Subgroups — C₄₁×#21410 #23797611

Order 10496.

1466 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1990	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1957	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1895	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1762	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₁	—	2	1	no	—
9	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
10	C₄₁×#532	—	2	4	no	—
11	C₄₁×#532	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₁	—	2	1	no	—
15	C₂×#121×C₄₁	—	2	1	no	—
16	C₂×#121×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₁	—	2	1	no	—
18	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
19	C₂×#117×C₄₁	—	2	1	no	—
20	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₄₁	C₂²	1	8	yes	—
22	C₄×M₁₆×C₄₁	—	2	4	no	—
23	C₂×#97×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#384	C₂²	1	2	yes	—
26	C₄₁×#382	—	2	1	no	—
27	C₄₁×#380	—	2	1	no	—
28	C₄₁×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#340	C₂²	1	8	yes	—
32	C₂×#41×C₄₁	—	2	8	no	—
33	C₂×#41×C₄₁	—	4	8	no	—
34	C₂²×Q₈×C₄₁	—	2	1	no	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	1	no	—
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₁	—	2	2	no	—
40	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₄₁	—	2	4	no	—
44	C₂×M₁₆×C₄₁	—	2	8	no	—
45	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
46	C₄⋊Q₈×C₄₁	—	2	2	no	—
47	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
48	#127×C₄₁	—	2	2	no	—
49	#127×C₄₁	C₂×C₄	1	4	yes	—
50	#124×C₄₁	—	2	8	no	—
51	#121×C₄₁	—	2	8	no	—
52	#121×C₄₁	—	2	4	no	—
53	#121×C₄₁	C₂×C₄	1	8	yes	—
54	C₄×D₄×C₄₁	—	2	8	no	—
55	C₄×D₄×C₄₁	—	2	4	no	—
56	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	—
57	#117×C₄₁	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄²×C₄₁	—	2	2	no	—
67	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	D₄	1	4	yes	—
71	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
73	#102×C₄₁	—	2	16	no	—
74	#97×C₄₁	—	2	4	no	—
75	C₄×C₈×C₄₁	—	2	4	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	2	no	—
78	C₂⁴×C₄₁	—	2	2	no	—
79	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
80	#41×C₄₁	—	4	32	no	—
81	C₂×Q₈×C₄₁	—	2	4	no	—
82	C₂×Q₈×C₄₁	—	4	4	no	—
83	C₂×D₄×C₄₁	—	2	8	no	—
84	C₂×D₄×C₄₁	—	2	4	no	—
85	C₂×D₄×C₄₁	—	2	4	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	8	no	—
88	C₂×D₄×C₄₁	—	4	8	no	—
89	C₂×D₄×C₄₁	—	4	2	no	—
90	C₂×D₄×C₄₁	—	4	4	no	—
91	C₂×D₄×C₄₁	—	4	2	no	—
92	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	8	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	4	8	no	—
101	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₄₁	—	2	16	no	—
112	C₂×C₈×C₄₁	—	2	4	no	—
113	C₂×C₈×C₄₁	—	2	4	no	—
114	C₂×C₈×C₄₁	#41	1	8	yes	complemented
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	8	no	—
118	C₄⋊C₄×C₄₁	—	4	4	no	—
119	C₄⋊C₄×C₄₁	—	4	4	no	—
120	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₄₁	—	2	8	no	—
122	C₂²⋊C₄×C₄₁	—	2	8	no	—
123	C₂²⋊C₄×C₄₁	—	4	4	no	—
124	C₄²×C₄₁	—	4	4	no	—
125	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
126	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
127	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
129	C₄²×C₄₁	C₂×D₄	1	2	yes	—
130	C₄²×C₄₁	C₂×D₄	1	2	yes	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	1	no	—
133	C₂³×C₄₁	—	2	2	no	—
134	C₂³×C₄₁	—	2	1	no	—
135	C₂³×C₄₁	—	2	4	no	—
136	C₂³×C₄₁	—	4	4	no	—
137	C₂³×C₄₁	—	4	4	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	2	no	—
140	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₄₁	—	4	8	no	—
143	D₄×C₄₁	—	2	8	no	—
144	D₄×C₄₁	—	4	16	no	—
145	D₄×C₄₁	—	4	4	no	—
146	D₄×C₄₁	—	4	8	no	—
147	D₄×C₄₁	—	4	8	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	1	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	4	no	—
153	C₂×C₄×C₄₁	—	2	4	no	—
154	C₂×C₄×C₄₁	—	2	8	no	—
155	C₂×C₄×C₄₁	—	2	8	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	4	16	no	—
158	C₂×C₄×C₄₁	—	4	4	no	—
159	C₂×C₄×C₄₁	—	4	4	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	4	4	no	—
162	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
169	C₂×C₄×C₄₁	#137	1	2	yes	—
170	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
173	C₈×C₄₁	—	2	8	no	—
174	#21410	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₁	—	2	2	no	—
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	4	2	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	4	4	no	—
181	C₂²×C₄₁	—	4	4	no	—
182	C₂²×C₄₁	—	4	4	no	—
183	C₂²×C₄₁	—	8	4	no	—
184	C₂²×C₄₁	—	8	4	no	—
185	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₁	#532	1	2	yes	—
187	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
188	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
190	C₄×C₄₁	—	2	2	no	—
191	C₄×C₄₁	—	2	2	no	—
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	4	4	no	—
194	C₄×C₄₁	—	8	4	no	—
195	C₄×C₄₁	#417	1	4	yes	—
196	C₄×C₄₁	#418	1	4	yes	—
