Finite Group Databasebeta

← C22×C4×#120⋊C3 #72341256

Subgroups — C22×C4×#120⋊C3 #72341256

Order 1536.

14382 conjugacy classes of subgroups; only the 381 normal subgroups are shown.

normal subgroups only

This group has 14382 conjugacy classes of subgroups — too many to draw. Only its 381 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×C4×C22⋊A4C211yesmaximal, characteristic, complemented
2C23×#120⋊C3C211yesmaximal, characteristic
3C2×C4×#120⋊C3C2112yesmaximal, direct product factor
4C22×#379⋊C3C211yesmaximal, characteristic, complemented
5C22×C4×#120C311yesmaximal, characteristic, complemented, Sylow
6C23×C22⋊A4C2211yescharacteristic
7C2×C4×C22⋊A4C2216yescomplemented
8C23×C4×A4—41nomaximal
9C22×#120⋊C3C418yesdirect product factor
10C22×#120⋊C3C2216yes—
11C4×#120⋊C3C22116yesdirect product factor
12C2×#379⋊C3C2216yescomplemented
13C26×C4C2×C311yescharacteristic, complemented
14C23×#120C2×C311yescharacteristic
15C23×C4×D4—31no—
16C2×C4×#120—312no—
17C2×C4×#120C2×C3112yescomplemented
18C22×#386—31no—
19C22×#385—31no—
20C22×#379C2×C311yescharacteristic, complemented
21C22×C4×C22⋊C4—31no—
22C22×C22⋊A4C2×C414yescomplemented
23C22×C22⋊A4C2313yes—
24C24×A4—41no—
25C4×C22⋊A4C2314yescomplemented
26C22×C4×A4—41no—
27C22×C4×A4—41no—
28C22×C4×A4—412no—
29C22×C4×A4—82no—
30C2×#120⋊C3C2×C4124yesdirect product factor
31C2×#120⋊C3C2314yes—
32#379⋊C3C2314yescomplemented
33C27C22×C311yescharacteristic
34C24×D4—31no—
35C25×C4—31no—
36C25×C4—31no—
37C25×C4—36no—
38C25×C4—62no—
39C25×C4—612no—
40C25×C4—62no—
41C25×C4A411yescharacteristic, complemented
42C25×C4C22×C316yescomplemented
43C22×#120—38no—
44C22×#120—36no—
45C22×#120C3×C418yescomplemented
46C22×#120C22×C316yes—
47C22×C4×D4—312no—
48C22×C4×D4—312no—
49C22×C4×D4—62no—
50C22×C4×D4—62no—
51C22×C4×D4—612no—
52C23×C4⋊C4—31no—
53C23×C22⋊C4—31no—
54C23×C22⋊C4—31no—
55C23×C22⋊C4—31no—
56C23×C22⋊C4—31no—
57C23×C42—31no—
58C4×#120—332no—
59C4×#120—348no—
60C4×#120C22×C3116yescomplemented
61C2×#386—312no—
62C2×#386—312no—
63C2×#385—312no—
64C2×#385—312no—
65C2×#379—36no—
66C2×#379C22×C316yescomplemented
67C2×C4×C22⋊C4—312no—
68C2×C4×C22⋊C4—312no—
69C22×#95—32no—
70C2×C22⋊A4C22×C416yescomplemented
71C2×C22⋊A4C2411yescharacteristic
72C23×A4—48no—
73C23×A4—41no—
74C23×A4—46no—
75C23×A4—82no—
76C23×C3×C4—161no—
77C2×C4×A4—46no—
78C2×C4×A4—46no—
79C2×C4×A4—416no—
80C2×C4×A4—812no—
81#120⋊C3C22×C418yesdirect product factor
82C26—31no—
83C26—33no—
84C26—34no—
85C26—62no—
86C26—66no—
87C26—68no—
