Finite Group Databasebeta

← #11870426

Subgroups — #11870426

Order 1152.

1139 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596067C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic, complemented
3C3×#5036C211yesmaximal, characteristic, complemented
4C3×#5033C211yesmaximal, characteristic, complemented
5#10591435C212yesmaximal, complemented
6#10591433C212yesmaximal, complemented
7#10591162C211yesmaximal, characteristic, complemented
8#10591133C211yesmaximal, characteristic, complemented
9#10591061C211yesmaximal, characteristic, complemented
10#10590471C212yesmaximal, complemented
11#10590459C212yesmaximal, complemented
12#81268—31nomaximal
13#79988—31nomaximal
14C2×#3830—21no—
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17C32×#121C2211yescharacteristic
18#64149C2211yescharacteristic, complemented
19#64148—21no—
20D4×C3⋊Dic3C2211yescharacteristic, complemented
21#64139C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64102C2211yescharacteristic, complemented
24#64097C2211yescharacteristic, complemented
25#64094—21no—
26#64090—21no—
27C2×C3×#213C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3—21no—
30#63898—21no—
31#63898—21no—
32#63898C2212yes—
33#63898C2212yes—
34C2×#3714C2212yes—
35C3×#832C2212yescomplemented
36C3×#830C2211yescharacteristic
37C3×#830C2211yescharacteristic
38C3×#809C2212yes—
39C3×#807C2212yescomplemented
40#63575C2212yescomplemented
41#63572C2212yescomplemented
42#63564C2212yescomplemented
43#63563C2212yes—
44#63553C2212yescomplemented
45C2×D4×Dic3—31no—
46#5596—31no—
47#5596—31no—
48#5596—61no—
49C2×#893—31no—
50C3×#480—31no—
51C3×#447—31no—
52#5217—31no—
53#5150—32no—
54Dic3×D8—32no—
55#5036D311yescharacteristic, complemented
56#5033D311yescharacteristic, complemented
57#4967—31no—
58#4890—32no—
59#4872—32no—
60#4786—32no—
61#4759—32no—
62#4756—32no—
63#4756—32no—
64#4736—31no—
65#4732—31no—
66#4718—31no—
67#4718—31no—
68C23×C3×D3—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×#638—21no—
73C2×#638—21no—
74C2×#638—21no—
75C22×C3⋊Dic3—21no—
76C22×C3⋊Dic3D411yescharacteristic
77C22×C3⋊Dic3D411yescharacteristic
78#3830—44no—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4×C3⋊D3—21no—
81C2×#634—21no—
82C22×C3×Dic3—21no—
83C2×C3×D12—21no—
84C2×C3×D12—24no—
85C2×C3×D12C2312yes—
86C2×D3×Dic3—22no—
87C2×D3×Dic3—22no—
88C2×D3×Dic3—44no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91#3757—21no—
92#3752—21no—
93#3752—21no—
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95#3750—21no—
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3D411yescharacteristic
98C4×C3⋊Dic3C2311yescharacteristic
99C4×C3⋊Dic3C2311yescharacteristic
100C3×#213—24no—
101C3×C4⋊Dic3—21no—
102C3×C4⋊Dic3C2312yes—
103C2×C3×C3⋊C8C2312yes—
104C2×C3×C3⋊C8C2312yes—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107#3714—24no—
108#3100—91noSylow
109C22×C3×D4—31no—
110C23×Dic3—61no—
111C2×#237—61no—
112C2×#237—61no—
113C2×#237—62no—
114C22×D12C2×D311yescharacteristic
115C22×C4×D3—61no—
116C2×C3×D8—32no—
117C3×#121—21no—
118C3×#121C2×D311yescharacteristic
119C3×#121C2×D311yescharacteristic
120C2×C3×C4⋊C4—31no—
121C2×#217—61no—
122#940—31no—
123#940—31no—
124#940—61no—
125#939—61no—
126#939—61no—
127#939—62no—
128D4×Dic3—31no—
129D4×Dic3—31no—
130D4×Dic3—32no—
131D4×Dic3—32no—
132D4×Dic3—61no—
133D4×Dic3—61no—
134D4×Dic3—61no—
135C2×#213—32no—
136C2×#213C2×D312yes—
137#930—31no—
138#930—31no—
139#930—61no—
140C2×(C2×D3)⋊C4—61no—
