Finite Group Databasebeta

← A4×#938 #11923360

Subgroups — A4×#938 #11923360

Order 1152.

1210 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 105 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, complemented
2C2×A4×#67C212yesmaximal, complemented
3C2×C4×D3×A4C211yesmaximal, characteristic, complemented
4A4×#217C212yesmaximal, complemented
5A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C22×#938C311yesmaximal, characteristic, complemented
7A4×#121—31nomaximal
8C23×C3×A4C2212yes—
9C22×D3×A4C2211yescharacteristic
10C3×D4×A4—22no—
11C2×C3×C4×A4C2211yescharacteristic
12A4×#67—24no—
13C2×Dic3×A4C2211yescharacteristic
14C2×Dic3×A4C2212yes—
15C4×D3×A4—22no—
16C3×#938—41nomaximal
17C23×C3×D4C2×C311yescharacteristic, complemented
18C23×#67C2×C312yescomplemented
19C23×C4×D3C2×C311yescharacteristic, complemented
20C2×D4×A4—21no—
21C2×D4×A4—32no—
22C2×D4×A4D311yescharacteristic, complemented
23C22×C4×A4—31no—
24C22×#217C2×C312yescomplemented
25C2×#938—31no—
26C2×#938—31no—
27C2×#938—31no—
28C2×#938—32no—
29C2×#938—31no—
30C2×#938—32no—
31C22×C4⋊Dic3C2×C311yescharacteristic, complemented
32A4×C4⋊C4—31no—
33A4×C22⋊C4—32no—
34C22×C3×A4—22no—
35C22×C3×A4—22no—
36C22×C3×A4—22no—
37C22×C3×A4C2311yescharacteristic
38C2×D3×A4—21no—
39C2×D3×A4—21no—
40C2×D3×A4D412yescomplemented
41C2×C32×D4—41no—
42C2×C3×#67—42no—
43C2×C3×C4×D3—41no—
44C3×C4×A4D412yescomplemented
45Dic3×A4—21no—
46Dic3×A4—22no—
47C3×#217—42no—
48C3×C4⋊Dic3—41no—
49C22×#121—31noSylow
50C25×C3C22×C312yes—
51C24×D3C22×C311yescharacteristic
52C23×A4—22no—
53C23×A4—31no—
54C23×A4C2×D312yes—
55C22×C3×D4—22no—
56C22×C3×D4—31no—
57C22×C3×D4—31no—
58C22×C3×D4—32no—
59C22×C3×D4—62no—
60C23×C3×C4C22×C311yescharacteristic
61C22×#67—24no—
62C22×#67—32no—
63C22×#67—32no—
64C22×#67—32no—
65C22×#67—32no—
66C22×#67—64no—
67C23×Dic3C22×C311yescharacteristic
68C23×Dic3C22×C312yes—
69C22×C4×D3—22no—
70C22×C4×D3—31no—
71C22×C4×D3—31no—
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3—62no—
75D4×A4—24no—
76D4×A4—22no—
77D4×A4—64no—
78C2×C4×A4—21no—
79C2×C4×A4—31no—
80C2×C4×A4—32no—
81C2×C4×A4—62no—
82C2×C4×A4C2×D311yescharacteristic
83C3×#121—121no—
84C2×#217—32no—
85C2×#217—32no—
86C2×#217—32no—
87C2×#217—32no—
88#938—32no—
89#938—34no—
90#938—32no—
91#938—32no—
92#938—34no—
93#938—31no—
94#938—32no—
95#938—31no—
96#938—32no—
97#938—31no—
98#938A411yescharacteristic, direct product factor
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—32no—
102C23×C32—42no—
103C22×C3×D3—41no—
104C2×C3×A4—42no—
105C2×C3×A4C2×D411yescharacteristic
106C2×C3×A4C2×D411yescharacteristic
107C2×C3×A4#4111yescharacteristic
108D3×A4—22no—
109C32×D4—82no—
110C2×C32×C4—41no—
111C3×#67—84no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—41no—
114C3×C4×D3—82no—
115C23×D4—32no—
116C23×D4C3×D311yescharacteristic, complemented
117C24×C4—31no—
118C2×#121—91no—
119C2×#121—92no—
120C2×#121—91no—
121C2×#121—91no—
122C2×#121—92no—
123C2×#121—91no—
124C22×C4⋊C4—31no—
125C22×C22⋊C4—32no—
126C24×C3—22no—
127C24×C3—22no—
128C24×C3—22no—
129C24×C3—32no—
130C24×C3—32no—
131C24×C3—62no—
132C24×C3—62no—
133C24×C3—62no—
134C24×C3C23×C311yescharacteristic
135C23×D3—21no—
136C23×D3—21no—
137C23×D3—31no—
138C23×D3—31no—
139C23×D3—32no—
140C23×D3—61no—
141C23×D3—61no—
142C23×D3C3×D412yescomplemented
143C22×A4—24no—
