Finite Group Databasebeta

← A4×#950 #11923382

Subgroups — A4×#950 #11923382

Order 1152.

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

normal subgroups only

This group has 748 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×#41C211yesmaximal, characteristic, complemented
2A4×#235C211yesmaximal, characteristic, complemented
3A4×#216C211yesmaximal, characteristic, complemented
4A4×#215C211yesmaximal, characteristic, complemented
5A4×#214C211yesmaximal, characteristic, complemented
6A4×#213C211yesmaximal, characteristic, complemented
7C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
8C22×#950C311yesmaximal, characteristic, complemented
9A4×#135—31nomaximal
10C3×Q8×A4C2211yescharacteristic
11C3×D4×A4—21no—
12C3×D4×A4C2211yescharacteristic
13C2×C3×C4×A4—21no—
14C2×C3×C4×A4C2211yescharacteristic
15A4×#67—21no—
16A4×D12C2211yescharacteristic
17C4×D3×A4—21no—
18A4×Dic6C2211yescharacteristic
19C3×#950—41nomaximal
20A4×C3⋊C8C2211yescharacteristic
21A4×C3⋊C8C2211yescharacteristic
22C22×C3×#41C2×C311yescharacteristic, complemented
23C22×#235C2×C311yescharacteristic, complemented
24A4×#41—21no—
25A4×#41—31no—
26A4×#41D311yescharacteristic, complemented
27C2×#950—31no—
28C2×#950—31no—
29C2×#950—31no—
30C2×#950—31no—
31C2×#950—31no—
32C2×#950—31no—
33C2×#950—31no—
34C2×#950—31no—
35C22×#216C2×C311yescharacteristic, complemented
36C22×#215C2×C311yescharacteristic, complemented
37C22×#214C2×C311yescharacteristic, complemented
38C22×#213C2×C311yescharacteristic, complemented
39C23×C3⋊C8C2×C311yescharacteristic, complemented
40A4×Q16—31no—
41A4×SD16—31no—
42A4×SD16—31no—
43A4×D8—31no—
44C2×C8×A4—31no—
45C22×C3×A4—21no—
46C22×C3×A4D411yescharacteristic
47C2×D3×A4—21no—
48C32×#41—41no—
49C3×#235—41no—
50C3×C4×A4—21no—
51C3×C4×A4D411yescharacteristic
52C3×C4×A4C2311yescharacteristic
53Dic3×A4—21no—
54C3×#216—41no—
55C3×#215—41no—
56C3×#214—41no—
57C3×#213—41no—
58C2×C3×C3⋊C8—41no—
59C22×#135—31noSylow
60C2×C3×#41—31no—
61C2×C3×#41—31no—
62C2×C3×#41—31no—
63C2×C3×#41—31no—
64C2×C3×#41—61no—
65C2×C3×#41—61no—
66C22×C3×Q8C22×C311yescharacteristic
67C22×C3×D4—21no—
68C22×C3×D4C22×C311yescharacteristic
69C23×C3×C4—21no—
70C23×C3×C4C22×C311yescharacteristic
71C22×#67—21no—
72C2×#235—31no—
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—31no—
76C2×#235—61no—
77C2×#235—61no—
78C22×D12C22×C311yescharacteristic
79C22×C4×D3—21no—
80C22×Dic6C22×C311yescharacteristic
81Q8×A4—21no—
82Q8×A4—31no—
83Q8×A4C2×D311yescharacteristic
84D4×A4—22no—
85D4×A4—21no—
86D4×A4—21no—
87D4×A4—31no—
88D4×A4—61no—
89D4×A4C2×D311yescharacteristic
90C2×C4×A4—22no—
91C2×C4×A4—21no—
92C2×C4×A4—21no—
93C2×C4×A4—61no—
94C2×C4×A4C2×D311yescharacteristic
95C3×#135—121no—
96#950—32no—
97#950—32no—
98#950—32no—
99#950—32no—
100#950—32no—
101#950—32no—
102#950—32no—
103#950—31no—
104#950—31no—
105#950—31no—
106#950—31no—
107#950—31no—
108#950—31no—
109#950—31no—
110#950A411yescharacteristic, direct product factor
111C2×#216—31no—
112C2×#216—31no—
113C2×#216—31no—
114C2×#216—31no—
115C2×#215—31no—
116C2×#215—31no—
117C2×#215—31no—
118C2×#215—31no—
119C2×#214—31no—
120C2×#214—31no—
121C2×#214—31no—
122C2×#214—31no—
123C2×#213—31no—
124C2×#213—31no—
125C2×#213—31no—
126C2×#213—31no—
127C22×C3⋊C8—31no—
128C22×C3⋊C8—31no—
129C22×C3⋊C8—31no—
130C22×C3⋊C8—31no—
131C22×C3⋊C8C22×C311yescharacteristic
132C22×C3⋊C8C22×C311yescharacteristic
133C8×A4—31no—
134C8×A4—31no—
