Subgroups — C₄₁×#36631 #23812832

Order 10496.

2670 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#529	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2861	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2860	C₂	1	4	yes	maximal, complemented
4	C₄₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2858	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2856	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#2854	C₂	1	4	yes	maximal, complemented
9	C₄₁×#2850	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#127×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#124×C₄₁	C₂	1	2	yes	maximal, complemented
13	C₄×#121×C₄₁	C₂	1	4	yes	maximal, complemented
14	C₄₁×#2293	C₂	1	4	yes	maximal, complemented
15	C₂×C₄³×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#529	—	2	16	no	—
19	C₂×#126×C₄₁	C₂²	1	4	yes	—
20	C₂×#125×C₄₁	C₂²	1	2	yes	—
21	C₂×#124×C₄₁	C₂²	1	2	yes	—
22	C₂×#124×C₄₁	C₂²	1	2	yes	—
23	C₂×#123×C₄₁	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
25	C₂×#121×C₄₁	C₂²	1	4	yes	—
26	C₂×#121×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
31	C₂×#117×C₄₁	C₂²	1	4	yes	—
32	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
35	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#391	C₂²	1	2	yes	—
38	C₄₁×#391	C₂²	1	2	yes	—
39	C₄₁×#390	C₂²	1	4	yes	—
40	C₄₁×#390	C₂²	1	4	yes	—
41	C₄₁×#390	C₂²	1	4	yes	—
42	C₄₁×#390	C₂²	1	2	yes	—
43	C₄₁×#390	C₂²	1	2	yes	—
44	C₄₁×#390	C₂²	1	4	yes	—
45	C₄₁×#389	C₂²	1	4	yes	—
46	C₄₁×#389	C₂²	1	4	yes	—
47	C₄₁×#389	C₂²	1	4	yes	—
48	C₄₁×#389	C₂²	1	4	yes	—
49	C₄₁×#388	C₂²	1	8	yes	—
50	C₄₁×#388	C₂²	1	8	yes	—
51	C₄₁×#388	C₂²	1	8	yes	—
52	C₄₁×#388	C₂²	1	8	yes	—
53	C₄₁×#386	C₂²	1	8	yes	—
54	C₄₁×#384	C₂²	1	1	yes	characteristic
55	C₄₁×#384	C₂²	1	1	yes	characteristic
56	C₄₁×#382	C₂²	1	2	yes	—
57	C₄₁×#380	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
59	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	—
60	C₄³×C₄₁	C₂²	1	2	yes	—
61	C₄³×C₄₁	C₂²	1	1	yes	characteristic
62	C₄³×C₄₁	C₂²	1	1	yes	characteristic
63	C₄³×C₄₁	C₂²	1	1	yes	characteristic
64	C₄³×C₄₁	C₂²	1	2	yes	—
65	C₄³×C₄₁	C₂²	1	1	yes	characteristic
66	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
67	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
68	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
70	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
71	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
72	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
76	C₄⋊Q₈×C₄₁	—	2	4	no	—
77	#127×C₄₁	—	2	4	no	—
78	#126×C₄₁	—	2	16	no	—
79	#125×C₄₁	—	2	8	no	—
80	#124×C₄₁	—	2	8	no	—
81	#124×C₄₁	—	2	8	no	—
82	#123×C₄₁	—	2	16	no	—
83	C₂²⋊Q₈×C₄₁	—	2	8	no	—
84	#121×C₄₁	—	2	8	no	—
85	#121×C₄₁	—	2	16	no	—
86	C₄×Q₈×C₄₁	—	2	8	no	—
87	C₄×D₄×C₄₁	—	2	16	no	—
88	C₄×D₄×C₄₁	—	2	8	no	—
89	C₄×D₄×C₄₁	—	2	16	no	—
90	#117×C₄₁	—	2	16	no	—
91	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
108	C₂×C₄²×C₄₁	—	2	8	no	—
109	C₂×C₄²×C₄₁	—	2	8	no	—
110	C₂×C₄²×C₄₁	—	2	4	no	—
111	C₂×C₄²×C₄₁	—	2	4	no	—
112	C₂×C₄²×C₄₁	D₄	1	8	yes	complemented
113	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
115	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
116	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
117	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
118	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
