Finite Group Databasebeta

← A4×#895 #11923169

Subgroups — A4×#895 #11923169

Order 1152.

1182 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 1182 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×A4×D12C211yesmaximal, characteristic, complemented
2C2×A4×D12C212yesmaximal, complemented
3C2×C4×D3×A4C211yesmaximal, characteristic, complemented
4C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
5A4×(C2×D3)⋊C4C212yesmaximal, complemented
6C22×#895C311yesmaximal, characteristic, complemented
7A4×#121—31nomaximal
8C22×D3×A4C2212yes—
9C22×D3×A4C2211yescharacteristic
10C2×C3×C4×A4C2212yes—
11C2×C3×C4×A4C2211yescharacteristic
12C2×Dic3×A4C2211yescharacteristic
13A4×D12—22no—
14A4×D12—24no—
15C4×D3×A4—22no—
16C3×#895—41nomaximal
17C23×D12C2×C312yescomplemented
18C23×D12C2×C311yescharacteristic, complemented
19C23×C4×D3C2×C311yescharacteristic, complemented
20C2×D4×A4—32no—
21C2×D4×A4—31no—
22C22×C4×A4—31no—
23C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
24C22×(C2×D3)⋊C4C2×C312yescomplemented
25C2×#895—31no—
26C2×#895—32no—
27C2×#895—31no—
28C2×#895—31no—
29C2×#895—31no—
30C2×#895—32no—
31A4×C4⋊C4—21no—
32A4×C4⋊C4D311yescharacteristic, complemented
33A4×C22⋊C4—32no—
34C22×C3×A4C2311yescharacteristic
35C2×D3×A4—21no—
36C2×D3×A4—21no—
37C2×D3×A4—22no—
38C2×D3×A4—22no—
39C2×D3×A4—22no—
40C2×D3×A4D412yescomplemented
41C2×C3×D12—41no—
42C2×C3×D12—42no—
43C2×C3×C4×D3—41no—
44C3×C4×A4—22no—
45C3×C4×A4D412yescomplemented
46Dic3×A4—21no—
47C32×C4⋊C4—41no—
48C3×(C2×D3)⋊C4—42no—
49C22×#121—31noSylow
50C24×D3C22×C312yes—
51C24×D3C22×C311yescharacteristic
52C23×A4—31no—
53C23×A4—32no—
54C23×C3×C4C22×C312yes—
55C23×C3×C4C22×C311yescharacteristic
56C23×Dic3C22×C311yescharacteristic
57C22×D12—24no—
58C22×D12—22no—
59C22×D12—31no—
60C22×D12—32no—
61C22×D12—32no—
62C22×D12—32no—
63C22×D12—32no—
64C22×D12—32no—
65C22×D12—31no—
66C22×D12—62no—
67C22×D12—64no—
68C22×C4×D3—22no—
69C22×C4×D3—31no—
70C22×C4×D3—31no—
71C22×C4×D3—31no—
72C22×C4×D3—31no—
73C22×C4×D3—62no—
74D4×A4—64no—
75D4×A4—62no—
76C2×C4×A4—21no—
77C2×C4×A4—22no—
78C2×C4×A4—31no—
79C2×C4×A4—62no—
80C2×C4×A4C2×D312yes—
81C2×C4×A4C2×D311yescharacteristic
82C3×#121—121no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—32no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—32no—
90#895—32no—
91#895—32no—
92#895—34no—
93#895—34no—
94#895—32no—
95#895—31no—
96#895—32no—
97#895—31no—
98#895—31no—
99#895—32no—
100#895A411yescharacteristic, direct product factor
101C22×C3×D3—41no—
102C22×C3×D3—42no—
103C2×C3×A4C2×D411yescharacteristic
104C2×C3×A4C2×D411yescharacteristic
105C2×C3×A4#4111yescharacteristic
106D3×A4—22no—
107D3×A4—42no—
108C2×C32×C4—41no—
109C2×C32×C4—42no—
110C2×C3×Dic3—41no—
111C3×D12—82no—
112C3×D12—84no—
113C3×C4×D3—82no—
114C23×D4—32no—
115C23×D4—31no—
116C24×C4—31no—
117C2×#121—91no—
118C2×#121—92no—
119C2×#121—91no—
120C2×#121—91no—
121C2×#121—91no—
122C2×#121—92no—
123C22×C4⋊C4C3×D311yescharacteristic, complemented
124C22×C22⋊C4—32no—
125C24×C3C23×C311yescharacteristic
126C23×D3—21no—
127C23×D3—21no—
128C23×D3—22no—
129C23×D3—22no—
130C23×D3—22no—
131C23×D3—31no—
132C23×D3—31no—
133C23×D3—32no—
134C23×D3—32no—
135C23×D3—32no—
