Finite Group Databasebeta

← C4×A4×#67 #11923348

Subgroups — C4×A4×#67 #11923348

Order 1152.

1210 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×A4C211yesmaximal, characteristic, complemented
2C2×A4×#67C211yesmaximal, characteristic
3C2×C4×D3×A4C211yesmaximal, characteristic, complemented
4A4×#217C211yesmaximal, characteristic, complemented
5A4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C4×Dic3×A4C211yesmaximal, characteristic, complemented
8C22×C4×#67C311yesmaximal, characteristic, complemented
9C4×D4×A4—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C22×D3×A4C2211yescharacteristic
12C2×C3×C4×A4—22no—
13C2×C3×C4×A4C2211yescharacteristic
14C2×C3×C4×A4C2211yescharacteristic
15A4×#67C414yesdirect product factor
16C2×Dic3×A4C2211yescharacteristic
17C2×Dic3×A4C2211yescharacteristic
18C2×Dic3×A4C2211yescharacteristic
19C4×D3×A4—22no—
20C3×C4×#67—41nomaximal
21C24×C3×C4C2×C311yescharacteristic, complemented
22C23×#67C2×C311yescharacteristic
23C23×C4×D3C2×C311yescharacteristic, complemented
24C2×D4×A4—31no—
25C22×C4×A4—21no—
26C22×C4×A4—31no—
27C22×C4×A4D311yescharacteristic, complemented
28C22×#217C2×C311yescharacteristic, complemented
29C2×C4×#67—31no—
30C2×C4×#67—31no—
31C2×C4×#67—31no—
32C2×C4×#67—31no—
33C2×C4×#67—31no—
34C2×C4×#67—31no—
35C2×C4×#67—31no—
36C2×C4×#67—31no—
37C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
38C22×Dic3⋊C4C2×C311yescharacteristic, complemented
39C22×C4×Dic3C2×C311yescharacteristic, complemented
40A4×C4⋊C4—31no—
41A4×C22⋊C4—31no—
42A4×C22⋊C4—31no—
43C42×A4—31no—
44C22×C3×A4—21no—
45C22×C3×A4—21no—
46C22×C3×A4C2×C412yescomplemented
47C22×C3×A4C2311yescharacteristic
48C2×D3×A4—21no—
49C2×D3×A4—21no—
50C2×D3×A4C2×C412yescomplemented
51C22×C32×C4—41no—
52C2×C3×#67—41no—
53C2×C3×C4×D3—41no—
54C3×C4×A4—21no—
55C3×C4×A4D412yescomplemented
56Dic3×A4—21no—
57Dic3×A4—21no—
58Dic3×A4C2×C412yescomplemented
59C3×#217—41no—
60C3×(C2×D3)⋊C4—41no—
61C3×Dic3⋊C4—41no—
62C3×C4×Dic3—41no—
63C22×C4×D4—31noSylow
64C25×C3C22×C311yescharacteristic
65C24×D3C22×C311yescharacteristic
66C23×A4—21no—
67C23×A4—31no—
68C23×A4C2×D311yescharacteristic
69C23×C3×C4—22no—
70C23×C3×C4—31no—
71C23×C3×C4—31no—
72C23×C3×C4—31no—
73C23×C3×C4—31no—
74C23×C3×C4—62no—
75C23×C3×C4C22×C311yescharacteristic
76C23×C3×C4C22×C311yescharacteristic
77C22×#67—31no—
78C22×#67—34no—
79C22×#67—31no—
80C22×#67—31no—
81C22×#67—31no—
82C22×#67C3×C414yescomplemented
83C23×Dic3C22×C311yescharacteristic
84C23×Dic3C22×C311yescharacteristic
85C23×Dic3C22×C311yescharacteristic
86C22×C4×D3—22no—
87C22×C4×D3—31no—
88C22×C4×D3—31no—
89C22×C4×D3—31no—
90C22×C4×D3—31no—
91C22×C4×D3—62no—
92D4×A4—34no—
93C2×C4×A4—24no—
94C2×C4×A4—22no—
95C2×C4×A4—21no—
96C2×C4×A4—21no—
97C2×C4×A4—31no—
98C2×C4×A4—31no—
99C2×C4×A4—31no—
100C2×C4×A4—62no—
101C2×C4×A4C2×D311yescharacteristic
102C2×C4×A4C2×D311yescharacteristic
103C3×C4×D4—121no—
104C2×#217—31no—
105C2×#217—31no—
106C2×#217—31no—
107C2×#217—31no—
108C4×#67—32no—
109C4×#67—32no—
110C4×#67—32no—
111C4×#67—32no—
112C4×#67—32no—
113C4×#67—32no—
114C4×#67—32no—
115C4×#67—31no—
116C4×#67—31no—
117C4×#67—31no—
118C4×#67—31no—
119C4×#67—31no—
120C4×#67—31no—
121C4×#67—31no—
