Finite Group Databasebeta

← D3×#4897 #11867924

Subgroups — D3×#4897 #11867924

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
1D3×#908C212yesmaximal, complemented
2C2×D3×D24C211yesmaximal, characteristic, complemented
3D3×#901C211yesmaximal, characteristic, complemented
4#10592596C211yesmaximal, characteristic, complemented
5C3×#4897C211yesmaximal, characteristic, complemented
6C3×D3×#108C211yesmaximal, characteristic, complemented
7D3×#823C212yesmaximal, complemented
8#10590987C212yesmaximal, complemented
9#10590984C212yesmaximal, complemented
10#10590929C211yesmaximal, characteristic, complemented
11#10590927C211yesmaximal, characteristic, complemented
12D3×#472—31nomaximal
13C2×#4897—31nomaximal
14D3×#235C2211yescharacteristic
15C2×D3×D12C2212yes—
16#64117C2212yescomplemented
17C2×#3745C2211yescharacteristic, complemented
18#64110C2211yescharacteristic, complemented
19C3×#908C2212yescomplemented
20C3×D3×M16C2212yes—
21C2×C3×D24C2211yescharacteristic, complemented
22C3×#901C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24#63830C2212yescomplemented
25#63825C2212yescomplemented
26C2×#3714C2212yescomplemented
27#63817C2211yescharacteristic, complemented
28#63814C2211yescharacteristic, complemented
29D3×#208C2211yescharacteristic
30#63804—21no—
31#63803—21no—
32#63795—22no—
33#63794—22no—
34D3×D24—22no—
35D3×D24—21no—
36D3×D24—21no—
37D3×D24—21no—
38D3×D24—21no—
39D3×#204—22no—
40D3×ΓL(1,𝔽25)—21no—
41D32×C8—21no—
42C32×#108C2211yescharacteristic, complemented
43#63650C2212yescomplemented
44C3×#823C2212yescomplemented
45C3×#822C2212yescomplemented
46C3×#819C2211yescharacteristic, complemented
47#63559C2212yescomplemented
48#63558C2212yescomplemented
49D3×AGL(1,ℤ/8)—32no—
50C2×D3×D8—31no—
51D3×#131—31no—
52C2×#908—32no—
53C22×D24—31no—
54C2×#901—31no—
55C3×#472—31no—
56C2×C3×#108—31no—
57#5199—32no—
58#5160—31no—
59#5142—31no—
60C2×#823—32no—
61#4897—32no—
62#4897—31no—
63#4897—31no—
64#4897—31no—
65#4897—31no—
66#4897—32no—
67#4897—61no—
68#4897D311yescharacteristic, direct product factor
69D3×#108D311yescharacteristic, complemented
70#4749—32no—
71D3×#100—32no—
72C22×D32—22no—
73#3828C2311yescharacteristic
74C2×C4⋊(C3⋊D3)C2312yes—
75C3×#235C2311yescharacteristic
76C2×C3×D12C2312yes—
77C2×C3×C4×D3C2311yescharacteristic
78D3×#67—21no—
79C2×#626—22no—
80#3804—21no—
81D3×D12—22no—
82D3×D12—22no—
83D3×D12—22no—
84D3×D12—22no—
85D3×D12D411yescharacteristic
86C4×D32—21no—
87#3799D411yescharacteristic
88#3798—21no—
89#3795D411yescharacteristic
90D3×Dic6D411yescharacteristic
91C32×M16C2312yes—
92C2×C32×C8C2311yescharacteristic
93#3748C2311yescharacteristic
94#3745—22no—
95#3745—21no—
96#3745—21no—
97#3744—22no—
98#3743—21no—
99C8×C3⋊D3—21no—
100C3×#208C2311yescharacteristic
101C3×#208C2312yes—
102C2×C3×C3⋊C8C2311yescharacteristic
103C3×D24—22no—
104C3×D24—21no—
105C3×D24—21no—
106C3×#204—22no—
107C3×ΓL(1,𝔽25)—22no—
108C3×ΓL(1,𝔽25)—21no—
109C3×D3×C8—22no—
110C3×D3×C8—21no—
111C3×D3×C8D411yescharacteristic
112C3×D3×C8D411yescharacteristic
