Subgroups — C₄₃×#8667 #24928684

Order 11008.

454 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1806	C₂	1	2	yes	maximal
3	C₄×#107×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1303	C₂	1	2	yes	maximal, complemented
6	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
7	C₈×Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
8	C₈×Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
9	C₈×D₄×C₄₃	—	2	1	no	—
10	C₈×D₄×C₄₃	—	2	1	no	—
11	C₈×D₄×C₄₃	C₄	1	1	yes	characteristic, complemented
12	C₈×D₄×C₄₃	C₄	1	1	yes	characteristic, complemented
13	C₄₃×#431	—	2	1	no	—
14	C₄₃×#431	C₂²	1	1	yes	characteristic
15	C₂×#107×C₄₃	—	2	1	no	—
16	C₄₃×#423	C₂²	1	2	yes	—
17	C₂×#104×C₄₃	—	2	2	no	—
18	C₂×C₄×C₈×C₄₃	—	2	1	no	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
21	C₄₃×#340	—	2	1	no	—
22	C₄₃×#339	—	2	2	no	—
23	C₄₃×#335	—	2	1	no	—
24	C₄₃×#335	—	2	1	no	—
25	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
26	C₂×M₁₆×C₄₃	—	2	2	no	—
27	C₂²×C₈×C₄₃	—	2	1	no	—
28	C₂²×C₈×C₄₃	—	2	1	no	—
29	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
31	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₄×Q₈×C₄₃	Q₈	1	1	yes	characteristic
33	C₄×D₄×C₄₃	—	2	1	no	—
34	C₄×D₄×C₄₃	—	2	1	no	—
35	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
36	C₄×D₄×C₄₃	Q₈	1	1	yes	characteristic
37	#117×C₄₃	—	2	1	no	—
38	#117×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₄²×C₄₃	—	2	1	no	—
41	C₂×C₄²×C₄₃	—	2	2	no	—
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	#107×C₄₃	—	2	4	no	—
44	C₄⋊C₈×C₄₃	—	2	1	no	—
45	C₄⋊C₈×C₄₃	—	2	1	no	—
46	C₄⋊C₈×C₄₃	—	2	2	no	—
47	C₄⋊C₈×C₄₃	—	2	2	no	—
48	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
49	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
50	#104×C₄₃	—	4	4	no	—
51	C₂²⋊C₈×C₄₃	—	2	1	no	—
52	C₂²⋊C₈×C₄₃	—	2	1	no	—
53	C₂²⋊C₈×C₄₃	—	2	1	no	—
54	C₄×C₈×C₄₃	—	2	1	no	—
55	C₄×C₈×C₄₃	—	2	1	no	—
56	C₄×C₈×C₄₃	—	2	1	no	—
57	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
58	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
60	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
61	#95×C₄₃	—	2	2	no	—
62	#41×C₄₃	—	2	1	no	—
63	#41×C₄₃	—	2	1	no	—
64	#41×C₄₃	D₈	1	2	yes	—
65	#41×C₄₃	Q₁₆	1	2	yes	—
66	C₂×Q₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
67	C₂×D₄×C₄₃	—	2	1	no	—
68	C₂×D₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	—	2	1	no	—
70	C₂²×C₄×C₄₃	—	2	1	no	—
71	C₂²×C₄×C₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	—	4	2	no	—
73	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
76	M₁₆×C₄₃	—	4	2	no	—
77	M₁₆×C₄₃	—	4	2	no	—
78	C₂×C₈×C₄₃	—	2	2	no	—
79	C₂×C₈×C₄₃	—	2	1	no	—
80	C₂×C₈×C₄₃	—	2	1	no	—
81	C₂×C₈×C₄₃	—	4	1	no	—
82	C₂×C₈×C₄₃	—	4	2	no	—
83	C₂×C₈×C₄₃	—	4	2	no	—
84	C₂×C₈×C₄₃	—	4	2	no	—
85	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₄⋊C₄×C₄₃	—	2	1	no	—
91	C₄⋊C₄×C₄₃	—	2	4	no	—
92	C₄⋊C₄×C₄₃	—	4	2	no	—
