Finite Group Databasebeta

← A4×#879 #11923153

Subgroups — A4×#879 #11923153

Order 1152.

674 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 674 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C3×A4×C22⋊C4C211yesmaximal, characteristic
2A4×#217C211yesmaximal, characteristic
3A4×#217C211yesmaximal, characteristic
4A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C4×Dic3×A4C211yesmaximal, characteristic, complemented
8C22×#879C311yesmaximal, characteristic, complemented
9A4×#126—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×Dic3×A4C2211yescharacteristic
14C2×Dic3×A4C2211yescharacteristic
15C2×Dic3×A4C2211yescharacteristic
16C2×Dic3×A4C2211yescharacteristic
17C3×#879—41nomaximal
18C22×C3×C22⋊C4C2×C311yescharacteristic
19C22×#217C2×C311yescharacteristic
20C22×#217C2×C311yescharacteristic
21C22×C4⋊Dic3C2×C311yescharacteristic, complemented
22C22×Dic3⋊C4C2×C311yescharacteristic, complemented
23C22×Dic3⋊C4C2×C311yescharacteristic, complemented
24C22×C4×Dic3C2×C311yescharacteristic, complemented
25C2×#879—31no—
26C2×#879—31no—
27C2×#879—31no—
28C2×#879—31no—
29C2×#879—31no—
30C2×#879—31no—
31C2×#879—31no—
32C2×#879—31no—
33A4×C4⋊C4—31no—
34A4×C4⋊C4—31no—
35A4×C4⋊C4—31no—
36A4×C22⋊C4—21no—
37A4×C22⋊C4—31no—
38A4×C22⋊C4—31no—
39A4×C22⋊C4D311yescharacteristic
40C42×A4—31no—
41C22×C3×A4—21no—
42C22×C3×A4—21no—
43C22×C3×A4—21no—
44C22×C3×A4C2311yescharacteristic
45C3×C4×A4—21no—
46C3×C4×A4—21no—
47Dic3×A4—21no—
48Dic3×A4—21no—
49Dic3×A4—21no—
50Dic3×A4—21no—
51C32×C22⋊C4—41no—
52C3×#217—41no—
53C3×#217—41no—
54C3×C4⋊Dic3—41no—
55C3×Dic3⋊C4—41no—
56C3×Dic3⋊C4—41no—
57C3×C4×Dic3—41no—
58C22×#126—31noSylow
59C25×C3C22×C311yescharacteristic
60C23×A4—21no—
61C23×A4C2×D311yescharacteristic
62C23×C3×C4C22×C311yescharacteristic
63C23×C3×C4C22×C311yescharacteristic
64C23×Dic3C22×C311yescharacteristic
65C23×Dic3C22×C311yescharacteristic
66C23×Dic3C22×C311yescharacteristic
67C23×Dic3C22×C311yescharacteristic
68C2×C4×A4—21no—
69C2×C4×A4—21no—
70C2×C4×A4—31no—
71C2×C4×A4—31no—
72C2×C4×A4—31no—
73C2×C4×A4—31no—
74C2×C4×A4C2×D311yescharacteristic
75C2×C4×A4C2×D311yescharacteristic
76C3×#126—121no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—31no—
81C2×#217—31no—
82C2×#217—31no—
83C2×#217—31no—
84C2×#217—31no—
85C2×#217—31no—
86C2×#217—31no—
87C2×#217—31no—
88C2×#217—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—31no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—31no—
105#879—32no—
106#879—32no—
107#879—32no—
108#879—32no—
109#879—32no—
110#879—32no—
111#879—32no—
112#879—31no—
113#879—31no—
114#879—31no—
115#879—31no—
116#879—31no—
117#879—31no—
118#879—31no—
119#879A411yescharacteristic, direct product factor
120C23×C32—41no—
121C2×C3×A4—41no—
122C2×C3×A4#4111yescharacteristic
123C2×C3×A4#4111yescharacteristic
124C2×C3×A4#4111yescharacteristic
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×#126—91no—
132C2×#126—91no—
133C2×#126—91no—
134C2×#126—91no—
135C2×#126—91no—
136C2×#126—91no—
137C2×#126—91no—
138C2×#126—91no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4—31no—
141C22×C4⋊C4—31no—
142C22×C22⋊C4—31no—
143C22×C22⋊C4—31no—
144C22×C22⋊C4C3×D311yescharacteristic
145C22×C42—31no—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—31no—
150C24×C3—31no—
151C24×C3—61no—
152C24×C3—61no—
153C24×C3—61no—
154C24×C3C23×C311yescharacteristic
155C22×A4—22no—
156C22×A4—21no—
157C22×A4—21no—
158C22×A4—21no—
159C22×A4—21no—
160C22×A4—41no—
161C22×A4—41no—
162C22×A4C22×D311yescharacteristic
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C4×A4—21no—
188C4×A4—21no—
189C4×A4—41no—
190C4×A4—41no—
191C4×A4—61no—
192C4×A4—61no—
193C4×A4—61no—
194C4×A4—61no—
195C3×C4⋊C4—121no—
196C3×C4⋊C4—121no—
197C3×C4⋊C4—121no—
198C3×C22⋊C4—32no—
