Subgroups — #435×Dic₄₇ #26214625

Order 12032.

1282 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689195	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#20243265	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243260	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243174	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243169	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243167	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#435	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×D₄×Dic₄₇	C₄	1	2	yes	—
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
21	#15689195	C₄	1	8	yes	complemented
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	M₁₆×Dic₄₇	—	2	4	no	—
26	C₂×#13093935	C₂²	1	1	yes	characteristic
27	C₂×#13093934	C₂²	1	1	yes	characteristic
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×#13093934	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₇	—	2	4	no	—
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
39	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
40	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
41	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
42	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
44	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
45	#15688877	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
52	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
54	C₄₇×#435	C₄	1	8	yes	complemented
55	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
58	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
59	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
61	C₂×#10625329	—	2	2	no	—
62	C₂×#10625329	—	2	2	no	—
63	C₂×#10625329	C₂×C₄	1	4	yes	complemented
64	C₂²×C₄₇⋊C₈	—	2	2	no	—
65	C₂²×C₄₇⋊C₈	—	2	2	no	—
66	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	D₄×Dic₄₇	—	2	8	no	—
72	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₄₇	—	2	2	no	—
76	C₂×C₄×Dic₄₇	—	2	2	no	—
77	C₂×C₄×Dic₄₇	—	2	2	no	—
78	C₂×C₄×Dic₄₇	—	2	2	no	—
79	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
83	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
87	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
88	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
89	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
90	#13093935	C₂×C₄	1	4	yes	complemented
91	#13093934	—	2	2	no	—
92	#13093934	—	2	2	no	—
93	#13093934	—	2	2	no	—
94	#13093934	—	2	2	no	—
95	C₈×Dic₄₇	—	2	2	no	—
96	C₈×Dic₄₇	—	2	2	no	—
97	C₈×Dic₄₇	—	2	2	no	—
98	C₈×Dic₄₇	—	2	2	no	—
99	C₈×Dic₄₇	—	2	2	no	—
100	C₈×Dic₄₇	D₄	1	4	yes	complemented
101	C₄₇⋊#95	C₂×C₄	1	2	yes	—
102	C₄₇⋊#95	C₂×C₄	1	2	yes	—
103	C₄₇⋊#95	C₂×C₄	1	2	yes	—
104	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₄₇	—	2	2	no	—
108	C₂×M₁₆×C₄₇	—	2	2	no	—
109	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
110	C₂²×C₈×C₄₇	—	2	2	no	—
111	C₂²×C₈×C₄₇	—	2	2	no	—
112	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
118	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
119	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
124	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
125	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
126	#97×C₄₇	C₂×C₄	1	4	yes	complemented
127	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₄₇	—	2	4	no	—
130	C₂×D₄×C₄₇	C₄²	1	4	yes	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	2	1	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂²×Dic₄₇	—	2	4	no	—
149	C₂²×Dic₄₇	—	2	4	no	—
150	C₂²×Dic₄₇	—	2	4	no	—
151	C₂²×Dic₄₇	—	2	4	no	—
152	C₂²×Dic₄₇	—	2	4	no	—
153	C₂²×Dic₄₇	M₁₆	1	8	yes	complemented
