Finite Group Databasebeta

← #11886914

Subgroups — #11886914

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5752C211yesmaximal, characteristic, complemented
2#10595454C212yesmaximal, complemented
3#10594687C211yesmaximal, characteristic, complemented
4#10592843C211yesmaximal, characteristic, complemented
5C3×#5142C211yesmaximal, characteristic, complemented
6#10591665C212yesmaximal, complemented
7#10591014C212yesmaximal, complemented
8#10590982C212yesmaximal, complemented
9#10590929C211yesmaximal, characteristic, complemented
10#10590919C211yesmaximal, characteristic, complemented
11#10590886C211yesmaximal, characteristic, complemented
12#84010—31nomaximal
13#80941—31nomaximal
14C3×#1009C2212yescomplemented
15#64307C2212yescomplemented
16C32×#131C2211yescharacteristic, complemented
17#64159C2211yescharacteristic
18#64110C2211yescharacteristic, complemented
19C3×#949C2212yescomplemented
20C3×#908—22no—
21C3×#908C2212yescomplemented
22C3×#904—21no—
23C3×#904C2211yescharacteristic
24C2×C3×D24—21no—
25C2×C3×D24C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic, complemented
27#63947—22no—
28#63939—22no—
29#63932—22no—
30D3×#213—22no—
31#63914C2212yescomplemented
32#63830C2212yescomplemented
33#63823C2212yescomplemented
34C2×#3713C2212yescomplemented
35#63815C2212yescomplemented
36#63810—21no—
37#63798—22no—
38#63797—21no—
39#63664C2211yescharacteristic, complemented
40#63652C2211yescharacteristic, complemented
41#63649C2211yescharacteristic, complemented
42C8×C3⋊Dic3C2211yescharacteristic, complemented
43C3×#823C2212yescomplemented
44C3×#819C2211yescharacteristic, complemented
45#63568C2212yescomplemented
46#63558C2212yescomplemented
47C3×#576—31no—
48#5835—32no—
49#5774—32no—
50#5769—31no—
51#5757—31no—
52#5752D311yescharacteristic, complemented
53C3×#472—31no—
54#5241—32no—
55#5199—32no—
56#5198—32no—
57#5198—32no—
58#5196—31no—
59#5160—31no—
60#5151—31no—
61#5151—31no—
62#5144—31no—
63#5144—31no—
64#5144—61no—
65#5142D311yescharacteristic, complemented
66#4897—31no—
67#4895—31no—
68#4749—32no—
69#4747—32no—
70C32×#41C2311yescharacteristic
71#3828C2311yescharacteristic
72C3×#239—22no—
73C3×D3×D4—22no—
74C3×D3×D4—42no—
75C3×#235—22no—
76C3×#235C2312yes—
77C2×C3×D12—22no—
78C2×C3×D12C2312yes—
79C2×C3×D12C2312yes—
80D3×#67—42no—
81C2×#625—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#3756D411yescharacteristic, complemented
91#3755D411yescharacteristic, complemented
92#3754D411yescharacteristic, complemented
93#3753D411yescharacteristic, complemented
94C4×C3⋊Dic3C2311yescharacteristic
95#3748C2311yescharacteristic
96C2×C3⋊(C3⋊C8)C2311yescharacteristic
97#3743—21no—
98C8×C3⋊D3—21no—
99C3×#215—22no—
100C3×#213—22no—
101C3×#208C2312yes—
102C3×Dic12D411yescharacteristic, complemented
103C3×D24—22no—
104C3×D24—21no—
105C3×D24—21no—
106C3×D24—21no—
107C3×D24—21no—
108C3×D24D411yescharacteristic, complemented
109C3×#204—22no—
