Finite Group Databasebeta

← #27098850

Subgroups — #27098850

Order 12032.

2010 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257422C212yesmaximal, complemented
2#20256363C211yesmaximal, characteristic, complemented
3#20256256C211yesmaximal, characteristic, complemented
4#20256097C212yesmaximal, complemented
5#20255811C211yesmaximal, characteristic, complemented
6#20255791C212yesmaximal, complemented
7#20255631C212yesmaximal, complemented
8#20255531C214yesmaximal, complemented
9D4×D376C211yesmaximal, characteristic, complemented
10D4×D376C212yesmaximal, complemented
11#20254038C212yesmaximal, complemented
12#20253967C211yesmaximal, characteristic, complemented
13#20253632C214yesmaximal, complemented
14#20253480C212yesmaximal, complemented
15#20252241C212yesmaximal, complemented
16C2×C4×D376C211yesmaximal, characteristic, complemented
17C47×#2966C211yesmaximal, characteristic, complemented
18C22×D376C2212yes—
19C22×D376C2211yescharacteristic
20#15689838C2212yescomplemented
21#15689833C2212yescomplemented
22#15689826—22no—
23#15689819C2214yescomplemented
24#15689795C2212yescomplemented
25#15689766—22no—
26#15689765—24no—
27D4×D188C2214yescomplemented
28D4×D188C2212yescomplemented
29#15689728C2214yescomplemented
30#15689712—24no—
31#15689673C2212yescomplemented
32#15689636—22no—
33#121×D47—22no—
34#15689597C2214yescomplemented
35C2×C4×D188C2212yescomplemented
36#15689528C2211yescharacteristic, complemented
37#15689525C2212yescomplemented
38#15689500C2211yescharacteristic, complemented
39#15689500C2212yescomplemented
40#15689488C2214yescomplemented
41#15689470C2212yescomplemented
42#15689448C2214yescomplemented
43#15689448C2214yescomplemented
44#15689442C2214yescomplemented
45#15689424C2214yescomplemented
46#15689424C2214yescomplemented
47#15689414C2212yescomplemented
48#15689414C2212yescomplemented
49#15689376C2214yescomplemented
50#15689359C2212yescomplemented
51#15689359C2212yescomplemented
52#15689359C2212yescomplemented
53#15689359C2212yescomplemented
54#15689319C2212yescomplemented
55#15689319C2212yescomplemented
56#15689319C2214yescomplemented
57#15689319C2214yescomplemented
58#15689259C2214yescomplemented
59#15689259C2214yescomplemented
60#15689259C2214yescomplemented
61#15689236C2214yescomplemented
62#15689236C2214yescomplemented
63#15689236C2214yescomplemented
64C4×D376C2212yes—
65C4×D376C2211yescharacteristic
66C4×D376C2211yescharacteristic
67C4×D376C2212yescomplemented
68C4×D376C2212yescomplemented
69C4×D376C2212yescomplemented
70C4×D376C2211yescharacteristic, complemented
71C4×D376C2211yescharacteristic, complemented
72C4×D376C2212yescomplemented
73C4×D376C2212yescomplemented
74#15689161C2212yescomplemented
75C2×#13093958C2211yescharacteristic, complemented
76#15689129C2214yescomplemented
77C2×#13093946C2212yescomplemented
78C47×#529C2211yescharacteristic
79C47×#446C2211yescharacteristic, complemented
80C8×Q8×C47C2211yescharacteristic, complemented
81C47×#436C2211yescharacteristic, complemented
82C47×#435C2212yescomplemented
83C8×D4×C47C2212yescomplemented
84C8×D4×C47C2211yescharacteristic, complemented
85C47×#433C2212yescomplemented
86C47×#432C2211yescharacteristic, complemented
87C47×#405C2212yescomplemented
88C2×C4×C8×C47C2211yescharacteristic, complemented
89C2×#10625354—22no—
