Finite Group Databasebeta

← C4×#64207 #11921991

Subgroups — C4×#64207 #11921991

Order 1152.

920 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 920 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3⋊S4C211yesmaximal, characteristic, complemented
2C2×C3×C4×S4C211yesmaximal, characteristic, complemented
3C2×#64207C211yesmaximal, characteristic
4C4×Dic3×A4C211yesmaximal, characteristic, complemented
5#10593242C211yesmaximal, characteristic, complemented
6(C2×S4)⋊Dic3C211yesmaximal, characteristic, complemented
7Dic3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
8C4×C4⋊S4—31nomaximal
9C4×#939—31nomaximal
10C22×C3⋊S4C2211yescharacteristic
11C22×C3×S4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×Dic3×A4C2211yescharacteristic
14C2×Dic3×A4C2211yescharacteristic
15C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
16C4×C3⋊S4—22no—
17C2×C3×SL(2,ℤ/4)C2211yescharacteristic
18C3×C4×S4—22no—
19#64207C414yesdirect product factor
20C4×#626—41nomaximal
21C2×C4⋊S4—31no—
22C2×C4×S4—31no—
23C2×C4×S4—61no—
24C2×C4×S4D311yescharacteristic, complemented
25C2×C3×C4×D4—31no—
26C2×#939—31no—
27C2×C4×#67—31no—
28C2×C4×#67—31no—
29C22×C4×Dic3D311yescharacteristic, complemented
30C42×A4—31no—
31(C2×S4)⋊C4—31no—
32(C2×S4)⋊C4—31no—
33C4⋊SL(2,ℤ/4)—31no—
34#5220—31no—
35C4×#217—31no—
36#4990—31no—
37#4976—31no—
38#4958—31no—
39#4957—31no—
40#4945—31no—
41#4942—31no—
42C4×(C2×D3)⋊C4—31no—
43C4×Dic3⋊C4—31no—
44C22×C3×A4C2311yescharacteristic
45C2×C3⋊S4—21no—
46C2×C3⋊S4—21no—
47C2×C3⋊S4C2×C412yescomplemented
48C2×C3×S4—21no—
49C2×C3×S4—21no—
50C2×C3×S4C2×C412yescomplemented
51C2×C4×C3⋊D3—41no—
52C2×C3×C4×D3—41no—
53C3×C4×A4D412yescomplemented
54C2×#626—41no—
55Dic3×A4—21no—
56Dic3×A4C2×C412yescomplemented
57C3⋊SL(2,ℤ/4)—21no—
58C3×SL(2,ℤ/4)—21no—
59C3×C4×Dic3—41no—
60Dic3⋊Dic3—41no—
61#3722—41no—
62(C2×D3)⋊Dic3—41no—
63C4×#121—91noSylow
64C22×S4—31no—
65C22×S4—61no—
66C22×S4C2×D311yescharacteristic
67C22×C3×D4—31no—
68C23×C3×C4—31no—
69C23×C3×C4C2×D311yescharacteristic
70C22×#67—31no—
71C22×#67—31no—
72C23×Dic3C2×D311yescharacteristic
73C23×Dic3C2×D311yescharacteristic
74C22×C4×D3—31no—
75C2×C4×A4—21no—
76C2×C4×A4—31no—
77C2×C4×A4—31no—
78C2×C4×A4C2×D311yescharacteristic
79C2×SL(2,ℤ/4)—31no—
80C2×SL(2,ℤ/4)—61no—
81C2×SL(2,ℤ/4)C2×D311yescharacteristic
82C4⋊S4—34no—
83C4×S4—22no—
84C4×S4—64no—
85C4×S4—62no—
86C3×C4×D4—62no—
87C3×C4×D4—62no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C22⋊C4—31no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C42—31no—
92C2×#217—31no—
93C2×#217—31no—
94C2×#217—31no—
95C2×#217—31no—
96#939—34no—
97#939—34no—
98C4×#67—61no—
99C4×#67—61no—
100C4×#67—61no—
101C4×#67—62no—
102C4×#67—62no—
103C4×#67—61no—
104C2×(C2×D3)⋊C4—31no—
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×Dic3⋊C4—31no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C4×D12—121no—
118C3⋊#95—31no—
119C3⋊#95—31no—
120C3⋊#95—31no—
121C3⋊#95—31no—
122C3⋊#95—31no—
123C3⋊#95—31no—
124C22×C3⋊D3—41no—
125C22×C3×D3—41no—
126C2×C3×A4C22×C411yescharacteristic
127C2×C3×A4C2×D411yescharacteristic
128C2×C3×A4#4111yescharacteristic
129C3⋊S4—22no—
130C3×S4—22no—
131C2×C32×C4—41no—
132C2×C3⋊Dic3—41no—
133C4×C3⋊D3—82no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×C4×D3—82no—
