Subgroups — C₄₁×#20848 #23797049

Order 10496.

1462 conjugacy classes of subgroups.

The subgroup lattice has 496 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
2	C₂×C₄₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#106×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#408	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2311	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1854	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1853	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#520	—	2	4	no	—
14	C₄₁×#520	—	2	4	no	—
15	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
16	C₂×C₄×D₄×C₄₁	—	2	2	no	—
17	C₂×C₄×D₄×C₄₁	—	2	1	no	—
18	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₁	C₂²	1	2	yes	—
20	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×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×#428	—	2	4	no	—
25	C₂×#107×C₄₁	C₂²	1	2	yes	—
26	C₂×#106×C₄₁	—	2	4	no	—
27	C₂×#106×C₄₁	C₂²	1	2	yes	—
28	C₂×#106×C₄₁	C₂²	1	4	yes	—
29	C₄₁×#408	C₄	1	8	yes	complemented
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
31	C₄₁×#391	—	2	1	no	—
32	C₄₁×#390	—	2	1	no	—
33	C₄₁×#386	—	2	2	no	—
34	C₄₁×#380	C₂²	1	4	yes	—
35	C₄₁×#340	C₂²	1	2	yes	—
36	C₄₁×#340	C₂²	1	4	yes	—
37	C₄₁×#340	C₂²	1	2	yes	—
38	C₂×#41×C₄₁	—	2	2	no	—
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	2	no	—
42	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
43	C₂×#41×C₄₁	Q₈	1	4	yes	—
44	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	D₄	1	2	yes	—
46	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	—	2	2	no	—
48	C₂³×C₄×C₄₁	—	2	1	no	—
49	C₂³×C₄×C₄₁	—	2	1	no	—
50	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₄₁	—	2	2	no	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
55	C₂²×C₈×C₄₁	—	2	2	no	—
56	C₂²×C₈×C₄₁	—	2	2	no	—
57	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
58	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
60	C₄×Q₈×C₄₁	—	2	8	no	—
61	C₄×D₄×C₄₁	—	2	16	no	—
62	C₄×D₄×C₄₁	—	2	8	no	—
63	#117×C₄₁	—	2	2	no	—
64	#117×C₄₁	—	2	4	no	—
65	#117×C₄₁	—	2	4	no	—
66	#117×C₄₁	—	2	2	no	—
67	#117×C₄₁	—	2	2	no	—
68	#117×C₄₁	D₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
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	2	yes	—
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
87	C₂×C₄²×C₄₁	—	2	2	no	—
88	C₂×C₄²×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	—	2	1	no	—
90	#107×C₄₁	—	2	4	no	—
91	#106×C₄₁	—	2	8	no	—
92	#106×C₄₁	—	2	4	no	—
93	C₂²⋊C₈×C₄₁	C₂×C₄	1	16	yes	complemented
94	#95×C₄₁	—	2	4	no	—
95	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
96	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
97	#41×C₄₁	—	2	8	no	—
98	#41×C₄₁	—	2	8	no	—
99	#41×C₄₁	—	2	8	no	—
100	#41×C₄₁	—	2	8	no	—
101	C₂×Q₈×C₄₁	—	2	2	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	C₄⋊C₄	1	4	yes	—
104	C₂×D₄×C₄₁	—	2	4	no	—
105	C₂×D₄×C₄₁	—	2	4	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	C₄⋊C₄	1	8	yes	—
109	C₂×D₄×C₄₁	C₄⋊C₄	1	4	yes	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	1	no	—
115	C₂²×C₄×C₄₁	—	2	2	no	—
116	C₂²×C₄×C₄₁	—	2	1	no	—
117	C₂²×C₄×C₄₁	—	2	8	no	—
118	C₂²×C₄×C₄₁	—	2	4	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	—	8	2	no	—
123	C₂²×C₄×C₄₁	—	8	4	no	—
124	C₂²×C₄×C₄₁	—	8	2	no	—
125	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
132	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₄₁	#41	1	2	yes	—
134	C₂²×C₄×C₄₁	#41	1	2	yes	—
135	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₄₁	—	2	8	no	—
137	C₂×C₈×C₄₁	—	2	8	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	—	2	2	no	—
140	C₂×C₈×C₄₁	—	2	2	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
143	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
144	C₄⋊C₄×C₄₁	—	2	8	no	—
145	C₄⋊C₄×C₄₁	—	2	4	no	—
146	C₄⋊C₄×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	2	1	no	—
148	C₄⋊C₄×C₄₁	—	2	1	no	—
149	C₄⋊C₄×C₄₁	—	2	2	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	2	no	—
153	C₄⋊C₄×C₄₁	—	4	2	no	—
154	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
156	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₄₁	—	2	8	no	—
158	C₂²⋊C₄×C₄₁	—	2	4	no	—
159	C₂²⋊C₄×C₄₁	—	4	2	no	—
160	C₂²⋊C₄×C₄₁	—	8	4	no	—
161	C₄²×C₄₁	—	2	8	no	—
162	C₄²×C₄₁	—	2	4	no	—
163	C₄²×C₄₁	—	4	2	no	—
