Subgroups — C₄₁×#18052 #23794253

Order 10496.

674 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2974	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1581	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1569	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1488	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1486	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₄₁	C₄	1	1	yes	characteristic
17	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
20	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
21	C₄₁×#442	C₄	1	1	yes	characteristic
22	C₄₁×#442	C₄	1	1	yes	characteristic
23	C₄₁×#440	C₄	1	1	yes	characteristic
24	C₄₁×#440	C₄	1	1	yes	characteristic
25	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#436	—	2	1	no	—
30	C₄₁×#436	—	2	1	no	—
31	C₄₁×#436	C₂²	1	1	yes	characteristic
32	C₄₁×#436	C₂²	1	1	yes	characteristic
33	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
34	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#435	—	2	1	no	—
36	C₄₁×#435	—	2	1	no	—
37	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#432	C₂²	1	1	yes	characteristic
40	C₄₁×#431	—	2	1	no	—
41	C₄₁×#431	C₂²	1	1	yes	characteristic
42	C₄₁×#431	C₂²	1	1	yes	characteristic
43	C₄₁×#428	C₄	1	1	yes	characteristic
44	C₄₁×#423	—	2	1	no	—
45	C₄₁×#423	C₂²	1	1	yes	characteristic
46	C₄₁×#418	C₄	1	1	yes	characteristic
47	C₄₁×#417	C₄	1	1	yes	characteristic
48	C₄₁×#407	—	2	1	no	—
49	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
50	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
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	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₄₁	—	2	1	no	—
70	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
71	C₂×SD₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
73	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
74	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
75	C₂×M₁₆×C₄₁	—	2	1	no	—
76	C₂×M₁₆×C₄₁	—	2	1	no	—
77	C₂×M₁₆×C₄₁	—	2	1	no	—
78	C₂×M₁₆×C₄₁	—	2	1	no	—
79	C₂×M₁₆×C₄₁	—	2	1	no	—
80	C₂×M₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
81	C₂×M₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₁	—	2	1	no	—
83	C₂²×C₈×C₄₁	—	2	1	no	—
84	C₄×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₄₁	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
96	#117×C₄₁	—	2	1	no	—
97	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
100	C₂×C₄²×C₄₁	—	2	1	no	—
101	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
102	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
103	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
104	#106×C₄₁	C₂×C₄	1	1	yes	characteristic
105	#106×C₄₁	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₈×C₄₁	—	2	1	no	—
107	C₄⋊C₈×C₄₁	—	2	1	no	—
108	C₄⋊C₈×C₄₁	—	2	1	no	—
109	C₄⋊C₈×C₄₁	—	2	1	no	—
110	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
111	C₄⋊C₈×C₄₁	D₄	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	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
116	#103×C₄₁	C₂×C₄	1	1	yes	characteristic
117	#103×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	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
132	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
133	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
134	#97×C₄₁	—	2	1	no	—
135	#97×C₄₁	C₂×C₄	1	1	yes	characteristic
136	#97×C₄₁	C₂×C₄	1	1	yes	characteristic
137	C₄×C₈×C₄₁	—	2	1	no	—
138	C₄×C₈×C₄₁	—	2	1	no	—
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	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
