Finite Group Databasebeta

← A4×#886 #11923159

Subgroups — A4×#886 #11923159

Order 1152.

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

normal subgroups only

This group has 950 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
1C2×A4×#67C211yesmaximal, characteristic
2C22×Dic3×A4C211yesmaximal, characteristic, complemented
3C3×A4×C22⋊C4C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C212yesmaximal, complemented
5A4×C4⋊Dic3C212yesmaximal, complemented
6C22×#886C311yesmaximal, characteristic, complemented
7A4×#123—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C22×D3×A4C2211yescharacteristic
10C2×C3×C4×A4C2212yes—
11A4×#67—22no—
12C2×Dic3×A4—22no—
13C2×Dic3×A4C2212yes—
14C2×Dic3×A4C2211yescharacteristic
15C3×#886—41nomaximal
16C23×#67C2×C311yescharacteristic
17C24×Dic3C2×C311yescharacteristic, complemented
18C2×D4×A4—31no—
19C22×C4×A4—31no—
20C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
21C22×(C2×D3)⋊C4C2×C312yescomplemented
22C22×C4⋊Dic3C2×C312yescomplemented
23C2×#886—31no—
24C2×#886—31no—
25C2×#886—31no—
26C2×#886—31no—
27C2×#886—32no—
28C2×#886—32no—
29A4×C4⋊C4—32no—
30A4×C22⋊C4—21no—
31A4×C22⋊C4—32no—
32A4×C22⋊C4D311yescharacteristic, complemented
33C22×C3×A4—22no—
34C22×C3×A4D412yes—
35C22×C3×A4C2311yescharacteristic
36C2×D3×A4—21no—
37C2×D3×A4—22no—
38C2×C3×#67—41no—
39C22×C3×Dic3—41no—
40C3×C4×A4—22no—
41Dic3×A4—22no—
42Dic3×A4—21no—
43C32×C22⋊C4—41no—
44C3×(C2×D3)⋊C4—42no—
45C3×C4⋊Dic3—42no—
46C22×#123—31noSylow
47C25×C3C22×C311yescharacteristic
48C24×D3C22×C311yescharacteristic
49C23×A4—21no—
50C23×A4—31no—
51C23×A4C2×D311yescharacteristic
52C23×C3×C4C22×C312yes—
53C22×#67—22no—
54C22×#67—31no—
55C22×#67—31no—
56C22×#67—31no—
57C22×#67—31no—
58C22×#67—62no—
59C23×Dic3—22no—
60C23×Dic3—31no—
61C23×Dic3—31no—
62C23×Dic3—32no—
63C23×Dic3—62no—
64C23×Dic3C22×C312yes—
65C23×Dic3C22×C311yescharacteristic
66D4×A4—62no—
67C2×C4×A4—22no—
68C2×C4×A4—32no—
69C2×C4×A4—31no—
70C2×C4×A4—62no—
71C2×C4×A4C2×D312yes—
72C3×#123—121no—
73C2×C3×C22⋊C4—31no—
74C2×C3×C22⋊C4—31no—
75C2×C3×C22⋊C4—32no—
76C2×(C2×D3)⋊C4—32no—
77C2×(C2×D3)⋊C4—32no—
78C2×(C2×D3)⋊C4—32no—
79C2×(C2×D3)⋊C4—32no—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—32no—
83C2×C4⋊Dic3—32no—
84#886—32no—
85#886—32no—
86#886—34no—
87#886—34no—
88#886—32no—
89#886—31no—
90#886—31no—
91#886—31no—
92#886—32no—
93#886—32no—
94#886A411yescharacteristic, direct product factor
95C23×C32—41no—
96C22×C3×D3—41no—
97C2×C3×A4—22no—
98C2×C3×A4C2×D411yescharacteristic
99C2×C3×A4#4112yes—
100D3×A4—41no—
101C2×C32×C4—42no—
102C3×#67—82no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—42no—
105C2×C3×Dic3—82no—
106C23×D4—31no—
107C24×C4—31no—
108C2×#123—91no—
109C2×#123—91no—
110C2×#123—92no—
111C2×#123—92no—
112C2×#123—91no—
113C2×#123—91no—
114C22×C4⋊C4—32no—
115C22×C22⋊C4—32no—
