Finite Group Databasebeta

← C4×#14583066 #25102469

Subgroups — C4×#14583066 #25102469

Order 11008.

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×#13063370C211yesmaximal, characteristic, complemented
2C2×#14583066C211yesmaximal, characteristic
3C4×#13063351C212yesmaximal, complemented
4#19134994C211yesmaximal, characteristic, complemented
5#19134974C212yesmaximal, complemented
6#19134820C212yesmaximal, complemented
7#19134804C211yesmaximal, characteristic, complemented
8#19134548C211yesmaximal, characteristic, complemented
9C4×#13063253C212yesmaximal, complemented
10C4×#13063242C211yesmaximal, characteristic, complemented
11C4×#127×C43C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C2×#13063351C2212yes—
14#14583380C2212yes—
15#14583378—22no—
16#14583374C2211yescharacteristic
17#14583372—22no—
18#14583371—22no—
19C4×#10621898C2212yes—
20C4×#10621900—22no—
21C2×C4×C22⋊D43—22no—
22C4×D4×D43—22no—
23#14583066C418yesdirect product factor
24#14583009—22no—
25#14582999—22no—
26C4×#10621883—22no—
27C4×#10621882—22no—
28#14582939C2212yescomplemented
29C2×#13063253C2212yes—
30C2×#13063253C2212yes—
31#14582904C2212yescomplemented
32#14582898C2212yes—
33C2×#13063242C2211yescharacteristic
34C2×#13063242C2211yescharacteristic
35C4×#10621877C2212yescomplemented
36#14582668C2212yescomplemented
37#14582659C2212yescomplemented
38#14582659C2212yescomplemented
39C2×#127×C43C2211yescharacteristic
40C2×C4×D4×C43—22no—
41C2×C4×D4×C43C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic, complemented
43C43×#390—22no—
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic, complemented
46C43×#384C2211yescharacteristic, complemented
47C43×C43C2211yescharacteristic, complemented
48#13063370—22no—
49#13063370—24no—
50#13063370C2×C414yescomplemented
51C2×#10621898C2312yes—
52C2×#10621900—22no—
53C22×C22⋊D43—22no—
54C2×D4×D43—22no—
55C22×C4×D43—22no—
56#13063351—24no—
57#13063351C2×C418yescomplemented
58C2×#10621883—22no—
59C2×#10621882—22no—
60C2×#10621877C2312yes—
61C2×#10621877C2312yes—
62C4×Dic86D412yescomplemented
63C4×Dic86D412yescomplemented
64#13063290—22no—
65C4×D172D412yescomplemented
66C4×D172D412yescomplemented
67D4×Dic43—22no—
68D4×Dic43—22no—
69#13063287—22no—
70C4×C22⋊D43—24no—
71C4×C22⋊D43—24no—
72C4×C22⋊D43—22no—
73C4×C22⋊D43—24no—
74C4×C22⋊D43—22no—
75(C22⋊D43)⋊C4—24no—
76(C22⋊D43)⋊C4—24no—
77#13063284C2312yes—
78#13063283—22no—
79#13063282—22no—
80#13063281—24no—
81C2×Dic43⋊C4—22no—
82C4⋊C4×D43—22no—
83C2×C22⋊Dic43—22no—
84C2×(C2×D43)⋊C4—22no—
85C22⋊C4×D43—24no—
86C2×C4×Dic43—22no—
87C42×D43—22no—
88#13063258—22no—
89#13063256—22no—
90#13063253—24no—
91#13063253C2×C418yescomplemented
92#13063248—22no—
93#13063246—22no—
94#13063246—22no—
95#13063245—22no—
96#13063242—22no—
97#13063242C2×C414yescomplemented
98#13063236—22no—
99C4×C43⋊C8—22no—
100C22×D4×C43—22no—
101C22×D4×C43C2311yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C23×C4×C43—21no—
104C23×C4×C43D412yes—
105#127×C43—22no—
106#127×C43C2×C414yescomplemented
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C4×D4×C43—48no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D412yes—
119C2×C42×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C24×C43—21no—
125C24×C43C2×D412yes—
126C23×D43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—21no—
