Subgroups — C₄₁×#36711 #23812912

Order 10496.

2422 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2848	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2694	C₂	1	8	yes	maximal, complemented
5	C₄₁×#2674	C₂	1	8	yes	maximal, complemented
6	C₄₁×#2626	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2583	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2482	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2482	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2435	C₂	1	2	yes	maximal
11	C₄₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#544	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
16	C₂×#125×C₄₁	C₂²	1	4	yes	complemented
17	C₂×#124×C₄₁	C₂²	1	4	yes	—
18	C₂×#123×C₄₁	—	2	8	no	—
19	C₂×#123×C₄₁	C₂²	1	8	yes	—
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
23	C₂×#117×C₄₁	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#399	C₂²	1	4	yes	complemented
30	C₄₁×#399	C₂²	1	4	yes	complemented
31	C₄₁×#399	C₂²	1	4	yes	complemented
32	C₄₁×#398	C₂²	1	4	yes	complemented
33	C₄₁×#397	C₂²	1	4	yes	complemented
34	C₄₁×#397	C₂²	1	4	yes	complemented
35	C₄₁×#396	C₂²	1	8	yes	complemented
36	C₄₁×#395	C₂²	1	4	yes	complemented
37	C₄₁×#394	C₂²	1	8	yes	—
38	C₄₁×#393	C₂²	1	4	yes	complemented
39	C₄₁×#390	C₂²	1	4	yes	—
40	C₄₁×#389	C₂²	1	8	yes	complemented
41	C₄₁×#388	C₂²	1	8	yes	complemented
42	C₄₁×#388	C₂²	1	8	yes	complemented
43	C₄₁×#387	C₂²	1	8	yes	complemented
44	C₄₁×#385	C₂²	1	4	yes	—
45	C₄₁×#385	C₂²	1	4	yes	—
46	C₄₁×#385	C₂²	1	8	yes	complemented
47	C₄₁×#381	C₂²	1	2	yes	—
48	C₄₁×#380	C₂²	1	2	yes	—
49	C₄₁×#380	C₂²	1	4	yes	complemented
50	C₄₁×#379	C₂²	1	4	yes	—
51	C₄₁×#379	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
53	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
54	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
57	C₂²×D₄×C₄₁	—	2	4	no	—
58	C₂²×D₄×C₄₁	—	4	4	no	—
59	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
60	C₂³×C₄×C₄₁	—	2	4	no	—
61	C₂³×C₄×C₄₁	—	4	4	no	—
62	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₄₁	—	2	16	no	—
69	#125×C₄₁	—	2	16	no	—
70	#124×C₄₁	—	4	8	no	—
71	#123×C₄₁	—	2	32	no	—
72	C₂²⋊Q₈×C₄₁	—	2	8	no	—
73	C₂²⋊Q₈×C₄₁	—	2	8	no	—
74	C₂²⋊Q₈×C₄₁	—	4	8	no	—
75	#117×C₄₁	—	2	8	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
101	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
102	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
103	#95×C₄₁	C₂³	1	4	yes	—
104	#95×C₄₁	C₂³	1	4	yes	—
105	#95×C₄₁	C₂³	1	8	yes	—
106	#95×C₄₁	C₂³	1	4	yes	—
107	#95×C₄₁	C₂³	1	4	yes	—
108	#95×C₄₁	C₂³	1	8	yes	—
109	C₂⁴×C₄₁	—	2	2	no	—
110	C₂⁴×C₄₁	—	2	4	no	—
111	C₂⁴×C₄₁	—	2	2	no	—
112	C₂⁴×C₄₁	—	2	4	no	—
113	C₂⁴×C₄₁	—	2	4	no	—
114	C₂⁴×C₄₁	—	4	2	no	—
115	C₂⁴×C₄₁	—	4	2	no	—
116	C₂⁴×C₄₁	—	4	2	no	—
117	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
118	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
119	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₄₁	—	2	4	no	—
121	C₂×Q₈×C₄₁	—	2	4	no	—
122	C₂×Q₈×C₄₁	—	4	4	no	—
123	C₂×Q₈×C₄₁	—	4	4	no	—
124	C₂×D₄×C₄₁	—	2	8	no	—
125	C₂×D₄×C₄₁	—	2	8	no	—
126	C₂×D₄×C₄₁	—	4	4	no	—
127	C₂×D₄×C₄₁	—	4	16	no	—
128	C₂²×C₄×C₄₁	—	2	4	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	8	no	—
132	C₂²×C₄×C₄₁	—	2	8	no	—
133	C₂²×C₄×C₄₁	—	4	2	no	—
134	C₂²×C₄×C₄₁	—	4	4	no	—
135	C₂²×C₄×C₄₁	—	4	2	no	—
136	C₂²×C₄×C₄₁	—	4	2	no	—
137	C₂²×C₄×C₄₁	—	4	2	no	—
138	C₂²×C₄×C₄₁	—	4	16	no	—
