Finite Group Databasebeta

← A4×#929 #11923349

Subgroups — A4×#929 #11923349

Order 1152.

970 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 970 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×C3×C4×A4C211yesmaximal, characteristic, complemented
2C2×A4×#67C211yesmaximal, characteristic
3A4×#217C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C212yesmaximal, complemented
5A4×Dic3⋊C4C212yesmaximal, complemented
6C22×#929C311yesmaximal, characteristic, complemented
7A4×#123—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C22×D3×A4C2211yescharacteristic
10C2×C3×C4×A4—22no—
11C2×C3×C4×A4C2212yes—
12A4×#67—22no—
13C2×Dic3×A4C2211yescharacteristic
14C2×Dic3×A4C2212yes—
15C3×#929—41nomaximal
16C24×C3×C4C2×C311yescharacteristic, complemented
17C23×#67C2×C311yescharacteristic
18C2×D4×A4—31no—
19C22×C4×A4—21no—
20C22×C4×A4D311yescharacteristic, complemented
21C22×#217C2×C311yescharacteristic, complemented
22C2×#929—31no—
23C2×#929—32no—
24C2×#929—32no—
25C2×#929—31no—
26C2×#929—31no—
27C2×#929—31no—
28C22×(C2×D3)⋊C4C2×C312yescomplemented
29C22×Dic3⋊C4C2×C312yescomplemented
30A4×C4⋊C4—32no—
31A4×C22⋊C4—31no—
32A4×C22⋊C4—32no—
33C22×C3×A4—22no—
34C22×C3×A4D412yes—
35C22×C3×A4C2311yescharacteristic
36C2×D3×A4—21no—
37C2×D3×A4—22no—
38C22×C32×C4—41no—
39C2×C3×#67—41no—
40C3×C4×A4—22no—
41Dic3×A4—21no—
42Dic3×A4—22no—
43C3×#217—41no—
44C3×(C2×D3)⋊C4—42no—
45C3×Dic3⋊C4—42no—
46C22×#123—31noSylow
47C25×C3C22×C311yescharacteristic
48C24×D3C22×C311yescharacteristic
49C23×A4—21no—
50C23×A4—31no—
51C23×A4C2×D311yescharacteristic
52C23×C3×C4—22no—
53C23×C3×C4—31no—
54C23×C3×C4—31no—
55C23×C3×C4—32no—
56C23×C3×C4—62no—
57C23×C3×C4C22×C312yes—
58C22×#67—22no—
59C22×#67—31no—
60C22×#67—31no—
61C22×#67—31no—
62C22×#67—31no—
63C22×#67—62no—
64C23×Dic3C22×C311yescharacteristic
65C23×Dic3C22×C312yes—
66D4×A4—62no—
67C2×C4×A4—24no—
68C2×C4×A4—22no—
69C2×C4×A4—22no—
70C2×C4×A4—31no—
71C2×C4×A4—32no—
72C2×C4×A4C2×D312yes—
73C3×#123—121no—
74C2×#217—31no—
75C2×#217—31no—
76C2×#217—32no—
77#929—32no—
78#929—32no—
79#929—34no—
80#929—34no—
81#929—32no—
82#929—31no—
83#929—31no—
84#929—31no—
85#929—32no—
86#929—32no—
87#929A411yescharacteristic, direct product factor
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—32no—
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C23×C32—41no—
97C22×C3×D3—41no—
98C2×C3×A4—22no—
99C2×C3×A4C2×D411yescharacteristic
100C2×C3×A4#4112yes—
101D3×A4—41no—
102C2×C32×C4—42no—
103C2×C32×C4—82no—
104C3×#67—82no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—42no—
107C23×D4—31no—
108C24×C4C3×D311yescharacteristic, complemented
109C2×#123—91no—
110C2×#123—92no—
111C2×#123—91no—
112C2×#123—92no—
113C2×#123—91no—
114C2×#123—91no—
115C22×C4⋊C4—32no—
116C22×C22⋊C4—31no—
117C22×C22⋊C4—32no—
118C24×C3—22no—
119C24×C3—31no—
120C24×C3—32no—
121C24×C3—31no—
