Finite Group Databasebeta

← D3×#5720 #11910168

Subgroups — D3×#5720 #11910168

Order 1152.

2814 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596191C211yesmaximal, characteristic, complemented
2C3×#5720C211yesmaximal, characteristic, complemented
3C3×D3×#127C211yesmaximal, characteristic, complemented
4#10595313C216yesmaximal, complemented
5D3×#939C216yesmaximal, complemented
6D3×#937C213yesmaximal, complemented
7#10595266C213yesmaximal, complemented
8#10595259C213yesmaximal, complemented
9D3×#935C213yesmaximal, complemented
10#10594022C212yesmaximal, complemented
11D3×#876C212yesmaximal, complemented
12D3×#560—31nomaximal
13C2×#5720—31nomaximal
14C23×D32C2211yescharacteristic
15C2×C3×D3×D4C2213yes—
16C2×C3×D3×D4C2213yescomplemented
17C2×D3×#67C2216yes—
18C22×D3×Dic3C2213yescomplemented
19C32×#127C2211yescharacteristic, complemented
20#64148C2216yescomplemented
21#64146C2213yescomplemented
22#64144C2213yescomplemented
23#64085C2212yescomplemented
24C3×#940C2213yescomplemented
25C3×#940C2213yescomplemented
26C3×#939C2216yescomplemented
27C3×#937C2213yescomplemented
28C3×#935C2213yescomplemented
29C3×#876C2212yescomplemented
30C3×#874C2211yescharacteristic, complemented
31C3×C42×D3C2211yescharacteristic, complemented
32#63983C2216yescomplemented
33#63981C2213yescomplemented
34#63980C2216yescomplemented
35#63978C2216yescomplemented
36#63976C2213yescomplemented
37#63971C2216yescomplemented
38#63970C2216yescomplemented
39#63969C2216yescomplemented
40D3×#217C2213yes—
41D3×#217C2213yescomplemented
42#63962C2213yescomplemented
43#63961C2213yescomplemented
44#63922C2216yescomplemented
45D3×(C2×D3)⋊C4C2216yes—
46#63886C2216yescomplemented
47#63885C2216yescomplemented
48#63884C2216yescomplemented
49D3×Dic3⋊C4C2216yescomplemented
50#63868C2216yescomplemented
51#63859C2216yescomplemented
52C3×#560—31no—
53C2×C3×#127—31no—
54C2×#939—36no—
55C2×#937—33no—
56C2×#935—33no—
57#5720—31no—
58#5720—31no—
59#5720—36no—
60#5720—33no—
61#5720—33no—
62#5720—32no—
63#5720—61no—
64#5720D311yescharacteristic, direct product factor
65D3×#127D311yescharacteristic, complemented
66#5711—32no—
67D3×#126—32no—
68#5666—33no—
69D3×#123—33no—
70#5620—36no—
71D3×#121—36no—
72#5595—33no—
73D3×#120—33no—
74C2×#876—32no—
75C23×C3⋊D3C2311yescharacteristic
76C23×C3×D3C2313yes—
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C22×D32—46no—
80C22×D32C2312yes—
81C22×D32C2312yes—
82C2×C32×D4C2313yes—
83C2×C32×D4C2313yescomplemented
84C2×#638C2316yes—
85C22×C3⋊Dic3C2313yescomplemented
86C2×C3×#67C2316yes—
87C2×C3×#67C2313yes—
88C2×C3×#67C2313yes—
89C2×C3×#67C2316yescomplemented
