Finite Group Databasebeta

← #11886913

Subgroups — #11886913

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#10596223C211yesmaximal, characteristic, complemented
2#10595461C212yesmaximal, complemented
3#10594678C211yesmaximal, characteristic, complemented
4C3×#5144C211yesmaximal, characteristic, complemented
5C3×#5142C211yesmaximal, characteristic, complemented
6#10591667C212yesmaximal, complemented
7#10591015C212yesmaximal, complemented
8#10590987C212yesmaximal, complemented
9#10590927C211yesmaximal, characteristic, complemented
10#10590917C211yesmaximal, characteristic, complemented
11#10590880C211yesmaximal, characteristic, complemented
12#80941—31nomaximal
13#79894—31nomaximal
14#64366C2212yescomplemented
15#64307C2212yescomplemented
16C32×#131C2211yescharacteristic, complemented
17#64117—22no—
18#64117C2212yescomplemented
19#64113—21no—
20#64113C2211yescharacteristic
21C2×#3745—21no—
22C2×#3745C2211yescharacteristic, complemented
23C3×#950C2211yescharacteristic
24C3×#949C2212yescomplemented
25C2×C3×D24C2211yescharacteristic, complemented
26C3×#901C2211yescharacteristic, complemented
27#63950—22no—
28#63941—22no—
29#63937—22no—
30#63926—22no—
31#63911C2212yescomplemented
32#63830C2212yescomplemented
33#63825C2212yescomplemented
34C2×#3714C2212yescomplemented
35#63817C2212yescomplemented
36#63807—21no—
37#63795—22no—
38D3×D24—21no—
39C3×#837C2211yescharacteristic, complemented
40C3×#825C2211yescharacteristic, complemented
41C3×#823C2212yescomplemented
42C3×#822C2211yescharacteristic, complemented
43C3×#819C2211yescharacteristic, complemented
44C3×C8×Dic3C2211yescharacteristic, complemented
45#63570C2212yescomplemented
46#63559C2212yescomplemented
47#5774—32no—
48#5769—32no—
49#5757—31no—
50#5752—31no—
51#5752—31no—
52#5752—31no—
53#5752—61no—
54C3×#472—31no—
55C3×#443—31no—
56#5198—32no—
57#5151—31no—
58#5144D311yescharacteristic, complemented
59#5142—31no—
60#5142D311yescharacteristic, complemented
61#4897—31no—
62#4897—32no—
63#4895—31no—
64#4822—32no—
65#4822—32no—
66#4749—32no—
67#4747—32no—
68#4700—31no—
69#4695—31no—
70C32×#41C2311yescharacteristic
71#3832—22no—
72D4×C3⋊D3—22no—
73D4×C3⋊D3—42no—
74#3828—22no—
75#3828C2312yes—
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4⋊(C3⋊D3)C2312yes—
78C3×#235C2311yescharacteristic
79C2×C3×D12C2312yes—
80D3×#67—42no—
81C2×#626—42no—
82#3802—22no—
83D3×D12—22no—
84#3796—22no—
85#3795—22no—
86C32×M16—21no—
87C32×M16C2311yescharacteristic
88C2×C32×C8—21no—
89C2×C32×C8C2311yescharacteristic
90#3746D411yescharacteristic, complemented
91#3745—22no—
92#3745—21no—
93#3745—21no—
94#3745D411yescharacteristic, complemented
95#3744—22no—
96#3744D412yescomplemented
97C3×#216D411yescharacteristic, complemented
98C3×#215—22no—
99C3×#215D411yescharacteristic, complemented
100C3×#214D411yescharacteristic, complemented
101C3×#213—22no—
102C3×#213D411yescharacteristic, complemented
103C3×C4×Dic3C2311yescharacteristic
104C3×#208C2311yescharacteristic
105C3×#208C2312yes—
106C2×C3×C3⋊C8C2311yescharacteristic
