Finite Group Databasebeta

← D12×#239 #11902855

Subgroups — D12×#239 #11902855

Order 1152.

3452 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C212yesmaximal, complemented
2#10596048C211yesmaximal, characteristic, complemented
3C3×Q8×D12C211yesmaximal, characteristic, complemented
4C3×C4×#239C211yesmaximal, characteristic, complemented
5#10595342C212yesmaximal, complemented
6#10594629C216yesmaximal, complemented
7#10594627C216yesmaximal, complemented
8D122C213yesmaximal, complemented
9C4×D3×D12C213yesmaximal, complemented
10#10593970C213yesmaximal, complemented
11#10593896C213yesmaximal, complemented
12D4×#239—31nomaximal
13#41×D12—31nomaximal
14C2×#3832C2212yescomplemented
15C2×C3×#239C2211yescharacteristic
16C2×C3×D3×Q8C2212yescomplemented
17D3×#239—216no—
18C2×D3×D12C2213yes—
19C2×D3×D12C2216yescomplemented
20C2×C4×D32C2216yescomplemented
21C2×#3799C2216yescomplemented
22C2×#3796C2216yescomplemented
23C32×C4×Q8C2211yescharacteristic, complemented
24#64104C2216yescomplemented
25#64083C2213yescomplemented
26C4×C4⋊(C3⋊D3)C2213yescomplemented
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C3×#897C2216yescomplemented
29C3×#893C2213yescomplemented
30C3×#892C2213yescomplemented
31C3×C4×D12C2213yes—
32C3×C4×D12C2213yescomplemented
33C3×C42×D3C2213yescomplemented
34C3×#869C2213yescomplemented
35#63923C22112yescomplemented
36D3×(C2×D3)⋊C4C2216yescomplemented
37#63909C2216yescomplemented
38#63909C2216yescomplemented
39#63909C2216yescomplemented
40C4×#626C2216yescomplemented
41#63894C2216yescomplemented
42#63894C2213yescomplemented
43Dic3×D12C2211yescharacteristic
44#63890C22112yescomplemented
45D3×C4⋊Dic3C2213yescomplemented
46#63880C2216yescomplemented
47#63871C2216yescomplemented
48#63864C2216yescomplemented
49C2×D3×#41—32no—
50C22×#239—32no—
51C3×D4×Q8—31no—
52C3×C4×#41—31no—
53#5817—32no—
54#5726—33no—
55#5725—33no—
56#5630—36no—
57#5627—36no—
58#5577—31no—
59#5577—31no—
60#5577—61no—
61#5576—32no—
62Q8×D12D311yescharacteristic, complemented
63C4×#239D311yescharacteristic, complemented
64#5555—33no—
65#5554—36no—
66D4×D12—33no—
67D4×D12—33no—
68C4×D3×D4—33no—
69#5524—36no—
70#5477—33no—
71C2×C4×D12—33no—
72C22×D32C2316yes—
73C2×C32×Q8C2311yescharacteristic
74#3832—28no—
75C2×C4⋊(C3⋊D3)C2316yes—
76C2×C4⋊(C3⋊D3)C2313yes—
77C2×C4⋊(C3⋊D3)C2316yes—
78C2×C4×C3⋊D3C2316yes—
79C3×#239D418yescomplemented
80C3×D3×Q8—28no—
81C2×C3×D12C2313yes—
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3C2316yes—
84C2×C3×C4×D3C2313yes—
