Subgroups — C₄₁×#25661 #23801862

Order 10496.

1048 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#489	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2043	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2042	C₂	1	2	yes	maximal
7	C₄₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1983	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1863	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1862	C₂	1	2	yes	maximal
11	C₄₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#556	—	2	4	no	—
13	C₄₁×#556	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₁	—	2	1	no	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#126×C₄₁	—	2	1	no	—
18	C₂×#126×C₄₁	—	2	1	no	—
19	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
22	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₁	—	2	1	no	—
27	C₄₁×#489	—	2	4	no	—
28	C₄₁×#477	—	2	4	no	—
29	C₂×#107×C₄₁	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×#103×C₄₁	C₂²	1	2	yes	—
33	C₂×#103×C₄₁	C₂²	1	2	yes	—
34	C₂×#103×C₄₁	C₂²	1	2	yes	—
35	C₂×#102×C₄₁	C₂²	1	2	yes	—
36	C₂×#102×C₄₁	C₂²	1	2	yes	—
37	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
38	C₄₁×#398	—	2	1	no	—
39	C₄₁×#398	—	2	1	no	—
40	C₄₁×#391	—	2	1	no	—
41	C₄₁×#389	C₂²	1	2	yes	—
42	C₄₁×#389	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₄₁×#336	C₂²	1	2	yes	—
46	C₄₁×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₁	—	2	1	no	—
48	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₁	—	2	1	no	—
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₄₁	—	2	2	no	—
56	C₄⋊Q₈×C₄₁	—	2	2	no	—
57	C₄⋊Q₈×C₄₁	—	2	2	no	—
58	C₄⋊Q₈×C₄₁	—	2	2	no	—
59	C₄⋊Q₈×C₄₁	—	4	4	no	—
60	#126×C₄₁	—	2	8	no	—
61	#126×C₄₁	—	2	8	no	—
62	#124×C₄₁	—	2	2	no	—
63	#124×C₄₁	—	2	2	no	—
64	#124×C₄₁	—	2	2	no	—
65	#124×C₄₁	D₄	1	4	yes	—
66	C₂²⋊Q₈×C₄₁	—	2	8	no	—
67	C₄×Q₈×C₄₁	—	2	2	no	—
68	C₄×Q₈×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×Q₈×C₄₁	—	2	2	no	—
71	C₄×Q₈×C₄₁	—	2	2	no	—
72	C₄×Q₈×C₄₁	D₄	1	4	yes	—
73	C₄×D₄×C₄₁	—	2	2	no	—
74	C₄×D₄×C₄₁	—	2	2	no	—
75	#117×C₄₁	—	2	8	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₄²×C₄₁	—	2	1	no	—
95	C₂×C₄²×C₄₁	—	2	1	no	—
96	C₂×C₄²×C₄₁	—	2	1	no	—
97	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
100	#107×C₄₁	—	2	4	no	—
101	C₄⋊C₈×C₄₁	—	2	2	no	—
102	#103×C₄₁	—	2	4	no	—
103	#103×C₄₁	—	2	4	no	—
104	#103×C₄₁	—	2	4	no	—
105	#103×C₄₁	—	2	4	no	—
106	#102×C₄₁	—	2	4	no	—
107	#102×C₄₁	—	2	4	no	—
108	#97×C₄₁	—	2	2	no	—
109	#95×C₄₁	—	2	1	no	—
110	#95×C₄₁	—	2	2	no	—
111	#95×C₄₁	—	2	2	no	—
112	C₂⁴×C₄₁	—	2	1	no	—
113	C₂×Q₈×C₄₁	—	2	2	no	—
114	C₂×Q₈×C₄₁	—	2	2	no	—
115	C₂×Q₈×C₄₁	—	2	1	no	—
116	C₂×Q₈×C₄₁	—	2	1	no	—
117	C₂×Q₈×C₄₁	—	2	2	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	4	1	no	—
122	C₂×Q₈×C₄₁	—	4	2	no	—
123	C₂×Q₈×C₄₁	—	4	2	no	—