145	C₂⁴×C₄₁	—	2	1	no	—
146	#41×C₄₁	—	2	2	no	—
147	#41×C₄₁	—	4	1	no	—
148	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₄₁	—	2	2	no	—
150	C₂×D₄×C₄₁	—	2	1	no	—
151	C₂×D₄×C₄₁	—	2	1	no	—
152	C₂×D₄×C₄₁	—	4	1	no	—
153	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	2	1	no	—
162	C₂²×C₄×C₄₁	—	2	1	no	—
163	C₂²×C₄×C₄₁	—	2	1	no	—
164	C₂²×C₄×C₄₁	—	8	1	no	—
165	C₂²×C₄×C₄₁	—	8	1	no	—
166	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
169	SD₁₆×C₄₁	—	2	2	no	—
170	SD₁₆×C₄₁	M₁₆	1	4	yes	complemented
171	D₈×C₄₁	—	2	2	no	—
172	D₈×C₄₁	—	2	2	no	—
173	M₁₆×C₄₁	—	2	2	no	—
174	M₁₆×C₄₁	—	4	1	no	—
175	M₁₆×C₄₁	—	8	1	no	—
176	M₁₆×C₄₁	—	8	1	no	—
177	M₁₆×C₄₁	—	8	1	no	—
178	M₁₆×C₄₁	—	8	1	no	—
179	M₁₆×C₄₁	—	8	1	no	—
180	C₂×C₈×C₄₁	—	2	1	no	—
181	C₂×C₈×C₄₁	—	2	1	no	—
182	C₂×C₈×C₄₁	—	2	1	no	—
183	C₂×C₈×C₄₁	—	2	1	no	—
184	C₂×C₈×C₄₁	—	2	1	no	—
185	C₂×C₈×C₄₁	—	2	1	no	—
186	C₂×C₈×C₄₁	—	8	1	no	—
187	C₂×C₈×C₄₁	—	8	1	no	—
188	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₄₁	—	2	1	no	—
197	C₄⋊C₄×C₄₁	—	2	1	no	—
198	C₄⋊C₄×C₄₁	—	2	1	no	—
199	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₄₁	—	2	1	no	—
208	C₂²⋊C₄×C₄₁	—	2	1	no	—
209	C₂²⋊C₄×C₄₁	—	2	1	no	—
210	C₄²×C₄₁	—	2	1	no	—
211	C₄²×C₄₁	—	2	1	no	—
212	C₄²×C₄₁	—	2	1	no	—
213	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₄₁	#41	1	1	yes	characteristic
216	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
217	C₂³×C₄₁	—	2	1	no	—
218	C₂³×C₄₁	—	2	1	no	—
219	C₂³×C₄₁	—	2	1	no	—
220	C₂³×C₄₁	—	4	2	no	—
221	C₂³×C₄₁	—	4	2	no	—
222	C₂³×C₄₁	—	8	1	no	—
223	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
224	Q₈×C₄₁	—	2	1	no	—
225	Q₈×C₄₁	C₂×M₁₆	1	2	yes	—
226	D₄×C₄₁	—	2	1	no	—
227	D₄×C₄₁	—	2	1	no	—
228	D₄×C₄₁	—	2	1	no	—
229	D₄×C₄₁	—	2	1	no	—
230	D₄×C₄₁	—	2	1	no	—
231	D₄×C₄₁	—	4	2	no	—
232	D₄×C₄₁	—	4	2	no	—
233	D₄×C₄₁	C₂×M₁₆	1	2	yes	—
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	—	2	1	no	—
239	C₂×C₄×C₄₁	—	2	1	no	—
240	C₂×C₄×C₄₁	—	2	1	no	—
241	C₂×C₄×C₄₁	—	2	1	no	—
242	C₂×C₄×C₄₁	—	2	1	no	—
243	C₂×C₄×C₄₁	—	4	1	no	—
244	C₂×C₄×C₄₁	—	4	2	no	—
245	C₂×C₄×C₄₁	—	4	2	no	—
246	C₂×C₄×C₄₁	—	4	1	no	—
247	C₂×C₄×C₄₁	—	4	1	no	—
248	C₂×C₄×C₄₁	—	4	1	no	—
249	C₂×C₄×C₄₁	—	4	1	no	—
250	C₂×C₄×C₄₁	—	4	1	no	—
251	C₂×C₄×C₄₁	—	4	1	no	—
252	C₂×C₄×C₄₁	—	8	1	no	—
253	C₂×C₄×C₄₁	—	8	1	no	—
254	C₂×C₄×C₄₁	—	8	1	no	—
255	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
261	C₈×C₄₁	—	2	1	no	—
262	C₈×C₄₁	—	2	1	no	—
263	C₈×C₄₁	—	2	1	no	—
264	C₈×C₄₁	—	2	1	no	—
265	C₈×C₄₁	—	2	1	no	—
266	C₈×C₄₁	—	2	1	no	—
267	C₈×C₄₁	—	2	1	no	—
268	C₈×C₄₁	—	4	1	no	—
269	C₈×C₄₁	—	4	1	no	—
270	C₈×C₄₁	—	4	1	no	—
271	C₈×C₄₁	—	4	1	no	—
272	C₈×C₄₁	—	4	1	no	—
273	C₈×C₄₁	—	4	1	no	—
274	C₈×C₄₁	C₂×M₁₆	1	2	yes	—
275	#18052	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂²×C₄₁	—	2	1	no	—
277	C₂²×C₄₁	—	2	2	no	—
278	C₂²×C₄₁	—	2	1	no	—
279	C₂²×C₄₁	—	2	1	no	—
280	C₂²×C₄₁	—	4	1	no	—
281	C₂²×C₄₁	—	4	1	no	—
282	C₂²×C₄₁	—	4	1	no	—
283	C₂²×C₄₁	—	4	1	no	—
284	C₂²×C₄₁	—	4	1	no	—
285	C₂²×C₄₁	—	4	1	no	—
286	C₂²×C₄₁	—	4	1	no	—
287	C₂²×C₄₁	—	4	1	no	—
288	C₂²×C₄₁	—	8	4	no	—
289	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
290	C₄×C₄₁	—	2	1	no	—
291	C₄×C₄₁	—	2	2	no	—
292	C₄×C₄₁	—	2	1	no	—
293	C₄×C₄₁	—	2	1	no	—
294	C₄×C₄₁	—	2	1	no	—
295	C₄×C₄₁	—	4	1	no	—
296	C₄×C₄₁	—	4	1	no	—
297	C₄×C₄₁	—	4	1	no	—
298	C₄×C₄₁	—	4	1	no	—
299	C₄×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
300	C₄×C₄₁	#568	1	1	yes	characteristic
301	C₄×C₄₁	#576	1	1	yes	characteristic
