Finite Group Databasebeta

← C2×A4×(C2×D3)⋊C4 #11923347

Subgroups — C2×A4×(C2×D3)⋊C4 #11923347

Order 1152.

2038 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 2038 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C23×D3×A4C211yesmaximal, characteristic
2C22×C3×C4×A4C211yesmaximal, characteristic, complemented
3C22×Dic3×A4C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C214yesmaximal, direct product factor
5C23×(C2×D3)⋊C4C311yesmaximal, characteristic, complemented
6C2×A4×C22⋊C4—31nomaximal
7C23×C3×A4C2211yescharacteristic
8C22×D3×A4—22no—
9C22×D3×A4—22no—
10C22×D3×A4C414yescomplemented
11C22×D3×A4C2212yes—
12C2×C3×C4×A4—22no—
13C2×C3×C4×A4C2212yescomplemented
14C2×Dic3×A4—22no—
15C2×Dic3×A4C2212yescomplemented
16C2×C3×(C2×D3)⋊C4—41nomaximal
17C25×D3C2×C311yescharacteristic
18C24×A4—31no—
19C24×C3×C4C2×C311yescharacteristic, complemented
20C24×Dic3C2×C311yescharacteristic, complemented
21C22×C4×A4—21no—
22C22×C4×A4—31no—
23C22×C4×A4D311yescharacteristic, complemented
24C22×(C2×D3)⋊C4—31no—
25C22×(C2×D3)⋊C4—31no—
26C22×(C2×D3)⋊C4—31no—
27C22×(C2×D3)⋊C4—31no—
28C22×(C2×D3)⋊C4—34no—
29C22×(C2×D3)⋊C4C2×C314yescomplemented
30A4×C22⋊C4—34no—
31C23×C3×D3—41no—
32C22×C3×A4C2×C412yes—
33C22×C3×A4D412yes—
34C22×C3×A4D412yes—
35C22×C3×A4C2311yescharacteristic
36C2×D3×A4—28no—
37C2×D3×A4—22no—
38C2×D3×A4—22no—
39C2×D3×A4C2×C414yescomplemented
40C22×C32×C4—41no—
41C22×C3×Dic3—41no—
42C3×C4×A4—22no—
43Dic3×A4—22no—
44C3×(C2×D3)⋊C4—44no—
45C23×C22⋊C4—31noSylow
46C25×C3C22×C311yescharacteristic
47C24×D3—22no—
48C24×D3—22no—
49C24×D3—31no—
50C24×D3—34no—
51C24×D3—31no—
52C24×D3—32no—
53C24×D3—62no—
54C24×D3—62no—
55C24×D3C3×C414yescomplemented
56C24×D3C22×C312yes—
57C23×A4—21no—
58C23×A4—34no—
59C23×A4—32no—
60C23×A4—62no—
61C23×A4—62no—
62C23×A4C2×D311yescharacteristic
63C23×C3×C4—22no—
64C23×C3×C4—31no—
65C23×C3×C4—31no—
66C23×C3×C4—32no—
67C23×C3×C4—62no—
68C23×C3×C4C22×C312yescomplemented
69C23×Dic3—22no—
70C23×Dic3—31no—
71C23×Dic3—31no—
72C23×Dic3—32no—
73C23×Dic3—62no—
74C23×Dic3C22×C312yescomplemented
75C2×C4×A4—24no—
76C2×C4×A4—22no—
77C2×C4×A4—22no—
78C2×C4×A4—32no—
79C2×C4×A4—62no—
80C2×C4×A4C2×D312yescomplemented
81C2×C3×C22⋊C4—121no—
82C2×(C2×D3)⋊C4—32no—
83C2×(C2×D3)⋊C4—34no—
84C2×(C2×D3)⋊C4—34no—
85C2×(C2×D3)⋊C4—34no—
86C2×(C2×D3)⋊C4—31no—
87C2×(C2×D3)⋊C4—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—34no—
91C2×(C2×D3)⋊C4—34no—
92C2×(C2×D3)⋊C4—34no—
93C2×(C2×D3)⋊C4—34no—
94C2×(C2×D3)⋊C4A411yescharacteristic, direct product factor
95C23×C32—41no—
96C22×C3×D3—44no—
97C22×C3×D3—42no—
98C22×C3×D3—82no—
99C22×C3×D3—82no—
100C2×C3×A4C22⋊C414yescomplemented
101C2×C3×A4C22×C411yescharacteristic
102C2×C3×A4C2×D411yescharacteristic
103C2×C3×A4C2×D411yescharacteristic
104D3×A4—24no—
105C2×C32×C4—42no—
106C2×C32×C4—82no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—82no—
109C26—31no—
110C24×C4—31no—
111C24×C4C3×D311yescharacteristic, complemented
