Subgroups — C₄₁×#33275 #23809476

Order 10496.

690 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2644	C₂	1	2	yes	maximal, complemented
2	C₄₁×#1972	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1972	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1970	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1936	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1934	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1934	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#102×C₄₁	C₂²	1	2	yes	—
17	C₂×#102×C₄₁	C₂²	1	2	yes	—
18	C₂×#102×C₄₁	C₂²	1	2	yes	—
19	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
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	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#397	—	2	2	no	—
26	C₄₁×#397	—	2	2	no	—
27	C₄₁×#397	—	2	2	no	—
28	C₄₁×#396	—	2	2	no	—
29	C₄₁×#390	C₂²	1	2	yes	—
30	C₄₁×#390	C₂²	1	2	yes	—
31	C₄₁×#390	C₂²	1	2	yes	—
32	C₄₁×#389	C₂²	1	2	yes	—
33	C₄₁×#389	C₂²	1	2	yes	—
34	C₄₁×#389	C₂²	1	2	yes	—
35	C₄₁×#376	C₂²	1	1	yes	characteristic
36	C₄₁×#340	C₂²	1	2	yes	—
37	C₄₁×#340	C₂²	1	2	yes	—
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
40	C₂×D₈×C₄₁	—	2	2	no	—
41	C₂×D₈×C₄₁	—	2	2	no	—
42	C₂×D₈×C₄₁	—	2	2	no	—
43	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	#107×C₄₁	—	2	2	no	—
63	#106×C₄₁	—	2	2	no	—
64	#106×C₄₁	—	2	2	no	—
65	#102×C₄₁	—	2	4	no	—
66	#102×C₄₁	—	2	4	no	—
67	#102×C₄₁	—	2	4	no	—
68	#97×C₄₁	—	2	2	no	—
69	#97×C₄₁	—	2	2	no	—
70	#97×C₄₁	—	2	2	no	—
71	C₄×C₈×C₄₁	—	2	2	no	—
72	C₄×C₈×C₄₁	—	2	2	no	—
73	C₄×C₈×C₄₁	—	2	2	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	D₄	1	2	yes	—
78	#95×C₄₁	D₄	1	2	yes	—
79	C₂⁴×C₄₁	—	2	2	no	—
80	C₂×D₄×C₄₁	—	2	2	no	—
81	C₂×D₄×C₄₁	—	2	2	no	—
82	C₂×D₄×C₄₁	—	2	2	no	—
83	C₂×D₄×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
94	D₈×C₄₁	—	4	4	no	—
95	C₂×C₈×C₄₁	—	2	1	no	—
96	C₂×C₈×C₄₁	—	2	1	no	—
97	C₂×C₈×C₄₁	—	2	1	no	—
98	C₂×C₈×C₄₁	—	2	1	no	—
99	C₂×C₈×C₄₁	—	2	1	no	—
100	C₂×C₈×C₄₁	—	2	1	no	—
101	C₂×C₈×C₄₁	#41	1	2	yes	—
102	C₂×C₈×C₄₁	#41	1	2	yes	—
103	C₂×C₈×C₄₁	#41	1	2	yes	—
104	C₂×C₈×C₄₁	#41	1	2	yes	—
105	C₂×C₈×C₄₁	#41	1	2	yes	—
106	C₂×C₈×C₄₁	#41	1	2	yes	—
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	—	8	2	no	—
114	C₄⋊C₄×C₄₁	—	8	2	no	—
115	C₄⋊C₄×C₄₁	—	8	2	no	—
116	C₂²⋊C₄×C₄₁	—	8	2	no	—
117	C₂²⋊C₄×C₄₁	—	8	2	no	—
118	C₂²⋊C₄×C₄₁	—	8	2	no	—
119	C₂²⋊C₄×C₄₁	—	8	2	no	—
120	C₂²⋊C₄×C₄₁	—	8	2	no	—
121	C₂²⋊C₄×C₄₁	—	8	2	no	—
122	C₄²×C₄₁	—	2	1	no	—
123	C₄²×C₄₁	—	2	1	no	—
124	C₄²×C₄₁	—	2	1	no	—
125	C₄²×C₄₁	—	2	1	no	—
126	C₄²×C₄₁	—	2	1	no	—
127	C₄²×C₄₁	—	2	1	no	—
128	C₂³×C₄₁	—	4	2	no	—
129	C₂³×C₄₁	—	4	2	no	—
130	C₂³×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	4	2	no	—