139	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
143	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
150	C₄⋊C₄×C₄₁	—	2	8	no	—
151	C₄⋊C₄×C₄₁	—	2	4	no	—
152	C₄⋊C₄×C₄₁	—	2	4	no	—
153	C₄⋊C₄×C₄₁	—	2	4	no	—
154	C₄⋊C₄×C₄₁	—	2	4	no	—
155	C₄⋊C₄×C₄₁	—	2	8	no	—
156	C₄⋊C₄×C₄₁	—	2	8	no	—
157	C₄⋊C₄×C₄₁	—	4	8	no	—
158	C₄⋊C₄×C₄₁	—	4	4	no	—
159	C₄⋊C₄×C₄₁	—	4	8	no	—
160	C₄⋊C₄×C₄₁	C₂×D₄	1	16	yes	—
161	C₂²⋊C₄×C₄₁	—	2	8	no	—
162	C₂²⋊C₄×C₄₁	—	2	16	no	—
163	C₂²⋊C₄×C₄₁	—	2	8	no	—
164	C₂²⋊C₄×C₄₁	—	2	8	no	—
165	C₂²⋊C₄×C₄₁	—	2	8	no	—
166	C₂²⋊C₄×C₄₁	—	2	8	no	—
167	C₂²⋊C₄×C₄₁	—	4	8	no	—
168	C₂²⋊C₄×C₄₁	—	4	8	no	—
169	C₂²⋊C₄×C₄₁	—	4	8	no	—
170	C₄²×C₄₁	—	2	8	no	—
171	C₄²×C₄₁	—	4	4	no	—
172	C₂³×C₄₁	—	2	2	no	—
173	C₂³×C₄₁	—	2	2	no	—
174	C₂³×C₄₁	—	2	8	no	—
175	C₂³×C₄₁	—	2	2	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	—	2	4	no	—
178	C₂³×C₄₁	—	2	4	no	—
179	C₂³×C₄₁	—	2	2	no	—
180	C₂³×C₄₁	—	2	4	no	—
181	C₂³×C₄₁	—	2	4	no	—
182	C₂³×C₄₁	—	2	4	no	—
183	C₂³×C₄₁	—	4	16	no	—
184	C₂³×C₄₁	—	4	4	no	—
185	C₂³×C₄₁	—	4	4	no	—
186	C₂³×C₄₁	—	4	4	no	—
187	C₂³×C₄₁	—	4	4	no	—
188	C₂³×C₄₁	—	4	4	no	—
189	C₂³×C₄₁	—	8	8	no	—
190	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
191	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
192	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
193	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
194	Q₈×C₄₁	—	8	4	no	—
195	Q₈×C₄₁	—	8	4	no	—
196	D₄×C₄₁	—	4	16	no	—
197	C₂×C₄×C₄₁	—	2	8	no	—
198	C₂×C₄×C₄₁	—	2	4	no	—
199	C₂×C₄×C₄₁	—	2	4	no	—
200	C₂×C₄×C₄₁	—	2	4	no	—
201	C₂×C₄×C₄₁	—	2	4	no	—
202	C₂×C₄×C₄₁	—	2	4	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	8	no	—
206	C₂×C₄×C₄₁	—	2	8	no	—
207	C₂×C₄×C₄₁	—	2	4	no	—
208	C₂×C₄×C₄₁	—	2	8	no	—
209	C₂×C₄×C₄₁	—	2	8	no	—
210	C₂×C₄×C₄₁	—	2	8	no	—
211	C₂×C₄×C₄₁	—	2	4	no	—
212	C₂×C₄×C₄₁	—	4	4	no	—
213	C₂×C₄×C₄₁	—	4	4	no	—
214	C₂×C₄×C₄₁	—	4	16	no	—
215	C₂×C₄×C₄₁	—	4	4	no	—
216	C₂×C₄×C₄₁	—	4	4	no	—
217	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
220	#36711	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₄₁	—	2	2	no	—
222	C₂²×C₄₁	—	2	2	no	—
223	C₂²×C₄₁	—	2	8	no	—
224	C₂²×C₄₁	—	2	4	no	—
225	C₂²×C₄₁	—	2	8	no	—
226	C₂²×C₄₁	—	4	16	no	—
227	C₂²×C₄₁	—	4	2	no	—
228	C₂²×C₄₁	—	4	2	no	—
229	C₂²×C₄₁	—	4	4	no	—
230	C₂²×C₄₁	—	4	2	no	—
231	C₂²×C₄₁	—	4	2	no	—
232	C₂²×C₄₁	—	4	2	no	—
233	C₂²×C₄₁	—	4	8	no	—
234	C₂²×C₄₁	—	8	8	no	—
235	C₂²×C₄₁	#536	1	4	yes	—
236	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
237	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
238	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
239	C₂²×C₄₁	#585	1	2	yes	—
240	C₄×C₄₁	—	2	4	no	—
241	C₄×C₄₁	—	2	4	no	—
242	C₄×C₄₁	—	2	4	no	—
243	C₄×C₄₁	—	4	2	no	—
244	C₄×C₄₁	—	4	4	no	—
245	C₄×C₄₁	—	4	4	no	—
246	C₄×C₄₁	—	4	2	no	—
247	C₄×C₄₁	—	4	8	no	—
248	C₂×#544	C₂×C₄₁	1	1	yes	characteristic, complemented
249	C₂²×#123	C₂×C₄₁	1	1	yes	characteristic
250	#2848	C₂×C₄₁	1	2	yes	complemented
251	#2694	C₂×C₄₁	1	8	yes	complemented
252	#2674	C₂×C₄₁	1	8	yes	complemented
253	#2626	C₂×C₄₁	1	2	yes	complemented
254	#2583	C₂×C₄₁	1	2	yes	complemented
255	#2482	C₂×C₄₁	1	2	yes	complemented
256	#2482	C₂×C₄₁	1	2	yes	complemented
257	#2435	C₂×C₄₁	1	2	yes	—
258	#2313	C₂×C₄₁	1	1	yes	characteristic, complemented
259	C₂×C₄₁	—	2	4	no	—
260	C₂×C₄₁	—	4	4	no	—
261	C₂×C₄₁	—	8	2	no	—
262	C₂×C₄₁	C₂×#536	1	1	yes	characteristic
263	C₂×C₄₁	#3484	1	1	yes	characteristic
264	C₂×C₄₁	#3487	1	1	yes	characteristic