107C3×D24—21no—
108C3×D24—21no—
109C3×ΓL(1,𝔽25)—21no—
110C3×D3×C8—21no—
111#3717—22no—
112#3716—22no—
113#3714—22no—
114#3714—22no—
115#3714—22no—
116#3714—22no—
117#3712—22no—
118#3710—22no—
119#3292—91noSylow
120#1009—32no—
121#1009—32no—
122#1009—32no—
123#1009—62no—
124#1004—32no—
125C3×AGL(1,ℤ/8)—32no—
126C3×#135—31no—
127C2×C3×D8—31no—
128C3×#131—21no—
129C3×#131—31no—
130C3×#131C2×D311yescharacteristic, complemented
131C3×#131C2×D311yescharacteristic, complemented
132#950C2×D311yescharacteristic
133#949—32no—
134#949C2×D312yescomplemented
135#940—32no—
136#932—32no—
137C2×#213—32no—
138#919—62no—
139#916—62no—
140#914—62no—
141#914—62no—
142#914—62no—
143#912—61no—
144#911—62no—
145#911—62no—
146D3×D8—61no—
147D3×D8—62no—
148D3×D8—62no—
149#908—32no—
150#908—32no—
151#908—32no—
152#908—32no—
153#908—62no—
154#908—62no—
155#908—62no—
156#908—62no—
157#908—64no—
158#907—32no—
159#904—31no—
160#904—31no—
161#904—61no—
162#904—61no—
163#904—61no—
164#904—61no—
165#904—62no—
166C2×D24—32no—
167C2×D24—31no—
168C2×D24—31no—
169C2×D24—61no—
170C2×D24—61no—
171C2×D24—61no—
172C2×D24—61no—
173C2×D24—62no—
174C2×D24C2×D311yescharacteristic, complemented
175#901—32no—
176#901C2×D311yescharacteristic, complemented
177#874—32no—
178C3×#108—31no—
179C3×#108—31no—
180C3×#104—31no—
181C3×#104—31no—
182C3×#100—32no—
183C3×C4×C8—31no—
184#837C2×D311yescharacteristic, complemented
185#825—32no—
186#825C2×D311yescharacteristic, complemented
187#823—32no—
188#823—32no—
189#823C2×D312yescomplemented
190#822C2×D311yescharacteristic, complemented
191#819C2×D311yescharacteristic, complemented
192C8×Dic3C2×D311yescharacteristic, complemented
193#805—32no—
194C22×C3⋊D3—22no—
195C22×C3⋊D3—42no—
196C22×C3×D3—22no—
197C2×D32—42no—
198C32×Q8C2×D411yescharacteristic
199C32×D4—21no—
200C32×D4C2×D411yescharacteristic
201C2×C32×C4—21no—
202C2×C32×C4C2411yescharacteristic
203#638—22no—
204#638—42no—
205C4⋊(C3⋊D3)—22no—
206C4⋊(C3⋊D3)—22no—
207C4⋊(C3⋊D3)—42no—
208C4⋊(C3⋊D3)C2×D412yes—
209C4×C3⋊D3—22no—
210C4×C3⋊D3—42no—
211#634C2×D412yes—
212C3×#67—21no—
213C2×C3×Dic3—21no—
214C3×D12—22no—
215C3×D12—22no—
216C3×D12C2×D411yescharacteristic
217C3×C4×D3—21no—
218C3×Dic6C2×D411yescharacteristic
219#626—42no—
220#626—84no—
221#625—42no—
222D3×Dic3—42no—
223C32×C8—21no—
224C32×C8C2×D411yescharacteristic
225C32×C8C2×D411yescharacteristic
226C3×C3⋊C8—22no—
227C3×C3⋊C8—21no—
228C3×C3⋊C8C2×D411yescharacteristic
229C3×C3⋊C8C2×D411yescharacteristic
230#576—91no—
231#576—92no—
232#576—91no—
233#493—91no—
234#472—31no—
235#472—92no—
236#472—91no—
237#453—92no—
238#453—92no—
239#443—31no—
240#443—91no—
241C3×#41—21no—
242C3×#41—31no—
243C3×#41C22×D311yescharacteristic
244C3×#41C22×D311yescharacteristic
245C2×C3×D4—32no—
246C2×#67—122no—
247C2×#67—122no—
248#239—62no—
249#239—62no—
250#239—62no—
251#239—122no—
252#237—62no—
253#237—62no—
254D3×D4—62no—
255D3×D4—62no—
256D3×D4—62no—
257D3×D4—62no—
258D3×D4—62no—
259D3×D4—122no—
260D3×D4—122no—
261D3×D4—122no—
262D3×D4—122no—
263D3×D4—124no—
264#235—32no—
265#235—32no—
