Subgroups — C₄₁×#11052 #23787253

Order 10496.

1022 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#103×C₄₁	C₂	1	2	yes	maximal
2	C₂×C₄₁×#391	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#382	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#340	C₂	1	2	yes	maximal
5	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#103×C₄₁	—	2	4	no	—
12	C₂×#103×C₄₁	—	2	4	no	—
13	C₂×#103×C₄₁	—	2	4	no	—
14	C₄₁×#391	—	2	2	no	—
15	C₄₁×#391	C₄	1	4	yes	complemented
16	C₄₁×#382	—	2	4	no	—
17	C₂×#95×C₄₁	—	2	2	no	—
18	C₂×#95×C₄₁	—	2	2	no	—
19	C₄₁×#340	—	2	4	no	—
20	C₄₁×#336	—	2	2	no	—
21	C₂²×Q₈×C₄₁	—	2	1	no	—
22	C₂²×Q₈×C₄₁	—	2	1	no	—
23	C₂²×Q₈×C₄₁	—	2	1	no	—
24	C₂²×Q₈×C₄₁	—	2	2	no	—
25	C₂²×Q₈×C₄₁	—	2	2	no	—
26	C₂²×Q₈×C₄₁	—	2	2	no	—
27	C₂²×Q₈×C₄₁	—	2	2	no	—
28	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
29	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
30	C₂²×Q₈×C₄₁	Q₈	1	2	yes	—
31	C₂³×C₄×C₄₁	—	2	1	no	—
32	C₂³×C₄×C₄₁	—	2	1	no	—
33	C₂³×C₄×C₄₁	—	2	2	no	—
34	C₂³×C₄×C₄₁	D₄	1	2	yes	—
35	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₄₁	—	2	2	no	—
37	C₂²×C₈×C₄₁	—	2	2	no	—
38	C₂²×C₈×C₄₁	—	2	2	no	—
39	C₂²×C₈×C₄₁	—	2	2	no	—
40	C₂²×C₈×C₄₁	—	2	2	no	—
41	C₂²×C₈×C₄₁	—	2	2	no	—
42	C₂²×C₈×C₄₁	D₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
53	C₂×C₄²×C₄₁	—	2	2	no	—
54	C₂×C₄²×C₄₁	—	2	2	no	—
55	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₁	D₄	1	2	yes	—
57	#103×C₄₁	—	2	16	no	—
58	#95×C₄₁	—	2	8	no	—
59	#95×C₄₁	—	2	8	no	—
60	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
61	C₂×Q₈×C₄₁	—	2	2	no	—
62	C₂×Q₈×C₄₁	—	2	2	no	—
63	C₂×Q₈×C₄₁	—	2	2	no	—
64	C₂×Q₈×C₄₁	—	2	4	no	—
65	C₂×Q₈×C₄₁	—	2	4	no	—
66	C₂×Q₈×C₄₁	—	2	4	no	—
67	C₂×Q₈×C₄₁	—	2	4	no	—
68	C₂×Q₈×C₄₁	—	2	4	no	—
69	C₂×Q₈×C₄₁	—	2	4	no	—
70	C₂×Q₈×C₄₁	—	4	2	no	—
71	C₂×Q₈×C₄₁	—	4	2	no	—
72	C₂×Q₈×C₄₁	—	4	2	no	—
73	C₂×Q₈×C₄₁	—	4	2	no	—
74	C₂×Q₈×C₄₁	—	4	2	no	—
75	C₂×Q₈×C₄₁	—	4	2	no	—
76	C₂×Q₈×C₄₁	C₄⋊C₄	1	4	yes	—
77	C₂²×C₄×C₄₁	—	2	2	no	—
78	C₂²×C₄×C₄₁	—	2	2	no	—
79	C₂²×C₄×C₄₁	—	2	2	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	4	no	—
83	C₂²×C₄×C₄₁	—	2	4	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	2	4	no	—
86	C₂²×C₄×C₄₁	—	4	1	no	—
87	C₂²×C₄×C₄₁	—	4	1	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	—	4	1	no	—
92	C₂²×C₄×C₄₁	—	4	1	no	—
93	C₂²×C₄×C₄₁	—	4	2	no	—
94	C₂²×C₄×C₄₁	—	4	4	no	—
95	C₂²×C₄×C₄₁	—	4	4	no	—
96	C₂²×C₄×C₄₁	—	4	4	no	—
97	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	#41	1	2	yes	—
107	C₂²×C₄×C₄₁	#41	1	2	yes	—
108	C₂×C₈×C₄₁	—	2	4	no	—
109	C₂×C₈×C₄₁	—	2	4	no	—
110	C₂×C₈×C₄₁	—	2	4	no	—
111	C₂×C₈×C₄₁	—	4	2	no	—
112	C₂×C₈×C₄₁	—	4	2	no	—
113	C₂×C₈×C₄₁	—	4	2	no	—
114	C₂×C₈×C₄₁	—	4	2	no	—
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₄⋊C₄×C₄₁	—	2	4	no	—
118	C₄⋊C₄×C₄₁	—	4	2	no	—
119	C₄⋊C₄×C₄₁	—	4	2	no	—
120	C₄⋊C₄×C₄₁	—	4	2	no	—
121	C₄²×C₄₁	—	2	4	no	—
122	C₄²×C₄₁	—	2	4	no	—
123	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂³×C₄₁	#120	1	1	yes	characteristic
125	C₂³×C₄₁	#121	1	1	yes	characteristic
126	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₄₁	#123	1	1	yes	characteristic
128	C₂³×C₄₁	#124	1	1	yes	characteristic
