Subgroups — C₄₁×#24971 #23801172

Order 10496.

842 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2538	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2076	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2036	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1954	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1872	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1824	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₁	—	2	1	no	—
15	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
17	C₂×#107×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#103×C₄₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#396	—	2	2	no	—
26	C₄₁×#390	—	2	1	no	—
27	C₄₁×#389	—	2	1	no	—
28	C₄₁×#389	—	2	1	no	—
29	C₄₁×#385	—	2	2	no	—
30	C₄₁×#384	C₂²	1	1	yes	characteristic
31	C₄₁×#384	C₂²	1	1	yes	characteristic
32	C₄₁×#380	C₂²	1	2	yes	—
33	C₄₁×#380	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#340	C₂²	1	1	yes	characteristic
36	C₄₁×#340	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	C₄₁×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₁	—	2	2	no	—
44	C₂³×C₄×C₄₁	C₂³	1	2	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	2	yes	—
48	C₂²⋊Q₈×C₄₁	—	2	4	no	—
49	C₂²⋊Q₈×C₄₁	—	4	2	no	—
50	C₄×Q₈×C₄₁	—	2	2	no	—
51	C₄×Q₈×C₄₁	—	2	2	no	—
52	C₄×D₄×C₄₁	—	2	2	no	—
53	C₄×D₄×C₄₁	—	2	2	no	—
54	C₄×D₄×C₄₁	—	4	4	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
64	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
74	C₂×C₄²×C₄₁	—	2	1	no	—
75	C₂×C₄²×C₄₁	—	2	1	no	—
76	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
77	#107×C₄₁	—	4	2	no	—
78	C₄⋊C₈×C₄₁	—	2	2	no	—
79	#103×C₄₁	—	2	2	no	—
80	#103×C₄₁	—	2	2	no	—
81	#103×C₄₁	—	4	2	no	—
82	C₂²⋊C₈×C₄₁	—	4	2	no	—
83	C₂²⋊C₈×C₄₁	—	4	2	no	—
84	C₄×C₈×C₄₁	—	2	2	no	—
85	#95×C₄₁	—	2	1	no	—
86	#95×C₄₁	—	2	2	no	—
87	#95×C₄₁	—	2	2	no	—
88	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
89	C₂×Q₈×C₄₁	—	2	1	no	—
90	C₂×Q₈×C₄₁	—	2	1	no	—
91	C₂×Q₈×C₄₁	—	2	1	no	—
92	C₂×Q₈×C₄₁	—	2	1	no	—
93	C₂×Q₈×C₄₁	—	2	1	no	—
94	C₂×Q₈×C₄₁	#41	1	2	yes	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	2	2	no	—
97	C₂×D₄×C₄₁	Q₁₆	1	4	yes	—
98	C₂²×C₄×C₄₁	—	2	1	no	—
99	C₂²×C₄×C₄₁	—	2	1	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	2	2	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	4	4	no	—
111	C₂²×C₄×C₄₁	—	4	4	no	—
112	C₂²×C₄×C₄₁	—	8	2	no	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₄₁	—	2	1	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	1	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	2	1	no	—
123	C₂×C₈×C₄₁	—	2	1	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	2	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	1	no	—
131	C₄⋊C₄×C₄₁	—	2	1	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	2	1	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	4	4	no	—
137	C₄⋊C₄×C₄₁	—	4	4	no	—
138	C₄⋊C₄×C₄₁	—	4	2	no	—
139	C₄⋊C₄×C₄₁	—	4	2	no	—
140	C₄⋊C₄×C₄₁	—	4	2	no	—
141	C₄⋊C₄×C₄₁	—	8	1	no	—
142	C₄⋊C₄×C₄₁	—	8	1	no	—
143	C₄⋊C₄×C₄₁	#41	1	2	yes	—
144	C₂²⋊C₄×C₄₁	—	2	4	no	—
145	C₂²⋊C₄×C₄₁	—	4	4	no	—
146	C₂²⋊C₄×C₄₁	—	4	4	no	—
147	C₂²⋊C₄×C₄₁	—	8	2	no	—
148	C₄²×C₄₁	—	4	2	no	—
149	C₄²×C₄₁	—	4	2	no	—
150	C₄²×C₄₁	#41	1	2	yes	—
151	C₄²×C₄₁	#41	1	2	yes	—
152	C₂³×C₄₁	—	2	2	no	—
153	C₂³×C₄₁	—	2	2	no	—
154	C₂³×C₄₁	—	2	2	no	—
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	2	2	no	—
