Subgroups — C₄₁×#23351 #23799552

Order 10496.

696 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2398	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1924	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1923	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1870	C₂	1	2	yes	maximal
7	C₄₁×#1851	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1851	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1832	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
11	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
20	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#400	C₄	1	1	yes	characteristic
23	C₄₁×#400	C₄	1	1	yes	characteristic
24	C₄₁×#397	C₄	1	2	yes	—
25	C₄₁×#394	C₄	1	1	yes	characteristic
26	C₄₁×#394	C₄	1	1	yes	characteristic
27	C₄₁×#393	C₄	1	2	yes	—
28	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#376	C₂²	1	1	yes	characteristic
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	2	yes	—
36	C₄₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
40	C₂×M₁₆×C₄₁	—	4	2	no	—
41	C₂×M₁₆×C₄₁	—	4	2	no	—
42	C₂×M₁₆×C₄₁	—	4	2	no	—
43	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
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	C₄×Q₈×C₄₁	—	4	1	no	—
48	C₄×Q₈×C₄₁	—	4	1	no	—
49	C₄×D₄×C₄₁	—	4	1	no	—
50	C₄×D₄×C₄₁	—	4	1	no	—
51	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₄₁	C₂³	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	C₄⋊C₈×C₄₁	—	4	2	no	—
65	C₄⋊C₈×C₄₁	—	4	2	no	—
66	C₄⋊C₈×C₄₁	—	4	1	no	—
67	C₄⋊C₈×C₄₁	—	4	1	no	—
68	C₂²⋊C₈×C₄₁	—	4	2	no	—
69	C₂²⋊C₈×C₄₁	—	4	2	no	—
70	C₂²⋊C₈×C₄₁	—	4	2	no	—
71	#97×C₄₁	—	4	1	no	—
72	C₄×C₈×C₄₁	—	4	1	no	—
73	#95×C₄₁	C₂×C₄	1	2	yes	—
74	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
75	#95×C₄₁	C₂×C₄	1	1	yes	characteristic
76	#95×C₄₁	C₂×C₄	1	2	yes	—
77	#95×C₄₁	C₂×C₄	1	2	yes	—
78	#95×C₄₁	C₂×C₄	1	2	yes	—
79	#95×C₄₁	C₂×C₄	1	2	yes	—
80	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	4	1	no	—
83	C₂×Q₈×C₄₁	—	4	1	no	—
84	C₂×D₄×C₄₁	—	4	1	no	—
85	C₂×D₄×C₄₁	—	4	2	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
102	M₁₆×C₄₁	—	4	8	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	—	2	2	no	—
113	C₂×C₈×C₄₁	—	2	2	no	—
114	C₂×C₈×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	4	1	no	—
116	C₄⋊C₄×C₄₁	—	4	1	no	—
117	C₄⋊C₄×C₄₁	—	4	1	no	—
118	C₄⋊C₄×C₄₁	—	4	1	no	—
119	C₂²⋊C₄×C₄₁	—	2	4	no	—
120	C₂²⋊C₄×C₄₁	—	4	2	no	—
121	C₂²⋊C₄×C₄₁	—	4	2	no	—
122	C₂²⋊C₄×C₄₁	—	4	2	no	—
123	C₂²⋊C₄×C₄₁	—	4	2	no	—
124	C₄²×C₄₁	—	2	1	no	—
125	C₄²×C₄₁	—	2	1	no	—
126	C₄²×C₄₁	—	2	2	no	—
127	C₄²×C₄₁	—	2	1	no	—
128	C₄²×C₄₁	—	2	1	no	—
129	C₄²×C₄₁	—	2	1	no	—
130	C₄²×C₄₁	—	2	1	no	—
131	C₄²×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	2	no	—
133	C₂³×C₄₁	—	2	2	no	—
134	C₂³×C₄₁	—	2	2	no	—
135	C₂³×C₄₁	—	2	2	no	—
136	C₂³×C₄₁	—	2	2	no	—
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
140	Q₈×C₄₁	—	4	4	no	—
141	D₄×C₄₁	—	4	4	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	1	no	—
144	C₂×C₄×C₄₁	—	2	1	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	1	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	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	2	no	—
155	C₂×C₄×C₄₁	—	2	1	no	—
156	C₂×C₄×C₄₁	—	2	1	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	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	1	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	#131	1	2	yes	—
170	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₄₁	—	4	2	no	—
175	C₈×C₄₁	—	4	2	no	—
176	C₈×C₄₁	—	4	2	no	—
177	C₈×C₄₁	—	4	2	no	—
178	#23351	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	4	2	no	—
181	C₂²×C₄₁	—	4	2	no	—
182	C₂²×C₄₁	—	4	2	no	—
183	C₂²×C₄₁	—	4	2	no	—
184	C₂²×C₄₁	—	4	2	no	—
185	C₂²×C₄₁	—	4	2	no	—
186	C₂²×C₄₁	#518	1	1	yes	characteristic
187	C₂²×C₄₁	#520	1	2	yes	—
188	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
189	C₂²×C₄₁	#568	1	1	yes	characteristic
190	C₂²×C₄₁	#568	1	2	yes	—
191	C₄×C₄₁	—	2	2	no	—
192	C₄×C₄₁	—	4	2	no	—
193	C₄×C₄₁	—	4	1	no	—
194	C₄×C₄₁	—	4	1	no	—
195	C₄×C₄₁	—	4	1	no	—
196	C₄×C₄₁	—	4	1	no	—
197	C₄×C₄₁	—	4	1	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	—	4	2	no	—
200	C₄×C₄₁	H(3,𝔽₄)	1	1	yes	characteristic
201	C₄×C₄₁	#562	1	2	yes	—
202	C₄×C₄₁	#563	1	1	yes	characteristic
