Subgroups — C₂×C₄₁×#2536 #23811095

Order 10496.

3526 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₄₁	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2536	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₁×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#394	C₂	1	2	yes	maximal
7	C₂×C₄₁×#388	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#380	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
13	C₂×C₂²⋊Q₈×C₄₁	—	2	16	no	—
14	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	16	yes	complemented
15	C₂×C₄×Q₈×C₄₁	—	2	8	no	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	8	yes	complemented
17	C₂×C₄×D₄×C₄₁	—	2	8	no	—
18	C₂×C₄×D₄×C₄₁	C₂²	1	8	yes	—
19	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
25	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
27	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#398	C₂²	1	16	yes	complemented
30	C₄₁×#394	C₂²	1	16	yes	—
31	C₄₁×#388	C₂²	1	32	yes	complemented
32	C₄₁×#382	C₂²	1	8	yes	complemented
33	C₄₁×#380	C₂²	1	16	yes	complemented
34	C₂×#95×C₄₁	C₂²	1	4	yes	—
35	C₂×#95×C₄₁	C₂²	1	2	yes	—
36	C₂×#95×C₄₁	C₂²	1	2	yes	—
37	C₂⁵×C₄₁	C₂³	1	2	yes	—
38	C₂²×Q₈×C₄₁	—	2	4	no	—
39	C₂²×Q₈×C₄₁	—	2	4	no	—
40	C₂²×Q₈×C₄₁	D₄	1	8	yes	complemented
41	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
42	C₂²×D₄×C₄₁	—	2	8	no	—
43	C₂²×D₄×C₄₁	—	2	4	no	—
44	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₄₁	—	2	8	no	—
46	C₂³×C₄×C₄₁	—	2	8	no	—
47	C₂³×C₄×C₄₁	—	2	8	no	—
48	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
49	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
51	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²⋊Q₈×C₄₁	—	2	64	no	—
57	C₄×Q₈×C₄₁	—	2	32	no	—
58	C₄×D₄×C₄₁	—	2	32	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
72	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
74	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
75	C₂×C₄²×C₄₁	—	2	8	no	—
76	C₂×C₄²×C₄₁	D₄	1	8	yes	—
77	C₂×C₄²×C₄₁	C₂³	1	8	yes	—
78	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
79	#95×C₄₁	C₂³	1	16	yes	—
80	#95×C₄₁	C₂³	1	8	yes	—
81	#95×C₄₁	C₂³	1	8	yes	—
82	C₂⁴×C₄₁	—	2	4	no	—
83	C₂⁴×C₄₁	—	2	4	no	—
84	C₂⁴×C₄₁	—	2	4	no	—
85	C₂⁴×C₄₁	—	2	4	no	—
86	C₂⁴×C₄₁	—	2	4	no	—
87	C₂⁴×C₄₁	—	2	4	no	—
88	C₂⁴×C₄₁	#41	1	8	yes	—
89	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
90	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
91	C₂×Q₈×C₄₁	—	2	32	no	—
92	C₂×Q₈×C₄₁	—	2	8	no	—
93	C₂×Q₈×C₄₁	—	2	8	no	—
94	C₂×Q₈×C₄₁	C₂×D₄	1	16	yes	complemented
95	C₂×D₄×C₄₁	—	2	32	no	—
96	C₂×D₄×C₄₁	—	2	16	no	—
97	C₂×D₄×C₄₁	—	2	8	no	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	4	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	—	2	8	no	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	4	no	—
106	C₂²×C₄×C₄₁	—	2	8	no	—
107	C₂²×C₄×C₄₁	—	2	8	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	8	no	—
110	C₂²×C₄×C₄₁	—	2	16	no	—
111	C₂²×C₄×C₄₁	—	2	16	no	—
112	C₂²×C₄×C₄₁	—	2	16	no	—
113	C₂²×C₄×C₄₁	—	4	32	no	—
114	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₄₁	#41	1	4	yes	—
120	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
121	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
127	C₄⋊C₄×C₄₁	—	2	8	no	—
128	C₄⋊C₄×C₄₁	—	2	16	no	—
129	C₄⋊C₄×C₄₁	—	2	8	no	—
130	C₄⋊C₄×C₄₁	—	2	16	no	—
131	C₄⋊C₄×C₄₁	—	2	32	no	—
132	C₂²⋊C₄×C₄₁	—	2	32	no	—