88C26C2×C3×C414yescomplemented
89C26C2×A411yescharacteristic
90C26C23×C313yes—
91C23×D4—38no—
92C23×D4—38no—
93C23×D4—36no—
94C23×D4—36no—
95C23×D4—68no—
96C23×D4—62no—
97C23×D4—66no—
98C24×C4—22no—
99C24×C4—32no—
100C24×C4—32no—
101C24×C4—312no—
102C24×C4—31no—
103C24×C4—31no—
104C24×C4—36no—
105C24×C4—36no—
106C24×C4—36no—
107C24×C4—38no—
108C24×C4—31no—
109C24×C4—36no—
110C24×C4—312no—
111C24×C4—612no—
112C24×C4—612no—
113C24×C4—61no—
114C24×C4—62no—
115C24×C4—62no—
116C24×C4—612no—
117C24×C4—612no—
118C24×C4—64no—
119C24×C4—612no—
120C24×C4—624no—
121C24×C4—648no—
122C24×C4—624no—
123C24×C4—612no—
124C24×C4—624no—
125C24×C4—624no—
126C24×C4—612no—
127C24×C4—66no—
128C24×C4—61no—
129C24×C4—62no—
130C24×C4—66no—
131C24×C4—62no—
132C24×C4—616no—
133C24×C4—612no—
134C24×C4—612no—
135C24×C4—64no—
136C24×C4—624no—
137C24×C4—648no—
138C24×C4—624no—
139C24×C4—62no—
140C24×C4—612no—
141C24×C4—62no—
142C24×C4C2×A411yescharacteristic
143C24×C4C2×A411yescharacteristic
144C24×C4C2×A4112yescomplemented
145C24×C4C23×C314yescomplemented
146C2×#120—348no—
147C2×#120—38no—
148C2×#120—348no—
149C2×#120—324no—
150C2×#120—312no—
151C2×#120C2×C3×C4124yescomplemented
152C2×#120C23×C314yes—
153C2×C4×D4—348no—
154C2×C4×D4—316no—
155C2×C4×D4—624no—
156C2×C4×D4—624no—
157C2×C4×D4—624no—
158C2×C4×D4—648no—
159C2×C4×D4—624no—
160C2×C4×D4—648no—
161C22×C4⋊C4—312no—
162C22×C4⋊C4—62no—
163C22×C4⋊C4—66no—
164C22×C22⋊C4—38no—
165C22×C22⋊C4—36no—
166C22×C22⋊C4—38no—
167C22×C22⋊C4—36no—
168C22×C22⋊C4—36no—
169C22×C22⋊C4—312no—
170C22×C22⋊C4—36no—
171C22×C22⋊C4—36no—
172C22×C22⋊C4—36no—
173C22×C22⋊C4—62no—
174C22×C22⋊C4—66no—
175C22×C22⋊C4—68no—
176C22×C22⋊C4—62no—
177C22×C22⋊C4—66no—
178C22×C42—312no—
179C22×C42—61no—
180C22×C42—66no—
181C22×C42—61no—
182#386—348no—
183#386—316no—
184#385—348no—
185#385—316no—
186#379—38no—
187#379—312no—
188#379C23×C314yescomplemented
189C4×C22⋊C4—348no—
190C4×C22⋊C4—316no—
191C2×#95—324no—
192C24×C3—161no—
193C22⋊A4C23×C411yescharacteristic, complemented
194C22×A4—44no—
195C22×A4—424no—
196C22×A4—44no—
197C22×A4—43no—
198C22×A4—88no—
199C22×A4—86no—
200C22×C3×C4—161no—
201C22×C3×C4—1612no—
202C22×C3×C4—161no—
203C4×A4—44no—
204C4×A4—44no—
205C4×A4—88no—
206C25—22no—
207C25—36no—
208C25—32no—
209C25—38no—
210C25—34no—
211C25—34no—
212C25—33no—
213C25—33no—
214C25—32no—
215C25—312no—
216C25—33no—
217C25—312no—
218C25—36no—
219C25—66no—
220C25—68no—
221C25—66no—
222C25—68no—
223C25—61no—
224C25—66no—
225C25—624no—
226C25—612no—