124	C₂×Q₈×C₄₁	—	4	2	no	—
125	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
126	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₄₁	—	2	1	no	—
128	C₂×D₄×C₄₁	—	2	2	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₁	—	2	4	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	1	no	—
134	C₂²×C₄×C₄₁	—	2	1	no	—
135	C₂²×C₄×C₄₁	—	2	1	no	—
136	C₂²×C₄×C₄₁	—	2	2	no	—
137	C₂²×C₄×C₄₁	—	4	2	no	—
138	C₂²×C₄×C₄₁	—	4	2	no	—
139	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₄₁	—	2	2	no	—
147	C₂×C₈×C₄₁	—	2	2	no	—
148	C₂×C₈×C₄₁	—	2	2	no	—
149	C₂×C₈×C₄₁	—	2	2	no	—
150	C₂×C₈×C₄₁	—	2	2	no	—
151	C₂×C₈×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	4	no	—
153	C₄⋊C₄×C₄₁	—	2	4	no	—
154	C₄⋊C₄×C₄₁	—	2	4	no	—
155	C₄⋊C₄×C₄₁	—	2	4	no	—
156	C₄⋊C₄×C₄₁	—	2	2	no	—
157	C₄⋊C₄×C₄₁	—	2	2	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	2	1	no	—
160	C₄⋊C₄×C₄₁	—	2	2	no	—
161	C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₄⋊C₄×C₄₁	—	2	2	no	—
163	C₄⋊C₄×C₄₁	—	4	4	no	—
164	C₄⋊C₄×C₄₁	—	4	2	no	—
165	C₄⋊C₄×C₄₁	—	4	4	no	—
166	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₄₁	#41	1	4	yes	—
168	C₂²⋊C₄×C₄₁	—	2	4	no	—
169	C₂²⋊C₄×C₄₁	—	2	4	no	—
170	C₂²⋊C₄×C₄₁	—	2	4	no	—
171	C₂²⋊C₄×C₄₁	—	2	4	no	—
172	C₂²⋊C₄×C₄₁	—	2	4	no	—
173	C₄²×C₄₁	—	2	4	no	—
174	C₄²×C₄₁	—	2	4	no	—
175	C₄²×C₄₁	—	2	1	no	—
176	C₄²×C₄₁	—	2	1	no	—
177	C₄²×C₄₁	—	2	1	no	—
178	C₄²×C₄₁	—	2	1	no	—
179	C₄²×C₄₁	—	4	2	no	—
180	C₄²×C₄₁	C₂×D₄	1	2	yes	—
181	C₄²×C₄₁	C₂×D₄	1	2	yes	—
182	C₂³×C₄₁	—	2	2	no	—
183	C₂³×C₄₁	—	4	2	no	—
184	C₂³×C₄₁	—	4	1	no	—
185	C₂³×C₄₁	—	4	1	no	—
186	C₂³×C₄₁	—	4	2	no	—
187	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₄₁	—	2	2	no	—
189	Q₈×C₄₁	—	2	2	no	—
190	Q₈×C₄₁	—	2	4	no	—
191	Q₈×C₄₁	—	4	4	no	—
192	Q₈×C₄₁	—	4	1	no	—
193	Q₈×C₄₁	—	4	1	no	—
194	Q₈×C₄₁	—	4	2	no	—
195	Q₈×C₄₁	—	8	4	no	—
196	D₄×C₄₁	—	2	4	no	—
197	D₄×C₄₁	—	4	1	no	—
198	D₄×C₄₁	—	4	1	no	—
199	C₂×C₄×C₄₁	—	2	1	no	—
200	C₂×C₄×C₄₁	—	2	1	no	—
201	C₂×C₄×C₄₁	—	2	1	no	—
202	C₂×C₄×C₄₁	—	2	1	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	1	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	1	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	2	no	—
209	C₂×C₄×C₄₁	—	2	1	no	—
210	C₂×C₄×C₄₁	—	2	4	no	—
211	C₂×C₄×C₄₁	—	2	1	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	4	8	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	4	2	no	—
218	C₂×C₄×C₄₁	—	4	2	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	#120	1	2	yes	—
226	C₂×C₄×C₄₁	#120	1	2	yes	—
227	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
231	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
232	C₈×C₄₁	—	4	2	no	—
233	C₈×C₄₁	—	4	2	no	—
234	#25661	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₄₁	—	4	2	no	—
236	C₂²×C₄₁	—	4	2	no	—
237	C₂²×C₄₁	—	4	2	no	—