122C4×#67A411yescharacteristic, direct product factor
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C23×C32—41no—
136C22×C3×D3—41no—
137C2×C3×A4—22no—
138C2×C3×A4C22×C411yescharacteristic
139C2×C3×A4C2×D411yescharacteristic
140C2×C3×A4#4111yescharacteristic
141D3×A4—22no—
142C2×C32×C4—41no—
143C2×C32×C4—41no—
144C2×C32×C4—82no—
145C3×#67—44no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×C4×D3—82no—
150C23×D4—31no—
151C24×C4—31no—
152C24×C4C3×D311yescharacteristic, complemented
153C2×C4×D4—91no—
154C2×C4×D4—91no—
155C2×C4×D4—91no—
156C2×C4×D4—91no—
157C2×C4×D4—91no—
158C2×C4×D4—91no—
159C2×C4×D4—91no—
160C2×C4×D4—91no—
161C22×C4⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C42—31no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—31no—
168C24×C3—32no—
169C24×C3—31no—
170C24×C3—61no—
171C24×C3—61no—
172C24×C3C2×C3×C412yescomplemented
173C24×C3C23×C311yescharacteristic
174C23×D3—21no—
175C23×D3—21no—
176C23×D3—31no—
177C23×D3—31no—
178C23×D3—32no—
179C23×D3—61no—
180C23×D3—61no—
181C23×D3C2×C3×C412yescomplemented
182C22×A4—22no—
183C22×A4—22no—
184C22×A4—21no—
185C22×A4—21no—
186C22×A4—22no—
187C22×A4—21no—
188C22×A4—32no—
189C22×A4—61no—
190C22×A4—61no—
191C22×A4C4×D312yescomplemented
192C22×A4C22×D311yescharacteristic
193C2×C3×D4—121no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—41no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C22×C3×C4—81no—
215C22×C3×C4—121no—
216C22×C3×C4C3×D412yescomplemented
217C22×C3×C4C2×A411yescharacteristic, complemented
218C2×#67—32no—
219C2×#67—34no—
220C2×#67—34no—
221C2×#67—34no—
222C2×#67—31no—
223C2×#67—31no—
224C2×#67—34no—
225C2×#67—34no—
226C2×#67—34no—
227C2×#67—34no—
228C2×#67—34no—
229C2×#67—31no—
230C2×#67C2×A411yescharacteristic
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—32no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3C2×C3×C412yescomplemented
243C2×C4×D3—32no—
244C2×C4×D3—31no—
245C2×C4×D3—31no—
246C2×C4×D3—31no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3C2×A411yescharacteristic, complemented
256C4×A4—22no—
257C4×A4—21no—
258C4×A4—22no—
259C4×A4—32no—
260C4×A4—61no—
261C4×A4—61no—
262C4×A4#6712yesdirect product factor
263C3×C4⋊C4—121no—
264C3×C22⋊C4—121no—
265C3×C22⋊C4—121no—
266C3×C42—121no—
267#217—32no—
268#217—31no—
269#217—31no—
270#217—31no—
271#217C2×A411yescharacteristic, complemented
272(C2×D3)⋊C4—32no—
273(C2×D3)⋊C4—31no—
274(C2×D3)⋊C4—31no—
275(C2×D3)⋊C4—31no—
276(C2×D3)⋊C4C2×A411yescharacteristic, complemented
277Dic3⋊C4—32no—
278Dic3⋊C4—31no—
279Dic3⋊C4—31no—
280Dic3⋊C4—31no—
281Dic3⋊C4C2×A411yescharacteristic, complemented
282C4×Dic3—32no—
283C4×Dic3—31no—
284C4×Dic3—31no—
285C4×Dic3—31no—
286C4×Dic3C2×A411yescharacteristic, complemented
287C22×C32—42no—
288C22×C32—41no—
289C22×C32—81no—
290C22×C32—81no—
291C2×C3×D3—42no—
292C2×C3×D3—81no—
293C2×C3×D3—81no—
294C3×A4C4×D411yescharacteristic, complemented
295C32×C4—42no—
296C32×C4—81no—
297C3×Dic3—42no—
298C3×Dic3—81no—
299C3×Dic3—81no—
300C25—31no—
301C25C2×C3×D311yescharacteristic
302C22×D4—34no—
303C22×D4—91no—
304C22×D4—91no—
305C22×D4—91no—
306C22×D4—91no—
307C22×D4—94no—
308C23×C4—22no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—62no—