157	C₂³×C₄₁	—	2	2	no	—
158	C₂³×C₄₁	C₂×Q₁₆	1	4	yes	—
159	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₄₁	—	2	2	no	—
161	Q₈×C₄₁	—	2	2	no	—
162	Q₈×C₄₁	—	4	1	no	—
163	Q₈×C₄₁	—	4	1	no	—
164	D₄×C₄₁	—	2	8	no	—
165	C₂×C₄×C₄₁	—	2	1	no	—
166	C₂×C₄×C₄₁	—	2	1	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	4	1	no	—
173	C₂×C₄×C₄₁	—	4	1	no	—
174	C₂×C₄×C₄₁	—	4	1	no	—
175	C₂×C₄×C₄₁	—	4	1	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	1	no	—
184	C₂×C₄×C₄₁	—	4	1	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	1	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	1	no	—
191	C₂×C₄×C₄₁	—	4	1	no	—
192	C₂×C₄×C₄₁	—	8	8	no	—
193	C₂×C₄×C₄₁	#123	1	2	yes	—
194	C₂×C₄×C₄₁	#123	1	2	yes	—
195	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
196	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
203	C₈×C₄₁	—	4	2	no	—
204	C₈×C₄₁	—	4	1	no	—
205	C₈×C₄₁	—	4	1	no	—
206	#24971	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₁	—	2	4	no	—
208	C₂²×C₄₁	—	2	4	no	—
209	C₂²×C₄₁	—	2	4	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	—	4	2	no	—
212	C₂²×C₄₁	—	4	2	no	—
213	C₂²×C₄₁	—	4	2	no	—
214	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
215	C₂²×C₄₁	#546	1	1	yes	characteristic
216	C₂²×C₄₁	#546	1	1	yes	characteristic
217	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
218	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂²×C₄₁	#577	1	1	yes	characteristic
220	C₂²×C₄₁	#577	1	1	yes	characteristic
221	C₄×C₄₁	—	2	2	no	—
222	C₄×C₄₁	—	4	2	no	—
223	C₄×C₄₁	—	4	2	no	—
224	C₄×C₄₁	—	4	2	no	—
225	C₄×C₄₁	—	8	2	no	—
226	C₄×C₄₁	—	8	1	no	—
227	C₄×C₄₁	—	8	1	no	—
228	C₄×C₄₁	—	8	2	no	—
229	C₄×C₄₁	#484	1	4	yes	—
230	C₄×C₄₁	#529	1	1	yes	characteristic
231	C₄×C₄₁	#540	1	1	yes	characteristic
232	C₄×C₄₁	#553	1	1	yes	characteristic
233	C₄×C₄₁	#555	1	1	yes	characteristic
234	#2538	C₂×C₄₁	1	1	yes	characteristic
235	D₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
236	#2076	C₂×C₄₁	1	2	yes	complemented
237	#2036	C₂×C₄₁	1	2	yes	complemented
238	#1954	C₂×C₄₁	1	1	yes	characteristic
239	#1947	C₂×C₄₁	1	1	yes	characteristic, complemented
240	#1872	C₂×C₄₁	1	2	yes	complemented
241	#1834	C₂×C₄₁	1	1	yes	characteristic, complemented
242	#1824	C₂×C₄₁	1	2	yes	complemented
243	#1803	C₂×C₄₁	1	1	yes	characteristic, complemented
244	C₄×#103	C₂×C₄₁	1	1	yes	characteristic, complemented
245	C₂×C₄₁	—	4	4	no	—
246	C₂×C₄₁	#2420	1	1	yes	characteristic
247	C₂×C₄₁	C₂×#484	1	1	yes	characteristic
248	C₂×C₄₁	#3099	1	1	yes	characteristic
249	C₂×C₄₁	#3299	1	1	yes	characteristic
250	C₂×C₄₁	#3299	1	1	yes	characteristic
251	C₂×C₄₁	#3324	1	1	yes	characteristic
252	C₂×C₄₁	#3332	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×C₄×D₄	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
258	C₂×#107	C₂²×C₄₁	1	2	yes	—
259	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
261	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×#103	C₂²×C₄₁	1	2	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
266	#396	—	2	2	no	—
267	#390	—	2	1	no	—
268	#389	—	2	1	no	—
269	#389	—	2	1	no	—
270	#385	—	2	2	no	—
271	#384	C₂²×C₄₁	1	1	yes	characteristic
272	#384	C₂²×C₄₁	1	1	yes	characteristic
273	#380	C₂²×C₄₁	1	2	yes	—
274	#380	C₂²×C₄₁	1	2	yes	—
275	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
276	#340	C₂²×C₄₁	1	2	yes	—
277	#340	C₂²×C₄₁	1	1	yes	characteristic
278	#340	C₂²×C₄₁	1	2	yes	—