266#235—62no—
267#235—62no—
268#235—62no—
269#235—62no—
270#235—64no—
271#235C22×D311yescharacteristic
272C2×D12—32no—
273C2×D12—32no—
274C2×D12—62no—
275C2×D12—62no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—64no—
279C2×D12—122no—
280C2×D12C22×D312yes—
281C3×Q16—31no—
282C3×SD16—31no—
283C3×SD16—31no—
284C3×SD16—62no—
285C3×D8—31no—
286C3×D8—62no—
287C3×D8—61no—
288C3×D8—61no—
289C3×M16—22no—
290C3×M16—21no—
291C3×M16—21no—
292C3×M16—21no—
293C3×M16—31no—
294C3×M16—32no—
295C3×M16—61no—
296C3×M16C22×D311yescharacteristic
297C3×M16C22×D311yescharacteristic
298C2×C3×C8—22no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—31no—
303C2×C3×C8—61no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C42—31no—
307#216D1211yescharacteristic, complemented
308#215—22no—
309#215—62no—
310#215D1211yescharacteristic, complemented
311#214—62no—
312#214D1211yescharacteristic, complemented
313#213—22no—
314#213—62no—
315#213—62no—
316#213—62no—
317#213—62no—
318#213D1211yescharacteristic, complemented
319C4×Dic3C22×D311yescharacteristic
320#208C22×D312yes—
321#208C22×D311yescharacteristic
322C2×C3⋊C8C22×D311yescharacteristic
323Dic12—31no—
324Dic12—31no—
325Dic12—61no—
326D24—21no—
327D24—21no—
328D24—31no—
329D24—31no—
330D24—61no—
331D24—62no—
332D24—62no—
333D24—62no—
334D24—64no—
335D24—62no—
336D24—62no—
337D24—62no—
338D24—62no—
339D24—62no—
340D24—61no—
341D24—61no—
342D24—61no—
343D24—61no—
344#204—32no—
345#204—32no—
346#204—62no—
347#204—62no—
348#204—62no—
349#204—64no—
350#204—62no—
351#204—62no—
352ΓL(1,𝔽25)—21no—
353ΓL(1,𝔽25)—62no—
354ΓL(1,𝔽25)—62no—
355D3×C8—21no—
356D3×C8—62no—
357D3×C8—62no—
358C22×C32—21no—
359C22×C32H(5,𝔽2)11yescharacteristic
360C2×C3⋊D3—22no—
361C2×C3⋊D3—42no—
362C2×C3⋊D3—82no—
363C2×C3⋊D3—162no—
364C2×C3×D3—21no—
365C2×C3×D3—42no—
366C2×C3×D3—82no—
367D32—162no—
368C32×C4—21no—
369C32×C4C22×D411yescharacteristic
370C32×C4C22×D411yescharacteristic
371C3⋊Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3—21no—
374H(5,𝔽2)—92no—
375H(5,𝔽2)—92no—
376AGL(1,ℤ/8)—32no—
377AGL(1,ℤ/8)—92no—
378AGL(1,ℤ/8)—92no—
379AGL(1,ℤ/8)—92no—
380AGL(1,ℤ/8)—182no—
381AGL(1,ℤ/8)—182no—
382AGL(1,ℤ/8)—182no—
383AGL(1,ℤ/8)—182no—
384#135—31no—
385#135—91no—
386#135—181no—
387#135—181no—
388#135—182no—
389C2×D8—31no—
390C2×D8—92no—
391C2×D8—91no—
392C2×D8—181no—
393C2×D8—181no—
394C2×D8—182no—
395#131—31no—
396#131—92no—
397#131D3211yescharacteristic, complemented
398#127—92no—
399#108—31no—
400#108—31no—
401#104—31no—
402#104—31no—
403#104—92no—
404#100—32no—
405#100—92no—
406C4×C8—31no—
407C23×C3—62no—
408C22×D3—22no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—122no—
412C22×D3—122no—
413C22×D3—122no—
414C22×D3—122no—
415C22×D3—122no—
416C22×D3—124no—
417C3×Q8—21no—
418C3×Q8—31no—
419C3×Q8C2×D1211yescharacteristic
420C3×Q8D3×D411yescharacteristic
421C3×D4—22no—
422C3×D4—21no—
423C3×D4—21no—
424C3×D4—21no—
425C3×D4—31no—
426C3×D4—61no—
427C3×D4—62no—
428C3×D4—62no—
429C3×D4C2×D1211yescharacteristic
430C3×D4D3×D411yescharacteristic
