Finite Group Databasebeta

← #11885778

Subgroups — #11885778

Order 1152.

1310 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
1C2×D3×D24C212yesmaximal, complemented
2#10594004C211yesmaximal, characteristic, complemented
3D122C211yesmaximal, characteristic, complemented
4#10592542C211yesmaximal, characteristic, complemented
5C3×#4843C211yesmaximal, characteristic, complemented
6C3×#4834C211yesmaximal, characteristic, complemented
7#10590947C212yesmaximal, complemented
8#10590944C212yesmaximal, complemented
9#10590826C212yesmaximal, complemented
10#10590350C211yesmaximal, characteristic, complemented
11C4×#3714C211yesmaximal, characteristic, complemented
12#80350—31nomaximal
13D4×D24—31nomaximal
14C2×#3802—21no—
15C2×D3×D12—21no—
16C2×D3×D12C2212yescomplemented
17C2×D3×D12C2212yescomplemented
18C2×#3745C2212yescomplemented
19#64083C2211yescharacteristic, complemented
20C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×D24C2212yescomplemented
22C2×C3×D3×C8C2212yescomplemented
23C3×#874C2211yescharacteristic, complemented
24C3×C4×D12C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic, complemented
26#63923—22no—
27#63922—22no—
28#63916—21no—
29#63909—21no—
30#63909C2212yescomplemented
31#63908C2212yescomplemented
32C2×#3714C2211yescharacteristic
33C2×#3714C2212yescomplemented
34C2×#3714C2212yescomplemented
35D3×D24—28no—
36C32×C4⋊C8C2211yescharacteristic, complemented
37#63648C2212yescomplemented
38C3×#821C2212yescomplemented
39C3×(C2×D3)⋊C8C2212yescomplemented
40C3×C4×C3⋊C8C2211yescharacteristic, complemented
41#63575C2211yescharacteristic, complemented
42#63564C2211yescharacteristic, complemented
43#63563C2211yescharacteristic, complemented
44C2×D3×D8—32no—
45C22×D24—32no—
46#5717—31no—
47D4×D12—31no—
48D4×D12—31no—
49D4×D12—31no—
50C3×#459—31no—
51C3×C8×D4—31no—
52#5156—32no—
53#5115—32no—
54#5073—31no—
55C4×#213—31no—
56#4843—31no—
57#4843—31no—
58#4843—61no—
59#4843D311yescharacteristic, complemented
60#4834D311yescharacteristic, complemented
61#4775—32no—
62#4773—32no—
63#4732—32no—
64#4732—32no—
65#4695—31no—
66C4×D24—31no—
67C22×D32—22no—
68C22×D32—22no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3C2312yes—
81C2×#626—22no—
82C2×#626—22no—
83C2×#626—22no—
84C2×#625—22no—
85#3802—44no—
86D3×D12—24no—
87D3×D12—24no—
88D3×D12—42no—
89D3×D12—42no—
90D3×D12—44no—
91C2×C32×C8C2312yes—
92C32×C42C2311yescharacteristic
93#3752—21no—
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95#3745—24no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4D412yes—
98C3×C4⋊Dic3D411yescharacteristic
99C3×C4⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C3×D24—24no—
103C3×D3×C8—24no—
104#3722—22no—
105(C2×D3)⋊Dic3—22no—
106#3714—24no—
107#3714—42no—
108#3714D414yescomplemented
109D4×D8—91noSylow
110C2×D3×D4—32no—
111C2×D3×D4—32no—
112C2×D3×D4—61no—
113C2×D3×D4—61no—
114C2×D3×D4—61no—
115C22×D12—32no—
116C22×D12—32no—
117C22×D12—61no—
118C2×C3×D8—32no—
119C22×C3×C8—32no—
120C3×#127—31no—
