Subgroups — C₄₁×#20899 #23797100

Order 10496.

1938 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#525	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1870	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1869	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#131×C₄₁	—	2	4	no	—
13	C₂×#131×C₄₁	—	2	4	no	—
14	C₂×#131×C₄₁	—	2	4	no	—
15	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	complemented
18	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₄₁	C₂²	1	2	yes	complemented
21	C₄₁×#525	—	2	4	no	—
22	C₄₁×#525	—	2	4	no	—
23	C₂×#123×C₄₁	C₄	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₄₁	C₄	1	2	yes	—
25	C₂×#121×C₄₁	C₄	1	2	yes	—
26	C₂×#120×C₄₁	C₄	1	2	yes	—
27	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
28	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#408	—	2	4	no	—
30	C₄₁×#407	—	2	4	no	—
31	C₂×C₂²⋊C₈×C₄₁	—	2	4	no	—
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
35	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	complemented
36	C₄₁×#336	C₂²	1	2	yes	complemented
37	C₄₁×#336	C₂²	1	4	yes	complemented
38	C₄₁×#336	C₂²	1	2	yes	complemented
39	C₂⁵×C₄₁	C₂×C₄	1	1	yes	characteristic
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	2	no	—
42	C₂×#41×C₄₁	—	2	2	no	—
43	C₂×#41×C₄₁	—	2	2	no	—
44	C₂×#41×C₄₁	D₄	1	4	yes	—
45	C₂×#41×C₄₁	D₄	1	4	yes	—
46	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₁	—	2	2	no	—
51	C₂³×C₄×C₄₁	—	2	2	no	—
52	C₂³×C₄×C₄₁	—	2	2	no	—
53	C₂³×C₄×C₄₁	—	2	2	no	—
54	C₂³×C₄×C₄₁	—	2	2	no	—
55	C₂³×C₄×C₄₁	—	2	2	no	—
56	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
57	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
61	#131×C₄₁	—	2	32	no	—
62	C₂×M₁₆×C₄₁	—	2	2	no	—
63	C₂×M₁₆×C₄₁	—	2	2	no	—
64	C₂×M₁₆×C₄₁	—	2	4	no	—
65	C₂×M₁₆×C₄₁	—	2	2	no	—
66	C₂×M₁₆×C₄₁	—	2	2	no	—
67	C₂×M₁₆×C₄₁	—	2	2	no	—
68	C₂×M₁₆×C₄₁	—	2	4	no	—
69	C₂×M₁₆×C₄₁	—	2	4	no	—
70	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
71	C₂²×C₈×C₄₁	—	2	2	no	—
72	C₂²×C₈×C₄₁	—	2	2	no	—
73	C₂²×C₈×C₄₁	—	2	4	no	—
74	C₂²×C₈×C₄₁	—	2	4	no	—
75	C₂²×C₈×C₄₁	—	2	4	no	—
76	C₂²×C₈×C₄₁	—	2	2	no	—
77	C₂²×C₈×C₄₁	—	2	2	no	—
78	C₂²×C₈×C₄₁	—	2	2	no	—
79	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
80	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
81	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
85	#123×C₄₁	—	2	8	no	—
86	C₂²⋊Q₈×C₄₁	—	2	8	no	—
87	#121×C₄₁	—	2	8	no	—
88	#120×C₄₁	—	2	8	no	—
89	C₄×D₄×C₄₁	—	2	8	no	—
90	C₄×D₄×C₄₁	—	2	8	no	—
91	#117×C₄₁	—	2	2	no	—
92	#117×C₄₁	—	2	2	no	—
93	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
95	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
96	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
97	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
98	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
99	C₂²⋊C₈×C₄₁	—	2	8	no	—
100	C₂²⋊C₈×C₄₁	—	2	4	no	—
101	C₂²⋊C₈×C₄₁	—	2	4	no	—
102	C₂²⋊C₈×C₄₁	—	2	8	no	—
103	C₂⁴×C₄₁	—	2	2	no	—
104	C₂⁴×C₄₁	—	2	4	no	—
105	C₂⁴×C₄₁	—	2	2	no	—
106	C₂⁴×C₄₁	—	2	2	no	—
107	C₂⁴×C₄₁	—	4	2	no	—
108	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
109	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
