Subgroups — C₄₁×#32986 #23809187

Order 10496.

1358 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2615	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1875	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1874	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1854	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1852	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1825	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1780	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#520	—	2	4	no	—
16	C₄₁×#520	—	2	4	no	—
17	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
18	C₂×C₄×D₄×C₄₁	—	2	2	no	—
19	C₂×C₄×D₄×C₄₁	—	2	1	no	—
20	C₂×#117×C₄₁	C₂²	1	2	yes	—
21	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#482	—	2	4	no	—
25	C₄₁×#480	—	2	4	no	—
26	C₂×#107×C₄₁	C₂²	1	2	yes	—
27	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
36	C₄₁×#393	—	2	1	no	—
37	C₄₁×#392	—	2	1	no	—
38	C₄₁×#392	—	2	2	no	—
39	C₄₁×#380	C₂²	1	1	yes	characteristic
40	C₄₁×#380	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	—	2	2	no	—
47	C₂×#41×C₄₁	—	2	4	no	—
48	C₂×#41×C₄₁	—	2	4	no	—
49	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	2	no	—
52	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	D₄	1	2	yes	—
54	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₁	—	2	2	no	—
56	C₂³×C₄×C₄₁	—	2	1	no	—
57	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
62	#121×C₄₁	—	2	2	no	—
63	#121×C₄₁	—	2	2	no	—
64	#121×C₄₁	—	2	4	no	—
65	#121×C₄₁	—	2	4	no	—
66	C₄×Q₈×C₄₁	—	2	8	no	—
67	C₄×D₄×C₄₁	—	2	16	no	—
68	C₄×D₄×C₄₁	—	2	8	no	—
69	#117×C₄₁	—	2	2	no	—
70	#117×C₄₁	—	2	4	no	—
71	#117×C₄₁	—	2	4	no	—
72	#117×C₄₁	D₄	1	4	yes	complemented
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	complemented
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₄²×C₄₁	—	2	2	no	—
91	C₂×C₄²×C₄₁	—	2	1	no	—
92	#107×C₄₁	—	2	4	no	—
93	#107×C₄₁	—	2	2	no	—
94	#106×C₄₁	—	2	2	no	—
95	#102×C₄₁	—	2	4	no	—
96	#102×C₄₁	—	2	2	no	—
97	#102×C₄₁	—	2	2	no	—
98	C₂²⋊C₈×C₄₁	—	2	2	no	—
99	C₂²⋊C₈×C₄₁	—	2	2	no	—
100	C₂²⋊C₈×C₄₁	—	2	4	no	—
101	C₂²⋊C₈×C₄₁	—	2	4	no	—
102	#95×C₄₁	—	2	1	no	—
103	#95×C₄₁	—	2	2	no	—
104	C₂⁴×C₄₁	—	2	1	no	—
105	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
107	#41×C₄₁	—	2	8	no	—
108	#41×C₄₁	—	2	8	no	—
109	#41×C₄₁	—	2	16	no	—
110	C₂×Q₈×C₄₁	—	2	2	no	—
111	C₂×Q₈×C₄₁	—	2	4	no	—
112	C₂×D₄×C₄₁	—	2	4	no	—
113	C₂×D₄×C₄₁	—	2	4	no	—
114	C₂×D₄×C₄₁	—	2	4	no	—
115	C₂×D₄×C₄₁	—	2	2	no	—
116	C₂×D₄×C₄₁	—	2	4	no	—
117	C₂×D₄×C₄₁	—	2	1	no	—
118	C₂×D₄×C₄₁	—	2	1	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	4	2	no	—
122	C₂×D₄×C₄₁	—	4	4	no	—
123	C₂×D₄×C₄₁	—	8	2	no	—
124	C₂×D₄×C₄₁	—	8	2	no	—
125	C₂×D₄×C₄₁	—	8	2	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	1	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	1	no	—
135	C₂²×C₄×C₄₁	—	2	8	no	—
136	C₂²×C₄×C₄₁	—	2	4	no	—
137	C₂²×C₄×C₄₁	—	2	1	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	8	2	no	—
140	C₂²×C₄×C₄₁	—	8	2	no	—
141	C₂²×C₄×C₄₁	—	8	2	no	—
142	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₁	#41	1	4	yes	—
