Subgroups — C₄₁×#10772 #23786973

Order 10496.

1298 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1740	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₄×#41×C₄₁	—	2	2	no	—
12	C₄×#41×C₄₁	—	2	2	no	—
13	C₄×#41×C₄₁	—	2	2	no	—
14	C₄×#41×C₄₁	C₄	1	4	yes	complemented
15	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
16	C₂×C₄×D₄×C₄₁	—	2	1	no	—
17	C₂×C₄×D₄×C₄₁	—	2	2	no	—
18	C₂×#117×C₄₁	—	2	1	no	—
19	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₁	—	2	1	no	—
23	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#421	—	2	2	no	—
25	C₄₁×#421	C₄	1	4	yes	complemented
26	C₂×#104×C₄₁	—	2	2	no	—
27	C₄₁×#419	—	2	1	no	—
28	C₄₁×#418	—	2	1	no	—
29	C₄₁×#417	C₄	1	4	yes	complemented
30	C₄₁×#416	—	2	2	no	—
31	C₄₁×#344	—	2	2	no	—
32	C₄₁×#342	—	2	2	no	—
33	C₄₁×#339	—	2	1	no	—
34	C₄₁×#339	—	2	1	no	—
35	C₄₁×#339	—	2	2	no	—
36	C₂×#41×C₄₁	—	2	1	no	—
37	C₂×#41×C₄₁	—	2	1	no	—
38	C₂×#41×C₄₁	—	2	1	no	—
39	C₂×#41×C₄₁	—	2	1	no	—
40	C₂×#41×C₄₁	—	2	1	no	—
41	C₂×#41×C₄₁	—	2	1	no	—
42	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
43	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
44	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
45	C₂×#41×C₄₁	D₄	1	2	yes	—
46	C₂×#41×C₄₁	D₄	1	2	yes	—
47	C₂×#41×C₄₁	Q₈	1	2	yes	—
48	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₄₁	—	2	1	no	—
50	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	—	2	1	no	—
52	C₂³×C₄×C₄₁	—	2	2	no	—
53	C₂³×C₄×C₄₁	—	2	1	no	—
54	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₄₁	—	2	1	no	—
56	C₂×M₁₆×C₄₁	—	2	1	no	—
57	C₂×M₁₆×C₄₁	—	2	1	no	—
58	C₂×M₁₆×C₄₁	—	2	1	no	—
59	C₂×M₁₆×C₄₁	—	2	1	no	—
60	C₂×M₁₆×C₄₁	—	2	1	no	—
61	C₂×M₁₆×C₄₁	—	2	1	no	—
62	C₂×M₁₆×C₄₁	—	2	1	no	—
63	C₂×M₁₆×C₄₁	—	2	1	no	—
64	C₂×M₁₆×C₄₁	—	2	1	no	—
65	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	complemented
66	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	complemented
67	C₂²×C₈×C₄₁	—	2	1	no	—
68	C₂²×C₈×C₄₁	—	2	1	no	—
69	C₄×Q₈×C₄₁	—	2	4	no	—
70	C₄×Q₈×C₄₁	—	2	4	no	—
71	C₄×D₄×C₄₁	—	2	8	no	—
72	C₄×D₄×C₄₁	—	2	4	no	—
73	C₄×D₄×C₄₁	—	2	4	no	—
74	C₄×D₄×C₄₁	—	2	8	no	—
75	#117×C₄₁	—	2	4	no	—
76	#117×C₄₁	—	2	1	no	—
77	#117×C₄₁	—	2	1	no	—
78	#117×C₄₁	—	2	1	no	—
79	#117×C₄₁	—	2	4	no	—
80	#117×C₄₁	—	2	1	no	—
81	#117×C₄₁	—	2	1	no	—
82	#117×C₄₁	—	2	1	no	—
83	#117×C₄₁	—	2	1	no	—
84	#117×C₄₁	—	2	1	no	—
85	#117×C₄₁	—	2	1	no	—
86	#117×C₄₁	C₂×C₄	1	2	yes	—
87	#117×C₄₁	C₂×C₄	1	2	yes	complemented
88	#117×C₄₁	D₄	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	complemented
93	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
97	C₂×C₄²×C₄₁	—	2	2	no	—
98	C₂×C₄²×C₄₁	—	2	4	no	—
99	C₂×C₄²×C₄₁	—	2	1	no	—
100	C₂×C₄²×C₄₁	—	2	1	no	—
101	C₂×C₄²×C₄₁	—	2	1	no	—
102	C₂×C₄²×C₄₁	—	2	1	no	—
103	C₂×C₄²×C₄₁	—	2	4	no	—
104	C₂×C₄²×C₄₁	—	2	1	no	—
105	C₂×C₄²×C₄₁	—	2	1	no	—
106	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
107	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₁	D₄	1	2	yes	—
110	#104×C₄₁	—	2	8	no	—
111	#103×C₄₁	—	2	4	no	—
112	#102×C₄₁	—	2	4	no	—
113	C₂⁴×C₄₁	—	2	1	no	—
114	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
115	#41×C₄₁	—	2	2	no	—
