Finite Group Databasebeta

← #11870873

Subgroups — #11870873

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596095C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic, complemented
3C3×#5046C211yesmaximal, characteristic, complemented
4C3×#5044C211yesmaximal, characteristic, complemented
5#10591571C212yesmaximal, complemented
6#10591570C212yesmaximal, complemented
7#10591162C211yesmaximal, characteristic
8#10591125C211yesmaximal, characteristic, complemented
9#10591061C211yesmaximal, characteristic, complemented
10#10590473C212yesmaximal, complemented
11#10590459C212yesmaximal, complemented
12#81453—31nomaximal
13#80133—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C32×C22⋊Q8C2211yescharacteristic
17#64156C2211yescharacteristic, complemented
18Q8×C3⋊Dic3C2211yescharacteristic, complemented
19#64139C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64107—21no—
22#64102C2211yescharacteristic, complemented
23#64101—21no—
24#64099C2211yescharacteristic, complemented
25#64095—21no—
26#64090—21no—
27C2×C3×#215C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3—21no—
30#63898—21no—
31#63898—21no—
32#63898C2212yes—
33#63898C2212yes—
34C2×#3714C2212yes—
35C3×#835C2212yescomplemented
36C3×#830C2211yescharacteristic
37C3×#830C2211yescharacteristic
38C3×#809C2212yes—
39C3×#807C2212yescomplemented
40#63573C2212yescomplemented
41#63572C2212yescomplemented
42#63564C2212yescomplemented
43#63563C2212yes—
44#63553C2212yescomplemented
45C2×D4×Dic3—31no—
46#5624—31no—
47#5624—31no—
48#5624—61no—
49C2×#893—31no—
50C3×#484—31no—
51C3×#450—31no—
52#5217—31no—
53#5165—32no—
54Dic3×SD16—32no—
55#5046D311yescharacteristic, complemented
56#5044D311yescharacteristic, complemented
57#4968—31no—
58#4891—32no—
59#4872—32no—
60#4819—32no—
61#4788—32no—
62#4763—32no—
63#4756—32no—
64#4735—31no—
65#4732—31no—
66#4718—31no—
67#4718—31no—
68C23×C3×D3—21no—
69C2×C32×Q8C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72C22×C3⋊Dic3D411yescharacteristic
73C22×C3⋊Dic3D411yescharacteristic
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3—21no—
76C22×C3×Dic3—21no—
77C2×C3×D12—21no—
78C2×C3×D12—24no—
79C2×C3×D12C2312yes—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—22no—
82C2×D3×Dic3—44no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86#3752—21no—
87#3752—21no—
88#3752—21no—
89#3752—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—21no—
94C4×C3⋊Dic3—21no—
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3C2311yescharacteristic
98C4×C3⋊Dic3C2311yescharacteristic
99C3×#215—24no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2312yes—
102C2×C3×C3⋊C8C2312yes—
103C2×C3×C3⋊C8C2312yes—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106#3714—24no—
107#3105—91noSylow
108C22×C3×D4—31no—
109C23×Dic3—61no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—61no—
112C2×C3×SD16—32no—
113C3×C22⋊Q8—21no—
114C3×C22⋊Q8C2×D311yescharacteristic
115C3×C22⋊Q8C2×D311yescharacteristic
116C2×C3×C4⋊C4—31no—
117C2×#217—61no—
118#947—31no—
119#947—31no—
120#947—61no—
121Q8×Dic3—31no—
122Q8×Dic3—31no—
123Q8×Dic3—61no—
124C2×#215C2×D312yes—
125D4×Dic3—32no—
126D4×Dic3—32no—
127D4×Dic3—61no—
128D4×Dic3—61no—
129C2×#213—32no—
130#930—31no—
131#930—31no—
132#930—61no—
133C2×(C2×D3)⋊C4—61no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×C4×Dic3—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—61no—
138C2×D24—32no—
139#898—61no—
140#898—61no—
141#898—62no—
142#893—32no—
143#893—32no—
144#893—31no—
145#893—31no—
146#893—61no—
147#893—61no—
148#893—61no—
149#892—61no—
150#892—61no—
151#892—62no—
152#890—31no—
153#890—31no—
154#890—61no—
155#886—61no—
156#886—61no—
157#886—62no—
158#67⋊C4—61no—
159#67⋊C4—61no—
160#67⋊C4—62no—
161C3×#107—32no—
162C3×#103—32no—
163C3×#102—32no—
164C3×C22⋊C8—31no—
165C3×C22⋊C8—31no—
166#835C2×D312yescomplemented
167#832—32no—
168#830C2×D311yescharacteristic
169#830C2×D311yescharacteristic
170#821—32no—
171#821—32no—
172#817—32no—
173Dic3⋊C8—32no—
174Dic3⋊C8—32no—
175C8×Dic3—32no—
176C8×Dic3—32no—
177#809—32no—
178#809C2×D312yes—
179#808—32no—
