Finite Group Databasebeta

← A4×#893 #11923167

Subgroups — A4×#893 #11923167

Order 1152.

1182 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 129 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×D12C211yesmaximal, characteristic
2C2×C4×D3×A4C212yesmaximal, complemented
3C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C212yesmaximal, complemented
5C4×Dic3×A4C211yesmaximal, characteristic, complemented
6C22×#893C311yesmaximal, characteristic, complemented
7C4×D4×A4—31nomaximal
8C22×D3×A4C2212yes—
9C2×C3×C4×A4C2212yes—
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2211yescharacteristic
12C2×Dic3×A4C2211yescharacteristic
13A4×D12C414yescomplemented
14C4×D3×A4—24no—
15C3×#893—41nomaximal
16C23×D12C2×C311yescharacteristic
17C23×C4×D3C2×C312yescomplemented
18C2×D4×A4—31no—
19C22×C4×A4—32no—
20C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
21C22×(C2×D3)⋊C4C2×C312yescomplemented
22C22×C4×Dic3C2×C311yescharacteristic, complemented
23C2×#893—31no—
24C2×#893—31no—
25C2×#893—32no—
26C2×#893—31no—
27C2×#893—32no—
28C2×#893—31no—
29A4×C4⋊C4—21no—
30A4×C4⋊C4D311yescharacteristic, complemented
31A4×C22⋊C4—32no—
32C42×A4—31no—
33C22×C3×A4C2311yescharacteristic
34C2×D3×A4—22no—
35C2×D3×A4—22no—
36C2×D3×A4C2×C414yescomplemented
37C2×C3×D12—41no—
38C2×C3×C4×D3—42no—
39C3×C4×A4—22no—
40C3×C4×A4C2×C412yescomplemented
41Dic3×A4—21no—
42Dic3×A4D412yescomplemented
43C32×C4⋊C4—41no—
44C3×(C2×D3)⋊C4—42no—
45C3×C4×Dic3—41no—
46C22×C4×D4—31noSylow
47C24×D3C22×C312yes—
48C23×A4—32no—
49C23×C3×C4C22×C312yes—
50C23×C3×C4C22×C311yescharacteristic
51C23×Dic3C22×C311yescharacteristic
52C23×Dic3C22×C311yescharacteristic
53C22×D12—31no—
54C22×D12—34no—
55C22×D12—32no—
56C22×D12—31no—
57C22×D12C3×C414yescomplemented
58C22×C4×D3—24no—
59C22×C4×D3—32no—
60C22×C4×D3—32no—
61C22×C4×D3—32no—
62C22×C4×D3—32no—
63C22×C4×D3—64no—
64D4×A4—34no—
65C2×C4×A4—21no—
66C2×C4×A4—22no—
67C2×C4×A4—31no—
68C2×C4×A4—31no—
69C2×C4×A4—64no—
70C2×C4×A4C2×D312yes—
71C2×C4×A4C2×D311yescharacteristic
72C3×C4×D4—121no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—32no—
76C2×(C2×D3)⋊C4—32no—
77C2×(C2×D3)⋊C4—32no—
78C2×(C2×D3)⋊C4—32no—
79C2×(C2×D3)⋊C4—32no—
80C2×C4×Dic3—31no—
81C2×C4×Dic3—31no—
82C2×C4×Dic3—31no—
83C2×C4×Dic3—31no—
84#893—34no—
85#893—34no—
86#893—32no—
87#893—32no—
88#893—32no—
89#893—31no—
90#893—32no—
91#893—31no—
92#893—32no—
93#893—31no—
94#893A411yescharacteristic, direct product factor
95C22×C3×D3—42no—
96C2×C3×A4C22×C411yescharacteristic
97C2×C3×A4C2×D411yescharacteristic
98C2×C3×A4#4111yescharacteristic
99D3×A4—24no—
100C2×C32×C4—41no—
101C2×C32×C4—42no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C3×D12—44no—
105C3×C4×D3—84no—
106C23×D4—31no—
107C24×C4—32no—
108C2×C4×D4—91no—
109C2×C4×D4—91no—
110C2×C4×D4—92no—
111C2×C4×D4—91no—
112C2×C4×D4—92no—
113C2×C4×D4—91no—
114C22×C4⋊C4C3×D311yescharacteristic, complemented
115C22×C22⋊C4—32no—
116C22×C42—31no—
117C24×C3C23×C311yescharacteristic
118C23×D3—22no—
119C23×D3—22no—
120C23×D3—32no—
121C23×D3—32no—
