Finite Group Databasebeta

← D3×#5159 #11866962

Subgroups — D3×#5159 #11866962

Order 1152.

1257 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2D3×#938C212yesmaximal, complemented
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#10592858C211yesmaximal, characteristic, complemented
5C3×#5159C211yesmaximal, characteristic, complemented
6#10591454C212yesmaximal, complemented
7#10591451C212yesmaximal, complemented
8D3×#832C212yesmaximal, complemented
9#10590846C211yesmaximal, characteristic, complemented
10#10590836C211yesmaximal, characteristic, complemented
11D3×#817C211yesmaximal, characteristic, complemented
12C2×#5159—31nomaximal
13D3×#469—31nomaximal
14C2×C3×D3×D4C2212yes—
15C2×D3×#67—22no—
16C2×C4×D32C2211yescharacteristic
17C2×C32×D8C2211yescharacteristic, complemented
18#64147C2212yescomplemented
19C2×#3743C2211yescharacteristic, complemented
20C3×#938C2212yescomplemented
21C2×C3×#213C2212yescomplemented
22C3×D3×D8—24no—
23C2×C3×D24C2211yescharacteristic, complemented
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic
26#63970—22no—
27D3×#217—22no—
28#63958—22no—
29#63916C2212yescomplemented
30#63908C2212yescomplemented
31D3×C4⋊Dic3C2212yes—
32C2×#3712C2211yescharacteristic, complemented
33C2×#3711C2211yescharacteristic, complemented
34C2×D3×C3⋊C8C2211yescharacteristic
35D3×ΓL(1,𝔽25)—24no—
36#63659C2212yescomplemented
37#63644C2211yescharacteristic, complemented
38C3×#832C2212yescomplemented
39C3×#817C2211yescharacteristic, complemented
40#63573C2212yescomplemented
41#63563C2212yescomplemented
42#63562C2212yescomplemented
43C22×C3×D8—31no—
44C2×#938—32no—
45C2×D3×D8D311yescharacteristic, complemented
46C2×D3×M16—31no—
47C22×ΓL(1,𝔽25)—31no—
48D3×#121—32no—
49C3×#469—31no—
50C2×#832—32no—
51#5159—31no—
52#5159—31no—
53#5159—32no—
54#5159—31no—
55#5159—32no—
56#5159—31no—
57#5159—61no—
58#5159D311yescharacteristic, direct product factor
59#5135—31no—
60C2×#817—31no—
61#5039—32no—
62#4865—31no—
63D3×#106—31no—
64#4782—32no—
65D3×#102—32no—
66C23×C3×D3—22no—
67C22×D32D411yescharacteristic
68C2×C32×D4C2312yes—
69C2×#638—22no—
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C3×D3×D4—24no—
74C3×D3×D4—24no—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78D3×#67—48no—
79C2×#626—22no—
80C2×#625—22no—
81C2×#624D411yescharacteristic
82C2×D3×Dic3—22no—
83C2×D3×Dic3D411yescharacteristic
84C2×D3×Dic3D411yescharacteristic
85C4×D32—22no—
86C4×D32—22no—
87C32×D8—22no—
88C2×C32×C8C2311yescharacteristic
89#3757—22no—
90C4⋊(C3⋊Dic3)C2312yes—
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92#3743—22no—
93C3×#217—22no—
94C3×#213—24no—
95C3×C4⋊Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×D24—22no—
99C3×ΓL(1,𝔽25)—22no—
100C3×D3×C8D414yescomplemented
101Dic3⋊Dic3—22no—
102(C2×D3)⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104#3712—22no—
105#3711—22no—
