Finite Group Databasebeta

← A4×#892 #11923166

Subgroups — A4×#892 #11923166

Order 1152.

906 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 123 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×C4×D3×A4C211yesmaximal, characteristic
2C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
3A4×(C2×D3)⋊C4C212yesmaximal
4A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C4×Dic3×A4C212yesmaximal, complemented
6C22×#892C311yesmaximal, characteristic, complemented
7A4×#117—31nomaximal
8C22×D3×A4C2211yescharacteristic
9C2×C3×C4×A4C2212yes—
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2212yes—
12C2×Dic3×A4C2211yescharacteristic
13C4×D3×A4C414yescomplemented
14C3×#892—41nomaximal
15C23×C4×D3C2×C311yescharacteristic
16C22×C4×A4—31no—
17C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
18C22×(C2×D3)⋊C4C2×C312yes—
19C22×C4⋊Dic3C2×C311yescharacteristic, complemented
20C22×C4×Dic3C2×C312yescomplemented
21C2×#892—31no—
22C2×#892—31no—
23C2×#892—31no—
24C2×#892—32no—
25C2×#892—31no—
26C2×#892—32no—
27A4×C4⋊C4—21no—
28A4×C4⋊C4—31no—
29A4×C4⋊C4D311yescharacteristic, complemented
30A4×C22⋊C4—32no—
31C42×A4—32no—
32C22×C3×A4C2311yescharacteristic
33C2×D3×A4—21no—
34C2×D3×A4—21no—
35C2×D3×A4C2×C412yes—
36C2×C3×C4×D3—41no—
37C3×C4×A4—22no—
38C3×C4×A4C2×C412yes—
39Dic3×A4—22no—
40Dic3×A4C2×C412yes—
41C32×C4⋊C4—41no—
42C3×(C2×D3)⋊C4—42no—
43C3×C4⋊Dic3—41no—
44C3×C4×Dic3—42no—
45C22×#117—31noSylow
46C24×D3C22×C311yescharacteristic
47C23×A4—31no—
48C23×C3×C4C22×C312yes—
49C23×C3×C4C22×C311yescharacteristic
50C23×Dic3C22×C312yes—
51C23×Dic3C22×C311yescharacteristic
52C22×C4×D3—31no—
53C22×C4×D3—34no—
54C22×C4×D3—31no—
55C22×C4×D3—31no—
56C22×C4×D3—31no—
57C22×C4×D3C3×C414yescomplemented
58C2×C4×A4—21no—
59C2×C4×A4—22no—
60C2×C4×A4—31no—
61C2×C4×A4—34no—
62C2×C4×A4—32no—
63C2×C4×A4C2×D312yes—
64C2×C4×A4C2×D311yescharacteristic
65C3×#117—121no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C4⋊C4—31no—
68C2×C3×C4⋊C4—32no—
69C2×(C2×D3)⋊C4—32no—
70C2×(C2×D3)⋊C4—32no—
71C2×(C2×D3)⋊C4—32no—
72C2×(C2×D3)⋊C4—32no—
73C2×C4⋊Dic3—31no—
74C2×C4⋊Dic3—31no—
75C2×C4⋊Dic3—32no—
76C2×C4×Dic3—32no—
77C2×C4×Dic3—32no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—32no—
80#892—32no—
81#892—32no—
82#892—34no—
83#892—34no—
84#892—32no—
85#892—31no—
86#892—31no—
87#892—32no—
88#892—31no—
89#892—32no—
90#892A411yescharacteristic, direct product factor
91C22×C3×D3—41no—
92C2×C3×A4C22×C411yescharacteristic
93C2×C3×A4#4111yescharacteristic
94C2×C3×A4#4111yescharacteristic
95D3×A4—22no—
96C2×C32×C4—41no—
97C2×C32×C4—42no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—42no—
100C3×C4×D3—44no—
101C24×C4—31no—
102C2×#117—91no—
103C2×#117—92no—
104C2×#117—92no—
105C2×#117—91no—
106C2×#117—91no—
107C2×#117—91no—
108C22×C4⋊C4—31no—
