Finite Group Databasebeta

← C2×C3×A4×#67 #13181455

Subgroups — C2×C3×A4×#67 #13181455

Order 1728.

1854 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×A4C211yesmaximal, characteristic, complemented
2C22×C3×D3×A4C211yesmaximal, characteristic, complemented
3C3×A4×#67C214yesmaximal, direct product factor
4C2×C3×Dic3×A4C211yesmaximal, characteristic, complemented
5C23×C3×#67C311yesmaximal, characteristic, complemented
6C2×C3×D4×A4—31nomaximal
7C2×A4×#67C313yesmaximal, direct product factor
8C22×C32×A4—22no—
9C22×C32×A4C2211yescharacteristic
10C22×C32×A4C2212yescomplemented
11C2×C3×D3×A4—22no—
12C2×C3×D3×A4C2212yescomplemented
13C2×C32×#67—41nomaximal
14C3×Dic3×A4C2212yescomplemented
15C25×C32C2×C311yescharacteristic, complemented
16C24×C3×D3C2×C311yescharacteristic, complemented
17C23×C3×A4—23no—
18C23×C3×A4—21no—
19C23×C3×A4—31no—
20C23×C3×A4D311yescharacteristic, complemented
21C23×C3×A4C2×C313yescomplemented
22C22×D3×A4C2×C313yescomplemented
23C22×C3×#67—31no—
24C22×C3×#67—31no—
25C22×C3×#67—31no—
26C22×C3×#67—31no—
27C22×C3×#67—34no—
28C22×C3×#67C2×C314yescomplemented
29C23×C3×Dic3C2×C311yescharacteristic, complemented
30C3×D4×A4—34no—
31C2×C3×C4×A4—31no—
32A4×#67C2×C3112yesdirect product factor
33C2×Dic3×A4C2×C313yescomplemented
34C23×C33—41no—
35C22×C32×D3—41no—
36C2×C32×A4—22no—
37C2×C32×A4D412yescomplemented
38C2×C32×A4C2311yescharacteristic
39C3×D3×A4—22no—
40C32×#67—44no—
41C2×C32×Dic3—41no—
42C23×C3×D4—31no—
43C23×#67C3211yescharacteristic, complemented
44C2×D4×A4—33no—
45C24×C32—22no—
46C24×C32—31no—
47C24×C32—32no—
48C24×C32—31no—
49C24×C32—62no—
50C24×C32C22×C311yescharacteristic
51C24×C32C22×C312yescomplemented
52C23×C3×D3—22no—
53C23×C3×D3—31no—
54C23×C3×D3—31no—
55C23×C3×D3—32no—
56C23×C3×D3—62no—
57C23×C3×D3C22×C312yescomplemented
58C22×C3×A4—24no—
59C22×C3×A4—212no—
60C22×C3×A4—21no—
61C22×C3×A4—22no—
62C22×C3×A4—23no—
63C22×C3×A4—26no—
64C22×C3×A4—22no—
65C22×C3×A4—26no—
66C22×C3×A4—32no—
67C22×C3×A4—62no—
68C22×C3×A4C2×D311yescharacteristic
69C22×C3×A4C2×D312yescomplemented
70C22×C3×A4C22×C313yes—
71C22×C3×A4C22×C316yescomplemented
72C2×D3×A4—26no—
73C2×D3×A4C22×C316yescomplemented
74C2×C32×D4—121no—
75C2×C3×#67—34no—
76C2×C3×#67—34no—
77C2×C3×#67—32no—
78C2×C3×#67—34no—
79C2×C3×#67—31no—
80C2×C3×#67—31no—
81C2×C3×#67—34no—
82C2×C3×#67—34no—
83C2×C3×#67—34no—
84C2×C3×#67—34no—
85C2×C3×#67—34no—
86C2×C3×#67—31no—
87C2×C3×#67—43no—
88C2×C3×#67A411yescharacteristic, direct product factor
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—32no—
92C22×C3×Dic3C22×C312yescomplemented
93C3×C4×A4—32no—
94Dic3×A4C22×C316yescomplemented
95C22×C33—41no—
96C22×C33—42no—
97C22×C33—82no—
98C2×C32×D3—42no—
99C2×C32×D3—82no—
100C32×A4C2×D411yescharacteristic, complemented
101C32×Dic3—42no—
102C25×C3—21no—
103C25×C3—31no—
104C25×C3C3×D311yescharacteristic, complemented
105C25×C3C2×C3211yescharacteristic, complemented