106D3×C3⋊C8—22no—
107C2×#469—91noSylow
108C22×C3×D4—32no—
109C22×#67—62no—
110C2×D3×D4—62no—
111C2×D3×D4C2×D312yes—
112C22×C4×D3—31no—
113C22×C4×D3—31no—
114C2×C3×D8—21no—
115C2×C3×D8—32no—
116C2×C3×D8—31no—
117C2×C3×D8—64no—
118C2×C3×D8C2×D311yescharacteristic, complemented
119C2×C3×D8C2×D311yescharacteristic, complemented
120C2×C3×M16—31no—
121C22×C3×C8—31no—
122C3×#121—32no—
123C2×#217—62no—
124#939—62no—
125#938—32no—
126#938—32no—
127#938—32no—
128#938—32no—
129#938—62no—
130#938—62no—
131#938—62no—
132#938C2×D312yescomplemented
133C2×#213C2×D312yescomplemented
134#930—32no—
135C2×C4⋊Dic3—32no—
136C2×#208—31no—
137C22×C3⋊C8—31no—
138D3×D8—24no—
139D3×M16—64no—
140C2×D24C2×D311yescharacteristic, complemented
141C2×ΓL(1,𝔽25)—31no—
142C2×ΓL(1,𝔽25)—31no—
143C2×ΓL(1,𝔽25)—31no—
144C2×ΓL(1,𝔽25)—31no—
145C2×ΓL(1,𝔽25)—31no—
146C2×ΓL(1,𝔽25)—61no—
147C2×ΓL(1,𝔽25)—64no—
148C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
149C2×D3×C8—31no—
150C2×D3×C8C2×D311yescharacteristic
151#895—32no—
152D3×C4⋊C4—32no—
153#884—62no—
154D3×C22⋊C4—62no—
155C3×#106—31no—
156C3×#102—32no—
157#832—32no—
158#832—32no—
159#832—32no—
160#832—32no—
161#832—62no—
162#832C2×D312yescomplemented
163#821—32no—
164#817—31no—
165#817—31no—
166#817—32no—
167#817—61no—
168#817C2×D311yescharacteristic, complemented
169#809—32no—
170#808—32no—
171C23×C32—22no—
172C22×C3⋊D3C2×D411yescharacteristic
173C22×C3×D3—22no—
174C22×C3×D3—44no—
175C22×C3×D3—44no—
176C22×C3×D3—44no—
177C22×C3×D3C2×D411yescharacteristic
178C22×C3×D3C2×D411yescharacteristic
179C2×D32—22no—
180C2×D32—24no—
181C32×D4—22no—
182C32×D4—22no—
183C2×C32×C4C2411yescharacteristic
184#638—44no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4×C3⋊D3—21no—
188C4×C3⋊D3—21no—
189C3×#67—44no—
190C3×#67—44no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×D12—22no—
195C3×D12—22no—
196C3×C4×D3—21no—
197C3×C4×D3—21no—
198C3×C4×D3C2×D412yes—
199C3×C4×D3#4112yes—
200#626—44no—
201#625—44no—
202#624—22no—
203D3×Dic3—22no—
204D3×Dic3—22no—
205D3×Dic3—44no—
206C32×C8C2×D412yescomplemented
207C3⋊(C3⋊C8)—21no—
208C3×C3⋊C8—21no—
209C3×C3⋊C8C2×D412yescomplemented
210C22×D8—31no—
211C22×M16—91no—
212C2×#121—92no—
213#469—31no—
214#469—92no—
215#469—91no—
216#469—92no—
217#469—91no—
218#469—91no—
219C2×#106—91no—
220C2×#102—92no—
221C24×C3—62no—
222C23×D3—22no—
223C23×D3—31no—
224C23×D3—31no—
225C2×C3×D4—22no—
226C2×C3×D4—32no—
227C2×C3×D4—64no—
228C2×C3×D4—64no—
229C2×C3×D4—62no—
230C2×C3×D4—62no—
231C2×C3×D4C22×D312yes—
232C2×C3×D4C22×D312yes—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C2×#67—22no—
236C2×#67—22no—
237C2×#67—62no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—122no—
243C2×#67—128no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—62no—
247D3×D4—24no—
248D3×D4—24no—
249D3×D4—128no—
250C2×D12—62no—
251C2×D12C22×D312yes—
252C2×C4×D3—31no—