93	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
94	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₄²×C₄₃	—	2	1	no	—
99	C₄²×C₄₃	—	2	1	no	—
100	C₄²×C₄₃	—	2	1	no	—
101	C₄²×C₄₃	—	4	2	no	—
102	C₄²×C₄₃	—	4	2	no	—
103	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
106	C₄²×C₄₃	#41	1	1	yes	characteristic
107	C₂³×C₄₃	—	2	1	no	—
108	C₂³×C₄₃	#121	1	1	yes	characteristic
109	Q₈×C₄₃	—	2	1	no	—
110	Q₈×C₄₃	#107	1	2	yes	complemented
111	D₄×C₄₃	—	2	2	no	—
112	D₄×C₄₃	—	2	2	no	—
113	D₄×C₄₃	—	2	1	no	—
114	D₄×C₄₃	#107	1	2	yes	complemented
115	C₂×C₄×C₄₃	—	2	1	no	—
116	C₂×C₄×C₄₃	—	2	1	no	—
117	C₂×C₄×C₄₃	—	2	1	no	—
118	C₂×C₄×C₄₃	—	2	2	no	—
119	C₂×C₄×C₄₃	—	2	2	no	—
120	C₂×C₄×C₄₃	—	2	1	no	—
121	C₂×C₄×C₄₃	—	2	1	no	—
122	C₂×C₄×C₄₃	—	4	1	no	—
123	C₂×C₄×C₄₃	—	4	2	no	—
124	C₂×C₄×C₄₃	—	4	1	no	—
125	C₂×C₄×C₄₃	—	4	1	no	—
126	C₂×C₄×C₄₃	—	4	4	no	—
127	C₂×C₄×C₄₃	—	8	2	no	—
128	C₂×C₄×C₄₃	—	8	2	no	—
129	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
132	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
133	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
136	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
137	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
138	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
139	C₈×C₄₃	—	2	1	no	—
140	C₈×C₄₃	—	2	1	no	—
141	C₈×C₄₃	—	2	1	no	—
142	C₈×C₄₃	—	4	1	no	—
143	C₈×C₄₃	—	4	1	no	—
144	C₈×C₄₃	—	8	2	no	—
145	C₈×C₄₃	#104	1	2	yes	complemented
146	#8667	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂²×C₄₃	—	2	1	no	—
148	C₂²×C₄₃	—	2	1	no	—
149	C₂²×C₄₃	—	2	2	no	—
150	C₂²×C₄₃	—	4	1	no	—
151	C₂²×C₄₃	—	4	1	no	—
152	C₂²×C₄₃	#380	1	1	yes	characteristic
153	C₂²×C₄₃	#466	1	1	yes	characteristic
154	C₂²×C₄₃	#467	1	1	yes	characteristic
155	C₄×C₄₃	—	2	1	no	—
156	C₄×C₄₃	—	2	2	no	—
157	C₄×C₄₃	—	2	1	no	—
158	C₄×C₄₃	—	2	1	no	—
159	C₄×C₄₃	—	4	1	no	—
160	C₄×C₄₃	—	4	1	no	—
161	C₄×C₄₃	—	8	4	no	—
162	C₄×C₄₃	C₂×#104	1	1	yes	characteristic
163	C₄×C₄₃	#421	1	1	yes	characteristic
164	C₄×C₄₃	C₂×#107	1	1	yes	characteristic
165	C₄×C₄₃	#427	1	1	yes	characteristic
166	C₄×C₄₃	#466	1	1	yes	characteristic
167	C₄×C₄₃	#467	1	1	yes	characteristic
168	C₈×#41	C₂×C₄₃	1	1	yes	characteristic
169	#1806	C₂×C₄₃	1	2	yes	—
170	C₄×#107	C₂×C₄₃	1	1	yes	characteristic, complemented
171	#1567	C₂×C₄₃	1	1	yes	characteristic, complemented
172	#1303	C₂×C₄₃	1	2	yes	complemented
173	C₂×C₄₃	—	2	1	no	—
174	C₂×C₄₃	—	2	1	no	—
175	C₂×C₄₃	—	4	2	no	—
176	C₂×C₄₃	#1806	1	1	yes	characteristic
177	C₂×C₄₃	#1808	1	1	yes	characteristic
178	C₂×C₄₃	#1814	1	1	yes	characteristic
179	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
180	C₈×Q₈	C₄×C₄₃	1	1	yes	characteristic, complemented
181	C₈×Q₈	C₄×C₄₃	1	1	yes	characteristic, complemented
182	C₈×D₄	—	2	1	no	—
183	C₈×D₄	—	2	1	no	—
184	C₈×D₄	C₄×C₄₃	1	1	yes	characteristic, complemented
185	C₈×D₄	C₄×C₄₃	1	1	yes	characteristic, complemented
186	#431	—	2	1	no	—
