Finite Group Databasebeta

← #11886915

Subgroups — #11886915

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×#5752C211yesmaximal, characteristic, complemented
2#10595456C212yesmaximal, complemented
3#10594680C211yesmaximal, characteristic, complemented
4#10592841C211yesmaximal, characteristic, complemented
5C3×#5144C211yesmaximal, characteristic, complemented
6#10591666C212yesmaximal, complemented
7#10591013C212yesmaximal, complemented
8#10590984C212yesmaximal, complemented
9#10590926C211yesmaximal, characteristic, complemented
10#10590915C211yesmaximal, characteristic, complemented
11#10590880C211yesmaximal, characteristic, complemented
12#84010—31nomaximal
13#79894—31nomaximal
14C3×#1009C2212yescomplemented
15#64308C2212yescomplemented
16C32×#131C2211yescharacteristic, complemented
17#64158C2212yescomplemented
18C2×#3745C2211yescharacteristic, complemented
19C3×#950C2211yescharacteristic
20C3×#908—22no—
21C3×#908C2212yescomplemented
22C3×#904—21no—
23C3×#904C2211yescharacteristic
24C2×C3×D24—21no—
25C2×C3×D24C2211yescharacteristic, complemented
26C3×#901C2211yescharacteristic, complemented
27#63949—22no—
28#63939—22no—
29#63934—22no—
30D3×#213—22no—
31#63911C2212yescomplemented
32#63825C2212yescomplemented
33C2×#3714C2212yescomplemented
34#63823C2212yescomplemented
35#63814C2212yescomplemented
36#63808—21no—
37#63794—22no—
38D3×D24—21no—
39#63650C2212yescomplemented
40#63646C2211yescharacteristic, complemented
41C3×#837C2211yescharacteristic, complemented
42C3×#825C2211yescharacteristic, complemented
43C3×#822C2211yescharacteristic, complemented
44C3×C8×Dic3C2211yescharacteristic, complemented
45#63569C2212yescomplemented
46#63558C2212yescomplemented
47C3×#576—31no—
48#5835—32no—
49#5769—32no—
50#5769—31no—
51#5752—31no—
52#5752D311yescharacteristic, complemented
53C3×#443—31no—
54#5241—32no—
55#5199—32no—
56#5198—32no—
57#5196—31no—
58#5160—31no—
59#5151—31no—
60#5144D311yescharacteristic, complemented
61#5142—31no—
62#5142—31no—
63#5142—31no—
64#5142—61no—
65#4897—32no—
66#4822—32no—
67#4822—32no—
68#4700—31no—
69#4695—31no—
70C32×#41C2311yescharacteristic
71C2×C4⋊(C3⋊D3)C2312yes—
72C3×#239—22no—
73C3×D3×D4—22no—
74C3×D3×D4—42no—
75C3×#235—22no—
76C3×#235C2311yescharacteristic
77C3×#235C2312yes—
78C2×C3×D12—22no—
79C2×C3×D12C2312yes—
80#3811—42no—
81C2×#626—42no—
82D3×D12—22no—
83D3×D12—22no—
84#3799—22no—
85#3799—22no—
86C32×M16—21no—
87C32×M16C2311yescharacteristic
88C2×C32×C8—21no—
89C2×C32×C8C2311yescharacteristic
90#3755—22no—
91#3753—22no—
92#3748C2312yes—
93#3745—21no—
94#3745—21no—
95C3×#216D411yescharacteristic, complemented
96C3×#215D411yescharacteristic, complemented
97C3×#214D411yescharacteristic, complemented
98C3×#213D411yescharacteristic, complemented
99C3×C4×Dic3C2311yescharacteristic
100C3×#208C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C3×Dic12D411yescharacteristic, complemented
103C3×D24—22no—
104C3×D24—21no—
105C3×D24—21no—
