Finite Group Databasebeta

← #11886916

Subgroups — #11886916

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 679 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596240C211yesmaximal, characteristic, complemented
2C3×#5769C211yesmaximal, characteristic, complemented
3#10595449C212yesmaximal, complemented
4C3×#5196C211yesmaximal, characteristic, complemented
5#10591677C212yesmaximal, complemented
6#10591667C212yesmaximal, complemented
7#10591666C212yesmaximal, complemented
8#10590929C211yesmaximal, characteristic, complemented
9#10590927C211yesmaximal, characteristic, complemented
10#10590923C211yesmaximal, characteristic, complemented
11#10590880C211yesmaximal, characteristic, complemented
12#84010—31nomaximal
13#79894—31nomaximal
14#64366C2212yescomplemented
15C3×#1009C2212yescomplemented
16C32×#135C2211yescharacteristic
17#64158C2212yescomplemented
18#64128—21no—
19#64123—22no—
20D8×C3⋊D3—21no—
21C2×#3745C2211yescharacteristic, complemented
22#64110C2211yescharacteristic, complemented
23C3×#949C2212yescomplemented
24C3×#948C2212yescomplemented
25C3×#919—21no—
26C3×#914—22no—
27C3×D3×D8—21no—
28C2×C3×D24C2211yescharacteristic, complemented
29C3×#901C2211yescharacteristic, complemented
30#63911C2212yescomplemented
31#63830—22no—
32#63830C2212yescomplemented
33#63829—22no—
34#63829C2211yescharacteristic
35#63825—22no—
36#63825C2212yescomplemented
37C2×#3714—22no—
38C2×#3714C2212yescomplemented
39C3×#837C2212yescomplemented
40C3×#819C2211yescharacteristic, complemented
41C3×C8×Dic3C2211yescharacteristic, complemented
42#63577C2211yescharacteristic, complemented
43#63570C2211yescharacteristic, complemented
44#63569C2211yescharacteristic, complemented
45#63559C2212yescomplemented
46#63558C2212yescomplemented
47C3×#576—31no—
48#5835—32no—
49#5769—31no—
50#5769—31no—
51#5769—61no—
52#5769D311yescharacteristic, complemented
53#5752—32no—
54C3×#443—31no—
55#5241—32no—
56#5199—32no—
57#5198—32no—
58#5196D311yescharacteristic, complemented
59#5160—31no—
60#5151—31no—
61#5144—31no—
62#5142—32no—
63#5142—31no—
64#4897—31no—
65#4897—31no—
66#4822—32no—
67#4822—32no—
68#4700—31no—
69#4695—31no—
70C32×#41C2312yes—
71#3832—22no—
72D4×C3⋊D3—22no—
73D4×C3⋊D3—42no—
74#3828—22no—
75#3828C2311yescharacteristic
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4⋊(C3⋊D3)C2312yes—
78C3×#239—22no—
79C3×D3×D4—22no—
80C3×D3×D4—42no—
81C3×#235—22no—
82C3×#235C2311yescharacteristic
83C2×C3×D12—22no—
84C2×C3×D12C2312yes—
85C2×#626—42no—
86C32×Q16D411yescharacteristic, complemented
87C32×SD16D412yescomplemented
88C32×D8D411yescharacteristic, complemented
89C2×C32×C8C2311yescharacteristic
90#3755—22no—
91#3753—22no—
92#3748C2311yescharacteristic
93#3745—21no—
94#3745—21no—
95#3743—21no—
96C8×C3⋊D3—21no—
97C3×#215—22no—
98C3×#213—22no—
99C3×C4×Dic3C2311yescharacteristic
100C3×#208—22no—
101C3×#208C2311yescharacteristic
102C3×#208C2312yes—
103C2×C3×C3⋊C8—22no—
104C2×C3×C3⋊C8C2311yescharacteristic
105C3×D24—21no—
106C3×D24—21no—
107C3×ΓL(1,𝔽25)—21no—
108C3×D3×C8—21no—
