Finite Group Databasebeta

← D3×#5192 #11867969

Subgroups — D3×#5192 #11867969

Order 1152.

946 conjugacy classes of subgroups.

The subgroup lattice has 699 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
2D3×#942C212yesmaximal
3D3×#901C211yesmaximal, characteristic
4#10592891C211yesmaximal, characteristic, complemented
5C3×#5192C211yesmaximal, characteristic, complemented
6#10591641C212yesmaximal, complemented
7D3×#836C212yesmaximal, complemented
8#10591543C212yesmaximal, complemented
9#10590933C211yesmaximal, characteristic, complemented
10#10590930C211yesmaximal, characteristic, complemented
11D3×#819C211yesmaximal, characteristic, complemented
12C2×#5192—31nomaximal
13D3×#473—31nomaximal
14C2×C3×D3×Q8C2212yes—
15D3×#235C2211yescharacteristic
16C2×C32×Q16C2211yescharacteristic, complemented
17#64151C2212yes—
18#64110C2211yescharacteristic
19C2×C3×#216C2212yescomplemented
20C3×#942C2212yes—
21C3×D3×Q16—21no—
22C3×D3×Q16—21no—
23C3×D3×Q16—21no—
24C3×D3×Q16—21no—
25C2×C3×Dic12C2211yescharacteristic, complemented
26C3×#901C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63948—22no—
29#63946—22no—
30D3×#216—22no—
31D3×#215—22no—
32#63833C2212yes—
33#63827C2212yes—
34#63817C2211yescharacteristic
35#63814C2211yescharacteristic
36D3×#208C2211yescharacteristic
37D3×#208C2212yes—
38#63804—21no—
39#63803—21no—
40D3×ΓL(1,𝔽25)—21no—
41D32×C8—21no—
42#63663C2212yescomplemented
43#63646C2211yescharacteristic, complemented
44C3×#836C2212yescomplemented
45C3×#819C2211yescharacteristic, complemented
46#63577C2212yescomplemented
47#63560C2212yescomplemented
48#63560C2212yescomplemented
49C22×C3×Q16—31no—
50C2×#942—32no—
51D3×#137—32no—
52C2×D3×Q16D311yescharacteristic, complemented
53D3×#131—31no—
54C2×#901—31no—
55C3×#473—31no—
56C2×#836—32no—
57#5204—32no—
58#5192—31no—
59#5192—31no—
60#5192—32no—
61#5192—31no—
62#5192—32no—
63#5192—31no—
64#5192—61no—
65#5192D311yescharacteristic, direct product factor
66#5143—31no—
67C2×#819—31no—
68#4896—31no—
69D3×#108—31no—
70#4755—32no—
71D3×#101—32no—
72C2×C32×Q8C2312yes—
73#3828C2311yescharacteristic
74C3×D3×Q8—22no—
75C3×D3×Q8—22no—
76C3×D3×Q8—22no—
77C3×D3×Q8—22no—
78C3×#235C2311yescharacteristic
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—22no—
82C2×C3×Dic6C2312yes—
83D3×#67—21no—
84#3804—21no—
85D3×D12D411yescharacteristic
86C4×D32—21no—
87#3799D411yescharacteristic
88#3798—21no—
89#3795D411yescharacteristic
90D3×Dic6D411yescharacteristic
91C32×Q16—21no—
92C32×Q16—21no—
93C2×C32×C8C2311yescharacteristic
94#3756—22no—
95#3755—22no—
96#3748C2311yescharacteristic
97#3748C2312yes—
98#3743—21no—
99C8×C3⋊D3—21no—
100C3×#216—22no—
101C3×#216—22no—
102C3×#216—22no—
103C3×#215—22no—
104C3×#208C2311yescharacteristic
105C3×#208C2312yes—
106C2×C3×C3⋊C8C2311yescharacteristic
107C3×Dic12—21no—
108C3×Dic12—21no—
109C3×ΓL(1,𝔽25)—21no—
110C3×D3×C8—21no—
111C3×D3×C8D411yescharacteristic
112C3×D3×C8D411yescharacteristic