90C22×C3×Dic3C2313yescomplemented
91C3×D3×D4—46no—
92C3×D3×D4—46no—
93C2×C3×D12C2313yes—
94C2×C3×D12C2313yescomplemented
95C2×C3×C4×D3C2313yes—
96D3×#67—412no—
97C2×#626C2316yes—
98C2×#625C2316yes—
99C2×D3×Dic3—46no—
100C2×D3×Dic3C2316yes—
101C2×D3×Dic3C2316yescomplemented
102C32×C42C2311yescharacteristic, complemented
103#3757C2313yes—
104#3757C2313yescomplemented
105#3752C2316yes—
106#3750C2316yescomplemented
107C3×#217C2313yes—
108C3×#217C2313yescomplemented
109C3×(C2×D3)⋊C4C2316yes—
110C3×Dic3⋊C4C2316yescomplemented
111C3×C4×Dic3C2313yescomplemented
112#3724C2316yescomplemented
113Dic3⋊Dic3C2316yescomplemented
114#3722C2316yes—
115(C2×D3)⋊Dic3C2316yes—
116(C2×D3)⋊Dic3C2316yes—
117(C2×D3)⋊Dic3C2316yescomplemented
118C2×#560—91noSylow
119C24×D3—31no—
120C24×D3—31no—
121C22×C3×D4—33no—
122C22×C3×D4—33no—
123C22×#67—36no—
124C23×Dic3—33no—
125C2×D3×D4—36no—
126C2×D3×D4C2×D313yes—
127C2×D3×D4C2×D313yescomplemented
128C22×C4×D3—33no—
129C3×#127—21no—
130C3×#127—33no—
131C3×#127—33no—
132C3×#127—31no—
133C3×#127C2×D311yescharacteristic, complemented
134C3×#127C2×D311yescharacteristic, complemented
135C3×#126—32no—
136C3×#123—33no—
137C3×#121—36no—
138C3×#120—33no—
139C2×C3×C42—31no—
140#953—33no—
141C2×#217—33no—
142C2×#217—33no—
143#940C2×D313yescomplemented
144#940C2×D313yescomplemented
145#939—36no—
146#939—36no—
147#939—36no—
148#939—36no—
149#939—36no—
150#939—36no—
151#939—36no—
152#939—36no—
153#939—36no—
154#939—66no—
155#939C2×D316yescomplemented
156#938—36no—
157#937—33no—
158#937—33no—
159#937—33no—
160#937—36no—
161#937—36no—
162#937—33no—
163#937—36no—
164#937—63no—
165#937C2×D313yescomplemented
166#935—33no—
167#935—33no—
168#935—33no—
169#935—36no—
170#935—33no—
171#935—36no—
172#935—63no—
173#935C2×D313yescomplemented
174#930—36no—
175#929—33no—
176C2×(C2×D3)⋊C4—36no—
177C2×Dic3⋊C4—36no—
178#898—36no—
179#895—36no—
180#894—36no—
181D3×C4⋊C4—36no—
182#886—33no—
183#884—36no—
184#884—36no—
185#883—36no—
186#882—33no—
187#882—36no—
188D3×C22⋊C4—33no—
189D3×C22⋊C4—33no—
190D3×C22⋊C4—36no—
191#879—36no—
192#876—32no—
193#876—32no—
194#876—36no—
195#876—36no—
196#876—62no—
197#876C2×D312yescomplemented
198#874C2×D311yescharacteristic, complemented
199C42×D3C2×D311yescharacteristic, complemented
200C23×C32C2411yescharacteristic
201C23×C32C2413yes—
202C22×C3⋊D3—43no—
203C22×C3⋊D3C2412yes—
204C22×C3×D3—26no—
205C22×C3×D3—26no—
206C22×C3×D3—212no—
207C22×C3×D3—43no—
208C22×C3×D3C2411yescharacteristic
209C22×C3×D3C2412yes—
210C22×C3×D3C2413yes—
211C22×C3×D3C2411yescharacteristic
212C2×D32—212no—
213C2×D32—46no—
214C2×D32—416no—
215C32×D4—43no—
216C32×D4—43no—