133	C₂²⋊C₄×C₄₁	—	2	16	no	—
134	C₂²⋊C₄×C₄₁	—	2	32	no	—
135	C₄²×C₄₁	—	2	16	no	—
136	C₄²×C₄₁	C₂×D₄	1	16	yes	—
137	C₂³×C₄₁	—	2	16	no	—
138	C₂³×C₄₁	—	2	16	no	—
139	C₂³×C₄₁	—	2	16	no	—
140	C₂³×C₄₁	—	2	4	no	—
141	C₂³×C₄₁	—	2	4	no	—
142	C₂³×C₄₁	—	2	4	no	—
143	C₂³×C₄₁	—	2	4	no	—
144	C₂³×C₄₁	—	2	4	no	—
145	C₂³×C₄₁	—	2	4	no	—
146	C₂³×C₄₁	—	4	8	no	—
147	C₂³×C₄₁	—	4	8	no	—
148	C₂³×C₄₁	—	4	8	no	—
149	C₂³×C₄₁	—	4	8	no	—
150	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
151	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
152	C₂³×C₄₁	C₂×#41	1	8	yes	—
153	C₂³×C₄₁	C₂×#41	1	2	yes	—
154	C₂³×C₄₁	C₂×#41	1	4	yes	—
155	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
156	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
157	Q₈×C₄₁	—	2	32	no	—
158	D₄×C₄₁	—	2	32	no	—
159	C₂×C₄×C₄₁	—	2	16	no	—
160	C₂×C₄×C₄₁	—	2	8	no	—
161	C₂×C₄×C₄₁	—	2	8	no	—
162	C₂×C₄×C₄₁	—	2	4	no	—
163	C₂×C₄×C₄₁	—	2	4	no	—
164	C₂×C₄×C₄₁	—	2	4	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	2	4	no	—
167	C₂×C₄×C₄₁	—	2	8	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	2	4	no	—
170	C₂×C₄×C₄₁	—	2	8	no	—
171	C₂×C₄×C₄₁	—	2	8	no	—
172	C₂×C₄×C₄₁	—	2	4	no	—
173	C₂×C₄×C₄₁	—	2	8	no	—
174	C₂×C₄×C₄₁	—	4	8	no	—
175	C₂×C₄×C₄₁	—	4	8	no	—
176	C₂×C₄×C₄₁	—	4	16	no	—
177	C₂×C₄×C₄₁	—	4	32	no	—
178	C₂×C₄×C₄₁	#121	1	16	yes	—
179	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
180	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
181	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
182	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
183	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
184	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
185	C₂×#2536	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₁	—	2	8	no	—
187	C₂²×C₄₁	—	2	8	no	—
188	C₂²×C₄₁	—	2	8	no	—
189	C₂²×C₄₁	—	4	4	no	—
190	C₂²×C₄₁	—	4	4	no	—
191	C₂²×C₄₁	—	4	4	no	—
192	C₂²×C₄₁	—	4	4	no	—
193	C₂²×C₄₁	—	4	32	no	—
194	C₂²×C₄₁	C₂×#121	1	4	yes	—
195	C₂²×C₄₁	#525	1	4	yes	—
196	C₂²×C₄₁	#536	1	4	yes	—
197	C₂²×C₄₁	#548	1	8	yes	—
198	C₂²×C₄₁	#552	1	8	yes	—
199	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
200	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
201	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
202	C₂²×C₄₁	C₂²×#41	1	2	yes	—
203	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
204	C₄×C₄₁	—	2	8	no	—
205	C₄×C₄₁	—	2	4	no	—
206	C₄×C₄₁	—	2	4	no	—
207	C₄×C₄₁	—	4	4	no	—
208	C₄×C₄₁	—	4	4	no	—
209	C₄×C₄₁	—	4	8	no	—
210	C₄×C₄₁	C₂×#121	1	8	yes	—
211	C₂²×C₂²⋊Q₈	C₂×C₄₁	1	2	yes	complemented
212	C₂²×C₄×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic
214	#2536	C₂×C₄₁	1	16	yes	direct product factor
215	C₂×#398	C₂×C₄₁	1	2	yes	complemented
216	C₂×#394	C₂×C₄₁	1	2	yes	—
217	C₂×#388	C₂×C₄₁	1	4	yes	complemented
218	C₂×#382	C₂×C₄₁	1	1	yes	characteristic, complemented
219	C₂×#380	C₂×C₄₁	1	2	yes	complemented
220	C₂×C₄₁	—	4	8	no	—
221	C₂×C₄₁	#2536	1	8	yes	direct product factor
222	C₂×C₄₁	C₂²×#121	1	1	yes	characteristic
223	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
224	C₂×C₄₁	C₂×#536	1	1	yes	characteristic
225	C₂×C₄₁	C₂×#548	1	2	yes	—
226	C₂×C₄₁	C₂×#552	1	2	yes	—
227	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
228	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
229	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
