Subgroups — C₄₁×#11267 #23787468

Order 10496.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#384	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#340	C₂	1	2	yes	maximal
3	C₂×C₄₁×#340	C₂	1	2	yes	maximal
4	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic
5	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
9	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#384	—	2	4	no	—
14	C₂×#95×C₄₁	—	2	1	no	—
15	C₂×#95×C₄₁	—	2	1	no	—
16	C₄₁×#340	—	2	4	no	—
17	C₄₁×#340	—	2	4	no	—
18	C₄₁×#336	C₄	1	4	yes	complemented
19	C₂³×C₄×C₄₁	—	2	2	no	—
20	C₂³×C₄×C₄₁	—	2	1	no	—
21	C₂³×C₄×C₄₁	—	2	1	no	—
22	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₄₁	—	2	2	no	—
26	C₂²×C₈×C₄₁	—	2	2	no	—
27	C₂²×C₈×C₄₁	—	2	2	no	—
28	C₂²×C₈×C₄₁	—	2	2	no	—
29	C₂²×C₈×C₄₁	—	2	2	no	—
30	C₂²×C₈×C₄₁	—	2	2	no	—
31	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
32	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
44	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
46	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
47	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
48	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
49	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₄₁	Q₈	1	2	yes	—
52	C₂×C₄²×C₄₁	—	2	2	no	—
53	C₂×C₄²×C₄₁	—	2	2	no	—
54	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₁	Q₈	1	2	yes	—
56	#95×C₄₁	—	4	2	no	—
57	#95×C₄₁	—	4	2	no	—
58	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₁	—	2	1	no	—
60	C₂²×C₄×C₄₁	—	2	1	no	—
61	C₂²×C₄×C₄₁	—	2	1	no	—
62	C₂²×C₄×C₄₁	—	2	1	no	—
63	C₂²×C₄×C₄₁	—	2	1	no	—
64	C₂²×C₄×C₄₁	—	2	1	no	—
65	C₂²×C₄×C₄₁	—	2	1	no	—
66	C₂²×C₄×C₄₁	—	2	1	no	—
67	C₂²×C₄×C₄₁	—	2	4	no	—
68	C₂²×C₄×C₄₁	—	2	2	no	—
69	C₂²×C₄×C₄₁	—	2	2	no	—
70	C₂²×C₄×C₄₁	—	4	1	no	—
71	C₂²×C₄×C₄₁	—	4	2	no	—
72	C₂²×C₄×C₄₁	—	4	1	no	—
73	C₂²×C₄×C₄₁	—	4	1	no	—
74	C₂²×C₄×C₄₁	—	4	2	no	—
75	C₂²×C₄×C₄₁	—	4	1	no	—
76	C₂²×C₄×C₄₁	—	4	1	no	—
77	C₂²×C₄×C₄₁	—	4	1	no	—
78	C₂²×C₄×C₄₁	—	4	2	no	—
79	C₂²×C₄×C₄₁	—	4	1	no	—
80	C₂²×C₄×C₄₁	—	4	1	no	—
81	C₂²×C₄×C₄₁	—	4	2	no	—
82	C₂²×C₄×C₄₁	—	4	2	no	—
83	C₂²×C₄×C₄₁	—	4	2	no	—
84	C₂²×C₄×C₄₁	—	4	1	no	—
85	C₂²×C₄×C₄₁	—	4	1	no	—
86	C₂²×C₄×C₄₁	—	4	1	no	—
87	C₂²×C₄×C₄₁	—	4	1	no	—
88	C₂²×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₁	D₈	1	2	yes	—
91	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₄₁	Q₁₆	1	2	yes	—
94	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	#41	1	2	yes	—
100	C₂²×C₄×C₄₁	#41	1	2	yes	—
101	C₂²×C₄×C₄₁	#41	1	2	yes	—
102	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
104	C₂×C₈×C₄₁	—	2	4	no	—
105	C₂×C₈×C₄₁	—	2	4	no	—
106	C₂×C₈×C₄₁	—	2	4	no	—
107	C₂×C₈×C₄₁	—	4	2	no	—
108	C₂×C₈×C₄₁	—	4	2	no	—
109	C₂×C₈×C₄₁	—	4	2	no	—
110	C₂×C₈×C₄₁	—	4	2	no	—
111	C₄⋊C₄×C₄₁	—	2	4	no	—
112	C₄⋊C₄×C₄₁	—	2	4	no	—
113	C₄⋊C₄×C₄₁	—	2	4	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	4	8	no	—
116	C₄⋊C₄×C₄₁	—	4	8	no	—
117	C₄⋊C₄×C₄₁	—	4	2	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×C₄⋊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	#124	1	1	yes	characteristic
130	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
131	C₂³×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
132	C₂³×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₄₁	C₂×Q₁₆	1	1	yes	characteristic