187	#431	C₂²×C₄₃	1	1	yes	characteristic
188	C₂×#107	—	2	1	no	—
189	#423	C₂²×C₄₃	1	2	yes	—
190	C₂×#104	—	2	2	no	—
191	C₂×C₄×C₈	—	2	1	no	—
192	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
193	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
194	#340	—	2	1	no	—
195	#339	—	2	2	no	—
196	#335	—	2	1	no	—
197	#335	—	2	1	no	—
198	C₄₃	#8667	1	1	yes	characteristic, direct product factor, Sylow
199	C₂×#41	D₄×C₄₃	1	1	yes	characteristic
200	C₂×M₁₆	—	2	2	no	—
201	C₂²×C₈	—	2	1	no	—
202	C₂²×C₈	—	2	1	no	—
203	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
204	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
205	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
206	C₄×Q₈	Q₈×C₄₃	1	1	yes	characteristic
207	C₄×D₄	—	2	1	no	—
208	C₄×D₄	—	2	1	no	—
209	C₄×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
210	C₄×D₄	Q₈×C₄₃	1	1	yes	characteristic
211	#117	—	2	1	no	—
212	#117	D₄×C₄₃	1	1	yes	characteristic
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	—	2	2	no	—
216	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
217	#107	—	2	4	no	—
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	—	2	1	no	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
223	C₄⋊C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
224	#104	—	4	4	no	—
225	C₂²⋊C₈	—	2	1	no	—
226	C₂²⋊C₈	—	2	1	no	—
227	C₂²⋊C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
232	C₄×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
233	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
234	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
235	#95	—	2	2	no	—
236	#41	—	2	1	no	—
237	#41	—	2	1	no	—
238	#41	D₈×C₄₃	1	2	yes	—
239	#41	Q₁₆×C₄₃	1	2	yes	—
240	C₂×Q₈	C₄⋊C₄×C₄₃	1	1	yes	characteristic
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	C₄⋊C₄×C₄₃	1	1	yes	characteristic
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	4	2	no	—
247	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
249	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
250	M₁₆	—	4	2	no	—
251	M₁₆	—	4	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	4	1	no	—
256	C₂×C₈	—	4	2	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	4	2	no	—
259	C₂×C₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
260	C₂×C₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
261	C₂×C₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
262	C₂×C₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
263	C₄⋊C₄	—	2	1	no	—
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	—	4	2	no	—
267	C₄⋊C₄	C₄⋊C₄×C₄₃	1	1	yes	characteristic
268	C₄⋊C₄	C₄⋊C₄×C₄₃	1	1	yes	characteristic
269	C₂²⋊C₄	—	2	1	no	—
270	C₂²⋊C₄	—	2	1	no	—
271	C₂²⋊C₄	—	2	1	no	—
272	C₄²	—	2	1	no	—
273	C₄²	—	2	1	no	—
274	C₄²	—	2	1	no	—
275	C₄²	—	4	2	no	—
276	C₄²	—	4	2	no	—
277	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
278	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