106C3×D24D411yescharacteristic, complemented
107C3×#204—22no—
108C3×#204D412yescomplemented
109C3×ΓL(1,𝔽25)—21no—
110C3×D3×C8—21no—
111#3717—22no—
112#3715—22no—
113#3714—22no—
114#3714—22no—
115#3714—22no—
116#3713—22no—
117#3711—22no—
118D3×C3⋊C8—22no—
119#3292—91noSylow
120C3×H(5,𝔽2)—32no—
121#1009—32no—
122#1009—32no—
123#1009C2×D312yescomplemented
124C3×AGL(1,ℤ/8)—32no—
125C3×AGL(1,ℤ/8)—62no—
126C3×#135—31no—
127C3×#135—31no—
128C3×#135—61no—
129C2×C3×D8—31no—
130C2×C3×D8—61no—
131C3×#131—21no—
132C3×#131—31no—
133C3×#131C2×D311yescharacteristic, complemented
134C3×#131C2×D311yescharacteristic, complemented
135#950—62no—
136#950C2×D311yescharacteristic
137#949—32no—
138#949—32no—
139#949—32no—
140#949—32no—
141#949—62no—
142#949—62no—
143#948—32no—
144#940—32no—
145#932—32no—
146#932—62no—
147C2×#213—32no—
148C2×#213—62no—
149#919—61no—
150#919—62no—
151#914—62no—
152#914—62no—
153#914—62no—
154D3×D8—61no—
155D3×D8—62no—
156#908—22no—
157#908—32no—
158#908—62no—
159#908C2×D312yescomplemented
160#904—21no—
161#904—61no—
162#904C2×D311yescharacteristic
163C2×D24—21no—
164C2×D24—32no—
165C2×D24—31no—
166C2×D24—31no—
167C2×D24—61no—
168C2×D24—61no—
169C2×D24C2×D311yescharacteristic, complemented
170#901—32no—
171#901C2×D311yescharacteristic, complemented
172#874—32no—
173C3×#108—31no—
174C3×#104—31no—
175C3×#104—31no—
176C3×C4×C8—31no—
177#837—32no—
178#837C2×D311yescharacteristic, complemented
179#833—32no—
180#825C2×D311yescharacteristic, complemented
181#823—32no—
182#823—32no—
183#823—32no—
184#823—62no—
185#822C2×D311yescharacteristic, complemented
186#819—31no—
187#819—31no—
188#819—61no—
189C8×Dic3C2×D311yescharacteristic, complemented
190#805—32no—
191C22×C3⋊D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—42no—
194C2×D32—42no—
195C32×Q8C2×D411yescharacteristic
196C32×D4—21no—
197C32×D4C2×D411yescharacteristic
198C2×C32×C4—21no—
199C2×C32×C4C2411yescharacteristic
200C4⋊(C3⋊D3)—22no—
201C4⋊(C3⋊D3)—22no—
202C3×#67—21no—
203C3×#67—22no—
204C3×#67—42no—
205C2×C3×Dic3—21no—
206C3×D12—22no—
207C3×D12—22no—
208C3×D12—42no—
209C3×D12C2×D411yescharacteristic
210C3×D12C2×D412yes—
211C3×C4×D3—22no—
212C3×C4×D3—21no—
213C3×C4×D3—42no—
214C3×Dic6C2×D411yescharacteristic
215C3×Dic6C2×D412yes—
216#626—42no—
217#626—42no—
218#626—84no—
219#624—42no—
220C32×C8—21no—
221C32×C8C2×D411yescharacteristic
222C32×C8C2×D411yescharacteristic
223C3⋊(C3⋊C8)—22no—
224C3×C3⋊C8—21no—
225C3×C3⋊C8C2×D411yescharacteristic
226C3×C3⋊C8C2×D411yescharacteristic
227#576—31no—
228#576—91no—
229#576—92no—
230#493—91no—
231#472—92no—
232#472—91no—
233#472—91no—
234#453—92no—
235#453—92no—
236#443—31no—
237#443—91no—
238C3×#41—21no—
239C3×#41—32no—
240C3×#41—31no—
241C3×#41—62no—
242C3×#41—62no—
243C3×#41C22×D311yescharacteristic
244C3×#41C22×D311yescharacteristic
245C2×C3×D4—32no—
246C2×C3×D4—62no—
247C2×C3×D4—62no—
248C2×C3×D4—122no—
249C2×#67—122no—
250#239—22no—
251#239—62no—
252#239—62no—
253D3×D4—22no—
254D3×D4—42no—
255D3×D4—62no—
