Subgroups — C₂×C₄₁×#2046 #23799719

Order 10496.

1458 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic
5	C₂²×#101×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#100×C₄₁	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#2046	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₄₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₄₁	—	2	4	no	—
12	C₂²×SD₁₆×C₄₁	—	2	4	no	—
13	C₂²×SD₁₆×C₄₁	—	2	2	no	—
14	C₂²×SD₁₆×C₄₁	—	2	2	no	—
15	C₂²×SD₁₆×C₄₁	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#424	—	2	2	no	—
22	C₄₁×#424	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₄₁	—	2	2	no	—
24	C₄₁×#419	—	2	2	no	—
25	C₄₁×#419	C₂²	1	4	yes	complemented
26	C₄₁×#418	—	2	2	no	—
27	C₄₁×#418	C₂²	1	4	yes	—
28	C₂×#103×C₄₁	—	2	2	no	—
29	C₂×#102×C₄₁	—	2	2	no	—
30	C₂×#101×C₄₁	—	2	4	no	—
31	C₂×#101×C₄₁	C₂²	1	4	yes	complemented
32	C₂×#100×C₄₁	—	2	4	no	—
33	C₂×#100×C₄₁	C₂²	1	4	yes	—
34	C₄₁×#341	C₂²	1	4	yes	complemented
35	C₂⁵×C₄₁	—	2	1	no	—
36	C₂²×Q₈×C₄₁	—	2	2	no	—
37	C₂²×Q₈×C₄₁	—	2	1	no	—
38	C₂²×Q₈×C₄₁	—	2	1	no	—
39	C₂²×Q₈×C₄₁	—	2	1	no	—
40	C₂²×Q₈×C₄₁	—	2	2	no	—
41	C₂²×Q₈×C₄₁	—	2	1	no	—
42	C₂²×Q₈×C₄₁	—	2	1	no	—
43	C₂²×Q₈×C₄₁	—	2	2	no	—
44	C₂²×Q₈×C₄₁	D₄	1	4	yes	—
45	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	1	no	—
49	C₂²×D₄×C₄₁	—	2	1	no	—
50	C₂²×D₄×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	2	no	—
52	C₂²×D₄×C₄₁	—	2	1	no	—
53	C₂²×D₄×C₄₁	—	2	2	no	—
54	C₂²×D₄×C₄₁	D₄	1	4	yes	—
55	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₁	—	2	1	no	—
57	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₄₁	—	2	16	no	—
59	C₂×SD₁₆×C₄₁	—	2	16	no	—
60	C₂×SD₁₆×C₄₁	—	2	8	no	—
61	C₂×SD₁₆×C₄₁	—	2	8	no	—
62	C₂×SD₁₆×C₄₁	—	2	8	no	—
63	C₂×M₁₆×C₄₁	—	2	1	no	—
64	C₂×M₁₆×C₄₁	—	2	1	no	—
65	C₂×M₁₆×C₄₁	—	2	1	no	—
66	C₂×M₁₆×C₄₁	—	2	2	no	—
67	C₂×M₁₆×C₄₁	—	2	2	no	—
68	C₂×M₁₆×C₄₁	—	2	2	no	—
69	C₂×M₁₆×C₄₁	—	2	2	no	—
70	C₂×M₁₆×C₄₁	—	2	2	no	—
71	C₂×M₁₆×C₄₁	—	2	2	no	—
72	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
73	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
74	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₁	—	2	2	no	—
76	C₂²×C₈×C₄₁	—	2	2	no	—
77	C₂²×C₈×C₄₁	—	2	1	no	—
78	C₂²×C₈×C₄₁	—	2	1	no	—
79	C₂²×C₈×C₄₁	—	2	1	no	—
80	C₂²×C₈×C₄₁	D₄	1	2	yes	—
81	C₂²×C₈×C₄₁	D₄	1	2	yes	—
82	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
83	#117×C₄₁	—	2	1	no	—
84	#117×C₄₁	—	2	1	no	—
85	#117×C₄₁	D₄	1	2	yes	—
86	#117×C₄₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	—	2	1	no	—
90	C₄⋊C₈×C₄₁	—	2	8	no	—
91	#103×C₄₁	—	2	8	no	—
92	#102×C₄₁	—	2	8	no	—
93	#101×C₄₁	—	2	8	no	—
94	#100×C₄₁	—	2	8	no	—
95	C₂⁴×C₄₁	—	2	4	no	—
96	C₂⁴×C₄₁	—	2	2	no	—
97	C₂⁴×C₄₁	—	4	1	no	—
98	C₂⁴×C₄₁	—	4	1	no	—
