Finite Group Databasebeta

← D3×#5160 #11867922

Subgroups — D3×#5160 #11867922

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 729 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2D3×#932C212yesmaximal, complemented
3D3×#901C211yesmaximal, characteristic, complemented
4#10592859C211yesmaximal, characteristic, complemented
5C3×#5160C211yesmaximal, characteristic, complemented
6#10591505C212yesmaximal, complemented
7D3×#833C212yesmaximal, complemented
8#10591406C212yesmaximal, complemented
9#10590929C211yesmaximal, characteristic, complemented
10#10590926C211yesmaximal, characteristic, complemented
11D3×#819C211yesmaximal, characteristic, complemented
12C2×#5160—31nomaximal
13D3×#472—31nomaximal
14C2×C3×D3×D4C2212yes—
15D3×#235C2211yescharacteristic
16C2×C32×D8C2211yescharacteristic, complemented
17#64141C2212yescomplemented
18#64110C2211yescharacteristic, complemented
19C3×#932C2212yescomplemented
20C2×C3×#213C2212yescomplemented
21C3×D3×D8—21no—
22C3×D3×D8—21no—
23C3×D3×D8—21no—
24C3×D3×D8—21no—
25C2×C3×D24C2211yescharacteristic, complemented
26C3×#901C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic
28#63934—22no—
29#63932—22no—
30D3×#214—22no—
31D3×#213—22no—
32#63830C2212yescomplemented
33#63823C2212yescomplemented
34#63817C2211yescharacteristic, complemented
35#63814C2211yescharacteristic, complemented
36D3×#208C2211yescharacteristic
37D3×#208C2212yes—
38#63804—21no—
39#63803—21no—
40D3×ΓL(1,𝔽25)—21no—
41D32×C8—21no—
42#63660C2212yescomplemented
43#63646C2211yescharacteristic, complemented
44C3×#833C2212yescomplemented
45C3×#819C2211yescharacteristic, complemented
46#63577C2212yescomplemented
47#63558C2212yescomplemented
48#63558C2212yescomplemented
49C22×C3×D8—31no—
50C2×#932—32no—
51D3×AGL(1,ℤ/8)—32no—
52C2×D3×D8D311yescharacteristic, complemented
53D3×#131—31no—
54C2×#901—31no—
55C3×#472—31no—
56C2×#833—32no—
57#5199—32no—
58#5160—31no—
59#5160—31no—
60#5160—32no—
61#5160—31no—
62#5160—32no—
63#5160—31no—
64#5160—61no—
65#5160D311yescharacteristic, direct product factor
66#5142—31no—
67C2×#819—31no—
68#4897—31no—
69D3×#108—31no—
70#4749—32no—
71D3×#100—32no—
72C23×C3×D3—22no—
73C2×C32×D4C2312yes—
74#3828C2311yescharacteristic
75C2×C3×#67—22no—
76C3×D3×D4—22no—
77C3×D3×D4—22no—
78C3×D3×D4—22no—
79C3×D3×D4—22no—
80C3×#235C2311yescharacteristic
81C2×C3×D12C2312yes—
82C2×C3×C4×D3C2311yescharacteristic
83D3×#67—21no—
84#3804—21no—
85D3×D12D411yescharacteristic
86C4×D32—21no—
87#3799D411yescharacteristic
88#3798—21no—
89#3795D411yescharacteristic
90D3×Dic6D411yescharacteristic
91C32×D8—21no—
92C32×D8—21no—
93C2×C32×C8C2311yescharacteristic
94#3754—22no—
95#3753—22no—
96#3748C2311yescharacteristic
97#3748C2312yes—
98#3743—21no—
99C8×C3⋊D3—21no—
100C3×#214—22no—
101C3×#213—22no—
102C3×#213—22no—
103C3×#213—22no—
104C3×#208C2311yescharacteristic
105C3×#208C2312yes—
106C2×C3×C3⋊C8C2311yescharacteristic
107C3×D24—21no—
108C3×D24—21no—
109C3×ΓL(1,𝔽25)—21no—
110C3×D3×C8—21no—
111C3×D3×C8D411yescharacteristic
112C3×D3×C8D411yescharacteristic
113C3×D3×C8D411yescharacteristic
114C3×D3×C8D411yescharacteristic
115#3716—22no—
