Finite Group Databasebeta

← #11885767

Subgroups — #11885767

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
1C3×#5717C211yesmaximal, characteristic, complemented
2C2×D3×#213C212yesmaximal, complemented
3#10594004C211yesmaximal, characteristic, complemented
4#10592771C211yesmaximal, characteristic, complemented
5C3×#5073C211yesmaximal, characteristic, complemented
6#10591515C212yesmaximal, complemented
7#10591498C212yesmaximal, complemented
8#10591447C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11C3⋊C8×D12C211yesmaximal, characteristic, complemented
12D4×#213—31nomaximal
13#81789—31nomaximal
14C2×C3×D3×D4—21no—
15C2×C3×D3×D4C2212yescomplemented
16C2×#3802—21no—
17C2×D3×D12C2212yescomplemented
18C32×#127C2211yescharacteristic, complemented
19C2×#3753C2212yescomplemented
20C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C3×#938—21no—
22C3×#938C2212yescomplemented
23C3×#937—22no—
24C2×C3×#213C2212yescomplemented
25C2×C3×#213C2212yescomplemented
26C3×#874C2211yescharacteristic, complemented
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic, complemented
29D3×#213—28no—
30#63922—22no—
31#63916—21no—
32#63908C2212yescomplemented
33C2×#3714C2211yescharacteristic
34C2×#3713C2212yescomplemented
35C2×D3×C3⋊C8C2212yescomplemented
36#63659C2212yescomplemented
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
38C3×C4×C3⋊C8C2211yescharacteristic, complemented
39#63575C2211yescharacteristic, complemented
40#63564C2211yescharacteristic, complemented
41#63563C2211yescharacteristic, complemented
42#63562C2212yescomplemented
43(C2×D3)⋊(C3⋊C8)C2212yescomplemented
44C3×D42—31no—
45C22×#213—32no—
46C2×D3×D8—32no—
47#5717—31no—
48#5717D311yescharacteristic, complemented
49D4×D12—31no—
50C3×#493—31no—
51#5217—32no—
52#5157—32no—
53#5156—32no—
54#5156—32no—
55#5073D311yescharacteristic, complemented
56#5072—31no—
57#5072—31no—
58#5072—31no—
59#5072—61no—
60#5038—32no—
61#5036—32no—
62#5015—31no—
63C4×#213—31no—
64D4×C3⋊C8—31no—
65C4×D24—31no—
66C8×D12—31no—
67C23×C3×D3—22no—
68C22×D32—22no—
69C2×C32×D4—21no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C3×#67—22no—
75C2×C3×#67—22no—
76C3×D3×D4—24no—
77C3×D3×D4—42no—
78C3×D3×D4—44no—
79C2×C3×D12—21no—
80C2×C3×D12—21no—
81C2×C3×D12D411yescharacteristic
82C2×C3×D12C2312yes—
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3C2312yes—
86C2×#626—22no—
87C2×#625—22no—
88#3802—44no—
89D3×D12—24no—
90D3×D12—42no—
91C32×C42C2311yescharacteristic
92#3753—24no—
93#3752—21no—
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—22no—
97C3×#213—24no—
98C3×#213—42no—
99C3×(C2×D3)⋊C4—21no—
100C3×(C2×D3)⋊C4D412yes—
101C3×C4⋊Dic3D411yescharacteristic
102C3×C4⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104C2×C3×C3⋊C8C2311yescharacteristic
105(C2×D3)⋊Dic3—22no—
106#3714D414yescomplemented
107#3713—24no—
108D3×C3⋊C8—24no—
109D4×D8—91noSylow
110C22×C3×D4—32no—
111C22×C3×D4—61no—
112C2×D3×D4—21no—
113C2×D3×D4—32no—
114C2×D3×D4—61no—
115C2×D3×D4—61no—
