Finite Group Databasebeta

← A4×#930 #11923350

Subgroups — A4×#930 #11923350

Order 1152.

1210 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C22×C3×C4×A4C211yesmaximal, characteristic, complemented
2C2×A4×#67C212yesmaximal, complemented
3C2×A4×D12C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C212yesmaximal, complemented
5A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C22×#930C311yesmaximal, characteristic, complemented
7A4×#121—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C22×D3×A4C2212yes—
10C2×C3×C4×A4—22no—
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13A4×#67—24no—
14C2×Dic3×A4C2212yes—
15A4×D12—22no—
16C3×#930—41nomaximal
17C24×C3×C4C2×C311yescharacteristic, complemented
18C23×#67C2×C312yescomplemented
19C23×D12C2×C311yescharacteristic, complemented
20C2×D4×A4—32no—
21C2×D4×A4—31no—
22C22×C4×A4—21no—
23C22×C4×A4D311yescharacteristic, complemented
24C2×#930—31no—
25C2×#930—31no—
26C2×#930—32no—
27C2×#930—31no—
28C2×#930—32no—
29C2×#930—31no—
30C22×(C2×D3)⋊C4C2×C312yescomplemented
31C22×C4⋊Dic3C2×C311yescharacteristic, complemented
32A4×C4⋊C4—31no—
33A4×C22⋊C4—32no—
34C22×C3×A4—21no—
35C22×C3×A4—21no—
36C22×C3×A4D412yescomplemented
37C22×C3×A4C2311yescharacteristic
38C2×D3×A4—22no—
39C2×D3×A4—22no—
40C2×D3×A4—22no—
41C22×C32×C4—41no—
42C2×C3×#67—42no—
43C2×C3×D12—41no—
44C3×C4×A4—21no—
45C3×C4×A4D412yescomplemented
46Dic3×A4—22no—
47C3×(C2×D3)⋊C4—42no—
48C3×C4⋊Dic3—41no—
49C22×#121—31noSylow
50C25×C3C22×C311yescharacteristic
51C24×D3C22×C312yes—
52C23×A4—21no—
53C23×A4—32no—
54C23×A4C2×D311yescharacteristic
55C23×C3×C4—22no—
56C23×C3×C4—31no—
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C23×C3×C4—62no—
61C23×C3×C4C22×C311yescharacteristic
62C23×C3×C4C22×C311yescharacteristic
63C22×#67—24no—
64C22×#67—32no—
65C22×#67—32no—
66C22×#67—32no—
67C22×#67—32no—
68C22×#67—64no—
69C23×Dic3C22×C312yes—
70C22×D12—22no—
71C22×D12—31no—
72C22×D12—32no—
73C22×D12—31no—
74C22×D12—62no—
75D4×A4—64no—
76D4×A4—62no—
77C2×C4×A4—24no—
78C2×C4×A4—22no—
79C2×C4×A4—21no—
80C2×C4×A4—21no—
81C2×C4×A4—32no—
82C2×C4×A4C2×D311yescharacteristic
83C2×C4×A4C2×D311yescharacteristic
84C3×#121—121no—
85#930—32no—
86#930—34no—
87#930—32no—
88#930—32no—
89#930—34no—
90#930—31no—
91#930—32no—
92#930—31no—
93#930—32no—
94#930—31no—
95#930A411yescharacteristic, direct product factor
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—32no—
103C23×C32—41no—
104C22×C3×D3—42no—
105C2×C3×A4—22no—
106C2×C3×A4C2×D411yescharacteristic
107C2×C3×A4C2×D411yescharacteristic
108C2×C3×A4#4111yescharacteristic
109D3×A4—42no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4—82no—
113C3×#67—84no—
114C2×C3×Dic3—42no—
115C3×D12—82no—
116C23×D4—32no—
117C23×D4—31no—
118C24×C4C3×D311yescharacteristic, complemented
119C2×#121—91no—
120C2×#121—92no—
121C2×#121—91no—
122C2×#121—91no—
123C2×#121—92no—
124C2×#121—91no—
125C22×C4⋊C4—31no—
126C22×C22⋊C4—32no—
127C24×C3—21no—
128C24×C3—21no—
129C24×C3—31no—
130C24×C3—32no—
131C24×C3—31no—
132C24×C3—61no—
133C24×C3—61no—
134C24×C3C3×D412yescomplemented
135C24×C3C23×C311yescharacteristic
136C23×D3—22no—
137C23×D3—22no—
138C23×D3—22no—
139C23×D3—32no—
140C23×D3—32no—
141C23×D3—62no—
142C23×D3—62no—
143C23×D3—62no—
144C22×A4—22no—
145C22×A4—22no—
146C22×A4—21no—
147C22×A4—21no—
148C22×A4—22no—
149C22×A4—21no—