138#626—44no—
139C2×#121—91no—
140C2×C4×D4—31no—
141C2×C4×D4—91no—
142C2×C4×D4—91no—
143C22×C42—31no—
144#390—91no—
145#389—91no—
146#388—91no—
147#388—91no—
148#386—91no—
149#386—91no—
150#380—91no—
151C4×C4⋊C4—91no—
152C4×C22⋊C4—91no—
153C4×C22⋊C4—91no—
154C24×C3—31no—
155C24×C3C22×D311yescharacteristic
156C23×D3—31no—
157C22×A4—21no—
158C22×A4C22×D311yescharacteristic
159C2×S4—21no—
160C2×S4—21no—
161C2×S4—32no—
162C2×S4—62no—
163C2×S4—62no—
164C2×S4—62no—
165C2×S4—61no—
166C2×S4—61no—
167C2×S4C4×D312yescomplemented
168C2×C3×D4—32no—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—32no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—61no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4—61no—
184C22×C3×C4D1212yescomplemented
185C2×#67—34no—
186C2×#67—32no—
187C2×#67—32no—
188C2×#67—61no—
189C2×#67—62no—
190C2×#67—61no—
191C2×#67—61no—
192C2×#67—61no—
193C2×#67—61no—
194C2×#67—61no—
195C22×Dic3—21no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—32no—
200C22×Dic3—31no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—61no—
205C22×Dic3C4×D312yescomplemented
206C2×D12—121no—
207C2×C4×D3—41no—
208C2×C4×D3—61no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—61no—
212C2×C4×D3—121no—
213C2×C4×D3—241no—
214C4×A4—22no—
215C4×A4—32no—
216C4×A4—61no—
217C4×A4#6712yescomplemented
218SL(2,ℤ/4)—21no—
219SL(2,ℤ/4)—62no—
220SL(2,ℤ/4)—61no—
221C3×C4⋊C4—62no—
222C3×C22⋊C4—62no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C42—62no—
226C3×C42—121no—
227#217—34no—
228#217—61no—
229#217—62no—
230#217—61no—
231#217—61no—
232#217—61no—
233(C2×D3)⋊C4—34no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—61no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—61no—
238(C2×D3)⋊C4—121no—
239(C2×D3)⋊C4—121no—
240C4⋊Dic3—121no—
241Dic3⋊C4—34no—
242Dic3⋊C4—62no—
243Dic3⋊C4—61no—
244Dic3⋊C4—62no—
245Dic3⋊C4—61no—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—61no—
250C4×Dic3—62no—
251C4×Dic3S411yescharacteristic, complemented
252C22×C32—41no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—81no—
255C2×C3⋊D3—81no—
256C2×C3×D3—42no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C3×A4C4×D411yescharacteristic, complemented
260C32×C4—42no—
261C3⋊Dic3—81no—
262C3×Dic3—42no—
263C3×Dic3—81no—
264C3×Dic3—81no—
265C22×D4—31no—
266C22×D4—91no—
267C22×D4—91no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4—31no—
271C23×C4—91no—
272C23×C4D3211yescharacteristic
273#121—94no—
274#121—94no—
275C4×D4—62no—
276C4×D4—62no—
277C4×D4—181no—
278C4×D4—181no—
279C4×D4—181no—
280C4×D4—181no—
281C4×D4—182no—
282C4×D4—182no—
283C2×C4⋊C4—31no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—31no—
289C2×C22⋊C4—31no—
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×C42—31no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
302C2×C42—91no—
303C2×C42—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95—91no—
309#95—91no—
310C23×C3—31no—
311C23×C3—31no—
312C23×C3—31no—
313C23×C3—31no—
314C23×C3—32no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3—61no—
318C23×C3—61no—
319C23×C3—61no—
320C23×C3—61no—
321C23×C3C2×C4×D311yescharacteristic
322C23×C3C2×D1211yescharacteristic
323C23×C3#23511yescharacteristic
324C22×D3—32no—