217C2×C32×C4C2413yes—
218#638—46no—
219C2×C3⋊Dic3—43no—
220C2×C3⋊Dic3C2416yes—
221C3×#67—46no—
222C3×#67—43no—
223C3×#67—43no—
224C3×#67—46no—
225C2×C3×Dic3—43no—
226C2×C3×Dic3C2413yes—
227C2×C3×Dic3C2416yes—
228C3×D12—43no—
229C3×D12—43no—
230C3×C4×D3—26no—
231#626—46no—
232#625—46no—
233D3×Dic3—212no—
234D3×Dic3—46no—
235#560—31no—
236#560—93no—
237#560—96no—
238#560—93no—
239#560—92no—
240#560—91no—
241C2×#127—31no—
242C2×#126—92no—
243C2×#123—93no—
244C2×#121—96no—
245C2×#120—93no—
246C24×C3—31no—
247C24×C3—33no—
248C24×C3—31no—
249C23×D3—31no—
250C23×D3—31no—
251C23×D3—32no—
252C23×D3—32no—
253C23×D3—32no—
254C23×D3—32no—
255C23×D3—61no—
256C23×D3—126no—
257C23×D3—126no—
258C23×D3C22×D311yescharacteristic
259C23×D3C22×D313yes—
260C23×D3C22×D311yescharacteristic
261C2×C3×D4—23no—
262C2×C3×D4—23no—
263C2×C3×D4—33no—
264C2×C3×D4—33no—
265C2×C3×D4—36no—
266C2×C3×D4—36no—
267C2×C3×D4—33no—
268C2×C3×D4—33no—
269C2×C3×D4—126no—
270C2×C3×D4—126no—
271C2×C3×D4C22×D313yes—
272C2×C3×D4C22×D313yes—
273C2×C3×D4C22×D313yescomplemented
274C2×C3×D4C22×D313yescomplemented
275C22×C3×C4—33no—
276C22×C3×C4—33no—
277C2×#67—36no—
278C2×#67—36no—
279C2×#67—36no—
280C2×#67—36no—
281C2×#67—36no—
282C2×#67—66no—
283C2×#67—1212no—
284C2×#67C22×D313yes—
285C2×#67C22×D313yes—
286C2×#67C22×D316yes—
287C2×#67C22×D316yescomplemented
288C22×Dic3—33no—
289C22×Dic3—33no—
290C22×Dic3—36no—
291C22×Dic3—36no—
292C22×Dic3—63no—
293C22×Dic3—126no—
294C22×Dic3C22×D313yescomplemented
295D3×D4—46no—
296D3×D4—46no—
297D3×D4—1212no—
298C2×D12—36no—
299C2×D12C22×D313yes—
300C2×D12C22×D313yescomplemented
301C2×C4×D3—36no—
302C2×C4×D3—36no—
303C2×C4×D3—126no—
304C2×C4×D3C22×D313yes—
305C3×C4⋊C4—36no—
306C3×C22⋊C4—33no—
307C3×C22⋊C4—33no—
308C3×C22⋊C4—36no—
309C3×C42—21no—
310C3×C42—33no—
311C3×C42C22×D311yescharacteristic, complemented
312C3×C42C22×D311yescharacteristic, complemented
313#217—33no—
314#217—33no—
315#217—33no—
316#217—33no—
317#217—36no—
318#217—36no—
319#217—36no—
320#217—63no—
321#217—63no—
322#217C22×D313yes—
323#217C22×D313yescomplemented
324(C2×D3)⋊C4—36no—
325(C2×D3)⋊C4—36no—
326(C2×D3)⋊C4—36no—
327(C2×D3)⋊C4—36no—
328(C2×D3)⋊C4—36no—
329(C2×D3)⋊C4—36no—
330(C2×D3)⋊C4—36no—
331(C2×D3)⋊C4—66no—
332(C2×D3)⋊C4C22×D316yes—
333C4⋊Dic3—36no—
334Dic3⋊C4—36no—
335Dic3⋊C4—36no—
336Dic3⋊C4—36no—
337Dic3⋊C4—36no—
338Dic3⋊C4—36no—
339Dic3⋊C4—66no—
340Dic3⋊C4C22×D316yescomplemented
341C4×Dic3C22×D313yescomplemented
342C22×C32—23no—
343C22×C32—26no—
344C22×C32—23no—
345C22×C32C2511yescharacteristic
346C2×C3⋊D3—26no—
347C2×C3⋊D3—44no—
348C2×C3×D3—23no—
349C2×C3×D3—26no—
350C2×C3×D3—26no—
351C2×C3×D3—23no—