110	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
111	#41×C₄₁	—	2	8	no	—
112	#41×C₄₁	—	2	8	no	—
113	#41×C₄₁	—	2	8	no	—
114	#41×C₄₁	—	2	8	no	—
115	C₂×Q₈×C₄₁	—	2	2	no	—
116	C₂×Q₈×C₄₁	—	2	2	no	—
117	C₂×Q₈×C₄₁	C₂²⋊C₄	1	4	yes	—
118	C₂×D₄×C₄₁	—	2	4	no	—
119	C₂×D₄×C₄₁	—	2	4	no	—
120	C₂×D₄×C₄₁	—	2	8	no	—
121	C₂×D₄×C₄₁	—	2	8	no	—
122	C₂×D₄×C₄₁	—	2	2	no	—
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	4	4	no	—
125	C₂×D₄×C₄₁	C₂²⋊C₄	1	8	yes	—
126	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	4	no	—
135	C₂²×C₄×C₄₁	—	2	4	no	—
136	C₂²×C₄×C₄₁	—	2	4	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	2	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	4	4	no	—
144	C₂²×C₄×C₄₁	—	4	4	no	—
145	C₂²×C₄×C₄₁	—	4	4	no	—
146	C₂²×C₄×C₄₁	—	4	4	no	—
147	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₁	#41	1	2	yes	—
158	C₂²×C₄×C₄₁	#41	1	2	yes	—
159	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
160	M₁₆×C₄₁	—	2	16	no	—
161	M₁₆×C₄₁	—	2	8	no	—
162	M₁₆×C₄₁	—	4	4	no	—
163	C₂×C₈×C₄₁	—	2	16	no	—
164	C₂×C₈×C₄₁	—	2	8	no	—
165	C₂×C₈×C₄₁	—	2	1	no	—
166	C₂×C₈×C₄₁	—	2	1	no	—
167	C₂×C₈×C₄₁	—	2	1	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	—	2	1	no	—
170	C₂×C₈×C₄₁	—	2	2	no	—
171	C₂×C₈×C₄₁	—	2	2	no	—
172	C₂×C₈×C₄₁	—	2	2	no	—
173	C₂×C₈×C₄₁	—	2	2	no	—
174	C₂×C₈×C₄₁	—	2	2	no	—
175	C₂×C₈×C₄₁	—	2	2	no	—
176	C₂×C₈×C₄₁	—	2	2	no	—
177	C₂×C₈×C₄₁	—	4	4	no	—
178	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₄₁	—	2	4	no	—
182	C₄⋊C₄×C₄₁	—	2	8	no	—
183	C₂²⋊C₄×C₄₁	—	2	4	no	—
184	C₂²⋊C₄×C₄₁	—	2	8	no	—
185	C₂²⋊C₄×C₄₁	—	2	8	no	—
186	C₄²×C₄₁	—	2	2	no	—
187	C₄²×C₄₁	—	2	2	no	—
188	C₂³×C₄₁	—	2	2	no	—
189	C₂³×C₄₁	—	2	2	no	—
190	C₂³×C₄₁	—	2	8	no	—
191	C₂³×C₄₁	—	2	2	no	—
192	C₂³×C₄₁	—	2	2	no	—
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	—	2	2	no	—
195	C₂³×C₄₁	—	2	2	no	—
196	C₂³×C₄₁	—	2	4	no	—
197	C₂³×C₄₁	—	2	2	no	—
198	C₂³×C₄₁	—	2	2	no	—
199	C₂³×C₄₁	—	2	4	no	—
200	C₂³×C₄₁	—	2	2	no	—
201	C₂³×C₄₁	—	4	8	no	—
202	C₂³×C₄₁	—	4	8	no	—
203	C₂³×C₄₁	—	4	4	no	—
204	C₂³×C₄₁	—	4	4	no	—
205	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂³×C₄₁	C₄×D₄	1	2	yes	—
208	C₂³×C₄₁	C₄×D₄	1	2	yes	—
209	C₂³×C₄₁	#131	1	4	yes	complemented
210	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
211	Q₈×C₄₁	—	2	8	no	—
212	D₄×C₄₁	—	2	16	no	—
213	D₄×C₄₁	—	2	8	no	—
214	D₄×C₄₁	—	4	16	no	—
215	C₂×C₄×C₄₁	—	2	2	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	4	no	—
218	C₂×C₄×C₄₁	—	2	4	no	—
219	C₂×C₄×C₄₁	—	2	4	no	—
220	C₂×C₄×C₄₁	—	2	4	no	—
221	C₂×C₄×C₄₁	—	2	4	no	—
222	C₂×C₄×C₄₁	—	2	2	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	4	no	—
226	C₂×C₄×C₄₁	—	2	4	no	—
227	C₂×C₄×C₄₁	—	4	4	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	4	2	no	—
232	C₂×C₄×C₄₁	—	4	8	no	—
233	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
234	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
235	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
236	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
237	C₂×C₄×C₄₁	#120	1	4	yes	—
238	C₂×C₄×C₄₁	#121	1	4	yes	—
239	C₂×C₄×C₄₁	#121	1	4	yes	—
240	C₂×C₄×C₄₁	#123	1	4	yes	—
