Finite Group Databasebeta

← C4×#64269 #11923033

Subgroups — C4×#64269 #11923033

Order 1152.

1182 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 123 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×C3×C4×A4C211yesmaximal, characteristic, complemented
2C2×#64269C211yesmaximal, characteristic
3C2×C4×C3⋊S4C211yesmaximal, characteristic, complemented
4#10593666C211yesmaximal, characteristic, complemented
5#10593647C211yesmaximal, characteristic, complemented
6#10593645C211yesmaximal, characteristic, complemented
7C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
8C4×GL(2,ℤ/4)—33nomaximal
9C4×#953—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C22×C3⋊S4C2211yescharacteristic
12C2×C3×C4×A4—22no—
13C2×C3×C4×A4C2211yescharacteristic
14C2×C3×C4×A4C2211yescharacteristic
15#64269C414yesdirect product factor
16C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
17C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
18C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
19C4×C3⋊S4—22no—
20C4×#638—41nomaximal
21C24×C3×C4D311yescharacteristic, complemented
22C22×C4×A4D313yescomplemented
23C2×GL(2,ℤ/4)—33no—
24C2×C4×S4—33no—
25C2×#953—31no—
26C2×C4×#67—31no—
27C2×C4×#67—31no—
28C2×C4×#67—31no—
29#5432—33no—
30(C2×S4)⋊C4—33no—
31SL(2,ℤ/4)⋊C4—33no—
32C4×SL(2,ℤ/4)—33no—
33#5247—31no—
34#5213—31no—
35#5213—31no—
36#5213—31no—
37#5210—31no—
38#5210—31no—
39#5210—31no—
40C4×#217—31no—
41C4×#217—31no—
42C4×#217—31no—
43C22×C3×A4—21no—
44C22×C3×A4—21no—
45C22×C3×A4C2×C412yescomplemented
46C22×C3×A4C2311yescharacteristic
47C2×C3⋊S4—21no—
48C2×C3⋊S4—21no—
49C2×C3⋊S4C2×C412yescomplemented
50C22×C32×C4—41no—
51C2×#638—41no—
52C2×C4×C3⋊D3—41no—
53C3×C4×A4—21no—
54C3×C4×A4D412yescomplemented
55C3⋊SL(2,ℤ/4)—21no—
56C3⋊SL(2,ℤ/4)—21no—
57C3⋊SL(2,ℤ/4)C2×C412yescomplemented
58#3757—41no—
59#3752—41no—
60#3750—41no—
61C4×C3⋊Dic3—41no—
62C4×#120—91noSylow
63C25×C3C2×D311yescharacteristic
64C23×A4C2×D313yes—
65C22×S4—33no—
66C23×C3×C4—22no—
67C23×C3×C4—31no—
68C23×C3×C4—31no—
69C23×C3×C4—31no—
70C23×C3×C4—31no—
71C23×C3×C4—62no—
72C23×C3×C4C2×D311yescharacteristic
73C23×C3×C4C2×D311yescharacteristic
74C22×#67—31no—
75C22×#67—31no—
76C22×#67—31no—
77C22×C4×D3—31no—
78C2×C4×A4—26no—
79C2×C4×A4C2×D313yes—
80C2×C4×A4C2×D313yes—
81GL(2,ℤ/4)—312no—
82C2×SL(2,ℤ/4)—33no—
83C2×SL(2,ℤ/4)—33no—
84C2×SL(2,ℤ/4)—33no—
85C4×S4—66no—
86#953—34no—
87#953—34no—
88C2×#217—31no—
89C2×#217—31no—
90C2×#217—31no—
91C2×#217—31no—
92C2×#217—31no—
93C2×#217—31no—
94C2×#217—31no—
95C2×#217—31no—
96C2×#217—31no—
97C4×#67—62no—
98C4×#67—64no—
99C4×#67—61no—
100C4×#67—61no—
101C4×#67—61no—
102C4×#67—62no—
103C4×#67—61no—
104C4×#67—123no—
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C3⋊#95—31no—
115C3⋊#95—31no—
116C3⋊#95—31no—
117C3⋊#95—31no—
118C3⋊#95—31no—
119C3⋊#95—31no—
120C23×C32—41no—
121C22×C3⋊D3—41no—
122C2×C3×A4—22no—
123C2×C3×A4C22×C411yescharacteristic
124C2×C3×A4C2×D411yescharacteristic
125C2×C3×A4#4111yescharacteristic
126C3⋊S4—22no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—82no—
130#638—44no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C4×C3⋊D3—82no—
135C24×C4C3⋊D311yescharacteristic, complemented
136C2×#120—91no—
137C2×C4×D4—91no—
138C2×C4×D4—91no—
139C2×C4×D4—91no—
140#386—91no—
141#386—91no—
142#386—91no—