85C2×C3×C4×D3C2313yes—
86C2×C3×C4×D3C2313yes—
87C2×C3×Dic6C2316yes—
88C2×#626C23112yes—
89C2×#626C2316yes—
90C2×#624C2316yes—
91C2×D3×Dic3C2316yes—
92C2×D3×Dic3C2312yes—
93D3×D12—224no—
94D3×D12—212no—
95C4×D32—224no—
96#3799—224no—
97#3796—224no—
98C32×C4⋊C4C2313yes—
99C32×C42C2313yes—
100#3752C2316yes—
101C4⋊(C3⋊Dic3)C2311yescharacteristic
102C3×(C2×D3)⋊C4C2316yes—
103C3×(C2×D3)⋊C4C2316yes—
104C3×C4⋊Dic3C2313yes—
105C3×C4⋊Dic3C2316yes—
106C3×C4⋊Dic3C2313yes—
107C3×C4×Dic3C2313yes—
108C3×C4×Dic3C2313yes—
109C3×C4×Dic3C2311yescharacteristic
110Dic3⋊Dic3C2316yes—
111#3722C2316yes—
112#3722C23112yes—
113(C2×D3)⋊Dic3C2312yes—
114D4×#41—91noSylow
115C2×C3×#41—31no—
116C22×C3×Q8—32no—
117D3×#41—616no—
118C2×#239—32no—
119C2×#239—32no—
120C2×#239—36no—
121C2×#239—36no—
122C2×#239—62no—
123C2×#239—616no—
124C2×#239C2×D311yescharacteristic
125C2×D3×Q8C2×D312yescomplemented
126C2×#237—36no—
127C2×D3×D4—33no—
128C2×D3×D4—36no—
129C2×#235—36no—
130C22×D12—33no—
131C22×D12—36no—
132C22×C4×D3—36no—
133C22×C4×D3—36no—
134C3×C4⋊Q8—33no—
135C3×C22⋊Q8—36no—
136C3×C4×Q8—21no—
137C3×C4×Q8—31no—
138C3×C4×Q8C2×D311yescharacteristic, complemented
139C3×C4×Q8C2×D311yescharacteristic, complemented
140C3×C4×D4—33no—
141C3×C4×D4—33no—
142C3×C4×D4—33no—
143C3×#117—33no—
144C2×C3×C42—33no—
145#947—36no—
146#946—36no—
147Q8×Dic3C2×D311yescharacteristic, complemented
148D4×Dic3—31no—
149#930—36no—
150#930—36no—
151#930—36no—
152C4×#67—36no—
153C2×(C2×D3)⋊C4—36no—
154C2×C4⋊Dic3—33no—
155#897—36no—
156#897C2×D316yescomplemented
157#895—36no—
158#895—36no—
159#895—36no—
160#895—36no—
161#895—36no—
162#895—66no—
163#894—312no—
164#893—33no—
165#893—36no—
166#893C2×D313yescomplemented
167#892C2×D313yescomplemented
168D3×C4⋊C4—33no—
169#886—312no—
170#882—312no—
171#882—312no—
172#67⋊C4—36no—
173D3×C22⋊C4—36no—
174#875—36no—
175#874—33no—
176#874—33no—
177#874—63no—
178C4×D12—31no—
179C4×D12—36no—
180C4×D12—33no—
181C4×D12—33no—
182C4×D12—36no—
183C4×D12—33no—
184C4×D12—36no—
185C4×D12—63no—
186C4×D12C2×D313yes—
187C4×D12C2×D313yescomplemented
188C42×D3C2×D313yescomplemented
189#869C2×D313yescomplemented
190C22×C3⋊D3C2416yes—
191C22×C3×D3C2413yes—
192C22×C3×D3C2412yes—
193C2×D32—212no—
194C2×D32—212no—
195C2×D32—46no—
196C32×Q8C2×D414yescomplemented
197C2×C32×C4C2413yes—
198C2×C32×C4C2413yes—
199C2×C32×C4C2411yescharacteristic
200C2×C3⋊Dic3C2412yes—
201C4⋊(C3⋊D3)—212no—
202C4⋊(C3⋊D3)—26no—
203C4⋊(C3⋊D3)—46no—
204C4×C3⋊D3—212no—
205C2×C3×Dic3C2411yescharacteristic
