Subgroups — C₄₁×#22396 #23798597

Order 10496.

738 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2398	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1985	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1924	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1923	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1869	C₂	1	2	yes	maximal
6	C₄₁×#1850	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1840	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1752	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
11	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
18	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#97×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#400	C₄	1	2	yes	—
22	C₄₁×#397	C₄	1	2	yes	—
23	C₄₁×#394	C₄	1	2	yes	—
24	C₄₁×#393	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#376	C₂²	1	1	yes	characteristic
28	C₄₁×#336	C₂²	1	2	yes	—
29	C₄₁×#336	C₂²	1	1	yes	characteristic
30	C₄₁×#336	C₂²	1	2	yes	—
31	C₄₁×#336	C₂²	1	2	yes	—
32	C₄₁×#336	C₂²	1	1	yes	characteristic
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₄₁	—	2	4	no	—
39	C₂²×C₈×C₄₁	—	4	2	no	—
40	C₂²×C₈×C₄₁	—	4	2	no	—
41	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
45	C₄×Q₈×C₄₁	—	4	2	no	—
46	C₄×D₄×C₄₁	—	4	2	no	—
47	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₄₁	—	2	4	no	—
60	C₄⋊C₈×C₄₁	—	4	2	no	—
61	C₂²⋊C₈×C₄₁	—	2	4	no	—
62	C₂²⋊C₈×C₄₁	—	4	2	no	—
63	C₂²⋊C₈×C₄₁	—	4	2	no	—
64	#97×C₄₁	—	4	1	no	—
65	#97×C₄₁	—	4	2	no	—
66	C₄×C₈×C₄₁	—	4	1	no	—
67	#95×C₄₁	C₂×C₄	1	2	yes	—
68	#95×C₄₁	C₂×C₄	1	2	yes	—
69	#95×C₄₁	C₂×C₄	1	2	yes	—
70	#95×C₄₁	C₂×C₄	1	2	yes	—
71	#95×C₄₁	C₂×C₄	1	2	yes	—
72	#95×C₄₁	C₂×C₄	1	2	yes	—
73	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
74	C₂×Q₈×C₄₁	—	4	1	no	—
75	C₂×Q₈×C₄₁	—	4	2	no	—
76	C₂×D₄×C₄₁	—	2	4	no	—
77	C₂×D₄×C₄₁	—	4	1	no	—
78	C₂²×C₄×C₄₁	—	2	2	no	—
79	C₂²×C₄×C₄₁	—	2	2	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	2	no	—
84	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₄₁	—	2	2	no	—
93	C₂×C₈×C₄₁	—	2	2	no	—
94	C₂×C₈×C₄₁	—	2	2	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	8	no	—
104	C₂×C₈×C₄₁	#41	1	4	yes	—
105	C₄⋊C₄×C₄₁	—	4	1	no	—
106	C₄⋊C₄×C₄₁	—	4	1	no	—
107	C₄⋊C₄×C₄₁	—	4	2	no	—
108	C₂²⋊C₄×C₄₁	—	2	4	no	—
109	C₂²⋊C₄×C₄₁	—	2	4	no	—
110	C₂²⋊C₄×C₄₁	—	4	2	no	—
111	C₂²⋊C₄×C₄₁	—	4	2	no	—
112	C₂²⋊C₄×C₄₁	—	4	2	no	—
113	C₄²×C₄₁	—	2	2	no	—
114	C₄²×C₄₁	—	2	1	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	2	no	—
118	C₄²×C₄₁	—	2	1	no	—
119	C₂³×C₄₁	—	2	2	no	—
120	C₂³×C₄₁	—	2	2	no	—
121	C₂³×C₄₁	—	2	2	no	—
122	C₂³×C₄₁	—	2	2	no	—
123	C₂³×C₄₁	—	2	2	no	—
124	C₂³×C₄₁	—	2	2	no	—
125	C₂³×C₄₁	#131	1	4	yes	—
126	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
127	Q₈×C₄₁	—	4	4	no	—
128	D₄×C₄₁	—	4	4	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	2	no	—
131	C₂×C₄×C₄₁	—	2	1	no	—
132	C₂×C₄×C₄₁	—	2	1	no	—
133	C₂×C₄×C₄₁	—	2	2	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	2	no	—
138	C₂×C₄×C₄₁	—	2	2	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	2	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	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	C₂×#41	1	2	yes	—
153	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
155	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
156	C₈×C₄₁	—	2	4	no	—
157	C₈×C₄₁	—	4	2	no	—
158	C₈×C₄₁	—	4	2	no	—
159	C₈×C₄₁	—	4	2	no	—
160	#22396	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₄₁	—	2	4	no	—
162	C₂²×C₄₁	—	2	4	no	—
163	C₂²×C₄₁	—	2	4	no	—
164	C₂²×C₄₁	—	4	2	no	—
165	C₂²×C₄₁	—	4	2	no	—
166	C₂²×C₄₁	—	4	2	no	—
167	C₂²×C₄₁	—	4	2	no	—
168	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
169	C₂²×C₄₁	#518	1	1	yes	characteristic
170	C₂²×C₄₁	#520	1	1	yes	characteristic
171	C₂²×C₄₁	C₂×#131	1	2	yes	—
172	C₂²×C₄₁	#568	1	2	yes	—
173	C₄×C₄₁	—	4	2	no	—
174	C₄×C₄₁	—	4	2	no	—
175	C₄×C₄₁	—	4	2	no	—
176	C₄×C₄₁	—	4	1	no	—
177	C₄×C₄₁	—	4	1	no	—
178	C₄×C₄₁	—	4	2	no	—
179	C₄×C₄₁	—	4	2	no	—
180	C₄×C₄₁	#538	1	2	yes	—
181	C₄×C₄₁	#542	1	2	yes	—
182	#2398	C₂×C₄₁	1	1	yes	characteristic
183	#1985	C₂×C₄₁	1	2	yes	complemented
184	#1924	C₂×C₄₁	1	2	yes	complemented
185	#1923	C₂×C₄₁	1	2	yes	complemented
