Finite Group Databasebeta

← A4×#946 #11923370

Subgroups — A4×#946 #11923370

Order 1152.

898 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 105 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×Q8×A4C211yesmaximal, characteristic, complemented
2C2×C4×D3×A4C211yesmaximal, characteristic
3A4×(C2×D3)⋊C4C212yesmaximal
4A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5A4×Dic3⋊C4C212yesmaximal, complemented
6C22×#946C311yesmaximal, characteristic, complemented
7A4×C22⋊Q8—31nomaximal
8C22×D3×A4C2211yescharacteristic
9C3×Q8×A4—22no—
10C2×C3×C4×A4C2212yes—
11C2×C3×C4×A4C2211yescharacteristic
12C2×Dic3×A4C2211yescharacteristic
13C2×Dic3×A4C2212yes—
14C4×D3×A4—22no—
15C3×#946—41nomaximal
16C23×C3×Q8C2×C311yescharacteristic, complemented
17C23×C4×D3C2×C311yescharacteristic
18C2×Q8×A4—21no—
19C2×Q8×A4D311yescharacteristic, complemented
20C22×C4×A4—31no—
21C2×#946—31no—
22C2×#946—32no—
23C2×#946—31no—
24C2×#946—32no—
25C2×#946—31no—
26C2×#946—31no—
27C22×(C2×D3)⋊C4C2×C312yes—
28C22×C4⋊Dic3C2×C311yescharacteristic, complemented
29C22×Dic3⋊C4C2×C312yescomplemented
30A4×C4⋊C4—32no—
31A4×C4⋊C4—31no—
32A4×C22⋊C4—32no—
33C22×C3×A4C2311yescharacteristic
34C2×D3×A4—21no—
35C2×D3×A4—21no—
36C2×D3×A4Q812yescomplemented
37C2×C32×Q8—41no—
38C2×C3×C4×D3—41no—
39C3×C4×A4—22no—
40C3×C4×A4D412yes—
41Dic3×A4—21no—
42Dic3×A4—22no—
43C3×(C2×D3)⋊C4—42no—
44C3×C4⋊Dic3—41no—
45C3×Dic3⋊C4—42no—
46C22×C22⋊Q8—31noSylow
47C24×D3C22×C311yescharacteristic
48C23×A4—31no—
49C22×C3×Q8—22no—
50C22×C3×Q8—31no—
51C22×C3×Q8—32no—
52C22×C3×Q8—31no—
53C22×C3×Q8—62no—
54C23×C3×C4C22×C312yes—
55C23×C3×C4C22×C311yescharacteristic
56C23×Dic3C22×C311yescharacteristic
57C23×Dic3C22×C312yes—
58C22×C4×D3—22no—
59C22×C4×D3—31no—
60C22×C4×D3—31no—
61C22×C4×D3—31no—
62C22×C4×D3—31no—
63C22×C4×D3—62no—
64Q8×A4—24no—
65Q8×A4—22no—
66C2×C4×A4—22no—
67C2×C4×A4—21no—
68C2×C4×A4—31no—
69C2×C4×A4—32no—
70C2×C4×A4—62no—
71C2×C4×A4C2×D312yes—
72C2×C4×A4C2×D311yescharacteristic
73C3×C22⋊Q8—121no—
74#946—32no—
75#946—32no—
76#946—34no—
77#946—34no—
78#946—32no—
79#946—31no—
80#946—31no—
81#946—32no—
82#946—31no—
83#946—32no—
84#946A411yescharacteristic, direct product factor
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—32no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C22×C3×D3—41no—
97C2×C3×A4C2×D411yescharacteristic
98C2×C3×A4C2×Q811yescharacteristic
99C2×C3×A4#4111yescharacteristic
100D3×A4—22no—
101C32×Q8—82no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—42no—
106C3×C4×D3—82no—
107C23×Q8C3×D311yescharacteristic, complemented
108C24×C4—31no—
109C2×C22⋊Q8—91no—
110C2×C22⋊Q8—92no—
111C2×C22⋊Q8—92no—
112C2×C22⋊Q8—91no—
113C2×C22⋊Q8—91no—
114C2×C22⋊Q8—91no—
115C22×C4⋊C4—32no—
116C22×C4⋊C4—31no—
117C22×C22⋊C4—32no—
118C24×C3C23×C311yescharacteristic
119C23×D3—21no—
120C23×D3—21no—
121C23×D3—31no—
