Finite Group Databasebeta

← D3×A4×D12 #13180887

Subgroups — D3×A4×D12 #13180887

Order 1728.

1410 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 1410 conjugacy classes of subgroups — too many to draw. Only its 108 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×D32×A4C212yesmaximal, complemented
2A4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×A4×D12C211yesmaximal, characteristic, complemented
4C3×C4×D3×A4C211yesmaximal, characteristic, complemented
5A4×#626C212yesmaximal, complemented
6C22×D3×D12C311yesmaximal, characteristic, complemented
7D3×D4×A4—31nomaximal
8C2×A4×D12—31nomaximal
9C2×A4×C3⋊D3C2212yescomplemented
10C2×C3×D3×A4C2211yescharacteristic
11C2×C3×D3×A4C2212yescomplemented
12D32×A4—24no—
13C32×C4×A4C2211yescharacteristic, complemented
14C3×D3×D12—41nomaximal
15C3×Dic3×A4C2211yescharacteristic, complemented
16C23×D32C2×C312yescomplemented
17C22×D3×A4—32no—
18C22×D3×A4—32no—
19C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
20C22×C3×D12C2×C311yescharacteristic, complemented
21C22×C3×C4×D3C2×C311yescharacteristic, complemented
22C3×D4×A4—31no—
23C2×C3×C4×A4—31no—
24C22×#626C2×C312yescomplemented
25C2×D3×D12—31no—
26C2×D3×D12—32no—
27C2×D3×D12—31no—
28C2×D3×D12—31no—
29C2×D3×D12—31no—
30C2×D3×D12—32no—
31A4×#67—32no—
32A4×D12—21no—
33A4×D12—31no—
34A4×D12—31no—
35A4×D12—32no—
36A4×D12—61no—
37A4×D12D311yescharacteristic, direct product factor
38C4×D3×A4—21no—
39C4×D3×A4D311yescharacteristic, complemented
40C2×C32×A4C2311yescharacteristic
41C2×C3×D32—42no—
42A4×C3⋊D3—22no—
43C3×D3×A4—22no—
44C3×D3×A4D412yescomplemented
45C3×C4⋊(C3⋊D3)—41no—
46C32×D12—41no—
47C32×C4×D3—41no—
48C3×#626—42no—
49C22×D3×D4—31no—
50C23×D12—31no—
51C2×D4×A4—91no—
52C23×C3⋊D3C22×C312yescomplemented
53C23×C3×D3C22×C311yescharacteristic
54C23×C3×D3C22×C312yescomplemented
55C22×C3×A4—31no—
56C22×C3×A4—32no—
57C22×D32—24no—
58C22×D32—32no—
59C22×D32—32no—
60C22×D32—32no—
61C22×D32—32no—
62C22×D32—64no—
63C2×D3×A4—21no—
64C2×D3×A4—22no—
65C2×D3×A4—32no—
66C2×D3×A4—32no—
67C2×D3×A4—64no—
68C2×D3×A4—64no—
69C2×D3×A4—62no—
70C2×D3×A4C2×D311yescharacteristic
71C2×D3×A4C2×D312yescomplemented
72C22×C32×C4C22×C311yescharacteristic, complemented
73C2×C4⋊(C3⋊D3)—31no—
74C2×C4⋊(C3⋊D3)—32no—
75C2×C4⋊(C3⋊D3)—31no—
76C22×C3×Dic3C22×C311yescharacteristic, complemented
77C3×D3×D4—121no—
78C2×C3×D12—31no—
79C2×C3×D12—32no—
80C2×C3×D12—31no—
81C2×C3×D12—121no—
82C2×C3×C4×D3—31no—
83C2×C3×C4×D3—31no—
84C2×C3×C4×D3—31no—
85C2×C3×C4×D3—31no—