112C22×C22⋊C4—34no—
113C22×C22⋊C4—91no—
114C22×C22⋊C4—94no—
115C22×C22⋊C4—91no—
116C22×C22⋊C4—91no—
117C22×C22⋊C4—91no—
118C24×C3—31no—
119C24×C3—32no—
120C24×C3—32no—
121C24×C3—32no—
122C24×C3—31no—
123C24×C3—121no—
124C24×C3C2×C3×C412yes—
125C24×C3C3×D412yes—
126C24×C3C3×D412yes—
127C24×C3C23×C311yescharacteristic
128C23×D3—28no—
129C23×D3—22no—
130C23×D3—22no—
131C23×D3—32no—
132C23×D3—34no—
133C23×D3—38no—
134C23×D3—31no—
135C23×D3—34no—
136C23×D3—34no—
137C23×D3—32no—
138C23×D3—32no—
139C23×D3—32no—
140C23×D3—34no—
141C23×D3—38no—
142C23×D3—34no—
143C23×D3—62no—
144C23×D3—62no—
145C23×D3—62no—
146C23×D3—62no—
147C23×D3—64no—
148C23×D3—64no—
149C23×D3—616no—
150C23×D3—64no—
151C23×D3—64no—
152C23×D3—68no—
153C23×D3—68no—
154C23×D3—62no—
155C23×D3—62no—
156C23×D3—62no—
157C23×D3—62no—
158C23×D3—68no—
159C23×D3—62no—
160C23×D3—62no—
161C23×D3C2×C3×C414yescomplemented
162C23×D3C2×A411yescharacteristic
163C22×A4—22no—
164C22×A4—22no—
165C22×A4—22no—
166C22×A4—21no—
167C22×A4—34no—
168C22×A4—68no—
169C22×A4—62no—
170C22×A4—62no—
171C22×A4C4×D312yes—
172C22×A4D1212yes—
173C22×A4#6712yes—
174C22×A4C22×D311yescharacteristic
175C22×C3×C4—22no—
176C22×C3×C4—32no—
177C22×C3×C4—31no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—41no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4—64no—
185C22×C3×C4—64no—
186C22×C3×C4—62no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4—81no—
190C22×C3×C4—121no—
191C22×C3×C4C2×A411yescharacteristic, complemented
192C22×Dic3—22no—
193C22×Dic3—32no—
194C22×Dic3—31no—
195C22×Dic3—32no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200C22×Dic3—64no—
201C22×Dic3—64no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204C22×Dic3—62no—
205C22×Dic3C2×A411yescharacteristic, complemented
206C4×A4—24no—
207C4×A4—22no—
208C4×A4—62no—
209C3×C22⋊C4—124no—
210(C2×D3)⋊C4—38no—
211(C2×D3)⋊C4—34no—
212(C2×D3)⋊C4—34no—
213(C2×D3)⋊C4—34no—
214(C2×D3)⋊C4C2×A414yesdirect product factor
215C22×C32—42no—
216C22×C32—42no—
217C22×C32—42no—
218C22×C32—41no—
219C2×C3×D3—44no—
220C2×C3×D3—82no—
221C2×C3×D3—82no—
222C2×C3×D3—88no—
223C3×A4C2×C22⋊C411yescharacteristic, complemented
224C32×C4—82no—
225C3×Dic3—82no—
226C25—34no—
227C25—32no—
228C25—62no—
229C25—62no—
230C25—91no—
231C25—92no—
232C25—91no—
233C25—94no—
234C25—182no—
235C25—182no—
236C25C2×C3×D311yescharacteristic
237C23×C4—22no—
238C23×C4—31no—
239C23×C4—31no—
240C23×C4—32no—
241C23×C4—32no—
242C23×C4—62no—
243C23×C4—62no—
244C23×C4—91no—
245C23×C4—92no—
246C23×C4—91no—
247C23×C4—182no—
248C23×C4C2×C3×D312yescomplemented
249C2×C22⋊C4—31no—
250C2×C22⋊C4—94no—
251C2×C22⋊C4—94no—
252C2×C22⋊C4—91no—
253C2×C22⋊C4—91no—
254C2×C22⋊C4—94no—
255C2×C22⋊C4—94no—
256C2×C22⋊C4—92no—
257C2×C22⋊C4—94no—
258C2×C22⋊C4—91no—
259C2×C22⋊C4—94no—
260C2×C22⋊C4—94no—
261C2×C22⋊C4—94no—
262C23×C3—32no—
263C23×C3—31no—
264C23×C3—32no—
265C23×C3—31no—
266C23×C3—32no—
267C23×C3—31no—
268C23×C3—34no—
269C23×C3—34no—
270C23×C3—34no—
