Finite Group Databasebeta

← A4×#935 #11923354

Subgroups — A4×#935 #11923354

Order 1152.

970 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 970 conjugacy classes of subgroups — too many to draw. Only its 99 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×D4×A4C211yesmaximal, characteristic
2C22×Dic3×A4C211yesmaximal, characteristic, complemented
3A4×#217C212yesmaximal, complemented
4A4×#217C211yesmaximal, characteristic, complemented
5A4×Dic3⋊C4C212yesmaximal, complemented
6C22×#935C311yesmaximal, characteristic, complemented
7A4×#123—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C23×C3×A4C2211yescharacteristic
10C3×D4×A4—22no—
11C2×C3×C4×A4C2211yescharacteristic
12C2×Dic3×A4—22no—
13C2×Dic3×A4C2212yes—
14C2×Dic3×A4C2212yes—
15C3×#935—41nomaximal
16C23×C3×D4C2×C311yescharacteristic
17C24×Dic3C2×C311yescharacteristic, complemented
18C2×D4×A4—21no—
19C2×D4×A4D311yescharacteristic
20C22×C4×A4—31no—
21C22×#217C2×C312yescomplemented
22C22×#217C2×C311yescharacteristic, complemented
23C2×#935—31no—
24C2×#935—32no—
25C2×#935—31no—
26C2×#935—31no—
27C2×#935—31no—
28C2×#935—32no—
29C22×Dic3⋊C4C2×C312yescomplemented
30A4×C4⋊C4—32no—
31A4×C22⋊C4—32no—
32A4×C22⋊C4—31no—
33C22×C3×A4—22no—
34C22×C3×A4—21no—
35C22×C3×A4—22no—
36C22×C3×A4D412yes—
37C22×C3×A4C2311yescharacteristic
38C2×C32×D4—41no—
39C22×C3×Dic3—41no—
40C3×C4×A4—21no—
41Dic3×A4—22no—
42Dic3×A4—22no—
43C3×#217—41no—
44C3×#217—42no—
45C3×Dic3⋊C4—42no—
46C22×#123—31noSylow
47C25×C3C22×C311yescharacteristic
48C25×C3C22×C311yescharacteristic
49C23×A4—21no—
50C23×A4—21no—
51C23×A4C2×D311yescharacteristic
52C23×A4C2×D311yescharacteristic
53C22×C3×D4—22no—
54C22×C3×D4—31no—
55C22×C3×D4—31no—
56C22×C3×D4—31no—
57C22×C3×D4—31no—
58C22×C3×D4—62no—
59C23×C3×C4C22×C311yescharacteristic
60C23×Dic3—22no—
61C23×Dic3—31no—
62C23×Dic3—31no—
63C23×Dic3—32no—
64C23×Dic3—62no—
65C23×Dic3C22×C312yes—
66C23×Dic3C22×C312yes—
67D4×A4—24no—
68D4×A4—22no—
69C2×C4×A4—21no—
70C2×C4×A4—32no—
71C2×C4×A4—32no—
72C2×C4×A4—62no—
73C2×C4×A4C2×D311yescharacteristic
74C3×#123—121no—
75C2×#217—31no—
76C2×#217—32no—
77C2×#217—31no—
78C2×#217—32no—
79C2×#217—32no—
80C2×#217—32no—
81C2×#217—32no—
82#935—32no—
83#935—32no—
84#935—34no—
85#935—34no—
86#935—32no—
87#935—31no—
88#935—31no—
89#935—32no—
90#935—31no—
91#935—32no—
92#935A411yescharacteristic, direct product factor
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C23×C32—41no—
98C23×C32—41no—
99C2×C3×A4—22no—
100C2×C3×A4—41no—
101C2×C3×A4C2×D411yescharacteristic
102C2×C3×A4#4112yes—
103C32×D4—82no—
104C2×C32×C4—41no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3—82no—
108C23×D4C3×D311yescharacteristic
109C24×C4—31no—
110C2×#123—91no—
111C2×#123—91no—
112C2×#123—92no—
113C2×#123—92no—
114C2×#123—91no—
