Finite Group Databasebeta

← #11904787

Subgroups — #11904787

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 675 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×C3×D3×#41C211yesmaximal, characteristic, complemented
3C3×#5827C211yesmaximal, characteristic, complemented
4#10595414C212yesmaximal, complemented
5Q8×#626C212yesmaximal, complemented
6#10595248C216yesmaximal, complemented
7#10595246C216yesmaximal, complemented
8#10595043C213yesmaximal, complemented
9#10595023C213yesmaximal, complemented
10#10594856C213yesmaximal, complemented
11C2×#63857C213yesmaximal, complemented
12#87264—31nomaximal
13#85901—31nomaximal
14C2×C32×#41C2211yescharacteristic
15#64367—28no—
16C2×Q8×C3⋊D3C2212yescomplemented
17C2×#3830C2216yescomplemented
18C2×#3828C2213yescomplemented
19C22×#634C2213yescomplemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237C2213yes—
24C2×C3×D3×D4C2213yes—
25C2×C3×#235C2213yes—
26C22×C3×C4×D3C2213yes—
27C3×Q8×Dic3C2212yescomplemented
28C3×D4×Dic3C2216yescomplemented
29C3×#926C2213yescomplemented
30C2×C3×C4⋊Dic3C2213yescomplemented
31#63978C22112yescomplemented
32#63977C2216yes—
33#63966C2216yescomplemented
34C2×Dic3⋊Dic3C2216yescomplemented
35#63962C22112yescomplemented
36C2×(C2×D3)⋊Dic3C2216yes—
37#63916C2216yescomplemented
38#63909C2211yescharacteristic
39#63909C2213yescomplemented
40C4×#626C2216yes—
41C4×#626C2216yescomplemented
42#63871C2216yescomplemented
43#63866C2216yescomplemented
44#63860C2216yescomplemented
45#63857C2213yes—
46#63857C2216yes—
47#63857C2216yescomplemented
48#63857C2216yescomplemented
49#63857C2213yescomplemented
50C22×C3×#41—31no—
51C2×#1010—31no—
52C2×#1010—31no—
53C2×#1010—61no—
54C2×D3×#41D311yescharacteristic, complemented
55C3×#520—31no—
56#5833—33no—
57#5831—32no—
58#5827D311yescharacteristic, complemented
59#5825—33no—
60#5824—36no—
61Q8×#67—32no—
62#5806—36no—
63#5791—33no—
64C2×#924—33no—
65#5576—32no—
66Q8×D12—32no—
67#5555—36no—
68#5554—36no—
69#5526—33no—
70#5524—33no—
71#5510—33no—
72C2×#897—33no—
73C23×C3×D3C2313yes—
74C32×#41D418yescomplemented
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4C2313yes—
77C22×C32×C4C2313yes—
78C2×#638C2316yes—
79C22×C3⋊Dic3C2316yes—
80Q8×C3⋊D3—28no—
81#3830—224no—
82#3828—212no—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3C2316yes—
85C2×#634—212no—
86C2×#634C2313yes—
87C2×#634C2316yes—
88C2×C3×#67C2316yes—
89C22×C3×Dic3C2313yes—
90C22×C3×Dic3C2316yes—
91C3×#239—24no—
