Finite Group Databasebeta

← D3×#5734 #11903322

Subgroups — D3×#5734 #11903322

Order 1152.

2598 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596205C211yesmaximal, characteristic, complemented
2C3×#5734C211yesmaximal, characteristic, complemented
3C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
4D3×#947C214yesmaximal, complemented
5#10595385C214yesmaximal, complemented
6D3×#895C214yesmaximal, complemented
7D3×#892C214yesmaximal, complemented
8#10594564C214yesmaximal, complemented
9#10594463C214yesmaximal, complemented
10C4×D3×D12C212yesmaximal, complemented
11#10593987C212yesmaximal, complemented
12D3×#555—31nomaximal
13C2×#5734—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×D3×D12C2212yes—
16C2×D3×D12C2214yes—
17C2×C4×D32C2214yes—
18C32×C4⋊Q8C2211yescharacteristic, complemented
19#64156C2214yescomplemented
20#64104C2214yescomplemented
21#64101C2214yescomplemented
22C4×C4⋊(C3⋊D3)C2212yescomplemented
23C3×#947C2214yescomplemented
24C3×#944C2212yescomplemented
25C3×#895C2214yescomplemented
26C3×#892C2214yescomplemented
27C3×D3×C4⋊C4C2214yes—
28C3×#888C2214yescomplemented
29C3×C4×D12C2212yescomplemented
30C3×C42×D3C2211yescharacteristic
31C3×#869C2211yescharacteristic, complemented
32D3×(C2×D3)⋊C4C2218yes—
33D3×(C2×D3)⋊C4C2214yes—
34#63916C2214yescomplemented
35#63910C2218yescomplemented
36#63909C2214yescomplemented
37#63907C2218yescomplemented
38#63907C2218yescomplemented
39C4×#626C2214yescomplemented
40#63894C2212yescomplemented
41Dic3×D12C2212yescomplemented
42D3×C4⋊Dic3C2212yes—
43#63886C2218yescomplemented
44#63880C2214yescomplemented
45#63878C2218yescomplemented
46C4×D3×Dic3C2214yes—
47#63864C2214yescomplemented
48#63863C2214yescomplemented
49#63849C2214yescomplemented
50#63841C2214yescomplemented
51#63836C2218yescomplemented
52C3×#555—31no—
53C2×C3×C4⋊Q8—31no—
54C2×#947—34no—
55#5734—31no—
56#5734—31no—
57#5734—34no—
58#5734—34no—
59#5734—34no—
60#5734—32no—
61#5734—61no—
62#5734D311yescharacteristic, direct product factor
63D3×C4⋊Q8D311yescharacteristic, complemented
64D3×#124—34no—
65#5670—34no—
66#5616—34no—
67D3×#121—34no—
68#5563—32no—
69C4×D3×D4—32no—
70#5532—34no—
71D3×#117—34no—
72C2×#895—34no—
73C2×#892—34no—
74C2×C4×D12—32no—
75C22×D32C2314yes—
76C2×C32×Q8C2312yes—
77C2×C4⋊(C3⋊D3)C2312yes—
78C2×C4⋊(C3⋊D3)C2314yes—
79C2×C4×C3⋊D3C2314yes—
80C3×D3×Q8—44no—
81C2×C3×D12C2312yes—
82C2×C3×D12C2314yes—
83C2×C3×C4×D3C2314yes—
84C2×C3×C4×D3C2314yes—
85C2×C3×C4×D3C2311yescharacteristic
86C2×C3×C4×D3C2312yes—
87C2×C3×Dic6C2314yes—
88C2×C3×Dic6C2312yes—
89C2×#626C2314yes—
90C2×#626C2318yes—
91C2×#624C2314yes—
92C2×D3×Dic3C2314yes—
93C2×D3×Dic3C2314yes—
94D3×D12—28no—
95D3×D12—48no—
96C4×D32—216no—
97C32×C4⋊C4C2314yes—
98C32×C42C2311yescharacteristic
99#3752C2314yes—
100#3752C2318yes—
101C4⋊(C3⋊Dic3)C2312yes—