86C3×C4×A4—21no—
87C3×C4×A4—21no—
88C3×C4×A4—21no—
89C3×C4×A4—31no—
90C3×C4×A4—41no—
91C3×C4×A4C2×D311yescharacteristic, complemented
92C3×C4×A4C2×D311yescharacteristic, complemented
93C2×#626—32no—
94C2×#626—32no—
95C2×#626—32no—
96C2×#626—32no—
97D3×D12—32no—
98D3×D12—32no—
99D3×D12—34no—
100D3×D12—34no—
101D3×D12—32no—
102D3×D12—32no—
103D3×D12—31no—
104D3×D12—31no—
105D3×D12—31no—
106D3×D12—32no—
107D3×D12A411yescharacteristic, direct product factor
108Dic3×A4—21no—
109Dic3×A4C2×D311yescharacteristic, complemented
110C2×C3×C3⋊D3—42no—
111C2×C32×D3—41no—
112C2×C32×D3—42no—
113C32×A4C2×D411yescharacteristic, complemented
114C3×D32—84no—
115C33×C4—41no—
116C32×Dic3—41no—
117C24×D3—32no—
118C24×D3—32no—
119C23×A4—92no—
120C22×C3×D4—31no—
121C23×C3×C4—31no—
122C22×#67—32no—
123C2×D3×D4—91no—
124C2×D3×D4—91no—
125C2×D3×D4—91no—
126C2×D3×D4—92no—
127C2×D3×D4—91no—
128C2×D3×D4—92no—
129C22×D12—32no—
130C22×D12—31no—
131C22×D12—31no—
132C22×D12—61no—
133C22×D12—91no—
134C22×D12—91no—
135C22×D12—91no—
136C22×D12—92no—
137C22×D12—91no—
138C22×D12—92no—
139C22×D12C3×D311yescharacteristic, complemented
140C22×C4×D3C3×D311yescharacteristic, complemented
141D4×A4—31no—
142D4×A4—61no—
143D4×A4—92no—
144D4×A4—91no—
145C2×C4×A4—31no—
146C2×C4×A4—61no—
147C23×C32C23×C311yescharacteristic
148C22×C3⋊D3—22no—
149C22×C3⋊D3—32no—
150C22×C3⋊D3—32no—
151C22×C3⋊D3—62no—
152C22×C3×D3—22no—
153C22×C3×D3—31no—
154C22×C3×D3—31no—
155C22×C3×D3—32no—
156C22×C3×D3—32no—
157C22×C3×D3—32no—
158C22×C3×D3—62no—
159C22×C3×D3—122no—
160C22×C3×D3—122no—
161C22×C3×D3C3×D412yescomplemented
162C2×C3×A4—21no—
163C2×C3×A4—21no—
164C2×C3×A4—21no—
165C2×C3×A4—32no—
166C2×C3×A4—41no—
167C2×C3×A4—62no—
168C2×C3×A4C22×D311yescharacteristic
169C2×C3×A4C22×D311yescharacteristic
170C2×D32—34no—
171C2×D32—32no—
172C2×D32—32no—
173C2×D32—32no—
174C2×D32—64no—
175C2×D32—64no—
176C2×D32—64no—
177C2×D32—64no—
178C2×D32—64no—
179C2×D32—64no—
180C2×D32—64no—
181C2×D32—64no—
182C2×D32C2×A412yescomplemented
183D3×A4—22no—
184D3×A4—22no—
185D3×A4—42no—
186D3×A4—62no—
187D3×A4—62no—
188D3×A4—122no—
189D3×A4D1212yesdirect product factor
190C32×D4—121no—
191C2×C32×C4—31no—
192C2×C32×C4—31no—
193C2×C32×C4—121no—
194C4⋊(C3⋊D3)—32no—
195C4⋊(C3⋊D3)—32no—
196C4⋊(C3⋊D3)—31no—
197C4⋊(C3⋊D3)C2×A411yescharacteristic, complemented
198C3×#67—122no—
199C2×C3×Dic3—31no—
200C2×C3×Dic3—31no—
201C3×D12—32no—
202C3×D12—32no—
203C3×D12—31no—
204C3×D12—41no—
205C3×D12—81no—
206C3×D12—121no—
207C3×D12—121no—