238	C₂²×C₄₁	—	8	2	no	—
239	C₂²×C₄₁	—	8	2	no	—
240	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
241	C₂²×C₄₁	#548	1	2	yes	—
242	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₄₁	#575	1	1	yes	characteristic
244	C₂²×C₄₁	#578	1	2	yes	—
245	C₄×C₄₁	—	2	2	no	—
246	C₄×C₄₁	—	2	2	no	—
247	C₄×C₄₁	—	2	2	no	—
248	C₄×C₄₁	—	4	4	no	—
249	C₄×C₄₁	—	4	2	no	—
250	C₄×C₄₁	—	4	2	no	—
251	C₄×C₄₁	—	4	1	no	—
252	C₄×C₄₁	—	4	2	no	—
253	C₄×C₄₁	—	4	1	no	—
254	C₄×C₄₁	—	4	1	no	—
255	C₄×C₄₁	—	8	2	no	—
256	C₄×C₄₁	#532	1	1	yes	characteristic
257	C₄×C₄₁	#536	1	1	yes	characteristic
258	C₄×C₄₁	#547	1	2	yes	—
259	C₂×#556	C₂×C₄₁	1	1	yes	characteristic
260	C₂×#489	C₂×C₄₁	1	1	yes	characteristic
261	C₂×#477	C₂×C₄₁	1	1	yes	characteristic, complemented
262	#2546	C₂×C₄₁	1	1	yes	characteristic, complemented
263	#2043	C₂×C₄₁	1	2	yes	complemented
264	#2042	C₂×C₄₁	1	2	yes	—
265	#1985	C₂×C₄₁	1	1	yes	characteristic, complemented
266	#1983	C₂×C₄₁	1	1	yes	characteristic
267	#1863	C₂×C₄₁	1	2	yes	complemented
268	#1862	C₂×C₄₁	1	2	yes	—
269	#1763	C₂×C₄₁	1	1	yes	characteristic, complemented
270	C₂×C₄₁	—	8	2	no	—
271	C₂×C₄₁	#2432	1	1	yes	characteristic
272	C₂×C₄₁	#3006	1	1	yes	characteristic
273	C₂×C₄₁	#3011	1	1	yes	characteristic
274	C₂×C₄₁	#3367	1	2	yes	—
275	C₂×C₄₁	#3377	1	2	yes	—
276	#556	—	2	4	no	—
277	#556	—	2	4	no	—
278	C₂×C₄⋊Q₈	—	2	1	no	—
279	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
281	C₂×#126	—	2	1	no	—
282	C₂×#126	—	2	1	no	—
283	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
284	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
285	C₂×C₂²⋊Q₈	—	2	1	no	—
286	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
290	C₂×#117	—	2	1	no	—
291	#489	—	2	4	no	—
292	#477	—	2	4	no	—
293	C₂×#107	C₂²×C₄₁	1	2	yes	—
294	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
295	C₂×#103	C₂²×C₄₁	1	2	yes	—
296	C₂×#103	C₂²×C₄₁	1	2	yes	—
297	C₂×#103	C₂²×C₄₁	1	2	yes	—
298	C₂×#103	C₂²×C₄₁	1	2	yes	—
299	C₂×#102	C₂²×C₄₁	1	2	yes	—
300	C₂×#102	C₂²×C₄₁	1	2	yes	—
301	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
302	#398	—	2	1	no	—
303	#398	—	2	1	no	—
304	#391	—	2	1	no	—
305	#389	C₂²×C₄₁	1	2	yes	—
306	#389	C₂²×C₄₁	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
308	#340	C₂²×C₄₁	1	2	yes	—
309	#336	C₂²×C₄₁	1	2	yes	—
310	#336	C₂²×C₄₁	1	2	yes	—
311	C₄₁	#25661	1	1	yes	characteristic, direct product factor, Sylow
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
314	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
316	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
319	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	4	4	no	—
325	#126	—	2	8	no	—
326	#126	—	2	8	no	—
327	#124	—	2	2	no	—
328	#124	—	2	2	no	—
329	#124	—	2	2	no	—
330	#124	D₄×C₄₁	1	4	yes	—