135C2×C3×A4—21no—
136C2×C3×A4—41no—
137C2×C3×A4C2×D411yescharacteristic
138D3×A4—41no—
139C32×Q8—41no—
140C32×D4—41no—
141C32×D4—81no—
142C2×C32×C4—41no—
143C2×C32×C4—81no—
144C3×#67—81no—
145C3×D12—41no—
146C3×C4×D3—81no—
147C3×Dic6—41no—
148C3×C3⋊C8—41no—
149C3×C3⋊C8—41no—
150C22×#41—31no—
151C22×#41C3×D311yescharacteristic, complemented
152C2×#135—91no—
153C2×#135—91no—
154C2×#135—91no—
155C2×#135—91no—
156C2×#135—91no—
157C2×#135—91no—
158C2×#135—91no—
159C2×#135—91no—
160C22×Q16—31no—
161C22×SD16—31no—
162C22×SD16—31no—
163C22×D8—31no—
164C23×C8—31no—
165C24×C3—21no—
166C24×C3C3×D411yescharacteristic
167C23×D3—21no—
168C22×A4—22no—
169C22×A4—21no—
170C22×A4—21no—
171C22×A4—61no—
172C22×A4#6711yescharacteristic
173C3×#41—32no—
174C3×#41—31no—
175C3×#41—31no—
176C3×#41—31no—
177C3×#41—41no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—62no—
181C3×#41—62no—
182C3×#41—61no—
183C3×#41—61no—
184C3×#41—81no—
185C3×#41—121no—
186C3×#41C2×A411yescharacteristic, complemented
187C2×C3×Q8—31no—
188C2×C3×Q8—31no—
189C2×C3×Q8—61no—
190C2×C3×D4—31no—
191C2×C3×D4—31no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4C3×D411yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C2×#67—61no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—61no—
212C22×Dic3—21no—
213#235—32no—
214#235—31no—
215#235—31no—
216#235—31no—
217#235—61no—
218#235—61no—
219#235—62no—
220#235—62no—
221#235—61no—
222#235—61no—
223#235C2×A411yescharacteristic, complemented
224C2×D12—31no—
225C2×D12—31no—
226C2×D12—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×Dic6—31no—
232C2×Dic6—31no—
233C2×Dic6—61no—
234C4×A4—22no—
235C4×A4—21no—
236C4×A4—21no—
237C4×A4—21no—
238C4×A4—61no—
239C4×A4#6711yescharacteristic
240C4×A4C22×D311yescharacteristic
241C3×Q16—121no—
242C3×SD16—121no—
243C3×SD16—121no—
244C3×D8—121no—
245C2×C3×C8—121no—
246#216—32no—
247#216—31no—
248#216—31no—
249#216—31no—
250#216C2×A411yescharacteristic, complemented
251#215—32no—
252#215—31no—
253#215—31no—
254#215—31no—
255#215C2×A411yescharacteristic, complemented
256#214—32no—
257#214—31no—
258#214—31no—
259#214—31no—
260#214C2×A411yescharacteristic, complemented
261#213—32no—
262#213—31no—
263#213—31no—
264#213—31no—
265#213C2×A411yescharacteristic, complemented
266C2×C3⋊C8—32no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8C2×A411yescharacteristic, complemented
275C22×C32—41no—
276C22×C32—81no—
277C2×C3×D3—81no—
278C3×A4#13511yescharacteristic, complemented
279C32×C4—41no—
280C32×C4—41no—
281C32×C4—81no—
282C3×Dic3—81no—
283C2×#41—31no—
284C2×#41—31no—
285C2×#41—31no—
286C2×#41—31no—
287C2×#41—61no—
288C2×#41—61no—
289C2×#41—91no—
290C2×#41—91no—
291C2×#41—91no—
292C2×#41—91no—
293C2×#41—181no—
294C2×#41—181no—
295C22×Q8—31no—
296C22×Q8C2×C3×D311yescharacteristic
297C22×D4—21no—
298C22×D4—31no—
299C22×D4—61no—
300C22×D4C2×C3×D311yescharacteristic
301C23×C4—21no—
302C23×C4—61no—
303C23×C4C2×C3×D311yescharacteristic
304#135—31no—
305#135—91no—
306#135—91no—
307#135—91no—
308#135—91no—
309#135—91no—
310#135—91no—
311#135—92no—
312#135—92no—
313#135—92no—
314#135—92no—
315#135—92no—
316#135—92no—
317#135—92no—
318#135—91no—
319C2×Q16—91no—
320C2×Q16—91no—
321C2×Q16—91no—
322C2×Q16—91no—
323C2×SD16—91no—
324C2×SD16—91no—
325C2×SD16—91no—
326C2×SD16—91no—
327C2×SD16—91no—
328C2×SD16—91no—
329C2×SD16—91no—
330C2×SD16—91no—
331C2×D8—91no—
332C2×D8—91no—
333C2×D8—91no—
