Subgroups — C₄₁×#17918 #23794119

Order 10496.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3105	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1586	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1585	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1582	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1581	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1580	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1574	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#484	C₄	1	1	yes	characteristic
19	C₄₁×#481	C₄	1	1	yes	characteristic
20	C₄₁×#478	C₄	1	1	yes	characteristic
21	C₄₁×#478	C₄	1	1	yes	characteristic
22	C₄₁×#463	C₄	1	1	yes	characteristic
23	C₄₁×#463	C₄	1	1	yes	characteristic
24	C₄₁×#450	C₄	1	1	yes	characteristic
25	C₄₁×#447	C₄	1	1	yes	characteristic
26	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
27	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
29	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
30	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#436	—	2	1	no	—
33	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
34	C₄₁×#435	—	2	1	no	—
35	C₈×D₄×C₄₁	—	2	1	no	—
36	C₈×D₄×C₄₁	—	2	1	no	—
37	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#433	—	2	1	no	—
43	C₄₁×#431	C₂²	1	1	yes	characteristic
44	C₄₁×#431	C₂²	1	1	yes	characteristic
45	C₄₁×#431	C₂²	1	1	yes	characteristic
46	C₄₁×#431	C₂²	1	1	yes	characteristic
47	C₄₁×#424	—	2	1	no	—
48	C₄₁×#423	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
50	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
51	C₄₁×#335	C₂²	1	1	yes	characteristic, complemented
52	C₄₁×#335	C₂²	1	1	yes	characteristic, complemented
53	C₄₁×#334	C₂²	1	1	yes	characteristic, complemented
54	C₄₁×#334	C₂²	1	1	yes	characteristic, complemented
55	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#322	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#322	C₂²	1	1	yes	characteristic, complemented
65	C₄₁×#322	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₄₁	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	—	2	1	no	—
69	C₂×SD₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
71	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
72	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
73	C₂×M₁₆×C₄₁	—	2	1	no	—
74	C₂×M₁₆×C₄₁	—	2	1	no	—
75	C₂²×C₈×C₄₁	—	2	1	no	—
76	C₂²×C₈×C₄₁	—	2	1	no	—
77	C₂²×C₈×C₄₁	—	2	1	no	—
78	C₂²×C₈×C₄₁	—	2	1	no	—
79	C₂²×C₈×C₄₁	—	2	1	no	—
80	#126×C₄₁	—	2	1	no	—
81	#125×C₄₁	C₂×C₄	1	1	yes	characteristic
82	#124×C₄₁	C₂×C₄	1	1	yes	characteristic
83	#123×C₄₁	—	2	1	no	—
84	C₂²⋊Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
85	#121×C₄₁	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₄₁	—	2	1	no	—
88	C₄×D₄×C₄₁	—	2	1	no	—
89	C₄×D₄×C₄₁	—	2	1	no	—
90	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
95	#117×C₄₁	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
100	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
101	#106×C₄₁	C₂×C₄	1	1	yes	characteristic
102	#106×C₄₁	C₂×C₄	1	1	yes	characteristic
103	C₄⋊C₈×C₄₁	—	2	1	no	—
104	C₄⋊C₈×C₄₁	—	2	1	no	—
105	C₄⋊C₈×C₄₁	—	2	1	no	—
106	C₄⋊C₈×C₄₁	—	2	1	no	—
107	C₄⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
109	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
110	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
111	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
115	#103×C₄₁	C₂×C₄	1	1	yes	characteristic
116	#103×C₄₁	C₂×C₄	1	1	yes	characteristic
117	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