143#385—91no—
144#385—91no—
145#385—91no—
146#379—91no—
147C4×C22⋊C4—91no—
148C4×C22⋊C4—91no—
149C4×C22⋊C4—91no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—31no—
153C24×C3—31no—
154C24×C3—32no—
155C24×C3—61no—
156C24×C3—61no—
157C24×C3C4×D312yescomplemented
158C24×C3C22×D311yescharacteristic
159C23×D3—31no—
160C22×A4—23no—
161C22×A4—23no—
162C22×A4C4×D316yescomplemented
163C22×A4C22×D313yes—
164C2×S4—36no—
165C2×S4—63no—
166C2×S4—63no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—32no—
172C22×C3×C4—34no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—43no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—62no—
187C22×C3×C4#6712yescomplemented
188C22×C3×C4S411yescharacteristic, complemented
189C2×#67—34no—
190C2×#67—32no—
191C2×#67—34no—
192C2×#67—32no—
193C2×#67—61no—
194C2×#67—62no—
195C2×#67—61no—
196C2×#67—61no—
197C2×#67—62no—
198C2×#67—62no—
199C2×#67—61no—
200C2×#67—61no—
201C2×#67—61no—
202C2×#67—123no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C2×C4×D3—61no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—123no—
215C4×A4—23no—
216C4×A4#6716yescomplemented
217SL(2,ℤ/4)—36no—
218SL(2,ℤ/4)—63no—
219SL(2,ℤ/4)—63no—
220#217—34no—
221#217—32no—
222#217—34no—
223#217—32no—
224#217—61no—
225#217—62no—
226#217—61no—
227#217—61no—
228#217—62no—
229#217—62no—
230#217—61no—
231#217—61no—
232#217—61no—
233#217—123no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—61no—
237(C2×D3)⋊C4—61no—
238(C2×D3)⋊C4—123no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—123no—
244C4×Dic3—62no—
245C4×Dic3—62no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—123no—
249C22×C32—42no—
250C22×C32—41no—
251C22×C32—81no—
252C22×C32—81no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—81no—
255C2×C3⋊D3—81no—
256C3×A4C4×D411yescharacteristic, complemented
257C32×C4—42no—
258C32×C4—81no—
259C3⋊Dic3—42no—
260C3⋊Dic3—81no—
261C3⋊Dic3—81no—
262C25C2×C3⋊D311yescharacteristic
263C22×D4—91no—
264C22×D4—91no—
265C22×D4—91no—
266C23×C4—22no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4—31no—
271C23×C4—62no—
272C23×C4—91no—
273C23×C4C2×C3⋊D311yescharacteristic
274C23×C4C2×C3⋊D311yescharacteristic
275#120—94no—
276#120—94no—
277C4×D4—182no—
278C4×D4—184no—
279C4×D4—181no—
280C4×D4—181no—
281C4×D4—181no—
282C4×D4—182no—
283C4×D4—181no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C22⋊C4—91no—
288C2×C22⋊C4—91no—
289C2×C22⋊C4—91no—
290C2×C22⋊C4—91no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
302#95—91no—
303#95—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308C23×C3—22no—
309C23×C3—31no—
310C23×C3—32no—
311C23×C3—31no—
312C23×C3—31no—
313C23×C3—31no—
314C23×C3—32no—
315C23×C3—32no—
316C23×C3—32no—
317C23×C3—32no—
318C23×C3—31no—
319C23×C3—43no—
320C23×C3—61no—
321C23×C3—61no—
322C23×C3—61no—
323C23×C3—61no—
324C23×C3—62no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—61no—
330C23×C3—64no—
331C23×C3C2×C4×D311yescharacteristic
332C23×C3#23511yescharacteristic
333C23×C3C2×#6711yescharacteristic
334C23×C3C2×S411yescharacteristic
335C22×D3—32no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—123no—
343C2×A4—26no—
344C2×A4C2×C4×D313yes—
345C2×A4#23513yes—
346C2×A4C2×#6713yes—
347S4—66no—
348C2×C3×C4—22no—
349C2×C3×C4—31no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—31no—
