Finite Group Databasebeta

← #11863951

Subgroups — #11863951

Order 1152.

2137 conjugacy classes of subgroups.

The subgroup lattice has 681 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5#10591651C214yesmaximal, complemented
6#10591515C214yesmaximal, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10591085C211yesmaximal, characteristic, complemented
9#10591069C211yesmaximal, characteristic, complemented
10#83944—31nomaximal
11#82927—31nomaximal
12C23×D32—21no—
13C2×C32×#41C2211yescharacteristic, complemented
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626—21no—
18C2×D3×D12—24no—
19C2×D3×D12—24no—
20C2×D3×D12—22no—
21C2×D3×D12C2214yes—
22#64158—24no—
23C2×#3755C2212yescomplemented
24C2×#3753C2212yescomplemented
25C2×#3748C2211yescharacteristic, complemented
26C3×#949—24no—
27C3×#946C2212yescomplemented
28C2×C3×#215C2212yescomplemented
29C3×#938C2212yescomplemented
30C3×#937—21no—
31C3×#935—21no—
32C2×C3×#213C2212yescomplemented
33C3×C4×#67—22no—
34C3×#926C2211yescharacteristic, complemented
35C2×C3×#208C2211yescharacteristic, complemented
36#63564C2214yescomplemented
37#63562C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C22×D3×D4—31no—
40C23×D12—31no—
41C2×C3×AGL(1,ℤ/8)—31no—
42C3×#525—31no—
43#5828D311yescharacteristic, complemented
44C2×#949—31no—
45C2×#949—31no—
46C2×#949—61no—
47C2×#949D311yescharacteristic, complemented
48#5215—31no—
49#5207—31no—
50#5169—34no—
51#5156—34no—
52#5131—31no—
53#5126—31no—
54#5046—34no—
55#5036—34no—
56#5001—31no—
57#5001—31no—
58C23×C3⋊D3—21no—
59C23×C3×D3—21no—
60C23×C3×D3D411yescharacteristic
61C22×D32—28no—
62C22×D32—24no—
63C22×D32—48no—
64C32×#41—22no—
65C32×#41—22no—
66C2×C32×Q8C2311yescharacteristic, complemented
67C2×C32×D4—21no—
68C2×C32×D4C2311yescharacteristic, complemented
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)D414yescomplemented
74C2×C4⋊(C3⋊D3)C2312yes—
75C2×C3×#67—22no—
76C22×C3×Dic3D411yescharacteristic
77C2×C3×D12—21no—
78C2×C3×D12—22no—
79C2×C3×D12D414yescomplemented
80C2×C3×D12C2312yes—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3D412yes—
84C2×C3×C4×D3C2312yes—
85C2×#626—28no—
86C2×#626—24no—
87D3×D12—216no—
88D3×D12—28no—
89D3×D12—28no—
90#3755—24no—
91#3753—24no—
92#3748—22no—
93C2×C3⋊(C3⋊C8)C2312yescomplemented
94C3×#217—21no—
95C3×#217—22no—
96C3×#215—24no—
97C3×#213—24no—
98C3×(C2×D3)⋊C4—22no—
99C3×C4⋊Dic3C2312yescomplemented
100C3×Dic3⋊C4—22no—
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yescomplemented
104#3003—91noSylow
105C24×D3—61no—
106C24×D3—61no—
107C2×C3×#41—21no—
108C2×C3×#41C2×D311yescharacteristic, complemented
109C2×C3×#41C2×D311yescharacteristic, complemented
110C22×C3×D4—31no—
111C23×C3×C4—31no—
112C22×#67—61no—
113C2×D3×D4—34no—
114C2×D3×D4—64no—
115C2×D3×D4—64no—
116C2×D3×D4—62no—
117C22×D12—31no—
118C22×D12—31no—
119C22×D12—34no—
120C22×D12—61no—
121C22×D12—64no—
122C22×D12—62no—
123C22×D12—61no—
124C22×D12—64no—
