Subgroups — C₄₁×#23240 #23799441

Order 10496.

764 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1985	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1917	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1916	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1851	C₂	1	2	yes	maximal
6	C₄₁×#1770	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1753	C₂	1	2	yes	maximal
8	C₄₁×#1749	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
11	C₂×C₂²⋊Q₈×C₄₁	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#97×C₄₁	C₂²	1	2	yes	—
19	C₂×#97×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#391	C₄	1	1	yes	characteristic
22	C₄₁×#389	C₄	1	1	yes	characteristic
23	C₄₁×#387	C₄	1	2	yes	—
24	C₄₁×#385	C₄	1	2	yes	—
25	C₄₁×#380	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₄₁×#336	C₂²	1	1	yes	characteristic
30	C₄₁×#336	C₂²	1	2	yes	—
31	C₄₁×#336	C₂²	1	2	yes	—
32	C₄₁×#336	C₂²	1	2	yes	—
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₄₁×#336	C₂²	1	1	yes	characteristic
36	C₄₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₄₁	—	2	4	no	—
42	C₂×M₁₆×C₄₁	—	2	4	no	—
43	C₂×M₁₆×C₄₁	—	4	2	no	—
44	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	C₂²⋊Q₈×C₄₁	—	2	4	no	—
49	C₄×Q₈×C₄₁	—	4	2	no	—
50	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₁	—	4	2	no	—
59	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
65	C₄⋊C₈×C₄₁	—	2	4	no	—
66	C₄⋊C₈×C₄₁	—	4	2	no	—
67	C₂²⋊C₈×C₄₁	—	2	2	no	—
68	C₂²⋊C₈×C₄₁	Q₈	1	4	yes	complemented
69	#97×C₄₁	—	4	2	no	—
70	#97×C₄₁	—	4	2	no	—
71	C₄×C₈×C₄₁	—	2	4	no	—
72	#95×C₄₁	C₂×C₄	1	2	yes	—
73	#95×C₄₁	C₂×C₄	1	2	yes	—
74	#95×C₄₁	C₂×C₄	1	2	yes	—
75	#95×C₄₁	C₂×C₄	1	2	yes	—
76	#95×C₄₁	C₂×C₄	1	2	yes	—
77	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
78	C₂×Q₈×C₄₁	—	2	2	no	—
79	C₂×Q₈×C₄₁	—	4	1	no	—
80	C₂×Q₈×C₄₁	—	4	1	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	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	—	4	1	no	—
89	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
94	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₁	#41	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
101	M₁₆×C₄₁	—	4	8	no	—
102	C₂×C₈×C₄₁	—	2	2	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	2	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	—	2	2	no	—
111	C₂×C₈×C₄₁	—	2	2	no	—
112	C₂×C₈×C₄₁	C₂×Q₈	1	4	yes	—
113	C₂×C₈×C₄₁	#41	1	4	yes	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	4	1	no	—
116	C₄⋊C₄×C₄₁	—	4	2	no	—
117	C₄⋊C₄×C₄₁	—	4	1	no	—
118	C₄⋊C₄×C₄₁	—	4	2	no	—
119	C₄⋊C₄×C₄₁	M₁₆	1	4	yes	complemented
120	C₂²⋊C₄×C₄₁	—	2	4	no	—
121	C₂²⋊C₄×C₄₁	—	4	2	no	—
122	C₄²×C₄₁	—	2	2	no	—
123	C₄²×C₄₁	—	2	2	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	—	2	2	no	—
127	C₄²×C₄₁	—	2	2	no	—
128	C₄²×C₄₁	—	4	1	no	—
129	C₄²×C₄₁	—	4	1	no	—
130	C₂³×C₄₁	—	2	1	no	—
131	C₂³×C₄₁	—	2	1	no	—
132	C₂³×C₄₁	—	2	1	no	—
133	C₂³×C₄₁	—	2	1	no	—
134	C₂³×C₄₁	—	2	1	no	—
135	C₂³×C₄₁	—	2	1	no	—
136	C₂³×C₄₁	C₄×Q₈	1	2	yes	—
137	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
138	Q₈×C₄₁	—	4	4	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	1	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	1	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	4	no	—
146	C₂×C₄×C₄₁	—	2	4	no	—
