Finite Group Databasebeta

← C2×A4×#626 #13180913

Subgroups — C2×A4×#626 #13180913

Order 1728.

1562 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 1562 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C22×A4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×D3×A4C211yesmaximal, characteristic, complemented
3C2×C3×Dic3×A4C211yesmaximal, characteristic, complemented
4A4×#626C214yesmaximal, direct product factor
5C23×#626C311yesmaximal, characteristic, complemented
6C2×A4×#67—31nomaximal
7C2×A4×D12—31nomaximal
8C22×C32×A4C2211yescharacteristic
9C2×A4×C3⋊D3—22no—
10C2×A4×C3⋊D3C2212yescomplemented
11C2×C3×D3×A4—22no—
12C2×C3×D3×A4C2212yescomplemented
13C2×C3×#626—41nomaximal
14C3×Dic3×A4C2212yescomplemented
15C24×C3⋊D3C2×C311yescharacteristic, complemented
16C24×C3×D3C2×C311yescharacteristic, complemented
17C23×C3×A4—31no—
18C22×D3×A4—21no—
19C22×D3×A4—31no—
20C22×D3×A4—31no—
21C22×D3×A4—61no—
22C22×D3×A4D311yescharacteristic, complemented
23C23×C3×Dic3C2×C311yescharacteristic, complemented
24C2×C3×C4×A4—31no—
25C22×#626—31no—
26C22×#626—31no—
27C22×#626—31no—
28C22×#626—31no—
29C22×#626—34no—
30C22×#626C2×C314yescomplemented
31A4×#67—34no—
32C2×Dic3×A4—21no—
33C2×Dic3×A4D311yescharacteristic, complemented
34A4×D12—34no—
35C22×C3×C3⋊D3—41no—
36C22×C32×D3—41no—
37C2×C32×A4D412yescomplemented
38C2×C32×A4C2311yescharacteristic
39A4×C3⋊D3—22no—
40C3×D3×A4—22no—
41C2×C32×Dic3—41no—
42C3×#626—44no—
43C23×#67—31no—
44C23×D12—31no—
45C2×D4×A4—91no—
46C24×C32C22×C311yescharacteristic
47C23×C3⋊D3—22no—
48C23×C3⋊D3—31no—
49C23×C3⋊D3—31no—
50C23×C3⋊D3—32no—
51C23×C3⋊D3—62no—
52C23×C3⋊D3C22×C312yescomplemented
53C23×C3×D3—22no—
54C23×C3×D3—31no—
55C23×C3×D3—31no—
56C23×C3×D3—32no—
57C23×C3×D3—62no—
58C23×C3×D3C22×C312yescomplemented
59C22×C3×A4—21no—
60C22×C3×A4—21no—
61C22×C3×A4—21no—
62C22×C3×A4—32no—
63C22×C3×A4—41no—
64C22×C3×A4—62no—
65C22×C3×A4C2×D311yescharacteristic
66C22×C3×A4C2×D311yescharacteristic
67C2×D3×A4—24no—
68C2×D3×A4—22no—
69C2×D3×A4—22no—
70C2×D3×A4—32no—
71C2×D3×A4—32no—
72C2×D3×A4—62no—
73C2×D3×A4—64no—
74C2×D3×A4—62no—
75C2×D3×A4—62no—
76C2×D3×A4C2×D312yescomplemented
77C2×C3×#67—121no—
78C22×C3×Dic3—31no—
79C22×C3×Dic3—31no—
80C22×C3×Dic3—32no—
81C22×C3×Dic3C22×C312yescomplemented
82C2×C3×D12—121no—
83C3×C4×A4—32no—
84C2×#626—32no—
85C2×#626—34no—
86C2×#626—34no—
87C2×#626—34no—
88C2×#626—31no—
89C2×#626—31no—
90C2×#626—31no—
91C2×#626—34no—
92C2×#626—34no—
93C2×#626—34no—
94C2×#626—34no—
95C2×#626—34no—
96C2×#626A411yescharacteristic, direct product factor
97Dic3×A4—22no—
98Dic3×A4C2×D312yescomplemented
99C22×C33—41no—
100C2×C3×C3⋊D3—42no—
101C2×C3×C3⋊D3—82no—
102C2×C32×D3—42no—
103C2×C32×D3—82no—
104C32×A4C2×D411yescharacteristic, complemented
105C32×Dic3—42no—
106C25×C3—31no—
107C24×D3—31no—
