Finite Group Databasebeta

← #2847×D71 #32203279

Subgroups — #2847×D71 #32203279

Order 18176.

8582 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D71C211yesmaximal, characteristic, complemented
2C2×#121×D71C213yesmaximal, complemented
3C2×#120×D71C212yesmaximal, complemented
4#22596623C213yesmaximal, complemented
5#22596622C211yesmaximal, characteristic, complemented
6#22596621C216yesmaximal, complemented
7#22596620C212yesmaximal, complemented
8#22596619C213yesmaximal, complemented
9#386×D71C216yesmaximal, complemented
10#380×D71C213yesmaximal, complemented
11C71×#2847C211yesmaximal, characteristic, complemented
12C25×D71C2211yescharacteristic
13C22×D4×D71C2216yes—
14C22×D4×D71C2211yescharacteristic, complemented
15C24×Dic71C2211yescharacteristic, complemented
16C23×C4×D71—224no—
17C23×C4×D71C2213yes—
18C23×C4×D71C2213yes—
19C23×C4×D71C2213yescomplemented
20C23×C4×D71C2213yescomplemented
21C2×#14556103C2213yescomplemented
22C2×#14556102C2213yescomplemented
23C2×#14556101C2216yescomplemented
24C2×#14556100C2216yescomplemented
25C2×#14556099C2213yescomplemented
26#121×D71—224no—
27C2×#14556098C2216yescomplemented
28C2×#14556097C2212yescomplemented
29C2×#14556096C2216yescomplemented
30#120×D71—216no—
31C2×C4⋊C4×D71C2213yescomplemented
32C2×C22⋊C4×D71C2216yes—
33C2×C22⋊C4×D71C2216yescomplemented
34#17985879C2216yescomplemented
35#17985878C2216yescomplemented
36#17985877C22112yescomplemented
37#17985876C2216yescomplemented
38#17985875C22112yescomplemented
39#17985859C2213yescomplemented
40#17985858C2216yescomplemented
41#17985857C2216yescomplemented
42#17985856C2216yescomplemented
43#95×D71C2216yescomplemented
44C24×C4×C71C2211yescharacteristic, complemented
45C2×#121×C71C2213yescomplemented
46C2×#120×C71C2212yescomplemented
47#386×C71C2216yescomplemented
48#380×C71C2213yescomplemented
49C24×D71—212no—
50C24×D71—212no—
51C24×D71D418yescomplemented
52C24×D71C2312yes—
53C24×D71C2313yes—
54C24×D71C2313yes—
55C22×D284C2316yes—
56C22×D284C2311yescharacteristic, complemented
57C22×C22⋊D71C2316yes—
58C22×C22⋊D71C2316yes—
59C22×C22⋊D71C2312yescomplemented
60C2×D4×D71—224no—
61C2×D4×D71—224no—
62C2×D4×D71—224no—
63C2×D4×D71—212no—
64C23×Dic71—212no—
65C23×Dic71C2313yes—
66C23×Dic71C2313yes—
67C22×C4×D71—2128no—
68C22×C4×D71—212no—
69C22×C4×D71—212no—
70C22×C4×D71—224no—
71C22×C4×D71—224no—
72C22×C4×D71—224no—
73C22×C4×D71—224no—
74C22×C4×D71—212no—
75C22×C4×D71D4124yescomplemented
76C22×C4×D71C2316yes—
77C22×C4×D71C2316yes—
78C22×C4×D71C2313yes—
79C22×C4×D71C2313yes—
80C22×C4×D71C2313yes—
81C22×C4×D71C2311yescharacteristic
82#14556103—212no—
83#14556102—212no—
