Finite Group Databasebeta

← C4×#15689290 #26222150

Subgroups — C4×#15689290 #26222150

Order 12032.

1578 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094069C211yesmaximal, characteristic, complemented
2C2×#15689290C211yesmaximal, characteristic
3C4×#13094050C212yesmaximal, complemented
4#20243787C211yesmaximal, characteristic, complemented
5#20243767C212yesmaximal, complemented
6#20243613C212yesmaximal, complemented
7#20243597C211yesmaximal, characteristic, complemented
8#20243341C211yesmaximal, characteristic, complemented
9C4×#13093952C212yesmaximal, complemented
10C4×#13093941C211yesmaximal, characteristic, complemented
11C4×#127×C47C211yesmaximal, characteristic, complemented
12C2×#13094069C2211yescharacteristic
13C2×#13094050C2212yes—
14#15689604C2212yes—
15#15689602—22no—
16#15689598C2211yescharacteristic
17#15689596—22no—
18#15689595—22no—
19C4×#10625350C2212yes—
20C4×#10625352—22no—
21C2×C4×C22⋊D47—22no—
22C4×D4×D47—22no—
23#15689290C418yesdirect product factor
24#15689233—22no—
25#15689223—22no—
26C4×#10625335—22no—
27C4×#10625334—22no—
28#15689163C2212yescomplemented
29C2×#13093952C2212yes—
30C2×#13093952C2212yes—
31#15689128C2212yescomplemented
32#15689122C2212yes—
33C2×#13093941C2211yescharacteristic
34C2×#13093941C2211yescharacteristic
35C4×#10625329C2212yescomplemented
36#15688892C2212yescomplemented
37#15688883C2212yescomplemented
38#15688883C2212yescomplemented
39C2×#127×C47C2211yescharacteristic
40C2×C4×D4×C47—22no—
41C2×C4×D4×C47C2211yescharacteristic
42C2×C4×D4×C47C2211yescharacteristic, complemented
43C47×#390—22no—
44C47×#390C2211yescharacteristic
45C47×#390C2211yescharacteristic, complemented
46C47×#384C2211yescharacteristic, complemented
47C43×C47C2211yescharacteristic, complemented
48#13094069—22no—
49#13094069—24no—
50#13094069C2×C414yescomplemented
51C2×#10625350C2312yes—
52C2×#10625352—22no—
53C22×C22⋊D47—22no—
54C2×D4×D47—22no—
55C22×C4×D47—22no—
56#13094050—24no—
57#13094050C2×C418yescomplemented
58C2×#10625335—22no—
59C2×#10625334—22no—
60C2×#10625329C2312yes—
61C2×#10625329C2312yes—
62C4×Dic94D412yescomplemented
63C4×Dic94D412yescomplemented
64#13093989—22no—
65C4×D188D412yescomplemented
66C4×D188D412yescomplemented
67D4×Dic47—22no—
68D4×Dic47—22no—
69#13093986—22no—
70C4×C22⋊D47—24no—
71C4×C22⋊D47—24no—
72C4×C22⋊D47—22no—
73C4×C22⋊D47—24no—
74C4×C22⋊D47—22no—
75(C22⋊D47)⋊C4—24no—
76(C22⋊D47)⋊C4—24no—
77#13093983C2312yes—
78#13093982—22no—
79#13093981—22no—
80#13093980—24no—
81C2×Dic47⋊C4—22no—
82C4⋊C4×D47—22no—
83C2×C22⋊Dic47—22no—
84C2×(C2×D47)⋊C4—22no—
85C22⋊C4×D47—24no—
86C2×C4×Dic47—22no—
87C42×D47—22no—
88#13093957—22no—
89#13093955—22no—
90#13093952—24no—
91#13093952C2×C418yescomplemented
92#13093947—22no—
93#13093945—22no—
94#13093945—22no—
95#13093944—22no—
96#13093941—22no—
97#13093941C2×C414yescomplemented
98#13093935—22no—
99C4×C47⋊C8—22no—
100C22×D4×C47—22no—
101C22×D4×C47C2311yescharacteristic
102C22×D4×C47C2311yescharacteristic
103C23×C4×C47—21no—
104C23×C4×C47D412yes—
105#127×C47—22no—
106#127×C47C2×C414yescomplemented
107C4×D4×C47—22no—
108C4×D4×C47—22no—
109C4×D4×C47—22no—
110C4×D4×C47—22no—
111C4×D4×C47—48no—
112C2×C4⋊C4×C47—22no—
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47D412yes—
119C2×C42×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124C24×C47—21no—
125C24×C47C2×D412yes—
126C23×D47—22no—
127C2×D4×C47—28no—
128C2×D4×C47—22no—
129C2×D4×C47—22no—
130C2×D4×C47—22no—
