Finite Group Databasebeta

← D3×#5135 #11866968

Subgroups — D3×#5135 #11866968

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×M16C211yesmaximal, characteristic, complemented
2D3×#930C212yesmaximal, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10592834C211yesmaximal, characteristic, complemented
5C3×#5135C211yesmaximal, characteristic, complemented
6#10591165C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590836C211yesmaximal, characteristic, complemented
9#10590835C211yesmaximal, characteristic, complemented
10#10590827C212yesmaximal, complemented
11D3×#817C211yesmaximal, characteristic, complemented
12C2×#5135—31nomaximal
13D3×#469—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×D3×#67—22no—
16C2×D3×D12C2212yes—
17C2×C32×M16C2211yescharacteristic, complemented
18#64139C2212yescomplemented
19C2×#3745C2211yescharacteristic, complemented
20C3×#930C2212yescomplemented
21C2×C3×#208C2211yescharacteristic, complemented
22C3×D3×M16—24no—
23C2×C3×D24C2211yescharacteristic, complemented
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63978—22no—
29D3×(C2×D3)⋊C4—22no—
30#63909C2212yescomplemented
31#63908C2212yescomplemented
32#63906—22no—
33D3×C4⋊Dic3C2212yes—
34C2×#3714C2212yescomplemented
35D3×D24—24no—
36#63648C2212yescomplemented
37#63644C2211yescharacteristic, complemented
38C3×#821C2212yescomplemented
39C3×#817C2211yescharacteristic, complemented
40#63573C2212yescomplemented
41#63564C2212yescomplemented
42#63563C2212yescomplemented
43C22×C3×M16—31no—
44C2×#930—32no—
45C2×D3×D8—31no—
46C2×D3×M16D311yescharacteristic, complemented
47C22×D24—31no—
48D3×#121—32no—
49C3×#469—31no—
50#5159—31no—
51#5135—31no—
52#5135—31no—
53#5135—32no—
54#5135—31no—
55#5135—32no—
56#5135—31no—
57#5135—61no—
58#5135D311yescharacteristic, direct product factor
59C2×#821—32no—
60C2×#817—31no—
61#5039—32no—
62#4865—31no—
63D3×#106—31no—
64#4782—32no—
65D3×#102—32no—
66C23×C3×D3D411yescharacteristic
67C22×D32—22no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—22no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C3×#67—22no—
72C22×C3×Dic3D411yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80D3×#67—48no—
81C2×#626—22no—
82C2×#626—22no—
83C2×#625—22no—
84C2×D3×Dic3—22no—
85D3×D12—24no—
86D3×D12—24no—
87C32×M16—22no—
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90#3752—22no—
91C4⋊(C3⋊Dic3)C2312yes—
92#3745—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3C2312yes—
95C3×#208—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×D24—22no—
99C3×ΓL(1,𝔽25)—22no—
100C3×ΓL(1,𝔽25)—22no—
101C3×D3×C8—22no—
102C3×D3×C8D414yescomplemented
103Dic3⋊Dic3—22no—
104#3722—22no—
105(C2×D3)⋊Dic3—22no—
106#3714—24no—
107C2×#469—91noSylow
108C23×C3×C4—31no—
109C22×#67—62no—
110C2×D3×D4—32no—
111C2×D3×D4—62no—
112C22×D12—32no—
113C22×C4×D3C2×D311yescharacteristic
114C2×C3×D8—31no—
115C2×C3×M16—21no—
116C2×C3×M16—31no—
117C2×C3×M16—31no—
118C2×C3×M16—31no—
119C2×C3×M16—64no—
120C2×C3×M16C2×D311yescharacteristic, complemented
121C2×C3×M16C2×D311yescharacteristic, complemented
122C22×C3×C8—31no—
123C22×C3×C8—31no—
124C3×#121—32no—
125#939—62no—
126#938—32no—
127C2×#213—32no—
128#930—32no—
129#930—32no—
130#930—32no—
131#930—32no—
132#930—62no—
133#930—62no—
134#930—62no—
135#930C2×D312yescomplemented
136C2×(C2×D3)⋊C4—62no—
137C2×C4⋊Dic3—32no—
