Finite Group Databasebeta

← #11886923

Subgroups — #11886923

Order 1152.

1006 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5757C211yesmaximal, characteristic, complemented
2#10595096C212yesmaximal, complemented
3#10594687C211yesmaximal, characteristic, complemented
4#10592859C211yesmaximal, characteristic, complemented
5C3×#5151C211yesmaximal, characteristic, complemented
6#10591523C212yesmaximal, complemented
7#10591509C212yesmaximal, complemented
8#10591505C212yesmaximal, complemented
9#10590926C211yesmaximal, characteristic, complemented
10#10590923C211yesmaximal, characteristic, complemented
11#10590915C211yesmaximal, characteristic, complemented
12#84010—31nomaximal
13#81791—31nomaximal
14C3×#1004C2212yescomplemented
15#64307C2212yescomplemented
16C2×C32×D8C2211yescharacteristic, complemented
17#64141C2212yescomplemented
18#64110C2211yescharacteristic, complemented
19C3×#940C2212yescomplemented
20C3×#932C2212yescomplemented
21C2×C3×#213C2212yescomplemented
22C3×#912—21no—
23C3×#911—22no—
24C3×D3×D8—21no—
25C3×#904C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic, complemented
27C3×#901C2211yescharacteristic, complemented
28#63933—22no—
29#63932—22no—
30#63925—22no—
31D3×#213—22no—
32#63829C2211yescharacteristic
33#63823C2212yescomplemented
34#63823C2212yescomplemented
35#63814C2212yescomplemented
36#63810—21no—
37#63798—22no—
38#63797—21no—
39#63660C2212yescomplemented
40#63646C2211yescharacteristic, complemented
41C3×C8×Dic3C2211yescharacteristic, complemented
42#63577C2211yescharacteristic, complemented
43#63570C2211yescharacteristic, complemented
44#63569C2211yescharacteristic, complemented
45#63569C2212yescomplemented
46#63558C2212yescomplemented
47C3×#576—31no—
48#5835—32no—
49#5769—31no—
50#5757—32no—
51#5757—31no—
52#5757D311yescharacteristic, complemented
53C3×#493—31no—
54#5241—32no—
55#5199—32no—
56#5198—32no—
57#5196—31no—
58#5160—31no—
59#5160—31no—
60#5160—32no—
61#5160—31no—
62#5160—61no—
63#5151D311yescharacteristic, complemented
64#5144—31no—
65#5142—31no—
66#5077—32no—
67#5077—32no—
68#4700—31no—
69#4700—31no—
70C2×C32×D4C2312yes—
71#3828C2311yescharacteristic
72C2×C3×#67—42no—
73C2×C3×#67—42no—
74C3×#237—22no—
75C3×#237—22no—
76C3×D3×D4—22no—
77C3×D3×D4—22no—
78C3×#235C2311yescharacteristic
79C3×#235C2312yes—
80C2×C3×D12C2312yes—
81D3×#67—42no—
82#3802—22no—
83D3×D12—22no—
84#3796—22no—
85#3795—22no—
86C32×D8—21no—
87C32×D8—21no—
88C2×C32×C8C2311yescharacteristic
89#3754—22no—
90#3753—22no—
91#3748C2312yes—
92#3748C2311yescharacteristic
93#3743—21no—
94C8×C3⋊D3—21no—
95C3×#214—22no—
96C3×#213—22no—
97C3×#213—22no—
98C3×#213—22no—
99C3×C4×Dic3C2311yescharacteristic
100C3×#208C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C3×Dic12D411yescharacteristic, complemented
103C3×D24—21no—
104C3×D24—21no—
105C3×D24D411yescharacteristic, complemented
106C3×#204D412yescomplemented
