Subgroups — C₄₁×#17879 #23794080

Order 10496.

678 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2972	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1585	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1582	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1478	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#446	—	2	2	no	—
14	C₄₁×#446	C₂²	1	4	yes	complemented
15	C₄×SD₁₆×C₄₁	C₄	1	2	yes	—
16	C₄×SD₁₆×C₄₁	C₄	1	2	yes	—
17	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
18	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
19	C₈×D₄×C₄₁	—	2	2	no	—
20	C₈×D₄×C₄₁	C₂²	1	4	yes	—
21	C₄₁×#432	—	2	2	no	—
22	C₄₁×#431	C₂²	1	1	yes	characteristic
23	C₄₁×#431	C₂²	1	1	yes	characteristic
24	C₄₁×#431	C₂²	1	1	yes	characteristic
25	C₄₁×#431	C₂²	1	1	yes	characteristic
26	C₂×#106×C₄₁	C₄	1	1	yes	characteristic
27	C₂×#103×C₄₁	C₄	1	1	yes	characteristic
28	C₂×#102×C₄₁	C₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₄₁	—	2	2	no	—
30	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#335	C₂²	1	2	yes	complemented
32	C₄₁×#334	C₂²	1	2	yes	complemented
33	C₄₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
34	C₄₁×D₄⋊C₈	C₂²	1	4	yes	—
35	C₄₁×#322	C₂²	1	2	yes	complemented
36	C₄₁×#322	C₂²	1	2	yes	complemented
37	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	—	2	1	no	—
40	C₂×SD₁₆×C₄₁	—	2	4	no	—
41	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
42	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₄₁	—	2	4	no	—
44	C₂²×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
46	C₄×Q₈×C₄₁	—	2	1	no	—
47	C₄×Q₈×C₄₁	—	2	1	no	—
48	C₄×Q₈×C₄₁	C₂×C₄	1	2	yes	—
49	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
50	C₄×D₄×C₄₁	—	2	1	no	—
51	C₄×D₄×C₄₁	—	2	1	no	—
52	C₄×D₄×C₄₁	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₄₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄²×C₄₁	—	2	1	no	—
59	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
60	#106×C₄₁	C₂×C₄	1	2	yes	—
61	#106×C₄₁	C₂×C₄	1	2	yes	—
62	C₄⋊C₈×C₄₁	—	2	4	no	—
63	C₄⋊C₈×C₄₁	—	2	1	no	—
64	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
65	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
66	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
67	#103×C₄₁	C₂×C₄	1	2	yes	—
68	#103×C₄₁	C₂×C₄	1	2	yes	—
69	#102×C₄₁	C₂×C₄	1	2	yes	—
70	#102×C₄₁	C₂×C₄	1	2	yes	—
71	C₂²⋊C₈×C₄₁	—	2	1	no	—
72	C₂²⋊C₈×C₄₁	—	2	1	no	—
73	C₂²⋊C₈×C₄₁	—	2	1	no	—
74	C₂²⋊C₈×C₄₁	—	2	4	no	—
75	C₂²⋊C₈×C₄₁	D₄	1	2	yes	—
76	#97×C₄₁	—	2	4	no	—
77	C₄×C₈×C₄₁	—	2	1	no	—
78	C₄×C₈×C₄₁	—	2	1	no	—
79	C₄×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₄₁	C₂³	1	2	yes	—
82	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₄₁	C₂³	1	2	yes	—
85	C₂⁴×C₄₁	—	2	1	no	—
86	C₂×Q₈×C₄₁	—	2	1	no	—
87	C₂×Q₈×C₄₁	—	2	2	no	—
88	C₂×Q₈×C₄₁	—	2	2	no	—
89	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₄₁	—	2	1	no	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂×D₄×C₄₁	M₁₆	1	4	yes	—
93	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₁	—	2	1	no	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	—	2	1	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	8	2	no	—
100	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
103	SD₁₆×C₄₁	—	2	4	no	—
104	SD₁₆×C₄₁	—	2	4	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	2	no	—
108	C₂×C₈×C₄₁	—	2	2	no	—
109	C₂×C₈×C₄₁	—	2	2	no	—
110	C₂×C₈×C₄₁	—	8	4	no	—
111	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	1	no	—
118	C₄⋊C₄×C₄₁	—	2	1	no	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
121	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