271C23×C3—32no—
272C23×C3—32no—
273C23×C3—32no—
274C23×C3—38no—
275C23×C3—32no—
276C23×C3—32no—
277C23×C3—32no—
278C23×C3—32no—
279C23×C3—32no—
280C23×C3—32no—
281C23×C3—31no—
282C23×C3—31no—
283C23×C3—41no—
284C23×C3—81no—
285C23×C3—122no—
286C23×C3—124no—
287C23×C3—242no—
288C23×C3—242no—
289C23×C3C3×C22⋊C414yescomplemented
290C23×C3C22×C3×C411yescharacteristic
291C23×C3C2×C3×D411yescharacteristic
292C23×C3C2×C3×D411yescharacteristic
293C23×C3C22×A411yescharacteristic
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—24no—
297C22×D3—38no—
298C22×D3—34no—
299C22×D3—34no—
300C22×D3—32no—
301C22×D3—34no—
302C22×D3—38no—
303C22×D3—34no—
304C22×D3—34no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—68no—
308C22×D3—64no—
309C22×D3—62no—
310C22×D3—64no—
311C22×D3—62no—
312C22×D3—68no—
313C22×D3—68no—
314C22×D3—68no—
315C22×D3—616no—
316C22×D3—616no—
317C22×D3—616no—
318C22×D3—68no—
319C22×D3—64no—
320C22×D3—64no—
321C22×D3—68no—
322C22×D3—68no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—616no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—68no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—68no—
334C22×D3—64no—
335C22×D3C4×A414yescomplemented
336C22×D3C22×A412yes—
337C2×A4—24no—
338C2×A4—21no—
339C2×A4—21no—
340C2×A4—21no—
341C2×A4—64no—
342C2×A4(C2×D3)⋊C414yesdirect product factor
343C2×A4C2×C4×D311yescharacteristic
344C2×A4C2×D1211yescharacteristic
345C2×A4C2×#6711yescharacteristic
346C2×C3×C4—22no—
347C2×C3×C4—32no—
348C2×C3×C4—42no—
349C2×C3×C4—62no—
350C2×C3×C4—64no—
351C2×C3×C4—62no—
352C2×C3×C4—64no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—82no—
357C2×C3×C4—84no—
358C2×C3×C4—82no—
359C2×C3×C4—122no—
360C2×C3×C4—242no—
361C2×C3×C4C22×A412yescomplemented
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—62no—
365C2×Dic3—64no—
366C2×Dic3—62no—
367C2×Dic3—64no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3C22×A412yescomplemented
372C2×C32—41no—
373C2×C32—41no—
374C2×C32—41no—
375C2×C32—44no—
376C3×D3—84no—
377C24—31no—
378C24—32no—
379C24—32no—
380C24—32no—
381C24—31no—
382C24—31no—
383C24—34no—
384C24—68no—
385C24—62no—
386C24—62no—
387C24—92no—
388C24—92no—
389C24—94no—
390C24—94no—
391C24—92no—
392C24—98no—
393C24—94no—
394C24—92no—
395C24—98no—
396C24—94no—
397C24—94no—
398C24—91no—
399C24—182no—
400C24—182no—
401C24—182no—
402C24—182no—
403C24—182no—
404C24—182no—
405C24—188no—
406C24—184no—
407C24—184no—
408C24—188no—
409C24—188no—
410C24—182no—
411C24—182no—
412C24—182no—
413C24—182no—
414C24—184no—
415C24—184no—
416C24—1816no—
417C24C3×C4×D312yes—
418C24C3×D1212yes—
419C24C3×#6712yes—
420C24C22×C3×D311yescharacteristic
421C22×C4—22no—
422C22×C4—32no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—32no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—62no—
429C22×C4—62no—
430C22×C4—64no—
431C22×C4—64no—
432C22×C4—62no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4—92no—
437C22×C4—92no—
438C22×C4—92no—
