Finite Group Databasebeta

← A4×#3805 #13180910

Subgroups — A4×#3805 #13180910

Order 1728.

1010 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 96 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×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×A4×#67C212yesmaximal, complemented
3A4×#627C211yesmaximal, characteristic, complemented
4A4×#625C211yesmaximal, characteristic, complemented
5D3×Dic3×A4C212yesmaximal, complemented
6C22×#3805C311yesmaximal, characteristic, complemented
7A4×#237—32nomaximal
8C22×C32×A4C2211yescharacteristic
9C2×C3×D3×A4C2212yes—
10C3×#3805—41nomaximal
11A4×C3⋊Dic3C2211yescharacteristic
12A4×C3⋊Dic3C2211yescharacteristic
13C3×Dic3×A4C2212yes—
14C23×C3⋊Dic3C2×C311yescharacteristic, complemented
15C22×C3×#67C2×C312yescomplemented
16C3×D4×A4—32no—
17C22×#627C2×C311yescharacteristic, complemented
18C22×#625C2×C311yescharacteristic, complemented
19C2×#3805—31no—
20C2×#3805—32no—
21C2×#3805—31no—
22C2×#3805—32no—
23C2×#3805—31no—
24C2×#3805—31no—
25C22×D3×Dic3C2×C312yescomplemented
26A4×#67—22no—
27A4×#67—32no—
28A4×#67D312yescomplemented
29C2×Dic3×A4—32no—
30C2×Dic3×A4—32no—
31C2×Dic3×A4—61no—
32C4×D3×A4—32no—
33A4×Dic6—32no—
34C2×C32×A4—21no—
35C2×C32×A4C2311yescharacteristic
36C3×D3×A4—22no—
37C2×C3×C3⋊Dic3—41no—
38C32×#67—42no—
39C3×#627—41no—
40C3×#625—41no—
41C3×D3×Dic3—42no—
42C22×#237—32no—
43A4×#41—91no—
44C24×C32C22×C311yescharacteristic
45C23×C3×D3C22×C312yes—
46C22×C3×A4—21no—
47C22×C3×A4—22no—
48C22×C3×A4—32no—
49C22×C3×A4—41no—
50C22×C3×A4C2×D312yes—
51C2×D3×A4—22no—
52C2×D3×A4C2×D312yes—
53C22×C3⋊Dic3—31no—
54C22×C3⋊Dic3—31no—
55C22×C3⋊Dic3—31no—
56C22×C3⋊Dic3—31no—
57C22×C3⋊Dic3C22×C311yescharacteristic
58C22×C3⋊Dic3C22×C311yescharacteristic
59C2×C3×#67—32no—
60C2×C3×#67—32no—
61C2×C3×#67—32no—
62C2×C3×#67—32no—
63C22×C3×Dic3C22×C312yes—
64C3×#237—122no—
65C3×C4×A4—32no—
66C2×#627—31no—
67C2×#627—31no—
68C2×#627—32no—
69C2×#625—31no—
70C2×#625—32no—
71C2×#625—31no—
72#3805—32no—
73#3805—32no—
74#3805—34no—
75#3805—34no—
76#3805—32no—
77#3805—31no—
78#3805—32no—
79#3805—31no—
80#3805—31no—
81#3805—32no—
82#3805A411yescharacteristic, direct product factor
83C2×D3×Dic3—32no—
84C2×D3×Dic3—32no—
85C2×D3×Dic3—32no—
86C2×D3×Dic3—32no—
87Dic3×A4—22no—
88Dic3×A4—32no—
89Dic3×A4—32no—
90Dic3×A4—61no—
91Dic3×A4—61no—
92Dic3×A4C2×D312yes—
93C22×C33—41no—
94C2×C32×D3—42no—
95C32×A4#4111yescharacteristic, complemented
96C3×C3⋊Dic3—41no—
97C3×C3⋊Dic3—41no—
98C32×Dic3—42no—
99C22×C3×D4—32no—
100C22×#67—32no—
101C22×#67C3×D312yescomplemented
102C23×Dic3—32no—
103C23×Dic3—32no—
104C23×Dic3—61no—
105C2×#237—92no—
106C2×#237—92no—
107C2×#237—92no—
108C2×#237—92no—
109C2×#237—92no—
110C2×#237—92no—
111C2×#237—92no—
112C2×#237—92no—
113C22×C4×D3—32no—
114C22×Dic6—32no—
115Q8×A4—91no—
116D4×A4—32no—
117D4×A4—62no—
118D4×A4—91no—
119C2×C4×A4—92no—
120C2×C4×A4—91no—
121C23×C32—21no—
122C23×C32—31no—
123C23×C32—31no—
124C23×C32—61no—
125C23×C32C23×C311yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—32no—