116	#41×C₄₁	—	2	2	no	—
117	#41×C₄₁	—	2	2	no	—
118	#41×C₄₁	—	2	2	no	—
119	#41×C₄₁	—	2	2	no	—
120	#41×C₄₁	—	2	2	no	—
121	#41×C₄₁	—	2	2	no	—
122	#41×C₄₁	—	2	2	no	—
123	#41×C₄₁	—	2	2	no	—
124	#41×C₄₁	—	2	2	no	—
125	#41×C₄₁	—	2	2	no	—
126	#41×C₄₁	—	2	2	no	—
127	#41×C₄₁	C₄²	1	4	yes	—
128	#41×C₄₁	C₂²⋊C₄	1	4	yes	—
129	#41×C₄₁	C₄⋊C₄	1	4	yes	—
130	#41×C₄₁	C₄⋊C₄	1	4	yes	—
131	C₂×Q₈×C₄₁	—	2	1	no	—
132	C₂×Q₈×C₄₁	—	2	1	no	—
133	C₂×Q₈×C₄₁	—	2	1	no	—
134	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
135	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
136	C₂×Q₈×C₄₁	C₄⋊C₄	1	2	yes	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	2	2	no	—
140	C₂×D₄×C₄₁	—	2	2	no	—
141	C₂×D₄×C₄₁	—	2	2	no	—
142	C₂×D₄×C₄₁	—	2	2	no	—
143	C₂×D₄×C₄₁	—	2	1	no	—
144	C₂×D₄×C₄₁	—	2	1	no	—
145	C₂×D₄×C₄₁	—	2	1	no	—
146	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
148	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	—
149	C₂²×C₄×C₄₁	—	2	1	no	—
150	C₂²×C₄×C₄₁	—	2	1	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	2	no	—
153	C₂²×C₄×C₄₁	—	2	2	no	—
154	C₂²×C₄×C₄₁	—	2	2	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	8	no	—
158	C₂²×C₄×C₄₁	—	2	2	no	—
159	C₂²×C₄×C₄₁	—	2	2	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	2	2	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	4	4	no	—
164	C₂²×C₄×C₄₁	—	4	8	no	—
165	C₂²×C₄×C₄₁	—	4	1	no	—
166	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
176	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
177	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
178	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
179	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
180	M₁₆×C₄₁	—	2	2	no	—
181	M₁₆×C₄₁	—	2	2	no	—
182	M₁₆×C₄₁	—	2	2	no	—
183	M₁₆×C₄₁	—	2	2	no	—
184	M₁₆×C₄₁	—	4	1	no	—
185	M₁₆×C₄₁	—	4	1	no	—
186	M₁₆×C₄₁	—	4	1	no	—
187	M₁₆×C₄₁	—	4	1	no	—
188	C₂×C₈×C₄₁	—	2	2	no	—
189	C₂×C₈×C₄₁	—	2	2	no	—
190	C₂×C₈×C₄₁	—	4	1	no	—
191	C₂×C₈×C₄₁	—	4	1	no	—
192	C₂×C₈×C₄₁	—	4	1	no	—
193	C₂×C₈×C₄₁	—	4	1	no	—
194	C₄⋊C₄×C₄₁	—	2	8	no	—
195	C₄⋊C₄×C₄₁	—	2	2	no	—
196	C₄⋊C₄×C₄₁	—	2	2	no	—
197	C₄⋊C₄×C₄₁	—	2	2	no	—
198	C₄⋊C₄×C₄₁	—	2	2	no	—
199	C₄⋊C₄×C₄₁	—	2	2	no	—
200	C₄⋊C₄×C₄₁	—	4	1	no	—
201	C₂²⋊C₄×C₄₁	—	2	8	no	—
202	C₂²⋊C₄×C₄₁	—	2	2	no	—
203	C₂²⋊C₄×C₄₁	—	2	2	no	—
204	C₂²⋊C₄×C₄₁	—	4	1	no	—
205	C₂²⋊C₄×C₄₁	—	4	1	no	—
206	C₂²⋊C₄×C₄₁	—	4	1	no	—
207	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
208	C₄²×C₄₁	—	2	8	no	—
209	C₄²×C₄₁	—	2	2	no	—
210	C₄²×C₄₁	—	2	2	no	—
211	C₄²×C₄₁	—	2	1	no	—
212	C₄²×C₄₁	—	2	2	no	—
213	C₄²×C₄₁	—	2	1	no	—
214	C₄²×C₄₁	—	2	2	no	—
215	C₄²×C₄₁	—	2	2	no	—
216	C₄²×C₄₁	—	4	1	no	—
217	C₄²×C₄₁	—	4	1	no	—
218	C₄²×C₄₁	—	4	1	no	—
219	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
220	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
221	C₂³×C₄₁	—	2	2	no	—
222	C₂³×C₄₁	—	2	2	no	—
223	C₂³×C₄₁	—	2	2	no	—
224	C₂³×C₄₁	—	4	2	no	—
225	C₂³×C₄₁	—	4	4	no	—
226	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
228	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
229	C₂³×C₄₁	#120	1	1	yes	characteristic
230	C₂³×C₄₁	#120	1	1	yes	characteristic
231	C₂³×C₄₁	#121	1	1	yes	characteristic