203	#2398	C₂×C₄₁	1	1	yes	characteristic
204	#1985	C₂×C₄₁	1	1	yes	characteristic, complemented
205	#1984	C₂×C₄₁	1	1	yes	characteristic, complemented
206	#1924	C₂×C₄₁	1	2	yes	complemented
207	#1923	C₂×C₄₁	1	2	yes	complemented
208	#1870	C₂×C₄₁	1	2	yes	—
209	#1851	C₂×C₄₁	1	2	yes	complemented
210	#1851	C₂×C₄₁	1	2	yes	complemented
211	#1832	C₂×C₄₁	1	2	yes	complemented
212	C₂×C₄₁	—	8	2	no	—
213	C₂×C₄₁	#2379	1	1	yes	characteristic
214	C₂×C₄₁	#2976	1	1	yes	characteristic
215	C₂×C₄₁	#2978	1	1	yes	characteristic
216	C₂×C₄₁	#2993	1	2	yes	—
217	C₂×C₄₁	#2995	1	2	yes	—
218	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
219	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
226	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
228	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
230	#400	C₄×C₄₁	1	1	yes	characteristic
231	#400	C₄×C₄₁	1	1	yes	characteristic
232	#397	C₄×C₄₁	1	2	yes	—
233	#394	C₄×C₄₁	1	1	yes	characteristic
234	#394	C₄×C₄₁	1	1	yes	characteristic
235	#393	C₄×C₄₁	1	2	yes	—
236	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
237	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
238	#376	C₂²×C₄₁	1	1	yes	characteristic
239	#336	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	C₄₁	#23351	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
247	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
249	C₂×M₁₆	—	4	2	no	—
250	C₂×M₁₆	—	4	2	no	—
251	C₂×M₁₆	—	4	2	no	—
252	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
253	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
254	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
255	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
256	C₄×Q₈	—	4	1	no	—
257	C₄×Q₈	—	4	1	no	—
258	C₄×D₄	—	4	1	no	—
259	C₄×D₄	—	4	1	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
269	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
273	C₄⋊C₈	—	4	2	no	—
274	C₄⋊C₈	—	4	2	no	—
275	C₄⋊C₈	—	4	1	no	—
276	C₄⋊C₈	—	4	1	no	—
277	C₂²⋊C₈	—	4	2	no	—
278	C₂²⋊C₈	—	4	2	no	—
279	C₂²⋊C₈	—	4	2	no	—
280	#97	—	4	1	no	—
281	C₄×C₈	—	4	1	no	—
282	#95	C₂×C₄×C₄₁	1	2	yes	—
283	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
284	#95	C₂×C₄×C₄₁	1	1	yes	characteristic
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	2	yes	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
311	M₁₆	—	4	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	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	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
349	Q₈	—	4	4	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	1	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	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	#131×C₄₁	1	2	yes	—
379	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
380	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
381	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
382	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	C₄₁×#518	1	1	yes	characteristic
395	C₂²	C₄₁×#520	1	2	yes	—
396	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
397	C₂²	C₄₁×#568	1	1	yes	characteristic
398	C₂²	C₄₁×#568	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	C₄₁×H(3,𝔽₄)	1	1	yes	characteristic
409	C₄	C₄₁×#562	1	2	yes	—
410	C₄	C₄₁×#563	1	1	yes	characteristic
411	C₂	—	8	2	no	—
412	C₂	C₄₁×#2379	1	1	yes	characteristic
413	C₂	C₄₁×#2976	1	1	yes	characteristic
414	C₂	C₄₁×#2978	1	1	yes	characteristic
415	C₂	C₄₁×#2993	1	2	yes	—
416	C₂	C₄₁×#2995	1	2	yes	—

	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	C₂²×D₄×C₄₁	C₂×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×#1984	C₂	semidirect
4. C₄₁×#1924	C₂	semidirect
5. C₄₁×#1923	C₂	semidirect
7. C₄₁×#1851	C₂	semidirect
8. C₄₁×#1851	C₂	semidirect
9. C₄₁×#1832	C₂	semidirect
178. #23351	C₄₁	direct (N × H)
204. #1985	C₂×C₄₁	semidirect
205. #1984	C₂×C₄₁	semidirect
206. #1924	C₂×C₄₁	semidirect
207. #1923	C₂×C₄₁	semidirect
209. #1851	C₂×C₄₁	semidirect
210. #1851	C₂×C₄₁	semidirect
211. #1832	C₂×C₄₁	semidirect
245. C₄₁	#23351	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×#2398	2
C₄₁×#1985	2
C₄₁×#1984	2
C₄₁×#1924	2
C₄₁×#1923	2
C₄₁×#1870	2
C₄₁×#1851	2
C₄₁×#1832	2
#23351	41

Subgroups — C41×#23351 #23799552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23351 #23799552