113C3×D3×C8D411yescharacteristic
114C3×D3×C8D411yescharacteristic
115#3719—22no—
116#3718—22no—
117#3717—22no—
118#3715—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×#473—91noSylow
128C22×C3×Q8—32no—
129D3×#41—31no—
130C2×D3×Q8C2×D312yes—
131C2×#235—31no—
132C3×#137—32no—
133C2×C3×Q16—21no—
134C2×C3×Q16—32no—
135C2×C3×Q16—31no—
136C2×C3×Q16—61no—
137C2×C3×Q16—61no—
138C2×C3×Q16—61no—
139C2×C3×Q16—61no—
140C2×C3×Q16C2×D311yescharacteristic, complemented
141C2×C3×Q16C2×D311yescharacteristic, complemented
142C3×#131—31no—
143C22×C3×C8—31no—
144#951—32no—
145#948—31no—
146C2×#216—62no—
147C2×#216C2×D312yescomplemented
148#942—32no—
149#942—32no—
150#942—32no—
151#942—32no—
152#942—62no—
153#942—62no—
154#942—62no—
155#942C2×D312yes—
156C2×#215—62no—
157C2×#208—31no—
158C2×#208—32no—
159#918—62no—
160D3×Q16—21no—
161D3×Q16—21no—
162D3×Q16—21no—
163D3×Q16—21no—
164D3×Q16—62no—
165#915—62no—
166D3×SD16—62no—
167#909—32no—
168#907—31no—
169#907—61no—
170D3×M16—32no—
171D3×M16—31no—
172D3×M16—61no—
173C2×Dic12C2×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
183C2×ΓL(1,𝔽25)—61no—
184C2×D3×C8—61no—
185C2×D3×C8—61no—
186C2×D3×C8C2×D311yescharacteristic
187C3×#108—31no—
188C3×#101—32no—
189#836—32no—
190#836—32no—
191#836—32no—
192#836—32no—
193#836—62no—
194#836C2×D312yescomplemented
195#824—32no—
196#824—32no—
197#822—32no—
198#819—31no—
199#819—31no—
200#819—32no—
201#819—61no—
202#819C2×D311yescharacteristic, complemented
203C22×C3×D3#4111yescharacteristic
204C2×D32—21no—
205C32×Q8—22no—
206C32×Q8—22no—
207C2×C32×C4—22no—
208C2×C32×C4C2411yescharacteristic
209#638—21no—
210C4⋊(C3⋊D3)C2×D411yescharacteristic
211C4×C3⋊D3—21no—
212#634C2×D411yescharacteristic
213C3×#67—21no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3#4111yescharacteristic
216C3×D12C2×D411yescharacteristic
217C3×C4×D3—21no—
218C3×C4×D3—42no—
219C3×C4×D3—42no—
220C3×C4×D3C2×D411yescharacteristic
221C3×C4×D3C2×D411yescharacteristic
222C3×C4×D3C2×D411yescharacteristic
223C3×C4×D3C2×D411yescharacteristic
224C3×Dic6—22no—
225C3×Dic6—22no—
226C3×Dic6—42no—
227C3×Dic6—42no—
228C3×Dic6C2×D411yescharacteristic
229#627—21no—
230#626—21no—
231#626—21no—
232#625—21no—
233#624—21no—
234D3×Dic3—21no—
235D3×Dic3—21no—
236C32×C8C2×D411yescharacteristic
237C32×C8C2×D411yescharacteristic
238C3⋊(C3⋊C8)—21no—
239C3⋊(C3⋊C8)—22no—
240C3×C3⋊C8—21no—
241C3×C3⋊C8—22no—
242C3×C3⋊C8C2×D411yescharacteristic
243C3×C3⋊C8C2×D411yescharacteristic
244C2×#137—92no—
245C22×Q16—31no—
246C2×#131—91no—
247#473—31no—
248#473—92no—
249#473—91no—
250#473—91no—
251#473—92no—
252#473—91no—
253C2×#108—91no—
254C2×#101—92no—
255C3×#41—31no—
256C2×C3×Q8—22no—
257C2×C3×Q8—32no—
258C2×C3×Q8—62no—
259C2×C3×Q8—62no—
260C2×C3×Q8—62no—
261C2×C3×Q8—62no—
262C2×C3×Q8—62no—
263C2×C3×Q8C22×D312yes—
264C2×C3×Q8C22×D312yes—
265C22×C3×C4—31no—
266C22×C3×C4—62no—
267C2×#67—61no—
268#239—31no—
269D3×Q8—22no—
