Finite Group Databasebeta

← #11868036

Subgroups — #11868036

Order 1152.

954 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#131C211yesmaximal, characteristic, complemented
2#10595469C212yesmaximal, complemented
3C2×#63807C211yesmaximal, characteristic, complemented
4#10592842C211yesmaximal, characteristic, complemented
5C3×#5142C211yesmaximal, characteristic, complemented
6#10591679C212yesmaximal, complemented
7#10591006C212yesmaximal, complemented
8#10590996C212yesmaximal, complemented
9#10590932C211yesmaximal, characteristic, complemented
10#10590926C211yesmaximal, characteristic, complemented
11D3×#819C211yesmaximal, characteristic, complemented
12#83805—31nomaximal
13#80937—31nomaximal
14C3×D3×#41C2211yescharacteristic
15C2×#3795C2212yes—
16C32×#131C2211yescharacteristic
17#64160C2212yes—
18C2×#3746C2211yescharacteristic, complemented
19C3×#949C2212yes—
20C3×#948C2211yescharacteristic
21C3×#907—21no—
22C3×#907C2211yescharacteristic
23C3×D3×M16—21no—
24C3×D3×M16C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic, complemented
26C3×#901—21no—
27C3×#901C2211yescharacteristic
28C2×C3×D3×C8—21no—
29C2×C3×D3×C8C2211yescharacteristic
30#63947—22no—
31#63946—22no—
32#63933—22no—
33#63932—22no—
34#63831C2212yes—
35C2×#3716C2212yescomplemented
36#63823C2212yes—
37D3×#208C2212yes—
38#63807—21no—
39#63807—21no—
40#63807—21no—
41#63807—21no—
42#63651C2212yescomplemented
43#63646C2211yescharacteristic, complemented
44C3×#823C2212yescomplemented
45C3×#819C2211yescharacteristic, complemented
46#63577C2212yescomplemented
47#63561C2212yescomplemented
48#63558C2212yescomplemented
49C2×C3×#131—31no—
50#5822—32no—
51#5773—32no—
52C2×#912—31no—
53D3×#131D311yescharacteristic, complemented
54C2×#904—31no—
55C3×#472—31no—
56#5200—32no—
57#5160—31no—
58#5143—31no—
59#5143—31no—
60#5143—31no—
61#5143—61no—
62#5142—31no—
63#5142D311yescharacteristic, complemented
64#5141—32no—
65#5141—32no—
66#5132—32no—
67C2×#819—31no—
68#4896—31no—
69D3×#108—31no—
70#4748—32no—
71#4745—32no—
72C32×#41C2311yescharacteristic
73C2×#634C2312yes—
74C3×#239D411yescharacteristic
75C3×D3×Q8D411yescharacteristic
76C3×#237—21no—
77C3×#237D411yescharacteristic
78C3×D3×D4—21no—
79C3×D3×D4D411yescharacteristic
80C3×#235—21no—
81C3×#235C2311yescharacteristic
82C2×C3×D12C2312yes—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3C2311yescharacteristic
85C2×#625—22no—
86C2×D3×Dic3—22no—
87#3795—22no—
88#3795—22no—
89#3795—22no—
90#3795—22no—
91C32×M16—21no—
92C32×M16C2311yescharacteristic
93C2×C32×C8—21no—
94C2×C32×C8C2311yescharacteristic
95#3756—22no—
96#3754—22no—
97#3748C2312yes—
98#3746—21no—
99#3746—21no—
100C3×#215—22no—
101C3×#213—22no—
102C3×#208—21no—
103C3×#208C2311yescharacteristic
104C3×#208C2312yes—
105C2×C3×C3⋊C8—21no—
106C2×C3×C3⋊C8C2311yescharacteristic
107C3×D24—21no—
108C3×D24—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#3719—22no—
120#3716—22no—
121#3716—22no—