92C3×D3×Q8—24no—
93C3×#237—212no—
94C3×D3×D4—212no—
95C3×#235—212no—
96C2×C3×D12C2313yes—
97C2×C3×C4×D3—212no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2313yes—
100C2×C3×C4×D3C2313yes—
101C2×C3×C4×D3C2313yes—
102C2×C3×Dic6C2313yes—
103C2×#626C2312yes—
104C2×#626C2316yes—
105C3×#217C2316yes—
106C3×C4⋊Dic3C2313yes—
107C3×C4⋊Dic3C2316yes—
108C3×C4⋊Dic3C2311yescharacteristic
109C3×C4×Dic3C2316yes—
110Dic3⋊Dic3C2316yes—
111Dic3⋊Dic3C23112yes—
112Dic3⋊Dic3C2316yes—
113#3722C2316yes—
114#3722C2312yes—
115(C2×D3)⋊Dic3C2316yes—
116(C2×D3)⋊Dic3C23112yes—
117(C2×D3)⋊Dic3C2316yes—
118#3489—91noSylow
119C2×C3×#41—21no—
120C2×C3×#41—31no—
121C2×C3×#41—33no—
122C2×C3×#41—33no—
123C2×C3×#41—68no—
124C2×C3×#41C2×D311yescharacteristic
125C2×C3×#41C2×D311yescharacteristic
126C22×C3×Q8—31no—
127C22×C3×D4—33no—
128C23×C3×C4—33no—
129#1010—616no—
130#1010—68no—
131#1010—68no—
132D3×#41—28no—
133C2×#239C2×D311yescharacteristic
134C2×D3×Q8—32no—
135C2×D3×Q8—32no—
136C2×D3×Q8—62no—
137C2×D3×Q8C2×D311yescharacteristic
138C2×#237—36no—
139C2×#237—36no—
140C2×#237—66no—
141C2×#237C2×D313yes—
142C2×D3×D4C2×D313yes—
143C2×#235—33no—
144C2×#235—33no—
145C2×#235—63no—
146C2×#235C2×D313yes—
147C22×C4×D3C2×D313yes—
148C22×Dic6—33no—
149C22×Dic6—33no—
150C22×Dic6—63no—
151C3×C4×Q8—32no—
152C3×C4×D4—36no—
153C3×#117—33no—
154C2×C3×C4⋊C4—33no—
155#953—36no—
156C2×#217—36no—
157#946—36no—
158Q8×Dic3C2×D312yescomplemented
159#944—36no—
160#939—312no—
161#938—36no—
162#936—36no—
163#935—312no—
164D4×Dic3C2×D316yescomplemented
165#930—312no—
166#930—31no—
167#930—33no—
168#929—36no—
169C4×#67—36no—
170C4×#67—36no—
171C2×(C2×D3)⋊C4—36no—
172#926C2×D313yescomplemented
173C2×C4⋊Dic3—36no—
174C2×C4⋊Dic3C2×D313yescomplemented
175#924—33no—
176#924—36no—
177#924—36no—
178#924—36no—
179#924—33no—
180C2×Dic3⋊C4—36no—
181#897—33no—
182#897—36no—
183#897—36no—
184#897—36no—
185#897—33no—
186#897—36no—
187#895—36no—
188#895—33no—
189#895—31no—
190#886—312no—
191#886—36no—
192#882—36no—
193#875—36no—
194C4×D12—36no—
195C4×D12—36no—
196#869—36no—
197C23×C32C2413yes—
198C22×C3⋊D3C2412yes—
199C22×C3×D3—26no—
200C22×C3×D3—26no—
201C22×C3×D3—43no—
202C22×C3×D3C2413yes—
203C22×C3×D3C2411yescharacteristic
204C32×Q8C2×D414yes—
205C32×D4C2×D4112yes—
206C2×C32×C4C2×D4112yes—
207C2×C32×C4C2413yes—
208C2×C32×C4C2411yescharacteristic
209#638—212no—
210C2×C3⋊Dic3—212no—
211C2×C3⋊Dic3C2416yes—
212C4⋊(C3⋊D3)—22no—
213C4×C3⋊D3—212no—
