Finite Group Databasebeta

← C4×C4⋊#1020 #72341543

Subgroups — C4×C4⋊#1020 #72341543

Order 1536.

5598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 5598 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C4⋊#1020C211yesmaximal, characteristic
2C2×C4×#1020C212yesmaximal, complemented
3#11715572C212yesmaximal, complemented
4C4⋊#5936C211yesmaximal, characteristic, complemented
5C42×C22⋊A4C211yesmaximal, characteristic, complemented
6C4×#2847—31nomaximal, Sylow
7C22×#1020C2212yes—
8C2×C4×C22⋊A4C2211yescharacteristic
9C2×C4×C22⋊A4C2211yescharacteristic
10C2×C4×C22⋊A4C2211yescharacteristic
11C2×#5936C2212yes—
12C4⋊#1020C414yesdirect product factor
13C4×#1020—24no—
14C4×C4⋊S4—43nomaximal
15C24×C42D311yescharacteristic, complemented
16C2×#2847—31no—
17C2×C4×#121—33no—
18C2×C4×#120—32no—
19#14698—33no—
20#14697—33no—
21#14696—36no—
22#14694—32no—
23#14680—31no—
24C4×#380—33no—
25C4×#386—36no—
26C22×C22⋊A4C2311yescharacteristic
27C2×#1020—22no—
28C2×#1020—22no—
29C2×#1020C2×C414yescomplemented
30C4×C22⋊A4—21no—
31C4×C22⋊A4C2×C412yescomplemented
32C4×C22⋊A4D412yescomplemented
33#5936—22no—
34C2×C4⋊S4—43no—
35C2×C4×S4—46no—
36C42×A4—43no—
37C42×A4—81no—
38(C2×S4)⋊C4—46no—
39C4⋊SL(2,ℤ/4)—43no—
40C25×C4C2×D311yescharacteristic
41C25×C4C2×D311yescharacteristic
42C25×C4C2×D311yescharacteristic
43C22×#121—33no—
44C22×#120—32no—
45C22×C4×D4—36no—
46C22×C4×D4—31no—
47C23×C42—33no—
48C23×C42—33no—
49C23×C42—33no—
50C23×C42—33no—
51C23×C42—61no—
52C23×C42—61no—
53C23×C42—61no—
54C23×C42—61no—
55#2847—312no—
56#2847—34no—
57C4×#121—63no—
58C4×#121—63no—
59C4×#121—63no—
60C4×#121—63no—
61C4×#121—63no—
62C4×#121—63no—
63C4×#121—63no—
64C4×#121—63no—
65C4×#120—612no—
66C4×#120—64no—
67C2×#390—33no—
68C2×#389—33no—
69C2×#388—36no—
70C2×#386—36no—
71C2×#386—36no—
72C2×#386—36no—
73C2×#386—36no—
74C2×#385—36no—
75C2×#380—33no—
76C2×#380—33no—
77C2×#380—33no—
78C2×#379—32no—
79C2×C4×C4⋊C4—33no—
80C2×C4×C22⋊C4—36no—
81C2×C4×C22⋊C4—36no—
82#1437—312no—
83#1436—312no—
84C4⋊#95—36no—
85#1434—36no—
86C22⋊#95—36no—
87C22⋊#95—36no—
88C22⋊#95—36no—
89C4×#95—36no—
90C2×C22⋊A4C22×C411yescharacteristic
91C2×C22⋊A4C2×D411yescharacteristic
92C2×C22⋊A4#4111yescharacteristic
93#1020—24no—
94C22×S4—46no—
95C2×C4×A4—43no—
96C2×C4×A4—43no—
97C2×C4×A4—43no—
98C2×C4×A4—81no—
99C2×C4×A4—81no—
100C2×C4×A4—81no—
101C2×SL(2,ℤ/4)—46no—
102C4⋊S4—412no—
103C4×S4—812no—
104C4×D12—161no—
105C26C22×D311yescharacteristic
106C23×D4—36no—
107C23×D4—31no—
108C24×C4—21no—
109C24×C4—33no—
110C24×C4—33no—
111C24×C4—36no—
112C24×C4—33no—
113C24×C4—33no—
114C24×C4—33no—
115C24×C4—36no—
116C24×C4—33no—
117C24×C4—32no—
118C24×C4—61no—
119C24×C4—61no—
120C24×C4—61no—
121C24×C4—62no—
122C24×C4—62no—
123C24×C4—62no—
124C24×C4—61no—
125C24×C4—61no—
126C24×C4—61no—
