Finite Group Databasebeta

← #11886818

Subgroups — #11886818

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594691C211yesmaximal, characteristic, complemented
2#10594686C212yesmaximal, complemented
3#10594678C211yesmaximal, characteristic, complemented
4#10592399C211yesmaximal, characteristic, complemented
5C3×#4700C211yesmaximal, characteristic, complemented
6C3×#4696C211yesmaximal, characteristic, complemented
7#10590930C211yesmaximal, characteristic, complemented
8#10590928C212yesmaximal, complemented
9#10590926C211yesmaximal, characteristic, complemented
10#10590400C212yesmaximal, complemented
11#10590396C212yesmaximal, complemented
12#81835—31nomaximal
13#79891—31nomaximal
14#64307C2212yes—
15#64297C2212yescomplemented
16#64113C2211yescharacteristic
17#64110C2212yescomplemented
18C2×C3×Dic12C2211yescharacteristic, complemented
19C3×#904C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21C2×C3×#204C2212yescomplemented
22C3×#901C2211yescharacteristic
23C3×#901C2211yescharacteristic, complemented
24C3×#875C2212yescomplemented
25#63833C2212yescomplemented
26#63830C2212yes—
27#63827C2212yes—
28#63823C2212yescomplemented
29#63811—22no—
30#63809—22no—
31#63808—21no—
32#63807—21no—
33#63801—22no—
34D3×Dic12—21no—
35#63798—22no—
36#63796—22no—
37#63795—22no—
38D3×D24—21no—
39C32×C4×C8C2211yescharacteristic, complemented
40#63646C2211yescharacteristic, complemented
41#63632C2212yescomplemented
42C3×#819C2211yescharacteristic, complemented
43C3×#805C2211yescharacteristic
44C3×#805C2211yescharacteristic, complemented
45#63560C2212yescomplemented
46#63558C2212yescomplemented
47#5770—32no—
48#5766—31no—
49#5762—32no—
50#5757—31no—
51#5753—31no—
52#5752—31no—
53C3×#495—31no—
54C3×#443—31no—
55#5192—31no—
56#5177—32no—
57#5160—31no—
58#5143—31no—
59#5142—31no—
60#5062—32no—
61#5061—32no—
62#4898—32no—
63#4827—32no—
64#4825—32no—
65#4700—31no—
66#4700—31no—
67#4700—61no—
68#4700D311yescharacteristic, complemented
69#4696D311yescharacteristic, complemented
70#3828C2312yes—
71C3×#235C2311yescharacteristic
72C3×#235C2311yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×Dic6C2312yes—
75D3×#67—42no—
76#3804—42no—
77#3802—22no—
78D3×D12—22no—
79#3799—22no—
80#3797—22no—
81#3796—22no—
82#3796—22no—
83#3795—22no—
84D3×Dic6—22no—
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C42C2311yescharacteristic
88#3748C2312yes—
89#3746D411yescharacteristic
90#3745D411yescharacteristic
91#3744D412yes—
92#3743—22no—
93C8×C3⋊D3—22no—
94C3×(C2×D3)⋊C4—42no—
95C3×#208C2311yescharacteristic
96C3×#208C2311yescharacteristic
97C3×Dic12—21no—
98C3×Dic12—21no—
99C3×Dic12D411yescharacteristic
100C3×D24—21no—
101C3×D24—21no—
102C3×D24D411yescharacteristic
103C3×#204—22no—
104C3×#204—22no—
105C3×#204D411yescharacteristic
