Subgroups — C₄₁×#10863 #23787064

Order 10496.

942 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#107×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#106×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#97×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#340	C₂	1	2	yes	maximal
5	C₄₁×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#107×C₄₁	—	2	2	no	—
12	C₂×#107×C₄₁	—	2	2	no	—
13	C₂×#107×C₄₁	C₄	1	4	yes	complemented
14	C₂×#106×C₄₁	—	2	2	no	—
15	C₂×#106×C₄₁	—	2	2	no	—
16	C₂×#106×C₄₁	C₄	1	4	yes	complemented
17	C₂×#97×C₄₁	—	2	2	no	—
18	C₂×#97×C₄₁	—	2	2	no	—
19	C₂×#97×C₄₁	C₄	1	4	yes	complemented
20	C₂×#95×C₄₁	—	2	4	no	—
21	C₄₁×#340	—	2	4	no	—
22	C₂³×C₄×C₄₁	—	2	2	no	—
23	C₂³×C₄×C₄₁	—	2	2	no	—
24	C₂³×C₄×C₄₁	D₄	1	2	yes	—
25	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₄₁	—	2	1	no	—
27	C₂²×C₈×C₄₁	—	2	1	no	—
28	C₂²×C₈×C₄₁	—	2	1	no	—
29	C₂²×C₈×C₄₁	—	2	1	no	—
30	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₄₁	D₄	1	2	yes	—
35	C₂²×C₈×C₄₁	D₄	1	2	yes	—
36	C₂²×C₈×C₄₁	D₄	1	2	yes	—
37	C₂²×C₈×C₄₁	D₄	1	2	yes	—
38	C₂²×C₈×C₄₁	Q₈	1	2	yes	—
39	C₂²×C₈×C₄₁	Q₈	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
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	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₄₁	—	2	1	no	—
53	C₂×C₄²×C₄₁	—	2	1	no	—
54	C₂×C₄²×C₄₁	—	2	1	no	—
55	C₂×C₄²×C₄₁	—	2	1	no	—
56	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₁	Q₈	1	2	yes	—
58	#107×C₄₁	—	2	8	no	—
59	#106×C₄₁	—	2	8	no	—
60	#97×C₄₁	—	2	8	no	—
61	#95×C₄₁	—	4	8	no	—
62	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₁	—	2	2	no	—
64	C₂²×C₄×C₄₁	—	2	2	no	—
65	C₂²×C₄×C₄₁	—	2	4	no	—
66	C₂²×C₄×C₄₁	—	2	4	no	—
67	C₂²×C₄×C₄₁	—	2	4	no	—
68	C₂²×C₄×C₄₁	—	2	4	no	—
69	C₂²×C₄×C₄₁	—	4	2	no	—
70	C₂²×C₄×C₄₁	—	4	2	no	—
71	C₂²×C₄×C₄₁	—	4	2	no	—
72	C₂²×C₄×C₄₁	—	4	2	no	—
73	C₂²×C₄×C₄₁	—	4	4	no	—
74	C₂²×C₄×C₄₁	—	4	4	no	—
75	C₂²×C₄×C₄₁	—	4	4	no	—
76	C₂²×C₄×C₄₁	—	4	4	no	—
77	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
78	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
91	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
92	C₂×C₈×C₄₁	—	2	2	no	—
93	C₂×C₈×C₄₁	—	2	2	no	—
94	C₂×C₈×C₄₁	—	2	2	no	—
95	C₂×C₈×C₄₁	—	2	2	no	—
96	C₂×C₈×C₄₁	—	2	2	no	—
97	C₂×C₈×C₄₁	—	2	2	no	—
98	C₂×C₈×C₄₁	C₄²	1	4	yes	—
99	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
100	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
101	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
102	C₂×C₈×C₄₁	C₄⋊C₄	1	4	yes	—
103	C₂×C₈×C₄₁	C₄⋊C₄	1	4	yes	—
104	C₂×C₈×C₄₁	C₄⋊C₄	1	4	yes	—
105	C₂×C₈×C₄₁	C₄⋊C₄	1	4	yes	—
106	C₄⋊C₄×C₄₁	—	2	4	no	—
107	C₄⋊C₄×C₄₁	—	2	4	no	—
108	C₄⋊C₄×C₄₁	—	2	4	no	—
109	C₄⋊C₄×C₄₁	—	2	4	no	—
110	C₄⋊C₄×C₄₁	—	4	2	no	—
111	C₄⋊C₄×C₄₁	—	4	2	no	—
112	C₄⋊C₄×C₄₁	—	4	2	no	—
113	C₄⋊C₄×C₄₁	—	4	2	no	—
114	C₄²×C₄₁	—	2	2	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	2	no	—
