Finite Group Databasebeta

← #11902854

Subgroups — #11902854

Order 1152.

3451 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C212yesmaximal, complemented
2C4×#3832C211yesmaximal, characteristic, complemented
3C3×#5577C211yesmaximal, characteristic, complemented
4C3×Q8×D12C211yesmaximal, characteristic, complemented
5#10595409C212yesmaximal, complemented
6#10594633C216yesmaximal, complemented
7#10594632C216yesmaximal, complemented
8#10594004C213yesmaximal, complemented
9C4×#3802C213yesmaximal, complemented
10#10593907C213yesmaximal, complemented
11#10593869C213yesmaximal, complemented
12#86766—31nomaximal
13D4×#239—31nomaximal
14C2×#3832C2211yescharacteristic
15C2×C3×#239C2212yescomplemented
16C2×C3×D3×Q8C2212yescomplemented
17D3×#239—216no—
18C2×#3802C2213yes—
19C2×D3×D12C2216yescomplemented
20C2×C4×D32C2216yescomplemented
21C2×#3799C2216yescomplemented
22C2×#3796C2216yescomplemented
23C32×C4×Q8C2211yescharacteristic, complemented
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25#64102C2213yescomplemented
26#64101C2213yescomplemented
27C4×C4⋊(C3⋊D3)C2213yescomplemented
28C42×C3⋊D3C2213yescomplemented
29C3×#897C2216yescomplemented
30C3×#895C2216yescomplemented
31C3×#874C2213yescomplemented
32C3×C4×D12C2213yes—
33C3×C4×D12C2213yescomplemented
34C3×#869C2213yescomplemented
35#63922C22112yescomplemented
36#63921C2216yescomplemented
37#63916C2216yescomplemented
38#63916C2216yescomplemented
39#63908C2216yescomplemented
40#63902C2216yescomplemented
41C4×#625C2216yescomplemented
42#63900C2213yescomplemented
43#63898C2211yescharacteristic
44#63898C2216yescomplemented
45#63898C2213yescomplemented
46#63863C2216yescomplemented
47#63856C2216yescomplemented
48#63854C22112yescomplemented
49C2×D3×#41—32no—
50C22×#239—32no—
51C3×#550—31no—
52C3×D4×Q8—31no—
53#5831—32no—
54#5817—32no—
55#5726—33no—
56#5725—33no—
57#5717—33no—
58#5716—33no—
59#5630—36no—
60#5627—36no—
61#5612—36no—
62#5606—36no—
63#5577D311yescharacteristic, complemented
64Q8×D12D311yescharacteristic, complemented
65C4×#239—31no—
66C4×#239—31no—
67C4×#239—61no—
68#5551—33no—
69D4×D12—33no—
70C4×D3×D4—33no—
71C4×D3×D4—33no—
72C22×D32C2316yes—
73C2×C32×Q8C2311yescharacteristic
74#3832D418yescomplemented
75C2×C4⋊(C3⋊D3)C2313yes—
76C2×C4×C3⋊D3C2313yes—
77C2×C4×C3⋊D3C2313yes—
78C2×C4×C3⋊D3C2313yes—
79C3×#239—28no—
80C3×D3×Q8—28no—
81C2×C3×D12C2316yes—
82C2×C3×D12C2313yes—
83C2×C3×D12C2316yes—
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3C2316yes—