136C23×D3—61no—
137C23×D3—61no—
138C23×D3—62no—
139C23×D3—62no—
140C23×D3—62no—
141C23×D3C3×D412yescomplemented
142C22×A4—21no—
143C22×A4—32no—
144C22×A4—61no—
145C22×A4—61no—
146C22×A4—62no—
147C22×A4—62no—
148C22×A4—62no—
149C22×A4C22×D311yescharacteristic
150C2×C3×D4—121no—
151C2×C3×D4—122no—
152C22×C3×C4—22no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—62no—
159C22×C3×C4—121no—
160C22×C3×C4C3×D412yescomplemented
161C22×Dic3—21no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—61no—
165C2×D12—32no—
166C2×D12—34no—
167C2×D12—32no—
168C2×D12—32no—
169C2×D12—32no—
170C2×D12—32no—
171C2×D12—31no—
172C2×D12—62no—
173C2×D12—62no—
174C2×D12—64no—
175C2×D12—64no—
176C2×D12—64no—
177C2×D12—64no—
178C2×D12—64no—
179C2×D12—64no—
180C2×D12—62no—
181C2×D12—62no—
182C2×D12—64no—
183C2×D12—64no—
184C2×D12—64no—
185C2×D12—64no—
186C2×D12C2×A412yescomplemented
187C2×D12C2×A411yescharacteristic, complemented
188C2×C4×D3—32no—
189C2×C4×D3—31no—
190C2×C4×D3—31no—
191C2×C4×D3—31no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3C2×A411yescharacteristic, complemented
201C4×A4—22no—
202C4×A4—22no—
203C4×A4—42no—
204C4×A4—61no—
205C4×A4D1212yescomplemented
206C3×C4⋊C4—32no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—31no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4—81no—
211C3×C4⋊C4C2×A411yescharacteristic, complemented
212C3×C22⋊C4—122no—
213(C2×D3)⋊C4—34no—
214(C2×D3)⋊C4—32no—
215(C2×D3)⋊C4—32no—
216(C2×D3)⋊C4—32no—
217(C2×D3)⋊C4C2×A412yescomplemented
218C22×C32—41no—
219C2×C3×D3—42no—
220C2×C3×D3—81no—
221C2×C3×D3—81no—
222C2×C3×D3—82no—
223C2×C3×D3—82no—
224C2×C3×D3—82no—
225C3×A4#12111yescharacteristic, complemented
226C32×C4—42no—
227C32×C4—82no—
228C3×Dic3—81no—
229C25—31no—
230C25—32no—
231C22×D4—64no—
232C22×D4—62no—
233C22×D4—91no—
234C22×D4—92no—
235C22×D4—91no—
236C22×D4—92no—
237C22×D4—92no—
238C22×D4—92no—
239C22×D4—92no—
240C22×D4—182no—
241C22×D4—184no—
242C23×C4—31no—
243C23×C4—62no—
244C23×C4—91no—
245C23×C4—91no—
246C23×C4—91no—
247C23×C4—91no—
248C23×C4—182no—
249C23×C4C2×C3×D312yes—
250C23×C4C2×C3×D311yescharacteristic
251#121—31no—
252#121—92no—
253#121—91no—
254#121—91no—
255#121—92no—
256#121—92no—
257#121—94no—
258#121—92no—
259#121—92no—
260#121—94no—
261#121—91no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—32no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C23×C3—31no—
270C23×C3—31no—
271C23×C3—31no—
272C23×C3—31no—
273C23×C3—121no—
274C23×C3—122no—
275C23×C3C2×C3×D411yescharacteristic
276C23×C3C2×C3×D411yescharacteristic
277C23×C3C3×#4111yescharacteristic
278C22×D3—22no—
279C22×D3—32no—
280C22×D3—31no—
281C22×D3—32no—
282C22×D3—32no—
283C22×D3—32no—
284C22×D3—32no—
285C22×D3—42no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—61no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—64no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—124no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3C22×A412yes—
315C22×D3C22×A411yescharacteristic
316C2×A4—21no—
317C2×A4—21no—
318C2×A4—21no—
319C2×A4—62no—
320C2×A4—122no—
321C2×A4C2×D1211yescharacteristic
322C2×A4D3×D411yescharacteristic
323C2×A4#23911yescharacteristic
324C3×D4—242no—
325C3×D4—244no—