154	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
155	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
156	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
157	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
158	M₁₆×C₄₇	—	2	8	no	—
159	C₂×C₈×C₄₇	—	2	1	no	—
160	C₂×C₈×C₄₇	—	2	1	no	—
161	C₂×C₈×C₄₇	—	2	1	no	—
162	C₂×C₈×C₄₇	—	2	1	no	—
163	C₂×C₈×C₄₇	—	2	1	no	—
164	C₂×C₈×C₄₇	—	2	1	no	—
165	C₂×C₈×C₄₇	—	2	8	no	—
166	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₄₇	#41	1	2	yes	—
172	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
173	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
174	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
175	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
176	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
177	C₂²⋊Dic₄₇	—	2	4	no	—
178	C₂²⋊Dic₄₇	—	2	4	no	—
179	C₄⋊Dic₄₇	—	2	4	no	—
180	C₄×Dic₄₇	—	2	1	no	—
181	C₄×Dic₄₇	—	2	1	no	—
182	C₄×Dic₄₇	—	2	1	no	—
183	C₄×Dic₄₇	—	2	1	no	—
184	C₄×Dic₄₇	—	2	1	no	—
185	C₄×Dic₄₇	—	2	1	no	—
186	C₄×Dic₄₇	—	2	4	no	—
187	C₄×Dic₄₇	—	2	4	no	—
188	C₄×Dic₄₇	—	2	4	no	—
189	C₄×Dic₄₇	—	2	4	no	—
190	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
191	C₄×Dic₄₇	#41	1	2	yes	—
192	#10625329	—	2	8	no	—
193	C₂×C₄₇⋊C₈	—	2	1	no	—
194	C₂×C₄₇⋊C₈	—	2	1	no	—
195	C₂×C₄₇⋊C₈	—	2	1	no	—
196	C₂×C₄₇⋊C₈	—	2	1	no	—
197	C₂×C₄₇⋊C₈	—	2	1	no	—
198	C₂×C₄₇⋊C₈	—	2	1	no	—
199	C₂×C₄₇⋊C₈	—	2	8	no	—
200	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
201	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
202	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
203	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
204	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
205	C₂×C₄₇⋊C₈	#41	1	2	yes	—
206	C₂³×C₄₇	—	2	1	no	—
207	C₂³×C₄₇	—	2	1	no	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	—	2	1	no	—
210	C₂³×C₄₇	—	2	1	no	—
211	C₂³×C₄₇	—	2	2	no	—
212	C₂³×C₄₇	—	2	2	no	—
213	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
214	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
215	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
216	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
217	D₄×C₄₇	—	2	8	no	—
218	C₂×C₄×C₄₇	—	2	1	no	—
219	C₂×C₄×C₄₇	—	2	1	no	—
220	C₂×C₄×C₄₇	—	2	1	no	—
221	C₂×C₄×C₄₇	—	2	1	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
233	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
234	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
235	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
236	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
242	C₂×Dic₄₇	—	2	2	no	—
243	C₂×Dic₄₇	—	2	2	no	—
244	C₂×Dic₄₇	—	2	16	no	—
245	C₂×Dic₄₇	—	2	2	no	—
246	C₂×Dic₄₇	—	2	2	no	—
247	C₂×Dic₄₇	—	2	2	no	—
248	C₂×Dic₄₇	—	2	2	no	—
249	C₂×Dic₄₇	—	2	2	no	—
250	C₂×Dic₄₇	—	2	2	no	—
251	C₂×Dic₄₇	—	4	8	no	—
252	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
253	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
254	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
255	C₂×Dic₄₇	#131	1	4	yes	—
256	C₈×C₄₇	—	2	2	no	—
257	C₈×C₄₇	—	2	2	no	—
258	C₈×C₄₇	—	2	2	no	—
259	C₈×C₄₇	C₄×D₄	1	4	yes	complemented
260	C₄₇⋊C₈	—	2	2	no	—
261	C₄₇⋊C₈	—	2	2	no	—
262	C₄₇⋊C₈	—	2	2	no	—
263	C₄₇⋊C₈	C₄×D₄	1	4	yes	complemented
264	C₄×#435	—	47	1	no	maximal, Sylow
265	C₂²×C₄₇	—	2	2	no	—
266	C₂²×C₄₇	—	2	4	no	—
267	C₂²×C₄₇	—	2	4	no	—
268	C₂²×C₄₇	—	2	2	no	—
269	C₂²×C₄₇	—	2	2	no	—
270	C₂²×C₄₇	—	2	2	no	—
271	C₂²×C₄₇	—	2	2	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	—	4	2	no	—
274	C₂²×C₄₇	C₄×M₁₆	1	4	yes	complemented
275	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
