Subgroups — C₄₁×#20439 #23796640

Order 10496.

1130 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1771	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1771	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1770	C₂	1	2	yes	maximal, complemented
9	C₈×C₄⋊C₄×C₄₁	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#424	C₄	1	8	yes	complemented
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#405	—	2	4	no	—
23	C₄₁×#405	C₄	1	8	yes	complemented
24	C₄×M₁₆×C₄₁	—	2	4	no	—
25	C₂×#97×C₄₁	C₂²	1	2	yes	—
26	C₂×#97×C₄₁	C₂²	1	2	yes	—
27	C₂×#97×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#389	C₄	1	2	yes	—
32	C₄₁×#389	C₄	1	2	yes	—
33	C₄₁×#385	C₄	1	4	yes	—
34	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
36	C₄₁×#336	C₂²	1	1	yes	characteristic
37	C₄₁×#336	C₂²	1	2	yes	—
38	C₄₁×#336	C₂²	1	1	yes	characteristic
39	C₄₁×#336	C₂²	1	1	yes	characteristic
40	C₄₁×#336	C₂²	1	1	yes	characteristic
41	C₄₁×#336	C₂²	1	2	yes	—
42	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₄₁	—	2	2	no	—
45	C₂×M₁₆×C₄₁	—	2	2	no	—
46	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	—
48	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
49	C₂×M₁₆×C₄₁	Q₈	1	4	yes	—
50	C₂²×C₈×C₄₁	—	2	2	no	—
51	C₂²×C₈×C₄₁	—	2	2	no	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	—	2	2	no	—
54	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
62	#117×C₄₁	—	2	2	no	—
63	#117×C₄₁	—	2	2	no	—
64	#117×C₄₁	C₂×C₄	1	4	yes	—
65	#117×C₄₁	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₄₁	C₂×C₄	1	8	yes	complemented
81	C₄⋊C₈×C₄₁	C₂×C₄	1	8	yes	complemented
82	#97×C₄₁	—	2	4	no	—
83	#97×C₄₁	—	2	4	no	—
84	#97×C₄₁	C₂×C₄	1	8	yes	complemented
85	C₄×C₈×C₄₁	—	2	4	no	—
86	C₄×C₈×C₄₁	—	2	4	no	—
87	C₄×C₈×C₄₁	C₂×C₄	1	8	yes	complemented
88	#95×C₄₁	C₂×C₄	1	4	yes	—
89	#95×C₄₁	C₂×C₄	1	4	yes	—
90	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₁	—	2	4	no	—
92	C₂²×C₄×C₄₁	—	2	4	no	—
93	C₂²×C₄×C₄₁	—	4	2	no	—
94	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₁	#41	1	2	yes	—
105	C₂²×C₄×C₄₁	#41	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₄₁	—	2	8	no	—
108	M₁₆×C₄₁	C₄⋊C₄	1	16	yes	complemented
109	C₂×C₈×C₄₁	—	2	8	no	—
110	C₂×C₈×C₄₁	—	2	8	no	—
111	C₂×C₈×C₄₁	—	2	1	no	—
112	C₂×C₈×C₄₁	—	2	2	no	—
113	C₂×C₈×C₄₁	—	2	1	no	—
114	C₂×C₈×C₄₁	—	2	1	no	—
115	C₂×C₈×C₄₁	—	2	1	no	—
116	C₂×C₈×C₄₁	—	2	1	no	—
117	C₂×C₈×C₄₁	—	2	1	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
128	C₂×C₈×C₄₁	C₂×Q₈	1	4	yes	—
129	C₄⋊C₄×C₄₁	—	2	4	no	—
130	C₄⋊C₄×C₄₁	—	2	8	no	—
131	C₄⋊C₄×C₄₁	—	4	4	no	—
132	C₄⋊C₄×C₄₁	C₄²	1	4	yes	—
133	C₄⋊C₄×C₄₁	C₄²	1	4	yes	—
134	C₂²⋊C₄×C₄₁	—	2	4	no	—
135	C₂²⋊C₄×C₄₁	C₄²	1	8	yes	—
136	C₄²×C₄₁	—	2	4	no	—
137	C₄²×C₄₁	—	2	1	no	—
138	C₄²×C₄₁	—	2	2	no	—
139	C₄²×C₄₁	—	2	1	no	—
140	C₄²×C₄₁	—	2	1	no	—
141	C₄²×C₄₁	—	2	1	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
144	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
145	C₂³×C₄₁	—	2	2	no	—
146	C₂³×C₄₁	—	2	2	no	—
147	C₂³×C₄₁	C₂×C₄²	1	2	yes	—
148	C₂³×C₄₁	C₄×D₄	1	2	yes	—
149	C₂³×C₄₁	C₄×Q₈	1	2	yes	—
150	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	4	no	—
153	C₂×C₄×C₄₁	—	2	4	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	4	no	—
161	C₂×C₄×C₄₁	—	4	8	no	—
162	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
163	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
164	C₂×C₄×C₄₁	C₂×C₄²	1	2	yes	—
165	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
166	C₂×C₄×C₄₁	#117	1	4	yes	—
167	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
168	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₁	C₄×Q₈	1	4	yes	—
170	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₄₁	#131	1	4	yes	—
172	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
178	C₈×C₄₁	—	2	2	no	—
179	C₈×C₄₁	—	2	2	no	—
180	C₈×C₄₁	—	2	2	no	—
181	C₈×C₄₁	—	2	2	no	—
