Finite Group Databasebeta

← A4×#942 #11923367

Subgroups — A4×#942 #11923367

Order 1152.

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

normal subgroups only

This group has 726 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
1C2×C3×Q8×A4C211yesmaximal, characteristic, complemented
2A4×#235C211yesmaximal, characteristic
3A4×#216C212yesmaximal, complemented
4A4×#215C212yesmaximal, complemented
5A4×#208C211yesmaximal, characteristic, complemented
6C22×#942C311yesmaximal, characteristic, complemented
7A4×#137—31nomaximal
8C3×Q8×A4—21no—
9C3×Q8×A4C2212yes—
10C2×C3×C4×A4—21no—
11C2×C3×C4×A4C2211yescharacteristic
12A4×#67—21no—
13A4×D12C2211yescharacteristic
14C4×D3×A4—21no—
15A4×Dic6C2211yescharacteristic
16C3×#942—41nomaximal
17A4×C3⋊C8C2212yes—
18C23×C3×Q8C2×C311yescharacteristic, complemented
19C22×#235C2×C311yescharacteristic
20A4×#41—31no—
21C2×Q8×A4—21no—
22C2×Q8×A4D311yescharacteristic, complemented
23C22×#216C2×C312yescomplemented
24C2×#942—31no—
25C2×#942—31no—
26C2×#942—32no—
27C2×#942—31no—
28C2×#942—31no—
29C2×#942—32no—
30C22×#215C2×C312yescomplemented
31C22×#208C2×C311yescharacteristic, complemented
32A4×Q16—32no—
33A4×SD16—32no—
34A4×M16—31no—
35C22×C3×A4D411yescharacteristic
36C2×D3×A4—21no—
37C2×C32×Q8—41no—
38C3×#235—41no—
39C3×C4×A4—22no—
40C3×C4×A4D411yescharacteristic
41C3×C4×A4C2311yescharacteristic
42Dic3×A4—21no—
43C3×#216—42no—
44C3×#215—42no—
45C3×#208—41no—
46C22×#137—31noSylow
47C22×C3×Q8—21no—
48C22×C3×Q8—31no—
49C22×C3×Q8—32no—
50C22×C3×Q8—31no—
51C22×C3×Q8—61no—
52C22×C3×Q8—61no—
53C22×C3×Q8C22×C312yes—
54C23×C3×C4—21no—
55C23×C3×C4C22×C311yescharacteristic
56C22×#67—21no—
57C2×#235—31no—
58C2×#235—31no—
59C2×#235—31no—
60C2×#235—31no—
61C2×#235—61no—
62C2×#235—61no—
63C22×D12C22×C311yescharacteristic
64C22×C4×D3—21no—
65C22×Dic6C22×C311yescharacteristic
66Q8×A4—22no—
67Q8×A4—21no—
68Q8×A4—22no—
69Q8×A4—31no—
70Q8×A4C2×D312yes—
71D4×A4—31no—
72D4×A4—61no—
73C2×C4×A4—22no—
74C2×C4×A4—21no—
75C2×C4×A4—21no—
76C2×C4×A4—61no—
77C2×C4×A4C2×D311yescharacteristic
78C3×#137—121no—
79C2×#216—32no—
80C2×#216—32no—
81C2×#216—32no—
82C2×#216—32no—
83#942—32no—
84#942—34no—
85#942—32no—
86#942—32no—
87#942—34no—
88#942—31no—
89#942—31no—
90#942—32no—
91#942—32no—
92#942—31no—
93#942A411yescharacteristic, direct product factor
94C2×#215—32no—
95C2×#215—32no—
96C2×#215—32no—
97C2×#215—32no—
98C2×#208—31no—
99C2×#208—32no—
100C2×#208—31no—
101C22×C3⋊C8C22×C312yes—
102C8×A4—32no—
103C2×C3×A4—21no—
104C2×C3×A4C2×D411yescharacteristic
105D3×A4—41no—
106C32×Q8—42no—
107C32×Q8—81no—
108C2×C32×C4—41no—
109C2×C32×C4—81no—
110C3×#67—81no—
111C3×D12—41no—
112C3×C4×D3—81no—
113C3×Dic6—41no—
114C3×C3⋊C8—42no—
115C22×#41—31no—