144C22×A4—22no—
145C22×A4—22no—
146C22×A4—22no—
147C22×A4—21no—
148C22×A4—32no—
149C22×A4—42no—
150C22×A4—42no—
151C22×A4—61no—
152C22×A4—61no—
153C22×A4C22×D311yescharacteristic
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—31no—
157C2×C3×D4—41no—
158C2×C3×D4—62no—
159C2×C3×D4—62no—
160C2×C3×D4—64no—
161C2×C3×D4—62no—
162C2×C3×D4—64no—
163C2×C3×D4—62no—
164C2×C3×D4—81no—
165C2×C3×D4—122no—
166C2×C3×D4C2×A411yescharacteristic, complemented
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—32no—
170C22×C3×C4—121no—
171C22×C3×C4C3×D412yescomplemented
172C2×#67—34no—
173C2×#67—32no—
174C2×#67—32no—
175C2×#67—32no—
176C2×#67—64no—
177C2×#67—64no—
178C2×#67—64no—
179C2×#67—64no—
180C2×#67—64no—
181C2×#67—64no—
182C2×#67—64no—
183C2×#67—64no—
184C2×#67C2×A412yescomplemented
185C22×Dic3—21no—
186C22×Dic3—22no—
187C22×Dic3—32no—
188C22×Dic3—31no—
189C22×Dic3—32no—
190C22×Dic3—31no—
191C22×Dic3—61no—
192C22×Dic3—62no—
193C2×C4×D3—32no—
194C2×C4×D3—31no—
195C2×C4×D3—31no—
196C2×C4×D3—31no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3C2×A411yescharacteristic, complemented
206C4×A4—22no—
207C4×A4—62no—
208C4×A4—61no—
209C4×A4#6712yescomplemented
210C3×C4⋊C4—121no—
211C3×C22⋊C4—122no—
212#217—34no—
213#217—32no—
214#217—32no—
215#217—32no—
216#217C2×A412yescomplemented
217C4⋊Dic3—32no—
218C4⋊Dic3—31no—
219C4⋊Dic3—32no—
220C4⋊Dic3C2×A411yescharacteristic, complemented
221C22×C32—41no—
222C22×C32—82no—
223C22×C32—82no—
224C22×C32—82no—
225C2×C3×D3—42no—
226C2×C3×D3—81no—
227C2×C3×D3—81no—
228C3×A4#12111yescharacteristic, complemented
229C32×C4—42no—
230C3×Dic3—81no—
231C3×Dic3—82no—
232C25—31no—
233C25C2×C3×D312yes—
234C22×D4—22no—
235C22×D4—31no—
236C22×D4—31no—
237C22×D4—32no—
238C22×D4—62no—
239C22×D4—64no—
240C22×D4—92no—
241C22×D4—92no—
242C22×D4—92no—
243C22×D4—92no—
244C22×D4—184no—
245C23×C4—31no—
246C23×C4—32no—
247C23×C4—62no—
248C23×C4—91no—
249C23×C4—91no—
250C23×C4—91no—
251C23×C4—91no—
252C23×C4—182no—
253C23×C4C2×C3×D311yescharacteristic
254#121—31no—
255#121—92no—
256#121—91no—
257#121—91no—
258#121—92no—
259#121—92no—
260#121—94no—
261#121—92no—
262#121—92no—
263#121—94no—
264#121—91no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—92no—
267C2×C4⋊C4—91no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4—92no—
272C23×C3—31no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—31no—
276C23×C3—32no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—62no—
280C23×C3—62no—
281C23×C3—62no—
282C23×C3—62no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—62no—
286C23×C3—62no—
287C23×C3—62no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3—62no—
291C23×C3—82no—
292C23×C3—121no—
293C23×C3—122no—
294C23×C3—122no—
295C23×C3—122no—
296C23×C3—124no—
297C23×C3C2×C3×D411yescharacteristic
298C23×C3C2×C3×D411yescharacteristic
299C23×C3C3×#4111yescharacteristic
300C23×C3C22×A412yes—
301C22×D3—22no—
302C22×D3—32no—
303C22×D3—31no—
304C22×D3—32no—
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—61no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—61no—
311C22×D3—64no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—62no—
319C22×D3C22×A411yescharacteristic
320C2×A4—21no—
321C2×A4—21no—
322C2×A4—21no—
323C2×A4—44no—
324C2×A4—42no—
325C2×A4—62no—
326C2×A4D3×D411yescharacteristic
327C2×A4#23711yescharacteristic