182	C₈×C₄₁	—	2	4	no	—
183	C₈×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
184	#20439	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₁	—	2	2	no	—
186	C₂²×C₄₁	—	2	2	no	—
187	C₂²×C₄₁	—	2	4	no	—
188	C₂²×C₄₁	—	2	4	no	—
189	C₂²×C₄₁	C₄×C₄⋊C₄	1	4	yes	—
190	C₂²×C₄₁	C₂²×C₄²	1	1	yes	characteristic
191	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
193	C₂²×C₄₁	C₂×#131	1	2	yes	—
194	C₂²×C₄₁	#568	1	2	yes	—
195	C₄×C₄₁	—	2	4	no	—
196	C₄×C₄₁	—	2	4	no	—
197	C₄×C₄₁	—	2	4	no	—
198	C₄×C₄₁	—	4	4	no	—
199	C₄×C₄₁	—	4	2	no	—
200	C₄×C₄₁	C₄×C₄⋊C₄	1	4	yes	—
201	C₄×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
203	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
205	C₂×#424	C₂×C₄₁	1	1	yes	characteristic
206	C₂×#405	C₂×C₄₁	1	1	yes	characteristic
207	C₂×#405	C₂×C₄₁	1	1	yes	characteristic
208	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic
209	#2296	C₂×C₄₁	1	1	yes	characteristic
210	#1771	C₂×C₄₁	1	2	yes	complemented
211	#1771	C₂×C₄₁	1	2	yes	complemented
212	#1770	C₂×C₄₁	1	2	yes	complemented
213	C₈×C₄⋊C₄	C₂×C₄₁	1	2	yes	complemented
214	#1729	C₂×C₄₁	1	1	yes	characteristic
215	C₂×#336	C₂×C₄₁	1	1	yes	characteristic
216	C₂×C₄₁	—	2	4	no	—
217	C₂×C₄₁	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄₁	C₄×#131	1	1	yes	characteristic
219	C₂×C₄₁	#2875	1	1	yes	characteristic
220	C₂×C₄₁	#2933	1	2	yes	—
221	C₂×C₄₁	#2962	1	2	yes	—
222	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
223	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
224	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
225	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
227	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
229	#424	C₄×C₄₁	1	8	yes	complemented
230	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
231	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
232	#405	—	2	4	no	—
233	#405	C₄×C₄₁	1	8	yes	complemented
234	C₄×M₁₆	—	2	4	no	—
235	C₂×#97	C₂²×C₄₁	1	2	yes	—
236	C₂×#97	C₂²×C₄₁	1	2	yes	—
237	C₂×#97	C₂²×C₄₁	1	2	yes	—
238	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
239	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
240	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
241	#389	C₄×C₄₁	1	2	yes	—
242	#389	C₄×C₄₁	1	2	yes	—
243	#385	C₄×C₄₁	1	4	yes	—
244	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
245	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
246	#336	C₂²×C₄₁	1	1	yes	characteristic
247	#336	C₂²×C₄₁	1	1	yes	characteristic
248	#336	C₂²×C₄₁	1	1	yes	characteristic
249	#336	C₂²×C₄₁	1	1	yes	characteristic
250	#336	C₂²×C₄₁	1	2	yes	—
251	#336	C₂²×C₄₁	1	2	yes	—
252	C₄₁	#20439	1	1	yes	characteristic, direct product factor, Sylow
253	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
254	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	—
258	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	—
259	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
260	C₂×M₁₆	Q₈×C₄₁	1	4	yes	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
266	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
267	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
272	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	C₂×C₄×C₄₁	1	4	yes	—
276	#117	C₂×C₄×C₄₁	1	4	yes	—
277	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
278	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
280	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
287	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
288	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
291	C₄⋊C₈	C₂×C₄×C₄₁	1	8	yes	complemented
292	C₄⋊C₈	C₂×C₄×C₄₁	1	8	yes	complemented
293	#97	—	2	4	no	—
294	#97	—	2	4	no	—
295	#97	C₂×C₄×C₄₁	1	8	yes	complemented
296	C₄×C₈	—	2	4	no	—
297	C₄×C₈	—	2	4	no	—
298	C₄×C₈	C₂×C₄×C₄₁	1	8	yes	complemented
299	#95	C₂×C₄×C₄₁	1	4	yes	—
