Subgroups — C₄₁×#22700 #23798901

Order 10496.

1020 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#436	C₂	1	2	yes	maximal
2	C₄²×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1939	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1851	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1797	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1728	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₄₁	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₄₁	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₄₁	C₄	1	1	yes	characteristic
12	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
14	C₄₁×#436	—	2	8	no	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	—
18	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
20	C₄×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊C₄×C₄₁	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₄₁	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₄³×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#336	C₂²	1	1	yes	characteristic
28	C₄₁×#336	C₂²	1	1	yes	characteristic
29	C₄₁×#336	C₂²	1	2	yes	—
30	C₄₁×#336	C₂²	1	2	yes	—
31	C₄₁×#336	C₂²	1	4	yes	—
32	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
36	C₂×M₁₆×C₄₁	—	2	8	no	—
37	C₂×M₁₆×C₄₁	—	2	8	no	—
38	C₂×M₁₆×C₄₁	—	4	4	no	—
39	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
40	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
42	C₄×D₄×C₄₁	—	2	4	no	—
43	C₄×D₄×C₄₁	—	2	4	no	—
44	C₄×D₄×C₄₁	D₄	1	4	yes	—
45	C₄×D₄×C₄₁	Q₈	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₁	—	4	4	no	—
53	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₁	—	2	4	no	—
64	C₄⋊C₈×C₄₁	—	2	4	no	—
65	C₄⋊C₈×C₄₁	—	4	4	no	—
66	C₂²⋊C₈×C₄₁	—	2	8	no	—
67	C₄×C₈×C₄₁	—	2	4	no	—
68	#95×C₄₁	C₂×C₄	1	2	yes	—
69	#95×C₄₁	C₂×C₄	1	2	yes	—
70	#95×C₄₁	C₂×C₄	1	2	yes	—
71	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
72	C₂×D₄×C₄₁	—	2	2	no	—
73	C₂×D₄×C₄₁	—	2	2	no	—
74	C₂×D₄×C₄₁	C₄⋊C₄	1	4	yes	—
75	C₂²×C₄×C₄₁	—	2	4	no	—
76	C₂²×C₄×C₄₁	—	2	4	no	—
77	C₂²×C₄×C₄₁	—	2	4	no	—
78	C₂²×C₄×C₄₁	—	2	4	no	—
79	C₂²×C₄×C₄₁	—	2	4	no	—
80	C₂²×C₄×C₄₁	—	4	2	no	—
81	C₂²×C₄×C₄₁	—	4	2	no	—
82	C₂²×C₄×C₄₁	—	4	2	no	—
83	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
95	M₁₆×C₄₁	—	4	16	no	—
96	C₂×C₈×C₄₁	—	2	2	no	—
97	C₂×C₈×C₄₁	—	2	2	no	—
98	C₂×C₈×C₄₁	—	2	2	no	—
99	C₂×C₈×C₄₁	—	2	4	no	—
100	C₂×C₈×C₄₁	—	2	2	no	—
101	C₂×C₈×C₄₁	—	2	4	no	—
102	C₂×C₈×C₄₁	—	2	2	no	—
103	C₂×C₈×C₄₁	—	2	4	no	—
104	C₂×C₈×C₄₁	#41	1	4	yes	—
105	C₄⋊C₄×C₄₁	—	2	2	no	—
106	C₄⋊C₄×C₄₁	C₄⋊C₄	1	4	yes	—
107	C₄⋊C₄×C₄₁	M₁₆	1	4	yes	complemented
108	C₂²⋊C₄×C₄₁	—	2	4	no	—
109	C₂²⋊C₄×C₄₁	—	2	4	no	—
110	C₂²⋊C₄×C₄₁	C₄⋊C₄	1	8	yes	—
111	C₄²×C₄₁	—	2	2	no	—
112	C₄²×C₄₁	—	2	2	no	—
113	C₄²×C₄₁	—	2	2	no	—
114	C₄²×C₄₁	—	2	4	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	4	2	no	—
117	C₄²×C₄₁	—	4	2	no	—
118	C₄²×C₄₁	—	4	1	no	—
119	C₄²×C₄₁	M₁₆	1	4	yes	complemented
120	C₄²×C₄₁	C₂×D₄	1	2	yes	—
121	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
122	C₂³×C₄₁	—	2	2	no	—
123	C₂³×C₄₁	—	2	2	no	—
124	C₂³×C₄₁	—	2	2	no	—
125	C₂³×C₄₁	—	2	2	no	—
126	C₂³×C₄₁	—	2	2	no	—
127	C₂³×C₄₁	—	2	2	no	—
128	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
129	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
130	D₄×C₄₁	—	2	8	no	—
131	C₂×C₄×C₄₁	—	2	1	no	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	1	no	—
134	C₂×C₄×C₄₁	—	2	1	no	—
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	2	no	—
137	C₂×C₄×C₄₁	—	2	1	no	—
138	C₂×C₄×C₄₁	—	2	1	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	1	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	8	no	—
