Finite Group Databasebeta

← A4×#932 #11923357

Subgroups — A4×#932 #11923357

Order 1152.

854 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×A4C211yesmaximal, characteristic, complemented
2A4×#235C211yesmaximal, characteristic, complemented
3A4×#214C212yesmaximal, complemented
4A4×#213C212yesmaximal, complemented
5A4×#208C211yesmaximal, characteristic, complemented
6C22×#932C311yesmaximal, characteristic, complemented
7A4×AGL(1,ℤ/8)—31nomaximal
8C23×C3×A4—21no—
9C3×D4×A4—21no—
10C3×D4×A4C2212yes—
11C2×C3×C4×A4C2211yescharacteristic
12A4×#67—21no—
13A4×D12C2211yescharacteristic, complemented
14C4×D3×A4—21no—
15A4×Dic6C2211yescharacteristic, complemented
16C3×#932—41nomaximal
17A4×C3⋊C8C2212yescomplemented
18C23×C3×D4C2×C311yescharacteristic, complemented
19C22×#235C2×C311yescharacteristic, complemented
20A4×#41—31no—
21C2×D4×A4—21no—
22C2×D4×A4D311yescharacteristic, complemented
23C22×#214C2×C312yescomplemented
24C2×#932—31no—
25C2×#932—31no—
26C2×#932—32no—
27C2×#932—31no—
28C2×#932—31no—
29C2×#932—32no—
30C22×#213C2×C312yescomplemented
31C22×#208C2×C311yescharacteristic, complemented
32A4×SD16—32no—
33A4×D8—32no—
34A4×M16—31no—
35C22×C3×A4—22no—
36C22×C3×A4—42no—
37C22×C3×A4D411yescharacteristic
38C2×D3×A4—21no—
39C2×C32×D4—41no—
40C3×#235—41no—
41C3×C4×A4D411yescharacteristic
42C3×C4×A4C2311yescharacteristic
43Dic3×A4—21no—
44C3×#214—42no—
45C3×#213—42no—
46C3×#208—41no—
47C22×AGL(1,ℤ/8)—31noSylow
48C25×C3—21no—
49C23×A4—22no—
50C23×A4—21no—
51C22×C3×D4—21no—
52C22×C3×D4—31no—
53C22×C3×D4—31no—
54C22×C3×D4—32no—
55C22×C3×D4—61no—
56C22×C3×D4—61no—
57C22×C3×D4C22×C312yes—
58C23×C3×C4C22×C311yescharacteristic
59C22×#67—21no—
60C2×#235—31no—
61C2×#235—31no—
62C2×#235—31no—
63C2×#235—31no—
64C2×#235—61no—
65C2×#235—61no—
66C22×D12C22×C311yescharacteristic, complemented
67C22×C4×D3—21no—
68C22×Dic6C22×C311yescharacteristic, complemented
69Q8×A4—31no—
70D4×A4—22no—
71D4×A4—21no—
72D4×A4—22no—
73D4×A4—31no—
74D4×A4—61no—
75D4×A4C2×D312yes—
76C2×C4×A4—21no—
77C2×C4×A4—61no—
78C2×C4×A4C2×D311yescharacteristic
79C3×AGL(1,ℤ/8)—121no—
80C2×#214—32no—
81C2×#214—32no—
82C2×#214—32no—
83C2×#214—32no—
84#932—32no—
85#932—34no—
86#932—32no—
87#932—32no—
88#932—34no—
89#932—31no—
90#932—31no—
91#932—32no—
92#932—32no—
93#932—31no—
94#932A411yescharacteristic, direct product factor
95C2×#213—32no—
96C2×#213—32no—
97C2×#213—32no—
98C2×#213—32no—
99C2×#208—31no—
100C2×#208—32no—
101C2×#208—31no—
102C22×C3⋊C8C22×C312yescomplemented
103C8×A4—32no—
104C23×C32—81no—
105C2×C3×A4—21no—
106C2×C3×A4—42no—
107C2×C3×A4C2×D411yescharacteristic
108D3×A4—41no—
109C32×D4—42no—
110C32×D4—81no—
111C2×C32×C4—41no—
112C3×#67—81no—
113C3×D12—41no—
114C3×C4×D3—81no—
115C3×Dic6—41no—
116C3×C3⋊C8—42no—
117C22×#41—31no—
118C23×D4C3×D311yescharacteristic, complemented
119C2×AGL(1,ℤ/8)—91no—
120C2×AGL(1,ℤ/8)—91no—
121C2×AGL(1,ℤ/8)—92no—
122C2×AGL(1,ℤ/8)—92no—
123C2×AGL(1,ℤ/8)—91no—
124C2×AGL(1,ℤ/8)—91no—
125C22×SD16—32no—
126C22×D8—32no—
127C22×M16—31no—
128C24×C3—22no—
129C24×C3—42no—