110C3×#204D412yescomplemented
111#3716—22no—
112#3715—22no—
113#3714—22no—
114#3713—22no—
115#3713—22no—
116#3713—22no—
117#3711—22no—
118D3×C3⋊C8—22no—
119#3292—91noSylow
120C3×H(5,𝔽2)—32no—
121#1009—32no—
122#1009C2×D312yescomplemented
123#1004—32no—
124C3×AGL(1,ℤ/8)—32no—
125C3×AGL(1,ℤ/8)—32no—
126C3×AGL(1,ℤ/8)—62no—
127C3×#135—31no—
128C3×#135—61no—
129C2×C3×D8—31no—
130C2×C3×D8—31no—
131C2×C3×D8—61no—
132C3×#131—21no—
133C3×#131C2×D311yescharacteristic, complemented
134C3×#131C2×D311yescharacteristic, complemented
135#950—31no—
136#950—31no—
137#950—61no—
138#950—62no—
139#949—32no—
140#949—62no—
141#949C2×D312yescomplemented
142#948—32no—
143#940—32no—
144#940—32no—
145#932—32no—
146#932—32no—
147#932—62no—
148C2×#213—32no—
149C2×#213—32no—
150C2×#213—62no—
151#919—61no—
152#916—62no—
153#914—62no—
154#914—62no—
155#912—61no—
156#911—62no—
157#911—62no—
158D3×D8—61no—
159D3×D8—62no—
160D3×D8—61no—
161#908—22no—
162#908—32no—
163#908C2×D312yescomplemented
164#907—32no—
165#904—21no—
166#904C2×D311yescharacteristic
167C2×D24—21no—
168C2×D24C2×D311yescharacteristic, complemented
169C2×D24C2×D311yescharacteristic, complemented
170#901—31no—
171#901—31no—
172#901—61no—
173C3×#108—31no—
174C3×#100—32no—
175#837—31no—
176#837—31no—
177#837—32no—
178#837—61no—
179#833—32no—
180#825—32no—
181#825—31no—
182#825—31no—
183#825—61no—
184#823—32no—
185#823C2×D312yescomplemented
186#822—31no—
187#822—31no—
188#822—61no—
189#819C2×D311yescharacteristic, complemented
190C8×Dic3—31no—
191C8×Dic3—31no—
192C8×Dic3—61no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—42no—
196C2×D32—42no—
197C32×Q8C2×D411yescharacteristic
198C32×D4—21no—
199C32×D4C2×D411yescharacteristic
200C2×C32×C4—21no—
201C2×C32×C4C2411yescharacteristic
202#638—21no—
203C2×C3⋊Dic3—21no—
204C4⋊(C3⋊D3)C2×D411yescharacteristic
205C4×C3⋊D3—21no—
206#634C2×D411yescharacteristic
207C3×#67—22no—
208C3×#67—42no—
209C3×D12—22no—
210C3×D12—22no—
211C3×D12—22no—
212C3×D12—22no—
213C3×D12—42no—
214C3×D12C2×D412yes—
215C3×C4×D3—22no—
216C3×C4×D3—42no—
217C3×Dic6C2×D412yes—
218#626—42no—
219#625—42no—
220#625—84no—
221D3×Dic3—42no—
222C32×C8—21no—
223C32×C8C2×D411yescharacteristic
224C32×C8C2×D411yescharacteristic
225C3⋊(C3⋊C8)—21no—
226C3⋊(C3⋊C8)C2×D411yescharacteristic
227C3⋊(C3⋊C8)C2×D411yescharacteristic
228C3×C3⋊C8—22no—
229#576—31no—
230#576—91no—
231#576—92no—
232#493—91no—
233#472—31no—
234#472—92no—
235#472—91no—
236#453—92no—
237#453—92no—
238#443—91no—
239#443—91no—
240C3×#41—21no—
241C3×#41—32no—
242C3×#41—62no—
243C3×#41—62no—
244C3×#41C22×D311yescharacteristic
245C3×#41C22×D311yescharacteristic
246C2×C3×D4—32no—
247C2×C3×D4—32no—
248C2×C3×D4—62no—
249C2×C3×D4—62no—
250C2×C3×D4—122no—
251C2×#67—122no—
252C2×#67—122no—
253C2×#67—122no—
254#239—22no—
255#239—62no—
256#237—62no—
257#237—62no—
258D3×D4—22no—
259D3×D4—42no—
260D3×D4—62no—
261D3×D4—62no—
262D3×D4—62no—
