Subgroups — C₄₁×#23180 #23799381

Order 10496.

914 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#444	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2935	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1980	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1975	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1876	C₂	1	4	yes	maximal, complemented
7	C₄×#108×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₄₁	C₂²	1	2	yes	—
10	C₂×#135×C₄₁	C₂²	1	2	yes	—
11	C₂×#131×C₄₁	C₂²	1	4	yes	—
12	C₄₁×#532	C₂²	1	2	yes	—
13	C₄₁×#495	C₄	1	2	yes	complemented
14	C₄₁×#495	C₄	1	2	yes	complemented
15	C₄₁×#494	C₄	1	1	yes	characteristic, complemented
16	C₄₁×#493	C₄	1	1	yes	characteristic, complemented
17	C₄₁×#492	C₄	1	2	yes	complemented
18	C₄₁×#444	—	2	8	no	—
19	C₄₁×#436	—	2	2	no	—
20	C₄₁×#435	—	2	4	no	—
21	C₈×D₄×C₄₁	—	2	2	no	—
22	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#104×C₄₁	C₂²	1	4	yes	—
26	C₂×#104×C₄₁	C₂²	1	4	yes	—
27	C₄₁×#408	C₂²	1	4	yes	—
28	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
29	C₂×#97×C₄₁	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#341	C₂²	1	2	yes	—
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₂×#41×C₄₁	C₂³	1	4	yes	—
35	#135×C₄₁	—	2	4	no	—
36	#135×C₄₁	—	2	4	no	—
37	#135×C₄₁	—	4	2	no	—
38	#135×C₄₁	—	4	2	no	—
39	C₂×Q₁₆×C₄₁	C₂×C₄	1	2	yes	—
40	C₂×Q₁₆×C₄₁	C₂×C₄	1	2	yes	—
41	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	—
42	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	—
43	C₂×D₈×C₄₁	C₂×C₄	1	2	yes	—
44	C₂×D₈×C₄₁	C₂×C₄	1	2	yes	—
45	#131×C₄₁	—	2	8	no	—
46	#131×C₄₁	—	4	4	no	—
47	C₂×M₁₆×C₄₁	—	2	4	no	—
48	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
49	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₁	—	2	4	no	—
51	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
55	#127×C₄₁	C₂×C₄	1	2	yes	—
56	#124×C₄₁	C₂×C₄	1	4	yes	—
57	#121×C₄₁	—	2	2	no	—
58	#121×C₄₁	—	2	2	no	—
59	C₄×D₄×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
64	#108×C₄₁	—	2	2	no	—
65	#108×C₄₁	D₄	1	4	yes	complemented
66	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
67	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
68	#104×C₄₁	—	2	8	no	—
69	#104×C₄₁	—	4	4	no	—
70	C₂²⋊C₈×C₄₁	—	2	4	no	—
71	C₂²⋊C₈×C₄₁	—	2	4	no	—
72	#97×C₄₁	—	2	4	no	—
73	#97×C₄₁	—	2	2	no	—
74	C₄×C₈×C₄₁	—	2	2	no	—
75	C₄×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
79	#95×C₄₁	—	2	1	no	—
80	#41×C₄₁	—	2	4	no	—
81	#41×C₄₁	—	2	4	no	—
82	#41×C₄₁	—	2	4	no	—
83	#41×C₄₁	—	2	4	no	—
84	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
85	C₂×D₄×C₄₁	—	2	4	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₁	—	2	4	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
94	Q₁₆×C₄₁	—	2	4	no	—
95	Q₁₆×C₄₁	—	4	2	no	—
96	SD₁₆×C₄₁	—	2	8	no	—
97	SD₁₆×C₄₁	—	4	4	no	—
98	D₈×C₄₁	—	2	4	no	—
99	D₈×C₄₁	—	4	2	no	—
100	M₁₆×C₄₁	—	2	2	no	—
101	M₁₆×C₄₁	—	2	2	no	—
102	M₁₆×C₄₁	—	2	2	no	—
103	M₁₆×C₄₁	—	4	8	no	—
104	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	2	no	—
108	C₂×C₈×C₄₁	—	2	1	no	—
109	C₂×C₈×C₄₁	—	2	1	no	—
110	C₂×C₈×C₄₁	—	2	2	no	—
111	C₂×C₈×C₄₁	—	4	8	no	—
112	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
117	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₁	#41	1	2	yes	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	—	2	2	no	—
121	C₄⋊C₄×C₄₁	—	4	2	no	—
122	C₂²⋊C₄×C₄₁	—	2	4	no	—
123	C₂²⋊C₄×C₄₁	—	2	4	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₄₁	—	2	4	no	—
131	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
132	Q₈×C₄₁	—	2	4	no	—
133	Q₈×C₄₁	—	2	4	no	—
134	D₄×C₄₁	—	2	4	no	—
135	D₄×C₄₁	—	2	4	no	—