86C2×C3×C4×D3C2316yes—
87C2×C3×Dic6C2316yes—
88C2×#626C23112yes—
89C2×#625C2316yes—
90C2×#624C2316yes—
91C2×D3×Dic3C2316yes—
92C2×D3×Dic3C2312yes—
93#3802—212no—
94D3×D12—224no—
95C4×D32—224no—
96#3799—224no—
97#3796—224no—
98C32×C4⋊C4C2313yes—
99C32×C42C2313yes—
100#3752C2316yes—
101C4⋊(C3⋊Dic3)C2313yes—
102C4×C3⋊Dic3C2311yescharacteristic
103C4×C3⋊Dic3C2313yes—
104C4×C3⋊Dic3C2313yes—
105C3×(C2×D3)⋊C4C2316yes—
106C3×(C2×D3)⋊C4C2316yes—
107C3×C4⋊Dic3C2316yes—
108C3×C4⋊Dic3C2311yescharacteristic
109C3×C4⋊Dic3C2313yes—
110#3724C2316yes—
111(C2×D3)⋊Dic3C23112yes—
112(C2×D3)⋊Dic3C2316yes—
113(C2×D3)⋊Dic3C2312yes—
114D4×#41—91noSylow
115C2×C3×#41—32no—
116C22×C3×Q8—32no—
117D3×#41—616no—
118C2×#239—31no—
119C2×#239—31no—
120C2×#239—36no—
121C2×#239—36no—
122C2×#239—61no—
123C2×#239—616no—
124C2×#239C2×D312yescomplemented
125C2×D3×Q8C2×D312yescomplemented
126C2×#237—36no—
127C2×D3×D4—33no—
128C2×D3×D4—33no—
129C2×D3×D4—36no—
130C2×#235—36no—
131C22×D12—36no—
132C22×C4×D3—36no—
133C22×C4×D3—36no—
134C3×C4⋊Q8—33no—
135C3×#127—33no—
136C3×C22⋊Q8—36no—
137C3×#121—36no—
138C3×C4×Q8—21no—
139C3×C4×Q8C2×D311yescharacteristic, complemented
140C3×C4×Q8C2×D311yescharacteristic, complemented
141C3×C4×D4—33no—
142C3×C4×D4—33no—
143#947—36no—
144#946—36no—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147Q8×Dic3—61no—
148#938—36no—
149#938—36no—
150#938—36no—
151#937—312no—
152#936—36no—
153D4×Dic3—33no—
154D4×Dic3—36no—
155D4×Dic3—31no—
156#930—36no—
157C4×#67—36no—
158C4×#67—36no—
159#924—36no—
160#897C2×D316yescomplemented
161#895—36no—
162#895—36no—
163#895C2×D316yescomplemented
164#894—312no—
165#893—33no—
166#893—36no—
167#893—31no—
168#893—33no—
169#893—33no—
170#893—63no—
171#892—33no—
172#892—33no—
173#892—63no—
174D3×C4⋊C4—33no—
175D3×C4⋊C4—33no—
176#883—312no—
177#882—312no—
178#67⋊C4—36no—
179#67⋊C4—36no—
180D3×C22⋊C4—36no—
181D3×C22⋊C4—36no—
182#874C2×D313yescomplemented
183C4×D12—33no—
184C4×D12—33no—
185C4×D12—63no—
186C4×D12C2×D313yes—
187C4×D12C2×D313yescomplemented
188C42×D3—33no—
189C42×D3—33no—
190C42×D3—63no—
191#869C2×D313yescomplemented
192C22×C3⋊D3C2413yes—
193C22×C3×D3C2416yes—
194C22×C3×D3C2412yes—
195C2×D32—212no—
196C2×D32—212no—
197C2×D32—46no—
198C32×Q8C2×D414yescomplemented
199C2×C32×C4C2413yes—
200C2×C32×C4C2413yes—
201C2×C32×C4C2411yescharacteristic
202C2×C3⋊Dic3C2411yescharacteristic
203C2×C3⋊Dic3C2413yes—
204C2×C3⋊Dic3C2411yescharacteristic