102C4×C3⋊Dic3C2314yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×(C2×D3)⋊C4C2314yes—
105C3×C4⋊Dic3C2314yes—
106C3×C4⋊Dic3C2312yes—
107C3×Dic3⋊C4C2318yes—
108C3×C4×Dic3C2312yes—
109C3×C4×Dic3C2314yes—
110C3×C4×Dic3C2311yescharacteristic
111Dic3⋊Dic3C2314yes—
112#3722C2318yes—
113#3722C2314yes—
114(C2×D3)⋊Dic3C2318yes—
115(C2×D3)⋊Dic3C2314yes—
116Dic32C2318yes—
117C2×#555—91noSylow
118C22×C3×Q8—32no—
119C2×D3×Q8C2×D312yes—
120C2×D3×D4—32no—
121C2×D3×D4—34no—
122C22×D12—32no—
123C22×D12—34no—
124C22×C4×D3—34no—
125C22×C4×D3—34no—
126C3×C4⋊Q8—21no—
127C3×C4⋊Q8—32no—
128C3×C4⋊Q8—34no—
129C3×C4⋊Q8—31no—
130C3×C4⋊Q8C2×D311yescharacteristic, complemented
131C3×C4⋊Q8C2×D311yescharacteristic, complemented
132C3×#124—34no—
133C3×#121—34no—
134C3×C4×D4—32no—
135C3×#117—34no—
136C2×C3×C4⋊C4—34no—
137C2×C3×C42—31no—
138#947—34no—
139#947—34no—
140#947—34no—
141#947—38no—
142#947—38no—
143#947—34no—
144#947—64no—
145#947C2×D314yescomplemented
146#944C2×D312yescomplemented
147#939—38no—
148#938—34no—
149#936—34no—
150D4×Dic3—32no—
151#930—34no—
152C4×#67—34no—
153C2×(C2×D3)⋊C4—34no—
154C2×(C2×D3)⋊C4—38no—
155#926—34no—
156C2×C4⋊Dic3—32no—
157C2×C4×Dic3—34no—
158#895—38no—
159#895—34no—
160#895—34no—
161#895—34no—
162#895—34no—
163#895—38no—
164#895—64no—
165#895C2×D314yescomplemented
166#893—32no—
167#892—34no—
168#892—34no—
169#892—34no—
170#892—38no—
171#892—34no—
172#892—34no—
173#892—38no—
174#892—64no—
175#892C2×D314yescomplemented
176D3×C4⋊C4—32no—
177D3×C4⋊C4C2×D314yes—
178#888C2×D314yescomplemented
179#885—38no—
180#885—38no—
181#884—38no—
182#67⋊C4—34no—
183D3×C22⋊C4—34no—
184D3×C22⋊C4—38no—
185#877—38no—
186#875—34no—
187C4×D12—32no—
188C4×D12—34no—
189C4×D12—32no—
190C4×D12—32no—
191C4×D12—34no—
192C4×D12—32no—
193C4×D12—62no—
194C4×D12C2×D312yescomplemented
195#872—38no—
196C42×D3—34no—
197C42×D3C2×D311yescharacteristic
198#869C2×D311yescharacteristic, complemented
199C22×C3⋊D3C2414yes—
200C22×C3×D3C2414yes—
201C22×C3×D3C2411yescharacteristic
202C2×D32—28no—
203C2×D32—28no—
204C2×D32—28no—
205C32×Q8—42no—
206C2×C32×C4C2414yes—
207C2×C32×C4C2411yescharacteristic
208C2×C32×C4C2412yes—
209C2×C3⋊Dic3C2414yes—
210C4⋊(C3⋊D3)—24no—
211C4⋊(C3⋊D3)—44no—
212C4×C3⋊D3—28no—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2411yescharacteristic
216C2×C3×Dic3C2412yes—
217C3×D12—24no—
218C3×D12—44no—
219C3×C4×D3—28no—
220C3×C4×D3—22no—
221C3×C4×D3—28no—
222C3×C4×D3#4118yes—
223C3×Dic6—42no—
224C3×Dic6—44no—
225#626—28no—
226#626—48no—
227#624—28no—
228D3×Dic3—28no—
229D3×Dic3—28no—
230#555—31no—
231#555—94no—
232#555—92no—
233#555—94no—
234#555—94no—
235#555—91no—
236C2×C4⋊Q8—31no—
237C2×#124—94no—
238C2×#121—94no—
239C2×C4×D4—92no—
240C2×#117—94no—
241C23×D3—34no—
242C23×D3—34no—
243C2×C3×Q8—22no—
244C2×C3×Q8—32no—
245C2×C3×Q8—34no—
246C2×C3×Q8—124no—
247C2×C3×Q8C22×D312yes—
248C2×C3×Q8C22×D312yes—