147	C₂×C₄×C₄₁	—	2	2	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	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	1	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	1	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	2	1	no	—
162	C₂×C₄×C₄₁	—	2	1	no	—
163	C₂×C₄×C₄₁	—	2	1	no	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	4	4	no	—
166	C₂×C₄×C₄₁	—	4	4	no	—
167	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
168	C₂×C₄×C₄₁	C₂×M₁₆	1	4	yes	—
169	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
173	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
174	C₈×C₄₁	—	2	4	no	—
175	C₈×C₄₁	—	2	4	no	—
176	C₈×C₄₁	—	4	2	no	—
177	C₈×C₄₁	—	4	2	no	—
178	#23240	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	—	4	1	no	—
184	C₂²×C₄₁	—	4	1	no	—
185	C₂²×C₄₁	—	4	1	no	—
186	C₂²×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
187	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
188	C₂²×C₄₁	#518	1	1	yes	characteristic
189	C₂²×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
190	C₂²×C₄₁	#568	1	1	yes	characteristic
191	C₂²×C₄₁	#568	1	1	yes	characteristic
192	C₂²×C₄₁	#568	1	1	yes	characteristic
193	C₄×C₄₁	—	2	2	no	—
194	C₄×C₄₁	—	2	4	no	—
195	C₄×C₄₁	—	2	2	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	—	4	1	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	—	4	2	no	—
200	C₄×C₄₁	—	4	1	no	—
201	C₄×C₄₁	—	4	1	no	—
202	C₄×C₄₁	#551	1	2	yes	—
203	C₄×C₄₁	#554	1	2	yes	—
204	C₄×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
205	#1985	C₂×C₄₁	1	2	yes	complemented
206	#1917	C₂×C₄₁	1	2	yes	complemented
207	#1916	C₂×C₄₁	1	2	yes	complemented
208	#1851	C₂×C₄₁	1	2	yes	—
209	#1770	C₂×C₄₁	1	2	yes	complemented
210	#1753	C₂×C₄₁	1	2	yes	—
211	#1749	C₂×C₄₁	1	1	yes	characteristic
212	#1728	C₂×C₄₁	1	1	yes	characteristic
213	C₂×C₄₁	—	4	2	no	—
214	C₂×C₄₁	#2368	1	1	yes	characteristic
215	C₂×C₄₁	#2961	1	1	yes	characteristic
216	C₂×C₄₁	Q₈×M₁₆	1	1	yes	characteristic
217	C₂×C₄₁	#2967	1	1	yes	characteristic
218	C₂×C₄₁	#2970	1	1	yes	characteristic
219	C₂×C₄₁	#2975	1	1	yes	characteristic
220	C₂×C₄₁	#2978	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
222	C₂×C₂²⋊Q₈	C₄×C₄₁	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
224	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
226	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×#97	C₂²×C₄₁	1	2	yes	—
230	C₂×#97	C₂²×C₄₁	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
232	#391	C₄×C₄₁	1	1	yes	characteristic
233	#389	C₄×C₄₁	1	1	yes	characteristic
234	#387	C₄×C₄₁	1	2	yes	—
235	#385	C₄×C₄₁	1	2	yes	—
236	#380	C₄×C₄₁	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
239	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
240	#336	C₂²×C₄₁	1	2	yes	—
241	#336	C₂²×C₄₁	1	2	yes	—
242	#336	C₂²×C₄₁	1	2	yes	—
243	#336	C₂²×C₄₁	1	2	yes	—
244	#336	C₂²×C₄₁	1	2	yes	—
245	#336	C₂²×C₄₁	1	1	yes	characteristic
246	#336	C₂²×C₄₁	1	2	yes	—
247	#336	C₂²×C₄₁	1	1	yes	characteristic
248	C₄₁	#23240	1	1	yes	characteristic, direct product factor, Sylow
249	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
250	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	2	4	no	—
255	C₂×M₁₆	—	4	2	no	—
256	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
257	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