197	C₄×C₄₁	C₄×#41	1	2	yes	—
198	C₄×C₄₁	#525	1	2	yes	—
199	C₂×#532	C₂×C₄₁	1	1	yes	characteristic
200	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
201	#2285	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#1990	C₂×C₄₁	1	2	yes	complemented
203	#1957	C₂×C₄₁	1	2	yes	complemented
204	#1895	C₂×C₄₁	1	4	yes	complemented
205	#1762	C₂×C₄₁	1	4	yes	complemented
206	C₂×C₄₁	—	4	2	no	—
207	C₂×C₄₁	—	8	4	no	—
208	C₂×C₄₁	#2297	1	1	yes	characteristic
209	C₂×C₄₁	C₂×#418	1	1	yes	characteristic
210	C₂×C₄₁	C₂×#417	1	1	yes	characteristic
211	C₂×C₄₁	#3182	1	2	yes	—
212	C₂×C₄₁	#3184	1	2	yes	—
213	C₂²×#41	—	2	1	no	—
214	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
215	#532	—	2	4	no	—
216	#532	C₄×C₄₁	1	8	yes	complemented
217	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×#124	—	2	1	no	—
220	C₂×#121	—	2	1	no	—
221	C₂×#121	C₂²×C₄₁	1	2	yes	—
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
224	C₂×#117	—	2	1	no	—
225	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#102	C₂²×C₄₁	1	8	yes	—
227	C₄×M₁₆	—	2	4	no	—
228	C₂×#97	C₂²×C₄₁	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
230	#384	C₂²×C₄₁	1	2	yes	—
231	#382	—	2	1	no	—
232	#380	—	2	1	no	—
233	#380	C₂²×C₄₁	1	2	yes	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
236	#340	C₂²×C₄₁	1	8	yes	—
237	C₄₁	#21410	1	1	yes	characteristic, direct product factor, Sylow
238	C₂×#41	—	2	8	no	—
239	C₂×#41	—	4	8	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	—	2	8	no	—
251	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
254	#127	—	2	2	no	—
255	#127	C₂×C₄×C₄₁	1	4	yes	—
256	#124	—	2	8	no	—
257	#121	—	2	8	no	—
258	#121	—	2	4	no	—
259	#121	C₂×C₄×C₄₁	1	8	yes	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	—
263	#117	—	4	4	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
274	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
275	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₄₁	1	4	yes	—
277	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
279	#102	—	2	16	no	—
280	#97	—	2	4	no	—
281	C₄×C₈	—	2	4	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
286	#41	—	4	32	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	4	8	no	—
307	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
308	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
317	M₁₆	—	2	16	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	#41×C₄₁	1	8	yes	complemented
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	8	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₄²	—	4	4	no	—
331	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
332	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
333	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
334	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
335	C₄²	C₂×D₄×C₄₁	1	2	yes	—
336	C₄²	C₂×D₄×C₄₁	1	2	yes	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
347	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
348	Q₈	—	4	8	no	—
349	D₄	—	2	8	no	—
350	D₄	—	4	16	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	8	no	—
353	D₄	—	4	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	16	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
373	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
374	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
375	C₂×C₄	#137×C₄₁	1	2	yes	—
376	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
379	C₈	—	2	8	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	8	4	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
391	C₂²	C₄₁×#532	1	2	yes	—
392	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
393	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
394	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	4	no	—
400	C₄	C₄₁×#417	1	4	yes	—
401	C₄	C₄₁×#418	1	4	yes	—
402	C₄	C₄×#41×C₄₁	1	2	yes	—
403	C₄	C₄₁×#525	1	2	yes	—
404	C₂	—	4	2	no	—
405	C₂	—	8	4	no	—
406	C₂	C₄₁×#2297	1	1	yes	characteristic
407	C₂	C₂×C₄₁×#418	1	1	yes	characteristic
408	C₂	C₂×C₄₁×#417	1	1	yes	characteristic
409	C₂	C₄₁×#3182	1	2	yes	—
410	C₂	C₄₁×#3184	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×M₁₆×C₄₁	C₂	semidirect
3. C₄₁×#2285	C₂	semidirect
4. C₄₁×#1990	C₂	semidirect
5. C₄₁×#1957	C₂	semidirect
6. C₄₁×#1895	C₂	semidirect
7. C₄₁×#1762	C₂	semidirect
11. C₄₁×#532	C₄	semidirect
114. C₂×C₈×C₄₁	#41	semidirect
174. #21410	C₄₁	direct (N × H)
200. C₂×C₄×M₁₆	C₂×C₄₁	semidirect
201. #2285	C₂×C₄₁	semidirect
202. #1990	C₂×C₄₁	semidirect
203. #1957	C₂×C₄₁	semidirect
204. #1895	C₂×C₄₁	semidirect
205. #1762	C₂×C₄₁	semidirect
216. #532	C₄×C₄₁	semidirect
237. C₄₁	#21410	direct (N × H)
320. C₂×C₈	#41×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×#532	2
C₂×C₄×M₁₆×C₄₁	2
C₄₁×#2285	2
C₄₁×#1990	2
C₄₁×#1957	2
C₄₁×#1895	2
C₄₁×#1762	2
#21410	41

Subgroups — C41×#21410 #23797611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21410 #23797611