227C25—66no—
228C25—62no—
229C25—66no—
230C25—612no—
231C25—612no—
232C25—66no—
233C25—68no—
234C25—624no—
235C25—612no—
236C25—68no—
237C25—616no—
238C25—648no—
239C25—624no—
240C25—63no—
241C25—64no—
242C25—66no—
243C25—62no—
244C25—68no—
245C25—64no—
246C25—612no—
247C25—612no—
248C25—624no—
249C25—616no—
250C25—624no—
251C25—648no—
252C25C4×A418yescomplemented
253C25C22×C3×C416yescomplemented
254C25C22×A411yescharacteristic
255C25C22×A416yes—
256C25C24×C311yescharacteristic
257C22×D4—324no—
258C22×D4—348no—
259C22×D4—324no—
260C22×D4—34no—
261C22×D4—312no—
262C22×D4—612no—
263C22×D4—612no—
264C22×D4—612no—
265C22×D4—612no—
266C22×D4—624no—
267C22×D4—624no—
268C22×D4—616no—
269C22×D4—616no—
270C22×D4—648no—
271C22×D4—648no—
272C23×C4—212no—
273C23×C4—31no—
274C23×C4—31no—
275C23×C4—36no—
276C23×C4—36no—
277C23×C4—32no—
278C23×C4—312no—
279C23×C4—312no—
280C23×C4—312no—
281C23×C4—324no—
282C23×C4—312no—
283C23×C4—324no—
284C23×C4—38no—
285C23×C4—36no—
286C23×C4—36no—
287C23×C4—34no—
288C23×C4—312no—
289C23×C4—312no—
290C23×C4—36no—
291C23×C4—34no—
292C23×C4—41no—
293C23×C4—68no—
294C23×C4—624no—
295C23×C4—612no—
296C23×C4—624no—
297C23×C4—612no—
298C23×C4—648no—
299C23×C4—62no—
300C23×C4—64no—
301C23×C4—612no—
302C23×C4—612no—
303C23×C4—612no—
304C23×C4—624no—
305C23×C4—612no—
306C23×C4—624no—
307C23×C4—612no—
308C23×C4—624no—
309C23×C4—624no—
310C23×C4—624no—
311C23×C4—624no—
312C23×C4—624no—
313C23×C4—648no—
314C23×C4—648no—
315C23×C4—624no—
316C23×C4—648no—
317C23×C4—624no—
318C23×C4—648no—
319C23×C4—68no—
320C23×C4—624no—
321C23×C4—612no—
322C23×C4—61no—
323C23×C4—612no—
324C23×C4—63no—
325C23×C4—61no—
326C23×C4—66no—
327C23×C4—62no—
328C23×C4—612no—
329C23×C4—612no—
330C23×C4—612no—
331C23×C4—612no—
332C23×C4—64no—
333C23×C4—624no—
334C23×C4—624no—
335C23×C4—624no—
336C23×C4—624no—
337C23×C4—648no—
338C23×C4—696no—
339C23×C4—696no—
340C23×C4—648no—
341C23×C4—624no—
342C23×C4—648no—
343C23×C4—624no—
344C23×C4—612no—
345C23×C4—624no—
346C23×C4—696no—
347C23×C4—612no—
348C23×C4—624no—
349C23×C4—696no—
350C23×C4—648no—
351C23×C4—648no—
352C23×C4—648no—
353C23×C4—648no—
354C23×C4—612no—
355C23×C4—624no—
356C23×C4—624no—
357C23×C4—612no—
358C23×C4—64no—
359C23×C4—624no—
360C23×C4—62no—
361C23×C4—62no—
362C23×C4—612no—
363C23×C4—612no—
364C23×C4—624no—
365C23×C4—62no—
366C23×C4—612no—
367C23×C4—612no—
368C23×C4—63no—
369C23×C4—61no—
370C23×C4—68no—
371C23×C4—63no—
372C23×C4—126no—
373C23×C4—121no—
374C23×C4—128no—