325C22×D3—41no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—121no—
333C22×D3—241no—
334C2×A4—21no—
335C2×A4—21no—
336C2×A4—21no—
337C2×A4C2×C4×D311yescharacteristic
338C2×A4#23511yescharacteristic
339C2×A4C2×#6711yescharacteristic
340S4—22no—
341S4—64no—
342S4—62no—
343C3×D4—62no—
344C3×D4—62no—
345C3×D4—62no—
346C3×D4—62no—
347C2×C3×C4—31no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—41no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—81no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—122no—
366C2×C3×C4—122no—
367C2×C3×C4C2×S411yescharacteristic
368#67—64no—
369#67—62no—
370#67—62no—
371#67—62no—
372#67—62no—
373#67—64no—
374C2×Dic3—31no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—31no—
381C2×Dic3—41no—
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—121no—
395C2×Dic3—241no—
396C2×Dic3C2×S411yescharacteristic
397C2×Dic3C2×S411yescharacteristic
398D12—124no—
399C4×D3—82no—
400C4×D3—122no—
401C4×D3—122no—
402C4×D3—242no—
403C4×D3—244no—
404C2×C32—41no—
405C2×C32—41no—
406C2×C32—41no—
407C3⋊D3—82no—
408C3×D3—82no—
409C24—31no—
410C24—91no—
411C24C2×D3211yescharacteristic
412C2×D4—32no—
413C2×D4—32no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—94no—
419C2×D4—92no—
420C2×D4—92no—
421C2×D4—181no—
422C2×D4—181no—
423C2×D4—182no—
424C2×D4—181no—
425C2×D4—181no—
426C2×D4—181no—
427C2×D4—181no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—32no—
435C22×C4—62no—
436C22×C4—61no—
437C22×C4—62no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—92no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—91no—
448C22×C4—181no—
449C22×C4—182no—
450C22×C4—182no—
451C22×C4—181no—
452C22×C4—181no—
453C22×C4#62612yescomplemented
454C4⋊C4—62no—
455C4⋊C4—94no—
456C4⋊C4—181no—
457C4⋊C4—182no—
458C4⋊C4—181no—
459C4⋊C4—182no—
460C22⋊C4—62no—
461C22⋊C4—61no—
462C22⋊C4—61no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C22⋊C4—182no—
468C22⋊C4—181no—
469C22⋊C4—182no—
470C22⋊C4—181no—
471C22⋊C4—182no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C42—31no—
475C42—62no—
476C42—91no—
477C42—91no—
478C42—91no—
479C42—181no—
480C42—182no—
481C22×C3—31no—
482C22×C3—31no—
483C22×C3—31no—
484C22×C3—31no—
485C22×C3—31no—
486C22×C3—31no—
487C22×C3—31no—
488C22×C3—31no—
489C22×C3—31no—
490C22×C3—41no—
491C22×C3—61no—
492C22×C3—62no—
493C22×C3—62no—
494C22×C3—62no—
495C22×C3—81no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3—121no—
499C22×C3—121no—
500C22×C3C4×D1211yescharacteristic, complemented
501C22×C3C22×S411yescharacteristic
502C2×D3—42no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—81no—
507C2×D3—81no—
508C2×D3—122no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—242no—
514C2×D3—241no—
515C2×D3—241no—
516C2×D3—242no—
517C2×D3—242no—
518A4—21no—
519A4C4×#6711yescharacteristic, complemented
520C3×C4—32no—
521C3×C4—42no—
522C3×C4—62no—
523C3×C4—82no—
524C3×C4—122no—
525C3×C4—121no—
526C3×C4—121no—
527C3×C4—241no—
528C3×C4C4⋊S412yescomplemented
529Dic3—21no—
530Dic3—32no—
531Dic3—62no—
532Dic3—61no—
533Dic3—81no—
534Dic3—121no—
535Dic3—121no—
536Dic3—241no—
537Dic3—242no—
538Dic3C4×S412yescomplemented
539C32—41noSylow
540C23—31no—
541C23—31no—
542C23—31no—
543C23—31no—
544C23—32no—
545C23—61no—
546C23—61no—
547C23—61no—
