Finite Group Databasebeta

← A4×#949 #11923381

Subgroups — A4×#949 #11923381

Order 1152.

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

normal subgroups only

This group has 840 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
1C3×A4×#41C211yesmaximal, characteristic, complemented
2C2×A4×D12C211yesmaximal, characteristic, complemented
3A4×#215C212yesmaximal, complemented
4A4×#213C212yesmaximal, complemented
5A4×#208C211yesmaximal, characteristic, complemented
6C22×#949C311yesmaximal, characteristic, complemented
7A4×AGL(1,ℤ/8)—31nomaximal
8C22×D3×A4—21no—
9C3×Q8×A4C2211yescharacteristic, complemented
10C3×D4×A4—21no—
11C3×D4×A4C2211yescharacteristic, complemented
12C2×C3×C4×A4—21no—
13C2×C3×C4×A4C2211yescharacteristic
14A4×D12—21no—
15A4×D12C2212yes—
16C3×#949—41nomaximal
17A4×C3⋊C8C2212yescomplemented
18C22×C3×#41C2×C311yescharacteristic, complemented
19C23×D12C2×C311yescharacteristic, complemented
20A4×#41—21no—
21A4×#41D311yescharacteristic, complemented
22C2×D4×A4—31no—
23C2×#949—31no—
24C2×#949—31no—
25C2×#949—32no—
26C2×#949—32no—
27C2×#949—31no—
28C2×#949—31no—
29C22×#215C2×C312yescomplemented
30C22×#213C2×C312yescomplemented
31C22×#208C2×C311yescharacteristic, complemented
32A4×SD16—32no—
33A4×D8—32no—
34A4×M16—31no—
35C22×C3×A4—21no—
36C22×C3×A4D411yescharacteristic
37C2×D3×A4—22no—
38C2×D3×A4—42no—
39C32×#41—41no—
40C2×C3×D12—41no—
41C3×C4×A4—21no—
42C3×C4×A4D411yescharacteristic
43C3×C4×A4C2311yescharacteristic
44C3×#215—42no—
45C3×#213—42no—
46C3×#208—41no—
47C22×AGL(1,ℤ/8)—31noSylow
48C24×D3—21no—
49C23×A4—61no—
50C2×C3×#41—31no—
51C2×C3×#41—31no—
52C2×C3×#41—31no—
53C2×C3×#41—31no—
54C2×C3×#41—61no—
55C2×C3×#41—61no—
56C22×C3×Q8C22×C311yescharacteristic, complemented
57C22×C3×D4—21no—
58C22×C3×D4C22×C311yescharacteristic, complemented
59C23×C3×C4—21no—
60C23×C3×C4C22×C311yescharacteristic
61C22×D12—21no—
62C22×D12—31no—
63C22×D12—31no—
64C22×D12—32no—
65C22×D12—61no—
66C22×D12—61no—
67C22×D12C22×C312yes—
68Q8×A4—21no—
69Q8×A4C2×D311yescharacteristic, complemented
70D4×A4—22no—
71D4×A4—21no—
72D4×A4—21no—
73D4×A4—32no—
74D4×A4—61no—
75D4×A4C2×D311yescharacteristic, complemented
76C2×C4×A4—22no—
77C2×C4×A4—21no—
78C2×C4×A4—21no—
79C2×C4×A4C2×D311yescharacteristic
80C3×AGL(1,ℤ/8)—121no—
81#949—32no—
82#949—34no—
83#949—32no—
84#949—32no—
85#949—34no—
86#949—31no—
87#949—31no—
88#949—32no—
89#949—32no—
90#949—31no—
91#949A411yescharacteristic, direct product factor
92C2×#215—32no—
93C2×#215—32no—
94C2×#215—32no—
95C2×#215—32no—
96C2×#213—32no—
97C2×#213—32no—
98C2×#213—32no—
99C2×#213—32no—
100C2×#208—31no—
101C2×#208—32no—
102C2×#208—31no—
103C22×C3⋊C8C22×C312yescomplemented
104C8×A4—32no—
105C22×C3×D3—81no—
106C2×C3×A4—21no—
107C2×C3×A4—41no—
108C2×C3×A4C2×D411yescharacteristic
109D3×A4—42no—
110C32×Q8—41no—
111C32×D4—41no—
112C32×D4—81no—
113C2×C32×C4—41no—
114C2×C32×C4—81no—
115C3×D12—42no—
116C3×D12—81no—
117C3×C3⋊C8—42no—
118C22×#41C3×D311yescharacteristic, complemented
119C23×D4—31no—
120C2×AGL(1,ℤ/8)—91no—
121C2×AGL(1,ℤ/8)—91no—
122C2×AGL(1,ℤ/8)—92no—
123C2×AGL(1,ℤ/8)—92no—