121C3×C4×D4—31no—
122C3×C4×D4—31no—
123#938—32no—
124#938—61no—
125#937—62no—
126C2×#213—31no—
127C2×#213—32no—
128C2×#213—32no—
129#930—32no—
130#930—32no—
131#930—61no—
132D3×D8—68no—
133C2×D24—31no—
134C2×D24—32no—
135C2×D24—32no—
136C2×D24—32no—
137C2×D24—32no—
138C2×D24—62no—
139C2×D24—68no—
140C2×D24C2×D312yescomplemented
141C2×D3×C8C2×D312yescomplemented
142#895—32no—
143#895—61no—
144#895—61no—
145#882—62no—
146#882—62no—
147#882—62no—
148#874—31no—
149#874—31no—
150#874—61no—
151#874C2×D311yescharacteristic, complemented
152C4×D12—31no—
153C4×D12—31no—
154C4×D12—61no—
155C4×D12C2×D311yescharacteristic
156C4×D12C2×D311yescharacteristic, complemented
157C3×C4⋊C8—21no—
158C3×C4⋊C8C2×D311yescharacteristic, complemented
159C3×C4⋊C8C2×D311yescharacteristic, complemented
160C3×#102—32no—
161C3×C22⋊C8—32no—
162C3×C4×C8—31no—
163#832—31no—
164#821—31no—
165#821—32no—
166#821—32no—
167#821—31no—
168#821—62no—
169#821C2×D312yescomplemented
170(C2×D3)⋊C8C2×D312yescomplemented
171#818—31no—
172#809—31no—
173#807—31no—
174C4×C3⋊C8C2×D311yescharacteristic, complemented
175C22×C3⋊D3—21no—
176C22×C3⋊D3—22no—
177C22×C3×D3—21no—
178C22×C3×D3—22no—
179C22×C3×D3C2×D412yes—
180C2×D32—44no—
181C2×D32—44no—
182C2×D32—44no—
183C2×D32—44no—
184C2×D32—82no—
185C2×D32—82no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C4⋊(C3⋊D3)—22no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)—22no—
193C4⋊(C3⋊D3)—42no—
194C4⋊(C3⋊D3)—81no—
195C4⋊(C3⋊D3)C2×D412yescomplemented
196C4×C3⋊D3—42no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3C2×D412yes—
199C3×D12—22no—
200C3×D12—21no—
201C3×D12—22no—
202C3×D12—42no—
203C3×D12—81no—
204C3×D12D814yescomplemented
205C3×D12C2×D412yescomplemented
206C3×C4×D3—22no—
207C3×C4×D3—22no—
208C3×C4×D3—42no—
209#626—44no—
210#626—44no—
211#626—44no—
212#625—44no—
213C32×C8—22no—
214C3×C3⋊C8—21no—
215C3×C3⋊C8C2×D412yescomplemented
216C22×D8—92no—
217D42—91no—
218D42—91no—
219#493—91no—
220#466—92no—
221#459—31no—
222#459—91no—
223#447—92no—
224#447—92no—
225C4×D8—91no—
226C8×D4—31no—
227C23×D3—62no—
228C23×D3—62no—
229C23×D3—62no—
230C23×D3—62no—
231C2×C3×D4—31no—
232C2×C3×D4—31no—
233C2×C3×D4—32no—
234C2×C3×D4—61no—
235C2×C3×D4—61no—
236C22×C3×C4—32no—
237C22×C3×C4—61no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243D3×D4—64no—
244D3×D4—64no—
245D3×D4—122no—
246D3×D4—122no—
247D3×D4—124no—
248D3×D4—124no—
249D3×D4—124no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—31no—
253C2×D12—31no—
254C2×D12—32no—
255C2×D12—32no—
256C2×D12—61no—
257C2×D12—62no—
258C2×D12—64no—
259C2×D12—64no—
260C2×D12—62no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—61no—
264C2×D12—61no—
265C2×D12—61no—
266C2×D12—61no—
267C2×D12—121no—
268C2×D12—121no—
269C2×D12—122no—
270C2×D12—122no—
271C2×D12—124no—
272C2×D12D1211yescharacteristic
273C2×D12C22×D312yes—
274C2×D12C22×D311yescharacteristic
275C2×C4×D3—21no—
276C2×C4×D3—61no—
277C2×C4×D3—61no—
278C2×C4×D3—121no—
279C2×C4×D3C22×D312yes—
