Subgroups — C₄₁×#34234 #23810435

Order 10496.

2214 conjugacy classes of subgroups.

The subgroup lattice has 596 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	1	yes	maximal, characteristic
2	C₄₁×#2368	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2364	C₂	1	2	yes	maximal
4	C₄₁×#2359	C₂	1	4	yes	maximal, complemented
5	C₄₁×#2356	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2353	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2347	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2343	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2337	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2336	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2318	C₂	1	2	yes	maximal, complemented
12	C₄×#126×C₄₁	C₂	1	4	yes	maximal, complemented
13	C₂×C₄₁×#383	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2275	C₂	1	2	yes	maximal, complemented
15	C₄×#117×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#529	C₄	1	16	yes	complemented
17	C₂×#126×C₄₁	C₂²	1	2	yes	—
18	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#123×C₄₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₁	C₂²	1	2	yes	—
28	C₂×#117×C₄₁	C₂²	1	2	yes	—
29	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#391	C₂²	1	4	yes	—
31	C₄₁×#389	C₂²	1	4	yes	—
32	C₄₁×#388	C₂²	1	4	yes	—
33	C₄₁×#388	C₂²	1	4	yes	—
34	C₄₁×#388	C₂²	1	4	yes	—
35	C₄₁×#388	C₂²	1	4	yes	—
36	C₄₁×#387	C₂²	1	4	yes	—
37	C₄₁×#387	C₂²	1	4	yes	—
38	C₄₁×#387	C₂²	1	4	yes	—
39	C₄₁×#387	C₂²	1	4	yes	—
40	C₄₁×#387	C₂²	1	4	yes	—
41	C₄₁×#387	C₂²	1	4	yes	—
42	C₄₁×#386	C₂²	1	4	yes	—
43	C₄₁×#386	C₂²	1	4	yes	—
44	C₄₁×#385	C₂²	1	4	yes	—
45	C₄₁×#385	C₂²	1	4	yes	—
46	C₄₁×#383	C₂²	1	2	yes	—
47	C₄₁×#383	C₂²	1	2	yes	—
48	C₄₁×#383	C₂²	1	1	yes	characteristic
49	C₄₁×#383	C₂²	1	1	yes	characteristic
50	C₄₁×#383	C₂²	1	2	yes	—
51	C₄₁×#383	C₂²	1	2	yes	—
52	C₄₁×#382	C₂²	1	2	yes	—
53	C₄₁×#381	C₂²	1	2	yes	—
54	C₄₁×#380	C₂²	1	2	yes	—
55	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
56	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
65	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
67	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
69	C₄₁×#376	C₂²	1	2	yes	—
70	C₄₁×#376	C₂²	1	2	yes	—
71	C₂×#95×C₄₁	C₂²	1	2	yes	—
72	C₂×#95×C₄₁	C₂²	1	2	yes	—
73	C₂×#95×C₄₁	C₂²	1	2	yes	—
74	C₂×#95×C₄₁	C₂²	1	2	yes	—
75	C₄³×C₄₁	C₂²	1	2	yes	—
76	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
81	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
82	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
85	#126×C₄₁	C₂×C₄	1	16	yes	complemented
86	#125×C₄₁	C₂×C₄	1	8	yes	complemented
87	#124×C₄₁	C₂×C₄	1	8	yes	complemented
88	#123×C₄₁	C₂×C₄	1	16	yes	complemented
89	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
90	#121×C₄₁	C₂×C₄	1	8	yes	—
91	C₄×Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
92	C₄×D₄×C₄₁	—	2	16	no	—
93	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
94	C₄×D₄×C₄₁	C₂×C₄	1	16	yes	complemented
95	#117×C₄₁	—	2	8	no	—
96	#117×C₄₁	C₂×C₄	1	16	yes	complemented
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×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
117	C₂×C₄²×C₄₁	C₂×C₄	1	8	yes	complemented
118	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
119	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
120	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
121	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
122	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
123	C₂×C₄²×C₄₁	C₂³	1	4	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	2	yes	—
130	#95×C₄₁	C₂³	1	2	yes	—
131	#95×C₄₁	C₂³	1	2	yes	—
132	#95×C₄₁	C₂³	1	2	yes	—
133	#95×C₄₁	C₂³	1	2	yes	—
134	#95×C₄₁	C₂³	1	4	yes	—
135	#95×C₄₁	C₂³	1	4	yes	—
136	#95×C₄₁	C₂³	1	4	yes	—
137	#95×C₄₁	C₂³	1	2	yes	—
138	#95×C₄₁	C₂³	1	2	yes	—
