Finite Group Databasebeta

← C3×D3×D4×A4 #13181439

Subgroups — C3×D3×D4×A4 #13181439

Order 1728.

1646 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×A4C212yesmaximal, complemented
2C32×D4×A4C211yesmaximal, characteristic, complemented
3C3×A4×#67C212yesmaximal, complemented
4C3×A4×D12C211yesmaximal, characteristic, complemented
5C3×C4×D3×A4C211yesmaximal, characteristic, complemented
6C22×C3×D3×D4C311yesmaximal, characteristic, complemented
7C2×C3×D4×A4—31nomaximal
8D3×D4×A4C313yesmaximal, direct product factor
9C22×C32×A4C2212yescomplemented
10C2×C3×D3×A4—24no—
11C2×C3×D3×A4C2211yescharacteristic
12C2×C3×D3×A4C2212yescomplemented
13C32×D3×D4—41nomaximal
14C32×C4×A4C2211yescharacteristic, complemented
15C3×Dic3×A4C2211yescharacteristic, complemented
16C24×C3×D3C2×C312yescomplemented
17C23×C3×A4—32no—
18C22×D3×A4C2×C316yescomplemented
19C22×C32×D4C2×C311yescharacteristic, complemented
20C22×C3×#67C2×C312yescomplemented
21C2×C3×D3×D4—31no—
22C2×C3×D3×D4—32no—
23C2×C3×D3×D4—31no—
24C2×C3×D3×D4—31no—
25C2×C3×D3×D4—31no—
26C2×C3×D3×D4—32no—
27C22×C3×D12C2×C311yescharacteristic, complemented
28C22×C3×C4×D3C2×C311yescharacteristic, complemented
29C3×D4×A4—21no—
30C3×D4×A4—23no—
31C3×D4×A4—31no—
32C3×D4×A4—32no—
33C3×D4×A4D311yescharacteristic, direct product factor
34C3×D4×A4C2×C313yescomplemented
35C2×C3×C4×A4—31no—
36A4×#67C2×C316yescomplemented
37A4×D12C2×C313yescomplemented
38C4×D3×A4C2×C313yescomplemented
39C22×C32×D3—42no—
40C2×C32×A4—22no—
41C2×C32×A4C2311yescharacteristic
42C3×D3×A4—22no—
43C3×D3×A4D412yesdirect product factor
44C33×D4—41no—
45C32×#67—42no—
46C32×D12—41no—
47C32×C4×D3—41no—
48C23×C3×D4—31no—
49C22×D3×D4C3211yescharacteristic, complemented
50C2×D4×A4—33no—
51C24×C32C22×C312yescomplemented
52C23×C3×D3—24no—
53C23×C3×D3—32no—
54C23×C3×D3—32no—
55C23×C3×D3—32no—
56C23×C3×D3—32no—
57C23×C3×D3—64no—
58C23×C3×D3C22×C311yescharacteristic
59C23×C3×D3C22×C312yescomplemented
60C22×C3×A4—22no—
61C22×C3×A4—26no—
62C22×C3×A4—31no—
63C22×C3×A4—32no—
64C22×C3×A4—64no—
65C22×C3×A4C2×D312yescomplemented
66C22×C3×A4C22×C316yescomplemented
67C2×D3×A4—212no—
68C2×D3×A4C22×C313yes—
69C2×D3×A4C22×C316yescomplemented
70C2×C32×D4—31no—
71C2×C32×D4—31no—
72C2×C32×D4—32no—
73C2×C32×D4—121no—
74C22×C32×C4C22×C311yescharacteristic, complemented
75C2×C3×#67—32no—
76C2×C3×#67—32no—
77C2×C3×#67—32no—
78C2×C3×#67—32no—
79C22×C3×Dic3C22×C311yescharacteristic, complemented
80C3×D3×D4—34no—
81C3×D3×D4—34no—
82C3×D3×D4—32no—
83C3×D3×D4—32no—
84C3×D3×D4—32no—
85C3×D3×D4—32no—
86C3×D3×D4—31no—
87C3×D3×D4—32no—
88C3×D3×D4—31no—
89C3×D3×D4—31no—