352C2×C3×D3—44no—
353C2×C3×D3—44no—
354C2×C3×D3—412no—
355C2×C3×D3H(5,𝔽2)16yes—
356D32—48no—
357D32—48no—
358C32×C4—23no—
359C3⋊Dic3—26no—
360C3×Dic3—26no—
361C3×Dic3—23no—
362C25—91no—
363C22×D4—33no—
364C22×D4—33no—
365C22×D4—96no—
366C23×C4—93no—
367#127—33no—
368#127—33no—
369#127—31no—
370#127D3211yescharacteristic, complemented
371#126—32no—
372#126—96no—
373#126—96no—
374#126—92no—
375#123—33no—
376#123—96no—
377#123—93no—
378#123—96no—
379#123—93no—
380#123—93no—
381#121—36no—
382#121—96no—
383#121—96no—
384#121—96no—
385#121—96no—
386#121—96no—
387#121—96no—
388#121—96no—
389#120—33no—
390#120—93no—
391#120—96no—
392#120—96no—
393#120—93no—
394#120—93no—
395C2×C4⋊C4—96no—
396C2×C22⋊C4—96no—
397C2×C22⋊C4—93no—
398C2×C22⋊C4—93no—
399C2×C42—31no—
400C23×C3—21no—
401C23×C3—23no—
402C23×C3—31no—
403C23×C3—31no—
404C23×C3—32no—
405C23×C3—33no—
406C23×C3—66no—
407C23×C3—612no—
408C23×C3—66no—
409C23×C3—123no—
410C23×C3C23×D311yescharacteristic
411C23×C3C23×D311yescharacteristic
412C23×C3C23×D313yes—
413C23×C3C23×D313yes—
414C22×D3—26no—
415C22×D3—212no—
416C22×D3—26no—
417C22×D3—32no—
418C22×D3—32no—
419C22×D3—43no—
420C22×D3—62no—
421C22×D3—612no—
422C22×D3—612no—
423C22×D3—126no—
424C22×D3—126no—
425C22×D3—1216no—
426C22×D3—1216no—
427C22×D3—123no—
428C22×D3—123no—
429C22×D3—243no—
430C22×D3C23×D311yescharacteristic
431C22×D3C23×D312yes—
432C22×D3C23×D313yes—
433C22×D3C23×D311yescharacteristic
434C3×D4—43no—
435C3×D4—43no—
436C3×D4—43no—
437C3×D4—43no—
438C3×D4—83no—
439C3×D4—83no—
440C3×D4—123no—
441C3×D4—123no—
442C3×D4—126no—
443C3×D4—123no—
444C3×D4—126no—
445C3×D4—123no—
446C2×C3×C4—23no—
447C2×C3×C4—33no—
448C2×C3×C4—36no—
449C2×C3×C4—66no—
450C2×C3×C4—123no—
451C2×C3×C4C23×D313yes—
452C2×C3×C4C23×D313yes—
453#67—43no—
454#67—43no—
455#67—46no—
456#67—46no—
457#67—126no—
458#67—126no—
459#67—126no—
460#67—126no—
461#67—126no—
462#67—246no—
463C2×Dic3—36no—
464C2×Dic3—36no—
465C2×Dic3—43no—
466C2×Dic3—66no—
467C2×Dic3—612no—
468C2×Dic3—126no—
469C2×Dic3—123no—
470C2×Dic3—123no—
471C2×Dic3—243no—
472C2×Dic3C23×D313yes—
473C2×Dic3C23×D316yes—
474D12—43no—
475D12—43no—
476D12—126no—
477C4×D3—26no—
478C4×D3—612no—
479C4×D3—126no—
480C2×C32—41no—
481C2×C32—43no—
482C2×C32C2×H(5,𝔽2)13yes—
483C3⋊D3—42no—
484C3×D3—42no—
485C3×D3—41no—
486C3×D3—43no—
487C3×D3#56014yescomplemented
488C24—31no—
489C24—33no—
490C24—31no—
491C24—92no—
492C24—92no—
493C24—91no—
494C24—366no—
495C2×D4—36no—
496C2×D4—33no—
497C2×D4—33no—
498C2×D4—36no—
499C2×D4—33no—
500C2×D4—33no—
501C2×D4—96no—
502C2×D4—96no—
503C2×D4—96no—
504C2×D4—126no—
505C2×D4—126no—
506C2×D4—3612no—