127C24×C4—63no—
128C24×C4C4×D312yescomplemented
129C24×C4D1212yescomplemented
130C2×#121—312no—
131C2×#121—312no—
132C2×#121—66no—
133C2×#121—66no—
134C2×#121—63no—
135C2×#121—63no—
136C2×#121—63no—
137C2×#121—63no—
138C2×#120—312no—
139C2×#120—34no—
140C2×#120—66no—
141C2×#120—66no—
142C2×#120—62no—
143C2×#120—62no—
144C2×C4×D4—63no—
145C2×C4×D4—63no—
146C2×C4×D4—63no—
147C2×C4×D4—63no—
148C2×C4×D4—612no—
149C2×C4×D4—612no—
150C2×C4×D4—612no—
151C2×C4×D4—612no—
152C2×C4×D4—66no—
153C2×C4×D4—66no—
154C2×C4×D4—66no—
155C2×C4×D4—66no—
156C22×C4⋊C4—33no—
157C22×C4⋊C4—36no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—33no—
160C22×C22⋊C4—36no—
161C22×C22⋊C4—36no—
162C22×C22⋊C4—36no—
163C22×C22⋊C4—36no—
164C22×C22⋊C4—32no—
165C22×C22⋊C4—36no—
166C22×C22⋊C4—36no—
167C22×C42—21no—
168C22×C42—31no—
169C22×C42—33no—
170C22×C42—33no—
171C22×C42—33no—
172C22×C42—33no—
173C22×C42—33no—
174C22×C42—33no—
175C22×C42—33no—
176C22×C42—33no—
177C22×C42—33no—
178C22×C42—33no—
179C22×C42—36no—
180C22×C42—36no—
181C22×C42—66no—
182C22×C42—66no—
183C22×C42—66no—
184C22×C42—63no—
185C22×C42—63no—
186C22×C42—66no—
187C22×C42—66no—
188C22×C42—63no—
189C22×C42—66no—
190C22×C42—63no—
191C22×C42—61no—
192C22×C42—61no—
193C22×C42—61no—
194C22×C42—63no—
195C22×C42—63no—
196C22×C42—63no—
197C22×C42—63no—
198C22×C42—63no—
199C22×C42—63no—
200C22×C42—63no—
201C22×C42—62no—
202C22×C42S413yescomplemented
203#390—63no—
204#390—63no—
205#390—63no—
206#390—63no—
207#389—63no—
208#389—63no—
209#389—63no—
210#389—63no—
211#388—66no—
212#388—66no—
213#388—66no—
214#388—66no—
215#386—324no—
216#386—324no—
217#386—612no—
218#386—612no—
219#386—612no—
220#386—612no—
221#386—66no—
222#386—66no—
223#386—66no—
224#386—66no—
225#385—612no—
226#385—612no—
227#380—312no—
228#380—312no—
229#380—66no—
230#380—66no—
231#380—63no—
232#380—63no—
233#380—63no—
234#380—63no—
235#379—66no—
236#379—62no—
237C4×C4⋊C4—63no—
238C4×C4⋊C4—63no—
239C4×C4⋊C4—63no—
240C4×C4⋊C4—63no—
241C4×C22⋊C4—66no—
242C4×C22⋊C4—66no—
243C4×C22⋊C4—66no—
244C4×C22⋊C4—66no—
245C4×C22⋊C4—612no—
246C4×C22⋊C4—612no—
247C2×#95—36no—
248C2×#95—36no—
249C2×#95—312no—
250C2×#95—36no—
251C2×#95—36no—
252C2×#95—36no—
253C2×#95—312no—
254C22⋊A4C4×D411yescharacteristic, complemented
255C22×A4—43no—
256C22×A4—81no—
257C2×S4—412no—
258C2×S4—86no—
259C2×S4—86no—
260C2×D12—161no—
261C2×C4×D3—162no—
262C4×A4—46no—
263C4×A4—46no—
264C4×A4—82no—
265C4×A4—82no—
266C4×A4—83no—
267C4×A4—82no—
268SL(2,ℤ/4)—86no—
269C3×C42—161no—
270(C2×D3)⋊C4—162no—
271C4⋊Dic3—161no—
272C25—33no—
273C25—33no—
274C25—33no—
275C25—33no—
276C25—32no—
277C25—61no—
278C25—61no—
279C25—61no—
280C25—61no—
281C25C2×C4×D311yescharacteristic
282C25C2×D1211yescharacteristic
283C25#23511yescharacteristic
284C22×D4—312no—
285C22×D4—312no—
