Subgroups — C₄₁×#8977 #23785178

Order 10496.

764 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1957	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₄₁	—	2	1	no	—
9	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₄₁	—	2	1	no	—
11	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
13	C₄₁×#459	—	2	2	no	—
14	C₄₁×#459	C₄	1	4	yes	complemented
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#102×C₄₁	—	2	1	no	—
18	C₂×#102×C₄₁	—	2	2	no	—
19	C₂×#102×C₄₁	—	2	1	no	—
20	C₂×#102×C₄₁	—	2	1	no	—
21	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#389	—	2	1	no	—
23	C₄₁×#385	—	2	2	no	—
24	C₄₁×#384	C₂²	1	1	yes	characteristic
25	C₄₁×#380	—	2	1	no	—
26	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×D₄⋊C₈	—	2	2	no	—
28	C₂²×D₄×C₄₁	—	2	1	no	—
29	C₂²×D₄×C₄₁	—	2	1	no	—
30	C₂²×D₄×C₄₁	—	2	1	no	—
31	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₁	—	2	1	no	—
33	C₂³×C₄×C₄₁	—	2	2	no	—
34	C₂×D₈×C₄₁	—	2	4	no	—
35	C₂×D₈×C₄₁	—	4	2	no	—
36	C₂×D₈×C₄₁	—	4	2	no	—
37	C₂²×C₈×C₄₁	—	2	1	no	—
38	C₂²×C₈×C₄₁	—	2	1	no	—
39	C₂²×C₈×C₄₁	—	2	1	no	—
40	#127×C₄₁	—	2	1	no	—
41	#127×C₄₁	—	2	1	no	—
42	#127×C₄₁	—	2	1	no	—
43	#127×C₄₁	C₂×C₄	1	2	yes	complemented
44	C₄×D₄×C₄₁	—	2	1	no	—
45	C₄×D₄×C₄₁	—	2	1	no	—
46	C₄×D₄×C₄₁	—	4	2	no	—
47	C₄×D₄×C₄₁	—	4	2	no	—
48	C₄×D₄×C₄₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₄₁	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
55	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	—	2	1	no	—
62	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₁	—	2	1	no	—
64	C₄⋊C₈×C₄₁	—	2	1	no	—
65	C₄⋊C₈×C₄₁	—	2	1	no	—
66	C₄⋊C₈×C₄₁	C₂×C₄	1	2	yes	complemented
67	#102×C₄₁	—	2	4	no	—
68	#102×C₄₁	—	4	2	no	—
69	#102×C₄₁	—	4	4	no	—
70	#102×C₄₁	—	4	2	no	—
71	C₄×C₈×C₄₁	—	2	1	no	—
72	C₄×C₈×C₄₁	—	2	1	no	—
73	#95×C₄₁	—	2	2	no	—
74	#95×C₄₁	—	2	1	no	—
75	C₂⁴×C₄₁	—	2	1	no	—
76	C₂⁴×C₄₁	—	4	1	no	—
77	C₂×D₄×C₄₁	—	2	2	no	—
78	C₂×D₄×C₄₁	—	2	2	no	—
79	C₂×D₄×C₄₁	—	2	2	no	—
80	C₂×D₄×C₄₁	—	2	1	no	—
81	C₂×D₄×C₄₁	—	2	1	no	—
82	C₂×D₄×C₄₁	—	2	1	no	—
83	C₂×D₄×C₄₁	—	4	2	no	—
84	C₂×D₄×C₄₁	—	4	2	no	—
85	C₂×D₄×C₄₁	—	4	1	no	—
86	C₂×D₄×C₄₁	—	4	1	no	—
87	C₂×D₄×C₄₁	—	4	1	no	—
88	C₂×D₄×C₄₁	—	4	1	no	—
89	C₂×D₄×C₄₁	—	4	1	no	—
90	C₂×D₄×C₄₁	—	4	1	no	—
91	C₂×D₄×C₄₁	—	4	1	no	—
92	C₂×D₄×C₄₁	—	4	1	no	—
93	C₂×D₄×C₄₁	—	4	1	no	—
94	C₂×D₄×C₄₁	—	4	1	no	—
95	C₂×D₄×C₄₁	—	4	1	no	—
96	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
97	C₂×D₄×C₄₁	D₈	1	2	yes	—
98	C₂×D₄×C₄₁	SD₁₆	1	2	yes	—
99	C₂²×C₄×C₄₁	—	2	1	no	—
100	C₂²×C₄×C₄₁	—	2	1	no	—
101	C₂²×C₄×C₄₁	—	2	2	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	4	4	no	—
106	C₂²×C₄×C₄₁	—	4	1	no	—
107	C₂²×C₄×C₄₁	—	4	1	no	—
108	C₂²×C₄×C₄₁	—	4	1	no	—
109	C₂²×C₄×C₄₁	—	4	1	no	—
110	C₂²×C₄×C₄₁	—	4	4	no	—
111	C₂²×C₄×C₄₁	—	8	2	no	—
112	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	D₈×C₄₁	—	4	8	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	4	1	no	—
119	C₂×C₈×C₄₁	—	4	1	no	—
120	C₂×C₈×C₄₁	—	4	1	no	—
121	C₂×C₈×C₄₁	—	4	1	no	—
122	C₂×C₈×C₄₁	—	4	1	no	—
123	C₂×C₈×C₄₁	—	4	1	no	—
124	C₂×C₈×C₄₁	—	4	1	no	—
125	C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₄⋊C₄×C₄₁	—	4	2	no	—