214#634—26no—
215#634—212no—
216C3×#67—212no—
217C2×C3×Dic3—26no—
218C2×C3×Dic3—46no—
219C2×C3×Dic3C2412yes—
220C2×C3×Dic3C2416yes—
221C2×C3×Dic3C2413yes—
222C2×C3×Dic3C2411yescharacteristic
223C3×D12—26no—
224C3×C4×D3—22no—
225C3×C4×D3—26no—
226C3×C4×D3—26no—
227C3×C4×D3—26no—
228C3×Dic6—26no—
229#626—24no—
230#626—46no—
231C2×2−1+4—91no—
232C22×#41—31no—
233D4×Q8—92no—
234#548—92no—
235#547—96no—
236#546—96no—
237#537—93no—
238#536—93no—
239#525—93no—
240C2×C22⋊Q8—93no—
241#520—31no—
242C24×C3—33no—
243C23×D3C22×D313yes—
244C3×#41—28no—
245C3×#41—64no—
246C3×#41—612no—
247C3×#41—612no—
248C3×#41D1218yescomplemented
249C3×#41#6718yescomplemented
250C2×C3×Q8—21no—
251C2×C3×Q8—33no—
252C2×C3×Q8—64no—
253C2×C3×Q8C22×D311yescharacteristic
254C2×C3×Q8C22×D311yescharacteristic
255C2×C3×D4—23no—
256C2×C3×D4—36no—
257C2×C3×D4—33no—
258C2×C3×D4—612no—
259C2×C3×D4C22×D313yes—
260C2×C3×D4C22×D313yes—
261C22×C3×C4—23no—
262C22×C3×C4—33no—
263C22×C3×C4—36no—
264C22×C3×C4—31no—
265C22×C3×C4—33no—
266C22×C3×C4—33no—
267C22×C3×C4—33no—
268C22×C3×C4—612no—
269C22×C3×C4C22×D313yes—
270C22×C3×C4C22×D313yes—
271C2×#67—36no—
272C2×#67—36no—
273C2×#67—32no—
274C2×#67—36no—
275C2×#67—66no—
276C2×#67C22×D316yes—
277C22×Dic3—36no—
278C22×Dic3—36no—
279C22×Dic3—66no—
280C22×Dic3C22×D313yes—
281C22×Dic3C22×D316yes—
282#239—24no—
283D3×Q8—24no—
284D3×Q8—616no—
285D3×Q8—68no—
286D3×Q8—68no—
287#237—212no—
288#237—648no—
289#237—624no—
290#237—624no—
291D3×D4—212no—
292#235—212no—
293#235—624no—
294#235—612no—
295#235—612no—
296C2×D12—32no—
297C2×D12—31no—
298C2×D12—31no—
299C2×D12—36no—
300C2×D12—61no—
301C2×D12C22×D313yes—
302C2×C4×D3—212no—
303C2×C4×D3—36no—
304C2×C4×D3—36no—
305C2×C4×D3—66no—
306C2×C4×D3C22×D313yes—
307C2×C4×D3C22×D313yes—
308C2×C4×D3C22×D311yescharacteristic
309C2×C4×D3C22×D313yes—
310C2×Dic6—36no—
311C2×Dic6—33no—
312C2×Dic6—33no—
313C2×Dic6—36no—
314C2×Dic6—63no—
315C2×Dic6—66no—
316C2×Dic6—624no—
317C2×Dic6—612no—
318C2×Dic6—612no—
319C2×Dic6C22×D313yes—
320C3×C4⋊C4—33no—
321C3×C4⋊C4—36no—
322C3×C4⋊C4—31no—
323C3×C22⋊C4—36no—
324C3×C42—36no—
325#217—36no—
326#217—312no—
327#217—36no—
328#217C22×D316yes—
329(C2×D3)⋊C4—36no—
330(C2×D3)⋊C4—36no—
331(C2×D3)⋊C4—312no—
332(C2×D3)⋊C4—32no—
333(C2×D3)⋊C4—36no—
334(C2×D3)⋊C4—32no—
335(C2×D3)⋊C4—36no—
336C4⋊Dic3—36no—
337C4⋊Dic3—312no—
338C4⋊Dic3—36no—
339C4⋊Dic3C22×D313yes—
340C4⋊Dic3C22×D311yescharacteristic
341C4⋊Dic3C22×D316yes—