139	#95×C₄₁	C₂³	1	4	yes	—
140	#95×C₄₁	C₂³	1	2	yes	—
141	#95×C₄₁	C₂³	1	4	yes	—
142	#95×C₄₁	C₂³	1	2	yes	—
143	#95×C₄₁	C₂³	1	4	yes	—
144	#95×C₄₁	C₂³	1	4	yes	—
145	#95×C₄₁	C₂³	1	4	yes	—
146	#95×C₄₁	C₂³	1	4	yes	—
147	#95×C₄₁	C₂³	1	4	yes	—
148	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
149	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
150	C₂×Q₈×C₄₁	—	4	2	no	—
151	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
152	C₂×D₄×C₄₁	—	2	8	no	—
153	C₂×D₄×C₄₁	—	4	2	no	—
154	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
155	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₄₁	—	2	4	no	—
157	C₂²×C₄×C₄₁	—	2	8	no	—
158	C₂²×C₄×C₄₁	—	2	8	no	—
159	C₂²×C₄×C₄₁	—	4	2	no	—
160	C₂²×C₄×C₄₁	—	4	2	no	—
161	C₂²×C₄×C₄₁	—	4	4	no	—
162	C₂²×C₄×C₄₁	—	4	4	no	—
163	C₂²×C₄×C₄₁	—	4	4	no	—
164	C₂²×C₄×C₄₁	—	4	4	no	—
165	C₂²×C₄×C₄₁	—	4	4	no	—
166	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
167	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
170	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
183	C₄⋊C₄×C₄₁	—	2	8	no	—
184	C₄⋊C₄×C₄₁	—	2	8	no	—
185	C₄⋊C₄×C₄₁	—	4	4	no	—
186	C₄⋊C₄×C₄₁	—	4	4	no	—
187	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
188	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
189	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
190	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
191	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
192	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
193	C₂²⋊C₄×C₄₁	—	2	4	no	—
194	C₂²⋊C₄×C₄₁	—	2	8	no	—
195	C₂²⋊C₄×C₄₁	—	4	4	no	—
196	C₂²⋊C₄×C₄₁	—	4	4	no	—
197	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
198	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
199	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
200	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
201	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
202	C₂²⋊C₄×C₄₁	#41	1	8	yes	—
203	C₄²×C₄₁	—	2	8	no	—
204	C₄²×C₄₁	—	2	8	no	—
205	C₄²×C₄₁	—	4	2	no	—
206	C₄²×C₄₁	—	4	4	no	—
207	C₄²×C₄₁	—	4	4	no	—
208	C₄²×C₄₁	—	4	4	no	—
209	C₄²×C₄₁	—	4	2	no	—
210	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
211	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
212	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
213	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
214	C₄²×C₄₁	C₂²×C₄	1	8	yes	—
215	C₂³×C₄₁	—	2	2	no	—
216	C₂³×C₄₁	—	2	2	no	—
217	C₂³×C₄₁	—	2	4	no	—
218	C₂³×C₄₁	—	2	2	no	—
219	C₂³×C₄₁	—	2	4	no	—
220	C₂³×C₄₁	—	2	2	no	—
221	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
222	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
223	C₂³×C₄₁	C₂×#41	1	4	yes	—
224	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
225	Q₈×C₄₁	—	4	4	no	—
226	D₄×C₄₁	—	2	16	no	—
227	D₄×C₄₁	—	4	4	no	—
228	C₂×C₄×C₄₁	—	2	8	no	—
229	C₂×C₄×C₄₁	—	2	2	no	—
230	C₂×C₄×C₄₁	—	2	4	no	—
231	C₂×C₄×C₄₁	—	2	2	no	—
232	C₂×C₄×C₄₁	—	2	2	no	—
233	C₂×C₄×C₄₁	—	2	2	no	—
234	C₂×C₄×C₄₁	—	2	4	no	—
235	C₂×C₄×C₄₁	—	2	4	no	—
236	C₂×C₄×C₄₁	—	2	2	no	—
237	C₂×C₄×C₄₁	—	2	4	no	—
238	C₂×C₄×C₄₁	—	2	2	no	—
239	C₂×C₄×C₄₁	—	2	2	no	—
240	C₂×C₄×C₄₁	—	2	2	no	—
241	C₂×C₄×C₄₁	—	2	4	no	—
242	C₂×C₄×C₄₁	—	2	4	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	4	no	—
248	C₂×C₄×C₄₁	—	2	4	no	—
249	C₂×C₄×C₄₁	—	2	4	no	—
250	C₂×C₄×C₄₁	—	4	4	no	—
251	C₂×C₄×C₄₁	—	4	8	no	—
252	C₂×C₄×C₄₁	—	4	4	no	—
253	C₂×C₄×C₄₁	—	8	8	no	—
254	C₂×C₄×C₄₁	—	8	8	no	—
255	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
256	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
257	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
258	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
259	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
260	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
261	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