141C2×C4⋊Dic3C2×D311yescharacteristic
142C2×C4×Dic3—31no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—61no—
145C2×D24—32no—
146#893—32no—
147#893—32no—
148#893—31no—
149#893—31no—
150#893—61no—
151#893—61no—
152#893—61no—
153#888—31no—
154#888—31no—
155#888—61no—
156#885—61no—
157#885—61no—
158#885—62no—
159#67⋊C4—61no—
160#67⋊C4—61no—
161#67⋊C4—62no—
162C3×#107—32no—
163C3×#102—32no—
164C3×#102—32no—
165C3×C22⋊C8—31no—
166C3×C22⋊C8—31no—
167#832—32no—
168#832C2×D312yescomplemented
169#830C2×D311yescharacteristic
170#830C2×D311yescharacteristic
171#821—32no—
172#821—32no—
173#818—32no—
174Dic3⋊C8—32no—
175Dic3⋊C8—32no—
176C8×Dic3—32no—
177C8×Dic3—32no—
178#809—32no—
179#809C2×D312yes—
180#807—32no—
181#807C2×D312yescomplemented
182C23×C32—21no—
183C23×C32C2×D411yescharacteristic
184C22×C3⋊D3—21no—
185C22×C3×D3—24no—
186C22×C3×D3—22no—
187C22×C3×D3—42no—
188C22×C3×D3—42no—
189C32×D4—22no—
190C32×D4—42no—
191C2×C32×C4—21no—
192C2×C32×C4—22no—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195#638—42no—
196#638—42no—
197#638—42no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—41no—
200C2×C3⋊Dic3—42no—
201C2×C3⋊Dic3D814yescomplemented
202C2×C3⋊Dic3C2×D411yescharacteristic
203C2×C3⋊Dic3C2×D411yescharacteristic
204C2×C3⋊Dic3C2×D411yescharacteristic
205C2×C3⋊Dic3C2×D411yescharacteristic
206C4⋊(C3⋊D3)—22no—
207C4×C3⋊D3—42no—
208#634—42no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—42no—
211C3×D12—24no—
212C3×D12—22no—
213C3×D12#4114yescomplemented
214D3×Dic3—44no—
215D3×Dic3—44no—
216C3×C3⋊C8—22no—
217C3×C3⋊C8—22no—
218#532—91no—
219C2×C4×D4—91no—
220#480—31no—
221#480—91no—
222#474—92no—
223#459—92no—
224#447—31no—
225#447—91no—
226C4×D8—92no—
227C4×D8—92no—
228#431—91no—
229C24×C3—61no—
230C23×D3—21no—
231C2×C3×D4—22no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—32no—
236C2×C3×D4—64no—
237C2×C3×D4—61no—
238C2×C3×D4C22×D311yescharacteristic
239C2×C3×D4C22×D311yescharacteristic
240C22×C3×C4—21no—
241C22×C3×C4—61no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C2×#67—61no—
245C2×#67—61no—
246C2×#67—61no—
247C2×#67—61no—
248C2×#67—62no—
249C2×#67—62no—
250C2×#67—62no—
251C2×#67—61no—
252C2×#67—61no—
253C22×Dic3—21no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—62no—
261C22×Dic3—62no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264C22×Dic3—62no—
265C22×Dic3—124no—
266#237—124no—
267#237—124no—
268#237—128no—
269C2×D12—21no—
270C2×D12—24no—
271C2×D12—31no—
272C2×D12—31no—
273C2×D12—61no—
274C2×D12C22×D312yes—
275C2×C4×D3—61no—
276C2×C4×D3—61no—
277C2×C4×D3—62no—
278C2×C4×D3—62no—
279C2×C4×D3—62no—
280C2×C4×D3—124no—
281C2×Dic6—61no—
282C2×Dic6—61no—
283C2×Dic6—62no—
284C3×D8—64no—
285C2×C3×C8—32no—
286C2×C3×C8—32no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—32no—
289C3×C4⋊C4—61no—
290C3×C4⋊C4C22×D311yescharacteristic
291C3×C4⋊C4C22×D311yescharacteristic
292C3×C22⋊C4—22no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—21no—
295#217—62no—
296#217—62no—
297#217—61no—
298#217—61no—
299#217—62no—
300#213—24no—
301#213—64no—
302(C2×D3)⋊C4—61no—
303(C2×D3)⋊C4—61no—
304(C2×D3)⋊C4—62no—
305(C2×D3)⋊C4—62no—
306(C2×D3)⋊C4—62no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—61no—
309(C2×D3)⋊C4—61no—
310C4⋊Dic3—21no—
311C4⋊Dic3—31no—
312C4⋊Dic3—31no—
313C4⋊Dic3—61no—
314C4⋊Dic3C22×D312yes—
315Dic3⋊C4—61no—
316Dic3⋊C4—61no—
317Dic3⋊C4—62no—
318C4×Dic3—31no—
319C4×Dic3—31no—
320C4×Dic3—31no—
321C4×Dic3—31no—
322C4×Dic3—31no—
323C4×Dic3—31no—