124C2×AGL(1,ℤ/8)—91no—
125C2×AGL(1,ℤ/8)—91no—
126C22×SD16—32no—
127C22×D8—32no—
128C22×M16—31no—
129C24×C3—21no—
130C24×C3C3×D411yescharacteristic
131C23×D3—22no—
132C23×D3—42no—
133C23×D3—61no—
134C23×D3—62no—
135C23×D3—61no—
136C23×D3—122no—
137C22×A4—22no—
138C22×A4—21no—
139C22×A4—21no—
140C22×A4—62no—
141C22×A4—122no—
142C22×A4#6711yescharacteristic
143C3×#41—32no—
144C3×#41—31no—
145C3×#41—31no—
146C3×#41—31no—
147C3×#41—41no—
148C3×#41—61no—
149C3×#41—61no—
150C3×#41—62no—
151C3×#41—62no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—81no—
155C3×#41C2×A411yescharacteristic, complemented
156C2×C3×Q8—31no—
157C2×C3×Q8—31no—
158C2×C3×Q8—61no—
159C2×C3×D4—31no—
160C2×C3×D4—31no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—121no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C3×D411yescharacteristic
177C22×C3×C4C23×C311yescharacteristic
178C2×D12—32no—
179C2×D12—31no—
180C2×D12—32no—
181C2×D12—32no—
182C2×D12—32no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—64no—
188C2×D12—62no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—62no—
192C2×D12C2×A411yescharacteristic, complemented
193C4×A4—22no—
194C4×A4—21no—
195C4×A4—21no—
196C4×A4—21no—
197C4×A4#6711yescharacteristic
198C4×A4C22×D311yescharacteristic
199C3×SD16—122no—
200C3×D8—122no—
201C3×M16—121no—
202#215—34no—
203#215—32no—
204#215—32no—
205#215—32no—
206#215C2×A412yescomplemented
207#213—34no—
208#213—32no—
209#213—32no—
210#213—32no—
211#213C2×A412yescomplemented
212#208—32no—
213#208—31no—
214#208—32no—
215#208C2×A411yescharacteristic, complemented
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C22×C32—41no—
219C22×C32—81no—
220C2×C3×D3—82no—
221C2×C3×D3—162no—
222C3×A4AGL(1,ℤ/8)11yescharacteristic, complemented
223C32×C4—41no—
224C32×C4—41no—
225C32×C4—81no—
226C25—61no—
227C2×#41—31no—
228C2×#41—31no—
229C2×#41—31no—
230C2×#41—31no—
231C2×#41—61no—
232C2×#41—61no—
233C22×Q8C2×C3×D311yescharacteristic, complemented
234C22×D4—21no—
235C22×D4—32no—
236C22×D4—61no—
237C22×D4—91no—
238C22×D4—91no—
239C22×D4—92no—
240C22×D4—181no—
241C22×D4—181no—
242C22×D4C2×C3×D311yescharacteristic, complemented
243C23×C4—21no—
244C23×C4C2×C3×D311yescharacteristic
245AGL(1,ℤ/8)—31no—
246AGL(1,ℤ/8)—91no—
247AGL(1,ℤ/8)—92no—
248AGL(1,ℤ/8)—92no—
249AGL(1,ℤ/8)—91no—
250AGL(1,ℤ/8)—94no—
251AGL(1,ℤ/8)—94no—
252AGL(1,ℤ/8)—92no—
253AGL(1,ℤ/8)—92no—
254AGL(1,ℤ/8)—92no—
255AGL(1,ℤ/8)—91no—
256C2×SD16—92no—
257C2×SD16—92no—
258C2×SD16—92no—
259C2×SD16—92no—
260C2×D8—92no—
261C2×D8—92no—
262C2×D8—92no—
263C2×D8—92no—
264C2×M16—91no—
265C2×M16—92no—
266C2×M16—91no—
267C22×C8—32no—
268C23×C3—21no—
269C23×C3—31no—
270C23×C3—31no—
271C23×C3—41no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3—61no—
275C23×C3—121no—
276C23×C3—241no—
277C23×C3C2×C3×D411yescharacteristic
278C22×D3—21no—
279C22×D3—42no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—61no—
284C22×D3—62no—
285C22×D3—122no—
286C22×D3—122no—
287C22×D3—124no—
288C22×D3—124no—
289C22×D3—122no—
290C22×D3—122no—
291C22×D3—122no—
292C2×A4—21no—
293C2×A4—21no—
294C2×A4—41no—
295C2×A4—42no—