134	C₂³×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂³×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂³×C₄₁	#137	1	1	yes	characteristic
137	C₂³×C₄₁	#137	1	1	yes	characteristic
138	C₂×C₄×C₄₁	—	2	2	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	2	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	4	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	4	no	—
154	C₂×C₄×C₄₁	—	4	4	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	8	1	no	—
160	C₂×C₄×C₄₁	—	8	1	no	—
161	C₂×C₄×C₄₁	—	8	2	no	—
162	C₂×C₄×C₄₁	—	8	2	no	—
163	C₂×C₄×C₄₁	—	8	1	no	—
164	C₂×C₄×C₄₁	—	8	1	no	—
165	C₂×C₄×C₄₁	—	8	1	no	—
166	C₂×C₄×C₄₁	—	8	1	no	—
167	C₂×C₄×C₄₁	—	8	2	no	—
168	C₂×C₄×C₄₁	—	8	1	no	—
169	C₂×C₄×C₄₁	—	8	1	no	—
170	C₂×C₄×C₄₁	—	8	2	no	—
171	C₂×C₄×C₄₁	#106	1	4	yes	—
172	C₂×C₄×C₄₁	#107	1	4	yes	—
173	C₂×C₄×C₄₁	#117	1	2	yes	—
174	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₄×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₄₁	#121	1	2	yes	—
178	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₄₁	#123	1	2	yes	—
181	C₂×C₄×C₄₁	#123	1	2	yes	—
182	C₂×C₄×C₄₁	#124	1	2	yes	—
183	C₂×C₄×C₄₁	#125	1	2	yes	—
184	C₂×C₄×C₄₁	#125	1	2	yes	—
185	C₂×C₄×C₄₁	#125	1	1	yes	characteristic
186	C₂×C₄×C₄₁	#126	1	2	yes	—
187	C₂×C₄×C₄₁	#126	1	2	yes	—
188	C₂×C₄×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
189	C₈×C₄₁	—	4	4	no	—
190	#11267	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₁	#382	1	1	yes	characteristic
192	C₂²×C₄₁	#385	1	1	yes	characteristic
193	C₂²×C₄₁	#389	1	1	yes	characteristic
194	C₂²×C₄₁	#393	1	1	yes	characteristic
195	C₂²×C₄₁	#394	1	1	yes	characteristic
196	C₂²×C₄₁	#397	1	1	yes	characteristic
197	C₂²×C₄₁	#400	1	1	yes	characteristic
198	C₂²×C₄₁	C₂×#106	1	1	yes	characteristic
199	C₂²×C₄₁	C₂×#107	1	1	yes	characteristic
200	C₂²×C₄₁	#428	1	1	yes	characteristic
201	C₂²×C₄₁	#428	1	1	yes	characteristic
202	C₂²×C₄₁	#447	1	1	yes	characteristic
203	C₂²×C₄₁	#448	1	1	yes	characteristic
204	C₂²×C₄₁	#450	1	1	yes	characteristic
205	C₂²×C₄₁	#451	1	1	yes	characteristic
206	C₂²×C₄₁	#459	1	1	yes	characteristic
207	C₂²×C₄₁	#460	1	1	yes	characteristic
208	C₂²×C₄₁	#461	1	1	yes	characteristic
209	C₂²×C₄₁	#462	1	1	yes	characteristic
210	C₂²×C₄₁	#474	1	1	yes	characteristic
211	C₂²×C₄₁	#475	1	1	yes	characteristic
212	C₂²×C₄₁	#476	1	1	yes	characteristic
213	C₂²×C₄₁	#477	1	1	yes	characteristic
214	C₂²×C₄₁	#480	1	1	yes	characteristic
215	C₂²×C₄₁	#481	1	1	yes	characteristic
216	C₂²×C₄₁	#483	1	1	yes	characteristic
217	C₂²×C₄₁	#484	1	1	yes	characteristic
218	C₂²×C₄₁	#486	1	1	yes	characteristic
219	C₂²×C₄₁	#486	1	1	yes	characteristic
220	C₂²×C₄₁	#487	1	1	yes	characteristic
221	C₂²×C₄₁	#487	1	1	yes	characteristic
222	C₂²×C₄₁	#489	1	1	yes	characteristic
223	C₂²×C₄₁	#489	1	1	yes	characteristic
224	C₂²×C₄₁	#490	1	1	yes	characteristic
225	C₂²×C₄₁	#491	1	1	yes	characteristic
226	C₄×C₄₁	—	2	4	no	—
227	C₄×C₄₁	—	2	4	no	—
228	C₄×C₄₁	—	8	2	no	—
229	C₄×C₄₁	—	8	2	no	—
230	C₄×C₄₁	—	8	4	no	—
231	C₄×C₄₁	#387	1	2	yes	—
232	C₄×C₄₁	#388	1	2	yes	—
233	C₄×C₄₁	#398	1	2	yes	—
234	C₄×C₄₁	#400	1	2	yes	—
235	C₂×#384	C₂×C₄₁	1	1	yes	characteristic
236	C₂×#340	C₂×C₄₁	1	2	yes	—
237	C₂×#340	C₂×C₄₁	1	2	yes	—
238	C₂×#336	C₂×C₄₁	1	1	yes	characteristic
239	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