90C3×D3×D4—43no—
91C3×D3×D4A411yescharacteristic, direct product factor
92C2×C3×D12—31no—
93C2×C3×D12—32no—
94C2×C3×D12—31no—
95C2×C3×C4×D3—31no—
96C2×C3×C4×D3—31no—
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C3×C4×A4—21no—
100C3×C4×A4—23no—
101C3×C4×A4—31no—
102C3×C4×A4C2×D311yescharacteristic, complemented
103C3×C4×A4C22×C313yescomplemented
104Dic3×A4C22×C313yescomplemented
105C22×C33—42no—
106C2×C32×D3—41no—
107C2×C32×D3—42no—
108C2×C32×D3—84no—
109C32×A4C2×D411yescharacteristic, complemented
110C33×C4—41no—
111C32×Dic3—41no—
112C25×C3—32no—
113C24×D3C2×C3212yescomplemented
114C23×A4—36no—
115C22×C3×D4—21no—
116C22×C3×D4—32no—
117C22×C3×D4—31no—
118C22×C3×D4—91no—
119C22×C3×D4—91no—
120C22×C3×D4—91no—
121C22×C3×D4—91no—
122C22×C3×D4—92no—
123C22×C3×D4—92no—
124C22×C3×D4C3×D311yescharacteristic, complemented
125C22×C3×D4C2×C3211yescharacteristic, complemented
126C23×C3×C4—31no—
127C22×#67C2×C3212yescomplemented
128C2×D3×D4—31no—
129C2×D3×D4—31no—
130C2×D3×D4—31no—
131C2×D3×D4—32no—
132C2×D3×D4—31no—
133C2×D3×D4—32no—
134C22×D12C2×C3211yescharacteristic, complemented
135C22×C4×D3C2×C3211yescharacteristic, complemented
136D4×A4—23no—
137D4×A4—36no—
138D4×A4—33no—
139D4×A4C3×D313yesdirect product factor
140C2×C4×A4—33no—
141C23×C32—22no—
142C23×C32—32no—
143C23×C32—32no—
144C23×C32—62no—
145C23×C32—122no—
146C23×C32C23×C311yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—31no—
149C22×C3×D3—31no—
150C22×C3×D3—32no—
151C22×C3×D3—34no—
152C22×C3×D3—32no—
153C22×C3×D3—32no—
154C22×C3×D3—32no—
155C22×C3×D3—32no—
156C22×C3×D3—32no—
157C22×C3×D3—46no—
158C22×C3×D3—64no—
159C22×C3×D3—64no—
160C22×C3×D3—64no—
161C22×C3×D3—64no—
162C22×C3×D3—64no—
163C22×C3×D3—64no—
164C22×C3×D3—64no—
165C22×C3×D3—64no—
166C22×C3×D3—62no—
167C22×C3×D3C3×D412yescomplemented
168C22×C3×D3C2×A412yescomplemented
169C2×C3×A4—22no—
170C2×C3×A4—21no—
171C2×C3×A4—23no—
172C2×C3×A4—26no—
173C2×C3×A4—32no—
174C2×C3×A4—46no—
175C2×C3×A4—42no—
176C2×C3×A4—62no—
177C2×C3×A4C22×D311yescharacteristic
178C2×C3×A4C23×C313yes—
179D3×A4—26no—
180D3×A4C3×D416yesdirect product factor
181C32×D4—32no—
182C32×D4—32no—
183C32×D4—31no—
184C32×D4—41no—
185C32×D4—43no—
186C32×D4—83no—
187C32×D4—81no—
188C32×D4—121no—
189C32×D4—122no—
190C32×D4C2×A411yescharacteristic, complemented
191C2×C32×C4—31no—
192C2×C32×C4—31no—
193C2×C32×C4—121no—
194C3×#67—34no—
195C3×#67—32no—
196C3×#67—32no—
197C3×#67—32no—
198C3×#67—46no—
199C3×#67C2×A412yescomplemented
200C2×C3×Dic3—31no—
201C2×C3×Dic3—31no—
202C3×D12—32no—
203C3×D12—32no—
204C3×D12—31no—
205C3×D12—43no—
206C3×D12C2×A411yescharacteristic, complemented
