Finite Group Databasebeta

← C22×#85513 #72344195

Subgroups — C22×#85513 #72344195

Order 1536.

16079 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊S4C211yesmaximal, characteristic, complemented
2C2×#85513C2124yesmaximal, direct product factor
3C22×#5417C212yesmaximal, complemented
4C22×#5415C212yesmaximal, complemented
5C22×#5409C211yesmaximal, characteristic, complemented
6C22×A4×#41C211yesmaximal, characteristic, complemented
7C22×#3006—31nomaximal, Sylow
8C24×S4—21no—
9C2×A4×#41—26no—
10C2×A4×#41C22112yescomplemented
11C22×Q8×A4C2211yescharacteristic, complemented
12C22×D4×A4—21no—
13C22×D4×A4C2211yescharacteristic, complemented
14C23×C4×A4—21no—
15C23×C4×A4C2211yescharacteristic
16C22×C4⋊S4—26no—
17C22×C4⋊S4—21no—
18C22×C4⋊S4C2212yes—
19C22×C4⋊S4C22112yescomplemented
20C22×#949—41nomaximal
21#85513C22164yesdirect product factor
22C2×#5417C22124yescomplemented
23C2×#5415C22124yescomplemented
24C2×#5409C22112yescomplemented
25C22×A4⋊C8C2212yescomplemented
26C24×#41D311yescharacteristic, complemented
27C23×AGL(1,ℤ/8)—31no—
28C23×AGL(1,ℤ/8)—31no—
29C23×#121—31no—
30C2×#3006—324no—
31C2×#3006—324no—
32C22×#449—32no—
33C22×#449—32no—
34C22×#448—32no—
35C22×#447—32no—
36C22×#417—31no—
37C22×#417—31no—
38C22×#407—31no—
39C24×A4—21no—
40C24×A4D411yescharacteristic
41C23×S4—22no—
42C23×S4—212no—
43C23×S4—48no—
44C22×C3×#41—41no—
45C23×D12—41no—
46A4×#41—224no—
47A4×#41C23116yescomplemented
48C2×Q8×A4—23no—
49C2×Q8×A4C2316yescomplemented
50C2×D4×A4—212no—
51C2×D4×A4—23no—
52C2×D4×A4C2316yescomplemented
53C22×C4×A4—21no—
54C22×C4×A4—212no—
55C22×C4×A4D411yescharacteristic
56C22×C4×A4D416yes—
57C22×C4×A4C2311yescharacteristic
58C22×C4×A4C2316yes—
59C2×C4⋊S4—26no—
60C2×C4⋊S4—224no—
61C2×C4⋊S4—212no—
62C2×C4⋊S4C23112yes—
63C2×C4⋊S4C23116yescomplemented
64C2×#949—424no—
65C22×#215—42no—
66C22×#213—42no—
67C22×#208—41no—
68#5417C23132yescomplemented
69#5415C23132yescomplemented
70#5409C23116yescomplemented
71C2×A4⋊C8C23112yescomplemented
72C23×#41—26no—
73C23×#41—31no—
74C23×#41—31no—
75C23×#41—31no—
76C23×#41—31no—
77C23×#41—312no—
78C23×#41—61no—
79C23×#41—61no—
80C23×#41—66no—
81C23×#41C2×D3112yescomplemented
82C24×Q8C2×D311yescharacteristic, complemented
83C24×D4—21no—
84C24×D4—31no—
85C24×D4—61no—
86C24×D4C2×D311yescharacteristic, complemented
87C25×C4—21no—
88C25×C4C2×D311yescharacteristic
89C22×AGL(1,ℤ/8)—324no—
90C22×AGL(1,ℤ/8)—324no—
91C22×AGL(1,ℤ/8)—62no—
92C22×AGL(1,ℤ/8)—612no—
93C22×AGL(1,ℤ/8)—62no—
94C22×AGL(1,ℤ/8)—612no—
95C22×AGL(1,ℤ/8)—61no—
96C22×AGL(1,ℤ/8)—61no—
97C22×AGL(1,ℤ/8)—61no—
98C22×AGL(1,ℤ/8)—61no—
99C23×SD16—32no—
100C23×SD16—32no—
101C23×D8—32no—
102C23×D8—32no—
103C23×M16—31no—
104C23×M16—31no—
105C22×#121—32no—
106C22×#121—312no—
107C22×#121—32no—
108C22×#121—312no—
109C22×#121—61no—
110C22×#121—66no—
111C22×#121—61no—
112C22×#121—66no—
113C23×C4⋊C4—31no—
114C23×C22⋊C4—61no—