138C2×#208C2×D311yescharacteristic, complemented
139D3×D8—64no—
140D3×M16—24no—
141C2×D24—32no—
142C2×D24—31no—
143C2×D24—31no—
144C2×D24—61no—
145C2×D24—64no—
146C2×D24C2×D311yescharacteristic, complemented
147C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
148C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
149C2×D3×C8C2×D311yescharacteristic
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#821—32no—
159#821—32no—
160#821—32no—
161#821—32no—
162#821—62no—
163#821C2×D312yescomplemented
164#817—31no—
165#817—31no—
166#817—32no—
167#817—61no—
168#817C2×D311yescharacteristic, complemented
169#809—32no—
170#808—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—24no—
175C22×C3×D3—22no—
176C22×C3×D3C2×D411yescharacteristic
177C22×C3×D3C2×D411yescharacteristic
178C2×D32—44no—
179C2×D32—44no—
180C2×D32—44no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185#638—44no—
186C2×C3⋊Dic3—22no—
187C4⋊(C3⋊D3)—22no—
188C4⋊(C3⋊D3)—22no—
189C3×#67—44no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×D12—22no—
195C3×D12—22no—
196C3×C4×D3—22no—
197C3×C4×D3—21no—
198C3×C4×D3—21no—
199C3×C4×D3—22no—
200C3×C4×D3C2×D412yes—
201C3×C4×D3#4112yes—
202#626—44no—
203#626—44no—
204#625—44no—
205D3×Dic3—44no—
206C32×C8—21no—
207C32×C8C2×D412yescomplemented
208C3×C3⋊C8—21no—
209C3×C3⋊C8C2×D412yescomplemented
210C22×D8—91no—
211C22×M16—31no—
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—31no—
222C23×D3—62no—
223C23×D3—62no—
224C23×D3D1211yescharacteristic
225C2×C3×D4—32no—
226C2×C3×D4—62no—
227C22×C3×C4—21no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—62no—
234C22×C3×C4—62no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—22no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—122no—
245C2×#67—128no—
246C22×Dic3—62no—
247C22×Dic3D1211yescharacteristic
248D3×D4—64no—
249D3×D4—64no—
250D3×D4—128no—
251C2×D12—32no—
252C2×D12—32no—
253C2×D12—62no—
254C2×D12—64no—
255C2×D12—64no—
256C2×D12—62no—
257C2×D12—62no—
258C2×D12C22×D312yes—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—62no—
262C2×C4×D3D1211yescharacteristic
263C2×C4×D3D1211yescharacteristic
264C2×C4×D3C22×D311yescharacteristic
265C2×C4×D3C22×D311yescharacteristic
266C3×D8—62no—
267C3×M16—22no—
268C3×M16—22no—
269C3×M16—42no—
270C3×M16—62no—
271C3×M16—62no—
272C3×M16—62no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—31no—
276C2×C3×C8—34no—
277C2×C3×C8—31no—
278C2×C3×C8—62no—
279C2×C3×C8C22×D311yescharacteristic
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D311yescharacteristic
282C2×C3×C8C22×D311yescharacteristic
283C3×C4⋊C4—32no—
284C3×C22⋊C4—62no—
285#217—62no—
286#213—64no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—122no—
294C4⋊Dic3—32no—
295C4⋊Dic3—32no—
296C4⋊Dic3—62no—
297C4⋊Dic3—62no—
298C4⋊Dic3C22×D312yes—
299Dic3⋊C4—62no—
300#208—22no—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303D24—22no—
304D24—64no—
305D24—62no—
306D24—62no—
307D24—122no—
308ΓL(1,𝔽25)—22no—
309ΓL(1,𝔽25)—22no—
310D3×C8—22no—
311D3×C8#6714yescomplemented
312C22×C32—21no—
313C22×C32—22no—
314C22×C32C22×D411yescharacteristic
315C2×C3⋊D3—42no—
316C2×C3⋊D3—42no—
317C2×C3⋊D3—42no—
318C2×C3×D3—21no—
319C2×C3×D3—22no—
320C2×C3×D3—44no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3#12112yes—
325C2×C3×D3AGL(1,ℤ/8)14yes—
326D32—88no—
327C32×C4—21no—
