Subgroups — C₄₁×#22076 #23798277

Order 10496.

980 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#481	C₂	1	1	yes	maximal, characteristic
2	C₄×#121×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1941	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1934	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1920	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1874	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1864	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1853	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₁	—	2	1	no	—
14	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#481	C₄	1	8	yes	complemented
20	C₂×#106×C₄₁	C₂²	1	2	yes	—
21	C₂×#106×C₄₁	C₂²	1	2	yes	—
22	C₂×#102×C₄₁	C₂²	1	2	yes	—
23	C₂×#102×C₄₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#390	C₂²	1	1	yes	characteristic
28	C₄₁×#389	—	2	1	no	—
29	C₄₁×#389	—	2	1	no	—
30	C₄₁×#389	C₂²	1	2	yes	—
31	C₄₁×#389	C₂²	1	2	yes	—
32	C₄₁×#389	C₂²	1	1	yes	characteristic
33	C₄₁×#388	—	2	1	no	—
34	C₄₁×#386	—	2	1	no	—
35	C₄₁×#380	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
38	C₂×#95×C₄₁	—	2	1	no	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₄₁	—	2	1	no	—
45	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂³×C₄×C₄₁	—	2	1	no	—
48	C₂³×C₄×C₄₁	—	2	1	no	—
49	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	#121×C₄₁	—	2	2	no	—
55	#121×C₄₁	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₄₁	—	4	2	no	—
57	C₄×D₄×C₄₁	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
66	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	complemented
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	—	2	1	no	—
78	C₂×C₄²×C₄₁	—	4	2	no	—
79	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
83	#106×C₄₁	—	4	2	no	—
84	#106×C₄₁	C₂×C₄	1	8	yes	complemented
85	#102×C₄₁	—	4	2	no	—
86	#102×C₄₁	C₂×C₄	1	8	yes	complemented
87	C₂²⋊C₈×C₄₁	—	2	2	no	—
88	C₂²⋊C₈×C₄₁	C₂×C₄	1	4	yes	complemented
89	C₄×C₈×C₄₁	—	4	2	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	—	2	1	no	—
93	#95×C₄₁	—	2	1	no	—
94	#95×C₄₁	—	2	1	no	—
95	C₂⁴×C₄₁	—	2	1	no	—
96	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₄₁	—	2	4	no	—
98	C₂×D₄×C₄₁	—	2	1	no	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	4	2	no	—
102	C₂×D₄×C₄₁	—	4	2	no	—
103	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	4	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	4	1	no	—
115	C₂²×C₄×C₄₁	—	4	1	no	—
116	C₂²×C₄×C₄₁	—	4	1	no	—
117	C₂²×C₄×C₄₁	—	4	2	no	—
118	C₂²×C₄×C₄₁	—	4	2	no	—
119	C₂²×C₄×C₄₁	—	4	2	no	—
120	C₂²×C₄×C₄₁	—	4	2	no	—
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	—	4	2	no	—
123	C₂²×C₄×C₄₁	—	4	2	no	—
124	C₂²×C₄×C₄₁	—	4	2	no	—
125	C₂²×C₄×C₄₁	SD₁₆	1	4	yes	—
126	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	#41	1	2	yes	—
133	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₄₁	—	2	2	no	—
135	C₂×C₈×C₄₁	—	2	2	no	—
136	C₂×C₈×C₄₁	—	2	2	no	—
137	C₂×C₈×C₄₁	—	2	2	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
140	C₄⋊C₄×C₄₁	—	2	4	no	—
141	C₄⋊C₄×C₄₁	—	2	2	no	—