507C2×D4C2×D3213yes—
508C2×D4C2×D3213yescomplemented
509C22×C4—33no—
510C22×C4—33no—
511C22×C4—96no—
512C22×C4—96no—
513C22×C4—93no—
514C22×C4—366no—
515C4⋊C4—36no—
516C4⋊C4—96no—
517C4⋊C4—96no—
518C4⋊C4—96no—
519C22⋊C4—33no—
520C22⋊C4—33no—
521C22⋊C4—36no—
522C22⋊C4—96no—
523C22⋊C4—96no—
524C22⋊C4—96no—
525C22⋊C4—96no—
526C22⋊C4—93no—
527C22⋊C4—93no—
528C22⋊C4—96no—
529C42—33no—
530C42C2×D3211yescharacteristic, complemented
531C22×C3—23no—
532C22×C3—26no—
533C22×C3—23no—
534C22×C3—23no—
535C22×C3—26no—
536C22×C3—23no—
537C22×C3—21no—
538C22×C3—36no—
539C22×C3—43no—
540C22×C3—46no—
541C22×C3—43no—
542C22×C3—66no—
543C22×C3—63no—
544C22×C3—66no—
545C22×C3—63no—
546C22×C3—124no—
547C22×C3—1212no—
548C22×C3—124no—
549C22×C3C24×D311yescharacteristic
550C22×C3C24×D311yescharacteristic
551C2×D3—23no—
552C2×D3—26no—
553C2×D3—23no—
554C2×D3—26no—
555C2×D3—44no—
556C2×D3—44no—
557C2×D3—412no—
558C2×D3—66no—
559C2×D3—66no—
560C2×D3—126no—
561C2×D3—128no—
562C2×D3—128no—
563C2×D3—128no—
564C2×D3—124no—
565C2×D3—124no—
566C2×D3—128no—
567C2×D3—244no—
568C2×D3#100416yes—
569C3×C4—23no—
570C3×C4—23no—
571C3×C4—43no—
572C3×C4—66no—
573C3×C4—63no—
574Dic3—23no—
575Dic3—26no—
576Dic3—66no—
577Dic3—66no—
578Dic3—126no—
579C32C2×#56011yescharacteristic, complemented, Sylow
580C23—31no—
581C23—32no—
582C23—31no—
583C23—33no—
584C23—66no—
585C23—612no—
586C23—66no—
587C23—92no—
588C23—123no—
589C23—1812no—
590C23—363no—
591C23—366no—
592C23—3616no—
593C23C22×D3211yescharacteristic
594C23C22×D3213yes—
595D4—43no—
596D4—43no—
597D4—123no—
598D4—123no—
599D4—123no—
600D4—126no—
601D4—123no—
602D4—126no—
603D4—366no—
604D4—366no—
605D4—366no—
606C2×C4—33no—
607C2×C4—36no—
608C2×C4—66no—
609C2×C4—96no—
610C2×C4—123no—
611C2×C4—1812no—
612C2×C4—366no—
613C2×C4—363no—
614C2×C4C22×D3213yes—
615C2×C3—23no—
616C2×C3—34no—
617C2×C3—41no—
618C2×C3—43no—
619C2×C3—41no—
620C2×C3—43no—
621C2×C3—81no—
622C2×C3—83no—
623C2×C3—121no—
624C2×C3—123no—
625C2×C3—122no—
626C2×C3C2×#100413yes—
627C2×C3D3×H(5,𝔽2)13yes—
628D3—42no—
629D3—41no—
630D3—43no—
631D3—122no—
632D3—122no—
633D3—242no—
634D3#572014yesdirect product factor
635C22—23no—
636C22—26no—
637C22—23no—
638C22—36no—
639C22—63no—
640C22—66no—
641C22—63no—
642C22—66no—
643C22—124no—
644C22—1212no—
645C22—124no—
646C22—186no—
647C22—368no—
648C22—364no—
649C22—368no—
650C22C23×D3211yescharacteristic
651C4—23no—
652C4—63no—
653C4—66no—
654C4—186no—
655C3—21no—
656C3C2×#572011yescharacteristic, complemented
657C3D3×#56011yescharacteristic, complemented
658C2—34no—
659C2—41no—
660C2—43no—
661C2—121no—
662C2—122no—
663C2—123no—
664C2—362no—