286C22×D4—34no—
287C22×D4—63no—
288C22×D4—63no—
289C22×D4—66no—
290C22×D4—66no—
291C22×D4—66no—
292C22×D4—66no—
293C22×D4—66no—
294C22×D4—66no—
295C22×D4—66no—
296C22×D4—66no—
297C22×D4—66no—
298C22×D4—66no—
299C22×D4—66no—
300C22×D4—66no—
301C22×D4—66no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—33no—
308C23×C4—33no—
309C23×C4—33no—
310C23×C4—31no—
311C23×C4—36no—
312C23×C4—36no—
313C23×C4—33no—
314C23×C4—33no—
315C23×C4—36no—
316C23×C4—36no—
317C23×C4—33no—
318C23×C4—33no—
319C23×C4—33no—
320C23×C4—33no—
321C23×C4—36no—
322C23×C4—36no—
323C23×C4—36no—
324C23×C4—36no—
325C23×C4—36no—
326C23×C4—36no—
327C23×C4—36no—
328C23×C4—36no—
329C23×C4—36no—
330C23×C4—36no—
331C23×C4—36no—
332C23×C4—33no—
333C23×C4—33no—
334C23×C4—33no—
335C23×C4—36no—
336C23×C4—32no—
337C23×C4—62no—
338C23×C4—62no—
339C23×C4—63no—
340C23×C4—63no—
341C23×C4—62no—
342C23×C4—62no—
343C23×C4—62no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—62no—
347C23×C4—63no—
348C23×C4—63no—
349C23×C4—612no—
350C23×C4—612no—
351C23×C4—612no—
352C23×C4—612no—
353C23×C4—66no—
354C23×C4—66no—
355C23×C4—66no—
356C23×C4—66no—
357C23×C4—66no—
358C23×C4—66no—
359C23×C4—63no—
360C23×C4—63no—
361C23×C4—66no—
362C23×C4—63no—
363C23×C4—63no—
364C23×C4—63no—
365C23×C4—63no—
366C23×C4—612no—
367C23×C4—612no—
368C23×C4—66no—
369C23×C4—66no—
370C23×C4—66no—
371C23×C4—66no—
372C23×C4—64no—
373C23×C4—66no—
374C23×C4—66no—
375C23×C4—612no—
376C23×C4—61no—
377C23×C4—61no—
378C23×C4—61no—
379C23×C4—63no—
380C23×C4—63no—
381C23×C4—63no—
382C23×C4—63no—
383C23×C4—63no—
384C23×C4—63no—
385C23×C4—63no—
386C23×C4—63no—
387C23×C4—66no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—66no—
392C23×C4—66no—
393C23×C4—66no—
394C23×C4—63no—
395C23×C4—62no—
396C23×C4C2×S413yes—
397C23×C4C2×S413yes—
398C23×C4C2×S413yes—
399#121—612no—
400#121—612no—
401#121—612no—
402#121—612no—
403#121—612no—
404#121—612no—
405#121—612no—
406#121—612no—
407#120—612no—
408#120—612no—
409#120—612no—
410#120—624no—
411#120—64no—
412C4×D4—126no—
413C4×D4—123no—
414C4×D4—123no—
415C4×D4—123no—
416C4×D4—1212no—
417C4×D4—1212no—
418C4×D4—1212no—
419C4×D4—1212no—
420C4×D4—1212no—
421C4×D4—1212no—
422C4×D4—1212no—
423C4×D4—1212no—
424C4×D4—121no—
425C2×C4⋊C4—312no—
426C2×C4⋊C4—66no—
427C2×C4⋊C4—63no—
428C2×C4⋊C4—63no—
429C2×C4⋊C4—612no—
430C2×C4⋊C4—63no—
431C2×C4⋊C4—63no—
432C2×C4⋊C4—612no—
433C2×C4⋊C4—66no—
434C2×C4⋊C4—66no—
435C2×C4⋊C4—63no—
436C2×C4⋊C4—63no—
437C2×C4⋊C4—612no—
438C2×C22⋊C4—312no—
439C2×C22⋊C4—312no—
440C2×C22⋊C4—324no—
441C2×C22⋊C4—612no—
442C2×C22⋊C4—66no—
443C2×C22⋊C4—66no—
444C2×C22⋊C4—66no—
445C2×C22⋊C4—66no—
446C2×C22⋊C4—66no—
447C2×C22⋊C4—66no—
448C2×C22⋊C4—612no—
449C2×C22⋊C4—612no—
450C2×C22⋊C4—66no—
451C2×C22⋊C4—66no—
452C2×C22⋊C4—66no—
453C2×C22⋊C4—66no—