129	C₂³×C₄₁	#127	1	1	yes	characteristic
130	C₂³×C₄₁	#135	1	4	yes	—
131	C₂³×C₄₁	#137	1	4	yes	—
132	Q₈×C₄₁	—	2	8	no	—
133	Q₈×C₄₁	—	4	4	no	—
134	Q₈×C₄₁	—	4	4	no	—
135	Q₈×C₄₁	—	4	4	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	4	no	—
139	C₂×C₄×C₄₁	—	2	4	no	—
140	C₂×C₄×C₄₁	—	4	2	no	—
141	C₂×C₄×C₄₁	—	4	2	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	4	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	4	4	no	—
150	C₂×C₄×C₄₁	—	4	4	no	—
151	C₂×C₄×C₄₁	—	4	8	no	—
152	C₂×C₄×C₄₁	—	8	4	no	—
153	C₂×C₄×C₄₁	—	8	2	no	—
154	C₂×C₄×C₄₁	—	8	2	no	—
155	C₂×C₄×C₄₁	—	8	2	no	—
156	C₂×C₄×C₄₁	—	8	2	no	—
157	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
159	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₁	#120	1	2	yes	—
162	C₂×C₄×C₄₁	#121	1	2	yes	—
163	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₁	#121	1	2	yes	—
165	C₂×C₄×C₄₁	#121	1	2	yes	—
166	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₁	#123	1	2	yes	—
170	C₂×C₄×C₄₁	#123	1	2	yes	—
171	C₂×C₄×C₄₁	#124	1	2	yes	—
172	C₂×C₄×C₄₁	#126	1	2	yes	—
173	C₈×C₄₁	—	4	4	no	—
174	#11052	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₁	#380	1	1	yes	characteristic
176	C₂²×C₄₁	#386	1	1	yes	characteristic
177	C₂²×C₄₁	#390	1	1	yes	characteristic
178	C₂²×C₄₁	#392	1	1	yes	characteristic
179	C₂²×C₄₁	#393	1	1	yes	characteristic
180	C₂²×C₄₁	#397	1	1	yes	characteristic
181	C₂²×C₄₁	#399	1	1	yes	characteristic
182	C₂²×C₄₁	#416	1	2	yes	—
183	C₂²×C₄₁	#419	1	2	yes	—
184	C₂²×C₄₁	#452	1	4	yes	—
185	C₂²×C₄₁	#464	1	4	yes	—
186	C₂²×C₄₁	#479	1	4	yes	—
187	C₂²×C₄₁	#485	1	4	yes	—
188	C₂²×C₄₁	#488	1	2	yes	—
189	C₂²×C₄₁	#491	1	2	yes	—
190	C₂²×C₄₁	#495	1	2	yes	—
191	C₂²×C₄₁	#497	1	2	yes	—
192	C₄×C₄₁	—	4	4	no	—
193	C₄×C₄₁	—	4	4	no	—
194	C₄×C₄₁	—	8	2	no	—
195	C₄×C₄₁	—	8	4	no	—
196	C₄×C₄₁	#385	1	2	yes	—
197	C₄×C₄₁	#388	1	2	yes	—
198	C₄×C₄₁	#394	1	2	yes	—
199	C₄×C₄₁	#396	1	2	yes	—
200	C₂²×#103	C₂×C₄₁	1	2	yes	—
201	C₂×#391	C₂×C₄₁	1	1	yes	characteristic
202	C₂×#382	C₂×C₄₁	1	1	yes	characteristic
203	C₂×#340	C₂×C₄₁	1	2	yes	—
204	C₂×#336	C₂×C₄₁	1	1	yes	characteristic
205	C₂×C₄₁	#1439	1	1	yes	characteristic
206	C₂×C₄₁	#1805	1	2	yes	—
207	C₂×C₄₁	#1873	1	2	yes	—
208	C₂×C₄₁	#1958	1	1	yes	characteristic
209	C₂×C₄₁	#1960	1	1	yes	characteristic
210	C₂×C₄₁	#2015	1	2	yes	—
211	C₂×C₄₁	#2026	1	2	yes	—
212	C₂×C₄₁	#2074	1	2	yes	—
213	C₂×C₄₁	#2097	1	2	yes	—
214	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
215	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
218	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×#103	—	2	4	no	—
220	C₂×#103	—	2	4	no	—
221	C₂×#103	—	2	4	no	—
222	#391	—	2	2	no	—
223	#391	C₄×C₄₁	1	4	yes	complemented
224	#382	—	2	4	no	—
225	C₂×#95	—	2	2	no	—
226	C₂×#95	—	2	2	no	—
227	#340	—	2	4	no	—
228	#336	—	2	2	no	—
229	C₄₁	#11052	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	—	2	2	no	—
237	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
238	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
239	C₂²×Q₈	Q₈×C₄₁	1	2	yes	—
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	D₄×C₄₁	1	2	yes	—
244	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	D₄×C₄₁	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