116C22×C22⋊C4C3×D311yescharacteristic, complemented
117C24×C3—22no—
118C24×C3—31no—
119C24×C3—32no—
120C24×C3—31no—
121C24×C3—62no—
122C24×C3C3×D412yes—
123C24×C3C23×C311yescharacteristic
124C23×D3—21no—
125C23×D3—22no—
126C23×D3—31no—
127C23×D3—31no—
128C23×D3—61no—
129C23×D3—62no—
130C22×A4—22no—
131C22×A4—22no—
132C22×A4—21no—
133C22×A4—42no—
134C22×A4—61no—
135C22×A4—62no—
136C22×A4D1212yes—
137C22×A4C22×D311yescharacteristic
138C2×C3×D4—121no—
139C22×C3×C4—22no—
140C22×C3×C4—32no—
141C22×C3×C4—32no—
142C22×C3×C4—62no—
143C22×C3×C4—121no—
144C2×#67—32no—
145C2×#67—31no—
146C2×#67—31no—
147C2×#67—31no—
148C2×#67—62no—
149C2×#67—62no—
150C2×#67—62no—
151C2×#67—62no—
152C2×#67—62no—
153C2×#67—62no—
154C2×#67—62no—
155C2×#67—62no—
156C2×#67C2×A411yescharacteristic
157C22×Dic3—22no—
158C22×Dic3—21no—
159C22×Dic3—32no—
160C22×Dic3—31no—
161C22×Dic3—32no—
162C22×Dic3—31no—
163C22×Dic3—32no—
164C22×Dic3—31no—
165C22×Dic3—32no—
166C22×Dic3—62no—
167C22×Dic3—62no—
168C22×Dic3—64no—
169C22×Dic3—64no—
170C22×Dic3—62no—
171C22×Dic3—62no—
172C22×Dic3—62no—
173C22×Dic3—61no—
174C22×Dic3C2×A411yescharacteristic, complemented
175C4×A4—22no—
176C4×A4—42no—
177C4×A4—62no—
178C4×A4—61no—
179C3×C4⋊C4—122no—
180C3×C22⋊C4—32no—
181C3×C22⋊C4—31no—
182C3×C22⋊C4—32no—
183C3×C22⋊C4—41no—
184C3×C22⋊C4—81no—
185C3×C22⋊C4—122no—
186C3×C22⋊C4C2×A411yescharacteristic, complemented
187(C2×D3)⋊C4—34no—
188(C2×D3)⋊C4—32no—
189(C2×D3)⋊C4—32no—
190(C2×D3)⋊C4—32no—
191(C2×D3)⋊C4C2×A412yescomplemented
192C4⋊Dic3—34no—
193C4⋊Dic3—32no—
194C4⋊Dic3—32no—
195C4⋊Dic3—32no—
196C4⋊Dic3C2×A412yescomplemented
197C22×C32—42no—
198C22×C32—41no—
199C22×C32—82no—
200C2×C3×D3—81no—
201C2×C3×D3—82no—
202C3×A4#12311yescharacteristic, complemented
203C32×C4—82no—
204C3×Dic3—82no—
205C3×Dic3—81no—
206C25—31no—
207C25C2×C3×D311yescharacteristic
208C22×D4—62no—
209C22×D4—91no—
210C22×D4—91no—
211C22×D4—91no—
212C22×D4—91no—
213C22×D4—182no—
214C23×C4—32no—
215C23×C4—31no—
216C23×C4—62no—
217C23×C4—91no—
218C23×C4—92no—
219C23×C4—91no—
220C23×C4—182no—
221C23×C4C2×C3×D312yes—
222#123—31no—
223#123—92no—
224#123—92no—
225#123—91no—
226#123—91no—
227#123—94no—
228#123—92no—
229#123—92no—
230#123—92no—
231#123—94no—
232#123—91no—
233C2×C4⋊C4—92no—
234C2×C4⋊C4—92no—
235C2×C4⋊C4—92no—
236C2×C4⋊C4—92no—
237C2×C22⋊C4—31no—
238C2×C22⋊C4—31no—
239C2×C22⋊C4—32no—
240C2×C22⋊C4—92no—
241C2×C22⋊C4—92no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—92no—
244C23×C3—22no—
245C23×C3—31no—
246C23×C3—32no—
247C23×C3—31no—
248C23×C3—32no—
249C23×C3—32no—
250C23×C3—32no—
251C23×C3—32no—
252C23×C3—31no—
253C23×C3—41no—
254C23×C3—62no—
255C23×C3—62no—
256C23×C3—62no—
257C23×C3—64no—
258C23×C3—62no—
259C23×C3—62no—
260C23×C3—64no—
261C23×C3—81no—
262C23×C3—121no—
263C23×C3C2×C3×D411yescharacteristic
264C23×C3C3×#4112yes—
265C23×C3C22×A411yescharacteristic