107C3×ΓL(1,𝔽25)—21no—
108C3×D3×C8—21no—
109#3719D411yescharacteristic, complemented
110#3717D411yescharacteristic, complemented
111#3716D411yescharacteristic, complemented
112#3715—22no—
113#3715—22no—
114#3714D411yescharacteristic, complemented
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#1004—32no—
123#1004C2×D312yescomplemented
124C3×AGL(1,ℤ/8)—32no—
125C3×AGL(1,ℤ/8)—62no—
126C3×#135—31no—
127C3×#135—61no—
128C2×C3×D8—21no—
129C2×C3×D8—32no—
130C2×C3×D8—31no—
131C2×C3×D8—61no—
132C2×C3×D8C2×D311yescharacteristic, complemented
133C2×C3×D8C2×D311yescharacteristic, complemented
134C3×#131—31no—
135C3×#127—32no—
136#950—31no—
137#950—62no—
138#949—32no—
139#949—32no—
140#949—62no—
141#948—32no—
142#940C2×D312yescomplemented
143#932—32no—
144#932—32no—
145#932—32no—
146#932—32no—
147#932—62no—
148#932—62no—
149#932C2×D312yescomplemented
150C2×#213—62no—
151C2×#213C2×D312yescomplemented
152#919—61no—
153#914—62no—
154#912—21no—
155#912—62no—
156#912—61no—
157#911—22no—
158#911—62no—
159#911—62no—
160#911—62no—
161D3×D8—21no—
162D3×D8—61no—
163D3×D8—62no—
164D3×D8—61no—
165#904—31no—
166#904C2×D311yescharacteristic
167C2×D24C2×D311yescharacteristic, complemented
168#901—32no—
169#901—31no—
170#901—31no—
171#901—61no—
172#901C2×D311yescharacteristic, complemented
173C3×C4×C8—31no—
174#837—31no—
175#837—32no—
176#833—32no—
177#833—32no—
178#833—32no—
179#833—62no—
180#825—31no—
181#823—32no—
182#822—31no—
183#819—31no—
184#819—31no—
185#819—31no—
186#819—61no—
187C8×Dic3C2×D311yescharacteristic, complemented
188#805—31no—
189#805—32no—
190#805—31no—
191C23×C32—22no—
192C22×C3×D3—22no—
193C22×C3×D3—42no—
194C2×D32—42no—
195C32×D4—22no—
196C32×D4—22no—
197C2×C32×C4C2411yescharacteristic
198#638—21no—
199C4⋊(C3⋊D3)C2×D411yescharacteristic
200C4×C3⋊D3—21no—
201#634C2×D411yescharacteristic
202C3×#67—22no—
203C3×#67—21no—
204C3×#67—42no—
205C3×#67—42no—
206C3×#67—84no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—42no—
209C3×D12—22no—
210C3×D12—22no—
211C3×D12C2×D411yescharacteristic
212C3×D12C2×D412yes—
213C3×C4×D3—22no—
214C3×C4×D3—21no—
215C3×Dic6C2×D411yescharacteristic
216C3×Dic6C2×D412yes—
217#626—42no—
218#625—42no—
219D3×Dic3—42no—
220C32×C8C2×D411yescharacteristic
221C32×C8C2×D411yescharacteristic
222C3⋊(C3⋊C8)—22no—
223C3⋊(C3⋊C8)—21no—
224C3×C3⋊C8—21no—
225C3×C3⋊C8C2×D411yescharacteristic
226C3×C3⋊C8C2×D411yescharacteristic
227#576—31no—
228#576—91no—
229#576—92no—
230#493—31no—
231#472—91no—
232#472—92no—
233#472—91no—
234#453—92no—
235#453—92no—
236#443—91no—
237#443—91no—
238C3×#41—32no—
239C3×#41—31no—
240C3×#41—62no—
241C3×#41—62no—
242C2×C3×D4—22no—
243C2×C3×D4—32no—
244C2×C3×D4—62no—
245C2×C3×D4—62no—
246C2×C3×D4—122no—
247C2×C3×D4—122no—
248C2×C3×D4C22×D312yes—
249C2×C3×D4C22×D312yes—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—122no—
253#239—62no—
254#237—22no—
255#237—22no—
256#237—62no—
257#237—62no—