199C3×C22⋊C4—31no—
200C3×C22⋊C4—31no—
201C3×C22⋊C4—31no—
202C3×C22⋊C4—41no—
203C3×C22⋊C4—81no—
204C3×C22⋊C4—121no—
205C3×C22⋊C4—121no—
206C3×C22⋊C4C2×A411yescharacteristic
207C3×C42—121no—
208#217—32no—
209#217—32no—
210#217—31no—
211#217—31no—
212#217—31no—
213#217—31no—
214#217—31no—
215#217—31no—
216#217C2×A411yescharacteristic
217#217C2×A411yescharacteristic
218C4⋊Dic3—32no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—31no—
222C4⋊Dic3C2×A411yescharacteristic, complemented
223Dic3⋊C4—32no—
224Dic3⋊C4—32no—
225Dic3⋊C4—31no—
226Dic3⋊C4—31no—
227Dic3⋊C4—31no—
228Dic3⋊C4—31no—
229Dic3⋊C4—31no—
230Dic3⋊C4—31no—
231Dic3⋊C4C2×A411yescharacteristic, complemented
232Dic3⋊C4C2×A411yescharacteristic, complemented
233C4×Dic3—32no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—31no—
237C4×Dic3C2×A411yescharacteristic, complemented
238C22×C32—41no—
239C22×C32—81no—
240C22×C32—81no—
241C22×C32—81no—
242C3×A4#12611yescharacteristic, complemented
243C32×C4—81no—
244C32×C4—81no—
245C3×Dic3—81no—
246C3×Dic3—81no—
247C3×Dic3—81no—
248C3×Dic3—81no—
249C25C2×C3×D311yescharacteristic
250C23×C4—31no—
251C23×C4—31no—
252C23×C4—31no—
253C23×C4—31no—
254C23×C4C2×C3×D311yescharacteristic
255C23×C4C2×C3×D311yescharacteristic
256#126—31no—
257#126—91no—
258#126—91no—
259#126—91no—
260#126—91no—
261#126—91no—
262#126—91no—
263#126—92no—
264#126—92no—
265#126—92no—
266#126—92no—
267#126—92no—
268#126—92no—
269#126—92no—
270#126—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C22⋊C4—31no—
284C2×C22⋊C4—31no—
285C2×C22⋊C4—31no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—91no—
288C2×C22⋊C4—91no—
289C2×C22⋊C4—91no—
290C2×C22⋊C4—91no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295C2×C42—91no—
296C2×C42—91no—
297C2×C42—91no—
298C2×C42—91no—
299C23×C3—31no—
300C23×C3—31no—
301C23×C3—31no—
302C23×C3—31no—
303C23×C3—31no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3—61no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—61no—
314C23×C3—61no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3—61no—
318C23×C3—81no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3—121no—
322C23×C3—122no—
323C23×C3C3×#4111yescharacteristic
324C23×C3C3×#4111yescharacteristic
325C23×C3C3×#4111yescharacteristic
326C23×C3C22×A411yescharacteristic
327C2×A4—21no—
328C2×A4—21no—
329C2×A4—21no—
330C2×A4—42no—
331C2×A4—41no—
332C2×A4#23511yescharacteristic
333C2×A4#23711yescharacteristic
334C2×A4#23711yescharacteristic
335C2×C3×C4—31no—
336C2×C3×C4—31no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—81no—
348C2×C3×C4—81no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4C22×A411yescharacteristic
354C2×C3×C4C22×A411yescharacteristic
355C2×Dic3—31no—
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3C22×A411yescharacteristic
376C2×Dic3C22×A411yescharacteristic
377C2×Dic3C22×A411yescharacteristic
378C2×Dic3C22×A411yescharacteristic
379C2×C32—41no—
380C2×C32—41no—
381C2×C32—41no—
382C2×C32—161no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—31no—
387C24—31no—
388C24—61no—
389C24—61no—
390C24—61no—
391C24C22×C3×D311yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—31no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—91no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4—181no—
416C4⋊C4—31no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—91no—
420C4⋊C4—91no—
421C4⋊C4—91no—
422C4⋊C4—91no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—92no—
426C4⋊C4—92no—
427C4⋊C4—92no—
428C4⋊C4—91no—
429C4⋊C4—91no—
430C4⋊C4—91no—
431C22⋊C4—32no—
432C22⋊C4—31no—
433C22⋊C4—31no—
434C22⋊C4—31no—
435C22⋊C4—31no—
436C22⋊C4—31no—
437C22⋊C4—91no—
438C22⋊C4—91no—
439C22⋊C4—91no—
440C22⋊C4—91no—
441C22⋊C4—92no—
442C22⋊C4—92no—
443C22⋊C4—91no—
444C22⋊C4—91no—