122#3716—22no—
123#3715—22no—
124#3713—22no—
125#3711—22no—
126D3×C3⋊C8—22no—
127#3067—91noSylow
128C2×C3×#41—31no—
129D3×#41C2×D311yescharacteristic
130C2×#237—32no—
131C2×#235—32no—
132C3×AGL(1,ℤ/8)—32no—
133C2×C3×D8—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#951—32no—
148#951—32no—
149#951—62no—
150#950—62no—
151#950—62no—
152#949—32no—
153#949C2×D312yes—
154#948C2×D311yescharacteristic
155#942—62no—
156C2×#214—32no—
157#932—32no—
158#932—62no—
159C2×#208—32no—
160#916—62no—
161#915—62no—
162#912—62no—
163#912—61no—
164#912—61no—
165#912—61no—
166#912—61no—
167#911—62no—
168#909—32no—
169#907—21no—
170#907C2×D311yescharacteristic
171D3×M16—21no—
172D3×M16—32no—
173D3×M16C2×D311yescharacteristic
174C2×Dic12—31no—
175C2×Dic12—31no—
176C2×Dic12—61no—
177#904—61no—
178#904—61no—
179#904—61no—
180#904—61no—
181C2×D24C2×D311yescharacteristic, complemented
182C2×#204—32no—
183#901—21no—
184#901C2×D311yescharacteristic
185C2×D3×C8—21no—
186C2×D3×C8C2×D311yescharacteristic
187C3×#108—31no—
188C3×#100—32no—
189#833—32no—
190#824—32no—
191#824—32no—
192#824—32no—
193#824—32no—
194#824—62no—
195#823—32no—
196#823C2×D312yescomplemented
197#822—32no—
198#819—31no—
199#819—31no—
200#819—32no—
201#819—61no—
202#819C2×D311yescharacteristic, complemented
203C22×C3×D3—21no—
204C22×C3×D3—22no—
205C22×C3×D3#4111yescharacteristic
206C32×Q8C2×D411yescharacteristic
207C32×D4—21no—
208C32×D4C2×D411yescharacteristic
209C2×C32×C4—21no—
210C2×C32×C4C2411yescharacteristic
211C2×C3⋊Dic3—22no—
212#634—22no—
213#634—22no—
214C3×#67—21no—
215C3×#67—21no—
216C3×#67—21no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3#4111yescharacteristic
219C3×D12—21no—
220C3×D12—22no—
221C3×D12—22no—
222C3×D12C2×D411yescharacteristic
223C3×C4×D3—21no—
224C3×C4×D3—21no—
225C3×C4×D3—21no—
226C3×C4×D3C2×D411yescharacteristic
227C3×C4×D3C2×D411yescharacteristic
228C3×C4×D3C2×D411yescharacteristic
229C3×C4×D3C2×D411yescharacteristic
230C3×Dic6—21no—
231C3×Dic6C2×D411yescharacteristic
232#625—42no—
233#625—42no—
234D3×Dic3—42no—
235D3×Dic3—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—91no—
248#473—91no—
249#472—31no—
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×D4—31no—
265C2×C3×D4—32no—
266C2×C3×D4—61no—
267C22×C3×C4—31no—
268C22×C3×C4—61no—
269C2×#67—62no—
270C2×#67—62no—
271C22×Dic3—62no—
272#239D1211yescharacteristic
273D3×Q8D1211yescharacteristic
274#237—21no—
275#237—62no—
276#237—62no—
277#237—62no—
278#237—62no—
279#237D1211yescharacteristic
280D3×D4—21no—
281D3×D4D1211yescharacteristic
282#235—21no—
283#235—62no—
284#235—62no—
285#235—62no—
286#235—62no—
287#235C22×D311yescharacteristic
288C2×D12C22×D312yes—
289C2×C4×D3—21no—
290C2×C4×D3—62no—
291C2×C4×D3C22×D311yescharacteristic
292C2×Dic6—32no—
293C2×Dic6—32no—
294C2×Dic6—62no—
295C3×SD16—62no—
296C3×D8—62no—
297C3×D8—61no—
298C3×D8—61no—
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—62no—