122C24×C3—62no—
123C24×C3C3×D412yes—
124C24×C3C23×C311yescharacteristic
125C23×D3—21no—
126C23×D3—22no—
127C23×D3—31no—
128C23×D3—31no—
129C23×D3—61no—
130C23×D3—62no—
131C22×A4—24no—
132C22×A4—22no—
133C22×A4—22no—
134C22×A4—21no—
135C22×A4—62no—
136C22×A4—61no—
137C22×A4#6712yes—
138C22×A4C22×D311yescharacteristic
139C2×C3×D4—121no—
140C22×C3×C4—22no—
141C22×C3×C4—32no—
142C22×C3×C4—31no—
143C22×C3×C4—32no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4—41no—
147C22×C3×C4—62no—
148C22×C3×C4—62no—
149C22×C3×C4—64no—
150C22×C3×C4—64no—
151C22×C3×C4—62no—
152C22×C3×C4—62no—
153C22×C3×C4—62no—
154C22×C3×C4—81no—
155C22×C3×C4C2×A411yescharacteristic, complemented
156C2×#67—32no—
157C2×#67—31no—
158C2×#67—31no—
159C2×#67—31no—
160C2×#67—62no—
161C2×#67—62no—
162C2×#67—62no—
163C2×#67—62no—
164C2×#67—62no—
165C2×#67—62no—
166C2×#67—62no—
167C2×#67—62no—
168C2×#67C2×A411yescharacteristic
169C22×Dic3—21no—
170C22×Dic3—22no—
171C22×Dic3—31no—
172C22×Dic3—32no—
173C22×Dic3—31no—
174C22×Dic3—32no—
175C22×Dic3—62no—
176C22×Dic3—61no—
177C4×A4—24no—
178C4×A4—22no—
179C4×A4—62no—
180C4×A4—61no—
181C3×C4⋊C4—122no—
182C3×C22⋊C4—122no—
183C3×C22⋊C4—121no—
184#217—32no—
185#217—31no—
186#217—32no—
187#217C2×A411yescharacteristic, complemented
188(C2×D3)⋊C4—34no—
189(C2×D3)⋊C4—32no—
190(C2×D3)⋊C4—32no—
191(C2×D3)⋊C4—32no—
192(C2×D3)⋊C4C2×A412yescomplemented
193Dic3⋊C4—34no—
194Dic3⋊C4—32no—
195Dic3⋊C4—32no—
196Dic3⋊C4—32no—
197Dic3⋊C4C2×A412yescomplemented
198C22×C32—42no—
199C22×C32—41no—
200C22×C32—82no—
201C2×C3×D3—81no—
202C2×C3×D3—82no—
203C3×A4#12311yescharacteristic, complemented
204C32×C4—82no—
205C3×Dic3—81no—
206C3×Dic3—82no—
207C25—31no—
208C25C2×C3×D311yescharacteristic
209C22×D4—62no—
210C22×D4—91no—
211C22×D4—91no—
212C22×D4—91no—
213C22×D4—91no—
214C22×D4—182no—
215C23×C4—22no—
216C23×C4—31no—
217C23×C4—31no—
218C23×C4—32no—
219C23×C4—32no—
220C23×C4—31no—
221C23×C4—62no—
222C23×C4C2×C3×D312yes—
223#123—31no—
224#123—91no—
225#123—92no—
226#123—92no—
227#123—91no—
228#123—94no—
229#123—92no—
230#123—92no—
231#123—92no—
232#123—94no—
233#123—91no—
234C2×C4⋊C4—92no—
235C2×C4⋊C4—92no—
236C2×C4⋊C4—92no—
237C2×C4⋊C4—92no—
238C2×C22⋊C4—92no—
239C2×C22⋊C4—91no—
240C2×C22⋊C4—92no—
241C2×C22⋊C4—92no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—92no—
244C2×C22⋊C4—91no—
245C23×C3—22no—
246C23×C3—31no—
247C23×C3—32no—
248C23×C3—31no—
249C23×C3—32no—
250C23×C3—32no—
251C23×C3—32no—
252C23×C3—32no—
253C23×C3—31no—
254C23×C3—41no—
255C23×C3—62no—
256C23×C3—62no—
257C23×C3—62no—
258C23×C3—64no—
259C23×C3—62no—
260C23×C3—62no—
261C23×C3—64no—
262C23×C3—81no—
263C23×C3—121no—
264C23×C3C2×C3×D411yescharacteristic
265C23×C3C3×#4112yes—
266C23×C3C22×A411yescharacteristic
267C22×D3—31no—
268C22×D3—41no—
269C22×D3—61no—
270C22×D3—61no—
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—61no—