208C3×D12—122no—
209C3×D12—241no—
210C3×D12C2×A411yescharacteristic, complemented
211C3×C4×D3—32no—
212C3×C4×D3—31no—
213C3×C4×D3—31no—
214C3×C4×D3—31no—
215C3×C4×D3—41no—
216C3×C4×D3—81no—
217C3×C4×D3C2×A411yescharacteristic, complemented
218#626—34no—
219#626—32no—
220#626—32no—
221#626—32no—
222#626C2×A412yescomplemented
223C23×D4—91noSylow
224C2×C33—41no—
225C3×C3⋊D3—82no—
226C32×D3—42no—
227C32×D3—82no—
228C24×C3—31no—
229C24×C3—32no—
230C23×D3—32no—
231C23×D3—32no—
232C23×D3—62no—
233C23×D3—64no—
234C23×D3—64no—
235C23×D3—92no—
236C23×D3—92no—
237C23×D3—92no—
238C23×D3—92no—
239C23×D3—92no—
240C23×D3—92no—
241C23×D3—92no—
242C23×D3—92no—
243C23×D3—184no—
244C23×D3—184no—
245C23×D3C2×C3×D311yescharacteristic
246C23×D3C2×C3×D312yescomplemented
247C22×A4—31no—
248C22×A4—32no—
249C22×A4—61no—
250C22×A4—62no—
251C22×A4—92no—
252C22×A4—184no—
253C2×C3×D4—91no—
254C2×C3×D4—91no—
255C2×C3×D4—92no—
256C2×C3×D4—361no—
257C22×C3×C4—21no—
258C22×C3×C4—31no—
259C22×C3×C4—91no—
260C22×C3×C4—91no—
261C22×C3×C4—91no—
262C22×C3×C4—91no—
263C22×C3×C4C2×C3×D311yescharacteristic, complemented
264C22×C3×C4C2×C3×D311yescharacteristic, complemented
265C2×#67—92no—
266C2×#67—92no—
267C2×#67—92no—
268C2×#67—92no—
269C22×Dic3C2×C3×D311yescharacteristic, complemented
270D3×D4—31no—
271D3×D4—91no—
272D3×D4—92no—
273D3×D4—91no—
274D3×D4—92no—
275D3×D4—94no—
276D3×D4—94no—
277D3×D4—92no—
278D3×D4—92no—
279D3×D4—92no—
280D3×D4—91no—
281C2×D12—31no—
282C2×D12—31no—
283C2×D12—32no—
284C2×D12—31no—
285C2×D12—92no—
286C2×D12—91no—
287C2×D12—91no—
288C2×D12—91no—
289C2×D12—91no—
290C2×D12—92no—
291C2×D12—92no—
292C2×D12—92no—
293C2×D12—94no—
294C2×D12—92no—
295C2×D12—94no—
296C2×D12—92no—
297C2×D12—91no—
298C2×D12—92no—
299C2×D12—91no—
300C2×D12—92no—
301C2×D12—91no—
302C2×D12—92no—
303C2×D12—92no—
304C2×D12—92no—
305C2×D12—181no—
306C2×D12—181no—
307C2×D12—182no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C4×A4—21no—
313C4×A4—21no—
314C4×A4—31no—
315C4×A4—41no—
316C4×A4—61no—
317C4×A4D3211yescharacteristic, complemented
318C22×C32—31no—
319C22×C32—31no—
320C22×C32—121no—
321C22×C32—122no—
322C22×C32C2×C3×D411yescharacteristic, complemented
323C2×C3⋊D3—32no—
324C2×C3⋊D3—62no—
325C2×C3⋊D3—62no—
326C2×C3⋊D3—62no—
327C2×C3⋊D3—62no—
328C2×C3⋊D3C22×A412yescomplemented
329C2×C3×D3—32no—
330C2×C3×D3—31no—
331C2×C3×D3—32no—
332C2×C3×D3—32no—
333C2×C3×D3—32no—
334C2×C3×D3—32no—
335C2×C3×D3—41no—
336C2×C3×D3—42no—
337C2×C3×D3—62no—
338C2×C3×D3—62no—
339C2×C3×D3—62no—