317C23×C4—62no—
318C23×C4—91no—
319C23×C4—91no—
320C23×C4—91no—
321C23×C4—91no—
322C23×C4—182no—
323C23×C4C2×C3×D311yescharacteristic
324C23×C4C2×C3×D311yescharacteristic
325C4×D4—31no—
326C4×D4—91no—
327C4×D4—91no—
328C4×D4—91no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—91no—
332C4×D4—92no—
333C4×D4—92no—
334C4×D4—92no—
335C4×D4—92no—
336C4×D4—92no—
337C4×D4—92no—
338C4×D4—92no—
339C4×D4—91no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—91no—
344C2×C22⋊C4—91no—
345C2×C22⋊C4—91no—
346C2×C22⋊C4—91no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—91no—
351C2×C22⋊C4—91no—
352C2×C42—91no—
353C2×C42—91no—
354C2×C42—91no—
355C2×C42—91no—
356C23×C3—22no—
357C23×C3—31no—
358C23×C3—31no—
359C23×C3—31no—
360C23×C3—31no—
361C23×C3—32no—
362C23×C3—32no—
363C23×C3—32no—
364C23×C3—32no—
365C23×C3—31no—
366C23×C3—41no—
367C23×C3—61no—
368C23×C3—61no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3—61no—
374C23×C3—62no—
375C23×C3—62no—
376C23×C3—61no—
377C23×C3—61no—
378C23×C3—64no—
379C23×C3—81no—
380C23×C3—121no—
381C23×C3C22×C3×C411yescharacteristic
382C23×C3C2×C3×D411yescharacteristic
383C23×C3C3×#4111yescharacteristic
384C23×C3C22×A411yescharacteristic
385C22×D3—22no—
386C22×D3—32no—
387C22×D3—31no—
388C22×D3—32no—
389C22×D3—32no—
390C22×D3—32no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—64no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—61no—
401C22×D3—61no—
402C22×D3—62no—
403C22×D3C22×A411yescharacteristic
404C2×A4—24no—
405C2×A4—22no—
406C2×A4—21no—
407C2×A4—21no—
408C2×A4—21no—
409C2×A4—62no—
410C2×A4C2×C4×D311yescharacteristic
411C2×A4#23511yescharacteristic
412C2×A4C2×#6711yescharacteristic
413C3×D4—124no—
414C2×C3×C4—22no—
415C2×C3×C4—32no—
416C2×C3×C4—31no—
417C2×C3×C4—32no—
418C2×C3×C4—32no—
419C2×C3×C4—32no—
420C2×C3×C4—31no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—62no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—62no—
427C2×C3×C4—64no—
428C2×C3×C4—62no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—82no—
432C2×C3×C4—84no—
433C2×C3×C4—81no—
434C2×C3×C4—81no—
435C2×C3×C4—121no—
436C2×C3×C4—121no—
437C2×C3×C4—121no—
438C2×C3×C4—242no—
439C2×C3×C4C22×A411yescharacteristic
440C2×C3×C4C22×A411yescharacteristic
441#67—38no—
442#67—34no—
443#67—34no—
444#67—34no—
445#67C4×A414yesdirect product factor
446C2×Dic3—32no—
447C2×Dic3—31no—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—32no—
451C2×Dic3—31no—
452C2×Dic3—31no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3C22×A411yescharacteristic
462C2×Dic3C22×A411yescharacteristic
463C2×Dic3C22×A411yescharacteristic
464C4×D3—22no—
465C4×D3—62no—
466C4×D3—62no—
467C4×D3—64no—
468C4×D3—62no—
469C2×C32—41no—
470C2×C32—41no—
471C2×C32—41no—
472C2×C32—82no—
473C3×D3—82no—
474C24—21no—
475C24—21no—
476C24—31no—
477C24—32no—
478C24—31no—
479C24—32no—
480C24—61no—
481C24—61no—
482C24—61no—
483C24—61no—
484C24—91no—
485C24—91no—
486C24—92no—
487C24—181no—
488C24—181no—
489C24C3×C4×D312yescomplemented
490C24C22×C3×D311yescharacteristic
491C2×D4—31no—
492C2×D4—91no—
493C2×D4—94no—
494C2×D4—94no—
495C2×D4—91no—
496C2×D4—92no—
497C2×D4—94no—
498C2×D4—94no—
499C2×D4—94no—
500C2×D4—91no—