136	D₄×C₄₁	—	4	4	no	—
137	D₄×C₄₁	—	4	4	no	—
138	D₄×C₄₁	—	4	4	no	—
139	D₄×C₄₁	—	8	2	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	4	no	—
142	C₂×C₄×C₄₁	—	4	1	no	—
143	C₂×C₄×C₄₁	—	4	4	no	—
144	C₂×C₄×C₄₁	—	4	4	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	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
158	C₈×C₄₁	—	2	1	no	—
159	C₈×C₄₁	—	2	1	no	—
160	C₈×C₄₁	—	2	4	no	—
161	C₈×C₄₁	—	2	4	no	—
162	C₈×C₄₁	—	4	2	no	—
163	C₈×C₄₁	C₄×D₄	1	2	yes	—
164	C₈×C₄₁	C₄×D₄	1	2	yes	—
165	#23180	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂²×C₄₁	—	2	1	no	—
167	C₂²×C₄₁	—	2	1	no	—
168	C₂²×C₄₁	—	4	4	no	—
169	C₂²×C₄₁	—	4	4	no	—
170	C₂²×C₄₁	—	4	4	no	—
171	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
172	C₂²×C₄₁	#550	1	1	yes	characteristic
173	C₂²×C₄₁	#559	1	1	yes	characteristic
174	C₄×C₄₁	—	2	1	no	—
175	C₄×C₄₁	—	2	1	no	—
176	C₄×C₄₁	—	2	1	no	—
177	C₄×C₄₁	—	4	4	no	—
178	C₄×C₄₁	—	8	2	no	—
179	C₄×C₄₁	#444	1	2	yes	complemented
180	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₄₁	#518	1	1	yes	characteristic
182	C₄×C₄₁	D₄²	1	1	yes	characteristic
183	C₄×C₄₁	#550	1	1	yes	characteristic
184	#3147	C₂×C₄₁	1	1	yes	characteristic
185	C₂×#444	C₂×C₄₁	1	2	yes	complemented
186	#2935	C₂×C₄₁	1	2	yes	complemented
187	#1980	C₂×C₄₁	1	2	yes	complemented
188	#1975	C₂×C₄₁	1	2	yes	complemented
189	#1876	C₂×C₄₁	1	4	yes	complemented
190	C₄×#108	C₂×C₄₁	1	1	yes	characteristic, complemented
191	#1770	C₂×C₄₁	1	1	yes	characteristic, complemented
192	C₂×C₄₁	—	2	1	no	—
193	C₂×C₄₁	—	2	1	no	—
194	C₂×C₄₁	—	8	4	no	—
195	C₂×C₄₁	#2366	1	1	yes	characteristic
196	C₂×C₄₁	C₂×#444	1	1	yes	characteristic
197	C₂×C₄₁	#2957	1	1	yes	characteristic
198	C₂×#135	C₂²×C₄₁	1	2	yes	—
199	C₂×#135	C₂²×C₄₁	1	2	yes	—
200	C₂×#131	C₂²×C₄₁	1	4	yes	—
201	#532	C₂²×C₄₁	1	2	yes	—
202	#495	C₄×C₄₁	1	2	yes	complemented
203	#495	C₄×C₄₁	1	2	yes	complemented
204	#494	C₄×C₄₁	1	1	yes	characteristic, complemented
205	#493	C₄×C₄₁	1	1	yes	characteristic, complemented
206	#492	C₄×C₄₁	1	2	yes	complemented
207	#444	—	2	8	no	—
208	#436	—	2	2	no	—
209	#435	—	2	4	no	—
210	C₈×D₄	—	2	2	no	—
211	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
212	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
214	C₂×#104	C₂²×C₄₁	1	4	yes	—
215	C₂×#104	C₂²×C₄₁	1	4	yes	—
216	#408	C₂²×C₄₁	1	4	yes	—
217	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
218	C₂×#97	C₂²×C₄₁	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
220	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
221	#341	C₂²×C₄₁	1	2	yes	—
222	#336	C₂²×C₄₁	1	2	yes	—
223	C₄₁	#23180	1	1	yes	characteristic, direct product factor, Sylow
224	C₂×#41	C₂³×C₄₁	1	4	yes	—
225	#135	—	2	4	no	—
226	#135	—	2	4	no	—
227	#135	—	4	2	no	—
228	#135	—	4	2	no	—
229	C₂×Q₁₆	C₂×C₄×C₄₁	1	2	yes	—
230	C₂×Q₁₆	C₂×C₄×C₄₁	1	2	yes	—
231	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	—
232	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	—
233	C₂×D₈	C₂×C₄×C₄₁	1	2	yes	—
234	C₂×D₈	C₂×C₄×C₄₁	1	2	yes	—
235	#131	—	2	8	no	—
236	#131	—	4	4	no	—
237	C₂×M₁₆	—	2	4	no	—
238	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
239	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
240	C₂²×C₈	—	2	4	no	—
241	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
243	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
245	#127	C₂×C₄×C₄₁	1	2	yes	—
246	#124	C₂×C₄×C₄₁	1	4	yes	—
247	#121	—	2	2	no	—
248	#121	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
253	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
254	#108	—	2	2	no	—
255	#108	D₄×C₄₁	1	4	yes	complemented