130C24×C3—61no—
131C24×C3—62no—
132C24×C3—61no—
133C24×C3—122no—
134C24×C3C3×D411yescharacteristic
135C23×D3—21no—
136C22×A4—24no—
137C22×A4—22no—
138C22×A4—21no—
139C22×A4—44no—
140C22×A4—42no—
141C22×A4—61no—
142C22×A4#6711yescharacteristic
143C3×#41—121no—
144C2×C3×D4—32no—
145C2×C3×D4—32no—
146C2×C3×D4—32no—
147C2×C3×D4—32no—
148C2×C3×D4—31no—
149C2×C3×D4—41no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—64no—
155C2×C3×D4—61no—
156C2×C3×D4—62no—
157C2×C3×D4—61no—
158C2×C3×D4—62no—
159C2×C3×D4—81no—
160C2×C3×D4C2×A411yescharacteristic, complemented
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4C3×D411yescharacteristic
166C22×C3×C4C23×C311yescharacteristic
167C2×#67—61no—
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—61no—
171C22×Dic3—21no—
172#235—32no—
173#235—31no—
174#235—31no—
175#235—31no—
176#235—61no—
177#235—61no—
178#235—62no—
179#235—62no—
180#235—61no—
181#235—61no—
182#235C2×A411yescharacteristic, complemented
183C2×D12—31no—
184C2×D12—31no—
185C2×D12—61no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×Dic6—31no—
191C2×Dic6—31no—
192C2×Dic6—61no—
193C4×A4—21no—
194C4×A4—21no—
195C4×A4—61no—
196C4×A4#6711yescharacteristic
197C4×A4C22×D311yescharacteristic
198C3×SD16—122no—
199C3×D8—122no—
200C3×M16—121no—
201#214—34no—
202#214—32no—
203#214—32no—
204#214—32no—
205#214C2×A412yescomplemented
206#213—34no—
207#213—32no—
208#213—32no—
209#213—32no—
210#213C2×A412yescomplemented
211#208—32no—
212#208—31no—
213#208—32no—
214#208C2×A411yescharacteristic, complemented
215C2×C3⋊C8—32no—
216C2×C3⋊C8—32no—
217C22×C32—41no—
218C22×C32—82no—
219C22×C32—162no—
220C2×C3×D3—81no—
221C3×A4AGL(1,ℤ/8)11yescharacteristic, complemented
222C32×C4—41no—
223C32×C4—41no—
224C3×Dic3—81no—
225C25—21no—
226C2×#41—91no—
227C2×#41—91no—
228C2×#41—91no—
229C2×#41—91no—
230C2×#41—181no—
231C2×#41—181no—
232C22×Q8—31no—
233C22×D4—21no—
234C22×D4—31no—
235C22×D4—31no—
236C22×D4—32no—
237C22×D4—31no—
238C22×D4—61no—
239C22×D4—61no—
240C22×D4—61no—
241C22×D4C2×C3×D312yes—
242C23×C4—61no—
243C23×C4C2×C3×D311yescharacteristic
244AGL(1,ℤ/8)—31no—
245AGL(1,ℤ/8)—91no—
246AGL(1,ℤ/8)—92no—
247AGL(1,ℤ/8)—92no—
248AGL(1,ℤ/8)—91no—
249AGL(1,ℤ/8)—94no—
250AGL(1,ℤ/8)—92no—
251AGL(1,ℤ/8)—92no—
252AGL(1,ℤ/8)—94no—
253AGL(1,ℤ/8)—92no—
254AGL(1,ℤ/8)—91no—
255C2×SD16—92no—
256C2×SD16—92no—
257C2×SD16—92no—
258C2×SD16—92no—
259C2×D8—92no—
260C2×D8—92no—
261C2×D8—92no—
262C2×D8—92no—
263C2×M16—91no—
264C2×M16—92no—
265C2×M16—91no—
266C22×C8—32no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—31no—
270C23×C3—31no—
271C23×C3—42no—
272C23×C3—62no—
273C23×C3—62no—
274C23×C3—61no—
275C23×C3—62no—
276C23×C3—62no—
277C23×C3—61no—
278C23×C3—81no—
279C23×C3—82no—
280C23×C3—122no—
281C23×C3—122no—
282C23×C3—122no—
283C23×C3—122no—
284C23×C3—124no—
285C23×C3—122no—
286C23×C3—124no—
287C23×C3C2×C3×D411yescharacteristic
288C22×D3—41no—
289C22×D3—61no—
290C22×D3—61no—
291C22×D3—121no—
292C2×A4—22no—
293C2×A4—21no—
294C2×A4—21no—
295C2×A4—44no—
296C2×A4—42no—
297C2×A4—121no—