150C22×A4—62no—
151C22×A4—62no—
152C22×A4—62no—
153C22×A4D1212yescomplemented
154C22×A4C22×D311yescharacteristic
155C2×C3×D4—121no—
156C2×C3×D4—122no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—32no—
161C22×C3×C4—32no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—41no—
168C22×C3×C4—62no—
169C22×C3×C4—62no—
170C22×C3×C4—62no—
171C22×C3×C4—62no—
172C22×C3×C4—62no—
173C22×C3×C4—62no—
174C22×C3×C4—62no—
175C22×C3×C4—62no—
176C22×C3×C4—61no—
177C22×C3×C4—81no—
178C22×C3×C4C3×D412yescomplemented
179C22×C3×C4C2×A411yescharacteristic, complemented
180C2×#67—34no—
181C2×#67—32no—
182C2×#67—32no—
183C2×#67—32no—
184C2×#67—64no—
185C2×#67—64no—
186C2×#67—64no—
187C2×#67—64no—
188C2×#67—64no—
189C2×#67—64no—
190C2×#67—64no—
191C2×#67—64no—
192C2×#67C2×A412yescomplemented
193C22×Dic3—22no—
194C22×Dic3—32no—
195C22×Dic3—32no—
196C22×Dic3—62no—
197C2×D12—32no—
198C2×D12—32no—
199C2×D12—31no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—64no—
203C2×D12—64no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12C2×A411yescharacteristic, complemented
207C4×A4—22no—
208C4×A4—21no—
209C4×A4—22no—
210C4×A4—62no—
211C4×A4#6712yescomplemented
212C3×C4⋊C4—121no—
213C3×C22⋊C4—122no—
214(C2×D3)⋊C4—34no—
215(C2×D3)⋊C4—32no—
216(C2×D3)⋊C4—32no—
217(C2×D3)⋊C4—32no—
218(C2×D3)⋊C4C2×A412yescomplemented
219C4⋊Dic3—32no—
220C4⋊Dic3—31no—
221C4⋊Dic3—32no—
222C4⋊Dic3C2×A411yescharacteristic, complemented
223C22×C32—42no—
224C22×C32—41no—
225C22×C32—81no—
226C22×C32—81no—
227C2×C3×D3—82no—
228C2×C3×D3—82no—
229C2×C3×D3—82no—
230C3×A4#12111yescharacteristic, complemented
231C32×C4—42no—
232C32×C4—81no—
233C3×Dic3—82no—
234C25—32no—
235C25C2×C3×D311yescharacteristic
236C22×D4—64no—
237C22×D4—62no—
238C22×D4—91no—
239C22×D4—91no—
240C22×D4—92no—
241C22×D4—92no—
242C22×D4—92no—
243C22×D4—92no—
244C22×D4—92no—
245C22×D4—182no—
246C22×D4—184no—
247C23×C4—22no—
248C23×C4—31no—
249C23×C4—31no—
250C23×C4—31no—
251C23×C4—31no—
252C23×C4—32no—
253C23×C4—62no—
254C23×C4C2×C3×D311yescharacteristic
255C23×C4C2×C3×D311yescharacteristic
256#121—31no—
257#121—92no—
258#121—91no—
259#121—92no—
260#121—91no—
261#121—94no—
262#121—94no—
263#121—92no—
264#121—92no—
265#121—92no—
266#121—91no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—92no—
269C2×C4⋊C4—91no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4—92no—
272C2×C22⋊C4—92no—
273C2×C22⋊C4—92no—
274C23×C3—22no—
275C23×C3—31no—
276C23×C3—31no—
277C23×C3—31no—
278C23×C3—31no—
279C23×C3—32no—
280C23×C3—32no—
281C23×C3—32no—
282C23×C3—32no—
283C23×C3—31no—
284C23×C3—41no—
285C23×C3—61no—
286C23×C3—61no—
287C23×C3—61no—
288C23×C3—61no—
289C23×C3—62no—
290C23×C3—61no—
291C23×C3—61no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3—61no—
295C23×C3—61no—
296C23×C3—64no—
297C23×C3—81no—
298C23×C3—122no—
299C23×C3C2×C3×D411yescharacteristic
300C23×C3C2×C3×D411yescharacteristic
301C23×C3C3×#4111yescharacteristic
302C23×C3C22×A411yescharacteristic
303C22×D3—32no—
304C22×D3—42no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—124no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3C22×A412yes—
322C2×A4—24no—
323C2×A4—22no—
324C2×A4—21no—
325C2×A4—21no—
326C2×A4—21no—
327C2×A4—122no—
328C2×A4C2×D1211yescharacteristic
329C2×A4#23511yescharacteristic
330C2×A4C2×#6711yescharacteristic
331C3×D4—242no—
332C3×D4—244no—
