Subgroups — C₄₁×#21286 #23797487

Order 10496.

950 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#442	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2293	C₂	1	2	yes	maximal, complemented
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×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1936	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1934	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1776	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1762	C₂	1	2	yes	maximal, complemented
11	C₄×#97×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
14	C₂×#117×C₄₁	—	2	2	no	—
15	C₄₁×#442	C₄	1	8	yes	complemented
16	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#102×C₄₁	C₂²	1	2	yes	—
20	C₂×#102×C₄₁	C₂²	1	2	yes	—
21	C₂×#102×C₄₁	C₂²	1	2	yes	—
22	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#390	C₂²	1	2	yes	—
29	C₄₁×#390	C₂²	1	2	yes	—
30	C₄₁×#389	C₂²	1	2	yes	—
31	C₄₁×#389	C₂²	1	2	yes	—
32	C₄₁×#388	—	2	2	no	—
33	C₄₁×#388	—	2	2	no	—
34	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
36	C₄³×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#340	C₂²	1	2	yes	—
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₁	—	2	2	no	—
42	C₂×D₈×C₄₁	—	2	2	no	—
43	C₂×D₈×C₄₁	—	2	2	no	—
44	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
49	C₄×D₄×C₄₁	—	2	4	no	—
50	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	—
51	#117×C₄₁	—	4	8	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
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	D₄	1	2	yes	—
64	C₂×C₄²×C₄₁	D₄	1	2	yes	—
65	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
68	#107×C₄₁	—	2	2	no	—
69	#106×C₄₁	—	2	2	no	—
70	#106×C₄₁	C₂×C₄	1	4	yes	—
71	#102×C₄₁	—	2	4	no	—
72	#102×C₄₁	—	2	4	no	—
73	#102×C₄₁	C₂×C₄	1	8	yes	—
74	#97×C₄₁	—	2	2	no	—
75	#97×C₄₁	—	2	2	no	—
76	#97×C₄₁	—	2	2	no	—
77	#97×C₄₁	C₂×C₄	1	4	yes	—
78	C₄×C₈×C₄₁	—	2	2	no	—
79	C₄×C₈×C₄₁	—	2	2	no	—
80	#95×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	2	no	—
82	#95×C₄₁	—	2	2	no	—
83	C₂⁴×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	8	no	—
92	C₂²×C₄×C₄₁	—	2	2	no	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	4	4	no	—
95	C₂²×C₄×C₄₁	—	4	4	no	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
101	D₈×C₄₁	—	2	8	no	—
102	C₂×C₈×C₄₁	—	2	1	no	—
103	C₂×C₈×C₄₁	—	2	1	no	—
104	C₂×C₈×C₄₁	—	2	1	no	—
105	C₂×C₈×C₄₁	—	2	1	no	—
106	C₂×C₈×C₄₁	—	2	1	no	—
107	C₂×C₈×C₄₁	—	2	1	no	—
108	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₁	#41	1	2	yes	—
111	C₂×C₈×C₄₁	#41	1	2	yes	—
112	C₂×C₈×C₄₁	#41	1	2	yes	—
113	C₂×C₈×C₄₁	#41	1	2	yes	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	2	no	—
118	C₄⋊C₄×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	—	4	4	no	—
120	C₄⋊C₄×C₄₁	—	4	4	no	—
121	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
122	C₂²⋊C₄×C₄₁	—	2	8	no	—
123	C₂²⋊C₄×C₄₁	—	4	4	no	—
124	C₂²⋊C₄×C₄₁	—	4	4	no	—
125	C₂²⋊C₄×C₄₁	—	4	4	no	—
126	C₂²⋊C₄×C₄₁	—	4	4	no	—
127	C₄²×C₄₁	—	2	4	no	—
128	C₄²×C₄₁	—	2	1	no	—
129	C₄²×C₄₁	—	2	1	no	—
130	C₄²×C₄₁	—	2	1	no	—
131	C₄²×C₄₁	—	2	1	no	—
132	C₄²×C₄₁	—	4	2	no	—
133	C₄²×C₄₁	—	4	4	no	—
134	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₁	#41	1	2	yes	—
136	C₂³×C₄₁	—	2	4	no	—
137	C₂³×C₄₁	—	4	2	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	2	no	—
140	C₂³×C₄₁	—	4	2	no	—
141	C₂³×C₄₁	—	4	2	no	—
142	C₂³×C₄₁	—	4	2	no	—
143	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
144	D₄×C₄₁	—	2	4	no	—
145	D₄×C₄₁	—	2	4	no	—
146	D₄×C₄₁	—	4	2	no	—
147	D₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	4	no	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	2	1	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	4	16	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
167	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
168	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₄₁	—	2	2	no	—
175	C₈×C₄₁	—	2	2	no	—
176	C₈×C₄₁	—	2	2	no	—
177	C₈×C₄₁	#117	1	4	yes	complemented
178	#21286	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	4	4	no	—
180	C₂²×C₄₁	—	4	4	no	—
181	C₂²×C₄₁	—	4	4	no	—
182	C₂²×C₄₁	—	8	2	no	—
183	C₂²×C₄₁	—	8	2	no	—
184	C₂²×C₄₁	—	8	2	no	—
185	C₂²×C₄₁	—	8	2	no	—
186	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₁	#532	1	1	yes	characteristic
188	C₂²×C₄₁	#532	1	1	yes	characteristic
189	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
190	C₂²×C₄₁	#575	1	2	yes	—
191	C₄×C₄₁	—	2	4	no	—
192	C₄×C₄₁	—	2	4	no	—
193	C₄×C₄₁	—	4	1	no	—
194	C₄×C₄₁	—	4	1	no	—
195	C₄×C₄₁	—	4	4	no	—
196	C₄×C₄₁	—	8	2	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
199	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