122	C₂²⋊C₄×C₄₁	—	2	2	no	—
123	C₂²⋊C₄×C₄₁	—	2	2	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₁	#41	1	1	yes	characteristic
129	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	2	4	no	—
132	C₂³×C₄₁	—	8	1	no	—
133	C₂³×C₄₁	—	8	1	no	—
134	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
135	Q₈×C₄₁	—	2	2	no	—
136	Q₈×C₄₁	—	2	2	no	—
137	Q₈×C₄₁	—	4	2	no	—
138	D₄×C₄₁	—	2	2	no	—
139	D₄×C₄₁	—	2	4	no	—
140	D₄×C₄₁	C₂×M₁₆	1	4	yes	—
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	—	4	1	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	8	2	no	—
149	C₂×C₄×C₄₁	—	8	1	no	—
150	C₂×C₄×C₄₁	—	8	1	no	—
151	C₂×C₄×C₄₁	C₄×D₄	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	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₄₁	#131	1	2	yes	—
156	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
159	C₈×C₄₁	—	2	1	no	—
160	C₈×C₄₁	—	2	1	no	—
161	C₈×C₄₁	—	2	1	no	—
162	C₈×C₄₁	—	2	1	no	—
163	C₈×C₄₁	—	2	4	no	—
164	C₈×C₄₁	—	4	2	no	—
165	C₈×C₄₁	—	4	2	no	—
166	C₈×C₄₁	—	4	2	no	—
167	#17879	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₄₁	—	2	1	no	—
169	C₂²×C₄₁	—	2	1	no	—
170	C₂²×C₄₁	—	2	4	no	—
171	C₂²×C₄₁	—	4	2	no	—
172	C₂²×C₄₁	—	4	2	no	—
173	C₂²×C₄₁	—	8	4	no	—
174	C₂²×C₄₁	#435	1	2	yes	—
175	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
176	C₄×C₄₁	—	2	1	no	—
177	C₄×C₄₁	—	2	1	no	—
178	C₄×C₄₁	—	2	1	no	—
179	C₄×C₄₁	—	4	2	no	—
180	C₄×C₄₁	—	4	2	no	—
181	C₄×C₄₁	—	4	2	no	—
182	C₄×C₄₁	#435	1	2	yes	—
183	C₄×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
184	C₄×C₄₁	C₂×#131	1	1	yes	characteristic
185	C₄×C₄₁	#577	1	2	yes	—
186	#2983	C₂×C₄₁	1	1	yes	characteristic, complemented
187	#2972	C₂×C₄₁	1	1	yes	characteristic
188	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic
189	#1585	C₂×C₄₁	1	4	yes	complemented
190	#1582	C₂×C₄₁	1	4	yes	complemented
191	#1564	C₂×C₄₁	1	1	yes	characteristic, complemented
192	#1479	C₂×C₄₁	1	1	yes	characteristic, complemented
193	#1478	C₂×C₄₁	1	1	yes	characteristic
194	#1452	C₂×C₄₁	1	1	yes	characteristic, complemented
195	C₂×C₄₁	—	2	2	no	—
196	C₂×C₄₁	—	4	4	no	—
197	C₂×C₄₁	C₂×#435	1	1	yes	characteristic
198	C₂×C₄₁	#2949	1	1	yes	characteristic
199	C₂×C₄₁	#2957	1	1	yes	characteristic
200	C₂²×SD₁₆	C₄×C₄₁	1	1	yes	characteristic
201	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
203	#446	—	2	2	no	—
204	#446	C₂²×C₄₁	1	4	yes	complemented
205	C₄×SD₁₆	C₄×C₄₁	1	2	yes	—
206	C₄×SD₁₆	C₄×C₄₁	1	2	yes	—
207	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
208	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
209	C₈×D₄	—	2	2	no	—
210	C₈×D₄	C₂²×C₄₁	1	4	yes	—
211	#432	—	2	2	no	—
212	#431	C₂²×C₄₁	1	1	yes	characteristic
213	#431	C₂²×C₄₁	1	1	yes	characteristic
214	#431	C₂²×C₄₁	1	1	yes	characteristic
215	#431	C₂²×C₄₁	1	1	yes	characteristic
216	C₂×#106	C₄×C₄₁	1	1	yes	characteristic
217	C₂×#103	C₄×C₄₁	1	1	yes	characteristic
218	C₂×#102	C₄×C₄₁	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	—	2	2	no	—
220	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
221	#335	C₂²×C₄₁	1	2	yes	complemented
222	#334	C₂²×C₄₁	1	2	yes	complemented
223	Q₈⋊C₈	C₂²×C₄₁	1	4	yes	complemented
224	D₄⋊C₈	C₂²×C₄₁	1	4	yes	—
225	#322	C₂²×C₄₁	1	2	yes	complemented
226	#322	C₂²×C₄₁	1	2	yes	complemented
227	C₄₁	#17879	1	1	yes	characteristic, direct product factor, Sylow
228	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
229	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂×SD₁₆	—	2	4	no	—
232	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
233	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