355C2×C3×C4—43no—
356C2×C3×C4—43no—
357C2×C3×C4—62no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—64no—
363C2×C3×C4—62no—
364C2×C3×C4—61no—
365C2×C3×C4—86no—
366C2×C3×C4C2×S411yescharacteristic
367C2×C3×C4C2×S411yescharacteristic
368#67—62no—
369#67—62no—
370#67—62no—
371#67—68no—
372#67—64no—
373#67—62no—
374#67—64no—
375#67—1212no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—123no—
398C2×Dic3—123no—
399C2×Dic3—123no—
400C4×D3—122no—
401C4×D3—122no—
402C4×D3—246no—
403C2×C32—41no—
404C2×C32—41no—
405C2×C32—41no—
406C2×C32—82no—
407C3⋊D3—82no—
408C24—21no—
409C24—21no—
410C24—31no—
411C24—31no—
412C24—32no—
413C24—61no—
414C24—61no—
415C24—91no—
416C24C4×C3⋊D312yescomplemented
417C24C22×C3⋊D311yescharacteristic
418C2×D4—94no—
419C2×D4—92no—
420C2×D4—94no—
421C2×D4—92no—
422C2×D4—181no—
423C2×D4—182no—
424C2×D4—181no—
425C2×D4—181no—
426C2×D4—182no—
427C2×D4—182no—
428C2×D4—181no—
429C2×D4—181no—
430C2×D4—181no—
431C22×C4—21no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—31no—
435C22×C4—32no—
436C22×C4—34no—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—62no—
442C22×C4—62no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—91no—
451C22×C4—91no—
452C22×C4—91no—
453C22×C4—91no—
454C22×C4—91no—
455C22×C4—91no—
456C22×C4—91no—
457C22×C4—181no—
458C22×C4—182no—
459C22×C4—182no—
460C22×C4—181no—
461C22×C4#63812yescomplemented
462C22×C4C3⋊S411yescharacteristic, complemented
463C4⋊C4—182no—
464C4⋊C4—182no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C22⋊C4—94no—
468C22⋊C4—92no—
469C22⋊C4—94no—
470C22⋊C4—92no—
471C22⋊C4—182no—
472C22⋊C4—182no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C22⋊C4—182no—
476C22⋊C4—181no—
477C22⋊C4—181no—
478C22⋊C4—182no—
479C22⋊C4—182no—
480C22⋊C4—181no—
481C22⋊C4—181no—
482C22⋊C4—181no—
483C22⋊C4—181no—
484C42—181no—
485C42—182no—
486C42—182no—
487C42—181no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—31no—
491C22×C3—31no—
492C22×C3—31no—
493C22×C3—31no—
494C22×C3—31no—
495C22×C3—31no—
496C22×C3—31no—
497C22×C3—31no—
498C22×C3—31no—
499C22×C3—34no—
500C22×C3—32no—
501C22×C3—46no—
502C22×C3—43no—
503C22×C3—62no—
504C22×C3—62no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—61no—
508C22×C3—62no—
509C22×C3—62no—
510C22×C3—62no—
511C22×C3—61no—
512C22×C3—61no—
513C22×C3—83no—
514C22×C3—83no—
515C22×C3C4×#6711yescharacteristic, complemented
516C22×C3C4×S412yescomplemented
517C22×C3C22×S411yescharacteristic
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—126no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—243no—
527C2×D3—243no—
528A4C4×#6713yescomplemented
529C3×C4—21no—
530C3×C4—32no—
531C3×C4—46no—
532C3×C4—61no—
533C3×C4—83no—
534C3×C4GL(2,ℤ/4)12yescomplemented
535Dic3—62no—
536Dic3—62no—
537Dic3—62no—
538Dic3—126no—
539Dic3—121no—
540Dic3—121no—
541Dic3—121no—
542Dic3—121no—
543Dic3—243no—
544Dic3—243no—
545C32—41noSylow
546C23—22no—
547C23—31no—
548C23—32no—
549C23—31no—
550C23—31no—
551C23—31no—
552C23—32no—
553C23—32no—
554C23—32no—
555C23—32no—
556C23—31no—
557C23—61no—
558C23—61no—
559C23—61no—
560C23—61no—
561C23—62no—
562C23—61no—
563C23—61no—
564C23—62no—
565C23—62no—
566C23—61no—
567C23—64no—
568C23—92no—
569C23—181no—
570C23—181no—
571C23—181no—
572C23—181no—
573C23—181no—
574C23—181no—