328C32×C4C22×D411yescharacteristic
329C32×C4C2×#4111yescharacteristic
330C3⋊Dic3—42no—
331C3×Dic3—21no—
332C3×Dic3—42no—
333C3×Dic3#12112yes—
334C22×D4—92no—
335C22×D4—182no—
336C23×C4—31no—
337C2×D8—31no—
338C2×D8—92no—
339C2×D8—91no—
340C2×D8—184no—
341C2×M16—31no—
342C2×M16—31no—
343C2×M16—31no—
344C2×M16—64no—
345C2×M16D3211yescharacteristic, complemented
346C22×C8—31no—
347C22×C8—31no—
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—21no—
364C23×C3—31no—
365C23×C3—31no—
366C23×C3—64no—
367C23×C3—62no—
368C23×C3—62no—
369C23×C3C2×D1211yescharacteristic
370C23×C3D3×D411yescharacteristic
371C22×D3—24no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—122no—
377C22×D3—124no—
378C22×D3—124no—
379C22×D3—124no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—124no—
383C22×D3C2×D1211yescharacteristic
384C22×D3C2×D1211yescharacteristic
385C3×D4—62no—
386C3×D4—62no—
387C3×D4—124no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—31no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—31no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—62no—
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—44no—
411#67—124no—
412#67—124no—
413#67—124no—
414#67—124no—
415#67—124no—
416#67—124no—
417#67—244no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—122no—
423C2×Dic3—124no—
424C2×Dic3C2×D1211yescharacteristic
425C2×Dic3C2×D1211yescharacteristic
426D12—22no—
427D12—22no—
428D12—62no—
429D12—62no—
430D12—62no—
431D12—62no—
432D12—122no—
433D12—122no—
434D12—124no—
435D12—124no—
436C4×D3—22no—
437C4×D3—21no—
438C4×D3—21no—
439C4×D3—22no—
440C4×D3—124no—
441C4×D3#23512yes—
442C4×D3C2×#6712yes—
443C3×C8—21no—
444C3×C8—21no—
445C3×C8—22no—
446C3×C8—32no—
447C3×C8—41no—
448C3×C8—61no—
449C3×C8D3×D412yescomplemented
450C3×C8C2×#6712yescomplemented
451C3⋊C8—21no—
452C3⋊C8C2×#6712yescomplemented
453C2×C32—41no—
454C2×C32C2×#12111yescharacteristic
455C2×C32C2×AGL(1,ℤ/8)12yes—
456C3⋊D3—82no—
457C3×D3—41no—
458C3×D3—82no—
459C3×D3#46914yescomplemented
460C24—31no—
461C24—182no—
462C2×D4—32no—
463C2×D4—62no—
464C2×D4—92no—
465C2×D4—184no—
466C2×D4—184no—
467C2×D4—182no—
468C2×D4—182no—
469C2×D4—182no—
470C2×D4—182no—
471C2×D4—368no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—62no—
478C22×C4—62no—
479C22×C4—182no—
480C22×C4C2×D3211yescharacteristic
481D8—62no—
482D8—184no—
483D8—182no—
484M16—22no—
485M16—62no—
486M16—62no—
487M16—62no—
488C2×C8—31no—
489C2×C8—34no—
490C2×C8—31no—
491C2×C8—62no—
492C2×C8C2×D3211yescharacteristic
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—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—34no—
507C22×C3—32no—
508C22×C3—42no—
509C22×C3—41no—
510C22×C3—62no—
511C22×C3—61no—
512C22×C3—124no—
513C22×C3—122no—
514C22×C3—122no—
515C22×C3—122no—
516C22×C3C22×D1211yescharacteristic
517C22×C3C2×D3×D411yescharacteristic
518C2×D3—22no—
519C2×D3—21no—
520C2×D3—44no—
521C2×D3—42no—
522C2×D3—42no—
523C2×D3—42no—
524C2×D3—122no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—242no—
531C2×D3—242no—
532C2×D3—242no—
533C2×D3—248no—
534C2×D3—248no—
535C2×D3#90814yes—
536C2×D3#93012yes—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—32no—
542C3×C4—41no—
543C3×C4—61no—
544C3×C4—122no—
545C3×C4C2×#23511yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547C3×C4D3×#4111yescharacteristic