262	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
263	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
264	C₂×C₄×C₄₁	C₂×#41	1	8	yes	—
265	#34234	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₄₁	—	2	2	no	—
267	C₂²×C₄₁	—	2	2	no	—
268	C₂²×C₄₁	—	2	8	no	—
269	C₂²×C₄₁	—	2	4	no	—
270	C₂²×C₄₁	—	2	4	no	—
271	C₂²×C₄₁	—	2	4	no	—
272	C₂²×C₄₁	—	4	4	no	—
273	C₂²×C₄₁	—	4	4	no	—
274	C₂²×C₄₁	C₄×#41	1	4	yes	—
275	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
276	C₂²×C₄₁	C₂²×#41	1	2	yes	—
277	C₂²×C₄₁	#585	1	2	yes	—
278	C₂²×C₄₁	#585	1	2	yes	—
279	C₄×C₄₁	—	2	2	no	—
280	C₄×C₄₁	—	2	2	no	—
281	C₄×C₄₁	—	2	4	no	—
282	C₄×C₄₁	—	2	2	no	—
283	C₄×C₄₁	—	2	2	no	—
284	C₄×C₄₁	—	2	2	no	—
285	C₄×C₄₁	—	2	4	no	—
286	C₄×C₄₁	—	2	2	no	—
287	C₄×C₄₁	—	2	4	no	—
288	C₄×C₄₁	—	2	8	no	—
289	C₄×C₄₁	—	4	4	no	—
290	C₄×C₄₁	—	4	4	no	—
291	C₄×C₄₁	—	4	4	no	—
292	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
293	#2368	C₂×C₄₁	1	2	yes	complemented
294	#2364	C₂×C₄₁	1	2	yes	—
295	#2359	C₂×C₄₁	1	4	yes	complemented
296	#2356	C₂×C₄₁	1	2	yes	complemented
297	#2353	C₂×C₄₁	1	2	yes	complemented
298	#2347	C₂×C₄₁	1	2	yes	complemented
299	#2343	C₂×C₄₁	1	2	yes	complemented
300	#2337	C₂×C₄₁	1	2	yes	complemented
301	#2336	C₂×C₄₁	1	2	yes	complemented
302	#2318	C₂×C₄₁	1	2	yes	complemented
303	C₄×#126	C₂×C₄₁	1	4	yes	complemented
304	C₂×#383	C₂×C₄₁	1	1	yes	characteristic, complemented
305	#2275	C₂×C₄₁	1	2	yes	complemented
306	C₄×#117	C₂×C₄₁	1	1	yes	characteristic, complemented
307	C₂×C₄₁	—	2	4	no	—
308	C₂×C₄₁	—	4	4	no	—
309	C₂×C₄₁	C₂×C₄×#41	1	1	yes	characteristic
310	C₂×C₄₁	#3428	1	1	yes	characteristic
311	C₂×C₄₁	#3428	1	1	yes	characteristic
312	C₂×C₄₁	#3521	1	4	yes	—
313	#529	C₄×C₄₁	1	16	yes	complemented
314	C₂×#126	C₂²×C₄₁	1	2	yes	—
315	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
316	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
317	C₂×#123	C₂²×C₄₁	1	2	yes	—
318	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
319	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
320	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
322	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
323	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
324	C₂×#117	C₂²×C₄₁	1	2	yes	—
325	C₂×#117	C₂²×C₄₁	1	2	yes	—
326	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
327	#391	C₂²×C₄₁	1	4	yes	—
328	#389	C₂²×C₄₁	1	4	yes	—
329	#388	C₂²×C₄₁	1	4	yes	—
330	#388	C₂²×C₄₁	1	4	yes	—
331	#388	C₂²×C₄₁	1	4	yes	—
332	#388	C₂²×C₄₁	1	4	yes	—
333	#387	C₂²×C₄₁	1	4	yes	—
334	#387	C₂²×C₄₁	1	4	yes	—
335	#387	C₂²×C₄₁	1	4	yes	—
336	#387	C₂²×C₄₁	1	4	yes	—
337	#387	C₂²×C₄₁	1	4	yes	—
338	#387	C₂²×C₄₁	1	4	yes	—
339	#386	C₂²×C₄₁	1	4	yes	—
340	#386	C₂²×C₄₁	1	4	yes	—
341	#385	C₂²×C₄₁	1	4	yes	—
342	#385	C₂²×C₄₁	1	4	yes	—
343	#383	C₂²×C₄₁	1	2	yes	—
344	#383	C₂²×C₄₁	1	2	yes	—
345	#383	C₂²×C₄₁	1	2	yes	—
346	#383	C₂²×C₄₁	1	1	yes	characteristic
347	#383	C₂²×C₄₁	1	1	yes	characteristic
348	#383	C₂²×C₄₁	1	2	yes	—
349	#382	C₂²×C₄₁	1	2	yes	—
350	#381	C₂²×C₄₁	1	2	yes	—
351	#380	C₂²×C₄₁	1	2	yes	—
352	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
353	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
354	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
355	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
357	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
361	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
362	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
363	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
364	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
365	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
366	#376	C₂²×C₄₁	1	2	yes	—
367	#376	C₂²×C₄₁	1	2	yes	—
368	C₂×#95	C₂²×C₄₁	1	2	yes	—
369	C₂×#95	C₂²×C₄₁	1	2	yes	—
370	C₂×#95	C₂²×C₄₁	1	2	yes	—
371	C₂×#95	C₂²×C₄₁	1	2	yes	—