113C3×D3×C8D411yescharacteristic
114C3×D3×C8D411yescharacteristic
115#3717—22no—
116#3716—22no—
117#3714—22no—
118#3714—22no—
119#3714—22no—
120#3714—22no—
121#3712—21no—
122#3711—21no—
123#3711—21no—
124#3710—21no—
125D3×C3⋊C8—21no—
126D3×C3⋊C8—21no—
127C2×#472—91noSylow
128D3×#41—31no—
129C2×D3×D4—32no—
130C2×#235—31no—
131C22×D12—32no—
132C3×AGL(1,ℤ/8)—32no—
133C2×C3×D8—31no—
134C3×#131—31no—
135C2×C3×M16—32no—
136C22×C3×C8—31no—
137#949—32no—
138#948—31no—
139#932—32no—
140C2×#213—32no—
141C2×#208—31no—
142#914—62no—
143D3×SD16—62no—
144#911—62no—
145D3×D8—62no—
146D3×D8—61no—
147D3×D8—61no—
148D3×D8—61no—
149D3×D8—61no—
150#908—32no—
151#908—32no—
152#908—32no—
153#908—32no—
154#908—62no—
155#908—62no—
156#908—62no—
157#908C2×D312yescomplemented
158#907—31no—
159#907—61no—
160D3×M16—31no—
161D3×M16—61no—
162D3×M16C2×D312yes—
163C2×D24—32no—
164C2×D24—31no—
165C2×D24—31no—
166C2×D24—61no—
167C2×D24—61no—
168C2×D24—61no—
169C2×D24—61no—
170C2×D24—61no—
171C2×D24—62no—
172C2×D24C2×D311yescharacteristic, complemented
173C2×#204—62no—
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—21no—
188C3×#108—32no—
189C3×#108—31no—
190C3×#108C2×D311yescharacteristic, complemented
191C3×#108C2×D311yescharacteristic, complemented
192C3×#100—32no—
193#833—32no—
194#823—32no—
195#823—32no—
196#823—32no—
197#823—32no—
198#823—32no—
199#823—62no—
200#823C2×D312yescomplemented
201#822C2×D312yescomplemented
202#819C2×D311yescharacteristic, complemented
203C22×C3⋊D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3#4111yescharacteristic
206C2×D32—21no—
207C2×D32—42no—
208C2×D32—42no—
209C2×D32—84no—
210C2×C32×C4C2411yescharacteristic
211#638—21no—
212C4⋊(C3⋊D3)—22no—
213C4⋊(C3⋊D3)—22no—
214C4⋊(C3⋊D3)C2×D411yescharacteristic
215C4×C3⋊D3—21no—
216#634C2×D411yescharacteristic
217C3×#67—21no—
218C2×C3×Dic3#4111yescharacteristic
219C3×D12—22no—
220C3×D12—22no—
221C3×D12C2×D411yescharacteristic
222C3×C4×D3—21no—
223C3×C4×D3C2×D411yescharacteristic
224C3×C4×D3C2×D411yescharacteristic
225C3×C4×D3C2×D411yescharacteristic
226C3×C4×D3C2×D411yescharacteristic
227C3×Dic6C2×D411yescharacteristic
228#627—21no—
229#626—21no—
230#626—21no—
231#626—42no—
232#626—42no—
233#625—21no—
234#624—21no—
235D3×Dic3—21no—
236D3×Dic3—21no—
237C32×C8—22no—
238C32×C8C2×D411yescharacteristic
239C32×C8C2×D411yescharacteristic
240C3⋊(C3⋊C8)—21no—
241C3×C3⋊C8—21no—
242C3×C3⋊C8—22no—
243C3×C3⋊C8C2×D411yescharacteristic
244C3×C3⋊C8C2×D411yescharacteristic
245C2×AGL(1,ℤ/8)—92no—
246C22×D8—91no—
247C2×#131—91no—
248#472—31no—
249#472—92no—
250#472—91no—
251#472—91no—
252#472—92no—
253#472—91no—
254C2×#108—31no—
255C2×#100—92no—
256C23×D3—62no—
257C23×D3—62no—
258C3×#41—31no—
259C2×C3×D4—32no—
260C22×C3×C4—31no—
261C2×#67—61no—
262C2×#67—62no—
263#239—31no—
264D3×Q8—31no—
265#237—31no—
266#237—61no—
267D3×D4—31no—
268D3×D4—61no—
269D3×D4—62no—
270D3×D4—62no—
271D3×D4—62no—
272D3×D4—62no—
273#235—31no—
274#235—31no—
275#235—31no—
276#235—31no—
277#235—61no—
278#235—61no—
279#235—61no—