263D3×D4—122no—
264#235—22no—
265#235—31no—
266#235—31no—
267#235—61no—
268#235—62no—
269#235C22×D312yes—
270C2×D12—22no—
271C2×D12—62no—
272C2×D12C22×D312yes—
273C2×D12C22×D312yes—
274C3×Q16—31no—
275C3×SD16—32no—
276C3×SD16—62no—
277C3×SD16—62no—
278C3×D8—31no—
279C3×D8—62no—
280C3×D8—62no—
281C3×D8—61no—
282C3×D8—61no—
283C3×D8—61no—
284C3×D8—61no—
285C3×M16—21no—
286C3×M16—21no—
287C3×M16—21no—
288C3×M16—32no—
289C3×M16—41no—
290C3×M16C22×D311yescharacteristic
291C3×M16C22×D311yescharacteristic
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—41no—
296C2×C3×C8C22×D311yescharacteristic
297C2×C3×C8C22×D311yescharacteristic
298#216—31no—
299#216—31no—
300#216—61no—
301#215—22no—
302#215—31no—
303#215—31no—
304#215—61no—
305#215—62no—
306#214—31no—
307#214—31no—
308#214—61no—
309#214—62no—
310#214—62no—
311#213—22no—
312#213—31no—
313#213—31no—
314#213—61no—
315#213—62no—
316#213—62no—
317#213—62no—
318#213—62no—
319#213—62no—
320#213—62no—
321#213—62no—
322C4×Dic3—31no—
323C4×Dic3—31no—
324C4×Dic3—61no—
325#208—31no—
326#208—31no—
327#208—61no—
328#208—62no—
329#208C22×D312yes—
330C2×C3⋊C8—31no—
331C2×C3⋊C8—31no—
332C2×C3⋊C8—61no—
333C2×C3⋊C8—62no—
334Dic12#6711yescharacteristic, complemented
335D24—22no—
336D24—21no—
337D24—21no—
338D24—21no—
339D24—21no—
340D24—62no—
341D24#6711yescharacteristic, complemented
342#204—22no—
343#204—62no—
344#204#6712yescomplemented
345ΓL(1,𝔽25)—62no—
346ΓL(1,𝔽25)—61no—
347ΓL(1,𝔽25)—61no—
348ΓL(1,𝔽25)—121no—
349D3×C8—62no—
350D3×C8—61no—
351D3×C8—61no—
352D3×C8—121no—
353C22×C32—21no—
354C22×C32H(5,𝔽2)11yescharacteristic
355C2×C3⋊D3—21no—
356C2×C3×D3—22no—
357C2×C3×D3—42no—
358C2×C3×D3—42no—
359C2×C3×D3—82no—
360C2×C3×D3—82no—
361C2×C3×D3—162no—
362D32—162no—
363C32×C4—21no—
364C32×C4C22×D411yescharacteristic
365C32×C4C22×D411yescharacteristic
366C3⋊Dic3—22no—
367C3⋊Dic3—21no—
368C3×Dic3—22no—
369H(5,𝔽2)—32no—
370H(5,𝔽2)—92no—
371AGL(1,ℤ/8)—32no—
372AGL(1,ℤ/8)—32no—
373AGL(1,ℤ/8)—62no—
374AGL(1,ℤ/8)—92no—
375AGL(1,ℤ/8)—92no—
376AGL(1,ℤ/8)—182no—
377AGL(1,ℤ/8)—182no—
378AGL(1,ℤ/8)—182no—
379#135—31no—
380#135—61no—
381#135—91no—
382#135—181no—
383#135—182no—
384C2×D8—31no—
385C2×D8—31no—
386C2×D8—61no—
387C2×D8—92no—
388C2×D8—181no—
389C2×D8—182no—
390#131—92no—
391#131—91no—
392#131D3211yescharacteristic, complemented
393#127—92no—
394#108—31no—
395#108—91no—
396#104—92no—
397#104—91no—
398#104—91no—
399#100—32no—
400#100—92no—
401C4×C8—91no—
402C23×C3—62no—
403C23×C3—62no—
404C23×C3—122no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—42no—
408C22×D3—122no—
409C22×D3—122no—
410C3×Q8—21no—
411C3×Q8—32no—
412C3×Q8D3×D411yescharacteristic
413C3×Q8D3×D411yescharacteristic
414C3×D4—21no—
415C3×D4—21no—
416C3×D4—21no—
417C3×D4—32no—
418C3×D4—41no—
419C3×D4—62no—
420C3×D4—62no—
421C3×D4—62no—
422C3×D4—62no—
423C3×D4—62no—
424C3×D4—122no—
425C3×D4—122no—
426C3×D4D3×D411yescharacteristic