115#3006—3192no—
116#3006—364no—
117C2×#449—348no—
118C2×#449—348no—
119C2×#448—324no—
120C2×#448—324no—
121C2×#447—324no—
122C2×#447—324no—
123C2×#417—324no—
124C2×#417—324no—
125C22×#103—32no—
126C22×#103—32no—
127C22×#102—32no—
128C22×#102—32no—
129C2×#407—312no—
130C2×#407—312no—
131C22×C22⋊C8—32no—
132C22×C22⋊C8—32no—
133C24×D3—81no—
134C23×A4—24no—
135C23×A4—26no—
136C23×A4—44no—
137C23×A4C2×D416yes—
138C23×A4C2×D411yescharacteristic
139C22×S4—212no—
140C22×S4—216no—
141C22×S4—448no—
142C22×S4—48no—
143C2×C3×#41—412no—
144C2×C3×#41—86no—
145C22×C3×Q8—41no—
146C22×C3×D4—41no—
147C22×C3×D4—81no—
148C23×C3×C4—41no—
149C23×C3×C4—81no—
150C22×D12—42no—
151C22×D12—412no—
152C22×D12—81no—
153C22×D12—86no—
154Q8×A4—26no—
155Q8×A4C2414yescomplemented
156D4×A4—216no—
157D4×A4—26no—
158D4×A4C2414yescomplemented
159C2×C4×A4—26no—
160C2×C4×A4—216no—
161C2×C4×A4C2×D416yes—
162C2×C4×A4C2×D413yes—
163C2×C4×A4C2×D4112yes—
164C2×C4×A4C2413yes—
165C2×C4×A4C2414yes—
166C4⋊S4—212no—
167C4⋊S4—216no—
168C4⋊S4C2418yes—
169#949—464no—
170C2×#215—424no—
171C2×#213—424no—
172C2×#208—412no—
173C22×C3⋊C8—42no—
174A4⋊C8C2418yescomplemented
175C26—21no—
176C26—61no—
177C26#6711yescharacteristic
178C22×#41—224no—
179C22×#41—312no—
180C22×#41—32no—
181C22×#41—312no—
182C22×#41—32no—
183C22×#41—312no—
184C22×#41—312no—
185C22×#41—312no—
186C22×#41—312no—
187C22×#41—348no—
188C22×#41—31no—
189C22×#41—31no—
190C22×#41—31no—
191C22×#41—61no—
192C22×#41—61no—
193C22×#41—61no—
194C22×#41—66no—
195C22×#41—66no—
196C22×#41—612no—
197C22×#41—612no—
198C22×#41—624no—
199C22×#41—66no—
200C22×#41—66no—
201C22×#41—612no—
202C22×#41—612no—
203C22×#41—66no—
204C22×#41—66no—
205C22×#41—648no—
206C22×#41—66no—
207C22×#41—62no—
208C22×#41—66no—
209C22×#41—66no—
210C22×#41—66no—
211C22×#41—62no—
212C22×#41—616no—
213C22×#41—624no—
214C22×#41—648no—
215C22×#41—624no—
216C22×#41S411yescharacteristic, complemented
217C22×#41C22×D3116yescomplemented
218C23×Q8—23no—
219C23×Q8—31no—
220C23×Q8—31no—
221C23×Q8—36no—
222C23×Q8—61no—
223C23×Q8—63no—
224C23×Q8C22×D316yescomplemented
225C23×D4—212no—
226C23×D4—23no—
227C23×D4—31no—
228C23×D4—31no—
229C23×D4—36no—
230C23×D4—32no—
231C23×D4—312no—
232C23×D4—61no—
233C23×D4—63no—
234C23×D4—61no—
235C23×D4—66no—
236C23×D4—61no—
237C23×D4—66no—
238C23×D4—61no—
239C23×D4—61no—
240C23×D4—66no—
241C23×D4—61no—
242C23×D4—61no—
243C23×D4—612no—
244C23×D4—61no—
245C23×D4—61no—
246C23×D4—62no—
247C23×D4—612no—
248C23×D4—612no—
249C23×D4—62no—
250C23×D4—61no—
251C23×D4—128no—
252C23×D4—128no—
253C23×D4C22×D316yescomplemented
254C24×C4—21no—
255C24×C4—212no—
256C24×C4—31no—
257C24×C4—31no—
258C24×C4—36no—
259C24×C4—31no—
260C24×C4—31no—
261C24×C4—36no—
262C24×C4—61no—
263C24×C4—61no—
264C24×C4—61no—
265C24×C4—61no—
266C24×C4—612no—
267C24×C4—61no—
268C24×C4#6711yescharacteristic
269C24×C4#6716yes—
270C24×C4C22×D311yescharacteristic
