Subgroups — C₄₁×#14699 #23790900

Order 10496.

1566 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#387	C₂	1	2	yes	maximal
4	C₂×C₄³×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1436	C₂	1	2	yes	maximal
6	C₄₁×#1436	C₂	1	2	yes	maximal
7	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1434	C₂	1	2	yes	maximal
12	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#389	—	2	4	no	—
26	C₄₁×#389	C₄	1	8	yes	complemented
27	C₄₁×#387	—	2	8	no	—
28	C₂×#95×C₄₁	C₂²	1	2	yes	—
29	C₂×#95×C₄₁	C₂²	1	2	yes	—
30	C₂×#95×C₄₁	C₂²	1	2	yes	—
31	C₂×#95×C₄₁	C₂²	1	2	yes	—
32	C₂×#95×C₄₁	C₂²	1	2	yes	—
33	C₂×#95×C₄₁	C₂²	1	2	yes	—
34	C₂×#95×C₄₁	C₂²	1	2	yes	—
35	C₂×#95×C₄₁	C₂²	1	2	yes	—
36	C₂×#95×C₄₁	C₂²	1	2	yes	—
37	C₂×#95×C₄₁	C₂²	1	2	yes	—
38	C₄³×C₄₁	—	2	4	no	—
39	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	—	2	2	no	—
70	C₂×C₄²×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	—	2	2	no	—
77	C₂×C₄²×C₄₁	—	2	2	no	—
78	C₂×C₄²×C₄₁	—	2	2	no	—
79	C₂×C₄²×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	—	2	2	no	—
81	C₂×C₄²×C₄₁	—	2	2	no	—
82	C₂×C₄²×C₄₁	—	2	2	no	—
83	C₂×C₄²×C₄₁	—	2	2	no	—
84	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
85	C₂×C₄²×C₄₁	D₄	1	4	yes	—
86	C₂×C₄²×C₄₁	D₄	1	4	yes	—
87	C₂×C₄²×C₄₁	Q₈	1	4	yes	—
88	C₂×C₄²×C₄₁	Q₈	1	4	yes	—
89	#95×C₄₁	—	2	4	no	—
90	#95×C₄₁	—	2	4	no	—
91	#95×C₄₁	—	2	4	no	—
92	#95×C₄₁	—	2	4	no	—
93	#95×C₄₁	—	2	4	no	—
94	#95×C₄₁	—	2	4	no	—
95	#95×C₄₁	—	2	4	no	—
96	#95×C₄₁	—	2	4	no	—
97	#95×C₄₁	—	2	4	no	—
98	#95×C₄₁	C₂×C₄	1	8	yes	—
99	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	—	2	1	no	—
101	C₂²×C₄×C₄₁	—	2	1	no	—
102	C₂²×C₄×C₄₁	—	2	1	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	1	no	—
105	C₂²×C₄×C₄₁	—	2	1	no	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	1	no	—
110	C₂²×C₄×C₄₁	—	2	1	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	2	1	no	—
114	C₂²×C₄×C₄₁	—	2	1	no	—
115	C₂²×C₄×C₄₁	—	2	1	no	—
116	C₂²×C₄×C₄₁	—	2	1	no	—
117	C₂²×C₄×C₄₁	—	2	1	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	1	no	—
121	C₂²×C₄×C₄₁	—	2	1	no	—
122	C₂²×C₄×C₄₁	—	2	1	no	—
123	C₂²×C₄×C₄₁	—	2	1	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	2	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	2	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	2	no	—
147	C₂²×C₄×C₄₁	—	2	2	no	—
148	C₂²×C₄×C₄₁	—	2	2	no	—
149	C₂²×C₄×C₄₁	—	2	2	no	—
150	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
162	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
163	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
164	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
165	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
166	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
167	C₂²×C₄×C₄₁	#41	1	2	yes	—
168	C₂²×C₄×C₄₁	#41	1	2	yes	—
169	C₂²×C₄×C₄₁	#41	1	2	yes	—
170	C₂²×C₄×C₄₁	#41	1	2	yes	—
171	C₂²×C₄×C₄₁	#41	1	2	yes	—
172	C₂²×C₄×C₄₁	#41	1	2	yes	—
173	C₂²×C₄×C₄₁	#41	1	2	yes	—
174	C₂²×C₄×C₄₁	#41	1	2	yes	—
175	C₂²×C₄×C₄₁	#41	1	2	yes	—
176	C₂²×C₄×C₄₁	#41	1	2	yes	—
177	C₄⋊C₄×C₄₁	—	2	8	no	—
178	C₄⋊C₄×C₄₁	—	2	16	no	—
179	C₄⋊C₄×C₄₁	—	2	8	no	—
180	C₄⋊C₄×C₄₁	—	4	8	no	—
181	C₄⋊C₄×C₄₁	—	4	4	no	—
182	C₄⋊C₄×C₄₁	—	4	4	no	—
183	C₄²×C₄₁	—	2	8	no	—
184	C₄²×C₄₁	—	2	8	no	—
185	C₄²×C₄₁	—	2	8	no	—
186	C₄²×C₄₁	—	2	8	no	—
187	C₄²×C₄₁	—	2	8	no	—
188	C₄²×C₄₁	—	2	8	no	—
189	C₄²×C₄₁	—	2	8	no	—
190	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
191	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
192	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