108C24×D3—31no—
109C24×D3—61no—
110C24×D3C3×D311yescharacteristic, complemented
111C23×A4—31no—
112C23×A4—61no—
113C23×A4—91no—
114C23×C3×C4—31no—
115C22×#67—34no—
116C22×#67—91no—
117C22×#67—91no—
118C22×#67—94no—
119C22×#67—91no—
120C22×#67—91no—
121C23×Dic3C3×D311yescharacteristic, complemented
122C22×D12—34no—
123C22×D12—91no—
124C22×D12—94no—
125C22×D12—91no—
126C22×D12—91no—
127C22×D12—91no—
128D4×A4—94no—
129C2×C4×A4—31no—
130C2×C4×A4—61no—
131C23×C32—31no—
132C23×C32—32no—
133C23×C32—31no—
134C23×C32—121no—
135C23×C32C3×D412yescomplemented
136C23×C32C23×C311yescharacteristic
137C22×C3⋊D3—22no—
138C22×C3⋊D3—32no—
139C22×C3⋊D3—31no—
140C22×C3⋊D3—32no—
141C22×C3⋊D3—32no—
142C22×C3⋊D3—32no—
143C22×C3⋊D3—62no—
144C22×C3⋊D3—62no—
145C22×C3⋊D3—64no—
146C22×C3⋊D3—64no—
147C22×C3⋊D3—62no—
148C22×C3⋊D3—62no—
149C22×C3⋊D3—62no—
150C22×C3⋊D3C2×A411yescharacteristic, complemented
151C22×C3×D3—22no—
152C22×C3×D3—32no—
153C22×C3×D3—31no—
154C22×C3×D3—32no—
155C22×C3×D3—32no—
156C22×C3×D3—32no—
157C22×C3×D3—41no—
158C22×C3×D3—62no—
159C22×C3×D3—62no—
160C22×C3×D3—64no—
161C22×C3×D3—64no—
162C22×C3×D3—62no—
163C22×C3×D3—62no—
164C22×C3×D3—62no—
165C22×C3×D3—81no—
166C22×C3×D3—121no—
167C22×C3×D3—121no—
168C22×C3×D3—241no—
169C22×C3×D3C2×A411yescharacteristic, complemented
170C2×C3×A4—22no—
171C2×C3×A4—22no—
172C2×C3×A4—21no—
173C2×C3×A4—21no—
174C2×C3×A4—22no—
175C2×C3×A4—21no—
176C2×C3×A4—42no—
177C2×C3×A4—41no—
178C2×C3×A4—62no—
179C2×C3×A4D1212yescomplemented
180C2×C3×A4#6712yescomplemented
181C2×C3×A4C22×D311yescharacteristic
182C2×C3×A4C22×D311yescharacteristic
183D3×A4—24no—
184D3×A4—22no—
185D3×A4—64no—
186D3×A4—62no—
187D3×A4—62no—
188C2×C32×C4—121no—
189C3×#67—124no—
190C2×C3×Dic3—32no—
191C2×C3×Dic3—31no—
192C2×C3×Dic3—32no—
193C2×C3×Dic3—32no—
194C2×C3×Dic3—32no—
195C2×C3×Dic3—41no—
196C2×C3×Dic3—81no—
197C2×C3×Dic3C2×A411yescharacteristic, complemented
198C3×D12—124no—
199#626—38no—
200#626—34no—
201#626—34no—
202#626—34no—
203#626C2×A414yesdirect product factor
204C23×D4—91noSylow
205C2×C33—42no—
206C2×C33—41no—
207C3×C3⋊D3—82no—
208C32×D3—82no—
209C24×C3—21no—
210C24×C3—32no—
211C24×C3—62no—
212C24×C3—91no—
213C24×C3—92no—
214C24×C3—91no—
215C24×C3—182no—
216C24×C3C2×C3×D311yescharacteristic
217C24×C3C2×C3×D311yescharacteristic
218C23×D3—22no—
219C23×D3—31no—
220C23×D3—31no—
221C23×D3—32no—
222C23×D3—32no—
223C23×D3—32no—
224C23×D3—62no—
225C23×D3—62no—
226C23×D3—64no—
227C23×D3—62no—
228C23×D3—62no—
229C23×D3—91no—
230C23×D3—91no—
231C23×D3—92no—
232C23×D3—91no—
233C23×D3—92no—
234C23×D3—91no—
235C23×D3—181no—
236C23×D3—182no—
237C23×D3—181no—
238C23×D3—184no—
239C23×D3—182no—
240C23×D3—182no—
241C23×D3C2×C3×D312yescomplemented
242C22×A4—21no—
243C22×A4—21no—
244C22×A4—32no—
245C22×A4—41no—
246C22×A4—62no—
247C22×A4—64no—