125C22×D12C2×D311yescharacteristic
126C22×C4×D3C2×D311yescharacteristic
127C3×AGL(1,ℤ/8)—64no—
128C2×C3×SD16—32no—
129C2×C3×D8—32no—
130C2×C3×M16—31no—
131C3×#123—61no—
132C3×C22⋊Q8—32no—
133C3×#121—32no—
134C3×#120—61no—
135C3×C4×D4—62no—
136C3×#117—31no—
137#949—24no—
138#949—64no—
139#949—64no—
140#949—68no—
141#946C2×D312yescomplemented
142C2×#215—32no—
143C2×#215—32no—
144C2×#215—62no—
145C2×#215C2×D312yescomplemented
146#938C2×D312yescomplemented
147#937—21no—
148#935—21no—
149C2×#213—32no—
150C2×#213—32no—
151C2×#213—62no—
152C2×#213C2×D312yescomplemented
153C4×#67—22no—
154#926C2×D311yescharacteristic, complemented
155C2×#208—31no—
156C2×#208—31no—
157C2×#208—61no—
158C2×#208C2×D311yescharacteristic, complemented
159#832—34no—
160#830—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163#809—34no—
164#809—34no—
165C23×C32—21no—
166C23×C32C2×D411yescharacteristic
167C22×C3⋊D3—24no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3—44no—
170C22×C3×D3—22no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3—22no—
174C22×C3×D3—44no—
175C22×C3×D3C2×D412yes—
176C2×D32—216no—
177C2×D32—432no—
178C2×D32—48no—
179C2×D32—48no—
180C32×Q8—21no—
181C32×Q8—21no—
182C32×D4—21no—
183C32×D4—21no—
184C32×D4—42no—
185C2×C32×C4—21no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D412yes—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D412yes—
190C2×C32×C4C2411yescharacteristic
191C4⋊(C3⋊D3)—24no—
192C4⋊(C3⋊D3)—22no—
193C4⋊(C3⋊D3)C2×D414yes—
194C3×#67—44no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C2×D412yes—
198C3×D12—24no—
199C3×D12—22no—
200C3×D12C2×D414yes—
201C3×C4×D3—24no—
202C3×C4×D3—22no—
203C3×C4×D3—22no—
204#626—216no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207C23×D4—91no—
208C2×AGL(1,ℤ/8)—31no—
209C2×AGL(1,ℤ/8)—91no—
210#525—31no—
211#450—94no—
212#447—94no—
213#418—91no—
214#418—91no—
215#407—91no—
216C24×C3—31no—
217C24×C3—61no—
218C23×D3—21no—
219C23×D3—64no—
220C23×D3—68no—
221C23×D3—68no—
222C23×D3—61no—
223C23×D3—61no—
224C23×D3—64no—
225C23×D3—121no—
226C23×D3—128no—
227C23×D3—128no—
228C23×D3#6711yescharacteristic
229C3×#41—24no—
230C3×#41—22no—
231C3×#41—22no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41—42no—
235C2×C3×Q8—21no—
236C2×C3×Q8C22×D311yescharacteristic, complemented
237C2×C3×Q8C22×D311yescharacteristic, complemented
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—34no—
242C2×C3×D4—32no—
243C2×C3×D4—41no—
244C2×C3×D4—62no—
245C2×C3×D4—62no—
246C2×C3×D4—61no—
247C2×C3×D4C22×D311yescharacteristic, complemented
248C2×C3×D4C22×D311yescharacteristic, complemented
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—41no—
256C22×C3×C4—62no—
257C22×C3×C4—62no—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—22no—
261C2×#67—68no—
262C2×#67—64no—
263C22×Dic3#6711yescharacteristic
264D3×D4—68no—
265D3×D4—68no—
266D3×D4—616no—
267C2×D12—21no—
268C2×D12—22no—
269C2×D12—34no—
270C2×D12—34no—
271C2×D12—32no—