206C2×C3×Dic3C2413yes—
207C2×C3×Dic3C2416yes—
208C2×C3×Dic3C2411yescharacteristic
209C3×D12C2×D4112yescomplemented
210C3×D12#4114yescomplemented
211C3×C4×D3—212no—
212C3×C4×D3—26no—
213C3×C4×D3—43no—
214C3×C4×D3C2×D4112yescomplemented
215C3×Dic6—212no—
216#626—224no—
217#626—212no—
218#624—212no—
219D3×Dic3—212no—
220D3×Dic3—24no—
221C22×#41—92no—
222#550—91no—
223D4×Q8—31no—
224#548—92no—
225#547—93no—
226#546—96no—
227D42—93no—
228#532—93no—
229#525—96no—
230C4×#41—31no—
231C2×C4×D4—93no—
232C23×D3—36no—
233C23×D3—36no—
234C3×#41—38no—
235C2×C3×Q8—21no—
236C2×C3×Q8—36no—
237C2×C3×Q8—68no—
238C2×C3×Q8C22×D311yescharacteristic
239C2×C3×Q8C22×D311yescharacteristic
240C2×C3×D4—31no—
241C2×C3×D4—33no—
242C22×C3×C4—33no—
243C22×C3×C4—33no—
244C22×C3×C4—36no—
245C22×C3×C4—33no—
246C2×#67—36no—
247C2×#67—312no—
248C22×Dic3—32no—
249C22×Dic3—36no—
250#239—68no—
251#239—68no—
252#239—624no—
253#239—624no—
254#239—128no—
255#239D1218yesdirect product factor
256D3×Q8—28no—
257#237—624no—
258D3×D4—612no—
259D3×D4—624no—
260#235—624no—
261C2×D12—36no—
262C2×D12—312no—
263C2×D12—33no—
264C2×D12—33no—
265C2×D12—36no—
266C2×D12—36no—
267C2×D12—36no—
268C2×D12—36no—
269C2×D12—63no—
270C2×D12—66no—
271C2×D12—66no—
272C2×D12—624no—
273C2×D12—612no—
274C2×D12C22×D313yes—
275C2×D12C22×D311yescharacteristic
276C2×C4×D3—32no—
277C2×C4×D3—36no—
278C2×C4×D3—36no—
279C2×C4×D3—36no—
280C2×C4×D3—36no—
281C2×C4×D3—36no—
282C2×C4×D3—66no—
283C2×C4×D3—624no—
284C2×C4×D3—624no—
285C2×C4×D3C22×D313yes—
286C2×C4×D3C22×D316yes—
287C2×C4×D3C22×D313yes—
288C2×C4×D3C22×D313yes—
289C2×Dic6C22×D316yes—
290C3×C4⋊C4—23no—
291C3×C4⋊C4—33no—
292C3×C4⋊C4—36no—
293C3×C4⋊C4—33no—
294C3×C4⋊C4C22×D313yes—
295C3×C4⋊C4C22×D313yes—
296C3×C22⋊C4—36no—
297C3×C22⋊C4—36no—
298C3×C42—23no—
299C3×C42—31no—
300C3×C42—33no—
301C3×C42—33no—
302C3×C42C22×D313yes—
303C3×C42C22×D313yes—
304#217—32no—
305(C2×D3)⋊C4—32no—
306(C2×D3)⋊C4—36no—
307(C2×D3)⋊C4—36no—
308(C2×D3)⋊C4—36no—
309(C2×D3)⋊C4—312no—
310(C2×D3)⋊C4—36no—
311(C2×D3)⋊C4—312no—
312(C2×D3)⋊C4—66no—
313(C2×D3)⋊C4C22×D316yes—
314(C2×D3)⋊C4C22×D316yes—
315C4⋊Dic3—31no—
316C4⋊Dic3—31no—
317C4⋊Dic3—36no—
318C4⋊Dic3—61no—
319C4⋊Dic3C22×D313yes—
320C4⋊Dic3C22×D316yes—
321C4⋊Dic3C22×D313yes—
322Dic3⋊C4—36no—
323C4×Dic3C22×D311yescharacteristic
324C4×Dic3C22×D313yes—
325C4×Dic3C22×D313yes—
326C22×C32C2511yescharacteristic
327C2×C3⋊D3—26no—
328C2×C3⋊D3—26no—
329C2×C3⋊D3—26no—
330C2×C3×D3—22no—
331C2×C3×D3—23no—