333C2×C3×C4—22no—
334C2×C3×C4—32no—
335C2×C3×C4—31no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—31no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—64no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—82no—
351C2×C3×C4—84no—
352C2×C3×C4—81no—
353C2×C3×C4—81no—
354C2×C3×C4—122no—
355C2×C3×C4C22×A411yescharacteristic
356C2×C3×C4C22×A411yescharacteristic
357#67—24no—
358#67—64no—
359#67—64no—
360#67—68no—
361#67—64no—
362C2×Dic3—32no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3C22×A412yes—
368D12—22no—
369D12—64no—
370D12—64no—
371D12—62no—
372C2×C32—41no—
373C2×C32—41no—
374C2×C32—41no—
375C2×C32—82no—
376C3×D3—162no—
377C24—21no—
378C24—21no—
379C24—31no—
380C24—32no—
381C24—31no—
382C24—61no—
383C24—61no—
384C24—62no—
385C24—62no—
386C24—62no—
387C24—92no—
388C24—92no—
389C24—182no—
390C24—182no—
391C24—182no—
392C24C3×D1212yescomplemented
393C24C22×C3×D311yescharacteristic
394C2×D4—32no—
395C2×D4—31no—
396C2×D4—92no—
397C2×D4—92no—
398C2×D4—92no—
399C2×D4—92no—
400C2×D4—94no—
401C2×D4—92no—
402C2×D4—91no—
403C2×D4—182no—
404C2×D4—182no—
405C2×D4—184no—
406C2×D4—182no—
407C2×D4—184no—
408C2×D4—182no—
409C2×D4—184no—
410C2×D4—184no—
411C2×D4—184no—
412C2×D4—184no—
413C2×D4—184no—
414C2×D4—184no—
415C2×D4—184no—
416C2×D4—184no—
417C22×C4—21no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—31no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—62no—
428C22×C4—62no—
429C22×C4—62no—
430C22×C4—62no—
431C22×C4—62no—
432C22×C4—62no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—61no—
436C22×C4—62no—
437C22×C4—92no—
438C22×C4—92no—
439C22×C4—182no—
440C22×C4C3×#6712yescomplemented
441C22×C4D3×A411yescharacteristic, complemented
442C4⋊C4—31no—
443C4⋊C4—92no—
444C4⋊C4—92no—
445C4⋊C4—91no—
446C22⋊C4—32no—
447C22⋊C4—92no—
448C22⋊C4—92no—
449C22⋊C4—94no—
450C22⋊C4—92no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—31no—
454C22×C3—31no—
455C22×C3—31no—
456C22×C3—32no—
457C22×C3—31no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—31no—
461C22×C3—31no—
462C22×C3—31no—
463C22×C3—32no—
464C22×C3—42no—
465C22×C3—41no—
466C22×C3—62no—
467C22×C3—62no—
468C22×C3—62no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—61no—
475C22×C3—61no—
476C22×C3—81no—
477C22×C3—81no—
478C22×C3—82no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—81no—
482C22×C3—242no—
483C22×C3—242no—
484C22×C3—242no—
485C22×C3C3×#12111yescharacteristic, complemented
486C22×C3D4×A412yescomplemented
487C22×C3C23×A411yescharacteristic
488C2×D3—22no—
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502A4—21no—
503A4#93011yescharacteristic, direct product factor
504C3×C4—21no—
505C3×C4—32no—
506C3×C4—42no—
507C3×C4—61no—
508C3×C4—81no—
509C3×C4—82no—
510C3×C4—82no—
511C3×C4—242no—
512C3×C4D4×A412yescomplemented
513Dic3—22no—
514Dic3—62no—
515C32—41noSylow
516C23—22no—
517C23—31no—
518C23—31no—
519C23—31no—
520C23—31no—
521C23—32no—
522C23—32no—
523C23—32no—
524C23—32no—
525C23—31no—
526C23—32no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—61no—
531C23—62no—
532C23—61no—
533C23—61no—
534C23—62no—
535C23—62no—
536C23—61no—
537C23—61no—
538C23—64no—
539C23—92no—
540C23—122no—
541C23—182no—
542C23—182no—
543C23—182no—
544C23—182no—
545C23—182no—
546C23—182no—
547C23—182no—
548C23—182no—
549C23—182no—
550C23—182no—