230	C₂×C₂²⋊Q₈	—	2	16	no	—
231	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	16	yes	complemented
232	C₂×C₄×Q₈	—	2	8	no	—
233	C₂×C₄×Q₈	C₂²×C₄₁	1	8	yes	complemented
234	C₂×C₄×D₄	—	2	8	no	—
235	C₂×C₄×D₄	C₂²×C₄₁	1	8	yes	—
236	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
237	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
239	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
244	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
245	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
246	#398	C₂²×C₄₁	1	16	yes	complemented
247	#394	C₂²×C₄₁	1	16	yes	—
248	#388	C₂²×C₄₁	1	32	yes	complemented
249	#382	C₂²×C₄₁	1	8	yes	complemented
250	#380	C₂²×C₄₁	1	16	yes	complemented
251	C₂×#95	C₂²×C₄₁	1	2	yes	—
252	C₂×#95	C₂²×C₄₁	1	4	yes	—
253	C₂×#95	C₂²×C₄₁	1	2	yes	—
254	C₄₁	C₂×#2536	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁵	C₂³×C₄₁	1	2	yes	—
256	C₂²×Q₈	—	2	4	no	—
257	C₂²×Q₈	—	2	4	no	—
258	C₂²×Q₈	D₄×C₄₁	1	8	yes	complemented
259	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
260	C₂²×D₄	—	2	8	no	—
261	C₂²×D₄	—	2	4	no	—
262	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
263	C₂³×C₄	—	2	8	no	—
264	C₂³×C₄	—	2	8	no	—
265	C₂³×C₄	—	2	8	no	—
266	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
267	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
268	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
269	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
270	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
271	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
274	C₂²⋊Q₈	—	2	64	no	—
275	C₄×Q₈	—	2	32	no	—
276	C₄×D₄	—	2	32	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	8	no	—
279	C₂×C₄⋊C₄	—	2	4	no	—
280	C₂×C₄⋊C₄	—	2	8	no	—
281	C₂×C₄⋊C₄	—	2	16	no	—
282	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
286	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	—
287	C₂×C₂²⋊C₄	—	2	16	no	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	—	2	16	no	—
290	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
293	C₂×C₄²	—	2	8	no	—
294	C₂×C₄²	D₄×C₄₁	1	8	yes	—
295	C₂×C₄²	C₂³×C₄₁	1	8	yes	—
296	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
297	#95	C₂³×C₄₁	1	16	yes	—
298	#95	C₂³×C₄₁	1	8	yes	—
299	#95	C₂³×C₄₁	1	8	yes	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	#41×C₄₁	1	8	yes	—
307	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
308	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
309	C₂×Q₈	—	2	32	no	—
310	C₂×Q₈	—	2	8	no	—
311	C₂×Q₈	—	2	8	no	—
312	C₂×Q₈	C₂×D₄×C₄₁	1	16	yes	complemented
313	C₂×D₄	—	2	32	no	—
314	C₂×D₄	—	2	16	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	16	no	—
329	C₂²×C₄	—	2	16	no	—
330	C₂²×C₄	—	2	16	no	—
331	C₂²×C₄	—	4	32	no	—
332	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
333	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
334	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
335	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
337	C₂²×C₄	#41×C₄₁	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
344	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	16	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	16	no	—
349	C₄⋊C₄	—	2	32	no	—
350	C₂²⋊C₄	—	2	32	no	—
351	C₂²⋊C₄	—	2	16	no	—
352	C₂²⋊C₄	—	2	32	no	—
353	C₄²	—	2	16	no	—
354	C₄²	C₂×D₄×C₄₁	1	16	yes	—
355	C₂³	—	2	16	no	—
356	C₂³	—	2	16	no	—