454C2×C22⋊C4—66no—
455C2×C22⋊C4—66no—
456C2×C22⋊C4—624no—
457C2×C22⋊C4—66no—
458C2×C22⋊C4—66no—
459C2×C22⋊C4—66no—
460C2×C22⋊C4—66no—
461C2×C22⋊C4—66no—
462C2×C22⋊C4—66no—
463C2×C22⋊C4—66no—
464C2×C22⋊C4—66no—
465C2×C22⋊C4—66no—
466C2×C22⋊C4—66no—
467C2×C22⋊C4—66no—
468C2×C22⋊C4—66no—
469C2×C42—33no—
470C2×C42—33no—
471C2×C42—33no—
472C2×C42—33no—
473C2×C42—33no—
474C2×C42—33no—
475C2×C42—33no—
476C2×C42—33no—
477C2×C42—33no—
478C2×C42—33no—
479C2×C42—33no—
480C2×C42—33no—
481C2×C42—33no—
482C2×C42—33no—
483C2×C42—33no—
484C2×C42—33no—
485C2×C42—63no—
486C2×C42—63no—
487C2×C42—63no—
488C2×C42—66no—
489C2×C42—66no—
490C2×C42—66no—
491C2×C42—66no—
492C2×C42—66no—
493C2×C42—66no—
494C2×C42—66no—
495C2×C42—66no—
496C2×C42—66no—
497C2×C42—63no—
498C2×C42—63no—
499C2×C42—63no—
500C2×C42—66no—
501C2×C42—66no—
502C2×C42—66no—
503C2×C42—66no—
504C2×C42—66no—
505C2×C42—66no—
506C2×C42—66no—
507C2×C42—63no—
508C2×C42—63no—
509C2×C42—63no—
510C2×C42—63no—
511C2×C42—63no—
512C2×C42—63no—
513C2×C42—61no—
514C2×C42—61no—
515C2×C42—61no—
516C2×C42—61no—
517C2×C42—612no—
518C2×C42—66no—
519C2×C42—66no—
520C2×C42—612no—
521#95—324no—
522#95—66no—
523#95—66no—
524#95—624no—
525#95—66no—
526#95—66no—
527#95—66no—
528#95—66no—
529#95—612no—
530#95—624no—
531C22×D3—162no—
532C2×A4—43no—
533C2×A4—43no—
534C2×A4—43no—
535C2×A4—81no—
536C2×A4—81no—
537C2×A4—81no—
538S4—812no—
539C2×C3×C4—161no—
540C2×C3×C4—161no—
541C2×C3×C4—161no—
542C2×Dic3—162no—
543D12—164no—
544C4×D3—324no—
545C24—21no—
546C24—31no—
547C24—33no—
548C24—33no—
549C24—33no—
550C24—33no—
551C24—33no—
552C24—33no—
553C24—33no—
554C24—33no—
555C24—33no—
556C24—33no—
557C24—33no—
558C24—33no—
559C24—33no—
560C24—33no—
561C24—33no—
562C24—33no—
563C24—36no—
564C24—34no—
565C24—61no—
566C24—61no—
567C24—61no—
568C24—61no—
569C24—61no—
570C24—61no—
571C24—61no—
572C24—61no—
573C24—61no—
574C24—63no—
575C24—63no—
576C24—66no—
577C24—66no—
578C24—66no—
579C24—63no—
580C24—63no—
581C24—63no—
582C24—66no—
583C24—66no—
584C24—66no—
585C24—63no—
586C24—63no—
587C24—63no—
588C24—63no—
589C24—63no—
590C24—63no—
591C24—66no—
592C24—62no—
593C24—66no—
594C24—66no—
595C24—66no—
596C24—62no—
597C24—62no—
598C24C4×D1211yescharacteristic, complemented
599C24C22×S413yes—
600C2×D4—612no—
601C2×D4—612no—
602C2×D4—612no—
603C2×D4—612no—
604C2×D4—612no—
605C2×D4—612no—
606C2×D4—612no—
607C2×D4—612no—
608C2×D4—612no—
609C2×D4—612no—
610C2×D4—612no—
611C2×D4—612no—
612C2×D4—612no—
613C2×D4—612no—
614C2×D4—123no—
615C2×D4—126no—
616C2×D4—126no—
617C2×D4—126no—
618C2×D4—126no—
619C2×D4—126no—
620C2×D4—126no—
621C2×D4—126no—
622C2×D4—126no—
623C2×D4—126no—
624C2×D4—126no—
625C2×D4—126no—
626C2×D4—126no—
627C2×D4—126no—
628C2×D4—126no—
629C2×D4—126no—
630C2×D4—126no—
631C2×D4—126no—
632C2×D4—126no—