271C24×C4C22×D316yes—
272C2×AGL(1,ℤ/8)—364no—
273C2×AGL(1,ℤ/8)—364no—
274C2×AGL(1,ℤ/8)—648no—
275C2×AGL(1,ℤ/8)—696no—
276C2×AGL(1,ℤ/8)—648no—
277C2×AGL(1,ℤ/8)—696no—
278C2×AGL(1,ℤ/8)—624no—
279C2×AGL(1,ℤ/8)—624no—
280C2×AGL(1,ℤ/8)—624no—
281C2×AGL(1,ℤ/8)—624no—
282C22×SD16—324no—
283C22×SD16—324no—
284C22×SD16—64no—
285C22×SD16—612no—
286C22×SD16—612no—
287C22×SD16—62no—
288C22×SD16—62no—
289C22×D8—324no—
290C22×D8—324no—
291C22×D8—64no—
292C22×D8—612no—
293C22×D8—612no—
294C22×D8—62no—
295C22×D8—62no—
296C22×M16—312no—
297C22×M16—312no—
298C22×M16—61no—
299C22×M16—61no—
300C22×M16—66no—
301C22×M16—66no—
302C22×M16—61no—
303C22×M16—61no—
304C23×C8—32no—
305C23×C8—32no—
306C2×#121—312no—
307C2×#121—324no—
308C2×#121—348no—
309C2×#121—312no—
310C2×#121—316no—
311C2×#121—612no—
312C2×#121—612no—
313C2×#121—612no—
314C2×#121—648no—
315C2×#121—66no—
316C2×#121—612no—
317C2×#121—624no—
318C2×#121—612no—
319C2×#121—66no—
320C2×#121—624no—
321C22×C4⋊C4—32no—
322C22×C4⋊C4—312no—
323C22×C4⋊C4—61no—
324C22×C4⋊C4—66no—
325C22×C22⋊C4—62no—
326C22×C22⋊C4—612no—
327C22×C22⋊C4—62no—
328C22×C22⋊C4—612no—
329#449—3128no—
330#449—3128no—
331#448—396no—
332#448—332no—
333#447—396no—
334#447—332no—
335#417—364no—
336#417—364no—
337C2×#103—324no—
338C2×#103—324no—
339C2×#102—324no—
340C2×#102—324no—
341#407—348no—
342#407—316no—
343C2×C22⋊C8—312no—
344C2×C22⋊C8—324no—
345C2×C22⋊C8—312no—
346C24×C3—41no—
347C24×C3—81no—
348C23×D3—812no—
349C23×D3—82no—
350C23×D3—168no—
351C22×A4—212no—
352C22×A4—24no—
353C22×A4—412no—
354C22×A4AGL(1,ℤ/8)14yescomplemented
355C22×A4C22×D414yes—
356C22×A4C22×D413yes—
357C2×S4—28no—
358C2×S4—432no—
359C2×S4—424no—
360C3×#41—416no—
361C3×#41—824no—
362C2×C3×Q8—46no—
363C2×C3×Q8—83no—
364C2×C3×D4—46no—
365C2×C3×D4—83no—
366C2×C3×D4—812no—
367C22×C3×C4—41no—
368C22×C3×C4—46no—
369C22×C3×C4—41no—
370C22×C3×C4—46no—
371C22×C3×C4—812no—
372C22×C3×C4—81no—
373C2×D12—412no—
374C2×D12—416no—
375C2×D12—812no—
376C2×D12—86no—
377C2×D12—824no—
378C4×A4—24no—
379C4×A4C22×D414yes—
380C4×A4C22×D413yes—
381C4×A4C2511yescharacteristic
382#215—432no—
383#213—432no—
384#208—416no—
385C2×C3⋊C8—412no—
386C25—24no—
387C25—26no—
388C25—31no—
389C25—31no—
390C25—36no—
391C25—44no—
392C25—61no—
393C25—64no—
394C25—61no—
395C25—66no—
396C25—62no—
397C25—612no—
398C25—124no—
399C25—126no—
400C25—121no—
401C25—128no—
402C25—128no—
403C25—121no—
404C25C2×#6716yes—
405C25C2×#6711yescharacteristic
406C2×#41—26no—
407C2×#41—316no—
408C2×#41—324no—
409C2×#41—348no—
410C2×#41—324no—
411C2×#41—316no—
412C2×#41—348no—
413C2×#41—316no—
414C2×#41—316no—
415C2×#41—312no—
416C2×#41—312no—
417C2×#41—312no—
418C2×#41—612no—
419C2×#41—612no—
420C2×#41—612no—
421C2×#41—612no—
422C2×#41—66no—
423C2×#41—612no—
424C2×#41—66no—
425C2×#41—624no—
426C2×#41—624no—
427C2×#41—648no—
428C2×#41—616no—
429C2×#41—616no—
430C2×#41—624no—