119	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
120	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
121	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
124	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
125	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
132	#95×C₄₁	C₂³	1	8	yes	—
133	#95×C₄₁	C₂³	1	8	yes	—
134	#95×C₄₁	C₂³	1	8	yes	—
135	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
136	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
137	C₂×Q₈×C₄₁	—	2	4	no	—
138	C₂×Q₈×C₄₁	—	2	4	no	—
139	C₂×Q₈×C₄₁	—	2	4	no	—
140	C₂×D₄×C₄₁	—	2	8	no	—
141	C₂×D₄×C₄₁	—	2	16	no	—
142	C₂×D₄×C₄₁	—	2	4	no	—
143	C₂×D₄×C₄₁	—	2	8	no	—
144	C₂×D₄×C₄₁	—	2	8	no	—
145	C₂×D₄×C₄₁	—	2	4	no	—
146	C₂×D₄×C₄₁	—	2	8	no	—
147	C₂×D₄×C₄₁	—	2	4	no	—
148	C₂²×C₄×C₄₁	—	2	4	no	—
149	C₂²×C₄×C₄₁	—	2	4	no	—
150	C₂²×C₄×C₄₁	—	2	4	no	—
151	C₂²×C₄×C₄₁	—	2	4	no	—
152	C₂²×C₄×C₄₁	—	2	4	no	—
153	C₂²×C₄×C₄₁	—	2	4	no	—
154	C₂²×C₄×C₄₁	—	2	4	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	8	no	—
158	C₂²×C₄×C₄₁	—	2	16	no	—
159	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₄₁	#41	1	8	yes	—
163	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
176	C₄⋊C₄×C₄₁	—	2	8	no	—
177	C₄⋊C₄×C₄₁	—	2	8	no	—
178	C₄⋊C₄×C₄₁	—	2	4	no	—
179	C₄⋊C₄×C₄₁	—	2	8	no	—
180	C₄⋊C₄×C₄₁	—	2	4	no	—
181	C₄⋊C₄×C₄₁	—	2	8	no	—
182	C₄⋊C₄×C₄₁	—	2	8	no	—
183	C₄⋊C₄×C₄₁	—	2	8	no	—
184	C₄⋊C₄×C₄₁	—	2	8	no	—
185	C₂²⋊C₄×C₄₁	—	2	8	no	—
186	C₂²⋊C₄×C₄₁	—	2	8	no	—
187	C₂²⋊C₄×C₄₁	—	2	8	no	—
188	C₂²⋊C₄×C₄₁	—	2	8	no	—
189	C₂²⋊C₄×C₄₁	—	2	8	no	—
190	C₂²⋊C₄×C₄₁	—	2	16	no	—
191	C₂²⋊C₄×C₄₁	—	2	16	no	—
192	C₂²⋊C₄×C₄₁	—	2	16	no	—
193	C₄²×C₄₁	—	2	8	no	—
194	C₄²×C₄₁	—	2	4	no	—
195	C₄²×C₄₁	—	2	4	no	—
196	C₄²×C₄₁	—	2	4	no	—
197	C₄²×C₄₁	—	2	4	no	—
198	C₄²×C₄₁	—	2	4	no	—
199	C₄²×C₄₁	—	2	4	no	—
200	C₄²×C₄₁	—	2	4	no	—
201	C₄²×C₄₁	—	2	4	no	—
202	C₄²×C₄₁	—	2	4	no	—
203	C₄²×C₄₁	—	2	2	no	—
204	C₄²×C₄₁	—	2	2	no	—
205	C₄²×C₄₁	C₂×D₄	1	4	yes	—
206	C₄²×C₄₁	C₂×D₄	1	4	yes	—
207	C₄²×C₄₁	C₂×D₄	1	4	yes	—
208	C₄²×C₄₁	C₂×D₄	1	4	yes	—
209	C₄²×C₄₁	#41	1	8	yes	—
210	C₄²×C₄₁	#41	1	4	yes	—
211	C₄²×C₄₁	#41	1	4	yes	—
212	C₂³×C₄₁	—	2	1	no	—
213	C₂³×C₄₁	—	2	2	no	—
214	C₂³×C₄₁	—	2	1	no	—
215	C₂³×C₄₁	—	2	4	no	—
216	C₂³×C₄₁	—	2	4	no	—
217	C₂³×C₄₁	—	2	8	no	—
218	C₂³×C₄₁	—	2	8	no	—
219	C₂³×C₄₁	—	2	4	no	—
220	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
221	C₂³×C₄₁	C₂×#41	1	4	yes	—
222	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
223	Q₈×C₄₁	—	4	8	no	—
224	D₄×C₄₁	—	4	16	no	—
225	D₄×C₄₁	—	4	16	no	—
226	D₄×C₄₁	—	4	8	no	—
227	C₂×C₄×C₄₁	—	2	16	no	—
228	C₂×C₄×C₄₁	—	2	8	no	—
229	C₂×C₄×C₄₁	—	2	2	no	—
230	C₂×C₄×C₄₁	—	2	2	no	—
231	C₂×C₄×C₄₁	—	2	1	no	—
232	C₂×C₄×C₄₁	—	2	2	no	—
233	C₂×C₄×C₄₁	—	2	2	no	—
234	C₂×C₄×C₄₁	—	2	2	no	—
235	C₂×C₄×C₄₁	—	2	1	no	—
236	C₂×C₄×C₄₁	—	2	2	no	—
237	C₂×C₄×C₄₁	—	2	2	no	—
238	C₂×C₄×C₄₁	—	2	2	no	—
239	C₂×C₄×C₄₁	—	2	2	no	—
240	C₂×C₄×C₄₁	—	2	16	no	—
241	C₂×C₄×C₄₁	—	2	8	no	—
242	C₂×C₄×C₄₁	—	2	8	no	—
243	C₂×C₄×C₄₁	—	2	4	no	—
244	C₂×C₄×C₄₁	—	2	4	no	—
245	C₂×C₄×C₄₁	—	2	4	no	—
246	C₂×C₄×C₄₁	—	2	4	no	—
247	C₂×C₄×C₄₁	—	2	8	no	—
248	C₂×C₄×C₄₁	—	2	8	no	—
249	C₂×C₄×C₄₁	—	2	4	no	—
250	C₂×C₄×C₄₁	—	4	16	no	—
251	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
258	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
259	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
260	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