280C3×D8—64no—
281C2×C3×C8—22no—
282C2×C3×C8—31no—
283C2×C3×C8—31no—
284C2×C3×C8—64no—
285C2×C3×C8C22×D312yes—
286C2×C3×C8C22×D312yes—
287C3×C4⋊C4—31no—
288C3×C4⋊C4—31no—
289C3×C22⋊C4—32no—
290C3×C22⋊C4—61no—
291C3×C42—21no—
292C3×C42C22×D311yescharacteristic
293C3×C42C22×D311yescharacteristic
294#217—62no—
295#213—34no—
296#213—64no—
297#213—122no—
298(C2×D3)⋊C4—21no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—61no—
302(C2×D3)⋊C4—61no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—121no—
305(C2×D3)⋊C4D1212yes—
306C4⋊Dic3—31no—
307C4⋊Dic3—31no—
308C4⋊Dic3—61no—
309C4⋊Dic3D1211yescharacteristic
310C4⋊Dic3C22×D311yescharacteristic
311C2×C3⋊C8C22×D311yescharacteristic
312C2×C3⋊C8C22×D311yescharacteristic
313D24—24no—
314D24—34no—
315D24—64no—
316D24—64no—
317D24—64no—
318D24—124no—
319D24—122no—
320D3×C8—24no—
321C22×C32C22×D411yescharacteristic
322C2×C3⋊D3—22no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—42no—
326C2×C3⋊D3—42no—
327C2×C3⋊D3—42no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3C2×D814yescomplemented
337D32—88no—
338D32—88no—
339C32×C4—21no—
340C32×C4C2×D812yescomplemented
341C32×C4C22×D411yescharacteristic
342C32×C4H(5,𝔽2)11yescharacteristic
343C3⋊Dic3—41no—
344C3×Dic3—22no—
345C3×Dic3—41no—
346C22×D4—92no—
347C22×D4—92no—
348C22×D4—181no—
349C22×D4—181no—
350C2×D8—32no—
351C2×D8—91no—
352C2×D8—92no—
353C2×D8—92no—
354C2×D8—92no—
355C2×D8—188no—
356C22×C8—32no—
357#127—31no—
358#127—91no—
359#121—92no—
360#121—92no—
361#121—181no—
362#121—181no—
363#120—182no—
364#120—182no—
365C4×D4—31no—
366C4×D4—31no—
367C4×D4—91no—
368#107—91no—
369C4⋊C8D3211yescharacteristic, complemented
370#102—32no—
371#102—91no—
372#102—91no—
373#102—92no—
374C22⋊C8—32no—
375C4×C8—31no—
376C23×C3—32no—
377C23×C3—61no—
378C23×C3—62no—
379C22×D3—21no—
380C22×D3—22no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—121no—
386C22×D3—122no—
387C22×D3—124no—
388C22×D3—124no—
389C22×D3—124no—
390C22×D3—124no—
391C22×D3—124no—
392C22×D3—124no—
393C22×D3—124no—
394C22×D3—124no—
395C22×D3—242no—
396C22×D3—242no—
397C22×D3—242no—
398C22×D3—242no—
399C22×D3C2×D1212yes—
400C3×D4—34no—
401C3×D4—32no—
402C3×D4—62no—
403C3×D4—61no—
404C3×D4—62no—
405C3×D4—122no—
406C3×D4—241no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—32no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—61no—
414C2×C3×C4—122no—
415C2×C3×C4C2×D1211yescharacteristic
416C2×C3×C4C2×D1211yescharacteristic
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—124no—
422#67—124no—
423#67—124no—
424#67—124no—
425#67—124no—
426C2×Dic3—21no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—121no—
430C2×Dic3C2×D1212yes—
431D12—22no—
432D12—21no—
433D12—22no—
434D12—32no—
435D12—32no—
436D12—42no—
437D12—62no—
438D12—62no—
439D12—62no—
440D12—61no—
441D12—61no—
442D12—62no—
443D12—62no—
444D12—81no—
445D12—121no—
446D12—122no—
447D12—122no—
448D12—124no—
449D12—124no—
450D12—124no—
451D12—122no—
452D12—122no—
453D12—242no—