280#235—61no—
281#235C22×D311yescharacteristic
282C2×D12—31no—
283C2×D12—32no—
284C2×D12—32no—
285C2×D12—62no—
286C2×D12—62no—
287C2×D12—62no—
288C2×D12—62no—
289C2×D12—62no—
290C2×D12—62no—
291C2×D12C22×D312yes—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3C22×D311yescharacteristic
295C2×Dic6—31no—
296C3×SD16—62no—
297C3×D8—62no—
298C3×D8—61no—
299C3×D8—61no—
300C3×M16—22no—
301C3×M16—31no—
302C3×M16—32no—
303C3×M16—62no—
304C3×M16—61no—
305C3×M16C22×D312yes—
306C3×M16C22×D312yes—
307C2×C3×C8—21no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—62no—
314C2×C3×C8—61no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317#215—62no—
318#214—62no—
319#213—62no—
320#213—62no—
321#213—62no—
322#213—62no—
323#208—31no—
324#208—31no—
325#208—61no—
326#208—61no—
327#208—61no—
328#208C22×D312yes—
329#208C22×D311yescharacteristic
330C2×C3⋊C8—61no—
331C2×C3⋊C8—61no—
332C2×C3⋊C8C22×D311yescharacteristic
333D24—22no—
334D24—21no—
335D24—21no—
336D24—62no—
337D24—62no—
338D24—62no—
339D24—62no—
340D24—62no—
341D24—62no—
342D24—61no—
343D24—61no—
344D24—61no—
345D24—61no—
346D24—121no—
347D24—121no—
348D24—122no—
349#204—22no—
350#204—62no—
351#204—62no—
352#204—62no—
353#204—62no—
354#204—122no—
355ΓL(1,𝔽25)—22no—
356ΓL(1,𝔽25)—21no—
357ΓL(1,𝔽25)—61no—
358ΓL(1,𝔽25)—61no—
359ΓL(1,𝔽25)—61no—
360ΓL(1,𝔽25)—61no—
361ΓL(1,𝔽25)—61no—
362ΓL(1,𝔽25)—61no—
363ΓL(1,𝔽25)—121no—
364D3×C8—22no—
365D3×C8—21no—
366D3×C8—61no—
367D3×C8—61no—
368D3×C8—61no—
369D3×C8—61no—
370D3×C8—61no—
371D3×C8—61no—
372D3×C8—121no—
373D3×C8D1211yescharacteristic
374D3×C8D1211yescharacteristic
375D3×C8D1211yescharacteristic
376D3×C8D1211yescharacteristic
377C22×C32C2×#4111yescharacteristic
378C2×C3⋊D3—21no—
379C2×C3⋊D3—42no—
380C2×C3⋊D3—82no—
381C2×C3×D3—22no—
382C2×C3×D3—21no—
383C2×C3×D3—42no—
384C2×C3×D3—82no—
385C2×C3×D3#12111yescharacteristic
386C2×C3×D3#12111yescharacteristic
387D32—42no—
388D32—84no—
389D32—84no—
390C32×C4C22×D411yescharacteristic
391C32×C4C22×D411yescharacteristic
392C3⋊Dic3—21no—
393C3×Dic3—21no—
394C3×Dic3#12111yescharacteristic
395C3×Dic3#12111yescharacteristic
396C2×#41—91no—
397C22×D4—92no—
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—31no—
406C2×D8—92no—
407C2×D8—91no—
408C2×D8—181no—
409C2×D8—181no—
410C2×D8—181no—
411C2×D8—181no—
412C2×D8—182no—
413#131—31no—
414#131—91no—
415#131—91no—
416#131—91no—
417#131—181no—
418#131—181no—
419C2×M16—32no—
420C2×M16—91no—
421C2×M16—181no—
422C22×C8—31no—
423C22×C8—181no—
424#108—32no—
425#108—31no—
426#108D3211yescharacteristic, complemented
427#100—32no—
428#100—92no—
429#100—92no—
430#100—92no—
431C23×C3—31no—
432C23×C3—62no—
433C22×D3—22no—
434C22×D3—61no—
435C22×D3—61no—
436C22×D3—62no—
437C22×D3—62no—
438C22×D3—122no—
439C22×D3—122no—
440C22×D3—122no—
441C22×D3—122no—
442C22×D3—122no—
443C22×D3—244no—
444C22×D3—244no—
445C22×D3#23911yescharacteristic
446C3×Q8—31no—
447C3×D4—31no—
448C3×D4—61no—
449C3×D4—62no—
450C3×D4—62no—
451C2×C3×C4—21no—
452C2×C3×C4—31no—
453C2×C3×C4—31no—