90C2×#10625350—22no—
91C22×D188C2312yes—
92C22×D188C2314yes—
93C2×D4×D47—24no—
94C2×D4×D47—22no—
95C22×C4×D47—22no—
96C2×D376—28no—
97C2×D376—24no—
98C2×D376C2314yes—
99C2×D376C2312yes—
100C2×D376C2311yescharacteristic
101C2×D376C2312yes—
102C2×D376C2314yes—
103C2×D376C2312yes—
104C2×D376C2311yescharacteristic
105#13094024C2312yes—
106#13094021C2314yes—
107#13094021C2312yes—
108#13094019—24no—
109#13094016C2314yes—
110#13094012—22no—
111#13094010—24no—
112#13094009—24no—
113#13094009—24no—
114#13094006—24no—
115#13094002—24no—
116#13094000—22no—
117#13093999—22no—
118#13093999—24no—
119#13093999—24no—
120#13093999—22no—
121#13093998—22no—
122#13093998C2314yes—
123#13093998C2314yes—
124#13093998C2314yes—
125#13093997—24no—
126#13093997—24no—
127#13093996—24no—
128#13093995—22no—
129#13093994—24no—
130#13093994—24no—
131#13093994—24no—
132C4×D188—22no—
133C4×D188—22no—
134C4×D188—22no—
135C4×D188C2312yes—
136C4×D188C2314yes—
137C4×D188C2312yes—
138C4×D188C2314yes—
139C4×D188C2314yes—
140C4×D188C2312yes—
141C4×D188C2312yes—
142#13093986—24no—
143#13093986—24no—
144(C22⋊D47)⋊C4—24no—
145#13093983C2314yes—
146#13093982—22no—
147C2×C4⋊Dic47C2312yes—
148C4⋊C4×D47—22no—
149C2×(C2×D47)⋊C4—22no—
150C22⋊C4×D47—24no—
151C22⋊C4×D47—24no—
152#13093958C2311yescharacteristic
153#13093958C2312yes—
154#13093958C2312yes—
155#13093958C2311yescharacteristic
156#13093958C2312yes—
157#13093956C2314yes—
158#13093956C2314yes—
159#13093946C2312yes—
160#13093946C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163#13093946C2312yes—
164#13093946C2314yes—
165#13093946C2314yes—
166#13093946C2312yes—
167#13093946C2314yes—
168#13093946C2312yes—
169C2×M16×C47C2312yes—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2312yes—
172C22×C8×C47C2311yescharacteristic
173#126×C47D412yes—
174#125×C47D411yescharacteristic
175#124×C47D411yescharacteristic
176#123×C47D412yes—
177C22⋊Q8×C47D411yescharacteristic
178#121×C47D411yescharacteristic
179C4×Q8×C47C2311yescharacteristic
180C4×D4×C47C2312yes—
181C4×D4×C47C2311yescharacteristic
182#117×C47C2312yes—
183C2×C42×C47C2311yescharacteristic
184C4⋊C8×C47C2311yescharacteristic
185C4⋊C8×C47C2311yescharacteristic
186C4⋊C8×C47C2312yes—
187C4⋊C8×C47C2312yes—
188C22⋊C8×C47C2312yes—
189C22⋊C8×C47C2312yes—
190C22⋊C8×C47C2312yes—
191#97×C47C2312yes—
192#97×C47C2312yes—
193C4×C8×C47C2312yes—
194C4×C8×C47C2311yescharacteristic
195C4×C8×C47C2311yescharacteristic
196C4×C8×C47C2311yescharacteristic
197C4×C8×C47C2311yescharacteristic
198C23×D47—22no—
199C23×D47—24no—
200C2×Q8×C47C2×D411yescharacteristic
201C2×D4×C47C2×D412yes—
202C2×D4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2411yescharacteristic
206C22×C4×C47C2412yes—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C22×Dic47—22no—
211#10625354—84no—
212D4×D47—84no—
213D4×D47—88no—
214#10625350—84no—
215C2×D188—24no—
216C2×D188—28no—
217C2×D188—24no—
218C2×D188—22no—
219C2×D188—22no—
220C2×D188—24no—
221C2×D188—22no—
222C2×D188—24no—
223C2×D188—42no—
224C2×D188—44no—
225C2×D188C2412yes—
226C2×D188C2414yes—
227C2×D188C2412yes—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47—24no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—22no—
235C2×C4×D47—84no—
236C2×Dic94—22no—
237M16×C47—42no—
238C2×C8×C47—22no—
239C2×C8×C47—24no—
240C2×C8×C47—41no—