207C3×C4×D3—32no—
208C3×C4×D3—31no—
209C3×C4×D3—31no—
210C3×C4×D3—31no—
211C3×C4×D3—43no—
212C3×C4×D3C2×A411yescharacteristic, complemented
213C23×D4—31noSylow
214C2×C33—41no—
215C2×C33—82no—
216C32×D3—42no—
217C32×D3—82no—
218C24×C3—22no—
219C24×C3—31no—
220C24×C3—32no—
221C24×C3—64no—
222C24×C3—92no—
223C24×C3—92no—
224C24×C3—92no—
225C24×C3—92no—
226C24×C3—184no—
227C24×C3C2×C3×D312yescomplemented
228C24×C3C22×C3212yescomplemented
229C23×D3—24no—
230C23×D3—32no—
231C23×D3—32no—
232C23×D3—32no—
233C23×D3—32no—
234C23×D3—64no—
235C23×D3C22×C3211yescharacteristic
236C23×D3C22×C3212yescomplemented
237C22×A4—26no—
238C22×A4—33no—
239C22×A4—36no—
240C22×A4—612no—
241C22×A4C2×C3×D316yescomplemented
242C2×C3×D4—31no—
243C2×C3×D4—31no—
244C2×C3×D4—31no—
245C2×C3×D4—31no—
246C2×C3×D4—32no—
247C2×C3×D4—31no—
248C2×C3×D4—32no—
249C2×C3×D4—61no—
250C2×C3×D4—61no—
251C2×C3×D4—62no—
252C2×C3×D4—91no—
253C2×C3×D4—91no—
254C2×C3×D4—91no—
255C2×C3×D4—92no—
256C2×C3×D4—92no—
257C2×C3×D4—91no—
258C2×C3×D4—92no—
259C2×C3×D4—92no—
260C2×C3×D4—92no—
261C2×C3×D4—92no—
262C2×C3×D4—94no—
263C2×C3×D4—94no—
264C2×C3×D4—92no—
265C2×C3×D4—91no—
266C2×C3×D4—92no—
267C2×C3×D4—92no—
268C2×C3×D4—92no—
269C2×C3×D4—123no—
270C22×C3×C4—21no—
271C22×C3×C4—31no—
272C22×C3×C4—91no—
273C22×C3×C4—91no—
274C22×C3×C4—91no—
275C22×C3×C4—91no—
276C22×C3×C4C2×C3×D311yescharacteristic, complemented
277C22×C3×C4C22×C3211yescharacteristic, complemented
278C2×#67—32no—
279C2×#67—32no—
280C2×#67—32no—
281C2×#67—32no—
282C22×Dic3C22×C3211yescharacteristic, complemented
283D3×D4—34no—
284D3×D4—34no—
285D3×D4—32no—
286D3×D4—32no—
287D3×D4—32no—
288D3×D4—32no—
289D3×D4—31no—
290D3×D4—32no—
291D3×D4—31no—
292D3×D4—31no—
293D3×D4C3×A411yescharacteristic, direct product factor
294C2×D12—31no—
295C2×D12—32no—
296C2×D12—31no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C4×A4—23no—
302C4×A4—33no—
303C4×A4C2×C3×D313yescomplemented
304C22×C32—31no—
305C22×C32—31no—
306C22×C32—32no—
307C22×C32—42no—
308C22×C32—46no—
309C22×C32—62no—
310C22×C32—62no—
311C22×C32—62no—
312C22×C32—62no—
313C22×C32—86no—
314C22×C32—82no—
315C22×C32—121no—
316C22×C32—122no—
317C22×C32—244no—
318C22×C32C2×C3×D411yescharacteristic, complemented
319C22×C32C22×A412yescomplemented
320C2×C3×D3—24no—
321C2×C3×D3—32no—
322C2×C3×D3—31no—
323C2×C3×D3—32no—
324C2×C3×D3—32no—
325C2×C3×D3—32no—
326C2×C3×D3—32no—
327C2×C3×D3—43no—
328C2×C3×D3—46no—
329C2×C3×D3—64no—
330C2×C3×D3—62no—
331C2×C3×D3—62no—
332C2×C3×D3—64no—
333C2×C3×D3—68no—
334C2×C3×D3—64no—
335C2×C3×D3—62no—
336C2×C3×D3—62no—
337C2×C3×D3—812no—