270D3×Q8—22no—
271D3×Q8—22no—
272D3×Q8—22no—
273D3×Q8—31no—
274#237—31no—
275#237—61no—
276D3×D4—31no—
277D3×D4—61no—
278#235—31no—
279#235—31no—
280#235—31no—
281#235—31no—
282#235—61no—
283#235—61no—
284#235—61no—
285#235—61no—
286#235C22×D311yescharacteristic
287C2×D12—31no—
288C2×C4×D3—22no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×C4×D3C22×D311yescharacteristic
292C2×Dic6—22no—
293C2×Dic6—31no—
294C2×Dic6C22×D312yes—
295C3×Q16—21no—
296C3×Q16—21no—
297C3×Q16—21no—
298C3×Q16—21no—
299C3×Q16—41no—
300C3×Q16—41no—
301C3×Q16—62no—
302C3×Q16—62no—
303C3×Q16—62no—
304C3×Q16—61no—
305C3×Q16—61no—
306C3×SD16—62no—
307C3×M16—32no—
308C3×M16—31no—
309C3×M16—61no—
310C2×C3×C8—21no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8—61no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319#216—22no—
320#216—22no—
321#216—22no—
322#216—62no—
323#216—62no—
324#216—62no—
325#216—62no—
326#216—62no—
327#216—122no—
328#215—22no—
329#215—62no—
330#215—62no—
331#215—62no—
332#215—62no—
333#215—122no—
334#214—62no—
335#208—32no—
336#208—32no—
337#208—31no—
338#208—31no—
339#208—62no—
340#208—61no—
341#208—61no—
342#208—62no—
343#208—61no—
344#208C22×D312yes—
345#208C22×D311yescharacteristic
346C2×C3⋊C8—61no—
347C2×C3⋊C8—62no—
348C2×C3⋊C8—61no—
349C2×C3⋊C8C22×D311yescharacteristic
350Dic12—21no—
351Dic12—21no—
352Dic12—62no—
353#204—62no—
354ΓL(1,𝔽25)—21no—
355ΓL(1,𝔽25)—61no—
356ΓL(1,𝔽25)—61no—
357ΓL(1,𝔽25)—62no—
358ΓL(1,𝔽25)—61no—
359ΓL(1,𝔽25)—61no—
360ΓL(1,𝔽25)—61no—
361ΓL(1,𝔽25)—61no—
362ΓL(1,𝔽25)—121no—
363D3×C8—21no—
364D3×C8—61no—
365D3×C8—61no—
366D3×C8—62no—
367D3×C8—61no—
368D3×C8—61no—
369D3×C8—61no—
370D3×C8—61no—
371D3×C8—121no—
372D3×C8#6711yescharacteristic
373D3×C8#6711yescharacteristic
374D3×C8#6711yescharacteristic
375D3×C8#6711yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C2×C3⋊D3—21no—
378C2×C3×D3—22no—
379C2×C3×D3—21no—
380C2×C3×D3#12111yescharacteristic
381C2×C3×D3#12111yescharacteristic
382D32—42no—
383C32×C4—42no—
384C32×C4C22×D411yescharacteristic
385C32×C4C22×D411yescharacteristic
386C3⋊Dic3—21no—
387C3×Dic3—21no—
388C3×Dic3—42no—
389C3×Dic3#12111yescharacteristic
390C3×Dic3#12111yescharacteristic
391C2×#41—91no—
392C22×Q8—32no—
393#137—32no—
394#137—92no—
395#137—92no—
396#137—92no—
397#137—182no—
398#137—182no—
399C2×Q16—32no—
400C2×Q16—31no—
401C2×Q16—61no—
402C2×Q16—61no—
403C2×Q16—61no—
404C2×Q16—61no—
405C2×Q16—182no—
406C2×Q16D3211yescharacteristic, complemented
407C2×SD16—182no—
408#131—31no—
409#131—91no—
410#131—91no—
411#131—91no—
412#131—181no—
413#131—181no—
414C2×M16—91no—
415C2×M16—92no—
416C2×M16—181no—
417C22×C8—31no—
418C22×C8—181no—
419#108—31no—
420#108—92no—
421#108—91no—
422#101—32no—
423#101—92no—
424#101—92no—
425#101—92no—
426C23×C3—31no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3#23711yescharacteristic
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8—22no—
434C3×Q8—31no—