131C2×D4×C47—22no—
132C2×D4×C47—21no—
133C2×D4×C47—44no—
134C2×D4×C47—44no—
135C2×D4×C47C22×C412yes—
136C2×D4×C47C22×C412yescomplemented
137C2×D4×C47#4112yes—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—44no—
144C22×C4×C47—44no—
145C22×C4×C47—41no—
146C22×C4×C47—41no—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2411yescharacteristic
151C2×C22⋊D47—24no—
152C2×C22⋊D47—28no—
153C2×C22⋊D47—28no—
154C2×C22⋊D47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158#10625352—28no—
159#10625352—28no—
160D4×D47—28no—
161D4×D47—28no—
162#10625350—22no—
163#10625350—22no—
164#10625350C22×C414yes—
165#10625350#4114yes—
166C2×D188C2×D412yes—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—24no—
170C2×C4×D47—22no—
171C2×C4×D47—84no—
172C2×Dic94C2×D412yes—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—44no—
176C22⋊C4×C47—24no—
177C22⋊C4×C47—44no—
178C22⋊C4×C47—44no—
179C22⋊C4×C47—42no—
180C42×C47—24no—
181C42×C47—21no—
182C42×C47—22no—
183C42×C47—42no—
184C42×C47C22×C412yescomplemented
185C42×C47C2×D412yes—
186C42×C47C2×D412yes—
187C22⋊Dic47—24no—
188C22⋊Dic47—22no—
189#10625335—28no—
190#10625334—28no—
191(C2×D47)⋊C4—24no—
192(C2×D47)⋊C4—22no—
193(C2×D47)⋊C4—22no—
194C4⋊Dic47C2×D412yes—
195C4⋊Dic47C2×D412yes—
196Dic47⋊C4—24no—
197Dic47⋊C4—22no—
198Dic47⋊C4—22no—
199C4×Dic47—24no—
200C4×Dic47—22no—
201C4×Dic47—22no—
202C4×Dic47—22no—
203#10625329—22no—
204#10625329—22no—
205#10625329—22no—
206#10625329C22×C414yescomplemented
207C2×C47⋊C8—22no—
208C2×C47⋊C8—22no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—42no—
213C23×C47—42no—
214C23×C47—42no—
215C23×C47—42no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47C4×D414yes—
219C23×C47C22×D411yescharacteristic
220C22×D47—22no—
221C22×D47—28no—
222C22×D47—82no—
223C22×D47—82no—
224D4×C47—24no—
225D4×C47—24no—
226D4×C47—24no—
227D4×C47—416no—
228D4×C47—42no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—44no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—41no—
242C2×C4×C47—82no—
243C2×C4×C47—82no—
244C2×C4×C47—82no—
245C2×C4×C47#12012yes—
246C2×C4×C47#12011yescharacteristic
247C2×C4×C47#12011yescharacteristic
248C2×C4×C47C23×C411yescharacteristic
249C2×C4×C47C22×D412yes—
250C2×C4×C47C2×#4112yes—
251C2×C4×C47C2×#4111yescharacteristic
252C22⋊D47—216no—
253C22⋊D47—24no—
254C22⋊D47—24no—
255C2×Dic47—28no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—82no—
260C2×Dic47—82no—
261D188—22no—
262D188C4×D414yescomplemented
263C4×D47—24no—
264C4×D47—24no—
265C4×D47—44no—
266C4×D47—82no—
267C4×D47—84no—
268Dic94—22no—
269Dic94C4×D414yescomplemented
270C47⋊C8—24no—
271C47⋊C8—42no—
272C4×#453—471nomaximal, Sylow
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—24no—
276C22×C47—44no—
277C22×C47—44no—
278C22×C47—42no—
279C22×C47—42no—
280C22×C47—42no—
281C22×C47—82no—
282C22×C47—82no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47C2×C4×D411yescharacteristic
286C22×C47C2×#12011yescharacteristic
287C22×C47#52511yescharacteristic
288C2×D47—24no—
289C2×D47—42no—
290C2×D47—42no—
291C2×D47—88no—
292C4×C47—24no—
293C4×C47—21no—
294C4×C47—22no—
295C4×C47—42no—
296C4×C47—42no—
297C4×C47—81no—
298C4×C47#45312yescomplemented
299C4×C47C2×C4×D412yes—
300C4×C47#52512yes—
301Dic47—24no—
302Dic47—42no—
303Dic47—42no—
304C4×H(5,𝔽2)—471no—
305C2×#453—471no—
306C4×AGL(1,ℤ/8)—472no—
307C4×#127D4711yescharacteristic, complemented
308#1887—471no—
309#1883—472no—
310#1859—472no—