342Dic3⋊C4—36no—
343Dic3⋊C4—312no—
344Dic3⋊C4—36no—
345C4×Dic3C22×D316yes—
346C22×C32—23no—
347C22×C32—23no—
348C22×C32C22×D416yes—
349C22×C32C2511yescharacteristic
350C2×C3⋊D3—22no—
351C2×C3⋊D3—22no—
352C2×C3⋊D3—22no—
353C2×C3×D3—21no—
354C2×C3×D3—21no—
355C2×C3×D3—23no—
356C2×C3×D3—23no—
357C2×C3×D3—23no—
358C2×C3×D3—412no—
359C2×C3×D32−1+412yescomplemented
360C32×C4C22×D416yes—
361C32×C4C22×D412yes—
362C3⋊Dic3—26no—
363C3×Dic3—23no—
364C3×Dic3—21no—
365C3×Dic3—22no—
366C3×Dic3—26no—
3672−1+4—188no—
368C2×#41—31no—
369C2×#41—33no—
370C2×#41—33no—
371C2×#41—68no—
372C2×#41—96no—
373C2×#41—93no—
374C2×#41D3211yescharacteristic
375C22×Q8—31no—
376C22×Q8—92no—
377C22×Q8—93no—
378C22×D4—33no—
379C23×C4—33no—
380C4⋊Q8—96no—
381#124—96no—
382#123—96no—
383#123—912no—
384C22⋊Q8—93no—
385C22⋊Q8—96no—
386C22⋊Q8—96no—
387C22⋊Q8—96no—
388C22⋊Q8—93no—
389C22⋊Q8—96no—
390#121—91no—
391#121—93no—
392#121—96no—
393#121—912no—
394#120—96no—
395C4×Q8—32no—
396C4×D4—36no—
397C4×D4—96no—
398C4×D4—96no—
399#117—33no—
400C2×C4⋊C4—33no—
401C2×C4⋊C4—96no—
402C2×C22⋊C4—96no—
403C23×C3—23no—
404C23×C3—31no—
405C23×C3—33no—
406C23×C3—66no—
407C23×C3—66no—
408C23×C3—123no—
409C23×C3C23×D313yes—
410C23×C3C23×D313yes—
411C22×D3—26no—
412C22×D3—26no—
413C22×D3—32no—
414C22×D3—32no—
415C22×D3—43no—
416C22×D3—62no—
417C22×D3C23×D313yes—
418C22×D3C23×D311yescharacteristic
419C3×Q8—24no—
420C3×Q8—66no—
421C3×Q8C2×D1214yes—
422C3×Q8C2×#6714yes—
423C3×D4—212no—
424C3×D4—612no—
425C3×D4—66no—
426C3×D4C2×D12112yes—
427C3×D4C2×#67112yes—
428C2×C3×C4—21no—
429C2×C3×C4—23no—
430C2×C3×C4—212no—
431C2×C3×C4—31no—
432C2×C3×C4—33no—
433C2×C3×C4—32no—
434C2×C3×C4—36no—
435C2×C3×C4—66no—
436C2×C3×C4—62no—
437C2×C3×C4—66no—
438C2×C3×C4—66no—
439C2×C3×C4—66no—
440C2×C3×C4—126no—
441C2×C3×C4C2×D12112yes—
442C2×C3×C4C2×#67112yes—
443C2×C3×C4C23×D313yes—
444C2×C3×C4C23×D311yescharacteristic
445C2×C3×C4C23×D313yes—
446C2×C3×C4C23×D311yescharacteristic
447#67—212no—
448#67—64no—
449#67—624no—
450#67—612no—
451#67—612no—
452#67—126no—
453C2×Dic3—26no—
454C2×Dic3—36no—
455C2×Dic3—36no—
456C2×Dic3—46no—
457C2×Dic3—66no—
458C2×Dic3—624no—
459C2×Dic3—612no—
460C2×Dic3—612no—
461C2×Dic3C23×D312yes—
462C2×Dic3C23×D316yes—
463C2×Dic3C23×D313yes—
464C2×Dic3C23×D311yescharacteristic
465D12—26no—
466D12—64no—
467D12—64no—
468D12—62no—
469D12—62no—
470D12—126no—
471C4×D3—22no—
472C4×D3—26no—
473C4×D3—26no—
474C4×D3—26no—
475C4×D3—624no—