548C3×C4C22×#6711yescharacteristic
549Dic3—21no—
550Dic3—42no—
551Dic3—122no—
552Dic3—122no—
553Dic3—242no—
554Dic3#93012yes—
555C32C2×#46911yescharacteristic, complemented, Sylow
556C23—31no—
557C23—31no—
558C23—62no—
559C23—64no—
560C23—62no—
561C23—182no—
562C23—364no—
563C23—364no—
564C23—364no—
565C23D3×D1211yescharacteristic
566D4—62no—
567D4—62no—
568D4—124no—
569D4—182no—
570D4—182no—
571D4—364no—
572D4—364no—
573D4—364no—
574D4—364no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—31no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—31no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—61no—
586C2×C4—62no—
587C2×C4—182no—
588C2×C4—364no—
589C2×C4D3×D1211yescharacteristic
590C2×C4C22×D3211yescharacteristic
591C8—21no—
592C8—32no—
593C8—61no—
594C8D3×#6712yescomplemented
595C2×C3—22no—
596C2×C3—21no—
597C2×C3—34no—
598C2×C3—41no—
599C2×C3—41no—
600C2×C3—81no—
601C2×C3—121no—
602C2×C3—242no—
603C2×C3D3×#12111yescharacteristic
604C2×C3C2×#90812yes—
605C2×C3D3×AGL(1,ℤ/8)12yes—
606C2×C3C2×#93011yescharacteristic
607D3—41no—
608D3—82no—
609D3—242no—
610D3—242no—
611D3—482no—
612D3#513514yesdirect product factor
613C22—22no—
614C22—21no—
615C22—34no—
616C22—32no—
617C22—62no—
618C22—61no—
619C22—124no—
620C22—122no—
621C22—122no—
622C22—122no—
623C22—362no—
624C22—362no—
625C22—362no—
626C22—728no—
627C22C2×D3×D1211yescharacteristic
628C4—21no—
629C4—32no—
630C4—61no—
631C4—122no—
632C4—362no—
633C4D3×#23511yescharacteristic
634C4C2×D3×#6711yescharacteristic
635C3—21no—
636C3D3×#46911yescharacteristic, complemented
637C3C2×#513511yescharacteristic, complemented
638C2—34no—
639C2—41no—
640C2—121no—
641C2—242no—
642C2—722no—
643C2D3×#90812yes—
644C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×M16C2semidirect
2. D3×#930C2semidirect
3. C2×D3×D24C2semidirect
4. #10592834C2semidirect
5. C3×#5135C2semidirect
6. #10591165C2semidirect
7. D3×#821C2semidirect
8. #10590836C2semidirect
9. #10590835C2semidirect
10. #10590827C2semidirect
11. D3×#817C2semidirect
17. C2×C32×M16C22semidirect
18. #64139C22semidirect
19. C2×#3745C22semidirect
20. C3×#930C22semidirect
21. C2×C3×#208C22semidirect
23. C2×C3×D24C22semidirect
24. C2×C3×ΓL(1,𝔽25)C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
30. #63909C22semidirect
31. #63908C22semidirect
34. C2×#3714C22semidirect
36. #63648C22semidirect
37. #63644C22semidirect
38. C3×#821C22semidirect
39. C3×#817C22semidirect
40. #63573C22semidirect
41. #63564C22semidirect
42. #63563C22semidirect
46. C2×D3×M16D3semidirect
58. #5135D3direct (N × H)
102. C3×D3×C8D4semidirect
120. C2×C3×M16C2×D3semidirect
121. C2×C3×M16C2×D3semidirect
135. #930C2×D3semidirect
138. C2×#208C2×D3semidirect
146. C2×D24C2×D3semidirect
147. C2×ΓL(1,𝔽25)C2×D3semidirect
148. C2×ΓL(1,𝔽25)C2×D3semidirect
163. #821C2×D3semidirect
168. #817C2×D3semidirect
207. C32×C8C2×D4semidirect
209. C3×C3⋊C8C2×D4semidirect
311. D3×C8#67semidirect
345. C2×M16D32semidirect
449. C3×C8D3×D4semidirect
450. C3×C8C2×#67semidirect
452. C3⋊C8C2×#67semidirect
459. C3×D3#469semidirect
555. C32C2×#469semidirect
594. C8D3×#67semidirect
612. D3#5135direct (N × H)
636. C3D3×#469semidirect
637. C3C2×#5135semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
D3×#9302
C2×D3×D242
#105928342
C3×#51352
#105911652
D3×#8212
#105908362
#105908352
#105908272
D3×#8172
C2×#51353
D3×#4693