340C2×C3×D3—62no—
341C2×C3×D3—81no—
342C2×C3×D3—82no—
343C2×C3×D3—122no—
344C2×C3×D3—122no—
345C2×C3×D3—242no—
346C2×C3×D3—244no—
347C2×C3×D3—244no—
348C2×C3×D3C22×A411yescharacteristic
349C2×C3×D3C22×A412yescomplemented
350C3×A4—21no—
351C3×A4—21no—
352C3×A4—21no—
353C3×A4—41no—
354C3×A4C2×D1211yescharacteristic, complemented
355C3×A4D3×D411yescharacteristic, complemented
356D32—24no—
357D32—64no—
358D32—64no—
359D32—68no—
360D32—64no—
361C32×C4—31no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—81no—
365C32×C4—81no—
366C32×C4—81no—
367C32×C4—121no—
368C32×C4—161no—
369C32×C4C22×A411yescharacteristic, complemented
370C3×Dic3—31no—
371C3×Dic3—41no—
372C3×Dic3—81no—
373C3×Dic3C22×A411yescharacteristic, complemented
374C25—92no—
375C22×D4—31no—
376C22×D4—92no—
377C22×D4—91no—
378C22×D4—271no—
379C22×D4—271no—
380C22×D4—271no—
381C22×D4—271no—
382C22×D4—272no—
383C22×D4—272no—
384C23×C4—31no—
385C33—41noSylow
386C23×C3—21no—
387C23×C3—32no—
388C23×C3—62no—
389C23×C3—91no—
390C23×C3—92no—
391C23×C3—91no—
392C23×C3—92no—
393C23×C3—92no—
394C23×C3—182no—
395C23×C3—362no—
396C23×C3C22×C3×D311yescharacteristic
397C23×C3C22×C3×D311yescharacteristic
398C22×D3—22no—
399C22×D3—31no—
400C22×D3—31no—
401C22×D3—32no—
402C22×D3—32no—
403C22×D3—32no—
404C22×D3—32no—
405C22×D3—32no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—92no—
410C22×D3—92no—
411C22×D3—92no—
412C22×D3—92no—
413C22×D3—92no—
414C22×D3—92no—
415C22×D3—94no—
416C22×D3—94no—
417C22×D3—92no—
418C22×D3—92no—
419C22×D3—92no—
420C22×D3—92no—
421C22×D3—122no—
422C22×D3—182no—
423C22×D3—182no—
424C22×D3—184no—
425C22×D3—184no—
426C22×D3—184no—
427C22×D3—184no—
428C22×D3—184no—
429C22×D3—184no—
430C22×D3—184no—
431C22×D3—184no—
432C22×D3—184no—
433C22×D3—184no—
434C22×D3—184no—
435C22×D3—184no—
436C22×D3—184no—
437C22×D3—184no—
438C22×D3—184no—
439C22×D3—184no—
440C22×D3—182no—
441C22×D3—182no—
442C22×D3—362no—
443C22×D3C3×D1212yescomplemented
444C2×A4—21no—
445C2×A4—21no—
446C2×A4—32no—
447C2×A4—41no—
448C2×A4—62no—
449C2×A4—62no—
450C2×A4—122no—
451C2×A4—182no—
452C2×A4C2×D3211yescharacteristic
453C3×D4—31no—
454C3×D4—92no—
455C3×D4—92no—
456C3×D4—91no—
457C3×D4—121no—
458C3×D4—241no—
459C3×D4—361no—
460C3×D4—362no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—91no—
469C2×C3×C4—91no—
470C2×C3×C4—91no—
471C2×C3×C4—92no—
472C2×C3×C4—91no—
473C2×C3×C4—91no—
474C2×C3×C4—121no—
475C2×C3×C4—241no—
476#67—32no—
477#67—92no—
478#67—92no—
479#67—94no—