241C2×C8×C47C2412yes—
242C2×C8×C47C2411yescharacteristic
243C2×C8×C47C2411yescharacteristic
244C2×C8×C47C2412yes—
245C2×C8×C47C2411yescharacteristic
246C2×C8×C47C2411yescharacteristic
247C4⋊C4×C47C2×D412yes—
248C4⋊C4×C47C2×D412yes—
249C4⋊C4×C47C2×D411yescharacteristic
250C4⋊C4×C47C2×D412yes—
251C4⋊C4×C47C2×D411yescharacteristic
252C4⋊C4×C47C2×D412yes—
253C22⋊C4×C47C2×D412yes—
254C22⋊C4×C47C2×D412yes—
255C22⋊C4×C47C2×D412yes—
256C22⋊C4×C47C2×D412yes—
257C22⋊C4×C47C2×D412yes—
258C42×C47C2×D411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2411yescharacteristic
261C42×C47C2412yes—
262C42×C47C2411yescharacteristic
263C22⋊Dic47—24no—
264(C2×D47)⋊C4—22no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—22no—
269(C2×D47)⋊C4—22no—
270(C2×D47)⋊C4—22no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274C4⋊Dic47—22no—
275C4⋊Dic47—22no—
276C4⋊Dic47C2412yes—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2414yes—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281C4×Dic47—24no—
282D376—28no—
283D376—24no—
284D376—24no—
285D376—22no—
286D376—42no—
287D376—44no—
288D376#4114yescomplemented
289C23×C47C22×D412yes—
290C23×C47C22×D411yescharacteristic
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—24no—
294C22×D47—44no—
295C22×D47—48no—
296C22×D47—44no—
297C22×D47—82no—
298C22×D47—84no—
299C22×D47—84no—
300Q8×C47—22no—
301D4×C47—24no—
302D4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—21no—
306C2×C4×C47—22no—
307C2×C4×C47—21no—
308C2×C4×C47—22no—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D412yes—
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C2511yescharacteristic
318C22⋊D47—48no—
319C22⋊D47—84no—
320C22⋊D47—84no—
321C2×Dic47—22no—
322C2×Dic47—24no—
323C2×Dic47—22no—
324C2×Dic47—82no—
325D188—22no—
326D188—24no—
327D188—22no—
328D188—22no—
329D188—24no—
330D188—48no—
331D188—44no—
332D188—44no—
333D188—82no—
334D188—84no—
335D188—84no—
336D188C2×#4114yes—
337C4×D47—44no—
338C4×D47—44no—
339C4×D47—82no—
340C4×D47—82no—
341C4×D47—84no—
342C4×D47—84no—
343C4×D47—84no—
344Dic94—82no—
345C8×C47—22no—
346C8×C47—21no—
347C8×C47—21no—
348C8×C47—22no—
349C8×C47—21no—
350C8×C47C2×#4112yes—
351#61480—471nomaximal, Sylow
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47#57612yes—
358C22×C47C23×D411yescharacteristic
359C2×D47—24no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—44no—
364C2×D47—42no—
365C2×D47—44no—
366C2×D47—44no—
367C2×D47—42no—
368C2×D47—88no—
369C2×D47—168no—
370C4×C47—21no—
371C4×C47—22no—
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—21no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47#57612yes—
378C4×C47C22×#4111yescharacteristic
379C4×C47#58511yescharacteristic
380Dic47—44no—
381Dic47—42no—
382Dic47—42no—
383#3519—472no—
384#3391—471no—
385#3380—471no—
386#3366—472no—
387#3341—471no—
388#3339—472no—
389#3325—472no—
390#3318—474no—
391D4×D8—472no—
392D4×D8—471no—
393#3176—472no—
394#3169—471no—
395#3122—474no—
396#3109—472no—
397#2966D4711yescharacteristic, complemented
398#2948—472no—
399C2×C4×D8—471no—
400C2×C47—22no—
401C2×C47—42no—
402C2×C47D4×#4111yescharacteristic
403C2×C47C2×#57611yescharacteristic
404C2×C47C2×#57611yescharacteristic
405D47—44no—
406D47—82no—
407D47—84no—
408C22×D8—471no—
409C22×D8—472no—
410#555—472no—
411#554—472no—