200	C₄×C₄₁	#529	1	1	yes	characteristic
201	C₄×C₄₁	#529	1	1	yes	characteristic
202	C₂×#442	C₂×C₄₁	1	1	yes	characteristic
203	#2293	C₂×C₄₁	1	2	yes	complemented
204	#1972	C₂×C₄₁	1	1	yes	characteristic
205	#1970	C₂×C₄₁	1	1	yes	characteristic
206	#1944	C₂×C₄₁	1	1	yes	characteristic, complemented
207	#1941	C₂×C₄₁	1	1	yes	characteristic, complemented
208	#1936	C₂×C₄₁	1	2	yes	complemented
209	#1934	C₂×C₄₁	1	2	yes	complemented
210	#1776	C₂×C₄₁	1	1	yes	characteristic, complemented
211	#1762	C₂×C₄₁	1	2	yes	complemented
212	C₄×#97	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₂×C₄₁	—	8	4	no	—
214	C₂×C₄₁	#2293	1	1	yes	characteristic
215	C₂×C₄₁	C₄×AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄₁	#3180	1	2	yes	—
217	C₂×C₄₁	#3183	1	1	yes	characteristic
218	C₂×C₄₁	#3184	1	1	yes	characteristic
219	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
221	C₂×#117	—	2	2	no	—
222	#442	C₄×C₄₁	1	8	yes	complemented
223	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#102	C₂²×C₄₁	1	2	yes	—
227	C₂×#102	C₂²×C₄₁	1	2	yes	—
228	C₂×#102	C₂²×C₄₁	1	2	yes	—
229	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
230	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
232	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
235	#390	C₂²×C₄₁	1	2	yes	—
236	#390	C₂²×C₄₁	1	2	yes	—
237	#389	C₂²×C₄₁	1	2	yes	—
238	#389	C₂²×C₄₁	1	2	yes	—
239	#388	—	2	2	no	—
240	#388	—	2	2	no	—
241	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
242	C₄×C₂²⋊C₄	—	2	2	no	—
243	C₄³	C₂²×C₄₁	1	1	yes	characteristic
244	#340	C₂²×C₄₁	1	2	yes	—
245	#340	C₂²×C₄₁	1	2	yes	—
246	#340	C₂²×C₄₁	1	2	yes	—
247	C₄₁	#21286	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂×D₈	—	2	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	—
253	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	—
259	#117	—	4	8	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	D₄×C₄₁	1	2	yes	—
272	C₂×C₄²	D₄×C₄₁	1	2	yes	—
273	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
276	#107	—	2	2	no	—
277	#106	—	2	2	no	—
278	#106	C₂×C₄×C₄₁	1	4	yes	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	#102	C₂×C₄×C₄₁	1	8	yes	—
282	#97	—	2	2	no	—
283	#97	—	2	2	no	—
284	#97	—	2	2	no	—
285	#97	C₂×C₄×C₄₁	1	4	yes	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂⁴	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
309	D₈	—	2	8	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
318	C₂×C₈	#41×C₄₁	1	2	yes	—
319	C₂×C₈	#41×C₄₁	1	2	yes	—
320	C₂×C₈	#41×C₄₁	1	2	yes	—
321	C₂×C₈	#41×C₄₁	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	4	4	no	—
342	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
343	C₄²	#41×C₄₁	1	2	yes	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
352	D₄	—	2	4	no	—
353	D₄	—	2	4	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
375	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
376	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	#117×C₄₁	1	4	yes	complemented
386	C₂²	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
394	C₂²	C₄₁×#532	1	1	yes	characteristic
395	C₂²	C₄₁×#532	1	1	yes	characteristic
396	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
397	C₂²	C₄₁×#575	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	4	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
406	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
407	C₄	C₄₁×#529	1	1	yes	characteristic
408	C₄	C₄₁×#529	1	1	yes	characteristic
409	C₂	—	8	4	no	—
410	C₂	C₄₁×#2293	1	1	yes	characteristic
411	C₂	C₄×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
412	C₂	C₄₁×#3180	1	2	yes	—
413	C₂	C₄₁×#3183	1	1	yes	characteristic
414	C₂	C₄₁×#3184	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2293	C₂	semidirect
5. C₄₁×#1944	C₂	semidirect
6. C₄₁×#1941	C₂	semidirect
7. C₄₁×#1936	C₂	semidirect
8. C₄₁×#1934	C₂	semidirect
9. C₄₁×#1776	C₂	semidirect
10. C₄₁×#1762	C₂	semidirect
11. C₄×#97×C₄₁	C₂	semidirect
15. C₄₁×#442	C₄	semidirect
177. C₈×C₄₁	#117	semidirect
178. #21286	C₄₁	direct (N × H)
203. #2293	C₂×C₄₁	semidirect
206. #1944	C₂×C₄₁	semidirect
207. #1941	C₂×C₄₁	semidirect
208. #1936	C₂×C₄₁	semidirect
209. #1934	C₂×C₄₁	semidirect
210. #1776	C₂×C₄₁	semidirect
211. #1762	C₂×C₄₁	semidirect
212. C₄×#97	C₂×C₄₁	semidirect
222. #442	C₄×C₄₁	semidirect
247. C₄₁	#21286	direct (N × H)
385. C₈	#117×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#442	2
C₄₁×#2293	2
C₄₁×#1972	2
C₄₁×#1970	2
C₄₁×#1944	2
C₄₁×#1941	2
C₄₁×#1936	2
C₄₁×#1934	2
C₄₁×#1776	2
C₄₁×#1762	2
C₄×#97×C₄₁	2
#21286	41

Subgroups — C41×#21286 #23797487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21286 #23797487