248C22×A4—62no—
249C22×A4—92no—
250C22×A4—182no—
251C22×A4D3211yescharacteristic
252C2×C3×D4—361no—
253C22×C3×C4—32no—
254C22×C3×C4—91no—
255C22×C3×C4—92no—
256C22×C3×C4—91no—
257C2×#67—31no—
258C2×#67—94no—
259C2×#67—94no—
260C2×#67—91no—
261C2×#67—91no—
262C2×#67—94no—
263C2×#67—94no—
264C2×#67—92no—
265C2×#67—94no—
266C2×#67—94no—
267C2×#67—94no—
268C2×#67—94no—
269C2×#67—91no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—32no—
273C22×Dic3C2×C3×D312yescomplemented
274C2×D12—31no—
275C2×D12—94no—
276C2×D12—94no—
277C2×D12—91no—
278C2×D12—91no—
279C2×D12—94no—
280C2×D12—94no—
281C2×D12—92no—
282C2×D12—94no—
283C2×D12—91no—
284C2×D12—94no—
285C2×D12—94no—
286C2×D12—94no—
287C4×A4—32no—
288C4×A4—62no—
289C22×C32—32no—
290C22×C32—31no—
291C22×C32—32no—
292C22×C32—32no—
293C22×C32—32no—
294C22×C32—31no—
295C22×C32—31no—
296C22×C32—41no—
297C22×C32—41no—
298C22×C32—81no—
299C22×C32—81no—
300C22×C32—81no—
301C22×C32—122no—
302C22×C32—161no—
303C22×C32—242no—
304C22×C32C2×C3×D411yescharacteristic, complemented
305C22×C32C22×A411yescharacteristic
306C2×C3⋊D3—22no—
307C2×C3⋊D3—32no—
308C2×C3⋊D3—62no—
309C2×C3⋊D3—62no—
310C2×C3⋊D3—64no—
311C2×C3⋊D3—64no—
312C2×C3⋊D3—62no—
313C2×C3⋊D3—62no—
314C2×C3⋊D3—62no—
315C2×C3⋊D3C22×A412yescomplemented
316C2×C3×D3—22no—
317C2×C3×D3—32no—
318C2×C3×D3—42no—
319C2×C3×D3—62no—
320C2×C3×D3—62no—
321C2×C3×D3—64no—
322C2×C3×D3—64no—
323C2×C3×D3—62no—
324C2×C3×D3—62no—
325C2×C3×D3—62no—
326C2×C3×D3—82no—
327C2×C3×D3—84no—
328C2×C3×D3—82no—
329C2×C3×D3—122no—
330C2×C3×D3—122no—
331C2×C3×D3—242no—
332C2×C3×D3—242no—
333C2×C3×D3—242no—
334C2×C3×D3—244no—
335C2×C3×D3C22×A412yescomplemented
336C3×A4—21no—
337C3×A4—21no—
338C3×A4—21no—
339C3×A4—41no—
340C3×A4C2×D1211yescharacteristic, complemented
341C3×A4C2×#6711yescharacteristic, complemented
342C32×C4—122no—
343C3×Dic3—32no—
344C3×Dic3—42no—
345C3×Dic3—82no—
346C3×Dic3C22×A412yescomplemented
347C25—31no—
348C25—91no—
349C22×D4—94no—
350C22×D4—271no—
351C22×D4—271no—
352C22×D4—274no—
353C22×D4—271no—
354C22×D4—271no—
355C23×C4—31no—
356C33—41noSylow
357C23×C3—22no—
358C23×C3—21no—
359C23×C3—31no—
360C23×C3—31no—
361C23×C3—32no—
362C23×C3—32no—
363C23×C3—31no—
364C23×C3—31no—
365C23×C3—31no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—62no—
369C23×C3—62no—
370C23×C3—92no—
371C23×C3—92no—
372C23×C3—92no—
373C23×C3—92no—
374C23×C3—91no—
375C23×C3—121no—
376C23×C3—182no—
377C23×C3—182no—
378C23×C3—182no—
379C23×C3—184no—
380C23×C3—182no—
381C23×C3—182no—
382C23×C3—184no—
383C23×C3—241no—
384C23×C3—361no—
385C23×C3C3×D1212yescomplemented
386C23×C3C3×#6712yescomplemented
387C23×C3C22×C3×D311yescharacteristic
388C23×C3C22×C3×D311yescharacteristic
389C22×D3—22no—
390C22×D3—32no—
391C22×D3—31no—
392C22×D3—31no—
393C22×D3—31no—
394C22×D3—32no—
395C22×D3—32no—