259	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₄×Q₈	—	4	2	no	—
262	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
265	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
270	C₂×C₄²	—	4	2	no	—
271	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
272	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
275	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
276	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
277	C₄⋊C₈	—	2	4	no	—
278	C₄⋊C₈	—	4	2	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	Q₈×C₄₁	1	4	yes	complemented
281	#97	—	4	2	no	—
282	#97	—	4	2	no	—
283	C₄×C₈	—	2	4	no	—
284	#95	C₂×C₄×C₄₁	1	2	yes	—
285	#95	C₂×C₄×C₄₁	1	2	yes	—
286	#95	C₂×C₄×C₄₁	1	2	yes	—
287	#95	C₂×C₄×C₄₁	1	2	yes	—
288	#95	C₂×C₄×C₄₁	1	2	yes	—
289	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
311	C₂²×C₄	#41×C₄₁	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
313	M₁₆	—	4	8	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×Q₈×C₄₁	1	4	yes	—
325	C₂×C₈	#41×C₄₁	1	4	yes	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	M₁₆×C₄₁	1	4	yes	complemented
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	1	no	—
341	C₄²	—	4	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	C₄×Q₈×C₄₁	1	2	yes	—
349	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
350	Q₈	—	4	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	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	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
380	C₂×C₄	C₂×M₁₆×C₄₁	1	4	yes	—
381	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
382	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
383	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
385	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
386	C₈	—	2	4	no	—
387	C₈	—	2	4	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
398	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
399	C₂²	C₄₁×#518	1	1	yes	characteristic
400	C₂²	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
401	C₂²	C₄₁×#568	1	1	yes	characteristic
402	C₂²	C₄₁×#568	1	1	yes	characteristic
403	C₂²	C₄₁×#568	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	4	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	2	no	—
413	C₄	C₄₁×#551	1	2	yes	—
414	C₄	C₄₁×#554	1	2	yes	—
415	C₂	—	4	2	no	—
416	C₂	C₄₁×#2368	1	1	yes	characteristic
417	C₂	C₄₁×#2961	1	1	yes	characteristic
418	C₂	Q₈×M₁₆×C₄₁	1	1	yes	characteristic
419	C₂	C₄₁×#2967	1	1	yes	characteristic
420	C₂	C₄₁×#2970	1	1	yes	characteristic
421	C₂	C₄₁×#2975	1	1	yes	characteristic
422	C₂	C₄₁×#2978	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄₁×#1985	C₂	semidirect
3. C₄₁×#1917	C₂	semidirect
4. C₄₁×#1916	C₂	semidirect
6. C₄₁×#1770	C₂	semidirect
68. C₂²⋊C₈×C₄₁	Q₈	semidirect
119. C₄⋊C₄×C₄₁	M₁₆	semidirect
178. #23240	C₄₁	direct (N × H)
205. #1985	C₂×C₄₁	semidirect
206. #1917	C₂×C₄₁	semidirect
207. #1916	C₂×C₄₁	semidirect
209. #1770	C₂×C₄₁	semidirect
248. C₄₁	#23240	direct (N × H)
280. C₂²⋊C₈	Q₈×C₄₁	semidirect
331. C₄⋊C₄	M₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊Q₈×C₄₁	2
C₄₁×#1985	2
C₄₁×#1917	2
C₄₁×#1916	2
C₄₁×#1851	2
C₄₁×#1770	2
C₄₁×#1753	2
C₄₁×#1749	2
C₄₁×#1728	2
#23240	41

Subgroups — C41×#23240 #23799441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23240 #23799441