118	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
119	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
120	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
121	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
122	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊C₈×C₄₁	—	2	1	no	—
124	C₂²⋊C₈×C₄₁	—	2	1	no	—
125	C₂²⋊C₈×C₄₁	—	2	1	no	—
126	C₂²⋊C₈×C₄₁	—	2	1	no	—
127	C₂²⋊C₈×C₄₁	—	2	1	no	—
128	C₂²⋊C₈×C₄₁	—	2	1	no	—
129	C₂²⋊C₈×C₄₁	—	2	1	no	—
130	C₂²⋊C₈×C₄₁	—	2	1	no	—
131	C₂²⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
132	C₂²⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
133	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
134	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
135	#97×C₄₁	—	2	1	no	—
136	C₄×C₈×C₄₁	—	2	1	no	—
137	C₄×C₈×C₄₁	—	2	1	no	—
138	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
144	C₂⁴×C₄₁	—	2	1	no	—
145	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₄₁	—	2	2	no	—
147	C₂×D₄×C₄₁	—	2	2	no	—
148	C₂×D₄×C₄₁	—	2	1	no	—
149	C₂×D₄×C₄₁	—	2	1	no	—
150	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	—	2	1	no	—
154	C₂²×C₄×C₄₁	—	2	1	no	—
155	C₂²×C₄×C₄₁	—	2	1	no	—
156	C₂²×C₄×C₄₁	—	2	1	no	—
157	C₂²×C₄×C₄₁	—	2	1	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	8	1	no	—
160	C₂²×C₄×C₄₁	—	8	1	no	—
161	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
164	SD₁₆×C₄₁	—	2	2	no	—
165	SD₁₆×C₄₁	—	2	2	no	—
166	D₈×C₄₁	—	2	2	no	—
167	D₈×C₄₁	—	2	2	no	—
168	M₁₆×C₄₁	—	8	1	no	—
169	M₁₆×C₄₁	—	8	1	no	—
170	C₂×C₈×C₄₁	—	2	1	no	—
171	C₂×C₈×C₄₁	—	2	1	no	—
172	C₂×C₈×C₄₁	—	2	1	no	—
173	C₂×C₈×C₄₁	—	2	1	no	—
174	C₂×C₈×C₄₁	—	2	1	no	—
175	C₂×C₈×C₄₁	—	2	1	no	—
176	C₂×C₈×C₄₁	—	8	1	no	—
177	C₂×C₈×C₄₁	—	8	1	no	—
178	C₂×C₈×C₄₁	—	8	1	no	—
179	C₂×C₈×C₄₁	—	8	1	no	—
180	C₂×C₈×C₄₁	—	8	1	no	—
181	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₄₁	—	2	1	no	—
190	C₄⋊C₄×C₄₁	—	2	1	no	—
191	C₄⋊C₄×C₄₁	—	2	1	no	—
192	C₄⋊C₄×C₄₁	—	2	1	no	—
193	C₄⋊C₄×C₄₁	—	2	1	no	—
194	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₄₁	—	2	1	no	—
199	C₂²⋊C₄×C₄₁	—	2	1	no	—
200	C₂²⋊C₄×C₄₁	—	2	1	no	—
201	C₂²⋊C₄×C₄₁	—	2	1	no	—
202	C₂²⋊C₄×C₄₁	—	2	1	no	—
203	C₂²⋊C₄×C₄₁	—	2	1	no	—
204	C₂²⋊C₄×C₄₁	—	2	1	no	—
205	C₂²⋊C₄×C₄₁	—	2	1	no	—
206	C₂²⋊C₄×C₄₁	—	2	1	no	—
207	C₄²×C₄₁	—	2	1	no	—
208	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₄₁	#41	1	1	yes	characteristic
211	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
212	C₂³×C₄₁	—	2	4	no	—
213	C₂³×C₄₁	—	2	1	no	—
214	C₂³×C₄₁	—	2	1	no	—
215	C₂³×C₄₁	—	2	1	no	—
216	C₂³×C₄₁	—	8	1	no	—
217	C₂³×C₄₁	—	8	1	no	—
218	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
219	Q₈×C₄₁	—	2	1	no	—
220	Q₈×C₄₁	—	2	1	no	—
221	D₄×C₄₁	—	2	4	no	—
222	D₄×C₄₁	—	2	1	no	—
223	D₄×C₄₁	—	2	1	no	—
224	D₄×C₄₁	—	2	1	no	—
225	D₄×C₄₁	—	2	1	no	—
226	D₄×C₄₁	—	8	1	no	—
227	D₄×C₄₁	#131	1	2	yes	—
228	D₄×C₄₁	#131	1	2	yes	—
229	C₂×C₄×C₄₁	—	2	1	no	—
230	C₂×C₄×C₄₁	—	2	1	no	—
231	C₂×C₄×C₄₁	—	2	1	no	—
232	C₂×C₄×C₄₁	—	2	1	no	—
233	C₂×C₄×C₄₁	—	2	1	no	—
234	C₂×C₄×C₄₁	—	2	1	no	—
235	C₂×C₄×C₄₁	—	2	1	no	—
236	C₂×C₄×C₄₁	—	2	1	no	—
237	C₂×C₄×C₄₁	—	2	1	no	—
238	C₂×C₄×C₄₁	—	4	1	no	—
239	C₂×C₄×C₄₁	—	4	1	no	—
240	C₂×C₄×C₄₁	—	4	1	no	—
241	C₂×C₄×C₄₁	—	4	1	no	—
242	C₂×C₄×C₄₁	—	4	1	no	—
243	C₂×C₄×C₄₁	—	4	1	no	—
244	C₂×C₄×C₄₁	—	4	1	no	—
245	C₂×C₄×C₄₁	—	8	1	no	—
246	C₂×C₄×C₄₁	—	8	1	no	—
247	C₂×C₄×C₄₁	—	8	1	no	—
248	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
254	C₈×C₄₁	—	2	1	no	—
255	C₈×C₄₁	—	2	1	no	—
256	C₈×C₄₁	—	2	1	no	—
257	C₈×C₄₁	—	2	1	no	—
258	C₈×C₄₁	—	2	1	no	—
259	C₈×C₄₁	—	2	1	no	—