130C2×D4×C43—28no—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—44no—
134C2×D4×C43—44no—
135C2×D4×C43C22×C412yes—
136C2×D4×C43C22×C412yescomplemented
137C2×D4×C43#4112yes—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—44no—
144C22×C4×C43—44no—
145C22×C4×C43—41no—
146C22×C4×C43—41no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—24no—
152C2×C22⋊D43—28no—
153C2×C22⋊D43—28no—
154C2×C22⋊D43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158#10621900—28no—
159#10621900—28no—
160D4×D43—28no—
161D4×D43—28no—
162#10621898—22no—
163#10621898—22no—
164#10621898C22×C414yes—
165#10621898#4114yes—
166C2×D172C2×D412yes—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—24no—
170C2×C4×D43—22no—
171C2×C4×D43—84no—
172C2×Dic86C2×D412yes—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—44no—
176C22⋊C4×C43—24no—
177C22⋊C4×C43—44no—
178C22⋊C4×C43—44no—
179C22⋊C4×C43—42no—
180C42×C43—24no—
181C42×C43—21no—
182C42×C43—22no—
183C42×C43—42no—
184C42×C43C22×C412yescomplemented
185C42×C43C2×D412yes—
186C42×C43C2×D412yes—
187C22⋊Dic43—24no—
188C22⋊Dic43—22no—
189#10621883—28no—
190#10621882—28no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194C4⋊Dic43C2×D412yes—
195C4⋊Dic43C2×D412yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199C4×Dic43—24no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43—22no—
203#10621877—22no—
204#10621877—22no—
205#10621877—22no—
206#10621877C22×C414yescomplemented
207C2×C43⋊C8—22no—
208C2×C43⋊C8—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43C4×D414yes—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—28no—
222C22×D43—82no—
223C22×D43—82no—
224D4×C43—24no—
225D4×C43—24no—
226D4×C43—24no—
227D4×C43—416no—
228D4×C43—42no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—44no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—41no—
242C2×C4×C43—82no—
243C2×C4×C43—82no—
244C2×C4×C43—82no—
245C2×C4×C43#12012yes—
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12011yescharacteristic
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D412yes—
250C2×C4×C43C2×#4112yes—
251C2×C4×C43C2×#4111yescharacteristic
252C22⋊D43—216no—
253C22⋊D43—24no—
254C22⋊D43—24no—
255C2×Dic43—28no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—82no—
260C2×Dic43—82no—
261D172—22no—
262D172C4×D414yescomplemented
263C4×D43—24no—
264C4×D43—24no—
265C4×D43—44no—
266C4×D43—82no—
267C4×D43—84no—
268Dic86—22no—
269Dic86C4×D414yescomplemented
270C43⋊C8—24no—
271C43⋊C8—42no—
272C4×#453—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—24no—
276C22×C43—44no—
277C22×C43—44no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—82no—
282C22×C43—82no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43C2×C4×D411yescharacteristic
286C22×C43C2×#12011yescharacteristic
287C22×C43#52511yescharacteristic
288C2×D43—24no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—88no—
292C4×C43—24no—
293C4×C43—21no—
294C4×C43—22no—
295C4×C43—42no—
296C4×C43—42no—
297C4×C43—81no—
298C4×C43#45312yescomplemented
299C4×C43C2×C4×D412yes—
300C4×C43#52512yes—
301Dic43—24no—
302Dic43—42no—
303Dic43—42no—
304C4×H(5,𝔽2)—431no—
305C2×#453—431no—
306C4×AGL(1,ℤ/8)—432no—
307C4×#127D4311yescharacteristic, complemented
308#1887—431no—
309#1883—432no—
310#1859—432no—
311#1856—431no—
312#1792—431no—
313C4×#104—432no—
314C4×#100—431no—