164	C₂³×C₄₁	—	2	2	no	—
165	C₂³×C₄₁	—	2	2	no	—
166	C₂³×C₄₁	—	2	2	no	—
167	C₂³×C₄₁	—	2	2	no	—
168	C₂³×C₄₁	—	2	4	no	—
169	C₂³×C₄₁	—	2	4	no	—
170	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
171	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
172	C₂³×C₄₁	#120	1	2	yes	—
173	C₂³×C₄₁	#123	1	2	yes	—
174	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₄₁	—	2	8	no	—
176	D₄×C₄₁	—	2	16	no	—
177	D₄×C₄₁	—	2	8	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	4	no	—
181	C₂×C₄×C₄₁	—	2	4	no	—
182	C₂×C₄×C₄₁	—	2	4	no	—
183	C₂×C₄×C₄₁	—	2	4	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	4	no	—
194	C₂×C₄×C₄₁	—	4	2	no	—
195	C₂×C₄×C₄₁	—	8	4	no	—
196	C₂×C₄×C₄₁	—	8	8	no	—
197	C₂×C₄×C₄₁	—	8	4	no	—
198	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
199	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
200	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
201	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
202	C₂×C₄×C₄₁	#120	1	2	yes	—
203	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
204	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
205	C₂×C₄×C₄₁	#123	1	2	yes	—
206	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
212	C₈×C₄₁	—	2	4	no	—
213	C₈×C₄₁	—	2	4	no	—
214	#20848	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₁	—	2	4	no	—
216	C₂²×C₄₁	—	2	4	no	—
217	C₂²×C₄₁	—	2	2	no	—
218	C₂²×C₄₁	—	2	2	no	—
219	C₂²×C₄₁	—	2	8	no	—
220	C₂²×C₄₁	—	2	4	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	—	4	2	no	—
223	C₂²×C₄₁	—	4	2	no	—
224	C₂²×C₄₁	#385	1	4	yes	—
225	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
226	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
227	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
228	C₂²×C₄₁	#577	1	2	yes	—
229	C₂²×C₄₁	#577	1	2	yes	—
230	C₄×C₄₁	—	2	4	no	—
231	C₄×C₄₁	—	4	4	no	—
232	C₄×C₄₁	—	4	2	no	—
233	C₄×C₄₁	—	4	2	no	—
234	C₄×C₄₁	—	8	2	no	—
235	C₄×C₄₁	—	8	2	no	—
236	C₄×C₄₁	#385	1	4	yes	—
237	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
240	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×#520	C₂×C₄₁	1	1	yes	characteristic
242	C₂×#428	C₂×C₄₁	1	1	yes	characteristic, complemented
243	C₂²×#106	C₂×C₄₁	1	1	yes	characteristic, complemented
244	C₂×#408	C₂×C₄₁	1	1	yes	characteristic
245	#2311	C₂×C₄₁	1	1	yes	characteristic
246	#1854	C₂×C₄₁	1	4	yes	complemented
247	#1853	C₂×C₄₁	1	4	yes	complemented
248	#1736	C₂×C₄₁	1	1	yes	characteristic, complemented
249	#1735	C₂×C₄₁	1	1	yes	characteristic, complemented
250	C₂×C₄₁	—	2	4	no	—
251	C₂×C₄₁	—	4	4	no	—
252	C₂×C₄₁	C₂×#385	1	1	yes	characteristic
253	C₂×C₄₁	#2912	1	2	yes	—
254	C₂×C₄₁	#3009	1	1	yes	characteristic
255	C₂×C₄₁	#3010	1	1	yes	characteristic
256	C₂×C₄₁	#3099	1	2	yes	—
257	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
258	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
260	#520	—	2	4	no	—
261	#520	—	2	4	no	—
262	C₂×C₄×Q₈	—	2	1	no	—
263	C₂×C₄×D₄	—	2	2	no	—
264	C₂×C₄×D₄	—	2	1	no	—
265	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×#117	C₂²×C₄₁	1	2	yes	—
267	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
270	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
271	#428	—	2	4	no	—
272	C₂×#107	C₂²×C₄₁	1	2	yes	—
273	C₂×#106	—	2	4	no	—
274	C₂×#106	C₂²×C₄₁	1	2	yes	—
275	C₂×#106	C₂²×C₄₁	1	4	yes	—
276	#408	C₄×C₄₁	1	8	yes	complemented
277	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
278	#391	—	2	1	no	—
279	#390	—	2	1	no	—
280	#386	—	2	2	no	—
281	#380	C₂²×C₄₁	1	4	yes	—
282	#340	C₂²×C₄₁	1	2	yes	—
283	#340	C₂²×C₄₁	1	4	yes	—
284	#340	C₂²×C₄₁	1	2	yes	—
285	C₄₁	#20848	1	1	yes	characteristic, direct product factor, Sylow
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	2	no	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
291	C₂×#41	Q₈×C₄₁	1	4	yes	—
292	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
293	C₂²×D₄	D₄×C₄₁	1	2	yes	—
294	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
299	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
306	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
307	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
308	C₄×Q₈	—	2	8	no	—
309	C₄×D₄	—	2	16	no	—
310	C₄×D₄	—	2	8	no	—
311	#117	—	2	2	no	—
312	#117	—	2	4	no	—