116C2×D3×D4C2×D312yescomplemented
117C22×D12—32no—
118C2×C3×D8—32no—
119C2×C3×D8—32no—
120C3×#127—21no—
121C3×#127—31no—
122C3×#127C2×D311yescharacteristic, complemented
123C3×#127C2×D311yescharacteristic, complemented
124C3×#121—32no—
125C3×#121—61no—
126C3×#120—62no—
127C3×C4×D4—31no—
128C3×C4×D4—31no—
129#938—21no—
130#938—32no—
131#938—61no—
132#938C2×D312yescomplemented
133#937—22no—
134#937—62no—
135C2×#213—32no—
136C2×#213—32no—
137C2×#213—32no—
138C2×#213—32no—
139C2×#213—31no—
140C2×#213—62no—
141C2×#213—68no—
142C2×#213C2×D312yescomplemented
143C2×#213C2×D312yescomplemented
144#930—32no—
145C22×C3⋊C8—32no—
146D3×D8—68no—
147C2×D24—31no—
148C2×D3×C8—32no—
149#895—61no—
150#882—62no—
151#874C2×D311yescharacteristic, complemented
152C4×D12—31no—
153C4×D12—31no—
154C4×D12—61no—
155C4×D12C2×D311yescharacteristic
156C4×D12C2×D311yescharacteristic, complemented
157C3×C4×C8—31no—
158#832—32no—
159#832—32no—
160#832—32no—
161#832—31no—
162#832—62no—
163#830—32no—
164#821—31no—
165#821—31no—
166(C2×D3)⋊C8—32no—
167#818—31no—
168#809—32no—
169#809—31no—
170#807—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—61no—
174C4×C3⋊C8C2×D311yescharacteristic, complemented
175C23×C32—22no—
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3—22no—
179C22×C3×D3—44no—
180C22×C3×D3—44no—
181C22×C3×D3—82no—
182C22×C3×D3C2×D412yes—
183C2×D32—44no—
184C2×D32—44no—
185C2×D32—82no—
186C32×D4—22no—
187C32×D4—22no—
188C32×D4—42no—
189C32×D4—81no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—21no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)C2×D412yescomplemented
196C4×C3⋊D3—42no—
197C3×#67—44no—
198C3×#67—44no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3C2×D412yes—
201C3×D12—22no—
202C3×D12—21no—
203C3×D12—22no—
204C3×D12—42no—
205C3×D12—81no—
206C3×D12D814yescomplemented
207C3×D12C2×D412yescomplemented
208C3×C4×D3—22no—
209C3×C4×D3—22no—
210C3×C4×D3—42no—
211#626—44no—
212#625—44no—
213C3⋊(C3⋊C8)—22no—
214C3×C3⋊C8—21no—
215C3×C3⋊C8C2×D412yescomplemented
216C22×D8—92no—
217D42—31no—
218D42—91no—
219#493—31no—
220#466—92no—
221#459—91no—
222#459—91no—
223#447—92no—
224#447—92no—
225C4×D8—91no—
226C8×D4—91no—
227C24×C3—62no—
228C23×D3—22no—
229C23×D3—62no—
230C23×D3—62no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—22no—
236C2×C3×D4—31no—
237C2×C3×D4—31no—
238C2×C3×D4—32no—
239C2×C3×D4—41no—
240C2×C3×D4—41no—
241C2×C3×D4—62no—
242C2×C3×D4—64no—
243C2×C3×D4—62no—
244C2×C3×D4—61no—
245C2×C3×D4—61no—
246C2×C3×D4—122no—
247C2×C3×D4—124no—
248C2×C3×D4C22×D312yes—
249C2×C3×D4C22×D312yes—
250C22×C3×C4—32no—
251C22×C3×C4—61no—
252C2×#67—22no—
253C2×#67—22no—
254C2×#67—62no—
255C2×#67—62no—
256C2×#67—62no—
257D3×D4—24no—
258D3×D4—42no—
259D3×D4—44no—
260D3×D4—64no—
261D3×D4—122no—
262D3×D4—124no—
263D3×D4—124no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—31no—
267C2×D12—31no—
268C2×D12—61no—
269C2×D12—64no—
270C2×D12—62no—
271C2×D12—122no—
272C2×D12#6711yescharacteristic