109C22×C4⋊C4C3×D311yescharacteristic, complemented
110C22×C22⋊C4—32no—
111C22×C42—32no—
112C24×C3C23×C311yescharacteristic
113C23×D3—21no—
114C23×D3—21no—
115C23×D3—31no—
116C23×D3—31no—
117C23×D3—32no—
118C23×D3—61no—
119C23×D3—61no—
120C23×D3C2×C3×C412yes—
121C22×A4—21no—
122C22×A4—32no—
123C22×A4—61no—
124C22×A4—61no—
125C22×A4C22×D311yescharacteristic
126C22×C3×C4—22no—
127C22×C3×C4—31no—
128C22×C3×C4—31no—
129C22×C3×C4—32no—
130C22×C3×C4—32no—
131C22×C3×C4—32no—
132C22×C3×C4—62no—
133C22×C3×C4—121no—
134C22×C3×C4C2×C3×C412yes—
135C22×Dic3—22no—
136C22×Dic3—31no—
137C22×Dic3—31no—
138C22×Dic3—32no—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C22×Dic3—62no—
142C22×Dic3C2×C3×C412yes—
143C2×C4×D3—32no—
144C2×C4×D3—34no—
145C2×C4×D3—34no—
146C2×C4×D3—34no—
147C2×C4×D3—31no—
148C2×C4×D3—31no—
149C2×C4×D3—31no—
150C2×C4×D3—34no—
151C2×C4×D3—34no—
152C2×C4×D3—34no—
153C2×C4×D3—34no—
154C2×C4×D3—34no—
155C2×C4×D3C2×A411yescharacteristic
156C4×A4—22no—
157C4×A4—22no—
158C4×A4—32no—
159C4×A4—42no—
160C4×A4—62no—
161C4×A4C4×D312yes—
162C3×C4⋊C4—32no—
163C3×C4⋊C4—32no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—41no—
166C3×C4⋊C4—81no—
167C3×C4⋊C4—121no—
168C3×C4⋊C4C2×A411yescharacteristic, complemented
169C3×C22⋊C4—122no—
170C3×C42—122no—
171(C2×D3)⋊C4—34no—
172(C2×D3)⋊C4—32no—
173(C2×D3)⋊C4—32no—
174(C2×D3)⋊C4—32no—
175(C2×D3)⋊C4C2×A412yes—
176C4⋊Dic3—32no—
177C4⋊Dic3—31no—
178C4⋊Dic3—32no—
179C4⋊Dic3C2×A411yescharacteristic, complemented
180C4×Dic3—34no—
181C4×Dic3—32no—
182C4×Dic3—32no—
183C4×Dic3—32no—
184C4×Dic3C2×A412yescomplemented
185C22×C32—41no—
186C2×C3×D3—42no—
187C2×C3×D3—81no—
188C2×C3×D3—81no—
189C3×A4#11711yescharacteristic, complemented
190C32×C4—42no—
191C32×C4—82no—
192C3×Dic3—42no—
193C3×Dic3—82no—
194C25—31no—
195C23×C4—31no—
196C23×C4—34no—
197C23×C4—32no—
198C23×C4—91no—
199C23×C4—91no—
200C23×C4—91no—
201C23×C4—91no—
202C23×C4—94no—
203C23×C4C2×C3×D312yes—
204C23×C4C2×C3×D311yescharacteristic
205#117—31no—
206#117—92no—
207#117—92no—
208#117—91no—
209#117—91no—
210#117—92no—
211#117—94no—
212#117—92no—
213#117—92no—
214#117—94no—
215#117—91no—
216C2×C4⋊C4—31no—
217C2×C4⋊C4—31no—
218C2×C4⋊C4—32no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—92no—
221C2×C4⋊C4—91no—
222C2×C22⋊C4—92no—
223C2×C22⋊C4—92no—
224C2×C22⋊C4—92no—
225C2×C22⋊C4—92no—
226C2×C42—92no—
227C2×C42—92no—
228C2×C42—92no—
229C2×C42—92no—
230C23×C3—31no—
231C23×C3—31no—
232C23×C3—31no—
233C23×C3—31no—
234C23×C3—121no—
235C23×C3C22×C3×C411yescharacteristic
236C23×C3C3×#4111yescharacteristic
237C23×C3C3×#4111yescharacteristic
238C22×D3—22no—
239C22×D3—32no—
240C22×D3—31no—
241C22×D3—32no—
242C22×D3—32no—
243C22×D3—32no—
244C22×D3—61no—
245C22×D3—61no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—64no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—61no—