313	#117	—	2	4	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	#117	D₄×C₄₁	1	4	yes	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	4	no	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	#107	—	2	4	no	—
339	#106	—	2	8	no	—
340	#106	—	2	4	no	—
341	C₂²⋊C₈	C₂×C₄×C₄₁	1	16	yes	complemented
342	#95	—	2	4	no	—
343	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
344	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
345	#41	—	2	8	no	—
346	#41	—	2	8	no	—
347	#41	—	2	8	no	—
348	#41	—	2	8	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	C₄⋊C₄×C₄₁	1	4	yes	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	C₄⋊C₄×C₄₁	1	8	yes	—
357	C₂×D₄	C₄⋊C₄×C₄₁	1	4	yes	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	8	2	no	—
371	C₂²×C₄	—	8	4	no	—
372	C₂²×C₄	—	8	2	no	—
373	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
374	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
379	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
380	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
381	C₂²×C₄	#41×C₄₁	1	2	yes	—
382	C₂²×C₄	#41×C₄₁	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
384	M₁₆	—	2	8	no	—
385	C₂×C₈	—	2	8	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
391	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
404	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	8	4	no	—
409	C₄²	—	2	8	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	4	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
419	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
420	C₂³	#120×C₄₁	1	2	yes	—
421	C₂³	#123×C₄₁	1	2	yes	—
422	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
423	Q₈	—	2	8	no	—
424	D₄	—	2	16	no	—
425	D₄	—	2	8	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	—	8	8	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
447	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
448	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
449	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
450	C₂×C₄	#120×C₄₁	1	2	yes	—
451	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
452	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
453	C₂×C₄	#123×C₄₁	1	2	yes	—
454	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
457	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
460	C₈	—	2	4	no	—
461	C₈	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	2	8	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₄₁×#385	1	4	yes	—
472	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
473	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
474	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
475	C₂²	C₄₁×#577	1	2	yes	—
476	C₂²	C₄₁×#577	1	2	yes	—
477	C₄	—	2	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	8	2	no	—
482	C₄	—	8	2	no	—
483	C₄	C₄₁×#385	1	4	yes	—
484	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
485	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
486	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
487	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
488	C₂	—	2	4	no	—
489	C₂	—	4	4	no	—
490	C₂	C₂×C₄₁×#385	1	1	yes	characteristic
491	C₂	C₄₁×#2912	1	2	yes	—
492	C₂	C₄₁×#3009	1	1	yes	characteristic
493	C₂	C₄₁×#3010	1	1	yes	characteristic
494	C₂	C₄₁×#3099	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×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
2. C₂×C₄₁×#428	C₂	semidirect
3. C₂²×#106×C₄₁	C₂	semidirect
6. C₄₁×#1854	C₂	semidirect
7. C₄₁×#1853	C₂	semidirect
8. C₄₁×#1736	C₂	semidirect
9. C₄₁×#1735	C₂	semidirect
29. C₄₁×#408	C₄	semidirect
54. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
57. C₂²×C₈×C₄₁	C₂×C₄	semidirect
93. C₂²⋊C₈×C₄₁	C₂×C₄	semidirect
214. #20848	C₄₁	direct (N × H)
242. C₂×#428	C₂×C₄₁	semidirect
243. C₂²×#106	C₂×C₄₁	semidirect
246. #1854	C₂×C₄₁	semidirect
247. #1853	C₂×C₄₁	semidirect
248. #1736	C₂×C₄₁	semidirect
249. #1735	C₂×C₄₁	semidirect
276. #408	C₄×C₄₁	semidirect
285. C₄₁	#20848	direct (N × H)
302. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
305. C₂²×C₈	C₂×C₄×C₄₁	semidirect
341. C₂²⋊C₈	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×C₄₁×#520	2
C₂×C₄₁×#428	2
C₂²×#106×C₄₁	2
C₂×C₄₁×#408	2
C₄₁×#2311	2
C₄₁×#1854	2
C₄₁×#1853	2
C₄₁×#1736	2
C₄₁×#1735	2
#20848	41

Subgroups — C41×#20848 #23797049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20848 #23797049