109#3719D411yescharacteristic, complemented
110#3717—22no—
111#3717D411yescharacteristic, complemented
112#3716—22no—
113#3716D411yescharacteristic, complemented
114#3714—22no—
115#3714—22no—
116#3714—22no—
117#3714—22no—
118#3714D411yescharacteristic, complemented
119#3292—91noSylow
120C3×H(5,𝔽2)—32no—
121#1009—32no—
122#1009—32no—
123#1009—62no—
124#1009C2×D312yescomplemented
125C3×AGL(1,ℤ/8)—32no—
126C3×AGL(1,ℤ/8)—62no—
127C3×#135—21no—
128C3×#135—61no—
129C3×#135C2×D311yescharacteristic
130C3×#135C2×D311yescharacteristic
131C2×C3×D8—31no—
132C2×C3×D8—61no—
133C3×#131—32no—
134C3×#131—31no—
135#950—31no—
136#950—62no—
137#949—32no—
138#949—32no—
139#949—32no—
140#949—62no—
141#949—62no—
142#949C2×D312yescomplemented
143#948C2×D312yescomplemented
144#940—32no—
145#932—32no—
146#932—62no—
147C2×#213—32no—
148C2×#213—62no—
149#919—21no—
150#919—62no—
151#919—61no—
152#919—61no—
153#914—22no—
154#914—64no—
155#914—62no—
156#914—62no—
157D3×D8—21no—
158D3×D8—62no—
159D3×D8—61no—
160D3×D8—61no—
161#908—32no—
162#908—32no—
163#908—62no—
164#908—62no—
165#904—31no—
166#904—62no—
167C2×D24—32no—
168C2×D24—31no—
169C2×D24—31no—
170C2×D24—61no—
171C2×D24—62no—
172C2×D24C2×D311yescharacteristic, complemented
173#901—31no—
174#901—31no—
175#901—61no—
176#901C2×D311yescharacteristic, complemented
177#874—32no—
178C3×#108—31no—
179C3×#104—32no—
180C3×C4×C8—31no—
181#837—31no—
182#837C2×D312yescomplemented
183#833—32no—
184#825—31no—
185#823—32no—
186#823—32no—
187#823—32no—
188#822—31no—
189#819—31no—
190#819C2×D311yescharacteristic, complemented
191C8×Dic3C2×D311yescharacteristic, complemented
192#805—31no—
193#805—31no—
194C22×C3⋊D3—22no—
195C22×C3⋊D3—42no—
196C22×C3×D3—22no—
197C22×C3×D3—42no—
198C32×Q8C2×D412yes—
199C32×D4—22no—
200C32×D4C2×D412yes—
201C2×C32×C4—22no—
202C2×C32×C4C2411yescharacteristic
203#638—21no—
204#638—42no—
205C4⋊(C3⋊D3)—22no—
206C4⋊(C3⋊D3)—22no—
207C4⋊(C3⋊D3)—42no—
208C4⋊(C3⋊D3)C2×D411yescharacteristic
209C4×C3⋊D3—21no—
210C4×C3⋊D3—42no—
211#634C2×D411yescharacteristic
212C3×#67—21no—
213C3×#67—42no—
214C2×C3×Dic3—21no—
215C3×D12—22no—
216C3×D12—22no—
217C3×D12—42no—
218C3×D12C2×D411yescharacteristic
219C3×C4×D3—21no—
220C3×C4×D3—42no—
221C3×Dic6C2×D411yescharacteristic
222#626—84no—
223C32×C8C2×D411yescharacteristic
224C32×C8C2×D411yescharacteristic
225C3⋊(C3⋊C8)—21no—
226C3×C3⋊C8—22no—
227C3×C3⋊C8—21no—
228C3×C3⋊C8C2×D411yescharacteristic
229C3×C3⋊C8C2×D411yescharacteristic
230#576—31no—
231#576—92no—
232#576—91no—
233#493—91no—
234#472—91no—
235#472—91no—
236#472—92no—
237#453—92no—
238#453—92no—
239#443—31no—
240#443—91no—
241C3×#41—22no—
242C3×#41—31no—
243C3×#41—62no—
244C3×#41—62no—
245C3×#41C22×D312yes—
246C3×#41C22×D312yes—
247C2×C3×D4—32no—
248C2×C3×D4—62no—
249C2×C3×D4—62no—
250C2×C3×D4—122no—
251C2×#67—122no—
252#239—22no—
253#239—64no—
254#239—62no—
255#239—62no—
256D3×D4—22no—
257D3×D4—42no—
258D3×D4—64no—
259D3×D4—62no—
260D3×D4—62no—
261D3×D4—122no—
262D3×D4—122no—
263D3×D4—124no—
264#235—22no—
265#235—31no—
266#235—31no—
267#235—61no—