232	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
233	Q₈×C₄₁	—	2	2	no	—
234	Q₈×C₄₁	—	2	2	no	—
235	Q₈×C₄₁	—	2	2	no	—
236	Q₈×C₄₁	#95	1	4	yes	—
237	D₄×C₄₁	—	2	4	no	—
238	D₄×C₄₁	—	2	4	no	—
239	D₄×C₄₁	—	2	4	no	—
240	D₄×C₄₁	—	2	4	no	—
241	D₄×C₄₁	—	2	2	no	—
242	D₄×C₄₁	—	2	2	no	—
243	D₄×C₄₁	—	2	2	no	—
244	D₄×C₄₁	#95	1	4	yes	—
245	C₂×C₄×C₄₁	—	2	4	no	—
246	C₂×C₄×C₄₁	—	2	2	no	—
247	C₂×C₄×C₄₁	—	2	2	no	—
248	C₂×C₄×C₄₁	—	2	2	no	—
249	C₂×C₄×C₄₁	—	2	2	no	—
250	C₂×C₄×C₄₁	—	2	4	no	—
251	C₂×C₄×C₄₁	—	2	4	no	—
252	C₂×C₄×C₄₁	—	2	4	no	—
253	C₂×C₄×C₄₁	—	2	4	no	—
254	C₂×C₄×C₄₁	—	2	4	no	—
255	C₂×C₄×C₄₁	—	2	2	no	—
256	C₂×C₄×C₄₁	—	4	4	no	—
257	C₂×C₄×C₄₁	—	4	4	no	—
258	C₂×C₄×C₄₁	—	4	16	no	—
259	C₂×C₄×C₄₁	—	4	4	no	—
260	C₂×C₄×C₄₁	—	4	2	no	—
261	C₂×C₄×C₄₁	—	4	2	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	8	2	no	—
264	C₂×C₄×C₄₁	—	8	2	no	—
265	C₂×C₄×C₄₁	C₂×C₄²	1	1	yes	characteristic
266	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
274	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
275	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
276	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
277	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
278	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
282	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
283	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
284	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
285	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
286	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
287	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
288	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
290	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
291	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
292	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
293	C₈×C₄₁	—	4	2	no	—
294	C₈×C₄₁	—	4	2	no	—
295	#10772	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂²×C₄₁	—	2	2	no	—
297	C₂²×C₄₁	—	2	2	no	—
298	C₂²×C₄₁	—	2	2	no	—
299	C₂²×C₄₁	—	2	4	no	—
300	C₂²×C₄₁	—	4	1	no	—
301	C₂²×C₄₁	—	4	1	no	—
302	C₂²×C₄₁	—	4	1	no	—
303	C₂²×C₄₁	—	4	1	no	—
304	C₂²×C₄₁	—	4	4	no	—
305	C₂²×C₄₁	—	4	4	no	—
306	C₂²×C₄₁	—	4	4	no	—
307	C₂²×C₄₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₄₁	#379	1	1	yes	characteristic
309	C₂²×C₄₁	#380	1	1	yes	characteristic
310	C₂²×C₄₁	#385	1	1	yes	characteristic
311	C₂²×C₄₁	#385	1	1	yes	characteristic
312	C₂²×C₄₁	#386	1	1	yes	characteristic
313	C₂²×C₄₁	#386	1	1	yes	characteristic
314	C₄×C₄₁	—	2	4	no	—
315	C₄×C₄₁	—	2	4	no	—
316	C₄×C₄₁	—	4	4	no	—
317	C₄×C₄₁	—	4	2	no	—
318	C₄×C₄₁	—	8	2	no	—
319	C₄×C₄₁	—	8	2	no	—
320	C₄×C₄₁	C₂×#95	1	1	yes	characteristic
321	C₄×C₄₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
322	C₄×C₄₁	#380	1	1	yes	characteristic
323	C₄×C₄₁	#381	1	1	yes	characteristic
324	C₄×C₄₁	#385	1	1	yes	characteristic
325	C₄×C₄₁	#385	1	1	yes	characteristic
326	C₄×C₄₁	#386	1	1	yes	characteristic
327	C₄×C₄₁	#386	1	1	yes	characteristic
328	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic
329	C₂×#421	C₂×C₄₁	1	1	yes	characteristic