84#14556101—224no—
85#14556100—224no—
86#14556099—212no—
87#14556098—224no—
88#14556097—28no—
89#14556096—224no—
90C2×C4⋊Dic71C2313yescomplemented
91C2×Dic71⋊C4C2316yescomplemented
92C4⋊C4×D71—212no—
93C2×C22⋊Dic71C2316yes—
94C2×C22⋊Dic71C2316yescomplemented
95C2×(C2×D71)⋊C4C23112yes—
96C2×(C2×D71)⋊C4C2316yescomplemented
97C2×(C2×D71)⋊C4C2316yescomplemented
98C22⋊C4×D71—224no—
99C22⋊C4×D71—224no—
100C71⋊#95C23112yescomplemented
101C71⋊#95C2316yescomplemented
102C25×C71C2311yescharacteristic
103C22×D4×C71C2316yes—
104C22×D4×C71C2311yescharacteristic, complemented
105C23×C4×C71—212no—
106C23×C4×C71C2313yes—
107C23×C4×C71C2313yes—
108#121×C71—212no—
109#120×C71—28no—
110C2×C4⋊C4×C71C2313yescomplemented
111C2×C22⋊C4×C71C2316yes—
112C2×C22⋊C4×C71C2316yescomplemented
113#95×C71C2316yescomplemented
114C23×D71—232no—
115C23×D71—296no—
116C23×D71—26no—
117C23×D71—26no—
118C23×D71—296no—
119C23×D71—212no—
120C23×D71—212no—
121C23×D71—212no—
122C23×D71—212no—
123C23×D71—24no—
124C23×D71—212no—
125C23×D71—212no—
126C23×D71C2×D4112yes—
127C23×D71C2×D4112yes—
128C23×D71C2×D4112yescomplemented
129C23×D71#41112yes—
130C23×D71C2412yes—
131C23×D71C2413yes—
132C23×D71C2411yescharacteristic
133C2×D284—212no—
134C2×D284—212no—
135C2×D284—212no—
136C2×D284—26no—
137C2×C22⋊D71—212no—
138C2×C22⋊D71—212no—
139C2×C22⋊D71—212no—
140C2×C22⋊D71—212no—
141C2×C22⋊D71—212no—
142C2×C22⋊D71—212no—
143C2×C22⋊D71—212no—
144D4×D71—496no—
145D4×D71—416no—
146C22×Dic71—232no—
147C22×Dic71—26no—
148C22×Dic71—212no—
149C22×Dic71—212no—
150C22×Dic71C2×D4112yescomplemented
151C22×Dic71C2416yes—
152C22×Dic71C2413yes—
153C22×Dic71C2411yescharacteristic
154C2×C4×D71—296no—
155C2×C4×D71—296no—
156C2×C4×D71—296no—
157C2×C4×D71—212no—
158C2×C4×D71—212no—
159C2×C4×D71—212no—
160C2×C4×D71—212no—
161C2×C4×D71—212no—
162C2×C4×D71—212no—
163C2×C4×D71—296no—
164C2×C4×D71—212no—
165C2×C4×D71—212no—
166C2×C4×D71—212no—
167C2×C4×D71C2×D4112yes—
168C2×C4×D71C2×D4112yes—
169C2×C4×D71C2×D4112yescomplemented
170C2×C4×D71C2×D4112yescomplemented
171C4⋊Dic71—26no—
172Dic71⋊C4—212no—
173C22⋊Dic71—212no—
174C22⋊Dic71—212no—
175(C2×D71)⋊C4—224no—
176(C2×D71)⋊C4—212no—
177(C2×D71)⋊C4—212no—
178C24×C71—26no—
179C24×C71—26no—
180C24×C71C2×D414yescomplemented
181C24×C71C2412yes—
182C24×C71C2413yes—
183C2×D4×C71—212no—
184C2×D4×C71—212no—
185C2×D4×C71—212no—
186C2×D4×C71—26no—
187C22×C4×C71—232no—
188C22×C4×C71—26no—
189C22×C4×C71—212no—
190C22×C4×C71—212no—
191C22×C4×C71C2×D4112yescomplemented
192C22×C4×C71C2416yes—
193C22×C4×C71C2413yes—
194C22×C4×C71C2411yescharacteristic
195C4⋊C4×C71—26no—
196C22⋊C4×C71—212no—