118	C₂³×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
120	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
121	C₂³×C₄₁	#121	1	1	yes	characteristic
122	C₂³×C₄₁	#121	1	1	yes	characteristic
123	C₂³×C₄₁	#127	1	1	yes	characteristic
124	C₂³×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
125	C₂³×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
126	C₂³×C₄₁	#137	1	4	yes	—
127	C₂×C₄×C₄₁	—	2	4	no	—
128	C₂×C₄×C₄₁	—	2	8	no	—
129	C₂×C₄×C₄₁	—	4	4	no	—
130	C₂×C₄×C₄₁	—	4	2	no	—
131	C₂×C₄×C₄₁	—	4	2	no	—
132	C₂×C₄×C₄₁	—	4	4	no	—
133	C₂×C₄×C₄₁	—	4	4	no	—
134	C₂×C₄×C₄₁	—	4	8	no	—
135	C₂×C₄×C₄₁	—	4	8	no	—
136	C₂×C₄×C₄₁	—	8	4	no	—
137	C₂×C₄×C₄₁	—	8	4	no	—
138	C₂×C₄×C₄₁	—	8	2	no	—
139	C₂×C₄×C₄₁	—	8	2	no	—
140	C₂×C₄×C₄₁	—	8	2	no	—
141	C₂×C₄×C₄₁	—	8	2	no	—
142	C₂×C₄×C₄₁	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
151	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
152	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₁	C₄×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₁	C₄×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₄×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₁	C₄×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
165	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
166	C₂×C₄×C₄₁	#125	1	1	yes	characteristic
167	C₂×C₄×C₄₁	#125	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
170	C₈×C₄₁	—	2	4	no	—
171	C₈×C₄₁	#95	1	8	yes	complemented
172	#10863	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₁	C₄×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×C₄₁	#380	1	1	yes	characteristic
175	C₂²×C₄₁	#384	1	1	yes	characteristic
176	C₂²×C₄₁	#389	1	1	yes	characteristic
177	C₂²×C₄₁	#389	1	1	yes	characteristic
178	C₂²×C₄₁	#390	1	1	yes	characteristic
179	C₂²×C₄₁	#390	1	1	yes	characteristic
180	C₂²×C₄₁	#428	1	4	yes	—
181	C₂²×C₄₁	#440	1	4	yes	—
182	C₂²×C₄₁	#441	1	2	yes	—
183	C₂²×C₄₁	#442	1	2	yes	—
184	C₂²×C₄₁	#468	1	4	yes	—
185	C₂²×C₄₁	#469	1	2	yes	—
186	C₂²×C₄₁	#470	1	2	yes	—
187	C₂²×C₄₁	#496	1	2	yes	—
188	C₂²×C₄₁	#497	1	2	yes	—
189	C₂²×C₄₁	#501	1	4	yes	—
190	C₄×C₄₁	—	4	4	no	—
191	C₄×C₄₁	—	8	4	no	—
192	C₄×C₄₁	—	8	4	no	—
193	C₄×C₄₁	C₂×#95	1	1	yes	characteristic
194	C₄×C₄₁	C₄×C₄⋊C₄	1	1	yes	characteristic
195	C₄×C₄₁	#380	1	1	yes	characteristic
196	C₄×C₄₁	#382	1	1	yes	characteristic
197	C₄×C₄₁	#389	1	1	yes	characteristic
198	C₄×C₄₁	#389	1	1	yes	characteristic
199	C₄×C₄₁	#391	1	1	yes	characteristic
200	C₄×C₄₁	#391	1	1	yes	characteristic
201	C₂²×#107	C₂×C₄₁	1	1	yes	characteristic
202	C₂²×#106	C₂×C₄₁	1	1	yes	characteristic
203	C₂²×#97	C₂×C₄₁	1	1	yes	characteristic
204	C₂×#340	C₂×C₄₁	1	2	yes	—
205	C₄⋊#95	C₂×C₄₁	1	2	yes	—
206	C₂×C₄₁	C₄⋊#95	1	1	yes	characteristic
207	C₂×C₄₁	#1776	1	2	yes	—
208	C₂×C₄₁	#1809	1	2	yes	—
209	C₂×C₄₁	#1847	1	2	yes	—
210	C₂×C₄₁	#1943	1	2	yes	—
211	C₂×C₄₁	#1944	1	2	yes	—