142	C₄⋊C₄×C₄₁	—	2	1	no	—
143	C₄⋊C₄×C₄₁	—	2	2	no	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	2	2	no	—
146	C₄⋊C₄×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	4	2	no	—
148	C₄⋊C₄×C₄₁	—	4	4	no	—
149	C₄⋊C₄×C₄₁	—	4	2	no	—
150	C₄⋊C₄×C₄₁	—	4	4	no	—
151	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
152	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₄₁	—	2	4	no	—
154	C₂²⋊C₄×C₄₁	—	4	2	no	—
155	C₂²⋊C₄×C₄₁	—	4	2	no	—
156	C₂²⋊C₄×C₄₁	—	4	2	no	—
157	C₂²⋊C₄×C₄₁	—	4	2	no	—
158	C₄²×C₄₁	—	2	2	no	—
159	C₄²×C₄₁	—	2	2	no	—
160	C₄²×C₄₁	—	4	1	no	—
161	C₄²×C₄₁	—	4	1	no	—
162	C₄²×C₄₁	—	4	2	no	—
163	C₂³×C₄₁	—	2	1	no	—
164	C₂³×C₄₁	—	2	1	no	—
165	C₂³×C₄₁	—	2	1	no	—
166	C₂³×C₄₁	—	2	1	no	—
167	C₂³×C₄₁	—	2	2	no	—
168	C₂³×C₄₁	—	4	1	no	—
169	C₂³×C₄₁	—	4	1	no	—
170	C₂³×C₄₁	—	4	1	no	—
171	C₂³×C₄₁	—	4	1	no	—
172	C₂³×C₄₁	—	4	1	no	—
173	C₂³×C₄₁	—	4	1	no	—
174	C₂³×C₄₁	C₄×D₄	1	2	yes	—
175	C₂³×C₄₁	C₂×SD₁₆	1	2	yes	—
176	C₂³×C₄₁	#135	1	2	yes	—
177	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
178	D₄×C₄₁	—	2	4	no	—
179	D₄×C₄₁	—	4	8	no	—
180	D₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	2	1	no	—
182	C₂×C₄×C₄₁	—	2	1	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	1	no	—
186	C₂×C₄×C₄₁	—	2	1	no	—
187	C₂×C₄×C₄₁	—	2	1	no	—
188	C₂×C₄×C₄₁	—	2	1	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	4	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	4	no	—
193	C₂×C₄×C₄₁	—	2	1	no	—
194	C₂×C₄×C₄₁	—	2	1	no	—
195	C₂×C₄×C₄₁	—	2	1	no	—
196	C₂×C₄×C₄₁	—	4	4	no	—
197	C₂×C₄×C₄₁	—	4	4	no	—
198	C₂×C₄×C₄₁	—	4	8	no	—
199	C₂×C₄×C₄₁	—	4	1	no	—
200	C₂×C₄×C₄₁	—	4	1	no	—
201	C₂×C₄×C₄₁	—	4	2	no	—
202	C₂×C₄×C₄₁	—	4	2	no	—
203	C₂×C₄×C₄₁	—	4	1	no	—
204	C₂×C₄×C₄₁	—	4	2	no	—
205	C₂×C₄×C₄₁	—	4	1	no	—
206	C₂×C₄×C₄₁	—	4	1	no	—
207	C₂×C₄×C₄₁	—	4	1	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	1	no	—
212	C₂×C₄×C₄₁	—	8	4	no	—
213	C₂×C₄×C₄₁	—	8	4	no	—
214	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
216	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
221	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
222	C₈×C₄₁	—	2	4	no	—
223	C₈×C₄₁	—	4	2	no	—
224	#22076	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₄₁	—	2	2	no	—
226	C₂²×C₄₁	—	2	2	no	—
227	C₂²×C₄₁	—	2	2	no	—
228	C₂²×C₄₁	—	2	2	no	—
229	C₂²×C₄₁	—	2	2	no	—
230	C₂²×C₄₁	—	2	2	no	—
231	C₂²×C₄₁	—	4	2	no	—
232	C₂²×C₄₁	—	4	2	no	—
233	C₂²×C₄₁	—	4	2	no	—
234	C₂²×C₄₁	—	8	1	no	—
235	C₂²×C₄₁	—	8	1	no	—
236	C₂²×C₄₁	—	8	1	no	—
237	C₂²×C₄₁	—	8	1	no	—
238	C₂²×C₄₁	C₄×SD₁₆	1	4	yes	—
239	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂²×C₄₁	#534	1	1	yes	characteristic
241	C₂²×C₄₁	#536	1	1	yes	characteristic
242	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
243	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
244	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₄₁	#575	1	1	yes	characteristic
246	C₄×C₄₁	—	2	2	no	—
247	C₄×C₄₁	—	2	2	no	—
248	C₄×C₄₁	—	2	2	no	—
249	C₄×C₄₁	—	2	2	no	—
250	C₄×C₄₁	—	4	1	no	—
251	C₄×C₄₁	—	4	2	no	—
252	C₄×C₄₁	—	4	4	no	—
253	C₄×C₄₁	—	8	1	no	—
