Finite Group Databasebeta

← #11868034

Subgroups — #11868034

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#131C211yesmaximal, characteristic, complemented
2#10595470C212yesmaximal, complemented
3C2×#63808C211yesmaximal, characteristic, complemented
4#10592841C211yesmaximal, characteristic, complemented
5C3×#5143C211yesmaximal, characteristic, complemented
6#10591680C212yesmaximal, complemented
7#10591007C212yesmaximal, complemented
8#10590998C212yesmaximal, complemented
9#10590930C211yesmaximal, characteristic, complemented
10#10590927C211yesmaximal, characteristic, complemented
11D3×#819C211yesmaximal, characteristic, complemented
12#83805—31nomaximal
13#80943—31nomaximal
14C3×D3×#41C2211yescharacteristic
15C2×#3799C2212yes—
16C32×#131C2211yescharacteristic
17#64158C2212yes—
18C2×#3745C2211yescharacteristic, complemented
19C3×#951C2212yes—
20C3×#948C2211yescharacteristic
21C3×#907—21no—
22C3×#907C2211yescharacteristic
23C3×D3×M16—21no—
24C3×D3×M16C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic, complemented
26C3×#901—21no—
27C3×#901C2211yescharacteristic
28C2×C3×D3×C8—21no—
29C2×C3×D3×C8C2211yescharacteristic
30#63949—22no—
31#63948—22no—
32#63935—22no—
33#63934—22no—
34C2×#3717C2212yescomplemented
35#63827C2212yes—
36#63825C2212yes—
37D3×#208C2212yes—
38#63808—21no—
39#63808—21no—
40#63808—21no—
41#63808—21no—
42#63650C2212yescomplemented
43#63646C2211yescharacteristic, complemented
44C3×#824C2212yescomplemented
45C3×#819C2211yescharacteristic, complemented
46#63577C2212yescomplemented
47#63560C2212yescomplemented
48#63559C2212yescomplemented
49C2×C3×#131—31no—
50#5822—32no—
51#5777—32no—
52C2×#919—31no—
53D3×#131D311yescharacteristic, complemented
54C2×#904—31no—
55C3×#473—31no—
56#5203—32no—
57#5192—31no—
58#5143—31no—
59#5143D311yescharacteristic, complemented
60#5142—31no—
61#5142—31no—
62#5142—31no—
63#5142—61no—
64#5141—32no—
65#5141—32no—
66#5132—32no—
67C2×#819—31no—
68#4897—31no—
69D3×#108—31no—
70#4754—32no—
71#4751—32no—
72C32×#41C2311yescharacteristic
73C2×C4⋊(C3⋊D3)C2312yes—
74C3×#239D411yescharacteristic
75C3×D3×Q8D411yescharacteristic
76C3×#237—21no—
77C3×#237D411yescharacteristic
78C3×D3×D4—21no—
79C3×D3×D4D411yescharacteristic
80C3×#235—21no—
81C3×#235C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3C2311yescharacteristic
84C2×C3×Dic6C2312yes—
85C2×#626—22no—
86C2×#624—22no—
87#3799—22no—
88#3799—22no—
89#3799—22no—
90#3799—22no—
91C32×M16—21no—
92C32×M16C2311yescharacteristic
93C2×C32×C8—21no—
94C2×C32×C8C2311yescharacteristic
95#3755—22no—
96#3753—22no—
97#3748C2312yes—
98#3745—21no—
99#3745—21no—
100C3×#216—22no—
101C3×#214—22no—
102C3×#208—21no—
103C3×#208C2311yescharacteristic
104C3×#208C2312yes—
105C2×C3×C3⋊C8—21no—
106C2×C3×C3⋊C8C2311yescharacteristic
107C3×Dic12—21no—
108C3×Dic12—21no—
109C3×ΓL(1,𝔽25)—21no—
110C3×ΓL(1,𝔽25)—21no—
111C3×ΓL(1,𝔽25)—21no—
112C3×D3×C8—21no—
113C3×D3×C8—21no—
114C3×D3×C8—21no—
