Finite Group Databasebeta

← D3×#4968 #11869557

Subgroups — D3×#4968 #11869557

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2D3×#930C211yesmaximal, characteristic
3#10592667C211yesmaximal, characteristic, complemented
4C3×#4968C211yesmaximal, characteristic, complemented
5D3×#830C211yesmaximal, characteristic, complemented
6#10591125C211yesmaximal, characteristic, complemented
7#10591091C211yesmaximal, characteristic, complemented
8D3×#809C212yesmaximal, complemented
9D3×#808C212yesmaximal, complemented
10#10590500C212yesmaximal, complemented
11#10590423C212yesmaximal, complemented
12C2×#4968—31nomaximal
13D3×#481—31nomaximal
14C22×C3×C4×D3—21no—
15C22×C3×C4×D3C2211yescharacteristic
16C2×D3×#67—21no—
17C2×D3×D12C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic, complemented
19#64139C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
22C2×C3×Dic3⋊C4—21no—
23C3×D3×C4⋊C4—21no—
24C3×D3×C4⋊C4—21no—
25C3×D3×C4⋊C4C2212yes—
26C3×D3×C4⋊C4C2212yescomplemented
27#63978—21no—
28D3×(C2×D3)⋊C4—21no—
29#63909C2211yescharacteristic
30#63908C2211yescharacteristic
31#63906—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33C2×D3×C3⋊C8C2212yes—
34#63657C2211yescharacteristic, complemented
35#63636C2212yescomplemented
36#63635C2212yescomplemented
37C3×#830C2211yescharacteristic, complemented
38C3×#809C2212yescomplemented
39C3×#808C2212yescomplemented
40#63574C2212yescomplemented
41#63573C2212yescomplemented
42#63564C2212yescomplemented
43#63562C2212yescomplemented
44(C2×D3)⋊(C3⋊C8)C2212yescomplemented
45C22×C3×C4⋊C4—31no—
46C2×#930—31no—
47D3×#121—31no—
48C2×D3×C4⋊C4D311yescharacteristic, complemented
49C3×#481—31no—
50C2×#830—31no—
51#5034—31no—
52#4968—31no—
53#4968—31no—
54#4968—31no—
55#4968—31no—
56#4968—32no—
57#4968—32no—
58#4968—61no—
59#4968D311yescharacteristic, direct product factor
60C2×#809—32no—
61C2×#808—32no—
62#4863—32no—
63D3×#106—32no—
64#4777—32no—
65D3×#102—32no—
66#4735—31no—
67D3×C22⋊C8—31no—
68C23×C3×D3D411yescharacteristic
69C22×D32—21no—
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C2×#638—21no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—44no—
82C2×C3×C4×D3D411yescharacteristic
83C2×C3×C4×D3D411yescharacteristic
84C2×C3×C4×D3C2311yescharacteristic
85C2×C3×C4×D3C2311yescharacteristic
86D3×#67—44no—
87C2×#626—21no—
88C2×#626—21no—
89C2×#625—21no—
90C2×D3×Dic3—21no—
91D3×D12—24no—
92C32×C4⋊C4—21no—
93C32×C4⋊C4C2312yes—
94#3752—21no—
95C4⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×Dic3⋊C4—22no—
102C3×Dic3⋊C4—22no—
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—21no—
105#3722—21no—
106(C2×D3)⋊Dic3—21no—
107D3×C3⋊C8—24no—
108C2×#481—91noSylow
109C23×C3×C4—31no—
110C23×C3×C4—61no—
111C22×#67—61no—
112C2×D3×D4—31no—
113C2×D3×D4—61no—
114C22×D12—31no—
115C22×C4×D3—21no—
116C22×C4×D3C2×D311yescharacteristic
117C3×#121—31no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4—61no—
123C2×C3×C4⋊C4—61no—
124C2×C3×C4⋊C4—61no—
125C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
126C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
127#939—61no—
128#938—31no—
129#930—31no—
130#930—31no—
131#930—31no—
132#930—31no—
133#930—61no—
134#930—61no—
135#930—61no—
136#930C2×D311yescharacteristic
137C2×(C2×D3)⋊C4—61no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3C2×D311yescharacteristic, complemented
140C2×Dic3⋊C4—21no—
141C22×C3⋊C8—32no—
142C2×D3×C8—32no—
143#895—31no—
144D3×C4⋊C4—21no—