106C3×#204D411yescharacteristic
107C3×ΓL(1,𝔽25)—21no—
108C3×ΓL(1,𝔽25)—21no—
109C3×D3×C8—21no—
110C3×D3×C8—21no—
111#3719—22no—
112#3718—22no—
113#3717—22no—
114#3716—22no—
115#3715—22no—
116#3715—22no—
117#3714—22no—
118#3713—22no—
119#3290—91noSylow
120#1010—32no—
121#1009—32no—
122#1007—32no—
123#1004—32no—
124C3×#135—31no—
125C2×C3×Q16—31no—
126C2×C3×SD16—32no—
127C2×C3×D8—31no—
128C3×#131—31no—
129C3×#131—31no—
130C3×#124—32no—
131#951—32no—
132#949—32no—
133#942—32no—
134#942—32no—
135#932—32no—
136#932—32no—
137#919—61no—
138#918—62no—
139#918—62no—
140D3×Q16—61no—
141#916—62no—
142#916—62no—
143#915—62no—
144#914—62no—
145D3×SD16—62no—
146D3×SD16—62no—
147#912—61no—
148#911—62no—
149#911—62no—
150D3×D8—61no—
151#909—32no—
152#909—62no—
153#908—32no—
154#908—62no—
155C2×Dic12—61no—
156C2×Dic12C2×D311yescharacteristic, complemented
157#904—31no—
158#904—31no—
159#904—61no—
160#904—61no—
161#904—61no—
162#904C2×D311yescharacteristic
163C2×D24—61no—
164C2×D24C2×D311yescharacteristic
165C2×#204C2×D312yescomplemented
166#901—32no—
167#901—32no—
168#901—62no—
169#901C2×D311yescharacteristic
170#901C2×D311yescharacteristic, complemented
171#875C2×D312yescomplemented
172C3×#108—31no—
173C3×#104—31no—
174C3×#104—31no—
175C3×C4×C8—21no—
176C3×C4×C8C2×D311yescharacteristic, complemented
177C3×C4×C8C2×D311yescharacteristic, complemented
178#836—32no—
179#833—32no—
180#824—32no—
181#823—32no—
182#819—31no—
183#819—31no—
184#819—61no—
185#819C2×D311yescharacteristic, complemented
186#805—32no—
187#805—32no—
188#805—62no—
189#805C2×D311yescharacteristic
190#805C2×D311yescharacteristic, complemented
191C22×C3×D3—22no—
192C2×D32—42no—
193C2×C32×C4—21no—
194C2×C32×C4C2411yescharacteristic
195#638—22no—
196C4⋊(C3⋊D3)C2×D412yes—
197C4×C3⋊D3—22no—
198#634C2×D412yes—
199C3×#67—21no—
200C3×#67—21no—
201C2×C3×Dic3—22no—
202C3×D12—22no—
203C3×D12—22no—
204C3×D12C2×D411yescharacteristic
205C3×D12C2×D411yescharacteristic
206C3×C4×D3—21no—
207C3×C4×D3—21no—
208C3×Dic6—22no—
209C3×Dic6—22no—
210C3×Dic6C2×D411yescharacteristic
211C3×Dic6C2×D411yescharacteristic
212#627—42no—
213#626—42no—
214#626—42no—
215#625—42no—
216#624—42no—
217D3×Dic3—42no—
218D3×Dic3—42no—
219C32×C8C2×D411yescharacteristic
220C32×C8C2×D411yescharacteristic
221C32×C8C2×D411yescharacteristic
222C32×C8C2×D411yescharacteristic
223C3⋊(C3⋊C8)—22no—
224C3×C3⋊C8—21no—
225C3×C3⋊C8—21no—
226#578—91no—
227#577—92no—
228#576—91no—
229#495—31no—
230#473—91no—
231#472—91no—
232#471—92no—
233#455—92no—
234#454—92no—
235#443—31no—
236#443—91no—
237C3×#41—31no—
238C3×#41—31no—
239C2×C3×Q8—32no—
240C2×C3×D4—32no—
241C2×#67—122no—
242#239—62no—
243#239—62no—
244#239—62no—
245D3×Q8—62no—
246D3×Q8—62no—
247D3×Q8—62no—
248#237—62no—
249#237—62no—
250#237—62no—
