Finite Group Databasebeta

← A4×#896 #11923161

Subgroups — A4×#896 #11923161

Order 1152.

886 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 886 conjugacy classes of subgroups — too many to draw. Only its 99 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×C4×D3×A4C211yesmaximal, characteristic
2C2×A4×Dic6C211yesmaximal, characteristic, complemented
3C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C211yesmaximal, characteristic
5A4×(C2×D3)⋊C4C211yesmaximal, characteristic
6A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8C22×#896C311yesmaximal, characteristic, complemented
9A4×C22⋊Q8—31nomaximal
10C22×D3×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14C2×Dic3×A4C2211yescharacteristic
15C2×Dic3×A4C2211yescharacteristic
16C2×Dic3×A4C2211yescharacteristic
17C4×D3×A4—22no—
18A4×Dic6—22no—
19C3×#896—41nomaximal
20C23×C4×D3C2×C311yescharacteristic
21C23×Dic6C2×C311yescharacteristic, complemented
22C2×Q8×A4—31no—
23C22×C4×A4—31no—
24C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
25C22×(C2×D3)⋊C4C2×C311yescharacteristic
26C22×(C2×D3)⋊C4C2×C311yescharacteristic
27C22×Dic3⋊C4C2×C311yescharacteristic, complemented
28C22×Dic3⋊C4C2×C311yescharacteristic, complemented
29C2×#896—31no—
30C2×#896—31no—
31C2×#896—31no—
32C2×#896—31no—
33C2×#896—31no—
34C2×#896—31no—
35C2×#896—31no—
36C2×#896—31no—
37A4×C4⋊C4—21no—
38A4×C4⋊C4—31no—
39A4×C4⋊C4—31no—
40A4×C4⋊C4D311yescharacteristic, complemented
41A4×C22⋊C4—31no—
42A4×C22⋊C4—31no—
43C22×C3×A4C2311yescharacteristic
44C2×D3×A4—21no—
45C2×D3×A4—21no—
46C2×D3×A4Q812yescomplemented
47C2×C3×C4×D3—41no—
48C2×C3×Dic6—41no—
49C3×C4×A4—21no—
50C3×C4×A4—21no—
51C3×C4×A4—21no—
52Dic3×A4—21no—
53Dic3×A4—21no—
54Dic3×A4D412yes—
55C32×C4⋊C4—41no—
56C3×(C2×D3)⋊C4—41no—
57C3×(C2×D3)⋊C4—41no—
58C3×Dic3⋊C4—41no—
59C3×Dic3⋊C4—41no—
60C22×C22⋊Q8—31noSylow
61C24×D3C22×C311yescharacteristic
62C23×A4—31no—
63C23×C3×C4C22×C311yescharacteristic
64C23×C3×C4C22×C311yescharacteristic
65C23×C3×C4C22×C311yescharacteristic
66C23×Dic3C22×C311yescharacteristic
67C23×Dic3C22×C311yescharacteristic
68C23×Dic3C22×C311yescharacteristic
69C22×C4×D3—22no—
70C22×C4×D3—31no—
71C22×C4×D3—31no—
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3—62no—
75C22×Dic6—22no—
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—31no—
79C22×Dic6—31no—
80C22×Dic6—62no—
81Q8×A4—62no—
82C2×C4×A4—21no—
83C2×C4×A4—21no—
84C2×C4×A4—21no—
85C2×C4×A4—31no—
86C2×C4×A4—31no—
87C2×C4×A4—31no—
88C2×C4×A4—62no—
89C2×C4×A4C2×D311yescharacteristic
90C2×C4×A4C2×D311yescharacteristic
91C2×C4×A4C2×D311yescharacteristic
92C3×C22⋊Q8—121no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×(C2×D3)⋊C4—31no—
98C2×(C2×D3)⋊C4—31no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—31no—
102C2×(C2×D3)⋊C4—31no—
103C2×(C2×D3)⋊C4—31no—
104C2×(C2×D3)⋊C4—31no—
105C2×Dic3⋊C4—31no—
106C2×Dic3⋊C4—31no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—31no—
113#896—32no—
114#896—32no—
115#896—32no—
116#896—32no—
117#896—32no—
118#896—32no—
119#896—32no—
120#896—31no—
121#896—31no—
122#896—31no—
123#896—31no—
124#896—31no—
125#896—31no—
126#896—31no—
127#896A411yescharacteristic, direct product factor
128C22×C3×D3—41no—