130	C₄⋊C₄×C₄₁	—	4	4	no	—
131	C₄⋊C₄×C₄₁	—	4	1	no	—
132	C₄⋊C₄×C₄₁	—	4	1	no	—
133	C₄⋊C₄×C₄₁	—	4	1	no	—
134	C₄⋊C₄×C₄₁	—	4	1	no	—
135	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₄₁	D₈	1	2	yes	complemented
137	C₂²⋊C₄×C₄₁	—	2	2	no	—
138	C₂²⋊C₄×C₄₁	—	2	2	no	—
139	C₂²⋊C₄×C₄₁	—	4	4	no	—
140	C₄²×C₄₁	—	4	1	no	—
141	C₄²×C₄₁	—	4	1	no	—
142	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₁	#41	1	1	yes	characteristic
145	C₄²×C₄₁	#41	1	1	yes	characteristic
146	C₂³×C₄₁	—	2	2	no	—
147	C₂³×C₄₁	—	2	2	no	—
148	C₂³×C₄₁	—	2	2	no	—
149	C₂³×C₄₁	—	4	1	no	—
150	C₂³×C₄₁	—	4	1	no	—
151	C₂³×C₄₁	—	4	1	no	—
152	C₂³×C₄₁	—	4	1	no	—
153	C₂³×C₄₁	—	4	2	no	—
154	C₂³×C₄₁	—	8	1	no	—
155	C₂³×C₄₁	—	8	1	no	—
156	C₂³×C₄₁	—	8	1	no	—
157	C₂³×C₄₁	—	8	1	no	—
158	C₂³×C₄₁	—	8	1	no	—
159	C₂³×C₄₁	—	8	1	no	—
160	C₂³×C₄₁	#120	1	1	yes	characteristic
161	D₄×C₄₁	—	2	2	no	—
162	D₄×C₄₁	—	2	2	no	—
163	D₄×C₄₁	—	2	2	no	—
164	D₄×C₄₁	—	4	4	no	—
165	D₄×C₄₁	—	4	2	no	—
166	D₄×C₄₁	—	4	2	no	—
167	D₄×C₄₁	—	4	2	no	—
168	D₄×C₄₁	—	4	2	no	—
169	D₄×C₄₁	—	8	2	no	—
170	D₄×C₄₁	—	8	1	no	—
171	D₄×C₄₁	—	8	1	no	—
172	D₄×C₄₁	—	8	1	no	—
173	D₄×C₄₁	—	8	1	no	—
174	D₄×C₄₁	#102	1	4	yes	complemented
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	1	no	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	—	4	1	no	—
182	C₂×C₄×C₄₁	—	4	1	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	1	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	1	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	8	8	no	—
194	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
198	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
199	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
203	C₂×C₄×C₄₁	#135	1	1	yes	characteristic
204	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂×C₄×C₄₁	#137	1	1	yes	characteristic
208	C₈×C₄₁	—	4	2	no	—
209	C₈×C₄₁	—	4	2	no	—
210	C₈×C₄₁	—	8	1	no	—
211	#8977	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₄₁	—	2	4	no	—
213	C₂²×C₄₁	—	4	2	no	—
214	C₂²×C₄₁	—	4	2	no	—
215	C₂²×C₄₁	—	4	2	no	—
216	C₂²×C₄₁	—	4	2	no	—
217	C₂²×C₄₁	—	4	2	no	—
218	C₂²×C₄₁	—	4	2	no	—
219	C₂²×C₄₁	—	8	2	no	—
220	C₂²×C₄₁	—	8	2	no	—
221	C₂²×C₄₁	—	8	2	no	—
222	C₂²×C₄₁	—	16	1	no	—
223	C₂²×C₄₁	—	16	1	no	—
224	C₂²×C₄₁	—	16	1	no	—
225	C₂²×C₄₁	—	16	1	no	—
226	C₂²×C₄₁	#386	1	1	yes	characteristic
227	C₂²×C₄₁	#447	1	1	yes	characteristic
228	C₂²×C₄₁	#447	1	1	yes	characteristic
229	C₂²×C₄₁	#448	1	1	yes	characteristic
230	C₂²×C₄₁	#449	1	1	yes	characteristic
231	C₂²×C₄₁	#453	1	1	yes	characteristic
232	C₂²×C₄₁	#454	1	1	yes	characteristic
233	C₄×C₄₁	—	2	1	no	—
234	C₄×C₄₁	—	2	1	no	—
235	C₄×C₄₁	—	4	2	no	—
236	C₄×C₄₁	—	4	2	no	—
237	C₄×C₄₁	—	8	2	no	—
238	C₄×C₄₁	—	8	1	no	—
239	C₄×C₄₁	C₂×#102	1	1	yes	characteristic
240	C₄×C₄₁	#417	1	1	yes	characteristic
241	C₄×C₄₁	C₄×D₈	1	1	yes	characteristic
242	C₄×C₄₁	#442	1	1	yes	characteristic
243	C₄×C₄₁	#459	1	1	yes	characteristic
244	C₄×C₄₁	#463	1	1	yes	characteristic
245	C₄×C₄₁	#480	1	1	yes	characteristic
246	C₄×C₄₁	#481	1	1	yes	characteristic
247	C₂×#459	C₂×C₄₁	1	1	yes	characteristic
248	D₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