276	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
277	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
278	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
279	C₂²×C₄₇	C₂×#131	1	2	yes	—
280	C₄×C₄₇	—	2	2	no	—
281	C₄×C₄₇	—	2	2	no	—
282	C₄×C₄₇	—	2	2	no	—
283	C₄×C₄₇	—	2	2	no	—
284	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
285	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
286	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
287	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
288	Dic₄₇	—	2	4	no	—
289	Dic₄₇	—	4	2	no	—
290	Dic₄₇	—	4	2	no	—
291	Dic₄₇	#435	1	8	yes	direct product factor
292	C₂×#435	—	47	1	no	—
293	C₂×#435	D₄₇	1	1	yes	characteristic
294	C₂×C₄×M₁₆	—	47	1	no	—
295	C₂²×C₄×C₈	—	47	1	no	—
296	C₄²×D₄	—	47	1	no	—
297	#1771	—	47	1	no	—
298	#1771	—	47	1	no	—
299	C₄×C₄⋊C₈	—	47	1	no	—
300	#1753	—	47	1	no	—
301	#1753	—	47	1	no	—
302	#1752	—	47	1	no	—
303	#1752	—	47	1	no	—
304	C₄×C₂²⋊C₈	—	47	1	no	—
305	C₄×C₂²⋊C₈	—	47	1	no	—
306	C₄×#97	—	47	1	no	—
307	C₂×C₄₇	—	2	4	no	—
308	C₂×C₄₇	—	4	2	no	—
309	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
310	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
311	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
312	C₂×C₄₇	C₂×#435	1	2	yes	—
313	C₂×C₄₇	#2965	1	2	yes	—
314	C₂²×M₁₆	—	47	1	no	—
315	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
316	C₂³×C₈	—	47	1	no	—
317	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
318	C₂×C₄×D₄	—	47	2	no	—
319	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
320	C₂²×C₄²	—	47	1	no	—
321	C₂²×C₄²	—	47	1	no	—
322	#435	—	47	8	no	—
323	#435	Dic₄₇	1	8	yes	direct product factor
324	C₂×C₄⋊C₈	—	47	1	no	—
325	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₈	—	47	1	no	—
327	C₂×C₂²⋊C₈	—	47	1	no	—
328	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
329	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
330	C₄×M₁₆	—	94	4	no	—
331	C₂×#97	—	47	1	no	—
332	C₂×#97	—	47	1	no	—
333	C₂×#97	—	47	1	no	—
334	C₂×#97	—	47	1	no	—
335	C₂×#97	—	47	1	no	—
336	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
337	C₂×C₄×C₈	—	47	1	no	—
338	C₂×C₄×C₈	—	47	1	no	—
339	C₂×C₄×C₈	—	47	1	no	—
340	C₂×C₄×C₈	—	47	1	no	—
341	C₂×C₄×C₈	—	47	1	no	—
342	C₂×C₄×C₈	—	47	1	no	—
343	C₂×C₄×C₈	—	94	4	no	—
344	C₄×C₄⋊C₄	—	47	2	no	—
345	C₄×C₄⋊C₄	—	47	1	no	—
346	C₄×C₂²⋊C₄	—	47	1	no	—
347	C₄×C₂²⋊C₄	—	47	1	no	—
348	C₄×C₂²⋊C₄	—	47	2	no	—
349	C₄×C₂²⋊C₄	—	47	2	no	—
350	C₄³	—	47	1	no	—
351	#336	—	47	1	no	—
352	#336	—	47	1	no	—
353	#336	—	47	1	no	—
354	#336	—	47	1	no	—
355	#336	—	47	1	no	—
356	#336	—	47	1	no	—
357	C₄₇	C₄×#435	1	1	yes	characteristic, complemented, Sylow
358	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
359	C₂³×C₄	—	47	2	no	—
360	C₂³×C₄	—	47	2	no	—
361	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
362	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	47	4	no	—
366	C₂×M₁₆	—	94	2	no	—
367	C₂×M₁₆	—	94	2	no	—
368	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	complemented
369	C₂²×C₈	—	2	2	no	—
370	C₂²×C₈	—	2	2	no	—
371	C₂²×C₈	—	47	1	no	—
372	C₂²×C₈	—	47	4	no	—
373	C₂²×C₈	—	47	1	no	—
374	C₂²×C₈	—	47	1	no	—
375	C₂²×C₈	—	47	1	no	—
376	C₂²×C₈	—	94	2	no	—
377	C₂²×C₈	—	94	2	no	—
378	C₂²×C₈	C₂×Dic₄₇	1	4	yes	complemented
379	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
380	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
381	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
382	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
383	C₄×D₄	—	94	8	no	—
384	C₄×D₄	C₄×D₄₇	1	4	yes	—
385	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