122C23×D3—34no—
123C23×D3—62no—
124C23×D3—62no—
125C23×D3C2×C3×C414yescomplemented
126C22×A4—21no—
127C22×A4—34no—
128C22×A4—62no—
129C22×A4—62no—
130C22×A4C22×D311yescharacteristic
131C2×C3×D4—121no—
132C22×C3×C4—22no—
133C22×C3×C4—31no—
134C22×C3×C4—31no—
135C22×C3×C4—32no—
136C22×C3×C4—32no—
137C22×C3×C4—32no—
138C22×C3×C4—62no—
139C22×C3×C4—122no—
140C22×C3×C4C2×C3×C412yescomplemented
141C22×Dic3—21no—
142C22×Dic3—31no—
143C22×Dic3—31no—
144C22×Dic3—32no—
145C22×Dic3—31no—
146C22×Dic3—31no—
147C22×Dic3—61no—
148C22×Dic3C3×D412yescomplemented
149C2×D12—32no—
150C2×D12—38no—
151C2×D12—34no—
152C2×D12—32no—
153C2×D12—31no—
154C2×D12—34no—
155C2×D12—34no—
156C2×D12—38no—
157C2×D12—34no—
158C2×D12C2×A411yescharacteristic
159C2×C4×D3—34no—
160C2×C4×D3—32no—
161C2×C4×D3—32no—
162C2×C4×D3—32no—
163C2×C4×D3—64no—
164C2×C4×D3—64no—
165C2×C4×D3—64no—
166C2×C4×D3—64no—
167C2×C4×D3—64no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×C4×D3—64no—
171C2×C4×D3C2×A412yescomplemented
172C4×A4—22no—
173C4×A4—22no—
174C4×A4—32no—
175C4×A4—42no—
176C4×A4—61no—
177C4×A4C4×D312yescomplemented
178C3×C4⋊C4—32no—
179C3×C4⋊C4—32no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—81no—
183C3×C4⋊C4C2×A411yescharacteristic, complemented
184C3×C22⋊C4—122no—
185C3×C42—121no—
186(C2×D3)⋊C4—34no—
187(C2×D3)⋊C4—32no—
188(C2×D3)⋊C4—32no—
189(C2×D3)⋊C4—32no—
190(C2×D3)⋊C4C2×A412yescomplemented
191C4×Dic3—32no—
192C4×Dic3—31no—
193C4×Dic3—31no—
194C4×Dic3—31no—
195C4×Dic3C2×A411yescharacteristic, complemented
196C22×C32—41no—
197C2×C3×D3—44no—
198C2×C3×D3—82no—
199C2×C3×D3—82no—
200C3×A4C4×D411yescharacteristic, complemented
201C32×C4—42no—
202C32×C4—82no—
203C3×Dic3—42no—
204C3×Dic3—81no—
205C25—32no—
206C22×D4—34no—
207C22×D4—91no—
208C22×D4—91no—
209C22×D4—92no—
210C22×D4—94no—
211C23×C4—31no—
212C23×C4—31no—
213C23×C4—64no—
214C23×C4—92no—
215C23×C4—92no—
216C23×C4—92no—
217C23×C4—92no—
218C23×C4—184no—
219C23×C4C2×C3×D312yes—
220C23×C4C2×C3×D311yescharacteristic
221C4×D4—31no—
222C4×D4—91no—
223C4×D4—92no—
224C4×D4—92no—
225C4×D4—91no—
226C4×D4—92no—
227C4×D4—92no—
228C4×D4—94no—
229C4×D4—94no—
230C4×D4—92no—
231C4×D4—91no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—31no—
234C2×C4⋊C4—32no—
235C2×C22⋊C4—92no—
236C2×C22⋊C4—92no—
237C2×C22⋊C4—92no—
238C2×C22⋊C4—92no—
239C2×C42—91no—
240C2×C42—91no—
241C2×C42—91no—
242C2×C42—91no—
243C23×C3—31no—
244C23×C3—31no—
245C23×C3—31no—
246C23×C3—31no—
247C23×C3—122no—
248C23×C3C22×C3×C411yescharacteristic
249C23×C3C2×C3×D411yescharacteristic
250C23×C3C3×#4111yescharacteristic
251C22×D3—24no—
252C22×D3—34no—
253C22×D3—32no—
254C22×D3—34no—
255C22×D3—34no—
256C22×D3—34no—
257C22×D3—62no—
258C22×D3—62no—
259C22×D3—62no—
260C22×D3—62no—
261C22×D3—68no—
262C22×D3—62no—
263C22×D3—62no—
264C22×D3—64no—
265C22×D3—64no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—64no—
269C22×D3C22×A412yes—
270C2×A4—21no—
271C2×A4—21no—
272C2×A4—21no—
273C2×A4—64no—
274C2×A4C2×C4×D311yescharacteristic
275C2×A4D3×D411yescharacteristic