272C2×D12—32no—
273C2×D12—62no—
274C2×D12—64no—
275C2×D12—68no—
276C2×D12—616no—
277C2×D12—64no—
278C2×D12—68no—
279C2×D12—61no—
280C2×D12—62no—
281C2×D12—62no—
282C2×D12—61no—
283C2×D12—68no—
284C2×D12—121no—
285C2×D12—122no—
286C2×D12#6714yescomplemented
287C2×D12C22×D312yes—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3#6712yes—
291C2×C4×D3C22×D312yes—
292C3×SD16—64no—
293C3×D8—64no—
294C3×M16—62no—
295C2×C3×C8—32no—
296C3×C4⋊C4—32no—
297C3×C4⋊C4—62no—
298C3×C22⋊C4—62no—
299C3×C22⋊C4—62no—
300C3×C22⋊C4—61no—
301C3×C42—61no—
302#217—21no—
303#217—22no—
304#215—24no—
305#215—64no—
306#215—64no—
307#215—68no—
308#213—24no—
309#213—64no—
310#213—64no—
311#213—68no—
312(C2×D3)⋊C4—22no—
313C4⋊Dic3C22×D312yescomplemented
314Dic3⋊C4—22no—
315C4×Dic3—21no—
316#208—22no—
317#208—64no—
318#208—62no—
319#208—62no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—32no—
322C2×C3⋊C8—62no—
323C2×C3⋊C8C22×D312yescomplemented
324C22×C32—22no—
325C22×C32—41no—
326C22×C32—42no—
327C22×C32#12012yes—
328C22×C32C22×D411yescharacteristic
329C2×C3⋊D3—24no—
330C2×C3⋊D3—48no—
331C2×C3⋊D3—44no—
332C2×C3×D3—28no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—24no—
336C2×C3×D3—48no—
337C2×C3×D3—44no—
338C2×C3×D3AGL(1,ℤ/8)14yescomplemented
339D32—432no—
340C32×C4—41no—
341C32×C4#12012yes—
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3×Dic3—22no—
345C3×Dic3—42no—
346C25—181no—
347C2×#41D3211yescharacteristic, complemented
348C22×D4—31no—
349C22×D4—94no—
350C22×D4—91no—
351C22×D4—182no—
352C22×D4—181no—
353C22×D4—184no—
354C22×D4—184no—
355C23×C4—31no—
356AGL(1,ℤ/8)—64no—
357AGL(1,ℤ/8)—184no—
358C2×SD16—32no—
359C2×SD16—92no—
360C2×D8—32no—
361C2×D8—92no—
362C2×M16—31no—
363C2×M16—91no—
364#123—61no—
365C22⋊Q8—32no—
366#121—32no—
367#120—61no—
368C4×D4—62no—
369#117—31no—
370#102—94no—
371#102—94no—
372C22⋊C8—94no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—32no—
377C23×C3—41no—
378C23×C3—64no—
379C23×C3—62no—
380C23×C3—64no—
381C23×C3—62no—
382C23×C3—124no—
383C23×C3D3×D411yescharacteristic
384C23×C3C2×#6711yescharacteristic
385C22×D3—22no—
386C22×D3—24no—
387C22×D3—24no—
388C22×D3—22no—
389C22×D3—44no—
390C22×D3—616no—
391C22×D3—616no—
392C22×D3—64no—
393C22×D3—64no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—122no—
397C22×D3—124no—
398C22×D3—1232no—
399C22×D3—128no—
400C22×D3—128no—
401C22×D3—1232no—
402C22×D3—128no—
403C22×D3—124no—
404C22×D3—124no—
405C22×D3—128no—
406C22×D3—244no—
407C22×D3C2×#6712yes—
408C3×Q8—22no—
409C3×Q8—21no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—21no—
413C3×Q8—41no—
414C3×D4—22no—
415C3×D4—21no—
416C3×D4—21no—
417C3×D4—21no—
418C3×D4—21no—
419C3×D4—34no—
420C3×D4—41no—
421C3×D4—44no—
422C3×D4—42no—
423C3×D4—42no—
424C3×D4—64no—
425C3×D4—62no—
426C3×D4—124no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—32no—
434C2×C3×C4—41no—
435C2×C3×C4—44no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—62no—