386	C₂×C₄⋊C₄	—	47	2	no	—
387	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	47	2	no	—
389	C₂×C₂²⋊C₄	—	47	2	no	—
390	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄²	—	47	1	no	—
393	C₂×C₄²	—	47	2	no	—
394	C₂×C₄²	—	47	2	no	—
395	C₂×C₄²	—	47	2	no	—
396	C₂×C₄²	—	47	2	no	—
397	C₂×C₄²	—	47	1	no	—
398	C₂×C₄²	—	47	1	no	—
399	C₂×C₄²	—	47	1	no	—
400	C₂×C₄²	—	94	2	no	—
401	C₂×C₄²	—	94	2	no	—
402	C₂×C₄²	—	94	2	no	—
403	C₂×C₄²	—	94	2	no	—
404	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
405	C₄⋊C₈	—	47	4	no	—
406	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
407	C₂²⋊C₈	—	47	4	no	—
408	C₂²⋊C₈	—	47	4	no	—
409	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
410	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
411	#97	—	47	4	no	—
412	#97	—	94	2	no	—
413	#97	—	94	2	no	—
414	#97	—	94	2	no	—
415	#97	—	94	2	no	—
416	#97	C₂×Dic₄₇	1	4	yes	complemented
417	C₄×C₈	—	47	4	no	—
418	C₄×C₈	—	94	2	no	—
419	C₄×C₈	—	94	2	no	—
420	C₄×C₈	—	94	2	no	—
421	C₄×C₈	—	94	2	no	—
422	C₄×C₈	—	94	2	no	—
423	#95	—	47	2	no	—
424	#95	—	47	2	no	—
425	#95	—	47	2	no	—
426	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
427	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	47	2	no	—
439	C₂²×C₄	—	47	8	no	—
440	C₂²×C₄	—	47	2	no	—
441	C₂²×C₄	—	47	2	no	—
442	C₂²×C₄	—	47	2	no	—
443	C₂²×C₄	—	94	4	no	—
444	C₂²×C₄	—	94	4	no	—
445	C₂²×C₄	—	94	4	no	—
446	C₂²×C₄	—	94	4	no	—
447	C₂²×C₄	—	94	4	no	—
448	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
453	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
454	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
455	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
456	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
457	M₁₆	—	2	8	no	—
458	M₁₆	—	94	8	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	8	no	—
466	C₂×C₈	—	47	2	no	—
467	C₂×C₈	—	47	2	no	—
468	C₂×C₈	—	47	2	no	—
469	C₂×C₈	—	47	2	no	—
470	C₂×C₈	—	47	2	no	—
471	C₂×C₈	—	47	2	no	—
472	C₂×C₈	—	94	8	no	—
473	C₂×C₈	—	94	1	no	—
474	C₂×C₈	—	94	1	no	—
475	C₂×C₈	—	94	1	no	—
476	C₂×C₈	—	94	1	no	—
477	C₂×C₈	—	94	1	no	—
478	C₂×C₈	—	94	1	no	—
479	C₂×C₈	D₄×D₄₇	1	2	yes	—
480	C₂×C₈	#10625352	1	2	yes	—
481	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
482	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
483	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
484	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
485	C₄⋊C₄	—	94	4	no	—
486	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
487	C₂²⋊C₄	—	94	4	no	—
488	C₂²⋊C₄	—	94	4	no	—
489	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
490	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
491	C₄²	—	47	2	no	—
492	C₄²	—	47	2	no	—
493	C₄²	—	94	4	no	—
494	C₄²	—	94	4	no	—
495	C₄²	—	94	4	no	—
496	C₄²	—	94	4	no	—
497	C₄²	—	94	1	no	—
498	C₄²	—	94	1	no	—
499	C₄²	—	94	1	no	—
500	C₄²	—	94	1	no	—
501	C₄²	—	94	1	no	—
502	C₄²	—	94	1	no	—
503	C₄²	C₂×C₄×D₄₇	1	2	yes	—
504	C₄²	C₂²×Dic₄₇	1	2	yes	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
513	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
514	C₂³	M₁₆×D₄₇	1	4	yes	—
515	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
516	D₄	—	2	8	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	47	4	no	—
532	C₂×C₄	—	47	4	no	—
533	C₂×C₄	—	47	4	no	—
534	C₂×C₄	—	47	4	no	—
535	C₂×C₄	—	94	16	no	—
536	C₂×C₄	—	94	2	no	—
537	C₂×C₄	—	94	2	no	—
538	C₂×C₄	—	94	2	no	—
539	C₂×C₄	—	94	2	no	—
540	C₂×C₄	—	94	2	no	—
541	C₂×C₄	—	94	2	no	—
542	C₂×C₄	—	94	2	no	—
543	C₂×C₄	—	94	2	no	—
544	C₂×C₄	—	188	8	no	—
545	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