256D3×D4—62no—
257D3×D4—122no—
258D3×D4—122no—
259#235—22no—
260#235—62no—
261#235—62no—
262#235C22×D311yescharacteristic
263#235C22×D312yes—
264C2×D12—22no—
265C2×D12—32no—
266C2×D12—32no—
267C2×D12—62no—
268C2×D12—62no—
269C2×D12—62no—
270C2×D12—122no—
271C2×D12C22×D312yes—
272C3×Q16—31no—
273C3×Q16—31no—
274C3×SD16—31no—
275C3×SD16—31no—
276C3×SD16—32no—
277C3×SD16—62no—
278C3×D8—31no—
279C3×D8—31no—
280C3×D8—62no—
281C3×D8—61no—
282C3×D8—61no—
283C3×M16—21no—
284C3×M16—21no—
285C3×M16—21no—
286C3×M16—31no—
287C3×M16—41no—
288C3×M16—61no—
289C3×M16C22×D311yescharacteristic
290C3×M16C22×D311yescharacteristic
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—31no—
295C2×C3×C8—41no—
296C2×C3×C8—61no—
297C2×C3×C8C22×D311yescharacteristic
298C2×C3×C8C22×D311yescharacteristic
299C3×C42—31no—
300#216D1211yescharacteristic, complemented
301#215—62no—
302#215—62no—
303#215—62no—
304#215—62no—
305#215—122no—
306#215D1211yescharacteristic, complemented
307#214—62no—
308#214D1211yescharacteristic, complemented
309#213—62no—
310#213—62no—
311#213—62no—
312#213—62no—
313#213—62no—
314#213—62no—
315#213—62no—
316#213—122no—
317#213D1211yescharacteristic, complemented
318C4×Dic3C22×D311yescharacteristic
319#208—32no—
320#208—32no—
321#208—62no—
322#208—62no—
323#208C22×D311yescharacteristic
324C2×C3⋊C8—62no—
325C2×C3⋊C8C22×D311yescharacteristic
326Dic12#6711yescharacteristic, complemented
327D24—22no—
328D24—21no—
329D24—21no—
330D24—62no—
331D24—62no—
332D24—62no—
333D24—61no—
334D24—61no—
335D24—61no—
336D24—61no—
337D24—121no—
338D24—121no—
339D24#6711yescharacteristic, complemented
340#204—22no—
341#204—62no—
342#204#6712yescomplemented
343ΓL(1,𝔽25)—21no—
344ΓL(1,𝔽25)—62no—
345D3×C8—21no—
346D3×C8—62no—
347C22×C32—21no—
348C22×C32H(5,𝔽2)11yescharacteristic
349C2×C3⋊D3—42no—
350C2×C3⋊D3—82no—
351C2×C3×D3—21no—
352C2×C3×D3—22no—
353C2×C3×D3—42no—
354C2×C3×D3—82no—
355C2×C3×D3—162no—
356D32—162no—
357C32×C4—21no—
358C32×C4C22×D411yescharacteristic
359C32×C4C22×D411yescharacteristic
360C3×Dic3—22no—
361C3×Dic3—21no—
362C3×Dic3—22no—
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—31no—
375#135—61no—
376#135—181no—
377#135—182no—
378C2×D8—31no—
379C2×D8—61no—
380C2×D8—92no—
381C2×D8—91no—
382C2×D8—181no—
383C2×D8—182no—
384#131—31no—
385#131—92no—
386#131D3211yescharacteristic, complemented
387#127—92no—
388#108—31no—
389#108—91no—
390#104—31no—
391#104—31no—
392#104—92no—
393#100—92no—
394#100—92no—
395C4×C8—31no—
396C23×C3—62no—
397C23×C3—122no—
398C22×D3—22no—
399C22×D3—42no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—122no—
403C22×D3—122no—
404C22×D3—122no—
405C3×Q8—21no—
406C3×Q8—31no—
407C3×Q8—32no—
408C3×Q8C2×D1211yescharacteristic
409C3×Q8D3×D411yescharacteristic
410C3×D4—21no—
411C3×D4—21no—
412C3×D4—21no—
413C3×D4—31no—
414C3×D4—32no—
415C3×D4—41no—
416C3×D4—61no—
417C3×D4—62no—
418C3×D4—62no—
419C3×D4—62no—
420C3×D4—122no—
421C3×D4—122no—
422C3×D4C2×D1211yescharacteristic
