Finite Group Databasebeta

← A4×#951 #11923383

Subgroups — A4×#951 #11923383

Order 1152.

728 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C3×A4×#41C211yesmaximal, characteristic
2C2×A4×Dic6C211yesmaximal, characteristic, complemented
3A4×#216C212yesmaximal, complemented
4A4×#214C212yesmaximal, complemented
5A4×#208C211yesmaximal, characteristic, complemented
6C22×#951C311yesmaximal, characteristic, complemented
7A4×#137—31nomaximal
8C3×Q8×A4C2211yescharacteristic
9C3×D4×A4—21no—
10C3×D4×A4C2211yescharacteristic
11C2×C3×C4×A4—21no—
12C2×C3×C4×A4C2211yescharacteristic
13C2×Dic3×A4—21no—
14A4×Dic6—21no—
15A4×Dic6C2212yes—
16C3×#951—41nomaximal
17A4×C3⋊C8C2212yes—
18C22×C3×#41C2×C311yescharacteristic
19C23×Dic6C2×C311yescharacteristic, complemented
20A4×#41—21no—
21A4×#41D311yescharacteristic
22C2×Q8×A4—31no—
23C2×#951—31no—
24C2×#951—31no—
25C2×#951—32no—
26C2×#951—32no—
27C2×#951—31no—
28C2×#951—31no—
29C22×#216C2×C312yescomplemented
30C22×#214C2×C312yescomplemented
31C22×#208C2×C311yescharacteristic, complemented
32A4×Q16—32no—
33A4×SD16—32no—
34A4×M16—31no—
35C22×C3×A4—21no—
36C22×C3×A4D411yescharacteristic
37C32×#41—41no—
38C2×C3×Dic6—41no—
39C3×C4×A4—21no—
40C3×C4×A4D411yescharacteristic
41C3×C4×A4C2311yescharacteristic
42Dic3×A4—22no—
43C3×#216—42no—
44C3×#214—42no—
45C3×#208—41no—
46C22×#137—31noSylow
47C2×C3×#41—31no—
48C2×C3×#41—31no—
49C2×C3×#41—31no—
50C2×C3×#41—31no—
51C2×C3×#41—61no—
52C2×C3×#41—61no—
53C22×C3×Q8C22×C311yescharacteristic
54C22×C3×D4—21no—
55C22×C3×D4C22×C311yescharacteristic
56C23×C3×C4—21no—
57C23×C3×C4C22×C311yescharacteristic
58C23×Dic3—21no—
59C22×Dic6—21no—
60C22×Dic6—31no—
61C22×Dic6—31no—
62C22×Dic6—32no—
63C22×Dic6—61no—
64C22×Dic6—61no—
65C22×Dic6C22×C312yes—
66Q8×A4—21no—
67Q8×A4—32no—
68Q8×A4—61no—
69Q8×A4C2×D311yescharacteristic
70D4×A4—22no—
71D4×A4—21no—
72D4×A4—21no—
73D4×A4C2×D311yescharacteristic
74C2×C4×A4—22no—
75C2×C4×A4—21no—
76C2×C4×A4—21no—
77C2×C4×A4—61no—
78C2×C4×A4C2×D311yescharacteristic
79C3×#137—121no—
80#951—32no—
81#951—34no—
82#951—32no—
83#951—32no—
84#951—34no—
85#951—31no—
86#951—31no—
87#951—32no—
88#951—32no—
89#951—31no—
90#951A411yescharacteristic, direct product factor
91C2×#216—32no—
92C2×#216—32no—
93C2×#216—32no—
94C2×#216—32no—
95C2×#214—32no—
96C2×#214—32no—
97C2×#214—32no—
98C2×#214—32no—
99C2×#208—31no—
100C2×#208—32no—
101C2×#208—31no—
102C22×C3⋊C8C22×C312yes—
103C8×A4—32no—
104C2×C3×A4—21no—
105C2×C3×A4—41no—
106C2×C3×A4C2×D411yescharacteristic
107C32×Q8—41no—
108C32×D4—41no—
109C32×D4—81no—
110C2×C32×C4—41no—
111C2×C32×C4—81no—
112C2×C3×Dic3—81no—
113C3×Dic6—42no—
114C3×Dic6—81no—