212	C₂×C₄₁	#1971	1	1	yes	characteristic
213	C₂×C₄₁	#1972	1	1	yes	characteristic
214	C₂×C₄₁	#1973	1	2	yes	—
215	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
219	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
220	C₂×#107	—	2	2	no	—
221	C₂×#107	—	2	2	no	—
222	C₂×#107	C₄×C₄₁	1	4	yes	complemented
223	C₂×#106	—	2	2	no	—
224	C₂×#106	—	2	2	no	—
225	C₂×#106	C₄×C₄₁	1	4	yes	complemented
226	C₂×#97	—	2	2	no	—
227	C₂×#97	—	2	2	no	—
228	C₂×#97	C₄×C₄₁	1	4	yes	complemented
229	C₂×#95	—	2	4	no	—
230	#340	—	2	4	no	—
231	C₄₁	#10863	1	1	yes	characteristic, direct product factor, Sylow
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	D₄×C₄₁	1	2	yes	—
235	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
241	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
242	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
243	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
244	C₂²×C₈	D₄×C₄₁	1	2	yes	—
245	C₂²×C₈	D₄×C₄₁	1	2	yes	—
246	C₂²×C₈	D₄×C₄₁	1	2	yes	—
247	C₂²×C₈	D₄×C₄₁	1	2	yes	—
248	C₂²×C₈	Q₈×C₄₁	1	2	yes	—
249	C₂²×C₈	Q₈×C₄₁	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
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	2	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
267	C₂×C₄²	Q₈×C₄₁	1	2	yes	—
268	#107	—	2	8	no	—
269	#106	—	2	8	no	—
270	#97	—	2	8	no	—
271	#95	—	4	8	no	—
272	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	4	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
298	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
299	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
300	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
301	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	C₄²×C₄₁	1	4	yes	—
309	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
310	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
311	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
312	C₂×C₈	C₄⋊C₄×C₄₁	1	4	yes	—
313	C₂×C₈	C₄⋊C₄×C₄₁	1	4	yes	—
314	C₂×C₈	C₄⋊C₄×C₄₁	1	4	yes	—
315	C₂×C₈	C₄⋊C₄×C₄₁	1	4	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₂³	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
329	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
330	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
331	C₂³	#121×C₄₁	1	1	yes	characteristic
332	C₂³	#121×C₄₁	1	1	yes	characteristic
333	C₂³	#127×C₄₁	1	1	yes	characteristic
334	C₂³	C₄⋊Q₈×C₄₁	1	1	yes	characteristic
335	C₂³	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
336	C₂³	#137×C₄₁	1	4	yes	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	C₂×C₄²×C₄₁	1	1	yes	characteristic
353	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
354	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
360	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
361	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
362	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