115C3×D3×C8D411yescharacteristic
116C3×D3×C8D411yescharacteristic
117C3×D3×C8D411yescharacteristic
118C3×D3×C8D411yescharacteristic
119#3718—22no—
120#3717—22no—
121#3717—22no—
122#3717—22no—
123#3715—22no—
124#3714—22no—
125#3711—22no—
126D3×C3⋊C8—22no—
127#3067—91noSylow
128C2×C3×#41—31no—
129D3×#41C2×D311yescharacteristic
130C2×#239—32no—
131C2×#235—32no—
132C3×#137—32no—
133C2×C3×Q16—31no—
134C3×#131—21no—
135C3×#131—31no—
136C3×#131—31no—
137C3×#131—31no—
138C3×#131—61no—
139C3×#131—61no—
140C3×#131C2×D311yescharacteristic
141C3×#131C2×D311yescharacteristic
142C2×C3×M16—31no—
143C2×C3×M16—61no—
144C22×C3×C8—31no—
145C22×C3×C8—61no—
146#951—32no—
147#951C2×D312yes—
148#950—62no—
149#950—62no—
150#949—32no—
151#949—32no—
152#949—32no—
153#949—62no—
154#948C2×D311yescharacteristic
155#942—32no—
156#942—62no—
157C2×#215—32no—
158#932—62no—
159C2×#208—32no—
160#919—62no—
161#919—61no—
162#919—61no—
163#919—61no—
164#919—61no—
165#918—62no—
166#916—62no—
167#914—62no—
168#908—32no—
169#907—21no—
170#907C2×D311yescharacteristic
171D3×M16—21no—
172D3×M16—32no—
173D3×M16C2×D311yescharacteristic
174C2×Dic12C2×D311yescharacteristic, complemented
175#904—61no—
176#904—61no—
177#904—61no—
178#904—61no—
179C2×D24—31no—
180C2×D24—31no—
181C2×D24—61no—
182C2×#204—32no—
183#901—21no—
184#901C2×D311yescharacteristic
185C2×D3×C8—21no—
186C2×D3×C8C2×D311yescharacteristic
187C3×#108—31no—
188C3×#101—32no—
189#836—32no—
190#824—32no—
191#824C2×D312yescomplemented
192#823—32no—
193#823—32no—
194#823—32no—
195#823—32no—
196#823—62no—
197#822—32no—
198#819—31no—
199#819—31no—
200#819—32no—
201#819—61no—
202#819C2×D311yescharacteristic, complemented
203C22×C3⋊D3—22no—
204C22×C3×D3—21no—
205C22×C3×D3#4111yescharacteristic
206C32×Q8C2×D411yescharacteristic
207C32×D4—21no—
208C32×D4C2×D411yescharacteristic
209C2×C32×C4—21no—
210C2×C32×C4C2411yescharacteristic
211C4⋊(C3⋊D3)—22no—
212C4⋊(C3⋊D3)—22no—
213C3×#67—21no—
214C3×#67—21no—
215C3×#67—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3#4111yescharacteristic
219C3×D12—21no—
220C3×D12C2×D411yescharacteristic
221C3×C4×D3—21no—
222C3×C4×D3—21no—
223C3×C4×D3—21no—
224C3×C4×D3C2×D411yescharacteristic
225C3×C4×D3C2×D411yescharacteristic
226C3×C4×D3C2×D411yescharacteristic
227C3×C4×D3C2×D411yescharacteristic
228C3×Dic6—21no—
229C3×Dic6—22no—
230C3×Dic6—22no—
231C3×Dic6C2×D411yescharacteristic
232#626—42no—
233#626—42no—
234#624—42no—
235#624—42no—
236C32×C8—21no—
237C32×C8C2×D411yescharacteristic
238C32×C8C2×D411yescharacteristic
239C3⋊(C3⋊C8)—22no—
240C3×C3⋊C8—22no—
241C3×C3⋊C8—21no—
242C3×C3⋊C8C2×D411yescharacteristic
243C3×C3⋊C8C2×D411yescharacteristic
244#575—92no—
245C2×#135—91no—
246C2×#131—31no—
247#473—31no—
248#473—91no—
249#472—91no—
250#472—91no—
251#471—92no—
252#471—92no—
253C2×#108—91no—
254#413—92no—
255C3×#41—21no—
256C3×#41—31no—
257C3×#41—31no—
258C3×#41—31no—
259C3×#41—61no—
260C3×#41—61no—
261C3×#41C22×D311yescharacteristic