144	C₂×C₄×C₄₁	—	2	8	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	1	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	—	4	8	no	—
152	C₂×C₄×C₄₁	—	4	8	no	—
153	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
155	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
157	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
158	C₂×C₄×C₄₁	C₂×M₁₆	1	4	yes	—
159	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
160	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₄₁	#131	1	2	yes	—
162	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
165	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
166	C₈×C₄₁	—	2	4	no	—
167	C₈×C₄₁	—	4	2	no	—
168	C₈×C₄₁	—	4	4	no	—
169	#22700	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₁	—	2	4	no	—
171	C₂²×C₄₁	—	2	4	no	—
172	C₂²×C₄₁	—	2	4	no	—
173	C₂²×C₄₁	—	4	2	no	—
174	C₂²×C₄₁	—	4	2	no	—
175	C₂²×C₄₁	—	4	2	no	—
176	C₂²×C₄₁	—	4	2	no	—
177	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
179	C₂²×C₄₁	#518	1	1	yes	characteristic
180	C₂²×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
181	C₂²×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
182	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
183	C₂²×C₄₁	#568	1	1	yes	characteristic
184	C₄×C₄₁	—	2	4	no	—
185	C₄×C₄₁	—	2	2	no	—
186	C₄×C₄₁	—	2	2	no	—
187	C₄×C₄₁	—	2	2	no	—
188	C₄×C₄₁	—	2	4	no	—
189	C₄×C₄₁	—	2	2	no	—
190	C₄×C₄₁	—	4	1	no	—
191	C₄×C₄₁	—	4	2	no	—
192	C₄×C₄₁	#423	1	4	yes	—
193	C₄×C₄₁	#546	1	2	yes	—
194	C₄×C₄₁	#554	1	2	yes	—
195	C₂×#436	C₂×C₄₁	1	2	yes	—
196	C₄²×D₄	C₂×C₄₁	1	1	yes	characteristic
197	#1939	C₂×C₄₁	1	2	yes	complemented
198	#1851	C₂×C₄₁	1	4	yes	complemented
199	#1831	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1797	C₂×C₄₁	1	2	yes	complemented
201	C₄×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#1728	C₂×C₄₁	1	2	yes	complemented
203	C₂×C₄₁	—	4	4	no	—
204	C₂×C₄₁	#2349	1	1	yes	characteristic
205	C₂×C₄₁	C₂×#423	1	1	yes	characteristic
206	C₂×C₄₁	#2906	1	1	yes	characteristic
207	C₂×C₄₁	#2965	1	1	yes	characteristic
208	C₂×C₄₁	#2971	1	1	yes	characteristic
209	C₂×C₄₁	#2974	1	1	yes	characteristic
210	C₂×C₄₁	#2975	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₄₁	1	4	yes	—
212	C₂×C₄×D₄	C₄×C₄₁	1	1	yes	characteristic
213	C₂×C₄×D₄	C₄×C₄₁	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
216	#436	—	2	8	no	—
217	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
221	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
222	C₄×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
225	C₄×C₂²⋊C₄	C₄×C₄₁	1	2	yes	—
226	C₄×C₂²⋊C₄	C₄×C₄₁	1	2	yes	—
227	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
228	C₄³	C₂²×C₄₁	1	1	yes	characteristic
229	#336	C₂²×C₄₁	1	1	yes	characteristic
230	#336	C₂²×C₄₁	1	2	yes	—
231	#336	C₂²×C₄₁	1	2	yes	—
232	#336	C₂²×C₄₁	1	4	yes	—
233	#336	C₂²×C₄₁	1	1	yes	characteristic
234	C₄₁	#22700	1	1	yes	characteristic, direct product factor, Sylow
235	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
237	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
238	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
239	C₂×M₁₆	—	2	8	no	—
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	—	4	4	no	—
242	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
243	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
244	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
245	C₄×D₄	—	2	4	no	—
246	C₄×D₄	—	2	4	no	—
247	C₄×D₄	D₄×C₄₁	1	4	yes	—
248	C₄×D₄	Q₈×C₄₁	1	4	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