501C2×D4—94no—
502C2×D4—94no—
503C2×D4—94no—
504C22×C4—21no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—31no—
515C22×C4—32no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—91no—
531C22×C4—91no—
532C22×C4—92no—
533C22×C4—91no—
534C22×C4—92no—
535C22×C4—91no—
536C22×C4—91no—
537C22×C4—91no—
538C22×C4—182no—
539C22×C4—182no—
540C22×C4—182no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4—182no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—181no—
547C22×C4—181no—
548C22×C4C3×#6712yescomplemented
549C22×C4D3×A411yescharacteristic, complemented
550C4⋊C4—31no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—92no—
554C4⋊C4—91no—
555C22⋊C4—31no—
556C22⋊C4—31no—
557C22⋊C4—91no—
558C22⋊C4—91no—
559C22⋊C4—91no—
560C22⋊C4—91no—
561C22⋊C4—92no—
562C22⋊C4—92no—
563C22⋊C4—91no—
564C22⋊C4—91no—
565C42—31no—
566C42—91no—
567C42—91no—
568C42—92no—
569C42—91no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—31no—
573C22×C3—31no—
574C22×C3—31no—
575C22×C3—32no—
576C22×C3—31no—
577C22×C3—31no—
578C22×C3—31no—
579C22×C3—31no—
580C22×C3—31no—
581C22×C3—31no—
582C22×C3—32no—
583C22×C3—42no—
584C22×C3—41no—
585C22×C3—62no—
586C22×C3—62no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—62no—
592C22×C3—62no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—82no—
600C22×C3—81no—
601C22×C3—122no—
602C22×C3—241no—
603C22×C3—241no—
604C22×C3C3×C4×D411yescharacteristic, complemented
605C22×C3C2×C4×A412yescomplemented
606C22×C3C23×A411yescharacteristic
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—32no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3C2×C4×A412yescomplemented
621A4—21no—
622A4C4×#6711yescharacteristic, direct product factor
623C3×C4—21no—
624C3×C4—32no—
625C3×C4—42no—
626C3×C4—61no—
627C3×C4—81no—
628C3×C4—82no—
629C3×C4—82no—
630C3×C4—122no—
631C3×C4—241no—
632C3×C4—241no—
633C3×C4D4×A412yescomplemented
634Dic3—21no—
635Dic3—21no—
636Dic3—32no—
637Dic3—61no—
638Dic3—61no—
639Dic3C2×C4×A412yescomplemented
640C32—41noSylow
641C23—22no—
642C23—31no—
643C23—31no—
644C23—31no—
645C23—31no—
646C23—32no—
647C23—32no—
648C23—32no—
649C23—32no—
650C23—31no—
651C23—31no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—62no—
657C23—61no—
658C23—61no—
659C23—62no—
660C23—62no—
661C23—61no—
662C23—61no—
663C23—64no—
664C23—62no—
665C23—92no—
666C23—92no—
667C23—92no—
668C23—92no—
669C23—91no—
670C23—181no—
671C23—181no—
672C23—181no—
673C23—181no—
674C23—182no—
675C23—181no—
676C23—181no—
677C23—182no—
678C23—182no—
679C23—181no—
680C23—181no—
681C23—184no—
682C23C2×C3×C4×D311yescharacteristic
683C23C3×#23511yescharacteristic
684C23C2×C3×#6711yescharacteristic
685C23C2×D3×A411yescharacteristic
686D4—34no—
687D4—94no—
688D4—94no—
689D4—98no—
690D4—94no—
691C2×C4—22no—
692C2×C4—32no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—64no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—92no—
711C2×C4—92no—
712C2×C4—92no—
713C2×C4—91no—
714C2×C4—92no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—182no—
718C2×C4—182no—
719C2×C4—184no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—182no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4C2×D3×A411yescharacteristic