296C2×A4—41no—
297C2×A4—122no—
298C2×A4C2×#6711yescharacteristic
299C3×Q8—31no—
300C3×Q8—41no—
301C3×Q8—61no—
302C3×Q8—61no—
303C3×Q8—81no—
304C3×Q8C22×A411yescharacteristic, complemented
305C3×D4—21no—
306C3×D4—31no—
307C3×D4—41no—
308C3×D4—61no—
309C3×D4—61no—
310C3×D4—61no—
311C3×D4—61no—
312C3×D4—62no—
313C3×D4—61no—
314C3×D4—81no—
315C3×D4—82no—
316C3×D4—81no—
317C3×D4—122no—
318C3×D4—241no—
319C3×D4C22×A411yescharacteristic, complemented
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—31no—
327C2×C3×C4—31no—
328C2×C3×C4—31no—
329C2×C3×C4—41no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—81no—
337C2×C3×C4—82no—
338C2×C3×C4—81no—
339C2×C3×C4C22×A411yescharacteristic
340D12—21no—
341D12—32no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—61no—
347D12C22×A412yes—
348C3×C8—122no—
349C3⋊C8—32no—
350C3⋊C8C22×A412yescomplemented
351C2×C32—41no—
352C2×C32—81no—
353C2×C32—161no—
354C3×D3—162no—
355C24—21no—
356C24—62no—
357C24—122no—
358C24—181no—
359C24—182no—
360C24—181no—
361C24—362no—
362C24C3×#6711yescharacteristic
363#41—32no—
364#41—31no—
365#41—31no—
366#41—31no—
367#41—61no—
368#41—61no—
369#41—62no—
370#41—62no—
371#41—61no—
372#41—61no—
373#41D3×A411yescharacteristic, complemented
374C2×Q8—31no—
375C2×Q8—31no—
376C2×Q8—61no—
377C2×D4—31no—
378C2×D4—31no—
379C2×D4—31no—
380C2×D4—61no—
381C2×D4—61no—
382C2×D4—61no—
383C2×D4—61no—
384C2×D4—61no—
385C2×D4—92no—
386C2×D4—92no—
387C2×D4—92no—
388C2×D4—92no—
389C2×D4—91no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—181no—
394C2×D4—184no—
395C2×D4—181no—
396C2×D4—182no—
397C2×D4—181no—
398C2×D4—182no—
399C22×C4—21no—
400C22×C4—31no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4C3×#6711yescharacteristic
409C22×C4C22×C3×D311yescharacteristic
410SD16—32no—
411SD16—92no—
412SD16—92no—
413SD16—94no—
414SD16—92no—
415D8—32no—
416D8—92no—
417D8—92no—
418D8—94no—
419D8—92no—
420M16—31no—
421M16—92no—
422M16—92no—
423M16—91no—
424C2×C8—92no—
425C2×C8—92no—
426C22×C3—21no—
427C22×C3—31no—
428C22×C3—31no—
429C22×C3—31no—
430C22×C3—41no—
431C22×C3—61no—
432C22×C3—61no—
433C22×C3—61no—
434C22×C3—61no—
435C22×C3—61no—
436C22×C3—81no—
437C22×C3—82no—
438C22×C3—81no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—242no—
444C22×C3—482no—
445C22×C3C3×AGL(1,ℤ/8)11yescharacteristic, complemented
446C22×C3D4×A411yescharacteristic
447C2×D3—22no—
448C2×D3—42no—
449C2×D3—62no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—124no—
453C2×D3—122no—
454C2×D3—124no—
455C2×D3—122no—
456C2×D3—122no—
457A4—21no—
458A4#94911yescharacteristic, direct product factor
459C3×C4—21no—
460C3×C4—31no—
461C3×C4—31no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—61no—
465C3×C4—81no—
466C3×C4—82no—
467C3×C4—81no—
468C3×C4—81no—
469C3×C4D4×A411yescharacteristic
470C3×C4C23×A411yescharacteristic
471C32—41noSylow
472C23—21no—
473C23—31no—
474C23—31no—
475C23—41no—
476C23—61no—
477C23—61no—
478C23—61no—
479C23—61no—
480C23—121no—
481C23—122no—
482C23—182no—
483C23—182no—
484C23—182no—
485C23—182no—
486C23—181no—
487C23—362no—
488C23—362no—
489C23—362no—
490C23—362no—
