₄×C₄₁	—	2	4	no	—
133	C₂×C₄×C₄₁	—	2	4	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	4	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	2	no	—
138	C₂×C₄×C₄₁	—	4	8	no	—
139	C₂×C₄×C₄₁	#117	1	2	yes	—
140	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
143	C₂×C₄×C₄₁	#123	1	4	yes	—
144	C₂×C₄×C₄₁	#125	1	4	yes	—
145	C₂×C₄×C₄₁	#126	1	4	yes	—
146	C₂×C₄×C₄₁	#131	1	4	yes	—
147	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
153	C₈×C₄₁	—	2	2	no	—
154	C₈×C₄₁	—	2	2	no	—
155	C₈×C₄₁	—	2	4	no	—
156	C₈×C₄₁	—	4	2	no	—
157	C₈×C₄₁	—	4	2	no	—
158	#21026	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₄₁	—	2	4	no	—
160	C₂²×C₄₁	—	2	4	no	—
161	C₂²×C₄₁	—	2	2	no	—
162	C₂²×C₄₁	—	2	2	no	—
163	C₂²×C₄₁	#387	1	4	yes	—
164	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
165	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
167	C₂²×C₄₁	C₂×#131	1	2	yes	—
168	C₂²×C₄₁	#568	1	2	yes	—
169	C₄×C₄₁	—	2	4	no	—
170	C₄×C₄₁	—	4	2	no	—
171	C₄×C₄₁	—	4	4	no	—
172	C₄×C₄₁	—	4	4	no	—
173	C₄×C₄₁	#387	1	4	yes	—
174	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
175	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
176	C₄×C₄₁	C₂×#125	1	1	yes	characteristic
177	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
178	C₂×#424	C₂×C₄₁	1	1	yes	characteristic
179	C₂×#405	C₂×C₄₁	1	1	yes	characteristic
180	#2285	C₂×C₄₁	1	1	yes	characteristic
181	#1917	C₂×C₄₁	1	4	yes	complemented
182	#1916	C₂×C₄₁	1	4	yes	complemented
183	#1729	C₂×C₄₁	1	1	yes	characteristic
184	#1729	C₂×C₄₁	1	1	yes	characteristic
185	#1728	C₂×C₄₁	1	1	yes	characteristic
186	C₂×#336	C₂×C₄₁	1	1	yes	characteristic
187	C₂×C₄₁	—	2	4	no	—
188	C₂×C₄₁	C₂×#387	1	1	yes	characteristic
189	C₂×C₄₁	#2924	1	2	yes	—
190	C₂×C₄₁	#2935	1	2	yes	—
191	C₂×C₄₁	#2960	1	1	yes	characteristic
192	C₂×C₄₁	#2961	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
194	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
195	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
197	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
198	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
199	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
200	#424	—	2	4	no	—
201	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	—
202	#405	—	2	4	no	—
203	C₂×#97	C₂²×C₄₁	1	2	yes	—
204	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
205	#384	C₄×C₄₁	1	2	yes	—
206	#382	C₄×C₄₁	1	2	yes	—
207	#380	C₄×C₄₁	1	4	yes	—
208	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
209	#336	C₂²×C₄₁	1	2	yes	—
210	#336	C₂²×C₄₁	1	2	yes	—
211	#336	C₂²×C₄₁	1	4	yes	—
212	#336	C₂²×C₄₁	1	4	yes	—
213	#336	C₂²×C₄₁	1	2	yes	—
214	#336	C₂²×C₄₁	1	2	yes	—
215	C₄₁	#21026	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
217	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	Q₈×C₄₁	1	4	yes	—
230	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
233	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
235	#117	—	2	2	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	—	2	2	no	—
239	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
248	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
251	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
252	C₄⋊C₈	—	2	8	no	—
253	#97	—	2	4	no	—
254	C₄×C₈	—	2	4	no	—
255	#95	C₂×C₄×C₄₁	1	8	yes	—
256	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
262	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
266	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
267	C₂²×C₄	#41×C₄₁	1	2	yes	—
268	C₂²×C₄	#41×C₄₁	1	2	yes	—
269	C₂²×C₄	#41×C₄₁	1	2	yes	—
270	C₂²×C₄	#41×C₄₁	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
272	M₁₆	—	2	8	no	—
273	M₁₆	—	4	4	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
289	C₂×C₈	C₂×Q₈×C₄₁	1	2	yes	—
290	C₂×C₈	C₂×Q₈×C₄₁	1	2	yes	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	4	4	no	—
295	C₂²⋊C₄	—	2	4	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	#117×C₄₁	1	2	yes	—
308	C₂³	C₄×D₄×C₄₁	1	2	yes	—
309	C₂³	C₄×Q₈×C₄₁	1	2	yes	—
310	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	#117×C₄₁	1	2	yes	—
324	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
325	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
326	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
327	C₂×C₄	#123×C₄₁	1	4	yes	—
328	C₂×C₄	#125×C₄₁	1	4	yes	—
329	C₂×C₄	#126×C₄₁	1	4	yes	—
330	C₂×C₄	#131×C₄₁	1	4	yes	—
331	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₈	—	2	4	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	C₄₁×#387	1	4	yes	—
347	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
348	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
349	C₂²	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
350	C₂²	C₂×#131×C₄₁	1	2	yes	—
351	C₂²	C₄₁×#568	1	2	yes	—
352	C₄	—	2	4	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	4	no	—
355	C₄	—	4	4	no	—
356	C₄	C₄₁×#387	1	4	yes	—
357	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
358	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
359	C₄	C₂×#125×C₄₁	1	1	yes	characteristic
360	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
361	C₂	—	2	4	no	—
362	C₂	C₂×C₄₁×#387	1	1	yes	characteristic
363	C₂	C₄₁×#2924	1	2	yes	—
364	C₂	C₄₁×#2935	1	2	yes	—
365	C₂	C₄₁×#2960	1	1	yes	characteristic
366	C₂	C₄₁×#2961	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₄₁×#1917	C₂	semidirect
5. C₄₁×#1916	C₂	semidirect
158. #21026	C₄₁	direct (N × H)
181. #1917	C₂×C₄₁	semidirect
182. #1916	C₂×C₄₁	semidirect
215. C₄₁	#21026	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×#424	2
C₂×C₄₁×#405	2
C₄₁×#2285	2
C₄₁×#1917	2
C₄₁×#1916	2
C₄₁×#1729	2
C₄₁×#1728	2
C₂×C₄₁×#336	2
#21026	41

Subgroups — C41×#21026 #23797227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21026 #23797227