122C23×D3—31no—
123C23×D3—32no—
124C23×D3—61no—
125C23×D3—61no—
126C23×D3C3×Q812yescomplemented
127C22×A4—21no—
128C22×A4—32no—
129C22×A4—61no—
130C22×A4—61no—
131C22×A4C22×D311yescharacteristic
132C2×C3×Q8—32no—
133C2×C3×Q8—32no—
134C2×C3×Q8—31no—
135C2×C3×Q8—41no—
136C2×C3×Q8—62no—
137C2×C3×Q8—62no—
138C2×C3×Q8—62no—
139C2×C3×Q8—64no—
140C2×C3×Q8—62no—
141C2×C3×Q8—64no—
142C2×C3×Q8—81no—
143C2×C3×Q8C2×A411yescharacteristic, complemented
144C22×C3×C4—22no—
145C22×C3×C4—31no—
146C22×C3×C4—31no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
149C22×C3×C4—32no—
150C22×C3×C4—62no—
151C22×C3×C4—121no—
152C22×C3×C4C3×D412yes—
153C22×Dic3—21no—
154C22×Dic3—22no—
155C22×Dic3—31no—
156C22×Dic3—32no—
157C22×Dic3—31no—
158C22×Dic3—32no—
159C22×Dic3—61no—
160C22×Dic3—62no—
161C2×C4×D3—32no—
162C2×C4×D3—31no—
163C2×C4×D3—31no—
164C2×C4×D3—31no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—62no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×C4×D3—62no—
171C2×C4×D3—62no—
172C2×C4×D3—62no—
173C2×C4×D3C2×A411yescharacteristic
174C4×A4—24no—
175C4×A4—22no—
176C4×A4—22no—
177C4×A4—62no—
178C4×A4—61no—
179C4×A4#6712yes—
180C3×C4⋊C4—122no—
181C3×C4⋊C4—121no—
182C3×C22⋊C4—122no—
183(C2×D3)⋊C4—34no—
184(C2×D3)⋊C4—32no—
185(C2×D3)⋊C4—32no—
186(C2×D3)⋊C4—32no—
187(C2×D3)⋊C4C2×A412yes—
188C4⋊Dic3—32no—
189C4⋊Dic3—31no—
190C4⋊Dic3—32no—
191C4⋊Dic3C2×A411yescharacteristic, complemented
192Dic3⋊C4—34no—
193Dic3⋊C4—32no—
194Dic3⋊C4—32no—
195Dic3⋊C4—32no—
196Dic3⋊C4C2×A412yescomplemented
197C22×C32—41no—
198C2×C3×D3—42no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C3×A4C22⋊Q811yescharacteristic, complemented
202C32×C4—42no—
203C32×C4—82no—
204C3×Dic3—81no—
205C3×Dic3—82no—
206C25—31no—
207C22×Q8—22no—
208C22×Q8—31no—
209C22×Q8—32no—
210C22×Q8—31no—
211C22×Q8—62no—
212C23×C4—32no—
213C23×C4—31no—
214C23×C4—62no—
215C23×C4—91no—
216C23×C4—91no—
217C23×C4—91no—
218C23×C4—91no—
219C23×C4—182no—
220C23×C4C2×C3×D312yes—
221C23×C4C2×C3×D311yescharacteristic
222C22⋊Q8—31no—
223C22⋊Q8—92no—
224C22⋊Q8—91no—
225C22⋊Q8—92no—
226C22⋊Q8—91no—
227C22⋊Q8—94no—
228C22⋊Q8—92no—
229C22⋊Q8—92no—
230C22⋊Q8—92no—
231C22⋊Q8—94no—
232C22⋊Q8—91no—
233C2×C4⋊C4—92no—
234C2×C4⋊C4—91no—
235C2×C4⋊C4—92no—
236C2×C4⋊C4—92no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—92no—
239C2×C4⋊C4—91no—
240C2×C22⋊C4—92no—
241C2×C22⋊C4—92no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—92no—
244C23×C3—31no—
245C23×C3—31no—
246C23×C3—31no—
247C23×C3—31no—
248C23×C3—121no—
249C23×C3C2×C3×D411yescharacteristic
250C23×C3C2×C3×Q811yescharacteristic
251C23×C3C3×#4111yescharacteristic
252C22×D3—22no—
253C22×D3—32no—
254C22×D3—31no—
255C22×D3—32no—
256C22×D3—32no—
257C22×D3—32no—
258C22×D3—61no—
259C22×D3—61no—
260C22×D3—61no—
261C22×D3—61no—
262C22×D3—64no—
263C22×D3—61no—
264C22×D3—61no—
265C22×D3—62no—
266C22×D3—62no—