197C22⋊C4×C71—212no—
198C23×C71—28no—
199C23×C71—224no—
200C23×C71—224no—
201C23×C71—26no—
202C23×C71—26no—
203C23×C71—26no—
204C23×C71—22no—
205C23×C71—26no—
206C23×C71C22×D416yes—
207C23×C71C22×D416yes—
208C23×C71C2×#4116yes—
209C23×C71C2511yescharacteristic
210C22×D71—224no—
211C22×D71—248no—
212C22×D71—224no—
213C22×D71—2256no—
214C22×D71—224no—
215C22×D71—26no—
216C22×D71—26no—
217C22×D71—224no—
218C22×D71—248no—
219C22×D71—248no—
220C22×D71—224no—
221C22×D71—248no—
222C22×D71—26no—
223C22×D71—22no—
224C22×D71—26no—
225C22×D71—48no—
226C22×D71—424no—
227C22×D71—424no—
228C22×D71#121148yescomplemented
229C22×D71C22×D416yes—
230C22×D71C22×D416yes—
231C22×D71C22×D416yes—
232C22×D71C22×D412yes—
233C22×D71C2×#4116yes—
234C22×D71C2×#4116yes—
235D4×C71—424no—
236D4×C71—44no—
237C2×C4×C71—224no—
238C2×C4×C71—26no—
239C2×C4×C71—224no—
240C2×C4×C71—26no—
241C2×C4×C71—26no—
242C2×C4×C71—26no—
243C2×C4×C71C22×D416yes—
244C2×C4×C71C22×D416yes—
245C22⋊D71—424no—
246C22⋊D71—424no—
247C22⋊D71—48no—
248C2×Dic71—224no—
249C2×Dic71—26no—
250C2×Dic71—224no—
251C2×Dic71—26no—
252C2×Dic71—26no—
253C2×Dic71—26no—
254C2×Dic71C22×D416yes—
255C2×Dic71C22×D416yes—
256D284—424no—
257D284—44no—
258C4×D71—248no—
259C4×D71—224no—
260C4×D71—224no—
261C4×D71—224no—
262C4×D71—424no—
263C4×D71#120116yescomplemented
264C22×C71—232no—
265C22×C71—26no—
266C22×C71—212no—
267C22×C71—26no—
268C22×C71—212no—
269C22×C71—42no—
270C22×C71—46no—
271C22×C71—46no—
272C22×C71C2×#121112yescomplemented
273C22×C71C23×D413yes—
274C22×C71C23×D411yescharacteristic
275C22×C71C22×#4113yes—
276C2×D71—296no—
277C2×D71—26no—
278C2×D71—212no—
279C2×D71—26no—
280C2×D71—212no—
281C2×D71—296no—
282C2×D71—42no—
283C2×D71—46no—
284C2×D71—46no—
285C2×D71—816no—
286C2×D71C2×#12014yes—
287C2×D71C2×#121112yes—
288C2×D71C2×#121112yescomplemented
289C2×D71#525112yes—
290C4×C71—26no—
291C4×C71—46no—
292C4×C71C2×#12014yescomplemented
293Dic71—26no—
294Dic71—46no—
295Dic71C2×#12014yescomplemented
296C2×#2847—711nomaximal, Sylow
297C2×C71—212no—
298C2×C71—82no—
299C2×C71C22×#12011yescharacteristic
300C2×C71C22×#12113yes—
301C2×C71C2×#52513yes—
302D71—212no—
303D71—82no—
304D71#284718yesdirect product factor
305C25×C4—711no—
306C22×#121—713no—
307C22×#120—712no—
308#2847—716no—
309#2847—713no—
310#2847—711no—
311#2847—713no—
312#2847—712no—
313#2847D7111yescharacteristic, direct product factor
314C2×#386—716no—
315C2×#380—713no—
316C71C2×#284711yescharacteristic, complemented, Sylow
317C26—711no—
318C23×D4—716no—
319C23×D4—711no—
320C24×C4—713no—
321C24×C4—711no—
322C24×C4—713no—
323C24×C4—713no—
324C24×C4—713no—
325C24×C4—14224no—