115C2×#123—91no—
116C22×C4⋊C4—32no—
117C22×C22⋊C4—31no—
118C22×C22⋊C4—32no—
119C24×C3—22no—
120C24×C3—21no—
121C24×C3—22no—
122C24×C3—31no—
123C24×C3—32no—
124C24×C3—31no—
125C24×C3—31no—
126C24×C3—31no—
127C24×C3—62no—
128C24×C3—62no—
129C24×C3—61no—
130C24×C3C3×D412yes—
131C24×C3C23×C311yescharacteristic
132C22×A4—22no—
133C22×A4—22no—
134C22×A4—22no—
135C22×A4—21no—
136C22×A4—22no—
137C22×A4—21no—
138C22×A4—42no—
139C22×A4—42no—
140C22×A4#6712yes—
141C22×A4C22×D311yescharacteristic
142C2×C3×D4—32no—
143C2×C3×D4—31no—
144C2×C3×D4—31no—
145C2×C3×D4—31no—
146C2×C3×D4—41no—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C2×C3×D4—62no—
150C2×C3×D4—62no—
151C2×C3×D4—62no—
152C2×C3×D4—62no—
153C2×C3×D4—62no—
154C2×C3×D4—62no—
155C2×C3×D4—81no—
156C2×C3×D4C2×A411yescharacteristic
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—61no—
161C22×C3×C4—121no—
162C22×Dic3—22no—
163C22×Dic3—22no—
164C22×Dic3—32no—
165C22×Dic3—31no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—32no—
170C22×Dic3—32no—
171C22×Dic3—62no—
172C22×Dic3—62no—
173C22×Dic3—64no—
174C22×Dic3—64no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3C2×A411yescharacteristic, complemented
180C4×A4—22no—
181C4×A4—21no—
182C4×A4—62no—
183C4×A4—62no—
184C3×C4⋊C4—122no—
185C3×C22⋊C4—121no—
186C3×C22⋊C4—122no—
187#217—32no—
188#217—34no—
189#217—31no—
190#217—32no—
191#217—32no—
192#217—32no—
193#217—32no—
194#217C2×A411yescharacteristic, complemented
195#217C2×A412yescomplemented
196Dic3⋊C4—34no—
197Dic3⋊C4—32no—
198Dic3⋊C4—32no—
199Dic3⋊C4—32no—
200Dic3⋊C4C2×A412yescomplemented
201C22×C32—42no—
202C22×C32—41no—
203C22×C32—81no—
204C22×C32—82no—
205C22×C32—82no—
206C3×A4#12311yescharacteristic, complemented
207C32×C4—81no—
208C3×Dic3—82no—
209C3×Dic3—82no—
210C25C2×C3×D311yescharacteristic
211C25C2×C3×D311yescharacteristic
212C22×D4—22no—
213C22×D4—31no—
214C22×D4—31no—
215C22×D4—31no—
216C22×D4—31no—
217C22×D4—62no—
218C23×C4—32no—
219C23×C4—32no—
220C23×C4—62no—
221C23×C4—91no—
222C23×C4—92no—
223C23×C4—91no—
224C23×C4—182no—
225C23×C4C2×C3×D311yescharacteristic
226#123—31no—
227#123—91no—
228#123—92no—
229#123—92no—
230#123—91no—
231#123—94no—
232#123—94no—
233#123—92no—
234#123—92no—
235#123—92no—
236#123—91no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—92no—
239C2×C4⋊C4—92no—
240C2×C4⋊C4—92no—
241C2×C22⋊C4—91no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—92no—
244C2×C22⋊C4—92no—
245C2×C22⋊C4—92no—
246C2×C22⋊C4—91no—
247C2×C22⋊C4—92no—
248C23×C3—22no—
249C23×C3—31no—
250C23×C3—32no—
251C23×C3—31no—
252C23×C3—32no—
253C23×C3—32no—
254C23×C3—32no—
255C23×C3—32no—
256C23×C3—31no—
257C23×C3—31no—
258C23×C3—41no—
259C23×C3—41no—
260C23×C3—41no—
261C23×C3—62no—
262C23×C3—62no—
263C23×C3—61no—