338C2×C3×D3C22×A411yescharacteristic
339C2×C3×D3C22×A412yescomplemented
340C3×A4—21no—
341C3×A4—23no—
342C3×A4D3×D411yescharacteristic, direct product factor
343C3×A4C2×C3×D413yescomplemented
344C32×C4—31no—
345C32×C4—41no—
346C32×C4—43no—
347C32×C4—83no—
348C32×C4—81no—
349C32×C4—121no—
350C32×C4C22×A411yescharacteristic, complemented
351C3×Dic3—31no—
352C3×Dic3—43no—
353C3×Dic3C22×A411yescharacteristic, complemented
354C25—32no—
355C22×D4—32no—
356C22×D4—31no—
357C22×D4—91no—
358C22×D4—91no—
359C22×D4—91no—
360C22×D4—91no—
361C22×D4—92no—
362C22×D4—92no—
363C22×D4C32×D311yescharacteristic, complemented
364C23×C4—31no—
365C33—41noSylow
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—21no—
369C23×C3—32no—
370C23×C3—32no—
371C23×C3—32no—
372C23×C3—32no—
373C23×C3—32no—
374C23×C3—32no—
375C23×C3—42no—
376C23×C3—62no—
377C23×C3—62no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—91no—
382C23×C3—92no—
383C23×C3—92no—
384C23×C3—92no—
385C23×C3—91no—
386C23×C3—92no—
387C23×C3—94no—
388C23×C3—92no—
389C23×C3—92no—
390C23×C3—126no—
391C23×C3—122no—
392C23×C3—182no—
393C23×C3—184no—
394C23×C3—184no—
395C23×C3—184no—
396C23×C3—184no—
397C23×C3—184no—
398C23×C3—184no—
399C23×C3—184no—
400C23×C3—184no—
401C23×C3C22×C3×D311yescharacteristic
402C23×C3C23×C3211yescharacteristic
403C22×D3—22no—
404C22×D3—31no—
405C22×D3—31no—
406C22×D3—32no—
407C22×D3—34no—
408C22×D3—32no—
409C22×D3—32no—
410C22×D3—32no—
411C22×D3—32no—
412C22×D3—32no—
413C22×D3—64no—
414C22×D3—64no—
415C22×D3—64no—
416C22×D3—64no—
417C22×D3—64no—
418C22×D3—64no—
419C22×D3—64no—
420C22×D3—64no—
421C22×D3—62no—
422C22×D3C32×D412yescomplemented
423C22×D3C2×C3×A412yescomplemented
424C2×A4—26no—
425C2×A4—23no—
426C2×A4—36no—
427C2×A4—46no—
428C2×A4—66no—
429C2×A4C22×C3×D313yes—
430C3×D4—21no—
431C3×D4—32no—
432C3×D4—32no—
433C3×D4—32no—
434C3×D4—32no—
435C3×D4—32no—
436C3×D4—31no—
437C3×D4—31no—
438C3×D4—31no—
439C3×D4—43no—
440C3×D4—61no—
441C3×D4—62no—
442C3×D4—62no—
443C3×D4—83no—
444C3×D4—92no—
445C3×D4—92no—
446C3×D4—92no—
447C3×D4—92no—
448C3×D4—94no—
449C3×D4—92no—
450C3×D4—91no—
451C3×D4—123no—
452C3×D4—126no—
453C3×D4D3×A411yescharacteristic, direct product factor
454C3×D4C2×C3×A411yescharacteristic, complemented
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—91no—
463C2×C3×C4—91no—
464C2×C3×C4—91no—
465C2×C3×C4—92no—
466C2×C3×C4—91no—
467C2×C3×C4—91no—
468C2×C3×C4—123no—
469#67—34no—
470#67—32no—
471#67—32no—
472#67—32no—
473#67C2×C3×A412yescomplemented
474C2×Dic3—31no—
475C2×Dic3—31no—
476D12—32no—
477D12—32no—
478D12—31no—
479D12C2×C3×A411yescharacteristic, complemented