302	C₄×C₄₁	#577	1	1	yes	characteristic
303	#2991	C₂×C₄₁	1	1	yes	characteristic, complemented
304	#2974	C₂×C₄₁	1	1	yes	characteristic, complemented
305	C₄×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic
306	#1594	C₂×C₄₁	1	1	yes	characteristic, complemented
307	#1589	C₂×C₄₁	1	1	yes	characteristic, complemented
308	#1588	C₂×C₄₁	1	1	yes	characteristic, complemented
309	#1586	C₂×C₄₁	1	1	yes	characteristic, complemented
310	#1583	C₂×C₄₁	1	1	yes	characteristic, complemented
311	#1581	C₂×C₄₁	1	1	yes	characteristic, complemented
312	SD₁₆⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
313	C₈×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
314	#1569	C₂×C₄₁	1	1	yes	characteristic, complemented
315	#1488	C₂×C₄₁	1	1	yes	characteristic, complemented
316	#1486	C₂×C₄₁	1	1	yes	characteristic, complemented
317	#1453	C₂×C₄₁	1	1	yes	characteristic, complemented
318	C₂×C₄₁	—	4	1	no	—
319	C₂×C₄₁	—	4	2	no	—
320	C₂×C₄₁	—	8	1	no	—
321	C₂×C₄₁	—	8	1	no	—
322	C₂×C₄₁	D₄×M₁₆	1	1	yes	characteristic
323	C₂×C₄₁	#2946	1	1	yes	characteristic
324	C₂×C₄₁	#2955	1	1	yes	characteristic
325	C₂×AGL(1,ℤ/8)	C₄×C₄₁	1	1	yes	characteristic
326	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
328	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
329	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
330	#442	C₄×C₄₁	1	1	yes	characteristic
331	#442	C₄×C₄₁	1	1	yes	characteristic
332	#440	C₄×C₄₁	1	1	yes	characteristic
333	#440	C₄×C₄₁	1	1	yes	characteristic
334	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
335	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
336	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
337	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
338	#436	—	2	1	no	—
339	#436	—	2	1	no	—
340	#436	C₂²×C₄₁	1	1	yes	characteristic
341	#436	C₂²×C₄₁	1	1	yes	characteristic
342	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
343	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
344	#435	—	2	1	no	—
345	#435	—	2	1	no	—
346	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
347	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
348	#432	C₂²×C₄₁	1	1	yes	characteristic
349	#431	—	2	1	no	—
350	#431	C₂²×C₄₁	1	1	yes	characteristic
351	#431	C₂²×C₄₁	1	1	yes	characteristic
352	#428	C₄×C₄₁	1	1	yes	characteristic
353	#423	—	2	1	no	—
354	#423	C₂²×C₄₁	1	1	yes	characteristic
355	#418	C₄×C₄₁	1	1	yes	characteristic
356	#417	C₄×C₄₁	1	1	yes	characteristic
357	#407	—	2	1	no	—
358	C₂×C₂²⋊C₈	—	2	1	no	—
359	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
360	#335	C₂²×C₄₁	1	1	yes	characteristic, complemented
361	#335	C₂²×C₄₁	1	1	yes	characteristic, complemented
362	#334	C₂²×C₄₁	1	1	yes	characteristic, complemented
363	#334	C₂²×C₄₁	1	1	yes	characteristic, complemented
364	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
365	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
366	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
367	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
368	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
369	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
370	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
371	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
372	#322	C₂²×C₄₁	1	1	yes	characteristic, complemented
373	#322	C₂²×C₄₁	1	1	yes	characteristic, complemented
374	#322	C₂²×C₄₁	1	1	yes	characteristic, complemented
375	C₈²	C₂²×C₄₁	1	1	yes	characteristic, complemented