265	C₂×C₄₁	#3535	1	4	yes	—
266	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
267	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
268	#544	—	2	8	no	—
269	C₂×C₄⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
270	C₂×#125	C₂²×C₄₁	1	4	yes	complemented
271	C₂×#124	C₂²×C₄₁	1	4	yes	—
272	C₂×#123	—	2	8	no	—
273	C₂×#123	C₂²×C₄₁	1	8	yes	—
274	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
275	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
276	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
277	C₂×#117	C₂²×C₄₁	1	2	yes	—
278	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
282	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
283	#399	C₂²×C₄₁	1	4	yes	complemented
284	#399	C₂²×C₄₁	1	4	yes	complemented
285	#399	C₂²×C₄₁	1	4	yes	complemented
286	#398	C₂²×C₄₁	1	4	yes	complemented
287	#397	C₂²×C₄₁	1	4	yes	complemented
288	#397	C₂²×C₄₁	1	4	yes	complemented
289	#396	C₂²×C₄₁	1	8	yes	complemented
290	#395	C₂²×C₄₁	1	4	yes	complemented
291	#394	C₂²×C₄₁	1	8	yes	—
292	#393	C₂²×C₄₁	1	4	yes	complemented
293	#390	C₂²×C₄₁	1	4	yes	—
294	#389	C₂²×C₄₁	1	8	yes	complemented
295	#388	C₂²×C₄₁	1	8	yes	complemented
296	#388	C₂²×C₄₁	1	8	yes	complemented
297	#387	C₂²×C₄₁	1	8	yes	complemented
298	#385	C₂²×C₄₁	1	4	yes	—
299	#385	C₂²×C₄₁	1	4	yes	—
300	#385	C₂²×C₄₁	1	8	yes	complemented
301	#381	C₂²×C₄₁	1	2	yes	—
302	#380	C₂²×C₄₁	1	2	yes	—
303	#380	C₂²×C₄₁	1	4	yes	complemented
304	#379	C₂²×C₄₁	1	4	yes	—
305	#379	C₂²×C₄₁	1	4	yes	—
306	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
307	C₄₁	#36711	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
309	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
311	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
312	C₂²×D₄	—	2	4	no	—
313	C₂²×D₄	—	4	4	no	—
314	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	4	4	no	—
317	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
318	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
323	C₄⋊Q₈	—	2	16	no	—
324	#125	—	2	16	no	—
325	#124	—	4	8	no	—
326	#123	—	2	32	no	—
327	C₂²⋊Q₈	—	2	8	no	—
328	C₂²⋊Q₈	—	2	8	no	—
329	C₂²⋊Q₈	—	4	8	no	—
330	#117	—	2	8	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
333	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
334	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
342	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
343	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	—	2	4	no	—
347	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
356	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
357	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
358	#95	C₂³×C₄₁	1	4	yes	—
359	#95	C₂³×C₄₁	1	4	yes	—
360	#95	C₂³×C₄₁	1	8	yes	—
361	#95	C₂³×C₄₁	1	4	yes	—
362	#95	C₂³×C₄₁	1	4	yes	—
363	#95	C₂³×C₄₁	1	8	yes	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	4	2	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
373	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
374	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	—	4	4	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	16	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	16	no	—
394	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
398	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	8	no	—
414	C₄⋊C₄	—	4	8	no	—
415	C₄⋊C₄	C₂×D₄×C₄₁	1	16	yes	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	2	16	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	4	8	no	—