180#807C2×D312yescomplemented
181C23×C32C2×D411yescharacteristic
182C22×C3⋊D3—21no—
183C22×C3×D3—24no—
184C22×C3×D3—22no—
185C22×C3×D3—42no—
186C22×C3×D3—42no—
187C32×Q8—22no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—22no—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193#638—42no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C4⋊(C3⋊D3)—22no—
202C4×C3⋊D3—42no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—42no—
205C3×D12—24no—
206C3×D12—22no—
207C3×D12#4114yes—
208D3×Dic3—44no—
209D3×Dic3—44no—
210C3×C3⋊C8—22no—
211C3×C3⋊C8—22no—
212#529—91no—
213C2×C4×D4—91no—
214#484—31no—
215#481—91no—
216#478—92no—
217#463—92no—
218#450—31no—
219#447—91no—
220C4×SD16—92no—
221C4×D8—92no—
222#431—91no—
223C24×C3—61no—
224C23×D3—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×D4—32no—
229C2×C3×D4—64no—
230C2×C3×D4—61no—
231C22×C3×C4—21no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—62no—
236C2×#67—61no—
237C2×#67—61no—
238C22×Dic3—21no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—124no—
248C2×D12—21no—
249C2×D12—24no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×D12C22×D312yes—
254C2×C4×D3—61no—
255C2×C4×D3—61no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—124no—
260C3×SD16—64no—
261C2×C3×C8—32no—
262C2×C3×C8—32no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—32no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4C22×D311yescharacteristic
270C3×C4⋊C4C22×D311yescharacteristic
271C3×C22⋊C4—22no—
272C3×C22⋊C4—21no—
273C3×C22⋊C4—21no—
274#217—62no—
275#217—62no—
276#215—24no—
277#213—64no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292C4⋊Dic3—21no—
293C4⋊Dic3—31no—
294C4⋊Dic3—31no—
295C4⋊Dic3—61no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3—61no—
300C4⋊Dic3—62no—
301C4⋊Dic3—62no—
302C4⋊Dic3C22×D312yes—
303Dic3⋊C4—61no—
304Dic3⋊C4—61no—
305Dic3⋊C4—62no—
306C4×Dic3—31no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—31no—
313C4×Dic3—31no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C4×Dic3—62no—
321C2×C3⋊C8C22×D312yes—
322C2×C3⋊C8C22×D312yes—
323D24—64no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32#13512yes—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3×D3—24no—
332C2×C3×D3—48no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C32×C4—21no—
336C32×C4—41no—
337C32×C4—41no—
338C32×C4C2×#4112yes—
339C3⋊Dic3—21no—
340C3⋊Dic3—21no—
341C3⋊Dic3—21no—
342C3⋊Dic3—41no—
343C3⋊Dic3AGL(1,ℤ/8)12yes—
344C3×Dic3—42no—
345C22×D4—31no—
346C23×C4—181no—
347C2×SD16—32no—
348C2×D8—92no—
349#126—181no—
350#125—91no—
351#124—91no—
352#123—181no—
353C22⋊Q8D3211yescharacteristic
354#121—91no—
355C4×Q8—91no—
356C4×D4—92no—
357C4×D4—92no—
358C4×D4—91no—
359C4×D4—181no—
360C4×D4—181no—
361C4×D4—181no—
362#117—181no—
363C2×C4⋊C4—31no—
364C2×C22⋊C4—181no—
365C2×C42—91no—
366#107—32no—
367#106—92no—
368C4⋊C8—92no—
369#103—32no—
370#102—32no—
371#102—92no—
372#102—92no—
373C22⋊C8—31no—
374C22⋊C8—31no—
375C4×C8—92no—
376C23×C3—21no—
377C23×C3—64no—
378C23×C3—62no—
379C23×C3—122no—
380C23×C3—122no—
381C23×C3D3×D411yescharacteristic
382C23×C3D3×D411yescharacteristic
383C22×D3—24no—
384C22×D3—22no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—62no—
388C22×D3—61no—
389C22×D3—61no—
390C3×Q8—22no—
391C3×Q8—22no—
392C3×Q8—42no—
393C3×D4—34no—
394C3×D4—64no—
395C3×D4—62no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—42no—
407C2×C3×C4—62no—
408C2×C3×C4—122no—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413#67—124no—
414#67—122no—
415#67—122no—
416C2×Dic3—22no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—31no—
420C2×Dic3—31no—
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—31no—
424C2×Dic3—31no—
425C2×Dic3—42no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3—124no—
440C2×Dic3—124no—
441D12—24no—
442D12—22no—
443D12—62no—
444D12—62no—
445D12—122no—
446D12#23714yes—
447C4×D3—122no—
448C4×D3—122no—
449C4×D3—124no—
450C4×D3—124no—
451C4×D3—124no—
452C3×C8—62no—
453C3×C8—62no—
454C3⋊C8—22no—
455C3⋊C8—22no—
456C2×C32—22no—
457C2×C32#52511yescharacteristic
458C2×C32C2×#13511yescharacteristic