431C2×#41—624no—
432C2×#41—648no—
433C2×#41—648no—
434C2×#41—624no—
435C2×#41—624no—
436C2×#41—612no—
437C2×#41—648no—
438C2×#41—612no—
439C2×#41—612no—
440C2×#41—624no—
441C2×#41—624no—
442C2×#41—624no—
443C2×#41—624no—
444C2×#41—624no—
445C2×#41—624no—
446C2×#41—696no—
447C2×#41—696no—
448C2×#41—696no—
449C2×#41—624no—
450C2×#41—648no—
451C2×#41—648no—
452C2×#41—624no—
453C2×#41—696no—
454C2×#41—66no—
455C2×#41C2×S4112yescomplemented
456C22×Q8—26no—
457C22×Q8—36no—
458C22×Q8—32no—
459C22×Q8—36no—
460C22×Q8—36no—
461C22×Q8—36no—
462C22×Q8—312no—
463C22×Q8—31no—
464C22×Q8—61no—
465C22×Q8—63no—
466C22×Q8—63no—
467C22×Q8—66no—
468C22×Q8—66no—
469C22×Q8—63no—
470C22×Q8—63no—
471C22×Q8—66no—
472C22×Q8—612no—
473C22×Q8—64no—
474C22×Q8—612no—
475C22×Q8—612no—
476C22×Q8C2×S411yescharacteristic, complemented
477C22×Q8C23×D314yescomplemented
478C22×D4—21no—
479C22×D4—216no—
480C22×D4—26no—
481C22×D4—36no—
482C22×D4—32no—
483C22×D4—36no—
484C22×D4—36no—
485C22×D4—36no—
486C22×D4—312no—
487C22×D4—312no—
488C22×D4—316no—
489C22×D4—31no—
490C22×D4—61no—
491C22×D4—63no—
492C22×D4—63no—
493C22×D4—63no—
494C22×D4—66no—
495C22×D4—66no—
496C22×D4—61no—
497C22×D4—63no—
498C22×D4—66no—
499C22×D4—612no—
500C22×D4—62no—
501C22×D4—66no—
502C22×D4—66no—
503C22×D4—612no—
504C22×D4—612no—
505C22×D4—624no—
506C22×D4—624no—
507C22×D4—612no—
508C22×D4—612no—
509C22×D4—66no—
510C22×D4—624no—
511C22×D4—612no—
512C22×D4—612no—
513C22×D4—64no—
514C22×D4—612no—
515C22×D4—612no—
516C22×D4—61no—
517C22×D4—612no—
518C22×D4—62no—
519C22×D4—612no—
520C22×D4—612no—
521C22×D4—632no—
522C22×D4—61no—
523C22×D4—612no—
524C22×D4—648no—
525C22×D4—612no—
526C22×D4—612no—
527C22×D4—612no—
528C22×D4—624no—
529C22×D4—648no—
530C22×D4—616no—
531C22×D4—612no—
532C22×D4—62no—
533C22×D4—612no—
534C22×D4—126no—
535C22×D4—121no—
536C22×D4—126no—
537C22×D4—126no—
538C22×D4—126no—
539C22×D4—1224no—
540C22×D4—1248no—
541C22×D4—128no—
542C22×D4—1216no—
543C22×D4—1248no—
544C22×D4—1296no—
545C22×D4—128no—
546C22×D4—126no—
547C22×D4—121no—
548C22×D4C2×S411yescharacteristic, complemented
549C22×D4C23×D314yescomplemented
550C23×C4—21no—
551C23×C4—26no—
552C23×C4—216no—
553C23×C4—31no—
554C23×C4—31no—
555C23×C4—36no—
556C23×C4—36no—
557C23×C4—31no—
558C23×C4—31no—
559C23×C4—36no—
560C23×C4—36no—
561C23×C4—31no—
562C23×C4—31no—
563C23×C4—36no—
564C23×C4—31no—
565C23×C4—36no—
566C23×C4—33no—
567C23×C4—36no—
568C23×C4—312no—
569C23×C4—36no—
570C23×C4—36no—
571C23×C4—36no—
572C23×C4—324no—
573C23×C4—33no—
574C23×C4—36no—
575C23×C4—312no—
576C23×C4—612no—
577C23×C4—61no—
578C23×C4—612no—
579C23×C4—61no—
580C23×C4—63no—
581C23×C4—66no—
582C23×C4—612no—
583C23×C4—63no—
584C23×C4—64no—
585C23×C4—66no—
586C23×C4—61no—
587C23×C4—61no—
588C23×C4—62no—
589C23×C4—612no—
590C23×C4—612no—
591C23×C4—612no—
592C23×C4—612no—
593C23×C4—648no—
594C23×C4—632no—
595C23×C4—612no—
596C23×C4—612no—