396C22×D3—32no—
397C22×D3—61no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—64no—
401C22×D3—64no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—64no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—92no—
409C22×D3—92no—
410C22×D3—92no—
411C22×D3—92no—
412C22×D3—92no—
413C22×D3—92no—
414C22×D3—91no—
415C22×D3—91no—
416C22×D3—92no—
417C22×D3—92no—
418C22×D3—182no—
419C22×D3—182no—
420C22×D3—181no—
421C22×D3—182no—
422C22×D3—182no—
423C22×D3—182no—
424C22×D3—182no—
425C22×D3—182no—
426C22×D3—182no—
427C22×D3—184no—
428C22×D3—184no—
429C22×D3—184no—
430C22×D3—184no—
431C22×D3—184no—
432C22×D3—188no—
433C22×D3—184no—
434C22×D3—184no—
435C22×D3—182no—
436C22×D3—182no—
437C22×D3—182no—
438C22×D3—182no—
439C22×D3—184no—
440C22×D3—188no—
441C22×D3—184no—
442C22×D3—182no—
443C22×D3—182no—
444C22×D3D3×A411yescharacteristic, complemented
445C2×A4—22no—
446C2×A4—22no—
447C2×A4—21no—
448C2×A4—21no—
449C2×A4—42no—
450C2×A4—41no—
451C2×A4—64no—
452C2×A4—62no—
453C2×A4—182no—
454C2×A4#62612yesdirect product factor
455C2×A4C2×D3211yescharacteristic
456C3×D4—364no—
457C2×C3×C4—31no—
458C2×C3×C4—92no—
459C2×C3×C4—92no—
460C2×C3×C4—92no—
461C2×C3×C4—91no—
462C2×C3×C4—92no—
463C2×C3×C4—121no—
464C2×C3×C4—241no—
465#67—34no—
466#67—94no—
467#67—94no—
468#67—98no—
469#67—94no—
470C2×Dic3—32no—
471C2×Dic3—31no—
472C2×Dic3—32no—
473C2×Dic3—32no—
474C2×Dic3—32no—
475C2×Dic3D3×A411yescharacteristic, complemented
476D12—34no—
477D12—94no—
478D12—94no—
479D12—98no—
480D12—94no—
481C2×C32—32no—
482C2×C32—31no—
483C2×C32—31no—
484C2×C32—42no—
485C2×C32—42no—
486C2×C32—41no—
487C2×C32—41no—
488C2×C32—81no—
489C2×C32—82no—
490C2×C32—82no—
491C2×C32—82no—
492C2×C32—81no—
493C2×C32—81no—
494C2×C32—161no—
495C2×C32—162no—
496C2×C32—242no—
497C2×C32D4×A412yescomplemented
498C2×C32C23×A411yescharacteristic
499C3⋊D3—22no—
500C3⋊D3—62no—
501C3×D3—22no—
502C3×D3—62no—
503C3×D3—82no—
504C3×D3—84no—
505C3×D3—242no—
506C3×D3—242no—
507C3×D3—244no—
508C24—32no—
509C24—62no—
510C24—91no—
511C24—92no—
512C24—91no—
513C24—92no—
514C24—182no—
515C24—182no—
516C24—271no—
517C24—272no—
518C24—271no—
519C24—542no—
520C24C3×D3211yescharacteristic
521C2×D4—91no—
522C2×D4—271no—
523C2×D4—274no—
524C2×D4—274no—
525C2×D4—271no—
526C2×D4—271no—
527C2×D4—274no—
528C2×D4—274no—
529C2×D4—274no—
530C2×D4—272no—
531C2×D4—274no—
532C2×D4—274no—
533C2×D4—274no—
534C22×C4—32no—
535C22×C4—91no—
536C22×C4—92no—
537C22×C4—91no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—32no—
541C22×C3—31no—
542C22×C3—32no—
543C22×C3—31no—
544C22×C3—32no—
545C22×C3—32no—
546C22×C3—32no—
547C22×C3—32no—
548C22×C3—32no—
549C22×C3—32no—
550C22×C3—31no—
551C22×C3—31no—
552C22×C3—31no—
553C22×C3—31no—
554C22×C3—32no—
555C22×C3—41no—
556C22×C3—61no—
557C22×C3—62no—
558C22×C3—61no—
559C22×C3—62no—