132	C₂³×C₄₁	—	4	2	no	—
133	C₂³×C₄₁	—	4	2	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₄₁	—	4	2	no	—
137	D₄×C₄₁	—	4	2	no	—
138	D₄×C₄₁	—	4	2	no	—
139	D₄×C₄₁	—	4	2	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	1	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	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	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	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
165	C₈×C₄₁	—	2	2	no	—
166	C₈×C₄₁	—	2	2	no	—
167	C₈×C₄₁	—	2	2	no	—
168	C₈×C₄₁	#126	1	4	yes	—
169	#33275	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₁	—	8	2	no	—
171	C₂²×C₄₁	—	8	2	no	—
172	C₂²×C₄₁	—	8	2	no	—
173	C₂²×C₄₁	—	8	2	no	—
174	C₂²×C₄₁	—	8	2	no	—
175	C₂²×C₄₁	—	8	2	no	—
176	C₂²×C₄₁	—	8	2	no	—
177	C₂²×C₄₁	#532	1	1	yes	characteristic
178	C₂²×C₄₁	#532	1	1	yes	characteristic
179	C₂²×C₄₁	#532	1	1	yes	characteristic
180	C₂²×C₄₁	#576	1	2	yes	—
181	C₂²×C₄₁	#577	1	2	yes	—
182	C₄×C₄₁	—	4	1	no	—
183	C₄×C₄₁	—	4	1	no	—
184	C₄×C₄₁	—	4	2	no	—
185	C₄×C₄₁	—	4	2	no	—
186	C₄×C₄₁	—	8	2	no	—
187	C₄×C₄₁	—	8	2	no	—
188	C₄×C₄₁	—	8	2	no	—
189	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
190	C₄×C₄₁	#529	1	1	yes	characteristic
191	C₄×C₄₁	#529	1	1	yes	characteristic
192	C₄×C₄₁	#529	1	1	yes	characteristic
193	#2644	C₂×C₄₁	1	2	yes	complemented
194	#1972	C₂×C₄₁	1	1	yes	characteristic
195	#1972	C₂×C₄₁	1	1	yes	characteristic
196	#1970	C₂×C₄₁	1	1	yes	characteristic
197	#1944	C₂×C₄₁	1	1	yes	characteristic, complemented
198	#1943	C₂×C₄₁	1	1	yes	characteristic, complemented
199	#1941	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1936	C₂×C₄₁	1	2	yes	complemented
201	#1934	C₂×C₄₁	1	2	yes	complemented
202	#1934	C₂×C₄₁	1	2	yes	complemented
203	#1726	C₂×C₄₁	1	1	yes	characteristic, complemented
204	C₂×C₄₁	—	16	2	no	—
205	C₂×C₄₁	#2860	1	1	yes	characteristic
206	C₂×C₄₁	#3173	1	1	yes	characteristic
207	C₂×C₄₁	#3176	1	1	yes	characteristic
208	C₂×C₄₁	#3179	1	2	yes	—
209	C₂×C₄₁	#3179	1	2	yes	—
210	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
212	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
213	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
214	C₂×#102	C₂²×C₄₁	1	2	yes	—
215	C₂×#102	C₂²×C₄₁	1	2	yes	—
216	C₂×#102	C₂²×C₄₁	1	2	yes	—
217	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
223	#397	—	2	2	no	—
224	#397	—	2	2	no	—
225	#397	—	2	2	no	—
226	#396	—	2	2	no	—
227	#390	C₂²×C₄₁	1	2	yes	—
228	#390	C₂²×C₄₁	1	2	yes	—
229	#390	C₂²×C₄₁	1	2	yes	—
230	#389	C₂²×C₄₁	1	2	yes	—
231	#389	C₂²×C₄₁	1	2	yes	—
232	#389	C₂²×C₄₁	1	2	yes	—
233	#376	C₂²×C₄₁	1	1	yes	characteristic
234	#340	C₂²×C₄₁	1	2	yes	—