115C3×C3⋊C8—42no—
116C22×#41C3×D311yescharacteristic
117C23×Q8—31no—
118C2×#137—91no—
119C2×#137—91no—
120C2×#137—92no—
121C2×#137—92no—
122C2×#137—91no—
123C2×#137—91no—
124C22×Q16—32no—
125C22×SD16—32no—
126C22×M16—31no—
127C24×C3—21no—
128C24×C3C3×D411yescharacteristic
129C22×A4—22no—
130C22×A4—21no—
131C22×A4—21no—
132C22×A4#6711yescharacteristic
133C3×#41—32no—
134C3×#41—31no—
135C3×#41—31no—
136C3×#41—31no—
137C3×#41—41no—
138C3×#41—61no—
139C3×#41—61no—
140C3×#41—62no—
141C3×#41—62no—
142C3×#41—61no—
143C3×#41—61no—
144C3×#41—81no—
145C3×#41C2×A411yescharacteristic
146C2×C3×Q8—31no—
147C2×C3×Q8—31no—
148C2×C3×Q8—61no—
149C2×C3×Q8—121no—
150C2×C3×D4—31no—
151C2×C3×D4—31no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C3×D411yescharacteristic
167C22×C3×C4C23×C311yescharacteristic
168C22×Dic3—22no—
169C22×Dic3—61no—
170C22×Dic3—62no—
171C22×Dic3—61no—
172C2×Dic6—32no—
173C2×Dic6—31no—
174C2×Dic6—32no—
175C2×Dic6—32no—
176C2×Dic6—32no—
177C2×Dic6—61no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—64no—
181C2×Dic6—61no—
182C2×Dic6—62no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—62no—
186C2×Dic6C2×A411yescharacteristic, complemented
187C4×A4—22no—
188C4×A4—21no—
189C4×A4—21no—
190C4×A4—21no—
191C4×A4—62no—
192C4×A4#6711yescharacteristic
193C4×A4C22×D311yescharacteristic
194C3×Q16—122no—
195C3×SD16—122no—
196C3×M16—121no—
197#216—34no—
198#216—32no—
199#216—32no—
200#216—32no—
201#216C2×A412yescomplemented
202#214—34no—
203#214—32no—
204#214—32no—
205#214—32no—
206#214C2×A412yescomplemented
207#208—32no—
208#208—31no—
209#208—32no—
210#208C2×A411yescharacteristic, complemented
211C2×C3⋊C8—32no—
212C2×C3⋊C8—32no—
213C22×C32—41no—
214C22×C32—81no—
215C3×A4#13711yescharacteristic, complemented
216C32×C4—41no—
217C32×C4—41no—
218C32×C4—81no—
219C3×Dic3—82no—
220C2×#41—31no—
221C2×#41—31no—
222C2×#41—31no—
223C2×#41—31no—
224C2×#41—61no—
225C2×#41—61no—
226C22×Q8—32no—
227C22×Q8—61no—
228C22×Q8—91no—
229C22×Q8—91no—
230C22×Q8—92no—
231C22×Q8—181no—
232C22×Q8—181no—
233C22×Q8C2×C3×D311yescharacteristic
234C22×D4—21no—
235C22×D4C2×C3×D311yescharacteristic
236C23×C4—21no—
237C23×C4—61no—
238C23×C4C2×C3×D311yescharacteristic
239#137—31no—
240#137—91no—
241#137—92no—
242#137—92no—
243#137—91no—
244#137—94no—
245#137—94no—
246#137—92no—
247#137—92no—
248#137—92no—
249#137—91no—
250C2×Q16—92no—
251C2×Q16—92no—
252C2×Q16—92no—
253C2×Q16—92no—
254C2×SD16—92no—
255C2×SD16—92no—
256C2×SD16—92no—
257C2×SD16—92no—
258C2×M16—91no—
259C2×M16—92no—
260C2×M16—91no—
261C22×C8—32no—
262C23×C3—21no—
263C23×C3—31no—
264C23×C3—31no—
265C23×C3—41no—
266C23×C3—61no—
267C23×C3—61no—