253C2×C4×D3—31no—
254C2×C4×D3—31no—
255C2×C4×D3—31no—
256C2×C4×D3—31no—
257C2×C4×D3—31no—
258C2×C4×D3—61no—
259C2×C4×D3—62no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3C22×D311yescharacteristic
265C2×C4×D3C22×D311yescharacteristic
266C3×D8—22no—
267C3×D8—22no—
268C3×D8—42no—
269C3×D8—64no—
270C3×D8—62no—
271C3×M16—62no—
272C2×C3×C8—21no—
273C2×C3×C8—31no—
274C2×C3×C8—34no—
275C2×C3×C8—31no—
276C2×C3×C8C22×D311yescharacteristic
277C2×C3×C8C22×D311yescharacteristic
278C3×C4⋊C4—32no—
279C3×C22⋊C4—62no—
280#217—22no—
281#217—62no—
282#217—62no—
283#217—62no—
284#217—62no—
285#217—122no—
286#213—24no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289C4⋊Dic3—32no—
290C4⋊Dic3—32no—
291C4⋊Dic3—62no—
292C4⋊Dic3—62no—
293C4⋊Dic3C22×D312yes—
294Dic3⋊C4—62no—
295#208—62no—
296C2×C3⋊C8—31no—
297C2×C3⋊C8—31no—
298C2×C3⋊C8—61no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8C22×D311yescharacteristic
301C2×C3⋊C8C22×D311yescharacteristic
302D24—22no—
303ΓL(1,𝔽25)—22no—
304ΓL(1,𝔽25)—62no—
305ΓL(1,𝔽25)—62no—
306ΓL(1,𝔽25)—62no—
307ΓL(1,𝔽25)—62no—
308ΓL(1,𝔽25)—62no—
309ΓL(1,𝔽25)—122no—
310D3×C8—62no—
311D3×C8#6714yescomplemented
312C22×C32—42no—
313C22×C32—42no—
314C22×C32—42no—
315C22×C32C22×D411yescharacteristic
316C2×C3⋊D3—21no—
317C2×C3⋊D3—22no—
318C2×C3×D3—21no—
319C2×C3×D3—22no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—88no—
324C2×C3×D3#12112yes—
325C2×C3×D3AGL(1,ℤ/8)14yes—
326D32—44no—
327C32×C4C22×D411yescharacteristic
328C32×C4C2×#4111yescharacteristic
329C3⋊Dic3—21no—
330C3⋊Dic3—42no—
331C3×Dic3—21no—
332C3×Dic3—42no—
333C3×Dic3#12112yes—
334C22×D4—32no—
335C22×D4—182no—
336C23×C4—91no—
337C2×D8—32no—
338C2×D8—31no—
339C2×D8—64no—
340C2×D8D3211yescharacteristic, complemented
341C2×M16—31no—
342C2×M16—91no—
343C2×M16—91no—
344C2×M16—91no—
345C2×M16—184no—
346C22×C8—31no—
347C22×C8—91no—
348#121—32no—
349#121—92no—
350#121—92no—
351#121—92no—
352#121—182no—
353#121—182no—
354C2×C4⋊C4—92no—
355C2×C22⋊C4—182no—
356#106—31no—
357#106—92no—
358#106—91no—
359#102—32no—
360#102—92no—
361#102—92no—
362#102—92no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—31no—
366C23×C3—31no—
367C23×C3—42no—
368C23×C3—62no—
369C23×C3—124no—
370C23×C3—124no—
371C23×C3—124no—
372C22×D3—22no—
373C22×D3—31no—
374C22×D3—31no—
375C22×D3—44no—
376C22×D3—44no—
377C22×D3—44no—
378C22×D3—61no—
379C22×D3—62no—
380C22×D3—64no—
381C22×D3—64no—
382C22×D3—62no—
383C22×D3D3×D411yescharacteristic
384C22×D3D3×D411yescharacteristic
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—42no—
390C3×D4—42no—
391C3×D4—62no—
392C3×D4—62no—
393C3×D4—124no—
394C3×D4—124no—
395C2×C3×C4—21no—
396C2×C3×C4—31no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—31no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—62no—
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—44no—
406#67—44no—
407#67—124no—