315C2×C43—21no—
316C2×C43—21no—
317C2×C43—44no—
318C2×C43—82no—
319C2×C43C4×#12011yescharacteristic
320C2×C43C2×#45311yescharacteristic
321C2×C43#301811yescharacteristic
322D43—44no—
323C2×H(5,𝔽2)—431no—
324C2×AGL(1,ℤ/8)—432no—
325C2×#127C2×D4311yescharacteristic
326#520—432no—
327#520—862no—
328#518—431no—
329#518—862no—
330#518—862no—
331C4×#41—432no—
332C4×#41—862no—
333C2×C4×D4—22no—
334C2×C4×D4—862no—
335C2×C4×D4—862no—
336C2×C4×D4C2×D4311yescharacteristic
337C2×C4×D4C2×D4311yescharacteristic, complemented
338#453—438no—
339#442—862no—
340#440—862no—
341C4×SD16—862no—
342C4×D8—862no—
343#428—432no—
344C2×#104—432no—
345C2×#104—432no—
346#418—432no—
347#417—432no—
348C2×#100—431no—
349C2×#100—431no—
350C4×M16—432no—
351#390—22no—
352#390C2×D4311yescharacteristic
353#390C2×D4311yescharacteristic, complemented
354#384C2×D4311yescharacteristic, complemented
355C43C2×D4311yescharacteristic, complemented
356#343—432no—
357#339—432no—
358#339—432no—
359C43C4×#45311yescharacteristic, complemented, Sylow
360H(5,𝔽2)—434no—
361H(5,𝔽2)—864no—
362H(5,𝔽2)—862no—
363C2×#41—432no—
364C2×#41—862no—
365C22×D4—22no—
366C22×D4—862no—
367C22×D4—862no—
368C22×D4C22×D4311yescharacteristic
369C22×D4C22×D4311yescharacteristic
370C23×C4—21no—
371C23×C4—862no—
372C23×C4C22⋊D4312yes—
373AGL(1,ℤ/8)—438no—
374AGL(1,ℤ/8)—864no—
375C2×SD16—862no—
376C2×D8—862no—
377C2×M16—432no—
378C2×M16—432no—
379#127—22no—
380#127C4×D4314yescomplemented
381C4×Q8—432no—
382C4×Q8—432no—
383C4×Q8—862no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—48no—
389C4×D4—432no—
390C4×D4—432no—
391C4×D4—864no—
392C4×D4—864no—
393C4×D4—862no—
394C4×D4—862no—
395C4×D4—862no—
396C4×D4—864no—
397C4×D4—864no—
398C4×D4—862no—
399C4×D4—864no—
400C4×D4—862no—
401#117—432no—
402#117—864no—
403#117—862no—
404#117—862no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—864no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—862no—
416C2×C22⋊C4C22⋊D4312yes—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—862no—
420C2×C42—862no—
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423C2×C42C22×D4311yescharacteristic
424#107—862no—
425#106—862no—
426#104—438no—
427#104—864no—
428#103—862no—
429#102—862no—
430#102—862no—
431#102—862no—
432#100—434no—
433#100—862no—
434#97—862no—
435C4×C8—862no—
436C24—21no—
437C24—862no—
438C24C2×C22⋊D4312yes—
439#41—434no—
440#41—434no—
441#41—868no—
442#41—868no—
443#41—862no—
444#41—862no—
445C2×Q8—432no—
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—432no—
455C2×D4—868no—
456C2×D4—868no—
457C2×D4—864no—
458C2×D4—868no—
459C2×D4—868no—
460C2×D4—862no—
461C2×D4C2×C4×D4312yes—
462C2×D4C2×C4×D4312yescomplemented
463C2×D4#1062189812yes—
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—864no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—3444no—
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4312yes—
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485SD16—868no—
486D8—868no—
487M16—434no—
488M16—862no—
489M16—862no—
490M16—862no—
491C2×C8—862no—
492C2×C8—862no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—44no—
496C4⋊C4—432no—
497C4⋊C4—432no—
498C4⋊C4—864no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C22⋊C4—24no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—42no—
505C22⋊C4—864no—