99	C₂⁴×C₄₁	—	4	2	no	—
100	C₂⁴×C₄₁	—	8	4	no	—
101	C₂⁴×C₄₁	#41	1	1	yes	characteristic
102	C₂×Q₈×C₄₁	—	2	4	no	—
103	C₂×Q₈×C₄₁	—	2	2	no	—
104	C₂×Q₈×C₄₁	—	2	4	no	—
105	C₂×Q₈×C₄₁	—	2	4	no	—
106	C₂×Q₈×C₄₁	—	2	4	no	—
107	C₂×Q₈×C₄₁	—	2	4	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	2	2	no	—
110	C₂×Q₈×C₄₁	—	2	2	no	—
111	C₂×Q₈×C₄₁	—	2	2	no	—
112	C₂×Q₈×C₄₁	—	4	1	no	—
113	C₂×Q₈×C₄₁	—	4	1	no	—
114	C₂×Q₈×C₄₁	—	4	2	no	—
115	C₂×Q₈×C₄₁	—	4	2	no	—
116	C₂×Q₈×C₄₁	—	4	2	no	—
117	C₂×Q₈×C₄₁	—	4	2	no	—
118	C₂×Q₈×C₄₁	—	4	2	no	—
119	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
120	C₂×D₄×C₄₁	—	2	4	no	—
121	C₂×D₄×C₄₁	—	2	4	no	—
122	C₂×D₄×C₄₁	—	2	4	no	—
123	C₂×D₄×C₄₁	—	2	4	no	—
124	C₂×D₄×C₄₁	—	2	4	no	—
125	C₂×D₄×C₄₁	—	2	2	no	—
126	C₂×D₄×C₄₁	—	2	2	no	—
127	C₂×D₄×C₄₁	—	2	2	no	—
128	C₂×D₄×C₄₁	—	2	2	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	4	2	no	—
131	C₂×D₄×C₄₁	—	4	2	no	—
132	C₂×D₄×C₄₁	—	4	1	no	—
133	C₂×D₄×C₄₁	—	4	1	no	—
134	C₂×D₄×C₄₁	—	4	2	no	—
135	C₂×D₄×C₄₁	—	4	2	no	—
136	C₂×D₄×C₄₁	—	4	2	no	—
137	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	2	4	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	4	1	no	—
142	C₂²×C₄×C₄₁	—	4	1	no	—
143	C₂²×C₄×C₄₁	—	4	2	no	—
144	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	#41	1	2	yes	—
152	C₂²×C₄×C₄₁	#41	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
154	SD₁₆×C₄₁	—	2	32	no	—
155	M₁₆×C₄₁	—	2	2	no	—
156	M₁₆×C₄₁	—	2	2	no	—
157	M₁₆×C₄₁	—	2	2	no	—
158	M₁₆×C₄₁	—	2	2	no	—
159	M₁₆×C₄₁	—	2	2	no	—
160	M₁₆×C₄₁	—	2	2	no	—
161	M₁₆×C₄₁	—	4	2	no	—
162	M₁₆×C₄₁	—	4	2	no	—
163	M₁₆×C₄₁	—	4	2	no	—
164	C₂×C₈×C₄₁	—	2	4	no	—
165	C₂×C₈×C₄₁	—	2	4	no	—
166	C₂×C₈×C₄₁	—	2	2	no	—
167	C₂×C₈×C₄₁	—	2	2	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	—	2	2	no	—
170	C₂×C₈×C₄₁	—	2	2	no	—
171	C₂×C₈×C₄₁	—	4	2	no	—
172	C₂×C₈×C₄₁	—	4	2	no	—
173	C₂×C₈×C₄₁	—	4	2	no	—
174	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
175	C₄⋊C₄×C₄₁	—	2	2	no	—
176	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
177	C₂²⋊C₄×C₄₁	—	2	2	no	—
178	C₂²⋊C₄×C₄₁	—	2	2	no	—
179	C₄²×C₄₁	—	2	2	no	—
180	C₄²×C₄₁	—	2	2	no	—
181	C₂³×C₄₁	—	2	4	no	—
182	C₂³×C₄₁	—	2	4	no	—
183	C₂³×C₄₁	—	4	2	no	—
184	C₂³×C₄₁	—	4	2	no	—
185	C₂³×C₄₁	—	4	4	no	—
186	C₂³×C₄₁	—	4	4	no	—
187	C₂³×C₄₁	—	8	4	no	—
188	C₂³×C₄₁	—	8	8	no	—
189	C₂³×C₄₁	—	8	4	no	—
190	C₂³×C₄₁	—	8	8	no	—
191	C₂³×C₄₁	—	8	4	no	—
192	C₂³×C₄₁	#121	1	1	yes	characteristic
193	C₂³×C₄₁	#121	1	1	yes	characteristic
194	C₂³×C₄₁	#123	1	2	yes	—
195	C₂³×C₄₁	#123	1	2	yes	—
196	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
197	Q₈×C₄₁	—	2	4	no	—
198	Q₈×C₄₁	—	2	4	no	—
199	Q₈×C₄₁	—	4	2	no	—
200	Q₈×C₄₁	—	4	2	no	—
201	Q₈×C₄₁	—	4	4	no	—
202	Q₈×C₄₁	—	4	4	no	—