262C3×#41C22×D311yescharacteristic
263C2×C3×Q8—31no—
264C2×C3×Q8—32no—
265C2×C3×D4—31no—
266C2×C3×D4—61no—
267C22×C3×C4—31no—
268C22×C3×C4—61no—
269C2×#67—62no—
270#239—62no—
271#239—62no—
272#239—62no—
273#239—62no—
274#239D1211yescharacteristic
275D3×Q8D1211yescharacteristic
276#237—21no—
277#237D1211yescharacteristic
278D3×D4—21no—
279D3×D4D1211yescharacteristic
280#235—21no—
281#235—62no—
282#235—62no—
283#235—62no—
284#235—62no—
285#235C22×D311yescharacteristic
286C2×D12—32no—
287C2×D12—32no—
288C2×D12—62no—
289C2×D12—62no—
290C2×C4×D3—21no—
291C2×C4×D3—62no—
292C2×C4×D3—62no—
293C2×C4×D3C22×D311yescharacteristic
294C2×Dic6C22×D312yes—
295C3×Q16—62no—
296C3×Q16—61no—
297C3×Q16—61no—
298C3×SD16—62no—
299C3×M16—21no—
300C3×M16—21no—
301C3×M16—21no—
302C3×M16—32no—
303C3×M16—31no—
304C3×M16—41no—
305C3×M16—61no—
306C3×M16—61no—
307C3×M16—61no—
308C3×M16—61no—
309C3×M16C22×D311yescharacteristic
310C3×M16C22×D311yescharacteristic
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C2×C3×C8—41no—
320C2×C3×C8—61no—
321C2×C3×C8—61no—
322C2×C3×C8—61no—
323C2×C3×C8—61no—
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C22×D311yescharacteristic
326#216—22no—
327#216—62no—
328#216—62no—
329#215—62no—
330#215—62no—
331#215—62no—
332#215—62no—
333#215—62no—
334#215—62no—
335#215—122no—
336#214—22no—
337#214—62no—
338#213—62no—
339#213—62no—
340#213—62no—
341#213—122no—
342#208—21no—
343#208—32no—
344#208—32no—
345#208—62no—
346#208—62no—
347#208C22×D312yes—
348#208C22×D311yescharacteristic
349C2×C3⋊C8—21no—
350C2×C3⋊C8—62no—
351C2×C3⋊C8C22×D311yescharacteristic
352Dic12—21no—
353Dic12—21no—
354D24—62no—
355D24—61no—
356D24—61no—
357D24—61no—
358D24—61no—
359D24—121no—
360D24—121no—
361#204—62no—
362#204—62no—
363#204—62no—
364ΓL(1,𝔽25)—21no—
365ΓL(1,𝔽25)—21no—
366ΓL(1,𝔽25)—21no—
367ΓL(1,𝔽25)—62no—
368D3×C8—21no—
369D3×C8—21no—
370D3×C8—21no—
371D3×C8—62no—
372D3×C8#6711yescharacteristic
373D3×C8#6711yescharacteristic
374D3×C8#6711yescharacteristic
375D3×C8#6711yescharacteristic
376C22×C32—21no—
377C22×C32C2×#4111yescharacteristic
378C2×C3⋊D3—42no—
379C2×C3⋊D3—82no—
380C2×C3×D3—21no—
381C2×C3×D3—41no—
382C2×C3×D3—42no—
383C2×C3×D3#12111yescharacteristic
384C2×C3×D3#12111yescharacteristic
385C32×C4—21no—
386C32×C4C22×D411yescharacteristic
387C32×C4C22×D411yescharacteristic
388C3×Dic3—21no—
389C3×Dic3—42no—
390C3×Dic3#12111yescharacteristic
391C3×Dic3#12111yescharacteristic
392C2×#41—31no—
393C2×#41—92no—
394#137—32no—
395#137—92no—
396#137—182no—
397AGL(1,ℤ/8)—92no—
398AGL(1,ℤ/8)—92no—
399AGL(1,ℤ/8)—182no—
400#135—181no—
401#135—181no—
402#135—181no—
403#135—181no—
404#135—182no—
405#135—182no—
406C2×Q16—31no—
407C2×SD16—92no—
408C2×D8—91no—
409#131—31no—
410#131—31no—
411#131—31no—
412#131—61no—
413#131—61no—
414#131D3211yescharacteristic
415C2×M16—31no—
416C2×M16—61no—
417C2×M16—92no—
418C22×C8—31no—
419C22×C8—61no—
420#108—31no—
421#108—92no—
422#108—91no—
423#101—32no—