254	C₄×C₄₁	—	8	2	no	—
255	C₄×C₄₁	—	8	1	no	—
256	C₄×C₄₁	#520	1	2	yes	—
257	C₄×C₄₁	#539	1	2	yes	—
258	C₂×#481	C₂×C₄₁	1	1	yes	characteristic
259	C₄×#121	C₂×C₄₁	1	1	yes	characteristic
260	C₂×#389	C₂×C₄₁	1	1	yes	characteristic, complemented
261	#1941	C₂×C₄₁	1	2	yes	complemented
262	#1934	C₂×C₄₁	1	2	yes	complemented
263	#1920	C₂×C₄₁	1	2	yes	complemented
264	#1874	C₂×C₄₁	1	1	yes	characteristic
265	#1864	C₂×C₄₁	1	2	yes	complemented
266	#1853	C₂×C₄₁	1	1	yes	characteristic, complemented
267	#1824	C₂×C₄₁	1	1	yes	characteristic, complemented
268	C₄×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
269	C₂×C₄₁	—	2	4	no	—
270	C₂×C₄₁	—	8	2	no	—
271	C₂×C₄₁	#2322	1	1	yes	characteristic
272	C₂×C₄₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
273	C₂×C₄₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂×C₄₁	#3187	1	1	yes	characteristic
275	C₂×C₄₁	#3188	1	1	yes	characteristic
276	C₂×C₄₁	#3227	1	1	yes	characteristic
277	C₂×C₄₁	#3232	1	1	yes	characteristic
278	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
279	C₂×C₄×D₄	—	2	1	no	—
280	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	—	2	1	no	—
282	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
284	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
285	#481	C₄×C₄₁	1	8	yes	complemented
286	C₂×#106	C₂²×C₄₁	1	2	yes	—
287	C₂×#106	C₂²×C₄₁	1	2	yes	—
288	C₂×#102	C₂²×C₄₁	1	2	yes	—
289	C₂×#102	C₂²×C₄₁	1	2	yes	—
290	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
293	#390	C₂²×C₄₁	1	1	yes	characteristic
294	#389	—	2	1	no	—
295	#389	—	2	1	no	—
296	#389	C₂²×C₄₁	1	2	yes	—
297	#389	C₂²×C₄₁	1	2	yes	—
298	#389	C₂²×C₄₁	1	1	yes	characteristic
299	#388	—	2	1	no	—
300	#386	—	2	1	no	—
301	#380	C₂²×C₄₁	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	—	2	1	no	—
304	C₂×#95	—	2	1	no	—
305	#340	C₂²×C₄₁	1	2	yes	—
306	#340	C₂²×C₄₁	1	2	yes	—
307	#340	C₂²×C₄₁	1	2	yes	—
308	#340	C₂²×C₄₁	1	2	yes	—
309	#336	C₂²×C₄₁	1	2	yes	—
310	C₄₁	#22076	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
317	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
320	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
321	#121	—	2	2	no	—
322	#121	C₂×C₄×C₄₁	1	4	yes	—
323	C₄×D₄	—	4	2	no	—
324	C₄×D₄	—	4	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	4	2	no	—
332	C₂×C₄⋊C₄	—	4	4	no	—
333	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	complemented
334	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	4	2	no	—
346	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
347	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
350	#106	—	4	2	no	—
351	#106	C₂×C₄×C₄₁	1	8	yes	complemented
352	#102	—	4	2	no	—
353	#102	C₂×C₄×C₄₁	1	8	yes	complemented
354	C₂²⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	C₂×C₄×C₄₁	1	4	yes	complemented
356	C₄×C₈	—	4	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	C₂⁴	—	2	1	no	—
363	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	SD₁₆×C₄₁	1	4	yes	—
393	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