261	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
262	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
263	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
264	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
265	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
266	#36631	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂²×C₄₁	—	2	4	no	—
268	C₂²×C₄₁	—	2	2	no	—
269	C₂²×C₄₁	—	2	2	no	—
270	C₂²×C₄₁	—	2	4	no	—
271	C₂²×C₄₁	—	4	8	no	—
272	C₂²×C₄₁	—	4	4	no	—
273	C₂²×C₄₁	—	4	4	no	—
274	C₂²×C₄₁	—	4	4	no	—
275	C₂²×C₄₁	—	4	8	no	—
276	C₂²×C₄₁	#532	1	4	yes	—
277	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
278	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
279	C₂²×C₄₁	C₂²×#41	1	2	yes	—
280	C₂²×C₄₁	C₂²×#41	1	2	yes	—
281	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
282	C₄×C₄₁	—	2	4	no	—
283	C₄×C₄₁	—	2	2	no	—
284	C₄×C₄₁	—	2	2	no	—
285	C₄×C₄₁	—	2	2	no	—
286	C₄×C₄₁	—	2	2	no	—
287	C₄×C₄₁	—	2	4	no	—
288	C₄×C₄₁	—	2	4	no	—
289	C₄×C₄₁	—	4	4	no	—
290	C₄×C₄₁	—	4	4	no	—
291	C₄×C₄₁	—	4	4	no	—
292	C₄×C₄₁	#529	1	8	yes	complemented
293	C₄×C₄₁	#532	1	4	yes	—
294	C₄×C₄₁	#532	1	4	yes	—
295	C₂×#529	C₂×C₄₁	1	2	yes	complemented
296	#2861	C₂×C₄₁	1	2	yes	complemented
297	#2860	C₂×C₄₁	1	4	yes	complemented
298	#2859	C₂×C₄₁	1	1	yes	characteristic, complemented
299	#2858	C₂×C₄₁	1	1	yes	characteristic, complemented
300	#2857	C₂×C₄₁	1	1	yes	characteristic, complemented
301	#2856	C₂×C₄₁	1	1	yes	characteristic
302	#2854	C₂×C₄₁	1	4	yes	complemented
303	#2850	C₂×C₄₁	1	2	yes	complemented
304	C₄×C₄⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
305	C₄×#127	C₂×C₄₁	1	1	yes	characteristic, complemented
306	C₄×#124	C₂×C₄₁	1	2	yes	complemented
307	C₄×#121	C₂×C₄₁	1	4	yes	complemented
308	#2293	C₂×C₄₁	1	4	yes	complemented
309	C₂×C₄³	C₂×C₄₁	1	1	yes	characteristic, complemented
310	C₂×C₄₁	—	2	4	no	—
311	C₂×C₄₁	—	8	4	no	—
312	C₂×C₄₁	C₂×#529	1	2	yes	—
313	C₂×C₄₁	C₂×#532	1	1	yes	characteristic
314	C₂×C₄₁	C₂×#532	1	1	yes	characteristic
315	C₂×C₄₁	C₂×#532	1	1	yes	characteristic
316	C₂×C₄₁	#3444	1	2	yes	—
317	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
318	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
319	#529	—	2	16	no	—
320	C₂×#126	C₂²×C₄₁	1	4	yes	—
321	C₂×#125	C₂²×C₄₁	1	2	yes	—
322	C₂×#124	C₂²×C₄₁	1	2	yes	—
323	C₂×#124	C₂²×C₄₁	1	2	yes	—
324	C₂×#123	C₂²×C₄₁	1	4	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
326	C₂×#121	C₂²×C₄₁	1	2	yes	—
327	C₂×#121	C₂²×C₄₁	1	4	yes	—
328	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
329	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
331	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
332	C₂×#117	C₂²×C₄₁	1	4	yes	—
333	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
334	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
335	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
337	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
338	#391	C₂²×C₄₁	1	2	yes	—
339	#391	C₂²×C₄₁	1	2	yes	—
340	#390	C₂²×C₄₁	1	2	yes	—
341	#390	C₂²×C₄₁	1	4	yes	—
342	#390	C₂²×C₄₁	1	4	yes	—
343	#390	C₂²×C₄₁	1	4	yes	—
344	#390	C₂²×C₄₁	1	2	yes	—
345	#390	C₂²×C₄₁	1	4	yes	—
346	#389	C₂²×C₄₁	1	4	yes	—
347	#389	C₂²×C₄₁	1	4	yes	—
348	#389	C₂²×C₄₁	1	4	yes	—
349	#389	C₂²×C₄₁	1	4	yes	—
350	#388	C₂²×C₄₁	1	8	yes	—
351	#388	C₂²×C₄₁	1	8	yes	—