241	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
247	C₈×C₄₁	—	2	2	no	—
248	C₈×C₄₁	—	2	4	no	—
249	C₈×C₄₁	—	2	2	no	—
250	C₈×C₄₁	—	4	2	no	—
251	C₈×C₄₁	—	4	2	no	—
252	#20899	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂²×C₄₁	—	2	4	no	—
254	C₂²×C₄₁	—	2	2	no	—
255	C₂²×C₄₁	—	2	2	no	—
256	C₂²×C₄₁	—	2	4	no	—
257	C₂²×C₄₁	—	2	4	no	—
258	C₂²×C₄₁	—	2	8	no	—
259	C₂²×C₄₁	—	2	4	no	—
260	C₂²×C₄₁	—	2	4	no	—
261	C₂²×C₄₁	—	2	4	no	—
262	C₂²×C₄₁	—	4	16	no	—
263	C₂²×C₄₁	—	4	2	no	—
264	C₂²×C₄₁	—	4	2	no	—
265	C₂²×C₄₁	—	4	2	no	—
266	C₂²×C₄₁	—	4	2	no	—
267	C₂²×C₄₁	—	4	4	no	—
268	C₂²×C₄₁	—	4	2	no	—
269	C₂²×C₄₁	—	4	2	no	—
270	C₂²×C₄₁	#386	1	4	yes	—
271	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂²×C₄₁	C₂×#131	1	2	yes	—
275	C₂²×C₄₁	#568	1	2	yes	—
276	C₄×C₄₁	—	2	4	no	—
277	C₄×C₄₁	—	4	4	no	—
278	C₄×C₄₁	—	4	2	no	—
279	C₄×C₄₁	#386	1	4	yes	—
280	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
281	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
282	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
283	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
284	C₂²×#131	C₂×C₄₁	1	1	yes	characteristic, complemented
285	C₂×#525	C₂×C₄₁	1	1	yes	characteristic
286	C₂×#408	C₂×C₄₁	1	1	yes	characteristic, complemented
287	C₂×#407	C₂×C₄₁	1	1	yes	characteristic, complemented
288	C₂²×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
289	#1870	C₂×C₄₁	1	4	yes	complemented
290	#1869	C₂×C₄₁	1	4	yes	complemented
291	#1729	C₂×C₄₁	1	1	yes	characteristic, complemented
292	#1729	C₂×C₄₁	1	1	yes	characteristic, complemented
293	C₂×C₄₁	—	2	4	no	—
294	C₂×C₄₁	—	4	4	no	—
295	C₂×C₄₁	—	4	4	no	—
296	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
297	C₂×C₄₁	#2880	1	2	yes	—
298	C₂×C₄₁	#2929	1	1	yes	characteristic
299	C₂×C₄₁	#2930	1	1	yes	characteristic
300	C₂×C₄₁	#2933	1	2	yes	—
301	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
302	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
303	C₂×#131	—	2	4	no	—
304	C₂×#131	—	2	4	no	—
305	C₂×#131	—	2	4	no	—
306	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
307	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
308	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	complemented
309	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
311	C₂³×C₈	C₂²×C₄₁	1	2	yes	complemented
312	#525	—	2	4	no	—
313	#525	—	2	4	no	—
314	C₂×#123	C₄×C₄₁	1	2	yes	—
315	C₂×C₂²⋊Q₈	C₄×C₄₁	1	2	yes	—
316	C₂×#121	C₄×C₄₁	1	2	yes	—
317	C₂×#120	C₄×C₄₁	1	2	yes	—
318	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
319	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
320	#408	—	2	4	no	—
321	#407	—	2	4	no	—
322	C₂×C₂²⋊C₈	—	2	4	no	—
323	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
324	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
325	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
326	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	complemented
327	#336	C₂²×C₄₁	1	2	yes	complemented
328	#336	C₂²×C₄₁	1	4	yes	complemented
329	#336	C₂²×C₄₁	1	2	yes	complemented
330	C₄₁	#20899	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁵	C₂×C₄×C₄₁	1	1	yes	characteristic