324C4×Dic3—31no—
325C4×Dic3—31no—
326C4×Dic3—61no—
327C4×Dic3—61no—
328C4×Dic3—61no—
329C4×Dic3—61no—
330C2×C3⋊C8C22×D312yes—
331C2×C3⋊C8C22×D312yes—
332D24—64no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32C2×D812yes—
339C22×C32C22×D411yescharacteristic
340C2×C3⋊D3—41no—
341C2×C3⋊D3—41no—
342C2×C3⋊D3—41no—
343C2×C3×D3—24no—
344C2×C3×D3—48no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C32×C4—21no—
348C32×C4—41no—
349C32×C4C2×#4112yes—
350C3⋊Dic3—21no—
351C3⋊Dic3—21no—
352C3⋊Dic3—41no—
353C3⋊Dic3C2×D812yes—
354C3⋊Dic3C2×D812yes—
355C3×Dic3—42no—
356C2×#41—181no—
357C22×D4—31no—
358C23×C4—181no—
359C2×D8—32no—
360C2×D8—92no—
361C4⋊Q8—91no—
362#127—91no—
363#124—181no—
364#121—91no—
365#121—181no—
366#121D3211yescharacteristic
367C4×D4—92no—
368C4×D4—92no—
369C4×D4—91no—
370C4×D4—91no—
371C4×D4—181no—
372C4×D4—181no—
373C4×D4—181no—
374C2×C4⋊C4—31no—
375C2×C22⋊C4—181no—
376C2×C42—91no—
377#107—32no—
378#107—92no—
379C4⋊C8—92no—
380#102—32no—
381#102—32no—
382#102—92no—
383#102—92no—
384C22⋊C8—31no—
385C22⋊C8—31no—
386C4×C8—92no—
387C23×C3—22no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—64no—
392C23×C3—62no—
393C23×C3—122no—
394C23×C3—122no—
395C23×C3D3×D411yescharacteristic
396C23×C3D3×D411yescharacteristic
397C22×D3—24no—
398C22×D3—22no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—62no—
402C22×D3—61no—
403C22×D3—61no—
404C3×D4—22no—
405C3×D4—22no—
406C3×D4—34no—
407C3×D4—42no—
408C3×D4—44no—
409C3×D4—42no—
410C3×D4—42no—
411C3×D4—64no—
412C3×D4—62no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—42no—
421C2×C3×C4—62no—
422C2×C3×C4—122no—
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427#67—122no—
428#67—122no—
429#67—124no—
430#67—124no—
431#67—122no—
432#67—122no—
433#67—124no—
434#67—122no—
435#67—122no—
436C2×Dic3—22no—
437C2×Dic3—34no—
438C2×Dic3—34no—
439C2×Dic3—31no—
440C2×Dic3—31no—
441C2×Dic3—31no—
442C2×Dic3—31no—
443C2×Dic3—31no—
444C2×Dic3—31no—
445C2×Dic3—31no—
446C2×Dic3—31no—
447C2×Dic3—42no—
448C2×Dic3—64no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—62no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—124no—
457C2×Dic3—124no—
458C2×Dic3—122no—
459C2×Dic3—122no—
460C2×Dic3—121no—
461C2×Dic3—121no—
462C2×Dic3—124no—
463C2×Dic3—122no—
464D12—24no—
465D12—22no—
466D12—62no—
467D12—62no—
468D12—122no—
469D12#23714yescomplemented
470C4×D3—122no—
471C4×D3—122no—
472C4×D3—124no—
473C4×D3—124no—
474C4×D3—124no—
475Dic6—122no—
476Dic6—122no—
477Dic6—124no—
478C3×C8—62no—
479C3×C8—62no—
480C3⋊C8—22no—
481C3⋊C8—22no—
482C2×C32—22no—
483C2×C32—81no—
484C2×C32#52511yescharacteristic
485C2×C32C22×D811yescharacteristic
486C2×C32#57511yescharacteristic
487C3⋊D3—81no—
488C3×D3—44no—
489C24—61no—
490#41—364no—
491C2×Q8—181no—
492C2×D4—21no—
493C2×D4—32no—
494C2×D4—64no—
495C2×D4—61no—
496C2×D4—91no—
497C2×D4—181no—
498C2×D4—181no—
499C2×D4—181no—
500C2×D4C2×D3211yescharacteristic
501C22×C4—61no—
502C22×C4—91no—
503C22×C4—91no—
504C22×C4—181no—
505C22×C4—182no—
506C22×C4—182no—
507C22×C4—181no—
508C22×C4—364no—
509C22×C4C2×D3211yescharacteristic
510D8—64no—
511D8—184no—
512C2×C8—32no—
513C2×C8—32no—
514C4⋊C4—32no—
515C4⋊C4—61no—
516C4⋊C4—91no—
517C4⋊C4—181no—
518C4⋊C4C2×D3211yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—181no—
521C22⋊C4—182no—
522C22⋊C4—182no—
523C22⋊C4—181no—
524C22⋊C4—181no—
525C42—91no—
526C42—91no—
527C42—91no—
528C42—91no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—22no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—64no—