372	C₄³	C₂²×C₄₁	1	2	yes	—
373	C₄₁	#34234	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
376	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
379	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
380	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
381	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
383	#126	C₂×C₄×C₄₁	1	16	yes	complemented
384	#125	C₂×C₄×C₄₁	1	8	yes	complemented
385	#124	C₂×C₄×C₄₁	1	8	yes	complemented
386	#123	C₂×C₄×C₄₁	1	16	yes	complemented
387	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
388	#121	C₂×C₄×C₄₁	1	8	yes	—
389	C₄×Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
390	C₄×D₄	—	2	16	no	—
391	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
392	C₄×D₄	C₂×C₄×C₄₁	1	16	yes	complemented
393	#117	—	2	8	no	—
394	#117	C₂×C₄×C₄₁	1	16	yes	complemented
395	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	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	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
415	C₂×C₄²	C₂×C₄×C₄₁	1	8	yes	complemented
416	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
417	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
418	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
419	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
420	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
421	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
422	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
423	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
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	#95	C₂³×C₄₁	1	2	yes	—
429	#95	C₂³×C₄₁	1	2	yes	—
430	#95	C₂³×C₄₁	1	2	yes	—
431	#95	C₂³×C₄₁	1	2	yes	—
432	#95	C₂³×C₄₁	1	4	yes	—
433	#95	C₂³×C₄₁	1	4	yes	—
434	#95	C₂³×C₄₁	1	4	yes	—
435	#95	C₂³×C₄₁	1	2	yes	—
436	#95	C₂³×C₄₁	1	2	yes	—
437	#95	C₂³×C₄₁	1	4	yes	—
438	#95	C₂³×C₄₁	1	2	yes	—
439	#95	C₂³×C₄₁	1	4	yes	—
440	#95	C₂³×C₄₁	1	2	yes	—
441	#95	C₂³×C₄₁	1	4	yes	—
442	#95	C₂³×C₄₁	1	4	yes	—
443	#95	C₂³×C₄₁	1	4	yes	—
444	#95	C₂³×C₄₁	1	4	yes	—
445	#95	C₂³×C₄₁	1	4	yes	—
446	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
447	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
448	C₂×Q₈	—	4	2	no	—
449	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
450	C₂×D₄	—	2	8	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
453	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	8	no	—
456	C₂²×C₄	—	2	8	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	—	4	4	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
465	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
466	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
467	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
468	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
471	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	4	4	no	—
484	C₄⋊C₄	—	4	4	no	—
485	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
486	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
487	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
488	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
489	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
490	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₂²⋊C₄	—	4	4	no	—
495	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
496	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
497	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
498	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
499	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
500	C₂²⋊C₄	#41×C₄₁	1	8	yes	—
501	C₄²	—	2	8	no	—
502	C₄²	—	2	8	no	—
503	C₄²	—	4	2	no	—
504	C₄²	—	4	4	no	—
505	C₄²	—	4	4	no	—
506	C₄²	—	4	4	no	—
507	C₄²	—	4	2	no	—
508	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
509	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