439C22×C4—91no—
440C22×C4—92no—
441C22×C4—182no—
442C22×C4—182no—
443C22×C4—184no—
444C22×C4—184no—
445C22×C4—182no—
446C22×C4—182no—
447C22×C4—182no—
448C22×C4D3×A411yescharacteristic, complemented
449C22⋊C4—34no—
450C22⋊C4—94no—
451C22⋊C4—94no—
452C22⋊C4—98no—
453C22⋊C4—94no—
454C22×C3—34no—
455C22×C3—31no—
456C22×C3—31no—
457C22×C3—31no—
458C22×C3—34no—
459C22×C3—32no—
460C22×C3—34no—
461C22×C3—34no—
462C22×C3—32no—
463C22×C3—31no—
464C22×C3—31no—
465C22×C3—32no—
466C22×C3—31no—
467C22×C3—31no—
468C22×C3—32no—
469C22×C3—31no—
470C22×C3—31no—
471C22×C3—34no—
472C22×C3—34no—
473C22×C3—34no—
474C22×C3—34no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—41no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—82no—
482C22×C3—81no—
483C22×C3—124no—
484C22×C3—242no—
485C22×C3—242no—
486C22×C3—248no—
487C22×C3C2×C3×C22⋊C411yescharacteristic, complemented
488C22×C3C2×C4×A412yes—
489C22×C3D4×A412yes—
490C22×C3D4×A412yes—
491C22×C3C23×A411yescharacteristic
492C2×D3—22no—
493C2×D3—22no—
494C2×D3—28no—
495C2×D3—34no—
496C2×D3—64no—
497C2×D3—616no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—64no—
501C2×D3—616no—
502C2×D3—64no—
503C2×D3—64no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—68no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3C2×C4×A414yescomplemented
510A4—21no—
511A4C2×(C2×D3)⋊C411yescharacteristic, direct product factor
512C3×C4—22no—
513C3×C4—62no—
514C3×C4—82no—
515C3×C4—84no—
516C3×C4—242no—
517Dic3—22no—
518Dic3—62no—
519C32—41noSylow
520C23—32no—
521C23—31no—
522C23—32no—
523C23—31no—
524C23—32no—
525C23—31no—
526C23—34no—
527C23—34no—
528C23—34no—
529C23—32no—
530C23—32no—
531C23—32no—
532C23—38no—
533C23—32no—
534C23—32no—
535C23—32no—
536C23—32no—
537C23—32no—
538C23—32no—
539C23—31no—
540C23—31no—
541C23—34no—
542C23—32no—
543C23—62no—
544C23—62no—
545C23—64no—
546C23—94no—
547C23—94no—
548C23—98no—
549C23—98no—
550C23—94no—
551C23—94no—
552C23—94no—
553C23—92no—
554C23—182no—
555C23—182no—
556C23—188no—
557C23—182no—
558C23—184no—
559C23—182no—
560C23—184no—
561C23—188no—
562C23—188no—
563C23—188no—
564C23—184no—
565C23—1816no—
566C23—184no—
567C23—184no—
568C23—182no—
569C23—182no—
570C23—188no—
571C23—182no—
572C23—182no—
573C23—188no—
574C23—188no—
575C23—1816no—
576C23—1816no—
577C23—1816no—
578C23—184no—
579C23—184no—
580C23—188no—
581C23—188no—
582C23—182no—
583C23—182no—
584C23C3×(C2×D3)⋊C414yescomplemented
585C23C2×C3×C4×D311yescharacteristic
586C23C2×C3×D1211yescharacteristic
587C23C2×C3×#6711yescharacteristic
588C23C2×D3×A411yescharacteristic
589C2×C4—22no—
590C2×C4—32no—
591C2×C4—32no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—64no—
595C2×C4—64no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—92no—
601C2×C4—182no—
602C2×C4—182no—
603C2×C4—184no—
604C2×C4—184no—
605C2×C4—182no—
606C2×C4—182no—
607C2×C4—182no—
608C2×C4C2×D3×A412yescomplemented
609C2×C3—34no—
610C2×C3—31no—
611C2×C3—31no—
612C2×C3—31no—