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4C23×D311yescharacteristic
438C2×C3×C4C23×D311yescharacteristic
439#67—21no—
440#67—62no—
441#67—62no—
442#67—122no—
443#67—122no—
444#67—122no—
445#67—122no—
446#67—122no—
447#67—122no—
448#67—124no—
449#67—244no—
450C2×Dic3—21no—
451C2×Dic3—122no—
452D12—22no—
453D12—22no—
454D12—32no—
455D12—32no—
456D12—62no—
457D12—64no—
458D12—62no—
459D12—62no—
460D12—62no—
461D12—62no—
462D12—122no—
463D12—122no—
464D12—122no—
465D12—124no—
466D12—122no—
467D12—244no—
468D12C2×D1211yescharacteristic
469C4×D3—21no—
470C4×D3—62no—
471C4×D3—62no—
472C4×D3—122no—
473C4×D3—122no—
474C4×D3—122no—
475C4×D3—122no—
476C4×D3—124no—
477Dic6—32no—
478Dic6—32no—
479Dic6—62no—
480Dic6C2×D1211yescharacteristic
481C3×C8—22no—
482C3×C8—21no—
483C3×C8—21no—
484C3×C8—21no—
485C3×C8—21no—
486C3×C8—31no—
487C3×C8—31no—
488C3×C8—62no—
489C3×C8—61no—
490C3×C8D3×D411yescharacteristic
491C3×C8D3×D411yescharacteristic
492C3×C8D3×D411yescharacteristic
493C3×C8D3×D411yescharacteristic
494C3⋊C8—21no—
495C3⋊C8—22no—
496C3⋊C8C2×D1211yescharacteristic
497C3⋊C8C2×D1211yescharacteristic
498C2×C32—21no—
499C2×C32—41no—
500C2×C32D4211yescharacteristic
501C3⋊D3—42no—
502C3⋊D3—82no—
503C3×D3—41no—
504C3×D3—82no—
505#41—31no—
506#41—92no—
507#41—182no—
508#41—182no—
509#41—182no—
510#41—182no—
511#41C2×D3211yescharacteristic
512C2×D4—32no—
513C2×D4—92no—
514C2×D4—182no—
515C2×D4—182no—
516C2×D4—182no—
517C2×D4—182no—
518C2×D4—362no—
519C2×D4—362no—
520C2×D4—362no—
521Q16—31no—
522Q16—91no—
523SD16—31no—
524SD16—31no—
525SD16—62no—
526SD16—92no—
527SD16—182no—
528SD16—182no—
529SD16—182no—
530D8—31no—
531D8—62no—
532D8—61no—
533D8—61no—
534D8—91no—
535D8—182no—
536D8—182no—
537D8—182no—
538D8—182no—
539D8—182no—
540D8—181no—
541D8—181no—
542M16—21no—
543M16—32no—
544M16—31no—
545M16—61no—
546M16—182no—
547M16C2×D3211yescharacteristic
548C2×C8—21no—
549C2×C8—31no—
550C2×C8—61no—
551C2×C8—182no—
552C2×C8C2×D3211yescharacteristic
553C42—31no—
554C22×C3—22no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—61no—
559C22×C3—122no—
560C22×C3—242no—
561C22×C3#100911yescharacteristic
562C22×C3#100911yescharacteristic
563C2×D3—21no—
564C2×D3—42no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—82no—
568C2×D3—122no—
569C2×D3—124no—
570C2×D3—122no—
571C2×D3—122no—
572C2×D3—242no—
573C2×D3—242no—
574C2×D3—482no—
575C2×D3—482no—
576C2×D3—482no—
577C2×D3—482no—
578C2×D3—482no—
579C2×D3—484no—
580C3×C4—22no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—62no—
586C3×C4—61no—
587C3×C4C22×D1211yescharacteristic
588C3×C4C2×D3×D411yescharacteristic
589C3×C4C2×D3×D411yescharacteristic
590C3×C4C2×D3×D411yescharacteristic
591Dic3—22no—
592Dic3—21no—
593Dic3—62no—
594Dic3—62no—
595Dic3—122no—
596C32#329211yescharacteristic, complemented, Sylow
597C23—62no—
598C23—182no—
599C23—362no—
600C23—362no—
601Q8—31no—
602Q8—92no—
603Q8D3×D1211yescharacteristic
604D4—21no—
605D4—31no—
606D4—61no—
607D4—62no—
608D4—62no—
609D4—92no—
610D4—182no—
611D4—182no—
612D4—182no—