435C3×Q8—42no—
436C3×Q8—42no—
437C3×Q8—62no—
438C3×Q8—62no—
439C3×Q8—122no—
440C3×Q8—122no—
441C3×D4—31no—
442C3×D4—61no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—31no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—42no—
452C2×C3×C4—61no—
453C2×C3×C4—62no—
454C2×C3×C4—122no—
455C2×C3×C4—122no—
456C2×C3×C4C23×D311yescharacteristic
457C2×C3×C4C23×D311yescharacteristic
458#67—21no—
459#67—61no—
460#67—61no—
461#67—61no—
462#67—61no—
463#67—61no—
464#67—61no—
465#67—121no—
466C2×Dic3—22no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3#23711yescharacteristic
470D12—31no—
471D12—31no—
472D12—61no—
473D12—61no—
474D12—61no—
475D12D3×D411yescharacteristic
476C4×D3—21no—
477C4×D3—42no—
478C4×D3—42no—
479C4×D3—61no—
480C4×D3—61no—
481C4×D3—61no—
482C4×D3—61no—
483C4×D3—61no—
484C4×D3—61no—
485C4×D3—121no—
486C4×D3D3×D411yescharacteristic
487C4×D3D3×D411yescharacteristic
488C4×D3C2×#6711yescharacteristic
489C4×D3C2×#6711yescharacteristic
490Dic6—22no—
491Dic6—22no—
492Dic6—31no—
493Dic6—31no—
494Dic6—42no—
495Dic6—42no—
496Dic6—61no—
497Dic6—61no—
498Dic6—61no—
499Dic6D3×D411yescharacteristic
500C3×C8—21no—
501C3×C8—21no—
502C3×C8—31no—
503C3×C8—31no—
504C3×C8—62no—
505C3×C8—61no—
506C3×C8D3×D411yescharacteristic
507C3×C8D3×D411yescharacteristic
508C3×C8C2×#6711yescharacteristic
509C3×C8C2×#6711yescharacteristic
510C3⋊C8—21no—
511C3⋊C8—22no—
512C3⋊C8—61no—
513C3⋊C8—62no—
514C3⋊C8—62no—
515C3⋊C8—61no—
516C3⋊C8—121no—
517C3⋊C8—122no—
518C3⋊C8C2×#6711yescharacteristic
519C3⋊C8C2×#6711yescharacteristic
520C2×C32—21no—
521C2×C32C2×#12111yescharacteristic
522C3⋊D3—41no—
523C3×D3—21no—
524C3×D3—41no—
525C3×D3#47312yescomplemented
526#41—31no—
527#41—91no—
528#41—91no—
529#41—91no—
530#41—181no—
531#41—181no—
532C2×Q8—32no—
533C2×Q8—62no—
534C2×Q8—62no—
535C2×Q8—62no—
536C2×Q8—62no—
537C2×Q8—62no—
538C2×Q8—91no—
539C2×Q8C2×D3212yes—
540C2×D4—91no—
541C2×D4—181no—
542C22×C4—31no—
543C22×C4—62no—
544C22×C4—181no—
545Q16—21no—
546Q16—21no—
547Q16—62no—
548Q16—62no—
549Q16—62no—
550Q16—61no—
551Q16—61no—
552Q16—182no—
553Q16—182no—
554Q16—182no—
555SD16—62no—
556SD16—182no—
557SD16—182no—
558SD16—182no—
559M16—31no—
560M16—32no—
561M16—61no—
562M16—91no—
563M16—92no—
564M16—181no—
565M16—181no—
566M16—181no—
567M16—182no—
568M16—181no—
569C2×C8—31no—
570C2×C8—31no—
571C2×C8—31no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—61no—
575C2×C8—181no—
576C2×C8—181no—
577C2×C8—181no—
578C2×C8—182no—
579C2×C8—181no—
580C2×C8C2×D3211yescharacteristic
581C22×C3—21no—
582C22×C3—31no—
583C22×C3—31no—
584C22×C3—62no—
585C22×C3—61no—
586C22×C3C2×#23711yescharacteristic
587C22×C3D3×#4111yescharacteristic
588C2×D3—22no—
589C2×D3—21no—
590C2×D3—61no—
591C2×D3—61no—
592C2×D3—121no—
593C2×D3—122no—
594C2×D3—122no—
595C2×D3#93811yescharacteristic
596C2×D3#93811yescharacteristic
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—31no—