251#237—122no—
252D3×D4—62no—
253D3×D4—62no—
254D3×D4—62no—
255D3×D4—122no—
256#235—32no—
257#235—32no—
258#235—62no—
259#235—62no—
260#235—62no—
261#235—122no—
262#235C22×D311yescharacteristic
263#235C22×D311yescharacteristic
264C2×D12—62no—
265C2×D12C22×D312yes—
266C2×Dic6—62no—
267C2×Dic6C22×D312yes—
268C3×Q16—31no—
269C3×Q16—61no—
270C3×Q16—61no—
271C3×SD16—31no—
272C3×SD16—31no—
273C3×SD16—62no—
274C3×SD16—62no—
275C3×D8—31no—
276C3×D8—61no—
277C3×D8—61no—
278C3×M16—31no—
279C3×M16—31no—
280C3×M16—61no—
281C3×M16—61no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—61no—
285C2×C3×C8—61no—
286C2×C3×C8C22×D311yescharacteristic
287C2×C3×C8C22×D311yescharacteristic
288C2×C3×C8C22×D311yescharacteristic
289C2×C3×C8C22×D311yescharacteristic
290C3×C22⋊C4—122no—
291C3×C42—21no—
292C3×C42C22×D311yescharacteristic
293C3×C42C22×D311yescharacteristic
294#216—62no—
295#216—62no—
296#216—62no—
297#215—62no—
298#215—62no—
299#215—62no—
300#214—62no—
301#214—62no—
302#214—62no—
303#213—62no—
304#213—62no—
305#213—62no—
306(C2×D3)⋊C4—42no—
307#208—32no—
308#208—32no—
309#208—62no—
310#208C22×D311yescharacteristic
311#208C22×D311yescharacteristic
312Dic12—21no—
313Dic12—21no—
314Dic12—31no—
315Dic12—31no—
316Dic12—61no—
317Dic12—62no—
318Dic12D1211yescharacteristic
319D24—21no—
320D24—21no—
321D24—31no—
322D24—31no—
323D24—61no—
324D24—62no—
325D24D1211yescharacteristic
326#204—22no—
327#204—22no—
328#204—32no—
329#204—32no—
330#204—62no—
331#204—62no—
332#204—62no—
333#204D1211yescharacteristic
334#204D1211yescharacteristic
335ΓL(1,𝔽25)—21no—
336ΓL(1,𝔽25)—21no—
337ΓL(1,𝔽25)—62no—
338ΓL(1,𝔽25)—62no—
339ΓL(1,𝔽25)—122no—
340D3×C8—21no—
341D3×C8—21no—
342D3×C8—62no—
343D3×C8—62no—
344D3×C8—122no—
345C22×C32H(5,𝔽2)11yescharacteristic
346C2×C3⋊D3—22no—
347C2×C3×D3—21no—
348C2×C3×D3—21no—
349C2×C3×D3—42no—
350C2×C3×D3—82no—
351D32—162no—
352C32×C4—41no—
353C32×C4C22×D411yescharacteristic
354C32×C4C22×D411yescharacteristic
355C3⋊Dic3—22no—
356C3×Dic3—21no—
357C3×Dic3—21no—
358C3×Dic3—42no—
3592−1+4—92no—
360H(5,𝔽2)—92no—
361#137—92no—
362#137—92no—
363#137—182no—
364#137—182no—
365AGL(1,ℤ/8)—92no—
366AGL(1,ℤ/8)—92no—
367AGL(1,ℤ/8)—182no—
368AGL(1,ℤ/8)—182no—
369#135—31no—
370#135—91no—
371#135—181no—
372#135—181no—
373#135—182no—
374C2×Q16—31no—
375C2×Q16—181no—
376C2×SD16—32no—
377C2×SD16—182no—
378C2×D8—31no—
379C2×D8—181no—
380#131—31no—
381#131—31no—
382#131—92no—
383#124—32no—
384#108—31no—
385#108—91no—
386#104—31no—
387#104—31no—
388#104—92no—
389#101—92no—
390#100—92no—
391C4×C8D3211yescharacteristic, complemented
392C23×C3—62no—
393C22×D3—22no—
394C22×D3—122no—
395C22×D3—122no—
396C3×Q8—31no—
397C3×Q8—31no—
398C3×Q8—62no—
399C3×Q8—62no—
400C3×D4—31no—
401C3×D4—31no—
402C3×D4—61no—
403C3×D4—61no—