480#67—92no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483D12—32no—
484D12—32no—
485D12—32no—
486D12—31no—
487D12—31no—
488D12—31no—
489D12—61no—
490D12—92no—
491D12—92no—
492D12—92no—
493D12—92no—
494D12—92no—
495D12—92no—
496D12—94no—
497D12—92no—
498D12—91no—
499D12—91no—
500D12—181no—
501D12—182no—
502D12—182no—
503D12D3×A411yescharacteristic, direct product factor
504C4×D3—32no—
505C4×D3—31no—
506C4×D3—31no—
507C4×D3—31no—
508C4×D3D3×A411yescharacteristic, complemented
509C2×C32—31no—
510C2×C32—31no—
511C2×C32—41no—
512C2×C32—41no—
513C2×C32—81no—
514C2×C32—81no—
515C2×C32—81no—
516C2×C32—122no—
517C2×C32—161no—
518C2×C32—242no—
519C2×C32C23×A411yescharacteristic
520C3⋊D3—22no—
521C3⋊D3—62no—
522C3×D3—22no—
523C3×D3—32no—
524C3×D3—42no—
525C3×D3—62no—
526C3×D3—82no—
527C3×D3—82no—
528C3×D3—162no—
529C3×D3—242no—
530C3×D3—242no—
531C3×D3—482no—
532C3×D3D4×A412yescomplemented
533C24—31no—
534C24—32no—
535C24—92no—
536C24—184no—
537C24—272no—
538C24—272no—
539C24—272no—
540C24—272no—
541C24—544no—
542C2×D4—91no—
543C2×D4—91no—
544C2×D4—91no—
545C2×D4—92no—
546C2×D4—271no—
547C2×D4—271no—
548C2×D4—271no—
549C2×D4—272no—
550C2×D4—271no—
551C2×D4—272no—
552C2×D4—271no—
553C2×D4—272no—
554C2×D4—272no—
555C2×D4—272no—
556C2×D4—272no—
557C2×D4—274no—
558C2×D4—274no—
559C2×D4—272no—
560C2×D4—272no—
561C2×D4—272no—
562C2×D4—272no—
563C22×C4—31no—
564C22×C4—91no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4C3×D3211yescharacteristic, complemented
569C22×C3—21no—
570C22×C3—31no—
571C22×C3—31no—
572C22×C3—31no—
573C22×C3—31no—
574C22×C3—31no—
575C22×C3—32no—
576C22×C3—61no—
577C22×C3—61no—
578C22×C3—92no—
579C22×C3—92no—
580C22×C3—92no—
581C22×C3—92no—
582C22×C3—91no—
583C22×C3—92no—
584C22×C3—121no—
585C22×C3—122no—
586C22×C3—182no—
587C22×C3—182no—
588C22×C3—182no—
589C22×C3—182no—
590C22×C3—241no—
591C22×C3—242no—
592C22×C3—362no—
593C22×C3—724no—
594C22×C3C2×C3×D1211yescharacteristic, complemented
595C22×C3C3×D3×D411yescharacteristic, complemented
596C2×D3—32no—
597C2×D3—31no—
598C2×D3—32no—
599C2×D3—32no—
600C2×D3—32no—
601C2×D3—32no—
602C2×D3—32no—
603C2×D3—32no—
604C2×D3—62no—
605C2×D3—62no—
606C2×D3—62no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—92no—
612C2×D3—92no—
613C2×D3—182no—
614C2×D3—184no—
615C2×D3—184no—
616C2×D3—184no—
617C2×D3—188no—
618C2×D3—184no—
619C2×D3—182no—
620C2×D3—182no—
621C2×D3—182no—
622C2×D3—182no—
623C2×D3—184no—
624C2×D3—188no—
625C2×D3—184no—
626C2×D3—182no—
627C2×D3—182no—
628C2×D3—182no—
629C2×D3—182no—