423C3×D4D3×D411yescharacteristic
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—41no—
428C2×C3×C4—61no—
429C2×C3×C4—62no—
430C2×C3×C4—61no—
431C2×C3×C4—122no—
432C2×C3×C4C23×D311yescharacteristic
433C2×C3×C4C23×D311yescharacteristic
434#67—22no—
435#67—21no—
436#67—42no—
437#67—122no—
438#67—122no—
439#67—244no—
440C2×Dic3—21no—
441D12—22no—
442D12—22no—
443D12—42no—
444D12—62no—
445D12—62no—
446D12—62no—
447D12—62no—
448D12—122no—
449D12—122no—
450D12—122no—
451D12—122no—
452D12—244no—
453D12C2×D1211yescharacteristic
454D12C2×#6712yes—
455C4×D3—21no—
456C4×D3—22no—
457C4×D3—42no—
458C4×D3—122no—
459C4×D3—122no—
460Dic6C2×D1211yescharacteristic
461Dic6C2×#6712yes—
462C3×C8—21no—
463C3×C8—21no—
464C3×C8—21no—
465C3×C8—21no—
466C3×C8—31no—
467C3×C8—31no—
468C3×C8—41no—
469C3×C8—61no—
470C3×C8D3×D411yescharacteristic
471C3×C8D3×D411yescharacteristic
472C3×C8C2×#6711yescharacteristic
473C3×C8C2×#6711yescharacteristic
474C3⋊C8—21no—
475C3⋊C8—62no—
476C3⋊C8—62no—
477C3⋊C8—122no—
478C3⋊C8C2×D1211yescharacteristic
479C3⋊C8C2×D1211yescharacteristic
480C2×C32—21no—
481C2×C32—41no—
482C2×C32D4211yescharacteristic
483C3⋊D3—82no—
484C3×D3—41no—
485C3×D3—42no—
486C3×D3—82no—
487#41—31no—
488#41—32no—
489#41—62no—
490#41—62no—
491#41—182no—
492#41—182no—
493#41C2×D3211yescharacteristic
494C2×D4—32no—
495C2×D4—62no—
496C2×D4—62no—
497C2×D4—92no—
498C2×D4—122no—
499C2×D4—182no—
500C2×D4—182no—
501C2×D4—362no—
502C2×D4—362no—
503Q16—31no—
504Q16—31no—
505SD16—31no—
506SD16—31no—
507SD16—32no—
508SD16—62no—
509SD16—182no—
510SD16—182no—
511SD16—182no—
512D8—31no—
513D8—31no—
514D8—62no—
515D8—61no—
516D8—61no—
517D8—182no—
518D8—182no—
519D8—182no—
520D8—182no—
521D8—182no—
522D8—181no—
523D8—181no—
524M16—21no—
525M16—31no—
526M16—61no—
527M16—92no—
528M16—182no—
529M16C2×D3211yescharacteristic
530C2×C8—21no—
531C2×C8—31no—
532C2×C8—61no—
533C2×C8—182no—
534C2×C8C2×D3211yescharacteristic
535C42—31no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—41no—
540C22×C3—61no—
541C22×C3—62no—
542C22×C3—122no—
543C22×C3—242no—
544C22×C3—482no—
545C22×C3#100411yescharacteristic
546C22×C3#100911yescharacteristic
547C2×D3—22no—
548C2×D3—21no—
549C2×D3—42no—
550C2×D3—82no—
551C2×D3—122no—
552C2×D3—122no—
553C2×D3—162no—
554C2×D3—242no—
555C2×D3—242no—
556C2×D3—242no—
557C2×D3—482no—
558C2×D3—482no—
559C2×D3—482no—
560C3×C4—21no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—21no—
564C3×C4—41no—
565C3×C4—62no—
566C3×C4—61no—
567C3×C4—62no—
568C3×C4C22×D1211yescharacteristic
569C3×C4C2×D3×D411yescharacteristic
570C3×C4C2×D3×D411yescharacteristic
571C3×C4C22×#6711yescharacteristic
572Dic3—22no—
573Dic3—22no—
574Dic3—21no—
575C32#329211yescharacteristic, complemented, Sylow
576C23—62no—
577C23—122no—
578C23—182no—
579C23—362no—
580Q8—31no—
581Q8—32no—
582Q8D3×D1211yescharacteristic
583D4—21no—
584D4—31no—
585D4—32no—
586D4—62no—
587D4—61no—
588D4—62no—
589D4—62no—
590D4—122no—
591D4—122no—
592D4—182no—