129C2×C3×A4C2×D411yescharacteristic
130C2×C3×A4C2×Q811yescharacteristic
131C2×C3×A4#4111yescharacteristic
132D3×A4—22no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×C4×D3—82no—
140C3×Dic6—82no—
141C23×Q8—31no—
142C24×C4—31no—
143C2×C22⋊Q8—91no—
144C2×C22⋊Q8—91no—
145C2×C22⋊Q8—91no—
146C2×C22⋊Q8—91no—
147C2×C22⋊Q8—91no—
148C2×C22⋊Q8—91no—
149C2×C22⋊Q8—91no—
150C2×C22⋊Q8—91no—
151C22×C4⋊C4—31no—
152C22×C4⋊C4—31no—
153C22×C4⋊C4C3×D311yescharacteristic, complemented
154C22×C22⋊C4—31no—
155C22×C22⋊C4—31no—
156C24×C3C23×C311yescharacteristic
157C23×D3—21no—
158C23×D3—21no—
159C23×D3—31no—
160C23×D3—31no—
161C23×D3—32no—
162C23×D3—61no—
163C23×D3—61no—
164C23×D3C3×Q812yescomplemented
165C22×A4—21no—
166C22×A4—32no—
167C22×A4—61no—
168C22×A4—61no—
169C22×A4C22×D311yescharacteristic
170C2×C3×Q8—121no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—121no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—32no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3C3×D412yes—
196C2×C4×D3—32no—
197C2×C4×D3—31no—
198C2×C4×D3—31no—
199C2×C4×D3—31no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3C2×A411yescharacteristic
209C2×Dic6—32no—
210C2×Dic6—31no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6C2×A411yescharacteristic, complemented
222C4×A4—22no—
223C4×A4—21no—
224C4×A4—21no—
225C4×A4—21no—
226C4×A4—32no—
227C4×A4—41no—
228C4×A4—41no—
229C4×A4—61no—
230C4×A4—61no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—81no—
237C3×C4⋊C4—121no—
238C3×C4⋊C4—121no—
239C3×C4⋊C4C2×A411yescharacteristic, complemented
240C3×C22⋊C4—121no—
241C3×C22⋊C4—121no—
242(C2×D3)⋊C4—32no—
243(C2×D3)⋊C4—32no—
244(C2×D3)⋊C4—31no—
245(C2×D3)⋊C4—31no—
246(C2×D3)⋊C4—31no—
247(C2×D3)⋊C4—31no—
248(C2×D3)⋊C4—31no—
249(C2×D3)⋊C4—31no—
250(C2×D3)⋊C4C2×A411yescharacteristic
251(C2×D3)⋊C4C2×A411yescharacteristic
252Dic3⋊C4—32no—
253Dic3⋊C4—32no—
254Dic3⋊C4—31no—
255Dic3⋊C4—31no—
256Dic3⋊C4—31no—
257Dic3⋊C4—31no—
258Dic3⋊C4—31no—
259Dic3⋊C4—31no—
260Dic3⋊C4C2×A411yescharacteristic, complemented
261Dic3⋊C4C2×A411yescharacteristic, complemented
262C22×C32—41no—
263C2×C3×D3—42no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C3×A4C22⋊Q811yescharacteristic, complemented
267C32×C4—81no—
268C32×C4—81no—
269C32×C4—81no—
270C3×Dic3—42no—
271C3×Dic3—81no—
272C3×Dic3—81no—
273C25—31no—
274C22×Q8—62no—
275C22×Q8—91no—
276C22×Q8—91no—
277C22×Q8—91no—
278C22×Q8—91no—
279C22×Q8—182no—
280C23×C4—31no—
281C23×C4—31no—
282C23×C4—31no—
283C23×C4—62no—
284C23×C4—91no—
285C23×C4—91no—
286C23×C4—91no—
287C23×C4—91no—
288C23×C4—182no—
289C23×C4C2×C3×D311yescharacteristic
290C23×C4C2×C3×D311yescharacteristic
291C23×C4C2×C3×D311yescharacteristic
292C22⋊Q8—31no—
293C22⋊Q8—91no—
294C22⋊Q8—91no—
295C22⋊Q8—91no—
296C22⋊Q8—91no—
297C22⋊Q8—91no—
298C22⋊Q8—91no—
299C22⋊Q8—92no—
300C22⋊Q8—92no—
301C22⋊Q8—92no—
302C22⋊Q8—92no—
303C22⋊Q8—92no—
304C22⋊Q8—92no—
305C22⋊Q8—92no—
306C22⋊Q8—91no—
307C2×C4⋊C4—31no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—91no—
318C2×C4⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4—91no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—91no—
327C23×C3—31no—
328C23×C3—31no—
329C23×C3—31no—
330C23×C3—31no—
331C23×C3—121no—