106C24×D3C2×C3211yescharacteristic, complemented
107C23×A4—23no—
108C23×A4—33no—
109C23×A4C3×D313yescomplemented
110C22×C3×D4—34no—
111C22×C3×D4—91no—
112C22×C3×D4—91no—
113C22×C3×D4—94no—
114C22×C3×D4—91no—
115C22×C3×D4—91no—
116C23×C3×C4—31no—
117C22×#67—31no—
118C22×#67—31no—
119C22×#67—31no—
120C22×#67—31no—
121C22×#67—34no—
122C22×#67C2×C3214yescomplemented
123C23×Dic3C2×C3211yescharacteristic, complemented
124D4×A4—312no—
125C2×C4×A4—33no—
126C23×C32—22no—
127C23×C32—31no—
128C23×C32—32no—
129C23×C32—31no—
130C23×C32—32no—
131C23×C32—32no—
132C23×C32—31no—
133C23×C32—32no—
134C23×C32—32no—
135C23×C32—41no—
136C23×C32—43no—
137C23×C32—62no—
138C23×C32—62no—
139C23×C32—62no—
140C23×C32—64no—
141C23×C32—62no—
142C23×C32—62no—
143C23×C32—64no—
144C23×C32—83no—
145C23×C32—81no—
146C23×C32—121no—
147C23×C32C3×D412yescomplemented
148C23×C32C2×A411yescharacteristic, complemented
149C23×C32C23×C311yescharacteristic
150C22×C3×D3—22no—
151C22×C3×D3—32no—
152C22×C3×D3—31no—
153C22×C3×D3—32no—
154C22×C3×D3—32no—
155C22×C3×D3—32no—
156C22×C3×D3—43no—
157C22×C3×D3—62no—
158C22×C3×D3—62no—
159C22×C3×D3—64no—
160C22×C3×D3—64no—
161C22×C3×D3—62no—
162C22×C3×D3—62no—
163C22×C3×D3—62no—
164C22×C3×D3C2×A411yescharacteristic, complemented
165C2×C3×A4—24no—
166C2×C3×A4—212no—
167C2×C3×A4—22no—
168C2×C3×A4—26no—
169C2×C3×A4—22no—
170C2×C3×A4—21no—
171C2×C3×A4—26no—
172C2×C3×A4—23no—
173C2×C3×A4—62no—
174C2×C3×A4#6712yesdirect product factor
175C2×C3×A4C3×D416yescomplemented
176C2×C3×A4C22×D311yescharacteristic
177C2×C3×A4C23×C313yes—
178D3×A4—26no—
179C32×D4—124no—
180C2×C32×C4—121no—
181C3×#67—38no—
182C3×#67—34no—
183C3×#67—34no—
184C3×#67—34no—
185C3×#67—412no—
186C3×#67C2×A414yesdirect product factor
187C2×C3×Dic3—32no—
188C2×C3×Dic3—31no—
189C2×C3×Dic3—32no—
190C2×C3×Dic3—32no—
191C2×C3×Dic3—32no—
192C2×C3×Dic3—43no—
193C2×C3×Dic3C2×A411yescharacteristic, complemented
194C23×D4—31noSylow
195C2×C33—42no—
196C2×C33—41no—
197C2×C33—82no—
198C32×D3—82no—
199C24×C3—24no—
200C24×C3—22no—
201C24×C3—22no—
202C24×C3—21no—
203C24×C3—22no—
204C24×C3—32no—
205C24×C3—31no—
206C24×C3—32no—
207C24×C3—31no—
208C24×C3—31no—
209C24×C3—31no—
210C24×C3—32no—
211C24×C3—61no—
212C24×C3—62no—
213C24×C3—61no—
214C24×C3—62no—
215C24×C3—62no—
216C24×C3—64no—
217C24×C3—62no—
218C24×C3—91no—
219C24×C3—92no—
220C24×C3—91no—
221C24×C3—182no—
222C24×C3C2×C3×D311yescharacteristic
223C24×C3C2×C3×D312yescomplemented
224C24×C3C22×C3211yescharacteristic
225C24×C3C22×C3212yescomplemented
226C23×D3—22no—
227C23×D3—31no—
228C23×D3—31no—
229C23×D3—32no—
230C23×D3—62no—
231C23×D3C22×C3212yescomplemented
232C22×A4—212no—
233C22×A4—26no—
234C22×A4—23no—
235C22×A4—26no—
236C22×A4—36no—
237C22×A4—66no—
238C22×A4C2×C3×D313yes—
239C22×A4C2×C3×D316yescomplemented
240C2×C3×D4—31no—
241C2×C3×D4—91no—
242C2×C3×D4—94no—
243C2×C3×D4—94no—
244C2×C3×D4—91no—