510	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
511	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
512	C₄²	C₂²×C₄×C₄₁	1	8	yes	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	2	no	—
519	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
520	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
521	C₂³	C₂×#41×C₄₁	1	4	yes	—
522	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
523	Q₈	—	4	4	no	—
524	D₄	—	2	16	no	—
525	D₄	—	4	4	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	8	8	no	—
552	C₂×C₄	—	8	8	no	—
553	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
554	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
555	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
556	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
557	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
558	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
559	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
560	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
561	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
562	C₂×C₄	C₂×#41×C₄₁	1	8	yes	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	8	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	4	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	C₄×#41×C₄₁	1	4	yes	—
572	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
573	C₂²	C₂²×#41×C₄₁	1	2	yes	—
574	C₂²	C₄₁×#585	1	2	yes	—
575	C₂²	C₄₁×#585	1	2	yes	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	4	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	4	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	8	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	4	no	—
588	C₄	—	4	4	no	—
589	C₂	—	2	4	no	—
590	C₂	—	4	4	no	—
591	C₂	C₂×C₄×#41×C₄₁	1	1	yes	characteristic
592	C₂	C₄₁×#3428	1	1	yes	characteristic
593	C₂	C₄₁×#3428	1	1	yes	characteristic
594	C₂	C₄₁×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2368	C₂	semidirect
4. C₄₁×#2359	C₂	semidirect
5. C₄₁×#2356	C₂	semidirect
6. C₄₁×#2353	C₂	semidirect
7. C₄₁×#2347	C₂	semidirect
8. C₄₁×#2343	C₂	semidirect
9. C₄₁×#2337	C₂	semidirect
10. C₄₁×#2336	C₂	semidirect
11. C₄₁×#2318	C₂	semidirect
12. C₄×#126×C₄₁	C₂	semidirect
13. C₂×C₄₁×#383	C₂	semidirect
14. C₄₁×#2275	C₂	semidirect
15. C₄×#117×C₄₁	C₂	semidirect
16. C₄₁×#529	C₄	semidirect
85. #126×C₄₁	C₂×C₄	semidirect
86. #125×C₄₁	C₂×C₄	semidirect
87. #124×C₄₁	C₂×C₄	semidirect
88. #123×C₄₁	C₂×C₄	semidirect
89. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
91. C₄×Q₈×C₄₁	C₂×C₄	semidirect
93. C₄×D₄×C₄₁	C₂×C₄	semidirect
94. C₄×D₄×C₄₁	C₂×C₄	semidirect
96. #117×C₄₁	C₂×C₄	semidirect
117. C₂×C₄²×C₄₁	C₂×C₄	semidirect
265. #34234	C₄₁	direct (N × H)
293. #2368	C₂×C₄₁	semidirect
295. #2359	C₂×C₄₁	semidirect
296. #2356	C₂×C₄₁	semidirect
297. #2353	C₂×C₄₁	semidirect
298. #2347	C₂×C₄₁	semidirect
299. #2343	C₂×C₄₁	semidirect
300. #2337	C₂×C₄₁	semidirect
301. #2336	C₂×C₄₁	semidirect
302. #2318	C₂×C₄₁	semidirect
303. C₄×#126	C₂×C₄₁	semidirect
304. C₂×#383	C₂×C₄₁	semidirect
305. #2275	C₂×C₄₁	semidirect
306. C₄×#117	C₂×C₄₁	semidirect
313. #529	C₄×C₄₁	semidirect
373. C₄₁	#34234	direct (N × H)
383. #126	C₂×C₄×C₄₁	semidirect
384. #125	C₂×C₄×C₄₁	semidirect
385. #124	C₂×C₄×C₄₁	semidirect
386. #123	C₂×C₄×C₄₁	semidirect
387. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
389. C₄×Q₈	C₂×C₄×C₄₁	semidirect
391. C₄×D₄	C₂×C₄×C₄₁	semidirect
392. C₄×D₄	C₂×C₄×C₄₁	semidirect
394. #117	C₂×C₄×C₄₁	semidirect
415. C₂×C₄²	C₂×C₄×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×#529	2
C₄₁×#2368	2
C₄₁×#2364	2
C₄₁×#2359	2
C₄₁×#2356	2
C₄₁×#2353	2
C₄₁×#2347	2
C₄₁×#2343	2
C₄₁×#2337	2
C₄₁×#2336	2
C₄₁×#2318	2
C₄×#126×C₄₁	2
C₂×C₄₁×#383	2
C₄₁×#2275	2
C₄×#117×C₄₁	2
#34234	41

Subgroups — C41×#34234 #23810435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34234 #23810435