375C23×C4—126no—
376C23×C4C22×A416yes—
377C23×C4C22×A416yes—
378C23×C4C22×A4116yescomplemented
379#120—348no—
380#120—364no—
381#120—348no—
382#120—38no—
383#120C22×C3×C418yescomplemented
384C4×D4—696no—
385C4×D4—632no—
386C4×D4—696no—
387C4×D4—632no—
388C2×C4⋊C4—316no—
389C2×C4⋊C4—624no—
390C2×C4⋊C4—624no—
391C2×C22⋊C4—324no—
392C2×C22⋊C4—348no—
393C2×C22⋊C4—312no—
394C2×C22⋊C4—324no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—312no—
397C2×C22⋊C4—316no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—312no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—624no—
402C2×C22⋊C4—624no—
403C2×C22⋊C4—624no—
404C2×C22⋊C4—624no—
405C2×C22⋊C4—612no—
406C2×C22⋊C4—612no—
407C2×C22⋊C4—612no—
408C2×C22⋊C4—612no—
409C2×C42—316no—
410C2×C42—612no—
411C2×C42—624no—
412C2×C42—612no—
413#95—332no—
414C23×C3—166no—
415C23×C3—168no—
416C23×C3—161no—
417C2×A4—46no—
418C2×A4—48no—
419C2×A4—41no—
420C2×A4—82no—
421C2×A4—812no—
422C2×C3×C4—166no—
423C2×C3×C4—1616no—
424C2×C3×C4—166no—
425C24—26no—
426C24—28no—
427C24—33no—
428C24—34no—
429C24—31no—
430C24—36no—
431C24—36no—
432C24—36no—
433C24—36no—
434C24—312no—
435C24—312no—
436C24—324no—
437C24—324no—
438C24—38no—
439C24—38no—
440C24—36no—
441C24—312no—
442C24—36no—
443C24—33no—
444C24—31no—
445C24—38no—
446C24—36no—
447C24—36no—
448C24—31no—
449C24—41no—
450C24—62no—
451C24—612no—
452C24—66no—
453C24—612no—
454C24—624no—
455C24—66no—
456C24—68no—
457C24—612no—
458C24—62no—
459C24—66no—
460C24—66no—
461C24—612no—
462C24—66no—
463C24—66no—
464C24—66no—
465C24—612no—
466C24—66no—
467C24—612no—
468C24—612no—
469C24—612no—
470C24—612no—
471C24—624no—
472C24—624no—
473C24—624no—
474C24—648no—
475C24—68no—
476C24—68no—
477C24—68no—
478C24—616no—
479C24—612no—
480C24—612no—
481C24—66no—
482C24—624no—
483C24—648no—
484C24—612no—
485C24—624no—
486C24—648no—
487C24—624no—
488C24—624no—
489C24—648no—
490C24—648no—
491C24—624no—
492C24—624no—
493C24—612no—
494C24—66no—
495C24—624no—
496C24—612no—
497C24—66no—
498C24—66no—
499C24—66no—
500C24—66no—
501C24—68no—
502C24—612no—
503C24—624no—
504C24—68no—
505C24—68no—
506C24—612no—
507C24—612no—
508C24—624no—
509C24—624no—
510C24—612no—
511C24—612no—
512C24—612no—
513C24—616no—
514C24—624no—
515C24—648no—
516C24—624no—
517C24—624no—
518C24—624no—
519C24—648no—
520C24—648no—
521C24—648no—
522C24—612no—
523C24—624no—
524C24—648no—
525C24—648no—
526C24—648no—
527C24—648no—
528C24—648no—
529C24—696no—
530C24—624no—
531C24—648no—
532C24—648no—
533C24—696no—