255	C₂×C₄²	—	4	4	no	—
256	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
258	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
260	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
261	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
265	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
266	C₄⋊C₈	—	2	4	no	—
267	C₄⋊C₈	—	2	4	no	—
268	C₄⋊C₈	—	4	4	no	—
269	C₂²⋊C₈	—	2	8	no	—
270	C₄×C₈	—	2	4	no	—
271	#95	C₂×C₄×C₄₁	1	2	yes	—
272	#95	C₂×C₄×C₄₁	1	2	yes	—
273	#95	C₂×C₄×C₄₁	1	2	yes	—
274	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	C₄⋊C₄×C₄₁	1	4	yes	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
296	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
298	M₁₆	—	4	16	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	#41×C₄₁	1	4	yes	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₄⋊C₄×C₄₁	1	4	yes	—
310	C₄⋊C₄	M₁₆×C₄₁	1	4	yes	complemented
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	C₄⋊C₄×C₄₁	1	8	yes	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	4	2	no	—
321	C₄²	—	4	1	no	—
322	C₄²	M₁₆×C₄₁	1	4	yes	complemented
323	C₄²	C₂×D₄×C₄₁	1	2	yes	—
324	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
332	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
333	D₄	—	2	8	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
357	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
358	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
359	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
360	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
361	C₂×C₄	C₂×M₁₆×C₄₁	1	4	yes	—
362	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
363	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
364	C₂×C₄	#131×C₄₁	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
368	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
369	C₈	—	2	4	no	—
370	C₈	—	4	4	no	—
371	C₈	—	4	2	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
380	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
381	C₂²	C₄₁×#518	1	1	yes	characteristic
382	C₂²	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
383	C₂²	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
384	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
385	C₂²	C₄₁×#568	1	1	yes	characteristic
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	C₄₁×#423	1	4	yes	—
395	C₄	C₄₁×#546	1	2	yes	—
396	C₄	C₄₁×#554	1	2	yes	—
397	C₂	—	4	4	no	—
398	C₂	C₄₁×#2349	1	1	yes	characteristic
399	C₂	C₂×C₄₁×#423	1	1	yes	characteristic
400	C₂	C₄₁×#2906	1	1	yes	characteristic
401	C₂	C₄₁×#2965	1	1	yes	characteristic
402	C₂	C₄₁×#2971	1	1	yes	characteristic
403	C₂	C₄₁×#2974	1	1	yes	characteristic
404	C₂	C₄₁×#2975	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	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
3. C₄₁×#1939	C₂	semidirect
4. C₄₁×#1851	C₂	semidirect
5. C₄₁×#1831	C₂	semidirect
6. C₄₁×#1797	C₂	semidirect
7. C₄×C₄⋊C₈×C₄₁	C₂	semidirect
8. C₄₁×#1728	C₂	semidirect
107. C₄⋊C₄×C₄₁	M₁₆	semidirect
119. C₄²×C₄₁	M₁₆	semidirect
169. #22700	C₄₁	direct (N × H)
197. #1939	C₂×C₄₁	semidirect
198. #1851	C₂×C₄₁	semidirect
199. #1831	C₂×C₄₁	semidirect
200. #1797	C₂×C₄₁	semidirect
201. C₄×C₄⋊C₈	C₂×C₄₁	semidirect
202. #1728	C₂×C₄₁	semidirect
234. C₄₁	#22700	direct (N × H)
310. C₄⋊C₄	M₁₆×C₄₁	semidirect
322. C₄²	M₁₆×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×#436	2
C₄²×D₄×C₄₁	2
C₄₁×#1939	2
C₄₁×#1851	2
C₄₁×#1831	2
C₄₁×#1797	2
C₄×C₄⋊C₈×C₄₁	2
C₄₁×#1728	2
#22700	41

Subgroups — C41×#22700 #23798901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22700 #23798901