326C24×C4C2×D7111yescharacteristic, complemented
327C2×#121—716no—
328C2×#121—713no—
329C2×#121—713no—
330C2×#121—713no—
331C2×#121—716no—
332C2×#121—14224no—
333C2×#121C2×D7113yescomplemented
334C2×#120—712no—
335C2×#120—716no—
336C2×#120—716no—
337C2×#120—14216no—
338C2×#120C2×D7112yescomplemented
339C22×C4⋊C4—713no—
340C22×C22⋊C4—716no—
341C22×C22⋊C4—716no—
342#386—716no—
343#386—716no—
344#386—716no—
345#386—7112no—
346#386—7112no—
347#386C2×D7116yescomplemented
348#380—713no—
349#380—716no—
350#380—716no—
351#380—716no—
352#380C2×D7113yescomplemented
353C2×#95—716no—
354C25—713no—
355C25—718no—
356C25—713no—
357C25—712no—
358C25—14212no—
359C25—14212no—
360C25C22×D7111yescharacteristic
361C22×D4—716no—
362C22×D4—716no—
363C22×D4—712no—
364C22×D4—716no—
365C22×D4—711no—
366C22×D4—14212no—
367C22×D4—14224no—
368C22×D4—14224no—
369C22×D4—14224no—
370C22×D4C22×D7116yes—
371C22×D4C22×D7111yescharacteristic, complemented
372C23×C4—212no—
373C23×C4—711no—
374C23×C4—713no—
375C23×C4—7124no—
376C23×C4—713no—
377C23×C4—713no—
378C23×C4—713no—
379C23×C4—713no—
380C23×C4—716no—
381C23×C4—716no—
382C23×C4—14212no—
383C23×C4—14224no—
384C23×C4—14224no—
385C23×C4—14224no—
386C23×C4—14224no—
387C23×C4—14212no—
388C23×C4—142128no—
389C23×C4—14212no—
390C23×C4—14212no—
391C23×C4C22×D7113yes—
392C23×C4C22×D7113yes—
393#121—212no—
394#121—14224no—
395#121—14212no—
396#121—14212no—
397#121—14224no—
398#121—14212no—
399#120—28no—
400#120—14224no—
401#120—14224no—
402#120—1428no—
403C2×C4⋊C4—716no—
404C2×C4⋊C4—713no—
405C2×C4⋊C4—14212no—
406C2×C4⋊C4C22×D7113yescomplemented
407C2×C22⋊C4—716no—
408C2×C22⋊C4—716no—
409C2×C22⋊C4—7112no—
410C2×C22⋊C4—716no—
411C2×C22⋊C4—716no—
412C2×C22⋊C4—14224no—
413C2×C22⋊C4—14224no—
414C2×C22⋊C4C22×D7116yes—
415C2×C22⋊C4C22×D7116yescomplemented
416#95—7112no—
417#95—716no—
418#95C22×D7116yescomplemented
419C24—26no—
420C24—26no—
421C24—711no—
422C24—7112no—
423C24—7112no—
424C24—7112no—
425C24—713no—
426C24—7112no—
427C24—712no—
428C24—14212no—
429C24—1424no—
430C24—14212no—
431C24—14212no—
432C24—14212no—
433C24—14212no—
434C24—14212no—
435C24—14296no—
436C24—14232no—
437C24—14296no—
438C24—1426no—
439C24—1426no—
440C24D4×D7114yescomplemented
441C24C23×D7112yes—
442C24C23×D7113yes—
443C2×D4—212no—
444C2×D4—212no—
445C2×D4—212no—
446C2×D4—26no—
447C2×D4—28496no—
448C2×D4—28416no—
449C2×D4—14212no—
450C2×D4—14212no—
451C2×D4—14212no—
452C2×D4—14212no—
453C2×D4—14212no—
454C2×D4—14212no—
455C2×D4—14212no—
456C2×D4—14212no—
457C2×D4—14212no—
458C2×D4—14212no—
459C2×D4—1426no—
460C22×C4—232no—
461C22×C4—26no—
462C22×C4—212no—
463C22×C4—212no—