267C22×D3—61no—
268C22×D3—61no—
269C22×D3—62no—
270C22×D3C22×A411yescharacteristic
271C2×A4—21no—
272C2×A4—21no—
273C2×A4—21no—
274C2×A4—62no—
275C2×A4D3×Q811yescharacteristic
276C2×A4#23911yescharacteristic
277C2×A4C2×#6711yescharacteristic
278C3×Q8—22no—
279C3×Q8—64no—
280C3×Q8—64no—
281C3×Q8—62no—
282C3×Q8—82no—
283C3×Q8—84no—
284C2×C3×C4—32no—
285C2×C3×C4—31no—
286C2×C3×C4—32no—
287C2×C3×C4—32no—
288C2×C3×C4—32no—
289C2×C3×C4—32no—
290C2×C3×C4—41no—
291C2×C3×C4—42no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—82no—
297C2×C3×C4—81no—
298C2×C3×C4—122no—
299C2×C3×C4—121no—
300C2×C3×C4—242no—
301C2×C3×C4C22×A412yes—
302C2×C3×C4C22×A411yescharacteristic
303C2×Dic3—31no—
304C2×Dic3—32no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3C22×A411yescharacteristic
314C2×Dic3C22×A412yes—
315C4×D3—22no—
316C4×D3—62no—
317C4×D3—62no—
318C4×D3—64no—
319C4×D3—62no—
320C2×C32—41no—
321C2×C32—41no—
322C2×C32—41no—
323C3×D3—82no—
324C24—32no—
325C24—61no—
326C24—61no—
327C24—91no—
328C24—91no—
329C24—92no—
330C24—181no—
331C24—181no—
332C24C22×C3×D311yescharacteristic
333C2×Q8—32no—
334C2×Q8—32no—
335C2×Q8—31no—
336C2×Q8—62no—
337C2×Q8—62no—
338C2×Q8—62no—
339C2×Q8—64no—
340C2×Q8—62no—
341C2×Q8—64no—
342C2×Q8D3×A411yescharacteristic, complemented
343C22×C4—22no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—32no—
347C22×C4—32no—
348C22×C4—31no—
349C22×C4—32no—
350C22×C4—62no—
351C22×C4—62no—
352C22×C4—61no—
353C22×C4—91no—
354C22×C4—92no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—92no—
358C22×C4—91no—
359C22×C4—92no—
360C22×C4—91no—
361C22×C4—182no—
362C22×C4—182no—
363C22×C4—182no—
364C22×C4—182no—
365C22×C4—182no—
366C22×C4—182no—
367C22×C4—182no—
368C22×C4—182no—
369C22×C4—181no—
370C22×C4—182no—
371C22×C4C3×#6712yes—
372C4⋊C4—32no—
373C4⋊C4—31no—
374C4⋊C4—92no—
375C4⋊C4—92no—
376C4⋊C4—92no—
377C4⋊C4—94no—
378C4⋊C4—92no—
379C4⋊C4—92no—
380C4⋊C4—91no—
381C22⋊C4—32no—
382C22⋊C4—92no—
383C22⋊C4—92no—
384C22⋊C4—94no—
385C22⋊C4—92no—
386C22×C3—31no—
387C22×C3—31no—
388C22×C3—31no—
389C22×C3—32no—
390C22×C3—31no—
391C22×C3—31no—
392C22×C3—31no—
393C22×C3—31no—
394C22×C3—31no—
395C22×C3—31no—
396C22×C3—41no—
397C22×C3—81no—
398C22×C3—122no—
399C22×C3—241no—
400C22×C3—241no—
401C22×C3C3×C22⋊Q811yescharacteristic, complemented
402C22×C3C23×A411yescharacteristic
403C2×D3—21no—
404C2×D3—21no—
405C2×D3—32no—
406C2×D3—62no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—62no—
411C2×D3—62no—
412C2×D3—61no—
413C2×D3—61no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3Q8×A412yescomplemented
417A4—21no—
418A4#94611yescharacteristic, direct product factor
419C3×C4—22no—
420C3×C4—32no—
421C3×C4—42no—
422C3×C4—62no—
423C3×C4—82no—
424C3×C4—84no—
425C3×C4—82no—
426C3×C4—241no—
427C3×C4—242no—
428C3×C4D4×A412yes—
429Dic3—21no—
430Dic3—22no—
431Dic3—61no—
432Dic3—62no—