245C2×C3×D4—94no—
246C2×C3×D4—94no—
247C2×C3×D4—94no—
248C2×C3×D4—92no—
249C2×C3×D4—91no—
250C2×C3×D4—94no—
251C2×C3×D4—94no—
252C2×C3×D4—94no—
253C2×C3×D4—123no—
254C22×C3×C4—32no—
255C22×C3×C4—91no—
256C22×C3×C4—92no—
257C22×C3×C4—91no—
258C2×#67—34no—
259C2×#67—34no—
260C2×#67—32no—
261C2×#67—34no—
262C2×#67—31no—
263C2×#67—31no—
264C2×#67—34no—
265C2×#67—34no—
266C2×#67—34no—
267C2×#67—34no—
268C2×#67—34no—
269C2×#67—31no—
270C2×#67C3×A411yescharacteristic, direct product factor
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—32no—
274C22×Dic3C22×C3212yescomplemented
275C4×A4—36no—
276C22×C32—22no—
277C22×C32—32no—
278C22×C32—31no—
279C22×C32—32no—
280C22×C32—32no—
281C22×C32—32no—
282C22×C32—31no—
283C22×C32—31no—
284C22×C32—32no—
285C22×C32—41no—
286C22×C32—42no—
287C22×C32—43no—
288C22×C32—46no—
289C22×C32—62no—
290C22×C32—62no—
291C22×C32—64no—
292C22×C32—62no—
293C22×C32—62no—
294C22×C32—64no—
295C22×C32—62no—
296C22×C32—83no—
297C22×C32—86no—
298C22×C32—82no—
299C22×C32—86no—
300C22×C32—812no—
301C22×C32—84no—
302C22×C32—81no—
303C22×C32—82no—
304C22×C32—122no—
305C22×C32—242no—
306C22×C32C2×C3×D411yescharacteristic, complemented
307C22×C32C22×A411yescharacteristic
308C22×C32C22×A412yescomplemented
309C2×C3×D3—22no—
310C2×C3×D3—32no—
311C2×C3×D3—46no—
312C2×C3×D3—62no—
313C2×C3×D3—62no—
314C2×C3×D3—64no—
315C2×C3×D3—64no—
316C2×C3×D3—62no—
317C2×C3×D3—62no—
318C2×C3×D3—62no—
319C2×C3×D3—86no—
320C2×C3×D3C22×A412yescomplemented
321C3×A4—21no—
322C3×A4—23no—
323C3×A4C2×#6711yescharacteristic, direct product factor
324C3×A4C2×C3×D413yescomplemented
325C32×C4—122no—
326C3×Dic3—32no—
327C3×Dic3—46no—
328C3×Dic3C22×A412yescomplemented
329C25—31no—
330C25C32×D311yescharacteristic, complemented
331C22×D4—34no—
332C22×D4—91no—
333C22×D4—91no—
334C22×D4—94no—
335C22×D4—91no—
336C22×D4—91no—
337C23×C4—31no—
338C33—41noSylow
339C23×C3—24no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—31no—
346C23×C3—31no—
347C23×C3—32no—
348C23×C3—32no—
349C23×C3—31no—
350C23×C3—31no—
351C23×C3—32no—
352C23×C3—32no—
353C23×C3—32no—
354C23×C3—32no—
355C23×C3—31no—
356C23×C3—31no—
357C23×C3—32no—
358C23×C3—32no—
359C23×C3—31no—
360C23×C3—32no—
361C23×C3—32no—
362C23×C3—43no—
363C23×C3—61no—
364C23×C3—62no—
365C23×C3—61no—
366C23×C3—62no—
367C23×C3—61no—
368C23×C3—62no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—62no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—64no—
376C23×C3—64no—
377C23×C3—62no—
378C23×C3—62no—
379C23×C3—64no—
380C23×C3—64no—
381C23×C3—62no—
382C23×C3—62no—
383C23×C3—62no—
384C23×C3—62no—
385C23×C3—64no—
386C23×C3—64no—
387C23×C3—64no—
388C23×C3—64no—
389C23×C3—68no—
390C23×C3—64no—
391C23×C3—68no—
392C23×C3—62no—
393C23×C3—83no—
394C23×C3—92no—
395C23×C3—92no—
396C23×C3—92no—
397C23×C3—92no—
398C23×C3—91no—
399C23×C3—123no—
400C23×C3—182no—
401C23×C3—182no—
402C23×C3—182no—
403C23×C3—184no—