147	C₂²×C₄×C₄₁	#41	1	4	yes	—
148	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
149	C₂×C₈×C₄₁	—	2	1	no	—
150	C₂×C₈×C₄₁	—	2	2	no	—
151	C₂×C₈×C₄₁	—	2	1	no	—
152	C₂×C₈×C₄₁	—	2	2	no	—
153	C₂×C₈×C₄₁	—	2	2	no	—
154	C₂×C₈×C₄₁	—	2	2	no	—
155	C₂×C₈×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	8	no	—
157	C₄⋊C₄×C₄₁	—	2	4	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	2	1	no	—
160	C₄⋊C₄×C₄₁	—	2	1	no	—
161	C₄⋊C₄×C₄₁	—	2	1	no	—
162	C₄⋊C₄×C₄₁	—	2	1	no	—
163	C₄⋊C₄×C₄₁	—	2	2	no	—
164	C₄⋊C₄×C₄₁	—	2	2	no	—
165	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
168	C₂²⋊C₄×C₄₁	—	2	8	no	—
169	C₂²⋊C₄×C₄₁	—	2	4	no	—
170	C₂²⋊C₄×C₄₁	—	4	2	no	—
171	C₂²⋊C₄×C₄₁	—	4	4	no	—
172	C₂²⋊C₄×C₄₁	—	8	2	no	—
173	C₂²⋊C₄×C₄₁	—	8	1	no	—
174	C₄²×C₄₁	—	2	8	no	—
175	C₄²×C₄₁	—	2	4	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	—	2	2	no	—
178	C₂³×C₄₁	—	2	2	no	—
179	C₂³×C₄₁	—	2	2	no	—
180	C₂³×C₄₁	—	2	2	no	—
181	C₂³×C₄₁	—	2	2	no	—
182	C₂³×C₄₁	—	2	1	no	—
183	C₂³×C₄₁	—	2	2	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	1	no	—
186	C₂³×C₄₁	—	4	1	no	—
187	C₂³×C₄₁	—	4	2	no	—
188	C₂³×C₄₁	—	4	2	no	—
189	C₂³×C₄₁	—	4	1	no	—
190	C₂³×C₄₁	—	4	1	no	—
191	C₂³×C₄₁	#120	1	2	yes	—
192	C₂³×C₄₁	#123	1	4	yes	—
193	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₄₁	—	2	8	no	—
195	D₄×C₄₁	—	2	8	no	—
196	D₄×C₄₁	—	2	16	no	—
197	D₄×C₄₁	—	4	2	no	—
198	D₄×C₄₁	—	4	1	no	—
199	D₄×C₄₁	—	4	1	no	—
200	D₄×C₄₁	—	8	8	no	—
201	D₄×C₄₁	—	8	4	no	—
202	C₂×C₄×C₄₁	—	2	2	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	2	no	—
207	C₂×C₄×C₄₁	—	2	4	no	—
208	C₂×C₄×C₄₁	—	2	4	no	—
209	C₂×C₄×C₄₁	—	2	4	no	—
210	C₂×C₄×C₄₁	—	2	4	no	—
211	C₂×C₄×C₄₁	—	2	4	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	4	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	4	2	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	4	2	no	—
218	C₂×C₄×C₄₁	—	4	1	no	—
219	C₂×C₄×C₄₁	—	4	1	no	—
220	C₂×C₄×C₄₁	—	4	1	no	—
221	C₂×C₄×C₄₁	—	4	2	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	8	4	no	—
226	C₂×C₄×C₄₁	—	8	8	no	—
227	C₂×C₄×C₄₁	#120	1	2	yes	—
228	C₂×C₄×C₄₁	#123	1	4	yes	—
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
232	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
233	C₈×C₄₁	—	4	1	no	—
234	C₈×C₄₁	—	4	2	no	—
235	C₈×C₄₁	—	4	1	no	—
236	#32986	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₄₁	—	2	4	no	—
238	C₂²×C₄₁	—	2	4	no	—
239	C₂²×C₄₁	—	2	2	no	—
240	C₂²×C₄₁	—	2	4	no	—
241	C₂²×C₄₁	—	2	2	no	—
242	C₂²×C₄₁	—	2	2	no	—
243	C₂²×C₄₁	—	4	2	no	—
244	C₂²×C₄₁	—	4	2	no	—
245	C₂²×C₄₁	—	4	2	no	—
246	C₂²×C₄₁	—	4	2	no	—
247	C₂²×C₄₁	—	4	2	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	8	2	no	—
250	C₂²×C₄₁	—	8	2	no	—
251	C₂²×C₄₁	—	8	1	no	—
252	C₂²×C₄₁	—	8	1	no	—
253	C₂²×C₄₁	—	8	1	no	—
254	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
255	C₂²×C₄₁	C₂×#123	1	2	yes	—
256	C₂²×C₄₁	#576	1	2	yes	—
257	C₂²×C₄₁	#577	1	1	yes	characteristic
258	C₂²×C₄₁	#578	1	1	yes	characteristic
259	C₄×C₄₁	—	2	2	no	—
260	C₄×C₄₁	—	2	4	no	—
261	C₄×C₄₁	—	4	4	no	—