116#3715—22no—
117#3714—22no—
118#3713—22no—
119#3712—21no—
120#3711—21no—
121#3711—22no—
122#3711—21no—
123#3710—21no—
124D3×C3⋊C8—21no—
125D3×C3⋊C8—22no—
126D3×C3⋊C8—21no—
127C2×#472—91noSylow
128C22×C3×D4—32no—
129D3×#41—31no—
130C2×D3×D4C2×D312yes—
131C2×#235—31no—
132C3×AGL(1,ℤ/8)—32no—
133C2×C3×D8—21no—
134C2×C3×D8—32no—
135C2×C3×D8—31no—
136C2×C3×D8—61no—
137C2×C3×D8—61no—
138C2×C3×D8—61no—
139C2×C3×D8—61no—
140C2×C3×D8C2×D311yescharacteristic, complemented
141C2×C3×D8C2×D311yescharacteristic, complemented
142C3×#131—31no—
143C22×C3×C8—31no—
144#949—32no—
145#948—31no—
146C2×#214—62no—
147#932—32no—
148#932—32no—
149#932—32no—
150#932—32no—
151#932—62no—
152#932—62no—
153#932—62no—
154#932C2×D312yescomplemented
155C2×#213—62no—
156C2×#213C2×D312yescomplemented
157C2×#208—31no—
158C2×#208—32no—
159#914—62no—
160D3×SD16—62no—
161#911—62no—
162D3×D8—21no—
163D3×D8—21no—
164D3×D8—21no—
165D3×D8—21no—
166D3×D8—62no—
167#908—32no—
168#907—31no—
169#907—61no—
170D3×M16—32no—
171D3×M16—31no—
172D3×M16—61no—
173C2×D24C2×D311yescharacteristic, complemented
174#901—31no—
175#901—31no—
176#901—31no—
177#901—31no—
178#901—61no—
179#901—61no—
180#901—61no—
181#901—61no—
182#901C2×D311yescharacteristic, complemented
183C2×ΓL(1,𝔽25)—61no—
184C2×D3×C8—61no—
185C2×D3×C8—61no—
186C2×D3×C8C2×D311yescharacteristic
187C3×#108—31no—
188C3×#100—32no—
189#833—32no—
190#833—32no—
191#833—32no—
192#833—32no—
193#833—62no—
194#833C2×D312yescomplemented
195#823—32no—
196#823—32no—
197#822—32no—
198#819—31no—
199#819—31no—
200#819—32no—
201#819—61no—
202#819C2×D311yescharacteristic, complemented
203C23×C32—22no—
204C22×C3×D3—22no—
205C22×C3×D3—42no—
206C22×C3×D3—42no—
207C22×C3×D3—84no—
208C22×C3×D3#4111yescharacteristic
209C2×D32—21no—
210C32×D4—22no—
211C32×D4—22no—
212C2×C32×C4C2411yescharacteristic
213#638—21no—
214C4⋊(C3⋊D3)C2×D411yescharacteristic
215C4×C3⋊D3—21no—
216#634C2×D411yescharacteristic
217C3×#67—21no—
218C3×#67—42no—
219C3×#67—42no—
220C2×C3×Dic3#4111yescharacteristic
221C3×D12—22no—
222C3×D12—22no—
223C3×D12C2×D411yescharacteristic
224C3×C4×D3—21no—
225C3×C4×D3C2×D411yescharacteristic
226C3×C4×D3C2×D411yescharacteristic
227C3×C4×D3C2×D411yescharacteristic
228C3×C4×D3C2×D411yescharacteristic
229C3×Dic6C2×D411yescharacteristic
230#627—21no—
231#626—21no—
232#626—21no—
233#625—21no—
234#624—21no—
235D3×Dic3—21no—
236D3×Dic3—21no—
237C32×C8C2×D411yescharacteristic
238C32×C8C2×D411yescharacteristic
239C3⋊(C3⋊C8)—21no—
240C3⋊(C3⋊C8)—22no—
241C3×C3⋊C8—21no—
242C3×C3⋊C8—22no—
243C3×C3⋊C8C2×D411yescharacteristic
244C3×C3⋊C8C2×D411yescharacteristic
245C2×AGL(1,ℤ/8)—92no—
246C22×D8—31no—
247C2×#131—91no—
248#472—31no—
249#472—92no—
250#472—91no—
251#472—91no—
252#472—92no—
253#472—91no—
254C2×#108—91no—
255C2×#100—92no—
256C24×C3—62no—
257C23×D3—22no—
258C3×#41—31no—
259C2×C3×D4—22no—
260C2×C3×D4—32no—
261C2×C3×D4—62no—
262C2×C3×D4—62no—
263C2×C3×D4—62no—
264C2×C3×D4—62no—
265C2×C3×D4—62no—
266C2×C3×D4C22×D312yes—
267C2×C3×D4C22×D312yes—
268C22×C3×C4—31no—
269C2×#67—22no—
270C2×#67—61no—
271#239—31no—
272D3×Q8—31no—
273#237—31no—
274#237—61no—
275D3×D4—22no—