258D3×D4—22no—
259D3×D4—22no—
260D3×D4—62no—
261D3×D4—62no—
262D3×D4—62no—
263D3×D4—122no—
264#235—31no—
265#235—31no—
266#235—61no—
267#235—62no—
268#235C22×D311yescharacteristic
269#235C22×D312yes—
270C2×D12—62no—
271C2×D12C22×D312yes—
272C3×Q16—31no—
273C3×SD16—32no—
274C3×SD16—62no—
275C3×D8—21no—
276C3×D8—21no—
277C3×D8—21no—
278C3×D8—21no—
279C3×D8—31no—
280C3×D8—41no—
281C3×D8—41no—
282C3×D8—62no—
283C3×D8—62no—
284C3×D8—62no—
285C3×D8—61no—
286C3×D8—61no—
287C3×M16—31no—
288C3×M16—61no—
289C2×C3×C8—21no—
290C2×C3×C8—31no—
291C2×C3×C8—61no—
292C2×C3×C8C22×D311yescharacteristic
293C2×C3×C8C22×D311yescharacteristic
294C3×C42—31no—
295#216—31no—
296#215—31no—
297#215—62no—
298#215—62no—
299#214—22no—
300#214—31no—
301#214—62no—
302#214—62no—
303#214—62no—
304#214—62no—
305#214—122no—
306#213—22no—
307#213—22no—
308#213—22no—
309#213—31no—
310#213—62no—
311#213—62no—
312#213—62no—
313#213—62no—
314#213—62no—
315#213—62no—
316#213—122no—
317C4×Dic3C22×D311yescharacteristic
318#208—32no—
319#208—31no—
320#208—32no—
321#208—31no—
322#208—62no—
323#208—61no—
324#208—62no—
325#208C22×D311yescharacteristic
326C2×C3⋊C8—62no—
327C2×C3⋊C8C22×D311yescharacteristic
328Dic12—31no—
329Dic12#6711yescharacteristic, complemented
330D24—21no—
331D24—21no—
332D24—31no—
333D24#6711yescharacteristic, complemented
334#204—31no—
335#204—31no—
336#204#6712yescomplemented
337ΓL(1,𝔽25)—21no—
338ΓL(1,𝔽25)—62no—
339ΓL(1,𝔽25)—61no—
340ΓL(1,𝔽25)—61no—
341ΓL(1,𝔽25)—121no—
342D3×C8—21no—
343D3×C8—62no—
344D3×C8—61no—
345D3×C8—61no—
346D3×C8—121no—
347C22×C32—42no—
348C22×C32—82no—
349C22×C32H(5,𝔽2)11yescharacteristic
350C2×C3⋊D3—21no—
351C2×C3×D3—22no—
352C2×C3×D3—21no—
353C2×C3×D3—42no—
354C2×C3×D3—82no—
355C2×C3×D3—162no—
356D32—162no—
357C32×C4C22×D411yescharacteristic
358C32×C4C22×D411yescharacteristic
359C3⋊Dic3—21no—
360C3×Dic3—22no—
361C3×Dic3—22no—
362C3×Dic3—21no—
363H(5,𝔽2)—32no—
364H(5,𝔽2)—92no—
365AGL(1,ℤ/8)—32no—
366AGL(1,ℤ/8)—62no—
367AGL(1,ℤ/8)—92no—
368AGL(1,ℤ/8)—92no—
369AGL(1,ℤ/8)—92no—
370AGL(1,ℤ/8)—182no—
371AGL(1,ℤ/8)—182no—
372AGL(1,ℤ/8)—182no—
373#135—31no—
374#135—61no—
375#135—91no—
376#135—181no—
377#135—182no—
378C2×D8—32no—
379C2×D8—31no—
380C2×D8—61no—
381C2×D8—181no—
382C2×D8—182no—
383C2×D8D3211yescharacteristic, complemented
384#131—31no—
385#131—92no—
386#131—91no—
387#127—32no—
388#108—91no—
389#108—91no—
390#104—91no—
391#104—91no—
392#104—92no—
393#100—92no—
394#100—92no—
395C4×C8—31no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—42no—
399C23×C3—62no—
400C23×C3—122no—
401C22×D3—22no—
402C22×D3—42no—
403C22×D3—122no—
404C22×D3—122no—
405C3×Q8—31no—
406C3×Q8—32no—
407C3×D4—22no—
408C3×D4—22no—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—31no—
412C3×D4—32no—
413C3×D4—42no—
414C3×D4—42no—
415C3×D4—62no—
416C3×D4—61no—
417C3×D4—62no—
418C3×D4—62no—
419C3×D4—122no—
420C3×D4—122no—
421C3×D4—244no—