597C23×C4—61no—
598C23×C4—66no—
599C23×C4—61no—
600C23×C4—62no—
601C23×C4—612no—
602C23×C4—128no—
603C23×C4C2×#6716yes—
604C23×C4C2×#6713yes—
605C23×C4C2×#67112yes—
606C23×C4C2×S411yescharacteristic
607C23×C4C23×D313yes—
608C23×C4C23×D314yes—
609AGL(1,ℤ/8)—6128no—
610AGL(1,ℤ/8)—6128no—
611AGL(1,ℤ/8)—664no—
612AGL(1,ℤ/8)—664no—
613AGL(1,ℤ/8)—664no—
614AGL(1,ℤ/8)—664no—
615C2×SD16—332no—
616C2×SD16—332no—
617C2×SD16—648no—
618C2×SD16—648no—
619C2×SD16—648no—
620C2×SD16—624no—
621C2×SD16—624no—
622C2×D8—332no—
623C2×D8—332no—
624C2×D8—648no—
625C2×D8—648no—
626C2×D8—648no—
627C2×D8—624no—
628C2×D8—624no—
629C2×M16—316no—
630C2×M16—316no—
631C2×M16—612no—
632C2×M16—612no—
633C2×M16—624no—
634C2×M16—624no—
635C2×M16—612no—
636C2×M16—612no—
637C22×C8—312no—
638C22×C8—312no—
639C22×C8—62no—
640C22×C8—66no—
641C22×C8—66no—
642C22×C8—62no—
643#121—324no—
644#121—332no—
645#121—38no—
646#121—648no—
647#121—624no—
648#121—648no—
649#121—648no—
650#121—612no—
651#121—616no—
652#121—616no—
653#121—612no—
654C2×C4⋊C4—312no—
655C2×C4⋊C4—316no—
656C2×C4⋊C4—612no—
657C2×C4⋊C4—66no—
658C2×C4⋊C4—624no—
659C2×C22⋊C4—624no—
660C2×C22⋊C4—612no—
661C2×C22⋊C4—648no—
662C2×C22⋊C4—612no—
663C2×C22⋊C4—616no—
664#103—332no—
665#103—332no—
666#102—332no—
667#102—332no—
668C22⋊C8—324no—
669C22⋊C8—332no—
670C22⋊C8—38no—
671C23×C3—46no—
672C23×C3—41no—
673C23×C3—84no—
674C23×C3—86no—
675C23×C3—164no—
676C22×D3—812no—
677C22×D3—816no—
678C22×D3—168no—
679C22×D3—1648no—
680C2×A4—24no—
681C2×A4—44no—
682C2×A4C2×AGL(1,ℤ/8)16yescomplemented
683C2×A4C23×D411yescharacteristic
684S4—48no—
685C3×Q8—44no—
686C3×Q8—86no—
687C3×D4—44no—
688C3×D4—86no—
689C3×D4—816no—
690C2×C3×C4—46no—
691C2×C3×C4—43no—
692C2×C3×C4—412no—
693C2×C3×C4—43no—
694C2×C3×C4—44no—
695C2×C3×C4—816no—
696C2×C3×C4—86no—
697D12—48no—
698D12—816no—
699D12—812no—
700C3⋊C8—48no—
701C24—21no—
702C24—212no—
703C24—24no—
704C24—31no—
705C24—33no—
706C24—34no—
707C24—36no—
708C24—36no—
709C24—31no—
710C24—36no—
711C24—312no—
712C24—412no—
713C24—64no—
714C24—64no—
715C24—66no—
716C24—66no—
717C24—63no—
718C24—64no—
719C24—612no—
720C24—64no—
721C24—624no—
722C24—64no—
723C24—66no—
724C24—66no—
725C24—612no—
726C24—612no—
727C24—616no—
728C24—68no—
729C24—61no—
730C24—124no—
731C24—124no—
732C24—1212no—
733C24—124no—
734C24—1224no—
735C24—124no—
736C24—126no—
737C24—1224no—
738C24—1212no—
739C24—128no—
740C24—128no—
741C24—1212no—
742C24—1224no—
743C24—1248no—
744C24—1248no—
745C24—1212no—
746C24—122no—
747C24—248no—
748C24—2448no—
749C24—248no—
750C24#94914yescomplemented
751C24GL(2,ℤ/4)11yescharacteristic
752C24C22×#6714yes—
753C24C22×#6713yes—
754#41—224no—
755#41—332no—
756#41—332no—
757#41—316no—
758#41—316no—
759#41—316no—
760#41—616no—
761#41—648no—
762#41—616no—
763#41—648no—
764#41—624no—
765#41—616no—
766#41—624no—
767#41—648no—
768#41—648no—
769#41—648no—
770#41—632no—