205C4⋊(C3⋊D3)C2×D4112yescomplemented
206C4×C3⋊D3—26no—
207C4×C3⋊D3—43no—
208C4×C3⋊D3C2×D4112yescomplemented
209C2×C3×Dic3C2416yes—
210C2×C3×Dic3C2412yes—
211C3×D12—212no—
212C3×D12—26no—
213C3×D12—46no—
214C3×D12#4114yescomplemented
215C3×C4×D3—212no—
216C3×C4×D3—212no—
217C3×Dic6—212no—
218#626—224no—
219#625—212no—
220#624—212no—
221D3×Dic3—212no—
222D3×Dic3—24no—
223C22×#41—92no—
224#550—31no—
225D4×Q8—31no—
226#548—92no—
227#547—93no—
228#546—96no—
229D42—93no—
230#532—93no—
231#525—96no—
232C4×#41—91no—
233C2×C4×D4—93no—
234C23×D3—36no—
235C23×D3—36no—
236C3×#41—68no—
237C2×C3×Q8—21no—
238C2×C3×Q8—36no—
239C2×C3×Q8—68no—
240C2×C3×Q8C22×D311yescharacteristic
241C2×C3×Q8C22×D311yescharacteristic
242C2×C3×D4—31no—
243C2×C3×D4—33no—
244C2×C3×D4—36no—
245C2×C3×D4—36no—
246C22×C3×C4—36no—
247C22×C3×C4—36no—
248C2×#67—36no—
249C2×#67—36no—
250C2×#67—312no—
251C22×Dic3—32no—
252C22×Dic3—36no—
253#239—28no—
254#239—38no—
255#239—38no—
256#239—68no—
257#239—624no—
258#239—624no—
259D3×Q8—28no—
260#237—624no—
261D3×D4—624no—
262D3×D4—612no—
263D3×D4—612no—
264#235—624no—
265C2×D12—33no—
266C2×D12—33no—
267C2×D12—312no—
268C2×D12—63no—
269C2×D12—624no—
270C2×D12C22×D313yes—
271C2×D12C22×D316yes—
272C2×D12C22×D316yes—
273C2×D12C22×D311yescharacteristic
274C2×C4×D3—33no—
275C2×C4×D3—33no—
276C2×C4×D3—32no—
277C2×C4×D3—36no—
278C2×C4×D3—33no—
279C2×C4×D3—33no—
280C2×C4×D3—36no—
281C2×C4×D3—36no—
282C2×C4×D3—33no—
283C2×C4×D3—33no—
284C2×C4×D3—63no—
285C2×C4×D3—63no—
286C2×C4×D3—63no—
287C2×C4×D3—624no—
288C2×C4×D3—624no—
289C2×C4×D3C22×D316yes—
290C2×C4×D3C22×D316yes—
291C2×Dic6C22×D316yes—
292C3×C4⋊C4—23no—
293C3×C4⋊C4—31no—
294C3×C4⋊C4—33no—
295C3×C4⋊C4—36no—
296C3×C4⋊C4C22×D313yes—
297C3×C4⋊C4C22×D313yes—
298C3×C22⋊C4—36no—
299C3×C22⋊C4—36no—
300C3×C42—23no—
301C3×C42C22×D313yes—
302C3×C42C22×D313yes—
303#217—32no—
304#217—36no—
305#217—312no—
306(C2×D3)⋊C4—32no—
307(C2×D3)⋊C4—36no—
308(C2×D3)⋊C4—312no—
309(C2×D3)⋊C4—36no—
310(C2×D3)⋊C4—36no—
311(C2×D3)⋊C4—66no—
312(C2×D3)⋊C4C22×D316yes—
313(C2×D3)⋊C4C22×D316yes—
314C4⋊Dic3—33no—
315C4⋊Dic3—33no—
316C4⋊Dic3—63no—
317C4⋊Dic3C22×D313yes—
318C4⋊Dic3C22×D316yes—
319C4⋊Dic3C22×D311yescharacteristic
320Dic3⋊C4—36no—
321Dic3⋊C4—36no—
322C4×Dic3—31no—
323C4×Dic3—31no—
324C4×Dic3—33no—
325C4×Dic3—33no—
326C4×Dic3—33no—
327C4×Dic3—33no—
328C4×Dic3—61no—
329C4×Dic3—63no—
330C4×Dic3—63no—
331C22×C32C2511yescharacteristic
332C2×C3⋊D3—23no—
333C2×C3⋊D3—23no—
334C2×C3⋊D3C22×D416yes—