464C22×C4—711no—
465C22×C4—7112no—
466C22×C4—7112no—
467C22×C4—713no—
468C22×C4—7112no—
469C22×C4—7112no—
470C22×C4—7112no—
471C22×C4—716no—
472C22×C4—14212no—
473C22×C4—14212no—
474C22×C4—14212no—
475C22×C4—14212no—
476C22×C4—14212no—
477C22×C4—14296no—
478C22×C4—14212no—
479C22×C4—14212no—
480C22×C4—14296no—
481C22×C4—14296no—
482C22×C4—14296no—
483C22×C4—14212no—
484C22×C4—14212no—
485C22×C4—14232no—
486C22×C4—1426no—
487C22×C4—14212no—
488C22×C4—14212no—
489C22×C4D4×D71112yescomplemented
490C22×C4C23×D7116yes—
491C22×C4C23×D7113yes—
492C22×C4C23×D7111yescharacteristic
493C4⋊C4—26no—
494C4⋊C4—14212no—
495C4⋊C4—1426no—
496C22⋊C4—212no—
497C22⋊C4—212no—
498C22⋊C4—14212no—
499C22⋊C4—14224no—
500C22⋊C4—14212no—
501C22⋊C4—14212no—
502C22⋊C4—14212no—
503C23—28no—
504C23—224no—
505C23—26no—
506C23—26no—
507C23—224no—
508C23—26no—
509C23—22no—
510C23—26no—
511C23—2848no—
512C23—28424no—
513C23—28424no—
514C23—716no—
515C23—712no—
516C23—716no—
517C23—716no—
518C23—716no—
519C23—716no—
520C23—7148no—
521C23—14224no—
522C23—14248no—
523C23—14248no—
524C23—14224no—
525C23—14248no—
526C23—14224no—
527C23—142256no—
528C23—14224no—
529C23—14248no—
530C23—1426no—
531C23—1422no—
532C23—1426no—
533C23—1426no—
534C23—1426no—
535C23—14224no—
536C23C2×D4×D7116yes—
537C23C2×D4×D7116yes—
538C23#41×D7116yes—
539C23C24×D7111yescharacteristic
540D4—424no—
541D4—44no—
542D4—28424no—
543D4—28424no—
544D4—28424no—
545D4—2848no—
546D4—2844no—
547C2×C4—224no—
548C2×C4—26no—
549C2×C4—224no—
550C2×C4—26no—
551C2×C4—26no—
552C2×C4—26no—
553C2×C4—28424no—
554C2×C4—716no—
555C2×C4—7116no—
556C2×C4—716no—
557C2×C4—14224no—
558C2×C4—14224no—
559C2×C4—14248no—
560C2×C4—1426no—
561C2×C4—1426no—
562C2×C4—1426no—
563C2×C4—14224no—
564C2×C4—14224no—
565C2×C4—1426no—
566C2×C4—14224no—
567C2×C4C2×D4×D7116yes—
568C2×C4C2×D4×D7116yes—
569C22—232no—
570C22—26no—
571C22—212no—
572C22—26no—
573C22—212no—
574C22—42no—
575C22—46no—
576C22—46no—
577C22—2842no—
578C22—2846no—
579C22—2846no—
580C22—56816no—
581C22—714no—
582C22—7112no—
583C22—7112no—
584C22—7112no—
585C22—14296no—
586C22—14296no—
587C22—1426no—
588C22—14212no—
589C22—1426no—
590C22—14212no—
591C22#121×D71112yescomplemented
592C22C22×D4×D7113yes—
593C22C22×D4×D7111yescharacteristic
594C22C2×#41×D7113yes—
595C4—26no—
596C4—46no—
597C4—2846no—
598C4—714no—
599C4—1426no—
600C4#120×D7114yescomplemented
601C2—212no—
602C2—82no—
603C2—5682no—
604C2—718no—
605C2—14212no—
606C2C2×#120×D7111yescharacteristic
607C2C2×#121×D7113yes—
608C2#525×D7113yes—
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2847C2
hypercenter#2847D71
hypocenterC71C2×#2847