193	C₂³×C₄₁	C₂²×Q₈	1	1	yes	characteristic
194	C₂³×C₄₁	C₂²×Q₈	1	1	yes	characteristic
195	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
196	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
197	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
198	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
199	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
200	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
201	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
202	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
203	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
204	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	2	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	2	no	—
209	C₂×C₄×C₄₁	—	2	2	no	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	2	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	2	2	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	2	no	—
226	C₂×C₄×C₄₁	—	2	2	no	—
227	C₂×C₄×C₄₁	—	2	2	no	—
228	C₂×C₄×C₄₁	—	2	2	no	—
229	C₂×C₄×C₄₁	—	2	2	no	—
230	C₂×C₄×C₄₁	—	2	2	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	2	no	—
235	C₂×C₄×C₄₁	—	2	2	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	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	—	4	2	no	—
248	C₂×C₄×C₄₁	—	4	2	no	—
249	C₂×C₄×C₄₁	—	4	2	no	—
250	C₂×C₄×C₄₁	—	4	2	no	—
251	C₂×C₄×C₄₁	—	4	2	no	—
252	C₂×C₄×C₄₁	—	4	2	no	—
253	C₂×C₄×C₄₁	—	4	2	no	—
254	C₂×C₄×C₄₁	—	4	2	no	—
255	C₂×C₄×C₄₁	—	4	2	no	—
256	C₂×C₄×C₄₁	—	4	2	no	—
257	C₂×C₄×C₄₁	—	4	2	no	—
258	C₂×C₄×C₄₁	—	4	2	no	—
259	C₂×C₄×C₄₁	—	4	2	no	—
260	C₂×C₄×C₄₁	—	4	2	no	—
261	C₂×C₄×C₄₁	—	4	2	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	4	2	no	—
264	C₂×C₄×C₄₁	—	4	2	no	—
265	C₂×C₄×C₄₁	—	4	2	no	—
266	C₂×C₄×C₄₁	—	4	2	no	—
267	C₂×C₄×C₄₁	—	4	2	no	—
268	C₂×C₄×C₄₁	—	4	2	no	—
269	C₂×C₄×C₄₁	#117	1	4	yes	—
270	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
271	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
272	C₂×C₄×C₄₁	C₄×Q₈	1	4	yes	—
273	C₂×C₄×C₄₁	C₄×Q₈	1	4	yes	—
274	C₂×C₄×C₄₁	#121	1	4	yes	—
275	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
276	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
277	C₂×C₄×C₄₁	#123	1	4	yes	—
278	C₂×C₄×C₄₁	#125	1	4	yes	—
279	C₂×C₄×C₄₁	#125	1	4	yes	—
280	C₂×C₄×C₄₁	#126	1	4	yes	—
281	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
282	#14699	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
284	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂²×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
287	C₂²×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
288	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
289	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
290	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
291	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
292	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
293	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
294	C₂²×C₄₁	#525	1	1	yes	characteristic
295	C₂²×C₄₁	#525	1	1	yes	characteristic
296	C₂²×C₄₁	C₂×#125	1	1	yes	characteristic
297	C₂²×C₄₁	C₂×#125	1	1	yes	characteristic
298	C₂²×C₄₁	C₂×#126	1	1	yes	characteristic
299	C₂²×C₄₁	#529	1	1	yes	characteristic
300	C₂²×C₄₁	#529	1	1	yes	characteristic
301	C₂²×C₄₁	#529	1	1	yes	characteristic
302	C₂²×C₄₁	#529	1	1	yes	characteristic
303	C₂²×C₄₁	#529	1	1	yes	characteristic
304	C₂²×C₄₁	#529	1	1	yes	characteristic
305	C₂²×C₄₁	#529	1	1	yes	characteristic
306	C₂²×C₄₁	#529	1	1	yes	characteristic