480C4×D3—32no—
481C4×D3—31no—
482C4×D3—31no—
483C4×D3—31no—
484C4×D3C2×C3×A411yescharacteristic, complemented
485C2×C32—22no—
486C2×C32—31no—
487C2×C32—31no—
488C2×C32—41no—
489C2×C32—43no—
490C2×C32—62no—
491C2×C32—83no—
492C2×C32—82no—
493C2×C32—86no—
494C2×C32—81no—
495C2×C32—122no—
496C2×C32—162no—
497C2×C32—166no—
498C2×C32—242no—
499C2×C32C23×A411yescharacteristic
500C3×D3—22no—
501C3×D3—32no—
502C3×D3—46no—
503C3×D3—62no—
504C3×D3—86no—
505C3×D3D4×A412yesdirect product factor
506C24—31no—
507C24—32no—
508C24—64no—
509C24—92no—
510C24—92no—
511C24—92no—
512C24—92no—
513C24—184no—
514C24C2×C32×D312yescomplemented
515C2×D4—31no—
516C2×D4—31no—
517C2×D4—31no—
518C2×D4—32no—
519C2×D4—91no—
520C2×D4—91no—
521C2×D4—91no—
522C2×D4—92no—
523C2×D4—92no—
524C2×D4—91no—
525C2×D4—92no—
526C2×D4—92no—
527C2×D4—92no—
528C2×D4—92no—
529C2×D4—94no—
530C2×D4—94no—
531C2×D4—92no—
532C2×D4—91no—
533C2×D4—92no—
534C2×D4—92no—
535C2×D4—92no—
536C22×C4—31no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4C2×C32×D311yescharacteristic, complemented
542C22×C3—22no—
543C22×C3—21no—
544C22×C3—31no—
545C22×C3—31no—
546C22×C3—31no—
547C22×C3—31no—
548C22×C3—31no—
549C22×C3—32no—
550C22×C3—32no—
551C22×C3—32no—
552C22×C3—46no—
553C22×C3—61no—
554C22×C3—62no—
555C22×C3—61no—
556C22×C3—62no—
557C22×C3—62no—
558C22×C3—62no—
559C22×C3—62no—
560C22×C3—64no—
561C22×C3—62no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—86no—
566C22×C3—92no—
567C22×C3—92no—
568C22×C3—92no—
569C22×C3—92no—
570C22×C3—91no—
571C22×C3—92no—
572C22×C3—123no—
573C22×C3—126no—
574C22×C3—122no—
575C22×C3—122no—
576C22×C3—122no—
577C22×C3—122no—
578C22×C3—184no—
579C22×C3—182no—
580C22×C3—182no—
581C22×C3—184no—
582C22×C3—182no—
583C22×C3—182no—
584C22×C3—184no—
585C22×C3—188no—
586C22×C3—2412no—
587C22×C3C3×D3×D411yescharacteristic, complemented
588C22×C3C2×C32×D411yescharacteristic, complemented
589C22×C3C2×D3×A412yescomplemented
590C22×C3C22×C3×A412yescomplemented
591C2×D3—24no—
592C2×D3—32no—
593C2×D3—31no—
594C2×D3—32no—
595C2×D3—32no—
596C2×D3—32no—
597C2×D3—32no—
598C2×D3—64no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—64no—
602C2×D3—68no—
603C2×D3—64no—
604C2×D3—62no—
605C2×D3—62no—
606C2×D3C22×C3×A411yescharacteristic
607C2×D3C22×C3×A412yescomplemented
608A4—23no—
609A4C3×D3×D413yesdirect product factor
610C3×C4—21no—
611C3×C4—31no—
612C3×C4—31no—
613C3×C4—31no—
614C3×C4—43no—
615C3×C4—61no—
616C3×C4—83no—
617C3×C4—91no—
618C3×C4—123no—
619C3×C4C2×D3×A411yescharacteristic, complemented
620C3×C4C22×C3×A411yescharacteristic, complemented
621Dic3—31no—