279	#340	C₂²×C₄₁	1	1	yes	characteristic
280	#340	C₂²×C₄₁	1	2	yes	—
281	#340	C₂²×C₄₁	1	2	yes	—
282	C₄₁	#24971	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
284	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
287	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	4	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	4	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	4	2	no	—
306	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
319	#107	—	4	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#103	—	4	2	no	—
324	C₂²⋊C₈	—	4	2	no	—
325	C₂²⋊C₈	—	4	2	no	—
326	C₄×C₈	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	#41×C₄₁	1	2	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	Q₁₆×C₄₁	1	4	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	8	2	no	—
355	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	8	1	no	—
384	C₄⋊C₄	—	8	1	no	—
385	C₄⋊C₄	#41×C₄₁	1	2	yes	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₄²	—	4	2	no	—
391	C₄²	—	4	2	no	—
392	C₄²	#41×C₄₁	1	2	yes	—
393	C₄²	#41×C₄₁	1	2	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	C₂×Q₁₆×C₄₁	1	4	yes	—
401	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	D₄	—	2	8	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	8	8	no	—
435	C₂×C₄	#123×C₄₁	1	2	yes	—
436	C₂×C₄	#123×C₄₁	1	2	yes	—
437	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
438	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
439	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
443	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
444	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
445	C₈	—	4	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
456	C₂²	C₄₁×#546	1	1	yes	characteristic
457	C₂²	C₄₁×#546	1	1	yes	characteristic
458	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
459	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
460	C₂²	C₄₁×#577	1	1	yes	characteristic
461	C₂²	C₄₁×#577	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₄₁×#484	1	4	yes	—
471	C₄	C₄₁×#529	1	1	yes	characteristic
472	C₄	C₄₁×#540	1	1	yes	characteristic
473	C₄	C₄₁×#553	1	1	yes	characteristic
474	C₄	C₄₁×#555	1	1	yes	characteristic
475	C₂	—	4	4	no	—
476	C₂	C₄₁×#2420	1	1	yes	characteristic
477	C₂	C₂×C₄₁×#484	1	1	yes	characteristic
478	C₂	C₄₁×#3099	1	1	yes	characteristic
479	C₂	C₄₁×#3299	1	1	yes	characteristic
480	C₂	C₄₁×#3299	1	1	yes	characteristic
481	C₂	C₄₁×#3324	1	1	yes	characteristic
482	C₂	C₄₁×#3332	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄₁×#2076	C₂	semidirect
4. C₄₁×#2036	C₂	semidirect
6. C₄₁×#1947	C₂	semidirect
7. C₄₁×#1872	C₂	semidirect
8. C₄₁×#1834	C₂	semidirect
9. C₄₁×#1824	C₂	semidirect
10. C₄₁×#1803	C₂	semidirect
11. C₄×#103×C₄₁	C₂	semidirect
206. #24971	C₄₁	direct (N × H)
236. #2076	C₂×C₄₁	semidirect
237. #2036	C₂×C₄₁	semidirect
239. #1947	C₂×C₄₁	semidirect
240. #1872	C₂×C₄₁	semidirect
241. #1834	C₂×C₄₁	semidirect
242. #1824	C₂×C₄₁	semidirect
243. #1803	C₂×C₄₁	semidirect
244. C₄×#103	C₂×C₄₁	semidirect
282. C₄₁	#24971	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×#2538	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#2076	2
C₄₁×#2036	2
C₄₁×#1954	2
C₄₁×#1947	2
C₄₁×#1872	2
C₄₁×#1834	2
C₄₁×#1824	2
C₄₁×#1803	2
C₄×#103×C₄₁	2
#24971	41

Subgroups — C41×#24971 #23801172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24971 #23801172