307	C₂²×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
308	C₂²×C₄₁	#532	1	1	yes	characteristic
309	C₂²×C₄₁	#532	1	1	yes	characteristic
310	C₂²×C₄₁	#532	1	1	yes	characteristic
311	C₂²×C₄₁	#532	1	1	yes	characteristic
312	C₂²×C₄₁	#533	1	1	yes	characteristic
313	C₂²×C₄₁	#533	1	1	yes	characteristic
314	C₂²×C₄₁	#533	1	1	yes	characteristic
315	C₂²×C₄₁	#533	1	1	yes	characteristic
316	C₂²×C₄₁	#533	1	1	yes	characteristic
317	C₂²×C₄₁	#533	1	1	yes	characteristic
318	C₄×C₄₁	—	2	4	no	—
319	C₄×C₄₁	—	2	4	no	—
320	C₄×C₄₁	—	2	4	no	—
321	C₄×C₄₁	—	2	4	no	—
322	C₄×C₄₁	—	2	4	no	—
323	C₄×C₄₁	—	2	4	no	—
324	C₄×C₄₁	—	4	4	no	—
325	C₄×C₄₁	—	4	4	no	—
326	C₄×C₄₁	—	8	2	no	—
327	C₄×C₄₁	—	8	2	no	—
328	C₄×C₄₁	#387	1	8	yes	complemented
329	C₂×#389	C₂×C₄₁	1	1	yes	characteristic
330	C₂×#389	C₂×C₄₁	1	1	yes	characteristic
331	C₂×#387	C₂×C₄₁	1	2	yes	—
332	C₂×C₄³	C₂×C₄₁	1	1	yes	characteristic
333	#1436	C₂×C₄₁	1	2	yes	—
334	#1436	C₂×C₄₁	1	2	yes	—
335	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
336	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
337	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
338	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
339	#1434	C₂×C₄₁	1	2	yes	—
340	C₂×C₄₁	C₂×#387	1	1	yes	characteristic
341	C₂×C₄₁	#2293	1	1	yes	characteristic
342	C₂×C₄₁	#2295	1	1	yes	characteristic
343	C₂×C₄₁	C₄×#121	1	1	yes	characteristic
344	C₂×C₄₁	C₄×C₂²⋊Q₈	1	1	yes	characteristic
345	C₂×C₄₁	C₄×#125	1	1	yes	characteristic
346	C₂×C₄₁	C₄×C₄⋊Q₈	1	1	yes	characteristic
347	C₂×C₄₁	#2851	1	1	yes	characteristic
348	C₂×C₄₁	#2854	1	1	yes	characteristic
349	C₂×C₄₁	#2855	1	1	yes	characteristic
350	C₂×C₄₁	#2857	1	1	yes	characteristic
351	C₂×C₄₁	#2859	1	1	yes	characteristic
352	C₂×C₄₁	#2860	1	1	yes	characteristic
353	C₂×C₄₁	#2863	1	1	yes	characteristic
354	C₂×C₄₁	#2864	1	1	yes	characteristic
355	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
357	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
358	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
359	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
360	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
361	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
362	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
363	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
364	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
365	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
366	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
367	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
368	#389	—	2	4	no	—
369	#389	C₄×C₄₁	1	8	yes	complemented
370	#387	—	2	8	no	—
371	C₂×#95	C₂²×C₄₁	1	2	yes	—
372	C₂×#95	C₂²×C₄₁	1	2	yes	—
373	C₂×#95	C₂²×C₄₁	1	2	yes	—
374	C₂×#95	C₂²×C₄₁	1	2	yes	—
375	C₂×#95	C₂²×C₄₁	1	2	yes	—
376	C₂×#95	C₂²×C₄₁	1	2	yes	—
377	C₂×#95	C₂²×C₄₁	1	2	yes	—
378	C₂×#95	C₂²×C₄₁	1	2	yes	—
379	C₂×#95	C₂²×C₄₁	1	2	yes	—
380	C₂×#95	C₂²×C₄₁	1	2	yes	—
381	C₄³	—	2	4	no	—
382	C₄₁	#14699	1	1	yes	characteristic, direct product factor, Sylow
383	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
384	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
385	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
386	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
387	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
394	C₂×C₄⋊C₄	—	2	4	no	—
395	C₂×C₄⋊C₄	—	2	2	no	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	4	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	4	no	—