408#67—124no—
409#67—124no—
410#67—124no—
411#67—124no—
412#67—244no—
413C2×Dic3—22no—
414C2×Dic3—31no—
415C2×Dic3—31no—
416C2×Dic3—61no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—122no—
422C2×Dic3—124no—
423C2×Dic3D3×D411yescharacteristic
424C2×Dic3D3×D411yescharacteristic
425D12—22no—
426D12—22no—
427D12—124no—
428C4×D3—21no—
429C4×D3—21no—
430C4×D3—62no—
431C4×D3—62no—
432C4×D3—62no—
433C4×D3—61no—
434C4×D3—61no—
435C4×D3—61no—
436C4×D3—61no—
437C4×D3—62no—
438C4×D3—121no—
439C4×D3—121no—
440C4×D3—124no—
441C4×D3#23712yes—
442C4×D3C2×#6712yes—
443C3×C8—22no—
444C3×C8—32no—
445C3×C8—61no—
446C3×C8D3×D412yescomplemented
447C3×C8C2×#6712yescomplemented
448C3⋊C8—21no—
449C3⋊C8—61no—
450C3⋊C8—61no—
451C3⋊C8—121no—
452C3⋊C8C2×#6712yescomplemented
453C2×C32—82no—
454C2×C32C2×#12111yescharacteristic
455C2×C32C2×AGL(1,ℤ/8)12yes—
456C3⋊D3—41no—
457C3×D3—41no—
458C3×D3—82no—
459C3×D3#46914yescomplemented
460C24—62no—
461C24—91no—
462C2×D4—32no—
463C2×D4—64no—
464C2×D4—64no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—182no—
468C2×D4—182no—
469C2×D4—182no—
470C2×D4—368no—
471C2×D4C2×D3212yes—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—91no—
478C22×C4—182no—
479C22×C4—182no—
480C22×C4—182no—
481D8—22no—
482D8—64no—
483D8—62no—
484M16—62no—
485M16—182no—
486M16—182no—
487M16—182no—
488C2×C8—31no—
489C2×C8—34no—
490C2×C8—31no—
491C2×C8—91no—
492C2×C8—182no—
493C2×C8C2×D3211yescharacteristic
494C4⋊C4—32no—
495C4⋊C4—92no—
496C4⋊C4—182no—
497C22⋊C4—62no—
498C22⋊C4—182no—
499C22⋊C4—182no—
500C22⋊C4—182no—
501C22×C3—21no—
502C22×C3—34no—
503C22×C3—32no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—42no—
510C22×C3—62no—
511C22×C3—61no—
512C22×C3—82no—
513C22×C3—82no—
514C22×C3—82no—
515C22×C3—122no—
516C22×C3—122no—
517C22×C3—122no—
518C22×C3—248no—
519C22×C3C2×D3×D411yescharacteristic
520C22×C3C2×D3×D411yescharacteristic
521C2×D3—22no—
522C2×D3—21no—
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—42no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—61no—
529C2×D3—61no—
530C2×D3—88no—
531C2×D3—121no—
532C2×D3—122no—
533C2×D3—124no—
534C2×D3—124no—
535C2×D3#91114yes—
536C2×D3#93812yes—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—32no—
540C3×C4—61no—
541C3×C4—122no—
542C3×C4C2×D3×D411yescharacteristic
543C3×C4C2×#23711yescharacteristic
544C3×C4D3×#4111yescharacteristic
545C3×C4C22×#6711yescharacteristic
546Dic3—21no—
547Dic3—42no—
548Dic3—61no—
549Dic3—61no—
550Dic3—121no—
551Dic3—122no—
552Dic3—122no—
553Dic3—242no—
554Dic3#93812yes—
555C32C2×#46911yescharacteristic, complemented, Sylow
556C23—22no—
557C23—31no—
558C23—31no—
559C23—62no—
560C23—91no—
561C23—124no—
562C23—124no—
563C23—124no—
564C23—182no—
565C23—184no—
566D4—22no—
567D4—22no—
568D4—62no—
569D4—62no—
570D4—124no—
571D4—124no—
572D4—364no—
573D4—364no—
574D4—364no—