622Dic3C22×C3×A411yescharacteristic, complemented
623C32—41no—
624C32—43no—
625C32—83no—
626C32—81no—
627C32C2×D4×A411yescharacteristic, complemented
628C23—22no—
629C23—32no—
630C23—32no—
631C23—32no—
632C23—32no—
633C23—62no—
634C23—62no—
635C23—91no—
636C23—92no—
637C23—92no—
638C23—92no—
639C23—91no—
640C23—92no—
641C23—94no—
642C23—92no—
643C23—92no—
644C23—182no—
645C23—184no—
646C23—184no—
647C23—184no—
648C23—184no—
649C23—184no—
650C23—184no—
651C23—184no—
652C23—184no—
653C23C22×C32×D311yescharacteristic
654D4—32no—
655D4—32no—
656D4—32no—
657D4—31no—
658D4—31no—
659D4—92no—
660D4—92no—
661D4—92no—
662D4—92no—
663D4—94no—
664D4—92no—
665D4—91no—
666D4C3×D3×A411yescharacteristic, direct product factor
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—92no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C3—22no—
677C2×C3—22no—
678C2×C3—21no—
679C2×C3—31no—
680C2×C3—31no—
681C2×C3—32no—
682C2×C3—31no—
683C2×C3—31no—
684C2×C3—42no—
685C2×C3—43no—
686C2×C3—61no—
687C2×C3—61no—
688C2×C3—62no—
689C2×C3—62no—
690C2×C3—62no—
691C2×C3—86no—
692C2×C3—83no—
693C2×C3—92no—
694C2×C3—126no—
695C2×C3—122no—
696C2×C3—166no—
697C2×C3—182no—
698C2×C3—246no—
699C2×C3C22×D3×A411yescharacteristic
700C2×C3C23×C3×A411yescharacteristic
701D3—22no—
702D3—32no—
703D3—62no—
704D3C3×D4×A412yesdirect product factor
705C22—31no—
706C22—31no—
707C22—31no—
708C22—32no—
709C22—32no—
710C22—62no—
711C22—62no—
712C22—64no—
713C22—62no—
714C22—62no—
715C22—92no—
716C22—92no—
717C22—92no—
718C22—92no—
719C22—91no—
720C22—92no—
721C22—184no—
722C22—182no—
723C22—182no—
724C22—184no—
725C22—182no—
726C22—182no—
727C22—184no—
728C22—188no—
729C22C32×D3×D411yescharacteristic, complemented
730C22C2×C3×D3×A412yescomplemented
731C4—31no—
732C4—31no—
733C4—91no—
734C4C2×C3×D3×A411yescharacteristic, complemented
735C3—21no—
736C3—43no—
737C3—83no—
738C3D3×D4×A411yescharacteristic, direct product factor
739C3C2×C3×D4×A411yescharacteristic, complemented
740C2—22no—
741C2—31no—
742C2—31no—
743C2—32no—
744C2—62no—
745C2—62no—
746C2—92no—
747C2—182no—
748C2C22×C3×D3×A411yescharacteristic
subgroupG/H
centerC2×C3C22×D3×A4
commutator, cosocleC23×C3C23×C32
FrattiniC2C22×C3×D3×A4
FittingC22×C32×D4C2×C3
socleC23×C32C23×C3
hypercenterC3×D4D3×A4
hypocenterC22×C3C2×C32×D4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×A4C2semidirect
2. C32×D4×A4C2semidirect
3. C3×A4×#67C2semidirect
4. C3×A4×D12C2semidirect
5. C3×C4×D3×A4C2semidirect
6. C22×C3×D3×D4C3semidirect
8. D3×D4×A4C3direct (N × H)
9. C22×C32×A4C22semidirect
12. C2×C3×D3×A4C22semidirect
14. C32×C4×A4C22semidirect
15. C3×Dic3×A4C22semidirect