352	#388	C₂²×C₄₁	1	8	yes	—
353	#388	C₂²×C₄₁	1	8	yes	—
354	#386	C₂²×C₄₁	1	8	yes	—
355	#384	C₂²×C₄₁	1	1	yes	characteristic
356	#384	C₂²×C₄₁	1	1	yes	characteristic
357	#382	C₂²×C₄₁	1	2	yes	—
358	#380	C₂²×C₄₁	1	4	yes	—
359	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	—
361	C₄³	C₂²×C₄₁	1	1	yes	characteristic
362	C₄³	C₂²×C₄₁	1	1	yes	characteristic
363	C₄³	C₂²×C₄₁	1	2	yes	—
364	C₄³	C₂²×C₄₁	1	1	yes	characteristic
365	C₄³	C₂²×C₄₁	1	2	yes	—
366	C₄³	C₂²×C₄₁	1	1	yes	characteristic
367	C₄₁	#36631	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
369	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
370	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
371	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
372	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
373	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
374	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
378	C₄⋊Q₈	—	2	4	no	—
379	#127	—	2	4	no	—
380	#126	—	2	16	no	—
381	#125	—	2	8	no	—
382	#124	—	2	8	no	—
383	#124	—	2	8	no	—
384	#123	—	2	16	no	—
385	C₂²⋊Q₈	—	2	8	no	—
386	#121	—	2	8	no	—
387	#121	—	2	16	no	—
388	C₄×Q₈	—	2	8	no	—
389	C₄×D₄	—	2	16	no	—
390	C₄×D₄	—	2	8	no	—
391	C₄×D₄	—	2	16	no	—
392	#117	—	2	16	no	—
393	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
410	C₂×C₄²	—	2	8	no	—
411	C₂×C₄²	—	2	8	no	—
412	C₂×C₄²	—	2	4	no	—
413	C₂×C₄²	—	2	4	no	—
414	C₂×C₄²	D₄×C₄₁	1	8	yes	complemented
415	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
416	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
417	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
418	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
419	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
420	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
421	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
422	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
423	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
424	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
425	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
432	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
434	#95	C₂³×C₄₁	1	8	yes	—
435	#95	C₂³×C₄₁	1	8	yes	—
436	#95	C₂³×C₄₁	1	8	yes	—
437	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
438	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	16	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	8	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	8	no	—
460	C₂²×C₄	—	2	16	no	—
461	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
462	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
463	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
464	C₂²×C₄	#41×C₄₁	1	8	yes	—
465	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	8	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	2	8	no	—
492	C₂²⋊C₄	—	2	16	no	—
493	C₂²⋊C₄	—	2	16	no	—
494	C₂²⋊C₄	—	2	16	no	—
495	C₄²	—	2	8	no	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	4	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	C₂×D₄×C₄₁	1	4	yes	—
508	C₄²	C₂×D₄×C₄₁	1	4	yes	—
509	C₄²	C₂×D₄×C₄₁	1	4	yes	—
510	C₄²	C₂×D₄×C₄₁	1	4	yes	—
511	C₄²	#41×C₄₁	1	8	yes	—
512	C₄²	#41×C₄₁	1	4	yes	—
513	C₄²	#41×C₄₁	1	4	yes	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	4	no	—
522	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
523	C₂³	C₂×#41×C₄₁	1	4	yes	—