422C2×C3×C4—21no—
423C2×C3×C4—61no—
424C2×C3×C4—62no—
425C2×C3×C4—61no—
426C2×C3×C4—122no—
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—21no—
430#67—22no—
431#67—42no—
432#67—42no—
433#67—61no—
434#67—61no—
435#67—84no—
436#67—121no—
437#67—122no—
438#67—122no—
439#67—122no—
440C2×Dic3—21no—
441C2×Dic3—42no—
442C2×Dic3—122no—
443D12—22no—
444D12—22no—
445D12—31no—
446D12—31no—
447D12—61no—
448D12—122no—
449D12D3×D411yescharacteristic
450D12C2×#6712yes—
451C4×D3—22no—
452C4×D3—21no—
453C4×D3—61no—
454C4×D3—61no—
455C4×D3—121no—
456C4×D3—122no—
457Dic6—31no—
458Dic6—31no—
459Dic6—61no—
460Dic6D3×D411yescharacteristic
461Dic6C2×#6712yes—
462C3×C8—21no—
463C3×C8—21no—
464C3×C8—31no—
465C3×C8—31no—
466C3×C8—61no—
467C3×C8D3×D411yescharacteristic
468C3×C8D3×D411yescharacteristic
469C3×C8C2×#6711yescharacteristic
470C3×C8C2×#6711yescharacteristic
471C3⋊C8—21no—
472C3⋊C8—62no—
473C3⋊C8—61no—
474C3⋊C8—62no—
475C3⋊C8—61no—
476C3⋊C8—121no—
477C3⋊C8—122no—
478C3⋊C8D3×D411yescharacteristic
479C3⋊C8D3×D411yescharacteristic
480C2×C32—21no—
481C2×C32—82no—
482C2×C32D4211yescharacteristic
483C3⋊D3—41no—
484C3×D3—42no—
485C3×D3—41no—
486C3×D3—82no—
487#41—31no—
488#41—32no—
489#41—62no—
490#41—62no—
491#41—91no—
492#41—182no—
493#41—182no—
494C2×D4—32no—
495C2×D4—62no—
496C2×D4—62no—
497C2×D4—122no—
498C2×D4—122no—
499C2×D4—182no—
500C2×D4—182no—
501C2×D4—362no—
502C2×D4C2×D3212yes—
503Q16—31no—
504Q16—91no—
505SD16—32no—
506SD16—62no—
507SD16—91no—
508SD16—91no—
509SD16—182no—
510SD16—182no—
511SD16—182no—
512D8—21no—
513D8—21no—
514D8—31no—
515D8—62no—
516D8—62no—
517D8—62no—
518D8—61no—
519D8—61no—
520D8—91no—
521D8—182no—
522D8—182no—
523D8—182no—
524M16—31no—
525M16—61no—
526M16—92no—
527M16—91no—
528M16—182no—
529M16—181no—
530C2×C8—31no—
531C2×C8—61no—
532C2×C8—182no—
533C2×C8—181no—
534C2×C8C2×D3211yescharacteristic
535C42—31no—
536C22×C3—21no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—62no—
540C22×C3—61no—
541C22×C3—82no—
542C22×C3—82no—
543C22×C3—82no—
544C22×C3—122no—
545C22×C3—162no—
546C22×C3—242no—
547C22×C3—482no—
548C22×C3#100411yescharacteristic
549C22×C3#100411yescharacteristic
550C2×D3—21no—
551C2×D3—22no—
552C2×D3—42no—
553C2×D3—61no—
554C2×D3—61no—
555C2×D3—82no—
556C2×D3—121no—
557C2×D3—162no—
558C2×D3—482no—
559C2×D3—482no—
560C3×C4—21no—
561C3×C4—21no—
562C3×C4—62no—
563C3×C4—62no—
564C3×C4—61no—
565C3×C4C2×D3×D411yescharacteristic
566C3×C4C2×D3×D411yescharacteristic
567C3×C4C2×D3×D411yescharacteristic
568C3×C4C22×#6711yescharacteristic
569Dic3—22no—
570Dic3—21no—
571Dic3—22no—
572Dic3—61no—
573Dic3—61no—
574Dic3—121no—
575C32#329211yescharacteristic, complemented, Sylow
576C23—22no—
577C23—62no—
578C23—122no—
579C23—362no—
580Q8—31no—
581Q8—32no—
582Q8—91no—
583D4—22no—
584D4—22no—
585D4—31no—
586D4—32no—
587D4—61no—
588D4—62no—
589D4—62no—
590D4—62no—
591D4—91no—
592D4—122no—
593D4—122no—