252C22×D3—61no—
253C22×D3—61no—
254C22×D3—61no—
255C22×D3—62no—
256C22×D3C22×A411yescharacteristic
257C2×A4—21no—
258C2×A4—21no—
259C2×A4—21no—
260C2×A4—62no—
261C2×A4C2×C4×D311yescharacteristic
262C2×A4#23711yescharacteristic
263C2×A4#23911yescharacteristic
264C2×C3×C4—32no—
265C2×C3×C4—31no—
266C2×C3×C4—32no—
267C2×C3×C4—32no—
268C2×C3×C4—32no—
269C2×C3×C4—32no—
270C2×C3×C4—41no—
271C2×C3×C4—42no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—81no—
277C2×C3×C4—82no—
278C2×C3×C4—124no—
279C2×C3×C4—121no—
280C2×C3×C4—122no—
281C2×C3×C4C22×A412yes—
282C2×C3×C4C22×A411yescharacteristic
283C2×Dic3—32no—
284C2×Dic3—31no—
285C2×Dic3—32no—
286C2×Dic3—32no—
287C2×Dic3—32no—
288C2×Dic3—32no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3C22×A412yes—
294C2×Dic3C22×A411yescharacteristic
295C4×D3—38no—
296C4×D3—34no—
297C4×D3—34no—
298C4×D3—34no—
299C4×D3C4×A414yescomplemented
300C2×C32—41no—
301C2×C32—41no—
302C2×C32—41no—
303C3×D3—82no—
304C24—32no—
305C24—61no—
306C24—61no—
307C24—91no—
308C24—91no—
309C24—92no—
310C24—181no—
311C24—181no—
312C24C22×C3×D311yescharacteristic
313C22×C4—22no—
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—32no—
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—32no—
321C22×C4—62no—
322C22×C4—62no—
323C22×C4—91no—
324C22×C4—94no—
325C22×C4—94no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—92no—
329C22×C4—94no—
330C22×C4—94no—
331C22×C4—94no—
332C22×C4—94no—
333C22×C4—94no—
334C22×C4—94no—
335C22×C4—92no—
336C22×C4—91no—
337C22×C4—91no—
338C22×C4—92no—
339C22×C4—92no—
340C22×C4—182no—
341C22×C4C3×C4×D312yes—
342C4⋊C4—32no—
343C4⋊C4—32no—
344C4⋊C4—31no—
345C4⋊C4—31no—
346C4⋊C4—92no—
347C4⋊C4—92no—
348C4⋊C4—91no—
349C4⋊C4D3×A411yescharacteristic, complemented
350C22⋊C4—32no—
351C22⋊C4—92no—
352C22⋊C4—92no—
353C22⋊C4—94no—
354C22⋊C4—92no—
355C42—32no—
356C42—92no—
357C42—92no—
358C42—94no—
359C42—92no—
360C22×C3—31no—
361C22×C3—31no—
362C22×C3—31no—
363C22×C3—32no—
364C22×C3—31no—
365C22×C3—31no—
366C22×C3—31no—
367C22×C3—31no—
368C22×C3—31no—
369C22×C3—31no—
370C22×C3—41no—
371C22×C3—81no—
372C22×C3—122no—
373C22×C3—241no—
374C22×C3—241no—
375C22×C3C3×#11711yescharacteristic, complemented
376C22×C3C23×A411yescharacteristic
377C2×D3—21no—
378C2×D3—21no—
379C2×D3—32no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—61no—
387C2×D3—61no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3C2×C4×A412yes—
391A4—21no—
392A4#89211yescharacteristic, direct product factor
393C3×C4—22no—
394C3×C4—32no—
395C3×C4—42no—
396C3×C4—62no—
397C3×C4—82no—
398C3×C4—82no—
399C3×C4—122no—
400C3×C4—162no—
401C3×C4—242no—
402C3×C4C2×C4×A412yes—
403Dic3—22no—
404Dic3—32no—
405Dic3—62no—
406Dic3C2×C4×A412yes—
407C32—41noSylow
408C23—31no—
409C23—31no—
410C23—31no—
411C23—31no—
412C23—31no—
413C23—62no—
414C23—92no—