327#216—62no—
328#216—62no—
329#216—122no—
330#215—22no—
331#215—62no—
332#214—62no—
333#214—62no—
334#214—62no—
335#214—62no—
336#214—62no—
337#214—62no—
338#214—122no—
339#213—22no—
340#213—62no—
341#213—62no—
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—62no—
353Dic12—61no—
354Dic12—61no—
355Dic12—61no—
356Dic12—61no—
357Dic12—121no—
358Dic12—121no—
359D24—21no—
360D24—21no—
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—21no—
379C2×C3×D3—41no—
380C2×C3×D3—42no—
381C2×C3×D3—42no—
382C2×C3×D3—82no—
383C2×C3×D3#12111yescharacteristic
384C2×C3×D3#12111yescharacteristic
385C32×C4—21no—
386C32×C4C22×D411yescharacteristic
387C32×C4C22×D411yescharacteristic
388C3⋊Dic3—42no—
389C3×Dic3—21no—
390C3×Dic3#12111yescharacteristic
391C3×Dic3#12111yescharacteristic
392C2×#41—31no—
393C2×#41—92no—
394#137—92no—
395#137—92no—
396#137—182no—
397AGL(1,ℤ/8)—32no—
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—91no—
407C2×SD16—92no—
408C2×D8—31no—
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—92no—
424#101—92no—
425#100—32no—
426#100—92no—
427C23×C3—31no—
428C23×C3—61no—
429C23×C3—62no—
430C22×D3—21no—
431C22×D3—22no—
432C22×D3#23511yescharacteristic
433C3×Q8—21no—
434C3×Q8—31no—
435C3×Q8—61no—
436C3×Q8C2×D1211yescharacteristic
437C3×Q8D3×D411yescharacteristic
438C3×D4—21no—
439C3×D4—21no—
440C3×D4—21no—
441C3×D4—31no—
442C3×D4—41no—
443C3×D4—61no—
444C3×D4—61no—
445C3×D4—61no—
446C3×D4—61no—
447C3×D4—62no—
448C3×D4—62no—
449C3×D4C2×D1211yescharacteristic
450C3×D4D3×D411yescharacteristic
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—31no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—41no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4C23×D311yescharacteristic
465C2×C3×C4C23×D311yescharacteristic
466#67—21no—
467#67—21no—
468#67—21no—
469#67—122no—
470#67—122no—
471#67—122no—
472#67—122no—
473C2×Dic3—21no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—122no—
477C2×Dic3—122no—
478C2×Dic3—122no—
479C2×Dic3#23511yescharacteristic
480D12—21no—
481D12—22no—
482D12—22no—
483D12C2×D1211yescharacteristic
484C4×D3—21no—
485C4×D3—21no—
486C4×D3—21no—
487C4×D3—122no—
488C4×D3—122no—
489C4×D3C2×D1211yescharacteristic
490C4×D3C2×D1211yescharacteristic
491C4×D3C2×#6711yescharacteristic
492C4×D3C2×#6711yescharacteristic
493Dic6—21no—
494Dic6—62no—
495Dic6—62no—
496Dic6—62no—
497Dic6—62no—
498Dic6—122no—
499Dic6—122no—
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—21no—
525C3×D3—21no—
526C3×D3—41no—
527C3×D3—82no—
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—92no—
540C2×D4—31no—
541C2×D4—32no—
542C2×D4—61no—
543C2×D4—182no—
544C22×C4—31no—
545C22×C4—61no—
546C22×C4—182no—
547Q16—182no—
548Q16—182no—
549Q16—181no—
550Q16—181no—
551SD16—62no—
552SD16—182no—
553SD16—182no—
554SD16—182no—
555SD16—182no—
556SD16—182no—
557D8—62no—
558D8—61no—
559D8—61no—
560D8—182no—
561M16—21no—
562M16—32no—
563M16—31no—