203	D₄×C₄₁	—	2	4	no	—
204	D₄×C₄₁	—	2	4	no	—
205	D₄×C₄₁	—	4	2	no	—
206	D₄×C₄₁	—	4	2	no	—
207	D₄×C₄₁	—	4	4	no	—
208	D₄×C₄₁	—	4	4	no	—
209	C₂×C₄×C₄₁	—	2	4	no	—
210	C₂×C₄×C₄₁	—	2	4	no	—
211	C₂×C₄×C₄₁	—	4	2	no	—
212	C₂×C₄×C₄₁	—	4	2	no	—
213	C₂×C₄×C₄₁	—	4	4	no	—
214	C₂×C₄×C₄₁	—	4	4	no	—
215	C₂×C₄×C₄₁	—	4	4	no	—
216	C₂×C₄×C₄₁	#120	1	2	yes	—
217	C₂×C₄×C₄₁	#120	1	2	yes	—
218	C₂×C₄×C₄₁	#121	1	2	yes	—
219	C₂×C₄×C₄₁	#121	1	2	yes	—
220	C₂×C₄×C₄₁	#121	1	2	yes	—
221	C₂×C₄×C₄₁	#121	1	2	yes	—
222	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
223	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
224	C₂×C₄×C₄₁	#123	1	2	yes	—
225	C₂×C₄×C₄₁	#123	1	2	yes	—
226	C₂×C₄×C₄₁	#124	1	2	yes	—
227	C₂×C₄×C₄₁	#124	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	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
234	C₈×C₄₁	—	2	4	no	—
235	C₈×C₄₁	—	4	2	no	—
236	C₈×C₄₁	—	4	2	no	—
237	C₈×C₄₁	—	4	2	no	—
238	C₂×#2046	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₄₁	—	2	2	no	—
240	C₂²×C₄₁	—	2	2	no	—
241	C₂²×C₄₁	—	2	4	no	—
242	C₂²×C₄₁	—	2	4	no	—
243	C₂²×C₄₁	—	4	4	no	—
244	C₂²×C₄₁	—	8	4	no	—
245	C₂²×C₄₁	—	8	4	no	—
246	C₂²×C₄₁	—	8	8	no	—
247	C₂²×C₄₁	—	8	4	no	—
248	C₂²×C₄₁	—	8	8	no	—
249	C₂²×C₄₁	#394	1	2	yes	—
250	C₂²×C₄₁	#394	1	2	yes	—
251	C₂²×C₄₁	#471	1	4	yes	—
252	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
253	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
254	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
255	C₄×C₄₁	—	4	4	no	—
256	C₄×C₄₁	—	4	4	no	—
257	C₄×C₄₁	#394	1	2	yes	—
258	C₄×C₄₁	#394	1	2	yes	—
259	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
260	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
261	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
262	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
263	C₂³×SD₁₆	C₂×C₄₁	1	1	yes	characteristic
264	C₂×#424	C₂×C₄₁	1	1	yes	characteristic, complemented
265	C₂×#419	C₂×C₄₁	1	1	yes	characteristic, complemented
266	C₂×#418	C₂×C₄₁	1	1	yes	characteristic
267	C₂²×#101	C₂×C₄₁	1	1	yes	characteristic, complemented
268	C₂²×#100	C₂×C₄₁	1	1	yes	characteristic
269	#2046	C₂×C₄₁	1	8	yes	direct product factor
270	C₂×#341	C₂×C₄₁	1	1	yes	characteristic, complemented
271	C₂×C₄₁	—	2	1	no	—
272	C₂×C₄₁	—	2	1	no	—
273	C₂×C₄₁	—	2	2	no	—
274	C₂×C₄₁	—	8	4	no	—
275	C₂×C₄₁	#2046	1	4	yes	direct product factor
276	C₂×C₄₁	C₂×#394	1	1	yes	characteristic
277	C₂×C₄₁	C₂×#471	1	2	yes	—
278	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
279	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
280	C₂²×SD₁₆	—	2	4	no	—
281	C₂²×SD₁₆	—	2	4	no	—
282	C₂²×SD₁₆	—	2	2	no	—
283	C₂²×SD₁₆	—	2	2	no	—
284	C₂²×SD₁₆	C₂²×C₄₁	1	4	yes	—