276D3×D4—22no—
277D3×D4—22no—
278D3×D4—22no—
279D3×D4—31no—
280D3×D4—61no—
281#235—31no—
282#235—31no—
283#235—31no—
284#235—31no—
285#235—61no—
286#235—61no—
287#235—61no—
288#235—61no—
289#235C22×D311yescharacteristic
290C2×D12—31no—
291C2×D12C22×D312yes—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3C22×D311yescharacteristic
295C2×Dic6—31no—
296C3×SD16—62no—
297C3×D8—21no—
298C3×D8—21no—
299C3×D8—21no—
300C3×D8—21no—
301C3×D8—41no—
302C3×D8—41no—
303C3×D8—62no—
304C3×D8—62no—
305C3×D8—62no—
306C3×D8—61no—
307C3×D8—61no—
308C3×M16—32no—
309C3×M16—31no—
310C3×M16—61no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8—61no—
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320#215—62no—
321#214—22no—
322#214—62no—
323#214—62no—
324#214—62no—
325#214—62no—
326#214—122no—
327#213—22no—
328#213—22no—
329#213—22no—
330#213—62no—
331#213—62no—
332#213—62no—
333#213—62no—
334#213—62no—
335#213—122no—
336#208—32no—
337#208—32no—
338#208—31no—
339#208—31no—
340#208—62no—
341#208—61no—
342#208—61no—
343#208—62no—
344#208—61no—
345#208C22×D312yes—
346#208C22×D311yescharacteristic
347C2×C3⋊C8—61no—
348C2×C3⋊C8—62no—
349C2×C3⋊C8—61no—
350C2×C3⋊C8C22×D311yescharacteristic
351D24—21no—
352D24—21no—
353D24—62no—
354#204—62no—
355ΓL(1,𝔽25)—21no—
356ΓL(1,𝔽25)—61no—
357ΓL(1,𝔽25)—61no—
358ΓL(1,𝔽25)—62no—
359ΓL(1,𝔽25)—61no—
360ΓL(1,𝔽25)—61no—
361ΓL(1,𝔽25)—61no—
362ΓL(1,𝔽25)—61no—
363ΓL(1,𝔽25)—121no—
364D3×C8—21no—
365D3×C8—61no—
366D3×C8—61no—
367D3×C8—62no—
368D3×C8—61no—
369D3×C8—61no—
370D3×C8—61no—
371D3×C8—61no—
372D3×C8—121no—
373D3×C8#6711yescharacteristic
374D3×C8#6711yescharacteristic
375D3×C8#6711yescharacteristic
376D3×C8#6711yescharacteristic
377C22×C32—42no—
378C22×C32—82no—
379C22×C32C2×#4111yescharacteristic
380C2×C3⋊D3—21no—
381C2×C3×D3—22no—
382C2×C3×D3—21no—
383C2×C3×D3—42no—
384C2×C3×D3—84no—
385C2×C3×D3—84no—
386C2×C3×D3—82no—
387C2×C3×D3#12111yescharacteristic
388C2×C3×D3#12111yescharacteristic
389D32—42no—
390C32×C4C22×D411yescharacteristic
391C32×C4C22×D411yescharacteristic
392C3⋊Dic3—21no—
393C3×Dic3—21no—
394C3×Dic3#12111yescharacteristic
395C3×Dic3#12111yescharacteristic
396C2×#41—91no—
397C22×D4—32no—
398AGL(1,ℤ/8)—32no—
399AGL(1,ℤ/8)—92no—
400AGL(1,ℤ/8)—92no—
401AGL(1,ℤ/8)—92no—
402AGL(1,ℤ/8)—182no—
403AGL(1,ℤ/8)—182no—
404C2×SD16—182no—
405C2×D8—32no—
406C2×D8—31no—
407C2×D8—61no—
408C2×D8—61no—
409C2×D8—61no—
410C2×D8—61no—
411C2×D8—182no—
412C2×D8D3211yescharacteristic, complemented
413#131—31no—
414#131—91no—
415#131—91no—
416#131—91no—
417#131—181no—
418#131—181no—
419C2×M16—91no—
420C2×M16—92no—
421C2×M16—181no—
422C22×C8—31no—
423C22×C8—181no—
424#108—31no—
425#108—92no—
426#108—91no—
427#100—32no—
428#100—92no—
429#100—92no—
430#100—92no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—31no—
434C23×C3—42no—
435C23×C3—62no—
436C23×C3—122no—
437C23×C3—122no—
438C23×C3—244no—
439C22×D3—22no—
440C22×D3—42no—
441C22×D3—42no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—84no—
445C22×D3#23711yescharacteristic
446C3×Q8—31no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—22no—
450C3×D4—22no—