454C2×C3×C4—31no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—61no—
458C2×C3×C4C23×D311yescharacteristic
459C2×C3×C4C23×D311yescharacteristic
460#67—21no—
461#67—61no—
462#67—61no—
463#67—61no—
464#67—61no—
465#67—61no—
466#67—61no—
467#67—121no—
468#67—122no—
469#67—122no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3#23911yescharacteristic
473D12—22no—
474D12—22no—
475D12—31no—
476D12—31no—
477D12—61no—
478D12—61no—
479D12—61no—
480D12—62no—
481D12—62no—
482D12—62no—
483D12—62no—
484D12—122no—
485D12—122no—
486D12—122no—
487D12—122no—
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×D3C2×D1211yescharacteristic
498C4×D3C2×D1211yescharacteristic
499C4×D3D3×D411yescharacteristic
500C4×D3D3×D411yescharacteristic
501Dic6—31no—
502Dic6—31no—
503Dic6—61no—
504Dic6—61no—
505Dic6—61no—
506Dic6D3×D411yescharacteristic
507C3×C8—22no—
508C3×C8—22no—
509C3×C8—21no—
510C3×C8—21no—
511C3×C8—31no—
512C3×C8—31no—
513C3×C8—42no—
514C3×C8—61no—
515C3×C8—62no—
516C3×C8C2×D1211yescharacteristic
517C3×C8C2×D1211yescharacteristic
518C3×C8D3×D411yescharacteristic
519C3×C8D3×D411yescharacteristic
520C3⋊C8—21no—
521C3⋊C8—22no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C3⋊C8C2×D1211yescharacteristic
526C3⋊C8C2×D1211yescharacteristic
527C2×C32—21no—
528C2×C32C2×#12111yescharacteristic
529C3⋊D3—41no—
530C3⋊D3—82no—
531C3×D3—21no—
532C3×D3—41no—
533C3×D3—82no—
534C3×D3#47212yescomplemented
535C24—182no—
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—91no—
545C2×D4—92no—
546C2×D4—182no—
547C2×D4—182no—
548C2×D4—182no—
549C2×D4—182no—
550C2×D4—182no—
551C2×D4—181no—
552C22×C4—31no—
553C22×C4—181no—
554SD16—62no—
555SD16—182no—
556SD16—182no—
557SD16—182no—
558D8—62no—
559D8—61no—
560D8—61no—
561D8—182no—
562D8—182no—
563D8—182no—
564D8—182no—
565D8—182no—
566D8—181no—
567D8—181no—
568M16—31no—
569M16—32no—
570M16—62no—
571M16—61no—
572M16—91no—
573M16—181no—
574M16—181no—
575M16—181no—
576M16—181no—
577M16C2×D3212yes—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—31no—
582C2×C8—31no—
583C2×C8—62no—
584C2×C8—61no—
585C2×C8—181no—
586C2×C8—181no—
587C2×C8—181no—
588C2×C8—181no—
589C2×C8C2×D3211yescharacteristic
590C22×C3—21no—
591C22×C3—31no—
592C22×C3—31no—
593C22×C3—62no—
594C22×C3—61no—
595C22×C3—122no—
596C22×C3—242no—
597C22×C3C2×#23911yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C2×D3—22no—
600C2×D3—21no—
601C2×D3—42no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—82no—
605C2×D3—121no—
606C2×D3—122no—
607C2×D3—122no—
608C2×D3—122no—
609C2×D3—122no—
610C2×D3—242no—
611C2×D3—244no—
612C2×D3—244no—
613C2×D3—244no—
614C2×D3—244no—
615C2×D3—242no—
616C2×D3—242no—
617C2×D3—482no—
618C2×D3#89511yescharacteristic
619C2×D3#89511yescharacteristic
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—31no—
623C3×C4—31no—
624C3×C4—61no—
625C3×C4C22×D1211yescharacteristic
626C3×C4C2×D3×D411yescharacteristic
627C3×C4C2×D3×D411yescharacteristic
628C3×C4C2×D3×D411yescharacteristic
629Dic3—21no—
630Dic3—61no—
631Dic3—61no—