459C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
460C3⋊D3—81no—
461C3×D3—44no—
462C24—61no—
463C2×Q8C2×D3211yescharacteristic
464C2×D4—32no—
465C2×D4—64no—
466C2×D4—61no—
467C2×D4—91no—
468C2×D4—181no—
469C22×C4—61no—
470C22×C4—91no—
471C22×C4—91no—
472C22×C4—181no—
473C22×C4—182no—
474C22×C4—182no—
475C22×C4—364no—
476C22×C4C2×D3211yescharacteristic
477SD16—64no—
478D8—184no—
479C2×C8—32no—
480C2×C8—32no—
481C4⋊C4—21no—
482C4⋊C4—32no—
483C4⋊C4—61no—
484C4⋊C4—91no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C4⋊C4—181no—
488C4⋊C4C2×D3211yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—182no—
494C22⋊C4—182no—
495C22⋊C4—181no—
496C42—91no—
497C42—91no—
498C42—91no—
499C42—91no—
500C42—181no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—22no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—64no—
510C22×C3—128no—
511C22×C3—122no—
512C22×C3—122no—
513C22×C3#91612yes—
514C22×C3#91912yes—
515C22×C3C2×D3×D411yescharacteristic
516C22×C3C2×D3×D411yescharacteristic
517C2×D3—24no—
518C2×D3—48no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—121no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—22no—
533C3×C4—41no—
534C3×C4—42no—
535C3×C4—42no—
536C3×C4—41no—
537C3×C4—41no—
538C3×C4—41no—
539C3×C4—41no—
540C3×C4—122no—
541C3×C4C2×#23712yes—
542C3×C4D3×#4112yes—
543Dic3—32no—
544Dic3—32no—
545Dic3—42no—
546Dic3—62no—
547Dic3—61no—
548Dic3—61no—
549Dic3—61no—
550Dic3—61no—
551Dic3—61no—
552Dic3—61no—
553Dic3—121no—
554Dic3—121no—
555Dic3—121no—
556Dic3—122no—
557Dic3—121no—
558Dic3—121no—
559C32#310511yescharacteristic, complemented, Sylow
560C23—64no—
561C23—62no—
562C23—122no—
563C23—122no—
564C23—181no—
565C23#381111yescharacteristic
566Q8—22no—
567D4—34no—
568D4—64no—
569D4—62no—
570D4—182no—
571D4—362no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—62no—
576C2×C4—91no—
577C2×C4—91no—
578C2×C4—91no—
579C2×C4—91no—
580C2×C4—122no—
581C2×C4—182no—
582C2×C4—182no—
583C2×C4—181no—
584C2×C4—362no—
585C2×C4—364no—
586C2×C4—364no—
587C2×C4#381111yescharacteristic
588C2×C4C22×D3211yescharacteristic
589C8—62no—
590C8—62no—
591C2×C3—22no—
592C2×C3—22no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—42no—
597C2×C3—124no—
598C2×C3#558611yescharacteristic
599C2×C3#565611yescharacteristic
600C2×C3C2×#91611yescharacteristic
601C2×C3C2×#91911yescharacteristic
602C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
603C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
604D3—44no—
605D3—242no—
606D3—241no—
607D3—241no—
608C22—21no—
609C22—21no—
610C22—64no—
611C22—128no—
612C22—122no—
613C22—122no—
614C22—361no—
615C22—361no—
616C22—361no—
617C22#6395012yes—
618C22C2×#381111yescharacteristic
619C4—21no—
620C4—41no—
621C4—41no—
622C4—92no—
623C4—122no—
624C4—181no—
625C4—181no—
626C4—181no—
627C4—361no—
628C4D3×#23712yes—
629C3—21no—
630C3#8013311yescharacteristic, complemented
631C3#8145311yescharacteristic, complemented
632C2—22no—
633C2—124no—
634C2—721no—
635C2#1059516011yescharacteristic
636C2C2×#6395011yescharacteristic
637C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10591162C2
hypercenterC22⋊Q8D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596095C2semidirect
2. C2×#63898C2semidirect
3. C3×#5046C2semidirect
4. C3×#5044C2semidirect
5. #10591571C2semidirect
6. #10591570C2semidirect
8. #10591125C2semidirect
9. #10591061C2semidirect
10. #10590473C2semidirect
11. #10590459C2semidirect
17. #64156C22semidirect
18. Q8×C3⋊Dic3C22semidirect
22. #64102C22semidirect
24. #64099C22semidirect
35. C3×#835C22semidirect
39. C3×#807C22semidirect
40. #63573C22semidirect
41. #63572C22semidirect
42. #63564C22semidirect
44. #63553C22semidirect
55. #5046D3semidirect
56. #5044D3semidirect
166. #835C2×D3semidirect
180. #807C2×D3semidirect
559. C32#3105semidirect
630. C3#80133semidirect
631. C3#81453semidirect

Maximal subgroups

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

subgroupindex
#105960952
C2×#638982
C3×#50462
C3×#50442
#105915712
#105915702
#105911622
#105911252
#105910612
#105904732
#105904592
#814533
#801333