547C22×C3—128no—
548C22×C3—122no—
549C22×C3—122no—
550C22×C3D3×D812yes—
551C22×C3D3×D812yes—
552C22×C3C2×D3×D411yescharacteristic
553C22×C3C2×D3×D411yescharacteristic
554C2×D3—24no—
555C2×D3—48no—
556C2×D3—42no—
557C2×D3—42no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C2×D3—121no—
562C2×D3—121no—
563C2×D3—121no—
564C2×D3—121no—
565C2×D3—121no—
566C2×D3—121no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—22no—
570C3×C4—41no—
571C3×C4—42no—
572C3×C4—41no—
573C3×C4—41no—
574C3×C4—122no—
575C3×C4C2×#23712yes—
576C3×C4D3×#4112yes—
577Dic3—32no—
578Dic3—32no—
579Dic3—32no—
580Dic3—32no—
581Dic3—42no—
582Dic3—62no—
583Dic3—62no—
584Dic3—62no—
585Dic3—61no—
586Dic3—61no—
587Dic3—61no—
588Dic3—61no—
589Dic3—121no—
590Dic3—122no—
591Dic3—121no—
592Dic3—121no—
593C32#310011yescharacteristic, complemented, Sylow
594C23—21no—
595C23—64no—
596C23—62no—
597C23—122no—
598C23—122no—
599C23—181no—
600C23#381111yescharacteristic
601Q8—362no—
602D4—22no—
603D4—34no—
604D4—42no—
605D4—64no—
606D4—62no—
607D4—182no—
608D4—362no—
609D4—362no—
610D4—362no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—62no—
614C2×C4—91no—
615C2×C4—91no—
616C2×C4—94no—
617C2×C4—91no—
618C2×C4—91no—
619C2×C4—122no—
620C2×C4—181no—
621C2×C4—362no—
622C2×C4—364no—
623C2×C4—364no—
624C2×C4—362no—
625C2×C4—361no—
626C2×C4#381111yescharacteristic
627C2×C4C22×D3211yescharacteristic
628C8—62no—
629C8—62no—
630C2×C3—22no—
631C2×C3—22no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—42no—
636C2×C3—82no—
637C2×C3—81no—
638C2×C3—81no—
639C2×C3—124no—
640C2×C3#558611yescharacteristic
641C2×C3#565611yescharacteristic
642C2×C3C2×D3×D811yescharacteristic
643C2×C3C2×D3×D811yescharacteristic
644C2×C3#577311yescharacteristic
645C2×C3#577711yescharacteristic
646D3—44no—
647D3—242no—
648D3—241no—
649D3—241no—
650C22—21no—
651C22—21no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—64no—
656C22—128no—
657C22—122no—
658C22—122no—
659C22—361no—
660C22—361no—
661C22—361no—
662C22#6392612yes—
663C22C2×#381111yescharacteristic
664C4—21no—
665C4—41no—
666C4—92no—
667C4—92no—
668C4—122no—
669C4—181no—
670C4—181no—
671C4—361no—
672C4D3×#23712yes—
673C3—21no—
674C3#7998811yescharacteristic, complemented
675C3#8126811yescharacteristic, complemented
676C2—22no—
677C2—81no—
678C2—124no—
679C2—721no—
680C2C2×#6392611yescharacteristic
681C2#1059516011yescharacteristic
682C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596067C2semidirect
2. C2×#63898C2semidirect
3. C3×#5036C2semidirect
4. C3×#5033C2semidirect
5. #10591435C2semidirect
6. #10591433C2semidirect
7. #10591162C2semidirect
8. #10591133C2semidirect
9. #10591061C2semidirect
10. #10590471C2semidirect
11. #10590459C2semidirect
18. #64149C22semidirect
20. D4×C3⋊Dic3C22semidirect
23. #64102C22semidirect
24. #64097C22semidirect
35. C3×#832C22semidirect
39. C3×#807C22semidirect
40. #63575C22semidirect
41. #63572C22semidirect
42. #63564C22semidirect
44. #63553C22semidirect
55. #5036D3semidirect
56. #5033D3semidirect
168. #832C2×D3semidirect
181. #807C2×D3semidirect
201. C2×C3⋊Dic3D8semidirect
213. C3×D12#41semidirect
469. D12#237semidirect
593. C32#3100semidirect
674. C3#79988semidirect
675. C3#81268semidirect

Maximal subgroups

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

subgroupindex
#105960672
C2×#638982
C3×#50362
C3×#50332
#105914352
#105914332
#105911622
#105911332
#105910612
#105904712
#105904592
#812683
#799883