630C2×D3—362no—
631C2×D3—362no—
632C2×D3—362no—
633C2×D3—362no—
634C2×D3C2×D3×A411yescharacteristic
635C2×D3C2×D3×A412yescomplemented
636A4—21no—
637A4—21no—
638A4—41no—
639A4D3×D1211yescharacteristic, direct product factor
640C3×C4—21no—
641C3×C4—31no—
642C3×C4—31no—
643C3×C4—31no—
644C3×C4—41no—
645C3×C4—61no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—91no—
649C3×C4—121no—
650C3×C4—161no—
651C3×C4—241no—
652C3×C4C2×D3×A411yescharacteristic, complemented
653C3×C4C2×D3×A411yescharacteristic, complemented
654Dic3—31no—
655Dic3C2×D3×A411yescharacteristic, complemented
656C32—41no—
657C32—41no—
658C32—81no—
659C32—81no—
660C32—81no—
661C32—161no—
662C32C2×D4×A411yescharacteristic, complemented
663C23—32no—
664C23—62no—
665C23—91no—
666C23—92no—
667C23—92no—
668C23—91no—
669C23—92no—
670C23—92no—
671C23—182no—
672C23—182no—
673C23—272no—
674C23—272no—
675C23—272no—
676C23—272no—
677C23—272no—
678C23—274no—
679C23—542no—
680C23—544no—
681C23—544no—
682C23—544no—
683C23—544no—
684C23—544no—
685C23—544no—
686C23—544no—
687C23—544no—
688C23C2×C3×D3211yescharacteristic
689D4—31no—
690D4—92no—
691D4—92no—
692D4—92no—
693D4—91no—
694D4—91no—
695D4—272no—
696D4—272no—
697D4—272no—
698D4—272no—
699D4—272no—
700D4—274no—
701D4—271no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—92no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C3—21no—
712C2×C3—31no—
713C2×C3—31no—
714C2×C3—31no—
715C2×C3—31no—
716C2×C3—32no—
717C2×C3—41no—
718C2×C3—61no—
719C2×C3—61no—
720C2×C3—62no—
721C2×C3—81no—
722C2×C3—81no—
723C2×C3—92no—
724C2×C3—122no—
725C2×C3—161no—
726C2×C3—182no—
727C2×C3—242no—
728C2×C3—242no—
729C2×C3—482no—
730C2×C3—722no—
731C2×C3C22×D3×A411yescharacteristic
732C2×C3C22×D3×A411yescharacteristic
733D3—22no—
734D3—32no—
735D3—62no—
736D3—62no—
737D3—62no—
738D3—122no—
739D3—182no—
740D3—182no—
741D3—362no—
742D3A4×D1212yesdirect product factor
743C22—31no—
744C22—31no—
745C22—31no—
746C22—32no—
747C22—92no—
748C22—92no—
749C22—92no—
750C22—92no—
751C22—91no—
752C22—92no—
753C22—92no—
754C22—182no—
755C22—182no—
756C22—184no—
757C22—182no—
758C22—182no—
759C22—272no—
760C22—542no—
761C22—542no—
762C22—544no—
763C22—542no—
764C22—542no—
765C22—544no—
766C22—544no—
767C22—548no—
768C22C3×D3×D1211yescharacteristic, complemented
769C4—31no—
770C4—31no—
771C4—91no—
772C4D32×A411yescharacteristic, complemented
773C3—21no—
774C3—41no—
775C3—81no—
776C3—81no—
777C3—161no—
778C3C2×A4×D1211yescharacteristic, complemented