613C2×C3—31no—
614C2×C3—41no—
615C2×C3—41no—
616C2×C3—41no—
617C2×C3—44no—
618C2×C3—81no—
619C2×C3—81no—
620C2×C3—81no—
621C2×C3—84no—
622C2×C3—244no—
623C2×C3A4×C22⋊C414yescomplemented
624C2×C3C22×C4×A411yescharacteristic
625C2×C3C2×D4×A411yescharacteristic
626C2×C3C2×D4×A411yescharacteristic
627D3—24no—
628D3—64no—
629C22—34no—
630C22—31no—
631C22—31no—
632C22—31no—
633C22—34no—
634C22—32no—
635C22—34no—
636C22—34no—
637C22—31no—
638C22—32no—
639C22—31no—
640C22—31no—
641C22—32no—
642C22—31no—
643C22—31no—
644C22—32no—
645C22—31no—
646C22—34no—
647C22—34no—
648C22—34no—
649C22—34no—
650C22—34no—
651C22—62no—
652C22—62no—
653C22—68no—
654C22—94no—
655C22—184no—
656C22—184no—
657C22—1816no—
658C22—184no—
659C22—184no—
660C22—184no—
661C22—184no—
662C22—1816no—
663C22—184no—
664C22—184no—
665C22—182no—
666C22—182no—
667C22—188no—
668C22C2×C3×(C2×D3)⋊C411yescharacteristic, complemented
669C22C4×D3×A412yes—
670C22A4×D1212yes—
671C22A4×#6712yes—
672C22C22×D3×A411yescharacteristic
673C4—22no—
674C4—62no—
675C4—62no—
676C4—182no—
677C3—41no—
678C3—81no—
679C3C2×A4×C22⋊C411yescharacteristic, complemented
680C2—31no—
681C2—34no—
682C2—31no—
683C2—31no—
684C2—31no—
685C2—64no—
686C2—184no—
687C2A4×(C2×D3)⋊C414yesdirect product factor
688C2C2×C4×D3×A411yescharacteristic
689C2C2×A4×D1211yescharacteristic
690C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×A4
commutatorC23×C3C22×C3×C4
FrattiniC22C22×D3×A4
FittingC24×C3×C4C2×C3
socleC25×C3C22×C3
prime radicalC23×D3×A4C2
cosocleC24×C3C23×C3
hypercenterC22×C4D3×A4
hypocenterC22×C3C2×C3×C22⋊C4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×A4C2semidirect
3. C22×Dic3×A4C2semidirect
4. A4×(C2×D3)⋊C4C2direct (N × H)
5. C23×(C2×D3)⋊C4C3semidirect
10. C22×D3×A4C4semidirect
13. C2×C3×C4×A4C22semidirect
15. C2×Dic3×A4C22semidirect
19. C24×C3×C4C2×C3semidirect
20. C24×Dic3C2×C3semidirect
23. C22×C4×A4D3semidirect
29. C22×(C2×D3)⋊C4C2×C3semidirect
39. C2×D3×A4C2×C4semidirect
55. C24×D3C3×C4semidirect
68. C23×C3×C4C22×C3semidirect
74. C23×Dic3C22×C3semidirect
80. C2×C4×A4C2×D3semidirect
94. C2×(C2×D3)⋊C4A4direct (N × H)
100. C2×C3×A4C22⋊C4semidirect
111. C24×C4C3×D3semidirect
161. C23×D3C2×C3×C4semidirect
191. C22×C3×C4C2×A4semidirect
205. C22×Dic3C2×A4semidirect
214. (C2×D3)⋊C4C2×A4direct (N × H)
223. C3×A4C2×C22⋊C4semidirect
248. C23×C4C2×C3×D3semidirect
289. C23×C3C3×C22⋊C4semidirect
335. C22×D3C4×A4semidirect
342. C2×A4(C2×D3)⋊C4direct (N × H)
361. C2×C3×C4C22×A4semidirect
371. C2×Dic3C22×A4semidirect
448. C22×C4D3×A4semidirect
487. C22×C3C2×C3×C22⋊C4semidirect
509. C2×D3C2×C4×A4semidirect
511. A4C2×(C2×D3)⋊C4direct (N × H)
584. C23C3×(C2×D3)⋊C4semidirect
608. C2×C4C2×D3×A4semidirect
623. C2×C3A4×C22⋊C4semidirect
668. C22C2×C3×(C2×D3)⋊C4semidirect
679. C3C2×A4×C22⋊C4semidirect
687. C2A4×(C2×D3)⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×A42
C22×C3×C4×A42
C22×Dic3×A42
A4×(C2×D3)⋊C42
C23×(C2×D3)⋊C43
C2×A4×C22⋊C43
C2×C3×(C2×D3)⋊C44