404C3×D4—62no—
405C3×D4—62no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—41no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—21no—
416#67—21no—
417#67—62no—
418#67—62no—
419#67—122no—
420#67—122no—
421#67—122no—
422#67—122no—
423#67—122no—
424C2×Dic3—22no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427D12—22no—
428D12—22no—
429D12—32no—
430D12—32no—
431D12—62no—
432D12—122no—
433D12—122no—
434D12C2×D1211yescharacteristic
435D12C2×D1211yescharacteristic
436C4×D3—21no—
437C4×D3—21no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—122no—
441C4×D3—122no—
442C4×D3—122no—
443C4×D3—122no—
444C4×D3—122no—
445Dic6—22no—
446Dic6—22no—
447Dic6—32no—
448Dic6—32no—
449Dic6—62no—
450Dic6—122no—
451Dic6—122no—
452Dic6C2×D1211yescharacteristic
453Dic6C2×D1211yescharacteristic
454C3×C8—21no—
455C3×C8—21no—
456C3×C8—21no—
457C3×C8—21no—
458C3×C8—61no—
459C3×C8—61no—
460C3×C8C2×D1211yescharacteristic
461C3×C8C2×D1211yescharacteristic
462C3×C8D3×D411yescharacteristic
463C3×C8D3×D411yescharacteristic
464C3×C8D3×D411yescharacteristic
465C3×C8D3×D411yescharacteristic
466C3×C8D3×D411yescharacteristic
467C3×C8D3×D411yescharacteristic
468C3⋊C8—21no—
469C3⋊C8—21no—
470C3⋊C8—62no—
471C3⋊C8—62no—
472C3⋊C8—122no—
473C2×C32—21no—
474C2×C32D4211yescharacteristic
475C3⋊D3—42no—
476C3×D3—41no—
477C3×D3—41no—
478C3×D3—82no—
479#41—31no—
480#41—31no—
481#41—92no—
482#41—182no—
483#41—182no—
484#41—182no—
485#41—182no—
486#41—362no—
487C2×Q8—32no—
488C2×Q8—182no—
489C2×Q8—182no—
490C2×D4—32no—
491C2×D4—182no—
492C2×D4—182no—
493C2×D4—362no—
494Q16—31no—
495Q16—61no—
496Q16—61no—
497Q16—91no—
498Q16—182no—
499Q16—182no—
500SD16—31no—
501SD16—31no—
502SD16—62no—
503SD16—62no—
504SD16—92no—
505SD16—182no—
506SD16—182no—
507SD16—182no—
508SD16—182no—
509D8—31no—
510D8—61no—
511D8—61no—
512D8—91no—
513D8—182no—
514D8—182no—
515M16—31no—
516M16—31no—
517M16—61no—
518M16—61no—
519M16—92no—
520M16—182no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—182no—
524C2×C8C2×D3211yescharacteristic
525C2×C8C2×D3211yescharacteristic
526C22⋊C4—122no—
527C42C2×D3211yescharacteristic
528C22×C3—21no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—122no—
532C22×C3—242no—
533C22×C3#100411yescharacteristic
534C22×C3#100911yescharacteristic
535C2×D3—21no—
536C2×D3—21no—
537C2×D3—42no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—82no—
541C2×D3—122no—
542C2×D3—482no—
543C2×D3—482no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—41no—
547C3×C4—41no—
548C3×C4—42no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—122no—
552C3×C4C22×D1211yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C2×D3×D411yescharacteristic
555C3×C4C2×D3×D411yescharacteristic
556Dic3—21no—
557Dic3—21no—
558Dic3—42no—
559Dic3—62no—