266C22×D3—31no—
267C22×D3—41no—
268C22×D3—61no—
269C22×D3—61no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—122no—
277C22×D3—121no—
278C22×D3—122no—
279C22×D3C22×A411yescharacteristic
280C2×A4—22no—
281C2×A4—21no—
282C2×A4—22no—
283C2×A4—42no—
284C2×A4—121no—
285C2×A4C2×D1211yescharacteristic
286C2×A4#23712yes—
287C3×D4—242no—
288C2×C3×C4—32no—
289C2×C3×C4—42no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—82no—
295C2×C3×C4—122no—
296C2×C3×C4—121no—
297C2×C3×C4—242no—
298C2×C3×C4C22×A412yes—
299#67—22no—
300#67—62no—
301#67—62no—
302#67—64no—
303#67—62no—
304C2×Dic3—22no—
305C2×Dic3—31no—
306C2×Dic3—32no—
307C2×Dic3—62no—
308C2×Dic3—61no—
309C2×Dic3—62no—
310C2×Dic3—64no—
311C2×Dic3—61no—
312C2×Dic3—64no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—62no—
317C2×Dic3—61no—
318C2×Dic3C22×A411yescharacteristic
319C2×Dic3C22×A412yes—
320C2×C32—41no—
321C2×C32—42no—
322C2×C32—82no—
323C3×D3—161no—
324C24—22no—
325C24—31no—
326C24—32no—
327C24—31no—
328C24—62no—
329C24—61no—
330C24—62no—
331C24—91no—
332C24—91no—
333C24—181no—
334C24—182no—
335C24C3×D1212yes—
336C24C22×C3×D311yescharacteristic
337C2×D4—31no—
338C2×D4—91no—
339C2×D4—91no—
340C2×D4—92no—
341C2×D4—91no—
342C2×D4—182no—
343C2×D4—182no—
344C2×D4—182no—
345C2×D4—182no—
346C2×D4—182no—
347C2×D4—182no—
348C2×D4—182no—
349C2×D4—182no—
350C22×C4—22no—
351C22×C4—31no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—62no—
355C22×C4—62no—
356C22×C4—61no—
357C22×C4—92no—
358C22×C4—91no—
359C22×C4—92no—
360C22×C4—92no—
361C22×C4—91no—
362C22×C4—92no—
363C22×C4—91no—
364C22×C4—182no—
365C22×C4—182no—
366C22×C4—184no—
367C22×C4—184no—
368C22×C4—182no—
369C22×C4—182no—
370C22×C4—182no—
371C22×C4—181no—
372C4⋊C4—32no—
373C4⋊C4—92no—
374C4⋊C4—92no—
375C4⋊C4—94no—
376C4⋊C4—92no—
377C22⋊C4—32no—
378C22⋊C4—31no—
379C22⋊C4—32no—
380C22⋊C4—32no—
381C22⋊C4—92no—
382C22⋊C4—92no—
383C22⋊C4—94no—
384C22⋊C4—92no—
385C22⋊C4D3×A411yescharacteristic, complemented
386C22×C3—22no—
387C22×C3—31no—
388C22×C3—32no—
389C22×C3—32no—
390C22×C3—31no—
391C22×C3—31no—
392C22×C3—32no—
393C22×C3—32no—
394C22×C3—32no—
395C22×C3—42no—
396C22×C3—41no—
397C22×C3—62no—
398C22×C3—64no—
399C22×C3—62no—
400C22×C3—62no—
401C22×C3—62no—
402C22×C3—64no—
403C22×C3—62no—
404C22×C3—82no—
405C22×C3—82no—
406C22×C3—81no—
407C22×C3—162no—
408C22×C3—241no—
409C22×C3—242no—
410C22×C3C3×#12311yescharacteristic, complemented
411C22×C3D4×A412yes—
412C22×C3C23×A411yescharacteristic
413C2×D3—21no—
414C2×D3—22no—
415C2×D3—61no—
416C2×D3—62no—
417C2×D3—121no—
418C2×D3—121no—
419C2×D3—122no—
420C2×D3—121no—
421C2×D3—121no—
422C2×D3—122no—
423A4—21no—
424A4#88611yescharacteristic, direct product factor
425C3×C4—22no—
426C3×C4—62no—
427C3×C4—82no—
428C3×C4—162no—
429C3×C4—242no—
430C3×C4—241no—
431Dic3—22no—
432Dic3—21no—
433Dic3—62no—
434Dic3—61no—