334C2×D8—91no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—91no—
338C22×C8—91no—
339C22×C8—91no—
340C22×C8—91no—
341C23×C3—21no—
342C23×C3—31no—
343C23×C3—31no—
344C23×C3—41no—
345C23×C3—61no—
346C23×C3—61no—
347C23×C3—61no—
348C23×C3—121no—
349C23×C3C2×C3×D411yescharacteristic
350C22×D3—41no—
351C22×D3—61no—
352C22×D3—61no—
353C22×D3—121no—
354C2×A4—21no—
355C2×A4—21no—
356C2×A4—41no—
357C2×A4—42no—
358C2×A4—41no—
359C2×A4—121no—
360C2×A4C2×#6711yescharacteristic
361C3×Q8—31no—
362C3×Q8—41no—
363C3×Q8—61no—
364C3×Q8—61no—
365C3×Q8—81no—
366C3×Q8—121no—
367C3×Q8C22×A411yescharacteristic
368C3×D4—21no—
369C3×D4—31no—
370C3×D4—41no—
371C3×D4—61no—
372C3×D4—61no—
373C3×D4—61no—
374C3×D4—61no—
375C3×D4—62no—
376C3×D4—61no—
377C3×D4—81no—
378C3×D4—82no—
379C3×D4—81no—
380C3×D4—121no—
381C3×D4—241no—
382C3×D4C22×A411yescharacteristic
383C2×C3×C4—21no—
384C2×C3×C4—32no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—41no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—81no—
400C2×C3×C4—82no—
401C2×C3×C4—81no—
402C2×C3×C4—241no—
403C2×C3×C4C22×A411yescharacteristic
404#67—21no—
405#67—61no—
406#67—61no—
407#67—62no—
408#67—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411D12—31no—
412D12—61no—
413D12—61no—
414D12C22×A411yescharacteristic
415C4×D3—21no—
416C4×D3—61no—
417C4×D3—61no—
418C4×D3—62no—
419C4×D3—61no—
420Dic6—31no—
421Dic6—61no—
422Dic6—61no—
423Dic6C22×A411yescharacteristic
424C3×C8—121no—
425C3×C8—121no—
426C3⋊C8—31no—
427C3⋊C8—31no—
428C3⋊C8C22×A411yescharacteristic
429C3⋊C8C22×A411yescharacteristic
430C2×C32—41no—
431C2×C32—81no—
432C2×C32—161no—
433C3×D3—161no—
434C24—21no—
435C24—61no—
436C24C3×#6711yescharacteristic
437#41—32no—
438#41—31no—
439#41—31no—
440#41—31no—
441#41—31no—
442#41—61no—
443#41—61no—
444#41—62no—
445#41—62no—
446#41—61no—
447#41—61no—
448#41—91no—
449#41—91no—
450#41—92no—
451#41—91no—
452#41—181no—
453#41—181no—
454#41—182no—
455#41—182no—
456#41—181no—
457#41—181no—
458#41D3×A411yescharacteristic, complemented
459C2×Q8—31no—
460C2×Q8—31no—
461C2×Q8—61no—
462C2×Q8—91no—
463C2×Q8—91no—
464C2×Q8—181no—
465C2×D4—31no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—91no—
473C2×D4—91no—
474C2×D4—181no—
475C2×D4—181no—
476C2×D4—181no—
477C2×D4—181no—
478C2×D4—181no—
479C22×C4—21no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—181no—
490C22×C4—181no—
491C22×C4—181no—
492C22×C4—181no—
493C22×C4C3×#6711yescharacteristic
494C22×C4C22×C3×D311yescharacteristic
495Q16—31no—
496Q16—91no—
497Q16—91no—
498Q16—92no—
499Q16—91no—
500SD16—31no—
501SD16—31no—
502SD16—91no—
503SD16—91no—
504SD16—91no—
505SD16—91no—
506SD16—92no—
507SD16—92no—
508SD16—91no—
509SD16—91no—
510D8—31no—
511D8—91no—
512D8—91no—
513D8—92no—
514D8—91no—
515C2×C8—31no—
516C2×C8—91no—
517C2×C8—91no—
518C2×C8—91no—
519C2×C8—91no—
520C2×C8—92no—
521C2×C8—91no—
522C2×C8—91no—
523C2×C8—91no—
524C22×C3—21no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—31no—
528C22×C3—41no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—61no—
533C22×C3—61no—
534C22×C3—81no—
535C22×C3—82no—
536C22×C3—81no—
537C22×C3—121no—
538C22×C3—121no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—241no—
542C22×C3C3×#13511yescharacteristic, complemented
543C22×C3D4×A411yescharacteristic
544C2×D3—21no—
545C2×D3—61no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
549C2×D3—121no—
550A4—21no—