445C22⋊C4D3×A411yescharacteristic
446C42—31no—
447C42—91no—
448C42—91no—
449C42—92no—
450C42—91no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—31no—
455C22×C3—31no—
456C22×C3—31no—
457C22×C3—32no—
458C22×C3—31no—
459C22×C3—31no—
460C22×C3—31no—
461C22×C3—31no—
462C22×C3—31no—
463C22×C3—31no—
464C22×C3—41no—
465C22×C3—61no—
466C22×C3—61no—
467C22×C3—61no—
468C22×C3—81no—
469C22×C3—81no—
470C22×C3—81no—
471C22×C3—82no—
472C22×C3—81no—
473C22×C3—121no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—161no—
482C22×C3—161no—
483C22×C3C3×#12611yescharacteristic, complemented
484C22×C3C23×A411yescharacteristic
485A4—21no—
486A4#87911yescharacteristic, direct product factor
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—61no—
490C3×C4—61no—
491C3×C4—81no—
492C3×C4—81no—
493C3×C4—161no—
494C3×C4—161no—
495C3×C4—241no—
496C3×C4—241no—
497C3×C4—241no—
498C3×C4—241no—
499Dic3—21no—
500Dic3—21no—
501Dic3—21no—
502Dic3—21no—
503Dic3—61no—
504Dic3—61no—
505Dic3—61no—
506Dic3—61no—
507C32—41noSylow
508C23—31no—
509C23—31no—
510C23—31no—
511C23—31no—
512C23—31no—
513C23—41no—
514C23—61no—
515C23—61no—
516C23—61no—
517C23—61no—
518C23—61no—
519C23—61no—
520C23—61no—
521C23—61no—
522C23—61no—
523C23—61no—
524C23—61no—
525C23—61no—
526C23—121no—
527C23—121no—
528C23—121no—
529C23—122no—
530C23C3×#23511yescharacteristic
531C23C3×#23711yescharacteristic
532C23C3×#23711yescharacteristic
533C23C2×D3×A411yescharacteristic
534C2×C4—31no—
535C2×C4—31no—
536C2×C4—31no—
537C2×C4—31no—
538C2×C4—31no—
539C2×C4—31no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—91no—
549C2×C4—91no—
550C2×C4—91no—
551C2×C4—91no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4C2×D3×A411yescharacteristic
569C2×C4C2×D3×A411yescharacteristic
570C2×C3—31no—
571C2×C3—31no—
572C2×C3—31no—
573C2×C3—31no—
574C2×C3—41no—
575C2×C3—41no—
576C2×C3—41no—
577C2×C3—41no—
578C2×C3—81no—
579C2×C3—81no—
580C2×C3—81no—
581C2×C3—121no—
582C2×C3—161no—
583C2×C3—162no—
584C2×C3A4×#4111yescharacteristic
585C2×C3A4×#4111yescharacteristic
586C2×C3A4×#4111yescharacteristic
587C22—21no—
588C22—21no—
589C22—21no—
590C22—31no—
591C22—31no—
592C22—31no—
593C22—32no—
594C22—31no—
595C22—31no—
596C22—31no—
597C22—31no—
598C22—31no—
599C22—31no—
600C22—61no—
601C22—61no—
602C22—61no—
603C22—121no—
604C22—121no—
605C22—121no—
606C22—121no—
607C22—121no—
608C22—121no—
609C22—121no—
610C22—121no—
611C22C3×#87911yescharacteristic, complemented
612C22C22×D3×A411yescharacteristic
613C4—21no—
614C4—21no—
615C4—61no—
616C4—61no—
617C4—61no—
618C4—61no—
619C4—61no—
620C4—61no—
621C4—181no—
622C4—181no—
623C4—181no—
624C4—181no—
625C3—41no—
626C3—81no—
627C3A4×#12611yescharacteristic, complemented
628C2—31no—
629C2—31no—
630C2—31no—
631C2—31no—
632C2—41no—
633C2—121no—
634C2A4×#23511yescharacteristic
635C2A4×#23711yescharacteristic
636C2A4×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C22⋊C4C2×C3
prime radicalC23×C3×A4C22
hypercenterC22⋊C4D3×A4
hypocenterC22×C3C3×#126
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
4. A4×C4⋊Dic3C2semidirect
5. A4×Dic3⋊C4C2semidirect
6. A4×Dic3⋊C4C2semidirect
7. C4×Dic3×A4C2semidirect
8. C22×#879C3semidirect
21. C22×C4⋊Dic3C2×C3semidirect
22. C22×Dic3⋊C4C2×C3semidirect
23. C22×Dic3⋊C4C2×C3semidirect
24. C22×C4×Dic3C2×C3semidirect
119. #879A4direct (N × H)
222. C4⋊Dic3C2×A4semidirect
231. Dic3⋊C4C2×A4semidirect
232. Dic3⋊C4C2×A4semidirect
237. C4×Dic3C2×A4semidirect
242. C3×A4#126semidirect
483. C22×C3C3×#126semidirect
486. A4#879direct (N × H)
611. C22C3×#879semidirect
627. C3A4×#126semidirect

Maximal subgroups

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

subgroupindex
C3×A4×C22⋊C42
A4×#2172
A4×C4⋊Dic32
A4×Dic3⋊C42
C4×Dic3×A42
C22×#8793
A4×#1263
C3×#8794