186	#1869	C₂×C₄₁	1	2	yes	—
187	#1850	C₂×C₄₁	1	2	yes	complemented
188	#1840	C₂×C₄₁	1	1	yes	characteristic, complemented
189	#1768	C₂×C₄₁	1	1	yes	characteristic, complemented
190	#1752	C₂×C₄₁	1	2	yes	complemented
191	C₂×C₄₁	—	4	4	no	—
192	C₂×C₄₁	#2337	1	1	yes	characteristic
193	C₂×C₄₁	#2968	1	2	yes	—
194	C₂×C₄₁	#2977	1	1	yes	characteristic
195	C₂×C₄₁	#2978	1	1	yes	characteristic
196	C₂×C₄₁	#2992	1	2	yes	—
197	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
199	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
202	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
205	C₂×#97	C₂²×C₄₁	1	2	yes	—
206	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
208	#400	C₄×C₄₁	1	2	yes	—
209	#397	C₄×C₄₁	1	2	yes	—
210	#394	C₄×C₄₁	1	2	yes	—
211	#393	C₄×C₄₁	1	2	yes	—
212	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
214	#376	C₂²×C₄₁	1	1	yes	characteristic
215	#336	C₂²×C₄₁	1	1	yes	characteristic
216	#336	C₂²×C₄₁	1	2	yes	—
217	#336	C₂²×C₄₁	1	2	yes	—
218	#336	C₂²×C₄₁	1	1	yes	characteristic
219	#336	C₂²×C₄₁	1	2	yes	—
220	#336	C₂²×C₄₁	1	2	yes	—
221	#336	C₂²×C₄₁	1	2	yes	—
222	C₄₁	#22396	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
224	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	—	4	2	no	—
228	C₂²×C₈	—	4	2	no	—
229	C₂²×C₈	C₂³×C₄₁	1	2	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	C₄×Q₈	—	4	2	no	—
234	C₄×D₄	—	4	2	no	—
235	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
239	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
241	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
243	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
245	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
247	C₄⋊C₈	—	2	4	no	—
248	C₄⋊C₈	—	4	2	no	—
249	C₂²⋊C₈	—	2	4	no	—
250	C₂²⋊C₈	—	4	2	no	—
251	C₂²⋊C₈	—	4	2	no	—
252	#97	—	4	1	no	—
253	#97	—	4	2	no	—
254	C₄×C₈	—	4	1	no	—
255	#95	C₂×C₄×C₄₁	1	2	yes	—
256	#95	C₂×C₄×C₄₁	1	2	yes	—
257	#95	C₂×C₄×C₄₁	1	2	yes	—
258	#95	C₂×C₄×C₄₁	1	2	yes	—
259	#95	C₂×C₄×C₄₁	1	2	yes	—
260	#95	C₂×C₄×C₄₁	1	2	yes	—
261	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
276	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
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	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	4	8	no	—
292	C₂×C₈	#41×C₄₁	1	4	yes	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	1	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	#131×C₄₁	1	4	yes	—
314	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
315	Q₈	—	4	4	no	—
316	D₄	—	4	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	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	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
341	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
342	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
343	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
356	C₂²	C₄₁×#518	1	1	yes	characteristic
357	C₂²	C₄₁×#520	1	1	yes	characteristic
358	C₂²	C₂×#131×C₄₁	1	2	yes	—
359	C₂²	C₄₁×#568	1	2	yes	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₄₁×#538	1	2	yes	—
368	C₄	C₄₁×#542	1	2	yes	—
369	C₂	—	4	4	no	—
370	C₂	C₄₁×#2337	1	1	yes	characteristic
371	C₂	C₄₁×#2968	1	2	yes	—
372	C₂	C₄₁×#2977	1	1	yes	characteristic
373	C₂	C₄₁×#2978	1	1	yes	characteristic
374	C₂	C₄₁×#2992	1	2	yes	—

	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	C₂²×D₄×C₄₁	C₂×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
2. C₄₁×#1985	C₂	semidirect
3. C₄₁×#1924	C₂	semidirect
4. C₄₁×#1923	C₂	semidirect
6. C₄₁×#1850	C₂	semidirect
7. C₄₁×#1840	C₂	semidirect
8. C₄₁×#1768	C₂	semidirect
9. C₄₁×#1752	C₂	semidirect
160. #22396	C₄₁	direct (N × H)
183. #1985	C₂×C₄₁	semidirect
184. #1924	C₂×C₄₁	semidirect
185. #1923	C₂×C₄₁	semidirect
187. #1850	C₂×C₄₁	semidirect
188. #1840	C₂×C₄₁	semidirect
189. #1768	C₂×C₄₁	semidirect
190. #1752	C₂×C₄₁	semidirect
222. C₄₁	#22396	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2398	2
C₄₁×#1985	2
C₄₁×#1924	2
C₄₁×#1923	2
C₄₁×#1869	2
C₄₁×#1850	2
C₄₁×#1840	2
C₄₁×#1768	2
C₄₁×#1752	2
#22396	41

Subgroups — C41×#22396 #23798597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22396 #23798597