412#553—474no—
413#553—942no—
414#550—472no—
415#546—942no—
416#546—944no—
417D42—474no—
418D42—472no—
419#540—474no—
420#538—944no—
421#532—472no—
422#529C2×D4711yescharacteristic
423#525—942no—
424C2×#121—942no—
425#518—474no—
426C2×C4×D4—472no—
427#500—471no—
428#499—472no—
429#493—471no—
430#493—472no—
431#490—474no—
432#486—472no—
433#482—474no—
434#482—474no—
435#481—474no—
436#478—474no—
437#478—474no—
438#476—472no—
439#476—472no—
440#469—474no—
441#466—472no—
442#466—472no—
443#466—472no—
444#466—472no—
445#459—472no—
446#459—472no—
447#459—474no—
448#459—474no—
449#447—474no—
450#447—474no—
451#447—474no—
452#446C2×D4711yescharacteristic, complemented
453C8×Q8C2×D4711yescharacteristic, complemented
454#442—474no—
455#442—474no—
456#442—474no—
457C4×D8—472no—
458C4×D8—471no—
459C4×D8—472no—
460C4×D8—472no—
461C4×D8—472no—
462C4×D8—471no—
463C4×D8—472no—
464C4×D8—472no—
465C4×D8—471no—
466C4×D8—471no—
467#436C2×D4711yescharacteristic, complemented
468#435C2×D4712yescomplemented
469C8×D4C2×D4712yescomplemented
470C8×D4C2×D4711yescharacteristic, complemented
471#433C2×D4712yescomplemented
472#432C2×D4711yescharacteristic, complemented
473#427—472no—
474C2×#107—471no—
475#418—474no—
476C2×#102—472no—
477#405C2×D4712yescomplemented
478C2×C4×C8C2×D4711yescharacteristic, complemented
479C47#6148011yescharacteristic, complemented, Sylow
480C2×#41—942no—
481C2×#41—942no—
482C22×D4—472no—
483C22×D4—474no—
484C22×D4—944no—
485C22×D4—942no—
486C23×C4—942no—
487C2×D8—471no—
488C2×D8—472no—
489C2×D8—471no—
490C2×D8—472no—
491C2×D8—474no—
492C2×D8—472no—
493C2×D8—474no—
494C2×D8—944no—
495C2×D8—948no—
496C2×M16C22×D4712yes—
497C22×C8C22×D4711yescharacteristic
498C22×C8C22×D4712yes—
499C22×C8C22×D4711yescharacteristic
500C4⋊Q8—472no—
501#127—472no—
502#127—474no—
503#126—944no—
504#126D18812yes—
505#125—474no—
506#125D18811yescharacteristic
507#124—944no—
508#124—942no—
509#124D18811yescharacteristic
510#123—944no—
511#123—944no—
512#123—944no—
513#123D18812yes—
514C22⋊Q8—942no—
515C22⋊Q8—944no—
516C22⋊Q8D18811yescharacteristic
517#121—474no—
518#121—474no—
519#121—474no—
520#121—944no—
521#121—942no—
522#121—942no—
523#121—942no—
524#121—942no—
525#121—944no—
526#121—944no—
527#121—944no—
528#121—944no—
529#121D18811yescharacteristic
530#120—944no—
531#120—944no—
532#120—944no—
533C4×Q8C22×D4711yescharacteristic
534C4×D4—472no—
535C4×D4—472no—
536C4×D4—472no—
537C4×D4—472no—
538C4×D4—474no—
539C4×D4—474no—
540C4×D4—474no—
541C4×D4—944no—
542C4×D4—944no—
543C4×D4—944no—
544C4×D4—942no—
545C4×D4—942no—
546C4×D4—942no—
547C4×D4C22×D4712yes—
548C4×D4C22×D4711yescharacteristic
549#117—474no—
550#117—942no—
551#117C22×D4712yes—
552C2×C4⋊C4—472no—
553C2×C4⋊C4—942no—
554C2×C22⋊C4—942no—
555C2×C22⋊C4—944no—
556C2×C22⋊C4—944no—
557C2×C42C22×D4711yescharacteristic
558#107—471no—
559#107—471no—
560#107—472no—
561#107—472no—
562#107—472no—
563#106—474no—
564#106—474no—
565C4⋊C8C22×D4711yescharacteristic
566C4⋊C8C22×D4711yescharacteristic
567C4⋊C8C22×D4712yes—
568C4⋊C8C22×D4712yes—
569#102—472no—
570#102—472no—
571#102—472no—
572#102—472no—
573#102—474no—
574#102—474no—
575#102—474no—
576#102—474no—
577#102—474no—
578#102—474no—
579C22⋊C8C22×D4712yes—
580C22⋊C8C22×D4712yes—
581C22⋊C8C22×D4712yes—
582#97C22×D4712yes—