330	#2896	C₂×C₄₁	1	1	yes	characteristic
331	C₂×#344	C₂×C₄₁	1	1	yes	characteristic, complemented
332	#1740	C₂×C₄₁	1	1	yes	characteristic, complemented
333	C₂×#339	C₂×C₄₁	1	1	yes	characteristic, complemented
334	C₂×#339	C₂×C₄₁	1	1	yes	characteristic, complemented
335	C₂×C₄₁	—	2	1	no	—
336	C₂×C₄₁	—	2	1	no	—
337	C₂×C₄₁	—	2	1	no	—
338	C₂×C₄₁	—	2	1	no	—
339	C₂×C₄₁	—	2	1	no	—
340	C₂×C₄₁	—	2	1	no	—
341	C₂×C₄₁	—	4	4	no	—
342	C₂×C₄₁	C₂²⋊#95	1	1	yes	characteristic
343	C₂×C₄₁	#1906	1	2	yes	—
344	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
346	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
347	C₄×#41	—	2	2	no	—
348	C₄×#41	—	2	2	no	—
349	C₄×#41	—	2	2	no	—
350	C₄×#41	C₄×C₄₁	1	4	yes	complemented
351	C₂×C₄×Q₈	—	2	1	no	—
352	C₂×C₄×D₄	—	2	1	no	—
353	C₂×C₄×D₄	—	2	2	no	—
354	C₂×#117	—	2	1	no	—
355	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
356	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
357	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
358	C₂²×C₄²	—	2	1	no	—
359	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
360	#421	—	2	2	no	—
361	#421	C₄×C₄₁	1	4	yes	complemented
362	C₂×#104	—	2	2	no	—
363	#419	—	2	1	no	—
364	#418	—	2	1	no	—
365	#417	C₄×C₄₁	1	4	yes	complemented
366	#416	—	2	2	no	—
367	#344	—	2	2	no	—
368	#342	—	2	2	no	—
369	#339	—	2	1	no	—
370	#339	—	2	2	no	—
371	#339	—	2	1	no	—
372	C₄₁	#10772	1	1	yes	characteristic, direct product factor, Sylow
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂×#41	—	2	1	no	—
378	C₂×#41	—	2	1	no	—
379	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
380	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
381	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
382	C₂×#41	D₄×C₄₁	1	2	yes	—
383	C₂×#41	D₄×C₄₁	1	2	yes	—
384	C₂×#41	Q₈×C₄₁	1	2	yes	—
385	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	2	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	1	no	—
399	C₂×M₁₆	—	2	1	no	—
400	C₂×M₁₆	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	complemented
403	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	complemented
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	—	2	1	no	—
406	C₄×Q₈	—	2	4	no	—
407	C₄×Q₈	—	2	4	no	—
408	C₄×D₄	—	2	8	no	—
409	C₄×D₄	—	2	4	no	—
410	C₄×D₄	—	2	4	no	—
411	C₄×D₄	—	2	8	no	—
412	#117	—	2	4	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	2	1	no	—
416	#117	—	2	4	no	—
417	#117	—	2	1	no	—
418	#117	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	—	2	1	no	—
423	#117	C₂×C₄×C₄₁	1	2	yes	—
424	#117	C₂×C₄×C₄₁	1	2	yes	complemented
425	#117	D₄×C₄₁	1	2	yes	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	complemented
430	C₂×C₂²⋊C₄	—	2	2	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
434	C₂×C₄²	—	2	2	no	—
435	C₂×C₄²	—	2	4	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	4	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
444	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
445	C₂×C₄²	D₄×C₄₁	1	2	yes	—
446	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
447	#104	—	2	8	no	—
448	#103	—	2	4	no	—
449	#102	—	2	4	no	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	2	2	no	—