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C24×C4×D71C2semidirect
2. C2×#121×D71C2semidirect
3. C2×#120×D71C2semidirect
4. #22596623C2semidirect
5. #22596622C2semidirect
6. #22596621C2semidirect
7. #22596620C2semidirect
8. #22596619C2semidirect
9. #386×D71C2semidirect
10. #380×D71C2semidirect
11. C71×#2847C2semidirect
14. C22×D4×D71C22semidirect
15. C24×Dic71C22semidirect
19. C23×C4×D71C22semidirect
20. C23×C4×D71C22semidirect
21. C2×#14556103C22semidirect
22. C2×#14556102C22semidirect
23. C2×#14556101C22semidirect
24. C2×#14556100C22semidirect
25. C2×#14556099C22semidirect
27. C2×#14556098C22semidirect
28. C2×#14556097C22semidirect
29. C2×#14556096C22semidirect
31. C2×C4⋊C4×D71C22semidirect
33. C2×C22⋊C4×D71C22semidirect
34. #17985879C22semidirect
35. #17985878C22semidirect
36. #17985877C22semidirect
37. #17985876C22semidirect
38. #17985875C22semidirect
39. #17985859C22semidirect
40. #17985858C22semidirect
41. #17985857C22semidirect
42. #17985856C22semidirect
43. #95×D71C22semidirect
44. C24×C4×C71C22semidirect
45. C2×#121×C71C22semidirect
46. C2×#120×C71C22semidirect
47. #386×C71C22semidirect
48. #380×C71C22semidirect
51. C24×D71D4semidirect
56. C22×D284C23semidirect
59. C22×C22⋊D71C23semidirect
75. C22×C4×D71D4semidirect
90. C2×C4⋊Dic71C23semidirect
91. C2×Dic71⋊C4C23semidirect
94. C2×C22⋊Dic71C23semidirect
96. C2×(C2×D71)⋊C4C23semidirect
97. C2×(C2×D71)⋊C4C23semidirect
100. C71⋊#95C23semidirect
101. C71⋊#95C23semidirect
104. C22×D4×C71C23semidirect
110. C2×C4⋊C4×C71C23semidirect
112. C2×C22⋊C4×C71C23semidirect
113. #95×C71C23semidirect
128. C23×D71C2×D4semidirect
150. C22×Dic71C2×D4semidirect
169. C2×C4×D71C2×D4semidirect
170. C2×C4×D71C2×D4semidirect
180. C24×C71C2×D4semidirect
191. C22×C4×C71C2×D4semidirect
228. C22×D71#121semidirect
263. C4×D71#120semidirect
272. C22×C71C2×#121semidirect
288. C2×D71C2×#121semidirect
292. C4×C71C2×#120semidirect
295. Dic71C2×#120semidirect
304. D71#2847direct (N × H)
313. #2847D71direct (N × H)
316. C71C2×#2847semidirect
326. C24×C4C2×D71semidirect
333. C2×#121C2×D71semidirect
338. C2×#120C2×D71semidirect
347. #386C2×D71semidirect
352. #380C2×D71semidirect
371. C22×D4C22×D71semidirect
406. C2×C4⋊C4C22×D71semidirect
415. C2×C22⋊C4C22×D71semidirect
418. #95C22×D71semidirect
440. C24D4×D71semidirect
489. C22×C4D4×D71semidirect
591. C22#121×D71semidirect
600. C4#120×D71semidirect

Maximal subgroups

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

subgroupindex
C24×C4×D712
C2×#121×D712
C2×#120×D712
#225966232
#225966222
#225966212
#225966202
#225966192
#386×D712
#380×D712
C71×#28472
C2×#284771