274C22×D3—61no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—122no—
278C22×D3—121no—
279C22×D3—122no—
280C22×D3C22×A411yescharacteristic
281C2×A4—24no—
282C2×A4—22no—
283C2×A4—22no—
284C2×A4—21no—
285C2×A4—121no—
286C2×A4#23512yes—
287C2×A4C2×#6711yescharacteristic
288C3×D4—242no—
289C2×C3×C4—22no—
290C2×C3×C4—32no—
291C2×C3×C4—42no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—64no—
295C2×C3×C4—64no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—82no—
300C2×C3×C4—84no—
301C2×C3×C4—82no—
302C2×C3×C4—122no—
303C2×C3×C4—121no—
304C2×C3×C4C22×A412yes—
305#67—22no—
306#67—62no—
307#67—62no—
308#67—64no—
309#67—62no—
310C2×Dic3—31no—
311C2×Dic3—32no—
312C2×Dic3—62no—
313C2×Dic3—61no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—62no—
317C2×Dic3—61no—
318C2×Dic3—62no—
319C2×Dic3—61no—
320C2×Dic3C22×A411yescharacteristic
321C2×Dic3C22×A412yes—
322C2×C32—41no—
323C2×C32—42no—
324C2×C32—82no—
325C3×D3—161no—
326C24—22no—
327C24—31no—
328C24—32no—
329C24—31no—
330C24—62no—
331C24—62no—
332C24—61no—
333C24—91no—
334C24—91no—
335C24—181no—
336C24—182no—
337C24C3×#6712yes—
338C24C22×C3×D311yescharacteristic
339C2×D4—31no—
340C2×D4—91no—
341C2×D4—91no—
342C2×D4—92no—
343C2×D4—91no—
344C2×D4—182no—
345C2×D4—182no—
346C2×D4—182no—
347C2×D4—182no—
348C2×D4—182no—
349C2×D4—182no—
350C2×D4—182no—
351C2×D4—182no—
352C22×C4—22no—
353C22×C4—32no—
354C22×C4—31no—
355C22×C4—32no—
356C22×C4—32no—
357C22×C4—32no—
358C22×C4—62no—
359C22×C4—62no—
360C22×C4—64no—
361C22×C4—64no—
362C22×C4—62no—
363C22×C4—62no—
364C22×C4—62no—
365C22×C4—62no—
366C22×C4—61no—
367C22×C4—92no—
368C22×C4—91no—
369C22×C4—92no—
370C22×C4—91no—
371C22×C4—181no—
372C22×C4—182no—
373C22×C4D3×A411yescharacteristic, complemented
374C4⋊C4—32no—
375C4⋊C4—92no—
376C4⋊C4—92no—
377C4⋊C4—94no—
378C4⋊C4—92no—
379C22⋊C4—31no—
380C22⋊C4—32no—
381C22⋊C4—92no—
382C22⋊C4—92no—
383C22⋊C4—92no—
384C22⋊C4—94no—
385C22⋊C4—92no—
386C22⋊C4—91no—
387C22⋊C4—92no—
388C22×C3—22no—
389C22×C3—31no—
390C22×C3—32no—
391C22×C3—32no—
392C22×C3—31no—
393C22×C3—31no—
394C22×C3—32no—
395C22×C3—32no—
396C22×C3—32no—
397C22×C3—42no—
398C22×C3—41no—
399C22×C3—62no—
400C22×C3—64no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—62no—
404C22×C3—64no—
405C22×C3—62no—
406C22×C3—82no—
407C22×C3—84no—
408C22×C3—82no—
409C22×C3—81no—
410C22×C3—241no—
411C22×C3—242no—
412C22×C3C3×#12311yescharacteristic, complemented
413C22×C3D4×A412yes—
414C22×C3C23×A411yescharacteristic
415C2×D3—21no—
416C2×D3—22no—
417C2×D3—61no—
418C2×D3—62no—
419C2×D3—121no—
420C2×D3—121no—
421C2×D3—122no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—122no—
425A4—21no—
426A4#92911yescharacteristic, direct product factor
427C3×C4—22no—
428C3×C4—62no—
429C3×C4—82no—
430C3×C4—84no—
431C3×C4—241no—
432C3×C4—242no—
433Dic3—21no—
434Dic3—22no—