311#1856—471no—
312#1792—471no—
313C4×#104—472no—
314C4×#100—471no—
315C2×C47—21no—
316C2×C47—21no—
317C2×C47—44no—
318C2×C47—82no—
319C2×C47C4×#12011yescharacteristic
320C2×C47C2×#45311yescharacteristic
321C2×C47#301811yescharacteristic
322D47—44no—
323C2×H(5,𝔽2)—471no—
324C2×AGL(1,ℤ/8)—472no—
325C2×#127C2×D4711yescharacteristic
326#520—472no—
327#520—942no—
328#518—471no—
329#518—942no—
330#518—942no—
331C4×#41—472no—
332C4×#41—942no—
333C2×C4×D4—22no—
334C2×C4×D4—942no—
335C2×C4×D4—942no—
336C2×C4×D4C2×D4711yescharacteristic
337C2×C4×D4C2×D4711yescharacteristic, complemented
338#453—478no—
339#442—942no—
340#440—942no—
341C4×SD16—942no—
342C4×D8—942no—
343#428—472no—
344C2×#104—472no—
345C2×#104—472no—
346#418—472no—
347#417—472no—
348C2×#100—471no—
349C2×#100—471no—
350C4×M16—472no—
351#390—22no—
352#390C2×D4711yescharacteristic
353#390C2×D4711yescharacteristic, complemented
354#384C2×D4711yescharacteristic, complemented
355C43C2×D4711yescharacteristic, complemented
356#343—472no—
357#339—472no—
358#339—472no—
359C47C4×#45311yescharacteristic, complemented, Sylow
360H(5,𝔽2)—474no—
361H(5,𝔽2)—944no—
362H(5,𝔽2)—942no—
363C2×#41—472no—
364C2×#41—942no—
365C22×D4—22no—
366C22×D4—942no—
367C22×D4—942no—
368C22×D4C22×D4711yescharacteristic
369C22×D4C22×D4711yescharacteristic
370C23×C4—21no—
371C23×C4—942no—
372C23×C4C22⋊D4712yes—
373AGL(1,ℤ/8)—478no—
374AGL(1,ℤ/8)—944no—
375C2×SD16—942no—
376C2×D8—942no—
377C2×M16—472no—
378C2×M16—472no—
379#127—22no—
380#127C4×D4714yescomplemented
381C4×Q8—472no—
382C4×Q8—472no—
383C4×Q8—942no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—48no—
389C4×D4—472no—
390C4×D4—472no—
391C4×D4—944no—
392C4×D4—944no—
393C4×D4—942no—
394C4×D4—942no—
395C4×D4—942no—
396C4×D4—944no—
397C4×D4—944no—
398C4×D4—942no—
399C4×D4—944no—
400C4×D4—942no—
401#117—472no—
402#117—944no—
403#117—942no—
404#117—942no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4C22×D4711yescharacteristic
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—944no—
414C2×C22⋊C4—942no—
415C2×C22⋊C4—942no—
416C2×C22⋊C4C22⋊D4712yes—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—942no—
420C2×C42—942no—
421C2×C42C22×D4711yescharacteristic
422C2×C42C22×D4711yescharacteristic
423C2×C42C22×D4711yescharacteristic
424#107—942no—
425#106—942no—
426#104—478no—
427#104—944no—
428#103—942no—
429#102—942no—
430#102—942no—
431#102—942no—
432#100—474no—
433#100—942no—
434#97—942no—
435C4×C8—942no—
436C24—21no—
437C24—942no—
438C24C2×C22⋊D4712yes—
439#41—474no—
440#41—474no—
441#41—948no—
442#41—948no—
443#41—942no—
444#41—942no—
445C2×Q8—472no—
446C2×D4—28no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—472no—
455C2×D4—948no—
456C2×D4—948no—
457C2×D4—944no—
458C2×D4—948no—
459C2×D4—948no—
460C2×D4—942no—
461C2×D4C2×C4×D4712yes—
462C2×D4C2×C4×D4712yescomplemented
463C2×D4#1062535012yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—944no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—3764no—
481C22×C4C2×C22⋊D4711yescharacteristic
482C22×C4C2×C22⋊D4712yes—
483C22×C4C2×C22⋊D4711yescharacteristic
484C22×C4C23×D4711yescharacteristic
485SD16—948no—
486D8—948no—
487M16—474no—
488M16—942no—
489M16—942no—
490M16—942no—
491C2×C8—942no—
492C2×C8—942no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—44no—
496C4⋊C4—472no—
497C4⋊C4—472no—
498C4⋊C4—944no—
499C4⋊C4—942no—
500C4⋊C4—942no—
501C22⋊C4—24no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—42no—