404C23×C3—182no—
405C23×C3—182no—
406C23×C3—184no—
407C23×C3C3×#6712yescomplemented
408C23×C3C32×D412yescomplemented
409C23×C3D3×A411yescharacteristic, complemented
410C23×C3C2×C3×A411yescharacteristic, complemented
411C23×C3C22×C3×D311yescharacteristic
412C23×C3C23×C3211yescharacteristic
413C22×D3—22no—
414C22×D3—32no—
415C22×D3—31no—
416C22×D3—32no—
417C22×D3—32no—
418C22×D3—32no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—64no—
422C22×D3—64no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3C2×C3×A411yescharacteristic, complemented
427C2×A4—212no—
428C2×A4—26no—
429C2×A4—26no—
430C2×A4—23no—
431C2×A4—66no—
432C2×A4C3×#6716yesdirect product factor
433C2×A4C22×C3×D313yes—
434C3×D4—34no—
435C3×D4—94no—
436C3×D4—94no—
437C3×D4—98no—
438C3×D4—94no—
439C3×D4—1212no—
440C2×C3×C4—31no—
441C2×C3×C4—92no—
442C2×C3×C4—92no—
443C2×C3×C4—92no—
444C2×C3×C4—91no—
445C2×C3×C4—92no—
446C2×C3×C4—123no—
447#67—38no—
448#67—34no—
449#67—34no—
450#67—34no—
451#67C2×C3×A414yesdirect product factor
452C2×Dic3—32no—
453C2×Dic3—31no—
454C2×Dic3—32no—
455C2×Dic3—32no—
456C2×Dic3—32no—
457C2×Dic3C2×C3×A411yescharacteristic, complemented
458C2×C32—22no—
459C2×C32—32no—
460C2×C32—31no—
461C2×C32—31no—
462C2×C32—42no—
463C2×C32—41no—
464C2×C32—46no—
465C2×C32—43no—
466C2×C32—62no—
467C2×C32—86no—
468C2×C32—83no—
469C2×C32—82no—
470C2×C32—86no—
471C2×C32—812no—
472C2×C32—84no—
473C2×C32—82no—
474C2×C32—81no—
475C2×C32—242no—
476C2×C32D4×A412yescomplemented
477C2×C32C23×A411yescharacteristic
478C3×D3—22no—
479C3×D3—62no—
480C3×D3—86no—
481C24—22no—
482C24—32no—
483C24—31no—
484C24—31no—
485C24—32no—
486C24—62no—
487C24—62no—
488C24—91no—
489C24—92no—
490C24—91no—
491C24—182no—
492C24C2×C32×D311yescharacteristic
493C24C2×C32×D312yescomplemented
494C2×D4—31no—
495C2×D4—91no—
496C2×D4—94no—
497C2×D4—94no—
498C2×D4—91no—
499C2×D4—94no—
500C2×D4—94no—
501C2×D4—94no—
502C2×D4—92no—
503C2×D4—91no—
504C2×D4—94no—
505C2×D4—94no—
506C2×D4—94no—
507C22×C4—32no—
508C22×C4—91no—
509C22×C4—92no—
510C22×C4—91no—
511C22×C3—24no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—22no—
516C22×C3—21no—
517C22×C3—32no—
518C22×C3—31no—
519C22×C3—32no—
520C22×C3—31no—
521C22×C3—32no—
522C22×C3—32no—
523C22×C3—32no—
524C22×C3—32no—
525C22×C3—32no—
526C22×C3—32no—
527C22×C3—31no—
528C22×C3—31no—
529C22×C3—31no—
530C22×C3—31no—
531C22×C3—32no—
532C22×C3—32no—
533C22×C3—32no—
534C22×C3—43no—
535C22×C3—46no—
536C22×C3—62no—
537C22×C3—61no—
538C22×C3—62no—
539C22×C3—61no—
540C22×C3—62no—
541C22×C3—62no—
542C22×C3—61no—
543C22×C3—62no—
544C22×C3—62no—
545C22×C3—62no—
546C22×C3—64no—
547C22×C3—62no—
548C22×C3—64no—
549C22×C3—62no—
550C22×C3—64no—
551C22×C3—64no—
552C22×C3—68no—
553C22×C3—64no—
554C22×C3—62no—
555C22×C3—62no—
556C22×C3—62no—
557C22×C3—62no—
558C22×C3—64no—
559C22×C3—64no—
560C22×C3—64no—
561C22×C3—64no—
562C22×C3—68no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—62no—