264C23×C3—61no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3—64no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3—64no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3—62no—
275C23×C3—62no—
276C23×C3—81no—
277C23×C3—81no—
278C23×C3—121no—
279C23×C3—122no—
280C23×C3—122no—
281C23×C3C2×C3×D411yescharacteristic
282C23×C3C3×#4112yes—
283C23×C3C22×A411yescharacteristic
284C23×C3C22×A411yescharacteristic
285C2×A4—22no—
286C2×A4—22no—
287C2×A4—21no—
288C2×A4—42no—
289C2×A4—42no—
290C2×A4—41no—
291C2×A4#23712yes—
292C2×A4C2×#6711yescharacteristic
293C3×D4—22no—
294C3×D4—62no—
295C3×D4—62no—
296C3×D4—64no—
297C3×D4—62no—
298C3×D4—82no—
299C3×D4—84no—
300C2×C3×C4—31no—
301C2×C3×C4—41no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—81no—
307C2×C3×C4—122no—
308C2×C3×C4—122no—
309C2×C3×C4—242no—
310C2×C3×C4C22×A411yescharacteristic
311C2×Dic3—22no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3C22×A412yes—
326C2×Dic3C22×A412yes—
327C2×C32—41no—
328C2×C32—42no—
329C2×C32—82no—
330C2×C32—161no—
331C24—22no—
332C24—22no—
333C24—21no—
334C24—31no—
335C24—32no—
336C24—31no—
337C24—31no—
338C24—31no—
339C24—62no—
340C24—61no—
341C24—62no—
342C24C3×#6712yes—
343C24C22×C3×D311yescharacteristic
344C2×D4—32no—
345C2×D4—31no—
346C2×D4—31no—
347C2×D4—31no—
348C2×D4—62no—
349C2×D4—62no—
350C2×D4—62no—
351C2×D4—62no—
352C2×D4—62no—
353C2×D4—62no—
354C2×D4—62no—
355C2×D4—62no—
356C2×D4D3×A411yescharacteristic
357C22×C4—21no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—61no—
362C22×C4—62no—
363C22×C4—62no—
364C22×C4—92no—
365C22×C4—92no—
366C22×C4—92no—
367C22×C4—92no—
368C22×C4—91no—
369C22×C4—92no—
370C22×C4—92no—
371C22×C4—182no—
372C22×C4—182no—
373C22×C4—184no—
374C22×C4—184no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—182no—
379C4⋊C4—32no—
380C4⋊C4—92no—
381C4⋊C4—92no—
382C4⋊C4—94no—
383C4⋊C4—92no—
384C22⋊C4—31no—
385C22⋊C4—32no—
386C22⋊C4—92no—
387C22⋊C4—92no—
388C22⋊C4—92no—
389C22⋊C4—92no—
390C22⋊C4—94no—
391C22⋊C4—91no—
392C22⋊C4—92no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—22no—
396C22×C3—31no—
397C22×C3—32no—
398C22×C3—32no—
399C22×C3—31no—
400C22×C3—31no—
401C22×C3—32no—
402C22×C3—32no—
403C22×C3—32no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—62no—
407C22×C3—64no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—64no—
412C22×C3—62no—
413C22×C3—61no—
414C22×C3—62no—
415C22×C3—82no—
416C22×C3—81no—
417C22×C3—82no—
418C22×C3—82no—
419C22×C3—82no—
420C22×C3—81no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3—122no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3—122no—
427C22×C3—162no—
428C22×C3—162no—
429C22×C3C3×#12311yescharacteristic, complemented
430C22×C3D4×A412yes—
431C22×C3C23×A411yescharacteristic
432A4—21no—
433A4#93511yescharacteristic, direct product factor