260	C₈×C₄₁	—	2	1	no	—
261	C₈×C₄₁	—	2	1	no	—
262	C₈×C₄₁	—	4	1	no	—
263	C₈×C₄₁	—	4	1	no	—
264	C₈×C₄₁	—	4	1	no	—
265	C₈×C₄₁	—	4	1	no	—
266	C₈×C₄₁	—	4	1	no	—
267	C₈×C₄₁	—	4	1	no	—
268	#17918	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂²×C₄₁	—	2	1	no	—
270	C₂²×C₄₁	—	2	2	no	—
271	C₂²×C₄₁	—	2	2	no	—
272	C₂²×C₄₁	—	2	1	no	—
273	C₂²×C₄₁	—	2	1	no	—
274	C₂²×C₄₁	—	4	1	no	—
275	C₂²×C₄₁	—	4	1	no	—
276	C₂²×C₄₁	—	4	1	no	—
277	C₂²×C₄₁	—	4	1	no	—
278	C₂²×C₄₁	—	4	1	no	—
279	C₂²×C₄₁	—	4	1	no	—
280	C₂²×C₄₁	—	4	1	no	—
281	C₂²×C₄₁	—	8	4	no	—
282	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₄₁	—	2	1	no	—
284	C₄×C₄₁	—	2	1	no	—
285	C₄×C₄₁	—	2	1	no	—
286	C₄×C₄₁	—	2	1	no	—
287	C₄×C₄₁	—	4	1	no	—
288	C₄×C₄₁	—	4	1	no	—
289	C₄×C₄₁	—	4	1	no	—
290	C₄×C₄₁	—	4	1	no	—
291	C₄×C₄₁	—	4	1	no	—
292	C₄×C₄₁	C₂×#131	1	1	yes	characteristic
293	C₄×C₄₁	C₂×#131	1	1	yes	characteristic
294	C₄×C₄₁	#576	1	1	yes	characteristic
295	C₄×C₄₁	#577	1	1	yes	characteristic
296	#3105	C₂×C₄₁	1	1	yes	characteristic
297	#2993	C₂×C₄₁	1	1	yes	characteristic, complemented
298	#2972	C₂×C₄₁	1	1	yes	characteristic, complemented
299	#1586	C₂×C₄₁	1	1	yes	characteristic, complemented
300	#1585	C₂×C₄₁	1	1	yes	characteristic, complemented
301	#1582	C₂×C₄₁	1	1	yes	characteristic, complemented
302	#1581	C₂×C₄₁	1	1	yes	characteristic, complemented
303	#1580	C₂×C₄₁	1	1	yes	characteristic, complemented
304	SD₁₆⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
305	C₈×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
306	C₈×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
307	#1574	C₂×C₄₁	1	1	yes	characteristic, complemented
308	#1486	C₂×C₄₁	1	1	yes	characteristic, complemented
309	#1482	C₂×C₄₁	1	1	yes	characteristic, complemented
310	#1454	C₂×C₄₁	1	1	yes	characteristic, complemented
311	C₂×C₄₁	—	4	1	no	—
312	C₂×C₄₁	—	4	2	no	—
313	C₂×C₄₁	—	4	2	no	—
314	C₂×C₄₁	—	8	1	no	—
315	C₂×C₄₁	#2929	1	1	yes	characteristic
316	C₂×C₄₁	#2946	1	1	yes	characteristic
317	C₂×C₄₁	#2957	1	1	yes	characteristic
318	#529	C₂²×C₄₁	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
320	#484	C₄×C₄₁	1	1	yes	characteristic
321	#481	C₄×C₄₁	1	1	yes	characteristic
322	#478	C₄×C₄₁	1	1	yes	characteristic
323	#478	C₄×C₄₁	1	1	yes	characteristic
324	#463	C₄×C₄₁	1	1	yes	characteristic
325	#463	C₄×C₄₁	1	1	yes	characteristic
326	#450	C₄×C₄₁	1	1	yes	characteristic
327	#447	C₄×C₄₁	1	1	yes	characteristic
328	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
329	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
330	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
331	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
332	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
333	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
334	#436	—	2	1	no	—
335	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
336	#435	—	2	1	no	—
337	C₈×D₄	—	2	1	no	—
338	C₈×D₄	—	2	1	no	—
339	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
340	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
341	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
342	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
343	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
344	#433	—	2	1	no	—
345	#431	C₂²×C₄₁	1	1	yes	characteristic
346	#431	C₂²×C₄₁	1	1	yes	characteristic
347	#431	C₂²×C₄₁	1	1	yes	characteristic
348	#431	C₂²×C₄₁	1	1	yes	characteristic
349	#424	—	2	1	no	—
350	#423	C₂²×C₄₁	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	—	2	1	no	—
352	C₂×C₂²⋊C₈	—	2	1	no	—
353	#335	C₂²×C₄₁	1	1	yes	characteristic, complemented
