Subgroups — C₄₁×#9076 #23785277

Order 10496.

690 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#121×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1279	C₂	1	2	yes	maximal, complemented
6	C₂×#121×C₄₁	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄×C₄₁	—	2	1	no	—
8	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₄₁×#431	—	2	4	no	—
11	C₂×C₄⋊C₈×C₄₁	—	2	1	no	—
12	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
13	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
14	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
15	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#390	C₄	1	1	yes	characteristic
17	C₄₁×#389	C₄	1	1	yes	characteristic
18	C₄₁×#388	—	2	1	no	—
19	C₄₁×#386	—	2	1	no	—
20	C₄₁×#380	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
23	C₄₁×#336	—	2	1	no	—
24	C₄₁×D₄⋊C₈	—	2	4	no	—
25	C₂²×D₄×C₄₁	—	2	1	no	—
26	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₁	—	2	1	no	—
28	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₄₁	—	2	2	no	—
32	C₂²×C₈×C₄₁	—	2	2	no	—
33	#121×C₄₁	—	2	2	no	—
34	#121×C₄₁	—	2	2	no	—
35	C₄×D₄×C₄₁	—	2	2	no	—
36	C₄×D₄×C₄₁	—	2	2	no	—
37	C₄×D₄×C₄₁	—	4	2	no	—
38	C₄×D₄×C₄₁	—	4	2	no	—
39	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
48	C₂×C₄²×C₄₁	—	2	2	no	—
49	C₂×C₄²×C₄₁	—	2	2	no	—
50	C₂×C₄²×C₄₁	—	2	1	no	—
51	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₄₁	—	2	4	no	—
56	C₄⋊C₈×C₄₁	—	2	2	no	—
57	C₄⋊C₈×C₄₁	—	2	2	no	—
58	C₂²⋊C₈×C₄₁	—	2	4	no	—
59	C₂²⋊C₈×C₄₁	—	4	2	no	—
60	C₄×C₈×C₄₁	—	2	2	no	—
61	C₄×C₈×C₄₁	D₄	1	4	yes	complemented
62	#95×C₄₁	—	2	1	no	—
63	#95×C₄₁	—	2	1	no	—
64	#95×C₄₁	—	2	1	no	—
65	C₂⁴×C₄₁	—	2	1	no	—
66	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×D₄×C₄₁	—	2	4	no	—
68	C₂×D₄×C₄₁	—	2	2	no	—
69	C₂×D₄×C₄₁	—	2	1	no	—
70	C₂×D₄×C₄₁	—	2	2	no	—
71	C₂×D₄×C₄₁	—	4	2	no	—
72	C₂×D₄×C₄₁	—	4	2	no	—
73	C₂×D₄×C₄₁	M₁₆	1	2	yes	—
74	C₂²×C₄×C₄₁	—	2	2	no	—
75	C₂²×C₄×C₄₁	—	2	2	no	—
76	C₂²×C₄×C₄₁	—	2	1	no	—
77	C₂²×C₄×C₄₁	—	2	2	no	—
78	C₂²×C₄×C₄₁	—	2	1	no	—
79	C₂²×C₄×C₄₁	—	2	1	no	—
80	C₂²×C₄×C₄₁	—	2	1	no	—
81	C₂²×C₄×C₄₁	—	2	1	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	1	no	—
84	C₂²×C₄×C₄₁	—	2	1	no	—
85	C₂²×C₄×C₄₁	—	4	1	no	—
86	C₂²×C₄×C₄₁	—	4	1	no	—
87	C₂²×C₄×C₄₁	—	4	2	no	—
88	C₂²×C₄×C₄₁	—	4	1	no	—
89	C₂²×C₄×C₄₁	—	4	1	no	—
90	C₂²×C₄×C₄₁	—	4	2	no	—
91	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	D₈	1	2	yes	—
95	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
96	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₄₁	—	2	4	no	—
100	C₂×C₈×C₄₁	—	4	2	no	—
101	C₂×C₈×C₄₁	—	4	2	no	—
102	C₂×C₈×C₄₁	—	4	2	no	—
103	C₂×C₈×C₄₁	—	4	2	no	—
104	C₂×C₈×C₄₁	—	4	2	no	—
105	C₄⋊C₄×C₄₁	—	2	1	no	—
106	C₄⋊C₄×C₄₁	—	2	2	no	—
107	C₄⋊C₄×C₄₁	—	2	2	no	—
108	C₄⋊C₄×C₄₁	—	4	2	no	—
109	C₄⋊C₄×C₄₁	M₁₆	1	2	yes	—
110	C₂²⋊C₄×C₄₁	—	2	4	no	—
111	C₂²⋊C₄×C₄₁	—	4	2	no	—
112	C₂²⋊C₄×C₄₁	—	4	2	no	—
113	C₂²⋊C₄×C₄₁	—	4	2	no	—
114	C₂²⋊C₄×C₄₁	—	4	1	no	—
115	C₂²⋊C₄×C₄₁	—	4	1	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	1	no	—
118	C₄²×C₄₁	—	2	2	no	—
119	C₄²×C₄₁	—	2	1	no	—
120	C₄²×C₄₁	—	4	1	no	—
121	C₄²×C₄₁	—	4	1	no	—
122	C₄²×C₄₁	C₂×D₄	1	2	yes	—
123	C₄²×C₄₁	#41	1	2	yes	—
124	C₂³×C₄₁	—	2	1	no	—
125	C₂³×C₄₁	—	2	1	no	—
126	C₂³×C₄₁	—	2	1	no	—
127	C₂³×C₄₁	—	2	1	no	—
128	C₂³×C₄₁	—	2	1	no	—
129	C₂³×C₄₁	—	2	1	no	—
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	4	1	no	—
132	C₂³×C₄₁	—	4	1	no	—