439C2×C3×C4—64no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4D3×D411yescharacteristic
444C2×C3×C4D3×D412yes—
445C2×C3×C4D3×D412yes—
446C2×C3×C4D3×D412yes—
447C2×C3×C4C2×#6711yescharacteristic
448C2×C3×C4C2×#6712yes—
449C2×C3×C4C23×D311yescharacteristic
450C2×C3×C4C23×D311yescharacteristic
451#67—44no—
452#67—616no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3C2×#6712yes—
456D12—24no—
457D12—22no—
458D12—34no—
459D12—34no—
460D12—64no—
461D12—616no—
462D12—64no—
463D12—64no—
464D12—62no—
465D12—62no—
466D12—122no—
467D12—124no—
468D12C2×#6714yes—
469C4×D3—24no—
470C4×D3—22no—
471C4×D3—22no—
472C3×C8—62no—
473C3⋊C8—22no—
474C3⋊C8—64no—
475C3⋊C8—62no—
476C3⋊C8—62no—
477C2×C32—22no—
478C2×C32—81no—
479C2×C32C2×#12011yescharacteristic
480C2×C32C2×AGL(1,ℤ/8)12yes—
481C3⋊D3—44no—
482C3×D3—24no—
483C3×D3—44no—
484C24—31no—
485C24—61no—
486C24—184no—
487C24—188no—
488C24—181no—
489C24—368no—
490#41—22no—
491#41—22no—
492C2×Q8C2×D3211yescharacteristic, complemented
493C2×D4—21no—
494C2×D4—32no—
495C2×D4—34no—
496C2×D4—62no—
497C2×D4—61no—
498C2×D4—62no—
499C2×D4—92no—
500C2×D4—94no—
501C2×D4—184no—
502C2×D4—188no—
503C2×D4—188no—
504C2×D4—1816no—
505C2×D4—188no—
506C2×D4—182no—
507C2×D4—181no—
508C2×D4C2×D3211yescharacteristic, complemented
509C22×C4—21no—
510C22×C4—31no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4C2×D3211yescharacteristic
516SD16—64no—
517SD16—184no—
518D8—64no—
519D8—184no—
520M16—62no—
521M16—182no—
522C2×C8—32no—
523C2×C8—92no—
524C4⋊C4—32no—
525C4⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—62no—
528C22⋊C4—61no—
529C42—61no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—21no—
533C22×C3—22no—
534C22×C3—34no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—42no—
541C22×C3—68no—
542C22×C3—62no—
543C22×C3—62no—
544C22×C3—64no—
545C22×C3—82no—
546C22×C3—128no—
547C22×C3—124no—
548C22×C3#93712yes—
549C22×C3#93712yes—
550C22×C3C2×D3×D411yescharacteristic
551C22×C3C22×#6711yescharacteristic
552C2×D3—28no—
553C2×D3—22no—
554C2×D3—22no—
555C2×D3—24no—
556C2×D3—48no—
557C2×D3—44no—
558C2×D3—64no—
559C2×D3—64no—
560C2×D3—124no—
561C2×D3—1232no—
562C2×D3—1232no—
563C2×D3—128no—
564C2×D3—128no—
565C2×D3—124no—
566C2×D3—124no—
567C2×D3—244no—
568C2×D3—248no—
569C2×D3#94914yescomplemented
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—22no—
573C3×C4—42no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—62no—
577C3×C4—122no—
578C3×C4#93712yes—
579C3×C4#93712yes—
580C3×C4C2×D3×D411yescharacteristic
581C3×C4C2×D3×D411yescharacteristic
582C3×C4C2×D3×D411yescharacteristic
583C3×C4C22×#6711yescharacteristic
584Dic3—22no—
585Dic3—42no—
586C32#300311yescharacteristic, complemented, Sylow
587C23—21no—
588C23—32no—
589C23—64no—
590C23—62no—
591C23—62no—
592C23—64no—
593C23—124no—
594C23—1816no—
595C23—182no—
596C23—184no—
597C23—364no—
598C23—368no—
599C23—3632no—
600C23—368no—
601C23D3×#6711yescharacteristic