464	#41	C₄²×C₄₁	1	4	yes	—
465	#41	C₂²⋊C₄×C₄₁	1	4	yes	—
466	#41	C₄⋊C₄×C₄₁	1	4	yes	—
467	#41	C₄⋊C₄×C₄₁	1	4	yes	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
472	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
473	C₂×Q₈	C₄⋊C₄×C₄₁	1	2	yes	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
484	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
485	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	8	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	—	4	8	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
512	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
513	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
514	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
515	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
516	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
517	M₁₆	—	2	2	no	—
518	M₁₆	—	2	2	no	—
519	M₁₆	—	2	2	no	—
520	M₁₆	—	2	2	no	—
521	M₁₆	—	4	1	no	—
522	M₁₆	—	4	1	no	—
523	M₁₆	—	4	1	no	—
524	M₁₆	—	4	1	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	4	1	no	—
528	C₂×C₈	—	4	1	no	—
529	C₂×C₈	—	4	1	no	—
530	C₂×C₈	—	4	1	no	—
531	C₄⋊C₄	—	2	8	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	2	8	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₂²⋊C₄	—	4	1	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
545	C₄²	—	2	8	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	4	1	no	—
554	C₄²	—	4	1	no	—
555	C₄²	—	4	1	no	—
556	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
557	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	4	no	—
563	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
564	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
565	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
566	C₂³	#120×C₄₁	1	1	yes	characteristic
567	C₂³	#120×C₄₁	1	1	yes	characteristic
568	C₂³	#121×C₄₁	1	1	yes	characteristic
569	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
570	Q₈	—	2	2	no	—
571	Q₈	—	2	2	no	—
572	Q₈	—	2	2	no	—
573	Q₈	#95×C₄₁	1	4	yes	—
574	D₄	—	2	4	no	—
575	D₄	—	2	4	no	—
576	D₄	—	2	4	no	—
577	D₄	—	2	4	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	#95×C₄₁	1	4	yes	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	16	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	—	8	2	no	—
602	C₂×C₄	C₂×C₄²×C₄₁	1	1	yes	characteristic
603	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
604	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
605	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
606	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
607	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
608	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
609	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
610	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
611	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
612	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
613	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
614	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
615	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
616	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