633C2×D4—121no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—23no—
638C22×C4—33no—
639C22×C4—33no—
640C22×C4—32no—
641C22×C4—36no—
642C22×C4—32no—
643C22×C4—36no—
644C22×C4—33no—
645C22×C4—33no—
646C22×C4—33no—
647C22×C4—33no—
648C22×C4—33no—
649C22×C4—36no—
650C22×C4—36no—
651C22×C4—36no—
652C22×C4—36no—
653C22×C4—33no—
654C22×C4—33no—
655C22×C4—33no—
656C22×C4—36no—
657C22×C4—312no—
658C22×C4—33no—
659C22×C4—36no—
660C22×C4—36no—
661C22×C4—36no—
662C22×C4—36no—
663C22×C4—36no—
664C22×C4—36no—
665C22×C4—36no—
666C22×C4—36no—
667C22×C4—36no—
668C22×C4—36no—
669C22×C4—36no—
670C22×C4—36no—
671C22×C4—36no—
672C22×C4—33no—
673C22×C4—312no—
674C22×C4—63no—
675C22×C4—63no—
676C22×C4—63no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—66no—
682C22×C4—612no—
683C22×C4—66no—
684C22×C4—66no—
685C22×C4—612no—
686C22×C4—66no—
687C22×C4—66no—
688C22×C4—66no—
689C22×C4—66no—
690C22×C4—63no—
691C22×C4—66no—
692C22×C4—66no—
693C22×C4—66no—
694C22×C4—66no—
695C22×C4—66no—
696C22×C4—66no—
697C22×C4—63no—
698C22×C4—63no—
699C22×C4—63no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—66no—
703C22×C4—612no—
704C22×C4—66no—
705C22×C4—612no—
706C22×C4—66no—
707C22×C4—66no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—66no—
711C22×C4—612no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—66no—
715C22×C4—62no—
716C22×C4—62no—
717C22×C4—62no—
718C22×C4—61no—
719C22×C4—63no—
720C22×C4—63no—
721C22×C4—63no—
722C22×C4—66no—
723C22×C4—66no—
724C22×C4—66no—
725C22×C4—66no—
726C22×C4—66no—
727C22×C4—66no—
728C22×C4—63no—
729C22×C4—63no—
730C22×C4—63no—
731C22×C4—66no—
732C22×C4—66no—
733C22×C4—63no—
734C22×C4—63no—
735C22×C4—66no—
736C22×C4—612no—
737C22×C4—66no—
738C22×C4—66no—
739C22×C4—66no—
740C22×C4—66no—
741C22×C4—66no—
742C22×C4—66no—
743C22×C4—66no—
744C22×C4—66no—
745C22×C4—66no—
746C22×C4—66no—
747C22×C4—612no—
748C22×C4—612no—
749C22×C4—66no—
750C22×C4—66no—
751C22×C4—66no—
752C22×C4—63no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—62no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—66no—
763C22×C4—66no—
764C22×C4—66no—
765C22×C4—66no—
766C22×C4—66no—
767C22×C4—66no—
768C22×C4—66no—
769C22×C4—66no—
770C22×C4—66no—
771C22×C4—612no—
772C22×C4—612no—
773C22×C4—66no—
774C22×C4—62no—
775C22×C4—66no—
776C22×C4—1212no—
777C22×C4—126no—
778C22×C4—1212no—
779C22×C4—1212no—
780C22×C4—1212no—
781C22×C4—122no—
782C22×C4C4×S416yescomplemented
783C22×C4C4⋊S416yescomplemented
784C4⋊C4—612no—
785C4⋊C4—612no—
786C4⋊C4—126no—
787C4⋊C4—126no—
788C4⋊C4—123no—
789C4⋊C4—1212no—
790C4⋊C4—1212no—
791C4⋊C4—121no—
792C22⋊C4—624no—
793C22⋊C4—624no—
794C22⋊C4—612no—
795C22⋊C4—612no—
796C22⋊C4—612no—
797C22⋊C4—612no—
798C22⋊C4—1212no—
799C22⋊C4—1212no—
800C22⋊C4—1212no—
801C22⋊C4—1212no—
802C22⋊C4—126no—