249C2×C3×D4—32no—
250C2×C3×D4—34no—
251C22×C3×C4—32no—
252C22×C3×C4—34no—
253C22×C3×C4—34no—
254C22×C3×C4—31no—
255C2×#67—34no—
256C2×#67—38no—
257C22×Dic3—34no—
258C22×Dic3—34no—
259D3×Q8—44no—
260D3×D4—68no—
261D3×D4—128no—
262C2×D12—34no—
263C2×D12—32no—
264C2×D12—32no—
265C2×D12—38no—
266C2×D12—34no—
267C2×D12—34no—
268C2×D12—62no—
269C2×D12—64no—
270C2×D12—68no—
271C2×D12—128no—
272C2×D12C22×D312yes—
273C2×D12C22×D314yes—
274C2×C4×D3—34no—
275C2×C4×D3—34no—
276C2×C4×D3—34no—
277C2×C4×D3—34no—
278C2×C4×D3—34no—
279C2×C4×D3—34no—
280C2×C4×D3—64no—
281C2×C4×D3—616no—
282C2×C4×D3—616no—
283C2×C4×D3C22×D314yes—
284C2×C4×D3C22×D311yescharacteristic
285C2×C4×D3C22×D314yes—
286C2×C4×D3C22×D312yes—
287C2×Dic6C22×D312yes—
288C2×Dic6C22×D314yes—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—32no—
291C3×C4⋊C4—38no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4C22×D314yes—
294C3×C4⋊C4C22×D314yes—
295C3×C22⋊C4—38no—
296C3×C22⋊C4—34no—
297C3×C42—21no—
298C3×C42—34no—
299C3×C42—31no—
300C3×C42—32no—
301C3×C42C22×D311yescharacteristic
302C3×C42C22×D311yescharacteristic
303#217—38no—
304#217—34no—
305(C2×D3)⋊C4—34no—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—34no—
309(C2×D3)⋊C4—34no—
310(C2×D3)⋊C4—38no—
311(C2×D3)⋊C4—38no—
312(C2×D3)⋊C4—34no—
313(C2×D3)⋊C4—34no—
314(C2×D3)⋊C4—38no—
315(C2×D3)⋊C4—64no—
316(C2×D3)⋊C4—68no—
317(C2×D3)⋊C4C22×D314yes—
318(C2×D3)⋊C4C22×D318yes—
319C4⋊Dic3—32no—
320C4⋊Dic3—32no—
321C4⋊Dic3—34no—
322C4⋊Dic3—62no—
323C4⋊Dic3C22×D314yes—
324C4⋊Dic3C22×D312yes—
325Dic3⋊C4—34no—
326Dic3⋊C4C22×D318yes—
327C4×Dic3—34no—
328C4×Dic3—34no—
329C4×Dic3—38no—
330C4×Dic3—38no—
331C4×Dic3—64no—
332C4×Dic3C22×D311yescharacteristic
333C4×Dic3C22×D312yes—
334C4×Dic3C22×D314yes—
335C22×C32C2511yescharacteristic
336C2×C3⋊D3—24no—
337C2×C3⋊D3—24no—
338C2×C3⋊D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—24no—
342C2×C3×D3C2×#4114yes—
343C2×C3×D3H(5,𝔽2)12yes—
344D32—416no—
345C32×C4—21no—
346C32×C4—24no—
347C32×C4C2×#4114yes—
348C3⋊Dic3—24no—
349C3×Dic3—24no—
350C3×Dic3—24no—
351C3×Dic3—21no—
352C3×Dic3C2×#4114yes—
353C22×Q8—32no—
354C22×D4—92no—
355C22×D4—94no—
356C23×C4—94no—
357C4⋊Q8—32no—
358C4⋊Q8—34no—
359C4⋊Q8—31no—
360C4⋊Q8D3211yescharacteristic, complemented
361#124—34no—
362#124—94no—
363#124—98no—
364#124—98no—
365#124—94no—
366#124—94no—
367#121—34no—
368#121—98no—
369#121—94no—
370#121—94no—
371#121—98no—
372#121—94no—
373C4×D4—32no—
374C4×D4—94no—
375C4×D4—92no—
376C4×D4—94no—
377C4×D4—92no—
378C4×D4—92no—
379#117—34no—
380#117—98no—
381#117—98no—
382#117—94no—
383#117—94no—
384#117—94no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—92no—
387C2×C22⋊C4—98no—
388C2×C22⋊C4—94no—
389C2×C42—31no—
390C2×C42—94no—
391C23×C3—31no—
392C23×C3—34no—
393C22×D3—34no—
394C22×D3—34no—
395C22×D3—64no—
396C22×D3—68no—