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—
281C3×D8—122no—
282C2×C3×C8—31no—
283C2×C3×C8—31no—
284C3×C4⋊C4—31no—
285C3×C4⋊C4—31no—
286C3×C22⋊C4—32no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4—61no—
289C3×C42—21no—
290C3×C42C22×D311yescharacteristic
291C3×C42C22×D311yescharacteristic
292#217—22no—
293#217—62no—
294#213—24no—
295#213—34no—
296#213—42no—
297#213—64no—
298#213—64no—
299#213—64no—
300#213—64no—
301#213—124no—
302(C2×D3)⋊C4—21no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—61no—
305(C2×D3)⋊C4—61no—
306(C2×D3)⋊C4—121no—
307(C2×D3)⋊C4#6712yes—
308C4⋊Dic3—31no—
309C4⋊Dic3—31no—
310C4⋊Dic3—61no—
311C4⋊Dic3#6711yescharacteristic
312C4⋊Dic3C22×D311yescharacteristic
313C2×C3⋊C8—32no—
314C2×C3⋊C8—32no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8—64no—
317C2×C3⋊C8C22×D311yescharacteristic
318C2×C3⋊C8C22×D311yescharacteristic
319D24—34no—
320D3×C8—64no—
321C22×C32—42no—
322C22×C32—42no—
323C22×C32—42no—
324C22×C32C22×D411yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—41no—
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×D3—88no—
337C2×C3×D3C2×D814yescomplemented
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—32no—
347C22×D4—61no—
348C22×D4—92no—
349C22×D4—181no—
350C2×D8—32no—
351C2×D8—32no—
352C2×D8—91no—
353C2×D8—92no—
354C2×D8—92no—
355C2×D8—188no—
356C22×C8—92no—
357#127—31no—
358#127D3211yescharacteristic, complemented
359#121—32no—
360#121—61no—
361#121—92no—
362#121—181no—
363#120—62no—
364#120—182no—
365C4×D4—31no—
366C4×D4—31no—
367C4×D4—91no—
368#107—91no—
369C4⋊C8—91no—
370#102—91no—
371#102—92no—
372#102—91no—
373#102—92no—
374C22⋊C8—92no—
375C4×C8—31no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—32no—
379C23×C3—42no—
380C23×C3—61no—
381C23×C3—62no—
382C23×C3—124no—
383C23×C3—124no—
384C23×C3—242no—
385C22×D3—21no—
386C22×D3—22no—
387C22×D3—44no—
388C22×D3—44no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—82no—
392C22×D3—121no—
393C22×D3—124no—
394C22×D3—124no—
395C22×D3—124no—
396C22×D3—124no—
397C22×D3—242no—
398C22×D3—242no—
399C22×D3C2×#6712yes—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—34no—
405C3×D4—32no—
406C3×D4—42no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—42no—
410C3×D4—62no—
411C3×D4—61no—
412C3×D4—62no—
413C3×D4—82no—
414C3×D4—81no—
415C3×D4—81no—
416C3×D4—82no—
417C3×D4—124no—
418C3×D4—124no—
419C3×D4—122no—
420C3×D4—241no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—32no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—61no—
428C2×C3×C4—122no—
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4D3×D411yescharacteristic
431C2×C3×C4C2×#6711yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C23×D311yescharacteristic
434C2×C3×C4C23×D311yescharacteristic
435#67—44no—
436#67—44no—
437#67—124no—
438#67—124no—
439#67—124no—
440C2×Dic3—21no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—121no—
444C2×Dic3C2×#6712yes—
445D12—22no—
446D12—21no—
447D12—22no—
448D12—32no—