268#235—62no—
269#235—62no—
270#235—122no—
271#235C22×D311yescharacteristic
272C2×D12—22no—
273C2×D12—32no—
274C2×D12—32no—
275C2×D12—62no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—122no—
279C2×D12—122no—
280C2×D12C22×D312yes—
281C3×Q16—21no—
282C3×Q16D1211yescharacteristic, complemented
283C3×Q16#6711yescharacteristic, complemented
284C3×SD16—22no—
285C3×SD16—62no—
286C3×SD16D1212yescomplemented
287C3×SD16#6712yescomplemented
288C3×D8—21no—
289C3×D8—62no—
290C3×D8—61no—
291C3×D8—61no—
292C3×D8D1211yescharacteristic, complemented
293C3×D8#6711yescharacteristic, complemented
294C3×M16—31no—
295C3×M16—32no—
296C3×M16—62no—
297C3×M16—61no—
298C2×C3×C8—21no—
299C2×C3×C8—31no—
300C2×C3×C8—62no—
301C2×C3×C8—61no—
302C2×C3×C8C22×D311yescharacteristic
303C2×C3×C8C22×D311yescharacteristic
304C3×C42—31no—
305#216—31no—
306#215—22no—
307#215—31no—
308#215—62no—
309#215—64no—
310#215—62no—
311#215—62no—
312#214—31no—
313#214—62no—
314#213—22no—
315#213—31no—
316#213—62no—
317#213—62no—
318#213—64no—
319#213—62no—
320#213—62no—
321#213—62no—
322#213—62no—
323C4×Dic3C22×D311yescharacteristic
324#208—22no—
325#208—31no—
326#208—31no—
327#208—61no—
328#208C22×D311yescharacteristic
329#208C22×D312yes—
330C2×C3⋊C8—22no—
331C2×C3⋊C8C22×D311yescharacteristic
332Dic12—31no—
333D24—21no—
334D24—21no—
335D24—31no—
336D24—62no—
337D24—62no—
338D24—62no—
339D24—62no—
340D24—62no—
341D24—62no—
342D24—61no—
343D24—61no—
344D24—61no—
345D24—61no—
346#204—31no—
347#204—31no—
348#204—62no—
349#204—62no—
350ΓL(1,𝔽25)—21no—
351ΓL(1,𝔽25)—62no—
352ΓL(1,𝔽25)—61no—
353ΓL(1,𝔽25)—61no—
354D3×C8—21no—
355D3×C8—62no—
356D3×C8—61no—
357D3×C8—61no—
358C22×C32—22no—
359C22×C32H(5,𝔽2)11yescharacteristic
360C2×C3⋊D3—21no—
361C2×C3⋊D3—42no—
362C2×C3⋊D3—82no—
363C2×C3⋊D3—162no—
364C2×C3×D3—21no—
365C2×C3×D3—42no—
366C2×C3×D3—82no—
367C2×C3×D3—162no—
368C32×C4—22no—
369C32×C4C22×D411yescharacteristic
370C32×C4C22×D411yescharacteristic
371C3⋊Dic3—21no—
372C3×Dic3—22no—
373C3×Dic3—21no—
374H(5,𝔽2)—32no—
375H(5,𝔽2)—92no—
376AGL(1,ℤ/8)—32no—
377AGL(1,ℤ/8)—62no—
378AGL(1,ℤ/8)—92no—
379AGL(1,ℤ/8)—92no—
380AGL(1,ℤ/8)—92no—
381AGL(1,ℤ/8)—182no—
382AGL(1,ℤ/8)—182no—
383AGL(1,ℤ/8)—182no—
384#135—61no—
385#135—91no—
386#135—182no—
387#135—181no—
388#135D3211yescharacteristic
389C2×D8—31no—
390C2×D8—61no—
391C2×D8—92no—
392C2×D8—91no—
393C2×D8—182no—
394C2×D8—181no—
395#131—32no—
396#131—31no—
397#131—91no—
398#127—92no—
399#108—31no—
400#108—91no—
401#104—32no—
402#104—91no—
403#104—91no—
404#100—92no—
405#100—92no—
406C4×C8—31no—
407C23×C3—62no—
408C23×C3—122no—
409C22×D3—22no—
410C22×D3—42no—
411C22×D3—62no—
412C22×D3—62no—
413C22×D3—122no—
414C22×D3—122no—
415C22×D3—122no—
416C22×D3—124no—
417C3×Q8—22no—
418C3×Q8—31no—
419C3×Q8C2×D1212yes—
420C3×Q8C2×#6712yes—
421C3×D4—22no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—31no—
425C3×D4—42no—
426C3×D4—61no—
427C3×D4—62no—
428C3×D4—62no—
429C3×D4—122no—
430C3×D4—122no—
431C3×D4C2×D1212yes—