534C24—648no—
535C24—616no—
536C24—62no—
537C24—123no—
538C24—124no—
539C24—122no—
540C24—1212no—
541C24C2×C4×A414yes—
542C24C2×C4×A4124yescomplemented
543C24C23×C3×C411yescharacteristic, complemented
544C24C23×A413yes—
545C24C23×A414yes—
546C2×D4—38no—
547C2×D4—348no—
548C2×D4—38no—
549C2×D4—68no—
550C2×D4—624no—
551C2×D4—68no—
552C2×D4—624no—
553C2×D4—648no—
554C2×D4—696no—
555C2×D4—648no—
556C2×D4—648no—
557C2×D4—696no—
558C2×D4—648no—
559C22×C4—28no—
560C22×C4—36no—
561C22×C4—38no—
562C22×C4—31no—
563C22×C4—36no—
564C22×C4—36no—
565C22×C4—36no—
566C22×C4—312no—
567C22×C4—312no—
568C22×C4—312no—
569C22×C4—38no—
570C22×C4—324no—
571C22×C4—38no—
572C22×C4—324no—
573C22×C4—324no—
574C22×C4—34no—
575C22×C4—34no—
576C22×C4—34no—
577C22×C4—41no—
578C22×C4—412no—
579C22×C4—616no—
580C22×C4—648no—
581C22×C4—624no—
582C22×C4—648no—
583C22×C4—624no—
584C22×C4—612no—
585C22×C4—624no—
586C22×C4—612no—
587C22×C4—624no—
588C22×C4—68no—
589C22×C4—624no—
590C22×C4—624no—
591C22×C4—648no—
592C22×C4—624no—
593C22×C4—648no—
594C22×C4—68no—
595C22×C4—624no—
596C22×C4—648no—
597C22×C4—616no—
598C22×C4—616no—
599C22×C4—66no—
600C22×C4—68no—
601C22×C4—66no—
602C22×C4—66no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—66no—
608C22×C4—624no—
609C22×C4—68no—
610C22×C4—612no—
611C22×C4—624no—
612C22×C4—68no—
613C22×C4—648no—
614C22×C4—648no—
615C22×C4—648no—
616C22×C4—648no—
617C22×C4—696no—
618C22×C4—648no—
619C22×C4—616no—
620C22×C4—624no—
621C22×C4—648no—
622C22×C4—624no—
623C22×C4—648no—
624C22×C4—624no—
625C22×C4—696no—
626C22×C4—648no—
627C22×C4—648no—
628C22×C4—648no—
629C22×C4—624no—
630C22×C4—624no—
631C22×C4—612no—
632C22×C4—624no—
633C22×C4—612no—
634C22×C4—648no—
635C22×C4—648no—
636C22×C4—616no—
637C22×C4—62no—
638C22×C4—612no—
639C22×C4—612no—
640C22×C4—612no—
641C22×C4—624no—
642C22×C4—68no—
643C22×C4—612no—
644C22×C4—68no—
645C22×C4—624no—
646C22×C4—66no—
647C22×C4—66no—
648C22×C4—624no—
649C22×C4—66no—
650C22×C4—1224no—
651C22×C4—1212no—
652C22×C4—1224no—
653C22×C4—123no—
654C22×C4—1212no—
655C22×C4—124no—
656C22×C4—122no—
657C22×C4#120⋊C311yescharacteristic, direct product factor
658C22×C4C23×A414yes—
659C22×C4C23×A414yes—
660C4⋊C4—632no—
661C22⋊C4—38no—
662C22⋊C4—348no—
663C22⋊C4—38no—
664C22⋊C4—632no—
665C22⋊C4—624no—
666C22⋊C4—68no—
667C22⋊C4—68no—
668C22⋊C4—624no—
669C42—616no—
670C42—616no—
671C22×C3—164no—
672C22×C3—1624no—
673C22×C3—163no—
674C22×C3—164no—
675A4—41no—
676A4—82no—
677C3×C4—164no—
678C3×C4—164no—
679C23—22no—