332C23×C3C2×C3×D411yescharacteristic
333C23×C3C2×C3×Q811yescharacteristic
334C23×C3C3×#4111yescharacteristic
335C22×D3—22no—
336C22×D3—32no—
337C22×D3—31no—
338C22×D3—32no—
339C22×D3—32no—
340C22×D3—32no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—64no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—62no—
353C22×D3C22×A411yescharacteristic
354C2×A4—21no—
355C2×A4—21no—
356C2×A4—21no—
357C2×A4—62no—
358C2×A4#23511yescharacteristic
359C2×A4D3×D411yescharacteristic
360C2×A4D3×Q811yescharacteristic
361C3×Q8—242no—
362C2×C3×C4—31no—
363C2×C3×C4—31no—
364C2×C3×C4—31no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—81no—
381C2×C3×C4—81no—
382C2×C3×C4—81no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4—242no—
387C2×C3×C4C22×A411yescharacteristic
388C2×C3×C4C22×A411yescharacteristic
389C2×C3×C4C22×A411yescharacteristic
390C2×Dic3—32no—
391C2×Dic3—31no—
392C2×Dic3—32no—
393C2×Dic3—32no—
394C2×Dic3—32no—
395C2×Dic3—31no—
396C2×Dic3—31no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3C22×A411yescharacteristic
406C2×Dic3C22×A411yescharacteristic
407C2×Dic3C22×A411yescharacteristic
408C4×D3—22no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—64no—
412C4×D3—62no—
413Dic6—22no—
414Dic6—62no—
415Dic6—62no—
416Dic6—64no—
417Dic6—62no—
418C2×C32—41no—
419C2×C32—41no—
420C2×C32—41no—
421C3×D3—82no—
422C24—32no—
423C24—61no—
424C24—61no—
425C24—91no—
426C24—91no—
427C24—92no—
428C24—181no—
429C24—181no—
430C24C22×C3×D311yescharacteristic
431C2×Q8—31no—
432C2×Q8—91no—
433C2×Q8—91no—
434C2×Q8—92no—
435C2×Q8—91no—
436C2×Q8—182no—
437C2×Q8—182no—
438C2×Q8—182no—
439C2×Q8—182no—
440C2×Q8—182no—
441C2×Q8—182no—
442C2×Q8—182no—
443C2×Q8—182no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—92no—
466C22×C4—91no—
467C22×C4—92no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—91no—
471C22×C4—182no—
472C22×C4—182no—
473C22×C4—182no—
474C22×C4—182no—
475C22×C4—182no—
476C22×C4—182no—
477C22×C4—182no—
478C22×C4—182no—
479C22×C4—181no—
480C22×C4—181no—
481C4⋊C4—32no—
482C4⋊C4—31no—
483C4⋊C4—31no—
484C4⋊C4—31no—
485C4⋊C4—31no—
486C4⋊C4—31no—
487C4⋊C4—91no—
488C4⋊C4—91no—
489C4⋊C4—91no—
490C4⋊C4—91no—
491C4⋊C4—92no—
492C4⋊C4—92no—
493C4⋊C4—91no—
494C4⋊C4—91no—
495C4⋊C4D3×A411yescharacteristic, complemented
496C22⋊C4—31no—
497C22⋊C4—31no—
498C22⋊C4—91no—
499C22⋊C4—91no—
500C22⋊C4—91no—
501C22⋊C4—91no—
502C22⋊C4—92no—
503C22⋊C4—92no—
504C22⋊C4—91no—
505C22⋊C4—91no—
506C22×C3—31no—
507C22×C3—31no—
508C22×C3—31no—
509C22×C3—32no—
510C22×C3—31no—
511C22×C3—31no—
512C22×C3—31no—
513C22×C3—31no—
514C22×C3—31no—
515C22×C3—31no—
516C22×C3—41no—
517C22×C3—81no—
518C22×C3—122no—
519C22×C3—241no—
520C22×C3—241no—
521C22×C3C3×C22⋊Q811yescharacteristic, complemented
522C22×C3C23×A411yescharacteristic
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—32no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—61no—
533C2×D3—61no—
534C2×D3—62no—
535C2×D3—62no—
536C2×D3Q8×A412yescomplemented
537A4—21no—
538A4#89611yescharacteristic, direct product factor
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—61no—
543C3×C4—61no—
544C3×C4—61no—
545C3×C4—81no—
546C3×C4—81no—
547C3×C4—81no—
548C3×C4—82no—
549C3×C4—122no—
550C3×C4—161no—