771#41—632no—
772#41—696no—
773#41—696no—
774#41—624no—
775#41C22×S4116yescomplemented
776C2×Q8—23no—
777C2×Q8—34no—
778C2×Q8—312no—
779C2×Q8—312no—
780C2×Q8—34no—
781C2×Q8—312no—
782C2×Q8—36no—
783C2×Q8—66no—
784C2×Q8—66no—
785C2×Q8—66no—
786C2×Q8—66no—
787C2×Q8—612no—
788C2×Q8—64no—
789C2×Q8—66no—
790C2×Q8—66no—
791C2×Q8—612no—
792C2×Q8—66no—
793C2×Q8—612no—
794C2×Q8—624no—
795C2×Q8—624no—
796C2×Q8—63no—
797C2×Q8C22×S416yescomplemented
798C2×D4—212no—
799C2×D4—23no—
800C2×D4—34no—
801C2×D4—312no—
802C2×D4—312no—
803C2×D4—34no—
804C2×D4—312no—
805C2×D4—38no—
806C2×D4—36no—
807C2×D4—612no—
808C2×D4—66no—
809C2×D4—66no—
810C2×D4—612no—
811C2×D4—66no—
812C2×D4—64no—
813C2×D4—66no—
814C2×D4—66no—
815C2×D4—66no—
816C2×D4—612no—
817C2×D4—66no—
818C2×D4—612no—
819C2×D4—612no—
820C2×D4—612no—
821C2×D4—612no—
822C2×D4—616no—
823C2×D4—616no—
824C2×D4—616no—
825C2×D4—616no—
826C2×D4—612no—
827C2×D4—616no—
828C2×D4—648no—
829C2×D4—624no—
830C2×D4—612no—
831C2×D4—648no—
832C2×D4—624no—
833C2×D4—648no—
834C2×D4—624no—
835C2×D4—648no—
836C2×D4—612no—
837C2×D4—616no—
838C2×D4—616no—
839C2×D4—616no—
840C2×D4—624no—
841C2×D4—632no—
842C2×D4—68no—
843C2×D4—63no—
844C2×D4—612no—
845C2×D4—616no—
846C2×D4—1212no—
847C2×D4—126no—
848C2×D4—1224no—
849C2×D4—1224no—
850C2×D4—1212no—
851C2×D4—1224no—
852C2×D4—1224no—
853C2×D4—1232no—
854C2×D4—1248no—
855C2×D4—1224no—
856C2×D4—1296no—
857C2×D4—1232no—
858C2×D4—12192no—
859C2×D4—1224no—
860C2×D4—1212no—
861C2×D4—126no—
862C2×D4—1224no—
863C2×D4C22×S416yescomplemented
864C22×C4—21no—
865C22×C4—212no—
866C22×C4—24no—
867C22×C4—36no—
868C22×C4—36no—
869C22×C4—31no—
870C22×C4—31no—
871C22×C4—36no—
872C22×C4—33no—
873C22×C4—312no—
874C22×C4—33no—
875C22×C4—36no—
876C22×C4—312no—
877C22×C4—36no—
878C22×C4—36no—
879C22×C4—36no—
880C22×C4—324no—
881C22×C4—33no—
882C22×C4—34no—
883C22×C4—33no—
884C22×C4—36no—
885C22×C4—312no—
886C22×C4—33no—
887C22×C4—34no—
888C22×C4—36no—
889C22×C4—33no—
890C22×C4—312no—
891C22×C4—33no—
892C22×C4—34no—
893C22×C4—312no—
894C22×C4—36no—
895C22×C4—312no—
896C22×C4—312no—
897C22×C4—33no—
898C22×C4—34no—
899C22×C4—616no—
900C22×C4—612no—
901C22×C4—648no—
902C22×C4—66no—
903C22×C4—66no—
904C22×C4—64no—
905C22×C4—61no—
906C22×C4—63no—
907C22×C4—66no—
908C22×C4—66no—
909C22×C4—612no—
910C22×C4—612no—
911C22×C4—612no—
912C22×C4—63no—
913C22×C4—63no—
914C22×C4—66no—
915C22×C4—612no—
916C22×C4—66no—
917C22×C4—612no—
918C22×C4—612no—
919C22×C4—624no—
920C22×C4—648no—
921C22×C4—616no—
922C22×C4—616no—
923C22×C4—616no—
924C22×C4—66no—
925C22×C4—68no—
926C22×C4—648no—
927C22×C4—648no—
928C22×C4—61no—
929C22×C4—612no—
930C22×C4—612no—
931C22×C4—66no—
932C22×C4—612no—
933C22×C4—616no—
934C22×C4—128no—
935C22×C4—1248no—
936C22×C4GL(2,ℤ/4)16yes—
937C22×C4GL(2,ℤ/4)11yescharacteristic
938C22×C4C22×#6714yes—
939C22×C4C22×#6713yes—
940C22×C4C22×S416yes—
941C22×C4C22×S411yescharacteristic