335C2×C3×D3—22no—
336C2×C3×D3—22no—
337C2×C3×D3—26no—
338C2×C3×D3—26no—
339C2×C3×D3—26no—
340C2×C3×D3C2×#4114yescomplemented
341D32—424no—
342C32×C4—23no—
343C32×C4C22×D416yes—
344C32×C4C2×#4112yescomplemented
345C3⋊Dic3—21no—
346C3⋊Dic3—23no—
347C3⋊Dic3C22×D412yes—
348C3×Dic3—22no—
349C3×Dic3—26no—
350C2×#41—32no—
351C2×#41—96no—
352C2×#41—96no—
353C2×#41—91no—
354C2×#41—1816no—
355C22×Q8—32no—
356C22×D4—96no—
357C22×D4—93no—
358C23×C4—96no—
359C4⋊Q8—33no—
360#127—33no—
361#124—96no—
362#123—912no—
363C22⋊Q8—36no—
364C22⋊Q8—96no—
365#121—36no—
366#121—96no—
367#121—96no—
368#121—96no—
369#120—912no—
370C4×Q8—91no—
371C4×Q8D3211yescharacteristic, complemented
372C4×D4—33no—
373C4×D4—33no—
374C4×D4—96no—
375C4×D4—91no—
376C4×D4—93no—
377C4×D4—96no—
378C4×D4—96no—
379C4×D4—93no—
380C4×D4—93no—
381#117—93no—
382C2×C4⋊C4—93no—
383C2×C22⋊C4—96no—
384C2×C42—93no—
385C23×C3—32no—
386C23×C3—36no—
387C22×D3—33no—
388C22×D3—33no—
389C22×D3—63no—
390C22×D3—612no—
391C22×D3—612no—
392C22×D3—612no—
393C22×D3—612no—
394C22×D3—126no—
395C22×D3—126no—
396C22×D3C23×D316yes—
397C22×D3C23×D312yes—
398C3×Q8—24no—
399C3×Q8—612no—
400C3×Q8D3×D414yescomplemented
401C3×Q8D3×D414yescomplemented
402C3×D4—34no—
403C3×D4—612no—
404C3×D4—66no—
405C3×D4—126no—
406C2×C3×C4—23no—
407C2×C3×C4—21no—
408C2×C3×C4—23no—
409C2×C3×C4—32no—
410C2×C3×C4—36no—
411C2×C3×C4—612no—
412C2×C3×C4—612no—
413C2×C3×C4C23×D313yes—
414C2×C3×C4C23×D313yes—
415C2×C3×C4C23×D313yes—
416C2×C3×C4C23×D313yes—
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—624no—
420#67—612no—
421#67—612no—
422C2×Dic3—31no—
423C2×Dic3—31no—
424C2×Dic3—31no—
425C2×Dic3—31no—
426C2×Dic3—33no—
427C2×Dic3—33no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—63no—
431C2×Dic3—64no—
432C2×Dic3—612no—
433C2×Dic3C23×D312yes—
434C2×Dic3C23×D316yes—
435D12—212no—
436D12—26no—
437D12—312no—
438D12—312no—
439D12—46no—
440D12—612no—
441D12—624no—
442D12#23914yescomplemented
443C4×D3—212no—
444C4×D3—212no—
445C4×D3—312no—
446C4×D3—312no—
447C4×D3—612no—
448C4×D3—612no—
449C4×D3—612no—
450C4×D3—64no—
451C4×D3—612no—
452C4×D3—66no—
453C4×D3—66no—
454C4×D3—126no—
455C4×D3—123no—
456C4×D3—123no—
457C4×D3—126no—
458Dic6—212no—
459C2×C32C23×D411yescharacteristic
460C2×C32C22×#4111yescharacteristic
461C2×C32#58511yescharacteristic
462C3⋊D3—26no—
463C3×D3—24no—
464C3×D3—46no—
465C24—96no—
466#41—68no—
467#41—98no—
468#41—1824no—
469#41—1824no—
470C2×Q8—36no—
471C2×Q8—68no—