575C2×C4—31no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—31no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—62no—
582C2×C4—91no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—182no—
589C2×C4—364no—
590C2×C4C22×D3211yescharacteristic
591C8—32no—
592C8—61no—
593C8—181no—
594C8D3×#6712yescomplemented
595C2×C3—22no—
596C2×C3—21no—
597C2×C3—34no—
598C2×C3—82no—
599C2×C3—82no—
600C2×C3—121no—
601C2×C3—162no—
602C2×C3—242no—
603C2×C3D3×#12111yescharacteristic
604C2×C3C2×#91112yes—
605C2×C3D3×AGL(1,ℤ/8)12yes—
606C2×C3C2×#93811yescharacteristic
607D3—41no—
608D3—82no—
609D3—121no—
610D3—121no—
611D3—241no—
612D3#515914yesdirect product factor
613C22—34no—
614C22—32no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—62no—
619C22—61no—
620C22—122no—
621C22—122no—
622C22—122no—
623C22—182no—
624C22—181no—
625C22—248no—
626C22—364no—
627C22D32×D411yescharacteristic
628C4—32no—
629C4—61no—
630C4—122no—
631C4—181no—
632C4—362no—
633C4D3×#23711yescharacteristic
634C4C2×D3×#6711yescharacteristic
635C3—21no—
636C3D3×#46911yescharacteristic, complemented
637C3C2×#515911yescharacteristic, complemented
638C2—34no—
639C2—82no—
640C2—121no—
641C2—242no—
642C2—361no—
643C2D3×#91112yes—
644C2D3×#93811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ 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×#938C2semidirect
3. C2×D3×ΓL(1,𝔽25)C2semidirect
4. #10592858C2semidirect
5. C3×#5159C2semidirect
6. #10591454C2semidirect
7. #10591451C2semidirect
8. D3×#832C2semidirect
9. #10590846C2semidirect
10. #10590836C2semidirect
11. D3×#817C2semidirect
17. C2×C32×D8C22semidirect
18. #64147C22semidirect
19. C2×#3743C22semidirect
20. C3×#938C22semidirect
21. C2×C3×#213C22semidirect
23. C2×C3×D24C22semidirect
24. C2×C3×ΓL(1,𝔽25)C22semidirect
29. #63916C22semidirect
30. #63908C22semidirect
32. C2×#3712C22semidirect
33. C2×#3711C22semidirect
36. #63659C22semidirect
37. #63644C22semidirect
38. C3×#832C22semidirect
39. C3×#817C22semidirect
40. #63573C22semidirect
41. #63563C22semidirect
42. #63562C22semidirect
45. C2×D3×D8D3semidirect
58. #5159D3direct (N × H)
100. C3×D3×C8D4semidirect
118. C2×C3×D8C2×D3semidirect
119. C2×C3×D8C2×D3semidirect
132. #938C2×D3semidirect
133. C2×#213C2×D3semidirect
140. C2×D24C2×D3semidirect
148. C2×ΓL(1,𝔽25)C2×D3semidirect
162. #832C2×D3semidirect
168. #817C2×D3semidirect
206. C32×C8C2×D4semidirect
209. C3×C3⋊C8C2×D4semidirect
311. D3×C8#67semidirect
340. C2×D8D32semidirect
446. C3×C8D3×D4semidirect
447. C3×C8C2×#67semidirect
452. C3⋊C8C2×#67semidirect
459. C3×D3#469semidirect
555. C32C2×#469semidirect
594. C8D3×#67semidirect
612. D3#5159direct (N × H)
636. C3D3×#469semidirect
637. C3C2×#5159semidirect

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×#9382
C2×D3×ΓL(1,𝔽25)2
#105928582
C3×#51592
#105914542
#105914512
D3×#8322
#105908462
#105908362
D3×#8172
C2×#51593
D3×#4693