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	D₄×C₄₁	1	4	yes	—
337	C₂×#41	D₄×C₄₁	1	4	yes	—
338	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
339	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
340	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
341	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
342	C₂³×C₄	—	2	2	no	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	—	2	2	no	—
347	C₂³×C₄	—	2	2	no	—
348	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
349	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
351	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
352	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
353	#131	—	2	32	no	—
354	C₂×M₁₆	—	2	2	no	—
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	4	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	4	no	—
361	C₂×M₁₆	—	2	4	no	—
362	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
363	C₂²×C₈	—	2	2	no	—
364	C₂²×C₈	—	2	2	no	—
365	C₂²×C₈	—	2	4	no	—
366	C₂²×C₈	—	2	4	no	—
367	C₂²×C₈	—	2	4	no	—
368	C₂²×C₈	—	2	2	no	—
369	C₂²×C₈	—	2	2	no	—
370	C₂²×C₈	—	2	2	no	—
371	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
372	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
373	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
374	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
377	#123	—	2	8	no	—
378	C₂²⋊Q₈	—	2	8	no	—
379	#121	—	2	8	no	—
380	#120	—	2	8	no	—
381	C₄×D₄	—	2	8	no	—
382	C₄×D₄	—	2	8	no	—
383	#117	—	2	2	no	—
384	#117	—	2	2	no	—
385	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
386	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
390	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
391	C₂²⋊C₈	—	2	8	no	—
392	C₂²⋊C₈	—	2	4	no	—
393	C₂²⋊C₈	—	2	4	no	—
394	C₂²⋊C₈	—	2	8	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
401	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
402	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
403	#41	—	2	8	no	—
404	#41	—	2	8	no	—
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	C₂²⋊C₄×C₄₁	1	4	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	C₂²⋊C₄×C₄₁	1	8	yes	—
418	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
440	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
441	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
442	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
444	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
445	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
449	C₂²×C₄	#41×C₄₁	1	2	yes	—
450	C₂²×C₄	#41×C₄₁	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
452	M₁₆	—	2	16	no	—
453	M₁₆	—	2	8	no	—
454	M₁₆	—	4	4	no	—
455	C₂×C₈	—	2	16	no	—
456	C₂×C₈	—	2	8	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	4	4	no	—
470	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
471	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
472	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	8	no	—
494	C₂³	—	4	8	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
498	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
499	C₂³	C₄×D₄×C₄₁	1	2	yes	—
500	C₂³	C₄×D₄×C₄₁	1	2	yes	—
501	C₂³	#131×C₄₁	1	4	yes	complemented