583#97C22×D4712yes—
584C4×C8C22×D4711yescharacteristic
585C4×C8C22×D4711yescharacteristic
586C4×C8C22×D4711yescharacteristic
587C4×C8C22×D4711yescharacteristic
588C4×C8C22×D4712yes—
589C24—944no—
590C24—942no—
591#41—3764no—
592#41—3764no—
593C2×Q8—942no—
594C2×Q8C2×D18811yescharacteristic
595C2×D4—472no—
596C2×D4—472no—
597C2×D4—474no—
598C2×D4—944no—
599C2×D4—948no—
600C2×D4—944no—
601C2×D4—944no—
602C2×D4—944no—
603C2×D4—944no—
604C2×D4—942no—
605C2×D4—944no—
606C2×D4—944no—
607C2×D4—942no—
608C2×D4—942no—
609C2×D4—3768no—
610C2×D4—3764no—
611C2×D4—1882no—
612C2×D4—1884no—
613C2×D4C2×D18812yes—
614C2×D4C2×D18811yescharacteristic
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—944no—
618C22×C4—944no—
619C22×C4—944no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—3764no—
624C22×C4C2×D18811yescharacteristic
625C22×C4C2×D18811yescharacteristic
626C22×C4C23×D4711yescharacteristic
627C22×C4C23×D4712yes—
628D8—474no—
629D8—944no—
630D8—948no—
631D8—942no—
632D8—944no—
633D8—1882no—
634D8—1884no—
635M16—42no—
636C2×C8—22no—
637C2×C8—24no—
638C2×C8—41no—
639C2×C8C23×D4711yescharacteristic
640C2×C8C23×D4711yescharacteristic
641C2×C8C23×D4711yescharacteristic
642C2×C8C23×D4712yes—
643C2×C8C23×D4712yes—
644C2×C8C23×D4711yescharacteristic
645C4⋊C4—472no—
646C4⋊C4—472no—
647C4⋊C4—474no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—942no—
651C4⋊C4—942no—
652C4⋊C4C2×D18811yescharacteristic
653C4⋊C4C2×D18811yescharacteristic
654C4⋊C4C2×D18812yes—
655C4⋊C4C2×D18812yes—
656C4⋊C4C2×D18812yes—
657C4⋊C4C2×D18812yes—
658C22⋊C4—944no—
659C22⋊C4—942no—
660C22⋊C4—944no—
661C22⋊C4—942no—
662C22⋊C4—944no—
663C22⋊C4—942no—
664C22⋊C4—944no—
665C22⋊C4—942no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4C2×D18812yes—
670C22⋊C4C2×D18812yes—
671C22⋊C4C2×D18812yes—
672C22⋊C4C2×D18812yes—
673C22⋊C4C2×D18812yes—
674C42—944no—
675C42C2×D18811yescharacteristic
676C42C2×D18811yescharacteristic
677C42C23×D4711yescharacteristic
678C42C23×D4711yescharacteristic
679C42C23×D4712yes—
680C23—942no—
681C23—942no—
682C23—944no—
683C23—3762no—
684C23—3764no—
685C23—3764no—
686C23—1884no—
687C23—1888no—
688C23—1884no—
689C23C22×D18812yes—
690C23C22×D18811yescharacteristic
691Q8—22no—
692Q8—3762no—
693D4—24no—
694D4—22no—
695D4—474no—
696D4—942no—
697D4—944no—
698D4—942no—
699D4—942no—
700D4—944no—
701D4—3764no—
702D4—3762no—
703D4—3764no—
704D4—3764no—
705D4—3764no—
706D4—1884no—
707D4—1888no—
708D4—1888no—
709D4—1884no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—942no—
717C2×C4—944no—
718C2×C4—942no—
719C2×C4—3762no—
720C2×C4—3762no—
721C2×C4—3764no—
722C2×C4—3764no—
723C2×C4—3764no—
724C2×C4—3762no—
725C2×C4—1884no—
726C2×C4—1884no—
727C2×C4C22×D18812yes—
728C2×C4C22×D18811yescharacteristic
729C2×C4C22×D18811yescharacteristic
730C2×C4C22×D18811yescharacteristic
731C2×C4C22×D18811yescharacteristic
732C2×C4C22×D18812yes—
733C2×C4C22×D18812yes—
734C2×C4C22×D18811yescharacteristic
735C2×C4C24×D4711yescharacteristic
736C8—21no—
737C8—22no—
738C8—21no—
739C8—21no—
740C8—22no—
741C8#41×D4712yes—
742C22—21no—
743C22—21no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—944no—
748C22—3768no—
749C22—1882no—
750C22—1884no—
751C22—1884no—
752C22—1882no—
753C22—1882no—
754C22—1884no—
755C22—1882no—
756C22—1882no—
757C22—7528no—