332C2×C3×D3—23no—
333C2×C3×D3—22no—
334C2×C3×D3C22×D416yes—
335C2×C3×D3C2×#4114yescomplemented
336D32—424no—
337C32×C4—23no—
338C32×C4C22×D416yes—
339C32×C4C2×#4112yescomplemented
340C3⋊Dic3—22no—
341C3×Dic3—26no—
342C3×Dic3—23no—
343C3×Dic3—21no—
344C3×Dic3C22×D412yes—
345C2×#41—31no—
346C2×#41—96no—
347C2×#41—96no—
348C2×#41—92no—
349C2×#41—1816no—
350C22×Q8—32no—
351C22×D4—93no—
352C22×D4—96no—
353C23×C4—96no—
354C4⋊Q8—33no—
355#127—93no—
356#124—96no—
357#123—912no—
358C22⋊Q8—36no—
359C22⋊Q8—96no—
360#121—96no—
361#121—96no—
362#121—96no—
363#121—96no—
364#120—912no—
365C4×Q8—31no—
366C4×Q8D3211yescharacteristic, complemented
367C4×D4—33no—
368C4×D4—33no—
369C4×D4—33no—
370C4×D4—96no—
371C4×D4—93no—
372C4×D4—96no—
373C4×D4—96no—
374C4×D4—91no—
375C4×D4—93no—
376#117—33no—
377C2×C4⋊C4—93no—
378C2×C22⋊C4—96no—
379C2×C42—33no—
380C23×C3—32no—
381C23×C3—33no—
382C22×D3—36no—
383C22×D3—36no—
384C22×D3—66no—
385C22×D3—612no—
386C22×D3—612no—
387C22×D3—612no—
388C22×D3—612no—
389C22×D3—126no—
390C22×D3—126no—
391C22×D3C23×D313yes—
392C22×D3C23×D312yes—
393C3×Q8—24no—
394C3×Q8—612no—
395C3×Q8C2×D1214yescomplemented
396C3×Q8D3×D414yescomplemented
397C3×D4—312no—
398C3×D4—34no—
399C2×C3×C4—21no—
400C2×C3×C4—23no—
401C2×C3×C4—23no—
402C2×C3×C4—31no—
403C2×C3×C4—312no—
404C2×C3×C4—36no—
405C2×C3×C4—33no—
406C2×C3×C4—31no—
407C2×C3×C4—612no—
408C2×C3×C4—66no—
409C2×C3×C4—123no—
410C2×C3×C4C23×D313yes—
411C2×C3×C4C23×D313yes—
412C2×C3×C4C23×D313yes—
413C2×C3×C4C23×D313yes—
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416#67—624no—
417#67—612no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—62no—
421C2×Dic3—612no—
422C2×Dic3—64no—
423C2×Dic3C23×D311yescharacteristic
424C2×Dic3C23×D313yes—
425C2×Dic3C23×D316yes—
426C2×Dic3C23×D311yescharacteristic
427D12—624no—
428D12—612no—
429D12—612no—
430D12—612no—
431D12—66no—
432D12—66no—
433D12—126no—
434D12—1212no—
435D12—126no—
436D12—126no—
437D12—246no—
438D12C2×D12112yescomplemented
439D12#23914yesdirect product factor
440C4×D3—212no—
441C4×D3—26no—
442C4×D3—43no—
443C4×D3—612no—
444C4×D3—64no—
445C4×D3—612no—
446C4×D3—612no—
447C4×D3—612no—
448C4×D3—612no—
449C4×D3—1212no—
450C4×D3C2×D12112yescomplemented
451Dic6—212no—
452C2×C32C23×D411yescharacteristic
453C2×C32C22×#4111yescharacteristic
454C2×C32#58511yescharacteristic
455C3⋊D3—46no—
456C3×D3—24no—
457C3×D3—26no—
458C24—96no—
459#41—38no—
460#41—1824no—
461#41—1824no—
462#41—188no—
463C2×Q8—36no—
464C2×Q8—68no—