433C32—41noSylow
434C23—31no—
435C23—31no—
436C23—31no—
437C23—31no—
438C23—31no—
439C23—62no—
440C23—92no—
441C23—92no—
442C23—92no—
443C23—92no—
444C23—91no—
445C23—181no—
446C23—181no—
447C23—181no—
448C23—181no—
449C23—182no—
450C23—181no—
451C23—181no—
452C23—182no—
453C23—182no—
454C23—181no—
455C23—181no—
456C23—184no—
457C23C3×D3×Q811yescharacteristic
458C23C3×#23911yescharacteristic
459C23C2×C3×#6711yescharacteristic
460Q8—22no—
461Q8—64no—
462Q8—64no—
463Q8—62no—
464C2×C4—32no—
465C2×C4—31no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—31no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—92no—
478C2×C4—91no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—184no—
482C2×C4—181no—
483C2×C4—182no—
484C2×C4—181no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—181no—
488C2×C4—182no—
489C2×C4—181no—
490C2×C4—182no—
491C2×C4C2×D3×A412yes—
492C2×C4C2×D3×A411yescharacteristic
493C2×C3—31no—
494C2×C3—31no—
495C2×C3—31no—
496C2×C3—31no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3—81no—
501C2×C3—81no—
502C2×C3—81no—
503C2×C3—242no—
504C2×C3C2×D4×A411yescharacteristic
505C2×C3C2×Q8×A411yescharacteristic
506C2×C3A4×#4111yescharacteristic
507D3—22no—
508D3—62no—
509C22—31no—
510C22—31no—
511C22—31no—
512C22—32no—
513C22—31no—
514C22—31no—
515C22—31no—
516C22—31no—
517C22—31no—
518C22—31no—
519C22—32no—
520C22—61no—
521C22—61no—
522C22—92no—
523C22—182no—
524C22—182no—
525C22—182no—
526C22—182no—
527C22—182no—
528C22—182no—
529C22—182no—
530C22—182no—
531C22—181no—
532C22—181no—
533C22C3×#94611yescharacteristic, complemented
534C22C22×D3×A411yescharacteristic
535C4—22no—
536C4—32no—
537C4—62no—
538C4—62no—
539C4—61no—
540C4—182no—
541C4—181no—
542C4A4×#6712yes—
543C3—41no—
544C3—81no—
545C3A4×C22⋊Q811yescharacteristic, complemented
546C2—31no—
547C2—31no—
548C2—31no—
549C2—31no—
550C2—62no—
551C2—182no—
552C2D3×Q8×A411yescharacteristic
553C2A4×#23911yescharacteristic
554C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×Q8C2×C3
prime radicalC22×D3×A4C22
hypercenterC2×Q8D3×A4
hypocenterC22×C3C3×C22⋊Q8
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×A4C2semidirect
4. A4×C4⋊Dic3C2semidirect
5. A4×Dic3⋊C4C2semidirect
6. C22×#946C3semidirect
16. C23×C3×Q8C2×C3semidirect
19. C2×Q8×A4D3semidirect
28. C22×C4⋊Dic3C2×C3semidirect
29. C22×Dic3⋊C4C2×C3semidirect
36. C2×D3×A4Q8semidirect
84. #946A4direct (N × H)
107. C23×Q8C3×D3semidirect
126. C23×D3C3×Q8semidirect
143. C2×C3×Q8C2×A4semidirect
191. C4⋊Dic3C2×A4semidirect
196. Dic3⋊C4C2×A4semidirect
201. C3×A4C22⋊Q8semidirect
342. C2×Q8D3×A4semidirect
401. C22×C3C3×C22⋊Q8semidirect
416. C2×D3Q8×A4semidirect
418. A4#946direct (N × H)
533. C22C3×#946semidirect
545. C3A4×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C2×C4×D3×A42
A4×(C2×D3)⋊C42
A4×C4⋊Dic32
A4×Dic3⋊C42
C22×#9463
A4×C22⋊Q83
C3×#9464