268C23×C3—61no—
269C23×C3—121no—
270C23×C3C2×C3×D411yescharacteristic
271C2×A4—21no—
272C2×A4—21no—
273C2×A4—41no—
274C2×A4—42no—
275C2×A4—41no—
276C2×A4C2×#6711yescharacteristic
277C3×Q8—31no—
278C3×Q8—41no—
279C3×Q8—61no—
280C3×Q8—61no—
281C3×Q8—81no—
282C3×Q8—122no—
283C3×Q8—241no—
284C3×Q8C22×A411yescharacteristic
285C3×D4—21no—
286C3×D4—31no—
287C3×D4—41no—
288C3×D4—61no—
289C3×D4—61no—
290C3×D4—61no—
291C3×D4—61no—
292C3×D4—62no—
293C3×D4—61no—
294C3×D4—81no—
295C3×D4—82no—
296C3×D4—81no—
297C3×D4C22×A411yescharacteristic
298C2×C3×C4—21no—
299C2×C3×C4—32no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—31no—
304C2×C3×C4—31no—
305C2×C3×C4—31no—
306C2×C3×C4—31no—
307C2×C3×C4—41no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—62no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—81no—
315C2×C3×C4—82no—
316C2×C3×C4—81no—
317C2×C3×C4—241no—
318C2×C3×C4C22×A411yescharacteristic
319C2×Dic3—21no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—61no—
324C2×Dic3—62no—
325Dic6—21no—
326Dic6—32no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330Dic6—61no—
331Dic6—62no—
332Dic6C22×A412yes—
333C3×C8—122no—
334C3⋊C8—32no—
335C3⋊C8C22×A412yes—
336C2×C32—41no—
337C2×C32—81no—
338C2×C32—161no—
339C24—21no—
340C24C3×#6711yescharacteristic
341#41—32no—
342#41—31no—
343#41—31no—
344#41—31no—
345#41—61no—
346#41—61no—
347#41—62no—
348#41—62no—
349#41—61no—
350#41—61no—
351#41D3×A411yescharacteristic
352C2×Q8—31no—
353C2×Q8—31no—
354C2×Q8—31no—
355C2×Q8—61no—
356C2×Q8—92no—
357C2×Q8—92no—
358C2×Q8—92no—
359C2×Q8—92no—
360C2×Q8—91no—
361C2×Q8—181no—
362C2×Q8—181no—
363C2×Q8—181no—
364C2×Q8—182no—
365C2×Q8—181no—
366C2×Q8—182no—
367C2×Q8—181no—
368C2×Q8—184no—
369C2×Q8—181no—
370C2×D4—31no—
371C2×D4—31no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C22×C4—21no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4—61no—
386C22×C4—62no—
387C22×C4—181no—
388C22×C4—182no—
389C22×C4—181no—
390C22×C4C3×#6711yescharacteristic
391C22×C4C22×C3×D311yescharacteristic
392Q16—32no—
393Q16—92no—
394Q16—92no—
395Q16—94no—
396Q16—92no—
397SD16—32no—
398SD16—92no—
399SD16—92no—
400SD16—94no—
401SD16—92no—
402M16—31no—
403M16—92no—
404M16—92no—
405M16—91no—
406C2×C8—92no—
407C2×C8—92no—
408C22×C3—21no—
409C22×C3—31no—
410C22×C3—31no—
411C22×C3—31no—
412C22×C3—41no—
413C22×C3—61no—
414C22×C3—61no—
415C22×C3—61no—
416C22×C3—61no—
417C22×C3—61no—
418C22×C3—81no—
419C22×C3—82no—
420C22×C3—81no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3C3×#13711yescharacteristic, complemented
426C22×C3D4×A411yescharacteristic
427A4—21no—
428A4#95111yescharacteristic, direct product factor