803C22⋊C4—126no—
804C22⋊C4—126no—
805C22⋊C4—126no—
806C22⋊C4—126no—
807C22⋊C4—126no—
808C22⋊C4—126no—
809C22⋊C4—126no—
810C22⋊C4—126no—
811C22⋊C4—122no—
812C42—36no—
813C42—33no—
814C42—33no—
815C42—33no—
816C42—63no—
817C42—66no—
818C42—66no—
819C42—66no—
820C42—63no—
821C42—63no—
822C42—63no—
823C42—62no—
824C42—61no—
825C42—61no—
826C42—61no—
827C42—1212no—
828C42—1212no—
829C42#102011yescharacteristic, complemented
830C22×C3—161no—
831C2×D3—164no—
832C2×D3—322no—
833C2×D3—322no—
834A4—43no—
835A4—81no—
836C3×C4—162no—
837C3×C4—162no—
838C3×C4—321no—
839Dic3—322no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—31no—
844C23—31no—
845C23—33no—
846C23—33no—
847C23—33no—
848C23—31no—
849C23—33no—
850C23—33no—
851C23—33no—
852C23—33no—
853C23—33no—
854C23—33no—
855C23—33no—
856C23—33no—
857C23—33no—
858C23—33no—
859C23—33no—
860C23—33no—
861C23—33no—
862C23—33no—
863C23—33no—
864C23—33no—
865C23—33no—
866C23—33no—
867C23—33no—
868C23—33no—
869C23—33no—
870C23—33no—
871C23—33no—
872C23—33no—
873C23—33no—
874C23—33no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—63no—
880C23—66no—
881C23—63no—
882C23—63no—
883C23—66no—
884C23—63no—
885C23—63no—
886C23—66no—
887C23—63no—
888C23—66no—
889C23—66no—
890C23—66no—
891C23—66no—
892C23—66no—
893C23—66no—
894C23—63no—
895C23—63no—
896C23—63no—
897C23—63no—
898C23—63no—
899C23—63no—
900C23—66no—
901C23—66no—
902C23—66no—
903C23—66no—
904C23—66no—
905C23—66no—
906C23—63no—
907C23—63no—
908C23—63no—
909C23—66no—
910C23—66no—
911C23—66no—
912C23—612no—
913C23—64no—
914C23—612no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—63no—
919C23—63no—
920C23—63no—
921C23—63no—
922C23—63no—
923C23—63no—
924C23—66no—
925C23—61no—
926C23—126no—
927C23—126no—
928C23—126no—
929C23—126no—
930C23—126no—
931C23—126no—
932C23—126no—
933C23—1212no—
934C23—122no—
935C23C2×C4×S413yes—
936C23C2×C4⋊S413yes—
937C23#591213yes—
938D4—1212no—
939D4—1212no—
940D4—1212no—
941D4—1212no—
942D4—1212no—
943D4—1212no—
944D4—1212no—
945D4—1212no—
946D4—1212no—
947D4—124no—
948C2×C4—36no—
949C2×C4—36no—
950C2×C4—36no—
951C2×C4—36no—
952C2×C4—33no—
953C2×C4—33no—
954C2×C4—36no—
955C2×C4—36no—
956C2×C4—36no—
957C2×C4—36no—
958C2×C4—36no—
959C2×C4—36no—
960C2×C4—36no—
961C2×C4—36no—
962C2×C4—36no—
963C2×C4—36no—
964C2×C4—33no—
965C2×C4—63no—
966C2×C4—63no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—63no—
970C2×C4—63no—
971C2×C4—66no—
972C2×C4—66no—
973C2×C4—66no—
974C2×C4—66no—
975C2×C4—612no—
976C2×C4—612no—
977C2×C4—612no—
978C2×C4—612no—
979C2×C4—66no—
980C2×C4—66no—
981C2×C4—66no—
982C2×C4—66no—
983C2×C4—63no—
984C2×C4—63no—
985C2×C4—63no—
986C2×C4—612no—
987C2×C4—63no—
988C2×C4—63no—
989C2×C4—612no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—66no—
993C2×C4—66no—
994C2×C4—66no—