451C3×D4—31no—
452C3×D4—42no—
453C3×D4—42no—
454C3×D4—61no—
455C3×D4—62no—
456C3×D4—62no—
457C3×D4—122no—
458C3×D4—122no—
459C2×C3×C4—21no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—61no—
466C2×C3×C4C23×D311yescharacteristic
467C2×C3×C4C23×D311yescharacteristic
468#67—21no—
469#67—42no—
470#67—42no—
471#67—61no—
472#67—61no—
473#67—61no—
474#67—61no—
475#67—61no—
476#67—61no—
477#67—121no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3#23711yescharacteristic
481D12—22no—
482D12—22no—
483D12—31no—
484D12—31no—
485D12—61no—
486D12—61no—
487D12—61no—
488D12D3×D411yescharacteristic
489C4×D3—21no—
490C4×D3—61no—
491C4×D3—61no—
492C4×D3—61no—
493C4×D3—61no—
494C4×D3—61no—
495C4×D3—61no—
496C4×D3—121no—
497C4×D3D3×D411yescharacteristic
498C4×D3D3×D411yescharacteristic
499C4×D3C2×#6711yescharacteristic
500C4×D3C2×#6711yescharacteristic
501Dic6—31no—
502Dic6—31no—
503Dic6—61no—
504Dic6—61no—
505Dic6—61no—
506Dic6D3×D411yescharacteristic
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—31no—
510C3×C8—31no—
511C3×C8—62no—
512C3×C8—61no—
513C3×C8D3×D411yescharacteristic
514C3×C8D3×D411yescharacteristic
515C3×C8C2×#6711yescharacteristic
516C3×C8C2×#6711yescharacteristic
517C3⋊C8—21no—
518C3⋊C8—22no—
519C3⋊C8—61no—
520C3⋊C8—62no—
521C3⋊C8—62no—
522C3⋊C8—61no—
523C3⋊C8—121no—
524C3⋊C8—122no—
525C3⋊C8C2×#6711yescharacteristic
526C3⋊C8C2×#6711yescharacteristic
527C2×C32—21no—
528C2×C32—82no—
529C2×C32C2×#12111yescharacteristic
530C3⋊D3—41no—
531C3×D3—21no—
532C3×D3—41no—
533C3×D3—82no—
534C3×D3#47212yescomplemented
535C24—62no—
536#41—31no—
537#41—91no—
538#41—91no—
539#41—91no—
540#41—181no—
541#41—181no—
542C2×Q8—91no—
543C2×D4—32no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—91no—
550C2×D4—181no—
551C2×D4C2×D3212yes—
552C22×C4—31no—
553C22×C4—181no—
554SD16—62no—
555SD16—182no—
556SD16—182no—
557SD16—182no—
558D8—21no—
559D8—21no—
560D8—62no—
561D8—62no—
562D8—62no—
563D8—61no—
564D8—61no—
565D8—182no—
566D8—182no—
567D8—182no—
568M16—31no—
569M16—32no—
570M16—61no—
571M16—91no—
572M16—92no—
573M16—181no—
574M16—181no—
575M16—181no—
576M16—182no—
577M16—181no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—31no—
582C2×C8—31no—
583C2×C8—61no—
584C2×C8—181no—
585C2×C8—181no—
586C2×C8—181no—
587C2×C8—182no—
588C2×C8—181no—
589C2×C8C2×D3211yescharacteristic
590C22×C3—21no—
591C22×C3—31no—
592C22×C3—31no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—62no—
596C22×C3—61no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—82no—
600C22×C3—122no—
601C22×C3—162no—
602C22×C3—242no—
603C22×C3—244no—
604C22×C3—244no—
605C22×C3C2×#23711yescharacteristic
606C22×C3D3×#4111yescharacteristic
607C2×D3—22no—
608C2×D3—21no—
609C2×D3—42no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—84no—
613C2×D3—84no—
614C2×D3—82no—
615C2×D3—121no—
616C2×D3—122no—
617C2×D3—122no—
618C2×D3#93811yescharacteristic
619C2×D3#93811yescharacteristic
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—31no—
623C3×C4—31no—
624C3×C4—61no—
625C3×C4C2×D3×D411yescharacteristic
626C3×C4C2×D3×D411yescharacteristic
627C3×C4C2×D3×D411yescharacteristic