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×C3—122no—
593C22×C3—242no—
594C22×C3C2×#23511yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C2×D3—21no—
597C2×D3—41no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—82no—
601C2×D3#93011yescharacteristic
602C2×D3#93011yescharacteristic
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—31no—
608C3×C4—31no—
609C3×C4—41no—
610C3×C4—61no—
611C3×C4C22×D1211yescharacteristic
612C3×C4C2×D3×D411yescharacteristic
613C3×C4C2×D3×D411yescharacteristic
614C3×C4C22×#6711yescharacteristic
615Dic3—21no—
616Dic3—122no—
617Dic3—122no—
618Dic3—242no—
619Dic3#93011yescharacteristic
620Dic3#93011yescharacteristic
621C32#306711yescharacteristic, complemented, Sylow
622C23—31no—
623C23—61no—
624C23—62no—
625Q8—31no—
626Q8—61no—
627Q8—182no—
628Q8—182no—
629Q8D3×D1211yescharacteristic
630D4—21no—
631D4—31no—
632D4—61no—
633D4—61no—
634D4—61no—
635D4—61no—
636D4—62no—
637D4—62no—
638D4—362no—
639D4—362no—
640D4D3×D1211yescharacteristic
641C2×C4—21no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—182no—
652C2×C4—362no—
653C2×C4—362no—
654C2×C4C22×D3211yescharacteristic
655C8—21no—
656C8—31no—
657C8—31no—
658C8—62no—
659C8—61no—
660C8—182no—
661C8D3×#6711yescharacteristic
662C8D3×#6711yescharacteristic
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—41no—
667C2×C3—41no—
668C2×C3—41no—
669C2×C3—61no—
670C2×C3—61no—
671C2×C3—81no—
672C2×C3—121no—
673C2×C3—242no—
674C2×C3D3×#12111yescharacteristic
675C2×C3C2×#93011yescharacteristic
676D3—21no—
677D3—21no—
678D3—41no—
679D3—82no—
680C22—21no—
681C22—31no—
682C22—31no—
683C22—61no—
684C22—121no—
685C22—122no—
686C22—122no—
687C22—242no—
688C22D3×#23511yescharacteristic
689C4—21no—
690C4—31no—
691C4—31no—
692C4—61no—
693C4—362no—
694C4C2×D3×D1211yescharacteristic
695C4C2×D3×#6711yescharacteristic
696C3—21no—
697C3#8093711yescharacteristic, complemented
698C3#8380511yescharacteristic, complemented
699C2—21no—
700C2—41no—
701C2—61no—
702C2—61no—
703C2—121no—
704C2—242no—
705C2D3×#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. #10595469C2semidirect
3. C2×#63807C2semidirect
4. #10592842C2semidirect
5. C3×#5142C2semidirect
6. #10591679C2semidirect
7. #10591006C2semidirect
8. #10590996C2semidirect
9. #10590932C2semidirect
10. #10590926C2semidirect
11. D3×#819C2semidirect
18. C2×#3746C22semidirect
25. C2×C3×D24C22semidirect
35. C2×#3716C22semidirect
42. #63651C22semidirect
43. #63646C22semidirect
44. C3×#823C22semidirect
45. C3×#819C22semidirect
46. #63577C22semidirect
47. #63561C22semidirect
48. #63558C22semidirect
53. D3×#131D3semidirect
63. #5142D3semidirect
181. C2×D24C2×D3semidirect
196. #823C2×D3semidirect
202. #819C2×D3semidirect
621. C32#3067semidirect
697. C3#80937semidirect
698. 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
#105954692
C2×#638072
#105928422
C3×#51422
#105916792
#105910062
#105909962
#105909322
#105909262
D3×#8192
#838053
#809373