354	#335	C₂²×C₄₁	1	1	yes	characteristic, complemented
355	#334	C₂²×C₄₁	1	1	yes	characteristic, complemented
356	#334	C₂²×C₄₁	1	1	yes	characteristic, complemented
357	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
358	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
359	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
360	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
361	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
362	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
363	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
364	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
365	#322	C₂²×C₄₁	1	1	yes	characteristic, complemented
366	#322	C₂²×C₄₁	1	1	yes	characteristic, complemented
367	#322	C₂²×C₄₁	1	1	yes	characteristic, complemented
368	C₈²	C₂²×C₄₁	1	1	yes	characteristic, complemented
369	C₄₁	#17918	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂×SD₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
373	C₂×SD₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
374	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
375	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	#126	—	2	1	no	—
384	#125	C₂×C₄×C₄₁	1	1	yes	characteristic
385	#124	C₂×C₄×C₄₁	1	1	yes	characteristic
386	#123	—	2	1	no	—
387	C₂²⋊Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
388	#121	C₂×C₄×C₄₁	1	1	yes	characteristic
389	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
394	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
395	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
397	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
398	#117	—	2	1	no	—
399	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
402	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
403	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
404	#106	C₂×C₄×C₄₁	1	1	yes	characteristic
405	#106	C₂×C₄×C₄₁	1	1	yes	characteristic
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
411	C₄⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
412	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
413	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
418	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
419	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
420	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
421	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
422	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
423	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
424	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
425	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
435	C₂²⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
436	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
437	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
438	#97	—	2	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	2	1	no	—
441	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
442	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
444	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
447	C₂⁴	—	2	1	no	—
448	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
455	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	8	1	no	—
463	C₂²×C₄	—	8	1	no	—
464	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
466	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
467	SD₁₆	—	2	2	no	—
468	SD₁₆	—	2	2	no	—
469	D₈	—	2	2	no	—
470	D₈	—	2	2	no	—
471	M₁₆	—	8	1	no	—
472	M₁₆	—	8	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	8	1	no	—