758C22#1568992812yes—
759C22C23×D18811yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—22no—
764C4—22no—
765C4—21no—
766C4—22no—
767C4—1882no—
768C4—1882no—
769C4—1884no—
770C4#1568992812yes—
771C4C2×#41×D4711yescharacteristic
772C4#1568995911yescharacteristic
773C2—22no—
774C2—42no—
775C2—3762no—
776C2—3764no—
777C2—1884no—
778C2#41×D18811yescharacteristic
779C2C2×#1568992811yescharacteristic
780C2C2×#1568992811yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#2966C2
socleC22×C47C23×D4
hypercenter#2966D47
hypocenterC47#61480
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #529 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #20257422C2semidirect
2. #20256363C2semidirect
3. #20256256C2semidirect
4. #20256097C2semidirect
5. #20255811C2semidirect
6. #20255791C2semidirect
7. #20255631C2semidirect
8. #20255531C2semidirect
9. D4×D376C2semidirect
10. D4×D376C2semidirect
11. #20254038C2semidirect
12. #20253967C2semidirect
13. #20253632C2semidirect
14. #20253480C2semidirect
15. #20252241C2semidirect
16. C2×C4×D376C2semidirect
17. C47×#2966C2semidirect
20. #15689838C22semidirect
21. #15689833C22semidirect
23. #15689819C22semidirect
24. #15689795C22semidirect
27. D4×D188C22semidirect
28. D4×D188C22semidirect
29. #15689728C22semidirect
31. #15689673C22semidirect
34. #15689597C22semidirect
35. C2×C4×D188C22semidirect
36. #15689528C22semidirect
37. #15689525C22semidirect
38. #15689500C22semidirect
39. #15689500C22semidirect
40. #15689488C22semidirect
41. #15689470C22semidirect
42. #15689448C22semidirect
43. #15689448C22semidirect
44. #15689442C22semidirect
45. #15689424C22semidirect
46. #15689424C22semidirect
47. #15689414C22semidirect
48. #15689414C22semidirect
49. #15689376C22semidirect
50. #15689359C22semidirect
51. #15689359C22semidirect
52. #15689359C22semidirect
53. #15689359C22semidirect
54. #15689319C22semidirect
55. #15689319C22semidirect
56. #15689319C22semidirect
57. #15689319C22semidirect
58. #15689259C22semidirect
59. #15689259C22semidirect
60. #15689259C22semidirect
61. #15689236C22semidirect
62. #15689236C22semidirect
63. #15689236C22semidirect
67. C4×D376C22semidirect
68. C4×D376C22semidirect
69. C4×D376C22semidirect
70. C4×D376C22semidirect
71. C4×D376C22semidirect
72. C4×D376C22semidirect
73. C4×D376C22semidirect
74. #15689161C22semidirect
75. C2×#13093958C22semidirect
76. #15689129C22semidirect
77. C2×#13093946C22semidirect
79. C47×#446C22semidirect
80. C8×Q8×C47C22semidirect
81. C47×#436C22semidirect
82. C47×#435C22semidirect
83. C8×D4×C47C22semidirect
84. C8×D4×C47C22semidirect
85. C47×#433C22semidirect
86. C47×#432C22semidirect
87. C47×#405C22semidirect
88. C2×C4×C8×C47C22semidirect
288. D376#41semidirect
397. #2966D47semidirect
452. #446C2×D47semidirect
453. C8×Q8C2×D47semidirect
467. #436C2×D47semidirect
468. #435C2×D47semidirect
469. C8×D4C2×D47semidirect
470. C8×D4C2×D47semidirect
471. #433C2×D47semidirect
472. #432C2×D47semidirect
477. #405C2×D47semidirect
478. C2×C4×C8C2×D47semidirect
479. C47#61480semidirect

Maximal subgroups

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

subgroupindex
#202574222
#202563632
#202562562
#202560972
#202558112
#202557912
#202556312
#202555312
D4×D3762
#202540382
#202539672
#202536322
#202534802
#202522412
C2×C4×D3762
C47×#29662
#6148047