465C2×Q8C2×D3211yescharacteristic
466C2×D4—31no—
467C2×D4—33no—
468C2×D4—96no—
469C2×D4—912no—
470C2×D4—93no—
471C2×D4—96no—
472C2×D4—96no—
473C2×D4—1824no—
474C2×D4—1812no—
475C22×C4—33no—
476C22×C4—33no—
477C22×C4—36no—
478C22×C4—33no—
479C22×C4—96no—
480C22×C4—96no—
481C22×C4—92no—
482C22×C4—96no—
483C22×C4—1824no—
484C4⋊C4—33no—
485C4⋊C4—33no—
486C4⋊C4—36no—
487C4⋊C4—96no—
488C4⋊C4—91no—
489C4⋊C4C2×D3213yes—
490C22⋊C4—36no—
491C22⋊C4—36no—
492C22⋊C4—96no—
493C22⋊C4—912no—
494C22⋊C4—92no—
495C22⋊C4—96no—
496C42—31no—
497C42—33no—
498C42—33no—
499C42C2×D3213yes—
500C22×C3—21no—
501C22×C3—36no—
502C22×C3—34no—
503C22×C3—62no—
504C22×C3—63no—
505C22×C3—62no—
506C22×C3—63no—
507C22×C3C24×D311yescharacteristic
508C22×C3C24×D311yescharacteristic
509C2×D3—22no—
510C2×D3—23no—
511C2×D3—23no—
512C2×D3—22no—
513C2×D3—66no—
514C2×D3—66no—
515C2×D3—66no—
516C2×D3—66no—
517C2×D3—66no—
518C2×D3—66no—
519C2×D3—126no—
520C2×D3—126no—
521C2×D3—126no—
522C2×D3—1224no—
523C2×D3—1224no—
524C2×D3C22×D1216yes—
525C2×D3C2×#23914yescomplemented
526C3×C4—23no—
527C3×C4—23no—
528C3×C4—26no—
529C3×C4—22no—
530C3×C4—32no—
531C3×C4—43no—
532C3×C4—66no—
533C3×C4—63no—
534C3×C4—61no—
535C3×C4C22×D1216yes—
536C3×C4C2×D3×D416yes—
537C3×C4C2×#23912yescomplemented
538C3×C4D3×#4112yescomplemented
539Dic3—26no—
540Dic3—23no—
541Dic3—21no—
542Dic3—62no—
543Dic3—62no—
544Dic3—122no—
545Dic3C22×D1212yes—
546C32D4×#4111yescharacteristic, complemented, Sylow
547C23—32no—
548C23—33no—
549C23—96no—
550C23—1812no—
551C23—1812no—
552C23—366no—
553Q8—612no—
554Q8D3×D1214yescomplemented
555D4—312no—
556D4—34no—
557D4—1824no—
558D4—1812no—
559D4—1812no—
560D4—186no—
561D4—366no—
562C2×C4—31no—
563C2×C4—312no—
564C2×C4—31no—
565C2×C4—33no—
566C2×C4—36no—
567C2×C4—612no—
568C2×C4—66no—
569C2×C4—92no—
570C2×C4—123no—
571C2×C4—1812no—
572C2×C4—184no—
573C2×C4—1812no—
574C2×C4—1812no—
575C2×C4C22×D3213yes—
576C2×C4C22×D3213yes—
577C2×C4C22×D3211yescharacteristic
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—64no—
582C2×C3—66no—
583C2×C3C23×D1211yescharacteristic
584C2×C3C22×D3×D411yescharacteristic
585C2×C3C22×#23911yescharacteristic
586C2×C3C2×D3×#4111yescharacteristic
587C2×C3#596411yescharacteristic
588C2×C3#596811yescharacteristic
589D3—26no—
590D3—24no—
591D3—126no—
592D3—126no—
593D3—246no—
594C22—36no—
595C22—34no—
596C22—62no—
597C22—63no—
598C22—63no—
599C22—62no—
600C22—186no—
601C22—186no—
602C22—186no—
603C22—3624no—
604C22C23×D3211yescharacteristic
605C4—23no—