285	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
286	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
287	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
288	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
290	#424	—	2	2	no	—
291	#424	C₂²×C₄₁	1	4	yes	complemented
292	C₂×C₄⋊C₈	—	2	2	no	—
293	#419	—	2	2	no	—
294	#419	C₂²×C₄₁	1	4	yes	complemented
295	#418	—	2	2	no	—
296	#418	C₂²×C₄₁	1	4	yes	—
297	C₂×#103	—	2	2	no	—
298	C₂×#102	—	2	2	no	—
299	C₂×#101	—	2	4	no	—
300	C₂×#101	C₂²×C₄₁	1	4	yes	complemented
301	C₂×#100	—	2	4	no	—
302	C₂×#100	C₂²×C₄₁	1	4	yes	—
303	#341	C₂²×C₄₁	1	4	yes	complemented
304	C₄₁	C₂×#2046	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁵	—	2	1	no	—
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	D₄×C₄₁	1	4	yes	—
315	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	D₄×C₄₁	1	4	yes	—
325	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
326	C₂³×C₄	—	2	1	no	—
327	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
328	C₂×SD₁₆	—	2	16	no	—
329	C₂×SD₁₆	—	2	16	no	—
330	C₂×SD₁₆	—	2	8	no	—
331	C₂×SD₁₆	—	2	8	no	—
332	C₂×SD₁₆	—	2	8	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
343	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
344	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	2	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	1	no	—
350	C₂²×C₈	D₄×C₄₁	1	2	yes	—
351	C₂²×C₈	D₄×C₄₁	1	2	yes	—
352	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
353	#117	—	2	1	no	—
354	#117	—	2	1	no	—
355	#117	D₄×C₄₁	1	2	yes	—
356	#117	C₂³×C₄₁	1	2	yes	—
357	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₄⋊C₈	—	2	8	no	—
361	#103	—	2	8	no	—
362	#102	—	2	8	no	—
363	#101	—	2	8	no	—
364	#100	—	2	8	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	—	4	1	no	—
368	C₂⁴	—	4	1	no	—
369	C₂⁴	—	4	2	no	—
370	C₂⁴	—	8	4	no	—
371	C₂⁴	#41×C₄₁	1	1	yes	characteristic
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	—	4	2	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
421	C₂²×C₄	#41×C₄₁	1	2	yes	—
422	C₂²×C₄	#41×C₄₁	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
424	SD₁₆	—	2	32	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	4	2	no	—
432	M₁₆	—	4	2	no	—
433	M₁₆	—	4	2	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	4	2	no	—
442	C₂×C₈	—	4	2	no	—
443	C₂×C₈	—	4	2	no	—
444	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	8	4	no	—
458	C₂³	—	8	8	no	—
459	C₂³	—	8	4	no	—
460	C₂³	—	8	8	no	—
461	C₂³	—	8	4	no	—
462	C₂³	#121×C₄₁	1	1	yes	characteristic
463	C₂³	#121×C₄₁	1	1	yes	characteristic
464	C₂³	#123×C₄₁	1	2	yes	—
465	C₂³	#123×C₄₁	1	2	yes	—
466	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	4	no	—