300	#95	C₂×C₄×C₄₁	1	4	yes	—
301	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
307	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
314	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
315	C₂²×C₄	#41×C₄₁	1	2	yes	—
316	C₂²×C₄	#41×C₄₁	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
318	M₁₆	—	2	8	no	—
319	M₁₆	C₄⋊C₄×C₄₁	1	16	yes	complemented
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	—	2	8	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
334	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
335	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
336	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
337	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
338	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
339	C₂×C₈	C₂×Q₈×C₄₁	1	4	yes	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	C₄²×C₄₁	1	4	yes	—
344	C₄⋊C₄	C₄²×C₄₁	1	4	yes	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	C₄²×C₄₁	1	8	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	2	no	—
354	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
355	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	C₂×C₄²×C₄₁	1	2	yes	—
359	C₂³	C₄×D₄×C₄₁	1	2	yes	—
360	C₂³	C₄×Q₈×C₄₁	1	2	yes	—
361	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
374	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
375	C₂×C₄	C₂×C₄²×C₄₁	1	2	yes	—
376	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
377	C₂×C₄	#117×C₄₁	1	4	yes	—
378	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
379	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
380	C₂×C₄	C₄×Q₈×C₄₁	1	4	yes	—
381	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
382	C₂×C₄	#131×C₄₁	1	4	yes	—
383	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
384	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
386	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	2	4	no	—
394	C₈	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	C₄×C₄⋊C₄×C₄₁	1	4	yes	—
400	C₂²	C₂²×C₄²×C₄₁	1	1	yes	characteristic
401	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
402	C₂²	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
403	C₂²	C₂×#131×C₄₁	1	2	yes	—
404	C₂²	C₄₁×#568	1	2	yes	—
405	C₄	—	2	4	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	C₄×C₄⋊C₄×C₄₁	1	4	yes	—
411	C₄	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
412	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
413	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
414	C₄	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
415	C₂	—	2	4	no	—
416	C₂	C₂×C₄×C₄⋊C₄×C₄₁	1	1	yes	characteristic
417	C₂	C₄×#131×C₄₁	1	1	yes	characteristic
418	C₂	C₄₁×#2875	1	1	yes	characteristic
419	C₂	C₄₁×#2933	1	2	yes	—
420	C₂	C₄₁×#2962	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
6. C₄₁×#1771	C₂	semidirect
7. C₄₁×#1771	C₂	semidirect
8. C₄₁×#1770	C₂	semidirect
9. C₈×C₄⋊C₄×C₄₁	C₂	semidirect
19. C₄₁×#424	C₄	semidirect
23. C₄₁×#405	C₄	semidirect
80. C₄⋊C₈×C₄₁	C₂×C₄	semidirect
81. C₄⋊C₈×C₄₁	C₂×C₄	semidirect
84. #97×C₄₁	C₂×C₄	semidirect
87. C₄×C₈×C₄₁	C₂×C₄	semidirect
108. M₁₆×C₄₁	C₄⋊C₄	semidirect
184. #20439	C₄₁	direct (N × H)
210. #1771	C₂×C₄₁	semidirect
211. #1771	C₂×C₄₁	semidirect
212. #1770	C₂×C₄₁	semidirect
213. C₈×C₄⋊C₄	C₂×C₄₁	semidirect
229. #424	C₄×C₄₁	semidirect
233. #405	C₄×C₄₁	semidirect
252. C₄₁	#20439	direct (N × H)
291. C₄⋊C₈	C₂×C₄×C₄₁	semidirect
292. C₄⋊C₈	C₂×C₄×C₄₁	semidirect
295. #97	C₂×C₄×C₄₁	semidirect
298. C₄×C₈	C₂×C₄×C₄₁	semidirect
319. M₁₆	C₄⋊C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#424	2
C₂×C₄₁×#405	2
C₂×C₄×M₁₆×C₄₁	2
C₄₁×#2296	2
C₄₁×#1771	2
C₄₁×#1770	2
C₈×C₄⋊C₄×C₄₁	2
C₄₁×#1729	2
C₂×C₄₁×#336	2
#20439	41

Subgroups — C41×#20439 #23796640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20439 #23796640