435C32—41noSylow
436C23—22no—
437C23—32no—
438C23—31no—
439C23—31no—
440C23—32no—
441C23—32no—
442C23—32no—
443C23—32no—
444C23—31no—
445C23—31no—
446C23—62no—
447C23—62no—
448C23—62no—
449C23—64no—
450C23—62no—
451C23—62no—
452C23—64no—
453C23—91no—
454C23—121no—
455C23—181no—
456C23—181no—
457C23—182no—
458C23—182no—
459C23—181no—
460C23—181no—
461C23—182no—
462C23—182no—
463C23—361no—
464C23—362no—
465C23—362no—
466C23C2×C3×D1211yescharacteristic
467C23C3×#23712yes—
468C23C2×D3×A411yescharacteristic
469D4—62no—
470D4—182no—
471D4—182no—
472D4—184no—
473D4—182no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—31no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—92no—
483C2×C4—91no—
484C2×C4—182no—
485C2×C4—181no—
486C2×C4—182no—
487C2×C4—184no—
488C2×C4—181no—
489C2×C4—184no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—181no—
493C2×C4—182no—
494C2×C4—181no—
495C2×C4C2×D3×A412yes—
496C2×C3—22no—
497C2×C3—31no—
498C2×C3—32no—
499C2×C3—31no—
500C2×C3—41no—
501C2×C3—42no—
502C2×C3—62no—
503C2×C3—82no—
504C2×C3—81no—
505C2×C3—82no—
506C2×C3—162no—
507C2×C3—481no—
508C2×C3C2×D4×A411yescharacteristic
509C2×C3A4×#4112yes—
510D3—41no—
511D3—121no—
512C22—22no—
513C22—31no—
514C22—32no—
515C22—32no—
516C22—31no—
517C22—31no—
518C22—32no—
519C22—32no—
520C22—32no—
521C22—62no—
522C22—62no—
523C22—64no—
524C22—62no—
525C22—62no—
526C22—64no—
527C22—62no—
528C22—61no—
529C22—62no—
530C22—181no—
531C22—182no—
532C22—361no—
533C22—361no—
534C22—362no—
535C22—361no—
536C22—361no—
537C22—362no—
538C22C3×#88611yescharacteristic, complemented
539C22A4×D1212yes—
540C22C22×D3×A411yescharacteristic
541C4—22no—
542C4—62no—
543C4—61no—
544C4—62no—
545C4—182no—
546C4—181no—
547C3—41no—
548C3—81no—
549C3A4×#12311yescharacteristic, complemented
550C2—22no—
551C2—31no—
552C2—31no—
553C2—32no—
554C2—62no—
555C2—121no—
556C2—361no—
557C2C2×A4×D1211yescharacteristic
558C2A4×#23712yes—
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C22⋊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
2. C22×Dic3×A4C2semidirect
3. C3×A4×C22⋊C4C2semidirect
4. A4×(C2×D3)⋊C4C2semidirect
5. A4×C4⋊Dic3C2semidirect
6. C22×#886C3semidirect
17. C24×Dic3C2×C3semidirect
20. C22×C3×C22⋊C4C2×C3semidirect
21. C22×(C2×D3)⋊C4C2×C3semidirect
22. C22×C4⋊Dic3C2×C3semidirect
32. A4×C22⋊C4D3semidirect
94. #886A4direct (N × H)
116. C22×C22⋊C4C3×D3semidirect
174. C22×Dic3C2×A4semidirect
186. C3×C22⋊C4C2×A4semidirect
191. (C2×D3)⋊C4C2×A4semidirect
196. C4⋊Dic3C2×A4semidirect
202. C3×A4#123semidirect
385. C22⋊C4D3×A4semidirect
410. C22×C3C3×#123semidirect
424. A4#886direct (N × H)
538. C22C3×#886semidirect
549. C3A4×#123semidirect

Maximal subgroups

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

subgroupindex
C2×A4×#672
C22×Dic3×A42
C3×A4×C22⋊C42
A4×(C2×D3)⋊C42
A4×C4⋊Dic32
C22×#8863
A4×#1233
C3×#8864