551C23—182no—
552C23—182no—
553C23—362no—
554C23—362no—
555C23—362no—
556C23—364no—
557C23C2×C3×D1211yescharacteristic
558C23C3×#23511yescharacteristic
559C23C2×C3×#6711yescharacteristic
560C23C2×D3×A411yescharacteristic
561D4—64no—
562D4—62no—
563D4—184no—
564D4—184no—
565D4—184no—
566D4—184no—
567D4—188no—
568D4—184no—
569D4—182no—
570C2×C4—22no—
571C2×C4—32no—
572C2×C4—31no—
573C2×C4—32no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—31no—
578C2×C4—62no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—62no—
582C2×C4—64no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—61no—
586C2×C4—92no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4—182no—
591C2×C4C2×D3×A411yescharacteristic
592C2×C4C2×D3×A411yescharacteristic
593C2×C3—22no—
594C2×C3—31no—
595C2×C3—31no—
596C2×C3—31no—
597C2×C3—31no—
598C2×C3—41no—
599C2×C3—41no—
600C2×C3—41no—
601C2×C3—62no—
602C2×C3—82no—
603C2×C3—84no—
604C2×C3—81no—
605C2×C3—81no—
606C2×C3—81no—
607C2×C3—482no—
608C2×C3C2×D4×A411yescharacteristic
609C2×C3C2×D4×A411yescharacteristic
610C2×C3A4×#4111yescharacteristic
611D3—42no—
612D3—122no—
613C22—21no—
614C22—21no—
615C22—31no—
616C22—31no—
617C22—31no—
618C22—32no—
619C22—31no—
620C22—31no—
621C22—31no—
622C22—31no—
623C22—31no—
624C22—31no—
625C22—32no—
626C22—62no—
627C22—62no—
628C22—62no—
629C22—62no—
630C22—62no—
631C22—62no—
632C22—62no—
633C22—62no—
634C22—61no—
635C22—61no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—182no—
640C22—182no—
641C22—182no—
642C22—362no—
643C22—362no—
644C22—362no—
645C22—362no—
646C22—362no—
647C22—362no—
648C22—362no—
649C22—362no—
650C22C3×#93011yescharacteristic, complemented
651C22A4×D1212yescomplemented
652C22C22×D3×A411yescharacteristic
653C4—21no—
654C4—32no—
655C4—62no—
656C4—61no—
657C4—182no—
658C4A4×#6712yescomplemented
659C3—41no—
660C3—81no—
661C3A4×#12111yescharacteristic, complemented
662C2—22no—
663C2—31no—
664C2—31no—
665C2—31no—
666C2—31no—
667C2—62no—
668C2—122no—
669C2—362no—
670C2C2×A4×D1211yescharacteristic
671C2A4×#23511yescharacteristic
672C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC24×C3×C4C2×C3
hypercenterC22×C4D3×A4
hypocenterC22×C3C3×#121
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×A4C2semidirect
2. C2×A4×#67C2semidirect
3. C2×A4×D12C2semidirect
4. A4×(C2×D3)⋊C4C2semidirect
5. A4×C4⋊Dic3C2semidirect
6. C22×#930C3semidirect
17. C24×C3×C4C2×C3semidirect
18. C23×#67C2×C3semidirect
19. C23×D12C2×C3semidirect
23. C22×C4×A4D3semidirect
30. C22×(C2×D3)⋊C4C2×C3semidirect
31. C22×C4⋊Dic3C2×C3semidirect
36. C22×C3×A4D4semidirect
45. C3×C4×A4D4semidirect
95. #930A4direct (N × H)
118. C24×C4C3×D3semidirect
134. C24×C3C3×D4semidirect
153. C22×A4D12semidirect
178. C22×C3×C4C3×D4semidirect
179. C22×C3×C4C2×A4semidirect
192. C2×#67C2×A4semidirect
206. C2×D12C2×A4semidirect
211. C4×A4#67semidirect
218. (C2×D3)⋊C4C2×A4semidirect
222. C4⋊Dic3C2×A4semidirect
230. C3×A4#121semidirect
392. C24C3×D12semidirect
440. C22×C4C3×#67semidirect
441. C22×C4D3×A4semidirect
485. C22×C3C3×#121semidirect
486. C22×C3D4×A4semidirect
503. A4#930direct (N × H)
512. C3×C4D4×A4semidirect
650. C22C3×#930semidirect
651. C22A4×D12semidirect
658. C4A4×#67semidirect
661. C3A4×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C2×A4×#672
C2×A4×D122
A4×(C2×D3)⋊C42
A4×C4⋊Dic32
C22×#9303
A4×#1213
C3×#9304