449D12—32no—
450D12—42no—
451D12—62no—
452D12—61no—
453D12—61no—
454D12—81no—
455D12—121no—
456D12—124no—
457D12#21314yescomplemented
458D12D3×D412yescomplemented
459C4×D3—22no—
460C4×D3—22no—
461C4×D3—42no—
462C4×D3—122no—
463C4×D3—122no—
464C4×D3—242no—
465C3×C8—32no—
466C3×C8—61no—
467C3⋊C8—21no—
468C3⋊C8—62no—
469C3⋊C8—62no—
470C3⋊C8—122no—
471C3⋊C8D3×D412yescomplemented
472C2×C32—82no—
473C2×C32D4211yescharacteristic
474C2×C32C22×D811yescharacteristic
475C2×C32#57611yescharacteristic
476C3⋊D3—42no—
477C3×D3—24no—
478C3×D3—42no—
479C3×D3—82no—
480C24—62no—
481C24—182no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—31no—
485C2×D4—32no—
486C2×D4—31no—
487C2×D4—62no—
488C2×D4—64no—
489C2×D4—62no—
490C2×D4—61no—
491C2×D4—61no—
492C2×D4—91no—
493C2×D4—122no—
494C2×D4—124no—
495C2×D4—182no—
496C2×D4—184no—
497C2×D4—182no—
498C2×D4—362no—
499C2×D4—364no—
500C2×D4C2×D3212yes—
501C22×C4—32no—
502C22×C4—61no—
503C22×C4—181no—
504D8—64no—
505D8—94no—
506D8—122no—
507D8—184no—
508D8—184no—
509C2×C8—31no—
510C2×C8—31no—
511C2×C8—92no—
512C2×C8—184no—
513C4⋊C4—31no—
514C4⋊C4—31no—
515C4⋊C4—91no—
516C22⋊C4—32no—
517C22⋊C4—62no—
518C22⋊C4—61no—
519C22⋊C4—182no—
520C22⋊C4—181no—
521C42C2×D3211yescharacteristic
522C22×C3—21no—
523C22×C3—34no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—62no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3—82no—
534C22×C3—82no—
535C22×C3—82no—
536C22×C3—121no—
537C22×C3—121no—
538C22×C3—122no—
539C22×C3—122no—
540C22×C3—122no—
541C22×C3—248no—
542C22×C3C2×D3×D411yescharacteristic
543C22×C3C22×#6711yescharacteristic
544C2×D3—22no—
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—41no—
548C2×D3—41no—
549C2×D3—42no—
550C2×D3—42no—
551C2×D3—42no—
552C2×D3—62no—
553C2×D3—62no—
554C2×D3—88no—
555C2×D3—122no—
556C2×D3—121no—
557C2×D3—121no—
558C2×D3—121no—
559C2×D3—121no—
560C2×D3—241no—
561C2×D3—241no—
562C2×D3—248no—
563C2×D3—248no—
564C2×D3C2×#21314yescomplemented
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—22no—
570C3×C4—41no—
571C3×C4—62no—
572C3×C4—121no—
573C3×C4D3×D812yescomplemented
574C3×C4C2×#21312yescomplemented
575C3×C4C2×D3×D411yescharacteristic
576C3×C4C2×D3×D411yescharacteristic
577C3×C4#100411yescharacteristic
578C3×C4#100411yescharacteristic
579Dic3—22no—
580Dic3—41no—
581Dic3—121no—
582Dic3—121no—
583Dic3—241no—
584C32D4×D811yescharacteristic, complemented, Sylow
585C23—22no—
586C23—32no—
587C23—61no—
588C23—62no—
589C23—124no—
590C23—124no—
591C23—181no—
592C23—242no—
593C23—364no—
594C23—364no—
595C23—722no—
596D4—22no—
597D4—22no—
598D4—32no—
599D4—34no—
600D4—42no—
601D4—62no—
602D4—61no—
603D4—62no—
604D4—81no—
605D4—92no—
606D4—124no—
607D4—124no—
608D4—122no—
609D4—181no—
610D4—241no—
611D4—364no—
612D4—364no—
613C2×C4—32no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—61no—
617C2×C4—122no—
618C2×C4—181no—
619C2×C4—362no—
620C2×C4D3×#6711yescharacteristic
621C2×C4D3×#6711yescharacteristic
622C2×C4C22×D3211yescharacteristic