560C22×C3—62no—
561C22×C3—61no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—81no—
565C22×C3—81no—
566C22×C3—92no—
567C22×C3—122no—
568C22×C3—161no—
569C22×C3—182no—
570C22×C3—182no—
571C22×C3—184no—
572C22×C3—182no—
573C22×C3—182no—
574C22×C3—184no—
575C22×C3—182no—
576C22×C3—242no—
577C22×C3—242no—
578C22×C3—244no—
579C22×C3—362no—
580C22×C3—722no—
581C22×C3C2×C3×D1211yescharacteristic, complemented
582C22×C3C2×C3×#6711yescharacteristic, complemented
583C22×C3C2×D3×A411yescharacteristic
584C22×C3C2×D3×A411yescharacteristic
585C2×D3—22no—
586C2×D3—32no—
587C2×D3—32no—
588C2×D3—32no—
589C2×D3—62no—
590C2×D3—62no—
591C2×D3—64no—
592C2×D3—62no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—92no—
601C2×D3—92no—
602C2×D3—182no—
603C2×D3—182no—
604C2×D3—182no—
605C2×D3—182no—
606C2×D3—184no—
607C2×D3—182no—
608C2×D3—184no—
609C2×D3—184no—
610C2×D3—184no—
611C2×D3—188no—
612C2×D3—184no—
613C2×D3—184no—
614C2×D3—184no—
615C2×D3—184no—
616C2×D3—188no—
617C2×D3—182no—
618C2×D3—182no—
619C2×D3—182no—
620C2×D3—182no—
621C2×D3—182no—
622C2×D3—182no—
623C2×D3—184no—
624C2×D3C2×D3×A412yescomplemented
625A4—21no—
626A4—21no—
627A4—41no—
628A4C2×#62611yescharacteristic, direct product factor
629C3×C4—32no—
630C3×C4—92no—
631C3×C4—122no—
632C3×C4—242no—
633Dic3—32no—
634Dic3C2×D3×A412yescomplemented
635C32—41no—
636C32—41no—
637C32—81no—
638C32—81no—
639C32—81no—
640C32—161no—
641C32C2×D4×A411yescharacteristic, complemented
642C23—31no—
643C23—32no—
644C23—31no—
645C23—31no—
646C23—62no—
647C23—92no—
648C23—92no—
649C23—92no—
650C23—92no—
651C23—91no—
652C23—91no—
653C23—182no—
654C23—182no—
655C23—182no—
656C23—184no—
657C23—182no—
658C23—182no—
659C23—184no—
660C23—182no—
661C23—272no—
662C23—272no—
663C23—272no—
664C23—272no—
665C23—271no—
666C23—542no—
667C23—542no—
668C23—542no—
669C23—544no—
670C23—542no—
671C23—542no—
672C23—544no—
673C23C3×#62612yescomplemented
674C23C2×C3×D3211yescharacteristic
675D4—94no—
676D4—274no—
677D4—274no—
678D4—274no—
679D4—278no—
680C2×C4—31no—
681C2×C4—92no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—91no—
685C2×C4—92no—
686C2×C3—21no—
687C2×C3—22no—
688C2×C3—31no—
689C2×C3—32no—
690C2×C3—31no—
691C2×C3—31no—
692C2×C3—32no—
693C2×C3—31no—
694C2×C3—41no—
695C2×C3—42no—
696C2×C3—61no—
697C2×C3—62no—
698C2×C3—61no—
699C2×C3—62no—
700C2×C3—81no—
701C2×C3—81no—
702C2×C3—82no—
703C2×C3—82no—
704C2×C3—161no—
705C2×C3—162no—
706C2×C3—182no—
707C2×C3—242no—
708C2×C3—244no—
709C2×C3—722no—
710C2×C3A4×D1212yescomplemented
711C2×C3A4×#6712yescomplemented
712C2×C3C22×D3×A411yescharacteristic
713C2×C3C22×D3×A411yescharacteristic
714D3—22no—
715D3—64no—
716D3—62no—
717D3—62no—
718D3—62no—
719D3—184no—
720D3—182no—
721D3—182no—
722C22—32no—
723C22—31no—
724C22—32no—
725C22—31no—
726C22—31no—