575C23C2×C4×C3⋊D311yescharacteristic
576C23#382811yescharacteristic
577C23C2×#63811yescharacteristic
578C23C2×C3⋊S411yescharacteristic
579D4—182no—
580D4—182no—
581D4—182no—
582D4—188no—
583D4—184no—
584D4—184no—
585D4—182no—
586C2×C4—22no—
587C2×C4—31no—
588C2×C4—32no—
589C2×C4—32no—
590C2×C4—32no—
591C2×C4—32no—
592C2×C4—31no—
593C2×C4—62no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—62no—
598C2×C4—64no—
599C2×C4—62no—
600C2×C4—61no—
601C2×C4—92no—
602C2×C4—92no—
603C2×C4—92no—
604C2×C4—181no—
605C2×C4—181no—
606C2×C4—181no—
607C2×C4—181no—
608C2×C4—181no—
609C2×C4—181no—
610C2×C4—181no—
611C2×C4—181no—
612C2×C4—181no—
613C2×C4—181no—
614C2×C4—181no—
615C2×C4—181no—
616C2×C4—181no—
617C2×C4—181no—
618C2×C4—181no—
619C2×C4—181no—
620C2×C4—181no—
621C2×C4—181no—
622C2×C4—362no—
623C2×C4—362no—
624C2×C4C2×C3⋊S411yescharacteristic
625C2×C4C2×C3⋊S411yescharacteristic
626C2×C3—22no—
627C2×C3—31no—
628C2×C3—31no—
629C2×C3—31no—
630C2×C3—31no—
631C2×C3—43no—
632C2×C3—43no—
633C2×C3—43no—
634C2×C3—62no—
635C2×C3—86no—
636C2×C3C2×C4×S411yescharacteristic
637C2×C3#591211yescharacteristic
638C2×C3C2×GL(2,ℤ/4)11yescharacteristic
639D3—122no—
640D3—246no—
641C22—21no—
642C22—21no—
643C22—31no—
644C22—31no—
645C22—31no—
646C22—31no—
647C22—31no—
648C22—31no—
649C22—31no—
650C22—31no—
651C22—31no—
652C22—34no—
653C22—32no—
654C22—62no—
655C22—62no—
656C22—62no—
657C22—62no—
658C22—61no—
659C22—62no—
660C22—62no—
661C22—62no—
662C22—61no—
663C22—61no—
664C22—182no—
665C22—182no—
666C22—182no—
667C22—361no—
668C22—361no—
669C22—361no—
670C22—361no—
671C22C4×#63811yescharacteristic, complemented
672C22C4×C3⋊S412yescomplemented
673C22C22×C3⋊S411yescharacteristic
674C4—21no—
675C4—32no—
676C4—61no—
677C4—182no—
678C4—182no—
679C4—182no—
680C4—361no—
681C4—361no—
682C4—361no—
683C4—361no—
684C4#6426912yesdirect product factor
685C3—43no—
686C3C4×GL(2,ℤ/4)11yescharacteristic, complemented
687C2—22no—
688C2—31no—
689C2—31no—
690C2—31no—
691C2—31no—
692C2—62no—
693C2—362no—
694C2C2×C4×C3⋊S411yescharacteristic
695C2#1059657511yescharacteristic
696C2C2×#6426911yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC24×C3×C4D3
socleC24×C3C22×D3
prime radicalC2×#64269C2
cosocleC22×C3×A4C23
hypercenterC22×C4C3⋊S4
hypocenterC3×A4C4×D4
LCSG ▷ C2×C3×A4 ▷ C3×A4
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×C3⋊S4C2semidirect
4. #10593666C2semidirect
5. #10593647C2semidirect
6. #10593645C2semidirect
7. C4×C3⋊SL(2,ℤ/4)C2semidirect
15. #64269C4direct (N × H)
21. C24×C3×C4D3semidirect
22. C22×C4×A4D3semidirect
45. C22×C3×A4C2×C4semidirect
49. C2×C3⋊S4C2×C4semidirect
54. C3×C4×A4D4semidirect
57. C3⋊SL(2,ℤ/4)C2×C4semidirect
135. C24×C4C3⋊D3semidirect
157. C24×C3C4×D3semidirect
162. C22×A4C4×D3semidirect
187. C22×C3×C4#67semidirect
188. C22×C3×C4S4semidirect
216. C4×A4#67semidirect
256. C3×A4C4×D4semidirect
416. C24C4×C3⋊D3semidirect
461. C22×C4#638semidirect
462. C22×C4C3⋊S4semidirect
515. C22×C3C4×#67semidirect
516. C22×C3C4×S4semidirect
528. A4C4×#67semidirect
534. C3×C4GL(2,ℤ/4)semidirect
671. C22C4×#638semidirect
672. C22C4×C3⋊S4semidirect
684. C4#64269direct (N × H)
686. C3C4×GL(2,ℤ/4)semidirect

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×#642692
C2×C4×C3⋊S42
#105936662
#105936472
#105936452
C4×C3⋊SL(2,ℤ/4)2
C4×GL(2,ℤ/4)3
C4×#9533
C4×#6384