298C2×A4C2×#6711yescharacteristic
299C3×Q8—121no—
300C3×D4—21no—
301C3×D4—32no—
302C3×D4—42no—
303C3×D4—62no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—61no—
308C3×D4—81no—
309C3×D4—82no—
310C3×D4—82no—
311C3×D4—121no—
312C3×D4—241no—
313C3×D4C22×A412yes—
314C2×C3×C4—32no—
315C2×C3×C4—31no—
316C2×C3×C4—31no—
317C2×C3×C4—31no—
318C2×C3×C4—31no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—31no—
322C2×C3×C4—41no—
323C2×C3×C4—81no—
324C2×C3×C4—241no—
325C2×C3×C4C22×A411yescharacteristic
326#67—21no—
327#67—61no—
328#67—61no—
329#67—62no—
330#67—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333D12—31no—
334D12—61no—
335D12—61no—
336D12C22×A411yescharacteristic, complemented
337C4×D3—21no—
338C4×D3—61no—
339C4×D3—61no—
340C4×D3—62no—
341C4×D3—61no—
342Dic6—31no—
343Dic6—61no—
344Dic6—61no—
345Dic6C22×A411yescharacteristic, complemented
346C3×C8—122no—
347C3⋊C8—32no—
348C3⋊C8C22×A412yescomplemented
349C2×C32—41no—
350C2×C32—81no—
351C2×C32—162no—
352C3×D3—161no—
353C24—22no—
354C24—42no—
355C24—61no—
356C24—62no—
357C24—61no—
358C24—61no—
359C24—122no—
360C24C3×#6711yescharacteristic
361#41—31no—
362#41—91no—
363#41—91no—
364#41—92no—
365#41—91no—
366#41—181no—
367#41—181no—
368#41—182no—
369#41—182no—
370#41—181no—
371#41—181no—
372C2×Q8—91no—
373C2×Q8—91no—
374C2×Q8—181no—
375C2×D4—32no—
376C2×D4—32no—
377C2×D4—32no—
378C2×D4—32no—
379C2×D4—31no—
380C2×D4—61no—
381C2×D4—61no—
382C2×D4—61no—
383C2×D4—61no—
384C2×D4—64no—
385C2×D4—61no—
386C2×D4—62no—
387C2×D4—61no—
388C2×D4—62no—
389C2×D4—91no—
390C2×D4—91no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—181no—
394C2×D4—181no—
395C2×D4—181no—
396C2×D4D3×A411yescharacteristic, complemented
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—31no—
400C22×C4—31no—
401C22×C4—61no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4C3×#6711yescharacteristic
407C22×C4C22×C3×D311yescharacteristic
408SD16—32no—
409SD16—92no—
410SD16—92no—
411SD16—94no—
412SD16—92no—
413D8—32no—
414D8—92no—
415D8—92no—
416D8—94no—
417D8—92no—
418M16—31no—
419M16—92no—
420M16—92no—
421M16—91no—
422C2×C8—92no—
423C2×C8—92no—
424C22×C3—22no—
425C22×C3—31no—
426C22×C3—31no—
427C22×C3—31no—
428C22×C3—42no—
429C22×C3—41no—
430C22×C3—61no—
431C22×C3—61no—
432C22×C3—61no—
433C22×C3—61no—
434C22×C3—62no—
435C22×C3—82no—
436C22×C3—84no—
437C22×C3—81no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—124no—
444C22×C3—124no—
445C22×C3—162no—
446C22×C3—164no—
447C22×C3—241no—
448C22×C3C3×AGL(1,ℤ/8)11yescharacteristic, complemented
449C22×C3D4×A411yescharacteristic
450C2×D3—21no—
451C2×D3—61no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456A4—21no—
457A4#93211yescharacteristic, direct product factor
458C3×C4—31no—
459C3×C4—31no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—81no—
463C3×C4—81no—
464C3×C4—241no—
465C3×C4D4×A411yescharacteristic
466C3×C4C23×A411yescharacteristic
467Dic3—21no—
468Dic3—61no—
469C32—41noSylow
470C23—21no—
471C23—21no—
472C23—31no—
473C23—31no—
474C23—42no—
475C23—62no—