279	C₄²	C₂×Q₈×C₄₃	1	1	yes	characteristic
280	C₄²	#41×C₄₃	1	1	yes	characteristic
281	C₂³	—	2	1	no	—
282	C₂³	#121×C₄₃	1	1	yes	characteristic
283	Q₈	—	2	1	no	—
284	Q₈	#107×C₄₃	1	2	yes	complemented
285	D₄	—	2	2	no	—
286	D₄	—	2	2	no	—
287	D₄	—	2	1	no	—
288	D₄	#107×C₄₃	1	2	yes	complemented
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	8	2	no	—
302	C₂×C₄	—	8	2	no	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
304	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
305	C₂×C₄	#117×C₄₃	1	1	yes	characteristic
306	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
307	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
308	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
309	C₂×C₄	C₂×D₈×C₄₃	1	1	yes	characteristic
310	C₂×C₄	C₂×Q₁₆×C₄₃	1	1	yes	characteristic
311	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
312	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
313	C₈	—	2	1	no	—
314	C₈	—	2	1	no	—
315	C₈	—	2	1	no	—
316	C₈	—	4	1	no	—
317	C₈	—	4	1	no	—
318	C₈	—	8	2	no	—
319	C₈	#104×C₄₃	1	2	yes	complemented
320	C₂²	—	2	1	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	C₄₃×#380	1	1	yes	characteristic
326	C₂²	C₄₃×#466	1	1	yes	characteristic
327	C₂²	C₄₃×#467	1	1	yes	characteristic
328	C₄	—	2	2	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	1	no	—
331	C₄	—	2	1	no	—
332	C₄	—	4	1	no	—
333	C₄	—	4	1	no	—
334	C₄	—	8	4	no	—
335	C₄	C₂×#104×C₄₃	1	1	yes	characteristic
336	C₄	C₄₃×#421	1	1	yes	characteristic
337	C₄	C₂×#107×C₄₃	1	1	yes	characteristic
338	C₄	C₄₃×#427	1	1	yes	characteristic
339	C₄	C₄₃×#466	1	1	yes	characteristic
340	C₄	C₄₃×#467	1	1	yes	characteristic
341	C₂	—	2	1	no	—
342	C₂	—	2	1	no	—
343	C₂	—	4	2	no	—
344	C₂	C₄₃×#1806	1	1	yes	characteristic
345	C₂	C₄₃×#1808	1	1	yes	characteristic
346	C₂	C₄₃×#1814	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	#121
commutator	C₄²	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
socle	C₂²×C₄₃	#380
prime radical	C₂×#41×C₄₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×#107×C₄₃	C₂	semidirect
4. C₄₃×#1567	C₂	semidirect
5. C₄₃×#1303	C₂	semidirect
7. C₈×Q₈×C₄₃	C₄	semidirect
8. C₈×Q₈×C₄₃	C₄	semidirect
11. C₈×D₄×C₄₃	C₄	semidirect
12. C₈×D₄×C₄₃	C₄	semidirect
110. Q₈×C₄₃	#107	semidirect
114. D₄×C₄₃	#107	semidirect
145. C₈×C₄₃	#104	semidirect
146. #8667	C₄₃	direct (N × H)
170. C₄×#107	C₂×C₄₃	semidirect
171. #1567	C₂×C₄₃	semidirect
172. #1303	C₂×C₄₃	semidirect
180. C₈×Q₈	C₄×C₄₃	semidirect
181. C₈×Q₈	C₄×C₄₃	semidirect
184. C₈×D₄	C₄×C₄₃	semidirect
185. C₈×D₄	C₄×C₄₃	semidirect
198. C₄₃	#8667	direct (N × H)
284. Q₈	#107×C₄₃	semidirect
288. D₄	#107×C₄₃	semidirect
319. C₈	#104×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₈×#41×C₄₃	2
C₄₃×#1806	2
C₄×#107×C₄₃	2
C₄₃×#1567	2
C₄₃×#1303	2
#8667	43

Subgroups — C43×#8667 #24928684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8667 #24928684