548C23—61no—
549C23—61no—
550C23—61no—
551C23—92no—
552C23—181no—
553C23—181no—
554C23—181no—
555C23—181no—
556C23—181no—
557C23—181no—
558C23#379811yescharacteristic
559C23C4×D3211yescharacteristic
560C23C2×#62611yescharacteristic
561D4—62no—
562D4—62no—
563D4—62no—
564D4—62no—
565D4—184no—
566D4—184no—
567D4—182no—
568D4—182no—
569D4—182no—
570D4—182no—
571C2×C4—31no—
572C2×C4—31no—
573C2×C4—32no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—31no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—61no—
582C2×C4—61no—
583C2×C4—61no—
584C2×C4—61no—
585C2×C4—61no—
586C2×C4—61no—
587C2×C4—92no—
588C2×C4—92no—
589C2×C4—91no—
590C2×C4—92no—
591C2×C4—92no—
592C2×C4—92no—
593C2×C4—91no—
594C2×C4—122no—
595C2×C4—122no—
596C2×C4—181no—
597C2×C4—181no—
598C2×C4—181no—
599C2×C4—181no—
600C2×C4—181no—
601C2×C4—181no—
602C2×C4—181no—
603C2×C4—181no—
604C2×C4—181no—
605C2×C4—181no—
606C2×C4—181no—
607C2×C4—181no—
608C2×C4—362no—
609C2×C4—362no—
610C2×C4D3×S411yescharacteristic
611C2×C3—31no—
612C2×C3—31no—
613C2×C3—31no—
614C2×C3—31no—
615C2×C3—41no—
616C2×C3—41no—
617C2×C3—41no—
618C2×C3—81no—
619C2×C3—81no—
620C2×C3—81no—
621C2×C3—122no—
622C2×C3C2×C4×S411yescharacteristic
623C2×C3C2×C4⋊S411yescharacteristic
624C2×C3#591211yescharacteristic
625D3—82no—
626D3—122no—
627D3—242no—
628D3—244no—
629C22—31no—
630C22—31no—
631C22—31no—
632C22—31no—
633C22—31no—
634C22—31no—
635C22—31no—
636C22—31no—
637C22—31no—
638C22—61no—
639C22—62no—
640C22—62no—
641C22—62no—
642C22—121no—
643C22—121no—
644C22—121no—
645C22—121no—
646C22—182no—
647C22—182no—
648C22—182no—
649C22—361no—
650C22—361no—
651C22—361no—
652C22—361no—
653C22C4×#62611yescharacteristic, complemented
654C22C2×D3×S411yescharacteristic
655C4—32no—
656C4—32no—
657C4—62no—
658C4—61no—
659C4—92no—
660C4—121no—
661C4—121no—
662C4—182no—
663C4—181no—
664C4—361no—
665C4—361no—
666C4#6420712yesdirect product factor
667C3—41no—
668C3—81no—
669C3C4×C4⋊S411yescharacteristic, complemented
670C2—31no—
671C2—31no—
672C2—31no—
673C2—31no—
674C2—122no—
675C2—362no—
676C2#1059642611yescharacteristic
677C2C4×D3×S411yescharacteristic
678C2C2×#6420711yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×S4
commutatorC2×C3×A4C22×C4
FrattiniC22C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC2×#64207C2
cosocleC22×C3×A4C23
hypocenterC3×A4C4×D4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C3⋊S4C2semidirect
2. C2×C3×C4×S4C2semidirect
4. C4×Dic3×A4C2semidirect
5. #10593242C2semidirect
6. (C2×S4)⋊Dic3C2semidirect
7. Dic3⋊SL(2,ℤ/4)C2semidirect
19. #64207C4direct (N × H)
24. C2×C4×S4D3semidirect
29. C22×C4×Dic3D3semidirect
47. C2×C3⋊S4C2×C4semidirect
50. C2×C3×S4C2×C4semidirect
53. C3×C4×A4D4semidirect
56. Dic3×A4C2×C4semidirect
167. C2×S4C4×D3semidirect
184. C22×C3×C4D12semidirect
205. C22×Dic3C4×D3semidirect
217. C4×A4#67semidirect
251. C4×Dic3S4semidirect
259. C3×A4C4×D4semidirect
453. C22×C4#626semidirect
500. C22×C3C4×D12semidirect
519. A4C4×#67semidirect
528. C3×C4C4⋊S4semidirect
538. Dic3C4×S4semidirect
653. C22C4×#626semidirect
666. C4#64207direct (N × H)
669. C3C4×C4⋊S4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊S42
C2×C3×C4×S42
C2×#642072
C4×Dic3×A42
#105932422
(C2×S4)⋊Dic32
Dic3⋊SL(2,ℤ/4)2
C4×C4⋊S43
C4×#9393
C4×#6264