476C23—62no—
477C23—61no—
478C23—62no—
479C23—62no—
480C23—61no—
481C23—122no—
482C23—122no—
483C23—122no—
484C23—122no—
485C23—124no—
486C23—122no—
487C23—124no—
488C23—121no—
489C23—181no—
490C23—181no—
491C23—361no—
492C23C2×C3×#6711yescharacteristic
493Q8—31no—
494Q8—91no—
495Q8—181no—
496Q8—181no—
497D4—21no—
498D4—31no—
499D4—32no—
500D4—62no—
501D4—62no—
502D4—62no—
503D4—62no—
504D4—61no—
505D4—61no—
506D4—91no—
507D4—181no—
508D4—181no—
509D4—181no—
510D4—181no—
511D4—182no—
512D4—181no—
513D4C2×D3×A412yes—
514C2×C4—32no—
515C2×C4—31no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—31no—
522C2×C4—61no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—182no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4C2×D3×A411yescharacteristic
530C8—32no—
531C8—92no—
532C2×C3—21no—
533C2×C3—31no—
534C2×C3—31no—
535C2×C3—42no—
536C2×C3—41no—
537C2×C3—61no—
538C2×C3—81no—
539C2×C3—82no—
540C2×C3—81no—
541C2×C3—122no—
542C2×C3—162no—
543C2×C3—164no—
544C2×C3—481no—
545C2×C3C2×D4×A411yescharacteristic
546D3—41no—
547D3—121no—
548C22—22no—
549C22—31no—
550C22—31no—
551C22—31no—
552C22—42no—
553C22—61no—
554C22—61no—
555C22—61no—
556C22—61no—
557C22—61no—
558C22—62no—
559C22—122no—
560C22—122no—
561C22—122no—
562C22—122no—
563C22—122no—
564C22—124no—
565C22—124no—
566C22—181no—
567C22—361no—
568C22—361no—
569C22—361no—
570C22—361no—
571C22C3×#93211yescharacteristic, complemented
572C22A4×#6711yescharacteristic
573C4—31no—
574C4—31no—
575C4—61no—
576C4—181no—
577C4A4×#6711yescharacteristic
578C4C22×D3×A411yescharacteristic
579C3—41no—
580C3—81no—
581C3A4×AGL(1,ℤ/8)11yescharacteristic, complemented
582C2—21no—
583C2—31no—
584C2—31no—
585C2—42no—
586C2—61no—
587C2—122no—
588C2—121no—
589C2—361no—
590C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC2C2×A4×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC4C22×D3×A4
FittingC23×C3×D4C2×C3
socleC23×C3C2×C3×D4
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×AGL(1,ℤ/8)
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×A4C2semidirect
2. A4×#235C2semidirect
3. A4×#214C2semidirect
4. A4×#213C2semidirect
5. A4×#208C2semidirect
6. C22×#932C3semidirect
13. A4×D12C22semidirect
15. A4×Dic6C22semidirect
17. A4×C3⋊C8C22semidirect
18. C23×C3×D4C2×C3semidirect
19. C22×#235C2×C3semidirect
22. C2×D4×A4D3semidirect
23. C22×#214C2×C3semidirect
30. C22×#213C2×C3semidirect
31. C22×#208C2×C3semidirect
66. C22×D12C22×C3semidirect
68. C22×Dic6C22×C3semidirect
94. #932A4direct (N × H)
102. C22×C3⋊C8C22×C3semidirect
118. C23×D4C3×D3semidirect
160. C2×C3×D4C2×A4semidirect
182. #235C2×A4semidirect
205. #214C2×A4semidirect
210. #213C2×A4semidirect
214. #208C2×A4semidirect
221. C3×A4AGL(1,ℤ/8)semidirect
336. D12C22×A4semidirect
345. Dic6C22×A4semidirect
348. C3⋊C8C22×A4semidirect
396. C2×D4D3×A4semidirect
448. C22×C3C3×AGL(1,ℤ/8)semidirect
457. A4#932direct (N × H)
571. C22C3×#932semidirect
581. C3A4×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
A4×#2352
A4×#2142
A4×#2132
A4×#2082
C22×#9323
A4×AGL(1,ℤ/8)3
C3×#9324