502	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
503	Q₈	—	2	8	no	—
504	D₄	—	2	16	no	—
505	D₄	—	2	8	no	—
506	D₄	—	4	16	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
526	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
527	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
528	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
529	C₂×C₄	#120×C₄₁	1	4	yes	—
530	C₂×C₄	#121×C₄₁	1	4	yes	—
531	C₂×C₄	#121×C₄₁	1	4	yes	—
532	C₂×C₄	#123×C₄₁	1	4	yes	—
533	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
537	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
539	C₈	—	2	2	no	—
540	C₈	—	2	4	no	—
541	C₈	—	2	2	no	—
542	C₈	—	4	2	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	4	16	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	C₄₁×#386	1	4	yes	—
562	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
563	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
564	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
565	C₂²	C₂×#131×C₄₁	1	2	yes	—
566	C₂²	C₄₁×#568	1	2	yes	—
567	C₄	—	2	4	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	4	no	—
570	C₄	C₄₁×#386	1	4	yes	—
571	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
572	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
573	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
574	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
575	C₂	—	2	4	no	—
576	C₂	—	4	4	no	—
577	C₂	—	4	4	no	—
578	C₂	C₂×C₄₁×#386	1	1	yes	characteristic
579	C₂	C₄₁×#2880	1	2	yes	—
580	C₂	C₄₁×#2929	1	1	yes	characteristic
581	C₂	C₄₁×#2930	1	1	yes	characteristic
582	C₂	C₄₁×#2933	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₂×C₄₁×#525	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#131×C₄₁	C₂	semidirect
3. C₂×C₄₁×#408	C₂	semidirect
4. C₂×C₄₁×#407	C₂	semidirect
5. C₂²×C₂²⋊C₈×C₄₁	C₂	semidirect
6. C₄₁×#1870	C₂	semidirect
7. C₄₁×#1869	C₂	semidirect
8. C₄₁×#1729	C₂	semidirect
9. C₄₁×#1729	C₂	semidirect
17. C₂²×M₁₆×C₄₁	C₂²	semidirect
20. C₂³×C₈×C₄₁	C₂²	semidirect
35. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
36. C₄₁×#336	C₂²	semidirect
37. C₄₁×#336	C₂²	semidirect
38. C₄₁×#336	C₂²	semidirect
70. C₂×M₁₆×C₄₁	D₄	semidirect
79. C₂²×C₈×C₄₁	D₄	semidirect
209. C₂³×C₄₁	#131	semidirect
252. #20899	C₄₁	direct (N × H)
284. C₂²×#131	C₂×C₄₁	semidirect
286. C₂×#408	C₂×C₄₁	semidirect
287. C₂×#407	C₂×C₄₁	semidirect
288. C₂²×C₂²⋊C₈	C₂×C₄₁	semidirect
289. #1870	C₂×C₄₁	semidirect
290. #1869	C₂×C₄₁	semidirect
291. #1729	C₂×C₄₁	semidirect
292. #1729	C₂×C₄₁	semidirect
308. C₂²×M₁₆	C₂²×C₄₁	semidirect
311. C₂³×C₈	C₂²×C₄₁	semidirect
326. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
327. #336	C₂²×C₄₁	semidirect
328. #336	C₂²×C₄₁	semidirect
329. #336	C₂²×C₄₁	semidirect
330. C₄₁	#20899	direct (N × H)
362. C₂×M₁₆	D₄×C₄₁	semidirect
371. C₂²×C₈	D₄×C₄₁	semidirect
501. C₂³	#131×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#131×C₄₁	2
C₂×C₄₁×#525	2
C₂×C₄₁×#408	2
C₂×C₄₁×#407	2
C₂²×C₂²⋊C₈×C₄₁	2
C₄₁×#1870	2
C₄₁×#1869	2
C₄₁×#1729	2
#20899	41

Subgroups — C41×#20899 #23797100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20899 #23797100