128C22×C3×D3—32no—
129C22×C3×D3—62no—
130C2×C3×A4—22no—
131C2×C3×A4—22no—
132C2×C3×A4—22no—
133C2×C3×A4—21no—
134C2×C3×A4—41no—
135C2×C3×A4—42no—
136C2×C3×A4—42no—
137C2×C3×A4—62no—
138C2×C3×A4C22×D312yes—
139D3×A4—22no—
140D3×A4—42no—
141C32×D4—122no—
142C2×C3⋊Dic3—32no—
143C2×C3⋊Dic3—31no—
144C2×C3⋊Dic3—31no—
145C2×C3⋊Dic3—31no—
146C2×C3⋊Dic3—31no—
147C2×C3⋊Dic3—31no—
148C2×C3⋊Dic3—31no—
149C2×C3⋊Dic3—31no—
150C2×C3⋊Dic3C2×A411yescharacteristic, complemented
151C3×#67—34no—
152C3×#67—32no—
153C3×#67—32no—
154C3×#67—32no—
155C3×#67—42no—
156C3×#67—82no—
157C3×#67—122no—
158C3×#67C2×A412yescomplemented
159C2×C3×Dic3—32no—
160C2×C3×Dic3—32no—
161C2×C3×Dic3—122no—
162C2×C3×Dic3—122no—
163C2×C3×Dic3—241no—
164C3×C4×D3—122no—
165C3×Dic6—122no—
166#627—32no—
167#627—31no—
168#627—32no—
169#627C2×A411yescharacteristic, complemented
170#625—32no—
171#625—32no—
172#625—31no—
173#625C2×A411yescharacteristic, complemented
174D3×Dic3—34no—
175D3×Dic3—32no—
176D3×Dic3—32no—
177D3×Dic3—32no—
178D3×Dic3C2×A412yescomplemented
179C22×#41—91noSylow
180C2×C33—41no—
181C2×C33—81no—
182C32×D3—82no—
183C24×C3—21no—
184C24×C3—32no—
185C24×C3C2×C3×D312yes—
186C23×D3C2×C3×D312yes—
187C22×A4—22no—
188C22×A4—32no—
189C22×A4—41no—
190C22×A4—62no—
191C22×A4D3211yescharacteristic
192C3×#41—361no—
193C2×C3×D4—92no—
194C2×C3×D4—92no—
195C2×C3×D4—92no—
196C2×C3×D4—92no—
197C22×C3×C4—32no—
198C2×#67—32no—
199C2×#67—32no—
200C2×#67—32no—
201C2×#67—32no—
202C2×#67—92no—
203C2×#67—92no—
204C2×#67—92no—
205C2×#67—92no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—92no—
211C22×Dic3—92no—
212C22×Dic3—92no—
213C22×Dic3—92no—
214C22×Dic3—92no—
215C22×Dic3—92no—
216C22×Dic3—92no—
217C22×Dic3—92no—
218C22×Dic3—181no—
219C22×Dic3—181no—
220C22×Dic3—181no—
221C22×Dic3—181no—
222C22×Dic3C2×C3×D312yes—
223#237—32no—
224#237—92no—
225#237—92no—
226#237—92no—
227#237—92no—
228#237—92no—
229#237—92no—
230#237—94no—
231#237—94no—
232#237—94no—
233#237—94no—
234#237—94no—
235#237—94no—
236#237—94no—
237#237—92no—
238C2×C4×D3—92no—
239C2×C4×D3—92no—
240C2×C4×D3—92no—
241C2×C4×D3—92no—
242C2×Dic6—92no—
243C2×Dic6—92no—
244C2×Dic6—92no—
245C2×Dic6—92no—
246C4×A4—32no—
247C4×A4—62no—
248C4×A4—91no—
249C4×A4—91no—
250C22×C32—31no—
251C22×C32—31no—
252C22×C32—31no—
253C22×C32—42no—
254C22×C32—61no—
255C22×C32—61no—
256C22×C32—61no—
257C22×C32—61no—
258C22×C32—81no—
259C22×C32—82no—
260C22×C32—122no—
261C22×C32—161no—
262C22×C32C3×#4111yescharacteristic, complemented
263C22×C32C22×A411yescharacteristic
264C2×C3×D3—32no—
265C2×C3×D3—42no—
266C2×C3×D3—62no—
267C2×C3×D3—62no—
268C2×C3×D3—62no—
269C2×C3×D3—62no—
270C2×C3×D3—82no—
271C2×C3×D3C22×A412yes—
272C3×A4—22no—
273C3×A4—21no—
274C3×A4—41no—
275C3×A4#23712yescomplemented
276C32×C4—122no—
277C3⋊Dic3—31no—
278C3⋊Dic3—31no—
279C3⋊Dic3C22×A411yescharacteristic
280C3⋊Dic3C22×A411yescharacteristic
281C3×Dic3—32no—
282C3×Dic3—42no—
283C3×Dic3—82no—
284C3×Dic3—122no—
285C3×Dic3—122no—
286C3×Dic3—241no—