779C3D3×D4×A411yescharacteristic, complemented
780C2—31no—
781C2—31no—
782C2—32no—
783C2—62no—
784C2—92no—
785C2—182no—
786C2—182no—
787C2—542no—
788C2C2×D32×A411yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×A4
commutator, socle, cosocleC23×C32C23×C3
FittingC22×C32×C4C22×C3
hypercenterC4D32×A4
hypocenterC22×C32C2×C3×D4
LCSG ▷ C23×C32 ▷ C22×C32
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D32×A4C2semidirect
2. A4×C4⋊(C3⋊D3)C2semidirect
3. C3×A4×D12C2semidirect
4. C3×C4×D3×A4C2semidirect
5. A4×#626C2semidirect
6. C22×D3×D12C3semidirect
9. C2×A4×C3⋊D3C22semidirect
11. C2×C3×D3×A4C22semidirect
13. C32×C4×A4C22semidirect
15. C3×Dic3×A4C22semidirect
16. C23×D32C2×C3semidirect
19. C22×C4⋊(C3⋊D3)C2×C3semidirect
20. C22×C3×D12C2×C3semidirect
21. C22×C3×C4×D3C2×C3semidirect
24. C22×#626C2×C3semidirect
37. A4×D12D3direct (N × H)
39. C4×D3×A4D3semidirect
44. C3×D3×A4D4semidirect
52. C23×C3⋊D3C22×C3semidirect
54. C23×C3×D3C22×C3semidirect
71. C2×D3×A4C2×D3semidirect
72. C22×C32×C4C22×C3semidirect
76. C22×C3×Dic3C22×C3semidirect
91. C3×C4×A4C2×D3semidirect
92. C3×C4×A4C2×D3semidirect
107. D3×D12A4direct (N × H)
109. Dic3×A4C2×D3semidirect
113. C32×A4C2×D4semidirect
139. C22×D12C3×D3semidirect
140. C22×C4×D3C3×D3semidirect
161. C22×C3×D3C3×D4semidirect
182. C2×D32C2×A4semidirect
189. D3×A4D12direct (N × H)
197. C4⋊(C3⋊D3)C2×A4semidirect
210. C3×D12C2×A4semidirect
217. C3×C4×D3C2×A4semidirect
222. #626C2×A4semidirect
246. C23×D3C2×C3×D3semidirect
263. C22×C3×C4C2×C3×D3semidirect
264. C22×C3×C4C2×C3×D3semidirect
269. C22×Dic3C2×C3×D3semidirect
317. C4×A4D32semidirect
322. C22×C32C2×C3×D4semidirect
328. C2×C3⋊D3C22×A4semidirect
349. C2×C3×D3C22×A4semidirect
354. C3×A4C2×D12semidirect
355. C3×A4D3×D4semidirect
369. C32×C4C22×A4semidirect
373. C3×Dic3C22×A4semidirect
443. C22×D3C3×D12semidirect
503. D12D3×A4direct (N × H)
508. C4×D3D3×A4semidirect
532. C3×D3D4×A4semidirect
568. C22×C4C3×D32semidirect
594. C22×C3C2×C3×D12semidirect
595. C22×C3C3×D3×D4semidirect
635. C2×D3C2×D3×A4semidirect
639. A4D3×D12direct (N × H)
652. C3×C4C2×D3×A4semidirect
653. C3×C4C2×D3×A4semidirect
655. Dic3C2×D3×A4semidirect
662. C32C2×D4×A4semidirect
742. D3A4×D12direct (N × H)
768. C22C3×D3×D12semidirect
772. C4D32×A4semidirect
778. C3C2×A4×D12semidirect
779. C3D3×D4×A4semidirect

Maximal subgroups

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

subgroupindex
C2×D32×A42
A4×C4⋊(C3⋊D3)2
C3×A4×D122
C3×C4×D3×A42
A4×#6262
C22×D3×D123
D3×D4×A43
C2×A4×D123
C3×D3×D124