480	C₂×C₈	—	8	1	no	—
481	C₂×C₈	—	8	1	no	—
482	C₂×C₈	—	8	1	no	—
483	C₂×C₈	—	8	1	no	—
484	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
485	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
486	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
487	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
513	C₄²	#41×C₄₁	1	1	yes	characteristic
514	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
515	C₂³	—	2	4	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	8	1	no	—
520	C₂³	—	8	1	no	—
521	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	8	1	no	—
530	D₄	#131×C₄₁	1	2	yes	—
531	D₄	#131×C₄₁	1	2	yes	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
552	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
553	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
554	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
556	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	4	no	—
584	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	C₂×#131×C₄₁	1	1	yes	characteristic
595	C₄	C₂×#131×C₄₁	1	1	yes	characteristic
596	C₄	C₄₁×#576	1	1	yes	characteristic
597	C₄	C₄₁×#577	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	C₄₁×#2929	1	1	yes	characteristic
603	C₂	C₄₁×#2946	1	1	yes	characteristic
604	C₂	C₄₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₄₁×#447	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2993	C₂	semidirect
3. C₄₁×#2972	C₂	semidirect
4. C₄₁×#1586	C₂	semidirect
5. C₄₁×#1585	C₂	semidirect
6. C₄₁×#1582	C₂	semidirect
7. C₄₁×#1581	C₂	semidirect
8. C₄₁×#1580	C₂	semidirect
9. C₄₁×SD₁₆⋊C₈	C₂	semidirect
10. C₈×SD₁₆×C₄₁	C₂	semidirect
11. C₈×D₈×C₄₁	C₂	semidirect
12. C₄₁×#1574	C₂	semidirect
13. C₄₁×#1486	C₂	semidirect
14. C₄₁×#1482	C₂	semidirect
15. C₄₁×#1454	C₂	semidirect
26. C₄₁×#446	C₂²	semidirect
27. C₈×Q₈×C₄₁	C₂²	semidirect
33. C₄₁×#436	C₂²	semidirect
41. C₈×D₄×C₄₁	C₂²	semidirect
51. C₄₁×#335	C₂²	semidirect
52. C₄₁×#335	C₂²	semidirect
53. C₄₁×#334	C₂²	semidirect
54. C₄₁×#334	C₂²	semidirect
55. C₄₁×Q₈⋊C₈	C₂²	semidirect
56. C₄₁×Q₈⋊C₈	C₂²	semidirect
61. C₄₁×D₄⋊C₈	C₂²	semidirect
62. C₄₁×D₄⋊C₈	C₂²	semidirect
63. C₄₁×#322	C₂²	semidirect
64. C₄₁×#322	C₂²	semidirect
65. C₄₁×#322	C₂²	semidirect
66. C₈²×C₄₁	C₂²	semidirect
268. #17918	C₄₁	direct (N × H)
297. #2993	C₂×C₄₁	semidirect
298. #2972	C₂×C₄₁	semidirect
299. #1586	C₂×C₄₁	semidirect
300. #1585	C₂×C₄₁	semidirect
301. #1582	C₂×C₄₁	semidirect
302. #1581	C₂×C₄₁	semidirect
303. #1580	C₂×C₄₁	semidirect
304. SD₁₆⋊C₈	C₂×C₄₁	semidirect
305. C₈×SD₁₆	C₂×C₄₁	semidirect
306. C₈×D₈	C₂×C₄₁	semidirect
307. #1574	C₂×C₄₁	semidirect
308. #1486	C₂×C₄₁	semidirect
309. #1482	C₂×C₄₁	semidirect
310. #1454	C₂×C₄₁	semidirect
328. #446	C₂²×C₄₁	semidirect
329. C₈×Q₈	C₂²×C₄₁	semidirect
335. #436	C₂²×C₄₁	semidirect
343. C₈×D₄	C₂²×C₄₁	semidirect
353. #335	C₂²×C₄₁	semidirect
354. #335	C₂²×C₄₁	semidirect
355. #334	C₂²×C₄₁	semidirect
356. #334	C₂²×C₄₁	semidirect
357. Q₈⋊C₈	C₂²×C₄₁	semidirect
358. Q₈⋊C₈	C₂²×C₄₁	semidirect
363. D₄⋊C₈	C₂²×C₄₁	semidirect
364. D₄⋊C₈	C₂²×C₄₁	semidirect
365. #322	C₂²×C₄₁	semidirect
366. #322	C₂²×C₄₁	semidirect
367. #322	C₂²×C₄₁	semidirect
368. C₈²	C₂²×C₄₁	semidirect
369. C₄₁	#17918	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×#3105	2
C₄₁×#2993	2
C₄₁×#2972	2
C₄₁×#1586	2
C₄₁×#1585	2
C₄₁×#1582	2
C₄₁×#1581	2
C₄₁×#1580	2
C₄₁×SD₁₆⋊C₈	2
C₈×SD₁₆×C₄₁	2
C₈×D₈×C₄₁	2
C₄₁×#1574	2
C₄₁×#1486	2
C₄₁×#1482	2
C₄₁×#1454	2
#17918	41

Subgroups — C41×#17918 #23794119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17918 #23794119