628C3×C4C22×#6711yescharacteristic
629Dic3—21no—
630Dic3—61no—
631Dic3—61no—
632Dic3—121no—
633Dic3#93811yescharacteristic
634Dic3#93811yescharacteristic
635C32C2×#47211yescharacteristic, complemented, Sylow
636C23—22no—
637C23—31no—
638C23—62no—
639C23—122no—
640C23—122no—
641C23—181no—
642C23—244no—
643Q8—31no—
644Q8—91no—
645Q8—181no—
646D4—22no—
647D4—22no—
648D4—31no—
649D4—61no—
650D4—62no—
651D4—62no—
652D4—91no—
653D4—122no—
654D4—122no—
655D4—181no—
656D4—181no—
657D4—181no—
658D4—181no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—61no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4C22×D3211yescharacteristic
670C8—31no—
671C8—31no—
672C8—62no—
673C8—61no—
674C8—182no—
675C8—181no—
676C8D3×#6711yescharacteristic
677C8D3×#6711yescharacteristic
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—32no—
682C2×C3—41no—
683C2×C3—61no—
684C2×C3—82no—
685C2×C3—82no—
686C2×C3—121no—
687C2×C3—162no—
688C2×C3—242no—
689C2×C3D3×#12111yescharacteristic
690C2×C3C2×#93811yescharacteristic
691D3—21no—
692D3—41no—
693D3—82no—
694D3—121no—
695D3—121no—
696D3—241no—
697D3#516012yesdirect product factor
698C22—31no—
699C22—31no—
700C22—42no—
701C22—62no—
702C22—61no—
703C22—82no—
704C22—122no—
705C22—181no—
706C22—242no—
707C22—244no—
708C22—244no—
709C22—362no—
710C22D3×#23711yescharacteristic
711C4—31no—
712C4—31no—
713C4—61no—
714C4—181no—
715C4D32×D411yescharacteristic
716C4C2×D3×#6711yescharacteristic
717C3—21no—
718C3D3×#47211yescharacteristic, complemented
719C3C2×#516011yescharacteristic, complemented
720C2—21no—
721C2—32no—
722C2—61no—
723C2—82no—
724C2—121no—
725C2—242no—
726C2—361no—
727C2D3×#93811yescharacteristic
subgroupG/H
centerC2D3×#938
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC2×C32C2×#121
hypercenterC2×D8D32
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. D3×#932C2semidirect
3. D3×#901C2semidirect
4. #10592859C2semidirect
5. C3×#5160C2semidirect
6. #10591505C2semidirect
7. D3×#833C2semidirect
8. #10591406C2semidirect
9. #10590929C2semidirect
10. #10590926C2semidirect
11. D3×#819C2semidirect
16. C2×C32×D8C22semidirect
17. #64141C22semidirect
18. #64110C22semidirect
19. C3×#932C22semidirect
20. C2×C3×#213C22semidirect
25. C2×C3×D24C22semidirect
26. C3×#901C22semidirect
32. #63830C22semidirect
33. #63823C22semidirect
34. #63817C22semidirect
35. #63814C22semidirect
42. #63660C22semidirect
43. #63646C22semidirect
44. C3×#833C22semidirect
45. C3×#819C22semidirect
46. #63577C22semidirect
47. #63558C22semidirect
48. #63558C22semidirect
52. C2×D3×D8D3semidirect
65. #5160D3direct (N × H)
140. C2×C3×D8C2×D3semidirect
141. C2×C3×D8C2×D3semidirect
154. #932C2×D3semidirect
156. C2×#213C2×D3semidirect
173. C2×D24C2×D3semidirect
182. #901C2×D3semidirect
194. #833C2×D3semidirect
202. #819C2×D3semidirect
412. C2×D8D32semidirect
534. C3×D3#472semidirect
635. C32C2×#472semidirect
697. D3#5160direct (N × H)
718. C3D3×#472semidirect
719. C3C2×#5160semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
D3×#9322
D3×#9012
#105928592
C3×#51602
#105915052
D3×#8332
#105914062
#105909292
#105909262
D3×#8192
C2×#51603
D3×#4723