287C3×Dic3—241no—
288C3×Dic3C22×A412yes—
289C2×#41—271no—
290C2×#41—272no—
291C2×#41—271no—
292C2×#41—272no—
293C2×#41—271no—
294C2×#41—271no—
295C22×Q8—91no—
296C22×D4—32no—
297C22×D4—91no—
298C23×C4—92no—
299C23×C4—91no—
300C33—41noSylow
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—21no—
304C23×C3—32no—
305C23×C3—32no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3—62no—
309C23×C3—62no—
310C23×C3—62no—
311C23×C3—92no—
312C23×C3—92no—
313C23×C3—182no—
314C23×C3C22×C3×D312yes—
315C22×D3—22no—
316C22×D3—32no—
317C22×D3—32no—
318C22×D3—62no—
319C2×A4—21no—
320C2×A4—22no—
321C2×A4—42no—
322C2×A4—42no—
323C2×A4—41no—
324C2×A4—62no—
325C2×A4—122no—
326C2×A4C2×D3211yescharacteristic
327C3×Q8—361no—
328C3×D4—32no—
329C3×D4—92no—
330C3×D4—92no—
331C3×D4—94no—
332C3×D4—92no—
333C3×D4—122no—
334C3×D4—242no—
335C3×D4—361no—
336C2×C3×C4—92no—
337C2×C3×C4—92no—
338C2×C3×C4—362no—
339C2×C3×C4—361no—
340#67—34no—
341#67—32no—
342#67—32no—
343#67—32no—
344#67—32no—
345#67—92no—
346#67—92no—
347#67—94no—
348#67—92no—
349#67D3×A412yescomplemented
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—61no—
355C2×Dic3—92no—
356C2×Dic3—92no—
357C2×Dic3—92no—
358C2×Dic3—92no—
359C2×Dic3—92no—
360C2×Dic3—92no—
361C2×Dic3—94no—
362C2×Dic3—94no—
363C2×Dic3—92no—
364C2×Dic3—92no—
365C2×Dic3—92no—
366C2×Dic3—92no—
367C2×Dic3—181no—
368C2×Dic3—181no—
369C2×Dic3—181no—
370C2×Dic3—181no—
371C2×Dic3—181no—
372C2×Dic3—182no—
373C2×Dic3—181no—
374C2×Dic3—181no—
375C4×D3—32no—
376C4×D3—92no—
377C4×D3—92no—
378C4×D3—94no—
379C4×D3—92no—
380Dic6—32no—
381Dic6—92no—
382Dic6—92no—
383Dic6—94no—
384Dic6—92no—
385C2×C32—21no—
386C2×C32—31no—
387C2×C32—31no—
388C2×C32—42no—
389C2×C32—61no—
390C2×C32—81no—
391C2×C32—82no—
392C2×C32—82no—
393C2×C32—82no—
394C2×C32—161no—
395C2×C32—162no—
396C2×C32—162no—
397C2×C32—242no—
398C2×C32C23×A411yescharacteristic
399C3×D3—22no—
400C3×D3—62no—
401C3×D3—82no—
402C3×D3—162no—
403C24—32no—
404C24C3×D3211yescharacteristic
405#41—91no—
406#41—272no—
407#41—271no—
408#41—272no—
409#41—271no—
410#41—271no—
411#41—274no—
412#41—272no—
413#41—274no—
414#41—272no—
415#41—272no—
416C2×Q8—271no—
417C2×Q8—272no—
418C2×Q8—271no—
419C2×D4—92no—
420C2×D4—92no—
421C2×D4—92no—
422C2×D4—92no—
423C2×D4—271no—
424C2×D4—271no—
425C2×D4—272no—
426C22×C4—32no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—272no—
430C22×C4—271no—
431C22×C4—272no—
432C22×C4—272no—
433C22×C4—272no—
434C22×C4—271no—
435C22×C4—271no—
436C22×C4—271no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—32no—
440C22×C3—32no—
441C22×C3—32no—
442C22×C3—32no—
443C22×C3—41no—
444C22×C3—61no—
445C22×C3—61no—
446C22×C3—61no—
447C22×C3—62no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—82no—
456C22×C3—92no—
457C22×C3—122no—
458C22×C3—161no—
459C22×C3—182no—
460C22×C3—182no—
461C22×C3—182no—
462C22×C3—182no—
463C22×C3—242no—
464C22×C3C3×#23712yescomplemented
465C22×C3C2×D3×A412yes—
466C2×D3—32no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3C2×D3×A412yes—