401	C₂×C₄⋊C₄	—	2	4	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	4	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
410	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
411	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	—	2	2	no	—
414	C₂×C₄²	—	2	2	no	—
415	C₂×C₄²	—	2	2	no	—
416	C₂×C₄²	—	2	2	no	—
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	2	2	no	—
419	C₂×C₄²	—	2	2	no	—
420	C₂×C₄²	—	2	2	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	—	2	2	no	—
424	C₂×C₄²	—	2	2	no	—
425	C₂×C₄²	—	2	2	no	—
426	C₂×C₄²	—	2	2	no	—
427	C₂×C₄²	—	2	2	no	—
428	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
429	C₂×C₄²	D₄×C₄₁	1	4	yes	—
430	C₂×C₄²	D₄×C₄₁	1	4	yes	—
431	C₂×C₄²	Q₈×C₄₁	1	4	yes	—
432	C₂×C₄²	Q₈×C₄₁	1	4	yes	—
433	#95	—	2	4	no	—
434	#95	—	2	4	no	—
435	#95	—	2	4	no	—
436	#95	—	2	4	no	—
437	#95	—	2	4	no	—
438	#95	—	2	4	no	—
439	#95	—	2	4	no	—
440	#95	—	2	4	no	—
441	#95	—	2	4	no	—
442	#95	C₂×C₄×C₄₁	1	8	yes	—
443	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
495	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
496	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
497	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
498	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
499	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
500	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
501	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
502	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
503	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
504	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
505	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
506	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
507	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
508	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
509	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
510	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
511	C₂²×C₄	#41×C₄₁	1	2	yes	—
512	C₂²×C₄	#41×C₄₁	1	2	yes	—
513	C₂²×C₄	#41×C₄₁	1	2	yes	—
514	C₂²×C₄	#41×C₄₁	1	2	yes	—
515	C₂²×C₄	#41×C₄₁	1	2	yes	—
516	C₂²×C₄	#41×C₄₁	1	2	yes	—
517	C₂²×C₄	#41×C₄₁	1	2	yes	—
518	C₂²×C₄	#41×C₄₁	1	2	yes	—
519	C₂²×C₄	#41×C₄₁	1	2	yes	—
520	C₂²×C₄	#41×C₄₁	1	2	yes	—
521	C₄⋊C₄	—	2	8	no	—
522	C₄⋊C₄	—	2	16	no	—
523	C₄⋊C₄	—	2	8	no	—
524	C₄⋊C₄	—	4	8	no	—
525	C₄⋊C₄	—	4	4	no	—
526	C₄⋊C₄	—	4	4	no	—
527	C₄²	—	2	8	no	—
528	C₄²	—	2	8	no	—
529	C₄²	—	2	8	no	—
530	C₄²	—	2	8	no	—
531	C₄²	—	2	8	no	—
532	C₄²	—	2	8	no	—
533	C₄²	—	2	8	no	—
534	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
535	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
536	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
537	C₂³	C₂²×Q₈×C₄₁	1	1	yes	characteristic
538	C₂³	C₂²×Q₈×C₄₁	1	1	yes	characteristic
539	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
540	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
541	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
542	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
543	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
544	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
545	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
546	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
547	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
548	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	#117×C₄₁	1	4	yes	—
614	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
615	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