995C2×C4—66no—
996C2×C4—62no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—63no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—612no—
1009C2×C4—612no—
1010C2×C4—612no—
1011C2×C4—126no—
1012C2×C4—126no—
1013C2×C4—126no—
1014C2×C4—126no—
1015C2×C4—126no—
1016C2×C4—126no—
1017C2×C4—1212no—
1018C2×C4—126no—
1019C2×C4—126no—
1020C2×C4—1212no—
1021C2×C4—126no—
1022C2×C4—122no—
1023C2×C4—2412no—
1024C2×C4—244no—
1025C2×C4C2×#102011yescharacteristic
1026C2×C4C2×#102011yescharacteristic
1027C2×C4C2×#102011yescharacteristic
1028C2×C3—161no—
1029C2×C3—161no—
1030C2×C3—161no—
1031D3—324no—
1032C22—21no—
1033C22—33no—
1034C22—33no—
1035C22—33no—
1036C22—31no—
1037C22—33no—
1038C22—33no—
1039C22—33no—
1040C22—36no—
1041C22—33no—
1042C22—33no—
1043C22—33no—
1044C22—33no—
1045C22—33no—
1046C22—33no—
1047C22—33no—
1048C22—33no—
1049C22—33no—
1050C22—33no—
1051C22—63no—
1052C22—63no—
1053C22—66no—
1054C22—66no—
1055C22—66no—
1056C22—63no—
1057C22—66no—
1058C22—66no—
1059C22—63no—
1060C22—66no—
1061C22—63no—
1062C22—63no—
1063C22—63no—
1064C22—63no—
1065C22—63no—
1066C22—63no—
1067C22—63no—
1068C22—61no—
1069C22—61no—
1070C22—61no—
1071C22—62no—
1072C22—61no—
1073C22—61no—
1074C22—61no—
1075C22—61no—
1076C22—61no—
1077C22—61no—
1078C22—1212no—
1079C22—1212no—
1080C22—124no—
1081C22—246no—
1082C22—246no—
1083C22—242no—
1084C22—242no—
1085C22C4×C4⋊S413yescomplemented
1086C22C22×#102011yescharacteristic
1087C4—21no—
1088C4—36no—
1089C4—36no—
1090C4—62no—
1091C4—62no—
1092C4—62no—
1093C4—63no—
1094C4—1212no—
1095C4—246no—
1096C4—242no—
1097C4C4×#102012yescomplemented
1098C4C4⋊#102012yesdirect product factor
1099C3—161noSylow
1100C2—33no—
1101C2—33no—
1102C2—33no—
1103C2—33no—
1104C2—61no—
1105C2—61no—
1106C2—61no—
1107C2—61no—
1108C2—244no—
1109C2C2×C4×#102011yescharacteristic
1110C2C2×C4⋊#102011yescharacteristic
1111C2#1171580911yescharacteristic
subgroupG/H
centerC2×C4C2×#1020
commutatorC2×C22⋊A4C22×C4
FrattiniC22C22×#1020
FittingC24×C42D3
socleC26C22×D3
prime radicalC2×C4⋊#1020C2
cosocleC22×C22⋊A4C23
hypercenterC42#1020
hypocenterC22⋊A4C4×D4
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1020C2semidirect
3. #11715572C2semidirect
4. C4⋊#5936C2semidirect
5. C42×C22⋊A4C2semidirect
12. C4⋊#1020C4direct (N × H)
15. C24×C42D3semidirect
29. C2×#1020C2×C4semidirect
31. C4×C22⋊A4C2×C4semidirect
32. C4×C22⋊A4D4semidirect
128. C24×C4C4×D3semidirect
129. C24×C4D12semidirect
202. C22×C42S4semidirect
254. C22⋊A4C4×D4semidirect
598. C24C4×D12semidirect
782. C22×C4C4×S4semidirect
783. C22×C4C4⋊S4semidirect
829. C42#1020semidirect
1085. C22C4×C4⋊S4semidirect
1097. C4C4×#1020semidirect
1098. C4C4⋊#1020direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊#10202
C2×C4×#10202
#117155722
C4⋊#59362
C42×C22⋊A42
C4×#28473
C4×C4⋊S44