145D3×C4⋊C4—21no—
146D3×C4⋊C4—31no—
147D3×C4⋊C4C2×D312yes—
148D3×C4⋊C4C2×D312yescomplemented
149#884—61no—
150D3×C22⋊C4—61no—
151C3×#106—32no—
152C3×#102—32no—
153C3×C22⋊C8—31no—
154#832—32no—
155#830—31no—
156#830—31no—
157#830—32no—
158#830—61no—
159#830C2×D311yescharacteristic, complemented
160#821—32no—
161(C2×D3)⋊C8—32no—
162#817—32no—
163#809—32no—
164#809—32no—
165#809—32no—
166#809—32no—
167#809—62no—
168#809C2×D312yescomplemented
169#808—32no—
170#808—32no—
171#808—32no—
172#808—32no—
173#808—32no—
174#808—62no—
175#808C2×D312yescomplemented
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—21no—
181C22×C3×D3SD1614yes—
182C22×C3×D3C2×D411yescharacteristic
183C22×C3×D3C2×D411yescharacteristic
184C2×D32—42no—
185C2×D32—42no—
186C2×D32—42no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2411yescharacteristic
192#638—42no—
193C2×C3⋊Dic3—21no—
194C4⋊(C3⋊D3)—22no—
195C3×#67—42no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—42no—
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—22no—
203C3×C4×D3—22no—
204C3×C4×D3—22no—
205C3×C4×D3—22no—
206C3×C4×D3—44no—
207C3×C4×D3—44no—
208C3×C4×D3#4114yes—
209#626—42no—
210#626—42no—
211#625—42no—
212D3×Dic3—42no—
213C3⋊(C3⋊C8)—22no—
214C3×C3⋊C8—22no—
215C2×#121—91no—
216C22×C4⋊C4—31no—
217#481—31no—
218#481—91no—
219#481—92no—
220#481—92no—
221#481—91no—
222#481—91no—
223C2×#106—92no—
224C2×#102—92no—
225C2×C22⋊C8—91no—
226C24×C3—31no—
227C23×D3—61no—
228C23×D3—61no—
229C23×D3#6711yescharacteristic
230C2×C3×D4—31no—
231C2×C3×D4—61no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—41no—
241C22×C3×C4—64no—
242C22×C3×C4—62no—
243C22×C3×C4—62no—
244C22×C3×C4—61no—
245C22×C3×C4—124no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—21no—
249C2×#67—61no—
250C2×#67—61no—
251C2×#67—61no—
252C2×#67—61no—
253C2×#67—61no—
254C2×#67—61no—
255C2×#67—121no—
256C2×#67—124no—
257C22×Dic3—21no—
258C22×Dic3—61no—
259C22×Dic3#6711yescharacteristic
260D3×D4—64no—
261D3×D4—124no—
262C2×D12—31no—
263C2×D12—31no—
264C2×D12—61no—
265C2×D12—64no—
266C2×D12—61no—
267C2×D12—61no—
268C2×D12C22×D311yescharacteristic
269C2×C4×D3—24no—
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3—44no—
273C2×C4×D3—61no—
274C2×C4×D3#6711yescharacteristic
275C2×C4×D3#6711yescharacteristic
276C2×C4×D3C22×D311yescharacteristic
277C2×C4×D3C22×D311yescharacteristic
278C2×C3×C8—32no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—32no—
283C3×C4⋊C4—31no—
284C3×C4⋊C4—41no—
285C3×C4⋊C4—62no—
286C3×C4⋊C4—62no—
287C3×C4⋊C4—61no—
288C3×C4⋊C4C22×D312yes—
289C3×C4⋊C4C22×D312yes—
290C3×C22⋊C4—61no—
291#217—61no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—121no—
299C4⋊Dic3—21no—
300C4⋊Dic3—31no—
301C4⋊Dic3—31no—
302C4⋊Dic3—61no—
303C4⋊Dic3—61no—
304C4⋊Dic3C22×D311yescharacteristic
305C4⋊Dic3C22×D312yes—
306Dic3⋊C4—22no—
307Dic3⋊C4—22no—
308Dic3⋊C4—61no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—64no—
313C2×C3⋊C8C22×D312yes—
314D3×C8—64no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32C2×SD1612yes—
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—41no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3×D3—21no—
323C2×C3×D3—21no—
324C2×C3×D3—28no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3#12312yes—
329C2×C3×D3C2×SD1612yes—
330C2×C3×D3C2×SD1612yes—
331C2×C3×D3AGL(1,ℤ/8)12yes—
332D32—84no—
333C32×C4—21no—
334C32×C4—42no—
335C32×C4C2×#4112yes—
336C3⋊Dic3—41no—
337C3×Dic3—21no—
338C3×Dic3—41no—