616	C₂×C₄	C₄×Q₈×C₄₁	1	4	yes	—
617	C₂×C₄	C₄×Q₈×C₄₁	1	4	yes	—
618	C₂×C₄	#121×C₄₁	1	4	yes	—
619	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
620	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
621	C₂×C₄	#123×C₄₁	1	4	yes	—
622	C₂×C₄	#125×C₄₁	1	4	yes	—
623	C₂×C₄	#125×C₄₁	1	4	yes	—
624	C₂×C₄	#126×C₄₁	1	4	yes	—
625	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
626	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
627	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
628	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
629	C₂²	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
630	C₂²	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
631	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
632	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
633	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
634	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
635	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
636	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
637	C₂²	C₄₁×#525	1	1	yes	characteristic
638	C₂²	C₄₁×#525	1	1	yes	characteristic
639	C₂²	C₂×#125×C₄₁	1	1	yes	characteristic
640	C₂²	C₂×#125×C₄₁	1	1	yes	characteristic
641	C₂²	C₂×#126×C₄₁	1	1	yes	characteristic
642	C₂²	C₄₁×#529	1	1	yes	characteristic
643	C₂²	C₄₁×#529	1	1	yes	characteristic
644	C₂²	C₄₁×#529	1	1	yes	characteristic
645	C₂²	C₄₁×#529	1	1	yes	characteristic
646	C₂²	C₄₁×#529	1	1	yes	characteristic
647	C₂²	C₄₁×#529	1	1	yes	characteristic
648	C₂²	C₄₁×#529	1	1	yes	characteristic
649	C₂²	C₄₁×#529	1	1	yes	characteristic
650	C₂²	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
651	C₂²	C₄₁×#532	1	1	yes	characteristic
652	C₂²	C₄₁×#532	1	1	yes	characteristic
653	C₂²	C₄₁×#532	1	1	yes	characteristic
654	C₂²	C₄₁×#532	1	1	yes	characteristic
655	C₂²	C₄₁×#533	1	1	yes	characteristic
656	C₂²	C₄₁×#533	1	1	yes	characteristic
657	C₂²	C₄₁×#533	1	1	yes	characteristic
658	C₂²	C₄₁×#533	1	1	yes	characteristic
659	C₂²	C₄₁×#533	1	1	yes	characteristic
660	C₂²	C₄₁×#533	1	1	yes	characteristic
661	C₄	—	2	4	no	—
662	C₄	—	2	4	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	4	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	4	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	4	no	—
669	C₄	—	8	2	no	—
670	C₄	—	8	2	no	—
671	C₄	C₄₁×#387	1	8	yes	complemented
672	C₂	C₂×C₄₁×#387	1	1	yes	characteristic
673	C₂	C₄₁×#2293	1	1	yes	characteristic
674	C₂	C₄₁×#2295	1	1	yes	characteristic
675	C₂	C₄×#121×C₄₁	1	1	yes	characteristic
676	C₂	C₄×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
677	C₂	C₄×#125×C₄₁	1	1	yes	characteristic
678	C₂	C₄×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
679	C₂	C₄₁×#2851	1	1	yes	characteristic
680	C₂	C₄₁×#2854	1	1	yes	characteristic
681	C₂	C₄₁×#2855	1	1	yes	characteristic
682	C₂	C₄₁×#2857	1	1	yes	characteristic
683	C₂	C₄₁×#2859	1	1	yes	characteristic
684	C₂	C₄₁×#2860	1	1	yes	characteristic
685	C₂	C₄₁×#2863	1	1	yes	characteristic
686	C₂	C₄₁×#2864	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
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
26. C₄₁×#389	C₄	semidirect
282. #14699	C₄₁	direct (N × H)
328. C₄×C₄₁	#387	semidirect
369. #389	C₄×C₄₁	semidirect
382. C₄₁	#14699	direct (N × H)
671. C₄	C₄₁×#387	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#389	2
C₂×C₄₁×#387	2
C₂×C₄³×C₄₁	2
C₄₁×#1436	2
C₄₁×C₄⋊#95	2
C₄₁×#1434	2
#14699	41

Subgroups — C41×#14699 #23790900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#14699 #23790900