727C22—32no—
728C22—32no—
729C22—32no—
730C22—62no—
731C22—92no—
732C22—92no—
733C22—182no—
734C22—182no—
735C22—184no—
736C22—182no—
737C22—182no—
738C22—184no—
739C22—182no—
740C22—182no—
741C22—272no—
742C22—542no—
743C22—542no—
744C22—544no—
745C22—542no—
746C22—542no—
747C22—544no—
748C22—542no—
749C22C2×C3×#62611yescharacteristic, complemented
750C22D32×A411yescharacteristic
751C4—32no—
752C4—92no—
753C3—21no—
754C3—41no—
755C3—81no—
756C3—81no—
757C3—161no—
758C3C2×A4×D1211yescharacteristic, complemented
759C3C2×A4×#6711yescharacteristic, complemented
760C2—31no—
761C2—32no—
762C2—31no—
763C2—62no—
764C2—182no—
765C2—182no—
766C2—542no—
767C2A4×#62612yesdirect product factor
768C2C2×D32×A411yescharacteristic
subgroupG/H
center, hypercenterC22D32×A4
commutator, cosocleC23×C32C23×C3
FrattiniC2C2×D32×A4
Fitting, socleC24×C32C22×C3
hypocenterC22×C32C2×C3×D4
LCSG ▷ C23×C32 ▷ C22×C32
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×A4×C3⋊D3C2semidirect
2. C22×C3×D3×A4C2semidirect
3. C2×C3×Dic3×A4C2semidirect
4. A4×#626C2direct (N × H)
5. C23×#626C3semidirect
10. C2×A4×C3⋊D3C22semidirect
12. C2×C3×D3×A4C22semidirect
14. C3×Dic3×A4C22semidirect
15. C24×C3⋊D3C2×C3semidirect
16. C24×C3×D3C2×C3semidirect
22. C22×D3×A4D3semidirect
23. C23×C3×Dic3C2×C3semidirect
30. C22×#626C2×C3semidirect
33. C2×Dic3×A4D3semidirect
37. C2×C32×A4D4semidirect
52. C23×C3⋊D3C22×C3semidirect
58. C23×C3×D3C22×C3semidirect
76. C2×D3×A4C2×D3semidirect
81. C22×C3×Dic3C22×C3semidirect
96. C2×#626A4direct (N × H)
98. Dic3×A4C2×D3semidirect
104. C32×A4C2×D4semidirect
110. C24×D3C3×D3semidirect
121. C23×Dic3C3×D3semidirect
135. C23×C32C3×D4semidirect
150. C22×C3⋊D3C2×A4semidirect
169. C22×C3×D3C2×A4semidirect
179. C2×C3×A4D12semidirect
180. C2×C3×A4#67semidirect
197. C2×C3×Dic3C2×A4semidirect
203. #626C2×A4direct (N × H)
241. C23×D3C2×C3×D3semidirect
273. C22×Dic3C2×C3×D3semidirect
304. C22×C32C2×C3×D4semidirect
315. C2×C3⋊D3C22×A4semidirect
335. C2×C3×D3C22×A4semidirect
340. C3×A4C2×D12semidirect
341. C3×A4C2×#67semidirect
346. C3×Dic3C22×A4semidirect
385. C23×C3C3×D12semidirect
386. C23×C3C3×#67semidirect
444. C22×D3D3×A4semidirect
454. C2×A4#626direct (N × H)
475. C2×Dic3D3×A4semidirect
497. C2×C32D4×A4semidirect
581. C22×C3C2×C3×D12semidirect
582. C22×C3C2×C3×#67semidirect
624. C2×D3C2×D3×A4semidirect
628. A4C2×#626direct (N × H)
634. Dic3C2×D3×A4semidirect
641. C32C2×D4×A4semidirect
673. C23C3×#626semidirect
710. C2×C3A4×D12semidirect
711. C2×C3A4×#67semidirect
749. C22C2×C3×#626semidirect
758. C3C2×A4×D12semidirect
759. C3C2×A4×#67semidirect
767. C2A4×#626direct (N × H)

Maximal subgroups

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

subgroupindex
C22×A4×C3⋊D32
C22×C3×D3×A42
C2×C3×Dic3×A42
A4×#6262
C23×#6263
C2×A4×#673
C2×A4×D123
C2×C3×#6264