472	Q₈	—	4	4	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	4	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	4	no	—
478	D₄	—	4	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	#120×C₄₁	1	2	yes	—
487	C₂×C₄	#120×C₄₁	1	2	yes	—
488	C₂×C₄	#121×C₄₁	1	2	yes	—
489	C₂×C₄	#121×C₄₁	1	2	yes	—
490	C₂×C₄	#121×C₄₁	1	2	yes	—
491	C₂×C₄	#121×C₄₁	1	2	yes	—
492	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
493	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
494	C₂×C₄	#123×C₄₁	1	2	yes	—
495	C₂×C₄	#123×C₄₁	1	2	yes	—
496	C₂×C₄	#124×C₄₁	1	2	yes	—
497	C₂×C₄	#124×C₄₁	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
502	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
504	C₈	—	2	4	no	—
505	C₈	—	4	2	no	—
506	C₈	—	4	2	no	—
507	C₈	—	4	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	8	4	no	—
514	C₂²	—	8	4	no	—
515	C₂²	—	8	8	no	—
516	C₂²	—	8	4	no	—
517	C₂²	—	8	8	no	—
518	C₂²	C₄₁×#394	1	2	yes	—
519	C₂²	C₄₁×#394	1	2	yes	—
520	C₂²	C₄₁×#471	1	4	yes	—
521	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
522	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
523	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
524	C₄	—	4	4	no	—
525	C₄	—	4	4	no	—
526	C₄	C₄₁×#394	1	2	yes	—
527	C₄	C₄₁×#394	1	2	yes	—
528	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
529	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
530	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
531	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
532	C₂	—	2	1	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	2	no	—
535	C₂	—	8	4	no	—
536	C₂	C₄₁×#2046	1	4	yes	direct product factor
537	C₂	C₂×C₄₁×#394	1	1	yes	characteristic
538	C₂	C₂×C₄₁×#471	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#424	C₂	semidirect
3. C₂×C₄₁×#419	C₂	semidirect
5. C₂²×#101×C₄₁	C₂	semidirect
7. C₄₁×#2046	C₂	direct (N × H)
8. C₂×C₄₁×#341	C₂	semidirect
22. C₄₁×#424	C₂²	semidirect
25. C₄₁×#419	C₂²	semidirect
31. C₂×#101×C₄₁	C₂²	semidirect
34. C₄₁×#341	C₂²	semidirect
238. C₂×#2046	C₄₁	direct (N × H)
264. C₂×#424	C₂×C₄₁	semidirect
265. C₂×#419	C₂×C₄₁	semidirect
267. C₂²×#101	C₂×C₄₁	semidirect
269. #2046	C₂×C₄₁	direct (N × H)
270. C₂×#341	C₂×C₄₁	semidirect
275. C₂×C₄₁	#2046	direct (N × H)
291. #424	C₂²×C₄₁	semidirect
294. #419	C₂²×C₄₁	semidirect
300. C₂×#101	C₂²×C₄₁	semidirect
303. #341	C₂²×C₄₁	semidirect
304. C₄₁	C₂×#2046	direct (N × H)
536. C₂	C₄₁×#2046	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₄₁	2
C₂×C₄₁×#424	2
C₂×C₄₁×#419	2
C₂×C₄₁×#418	2
C₂²×#101×C₄₁	2
C₂²×#100×C₄₁	2
C₄₁×#2046	2
C₂×C₄₁×#341	2
C₂×#2046	41

Subgroups — C2×C41×#2046 #23799719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2046 #23799719