363	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
364	C₂×C₄	C₄×Q₈×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₄×Q₈×C₄₁	1	1	yes	characteristic
366	C₂×C₄	C₄×Q₈×C₄₁	1	1	yes	characteristic
367	C₂×C₄	C₄×Q₈×C₄₁	1	1	yes	characteristic
368	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
369	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
370	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
371	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
372	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
373	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
374	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
375	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
376	C₂×C₄	#125×C₄₁	1	1	yes	characteristic
377	C₂×C₄	#125×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₄⋊Q₈×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₄⋊Q₈×C₄₁	1	1	yes	characteristic
380	C₈	—	2	4	no	—
381	C₈	#95×C₄₁	1	8	yes	complemented
382	C₂²	C₄×C₄⋊C₄×C₄₁	1	1	yes	characteristic
383	C₂²	C₄₁×#380	1	1	yes	characteristic
384	C₂²	C₄₁×#384	1	1	yes	characteristic
385	C₂²	C₄₁×#389	1	1	yes	characteristic
386	C₂²	C₄₁×#389	1	1	yes	characteristic
387	C₂²	C₄₁×#390	1	1	yes	characteristic
388	C₂²	C₄₁×#390	1	1	yes	characteristic
389	C₂²	C₄₁×#428	1	4	yes	—
390	C₂²	C₄₁×#440	1	4	yes	—
391	C₂²	C₄₁×#441	1	2	yes	—
392	C₂²	C₄₁×#442	1	2	yes	—
393	C₂²	C₄₁×#468	1	4	yes	—
394	C₂²	C₄₁×#469	1	2	yes	—
395	C₂²	C₄₁×#470	1	2	yes	—
396	C₂²	C₄₁×#496	1	2	yes	—
397	C₂²	C₄₁×#497	1	2	yes	—
398	C₂²	C₄₁×#501	1	4	yes	—
399	C₄	—	4	4	no	—
400	C₄	—	8	4	no	—
401	C₄	—	8	4	no	—
402	C₄	C₂×#95×C₄₁	1	1	yes	characteristic
403	C₄	C₄×C₄⋊C₄×C₄₁	1	1	yes	characteristic
404	C₄	C₄₁×#380	1	1	yes	characteristic
405	C₄	C₄₁×#382	1	1	yes	characteristic
406	C₄	C₄₁×#389	1	1	yes	characteristic
407	C₄	C₄₁×#389	1	1	yes	characteristic
408	C₄	C₄₁×#391	1	1	yes	characteristic
409	C₄	C₄₁×#391	1	1	yes	characteristic
410	C₂	C₄₁×C₄⋊#95	1	1	yes	characteristic
411	C₂	C₄₁×#1776	1	2	yes	—
412	C₂	C₄₁×#1809	1	2	yes	—
413	C₂	C₄₁×#1847	1	2	yes	—
414	C₂	C₄₁×#1943	1	2	yes	—
415	C₂	C₄₁×#1944	1	2	yes	—
416	C₂	C₄₁×#1971	1	1	yes	characteristic
417	C₂	C₄₁×#1972	1	1	yes	characteristic
418	C₂	C₄₁×#1973	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
LCS	G ▷ C₂×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
13. C₂×#107×C₄₁	C₄	semidirect
16. C₂×#106×C₄₁	C₄	semidirect
19. C₂×#97×C₄₁	C₄	semidirect
171. C₈×C₄₁	#95	semidirect
172. #10863	C₄₁	direct (N × H)
222. C₂×#107	C₄×C₄₁	semidirect
225. C₂×#106	C₄×C₄₁	semidirect
228. C₂×#97	C₄×C₄₁	semidirect
231. C₄₁	#10863	direct (N × H)
381. C₈	#95×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#107×C₄₁	2
C₂²×#106×C₄₁	2
C₂²×#97×C₄₁	2
C₂×C₄₁×#340	2
C₄₁×C₄⋊#95	2
#10863	41

Subgroups — C41×#10863 #23787064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#10863 #23787064