593D4—182no—
594D4—362no—
595D4—362no—
596D4—724no—
597D4D3×D1211yescharacteristic
598C2×C4—21no—
599C2×C4—61no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—122no—
603C2×C4—362no—
604C2×C4C22×D3211yescharacteristic
605C8—21no—
606C8—31no—
607C8—31no—
608C8—61no—
609C8—182no—
610C8D3×#6711yescharacteristic
611C8D3×#6711yescharacteristic
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—41no—
616C2×C3—41no—
617C2×C3—41no—
618C2×C3—81no—
619C2×C3—122no—
620C2×C3—121no—
621C2×C3—242no—
622C2×C3D4×D1211yescharacteristic
623C2×C3D4×#6711yescharacteristic
624D3—41no—
625D3—42no—
626D3—82no—
627D3—242no—
628D3—242no—
629D3—482no—
630C22—21no—
631C22—62no—
632C22—61no—
633C22—122no—
634C22—242no—
635C22—362no—
636C22—482no—
637C22—722no—
638C22—1442no—
639C22#6430711yescharacteristic
640C4—21no—
641C4—62no—
642C4—62no—
643C4—61no—
644C4C2×D3×D1211yescharacteristic
645C4C2×D3×#6711yescharacteristic
646C3—21no—
647C3#7989411yescharacteristic, complemented
648C3#8401011yescharacteristic, complemented
649C2—21no—
650C2—41no—
651C2—122no—
652C2—121no—
653C2—242no—
654C2—722no—
655C2D12×#6711yescharacteristic
subgroupG/H
centerC2D12×#67
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. #10595456C2semidirect
3. #10594680C2semidirect
4. #10592841C2semidirect
5. C3×#5144C2semidirect
6. #10591666C2semidirect
7. #10591013C2semidirect
8. #10590984C2semidirect
9. #10590926C2semidirect
10. #10590915C2semidirect
11. #10590880C2semidirect
14. C3×#1009C22semidirect
15. #64308C22semidirect
16. C32×#131C22semidirect
17. #64158C22semidirect
18. C2×#3745C22semidirect
21. C3×#908C22semidirect
25. C2×C3×D24C22semidirect
26. C3×#901C22semidirect
31. #63911C22semidirect
32. #63825C22semidirect
33. C2×#3714C22semidirect
34. #63823C22semidirect
35. #63814C22semidirect
39. #63650C22semidirect
40. #63646C22semidirect
41. C3×#837C22semidirect
42. C3×#825C22semidirect
43. C3×#822C22semidirect
44. C3×C8×Dic3C22semidirect
45. #63569C22semidirect
46. #63558C22semidirect
52. #5752D3semidirect
60. #5144D3semidirect
95. C3×#216D4semidirect
96. C3×#215D4semidirect
97. C3×#214D4semidirect
98. C3×#213D4semidirect
102. C3×Dic12D4semidirect
106. C3×D24D4semidirect
108. C3×#204D4semidirect
123. #1009C2×D3semidirect
133. C3×#131C2×D3semidirect
134. C3×#131C2×D3semidirect
159. #908C2×D3semidirect
169. C2×D24C2×D3semidirect
171. #901C2×D3semidirect
178. #837C2×D3semidirect
180. #825C2×D3semidirect
185. #822C2×D3semidirect
189. C8×Dic3C2×D3semidirect
300. #216D12semidirect
306. #215D12semidirect
308. #214D12semidirect
317. #213D12semidirect
326. Dic12#67semidirect
339. D24#67semidirect
342. #204#67semidirect
386. #131D32semidirect
575. C32#3292semidirect
647. C3#79894semidirect
648. C3#84010semidirect

Maximal subgroups

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

subgroupindex
C3×#57522
#105954562
#105946802
#105928412
C3×#51442
#105916662
#105910132
#105909842
#105909262
#105909152
#105908802
#840103
#798943