423	C₂²⋊C₄	—	4	8	no	—
424	C₂²⋊C₄	—	4	8	no	—
425	C₄²	—	2	8	no	—
426	C₄²	—	4	4	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	4	16	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	8	8	no	—
445	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
446	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
447	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
448	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
449	Q₈	—	8	4	no	—
450	Q₈	—	8	4	no	—
451	D₄	—	4	16	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	16	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	8	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	8	no	—
480	C₂²	—	4	16	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	8	no	—
488	C₂²	—	8	8	no	—
489	C₂²	C₄₁×#536	1	4	yes	—
490	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
491	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
492	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
493	C₂²	C₄₁×#585	1	2	yes	—
494	C₄	—	2	4	no	—
495	C₄	—	2	4	no	—
496	C₄	—	2	4	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	8	no	—
502	C₂	—	2	4	no	—
503	C₂	—	4	4	no	—
504	C₂	—	8	2	no	—
505	C₂	C₂×C₄₁×#536	1	1	yes	characteristic
506	C₂	C₄₁×#3484	1	1	yes	characteristic
507	C₂	C₄₁×#3487	1	1	yes	characteristic
508	C₂	C₄₁×#3535	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#544	C₂	semidirect
3. C₄₁×#2848	C₂	semidirect
4. C₄₁×#2694	C₂	semidirect
5. C₄₁×#2674	C₂	semidirect
6. C₄₁×#2626	C₂	semidirect
7. C₄₁×#2583	C₂	semidirect
8. C₄₁×#2482	C₂	semidirect
9. C₄₁×#2482	C₂	semidirect
11. C₄₁×#2313	C₂	semidirect
15. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
16. C₂×#125×C₄₁	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
29. C₄₁×#399	C₂²	semidirect
30. C₄₁×#399	C₂²	semidirect
31. C₄₁×#399	C₂²	semidirect
32. C₄₁×#398	C₂²	semidirect
33. C₄₁×#397	C₂²	semidirect
34. C₄₁×#397	C₂²	semidirect
35. C₄₁×#396	C₂²	semidirect
36. C₄₁×#395	C₂²	semidirect
38. C₄₁×#393	C₂²	semidirect
40. C₄₁×#389	C₂²	semidirect
41. C₄₁×#388	C₂²	semidirect
42. C₄₁×#388	C₂²	semidirect
43. C₄₁×#387	C₂²	semidirect
46. C₄₁×#385	C₂²	semidirect
49. C₄₁×#380	C₂²	semidirect
220. #36711	C₄₁	direct (N × H)
248. C₂×#544	C₂×C₄₁	semidirect
250. #2848	C₂×C₄₁	semidirect
251. #2694	C₂×C₄₁	semidirect
252. #2674	C₂×C₄₁	semidirect
253. #2626	C₂×C₄₁	semidirect
254. #2583	C₂×C₄₁	semidirect
255. #2482	C₂×C₄₁	semidirect
256. #2482	C₂×C₄₁	semidirect
258. #2313	C₂×C₄₁	semidirect
269. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
270. C₂×#125	C₂²×C₄₁	semidirect
276. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
283. #399	C₂²×C₄₁	semidirect
284. #399	C₂²×C₄₁	semidirect
285. #399	C₂²×C₄₁	semidirect
286. #398	C₂²×C₄₁	semidirect
287. #397	C₂²×C₄₁	semidirect
288. #397	C₂²×C₄₁	semidirect
289. #396	C₂²×C₄₁	semidirect
290. #395	C₂²×C₄₁	semidirect
292. #393	C₂²×C₄₁	semidirect
294. #389	C₂²×C₄₁	semidirect
295. #388	C₂²×C₄₁	semidirect
296. #388	C₂²×C₄₁	semidirect
297. #387	C₂²×C₄₁	semidirect
300. #385	C₂²×C₄₁	semidirect
303. #380	C₂²×C₄₁	semidirect
307. C₄₁	#36711	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#544	2
C₂²×#123×C₄₁	2
C₄₁×#2848	2
C₄₁×#2694	2
C₄₁×#2674	2
C₄₁×#2626	2
C₄₁×#2583	2
C₄₁×#2482	2
C₄₁×#2435	2
C₄₁×#2313	2
#36711	41

Subgroups — C41×#36711 #23812912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#36711 #23812912