16. C24×C3×D3C2×C3semidirect
18. C22×D3×A4C2×C3semidirect
19. C22×C32×D4C2×C3semidirect
20. C22×C3×#67C2×C3semidirect
27. C22×C3×D12C2×C3semidirect
28. C22×C3×C4×D3C2×C3semidirect
33. C3×D4×A4D3direct (N × H)
34. C3×D4×A4C2×C3semidirect
36. A4×#67C2×C3semidirect
37. A4×D12C2×C3semidirect
38. C4×D3×A4C2×C3semidirect
43. C3×D3×A4D4direct (N × H)
49. C22×D3×D4C32semidirect
51. C24×C32C22×C3semidirect
59. C23×C3×D3C22×C3semidirect
65. C22×C3×A4C2×D3semidirect
66. C22×C3×A4C22×C3semidirect
69. C2×D3×A4C22×C3semidirect
74. C22×C32×C4C22×C3semidirect
79. C22×C3×Dic3C22×C3semidirect
91. C3×D3×D4A4direct (N × H)
102. C3×C4×A4C2×D3semidirect
103. C3×C4×A4C22×C3semidirect
104. Dic3×A4C22×C3semidirect
109. C32×A4C2×D4semidirect
113. C24×D3C2×C32semidirect
124. C22×C3×D4C3×D3semidirect
125. C22×C3×D4C2×C32semidirect
127. C22×#67C2×C32semidirect
134. C22×D12C2×C32semidirect
135. C22×C4×D3C2×C32semidirect
139. D4×A4C3×D3direct (N × H)
167. C22×C3×D3C3×D4semidirect
168. C22×C3×D3C2×A4semidirect
180. D3×A4C3×D4direct (N × H)
190. C32×D4C2×A4semidirect
199. C3×#67C2×A4semidirect
206. C3×D12C2×A4semidirect
212. C3×C4×D3C2×A4semidirect
227. C24×C3C2×C3×D3semidirect
228. C24×C3C22×C32semidirect
236. C23×D3C22×C32semidirect
241. C22×A4C2×C3×D3semidirect
276. C22×C3×C4C2×C3×D3semidirect
277. C22×C3×C4C22×C32semidirect
282. C22×Dic3C22×C32semidirect
293. D3×D4C3×A4direct (N × H)
303. C4×A4C2×C3×D3semidirect
318. C22×C32C2×C3×D4semidirect
319. C22×C32C22×A4semidirect
339. C2×C3×D3C22×A4semidirect
342. C3×A4D3×D4direct (N × H)
343. C3×A4C2×C3×D4semidirect
350. C32×C4C22×A4semidirect
353. C3×Dic3C22×A4semidirect
363. C22×D4C32×D3semidirect
422. C22×D3C32×D4semidirect
423. C22×D3C2×C3×A4semidirect
453. C3×D4D3×A4direct (N × H)
454. C3×D4C2×C3×A4semidirect
473. #67C2×C3×A4semidirect
479. D12C2×C3×A4semidirect
484. C4×D3C2×C3×A4semidirect
505. C3×D3D4×A4direct (N × H)
514. C24C2×C32×D3semidirect
541. C22×C4C2×C32×D3semidirect
587. C22×C3C3×D3×D4semidirect
588. C22×C3C2×C32×D4semidirect
589. C22×C3C2×D3×A4semidirect
590. C22×C3C22×C3×A4semidirect
607. C2×D3C22×C3×A4semidirect
609. A4C3×D3×D4direct (N × H)
619. C3×C4C2×D3×A4semidirect
620. C3×C4C22×C3×A4semidirect
622. Dic3C22×C3×A4semidirect
627. C32C2×D4×A4semidirect
666. D4C3×D3×A4direct (N × H)
704. D3C3×D4×A4direct (N × H)
729. C22C32×D3×D4semidirect
730. C22C2×C3×D3×A4semidirect
734. C4C2×C3×D3×A4semidirect
738. C3D3×D4×A4direct (N × H)
739. C3C2×C3×D4×A4semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×A42
C32×D4×A42
C3×A4×#672
C3×A4×D122
C3×C4×D3×A42
C22×C3×D3×D43
C2×C3×D4×A43
D3×D4×A43
C32×D3×D44