339C3×Dic3—42no—
340C3×Dic3#12312yes—
341C22×D4—91no—
342C22×D4—181no—
343C23×C4—31no—
344C23×C4—61no—
345C22×C8—92no—
346#121—31no—
347#121—91no—
348#121—91no—
349#121—91no—
350#121—181no—
351#121—181no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4D3211yescharacteristic, complemented
360C2×C22⋊C4—181no—
361#106—32no—
362#106—92no—
363#106—92no—
364#106—92no—
365#102—32no—
366#102—92no—
367#102—92no—
368#102—92no—
369C22⋊C8—31no—
370C22⋊C8—92no—
371C22⋊C8—91no—
372C23×C3—21no—
373C23×C3—31no—
374C23×C3—34no—
375C23×C3—31no—
376C23×C3—62no—
377C23×C3—62no—
378C23×C3—61no—
379C23×C3D3×D411yescharacteristic
380C23×C3C2×#6711yescharacteristic
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—21no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—121no—
387C22×D3—122no—
388C22×D3—122no—
389C22×D3—122no—
390C22×D3—122no—
391C22×D3—122no—
392C22×D3—122no—
393C22×D3#21514yes—
394C22×D3C2×#6711yescharacteristic
395C22×D3C2×#6711yescharacteristic
396C3×D4—62no—
397C3×D4—122no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—31no—
405C2×C3×C4—34no—
406C2×C3×C4—31no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—61no—
417C2×C3×C4—82no—
418C2×C3×C4—124no—
419C2×C3×C4—124no—
420C2×C3×C4—122no—
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—42no—
426#67—122no—
427#67—122no—
428#67—122no—
429#67—122no—
430#67—122no—
431#67—122no—
432#67—242no—
433C2×Dic3—22no—
434C2×Dic3—21no—
435C2×Dic3—22no—
436C2×Dic3—42no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—121no—
440C2×Dic3—122no—
441C2×Dic3C2×#6711yescharacteristic
442C2×Dic3C2×#6711yescharacteristic
443D12—22no—
444D12—62no—
445D12—62no—
446D12—122no—
447D12—122no—
448D12—122no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—44no—
453C4×D3—44no—
454C4×D3—122no—
455C4×D3#23514yes—
456C3×C8—62no—
457C3⋊C8—22no—
458C3⋊C8—62no—
459C3⋊C8—62no—
460C3⋊C8—122no—
461C2×C32—22no—
462C2×C32C2×#12311yescharacteristic
463C2×C32C22×SD1611yescharacteristic
464C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
465C3⋊D3—81no—
466C3×D3—22no—
467C3×D3—81no—
468C3×D3#48114yescomplemented
469C24—31no—
470C24—181no—
471C2×D4—31no—
472C2×D4—61no—
473C2×D4—91no—
474C2×D4—184no—
475C2×D4—181no—
476C2×D4—181no—
477C2×D4—181no—
478C2×D4—181no—
479C2×D4—364no—
480C22×C4—21no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—64no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—61no—
490C22×C4—124no—
491C22×C4—181no—
492C22×C4C2×D3211yescharacteristic
493C2×C8—32no—
494C2×C8—92no—
495C2×C8—184no—
496C4⋊C4—21no—
497C4⋊C4—32no—
498C4⋊C4—31no—
499C4⋊C4—62no—
500C4⋊C4—62no—
501C4⋊C4—61no—
502C4⋊C4—91no—
503C4⋊C4—181no—
504C4⋊C4C2×D3212yes—
505C22⋊C4—61no—
506C22⋊C4—181no—
507C22⋊C4—181no—
508C22⋊C4—181no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—22no—
515C22×C3—32no—
516C22×C3—32no—
517C22×C3—32no—
518C22×C3—32no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—68no—
522C22×C3—61no—
523C22×C3—61no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3D3×SD1612yes—
528C22×C3C2×#21512yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C2×D3—21no—
532C2×D3—21no—
533C2×D3—28no—
534C2×D3—41no—
535C2×D3—41no—
536C2×D3—41no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—121no—
540C2×D3—121no—
541C2×D3—121no—
542C2×D3—121no—
543C2×D3—241no—
544C2×D3—241no—
545C2×D3—241no—
546C2×D3—244no—
547C2×D3—244no—
548C2×D3#92912yes—
549C2×D3#93212yes—
550C2×D3C2×#21512yes—