454D12—241no—
455D12—241no—
456D12—242no—
457D12D2414yescomplemented
458D12D3×D412yescomplemented
459C4×D3—22no—
460C4×D3—22no—
461C4×D3—42no—
462C4×D3—122no—
463C4×D3—122no—
464C4×D3—242no—
465C3×C8—22no—
466C3×C8—22no—
467C3×C8—32no—
468C3×C8—42no—
469C3×C8—61no—
470C3⋊C8—21no—
471C3⋊C8D3×D412yescomplemented
472C2×C32D4211yescharacteristic
473C2×C32C22×D811yescharacteristic
474C2×C32#57611yescharacteristic
475C3⋊D3—42no—
476C3⋊D3—82no—
477C3×D3—24no—
478C3×D3—42no—
479C3×D3—82no—
480C24—182no—
481C24—182no—
482C2×D4—31no—
483C2×D4—32no—
484C2×D4—31no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—91no—
488C2×D4—92no—
489C2×D4—182no—
490C2×D4—182no—
491C2×D4—184no—
492C2×D4—184no—
493C2×D4—182no—
494C2×D4—182no—
495C2×D4—181no—
496C2×D4—181no—
497C2×D4—362no—
498C2×D4—362no—
499C2×D4—364no—
500C2×D4—364no—
501C22×C4—32no—
502C22×C4—61no—
503C22×C4—181no—
504D8—64no—
505D8—94no—
506D8—184no—
507D8—184no—
508D8—362no—
509C2×C8—31no—
510C2×C8—31no—
511C2×C8—64no—
512C2×C8C2×D3212yes—
513C4⋊C4—31no—
514C4⋊C4—31no—
515C4⋊C4—91no—
516C22⋊C4—32no—
517C22⋊C4—61no—
518C22⋊C4—182no—
519C22⋊C4—182no—
520C22⋊C4—181no—
521C42C2×D3211yescharacteristic
522C22×C3—21no—
523C22×C3—34no—
524C22×C3—62no—
525C22×C3—62no—
526C22×C3—62no—
527C22×C3—121no—
528C22×C3—121no—
529C22×C3—122no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3C22×D1211yescharacteristic
533C22×C3C2×D3×D411yescharacteristic
534C2×D3—22no—
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—41no—
538C2×D3—41no—
539C2×D3—42no—
540C2×D3—42no—
541C2×D3—42no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—122no—
545C2×D3—121no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
549C2×D3—122no—
550C2×D3—122no—
551C2×D3—122no—
552C2×D3—122no—
553C2×D3—122no—
554C2×D3—122no—
555C2×D3—241no—
556C2×D3—241no—
557C2×D3—242no—
558C2×D3—242no—
559C2×D3—242no—
560C2×D3—248no—
561C2×D3—248no—
562C2×D3—248no—
563C2×D3—248no—
564C2×D3C2×D2414yescomplemented
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—22no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—41no—
571C3×C4—62no—
572C3×C4—121no—
573C3×C4C2×D2412yescomplemented
574C3×C4D3×D812yescomplemented
575C3×C4C2×D3×D411yescharacteristic
576C3×C4C2×D3×D411yescharacteristic
577C3×C4#100911yescharacteristic
578C3×C4#100911yescharacteristic
579Dic3—22no—
580Dic3—41no—
581Dic3—121no—
582Dic3—121no—
583Dic3—241no—
584C32D4×D811yescharacteristic, complemented, Sylow
585C23—32no—
586C23—61no—
587C23—62no—
588C23—181no—
589C23—182no—
590C23—364no—
591C23—364no—
592C23—364no—
593C23—364no—
594C23—722no—
595C23—722no—
596D4—34no—
597D4—32no—
598D4—62no—
599D4—61no—
600D4—62no—
601D4—92no—
602D4—122no—
603D4—182no—
604D4—181no—
605D4—182no—
606D4—241no—
607D4—364no—
608D4—364no—
609D4—364no—
610D4—364no—
611D4—362no—
612D4—721no—
613C2×C4—32no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—61no—
617C2×C4—122no—
618C2×C4—181no—
619C2×C4—362no—
620C2×C4D3×D1211yescharacteristic