427C3×D4D3×D411yescharacteristic
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—41no—
432C2×C3×C4—62no—
433C2×C3×C4—122no—
434C2×C3×C4C23×D311yescharacteristic
435C2×C3×C4C23×D311yescharacteristic
436#67—22no—
437#67—42no—
438#67—61no—
439#67—61no—
440#67—121no—
441#67—122no—
442#67—122no—
443#67—122no—
444#67—244no—
445#67—244no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—121no—
449C2×Dic3—122no—
450D12—22no—
451D12—22no—
452D12—22no—
453D12—22no—
454D12—31no—
455D12—31no—
456D12—42no—
457D12—61no—
458D12—122no—
459D12C2×#6712yes—
460C4×D3—22no—
461C4×D3—42no—
462C4×D3—61no—
463C4×D3—61no—
464C4×D3—121no—
465C4×D3—122no—
466Dic6—31no—
467Dic6—31no—
468Dic6—61no—
469Dic6C2×#6712yes—
470C3×C8—21no—
471C3×C8—21no—
472C3×C8—21no—
473C3×C8—21no—
474C3×C8—41no—
475C3×C8—62no—
476C3×C8D3×D411yescharacteristic
477C3×C8D3×D411yescharacteristic
478C3×C8C2×#6711yescharacteristic
479C3×C8C2×#6711yescharacteristic
480C3⋊C8—22no—
481C3⋊C8—31no—
482C3⋊C8—31no—
483C3⋊C8—31no—
484C3⋊C8—31no—
485C3⋊C8—61no—
486C3⋊C8—61no—
487C3⋊C8—61no—
488C3⋊C8—61no—
489C3⋊C8—121no—
490C2×C32—21no—
491C2×C32—41no—
492C2×C32D4211yescharacteristic
493C3⋊D3—41no—
494C3×D3—42no—
495C3×D3—82no—
496C3×D3—82no—
497#41—32no—
498#41—62no—
499#41—62no—
500#41—91no—
501#41—182no—
502#41—182no—
503#41C2×D3211yescharacteristic
504C2×D4—32no—
505C2×D4—32no—
506C2×D4—62no—
507C2×D4—62no—
508C2×D4—122no—
509C2×D4—182no—
510C2×D4—182no—
511C2×D4—362no—
512C2×D4—362no—
513Q16—31no—
514Q16—91no—
515SD16—32no—
516SD16—62no—
517SD16—62no—
518SD16—91no—
519SD16—91no—
520SD16—182no—
521SD16—182no—
522D8—31no—
523D8—62no—
524D8—62no—
525D8—61no—
526D8—61no—
527D8—61no—
528D8—61no—
529D8—91no—
530D8—182no—
531D8—182no—
532D8—182no—
533D8—182no—
534M16—21no—
535M16—32no—
536M16—91no—
537M16—182no—
538M16—181no—
539M16C2×D3211yescharacteristic
540C2×C8—21no—
541C2×C8—91no—
542C2×C8—182no—
543C2×C8—181no—
544C2×C8C2×D3211yescharacteristic
545C42—91no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—41no—
550C22×C3—62no—
551C22×C3—122no—
552C22×C3—122no—
553C22×C3—242no—
554C22×C3—242no—
555C22×C3—482no—
556C22×C3#100411yescharacteristic
557C22×C3#100911yescharacteristic
558C2×D3—22no—
559C2×D3—42no—
560C2×D3—42no—
561C2×D3—61no—
562C2×D3—61no—
563C2×D3—82no—
564C2×D3—82no—
565C2×D3—121no—
566C2×D3—162no—
567C2×D3—482no—
568C2×D3—482no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—41no—
574C3×C4—62no—
575C3×C4C2×D3×D411yescharacteristic
576C3×C4C2×D3×D411yescharacteristic
577C3×C4C2×D3×D411yescharacteristic
578C3×C4C22×#6711yescharacteristic
579Dic3—22no—
580Dic3—62no—
581Dic3—62no—
582Dic3—61no—
583Dic3—61no—
584Dic3—121no—
585Dic3—122no—
586C32#329211yescharacteristic, complemented, Sylow
587C23—62no—
588C23—62no—
589C23—122no—
590C23—362no—
591Q8—32no—
592Q8—91no—
593Q8#380211yescharacteristic
594D4—21no—
595D4—32no—
596D4—62no—
597D4—62no—
598D4—62no—
599D4—62no—