472A4—22no—
473A4—41no—
474A4#380511yescharacteristic, direct product factor
475C3×C4—32no—
476C3×C4—92no—
477C3×C4—122no—
478C3×C4—242no—
479C3×C4—361no—
480C3×C4—361no—
481Dic3—32no—
482Dic3—32no—
483Dic3—32no—
484Dic3—61no—
485Dic3—61no—
486Dic3—92no—
487Dic3—92no—
488Dic3—181no—
489Dic3—181no—
490Dic3C2×D3×A412yes—
491C32—42no—
492C32—81no—
493C32—82no—
494C32—161no—
495C32A4×#4111yescharacteristic, complemented
496C23—21no—
497C23—31no—
498C23—31no—
499C23—61no—
500C23—62no—
501C23—92no—
502C23—92no—
503C23—182no—
504C23C2×C3×D3211yescharacteristic
505Q8—91no—
506Q8—272no—
507Q8—271no—
508Q8—272no—
509D4—32no—
510D4—92no—
511D4—92no—
512D4—91no—
513D4—94no—
514D4—92no—
515D4—271no—
516D4—272no—
517D4—272no—
518C2×C4—92no—
519C2×C4—92no—
520C2×C4—91no—
521C2×C4—92no—
522C2×C4—272no—
523C2×C4—272no—
524C2×C4—271no—
525C2×C4—271no—
526C2×C4—272no—
527C2×C4—271no—
528C2×C4—271no—
529C2×C4—274no—
530C2×C4—272no—
531C2×C4—271no—
532C2×C4—271no—
533C2×C4—271no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—32no—
538C2×C3—32no—
539C2×C3—41no—
540C2×C3—61no—
541C2×C3—61no—
542C2×C3—62no—
543C2×C3—62no—
544C2×C3—62no—
545C2×C3—81no—
546C2×C3—82no—
547C2×C3—162no—
548C2×C3—162no—
549C2×C3—161no—
550C2×C3—182no—
551C2×C3—242no—
552C2×C3—482no—
553C2×C3C22×D3×A412yes—
554D3—22no—
555D3—62no—
556C22—31no—
557C22—31no—
558C22—32no—
559C22—31no—
560C22—61no—
561C22—61no—
562C22—61no—
563C22—61no—
564C22—92no—
565C22—182no—
566C22—182no—
567C22—182no—
568C22—182no—
569C22C3×#380511yescharacteristic, complemented
570C22D32×A411yescharacteristic
571C4—32no—
572C4—91no—
573C4—92no—
574C4—91no—
575C4—271no—
576C4—271no—
577C3—21no—
578C3—41no—
579C3—82no—
580C3—161no—
581C3A4×#23712yescomplemented
582C2—21no—
583C2—31no—
584C2—31no—
585C2—61no—
586C2—62no—
587C2—182no—
588C2C2×D32×A411yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×A4
commutator, socle, cosocleC23×C32C23×C3
FittingC24×C32C22×C3
hypercenterC22D32×A4
hypocenterC22×C32C3×#41
LCSG ▷ C23×C32 ▷ C22×C32
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×A4×C3⋊Dic3C2semidirect
2. C3×A4×#67C2semidirect
3. A4×#627C2semidirect
4. A4×#625C2semidirect
5. D3×Dic3×A4C2semidirect
6. C22×#3805C3semidirect
14. C23×C3⋊Dic3C2×C3semidirect
15. C22×C3×#67C2×C3semidirect
17. C22×#627C2×C3semidirect
18. C22×#625C2×C3semidirect
25. C22×D3×Dic3C2×C3semidirect
28. A4×#67D3semidirect
82. #3805A4direct (N × H)
95. C32×A4#41semidirect
101. C22×#67C3×D3semidirect
150. C2×C3⋊Dic3C2×A4semidirect
158. C3×#67C2×A4semidirect
169. #627C2×A4semidirect
173. #625C2×A4semidirect
178. D3×Dic3C2×A4semidirect
262. C22×C32C3×#41semidirect
275. C3×A4#237semidirect
349. #67D3×A4semidirect
464. C22×C3C3×#237semidirect
474. A4#3805direct (N × H)
495. C32A4×#41semidirect
569. C22C3×#3805semidirect
581. C3A4×#237semidirect

Maximal subgroups

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

subgroupindex
C2×A4×C3⋊Dic32
C3×A4×#672
A4×#6272
A4×#6252
D3×Dic3×A42
C22×#38053
A4×#2373
C3×#38054