235	#340	C₂²×C₄₁	1	2	yes	—
236	#340	C₂²×C₄₁	1	2	yes	—
237	C₄₁	#33275	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	2	no	—
242	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
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	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
261	#107	—	2	2	no	—
262	#106	—	2	2	no	—
263	#106	—	2	2	no	—
264	#102	—	2	4	no	—
265	#102	—	2	4	no	—
266	#102	—	2	4	no	—
267	#97	—	2	2	no	—
268	#97	—	2	2	no	—
269	#97	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	D₄×C₄₁	1	2	yes	—
277	#95	D₄×C₄₁	1	2	yes	—
278	C₂⁴	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
293	D₈	—	4	4	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	#41×C₄₁	1	2	yes	—
301	C₂×C₈	#41×C₄₁	1	2	yes	—
302	C₂×C₈	#41×C₄₁	1	2	yes	—
303	C₂×C₈	#41×C₄₁	1	2	yes	—
304	C₂×C₈	#41×C₄₁	1	2	yes	—
305	C₂×C₈	#41×C₄₁	1	2	yes	—
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	—	8	2	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	—	8	2	no	—
319	C₂²⋊C₄	—	8	2	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	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	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
360	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	2	no	—
367	C₈	#126×C₄₁	1	4	yes	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	C₄₁×#532	1	1	yes	characteristic
376	C₂²	C₄₁×#532	1	1	yes	characteristic
377	C₂²	C₄₁×#532	1	1	yes	characteristic
378	C₂²	C₄₁×#576	1	2	yes	—
379	C₂²	C₄₁×#577	1	2	yes	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
388	C₄	C₄₁×#529	1	1	yes	characteristic
389	C₄	C₄₁×#529	1	1	yes	characteristic
390	C₄	C₄₁×#529	1	1	yes	characteristic
391	C₂	—	16	2	no	—
392	C₂	C₄₁×#2860	1	1	yes	characteristic
393	C₂	C₄₁×#3173	1	1	yes	characteristic
394	C₂	C₄₁×#3176	1	1	yes	characteristic
395	C₂	C₄₁×#3179	1	2	yes	—
396	C₂	C₄₁×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2644	C₂	semidirect
5. C₄₁×#1944	C₂	semidirect
6. C₄₁×#1943	C₂	semidirect
7. C₄₁×#1941	C₂	semidirect
8. C₄₁×#1936	C₂	semidirect
9. C₄₁×#1934	C₂	semidirect
10. C₄₁×#1934	C₂	semidirect
11. C₄₁×#1726	C₂	semidirect
169. #33275	C₄₁	direct (N × H)
193. #2644	C₂×C₄₁	semidirect
197. #1944	C₂×C₄₁	semidirect
198. #1943	C₂×C₄₁	semidirect
199. #1941	C₂×C₄₁	semidirect
200. #1936	C₂×C₄₁	semidirect
201. #1934	C₂×C₄₁	semidirect
202. #1934	C₂×C₄₁	semidirect
203. #1726	C₂×C₄₁	semidirect
237. C₄₁	#33275	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×#2644	2
C₄₁×#1972	2
C₄₁×#1970	2
C₄₁×#1944	2
C₄₁×#1943	2
C₄₁×#1941	2
C₄₁×#1936	2
C₄₁×#1934	2
C₄₁×#1726	2
#33275	41

Subgroups — C41×#33275 #23809476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33275 #23809476