602Q8—21no—
603Q8—21no—
604D4—21no—
605D4—21no—
606D4—34no—
607D4—42no—
608D4—62no—
609D4—64no—
610D4—94no—
611D4—124no—
612D4—1816no—
613D4—182no—
614D4—184no—
615C2×C4—21no—
616C2×C4—32no—
617C2×C4—42no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—64no—
622C2×C4—62no—
623C2×C4D3×#6712yes—
624C2×C4D3×#6711yescharacteristic
625C2×C4#381112yes—
626C2×C4C22×D3211yescharacteristic
627C8—62no—
628C8—182no—
629C2×C3—22no—
630C2×C3—22no—
631C2×C3—22no—
632C2×C3—21no—
633C2×C3—42no—
634C2×C3—64no—
635C2×C3—82no—
636C2×C3—81no—
637C2×C3—81no—
638C2×C3—124no—
639C2×C3D3×AGL(1,ℤ/8)12yes—
640C2×C3C2×#93711yescharacteristic
641C2×C3C2×#93711yescharacteristic
642C2×C3C2×#94912yes—
643D3—24no—
644D3—44no—
645D3—124no—
646D3—124no—
647D3—244no—
648C22—22no—
649C22—34no—
650C22—42no—
651C22—41no—
652C22—68no—
653C22—62no—
654C22—62no—
655C22—64no—
656C22—128no—
657C22—124no—
658C22—184no—
659C22—368no—
660C22—3632no—
661C22—364no—
662C22#6398312yes—
663C22C2×D3×#6711yescharacteristic
664C4—41no—
665C4—62no—
666C4—122no—
667C4#6398312yes—
668C4C2×D3×#6711yescharacteristic
669C4C2×#381111yescharacteristic
670C3—21no—
671C3#8292711yescharacteristic, complemented
672C3#8394411yescharacteristic, complemented
673C2—22no—
674C2—64no—
675C2—81no—
676C2—124no—
677C2—364no—
678C2D3×#94912yes—
679C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C22×D3×D12C2semidirect
2. C2×#64158C2semidirect
3. C3×#5828C2semidirect
4. C2×C3×#949C2semidirect
5. #10591651C2semidirect
6. #10591515C2semidirect
7. #10591096C2semidirect
8. #10591085C2semidirect
9. #10591069C2semidirect
13. C2×C32×#41C22semidirect
23. C2×#3755C22semidirect
24. C2×#3753C22semidirect
25. C2×#3748C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#938C22semidirect
32. C2×C3×#213C22semidirect
34. C3×#926C22semidirect
35. C2×C3×#208C22semidirect
36. #63564C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
43. #5828D3semidirect
47. C2×#949D3semidirect
66. C2×C32×Q8C23semidirect
68. C2×C32×D4C23semidirect
73. C2×C4⋊(C3⋊D3)D4semidirect
79. C2×C3×D12D4semidirect
93. C2×C3⋊(C3⋊C8)C23semidirect
99. C3×C4⋊Dic3C23semidirect
103. C2×C3×C3⋊C8C23semidirect
108. C2×C3×#41C2×D3semidirect
109. C2×C3×#41C2×D3semidirect
141. #946C2×D3semidirect
145. C2×#215C2×D3semidirect
146. #938C2×D3semidirect
152. C2×#213C2×D3semidirect
154. #926C2×D3semidirect
158. C2×#208C2×D3semidirect
236. C2×C3×Q8C22×D3semidirect
237. C2×C3×Q8C22×D3semidirect
247. C2×C3×D4C22×D3semidirect
248. C2×C3×D4C22×D3semidirect
286. C2×D12#67semidirect
313. C4⋊Dic3C22×D3semidirect
323. C2×C3⋊C8C22×D3semidirect
338. C2×C3×D3AGL(1,ℤ/8)semidirect
347. C2×#41D32semidirect
492. C2×Q8C2×D32semidirect
508. C2×D4C2×D32semidirect
569. C2×D3#949semidirect
586. C32#3003semidirect
671. C3#82927semidirect
672. C3#83944semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
C2×#641582
C3×#58282
C2×C3×#9492
#105916512
#105915152
#105910962
#105910852
#105910692
#839443
#829273