680C23—212no—
681C23—33no—
682C23—36no—
683C23—312no—
684C23—32no—
685C23—312no—
686C23—33no—
687C23—33no—
688C23—34no—
689C23—34no—
690C23—32no—
691C23—36no—
692C23—36no—
693C23—32no—
694C23—324no—
695C23—312no—
696C23—312no—
697C23—312no—
698C23—312no—
699C23—324no—
700C23—31no—
701C23—36no—
702C23—31no—
703C23—46no—
704C23—48no—
705C23—62no—
706C23—62no—
707C23—612no—
708C23—64no—
709C23—624no—
710C23—62no—
711C23—66no—
712C23—66no—
713C23—612no—
714C23—612no—
715C23—66no—
716C23—66no—
717C23—62no—
718C23—612no—
719C23—624no—
720C23—612no—
721C23—612no—
722C23—612no—
723C23—624no—
724C23—624no—
725C23—648no—
726C23—648no—
727C23—612no—
728C23—612no—
729C23—624no—
730C23—612no—
731C23—624no—
732C23—612no—
733C23—624no—
734C23—648no—
735C23—624no—
736C23—648no—
737C23—624no—
738C23—612no—
739C23—624no—
740C23—62no—
741C23—64no—
742C23—624no—
743C23—612no—
744C23—648no—
745C23—624no—
746C23—64no—
747C23—66no—
748C23—62no—
749C23—66no—
750C23—612no—
751C23—624no—
752C23—62no—
753C23—612no—
754C23—612no—
755C23—612no—
756C23—624no—
757C23—612no—
758C23—64no—
759C23—612no—
760C23—64no—
761C23—624no—
762C23—612no—
763C23—612no—
764C23—612no—
765C23—648no—
766C23—624no—
767C23—624no—
768C23—624no—
769C23—696no—
770C23—624no—
771C23—624no—
772C23—624no—
773C23—696no—
774C23—612no—
775C23—648no—
776C23—624no—
777C23—648no—
778C23—648no—
779C23—696no—
780C23—696no—
781C23—648no—
782C23—624no—
783C23—648no—
784C23—624no—
785C23—624no—
786C23—648no—
787C23—66no—
788C23—66no—
789C23—68no—
790C23—68no—
791C23—126no—
792C23—1212no—
793C23—1224no—
794C23—1212no—
795C23—1216no—
796C23C2×#120⋊C311yescharacteristic
797C23C22×C4×A416yes—
798C23C22×C4×A418yescomplemented
799C23C24×A411yescharacteristic
800D4—616no—
801D4—696no—
802D4—616no—
803C2×C4—312no—
804C2×C4—36no—
805C2×C4—34no—
806C2×C4—312no—
807C2×C4—34no—
808C2×C4—38no—
809C2×C4—38no—
810C2×C4—46no—
811C2×C4—416no—
812C2×C4—68no—
813C2×C4—616no—
814C2×C4—624no—
815C2×C4—648no—
816C2×C4—64no—
817C2×C4—64no—
818C2×C4—68no—
819C2×C4—624no—
820C2×C4—612no—
821C2×C4—64no—
822C2×C4—624no—
823C2×C4—624no—
824C2×C4—616no—
825C2×C4—624no—
826C2×C4—648no—
827C2×C4—624no—
828C2×C4—612no—
829C2×C4—68no—
830C2×C4—624no—
831C2×C4—68no—
832C2×C4—68no—
833C2×C4—64no—
834C2×C4—68no—
835C2×C4—1216no—
836C2×C4—126no—
837C2×C4—1212no—
838C2×C4—1212no—
839C2×C4C2×#120⋊C316yesdirect product factor
840C2×C3—168no—
841C2×C3—166no—
842C2×C3—161no—
843C22—22no—
844C22—31no—
845C22—36no—
846C22—36no—