249	#1982	C₂×C₄₁	1	1	yes	characteristic, complemented
250	#1957	C₂×C₄₁	1	1	yes	characteristic, complemented
251	C₂×D₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#1296	C₂×C₄₁	1	1	yes	characteristic, complemented
253	#1279	C₂×C₄₁	1	1	yes	characteristic, complemented
254	C₂×C₄₁	—	4	4	no	—
255	C₂×C₄₁	—	16	2	no	—
256	C₂×C₄₁	#1619	1	1	yes	characteristic
257	C₂×C₄₁	#1622	1	1	yes	characteristic
258	C₂×C₄₁	#1625	1	1	yes	characteristic
259	C₂×C₄₁	#1627	1	1	yes	characteristic
260	C₂×C₄₁	#1874	1	1	yes	characteristic
261	C₂×C₄₁	#1879	1	1	yes	characteristic
262	C₂×C₄₁	#1883	1	1	yes	characteristic
263	C₂²×D₈	—	2	1	no	—
264	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	—	2	1	no	—
268	#459	—	2	2	no	—
269	#459	C₄×C₄₁	1	4	yes	complemented
270	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
272	C₂×#102	—	2	1	no	—
273	C₂×#102	—	2	2	no	—
274	C₂×#102	—	2	1	no	—
275	C₂×#102	—	2	1	no	—
276	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
277	#389	—	2	1	no	—
278	#385	—	2	2	no	—
279	#384	C₂²×C₄₁	1	1	yes	characteristic
280	#380	—	2	1	no	—
281	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
282	D₄⋊C₈	—	2	2	no	—
283	C₄₁	#8977	1	1	yes	characteristic, direct product factor, Sylow
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂×D₈	—	2	4	no	—
291	C₂×D₈	—	4	2	no	—
292	C₂×D₈	—	4	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	—	2	1	no	—
296	#127	—	2	1	no	—
297	#127	—	2	1	no	—
298	#127	—	2	1	no	—
299	#127	C₂×C₄×C₄₁	1	2	yes	complemented
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	4	2	no	—
303	C₄×D₄	—	4	2	no	—
304	C₄×D₄	C₂×C₄×C₄₁	1	2	yes	—
305	C₄×D₄	D₄×C₄₁	1	2	yes	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	4	2	no	—
310	C₂×C₄⋊C₄	—	4	2	no	—
311	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
313	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
314	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	C₂×C₄×C₄₁	1	2	yes	complemented
323	#102	—	2	4	no	—
324	#102	—	4	2	no	—
325	#102	—	4	4	no	—
326	#102	—	4	2	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	—	2	1	no	—
331	C₂⁴	—	2	1	no	—
332	C₂⁴	—	4	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
353	C₂×D₄	D₈×C₄₁	1	2	yes	—
354	C₂×D₄	SD₁₆×C₄₁	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
371	D₈	—	4	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	4	1	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	1	no	—
380	C₂×C₈	—	4	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
392	C₄⋊C₄	D₈×C₄₁	1	2	yes	complemented
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	4	1	no	—
398	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
399	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
400	C₄²	#41×C₄₁	1	1	yes	characteristic
401	C₄²	#41×C₄₁	1	1	yes	characteristic
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	8	1	no	—
411	C₂³	—	8	1	no	—
412	C₂³	—	8	1	no	—
413	C₂³	—	8	1	no	—
414	C₂³	—	8	1	no	—
415	C₂³	—	8	1	no	—
416	C₂³	#120×C₄₁	1	1	yes	characteristic
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	1	no	—
429	D₄	—	8	1	no	—
430	D₄	#102×C₄₁	1	4	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	8	8	no	—