546	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
547	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
548	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
549	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
550	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
552	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
553	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
554	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	47	4	no	—
559	C₈	—	94	2	no	—
560	C₈	—	94	2	no	—
561	C₈	—	94	2	no	—
562	C₈	D₄×Dic₄₇	1	4	yes	complemented
563	C₂²	—	2	4	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	4	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	M₁₆×Dic₄₇	1	4	yes	complemented
573	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
574	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
575	C₂²	C₄×#10625352	1	1	yes	characteristic
576	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
577	C₂²	#131×D₄₇	1	2	yes	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	47	8	no	—
583	C₄	—	94	4	no	—
584	C₄	—	188	2	no	—
585	C₄	—	188	2	no	—
586	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
587	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
588	C₄	C₄×#10625352	1	1	yes	characteristic
589	C₄	#41×Dic₄₇	1	1	yes	characteristic
590	C₂	—	2	4	no	—
591	C₂	—	4	2	no	—
592	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
593	C₂	C₂×M₁₆×Dic₄₇	1	1	yes	characteristic
594	C₂	#131×Dic₄₇	1	1	yes	characteristic
595	C₂	#435×D₄₇	1	2	yes	—
596	C₂	#20252348	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄₇×#435	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#435	D₄₇
hypocenter	C₄₇	C₄×#435
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×Dic₄₇	C₂	semidirect
3. C₂²×C₈×Dic₄₇	C₂	semidirect
5. #20243265	C₂	semidirect
6. #20243260	C₂	semidirect
7. C₄⋊C₈×Dic₄₇	C₂	semidirect
8. #20243174	C₂	semidirect
9. #20243169	C₂	semidirect
10. #20243167	C₂	semidirect
11. #20243164	C₂	semidirect
12. C₂²⋊C₈×Dic₄₇	C₂	semidirect
13. C₂²⋊C₈×Dic₄₇	C₂	semidirect
14. #97×Dic₄₇	C₂	semidirect
21. #15689195	C₄	semidirect
54. C₄₇×#435	C₄	semidirect
63. C₂×#10625329	C₂×C₄	semidirect
66. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
87. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
88. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
89. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
90. #13093935	C₂×C₄	semidirect
100. C₈×Dic₄₇	D₄	semidirect
109. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
112. C₂²×C₈×C₄₇	C₂×C₄	semidirect
123. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
124. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
125. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
126. #97×C₄₇	C₂×C₄	semidirect
153. C₂²×Dic₄₇	M₁₆	semidirect
259. C₈×C₄₇	C₄×D₄	semidirect
263. C₄₇⋊C₈	C₄×D₄	semidirect
274. C₂²×C₄₇	C₄×M₁₆	semidirect
291. Dic₄₇	#435	direct (N × H)
323. #435	Dic₄₇	direct (N × H)
357. C₄₇	C₄×#435	semidirect
368. C₂×M₁₆	C₂×Dic₄₇	semidirect
378. C₂²×C₈	C₂×Dic₄₇	semidirect
406. C₄⋊C₈	C₂×Dic₄₇	semidirect
409. C₂²⋊C₈	C₂×Dic₄₇	semidirect
410. C₂²⋊C₈	C₂×Dic₄₇	semidirect
416. #97	C₂×Dic₄₇	semidirect
562. C₈	D₄×Dic₄₇	semidirect
572. C₂²	M₁₆×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689195	2
C₂×M₁₆×Dic₄₇	2
C₂²×C₈×Dic₄₇	2
C₄×D₄×Dic₄₇	2
#20243265	2
#20243260	2
C₄⋊C₈×Dic₄₇	2
#20243174	2
#20243169	2
#20243167	2
#20243164	2
C₂²⋊C₈×Dic₄₇	2
#97×Dic₄₇	2
C₂×C₄₇×#435	2
C₄×#435	47

Subgroups — #435×Dic47 #26214625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #435×Dic₄₇ #26214625