435Dic3—61no—
436Dic3—62no—
437C32—41noSylow
438C23—22no—
439C23—31no—
440C23—32no—
441C23—31no—
442C23—32no—
443C23—32no—
444C23—32no—
445C23—32no—
446C23—31no—
447C23—31no—
448C23—62no—
449C23—62no—
450C23—62no—
451C23—64no—
452C23—62no—
453C23—62no—
454C23—64no—
455C23—91no—
456C23—121no—
457C23—181no—
458C23—181no—
459C23—182no—
460C23—182no—
461C23—181no—
462C23—181no—
463C23—182no—
464C23—182no—
465C23—362no—
466C23—361no—
467C23—362no—
468C23C3×#23512yes—
469C23C2×C3×#6711yescharacteristic
470C23C2×D3×A411yescharacteristic
471D4—62no—
472D4—182no—
473D4—182no—
474D4—184no—
475D4—182no—
476C2×C4—22no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—31no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—64no—
483C2×C4—64no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—92no—
488C2×C4—91no—
489C2×C4—181no—
490C2×C4—182no—
491C2×C4—181no—
492C2×C4—182no—
493C2×C4—181no—
494C2×C4—182no—
495C2×C4—181no—
496C2×C4—182no—
497C2×C4C2×D3×A412yes—
498C2×C3—22no—
499C2×C3—31no—
500C2×C3—32no—
501C2×C3—31no—
502C2×C3—42no—
503C2×C3—41no—
504C2×C3—62no—
505C2×C3—82no—
506C2×C3—84no—
507C2×C3—82no—
508C2×C3—81no—
509C2×C3—481no—
510C2×C3C2×D4×A411yescharacteristic
511C2×C3A4×#4112yes—
512D3—41no—
513D3—121no—
514C22—22no—
515C22—32no—
516C22—31no—
517C22—32no—
518C22—32no—
519C22—32no—
520C22—31no—
521C22—31no—
522C22—32no—
523C22—62no—
524C22—62no—
525C22—64no—
526C22—62no—
527C22—62no—
528C22—64no—
529C22—62no—
530C22—62no—
531C22—61no—
532C22—182no—
533C22—181no—
534C22—361no—
535C22—361no—
536C22—362no—
537C22—361no—
538C22—361no—
539C22—362no—
540C22C3×#92911yescharacteristic, complemented
541C22A4×#6712yes—
542C22C22×D3×A411yescharacteristic
543C4—22no—
544C4—62no—
545C4—62no—
546C4—61no—
547C4—182no—
548C4—181no—
549C3—41no—
550C3—81no—
551C3A4×#12311yescharacteristic, complemented
552C2—22no—
553C2—31no—
554C2—32no—
555C2—31no—
556C2—62no—
557C2—121no—
558C2—361no—
559C2A4×#23512yes—
560C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC24×C3×C4C2×C3
prime radicalC2×A4×#67C2
hypercenterC22×C4D3×A4
hypocenterC22×C3C3×#123
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×A4C2semidirect
3. A4×#217C2semidirect
4. A4×(C2×D3)⋊C4C2semidirect
5. A4×Dic3⋊C4C2semidirect
6. C22×#929C3semidirect
16. C24×C3×C4C2×C3semidirect
20. C22×C4×A4D3semidirect
21. C22×#217C2×C3semidirect
28. C22×(C2×D3)⋊C4C2×C3semidirect
29. C22×Dic3⋊C4C2×C3semidirect
87. #929A4direct (N × H)
108. C24×C4C3×D3semidirect
155. C22×C3×C4C2×A4semidirect
187. #217C2×A4semidirect
192. (C2×D3)⋊C4C2×A4semidirect
197. Dic3⋊C4C2×A4semidirect
203. C3×A4#123semidirect
373. C22×C4D3×A4semidirect
412. C22×C3C3×#123semidirect
426. A4#929direct (N × H)
540. C22C3×#929semidirect
551. C3A4×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C2×A4×#672
A4×#2172
A4×(C2×D3)⋊C42
A4×Dic3⋊C42
C22×#9293
A4×#1233
C3×#9294