847C22—38no—
848C22—36no—
849C22—36no—
850C22—312no—
851C22—31no—
852C22—33no—
853C22—32no—
854C22—312no—
855C22—32no—
856C22—424no—
857C22—44no—
858C22—68no—
859C22—62no—
860C22—612no—
861C22—62no—
862C22—62no—
863C22—64no—
864C22—66no—
865C22—612no—
866C22—624no—
867C22—612no—
868C22—648no—
869C22—624no—
870C22—624no—
871C22—612no—
872C22—62no—
873C22—612no—
874C22—62no—
875C22—612no—
876C22—62no—
877C22—64no—
878C22—624no—
879C22—612no—
880C22—612no—
881C22—616no—
882C22—648no—
883C22—624no—
884C22—612no—
885C22—612no—
886C22—624no—
887C22—62no—
888C22—66no—
889C22—124no—
890C22—1224no—
891C22C4×#120⋊C314yesdirect product factor
892C22C22×#120⋊C313yes—
893C22C23×C4×A411yescharacteristic
894C4—34no—
895C4—44no—
896C4—68no—
897C4—68no—
898C4—124no—
899C4C22×#120⋊C314yesdirect product factor
900C3—161noSylow
901C2—31no—
902C2—31no—
903C2—36no—
904C2—48no—
905C2—62no—
906C2—612no—
907C2—62no—
908C2C2×C4×#120⋊C316yesdirect product factor
909C2C23×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22×C4#120⋊C3
commutator, hypocenterC24C23×C3×C4
FrattiniC23C24×A4
FittingC22×C4×#120C3
socleC25C22×A4
prime radicalC23×#120⋊C3C2
cosocleC25C24×C3
LCSG ▷ C24
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊A4C2semidirect
3. C2×C4×#120⋊C3C2direct (N × H)
4. C22×#379⋊C3C2semidirect
5. C22×C4×#120C3semidirect
7. C2×C4×C22⋊A4C22semidirect
9. C22×#120⋊C3C4direct (N × H)
11. C4×#120⋊C3C22direct (N × H)
12. C2×#379⋊C3C22semidirect
13. C26×C4C2×C3semidirect
17. C2×C4×#120C2×C3semidirect
20. C22×#379C2×C3semidirect
22. C22×C22⋊A4C2×C4semidirect
25. C4×C22⋊A4C23semidirect
30. C2×#120⋊C3C2×C4direct (N × H)
32. #379⋊C3C23semidirect
41. C25×C4A4semidirect
42. C25×C4C22×C3semidirect
45. C22×#120C3×C4semidirect
60. C4×#120C22×C3semidirect
66. C2×#379C22×C3semidirect
70. C2×C22⋊A4C22×C4semidirect
81. #120⋊C3C22×C4direct (N × H)
88. C26C2×C3×C4semidirect
144. C24×C4C2×A4semidirect
145. C24×C4C23×C3semidirect
151. C2×#120C2×C3×C4semidirect
188. #379C23×C3semidirect
193. C22⋊A4C23×C4semidirect
252. C25C4×A4semidirect
253. C25C22×C3×C4semidirect
378. C23×C4C22×A4semidirect
383. #120C22×C3×C4semidirect
542. C24C2×C4×A4semidirect
543. C24C23×C3×C4semidirect
657. C22×C4#120⋊C3direct (N × H)
798. C23C22×C4×A4semidirect
839. C2×C4C2×#120⋊C3direct (N × H)
891. C22C4×#120⋊C3direct (N × H)
899. C4C22×#120⋊C3direct (N × H)
908. C2C2×C4×#120⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊A42
C23×#120⋊C32
C2×C4×#120⋊C32
C22×#379⋊C32
C22×C4×#1203
C23×C4×A44