133	C₂³×C₄₁	—	4	1	no	—
134	C₂³×C₄₁	—	4	1	no	—
135	C₂³×C₄₁	—	4	1	no	—
136	C₂³×C₄₁	—	4	1	no	—
137	C₂³×C₄₁	#102	1	2	yes	—
138	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	D₄×C₄₁	—	2	4	no	—
140	D₄×C₄₁	—	4	8	no	—
141	D₄×C₄₁	—	4	2	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	1	no	—
144	C₂×C₄×C₄₁	—	2	1	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	4	no	—
147	C₂×C₄×C₄₁	—	2	4	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	1	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	1	no	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	2	1	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	1	no	—
158	C₂×C₄×C₄₁	—	4	1	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	1	no	—
162	C₂×C₄×C₄₁	—	4	1	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	—	4	1	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	1	no	—
167	C₂×C₄×C₄₁	—	8	2	no	—
168	C₂×C₄×C₄₁	—	8	2	no	—
169	C₂×C₄×C₄₁	#102	1	2	yes	—
170	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
172	C₂×C₄×C₄₁	#121	1	2	yes	—
173	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
174	C₂×C₄×C₄₁	C₂×M₁₆	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂×M₁₆	1	1	yes	characteristic
176	C₂×C₄×C₄₁	#131	1	2	yes	—
177	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
179	C₂×C₄×C₄₁	#135	1	2	yes	—
180	C₈×C₄₁	—	4	4	no	—
181	C₈×C₄₁	—	8	2	no	—
182	#9076	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₁	—	2	2	no	—
184	C₂²×C₄₁	—	2	2	no	—
185	C₂²×C₄₁	—	2	2	no	—
186	C₂²×C₄₁	—	4	1	no	—
187	C₂²×C₄₁	—	4	1	no	—
188	C₂²×C₄₁	—	4	1	no	—
189	C₂²×C₄₁	—	4	1	no	—
190	C₂²×C₄₁	—	4	2	no	—
191	C₂²×C₄₁	—	4	2	no	—
192	C₂²×C₄₁	—	4	2	no	—
193	C₂²×C₄₁	—	8	1	no	—
194	C₂²×C₄₁	—	8	1	no	—
195	C₂²×C₄₁	—	8	1	no	—
196	C₂²×C₄₁	—	8	1	no	—
197	C₂²×C₄₁	#386	1	1	yes	characteristic
198	C₂²×C₄₁	#407	1	1	yes	characteristic
199	C₂²×C₄₁	#408	1	1	yes	characteristic
200	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
201	C₂²×C₄₁	#416	1	1	yes	characteristic
202	C₂²×C₄₁	#421	1	1	yes	characteristic
203	C₂²×C₄₁	#421	1	1	yes	characteristic
204	C₄×C₄₁	—	2	2	no	—
205	C₄×C₄₁	—	2	1	no	—
206	C₄×C₄₁	—	2	1	no	—
207	C₄×C₄₁	—	4	1	no	—
208	C₄×C₄₁	—	4	1	no	—
209	C₄×C₄₁	—	4	2	no	—
210	C₄×C₄₁	—	8	1	no	—
211	C₄×C₄₁	—	8	1	no	—
212	C₄×C₄₁	#435	1	2	yes	—
213	C₄×C₄₁	#436	1	2	yes	—
214	C₄×C₄₁	#465	1	2	yes	—
215	C₄×C₄₁	#466	1	2	yes	—
216	C₂×#431	C₂×C₄₁	1	1	yes	characteristic, complemented
217	C₄×#121	C₂×C₄₁	1	1	yes	characteristic
218	#1797	C₂×C₄₁	1	1	yes	characteristic, complemented
219	C₂×D₄⋊C₈	C₂×C₄₁	1	2	yes	complemented
220	#1279	C₂×C₄₁	1	2	yes	complemented
221	C₂×C₄₁	—	4	2	no	—
222	C₂×C₄₁	—	8	2	no	—
223	C₂×C₄₁	#1480	1	1	yes	characteristic
224	C₂×C₄₁	#1482	1	1	yes	characteristic
225	C₂×C₄₁	#1486	1	1	yes	characteristic
226	C₂×C₄₁	#1488	1	1	yes	characteristic
227	C₂×C₄₁	#1870	1	1	yes	characteristic
228	C₂×C₄₁	#1893	1	1	yes	characteristic
229	C₂×C₄₁	#1897	1	1	yes	characteristic
230	C₂×#121	C₄×C₄₁	1	1	yes	characteristic
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
233	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
234	#431	—	2	4	no	—
235	C₂×C₄⋊C₈	—	2	1	no	—
236	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
237	C₂×C₂²⋊C₈	—	2	1	no	—
238	C₂×C₂²⋊C₈	—	2	1	no	—
239	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
240	#390	C₄×C₄₁	1	1	yes	characteristic
241	#389	C₄×C₄₁	1	1	yes	characteristic
242	#388	—	2	1	no	—