551C2×D3C2×#21512yes—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—22no—
555C3×C4—32no—
556C3×C4—41no—
557C3×C4—42no—
558C3×C4—42no—
559C3×C4—61no—
560C3×C4—82no—
561C3×C4—122no—
562C3×C4—121no—
563C3×C4C2×#23512yes—
564C3×C4D3×#4112yes—
565Dic3—21no—
566Dic3—41no—
567Dic3—42no—
568Dic3—121no—
569Dic3—121no—
570Dic3—241no—
571Dic3#92912yes—
572C32C2×#48111yescharacteristic, complemented, Sylow
573C23—31no—
574C23—31no—
575C23—34no—
576C23—62no—
577C23—62no—
578C23—61no—
579C23—181no—
580C23—362no—
581C23—362no—
582C23—362no—
583C23D3×#6711yescharacteristic
584D4—62no—
585D4—122no—
586D4—182no—
587D4—362no—
588D4—362no—
589D4—362no—
590D4—362no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—31no—
594C2×C4—34no—
595C2×C4—31no—
596C2×C4—42no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—62no—
603C2×C4—124no—
604C2×C4—124no—
605C2×C4—122no—
606C2×C4—181no—
607C2×C4—362no—
608C2×C4D3×#6711yescharacteristic
609C2×C4C22×D3211yescharacteristic
610C8—62no—
611C8—182no—
612C2×C3—22no—
613C2×C3—22no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—34no—
618C2×C3—42no—
619C2×C3—62no—
620C2×C3—241no—
621C2×C3D3×#12311yescharacteristic
622C2×C3C2×D3×SD1611yescharacteristic
623C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
624C2×C3C2×#92911yescharacteristic
625C2×C3C2×#93211yescharacteristic
626C2×C3C22×#21511yescharacteristic
627D3—22no—
628D3—81no—
629D3—241no—
630D3—241no—
631D3—481no—
632D3#496814yesdirect product factor
633C22—21no—
634C22—21no—
635C22—32no—
636C22—32no—
637C22—32no—
638C22—32no—
639C22—68no—
640C22—61no—
641C22—61no—
642C22—121no—
643C22—121no—
644C22—121no—
645C22—361no—
646C22—361no—
647C22—361no—
648C22—724no—
649C22D3×#21512yes—
650C22C2×D3×#6711yescharacteristic
651C4—21no—
652C4—32no—
653C4—42no—
654C4—61no—
655C4—122no—
656C4—121no—
657C4—361no—
658C4D3×#23512yes—
659C3—21no—
660C3D3×#48111yescharacteristic, complemented
661C3C2×#496811yescharacteristic, complemented
662C2—22no—
663C2—34no—
664C2—62no—
665C2—241no—
666C2—721no—
667C2D3×#92911yescharacteristic
668C2D3×#93211yescharacteristic
669C2C2×D3×#21511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalD3×#930C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#481
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
3. #10592667C2semidirect
4. C3×#4968C2semidirect
5. D3×#830C2semidirect
6. #10591125C2semidirect
7. #10591091C2semidirect
8. D3×#809C2semidirect
9. D3×#808C2semidirect
10. #10590500C2semidirect
11. #10590423C2semidirect
18. C2×C32×C4⋊C4C22semidirect
21. C2×C3×C4⋊Dic3C22semidirect
26. C3×D3×C4⋊C4C22semidirect
34. #63657C22semidirect
35. #63636C22semidirect
36. #63635C22semidirect
37. C3×#830C22semidirect
38. C3×#809C22semidirect
39. C3×#808C22semidirect
40. #63574C22semidirect
41. #63573C22semidirect
42. #63564C22semidirect
43. #63562C22semidirect
44. (C2×D3)⋊(C3⋊C8)C22semidirect
48. C2×D3×C4⋊C4D3semidirect
59. #4968D3direct (N × H)
125. C2×C3×C4⋊C4C2×D3semidirect
126. C2×C3×C4⋊C4C2×D3semidirect
139. C2×C4⋊Dic3C2×D3semidirect
148. D3×C4⋊C4C2×D3semidirect
159. #830C2×D3semidirect
168. #809C2×D3semidirect
175. #808C2×D3semidirect
359. C2×C4⋊C4D32semidirect
468. C3×D3#481semidirect
572. C32C2×#481semidirect
632. D3#4968direct (N × H)
660. C3D3×#481semidirect
661. C3C2×#4968semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
D3×#9302
#105926672
C3×#49682
D3×#8302
#105911252
#105910912
D3×#8092
D3×#8082
#105905002
#105904232
C2×#49683
D3×#4813