632Dic3—121no—
633Dic3#89511yescharacteristic
634Dic3#89511yescharacteristic
635C32C2×#47211yescharacteristic, complemented, Sylow
636C23—31no—
637C23—62no—
638C23—181no—
639C23—182no—
640C23—362no—
641C23—362no—
642C23—724no—
643Q8—31no—
644Q8—91no—
645Q8—181no—
646D4—31no—
647D4—61no—
648D4—62no—
649D4—62no—
650D4—91no—
651D4—181no—
652D4—181no—
653D4—181no—
654D4—181no—
655D4—182no—
656D4—182no—
657D4—362no—
658D4—362no—
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—22no—
671C8—31no—
672C8—31no—
673C8—61no—
674C8—62no—
675C8—181no—
676C8D3×D1211yescharacteristic
677C8D3×D1211yescharacteristic
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—32no—
682C2×C3—41no—
683C2×C3—61no—
684C2×C3—121no—
685C2×C3—242no—
686C2×C3C2×#89511yescharacteristic
687C2×C3D3×#12111yescharacteristic
688D3—21no—
689D3—41no—
690D3—82no—
691D3—121no—
692D3—121no—
693D3—241no—
694D3—242no—
695D3—242no—
696D3—482no—
697D3#489712yesdirect product factor
698C22—31no—
699C22—31no—
700C22—62no—
701C22—61no—
702C22—122no—
703C22—181no—
704C22—242no—
705C22—362no—
706C22—362no—
707C22—722no—
708C22—724no—
709C22—724no—
710C22D3×#23911yescharacteristic
711C4—31no—
712C4—31no—
713C4—61no—
714C4—181no—
715C4C2×D3×D1211yescharacteristic
716C4D32×D411yescharacteristic
717C3—21no—
718C3C2×#489711yescharacteristic, complemented
719C3D3×#47211yescharacteristic, complemented
720C2—21no—
721C2—32no—
722C2—61no—
723C2—121no—
724C2—242no—
725C2—361no—
726C2—722no—
727C2D3×#89511yescharacteristic
subgroupG/H
centerC2D3×#895
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×#121
hypercenter#108D32
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. D3×#908C2semidirect
2. C2×D3×D24C2semidirect
3. D3×#901C2semidirect
4. #10592596C2semidirect
5. C3×#4897C2semidirect
6. C3×D3×#108C2semidirect
7. D3×#823C2semidirect
8. #10590987C2semidirect
9. #10590984C2semidirect
10. #10590929C2semidirect
11. #10590927C2semidirect
16. #64117C22semidirect
17. C2×#3745C22semidirect
18. #64110C22semidirect
19. C3×#908C22semidirect
21. C2×C3×D24C22semidirect
22. C3×#901C22semidirect
24. #63830C22semidirect
25. #63825C22semidirect
26. C2×#3714C22semidirect
27. #63817C22semidirect
28. #63814C22semidirect
42. C32×#108C22semidirect
43. #63650C22semidirect
44. C3×#823C22semidirect
45. C3×#822C22semidirect
46. C3×#819C22semidirect
47. #63559C22semidirect
48. #63558C22semidirect
68. #4897D3direct (N × H)
69. D3×#108D3semidirect
157. #908C2×D3semidirect
172. C2×D24C2×D3semidirect
182. #901C2×D3semidirect
190. C3×#108C2×D3semidirect
191. C3×#108C2×D3semidirect
200. #823C2×D3semidirect
201. #822C2×D3semidirect
202. #819C2×D3semidirect
426. #108D32semidirect
534. C3×D3#472semidirect
635. C32C2×#472semidirect
697. D3#4897direct (N × H)
718. C3C2×#4897semidirect
719. C3D3×#472semidirect

Maximal subgroups

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

subgroupindex
D3×#9082
C2×D3×D242
D3×#9012
#105925962
C3×#48972
C3×D3×#1082
D3×#8232
#105909872
#105909842
#105909292
#105909272
D3×#4723
C2×#48973