262	C₄×C₄₁	—	4	2	no	—
263	C₄×C₄₁	—	4	2	no	—
264	C₄×C₄₁	—	8	2	no	—
265	C₄×C₄₁	—	8	1	no	—
266	C₄×C₄₁	#525	1	1	yes	characteristic
267	C₄×C₄₁	#525	1	1	yes	characteristic
268	C₄×C₄₁	#525	1	2	yes	—
269	C₂×#520	C₂×C₄₁	1	1	yes	characteristic, complemented
270	C₂×#482	C₂×C₄₁	1	1	yes	characteristic, complemented
271	C₂×#480	C₂×C₄₁	1	1	yes	characteristic, complemented
272	#2615	C₂×C₄₁	1	1	yes	characteristic
273	#1875	C₂×C₄₁	1	2	yes	complemented
274	#1874	C₂×C₄₁	1	2	yes	complemented
275	#1854	C₂×C₄₁	1	2	yes	complemented
276	#1852	C₂×C₄₁	1	2	yes	complemented
277	#1825	C₂×C₄₁	1	1	yes	characteristic, complemented
278	#1824	C₂×C₄₁	1	1	yes	characteristic, complemented
279	#1780	C₂×C₄₁	1	1	yes	characteristic, complemented
280	C₂×C₄₁	—	4	4	no	—
281	C₂×C₄₁	—	4	2	no	—
282	C₂×C₄₁	—	16	1	no	—
283	C₂×C₄₁	#2849	1	1	yes	characteristic
284	C₂×C₄₁	#3008	1	1	yes	characteristic
285	C₂×C₄₁	#3013	1	1	yes	characteristic
286	C₂×C₄₁	#3096	1	2	yes	—
287	C₂×C₄₁	#3098	1	2	yes	—
288	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
290	C₂×#121	C₂²×C₄₁	1	2	yes	—
291	#520	—	2	4	no	—
292	#520	—	2	4	no	—
293	C₂×C₄×Q₈	—	2	1	no	—
294	C₂×C₄×D₄	—	2	2	no	—
295	C₂×C₄×D₄	—	2	1	no	—
296	C₂×#117	C₂²×C₄₁	1	2	yes	—
297	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
299	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
300	#482	—	2	4	no	—
301	#480	—	2	4	no	—
302	C₂×#107	C₂²×C₄₁	1	2	yes	—
303	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
304	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
305	C₂×#102	C₂²×C₄₁	1	2	yes	—
306	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
307	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
310	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
312	#393	—	2	1	no	—
313	#392	—	2	1	no	—
314	#392	—	2	2	no	—
315	#380	C₂²×C₄₁	1	1	yes	characteristic
316	#380	C₂²×C₄₁	1	2	yes	—
317	#340	C₂²×C₄₁	1	2	yes	—
318	#340	C₂²×C₄₁	1	2	yes	—
319	#340	C₂²×C₄₁	1	2	yes	—
320	#340	C₂²×C₄₁	1	2	yes	—
321	C₄₁	#32986	1	1	yes	characteristic, direct product factor, Sylow
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	4	no	—
325	C₂×#41	—	2	4	no	—
326	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
330	C₂²×D₄	D₄×C₄₁	1	2	yes	—
331	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
336	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
339	#121	—	2	2	no	—
340	#121	—	2	2	no	—
341	#121	—	2	4	no	—
342	#121	—	2	4	no	—
343	C₄×Q₈	—	2	8	no	—
344	C₄×D₄	—	2	16	no	—
345	C₄×D₄	—	2	8	no	—
346	#117	—	2	2	no	—
347	#117	—	2	4	no	—
348	#117	—	2	4	no	—
349	#117	D₄×C₄₁	1	4	yes	complemented
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	complemented
356	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	1	no	—
369	#107	—	2	4	no	—
370	#107	—	2	2	no	—
371	#106	—	2	2	no	—
372	#102	—	2	4	no	—
373	#102	—	2	2	no	—
374	#102	—	2	2	no	—
375	C₂²⋊C₈	—	2	2	no	—
376	C₂²⋊C₈	—	2	2	no	—
377	C₂²⋊C₈	—	2	4	no	—
378	C₂²⋊C₈	—	2	4	no	—
379	#95	—	2	1	no	—
380	#95	—	2	2	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
383	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