623C8—32no—
624C8—61no—
625C8—182no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—64no—
630C2×C3—82no—
631C2×C3—82no—
632C2×C3—122no—
633C2×C3—162no—
634C2×C3—242no—
635C2×C3#571711yescharacteristic
636C2×C3C2×D3×D811yescharacteristic
637C2×C3#575711yescharacteristic
638C2×C3C22×#21311yescharacteristic
639C2×C3D4×#6711yescharacteristic
640C2×C3#583511yescharacteristic
641D3—24no—
642D3—42no—
643D3—82no—
644D3—122no—
645D3—122no—
646D3—242no—
647C22—34no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—62no—
652C22—62no—
653C22—62no—
654C22—121no—
655C22—121no—
656C22—122no—
657C22—122no—
658C22—122no—
659C22—182no—
660C22—248no—
661C22—361no—
662C22—361no—
663C22—728no—
664C22C2×D3×#6711yescharacteristic
665C4—21no—
666C4—62no—
667C4—121no—
668C4—361no—
669C4D3×#21312yescomplemented
670C4D32×D411yescharacteristic
671C4#6431311yescharacteristic
672C3—21no—
673C3#8178911yescharacteristic, complemented
674C3D4×#21311yescharacteristic, complemented
675C2—64no—
676C2—82no—
677C2—122no—
678C2—242no—
679C2—362no—
680C2C2×D3×#21311yescharacteristic
681C2#1059509611yescharacteristic
682C2#1059529311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5717C2semidirect
2. C2×D3×#213C2semidirect
3. #10594004C2semidirect
4. #10592771C2semidirect
5. C3×#5073C2semidirect
6. #10591515C2semidirect
7. #10591498C2semidirect
8. #10591447C2semidirect
9. #10590347C2semidirect
10. C4×#3714C2semidirect
11. C3⋊C8×D12C2semidirect
15. C2×C3×D3×D4C22semidirect
17. C2×D3×D12C22semidirect
18. C32×#127C22semidirect
19. C2×#3753C22semidirect
20. C4×C4⋊(C3⋊D3)C22semidirect
22. C3×#938C22semidirect
24. C2×C3×#213C22semidirect
25. C2×C3×#213C22semidirect
26. C3×#874C22semidirect
28. C3×C4×D12C22semidirect
32. #63908C22semidirect
34. C2×#3713C22semidirect
35. C2×D3×C3⋊C8C22semidirect
36. #63659C22semidirect
37. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×C4×C3⋊C8C22semidirect
39. #63575C22semidirect
40. #63564C22semidirect
41. #63563C22semidirect
42. #63562C22semidirect
43. (C2×D3)⋊(C3⋊C8)C22semidirect
48. #5717D3semidirect
55. #5073D3semidirect
106. #3714D4semidirect
116. C2×D3×D4C2×D3semidirect
122. C3×#127C2×D3semidirect
123. C3×#127C2×D3semidirect
132. #938C2×D3semidirect
142. C2×#213C2×D3semidirect
143. C2×#213C2×D3semidirect
151. #874C2×D3semidirect
156. C4×D12C2×D3semidirect
174. C4×C3⋊C8C2×D3semidirect
195. C4⋊(C3⋊D3)C2×D4semidirect
206. C3×D12D8semidirect
207. C3×D12C2×D4semidirect
215. C3×C3⋊C8C2×D4semidirect
337. C2×C3×D3C2×D8semidirect
340. C32×C4C2×D8semidirect
358. #127D32semidirect
457. D12#213semidirect
458. D12D3×D4semidirect
471. C3⋊C8D3×D4semidirect
564. C2×D3C2×#213semidirect
573. C3×C4D3×D8semidirect
574. C3×C4C2×#213semidirect
584. C32D4×D8semidirect
669. C4D3×#213semidirect
673. C3#81789semidirect
674. C3D4×#213semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
C2×D3×#2132
#105940042
#105927712
C3×#50732
#105915152
#105914982
#105914472
#105903472
C4×#37142
C3⋊C8×D122
D4×#2133
#817893