328C2×A4C2×#6711yescharacteristic
329C3×D4—22no—
330C3×D4—64no—
331C3×D4—64no—
332C3×D4—62no—
333C3×D4—82no—
334C3×D4—84no—
335C3×D4—244no—
336C2×C3×C4—32no—
337C2×C3×C4—31no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—41no—
342C2×C3×C4—81no—
343C2×C3×C4—121no—
344C2×C3×C4—122no—
345C2×C3×C4—242no—
346C2×C3×C4C22×A411yescharacteristic
347#67—24no—
348#67—64no—
349#67—64no—
350#67—68no—
351#67—64no—
352C2×Dic3—32no—
353C2×Dic3—31no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3C22×A412yes—
363C2×Dic3C22×A411yescharacteristic
364C4×D3—22no—
365C4×D3—62no—
366C4×D3—62no—
367C4×D3—64no—
368C4×D3—62no—
369C2×C32—41no—
370C2×C32—41no—
371C2×C32—41no—
372C2×C32—162no—
373C3×D3—82no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—32no—
378C24—32no—
379C24—32no—
380C24—62no—
381C24—62no—
382C24—62no—
383C24—61no—
384C24—61no—
385C24—91no—
386C24—91no—
387C24—92no—
388C24—181no—
389C24—181no—
390C24C22×C3×D311yescharacteristic
391C2×D4—32no—
392C2×D4—32no—
393C2×D4—32no—
394C2×D4—31no—
395C2×D4—62no—
396C2×D4—62no—
397C2×D4—64no—
398C2×D4—62no—
399C2×D4—64no—
400C2×D4—62no—
401C2×D4—92no—
402C2×D4—92no—
403C2×D4—94no—
404C2×D4—92no—
405C2×D4—184no—
406C2×D4—184no—
407C2×D4—184no—
408C2×D4—184no—
409C2×D4—184no—
410C2×D4—184no—
411C2×D4—184no—
412C2×D4—184no—
413C2×D4D3×A411yescharacteristic, complemented
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—32no—
417C22×C4—31no—
418C22×C4—62no—
419C22×C4—61no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—92no—
423C22×C4—91no—
424C22×C4—92no—
425C22×C4—91no—
426C22×C4—91no—
427C22×C4—92no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—182no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4—182no—
434C22×C4—182no—
435C22×C4—182no—
436C22×C4—181no—
437C22×C4—182no—
438C22×C4C3×#6712yescomplemented
439C4⋊C4—31no—
440C4⋊C4—92no—
441C4⋊C4—92no—
442C4⋊C4—91no—
443C22⋊C4—32no—
444C22⋊C4—92no—
445C22⋊C4—92no—
446C22⋊C4—94no—
447C22⋊C4—92no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—31no—
452C22×C3—31no—
453C22×C3—31no—
454C22×C3—32no—
455C22×C3—31no—
456C22×C3—31no—
457C22×C3—31no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—31no—
461C22×C3—41no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—82no—
466C22×C3—82no—
467C22×C3—82no—
468C22×C3—84no—
469C22×C3—81no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—162no—
480C22×C3—162no—
481C22×C3—241no—
482C22×C3—241no—
483C22×C3C3×#12111yescharacteristic, complemented
484C22×C3C23×A411yescharacteristic
485C2×D3—21no—
486C2×D3—21no—
487C2×D3—32no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—61no—
495C2×D3—61no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3D4×A412yescomplemented
499A4—21no—
500A4#93811yescharacteristic, direct product factor
501C3×C4—32no—
502C3×C4—42no—
503C3×C4—82no—
504C3×C4—241no—
505C3×C4—242no—
506C3×C4D4×A412yescomplemented
507Dic3—21no—
508Dic3—22no—
509Dic3—61no—
510Dic3—62no—
511C32—41noSylow
512C23—31no—
513C23—31no—
514C23—31no—
515C23—31no—
516C23—31no—
517C23—32no—
518C23—42no—
519C23—62no—
520C23—62no—
521C23—62no—
522C23—62no—
523C23—62no—
524C23—62no—
525C23—62no—
526C23—62no—
527C23—62no—
528C23—62no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23—92no—
533C23—92no—
534C23—92no—
535C23—92no—
536C23—91no—
537C23—122no—
538C23—122no—