326C2×C3×C4—32no—
327C2×C3×C4—31no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—41no—
333C2×C3×C4—42no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—81no—
339C2×C3×C4—82no—
340C2×C3×C4—121no—
341C2×C3×C4—242no—
342C2×C3×C4C22×A412yes—
343C2×C3×C4C22×A411yescharacteristic
344C2×Dic3—31no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3C22×A411yescharacteristic
350D12—24no—
351D12—22no—
352D12—64no—
353D12—64no—
354D12—64no—
355D12—64no—
356D12—68no—
357D12—64no—
358D12—62no—
359C4×D3—22no—
360C4×D3—62no—
361C4×D3—62no—
362C4×D3—64no—
363C4×D3—62no—
364C2×C32—41no—
365C2×C32—41no—
366C2×C32—41no—
367C3×D3—82no—
368C3×D3—162no—
369C24—32no—
370C24—61no—
371C24—61no—
372C24—62no—
373C24—62no—
374C24—62no—
375C24—91no—
376C24—92no—
377C24—91no—
378C24—92no—
379C24—92no—
380C24—181no—
381C24—181no—
382C24—182no—
383C24—182no—
384C24—182no—
385C24C22×C3×D311yescharacteristic
386C2×D4—32no—
387C2×D4—31no—
388C2×D4—92no—
389C2×D4—92no—
390C2×D4—92no—
391C2×D4—92no—
392C2×D4—94no—
393C2×D4—92no—
394C2×D4—91no—
395C2×D4—182no—
396C2×D4—182no—
397C2×D4—184no—
398C2×D4—182no—
399C2×D4—184no—
400C2×D4—182no—
401C2×D4—184no—
402C2×D4—184no—
403C2×D4—184no—
404C2×D4—184no—
405C2×D4—184no—
406C2×D4—184no—
407C2×D4—184no—
408C2×D4—184no—
409C22×C4—22no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—31no—
415C22×C4—32no—
416C22×C4—62no—
417C22×C4—61no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—92no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4—182no—
427C22×C4—182no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—182no—
431C22×C4—182no—
432C22×C4—181no—
433C22×C4C3×D1212yescomplemented
434C4⋊C4—32no—
435C4⋊C4—32no—
436C4⋊C4—31no—
437C4⋊C4D3×A411yescharacteristic, complemented
438C22⋊C4—32no—
439C22⋊C4—92no—
440C22⋊C4—92no—
441C22⋊C4—94no—
442C22⋊C4—92no—
443C22×C3—31no—
444C22×C3—31no—
445C22×C3—31no—
446C22×C3—32no—
447C22×C3—31no—
448C22×C3—31no—
449C22×C3—31no—
450C22×C3—31no—
451C22×C3—31no—
452C22×C3—31no—
453C22×C3—41no—
454C22×C3—81no—
455C22×C3—122no—
456C22×C3—241no—
457C22×C3—241no—
458C22×C3—242no—
459C22×C3—242no—
460C22×C3—242no—
461C22×C3C3×#12111yescharacteristic, complemented
462C22×C3C23×A411yescharacteristic
463C2×D3—21no—
464C2×D3—21no—
465C2×D3—22no—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—32no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—61no—
476C2×D3—61no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3D4×A412yescomplemented
491A4—21no—
492A4#89511yescharacteristic, direct product factor
493C3×C4—22no—
494C3×C4—32no—
495C3×C4—42no—
496C3×C4—62no—
497C3×C4—82no—
498C3×C4—82no—
499C3×C4—162no—
500C3×C4—241no—
501C3×C4D4×A412yescomplemented
502Dic3—21no—
503Dic3—61no—
504C32—41noSylow
505C23—31no—
506C23—31no—
507C23—31no—
508C23—31no—
509C23—31no—
510C23—32no—
511C23—62no—
512C23—92no—
513C23—92no—
514C23—92no—
515C23—92no—
516C23—91no—
517C23—92no—
518C23—122no—
519C23—181no—
520C23—181no—
521C23—181no—
522C23—181no—
523C23—182no—
524C23—182no—
525C23—182no—
526C23—182no—
527C23—182no—
528C23—182no—
529C23—182no—
530C23—181no—
531C23—181no—
532C23—182no—
533C23—182no—
534C23—181no—
535C23—181no—
536C23—184no—
537C23—182no—