665C2D3×#100413yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596191C2semidirect
2. C3×#5720C2semidirect
3. C3×D3×#127C2semidirect
4. #10595313C2semidirect
5. D3×#939C2semidirect
6. D3×#937C2semidirect
7. #10595266C2semidirect
8. #10595259C2semidirect
9. D3×#935C2semidirect
10. #10594022C2semidirect
11. D3×#876C2semidirect
16. C2×C3×D3×D4C22semidirect
18. C22×D3×Dic3C22semidirect
19. C32×#127C22semidirect
20. #64148C22semidirect
21. #64146C22semidirect
22. #64144C22semidirect
23. #64085C22semidirect
24. C3×#940C22semidirect
25. C3×#940C22semidirect
26. C3×#939C22semidirect
27. C3×#937C22semidirect
28. C3×#935C22semidirect
29. C3×#876C22semidirect
30. C3×#874C22semidirect
31. C3×C42×D3C22semidirect
32. #63983C22semidirect
33. #63981C22semidirect
34. #63980C22semidirect
35. #63978C22semidirect
36. #63976C22semidirect
37. #63971C22semidirect
38. #63970C22semidirect
39. #63969C22semidirect
41. D3×#217C22semidirect
42. #63962C22semidirect
43. #63961C22semidirect
44. #63922C22semidirect
46. #63886C22semidirect
47. #63885C22semidirect
48. #63884C22semidirect
49. D3×Dic3⋊C4C22semidirect
50. #63868C22semidirect
51. #63859C22semidirect
64. #5720D3direct (N × H)
65. D3×#127D3semidirect
83. C2×C32×D4C23semidirect
85. C22×C3⋊Dic3C23semidirect
89. C2×C3×#67C23semidirect
90. C22×C3×Dic3C23semidirect
94. C2×C3×D12C23semidirect
101. C2×D3×Dic3C23semidirect
102. C32×C42C23semidirect
104. #3757C23semidirect
106. #3750C23semidirect
108. C3×#217C23semidirect
110. C3×Dic3⋊C4C23semidirect
111. C3×C4×Dic3C23semidirect
112. #3724C23semidirect
113. Dic3⋊Dic3C23semidirect
117. (C2×D3)⋊Dic3C23semidirect
127. C2×D3×D4C2×D3semidirect
133. C3×#127C2×D3semidirect
134. C3×#127C2×D3semidirect
143. #940C2×D3semidirect
144. #940C2×D3semidirect
155. #939C2×D3semidirect
165. #937C2×D3semidirect
173. #935C2×D3semidirect
197. #876C2×D3semidirect
198. #874C2×D3semidirect
199. C42×D3C2×D3semidirect
273. C2×C3×D4C22×D3semidirect
274. C2×C3×D4C22×D3semidirect
287. C2×#67C22×D3semidirect
294. C22×Dic3C22×D3semidirect
300. C2×D12C22×D3semidirect
311. C3×C42C22×D3semidirect
312. C3×C42C22×D3semidirect
323. #217C22×D3semidirect
340. Dic3⋊C4C22×D3semidirect
341. C4×Dic3C22×D3semidirect
370. #127D32semidirect
487. C3×D3#560semidirect
508. C2×D4C2×D32semidirect
530. C42C2×D32semidirect
579. C32C2×#560semidirect
634. D3#5720direct (N × H)
656. C3C2×#5720semidirect
657. C3D3×#560semidirect

Maximal subgroups

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

subgroupindex
#105961912
C3×#57202
C3×D3×#1272
#105953132
D3×#9392
D3×#9372
#105952662
#105952592
D3×#9352
#105940222
D3×#8762
D3×#5603
C2×#57203