539C23—122no—
540C23—124no—
541C23—181no—
542C23—181no—
543C23—181no—
544C23—181no—
545C23—182no—
546C23—181no—
547C23—181no—
548C23—182no—
549C23—182no—
550C23—181no—
551C23—181no—
552C23—184no—
553C23C3×D3×D411yescharacteristic
554C23C3×#23711yescharacteristic
555C23C2×C3×#6711yescharacteristic
556C23C2×D3×A412yes—
557D4—22no—
558D4—64no—
559D4—64no—
560D4—64no—
561D4—62no—
562D4—184no—
563D4—184no—
564D4—184no—
565D4—188no—
566C2×C4—32no—
567C2×C4—31no—
568C2×C4—32no—
569C2×C4—32no—
570C2×C4—32no—
571C2×C4—31no—
572C2×C4—32no—
573C2×C4—62no—
574C2×C4—91no—
575C2×C4—92no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—184no—
579C2×C4—181no—
580C2×C4—182no—
581C2×C4—181no—
582C2×C4—182no—
583C2×C4—182no—
584C2×C4—181no—
585C2×C4—182no—
586C2×C4—181no—
587C2×C4—182no—
588C2×C4C2×D3×A411yescharacteristic
589C2×C3—31no—
590C2×C3—31no—
591C2×C3—31no—
592C2×C3—31no—
593C2×C3—42no—
594C2×C3—41no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—81no—
598C2×C3—81no—
599C2×C3—81no—
600C2×C3—122no—
601C2×C3—162no—
602C2×C3—164no—
603C2×C3—242no—
604C2×C3C2×D4×A411yescharacteristic
605C2×C3C2×D4×A411yescharacteristic
606C2×C3A4×#4111yescharacteristic
607D3—22no—
608D3—62no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—31no—
613C22—31no—
614C22—31no—
615C22—32no—
616C22—31no—
617C22—31no—
618C22—31no—
619C22—31no—
620C22—31no—
621C22—31no—
622C22—32no—
623C22—61no—
624C22—61no—
625C22—62no—
626C22—62no—
627C22—62no—
628C22—92no—
629C22—122no—
630C22—122no—
631C22—122no—
632C22—122no—
633C22—122no—
634C22—122no—
635C22—122no—
636C22—122no—
637C22—182no—
638C22—182no—
639C22—182no—
640C22—182no—
641C22—182no—
642C22—182no—
643C22—182no—
644C22—182no—
645C22—181no—
646C22—181no—
647C22C3×#93811yescharacteristic, complemented
648C22C22×D3×A411yescharacteristic
649C4—32no—
650C4—62no—
651C4—61no—
652C4—182no—
653C4—181no—
654C4A4×#6712yescomplemented
655C3—41no—
656C3—81no—
657C3A4×#12111yescharacteristic, complemented
658C2—31no—
659C2—31no—
660C2—31no—
661C2—31no—
662C2—42no—
663C2—62no—
664C2—122no—
665C2—182no—
666C2D3×D4×A411yescharacteristic
667C2A4×#23711yescharacteristic
668C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×D4C2×C3
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×#121
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×A4C2semidirect
2. C2×A4×#67C2semidirect
3. C2×C4×D3×A4C2semidirect
4. A4×#217C2semidirect
5. A4×C4⋊Dic3C2semidirect
6. C22×#938C3semidirect
17. C23×C3×D4C2×C3semidirect
18. C23×#67C2×C3semidirect
19. C23×C4×D3C2×C3semidirect
22. C2×D4×A4D3semidirect
24. C22×#217C2×C3semidirect
31. C22×C4⋊Dic3C2×C3semidirect
40. C2×D3×A4D4semidirect
44. C3×C4×A4D4semidirect
98. #938A4direct (N × H)
116. C23×D4C3×D3semidirect
142. C23×D3C3×D4semidirect
166. C2×C3×D4C2×A4semidirect
171. C22×C3×C4C3×D4semidirect
184. C2×#67C2×A4semidirect
205. C2×C4×D3C2×A4semidirect
209. C4×A4#67semidirect
216. #217C2×A4semidirect
220. C4⋊Dic3C2×A4semidirect
228. C3×A4#121semidirect
413. C2×D4D3×A4semidirect
438. C22×C4C3×#67semidirect
483. C22×C3C3×#121semidirect
498. C2×D3D4×A4semidirect
500. A4#938direct (N × H)
506. C3×C4D4×A4semidirect
647. C22C3×#938semidirect
654. C4A4×#67semidirect
657. C3A4×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×A4×#672
C2×C4×D3×A42
A4×#2172
A4×C4⋊Dic32
C22×#9383
A4×#1213
C3×#9384