424#101—92no—
425#100—92no—
426#100—92no—
427C23×C3—31no—
428C23×C3—61no—
429C22×D3—21no—
430C22×D3—62no—
431C22×D3—62no—
432C22×D3—122no—
433C22×D3#23511yescharacteristic
434C3×Q8—21no—
435C3×Q8—31no—
436C3×Q8—61no—
437C3×Q8—62no—
438C3×Q8—62no—
439C3×Q8C2×D1211yescharacteristic
440C3×Q8D3×D411yescharacteristic
441C3×D4—21no—
442C3×D4—21no—
443C3×D4—21no—
444C3×D4—31no—
445C3×D4—41no—
446C3×D4—61no—
447C3×D4—61no—
448C3×D4—61no—
449C3×D4—61no—
450C3×D4C2×D1211yescharacteristic
451C3×D4D3×D411yescharacteristic
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—41no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—62no—
466C2×C3×C4C23×D311yescharacteristic
467C2×C3×C4C23×D311yescharacteristic
468#67—21no—
469#67—21no—
470#67—21no—
471#67—122no—
472#67—122no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3#23511yescharacteristic
476D12—21no—
477D12—62no—
478D12—62no—
479D12—62no—
480D12—62no—
481D12—122no—
482D12—122no—
483D12—122no—
484D12—122no—
485D12C2×D1211yescharacteristic
486C4×D3—21no—
487C4×D3—21no—
488C4×D3—21no—
489C4×D3—122no—
490C4×D3—122no—
491C4×D3—122no—
492C4×D3—122no—
493C4×D3C2×D1211yescharacteristic
494C4×D3C2×D1211yescharacteristic
495C4×D3C2×#6711yescharacteristic
496C4×D3C2×#6711yescharacteristic
497Dic6—21no—
498Dic6—22no—
499Dic6—22no—
500Dic6C2×D1211yescharacteristic
501C3×C8—21no—
502C3×C8—21no—
503C3×C8—21no—
504C3×C8—21no—
505C3×C8—31no—
506C3×C8—31no—
507C3×C8—41no—
508C3×C8—62no—
509C3×C8—61no—
510C3×C8D3×D411yescharacteristic
511C3×C8D3×D411yescharacteristic
512C3×C8C2×#6711yescharacteristic
513C3×C8C2×#6711yescharacteristic
514C3⋊C8—22no—
515C3⋊C8—21no—
516C3⋊C8—62no—
517C3⋊C8—62no—
518C3⋊C8—122no—
519C3⋊C8C2×#6711yescharacteristic
520C3⋊C8C2×#6711yescharacteristic
521C2×C32—21no—
522C2×C32—41no—
523C2×C32C2×#12111yescharacteristic
524C3⋊D3—82no—
525C3×D3—21no—
526C3×D3—21no—
527C3×D3—41no—
528#41—31no—
529#41—31no—
530#41—31no—
531#41—61no—
532#41—61no—
533#41—182no—
534#41—182no—
535#41—182no—
536#41—182no—
537#41C2×D3211yescharacteristic
538C2×Q8—31no—
539C2×Q8—32no—
540C2×D4—31no—
541C2×D4—61no—
542C2×D4—92no—
543C2×D4—182no—
544C22×C4—31no—
545C22×C4—61no—
546C22×C4—182no—
547Q16—62no—
548Q16—61no—
549Q16—61no—
550Q16—182no—
551SD16—62no—
552SD16—182no—
553SD16—182no—
554SD16—182no—
555SD16—182no—
556SD16—182no—
557D8—182no—
558D8—182no—
559D8—181no—
560D8—181no—
561M16—21no—
562M16—31no—
563M16—32no—
564M16—61no—
565M16—61no—
566M16—61no—
567M16—61no—
568M16—92no—
569M16—182no—
570M16C2×D3211yescharacteristic
571C2×C8—21no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—182no—
582C2×C8C2×D3211yescharacteristic
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—31no—
587C22×C3—31no—
588C22×C3—41no—
589C22×C3—61no—
590C22×C3—121no—
591C22×C3—122no—
592C22×C3C2×#23511yescharacteristic
593C22×C3D3×#4111yescharacteristic
594C2×D3—21no—
595C2×D3—41no—
596C2×D3—42no—
597C2×D3—122no—
598C2×D3—122no—
599C2×D3—242no—