240	C₂×C₄₁	#1442	1	1	yes	characteristic
241	C₂×C₄₁	#1834	1	1	yes	characteristic
242	C₂×C₄₁	#1836	1	1	yes	characteristic
243	C₂×C₄₁	#1852	1	1	yes	characteristic
244	C₂×C₄₁	#1853	1	1	yes	characteristic
245	C₂×C₄₁	#1947	1	1	yes	characteristic
246	C₂×C₄₁	#1948	1	1	yes	characteristic
247	C₂×C₄₁	#2023	1	1	yes	characteristic
248	C₂×C₄₁	#2024	1	1	yes	characteristic
249	C₂×C₄₁	#2041	1	1	yes	characteristic
250	C₂×C₄₁	#2043	1	1	yes	characteristic
251	C₂×C₄₁	#2071	1	1	yes	characteristic
252	C₂×C₄₁	#2072	1	1	yes	characteristic
253	C₂×C₄₁	#2099	1	1	yes	characteristic
254	C₂×C₄₁	#2100	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
256	C₂²×C₄⋊C₄	—	2	1	no	—
257	C₂²×C₄⋊C₄	—	2	1	no	—
258	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
261	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
262	#384	—	2	4	no	—
263	C₂×#95	—	2	1	no	—
264	C₂×#95	—	2	1	no	—
265	#340	—	2	4	no	—
266	#340	—	2	4	no	—
267	#336	C₄×C₄₁	1	4	yes	complemented
268	C₄₁	#11267	1	1	yes	characteristic, direct product factor, Sylow
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
273	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	4	2	no	—
296	C₂×C₄⋊C₄	—	4	2	no	—
297	C₂×C₄⋊C₄	—	4	2	no	—
298	C₂×C₄⋊C₄	—	4	2	no	—
299	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
300	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
301	C₂×C₄⋊C₄	Q₈×C₄₁	1	2	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
305	C₂×C₄²	Q₈×C₄₁	1	2	yes	—
306	#95	—	4	2	no	—
307	#95	—	4	2	no	—
308	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
339	C₂²×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
340	C₂²×C₄	D₈×C₄₁	1	2	yes	—
341	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
342	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
343	C₂²×C₄	Q₁₆×C₄₁	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
347	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
349	C₂²×C₄	#41×C₄₁	1	2	yes	—
350	C₂²×C₄	#41×C₄₁	1	2	yes	—
351	C₂²×C₄	#41×C₄₁	1	2	yes	—
352	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
353	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	4	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	4	8	no	—
366	C₄⋊C₄	—	4	8	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₂³	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
374	C₂³	#120×C₄₁	1	1	yes	characteristic
375	C₂³	#121×C₄₁	1	1	yes	characteristic
376	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
377	C₂³	#123×C₄₁	1	1	yes	characteristic
378	C₂³	#124×C₄₁	1	1	yes	characteristic
379	C₂³	#124×C₄₁	1	1	yes	characteristic
380	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
381	C₂³	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
382	C₂³	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
383	C₂³	C₂×Q₁₆×C₄₁	1	1	yes	characteristic
384	C₂³	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
385	C₂³	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
386	C₂³	#137×C₄₁	1	1	yes	characteristic
387	C₂³	#137×C₄₁	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	8	1	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	—	8	1	no	—
418	C₂×C₄	—	8	1	no	—
419	C₂×C₄	—	8	1	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	#106×C₄₁	1	4	yes	—
422	C₂×C₄	#107×C₄₁	1	4	yes	—