276C2×A4#23911yescharacteristic
277C3×D4—124no—
278C2×C3×C4—32no—
279C2×C3×C4—31no—
280C2×C3×C4—32no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4—32no—
284C2×C3×C4—41no—
285C2×C3×C4—42no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—81no—
291C2×C3×C4—82no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—244no—
295C2×C3×C4C22×A412yes—
296C2×C3×C4C22×A411yescharacteristic
297C2×Dic3—32no—
298C2×Dic3—31no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—31no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3C22×A411yescharacteristic
308C2×Dic3C22×A411yescharacteristic
309D12—38no—
310D12—38no—
311D12—34no—
312D12C4×A414yescomplemented
313C4×D3—24no—
314C4×D3—64no—
315C4×D3—64no—
316C4×D3—68no—
317C4×D3—64no—
318C2×C32—41no—
319C2×C32—41no—
320C2×C32—41no—
321C3×D3—84no—
322C24—34no—
323C24—62no—
324C24—62no—
325C24—92no—
326C24—92no—
327C24—94no—
328C24—182no—
329C24—182no—
330C24C22×C3×D311yescharacteristic
331C2×D4—31no—
332C2×D4—94no—
333C2×D4—94no—
334C2×D4—92no—
335C2×D4—92no—
336C2×D4—98no—
337C2×D4—94no—
338C2×D4—94no—
339C2×D4—98no—
340C2×D4—91no—
341C22×C4—22no—
342C22×C4—31no—
343C22×C4—31no—
344C22×C4—32no—
345C22×C4—32no—
346C22×C4—32no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—62no—
350C22×C4—61no—
351C22×C4—92no—
352C22×C4—91no—
353C22×C4—91no—
354C22×C4—92no—
355C22×C4—94no—
356C22×C4—91no—
357C22×C4—92no—
358C22×C4—92no—
359C22×C4—91no—
360C22×C4—184no—
361C22×C4—184no—
362C22×C4—184no—
363C22×C4—184no—
364C22×C4—184no—
365C22×C4—184no—
366C22×C4—184no—
367C22×C4—184no—
368C22×C4—181no—
369C22×C4C3×C4×D312yescomplemented
370C4⋊C4—32no—
371C4⋊C4—32no—
372C4⋊C4—31no—
373C4⋊C4D3×A411yescharacteristic, complemented
374C22⋊C4—32no—
375C22⋊C4—92no—
376C22⋊C4—92no—
377C22⋊C4—94no—
378C22⋊C4—92no—
379C42—31no—
380C42—91no—
381C42—91no—
382C42—92no—
383C42—91no—
384C22×C3—31no—
385C22×C3—31no—
386C22×C3—31no—
387C22×C3—32no—
388C22×C3—31no—
389C22×C3—31no—
390C22×C3—31no—
391C22×C3—31no—
392C22×C3—31no—
393C22×C3—31no—
394C22×C3—41no—
395C22×C3—81no—
396C22×C3—124no—
397C22×C3—242no—
398C22×C3—242no—
399C22×C3C3×C4×D411yescharacteristic, complemented
400C22×C3C23×A411yescharacteristic
401C2×D3—22no—
402C2×D3—22no—
403C2×D3—34no—
404C2×D3—64no—
405C2×D3—64no—
406C2×D3—64no—
407C2×D3—64no—
408C2×D3—64no—
409C2×D3—64no—
410C2×D3—62no—
411C2×D3—62no—
412C2×D3—64no—
413C2×D3—64no—
414C2×D3C2×C4×A414yescomplemented
415A4—21no—
416A4#89311yescharacteristic, direct product factor
417C3×C4—22no—
418C3×C4—32no—
419C3×C4—42no—
420C3×C4—62no—
421C3×C4—82no—
422C3×C4—82no—
423C3×C4—122no—
424C3×C4—162no—
425C3×C4—241no—
426C3×C4C2×C4×A412yescomplemented
427Dic3—21no—
428Dic3—32no—
429Dic3—61no—
430Dic3D4×A412yescomplemented
431C32—41noSylow
432C23—31no—
433C23—31no—
434C23—31no—
435C23—31no—
436C23—32no—
437C23—64no—
438C23—94no—
439C23—94no—
440C23—94no—
441C23—94no—
442C23—92no—
443C23—182no—
444C23—182no—
445C23—182no—
446C23—182no—
447C23—184no—
448C23—182no—
449C23—182no—
450C23—184no—
451C23—184no—
452C23—182no—
453C23—182no—