476C4×D3—612no—
477C4×D3—612no—
478Dic6—26no—
479Dic6—612no—
480Dic6—624no—
481Dic6—66no—
482Dic6—612no—
483Dic6—66no—
484Dic6—612no—
485C2×C32—26no—
486C2×C32C23×D411yescharacteristic
487C2×C32C2×2−1+411yescharacteristic
488C2×C32#58511yescharacteristic
489C3⋊D3—42no—
490C3×D3—22no—
491C3×D3—43no—
492C24—33no—
493#41—64no—
494#41—612no—
495#41—612no—
496#41—1824no—
497#41—1812no—
498#41#62618yescomplemented
499C2×Q8—33no—
500C2×Q8—64no—
501C2×Q8—93no—
502C2×Q8—96no—
503C2×Q8—188no—
504C2×Q8—1812no—
505C2×Q8C2×D3211yescharacteristic
506C2×D4—36no—
507C2×D4—33no—
508C2×D4—612no—
509C2×D4—92no—
510C2×D4—96no—
511C2×D4—96no—
512C2×D4—91no—
513C2×D4C2×D3213yes—
514C22×C4—33no—
515C22×C4—36no—
516C22×C4—33no—
517C22×C4—33no—
518C22×C4—31no—
519C22×C4—33no—
520C22×C4—612no—
521C22×C4—96no—
522C22×C4—96no—
523C22×C4C2×D3213yes—
524C4⋊C4—33no—
525C4⋊C4—36no—
526C4⋊C4—31no—
527C4⋊C4—96no—
528C4⋊C4—912no—
529C4⋊C4—96no—
530C22⋊C4—36no—
531C22⋊C4—92no—
532C22⋊C4—96no—
533C22⋊C4—96no—
534C22⋊C4—912no—
535C22⋊C4—96no—
536C42—36no—
537C22×C3—23no—
538C22×C3—23no—
539C22×C3—23no—
540C22×C3—23no—
541C22×C3—26no—
542C22×C3—21no—
543C22×C3—32no—
544C22×C3—43no—
545C22×C3—43no—
546C22×C3—61no—
547C22×C3—61no—
548C22×C3—63no—
549C22×C3—63no—
550C22×C3—63no—
551C22×C3—1212no—
552C22×C3C22×D1216yes—
553C22×C3C22×#6716yes—
554C22×C3C24×D311yescharacteristic
555C22×C3C24×D311yescharacteristic
556C2×D3—21no—
557C2×D3—21no—
558C2×D3—23no—
559C2×D3—23no—
560C2×D3—23no—
561C2×D3—412no—
562C2×D3—64no—
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—62no—
568C2×D3—62no—
569C2×D3—122no—
570C2×D3—122no—
571C2×D3#101012yescomplemented
572C3×C4—22no—
573C3×C4—26no—
574C3×C4—61no—
575C3×C4—63no—
576C3×C4—62no—
577C3×C4—66no—
578C3×C4C22×D1212yes—
579C3×C4C22×D1216yes—
580C3×C4C22×#6716yes—
581C3×C4C22×#6712yes—
582Dic3—26no—
583Dic3—22no—
584Dic3—23no—
585Dic3—21no—
586Dic3—612no—
587Dic3—66no—
588Dic3—66no—
589C32#348911yescharacteristic, complemented, Sylow
590C23—31no—
591C23—33no—
592C23—66no—
593C23—66no—
594C23—92no—
595C23—123no—
596C23C22×D3213yes—
597Q8—66no—
598Q8—186no—
599Q8—1812no—
600Q8C2×#62614yes—
601D4—612no—
602D4—66no—
603D4—184no—
604D4—1812no—
605D4—182no—
606D4—366no—
607D4C2×#626112yes—
608C2×C4—32no—
609C2×C4—36no—
610C2×C4—31no—
611C2×C4—33no—
612C2×C4—66no—
613C2×C4—62no—
614C2×C4—66no—
615C2×C4—66no—
616C2×C4—66no—
617C2×C4—96no—
618C2×C4—126no—
619C2×C4—1812no—
620C2×C4—1812no—