376	C₄₁	#18052	1	1	yes	characteristic, direct product factor, Sylow
377	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
378	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	AGL(1,ℤ/8)	—	2	4	no	—
381	C₂×SD₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
382	C₂×SD₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
383	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
384	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
391	C₂×M₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₄×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
395	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
401	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
402	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
403	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
404	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
405	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
406	#117	—	2	1	no	—
407	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
412	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
413	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
414	#106	C₂×C₄×C₄₁	1	1	yes	characteristic
415	#106	C₂×C₄×C₄₁	1	1	yes	characteristic
416	C₄⋊C₈	—	2	1	no	—
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
421	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
424	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
425	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
426	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
427	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
428	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
429	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
430	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
431	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
432	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
433	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	C₂²⋊C₈	—	2	1	no	—
442	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
443	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
444	#97	—	2	1	no	—
445	#97	C₂×C₄×C₄₁	1	1	yes	characteristic
446	#97	C₂×C₄×C₄₁	1	1	yes	characteristic
447	C₄×C₈	—	2	1	no	—
448	C₄×C₈	—	2	1	no	—
449	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
450	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
451	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
452	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
453	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
454	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
455	C₂⁴	—	2	1	no	—
456	#41	—	2	2	no	—
457	#41	—	4	1	no	—
458	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
464	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
465	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	8	1	no	—
475	C₂²×C₄	—	8	1	no	—
476	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
478	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
479	SD₁₆	—	2	2	no	—
480	SD₁₆	M₁₆×C₄₁	1	4	yes	complemented
481	D₈	—	2	2	no	—
482	D₈	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	4	1	no	—
485	M₁₆	—	8	1	no	—
486	M₁₆	—	8	1	no	—
487	M₁₆	—	8	1	no	—
488	M₁₆	—	8	1	no	—
489	M₁₆	—	8	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	8	1	no	—
497	C₂×C₈	—	8	1	no	—
498	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
499	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
500	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
501	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