942C22×C4C24×D311yescharacteristic
943SD16—664no—
944SD16—632no—
945SD16—632no—
946D8—664no—
947D8—632no—
948D8—632no—
949M16—616no—
950M16—616no—
951M16—616no—
952M16—616no—
953C2×C8—38no—
954C2×C8—38no—
955C2×C8—612no—
956C2×C8—612no—
957C2×C8—612no—
958C2×C8—612no—
959C4⋊C4—38no—
960C4⋊C4—616no—
961C4⋊C4—612no—
962C22⋊C4—632no—
963C22⋊C4—624no—
964C22⋊C4—68no—
965C22×C3—44no—
966C22×C3—43no—
967C22×C3—44no—
968C22×C3—812no—
969C22×C3—84no—
970C22×C3—1612no—
971C2×D3—88no—
972C2×D3—1624no—
973C2×D3—1632no—
974A4C22×AGL(1,ℤ/8)11yescharacteristic, complemented
975C3×C4—41no—
976C3×C4—44no—
977C3×C4—43no—
978C3×C4—84no—
979C23—24no—
980C23—26no—
981C23—24no—
982C23—34no—
983C23—34no—
984C23—33no—
985C23—33no—
986C23—33no—
987C23—312no—
988C23—36no—
989C23—34no—
990C23—34no—
991C23—312no—
992C23—36no—
993C23—44no—
994C23—44no—
995C23—612no—
996C23—612no—
997C23—624no—
998C23—64no—
999C23—612no—
1000C23—61no—
1001C23—66no—
1002C23—66no—
1003C23—64no—
1004C23—624no—
1005C23—612no—
1006C23—612no—
1007C23—612no—
1008C23—64no—
1009C23—68no—
1010C23—64no—
1011C23—66no—
1012C23—1212no—
1013C23—1212no—
1014C23—1224no—
1015C23—1212no—
1016C23—124no—
1017C23—1224no—
1018C23—1212no—
1019C23—1212no—
1020C23—1224no—
1021C23—1212no—
1022C23—1216no—
1023C23—1224no—
1024C23—1224no—
1025C23—1212no—
1026C23—1216no—
1027C23—1224no—
1028C23—1232no—
1029C23—1232no—
1030C23—1232no—
1031C23—124no—
1032C23—1216no—
1033C23—1212no—
1034C23—2448no—
1035C23—2424no—
1036C23—2496no—
1037C23—2448no—
1038C23—248no—
1039C23C2×#94916yescomplemented
1040C23C2×GL(2,ℤ/4)16yes—
1041C23C2×GL(2,ℤ/4)11yescharacteristic
1042C23C23×#6711yescharacteristic
1043Q8—26no—
1044Q8—38no—
1045Q8—34no—
1046Q8—64no—
1047Q8—612no—
1048Q8—612no—
1049Q8—66no—
1050Q8C23×S414yescomplemented
1051D4—216no—
1052D4—26no—
1053D4—38no—
1054D4—34no—
1055D4—616no—
1056D4—64no—
1057D4—612no—
1058D4—612no—
1059D4—68no—
1060D4—616no—
1061D4—632no—
1062D4—616no—
1063D4—68no—
1064D4—66no—
1065D4—1216no—
1066D4—1212no—
1067D4—128no—
1068D4—1248no—
1069D4—1264no—
1070D4—128no—
1071D4—1216no—
1072D4—1212no—
1073D4C23×S414yescomplemented
1074C2×C4—26no—
1075C2×C4—216no—
1076C2×C4—33no—
1077C2×C4—34no—
1078C2×C4—36no—
1079C2×C4—33no—
1080C2×C4—312no—
1081C2×C4—31no—
1082C2×C4—33no—
1083C2×C4—34no—
1084C2×C4—34no—
1085C2×C4—33no—
1086C2×C4—33no—
1087C2×C4—34no—
1088C2×C4—312no—
1089C2×C4—36no—
1090C2×C4—312no—
1091C2×C4—312no—
1092C2×C4—34no—
1093C2×C4—33no—
1094C2×C4—31no—
1095C2×C4—616no—
1096C2×C4—64no—
1097C2×C4—612no—
1098C2×C4—66no—
1099C2×C4—63no—
1100C2×C4—63no—
1101C2×C4—64no—
1102C2×C4—612no—
1103C2×C4—616no—
1104C2×C4—632no—
1105C2×C4—612no—
1106C2×C4—66no—
1107C2×C4—616no—
1108C2×C4—64no—
1109C2×C4—68no—
1110C2×C4—1224no—
1111C2×C4—1232no—
1112C2×C4C2×GL(2,ℤ/4)16yes—
1113C2×C4C2×GL(2,ℤ/4)13yes—
1114C2×C4C2×GL(2,ℤ/4)112yes—
1115C2×C4C23×S413yes—
1116C2×C4C23×S414yes—