472C2×Q8C2×D3211yescharacteristic
473C2×D4—31no—
474C2×D4—33no—
475C2×D4—36no—
476C2×D4—36no—
477C2×D4—912no—
478C2×D4—96no—
479C2×D4—93no—
480C2×D4—1824no—
481C2×D4—1812no—
482C22×C4—36no—
483C22×C4—36no—
484C22×C4—96no—
485C22×C4—92no—
486C22×C4—96no—
487C22×C4—93no—
488C22×C4—93no—
489C22×C4—93no—
490C22×C4—1824no—
491C4⋊C4—31no—
492C4⋊C4—33no—
493C4⋊C4—36no—
494C4⋊C4—96no—
495C4⋊C4—93no—
496C4⋊C4C2×D3213yes—
497C22⋊C4—36no—
498C22⋊C4—36no—
499C22⋊C4—92no—
500C22⋊C4—96no—
501C22⋊C4—912no—
502C22⋊C4—96no—
503C42—91no—
504C42—93no—
505C42—93no—
506C42C2×D3213yes—
507C22×C3—21no—
508C22×C3—34no—
509C22×C3—62no—
510C22×C3—62no—
511C22×C3—66no—
512C22×C3—66no—
513C22×C3—66no—
514C22×C3C24×D311yescharacteristic
515C22×C3C24×D311yescharacteristic
516C2×D3—22no—
517C2×D3—22no—
518C2×D3—26no—
519C2×D3—26no—
520C2×D3—26no—
521C2×D3—36no—
522C2×D3—36no—
523C2×D3—66no—
524C2×D3—63no—
525C2×D3—63no—
526C2×D3—63no—
527C2×D3—63no—
528C2×D3—123no—
529C2×D3—123no—
530C2×D3—1224no—
531C2×D3—1224no—
532C2×D3C2×#23914yescomplemented
533C3×C4—23no—
534C3×C4—23no—
535C3×C4—26no—
536C3×C4—22no—
537C3×C4—43no—
538C3×C4—62no—
539C3×C4—66no—
540C3×C4C2×D3×D416yes—
541C3×C4C2×D3×D416yes—
542C3×C4C2×#23912yescomplemented
543C3×C4D3×#4112yescomplemented
544Dic3—26no—
545Dic3—22no—
546Dic3—32no—
547Dic3—32no—
548Dic3—62no—
549Dic3—62no—
550Dic3—63no—
551Dic3—63no—
552Dic3—61no—
553Dic3—61no—
554Dic3—123no—
555C32D4×#4111yescharacteristic, complemented, Sylow
556C23—32no—
557C23—36no—
558C23—93no—
559C23—1812no—
560C23—1812no—
561C23—366no—
562Q8—612no—
563Q8#380214yescomplemented
564D4—34no—
565D4—612no—
566D4—66no—
567D4—912no—
568D4—126no—
569D4—1824no—
570D4—1812no—
571C2×C4—32no—
572C2×C4—36no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—91no—
576C2×C4—912no—
577C2×C4—91no—
578C2×C4—93no—
579C2×C4—1812no—
580C2×C4—184no—
581C2×C4—1812no—
582C2×C4—186no—
583C2×C4—363no—
584C2×C4C22×D3213yes—
585C2×C4C22×D3213yes—
586C2×C4C22×D3211yescharacteristic
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—64no—
591C2×C3—126no—
592C2×C3C22×D3×D411yescharacteristic
593C2×C3C22×D3×D411yescharacteristic
594C2×C3C22×#23911yescharacteristic
595C2×C3C2×D3×#4111yescharacteristic
596C2×C3#596611yescharacteristic
597C2×C3#596811yescharacteristic
598D3—24no—
599D3—46no—
600D3—66no—
601D3—66no—
602D3—126no—
603C22—34no—
604C22—62no—
605C22—62no—
606C22—66no—
607C22—66no—
608C22—66no—
609C22—96no—
610C22—183no—
611C22—183no—