600C3×C4—31no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—61no—
604C3×C4—82no—
605C3×C4—122no—
606C3×C4C2×D3×D411yescharacteristic
607C3×C4C2×D3×D411yescharacteristic
608C3×C4C2×D3×D411yescharacteristic
609C3×C4C22×#6711yescharacteristic
610Dic3—21no—
611Dic3—42no—
612Dic3—61no—
613Dic3—61no—
614Dic3—121no—
615Dic3#93811yescharacteristic
616Dic3#93811yescharacteristic
617C32C2×#47311yescharacteristic, complemented, Sylow
618C23—31no—
619C23—181no—
620Q8—22no—
621Q8—22no—
622Q8—31no—
623Q8—62no—
624Q8—62no—
625Q8—91no—
626Q8—122no—
627Q8—122no—
628Q8—181no—
629D4—31no—
630D4—61no—
631D4—91no—
632D4—181no—
633D4—181no—
634D4—181no—
635D4—181no—
636C2×C4—22no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—61no—
643C2×C4—62no—
644C2×C4—122no—
645C2×C4—122no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4C22×D3211yescharacteristic
651C8—31no—
652C8—31no—
653C8—62no—
654C8—61no—
655C8—182no—
656C8—181no—
657C8D3×#6711yescharacteristic
658C8D3×#6711yescharacteristic
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—32no—
663C2×C3—41no—
664C2×C3—61no—
665C2×C3—121no—
666C2×C3D3×#12111yescharacteristic
667C2×C3C2×#93811yescharacteristic
668D3—21no—
669D3—41no—
670D3—121no—
671D3—121no—
672D3—241no—
673D3#519212yesdirect product factor
674C22—31no—
675C22—31no—
676C22—62no—
677C22—61no—
678C22—181no—
679C22—362no—
680C22D3×#23711yescharacteristic
681C4—31no—
682C4—31no—
683C4—42no—
684C4—61no—
685C4—122no—
686C4—181no—
687C4D32×D411yescharacteristic
688C4C2×D3×#6711yescharacteristic
689C3—21no—
690C3D3×#47311yescharacteristic, complemented
691C3C2×#519211yescharacteristic, complemented
692C2—21no—
693C2—32no—
694C2—61no—
695C2—121no—
696C2—361no—
697C2D3×#93811yescharacteristic
subgroupG/H
centerC2D3×#938
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC2×C32C2×#121
prime radicalD3×#235C22
hypercenterC2×Q16D32
hypocenterC32C2×#473
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
4. #10592891C2semidirect
5. C3×#5192C2semidirect
6. #10591641C2semidirect
7. D3×#836C2semidirect
8. #10591543C2semidirect
9. #10590933C2semidirect
10. #10590930C2semidirect
11. D3×#819C2semidirect
16. C2×C32×Q16C22semidirect
19. C2×C3×#216C22semidirect
25. C2×C3×Dic12C22semidirect
42. #63663C22semidirect
43. #63646C22semidirect
44. C3×#836C22semidirect
45. C3×#819C22semidirect
46. #63577C22semidirect
47. #63560C22semidirect
48. #63560C22semidirect
52. C2×D3×Q16D3semidirect
65. #5192D3direct (N × H)
140. C2×C3×Q16C2×D3semidirect
141. C2×C3×Q16C2×D3semidirect
147. C2×#216C2×D3semidirect
173. C2×Dic12C2×D3semidirect
194. #836C2×D3semidirect
202. #819C2×D3semidirect
406. C2×Q16D32semidirect
525. C3×D3#473semidirect
617. C32C2×#473semidirect
673. D3#5192direct (N × H)
690. C3D3×#473semidirect
691. C3C2×#5192semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9422
D3×#9012
#105928912
C3×#51922
#105916412
D3×#8362
#105915432
#105909332
#105909302
D3×#8192
C2×#51923
D3×#4733