434C3×C4—21no—
435C3×C4—61no—
436C3×C4—81no—
437C3×C4—82no—
438C3×C4—242no—
439C3×C4—242no—
440Dic3—22no—
441Dic3—22no—
442Dic3—62no—
443Dic3—62no—
444C32—41noSylow
445C23—22no—
446C23—31no—
447C23—32no—
448C23—31no—
449C23—32no—
450C23—32no—
451C23—32no—
452C23—32no—
453C23—31no—
454C23—31no—
455C23—41no—
456C23—62no—
457C23—62no—
458C23—61no—
459C23—61no—
460C23—62no—
461C23—62no—
462C23—62no—
463C23—64no—
464C23—62no—
465C23—62no—
466C23—64no—
467C23—61no—
468C23—61no—
469C23—62no—
470C23—62no—
471C23—122no—
472C23—121no—
473C23—122no—
474C23C3×#23712yes—
475C23C2×C3×#6711yescharacteristic
476C23C2×D3×A411yescharacteristic
477C23C2×D3×A411yescharacteristic
478D4—22no—
479D4—62no—
480D4—62no—
481D4—64no—
482D4—62no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—31no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—184no—
497C2×C4—182no—
498C2×C4—184no—
499C2×C4—182no—
500C2×C4—182no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4C2×D3×A411yescharacteristic
505C2×C3—22no—
506C2×C3—31no—
507C2×C3—32no—
508C2×C3—31no—
509C2×C3—41no—
510C2×C3—42no—
511C2×C3—41no—
512C2×C3—62no—
513C2×C3—82no—
514C2×C3—82no—
515C2×C3—81no—
516C2×C3—121no—
517C2×C3—162no—
518C2×C3—161no—
519C2×C3—162no—
520C2×C3C2×D4×A411yescharacteristic
521C2×C3A4×#4112yes—
522C22—22no—
523C22—22no—
524C22—21no—
525C22—32no—
526C22—31no—
527C22—32no—
528C22—32no—
529C22—32no—
530C22—31no—
531C22—31no—
532C22—32no—
533C22—62no—
534C22—62no—
535C22—64no—
536C22—62no—
537C22—62no—
538C22—64no—
539C22—62no—
540C22—62no—
541C22—61no—
542C22—121no—
543C22—121no—
544C22—122no—
545C22—121no—
546C22—121no—
547C22—122no—
548C22C3×#93511yescharacteristic, complemented
549C22A4×#6712yes—
550C22C22×D3×A411yescharacteristic
551C4—21no—
552C4—62no—
553C4—61no—
554C4—62no—
555C4—182no—
556C4—182no—
557C3—41no—
558C3—81no—
559C3A4×#12311yescharacteristic, complemented
560C2—22no—
561C2—31no—
562C2—32no—
563C2—31no—
564C2—41no—
565C2—62no—
566C2—121no—
567C2A4×#23712yes—
568C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×D4C2×C3
prime radicalC2×C3×D4×A4C2
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×#123
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3×A4C2semidirect
3. A4×#217C2semidirect
4. A4×#217C2semidirect
5. A4×Dic3⋊C4C2semidirect
6. C22×#935C3semidirect
17. C24×Dic3C2×C3semidirect
21. C22×#217C2×C3semidirect
22. C22×#217C2×C3semidirect
29. C22×Dic3⋊C4C2×C3semidirect
92. #935A4direct (N × H)
179. C22×Dic3C2×A4semidirect
194. #217C2×A4semidirect
195. #217C2×A4semidirect
200. Dic3⋊C4C2×A4semidirect
206. C3×A4#123semidirect
429. C22×C3C3×#123semidirect
433. A4#935direct (N × H)
548. C22C3×#935semidirect
559. C3A4×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C22×Dic3×A42
A4×#2172
A4×Dic3⋊C42
C22×#9353
A4×#1233
C3×#9354