551C3×C4—161no—
552C3×C4—241no—
553C3×C4—241no—
554Dic3—21no—
555Dic3—21no—
556Dic3—32no—
557Dic3—61no—
558Dic3—61no—
559Dic3D4×A412yes—
560C32—41noSylow
561C23—31no—
562C23—31no—
563C23—31no—
564C23—31no—
565C23—31no—
566C23—62no—
567C23—92no—
568C23—92no—
569C23—92no—
570C23—92no—
571C23—91no—
572C23—181no—
573C23—181no—
574C23—181no—
575C23—181no—
576C23—182no—
577C23—181no—
578C23—181no—
579C23—182no—
580C23—182no—
581C23—181no—
582C23—181no—
583C23—184no—
584C23C3×#23511yescharacteristic
585C23C3×D3×D411yescharacteristic
586C23C3×D3×Q811yescharacteristic
587Q8—62no—
588Q8—182no—
589Q8—182no—
590Q8—182no—
591Q8—184no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—62no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4—92no—
612C2×C4—92no—
613C2×C4—92no—
614C2×C4—91no—
615C2×C4—92no—
616C2×C4—91no—
617C2×C4—91no—
618C2×C4—182no—
619C2×C4—182no—
620C2×C4—182no—
621C2×C4—184no—
622C2×C4—181no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—181no—
628C2×C4—181no—
629C2×C4—181no—
630C2×C4C2×D3×A411yescharacteristic
631C2×C4C2×D3×A411yescharacteristic
632C2×C4C2×D3×A411yescharacteristic
633C2×C3—31no—
634C2×C3—31no—
635C2×C3—31no—
636C2×C3—31no—
637C2×C3—41no—
638C2×C3—41no—
639C2×C3—41no—
640C2×C3—81no—
641C2×C3—81no—
642C2×C3—81no—
643C2×C3—242no—
644C2×C3C2×D4×A411yescharacteristic
645C2×C3C2×Q8×A411yescharacteristic
646C2×C3A4×#4111yescharacteristic
647D3—22no—
648D3—62no—
649C22—31no—
650C22—31no—
651C22—31no—
652C22—32no—
653C22—31no—
654C22—31no—
655C22—31no—
656C22—31no—
657C22—31no—
658C22—31no—
659C22—32no—
660C22—61no—
661C22—61no—
662C22—92no—
663C22—182no—
664C22—182no—
665C22—182no—
666C22—182no—
667C22—182no—
668C22—182no—
669C22—182no—
670C22—182no—
671C22—181no—
672C22—181no—
673C22C3×#89611yescharacteristic, complemented
674C22C22×D3×A411yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—32no—
679C4—61no—
680C4—61no—
681C4—61no—
682C4—61no—
683C4—61no—
684C4—92no—
685C4—181no—
686C4—181no—
687C3—41no—
688C3—81no—
689C3A4×C22⋊Q811yescharacteristic, complemented
690C2—31no—
691C2—31no—
692C2—31no—
693C2—31no—
694C2—62no—
695C2—182no—
696C2A4×#23511yescharacteristic
697C2D3×D4×A411yescharacteristic
698C2D3×Q8×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C4⋊C4C2×C3
prime radicalC22×D3×A4C22
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C3×C22⋊Q8
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic6C2semidirect
3. C3×A4×C4⋊C4C2semidirect
6. A4×Dic3⋊C4C2semidirect
7. A4×Dic3⋊C4C2semidirect
8. C22×#896C3semidirect
21. C23×Dic6C2×C3semidirect
24. C22×C3×C4⋊C4C2×C3semidirect
27. C22×Dic3⋊C4C2×C3semidirect
28. C22×Dic3⋊C4C2×C3semidirect
40. A4×C4⋊C4D3semidirect
46. C2×D3×A4Q8semidirect
127. #896A4direct (N × H)
153. C22×C4⋊C4C3×D3semidirect
164. C23×D3C3×Q8semidirect
221. C2×Dic6C2×A4semidirect
239. C3×C4⋊C4C2×A4semidirect
260. Dic3⋊C4C2×A4semidirect
261. Dic3⋊C4C2×A4semidirect
266. C3×A4C22⋊Q8semidirect
495. C4⋊C4D3×A4semidirect
521. C22×C3C3×C22⋊Q8semidirect
536. C2×D3Q8×A4semidirect
538. A4#896direct (N × H)
673. C22C3×#896semidirect
689. C3A4×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×A42
C2×A4×Dic62
C3×A4×C4⋊C42
A4×(C2×D3)⋊C42
A4×Dic3⋊C42
C22×#8963
A4×C22⋊Q83
C3×#8964