236	C₂²×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	C₂×C₄×C₄₁	1	2	yes	—
240	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	C₂×C₄×C₄₁	1	2	yes	—
244	C₄×D₄	C₂³×C₄₁	1	2	yes	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
251	#106	C₂×C₄×C₄₁	1	2	yes	—
252	#106	C₂×C₄×C₄₁	1	2	yes	—
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
256	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
257	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
258	#103	C₂×C₄×C₄₁	1	2	yes	—
259	#103	C₂×C₄×C₄₁	1	2	yes	—
260	#102	C₂×C₄×C₄₁	1	2	yes	—
261	#102	C₂×C₄×C₄₁	1	2	yes	—
262	C₂²⋊C₈	—	2	1	no	—
263	C₂²⋊C₈	—	2	1	no	—
264	C₂²⋊C₈	—	2	1	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	C₂²⋊C₈	D₄×C₄₁	1	2	yes	—
267	#97	—	2	4	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
271	C₄×C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₄₁	1	2	yes	—
273	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₄₁	1	2	yes	—
276	C₂⁴	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	M₁₆×C₄₁	1	4	yes	—
284	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
294	SD₁₆	—	2	4	no	—
295	SD₁₆	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	8	4	no	—
302	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
305	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
312	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₄²	#41×C₄₁	1	1	yes	characteristic
320	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	8	1	no	—
324	C₂³	—	8	1	no	—
325	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	2	no	—
328	Q₈	—	4	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	2	4	no	—
331	D₄	C₂×M₁₆×C₄₁	1	4	yes	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	—	8	1	no	—
342	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
343	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
344	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
345	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
346	C₂×C₄	#131×C₄₁	1	2	yes	—
347	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	4	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	4	no	—
364	C₂²	C₄₁×#435	1	2	yes	—
365	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	C₄₁×#435	1	2	yes	—
373	C₄	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
374	C₄	C₂×#131×C₄₁	1	1	yes	characteristic
375	C₄	C₄₁×#577	1	2	yes	—
376	C₂	—	2	2	no	—
377	C₂	—	4	4	no	—
378	C₂	C₂×C₄₁×#435	1	1	yes	characteristic
379	C₂	C₄₁×#2949	1	1	yes	characteristic
380	C₂	C₄₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₂²×D₄×C₄₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2983	C₂	semidirect
4. C₄₁×#1585	C₂	semidirect
5. C₄₁×#1582	C₂	semidirect
6. C₄₁×#1564	C₂	semidirect
7. C₄₁×#1479	C₂	semidirect
9. C₄₁×#1452	C₂	semidirect
14. C₄₁×#446	C₂²	semidirect
31. C₄₁×#335	C₂²	semidirect
32. C₄₁×#334	C₂²	semidirect
33. C₄₁×Q₈⋊C₈	C₂²	semidirect
35. C₄₁×#322	C₂²	semidirect
36. C₄₁×#322	C₂²	semidirect
167. #17879	C₄₁	direct (N × H)
186. #2983	C₂×C₄₁	semidirect
189. #1585	C₂×C₄₁	semidirect
190. #1582	C₂×C₄₁	semidirect
191. #1564	C₂×C₄₁	semidirect
192. #1479	C₂×C₄₁	semidirect
194. #1452	C₂×C₄₁	semidirect
204. #446	C₂²×C₄₁	semidirect
221. #335	C₂²×C₄₁	semidirect
222. #334	C₂²×C₄₁	semidirect
223. Q₈⋊C₈	C₂²×C₄₁	semidirect
225. #322	C₂²×C₄₁	semidirect
226. #322	C₂²×C₄₁	semidirect
227. C₄₁	#17879	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2983	2
C₄₁×#2972	2
C₂×C₄×SD₁₆×C₄₁	2
C₄₁×#1585	2
C₄₁×#1582	2
C₄₁×#1564	2
C₄₁×#1479	2
C₄₁×#1478	2
C₄₁×#1452	2
#17879	41

Subgroups — C41×#17879 #23794080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17879 #23794080