560Dic3—62no—
561Dic3—122no—
562C32#329011yescharacteristic, complemented, Sylow
563C23—62no—
564C23—362no—
565Q8—31no—
566Q8—31no—
567Q8—62no—
568Q8—62no—
569Q8—92no—
570Q8—362no—
571D4—31no—
572D4—31no—
573D4—61no—
574D4—61no—
575D4—62no—
576D4—62no—
577D4—92no—
578D4—182no—
579D4—362no—
580D4—362no—
581D4—362no—
582C2×C4—21no—
583C2×C4—61no—
584C2×C4—61no—
585C2×C4—62no—
586C2×C4—182no—
587C2×C4—362no—
588C2×C4—362no—
589C2×C4—362no—
590C2×C4C22×D3211yescharacteristic
591C8—61no—
592C8—61no—
593C8—182no—
594C8D3×D1211yescharacteristic
595C8D3×D1211yescharacteristic
596C8#380211yescharacteristic
597C8#380211yescharacteristic
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—41no—
602C2×C3—121no—
603C2×C3—121no—
604C2×C3—242no—
605C2×C3D4×D1211yescharacteristic
606C2×C3#571711yescharacteristic
607D3—41no—
608D3—41no—
609D3—82no—
610D3—122no—
611D3—122no—
612D3—242no—
613C22—61no—
614C22—61no—
615C22—122no—
616C22—182no—
617C22—242no—
618C22—1442no—
619C22#6430711yescharacteristic
620C4—41no—
621C4—61no—
622C4—61no—
623C4—122no—
624C4—182no—
625C4C2×D3×D1211yescharacteristic
626C4C2×#380211yescharacteristic
627C3—21no—
628C3#7989111yescharacteristic, complemented
629C3#8183511yescharacteristic, complemented
630C2—21no—
631C2—121no—
632C2—121no—
633C2—242no—
634C2—362no—
635C2#1059400411yescharacteristic
subgroupG/H
centerC2#10594004
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC2×C32D42
hypercenterC4×C8D32
hypocenterC32#3290
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10594691C2semidirect
2. #10594686C2semidirect
3. #10594678C2semidirect
4. #10592399C2semidirect
5. C3×#4700C2semidirect
6. C3×#4696C2semidirect
7. #10590930C2semidirect
8. #10590928C2semidirect
9. #10590926C2semidirect
10. #10590400C2semidirect
11. #10590396C2semidirect
15. #64297C22semidirect
17. #64110C22semidirect
18. C2×C3×Dic12C22semidirect
21. C2×C3×#204C22semidirect
23. C3×#901C22semidirect
24. C3×#875C22semidirect
25. #63833C22semidirect
28. #63823C22semidirect
39. C32×C4×C8C22semidirect
40. #63646C22semidirect
41. #63632C22semidirect
42. C3×#819C22semidirect
44. C3×#805C22semidirect
45. #63560C22semidirect
46. #63558C22semidirect
68. #4700D3semidirect
69. #4696D3semidirect
156. C2×Dic12C2×D3semidirect
165. C2×#204C2×D3semidirect
170. #901C2×D3semidirect
171. #875C2×D3semidirect
176. C3×C4×C8C2×D3semidirect
177. C3×C4×C8C2×D3semidirect
185. #819C2×D3semidirect
190. #805C2×D3semidirect
391. C4×C8D32semidirect
562. C32#3290semidirect
628. C3#79891semidirect
629. C3#81835semidirect

Maximal subgroups

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

subgroupindex
#105946912
#105946862
#105946782
#105923992
C3×#47002
C3×#46962
#105909302
#105909282
#105909262
#105904002
#105903962
#818353
#798913