566C22×C3—86no—
567C22×C3—812no—
568C22×C3—83no—
569C22×C3—86no—
570C22×C3—92no—
571C22×C3—126no—
572C22×C3—182no—
573C22×C3—182no—
574C22×C3—184no—
575C22×C3—182no—
576C22×C3—182no—
577C22×C3—184no—
578C22×C3—182no—
579C22×C3—246no—
580C22×C3C2×C3×#6711yescharacteristic, complemented
581C22×C3C2×C32×D411yescharacteristic, complemented
582C22×C3C2×D3×A411yescharacteristic
583C22×C3C2×D3×A412yescomplemented
584C22×C3C22×C3×A411yescharacteristic
585C22×C3C22×C3×A412yescomplemented
586C2×D3—22no—
587C2×D3—32no—
588C2×D3—62no—
589C2×D3—64no—
590C2×D3—62no—
591C2×D3—64no—
592C2×D3—62no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3C22×C3×A412yescomplemented
596A4—23no—
597A4C2×C3×#6713yesdirect product factor
598C3×C4—32no—
599C3×C4—92no—
600C3×C4—126no—
601Dic3—32no—
602Dic3C22×C3×A412yescomplemented
603C32—41no—
604C32—43no—
605C32—83no—
606C32—81no—
607C32C2×D4×A411yescharacteristic, complemented
608C23—22no—
609C23—31no—
610C23—32no—
611C23—31no—
612C23—32no—
613C23—32no—
614C23—31no—
615C23—31no—
616C23—32no—
617C23—32no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23—64no—
622C23—62no—
623C23—62no—
624C23—64no—
625C23—62no—
626C23—92no—
627C23—92no—
628C23—92no—
629C23—92no—
630C23—91no—
631C23—182no—
632C23—182no—
633C23—182no—
634C23—184no—
635C23—182no—
636C23—182no—
637C23—184no—
638C23C32×#6712yescomplemented
639C23C3×D3×A411yescharacteristic, complemented
640C23C22×C32×D311yescharacteristic
641D4—34no—
642D4—94no—
643D4—94no—
644D4—98no—
645D4—94no—
646C2×C4—31no—
647C2×C4—92no—
648C2×C4—92no—
649C2×C4—92no—
650C2×C4—91no—
651C2×C4—92no—
652C2×C3—24no—
653C2×C3—22no—
654C2×C3—22no—
655C2×C3—22no—
656C2×C3—21no—
657C2×C3—31no—
658C2×C3—32no—
659C2×C3—31no—
660C2×C3—31no—
661C2×C3—32no—
662C2×C3—31no—
663C2×C3—46no—
664C2×C3—43no—
665C2×C3—61no—
666C2×C3—62no—
667C2×C3—61no—
668C2×C3—64no—
669C2×C3—62no—
670C2×C3—62no—
671C2×C3—62no—
672C2×C3—86no—
673C2×C3—812no—
674C2×C3—86no—
675C2×C3—83no—
676C2×C3—182no—
677C2×C3—246no—
678C2×C3A4×#6712yesdirect product factor
679C2×C3C3×D4×A412yescomplemented
680C2×C3C22×D3×A411yescharacteristic
681C2×C3C23×C3×A411yescharacteristic
682D3—22no—
683D3—62no—
684C22—22no—
685C22—32no—
686C22—31no—
687C22—32no—
688C22—32no—
689C22—32no—
690C22—31no—
691C22—31no—
692C22—32no—
693C22—32no—
694C22—62no—
695C22—62no—
696C22—64no—
697C22—62no—
698C22—62no—
699C22—64no—
700C22—62no—
701C22—62no—
702C22—92no—
703C22—182no—
704C22—182no—
705C22—184no—
706C22—182no—
707C22—182no—
708C22—184no—
709C22—182no—
710C22C2×C32×#6711yescharacteristic, complemented
711C22C2×C3×D3×A411yescharacteristic
712C22C2×C3×D3×A412yescomplemented
713C4—32no—
714C4—92no—
715C3—21no—
716C3—43no—
717C3—83no—
718C3C2×A4×#6711yescharacteristic, direct product factor
719C3C2×C3×D4×A411yescharacteristic, complemented
720C2—22no—
721C2—31no—
722C2—32no—
723C2—31no—