331	C₂²⋊Q₈	—	2	8	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	D₄×C₄₁	1	4	yes	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	#117	—	2	8	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
349	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
350	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
365	#107	—	2	4	no	—
366	C₄⋊C₈	—	2	2	no	—
367	#103	—	2	4	no	—
368	#103	—	2	4	no	—
369	#103	—	2	4	no	—
370	#103	—	2	4	no	—
371	#102	—	2	4	no	—
372	#102	—	2	4	no	—
373	#97	—	2	2	no	—
374	#95	—	2	1	no	—
375	#95	—	2	2	no	—
376	#95	—	2	2	no	—
377	C₂⁴	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	4	1	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
391	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	4	4	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	4	no	—
431	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
432	C₄⋊C₄	#41×C₄₁	1	4	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₄²	—	2	4	no	—
439	C₄²	—	2	4	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂×D₄×C₄₁	1	2	yes	—
446	C₄²	C₂×D₄×C₄₁	1	2	yes	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	4	no	—
456	Q₈	—	4	4	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	8	4	no	—
461	D₄	—	2	4	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	#120×C₄₁	1	2	yes	—
491	C₂×C₄	#120×C₄₁	1	2	yes	—
492	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
496	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
497	C₈	—	4	2	no	—
498	C₈	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
505	C₂²	C₄₁×#548	1	2	yes	—
506	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
507	C₂²	C₄₁×#575	1	1	yes	characteristic
508	C₂²	C₄₁×#578	1	2	yes	—
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	8	2	no	—
520	C₄	C₄₁×#532	1	1	yes	characteristic
521	C₄	C₄₁×#536	1	1	yes	characteristic
522	C₄	C₄₁×#547	1	2	yes	—
523	C₂	—	8	2	no	—
524	C₂	C₄₁×#2432	1	1	yes	characteristic
525	C₂	C₄₁×#3006	1	1	yes	characteristic
526	C₂	C₄₁×#3011	1	1	yes	characteristic
527	C₂	C₄₁×#3367	1	2	yes	—
528	C₂	C₄₁×#3377	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₁×#477	C₂	semidirect
4. C₄₁×#2546	C₂	semidirect
5. C₄₁×#2043	C₂	semidirect
7. C₄₁×#1985	C₂	semidirect
9. C₄₁×#1863	C₂	semidirect
11. C₄₁×#1763	C₂	semidirect
234. #25661	C₄₁	direct (N × H)
261. C₂×#477	C₂×C₄₁	semidirect
262. #2546	C₂×C₄₁	semidirect
263. #2043	C₂×C₄₁	semidirect
265. #1985	C₂×C₄₁	semidirect
267. #1863	C₂×C₄₁	semidirect
269. #1763	C₂×C₄₁	semidirect
311. C₄₁	#25661	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#556	2
C₂×C₄₁×#489	2
C₂×C₄₁×#477	2
C₄₁×#2546	2
C₄₁×#2043	2
C₄₁×#2042	2
C₄₁×#1985	2
C₄₁×#1983	2
C₄₁×#1863	2
C₄₁×#1862	2
C₄₁×#1763	2
#25661	41

Subgroups — C41×#25661 #23801862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25661 #23801862