730C2×C4C2×D3×A411yescharacteristic
731C2×C3—22no—
732C2×C3—31no—
733C2×C3—31no—
734C2×C3—31no—
735C2×C3—31no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—41no—
739C2×C3—62no—
740C2×C3—82no—
741C2×C3—84no—
742C2×C3—81no—
743C2×C3—81no—
744C2×C3—81no—
745C2×C3—242no—
746C2×C3C22×C4×A411yescharacteristic
747C2×C3C2×D4×A411yescharacteristic
748C2×C3A4×#4111yescharacteristic
749D3—22no—
750D3—62no—
751C22—21no—
752C22—21no—
753C22—31no—
754C22—31no—
755C22—31no—
756C22—32no—
757C22—31no—
758C22—31no—
759C22—31no—
760C22—31no—
761C22—31no—
762C22—31no—
763C22—32no—
764C22—32no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—62no—
773C22—61no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—92no—
778C22—182no—
779C22—182no—
780C22—182no—
781C22—182no—
782C22—182no—
783C22—182no—
784C22—182no—
785C22—182no—
786C22—181no—
787C22—181no—
788C22C3×C4×#6711yescharacteristic, complemented
789C22C4×D3×A412yescomplemented
790C22C22×D3×A411yescharacteristic
791C4—21no—
792C4—32no—
793C4—32no—
794C4—61no—
795C4—61no—
796C4—61no—
797C4—92no—
798C4—181no—
799C4—181no—
800C4A4×#6712yesdirect product factor
801C3—41no—
802C3—81no—
803C3C4×D4×A411yescharacteristic, complemented
804C2—22no—
805C2—31no—
806C2—31no—
807C2—31no—
808C2—31no—
809C2—62no—
810C2—62no—
811C2—182no—
812C2C2×C4×D3×A411yescharacteristic
813C2A4×#23511yescharacteristic
814C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC2×C4C2×D3×A4
commutatorC23×C3C22×C3×C4
FrattiniC22C22×D3×A4
FittingC24×C3×C4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC2×A4×#67C2
hypercenterC22×C4D3×A4
hypocenterC22×C3C3×C4×D4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×A4C2semidirect
3. C2×C4×D3×A4C2semidirect
4. A4×#217C2semidirect
5. A4×(C2×D3)⋊C4C2semidirect
6. A4×Dic3⋊C4C2semidirect
7. C4×Dic3×A4C2semidirect
8. C22×C4×#67C3semidirect
15. A4×#67C4direct (N × H)
21. C24×C3×C4C2×C3semidirect
23. C23×C4×D3C2×C3semidirect
27. C22×C4×A4D3semidirect
28. C22×#217C2×C3semidirect
37. C22×(C2×D3)⋊C4C2×C3semidirect
38. C22×Dic3⋊C4C2×C3semidirect
39. C22×C4×Dic3C2×C3semidirect
46. C22×C3×A4C2×C4semidirect
50. C2×D3×A4C2×C4semidirect
55. C3×C4×A4D4semidirect
58. Dic3×A4C2×C4semidirect
82. C22×#67C3×C4semidirect
122. C4×#67A4direct (N × H)
152. C24×C4C3×D3semidirect
172. C24×C3C2×C3×C4semidirect
181. C23×D3C2×C3×C4semidirect
191. C22×A4C4×D3semidirect
216. C22×C3×C4C3×D4semidirect
217. C22×C3×C4C2×A4semidirect
242. C22×Dic3C2×C3×C4semidirect
255. C2×C4×D3C2×A4semidirect
262. C4×A4#67direct (N × H)
271. #217C2×A4semidirect
276. (C2×D3)⋊C4C2×A4semidirect
281. Dic3⋊C4C2×A4semidirect
286. C4×Dic3C2×A4semidirect
294. C3×A4C4×D4semidirect
445. #67C4×A4direct (N × H)
489. C24C3×C4×D3semidirect
548. C22×C4C3×#67semidirect
549. C22×C4D3×A4semidirect
604. C22×C3C3×C4×D4semidirect
605. C22×C3C2×C4×A4semidirect
620. C2×D3C2×C4×A4semidirect
622. A4C4×#67direct (N × H)
633. C3×C4D4×A4semidirect
639. Dic3C2×C4×A4semidirect
788. C22C3×C4×#67semidirect
789. C22C4×D3×A4semidirect
800. C4A4×#67direct (N × H)
803. C3C4×D4×A4semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C2×A4×#672
C2×C4×D3×A42
A4×#2172
A4×(C2×D3)⋊C42
A4×Dic3⋊C42
C4×Dic3×A42
C22×C4×#673
C4×D4×A43
C3×C4×#674