524	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
525	Q₈	—	4	8	no	—
526	D₄	—	4	16	no	—
527	D₄	—	4	16	no	—
528	D₄	—	4	8	no	—
529	C₂×C₄	—	2	16	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	16	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	8	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	4	16	no	—
553	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
558	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
559	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
560	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
561	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
562	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
563	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
564	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
565	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
566	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
567	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
568	C₂²	—	2	4	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	4	8	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	8	no	—
577	C₂²	C₄₁×#532	1	4	yes	—
578	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
579	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
580	C₂²	C₂²×#41×C₄₁	1	2	yes	—
581	C₂²	C₂²×#41×C₄₁	1	2	yes	—
582	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
583	C₄	—	2	4	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	4	no	—
589	C₄	—	2	4	no	—
590	C₄	—	4	4	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	C₄₁×#529	1	8	yes	complemented
594	C₄	C₄₁×#532	1	4	yes	—
595	C₄	C₄₁×#532	1	4	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	8	4	no	—
598	C₂	C₂×C₄₁×#529	1	2	yes	—
599	C₂	C₂×C₄₁×#532	1	1	yes	characteristic
600	C₂	C₂×C₄₁×#532	1	1	yes	characteristic
601	C₂	C₂×C₄₁×#532	1	1	yes	characteristic
602	C₂	C₄₁×#3444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
socle	C₂³×C₄₁	C₂⁵
prime radical	C₄₁×#2856	C₂
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
1. C₂×C₄₁×#529	C₂	semidirect
2. C₄₁×#2861	C₂	semidirect
3. C₄₁×#2860	C₂	semidirect
4. C₄₁×#2859	C₂	semidirect
5. C₄₁×#2858	C₂	semidirect
6. C₄₁×#2857	C₂	semidirect
8. C₄₁×#2854	C₂	semidirect
9. C₄₁×#2850	C₂	semidirect
10. C₄×C₄⋊Q₈×C₄₁	C₂	semidirect
11. C₄×#127×C₄₁	C₂	semidirect
12. C₄×#124×C₄₁	C₂	semidirect
13. C₄×#121×C₄₁	C₂	semidirect
14. C₄₁×#2293	C₂	semidirect
15. C₂×C₄³×C₄₁	C₂	semidirect
112. C₂×C₄²×C₄₁	D₄	semidirect
266. #36631	C₄₁	direct (N × H)
292. C₄×C₄₁	#529	semidirect
295. C₂×#529	C₂×C₄₁	semidirect
296. #2861	C₂×C₄₁	semidirect
297. #2860	C₂×C₄₁	semidirect
298. #2859	C₂×C₄₁	semidirect
299. #2858	C₂×C₄₁	semidirect
300. #2857	C₂×C₄₁	semidirect
302. #2854	C₂×C₄₁	semidirect
303. #2850	C₂×C₄₁	semidirect
304. C₄×C₄⋊Q₈	C₂×C₄₁	semidirect
305. C₄×#127	C₂×C₄₁	semidirect
306. C₄×#124	C₂×C₄₁	semidirect
307. C₄×#121	C₂×C₄₁	semidirect
308. #2293	C₂×C₄₁	semidirect
309. C₂×C₄³	C₂×C₄₁	semidirect
367. C₄₁	#36631	direct (N × H)
414. C₂×C₄²	D₄×C₄₁	semidirect
593. C₄	C₄₁×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#529	2
C₄₁×#2861	2
C₄₁×#2860	2
C₄₁×#2859	2
C₄₁×#2858	2
C₄₁×#2857	2
C₄₁×#2856	2
C₄₁×#2854	2
C₄₁×#2850	2
C₄×C₄⋊Q₈×C₄₁	2
C₄×#127×C₄₁	2
C₄×#124×C₄₁	2
C₄×#121×C₄₁	2
C₄₁×#2293	2
C₂×C₄³×C₄₁	2
#36631	41

Subgroups — C41×#36631 #23812832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#36631 #23812832