384	#41	—	2	8	no	—
385	#41	—	2	8	no	—
386	#41	—	2	16	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	8	2	no	—
401	C₂×D₄	—	8	2	no	—
402	C₂×D₄	—	8	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	8	2	no	—
417	C₂²×C₄	—	8	2	no	—
418	C₂²×C₄	—	8	2	no	—
419	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
422	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
423	C₂²×C₄	#41×C₄₁	1	4	yes	—
424	C₂²×C₄	#41×C₄₁	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
444	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	—	8	2	no	—
450	C₂²⋊C₄	—	8	1	no	—
451	C₄²	—	2	8	no	—
452	C₄²	—	2	4	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	#120×C₄₁	1	2	yes	—
469	C₂³	#123×C₄₁	1	4	yes	—
470	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
471	Q₈	—	2	8	no	—
472	D₄	—	2	8	no	—
473	D₄	—	2	16	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	1	no	—
477	D₄	—	8	8	no	—
478	D₄	—	8	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	8	4	no	—
503	C₂×C₄	—	8	8	no	—
504	C₂×C₄	#120×C₄₁	1	2	yes	—
505	C₂×C₄	#123×C₄₁	1	4	yes	—
506	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
509	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
510	C₈	—	4	1	no	—
511	C₈	—	4	2	no	—
512	C₈	—	4	1	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
531	C₂²	C₂×#123×C₄₁	1	2	yes	—
532	C₂²	C₄₁×#576	1	2	yes	—
533	C₂²	C₄₁×#577	1	1	yes	characteristic
534	C₂²	C₄₁×#578	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	4	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	8	2	no	—
541	C₄	—	8	1	no	—
542	C₄	C₄₁×#525	1	1	yes	characteristic
543	C₄	C₄₁×#525	1	1	yes	characteristic
544	C₄	C₄₁×#525	1	2	yes	—
545	C₂	—	4	4	no	—
546	C₂	—	4	2	no	—
547	C₂	—	16	1	no	—
548	C₂	C₄₁×#2849	1	1	yes	characteristic
549	C₂	C₄₁×#3008	1	1	yes	characteristic
550	C₂	C₄₁×#3013	1	1	yes	characteristic
551	C₂	C₄₁×#3096	1	2	yes	—
552	C₂	C₄₁×#3098	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#2615	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#520	C₂	semidirect
2. C₂×C₄₁×#482	C₂	semidirect
3. C₂×C₄₁×#480	C₂	semidirect
5. C₄₁×#1875	C₂	semidirect
6. C₄₁×#1874	C₂	semidirect
7. C₄₁×#1854	C₂	semidirect
8. C₄₁×#1852	C₂	semidirect
9. C₄₁×#1825	C₂	semidirect
10. C₄₁×#1824	C₂	semidirect
11. C₄₁×#1780	C₂	semidirect
72. #117×C₄₁	D₄	semidirect
78. C₂×C₄⋊C₄×C₄₁	D₄	semidirect
236. #32986	C₄₁	direct (N × H)
269. C₂×#520	C₂×C₄₁	semidirect
270. C₂×#482	C₂×C₄₁	semidirect
271. C₂×#480	C₂×C₄₁	semidirect
273. #1875	C₂×C₄₁	semidirect
274. #1874	C₂×C₄₁	semidirect
275. #1854	C₂×C₄₁	semidirect
276. #1852	C₂×C₄₁	semidirect
277. #1825	C₂×C₄₁	semidirect
278. #1824	C₂×C₄₁	semidirect
279. #1780	C₂×C₄₁	semidirect
321. C₄₁	#32986	direct (N × H)
349. #117	D₄×C₄₁	semidirect
355. C₂×C₄⋊C₄	D₄×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×#520	2
C₂×C₄₁×#482	2
C₂×C₄₁×#480	2
C₄₁×#2615	2
C₄₁×#1875	2
C₄₁×#1874	2
C₄₁×#1854	2
C₄₁×#1852	2
C₄₁×#1825	2
C₄₁×#1824	2
C₄₁×#1780	2
#32986	41

Subgroups — C41×#32986 #23809187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#32986 #23809187