551A4#95011yescharacteristic, direct product factor
552C3×C4—21no—
553C3×C4—31no—
554C3×C4—31no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—61no—
558C3×C4—81no—
559C3×C4—82no—
560C3×C4—81no—
561C3×C4—81no—
562C3×C4—241no—
563C3×C4D4×A411yescharacteristic
564C3×C4C23×A411yescharacteristic
565Dic3—21no—
566Dic3—61no—
567C32—41noSylow
568C23—21no—
569C23—31no—
570C23—31no—
571C23—41no—
572C23—61no—
573C23—61no—
574C23—61no—
575C23—121no—
576C23—121no—
577C23—181no—
578C23—181no—
579C23—361no—
580C23C2×C3×#6711yescharacteristic
581Q8—31no—
582Q8—31no—
583Q8—61no—
584Q8—61no—
585Q8—91no—
586Q8—181no—
587Q8—181no—
588Q8C2×D3×A411yescharacteristic
589D4—21no—
590D4—31no—
591D4—31no—
592D4—61no—
593D4—61no—
594D4—61no—
595D4—61no—
596D4—62no—
597D4—61no—
598D4—61no—
599D4—91no—
600D4—181no—
601D4—181no—
602D4—181no—
603D4—181no—
604D4—182no—
605D4—181no—
606D4C2×D3×A411yescharacteristic
607C2×C4—21no—
608C2×C4—32no—
609C2×C4—31no—
610C2×C4—31no—
611C2×C4—31no—
612C2×C4—31no—
613C2×C4—31no—
614C2×C4—31no—
615C2×C4—31no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—62no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—182no—
626C2×C4—181no—
627C2×C4—181no—
628C2×C4—181no—
629C2×C4C2×D3×A411yescharacteristic
630C8—31no—
631C8—31no—
632C8—91no—
633C8—91no—
634C2×C3—21no—
635C2×C3—31no—
636C2×C3—31no—
637C2×C3—41no—
638C2×C3—41no—
639C2×C3—61no—
640C2×C3—81no—
641C2×C3—81no—
642C2×C3—121no—
643C2×C3—161no—
644C2×C3—161no—
645C2×C3—162no—
646C2×C3—481no—
647C2×C3C2×D4×A411yescharacteristic
648D3—41no—
649D3—121no—
650C22—21no—
651C22—31no—
652C22—31no—
653C22—31no—
654C22—61no—
655C22—61no—
656C22—61no—
657C22—61no—
658C22—61no—
659C22—61no—
660C22—121no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22—181no—
665C22—361no—
666C22—361no—
667C22—361no—
668C22—361no—
669C22C3×#95011yescharacteristic, complemented
670C22A4×#6711yescharacteristic
671C4—21no—
672C4—31no—
673C4—31no—
674C4—61no—
675C4—61no—
676C4—181no—
677C4A4×#6711yescharacteristic
678C4C22×D3×A411yescharacteristic
679C3—41no—
680C3—81no—
681C3A4×#13511yescharacteristic, complemented
682C2—21no—
683C2—31no—
684C2—31no—
685C2—41no—
686C2—61no—
687C2—121no—
688C2—121no—
689C2—361no—
690C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC4A4×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC4C22×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C2×C3×D4
hypercenter#41D3×A4
hypocenterC22×C3C3×#135
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×A4×#41C2semidirect
2. A4×#235C2semidirect
3. A4×#216C2semidirect
4. A4×#215C2semidirect
5. A4×#214C2semidirect
6. A4×#213C2semidirect
7. C2×A4×C3⋊C8C2semidirect
8. C22×#950C3semidirect
22. C22×C3×#41C2×C3semidirect
23. C22×#235C2×C3semidirect
26. A4×#41D3semidirect
35. C22×#216C2×C3semidirect
36. C22×#215C2×C3semidirect
37. C22×#214C2×C3semidirect
38. C22×#213C2×C3semidirect
39. C23×C3⋊C8C2×C3semidirect
110. #950A4direct (N × H)
151. C22×#41C3×D3semidirect
186. C3×#41C2×A4semidirect
223. #235C2×A4semidirect
250. #216C2×A4semidirect
255. #215C2×A4semidirect
260. #214C2×A4semidirect
265. #213C2×A4semidirect
274. C2×C3⋊C8C2×A4semidirect
278. C3×A4#135semidirect
458. #41D3×A4semidirect
542. C22×C3C3×#135semidirect
551. A4#950direct (N × H)
669. C22C3×#950semidirect
681. C3A4×#135semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
A4×#2352
A4×#2162
A4×#2152
A4×#2142
A4×#2132
C2×A4×C3⋊C82
C22×#9503
A4×#1353
C3×#9504