450	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
451	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
452	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
453	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
454	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
455	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
456	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
457	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
458	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
459	C₂×C₄	#135×C₄₁	1	1	yes	characteristic
460	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
461	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
462	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
463	C₂×C₄	#137×C₄₁	1	1	yes	characteristic
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	8	1	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	16	1	no	—
478	C₂²	—	16	1	no	—
479	C₂²	—	16	1	no	—
480	C₂²	—	16	1	no	—
481	C₂²	C₄₁×#386	1	1	yes	characteristic
482	C₂²	C₄₁×#447	1	1	yes	characteristic
483	C₂²	C₄₁×#447	1	1	yes	characteristic
484	C₂²	C₄₁×#448	1	1	yes	characteristic
485	C₂²	C₄₁×#449	1	1	yes	characteristic
486	C₂²	C₄₁×#453	1	1	yes	characteristic
487	C₂²	C₄₁×#454	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	2	no	—
493	C₄	—	8	1	no	—
494	C₄	C₂×#102×C₄₁	1	1	yes	characteristic
495	C₄	C₄₁×#417	1	1	yes	characteristic
496	C₄	C₄×D₈×C₄₁	1	1	yes	characteristic
497	C₄	C₄₁×#442	1	1	yes	characteristic
498	C₄	C₄₁×#459	1	1	yes	characteristic
499	C₄	C₄₁×#463	1	1	yes	characteristic
500	C₄	C₄₁×#480	1	1	yes	characteristic
501	C₄	C₄₁×#481	1	1	yes	characteristic
502	C₂	—	4	4	no	—
503	C₂	—	16	2	no	—
504	C₂	C₄₁×#1619	1	1	yes	characteristic
505	C₂	C₄₁×#1622	1	1	yes	characteristic
506	C₂	C₄₁×#1625	1	1	yes	characteristic
507	C₂	C₄₁×#1627	1	1	yes	characteristic
508	C₂	C₄₁×#1874	1	1	yes	characteristic
509	C₂	C₄₁×#1879	1	1	yes	characteristic
510	C₂	C₄₁×#1883	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	#120
commutator	C₄²	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
prime radical	C₂×C₄₁×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×C₄⋊C₄×C₄₁	C₂	semidirect
3. C₄₁×#1982	C₂	semidirect
4. C₄₁×#1957	C₂	semidirect
5. C₂×C₄₁×D₄⋊C₈	C₂	semidirect
6. C₄₁×#1296	C₂	semidirect
7. C₄₁×#1279	C₂	semidirect
14. C₄₁×#459	C₄	semidirect
43. #127×C₄₁	C₂×C₄	semidirect
66. C₄⋊C₈×C₄₁	C₂×C₄	semidirect
136. C₄⋊C₄×C₄₁	D₈	semidirect
174. D₄×C₄₁	#102	semidirect
211. #8977	C₄₁	direct (N × H)
248. D₄×C₄⋊C₄	C₂×C₄₁	semidirect
249. #1982	C₂×C₄₁	semidirect
250. #1957	C₂×C₄₁	semidirect
251. C₂×D₄⋊C₈	C₂×C₄₁	semidirect
252. #1296	C₂×C₄₁	semidirect
253. #1279	C₂×C₄₁	semidirect
269. #459	C₄×C₄₁	semidirect
283. C₄₁	#8977	direct (N × H)
299. #127	C₂×C₄×C₄₁	semidirect
322. C₄⋊C₈	C₂×C₄×C₄₁	semidirect
392. C₄⋊C₄	D₈×C₄₁	semidirect
430. D₄	#102×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×#459	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#1982	2
C₄₁×#1957	2
C₂×C₄₁×D₄⋊C₈	2
C₄₁×#1296	2
C₄₁×#1279	2
#8977	41

Subgroups — C41×#8977 #23785178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#8977 #23785178