621C2×C4D3×D1211yescharacteristic
622C2×C4C22×D3211yescharacteristic
623C8—22no—
624C8—32no—
625C8—61no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—64no—
630C2×C3—122no—
631C2×C3—242no—
632C2×C3D4×D1211yescharacteristic
633C2×C3#560911yescharacteristic
634C2×C3C22×D2411yescharacteristic
635C2×C3#575211yescharacteristic
636C2×C3C2×D3×D811yescharacteristic
637C2×C3#577411yescharacteristic
638D3—24no—
639D3—42no—
640D3—82no—
641D3—122no—
642D3—122no—
643D3—242no—
644D3—242no—
645D3—242no—
646D3—482no—
647C22—34no—
648C22—62no—
649C22—62no—
650C22—62no—
651C22—121no—
652C22—121no—
653C22—122no—
654C22—122no—
655C22—122no—
656C22—182no—
657C22—361no—
658C22—361no—
659C22—362no—
660C22—362no—
661C22—362no—
662C22—728no—
663C22—728no—
664C22C2×D3×D1211yescharacteristic
665C4—21no—
666C4—62no—
667C4—121no—
668C4—361no—
669C4D3×D2412yescomplemented
670C4D32×D411yescharacteristic
671C4#6432011yescharacteristic
672C3—21no—
673C3D4×D2411yescharacteristic, complemented
674C3#8035011yescharacteristic, complemented
675C2—64no—
676C2—122no—
677C2—242no—
678C2—362no—
679C2—722no—
680C2#1059462111yescharacteristic
681C2C2×D3×D2411yescharacteristic
682C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×D3×D24C2semidirect
2. #10594004C2semidirect
3. D122C2semidirect
4. #10592542C2semidirect
5. C3×#4843C2semidirect
6. C3×#4834C2semidirect
7. #10590947C2semidirect
8. #10590944C2semidirect
9. #10590826C2semidirect
10. #10590350C2semidirect
11. C4×#3714C2semidirect
16. C2×D3×D12C22semidirect
17. C2×D3×D12C22semidirect
18. C2×#3745C22semidirect
19. #64083C22semidirect
20. C4×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×D24C22semidirect
22. C2×C3×D3×C8C22semidirect
23. C3×#874C22semidirect
25. C3×C4×D12C22semidirect
30. #63909C22semidirect
31. #63908C22semidirect
33. C2×#3714C22semidirect
34. C2×#3714C22semidirect
36. C32×C4⋊C8C22semidirect
37. #63648C22semidirect
38. C3×#821C22semidirect
39. C3×(C2×D3)⋊C8C22semidirect
40. C3×C4×C3⋊C8C22semidirect
41. #63575C22semidirect
42. #63564C22semidirect
43. #63563C22semidirect
59. #4843D3semidirect
60. #4834D3semidirect
108. #3714D4semidirect
140. C2×D24C2×D3semidirect
141. C2×D3×C8C2×D3semidirect
151. #874C2×D3semidirect
156. C4×D12C2×D3semidirect
158. C3×C4⋊C8C2×D3semidirect
159. C3×C4⋊C8C2×D3semidirect
169. #821C2×D3semidirect
170. (C2×D3)⋊C8C2×D3semidirect
174. C4×C3⋊C8C2×D3semidirect
195. C4⋊(C3⋊D3)C2×D4semidirect
204. C3×D12D8semidirect
205. C3×D12C2×D4semidirect
215. C3×C3⋊C8C2×D4semidirect
336. C2×C3×D3C2×D8semidirect
340. C32×C4C2×D8semidirect
369. C4⋊C8D32semidirect
457. D12D24semidirect
458. D12D3×D4semidirect
471. C3⋊C8D3×D4semidirect
564. C2×D3C2×D24semidirect
573. C3×C4C2×D24semidirect
574. C3×C4D3×D8semidirect
584. C32D4×D8semidirect
669. C4D3×D24semidirect
673. C3D4×D24semidirect
674. C3#80350semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
#105940042
D1222
#105925422
C3×#48432
C3×#48342
#105909472
#105909442
#105908262
#105903502
C4×#37142
#803503
D4×D243