504	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
505	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
524	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
525	C₄²	#41×C₄₁	1	1	yes	characteristic
526	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	8	1	no	—
533	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
534	Q₈	—	2	1	no	—
535	Q₈	C₂×M₁₆×C₄₁	1	2	yes	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	C₂×M₁₆×C₄₁	1	2	yes	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	8	1	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
566	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
567	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
568	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
570	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	2	1	no	—
574	C₈	—	2	1	no	—
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	4	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	C₂×M₁₆×C₄₁	1	2	yes	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	8	4	no	—
598	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
599	C₄	—	2	1	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
609	C₄	C₄₁×#568	1	1	yes	characteristic
610	C₄	C₄₁×#576	1	1	yes	characteristic
611	C₄	C₄₁×#577	1	1	yes	characteristic
612	C₂	—	4	1	no	—
613	C₂	—	4	2	no	—
614	C₂	—	8	1	no	—
615	C₂	—	8	1	no	—
616	C₂	D₄×M₁₆×C₄₁	1	1	yes	characteristic
617	C₂	C₄₁×#2946	1	1	yes	characteristic
618	C₂	C₄₁×#2955	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	C₂×AGL(1,ℤ/8)×C₄₁	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
1. C₄₁×#2991	C₂	semidirect
2. C₄₁×#2974	C₂	semidirect
4. C₄₁×#1594	C₂	semidirect
5. C₄₁×#1589	C₂	semidirect
6. C₄₁×#1588	C₂	semidirect
7. C₄₁×#1586	C₂	semidirect
8. C₄₁×#1583	C₂	semidirect
9. C₄₁×#1581	C₂	semidirect
10. C₄₁×SD₁₆⋊C₈	C₂	semidirect
11. C₈×SD₁₆×C₄₁	C₂	semidirect
12. C₄₁×#1569	C₂	semidirect
13. C₄₁×#1488	C₂	semidirect
14. C₄₁×#1486	C₂	semidirect
15. C₄₁×#1453	C₂	semidirect
19. C₈×Q₈×C₄₁	C₂²	semidirect
20. C₈×Q₈×C₄₁	C₂²	semidirect
33. C₄₁×#436	C₂²	semidirect
34. C₄₁×#436	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
170. SD₁₆×C₄₁	M₁₆	semidirect
275. #18052	C₄₁	direct (N × H)
303. #2991	C₂×C₄₁	semidirect
304. #2974	C₂×C₄₁	semidirect
306. #1594	C₂×C₄₁	semidirect
307. #1589	C₂×C₄₁	semidirect
308. #1588	C₂×C₄₁	semidirect
309. #1586	C₂×C₄₁	semidirect
310. #1583	C₂×C₄₁	semidirect
311. #1581	C₂×C₄₁	semidirect
312. SD₁₆⋊C₈	C₂×C₄₁	semidirect
313. C₈×SD₁₆	C₂×C₄₁	semidirect
314. #1569	C₂×C₄₁	semidirect
315. #1488	C₂×C₄₁	semidirect
316. #1486	C₂×C₄₁	semidirect
317. #1453	C₂×C₄₁	semidirect
328. C₈×Q₈	C₂²×C₄₁	semidirect
329. C₈×Q₈	C₂²×C₄₁	semidirect
342. #436	C₂²×C₄₁	semidirect
343. #436	C₂²×C₄₁	semidirect
360. #335	C₂²×C₄₁	semidirect
361. #335	C₂²×C₄₁	semidirect
362. #334	C₂²×C₄₁	semidirect
363. #334	C₂²×C₄₁	semidirect
364. Q₈⋊C₈	C₂²×C₄₁	semidirect
365. Q₈⋊C₈	C₂²×C₄₁	semidirect
370. D₄⋊C₈	C₂²×C₄₁	semidirect
371. D₄⋊C₈	C₂²×C₄₁	semidirect
372. #322	C₂²×C₄₁	semidirect
373. #322	C₂²×C₄₁	semidirect
374. #322	C₂²×C₄₁	semidirect
375. C₈²	C₂²×C₄₁	semidirect
376. C₄₁	#18052	direct (N × H)
480. SD₁₆	M₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#2991	2
C₄₁×#2974	2
C₄×AGL(1,ℤ/8)×C₄₁	2
C₄₁×#1594	2
C₄₁×#1589	2
C₄₁×#1588	2
C₄₁×#1586	2
C₄₁×#1583	2
C₄₁×#1581	2
C₄₁×SD₁₆⋊C₈	2
C₈×SD₁₆×C₄₁	2
C₄₁×#1569	2
C₄₁×#1488	2
C₄₁×#1486	2
C₄₁×#1453	2
#18052	41

Subgroups — C41×#18052 #23794253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18052 #23794253