243	#386	—	2	1	no	—
244	#380	C₄×C₄₁	1	1	yes	characteristic
245	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	—	2	1	no	—
247	#336	—	2	1	no	—
248	D₄⋊C₈	—	2	4	no	—
249	C₄₁	#9076	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
254	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
255	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	#121	—	2	2	no	—
259	#121	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	4	2	no	—
263	C₄×D₄	—	4	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
280	C₄⋊C₈	—	2	4	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	4	no	—
284	C₂²⋊C₈	—	4	2	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	D₄×C₄₁	1	4	yes	complemented
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	C₂⁴	—	2	1	no	—
291	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	M₁₆×C₄₁	1	2	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
318	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	D₈×C₄₁	1	2	yes	—
320	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
321	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	M₁₆×C₄₁	1	2	yes	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	4	1	no	—
346	C₄²	—	4	1	no	—
347	C₄²	C₂×D₄×C₄₁	1	2	yes	—
348	C₄²	#41×C₄₁	1	2	yes	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	#102×C₄₁	1	2	yes	—
363	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
364	D₄	—	2	4	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	#102×C₄₁	1	2	yes	—
395	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
396	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
397	C₂×C₄	#121×C₄₁	1	2	yes	—
398	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
399	C₂×C₄	C₂×M₁₆×C₄₁	1	1	yes	characteristic
400	C₂×C₄	C₂×M₁₆×C₄₁	1	1	yes	characteristic
401	C₂×C₄	#131×C₄₁	1	2	yes	—
402	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
403	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
404	C₂×C₄	#135×C₄₁	1	2	yes	—
405	C₈	—	4	4	no	—
406	C₈	—	8	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	C₄₁×#386	1	1	yes	characteristic
422	C₂²	C₄₁×#407	1	1	yes	characteristic
423	C₂²	C₄₁×#408	1	1	yes	characteristic
424	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
425	C₂²	C₄₁×#416	1	1	yes	characteristic
426	C₂²	C₄₁×#421	1	1	yes	characteristic
427	C₂²	C₄₁×#421	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	1	no	—
436	C₄	C₄₁×#435	1	2	yes	—
437	C₄	C₄₁×#436	1	2	yes	—
438	C₄	C₄₁×#465	1	2	yes	—
439	C₄	C₄₁×#466	1	2	yes	—
440	C₂	—	4	2	no	—
441	C₂	—	8	2	no	—
442	C₂	C₄₁×#1480	1	1	yes	characteristic
443	C₂	C₄₁×#1482	1	1	yes	characteristic
444	C₂	C₄₁×#1486	1	1	yes	characteristic
445	C₂	C₄₁×#1488	1	1	yes	characteristic
446	C₂	C₄₁×#1870	1	1	yes	characteristic
447	C₂	C₄₁×#1893	1	1	yes	characteristic
448	C₂	C₄₁×#1897	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#431	C₂	semidirect
3. C₄₁×#1797	C₂	semidirect
4. C₂×C₄₁×D₄⋊C₈	C₂	semidirect
5. C₄₁×#1279	C₂	semidirect
61. C₄×C₈×C₄₁	D₄	semidirect
182. #9076	C₄₁	direct (N × H)
216. C₂×#431	C₂×C₄₁	semidirect
218. #1797	C₂×C₄₁	semidirect
219. C₂×D₄⋊C₈	C₂×C₄₁	semidirect
220. #1279	C₂×C₄₁	semidirect
249. C₄₁	#9076	direct (N × H)
286. C₄×C₈	D₄×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×#431	2
C₄×#121×C₄₁	2
C₄₁×#1797	2
C₂×C₄₁×D₄⋊C₈	2
C₄₁×#1279	2
#9076	41

Subgroups — C41×#9076 #23785277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#9076 #23785277