261	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
265	C₂×C₄²	D₄×C₄₁	1	2	yes	—
266	#103	—	2	16	no	—
267	#95	—	2	8	no	—
268	#95	—	2	8	no	—
269	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	C₄⋊C₄×C₄₁	1	4	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
307	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
313	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	#41×C₄₁	1	2	yes	—
316	C₂²×C₄	#41×C₄₁	1	2	yes	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	4	no	—
332	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
333	C₂³	#120×C₄₁	1	1	yes	characteristic
334	C₂³	#121×C₄₁	1	1	yes	characteristic
335	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
336	C₂³	#123×C₄₁	1	1	yes	characteristic
337	C₂³	#124×C₄₁	1	1	yes	characteristic
338	C₂³	#127×C₄₁	1	1	yes	characteristic
339	C₂³	#135×C₄₁	1	4	yes	—
340	C₂³	#137×C₄₁	1	4	yes	—
341	Q₈	—	2	8	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	4	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	8	4	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
367	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
368	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
369	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
370	C₂×C₄	#120×C₄₁	1	2	yes	—
371	C₂×C₄	#121×C₄₁	1	2	yes	—
372	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
373	C₂×C₄	#121×C₄₁	1	2	yes	—
374	C₂×C₄	#121×C₄₁	1	2	yes	—
375	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
376	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
377	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
378	C₂×C₄	#123×C₄₁	1	2	yes	—
379	C₂×C₄	#123×C₄₁	1	2	yes	—
380	C₂×C₄	#124×C₄₁	1	2	yes	—
381	C₂×C₄	#126×C₄₁	1	2	yes	—
382	C₈	—	4	4	no	—
383	C₂²	C₄₁×#380	1	1	yes	characteristic
384	C₂²	C₄₁×#386	1	1	yes	characteristic
385	C₂²	C₄₁×#390	1	1	yes	characteristic
386	C₂²	C₄₁×#392	1	1	yes	characteristic
387	C₂²	C₄₁×#393	1	1	yes	characteristic
388	C₂²	C₄₁×#397	1	1	yes	characteristic
389	C₂²	C₄₁×#399	1	1	yes	characteristic
390	C₂²	C₄₁×#416	1	2	yes	—
391	C₂²	C₄₁×#419	1	2	yes	—
392	C₂²	C₄₁×#452	1	4	yes	—
393	C₂²	C₄₁×#464	1	4	yes	—
394	C₂²	C₄₁×#479	1	4	yes	—
395	C₂²	C₄₁×#485	1	4	yes	—
396	C₂²	C₄₁×#488	1	2	yes	—
397	C₂²	C₄₁×#491	1	2	yes	—
398	C₂²	C₄₁×#495	1	2	yes	—
399	C₂²	C₄₁×#497	1	2	yes	—
400	C₄	—	4	4	no	—
401	C₄	—	4	4	no	—
402	C₄	—	8	4	no	—
403	C₄	—	8	2	no	—
404	C₄	C₄₁×#385	1	2	yes	—
405	C₄	C₄₁×#388	1	2	yes	—
406	C₄	C₄₁×#394	1	2	yes	—
407	C₄	C₄₁×#396	1	2	yes	—
408	C₂	C₄₁×#1439	1	1	yes	characteristic
409	C₂	C₄₁×#1805	1	2	yes	—
410	C₂	C₄₁×#1873	1	2	yes	—
411	C₂	C₄₁×#1958	1	1	yes	characteristic
412	C₂	C₄₁×#1960	1	1	yes	characteristic
413	C₂	C₄₁×#2015	1	2	yes	—
414	C₂	C₄₁×#2026	1	2	yes	—
415	C₂	C₄₁×#2074	1	2	yes	—
416	C₂	C₄₁×#2097	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
15. C₄₁×#391	C₄	semidirect
174. #11052	C₄₁	direct (N × H)
223. #391	C₄×C₄₁	semidirect
229. C₄₁	#11052	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#103×C₄₁	2
C₂×C₄₁×#391	2
C₂×C₄₁×#382	2
C₂×C₄₁×#340	2
C₂×C₄₁×#336	2
#11052	41

Subgroups — C41×#11052 #23787253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11052 #23787253