116C23×Q8C3×D311yescharacteristic, complemented
117C2×#137—91no—
118C2×#137—91no—
119C2×#137—92no—
120C2×#137—92no—
121C2×#137—91no—
122C2×#137—91no—
123C22×Q16—32no—
124C22×SD16—32no—
125C22×M16—31no—
126C24×C3C3×D411yescharacteristic
127C23×D3—21no—
128C22×A4—21no—
129C22×A4—61no—
130C22×A4#6711yescharacteristic
131C3×#41—121no—
132C2×C3×Q8—32no—
133C2×C3×Q8—32no—
134C2×C3×Q8—32no—
135C2×C3×Q8—32no—
136C2×C3×Q8—31no—
137C2×C3×Q8—41no—
138C2×C3×Q8—61no—
139C2×C3×Q8—61no—
140C2×C3×Q8—61no—
141C2×C3×Q8—62no—
142C2×C3×Q8—61no—
143C2×C3×Q8—62no—
144C2×C3×Q8—61no—
145C2×C3×Q8—64no—
146C2×C3×Q8—61no—
147C2×C3×Q8—81no—
148C2×C3×Q8C2×A411yescharacteristic, complemented
149C22×C3×C4—22no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—61no—
155C22×C3×C4—62no—
156C22×C3×C4—61no—
157C22×C3×C4C3×D411yescharacteristic
158C22×C3×C4C23×C311yescharacteristic
159C2×#67—61no—
160C2×#67—61no—
161C2×#67—61no—
162C2×#67—61no—
163C22×Dic3—21no—
164#235—32no—
165#235—31no—
166#235—31no—
167#235—31no—
168#235—61no—
169#235—61no—
170#235—62no—
171#235—62no—
172#235—61no—
173#235—61no—
174#235C2×A411yescharacteristic
175C2×D12—31no—
176C2×D12—31no—
177C2×D12—61no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×Dic6—31no—
183C2×Dic6—31no—
184C2×Dic6—61no—
185C4×A4—24no—
186C4×A4—22no—
187C4×A4—21no—
188C4×A4—21no—
189C4×A4—61no—
190C4×A4#6711yescharacteristic
191C4×A4C22×D311yescharacteristic
192C3×Q16—122no—
193C3×SD16—122no—
194C3×M16—121no—
195#216—34no—
196#216—32no—
197#216—32no—
198#216—32no—
199#216C2×A412yescomplemented
200#215—34no—
201#215—32no—
202#215—32no—
203#215—32no—
204#215C2×A412yescomplemented
205#208—32no—
206#208—31no—
207#208—32no—
208#208C2×A411yescharacteristic, complemented
209C2×C3⋊C8—32no—
210C2×C3⋊C8—32no—
211C22×C32—41no—
212C2×C3×D3—81no—
213C3×A4#13711yescharacteristic, complemented
214C32×C4—41no—
215C32×C4—41no—
216C32×C4—82no—
217C3×Dic3—81no—
218C2×#41—91no—
219C2×#41—91no—
220C2×#41—91no—
221C2×#41—91no—
222C2×#41—181no—
223C2×#41—181no—
224C22×Q8—21no—
225C22×Q8—31no—
226C22×Q8—32no—
227C22×Q8—31no—
228C22×Q8—31no—
229C22×Q8—61no—
230C22×Q8—61no—
231C22×Q8C2×C3×D312yes—
232C22×D4—31no—
233C22×D4—61no—
234C23×C4—21no—
235C23×C4—61no—
236C23×C4C2×C3×D311yescharacteristic
237#137—31no—
238#137—91no—
239#137—92no—
240#137—92no—
241#137—91no—
242#137—94no—
243#137—92no—
244#137—92no—
245#137—94no—
246#137—92no—
247#137—91no—
248C2×Q16—92no—
249C2×Q16—92no—
250C2×Q16—92no—
251C2×Q16—92no—
252C2×SD16—92no—
253C2×SD16—92no—
254C2×SD16—92no—
255C2×SD16—92no—
256C2×M16—91no—
257C2×M16—92no—
258C2×M16—91no—
259C22×C8—32no—
260C23×C3—21no—
261C23×C3—31no—
262C23×C3—31no—
263C23×C3—61no—
264C23×C3C2×C3×D411yescharacteristic
265C22×D3—41no—