454C23—188no—
455C23C2×C3×C4×D311yescharacteristic
456C23C3×D3×D411yescharacteristic
457C23C3×#23911yescharacteristic
458D4—34no—
459D4—98no—
460D4—98no—
461D4—94no—
462C2×C4—32no—
463C2×C4—31no—
464C2×C4—31no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—31no—
469C2×C4—32no—
470C2×C4—64no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—91no—
479C2×C4—92no—
480C2×C4—91no—
481C2×C4—184no—
482C2×C4—184no—
483C2×C4—184no—
484C2×C4—188no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4C2×D3×A412yes—
490C2×C4C2×D3×A411yescharacteristic
491C2×C3—31no—
492C2×C3—31no—
493C2×C3—31no—
494C2×C3—31no—
495C2×C3—41no—
496C2×C3—41no—
497C2×C3—41no—
498C2×C3—81no—
499C2×C3—81no—
500C2×C3—81no—
501C2×C3—244no—
502C2×C3C22×C4×A411yescharacteristic
503C2×C3C2×D4×A411yescharacteristic
504C2×C3A4×#4111yescharacteristic
505D3—24no—
506D3—64no—
507C22—31no—
508C22—31no—
509C22—31no—
510C22—32no—
511C22—31no—
512C22—31no—
513C22—31no—
514C22—31no—
515C22—31no—
516C22—31no—
517C22—34no—
518C22—62no—
519C22—62no—
520C22—94no—
521C22—184no—
522C22—184no—
523C22—184no—
524C22—184no—
525C22—184no—
526C22—184no—
527C22—184no—
528C22—184no—
529C22—182no—
530C22—182no—
531C22C3×#89311yescharacteristic, complemented
532C22C22×D3×A411yescharacteristic
533C4—22no—
534C4—32no—
535C4—32no—
536C4—62no—
537C4—61no—
538C4—92no—
539C4—181no—
540C4C4×D3×A412yescomplemented
541C3—41no—
542C3—81no—
543C3C4×D4×A411yescharacteristic, complemented
544C2—31no—
545C2—31no—
546C2—31no—
547C2—31no—
548C2—64no—
549C2—184no—
550C2C2×C4×D3×A411yescharacteristic
551C2D3×D4×A411yescharacteristic
552C2A4×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutatorC23×C3C22×C3×C4
FittingC22×C3×C4⋊C4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC2×A4×D12C2
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C3×C4×D4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×A4C2semidirect
3. C3×A4×C4⋊C4C2semidirect
4. A4×(C2×D3)⋊C4C2semidirect
5. C4×Dic3×A4C2semidirect
6. C22×#893C3semidirect
13. A4×D12C4semidirect
17. C23×C4×D3C2×C3semidirect
20. C22×C3×C4⋊C4C2×C3semidirect
21. C22×(C2×D3)⋊C4C2×C3semidirect
22. C22×C4×Dic3C2×C3semidirect
30. A4×C4⋊C4D3semidirect
36. C2×D3×A4C2×C4semidirect
40. C3×C4×A4C2×C4semidirect
42. Dic3×A4D4semidirect
57. C22×D12C3×C4semidirect
94. #893A4direct (N × H)
114. C22×C4⋊C4C3×D3semidirect
125. C23×D3C2×C3×C4semidirect
140. C22×C3×C4C2×C3×C4semidirect
148. C22×Dic3C3×D4semidirect
171. C2×C4×D3C2×A4semidirect
177. C4×A4C4×D3semidirect
183. C3×C4⋊C4C2×A4semidirect
190. (C2×D3)⋊C4C2×A4semidirect
195. C4×Dic3C2×A4semidirect
200. C3×A4C4×D4semidirect
312. D12C4×A4semidirect
369. C22×C4C3×C4×D3semidirect
373. C4⋊C4D3×A4semidirect
399. C22×C3C3×C4×D4semidirect
414. C2×D3C2×C4×A4semidirect
416. A4#893direct (N × H)
426. C3×C4C2×C4×A4semidirect
430. Dic3D4×A4semidirect
531. C22C3×#893semidirect
540. C4C4×D3×A4semidirect
543. C3C4×D4×A4semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D122
C2×C4×D3×A42
C3×A4×C4⋊C42
A4×(C2×D3)⋊C42
C4×Dic3×A42
C22×#8933
C4×D4×A43
C3×#8934