600D4—62no—
601D4—91no—
602D4—122no—
603D4—122no—
604D4—181no—
605D4—362no—
606D4—362no—
607D4—724no—
608D4#380211yescharacteristic
609C2×C4—21no—
610C2×C4—62no—
611C2×C4—122no—
612C2×C4—181no—
613C2×C4—181no—
614C2×C4—362no—
615C2×C4C22×D3211yescharacteristic
616C8—21no—
617C8—62no—
618C8—91no—
619C8—91no—
620C8—181no—
621C8D3×#6711yescharacteristic
622C8D3×#6711yescharacteristic
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—41no—
627C2×C3—41no—
628C2×C3—41no—
629C2×C3—81no—
630C2×C3—122no—
631C2×C3—242no—
632C2×C3—242no—
633C2×C3#560911yescharacteristic
634C2×C3D4×#6711yescharacteristic
635D3—42no—
636D3—82no—
637D3—82no—
638D3—121no—
639D3—121no—
640D3—241no—
641C22—21no—
642C22—62no—
643C22—122no—
644C22—122no—
645C22—181no—
646C22—242no—
647C22—242no—
648C22—482no—
649C22—1442no—
650C22#6430711yescharacteristic
651C4—21no—
652C4—62no—
653C4—182no—
654C4—181no—
655C4C2×#380211yescharacteristic
656C4C2×D3×#6711yescharacteristic
657C3—21no—
658C3#8094111yescharacteristic, complemented
659C3#8401011yescharacteristic, complemented
660C2—21no—
661C2—41no—
662C2—122no—
663C2—242no—
664C2—242no—
665C2—361no—
666C2#1059506911yescharacteristic
subgroupG/H
centerC2#10595069
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. C3×#5752C2semidirect
2. #10595454C2semidirect
3. #10594687C2semidirect
4. #10592843C2semidirect
5. C3×#5142C2semidirect
6. #10591665C2semidirect
7. #10591014C2semidirect
8. #10590982C2semidirect
9. #10590929C2semidirect
10. #10590919C2semidirect
11. #10590886C2semidirect
14. C3×#1009C22semidirect
15. #64307C22semidirect
16. C32×#131C22semidirect
18. #64110C22semidirect
19. C3×#949C22semidirect
21. C3×#908C22semidirect
25. C2×C3×D24C22semidirect
26. C2×C3×D24C22semidirect
31. #63914C22semidirect
32. #63830C22semidirect
33. #63823C22semidirect
34. C2×#3713C22semidirect
35. #63815C22semidirect
39. #63664C22semidirect
40. #63652C22semidirect
41. #63649C22semidirect
42. C8×C3⋊Dic3C22semidirect
43. C3×#823C22semidirect
44. C3×#819C22semidirect
45. #63568C22semidirect
46. #63558C22semidirect
52. #5752D3semidirect
65. #5142D3semidirect
90. #3756D4semidirect
91. #3755D4semidirect
92. #3754D4semidirect
93. #3753D4semidirect
102. C3×Dic12D4semidirect
108. C3×D24D4semidirect
110. C3×#204D4semidirect
122. #1009C2×D3semidirect
133. C3×#131C2×D3semidirect
134. C3×#131C2×D3semidirect
141. #949C2×D3semidirect
163. #908C2×D3semidirect
168. C2×D24C2×D3semidirect
169. C2×D24C2×D3semidirect
185. #823C2×D3semidirect
189. #819C2×D3semidirect
334. Dic12#67semidirect
341. D24#67semidirect
344. #204#67semidirect
392. #131D32semidirect
586. C32#3292semidirect
658. C3#80941semidirect
659. C3#84010semidirect

Maximal subgroups

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

subgroupindex
C3×#57522
#105954542
#105946872
#105928432
C3×#51422
#105916652
#105910142
#105909822
#105909292
#105909192
#105908862
#840103
#809413