594D4—181no—
595D4—244no—
596D4—362no—
597D4—362no—
598C2×C4—61no—
599C2×C4—62no—
600C2×C4—61no—
601C2×C4—122no—
602C2×C4—181no—
603C2×C4—362no—
604C2×C4C22×D3211yescharacteristic
605C8—31no—
606C8—31no—
607C8—61no—
608C8—182no—
609C8—181no—
610C8D3×#6711yescharacteristic
611C8D3×#6711yescharacteristic
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—41no—
616C2×C3—82no—
617C2×C3—82no—
618C2×C3—122no—
619C2×C3—121no—
620C2×C3—162no—
621C2×C3—242no—
622C2×C3#571711yescharacteristic
623C2×C3D4×#6711yescharacteristic
624D3—41no—
625D3—42no—
626D3—82no—
627D3—121no—
628D3—121no—
629D3—241no—
630C22—42no—
631C22—61no—
632C22—62no—
633C22—82no—
634C22—122no—
635C22—181no—
636C22—242no—
637C22—482no—
638C22—1442no—
639C22#6431311yescharacteristic
640C4—62no—
641C4—61no—
642C4—62no—
643C4—181no—
644C4D32×D411yescharacteristic
645C4C2×D3×#6711yescharacteristic
646C3—21no—
647C3#8179111yescharacteristic, complemented
648C3#8401011yescharacteristic, complemented
649C2—21no—
650C2—82no—
651C2—121no—
652C2—122no—
653C2—242no—
654C2—361no—
655C2#1059529311yescharacteristic
subgroupG/H
centerC2#10595293
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC2×C32D42
hypercenterC2×D8D32
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5757C2semidirect
2. #10595096C2semidirect
3. #10594687C2semidirect
4. #10592859C2semidirect
5. C3×#5151C2semidirect
6. #10591523C2semidirect
7. #10591509C2semidirect
8. #10591505C2semidirect
9. #10590926C2semidirect
10. #10590923C2semidirect
11. #10590915C2semidirect
14. C3×#1004C22semidirect
15. #64307C22semidirect
16. C2×C32×D8C22semidirect
17. #64141C22semidirect
18. #64110C22semidirect
19. C3×#940C22semidirect
20. C3×#932C22semidirect
21. C2×C3×#213C22semidirect
26. C2×C3×D24C22semidirect
27. C3×#901C22semidirect
33. #63823C22semidirect
34. #63823C22semidirect
35. #63814C22semidirect
39. #63660C22semidirect
40. #63646C22semidirect
41. C3×C8×Dic3C22semidirect
42. #63577C22semidirect
43. #63570C22semidirect
44. #63569C22semidirect
45. #63569C22semidirect
46. #63558C22semidirect
52. #5757D3semidirect
63. #5151D3semidirect
102. C3×Dic12D4semidirect
105. C3×D24D4semidirect
106. C3×#204D4semidirect
109. #3719D4semidirect
110. #3717D4semidirect
111. #3716D4semidirect
114. #3714D4semidirect
123. #1004C2×D3semidirect
132. C2×C3×D8C2×D3semidirect
133. C2×C3×D8C2×D3semidirect
142. #940C2×D3semidirect
149. #932C2×D3semidirect
151. C2×#213C2×D3semidirect
167. C2×D24C2×D3semidirect
172. #901C2×D3semidirect
187. C8×Dic3C2×D3semidirect
329. Dic12#67semidirect
333. D24#67semidirect
336. #204#67semidirect
383. C2×D8D32semidirect
575. C32#3292semidirect
647. C3#81791semidirect
648. C3#84010semidirect

Maximal subgroups

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

subgroupindex
C3×#57572
#105950962
#105946872
#105928592
C3×#51512
#105915232
#105915092
#105915052
#105909262
#105909232
#105909152
#840103
#817913