256	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
257	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
258	#104	—	2	8	no	—
259	#104	—	4	4	no	—
260	C₂²⋊C₈	—	2	4	no	—
261	C₂²⋊C₈	—	2	4	no	—
262	#97	—	2	4	no	—
263	#97	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
266	C₄×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
267	C₄×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
268	C₄×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
269	#95	—	2	1	no	—
270	#41	—	2	4	no	—
271	#41	—	2	4	no	—
272	#41	—	2	4	no	—
273	#41	—	2	4	no	—
274	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
282	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
284	Q₁₆	—	2	4	no	—
285	Q₁₆	—	4	2	no	—
286	SD₁₆	—	2	8	no	—
287	SD₁₆	—	4	4	no	—
288	D₈	—	2	4	no	—
289	D₈	—	4	2	no	—
290	M₁₆	—	2	2	no	—
291	M₁₆	—	2	2	no	—
292	M₁₆	—	2	2	no	—
293	M₁₆	—	4	8	no	—
294	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	8	no	—
302	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
305	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
307	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
308	C₂×C₈	#41×C₄₁	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
317	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₂³	—	2	4	no	—
321	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	8	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
342	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
346	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
347	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	2	4	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	C₄×D₄×C₄₁	1	2	yes	—
354	C₈	C₄×D₄×C₄₁	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	4	no	—
360	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
361	C₂²	C₄₁×#550	1	1	yes	characteristic
362	C₂²	C₄₁×#559	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	4	no	—
367	C₄	—	8	2	no	—
368	C₄	C₄₁×#444	1	2	yes	complemented
369	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
370	C₄	C₄₁×#518	1	1	yes	characteristic
371	C₄	D₄²×C₄₁	1	1	yes	characteristic
372	C₄	C₄₁×#550	1	1	yes	characteristic
373	C₂	—	2	1	no	—
374	C₂	—	2	1	no	—
375	C₂	—	8	4	no	—
376	C₂	C₄₁×#2366	1	1	yes	characteristic
377	C₂	C₂×C₄₁×#444	1	1	yes	characteristic
378	C₂	C₄₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₄₁×#3147	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₄⋊C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#444	C₂	semidirect
3. C₄₁×#2935	C₂	semidirect
4. C₄₁×#1980	C₂	semidirect
5. C₄₁×#1975	C₂	semidirect
6. C₄₁×#1876	C₂	semidirect
7. C₄×#108×C₄₁	C₂	semidirect
8. C₄₁×#1770	C₂	semidirect
13. C₄₁×#495	C₄	semidirect
14. C₄₁×#495	C₄	semidirect
15. C₄₁×#494	C₄	semidirect
16. C₄₁×#493	C₄	semidirect
17. C₄₁×#492	C₄	semidirect
65. #108×C₄₁	D₄	semidirect
165. #23180	C₄₁	direct (N × H)
179. C₄×C₄₁	#444	semidirect
185. C₂×#444	C₂×C₄₁	semidirect
186. #2935	C₂×C₄₁	semidirect
187. #1980	C₂×C₄₁	semidirect
188. #1975	C₂×C₄₁	semidirect
189. #1876	C₂×C₄₁	semidirect
190. C₄×#108	C₂×C₄₁	semidirect
191. #1770	C₂×C₄₁	semidirect
202. #495	C₄×C₄₁	semidirect
203. #495	C₄×C₄₁	semidirect
204. #494	C₄×C₄₁	semidirect
205. #493	C₄×C₄₁	semidirect
206. #492	C₄×C₄₁	semidirect
223. C₄₁	#23180	direct (N × H)
255. #108	D₄×C₄₁	semidirect
368. C₄	C₄₁×#444	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3147	2
C₂×C₄₁×#444	2
C₄₁×#2935	2
C₄₁×#1980	2
C₄₁×#1975	2
C₄₁×#1876	2
C₄×#108×C₄₁	2
C₄₁×#1770	2
#23180	41

Subgroups — C41×#23180 #23799381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23180 #23799381