397C22×D3—68no—
398C22×D3—68no—
399C22×D3—68no—
400C22×D3—68no—
401C22×D3—68no—
402C22×D3C23×D314yes—
403C22×D3C23×D311yescharacteristic
404C3×Q8—42no—
405C3×Q8—42no—
406C3×Q8—82no—
407C3×Q8—124no—
408C3×Q8—122no—
409C3×D4—64no—
410C3×D4—124no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—21no—
414C2×C3×C4—32no—
415C2×C3×C4—38no—
416C2×C3×C4—34no—
417C2×C3×C4—34no—
418C2×C3×C4—31no—
419C2×C3×C4—68no—
420C2×C3×C4—62no—
421C2×C3×C4—68no—
422C2×C3×C4C23×D314yes—
423C2×C3×C4C23×D314yes—
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D312yes—
427C2×C3×C4C23×D312yes—
428#67—68no—
429#67—128no—
430C2×Dic3—34no—
431C2×Dic3—34no—
432C2×Dic3—64no—
433C2×Dic3—68no—
434C2×Dic3—68no—
435C2×Dic3C23×D314yes—
436C2×Dic3C23×D314yes—
437C2×Dic3C23×D311yescharacteristic
438C2×Dic3C23×D312yes—
439D12—24no—
440D12—44no—
441D12—68no—
442D12—64no—
443D12—64no—
444D12—124no—
445D12—124no—
446D12—124no—
447D12—128no—
448D12—244no—
449C4×D3—28no—
450C4×D3—22no—
451C4×D3—28no—
452C4×D3—68no—
453C4×D3—68no—
454C4×D3—68no—
455C4×D3—68no—
456C4×D3—68no—
457C4×D3—68no—
458C4×D3—128no—
459C4×D3#23918yes—
460Dic6—44no—
461Dic6—42no—
462C2×C32C22×#4112yes—
463C2×C32C2×H(5,𝔽2)11yescharacteristic
464C3⋊D3—44no—
465C3×D3—44no—
466C3×D3#55514yescomplemented
467C24—94no—
468C2×Q8—34no—
469C2×Q8—32no—
470C2×Q8—124no—
471C2×Q8C2×D3212yes—
472C2×D4—32no—
473C2×D4—34no—
474C2×D4—94no—
475C2×D4—98no—
476C2×D4—92no—
477C2×D4—94no—
478C2×D4—188no—
479C2×D4—368no—
480C22×C4—32no—
481C22×C4—31no—
482C22×C4—34no—
483C22×C4—34no—
484C22×C4—94no—
485C22×C4—94no—
486C22×C4—94no—
487C22×C4—94no—
488C22×C4—1816no—
489C4⋊C4—38no—
490C4⋊C4—34no—
491C4⋊C4—32no—
492C4⋊C4—94no—
493C4⋊C4—92no—
494C4⋊C4C2×D3214yes—
495C22⋊C4—38no—
496C22⋊C4—34no—
497C22⋊C4—98no—
498C22⋊C4—94no—
499C22⋊C4—98no—
500C22⋊C4—94no—
501C22⋊C4—98no—
502C22⋊C4—94no—
503C42—31no—
504C42—32no—
505C42—34no—
506C42—98no—
507C42—94no—
508C42C2×D3211yescharacteristic
509C22×C3—21no—
510C22×C3—34no—
511C22×C3—32no—
512C22×C3—64no—
513C22×C3—64no—
514C22×C3—64no—
515C22×C3C24×D311yescharacteristic
516C22×C3C24×D311yescharacteristic
517C2×D3—24no—
518C2×D3—24no—
519C2×D3—24no—
520C2×D3—64no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—124no—
527C2×D3—124no—
528C2×D3—124no—
529C2×D3—1216no—
530C2×D3—1216no—
531C2×D3#100412yes—
532C2×D3C2×#23914yes—
533C3×C4—21no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—21no—
537C3×C4—24no—
538C3×C4—34no—
539C3×C4—44no—
540C3×C4—41no—
541C3×C4—64no—
542C3×C4—64no—
543C3×C4—61no—
544C3×C4C2×#23914yes—
545C3×C4D3×#4114yes—
546Dic3—21no—
547Dic3—24no—
548Dic3—24no—
549Dic3—64no—
550Dic3—64no—
551Dic3—124no—
552Dic3C2×#23914yes—
553C32C2×#55511yescharacteristic, complemented, Sylow
554C23—31no—
555C23—34no—
556C23—94no—
557C23—188no—
558C23—188no—
559C23—188no—
560Q8—42no—
561Q8—124no—
562Q8—122no—