617	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
618	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
619	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
620	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
621	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
622	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
623	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
624	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
625	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
626	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
627	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
628	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
629	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
630	C₈	—	4	2	no	—
631	C₈	—	4	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	C₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
644	C₂²	C₄₁×#379	1	1	yes	characteristic
645	C₂²	C₄₁×#380	1	1	yes	characteristic
646	C₂²	C₄₁×#385	1	1	yes	characteristic
647	C₂²	C₄₁×#385	1	1	yes	characteristic
648	C₂²	C₄₁×#386	1	1	yes	characteristic
649	C₂²	C₄₁×#386	1	1	yes	characteristic
650	C₄	—	2	4	no	—
651	C₄	—	2	4	no	—
652	C₄	—	4	4	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	2	no	—
655	C₄	—	8	2	no	—
656	C₄	C₂×#95×C₄₁	1	1	yes	characteristic
657	C₄	C₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
658	C₄	C₄₁×#380	1	1	yes	characteristic
659	C₄	C₄₁×#381	1	1	yes	characteristic
660	C₄	C₄₁×#385	1	1	yes	characteristic
661	C₄	C₄₁×#385	1	1	yes	characteristic
662	C₄	C₄₁×#386	1	1	yes	characteristic
663	C₄	C₄₁×#386	1	1	yes	characteristic
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	2	1	no	—
667	C₂	—	2	1	no	—
668	C₂	—	2	1	no	—
669	C₂	—	2	1	no	—
670	C₂	—	4	4	no	—
671	C₂	C₄₁×C₂²⋊#95	1	1	yes	characteristic
672	C₂	C₄₁×#1906	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	#121
commutator	C₂×C₄	C₂×C₄²×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂²×C₄₁	#386
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₁×#344	C₂	semidirect
5. C₄₁×#1740	C₂	semidirect
6. C₂×C₄₁×#339	C₂	semidirect
7. C₂×C₄₁×#339	C₂	semidirect
14. C₄×#41×C₄₁	C₄	semidirect
25. C₄₁×#421	C₄	semidirect
29. C₄₁×#417	C₄	semidirect
65. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
66. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
87. #117×C₄₁	C₂×C₄	semidirect
92. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
295. #10772	C₄₁	direct (N × H)
331. C₂×#344	C₂×C₄₁	semidirect
332. #1740	C₂×C₄₁	semidirect
333. C₂×#339	C₂×C₄₁	semidirect
334. C₂×#339	C₂×C₄₁	semidirect
350. C₄×#41	C₄×C₄₁	semidirect
361. #421	C₄×C₄₁	semidirect
365. #417	C₄×C₄₁	semidirect
372. C₄₁	#10772	direct (N × H)
402. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
403. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
424. #117	C₂×C₄×C₄₁	semidirect
429. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₄₁	2
C₂×C₄₁×#421	2
C₄₁×#2896	2
C₂×C₄₁×#344	2
C₄₁×#1740	2
C₂×C₄₁×#339	2
#10772	41

Subgroups — C41×#10772 #23786973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#10772 #23786973