621C2×C4C2×#626112yes—
622C2×C4C22×D3213yes—
623C2×C4C22×D3211yescharacteristic
624C2×C3—26no—
625C2×C3—26no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—46no—
630C2×C3—62no—
631C2×C3—123no—
632C2×C3C23×D1211yescharacteristic
633C2×C3C2×#101011yescharacteristic
634C2×C3#596411yescharacteristic
635C2×C3#596611yescharacteristic
636C2×C3D3×2−1+411yescharacteristic
637C2×C3C23×#6711yescharacteristic
638D3—22no—
639D3—43no—
640D3—124no—
641D3—122no—
642D3—122no—
643C22—23no—
644C22—23no—
645C22—32no—
646C22—61no—
647C22—61no—
648C22—63no—
649C22—63no—
650C22—63no—
651C22—1212no—
652C22—182no—
653C22—182no—
654C22—182no—
655C22C22×#62616yes—
656C22C23×D3211yescharacteristic
657C4—62no—
658C4—66no—
659C4—61no—
660C4—63no—
661C4—186no—
662C4C22×#62612yes—
663C4C22×#62616yes—
664C3—21no—
665C3#8590111yescharacteristic, complemented
666C3#8726411yescharacteristic, complemented
667C2—26no—
668C2—62no—
669C2—123no—
670C2—362no—
671C2D3×#101011yescharacteristic
672C2#1059669611yescharacteristic
673C2C23×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×C3×D3×#41C2semidirect
3. C3×#5827C2semidirect
4. #10595414C2semidirect
5. Q8×#626C2semidirect
6. #10595248C2semidirect
7. #10595246C2semidirect
8. #10595043C2semidirect
9. #10595023C2semidirect
10. #10594856C2semidirect
11. C2×#63857C2semidirect
16. C2×Q8×C3⋊D3C22semidirect
17. C2×#3830C22semidirect
18. C2×#3828C22semidirect
19. C22×#634C22semidirect
27. C3×Q8×Dic3C22semidirect
28. C3×D4×Dic3C22semidirect
29. C3×#926C22semidirect
30. C2×C3×C4⋊Dic3C22semidirect
31. #63978C22semidirect
33. #63966C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
35. #63962C22semidirect
37. #63916C22semidirect
39. #63909C22semidirect
41. C4×#626C22semidirect
42. #63871C22semidirect
43. #63866C22semidirect
44. #63860C22semidirect
47. #63857C22semidirect
48. #63857C22semidirect
49. #63857C22semidirect
54. C2×D3×#41D3semidirect
58. #5827D3semidirect
74. C32×#41D4semidirect
158. Q8×Dic3C2×D3semidirect
164. D4×Dic3C2×D3semidirect
172. #926C2×D3semidirect
174. C2×C4⋊Dic3C2×D3semidirect
248. C3×#41D12semidirect
249. C3×#41#67semidirect
359. C2×C3×D32−1+4semidirect
498. #41#626semidirect
571. C2×D3#1010semidirect
589. C32#3489semidirect
665. C3#85901semidirect
666. C3#87264semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C2×C3×D3×#412
C3×#58272
#105954142
Q8×#6262
#105952482
#105952462
#105950432
#105950232
#105948562
C2×#638572
#872643
#859013