563D4—64no—
564D4—124no—
565D4—188no—
566D4—184no—
567D4—364no—
568D4—368no—
569C2×C4—32no—
570C2×C4—38no—
571C2×C4—34no—
572C2×C4—31no—
573C2×C4—34no—
574C2×C4—68no—
575C2×C4—62no—
576C2×C4—68no—
577C2×C4—94no—
578C2×C4—188no—
579C2×C4—188no—
580C2×C4—188no—
581C2×C4—188no—
582C2×C4C22×D3214yes—
583C2×C4C22×D3211yescharacteristic
584C2×C4C22×D3212yes—
585C2×C3—21no—
586C2×C3—22no—
587C2×C3—34no—
588C2×C3—124no—
589C2×C3C2×#100411yescharacteristic
590C2×C3C22×#23912yes—
591C2×C3C2×D3×#4112yes—
592C2×C3D3×H(5,𝔽2)11yescharacteristic
593D3—44no—
594D3—124no—
595D3—124no—
596D3—244no—
597D3#573414yesdirect product factor
598C22—32no—
599C22—34no—
600C22—64no—
601C22—64no—
602C22—64no—
603C22—184no—
604C22—184no—
605C22—184no—
606C22—3616no—
607C22C23×D3211yescharacteristic
608C4—24no—
609C4—21no—
610C4—34no—
611C4—64no—
612C4—61no—
613C4—64no—
614C4—184no—
615C4D3×#23914yes—
616C3—21no—
617C3C2×#573411yescharacteristic, complemented
618C3D3×#55511yescharacteristic, complemented
619C2—34no—
620C2—124no—
621C2—364no—
622C2D3×#100411yescharacteristic
623C2C2×D3×#23912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#555
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596205C2semidirect
2. C3×#5734C2semidirect
3. C3×D3×C4⋊Q8C2semidirect
4. D3×#947C2semidirect
5. #10595385C2semidirect
6. D3×#895C2semidirect
7. D3×#892C2semidirect
8. #10594564C2semidirect
9. #10594463C2semidirect
10. C4×D3×D12C2semidirect
11. #10593987C2semidirect
18. C32×C4⋊Q8C22semidirect
19. #64156C22semidirect
20. #64104C22semidirect
21. #64101C22semidirect
22. C4×C4⋊(C3⋊D3)C22semidirect
23. C3×#947C22semidirect
24. C3×#944C22semidirect
25. C3×#895C22semidirect
26. C3×#892C22semidirect
28. C3×#888C22semidirect
29. C3×C4×D12C22semidirect
31. C3×#869C22semidirect
34. #63916C22semidirect
35. #63910C22semidirect
36. #63909C22semidirect
37. #63907C22semidirect
38. #63907C22semidirect
39. C4×#626C22semidirect
40. #63894C22semidirect
41. Dic3×D12C22semidirect
43. #63886C22semidirect
44. #63880C22semidirect
45. #63878C22semidirect
47. #63864C22semidirect
48. #63863C22semidirect
49. #63849C22semidirect
50. #63841C22semidirect
51. #63836C22semidirect
62. #5734D3direct (N × H)
63. D3×C4⋊Q8D3semidirect
130. C3×C4⋊Q8C2×D3semidirect
131. C3×C4⋊Q8C2×D3semidirect
145. #947C2×D3semidirect
146. #944C2×D3semidirect
165. #895C2×D3semidirect
175. #892C2×D3semidirect
178. #888C2×D3semidirect
194. C4×D12C2×D3semidirect
198. #869C2×D3semidirect
360. C4⋊Q8D32semidirect
466. C3×D3#555semidirect
553. C32C2×#555semidirect
597. D3#5734direct (N × H)
617. C3C2×#5734semidirect
618. C3D3×#555semidirect

Maximal subgroups

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

subgroupindex
#105962052
C3×#57342
C3×D3×C4⋊Q82
D3×#9472
#105953852
D3×#8952
D3×#8922
#105945642
#105944632
C4×D3×D122
#105939872
D3×#5553
C2×#57343