724C2—62no—
725C2—62no—
726C2—182no—
727C2C3×A4×#6712yesdirect product factor
728C2C22×C3×D3×A411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×A4
commutator, cosocleC23×C3C23×C32
FrattiniC2C22×C3×D3×A4
FittingC25×C32C2×C3
socleC24×C32C22×C3
hypercenterC23×C3D3×A4
hypocenterC22×C3C2×C32×D4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C23×C32×A4C2semidirect
2. C22×C3×D3×A4C2semidirect
3. C3×A4×#67C2direct (N × H)
4. C2×C3×Dic3×A4C2semidirect
5. C23×C3×#67C3semidirect
7. C2×A4×#67C3direct (N × H)
10. C22×C32×A4C22semidirect
12. C2×C3×D3×A4C22semidirect
14. C3×Dic3×A4C22semidirect
15. C25×C32C2×C3semidirect
16. C24×C3×D3C2×C3semidirect
20. C23×C3×A4D3semidirect
21. C23×C3×A4C2×C3semidirect
22. C22×D3×A4C2×C3semidirect
28. C22×C3×#67C2×C3semidirect
29. C23×C3×Dic3C2×C3semidirect
32. A4×#67C2×C3direct (N × H)
33. C2×Dic3×A4C2×C3semidirect
37. C2×C32×A4D4semidirect
43. C23×#67C32semidirect
51. C24×C32C22×C3semidirect
57. C23×C3×D3C22×C3semidirect
69. C22×C3×A4C2×D3semidirect
71. C22×C3×A4C22×C3semidirect
73. C2×D3×A4C22×C3semidirect
88. C2×C3×#67A4direct (N × H)
92. C22×C3×Dic3C22×C3semidirect
94. Dic3×A4C22×C3semidirect
100. C32×A4C2×D4semidirect
104. C25×C3C3×D3semidirect
105. C25×C3C2×C32semidirect
106. C24×D3C2×C32semidirect
109. C23×A4C3×D3semidirect
122. C22×#67C2×C32semidirect
123. C23×Dic3C2×C32semidirect
147. C23×C32C3×D4semidirect
148. C23×C32C2×A4semidirect
164. C22×C3×D3C2×A4semidirect
174. C2×C3×A4#67direct (N × H)
175. C2×C3×A4C3×D4semidirect
186. C3×#67C2×A4direct (N × H)
193. C2×C3×Dic3C2×A4semidirect
223. C24×C3C2×C3×D3semidirect
225. C24×C3C22×C32semidirect
231. C23×D3C22×C32semidirect
239. C22×A4C2×C3×D3semidirect
270. C2×#67C3×A4direct (N × H)
274. C22×Dic3C22×C32semidirect
306. C22×C32C2×C3×D4semidirect
308. C22×C32C22×A4semidirect
320. C2×C3×D3C22×A4semidirect
323. C3×A4C2×#67direct (N × H)
324. C3×A4C2×C3×D4semidirect
328. C3×Dic3C22×A4semidirect
330. C25C32×D3semidirect
407. C23×C3C3×#67semidirect
408. C23×C3C32×D4semidirect
409. C23×C3D3×A4semidirect
410. C23×C3C2×C3×A4semidirect
426. C22×D3C2×C3×A4semidirect
432. C2×A4C3×#67direct (N × H)
451. #67C2×C3×A4direct (N × H)
457. C2×Dic3C2×C3×A4semidirect
476. C2×C32D4×A4semidirect
493. C24C2×C32×D3semidirect
580. C22×C3C2×C3×#67semidirect
581. C22×C3C2×C32×D4semidirect
583. C22×C3C2×D3×A4semidirect
585. C22×C3C22×C3×A4semidirect
595. C2×D3C22×C3×A4semidirect
597. A4C2×C3×#67direct (N × H)
602. Dic3C22×C3×A4semidirect
607. C32C2×D4×A4semidirect
638. C23C32×#67semidirect
639. C23C3×D3×A4semidirect
678. C2×C3A4×#67direct (N × H)
679. C2×C3C3×D4×A4semidirect
710. C22C2×C32×#67semidirect
712. C22C2×C3×D3×A4semidirect
718. C3C2×A4×#67direct (N × H)
719. C3C2×C3×D4×A4semidirect
727. C2C3×A4×#67direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×A42
C22×C3×D3×A42
C3×A4×#672
C2×C3×Dic3×A42
C23×C3×#673
C2×C3×D4×A43
C2×A4×#673
C2×C32×#674