613D4—362no—
614D4—362no—
615D4—362no—
616D4—362no—
617D4—724no—
618D4D3×D1211yescharacteristic
619C2×C4—21no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—182no—
623C2×C4—362no—
624C2×C4—362no—
625C2×C4C22×D3211yescharacteristic
626C8—21no—
627C8—31no—
628C8—31no—
629C8—62no—
630C8—61no—
631C8#381111yescharacteristic
632C8#381111yescharacteristic
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—41no—
637C2×C3—42no—
638C2×C3—41no—
639C2×C3—41no—
640C2×C3—121no—
641C2×C3—242no—
642C2×C3D4×D1211yescharacteristic
643C2×C3#560911yescharacteristic
644D3—41no—
645D3—82no—
646D3—122no—
647D3—122no—
648D3—242no—
649D3—244no—
650D3—242no—
651D3—242no—
652C22—21no—
653C22—61no—
654C22—122no—
655C22—182no—
656C22—242no—
657C22—362no—
658C22—722no—
659C22—1442no—
660C22—1442no—
661C22#6430811yescharacteristic
662C4—21no—
663C4—62no—
664C4—61no—
665C4—182no—
666C4C2×D3×D1211yescharacteristic
667C4C2×#381111yescharacteristic
668C3—21no—
669C3#7989411yescharacteristic, complemented
670C3#8094111yescharacteristic, complemented
671C2—21no—
672C2—41no—
673C2—121no—
674C2—242no—
675C2—362no—
676C2—722no—
677C2#1059507411yescharacteristic
subgroupG/H
centerC2#10595074
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32D42
hypercenter#131D32
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. #10596223C2semidirect
2. #10595461C2semidirect
3. #10594678C2semidirect
4. C3×#5144C2semidirect
5. C3×#5142C2semidirect
6. #10591667C2semidirect
7. #10591015C2semidirect
8. #10590987C2semidirect
9. #10590927C2semidirect
10. #10590917C2semidirect
11. #10590880C2semidirect
14. #64366C22semidirect
15. #64307C22semidirect
16. C32×#131C22semidirect
18. #64117C22semidirect
22. C2×#3745C22semidirect
24. C3×#949C22semidirect
25. C2×C3×D24C22semidirect
26. C3×#901C22semidirect
31. #63911C22semidirect
32. #63830C22semidirect
33. #63825C22semidirect
34. C2×#3714C22semidirect
35. #63817C22semidirect
39. C3×#837C22semidirect
40. C3×#825C22semidirect
41. C3×#823C22semidirect
42. C3×#822C22semidirect
43. C3×#819C22semidirect
44. C3×C8×Dic3C22semidirect
45. #63570C22semidirect
46. #63559C22semidirect
58. #5144D3semidirect
60. #5142D3semidirect
90. #3746D4semidirect
94. #3745D4semidirect
96. #3744D4semidirect
97. C3×#216D4semidirect
99. C3×#215D4semidirect
100. C3×#214D4semidirect
102. C3×#213D4semidirect
130. C3×#131C2×D3semidirect
131. C3×#131C2×D3semidirect
134. #949C2×D3semidirect
174. C2×D24C2×D3semidirect
176. #901C2×D3semidirect
184. #837C2×D3semidirect
186. #825C2×D3semidirect
189. #823C2×D3semidirect
190. #822C2×D3semidirect
191. #819C2×D3semidirect
192. C8×Dic3C2×D3semidirect
307. #216D12semidirect
310. #215D12semidirect
312. #214D12semidirect
318. #213D12semidirect
397. #131D32semidirect
596. C32#3292semidirect
669. C3#79894semidirect
670. C3#80941semidirect

Maximal subgroups

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

subgroupindex
#105962232
#105954612
#105946782
C3×#51442
C3×#51422
#105916672
#105910152
#105909872
#105909272
#105909172
#105908802
#809413
#798943