429C3×C4—21no—
430C3×C4—31no—
431C3×C4—31no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—61no—
435C3×C4—81no—
436C3×C4—82no—
437C3×C4—81no—
438C3×C4—81no—
439C3×C4—242no—
440C3×C4D4×A411yescharacteristic
441C3×C4C23×A411yescharacteristic
442Dic3—22no—
443Dic3—62no—
444C32—41noSylow
445C23—21no—
446C23—31no—
447C23—31no—
448C23—41no—
449C23—61no—
450C23—61no—
451C23—61no—
452C23—121no—
453C23C2×C3×#6711yescharacteristic
454Q8—32no—
455Q8—31no—
456Q8—61no—
457Q8—61no—
458Q8—61no—
459Q8—92no—
460Q8—182no—
461Q8—182no—
462Q8—182no—
463Q8—182no—
464Q8—181no—
465Q8C2×D3×A411yescharacteristic
466D4—21no—
467D4—31no—
468D4—61no—
469D4—61no—
470D4—61no—
471D4—61no—
472D4—62no—
473D4—61no—
474D4C2×D3×A411yescharacteristic
475C2×C4—21no—
476C2×C4—32no—
477C2×C4—31no—
478C2×C4—31no—
479C2×C4—31no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C4—181no—
495C2×C4—182no—
496C2×C4C2×D3×A411yescharacteristic
497C8—32no—
498C8—92no—
499C2×C3—21no—
500C2×C3—31no—
501C2×C3—31no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—61no—
505C2×C3—81no—
506C2×C3—81no—
507C2×C3—121no—
508C2×C3—161no—
509C2×C3—161no—
510C2×C3—162no—
511C2×C3C2×D4×A411yescharacteristic
512C22—21no—
513C22—31no—
514C22—31no—
515C22—31no—
516C22—61no—
517C22—61no—
518C22—61no—
519C22—61no—
520C22—61no—
521C22—121no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22C3×#95111yescharacteristic, complemented
526C22A4×#6711yescharacteristic
527C4—21no—
528C4—31no—
529C4—31no—
530C4—61no—
531C4—62no—
532C4—182no—
533C4A4×#6711yescharacteristic
534C4C22×D3×A411yescharacteristic
535C3—41no—
536C3—81no—
537C3A4×#13711yescharacteristic, complemented
538C2—21no—
539C2—31no—
540C2—31no—
541C2—41no—
542C2—61no—
543C2—121no—
544C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC2C2×A4×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC4C22×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C2×C3×D4
prime radicalC3×A4×#41C2
hypercenter#41D3×A4
hypocenterC22×C3C3×#137
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic6C2semidirect
3. A4×#216C2semidirect
4. A4×#214C2semidirect
5. A4×#208C2semidirect
6. C22×#951C3semidirect
19. C23×Dic6C2×C3semidirect
29. C22×#216C2×C3semidirect
30. C22×#214C2×C3semidirect
31. C22×#208C2×C3semidirect
90. #951A4direct (N × H)
186. C2×Dic6C2×A4semidirect
201. #216C2×A4semidirect
206. #214C2×A4semidirect
210. #208C2×A4semidirect
215. C3×A4#137semidirect
425. C22×C3C3×#137semidirect
428. A4#951direct (N × H)
525. C22C3×#951semidirect
537. C3A4×#137semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
C2×A4×Dic62
A4×#2162
A4×#2142
A4×#2082
C22×#9513
A4×#1373
C3×#9514