423	C₂×C₄	#117×C₄₁	1	2	yes	—
424	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
425	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
426	C₂×C₄	C₄×Q₈×C₄₁	1	1	yes	characteristic
427	C₂×C₄	#121×C₄₁	1	2	yes	—
428	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
429	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
430	C₂×C₄	#123×C₄₁	1	2	yes	—
431	C₂×C₄	#123×C₄₁	1	2	yes	—
432	C₂×C₄	#124×C₄₁	1	2	yes	—
433	C₂×C₄	#125×C₄₁	1	2	yes	—
434	C₂×C₄	#125×C₄₁	1	2	yes	—
435	C₂×C₄	#125×C₄₁	1	1	yes	characteristic
436	C₂×C₄	#126×C₄₁	1	2	yes	—
437	C₂×C₄	#126×C₄₁	1	2	yes	—
438	C₂×C₄	C₄⋊Q₈×C₄₁	1	1	yes	characteristic
439	C₈	—	4	4	no	—
440	C₂²	C₄₁×#382	1	1	yes	characteristic
441	C₂²	C₄₁×#385	1	1	yes	characteristic
442	C₂²	C₄₁×#389	1	1	yes	characteristic
443	C₂²	C₄₁×#393	1	1	yes	characteristic
444	C₂²	C₄₁×#394	1	1	yes	characteristic
445	C₂²	C₄₁×#397	1	1	yes	characteristic
446	C₂²	C₄₁×#400	1	1	yes	characteristic
447	C₂²	C₂×#106×C₄₁	1	1	yes	characteristic
448	C₂²	C₂×#107×C₄₁	1	1	yes	characteristic
449	C₂²	C₄₁×#428	1	1	yes	characteristic
450	C₂²	C₄₁×#428	1	1	yes	characteristic
451	C₂²	C₄₁×#447	1	1	yes	characteristic
452	C₂²	C₄₁×#448	1	1	yes	characteristic
453	C₂²	C₄₁×#450	1	1	yes	characteristic
454	C₂²	C₄₁×#451	1	1	yes	characteristic
455	C₂²	C₄₁×#459	1	1	yes	characteristic
456	C₂²	C₄₁×#460	1	1	yes	characteristic
457	C₂²	C₄₁×#461	1	1	yes	characteristic
458	C₂²	C₄₁×#462	1	1	yes	characteristic
459	C₂²	C₄₁×#474	1	1	yes	characteristic
460	C₂²	C₄₁×#475	1	1	yes	characteristic
461	C₂²	C₄₁×#476	1	1	yes	characteristic
462	C₂²	C₄₁×#477	1	1	yes	characteristic
463	C₂²	C₄₁×#480	1	1	yes	characteristic
464	C₂²	C₄₁×#481	1	1	yes	characteristic
465	C₂²	C₄₁×#483	1	1	yes	characteristic
466	C₂²	C₄₁×#484	1	1	yes	characteristic
467	C₂²	C₄₁×#486	1	1	yes	characteristic
468	C₂²	C₄₁×#486	1	1	yes	characteristic
469	C₂²	C₄₁×#487	1	1	yes	characteristic
470	C₂²	C₄₁×#487	1	1	yes	characteristic
471	C₂²	C₄₁×#489	1	1	yes	characteristic
472	C₂²	C₄₁×#489	1	1	yes	characteristic
473	C₂²	C₄₁×#490	1	1	yes	characteristic
474	C₂²	C₄₁×#491	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	4	no	—
479	C₄	—	8	2	no	—
480	C₄	C₄₁×#387	1	2	yes	—
481	C₄	C₄₁×#388	1	2	yes	—
482	C₄	C₄₁×#398	1	2	yes	—
483	C₄	C₄₁×#400	1	2	yes	—
484	C₂	C₄₁×#1442	1	1	yes	characteristic
485	C₂	C₄₁×#1834	1	1	yes	characteristic
486	C₂	C₄₁×#1836	1	1	yes	characteristic
487	C₂	C₄₁×#1852	1	1	yes	characteristic
488	C₂	C₄₁×#1853	1	1	yes	characteristic
489	C₂	C₄₁×#1947	1	1	yes	characteristic
490	C₂	C₄₁×#1948	1	1	yes	characteristic
491	C₂	C₄₁×#2023	1	1	yes	characteristic
492	C₂	C₄₁×#2024	1	1	yes	characteristic
493	C₂	C₄₁×#2041	1	1	yes	characteristic
494	C₂	C₄₁×#2043	1	1	yes	characteristic
495	C₂	C₄₁×#2071	1	1	yes	characteristic
496	C₂	C₄₁×#2072	1	1	yes	characteristic
497	C₂	C₄₁×#2099	1	1	yes	characteristic
498	C₂	C₄₁×#2100	1	1	yes	characteristic

	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
18. C₄₁×#336	C₄	semidirect
190. #11267	C₄₁	direct (N × H)
267. #336	C₄×C₄₁	semidirect
268. C₄₁	#11267	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#384	2
C₂×C₄₁×#340	2
C₂×C₄₁×#336	2
C₄₁×C₄⋊#95	2
#11267	41

Subgroups — C41×#11267 #23787468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11267 #23787468