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—121no—
269C2×A4—22no—
270C2×A4—21no—
271C2×A4—21no—
272C2×A4—121no—
273C2×A4C2×#6711yescharacteristic
274C3×Q8—21no—
275C3×Q8—32no—
276C3×Q8—42no—
277C3×Q8—62no—
278C3×Q8—62no—
279C3×Q8—62no—
280C3×Q8—62no—
281C3×Q8—61no—
282C3×Q8—81no—
283C3×Q8—82no—
284C3×Q8—82no—
285C3×Q8—121no—
286C3×Q8C22×A412yes—
287C3×D4—121no—
288C3×D4—241no—
289C2×C3×C4—21no—
290C2×C3×C4—32no—
291C2×C3×C4—31no—
292C2×C3×C4—31no—
293C2×C3×C4—31no—
294C2×C3×C4—31no—
295C2×C3×C4—31no—
296C2×C3×C4—31no—
297C2×C3×C4—31no—
298C2×C3×C4—41no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—61no—
303C2×C3×C4—62no—
304C2×C3×C4—81no—
305C2×C3×C4—82no—
306C2×C3×C4—81no—
307C2×C3×C4—241no—
308C2×C3×C4C22×A411yescharacteristic
309#67—21no—
310#67—61no—
311#67—61no—
312#67—62no—
313#67—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316D12—31no—
317D12—61no—
318D12—61no—
319D12C22×A411yescharacteristic
320C4×D3—21no—
321C4×D3—61no—
322C4×D3—61no—
323C4×D3—62no—
324C4×D3—61no—
325Dic6—31no—
326Dic6—61no—
327Dic6—61no—
328Dic6C22×A411yescharacteristic
329C3×C8—122no—
330C3⋊C8—32no—
331C3⋊C8C22×A412yes—
332C2×C32—41no—
333C2×C32—81no—
334C3×D3—161no—
335C24—61no—
336C24C3×#6711yescharacteristic
337#41—31no—
338#41—91no—
339#41—91no—
340#41—92no—
341#41—91no—
342#41—181no—
343#41—181no—
344#41—182no—
345#41—182no—
346#41—181no—
347#41—181no—
348C2×Q8—32no—
349C2×Q8—32no—
350C2×Q8—32no—
351C2×Q8—32no—
352C2×Q8—31no—
353C2×Q8—61no—
354C2×Q8—61no—
355C2×Q8—61no—
356C2×Q8—62no—
357C2×Q8—61no—
358C2×Q8—62no—
359C2×Q8—61no—
360C2×Q8—64no—
361C2×Q8—61no—
362C2×Q8—91no—
363C2×Q8—91no—
364C2×Q8—181no—
365C2×Q8D3×A411yescharacteristic, complemented
366C2×D4—91no—
367C2×D4—91no—
368C2×D4—181no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4—181no—
372C2×D4—181no—
373C22×C4—22no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—61no—
379C22×C4—62no—
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—181no—
383C22×C4—181no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4C3×#6711yescharacteristic
387C22×C4C22×C3×D311yescharacteristic
388Q16—32no—
389Q16—92no—
390Q16—92no—
391Q16—94no—
392Q16—92no—
393SD16—32no—
394SD16—92no—
395SD16—92no—
396SD16—94no—
397SD16—92no—
398M16—31no—
399M16—92no—
400M16—92no—
401M16—91no—
402C2×C8—92no—
403C2×C8—92no—
404C22×C3—31no—
405C22×C3—31no—
406C22×C3—31no—
407C22×C3—41no—
408C22×C3—61no—
409C22×C3—61no—
410C22×C3—61no—
411C22×C3—61no—
412C22×C3—81no—
413C22×C3—241no—
414C22×C3C3×#13711yescharacteristic, complemented
415C22×C3D4×A411yescharacteristic
416C2×D3—21no—
417C2×D3—61no—
418C2×D3—121no—
419C2×D3—121no—
420C2×D3—121no—
421C2×D3—121no—
422A4—21no—
423A4#94211yescharacteristic, direct product factor