606C4—32no—
607C4—66no—
608C4—63no—
609C4—61no—
610C4—182no—
611C4C2×D3×D1216yes—
612C4D3×#23912yescomplemented
613C3—21no—
614C3#41×D1211yescharacteristic, complemented
615C3D4×#23911yescharacteristic, complemented
616C2—64no—
617C2—66no—
618C2—366no—
619C2C22×D3×D1211yescharacteristic
620C2C2×D3×#23911yescharacteristic
621C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. #10596048C2semidirect
3. C3×Q8×D12C2semidirect
4. C3×C4×#239C2semidirect
5. #10595342C2semidirect
6. #10594629C2semidirect
7. #10594627C2semidirect
8. D122C2semidirect
9. C4×D3×D12C2semidirect
10. #10593970C2semidirect
11. #10593896C2semidirect
14. C2×#3832C22semidirect
16. C2×C3×D3×Q8C22semidirect
19. C2×D3×D12C22semidirect
20. C2×C4×D32C22semidirect
21. C2×#3799C22semidirect
22. C2×#3796C22semidirect
23. C32×C4×Q8C22semidirect
24. #64104C22semidirect
25. #64083C22semidirect
26. C4×C4⋊(C3⋊D3)C22semidirect
27. C3×Q8×Dic3C22semidirect
28. C3×#897C22semidirect
29. C3×#893C22semidirect
30. C3×#892C22semidirect
32. C3×C4×D12C22semidirect
33. C3×C42×D3C22semidirect
34. C3×#869C22semidirect
35. #63923C22semidirect
36. D3×(C2×D3)⋊C4C22semidirect
37. #63909C22semidirect
38. #63909C22semidirect
39. #63909C22semidirect
40. C4×#626C22semidirect
41. #63894C22semidirect
42. #63894C22semidirect
44. #63890C22semidirect
45. D3×C4⋊Dic3C22semidirect
46. #63880C22semidirect
47. #63871C22semidirect
48. #63864C22semidirect
62. Q8×D12D3semidirect
63. C4×#239D3semidirect
79. C3×#239D4semidirect
125. C2×D3×Q8C2×D3semidirect
138. C3×C4×Q8C2×D3semidirect
139. C3×C4×Q8C2×D3semidirect
147. Q8×Dic3C2×D3semidirect
156. #897C2×D3semidirect
166. #893C2×D3semidirect
167. #892C2×D3semidirect
187. C4×D12C2×D3semidirect
188. C42×D3C2×D3semidirect
189. #869C2×D3semidirect
196. C32×Q8C2×D4semidirect
209. C3×D12C2×D4semidirect
210. C3×D12#41semidirect
214. C3×C4×D3C2×D4semidirect
255. #239D12direct (N × H)
335. C2×C3×D3C2×#41semidirect
339. C32×C4C2×#41semidirect
366. C4×Q8D32semidirect
395. C3×Q8C2×D12semidirect
396. C3×Q8D3×D4semidirect
438. D12C2×D12semidirect
439. D12#239direct (N × H)
450. C4×D3C2×D12semidirect
525. C2×D3C2×#239semidirect
537. C3×C4C2×#239semidirect
538. C3×C4D3×#41semidirect
546. C32D4×#41semidirect
554. Q8D3×D12semidirect
612. C4D3×#239semidirect
614. C3#41×D12semidirect
615. C3D4×#239semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
#105960482
C3×Q8×D122
C3×C4×#2392
#105953422
#105946292
#105946272
D1222
C4×D3×D122
#105939702
#105938962
D4×#2393
#41×D123