432C3×D4C2×#6712yes—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—42no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—122no—
440C2×C3×C4C23×D311yescharacteristic
441C2×C3×C4C23×D311yescharacteristic
442#67—21no—
443#67—42no—
444#67—62no—
445#67—61no—
446#67—61no—
447#67—122no—
448#67—122no—
449#67—124no—
450#67—244no—
451C2×Dic3—21no—
452D12—22no—
453D12—22no—
454D12—31no—
455D12—31no—
456D12—42no—
457D12—61no—
458D12—64no—
459D12—62no—
460D12—62no—
461D12—62no—
462D12—62no—
463D12—122no—
464D12—122no—
465D12—122no—
466D12—124no—
467D12—244no—
468D12D3×D411yescharacteristic
469C4×D3—21no—
470C4×D3—42no—
471C4×D3—62no—
472C4×D3—61no—
473C4×D3—61no—
474C4×D3—122no—
475C4×D3—122no—
476C4×D3—124no—
477Dic6—31no—
478Dic6—31no—
479Dic6—61no—
480Dic6D3×D411yescharacteristic
481C3×C8—21no—
482C3×C8—21no—
483C3×C8—31no—
484C3×C8—31no—
485C3×C8—61no—
486C3×C8—62no—
487C3×C8C2×D1211yescharacteristic
488C3×C8C2×D1211yescharacteristic
489C3×C8C2×#6711yescharacteristic
490C3×C8C2×#6711yescharacteristic
491C3⋊C8—22no—
492C3⋊C8—21no—
493C3⋊C8—62no—
494C3⋊C8—61no—
495C3⋊C8—61no—
496C3⋊C8D3×D411yescharacteristic
497C3⋊C8D3×D411yescharacteristic
498C2×C32—21no—
499C2×C32—42no—
500C2×C32D4211yescharacteristic
501C3⋊D3—41no—
502C3⋊D3—82no—
503C3×D3—41no—
504C3×D3—82no—
505#41—31no—
506#41—62no—
507#41—62no—
508#41—91no—
509#41—182no—
510#41—182no—
511#41C2×D3212yes—
512C2×D4—32no—
513C2×D4—62no—
514C2×D4—62no—
515C2×D4—92no—
516C2×D4—122no—
517C2×D4—182no—
518C2×D4—182no—
519C2×D4—362no—
520C2×D4—362no—
521Q16—91no—
522Q16#62611yescharacteristic, complemented
523SD16—62no—
524SD16—91no—
525SD16—91no—
526SD16—182no—
527SD16—182no—
528SD16—182no—
529SD16#62612yescomplemented
530D8—62no—
531D8—61no—
532D8—61no—
533D8—91no—
534D8—182no—
535D8—182no—
536D8—182no—
537D8—182no—
538D8—182no—
539D8—181no—
540D8—181no—
541D8#62611yescharacteristic, complemented
542M16—32no—
543M16—31no—
544M16—62no—
545M16—61no—
546M16—91no—
547M16—181no—
548C2×C8—31no—
549C2×C8—62no—
550C2×C8—61no—
551C2×C8—181no—
552C2×C8C2×D3211yescharacteristic
553C42—31no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—21no—
557C22×C3—42no—
558C22×C3—61no—
559C22×C3—122no—
560C22×C3—242no—
561C22×C3—482no—
562C22×C3#100411yescharacteristic
563C22×C3#100911yescharacteristic
564C2×D3—21no—
565C2×D3—42no—
566C2×D3—62no—
567C2×D3—61no—
568C2×D3—61no—
569C2×D3—82no—
570C2×D3—124no—
571C2×D3—122no—
572C2×D3—122no—
573C2×D3—162no—
574C2×D3—242no—
575C2×D3—242no—
576C2×D3—482no—
577C2×D3—482no—
578C2×D3—482no—
579C2×D3—484no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—42no—
585C3×C4—62no—
586C3×C4—61no—
587C3×C4C22×D1211yescharacteristic
588C3×C4C2×D3×D411yescharacteristic
589C3×C4C2×D3×D411yescharacteristic
590C3×C4C22×#6711yescharacteristic
591Dic3—22no—
592Dic3—21no—
593Dic3—62no—
594Dic3—61no—
595Dic3—61no—
596C32#329211yescharacteristic, complemented, Sylow
597C23—62no—
598C23—122no—
599C23—182no—
600C23—362no—
601Q8—31no—
602Q8—91no—
603Q8C2×#62612yes—
604D4—22no—
605D4—31no—
606D4—61no—
607D4—62no—
608D4—62no—
609D4—91no—
610D4—122no—
611D4—122no—
612D4—181no—