600C2×D3—242no—
601C2×D3—242no—
602C2×D3—482no—
603C2×D3#93011yescharacteristic
604C2×D3#93011yescharacteristic
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—31no—
610C3×C4—31no—
611C3×C4—41no—
612C3×C4—61no—
613C3×C4—122no—
614C3×C4C22×D1211yescharacteristic
615C3×C4C2×D3×D411yescharacteristic
616C3×C4C2×D3×D411yescharacteristic
617C3×C4C22×#6711yescharacteristic
618Dic3—21no—
619Dic3—42no—
620Dic3#93011yescharacteristic
621Dic3#93011yescharacteristic
622C32#306711yescharacteristic, complemented, Sylow
623C23—31no—
624C23—61no—
625C23—182no—
626Q8—31no—
627Q8—61no—
628Q8—62no—
629Q8—62no—
630Q8D3×D1211yescharacteristic
631D4—21no—
632D4—31no—
633D4—61no—
634D4—61no—
635D4—61no—
636D4—61no—
637D4—182no—
638D4—182no—
639D4—362no—
640D4—362no—
641D4D3×D1211yescharacteristic
642C2×C4—21no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—62no—
653C2×C4—362no—
654C2×C4—362no—
655C2×C4C22×D3211yescharacteristic
656C8—21no—
657C8—31no—
658C8—31no—
659C8—62no—
660C8—61no—
661C8—182no—
662C8D3×#6711yescharacteristic
663C8D3×#6711yescharacteristic
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—41no—
668C2×C3—41no—
669C2×C3—41no—
670C2×C3—61no—
671C2×C3—61no—
672C2×C3—81no—
673C2×C3—121no—
674C2×C3D3×#12111yescharacteristic
675C2×C3C2×#93011yescharacteristic
676D3—21no—
677D3—21no—
678D3—41no—
679D3—242no—
680D3—242no—
681D3—482no—
682C22—21no—
683C22—31no—
684C22—31no—
685C22—61no—
686C22—121no—
687C22—122no—
688C22—362no—
689C22—722no—
690C22D3×#23511yescharacteristic
691C4—21no—
692C4—31no—
693C4—31no—
694C4—61no—
695C4—122no—
696C4C2×D3×D1211yescharacteristic
697C4C2×D3×#6711yescharacteristic
698C3—21no—
699C3#8094311yescharacteristic, complemented
700C3#8380511yescharacteristic, complemented
701C2—21no—
702C2—41no—
703C2—61no—
704C2—61no—
705C2—121no—
706C2—722no—
707C2D3×#93011yescharacteristic
subgroupG/H
centerC2D3×#930
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32C2×#121
hypercenter#131D32
hypocenterC32#3067
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×D3×#131C2semidirect
2. #10595470C2semidirect
3. C2×#63808C2semidirect
4. #10592841C2semidirect
5. C3×#5143C2semidirect
6. #10591680C2semidirect
7. #10591007C2semidirect
8. #10590998C2semidirect
9. #10590930C2semidirect
10. #10590927C2semidirect
11. D3×#819C2semidirect
18. C2×#3745C22semidirect
25. C2×C3×Dic12C22semidirect
34. C2×#3717C22semidirect
42. #63650C22semidirect
43. #63646C22semidirect
44. C3×#824C22semidirect
45. C3×#819C22semidirect
46. #63577C22semidirect
47. #63560C22semidirect
48. #63559C22semidirect
53. D3×#131D3semidirect
59. #5143D3semidirect
174. C2×Dic12C2×D3semidirect
191. #824C2×D3semidirect
202. #819C2×D3semidirect
622. C32#3067semidirect
699. C3#80943semidirect
700. C3#83805semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1312
#105954702
C2×#638082
#105928412
C3×#51432
#105916802
#105910072
#105909982
#105909302
#105909272
D3×#8192
#838053
#809433