538C23—182no—
539C23—182no—
540C23—182no—
541C23—182no—
542C23—182no—
543C23—362no—
544C23—362no—
545C23—362no—
546C23—364no—
547C23C2×C3×D1211yescharacteristic
548C23C3×D3×D411yescharacteristic
549C23C3×#23911yescharacteristic
550D4—64no—
551D4—62no—
552D4—184no—
553D4—184no—
554D4—184no—
555D4—184no—
556D4—184no—
557D4—188no—
558D4—182no—
559C2×C4—32no—
560C2×C4—31no—
561C2×C4—32no—
562C2×C4—32no—
563C2×C4—32no—
564C2×C4—31no—
565C2×C4—32no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—91no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—184no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—182no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4C2×D3×A412yes—
581C2×C4C2×D3×A411yescharacteristic
582C2×C3—31no—
583C2×C3—31no—
584C2×C3—31no—
585C2×C3—31no—
586C2×C3—41no—
587C2×C3—41no—
588C2×C3—41no—
589C2×C3—81no—
590C2×C3—81no—
591C2×C3—81no—
592C2×C3—242no—
593C2×C3—482no—
594C2×C3C2×D4×A411yescharacteristic
595C2×C3C2×D4×A411yescharacteristic
596C2×C3A4×#4111yescharacteristic
597D3—22no—
598D3—42no—
599D3—62no—
600D3—122no—
601C22—31no—
602C22—31no—
603C22—31no—
604C22—32no—
605C22—31no—
606C22—31no—
607C22—31no—
608C22—31no—
609C22—31no—
610C22—31no—
611C22—32no—
612C22—61no—
613C22—61no—
614C22—62no—
615C22—62no—
616C22—62no—
617C22—92no—
618C22—182no—
619C22—182no—
620C22—182no—
621C22—182no—
622C22—182no—
623C22—182no—
624C22—182no—
625C22—182no—
626C22—181no—
627C22—181no—
628C22—182no—
629C22—182no—
630C22—182no—
631C22—362no—
632C22—362no—
633C22—362no—
634C22—362no—
635C22—362no—
636C22—362no—
637C22—362no—
638C22—362no—
639C22C3×#89511yescharacteristic, complemented
640C22C22×D3×A411yescharacteristic
641C4—22no—
642C4—32no—
643C4—61no—
644C4—62no—
645C4—181no—
646C4A4×D1212yescomplemented
647C3—41no—
648C3—81no—
649C3A4×#12111yescharacteristic, complemented
650C2—31no—
651C2—31no—
652C2—31no—
653C2—31no—
654C2—62no—
655C2—122no—
656C2—182no—
657C2—362no—
658C2C2×A4×D1211yescharacteristic
659C2D3×D4×A411yescharacteristic
660C2A4×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C4⋊C4C2×C3
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C3×#121
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×A4×D12C2semidirect
2. C2×A4×D12C2semidirect
3. C2×C4×D3×A4C2semidirect
4. C3×A4×C4⋊C4C2semidirect
5. A4×(C2×D3)⋊C4C2semidirect
6. C22×#895C3semidirect
17. C23×D12C2×C3semidirect
18. C23×D12C2×C3semidirect
19. C23×C4×D3C2×C3semidirect
23. C22×C3×C4⋊C4C2×C3semidirect
24. C22×(C2×D3)⋊C4C2×C3semidirect
32. A4×C4⋊C4D3semidirect
40. C2×D3×A4D4semidirect
45. C3×C4×A4D4semidirect
100. #895A4direct (N × H)
123. C22×C4⋊C4C3×D3semidirect
141. C23×D3C3×D4semidirect
160. C22×C3×C4C3×D4semidirect
186. C2×D12C2×A4semidirect
187. C2×D12C2×A4semidirect
200. C2×C4×D3C2×A4semidirect
205. C4×A4D12semidirect
211. C3×C4⋊C4C2×A4semidirect
217. (C2×D3)⋊C4C2×A4semidirect
225. C3×A4#121semidirect
433. C22×C4C3×D12semidirect
437. C4⋊C4D3×A4semidirect
461. C22×C3C3×#121semidirect
490. C2×D3D4×A4semidirect
492. A4#895direct (N × H)
501. C3×C4D4×A4semidirect
639. C22C3×#895semidirect
646. C4A4×D12semidirect
649. C3A4×#121semidirect

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
C22×#8953
A4×#1213
C3×#8954