613D4—182no—
614D4—182no—
615D4—362no—
616D4—362no—
617D4—724no—
618D4C2×#62612yes—
619C2×C4—22no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—122no—
623C2×C4—181no—
624C2×C4—362no—
625C2×C4C22×D3211yescharacteristic
626C8—31no—
627C8—31no—
628C8—62no—
629C8—61no—
630C8—181no—
631C8C2×#62611yescharacteristic
632C8C2×#62611yescharacteristic
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—41no—
637C2×C3—42no—
638C2×C3—42no—
639C2×C3—82no—
640C2×C3—121no—
641C2×C3—242no—
642C2×C3D4×D1211yescharacteristic
643C2×C3D4×#6711yescharacteristic
644D3—41no—
645D3—82no—
646D3—122no—
647D3—121no—
648D3—121no—
649D3—244no—
650D3—242no—
651D3—242no—
652C22—22no—
653C22—61no—
654C22—122no—
655C22—181no—
656C22—242no—
657C22—362no—
658C22—482no—
659C22—722no—
660C22—1442no—
661C22#6431411yescharacteristic
662C4—22no—
663C4—62no—
664C4—61no—
665C4—181no—
666C4D32×D411yescharacteristic
667C4C22×#62611yescharacteristic
668C3—21no—
669C3#7989411yescharacteristic, complemented
670C3#8401011yescharacteristic, complemented
671C2—21no—
672C2—42no—
673C2—121no—
674C2—242no—
675C2—361no—
676C2—722no—
677C2D4×#62611yescharacteristic
subgroupG/H
centerC2D4×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32D42
hypercenter#135D32
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #10596240C2semidirect
2. C3×#5769C2semidirect
3. #10595449C2semidirect
4. C3×#5196C2semidirect
5. #10591677C2semidirect
6. #10591667C2semidirect
7. #10591666C2semidirect
8. #10590929C2semidirect
9. #10590927C2semidirect
10. #10590923C2semidirect
11. #10590880C2semidirect
14. #64366C22semidirect
15. C3×#1009C22semidirect
17. #64158C22semidirect
21. C2×#3745C22semidirect
22. #64110C22semidirect
23. C3×#949C22semidirect
24. C3×#948C22semidirect
28. C2×C3×D24C22semidirect
29. C3×#901C22semidirect
30. #63911C22semidirect
32. #63830C22semidirect
36. #63825C22semidirect
38. C2×#3714C22semidirect
39. C3×#837C22semidirect
40. C3×#819C22semidirect
41. C3×C8×Dic3C22semidirect
42. #63577C22semidirect
43. #63570C22semidirect
44. #63569C22semidirect
45. #63559C22semidirect
46. #63558C22semidirect
52. #5769D3semidirect
58. #5196D3semidirect
86. C32×Q16D4semidirect
87. C32×SD16D4semidirect
88. C32×D8D4semidirect
109. #3719D4semidirect
111. #3717D4semidirect
113. #3716D4semidirect
118. #3714D4semidirect
124. #1009C2×D3semidirect
142. #949C2×D3semidirect
143. #948C2×D3semidirect
172. C2×D24C2×D3semidirect
176. #901C2×D3semidirect
182. #837C2×D3semidirect
190. #819C2×D3semidirect
191. C8×Dic3C2×D3semidirect
282. C3×Q16D12semidirect
283. C3×Q16#67semidirect
286. C3×SD16D12semidirect
287. C3×SD16#67semidirect
292. C3×D8D12semidirect
293. C3×D8#67semidirect
522. Q16#626semidirect
529. SD16#626semidirect
541. D8#626semidirect
596. C32#3292semidirect
669. C3#79894semidirect
670. C3#84010semidirect

Maximal subgroups

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

subgroupindex
#105962402
C3×#57692
#105954492
C3×#51962
#105916772
#105916672
#105916662
#105909292
#105909272
#105909232
#105908802
#840103
#798943