612C22—3624no—
613C22C23×D3211yescharacteristic
614C4—23no—
615C4—62no—
616C4—66no—
617C4—92no—
618C4—183no—
619C4—181no—
620C4C2×#380216yes—
621C4D3×#23912yescomplemented
622C3—21no—
623C3D4×#23911yescharacteristic, complemented
624C3#8676611yescharacteristic, complemented
625C2—64no—
626C2—126no—
627C2—186no—
628C2C22×#380211yescharacteristic
629C2C2×D3×#23911yescharacteristic
630C2#1059669811yescharacteristic
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. C4×#3832C2semidirect
3. C3×#5577C2semidirect
4. C3×Q8×D12C2semidirect
5. #10595409C2semidirect
6. #10594633C2semidirect
7. #10594632C2semidirect
8. #10594004C2semidirect
9. C4×#3802C2semidirect
10. #10593907C2semidirect
11. #10593869C2semidirect
15. C2×C3×#239C22semidirect
16. C2×C3×D3×Q8C22semidirect
19. C2×D3×D12C22semidirect
20. C2×C4×D32C22semidirect
21. C2×#3799C22semidirect
22. C2×#3796C22semidirect
23. C32×C4×Q8C22semidirect
24. Q8×C3⋊Dic3C22semidirect
25. #64102C22semidirect
26. #64101C22semidirect
27. C4×C4⋊(C3⋊D3)C22semidirect
28. C42×C3⋊D3C22semidirect
29. C3×#897C22semidirect
30. C3×#895C22semidirect
31. C3×#874C22semidirect
33. C3×C4×D12C22semidirect
34. C3×#869C22semidirect
35. #63922C22semidirect
36. #63921C22semidirect
37. #63916C22semidirect
38. #63916C22semidirect
39. #63908C22semidirect
40. #63902C22semidirect
41. C4×#625C22semidirect
42. #63900C22semidirect
44. #63898C22semidirect
45. #63898C22semidirect
46. #63863C22semidirect
47. #63856C22semidirect
48. #63854C22semidirect
63. #5577D3semidirect
64. Q8×D12D3semidirect
74. #3832D4semidirect
124. C2×#239C2×D3semidirect
125. C2×D3×Q8C2×D3semidirect
139. C3×C4×Q8C2×D3semidirect
140. C3×C4×Q8C2×D3semidirect
160. #897C2×D3semidirect
163. #895C2×D3semidirect
182. #874C2×D3semidirect
187. C4×D12C2×D3semidirect
191. #869C2×D3semidirect
198. C32×Q8C2×D4semidirect
205. C4⋊(C3⋊D3)C2×D4semidirect
208. C4×C3⋊D3C2×D4semidirect
214. C3×D12#41semidirect
340. C2×C3×D3C2×#41semidirect
344. C32×C4C2×#41semidirect
371. C4×Q8D32semidirect
400. C3×Q8D3×D4semidirect
401. C3×Q8D3×D4semidirect
442. D12#239semidirect
532. C2×D3C2×#239semidirect
542. C3×C4C2×#239semidirect
543. C3×C4D3×#41semidirect
555. C32D4×#41semidirect
563. Q8#3802semidirect
621. C4D3×#239semidirect
623. C3D4×#239semidirect
624. C3#86766semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C4×#38322
C3×#55772
C3×Q8×D122
#105954092
#105946332
#105946322
#105940042
C4×#38022
#105939072
#105938692
#867663
D4×#2393