399	C₂²×C₄	#41×C₄₁	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
419	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	4	1	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	2	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	C₄×D₄×C₄₁	1	2	yes	—
442	C₂³	C₂×SD₁₆×C₄₁	1	2	yes	—
443	C₂³	#135×C₄₁	1	2	yes	—
444	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
445	D₄	—	2	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	—	8	4	no	—
481	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
482	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
483	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
484	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
485	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
486	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
487	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
488	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
489	C₈	—	2	4	no	—
490	C₈	—	4	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	C₄×SD₁₆×C₄₁	1	4	yes	—
505	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
506	C₂²	C₄₁×#534	1	1	yes	characteristic
507	C₂²	C₄₁×#536	1	1	yes	characteristic
508	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
509	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
510	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
511	C₂²	C₄₁×#575	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	2	no	—
521	C₄	—	8	1	no	—
522	C₄	C₄₁×#520	1	2	yes	—
523	C₄	C₄₁×#539	1	2	yes	—
524	C₂	—	2	4	no	—
525	C₂	—	8	2	no	—
526	C₂	C₄₁×#2322	1	1	yes	characteristic
527	C₂	C₂×C₄×SD₁₆×C₄₁	1	1	yes	characteristic
528	C₂	C₄×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
529	C₂	C₄₁×#3187	1	1	yes	characteristic
530	C₂	C₄₁×#3188	1	1	yes	characteristic
531	C₂	C₄₁×#3227	1	1	yes	characteristic
532	C₂	C₄₁×#3232	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₁×#389	C₂	semidirect
4. C₄₁×#1941	C₂	semidirect
5. C₄₁×#1934	C₂	semidirect
6. C₄₁×#1920	C₂	semidirect
8. C₄₁×#1864	C₂	semidirect
9. C₄₁×#1853	C₂	semidirect
10. C₄₁×#1824	C₂	semidirect
11. C₄×C₂²⋊C₈×C₄₁	C₂	semidirect
19. C₄₁×#481	C₄	semidirect
66. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
84. #106×C₄₁	C₂×C₄	semidirect
86. #102×C₄₁	C₂×C₄	semidirect
88. C₂²⋊C₈×C₄₁	C₂×C₄	semidirect
224. #22076	C₄₁	direct (N × H)
260. C₂×#389	C₂×C₄₁	semidirect
261. #1941	C₂×C₄₁	semidirect
262. #1934	C₂×C₄₁	semidirect
263. #1920	C₂×C₄₁	semidirect
265. #1864	C₂×C₄₁	semidirect
266. #1853	C₂×C₄₁	semidirect
267. #1824	C₂×C₄₁	semidirect
268. C₄×C₂²⋊C₈	C₂×C₄₁	semidirect
285. #481	C₄×C₄₁	semidirect
310. C₄₁	#22076	direct (N × H)
333. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
351. #106	C₂×C₄×C₄₁	semidirect
353. #102	C₂×C₄×C₄₁	semidirect
355. 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×#481	2
C₄×#121×C₄₁	2
C₂×C₄₁×#389	2
C₄₁×#1941	2
C₄₁×#1934	2
C₄₁×#1920	2
C₄₁×#1874	2
C₄₁×#1864	2
C₄₁×#1853	2
C₄₁×#1824	2
C₄×C₂²⋊C₈×C₄₁	2
#22076	41

Subgroups — C41×#22076 #23798277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22076 #23798277