505C22⋊C4—944no—
506C22⋊C4—944no—
507C22⋊C4—942no—
508C22⋊C4—942no—
509C22⋊C4—942no—
510C42—24no—
511C42—21no—
512C42—22no—
513C42—42no—
514C42—944no—
515C42—942no—
516C42—942no—
517C42—942no—
518C42C2×C4×D4712yescomplemented
519C42D4×D4712yes—
520C42D4×D4712yes—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23—948no—
531C23—942no—
532C23—3762no—
533C23—3762no—
534C23C4×C22⋊D4714yes—
535C23C22×C22⋊D4711yescharacteristic
536Q8—474no—
537Q8—942no—
538D4—24no—
539D4—24no—
540D4—24no—
541D4—416no—
542D4—42no—
543D4—474no—
544D4—9416no—
545D4—944no—
546D4—944no—
547D4—942no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—948no—
565C2×C4—942no—
566C2×C4—944no—
567C2×C4—944no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—3762no—
571C2×C4—3764no—
572C2×C4—3762no—
573C2×C4—3762no—
574C2×C4—1884no—
575C2×C4#1309399212yes—
576C2×C4#1309399211yescharacteristic
577C2×C4#1309399211yescharacteristic
578C2×C4C22×C4×D4711yescharacteristic
579C2×C4C2×D4×D4712yes—
580C2×C4#41×D4712yes—
581C2×C4C2×#1062535011yescharacteristic
582C8—944no—
583C8—1882no—
584C22—21no—
585C22—21no—
586C22—24no—
587C22—44no—
588C22—44no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—944no—
597C22—3768no—
598C22—1882no—
599C22—1882no—
600C22C2×C4×C22⋊D4711yescharacteristic
601C22C2×#1309399211yescharacteristic
602C22#1568963011yescharacteristic
603C4—24no—
604C4—21no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—81no—
609C4—944no—
610C4—1882no—
611C4—1882no—
612C4#1568929012yesdirect product factor
613C4C4×D4×D4712yes—
614C4#1568963212yes—
615C2—21no—
616C2—21no—
617C2—44no—
618C2—82no—
619C2—1884no—
620C2C4×#1309399211yescharacteristic
621C2C2×#1568929011yescharacteristic
622C2#2025273611yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#127×C47C2
socleC22×C47C2×#120
prime radicalC2×#15689290C2
cosocleC22×C4×C47C24
hypercenterC4×#127D47
hypocenterC47C4×#453
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. C4×#13094069C2semidirect
3. C4×#13094050C2semidirect
4. #20243787C2semidirect
5. #20243767C2semidirect
6. #20243613C2semidirect
7. #20243597C2semidirect
8. #20243341C2semidirect
9. C4×#13093952C2semidirect
10. C4×#13093941C2semidirect
11. C4×#127×C47C2semidirect
23. #15689290C4direct (N × H)
28. #15689163C22semidirect
31. #15689128C22semidirect
35. C4×#10625329C22semidirect
36. #15688892C22semidirect
37. #15688883C22semidirect
38. #15688883C22semidirect
42. C2×C4×D4×C47C22semidirect
45. C47×#390C22semidirect
46. C47×#384C22semidirect
47. C43×C47C22semidirect
50. #13094069C2×C4semidirect
57. #13094050C2×C4semidirect
62. C4×Dic94D4semidirect
63. C4×Dic94D4semidirect
65. C4×D188D4semidirect
66. C4×D188D4semidirect
91. #13093952C2×C4semidirect
97. #13093941C2×C4semidirect
106. #127×C47C2×C4semidirect
136. C2×D4×C47C22×C4semidirect
184. C42×C47C22×C4semidirect
206. #10625329C22×C4semidirect
262. D188C4×D4semidirect
269. Dic94C4×D4semidirect
298. C4×C47#453semidirect
307. C4×#127D47semidirect
337. C2×C4×D4C2×D47semidirect
353. #390C2×D47semidirect
354. #384C2×D47semidirect
355. C43C2×D47semidirect
359. C47C4×#453semidirect
380. #127C4×D47semidirect
462. C2×D4C2×C4×D47semidirect
518. C42C2×C4×D47semidirect
612. C4#15689290direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130940692
C2×#156892902
C4×#130940502
#202437872
#202437672
#202436132
#202435972
#202433412
C4×#130939522
C4×#130939412
C4×#127×C472
C4×#45347