357	C₂³	—	2	16	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	4	8	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	8	no	—
367	C₂³	—	4	8	no	—
368	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
369	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
370	C₂³	C₂×#41×C₄₁	1	8	yes	—
371	C₂³	C₂×#41×C₄₁	1	2	yes	—
372	C₂³	C₂×#41×C₄₁	1	4	yes	—
373	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
374	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
375	Q₈	—	2	32	no	—
376	D₄	—	2	32	no	—
377	C₂×C₄	—	2	16	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	16	no	—
395	C₂×C₄	—	4	32	no	—
396	C₂×C₄	#121×C₄₁	1	16	yes	—
397	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
398	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
399	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
400	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
401	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
402	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	4	32	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	C₂×#121×C₄₁	1	4	yes	—
412	C₂²	C₄₁×#525	1	4	yes	—
413	C₂²	C₄₁×#536	1	4	yes	—
414	C₂²	C₄₁×#548	1	8	yes	—
415	C₂²	C₄₁×#552	1	8	yes	—
416	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
417	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
418	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
419	C₂²	C₂²×#41×C₄₁	1	2	yes	—
420	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
421	C₄	—	2	8	no	—
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	8	no	—
427	C₄	C₂×#121×C₄₁	1	8	yes	—
428	C₂	—	4	8	no	—
429	C₂	C₄₁×#2536	1	8	yes	direct product factor
430	C₂	C₂²×#121×C₄₁	1	1	yes	characteristic
431	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
432	C₂	C₂×C₄₁×#536	1	1	yes	characteristic
433	C₂	C₂×C₄₁×#548	1	2	yes	—
434	C₂	C₂×C₄₁×#552	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊Q₈×C₄₁	C₂	semidirect
2. C₂²×C₄×Q₈×C₄₁	C₂	semidirect
4. C₄₁×#2536	C₂	direct (N × H)
5. C₂×C₄₁×#398	C₂	semidirect
7. C₂×C₄₁×#388	C₂	semidirect
8. C₂×C₄₁×#382	C₂	semidirect
9. C₂×C₄₁×#380	C₂	semidirect
14. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
16. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
29. C₄₁×#398	C₂²	semidirect
31. C₄₁×#388	C₂²	semidirect
32. C₄₁×#382	C₂²	semidirect
33. C₄₁×#380	C₂²	semidirect
40. C₂²×Q₈×C₄₁	D₄	semidirect
94. C₂×Q₈×C₄₁	C₂×D₄	semidirect
185. C₂×#2536	C₄₁	direct (N × H)
211. C₂²×C₂²⋊Q₈	C₂×C₄₁	semidirect
212. C₂²×C₄×Q₈	C₂×C₄₁	semidirect
214. #2536	C₂×C₄₁	direct (N × H)
215. C₂×#398	C₂×C₄₁	semidirect
217. C₂×#388	C₂×C₄₁	semidirect
218. C₂×#382	C₂×C₄₁	semidirect
219. C₂×#380	C₂×C₄₁	semidirect
221. C₂×C₄₁	#2536	direct (N × H)
231. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
233. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
246. #398	C₂²×C₄₁	semidirect
248. #388	C₂²×C₄₁	semidirect
249. #382	C₂²×C₄₁	semidirect
250. #380	C₂²×C₄₁	semidirect
254. C₄₁	C₂×#2536	direct (N × H)
258. C₂²×Q₈	D₄×C₄₁	semidirect
312. C₂×Q₈	C₂×D₄×C₄₁	semidirect
429. C₂	C₄₁×#2536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₄₁	2
C₂²×C₄×Q₈×C₄₁	2
C₂²×C₄×D₄×C₄₁	2
C₄₁×#2536	2
C₂×C₄₁×#398	2
C₂×C₄₁×#394	2
C₂×C₄₁×#388	2
C₂×C₄₁×#382	2
C₂×C₄₁×#380	2
C₂×#2536	41

Subgroups — C2×C41×#2536 #23811095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2536 #23811095