1117C8—68no—
1118C8—68no—
1119C2×C3—46no—
1120C2×C3—41no—
1121C2×C3—84no—
1122C2×C3—164no—
1123D3—168no—
1124C22—212no—
1125C22—24no—
1126C22—31no—
1127C22—36no—
1128C22—36no—
1129C22—36no—
1130C22—312no—
1131C22—31no—
1132C22—33no—
1133C22—34no—
1134C22—412no—
1135C22—64no—
1136C22—64no—
1137C22—624no—
1138C22—63no—
1139C22—64no—
1140C22—64no—
1141C22—64no—
1142C22—612no—
1143C22—64no—
1144C22—124no—
1145C22—124no—
1146C22—1224no—
1147C22—1212no—
1148C22—124no—
1149C22—124no—
1150C22—1224no—
1151C22—128no—
1152C22—128no—
1153C22—1212no—
1154C22—128no—
1155C22—2432no—
1156C22—2424no—
1157C22—2432no—
1158C22—2424no—
1159C22#8551314yesdirect product factor
1160C22C22×#94911yescharacteristic, complemented
1161C22C22×GL(2,ℤ/4)14yes—
1162C22C22×GL(2,ℤ/4)13yes—
1163C4—24no—
1164C4—31no—
1165C4—34no—
1166C4—33no—
1167C4—64no—
1168C4—128no—
1169C4C22×GL(2,ℤ/4)14yes—
1170C4C22×GL(2,ℤ/4)13yes—
1171C4C24×S411yescharacteristic
1172C3—41noSylow
1173C2—24no—
1174C2—31no—
1175C2—31no—
1176C2—36no—
1177C2—44no—
1178C2—64no—
1179C2—124no—
1180C2—248no—
1181C2C2×#8551316yesdirect product factor
1182C2C23×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC23C2×GL(2,ℤ/4)
commutator, cosocleC4×A4C25
FrattiniC4C24×S4
FittingC24×#41D3
socleC25C2×#67
hypercenterC22×#41S4
hypocenterA4C22×AGL(1,ℤ/8)
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊S4C2semidirect
2. C2×#85513C2direct (N × H)
3. C22×#5417C2semidirect
4. C22×#5415C2semidirect
5. C22×#5409C2semidirect
6. C22×A4×#41C2semidirect
10. C2×A4×#41C22semidirect
11. C22×Q8×A4C22semidirect
13. C22×D4×A4C22semidirect
19. C22×C4⋊S4C22semidirect
21. #85513C22direct (N × H)
22. C2×#5417C22semidirect
23. C2×#5415C22semidirect
24. C2×#5409C22semidirect
25. C22×A4⋊C8C22semidirect
26. C24×#41D3semidirect
47. A4×#41C23semidirect
49. C2×Q8×A4C23semidirect
52. C2×D4×A4C23semidirect
63. C2×C4⋊S4C23semidirect
68. #5417C23semidirect
69. #5415C23semidirect
70. #5409C23semidirect
71. C2×A4⋊C8C23semidirect
81. C23×#41C2×D3semidirect
82. C24×Q8C2×D3semidirect
86. C24×D4C2×D3semidirect
155. Q8×A4C24semidirect
158. D4×A4C24semidirect
174. A4⋊C8C24semidirect
216. C22×#41S4semidirect
217. C22×#41C22×D3semidirect
224. C23×Q8C22×D3semidirect
253. C23×D4C22×D3semidirect
354. C22×A4AGL(1,ℤ/8)semidirect
455. C2×#41C2×S4semidirect
476. C22×Q8C2×S4semidirect
477. C22×Q8C23×D3semidirect
548. C22×D4C2×S4semidirect
549. C22×D4C23×D3semidirect
682. C2×A4C2×AGL(1,ℤ/8)semidirect
750. C24#949semidirect
775. #41C22×S4semidirect
797. C2×Q8C22×S4semidirect
863. C2×D4C22×S4semidirect
974. A4C22×AGL(1,ℤ/8)semidirect
1039. C23C2×#949semidirect
1050. Q8C23×S4semidirect
1073. D4C23×S4semidirect
1159. C22#85513direct (N × H)
1160. C22C22×#949semidirect
1181. C2C2×#85513direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊S42
C2×#855132
C22×#54172
C22×#54152
C22×#54092
C22×A4×#412
C22×#30063
C22×#9494