506C22⋊C4—864no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C22⋊C4—862no—
510C42—24no—
511C42—21no—
512C42—22no—
513C42—42no—
514C42—864no—
515C42—862no—
516C42—862no—
517C42—862no—
518C42C2×C4×D4312yescomplemented
519C42D4×D4312yes—
520C42D4×D4312yes—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23—868no—
531C23—862no—
532C23—3442no—
533C23—3442no—
534C23C4×C22⋊D4314yes—
535C23C22×C22⋊D4311yescharacteristic
536Q8—434no—
537Q8—862no—
538D4—24no—
539D4—24no—
540D4—24no—
541D4—416no—
542D4—42no—
543D4—434no—
544D4—8616no—
545D4—864no—
546D4—864no—
547D4—862no—
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—868no—
565C2×C4—862no—
566C2×C4—864no—
567C2×C4—864no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—3442no—
571C2×C4—3444no—
572C2×C4—3442no—
573C2×C4—3442no—
574C2×C4—1724no—
575C2×C4#1306329312yes—
576C2×C4#1306329311yescharacteristic
577C2×C4#1306329311yescharacteristic
578C2×C4C22×C4×D4311yescharacteristic
579C2×C4C2×D4×D4312yes—
580C2×C4#41×D4312yes—
581C2×C4C2×#1062189811yescharacteristic
582C8—864no—
583C8—1722no—
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—864no—
597C22—3448no—
598C22—1722no—
599C22—1722no—
600C22C2×C4×C22⋊D4311yescharacteristic
601C22C2×#1306329311yescharacteristic
602C22#1458340611yescharacteristic
603C4—24no—
604C4—22no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—81no—
609C4—864no—
610C4—1722no—
611C4—1722no—
612C4#1458306612yesdirect product factor
613C4C4×D4×D4312yes—
614C4#1458340812yes—
615C2—21no—
616C2—21no—
617C2—44no—
618C2—82no—
619C2—1724no—
620C2C4×#1306329311yescharacteristic
621C2C2×#1458306611yescharacteristic
622C2#1914394311yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#127×C43C2
socleC22×C43C2×#120
prime radicalC2×#14583066C2
cosocleC22×C4×C43C24
hypercenterC4×#127D43
hypocenterC43C4×#453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. C4×#13063370C2semidirect
3. C4×#13063351C2semidirect
4. #19134994C2semidirect
5. #19134974C2semidirect
6. #19134820C2semidirect
7. #19134804C2semidirect
8. #19134548C2semidirect
9. C4×#13063253C2semidirect
10. C4×#13063242C2semidirect
11. C4×#127×C43C2semidirect
23. #14583066C4direct (N × H)
28. #14582939C22semidirect
31. #14582904C22semidirect
35. C4×#10621877C22semidirect
36. #14582668C22semidirect
37. #14582659C22semidirect
38. #14582659C22semidirect
42. C2×C4×D4×C43C22semidirect
45. C43×#390C22semidirect
46. C43×#384C22semidirect
47. C43×C43C22semidirect
50. #13063370C2×C4semidirect
57. #13063351C2×C4semidirect
62. C4×Dic86D4semidirect
63. C4×Dic86D4semidirect
65. C4×D172D4semidirect
66. C4×D172D4semidirect
91. #13063253C2×C4semidirect
97. #13063242C2×C4semidirect
106. #127×C43C2×C4semidirect
136. C2×D4×C43C22×C4semidirect
184. C42×C43C22×C4semidirect
206. #10621877C22×C4semidirect
262. D172C4×D4semidirect
269. Dic86C4×D4semidirect
298. C4×C43#453semidirect
307. C4×#127D43semidirect
337. C2×C4×D4C2×D43semidirect
353. #390C2×D43semidirect
354. #384C2×D43semidirect
355. C43C2×D43semidirect
359. C43C4×#453semidirect
380. #127C4×D43semidirect
462. C2×D4C2×C4×D43semidirect
518. C42C2×C4×D43semidirect
612. C4#14583066direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130633702
C2×#145830662
C4×#130633512
#191349942
#191349742
#191348202
#191348042
#191345482
C4×#130632532
C4×#130632422
C4×#127×C432
C4×#45343