491C23—364no—
492C23—362no—
493C23—364no—
494C23C2×C3×#6711yescharacteristic
495Q8—31no—
496Q8—61no—
497Q8—61no—
498Q8C2×D3×A411yescharacteristic, complemented
499D4—21no—
500D4—32no—
501D4—31no—
502D4—61no—
503D4—61no—
504D4—61no—
505D4—61no—
506D4—62no—
507D4—61no—
508D4—61no—
509D4—92no—
510D4—182no—
511D4—182no—
512D4—182no—
513D4—182no—
514D4—181no—
515D4C2×D3×A411yescharacteristic, complemented
516C2×C4—21no—
517C2×C4—32no—
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—31no—
522C2×C4—31no—
523C2×C4—31no—
524C2×C4—31no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4C2×D3×A411yescharacteristic
532C8—32no—
533C8—92no—
534C2×C3—21no—
535C2×C3—31no—
536C2×C3—31no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3—61no—
540C2×C3—81no—
541C2×C3—81no—
542C2×C3—121no—
543C2×C3—161no—
544C2×C3—161no—
545C2×C3—162no—
546C2×C3—482no—
547C2×C3C2×D4×A411yescharacteristic
548D3—42no—
549D3—122no—
550C22—21no—
551C22—31no—
552C22—31no—
553C22—31no—
554C22—61no—
555C22—61no—
556C22—61no—
557C22—61no—
558C22—61no—
559C22—62no—
560C22—122no—
561C22—121no—
562C22—121no—
563C22—121no—
564C22—121no—
565C22—182no—
566C22—362no—
567C22—362no—
568C22—362no—
569C22—362no—
570C22—362no—
571C22—364no—
572C22—364no—
573C22C3×#94911yescharacteristic, complemented
574C22A4×#6711yescharacteristic
575C4—21no—
576C4—31no—
577C4—31no—
578C4—61no—
579C4A4×#6711yescharacteristic
580C4C22×D3×A411yescharacteristic
581C3—41no—
582C3—81no—
583C3A4×AGL(1,ℤ/8)11yescharacteristic, complemented
584C2—21no—
585C2—31no—
586C2—31no—
587C2—41no—
588C2—61no—
589C2—121no—
590C2—122no—
591C2—362no—
592C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC2C2×A4×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC4C22×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C2×C3×D4
hypercenter#41D3×A4
hypocenterC22×C3C3×AGL(1,ℤ/8)
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×A4×#41C2semidirect
2. C2×A4×D12C2semidirect
3. A4×#215C2semidirect
4. A4×#213C2semidirect
5. A4×#208C2semidirect
6. C22×#949C3semidirect
9. C3×Q8×A4C22semidirect
11. C3×D4×A4C22semidirect
17. A4×C3⋊C8C22semidirect
18. C22×C3×#41C2×C3semidirect
19. C23×D12C2×C3semidirect
21. A4×#41D3semidirect
29. C22×#215C2×C3semidirect
30. C22×#213C2×C3semidirect
31. C22×#208C2×C3semidirect
56. C22×C3×Q8C22×C3semidirect
58. C22×C3×D4C22×C3semidirect
69. Q8×A4C2×D3semidirect
75. D4×A4C2×D3semidirect
91. #949A4direct (N × H)
103. C22×C3⋊C8C22×C3semidirect
118. C22×#41C3×D3semidirect
155. C3×#41C2×A4semidirect
192. C2×D12C2×A4semidirect
206. #215C2×A4semidirect
211. #213C2×A4semidirect
215. #208C2×A4semidirect
222. C3×A4AGL(1,ℤ/8)semidirect
233. C22×Q8C2×C3×D3semidirect
242. C22×D4C2×C3×D3semidirect
304. C3×Q8C22×A4semidirect
319. C3×D4C22×A4semidirect
350. C3⋊C8C22×A4semidirect
373. #41D3×A4semidirect
445. C22×C3C3×AGL(1,ℤ/8)semidirect
458. A4#949direct (N × H)
498. Q8C2×D3×A4semidirect
515. D4C2×D3×A4semidirect
573. C22C3×#949semidirect
583. 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
C3×A4×#412
C2×A4×D122
A4×#2152
A4×#2132
A4×#2082
C22×#9493
A4×AGL(1,ℤ/8)3
C3×#9494