415C23—92no—
416C23—92no—
417C23—92no—
418C23—91no—
419C23—181no—
420C23—181no—
421C23—181no—
422C23—181no—
423C23—182no—
424C23—182no—
425C23—182no—
426C23—181no—
427C23—181no—
428C23—181no—
429C23—181no—
430C23—184no—
431C23C2×C3×C4×D311yescharacteristic
432C23C3×#23711yescharacteristic
433C23C3×#23911yescharacteristic
434C2×C4—32no—
435C2×C4—31no—
436C2×C4—31no—
437C2×C4—32no—
438C2×C4—32no—
439C2×C4—34no—
440C2×C4—32no—
441C2×C4—32no—
442C2×C4—32no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—94no—
448C2×C4—92no—
449C2×C4—94no—
450C2×C4—92no—
451C2×C4—98no—
452C2×C4—92no—
453C2×C4—91no—
454C2×C4—94no—
455C2×C4—92no—
456C2×C4—92no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—182no—
461C2×C4C2×D3×A412yes—
462C2×C4C2×D3×A411yescharacteristic
463C2×C3—31no—
464C2×C3—31no—
465C2×C3—31no—
466C2×C3—31no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—81no—
471C2×C3—81no—
472C2×C3—81no—
473C2×C3—242no—
474C2×C3C22×C4×A411yescharacteristic
475C2×C3A4×#4111yescharacteristic
476C2×C3A4×#4111yescharacteristic
477D3—22no—
478D3—62no—
479C22—31no—
480C22—31no—
481C22—31no—
482C22—32no—
483C22—31no—
484C22—31no—
485C22—31no—
486C22—31no—
487C22—31no—
488C22—31no—
489C22—32no—
490C22—61no—
491C22—61no—
492C22—92no—
493C22—182no—
494C22—182no—
495C22—182no—
496C22—182no—
497C22—182no—
498C22—182no—
499C22—182no—
500C22—182no—
501C22—181no—
502C22—181no—
503C22C3×#89211yescharacteristic, complemented
504C22C22×D3×A411yescharacteristic
505C4—22no—
506C4—32no—
507C4—32no—
508C4—62no—
509C4—62no—
510C4—92no—
511C4—182no—
512C4C4×D3×A412yes—
513C3—41no—
514C3—81no—
515C3A4×#11711yescharacteristic, complemented
516C2—31no—
517C2—31no—
518C2—31no—
519C2—31no—
520C2—62no—
521C2—182no—
522C2C2×C4×D3×A411yescharacteristic
523C2A4×#23711yescharacteristic
524C2A4×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutatorC23×C3C22×C3×C4
FittingC22×C3×C4⋊C4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC22×D3×A4C22
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C3×#117
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×A4×C4⋊C4C2semidirect
4. A4×C4⋊Dic3C2semidirect
5. C4×Dic3×A4C2semidirect
6. C22×#892C3semidirect
13. C4×D3×A4C4semidirect
17. C22×C3×C4⋊C4C2×C3semidirect
19. C22×C4⋊Dic3C2×C3semidirect
20. C22×C4×Dic3C2×C3semidirect
29. A4×C4⋊C4D3semidirect
57. C22×C4×D3C3×C4semidirect
90. #892A4direct (N × H)
109. C22×C4⋊C4C3×D3semidirect
168. C3×C4⋊C4C2×A4semidirect
179. C4⋊Dic3C2×A4semidirect
184. C4×Dic3C2×A4semidirect
189. C3×A4#117semidirect
299. C4×D3C4×A4semidirect
349. C4⋊C4D3×A4semidirect
375. C22×C3C3×#117semidirect
392. A4#892direct (N × H)
503. C22C3×#892semidirect
515. C3A4×#117semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×A42
C3×A4×C4⋊C42
A4×(C2×D3)⋊C42
A4×C4⋊Dic32
C4×Dic3×A42
C22×#8923
A4×#1173
C3×#8924