424C3×C4—22no—
425C3×C4—31no—
426C3×C4—31no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—62no—
430C3×C4—82no—
431C3×C4—84no—
432C3×C4—81no—
433C3×C4—81no—
434C3×C4—241no—
435C3×C4D4×A411yescharacteristic
436C3×C4C23×A411yescharacteristic
437Dic3—21no—
438Dic3—61no—
439C32—41noSylow
440C23—21no—
441C23—31no—
442C23—31no—
443C23—61no—
444C23—121no—
445C23—181no—
446C23—181no—
447C23—361no—
448C23C2×C3×#6711yescharacteristic
449Q8—21no—
450Q8—32no—
451Q8—31no—
452Q8—62no—
453Q8—62no—
454Q8—62no—
455Q8—62no—
456Q8—61no—
457Q8—91no—
458Q8—181no—
459Q8—181no—
460Q8C2×D3×A412yes—
461D4—31no—
462D4—61no—
463D4—91no—
464D4—181no—
465D4—181no—
466D4—181no—
467D4—181no—
468D4—182no—
469D4—181no—
470C2×C4—21no—
471C2×C4—32no—
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—31no—
477C2×C4—31no—
478C2×C4—31no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—182no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4C2×D3×A411yescharacteristic
492C8—32no—
493C8—92no—
494C2×C3—21no—
495C2×C3—31no—
496C2×C3—31no—
497C2×C3—41no—
498C2×C3—61no—
499C2×C3—81no—
500C2×C3—82no—
501C2×C3—81no—
502C2×C3—481no—
503C2×C3C2×D4×A411yescharacteristic
504D3—41no—
505D3—121no—
506C22—31no—
507C22—31no—
508C22—31no—
509C22—61no—
510C22—61no—
511C22—61no—
512C22—61no—
513C22—61no—
514C22—181no—
515C22—361no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22C3×#94211yescharacteristic, complemented
520C22A4×#6711yescharacteristic
521C4—22no—
522C4—31no—
523C4—31no—
524C4—62no—
525C4—61no—
526C4—181no—
527C4A4×#6711yescharacteristic
528C4C22×D3×A411yescharacteristic
529C3—41no—
530C3—81no—
531C3A4×#13711yescharacteristic, complemented
532C2—21no—
533C2—31no—
534C2—31no—
535C2—61no—
536C2—121no—
537C2—361no—
538C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC2C2×A4×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC4C22×D3×A4
FittingC23×C3×Q8C2×C3
socleC23×C3C2×C3×D4
prime radicalA4×#235C2
hypercenterC2×Q8D3×A4
hypocenterC22×C3C3×#137
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×A4C2semidirect
3. A4×#216C2semidirect
4. A4×#215C2semidirect
5. A4×#208C2semidirect
6. C22×#942C3semidirect
18. C23×C3×Q8C2×C3semidirect
22. C2×Q8×A4D3semidirect
23. C22×#216C2×C3semidirect
30. C22×#215C2×C3semidirect
31. C22×#208C2×C3semidirect
93. #942A4direct (N × H)
116. C23×Q8C3×D3semidirect
148. C2×C3×Q8C2×A4semidirect
199. #216C2×A4semidirect
204. #215C2×A4semidirect
208. #208C2×A4semidirect
213. C3×A4#137semidirect
365. C2×Q8D3×A4semidirect
414. C22×C3C3×#137semidirect
423. A4#942direct (N × H)
519. C22C3×#942semidirect
531. C3A4×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
A4×#2352
A4×#2162
A4×#2152
A4×#2082
C22×#9423
A4×#1373
C3×#9424