Finite Group Databasebeta

← D3×A4×C22⋊C4 #11923154

Subgroups — D3×A4×C22⋊C4 #11923154

Order 1152.

2018 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 2018 conjugacy classes of subgroups — too many to draw. Only its 147 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
2C2×C4×D3×A4C212yesmaximal, complemented
3C3×A4×C22⋊C4C211yesmaximal, characteristic, complemented
4A4×#217C211yesmaximal, characteristic, complemented
5A4×(C2×D3)⋊C4C212yesmaximal, complemented
6C22×D3×C22⋊C4C311yesmaximal, characteristic, complemented
7C2×A4×C22⋊C4—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C22×D3×A4—24no—
10C22×D3×A4C414yescomplemented
11C22×D3×A4C2211yescharacteristic
12C22×D3×A4C2211yescharacteristic
13C2×C3×C4×A4C2212yescomplemented
14C2×Dic3×A4C2212yescomplemented
15C4×D3×A4—24no—
16C3×D3×C22⋊C4—41nomaximal
17C25×D3C2×C311yescharacteristic
18C24×A4—31no—
19C23×C4×D3C2×C312yescomplemented
20C22×C4×A4—32no—
21C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
22C22×#217C2×C311yescharacteristic, complemented
23C22×(C2×D3)⋊C4C2×C312yescomplemented
24C2×D3×C22⋊C4—31no—
25C2×D3×C22⋊C4—31no—
26C2×D3×C22⋊C4—32no—
27C2×D3×C22⋊C4—31no—
28C2×D3×C22⋊C4—31no—
29C2×D3×C22⋊C4—32no—
30A4×C22⋊C4—21no—
31A4×C22⋊C4—31no—
32A4×C22⋊C4—32no—
33A4×C22⋊C4D311yescharacteristic, direct product factor
34C23×C3×D3—41no—
35C22×C3×A4—22no—
36C22×C3×A4C2×C412yescomplemented
37C22×C3×A4C2311yescharacteristic
38C2×D3×A4—22no—
39C2×D3×A4—28no—
40C2×D3×A4C2×C412yes—
41C2×D3×A4C2×C412yescomplemented
42C2×D3×A4D414yes—
43C2×C3×C4×D3—42no—
44C3×C4×A4—22no—
45Dic3×A4—22no—
46C32×C22⋊C4—41no—
47C3×#217—41no—
48C3×(C2×D3)⋊C4—42no—
49C23×C22⋊C4—31noSylow
50C25×C3C22×C311yescharacteristic
51C24×D3—24no—
52C24×D3—31no—
53C24×D3—34no—
54C24×D3—31no—
55C24×D3—31no—
56C24×D3—31no—
57C24×D3—64no—
58C24×D3C3×C414yescomplemented
59C24×D3C22×C311yescharacteristic
60C24×D3C22×C311yescharacteristic
61C23×A4—21no—
62C23×A4—31no—
63C23×A4—34no—
64C23×A4—31no—
65C23×A4—64no—
66C23×A4C2×D311yescharacteristic
67C23×C3×C4C22×C312yescomplemented
68C23×Dic3C22×C312yescomplemented
69C22×C4×D3—24no—
70C22×C4×D3—32no—
71C22×C4×D3—32no—
72C22×C4×D3—32no—
73C22×C4×D3—32no—
74C22×C4×D3—64no—
75C2×C4×A4—22no—
76C2×C4×A4—32no—
77C2×C4×A4—64no—
78C2×C4×A4C2×D312yescomplemented
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—31no—
81C2×C3×C22⋊C4—32no—
82C2×C3×C22⋊C4—121no—
83C2×#217—31no—
84C2×#217—31no—
85C2×#217—32no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—32no—
90D3×C22⋊C4—32no—
91D3×C22⋊C4—32no—
92D3×C22⋊C4—34no—
93D3×C22⋊C4—34no—
94D3×C22⋊C4—32no—
95D3×C22⋊C4—31no—
96D3×C22⋊C4—32no—
97D3×C22⋊C4—31no—
98D3×C22⋊C4—31no—
99D3×C22⋊C4—32no—
100D3×C22⋊C4A411yescharacteristic, direct product factor
101C23×C32—41no—
102C22×C3×D3—44no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—84no—
106C2×C3×A4—22no—
107C2×C3×A4C22×C411yescharacteristic
108C2×C3×A4C2×D412yes—
109D3×A4—22no—
110D3×A4C22⋊C414yesdirect product factor
111C2×C32×C4—42no—
112C2×C3×Dic3—42no—
113C3×C4×D3—84no—
114C26—31no—
115C24×C4—32no—
116C22×C22⋊C4—31no—
117C22×C22⋊C4—32no—
118C22×C22⋊C4—91no—
119C22×C22⋊C4—91no—
120C22×C22⋊C4—92no—
121C22×C22⋊C4—91no—
122C22×C22⋊C4—92no—
123C22×C22⋊C4—91no—
124C22×C22⋊C4C3×D311yescharacteristic, complemented
125C24×C3—22no—
126C24×C3—31no—
127C24×C3—32no—
128C24×C3—31no—
129C24×C3—62no—
130C24×C3—121no—
131C24×C3C2×C3×C412yescomplemented
132C24×C3C23×C311yescharacteristic
133C23×D3—22no—
134C23×D3—28no—
135C23×D3—31no—
136C23×D3—31no—
137C23×D3—34no—
138C23×D3—32no—
139C23×D3—32no—
140C23×D3—34no—
141C23×D3—34no—
142C23×D3—34no—
143C23×D3—31no—
144C23×D3—34no—
145C23×D3—34no—
146C23×D3—31no—
147C23×D3—31no—
148C23×D3—31no—
149C23×D3—31no—
150C23×D3—34no—
151C23×D3—34no—
152C23×D3—34no—
153C23×D3—32no—
154C23×D3—64no—
155C23×D3—64no—
156C23×D3—64no—
157C23×D3—64no—
158C23×D3—616no—
159C23×D3—64no—
160C23×D3—64no—
161C23×D3—64no—
162C23×D3—616no—
163C23×D3—64no—
164C23×D3—68no—
165C23×D3—62no—
166C23×D3C2×C3×C412yes—
167C23×D3C2×C3×C412yescomplemented
168C23×D3C3×D414yes—
169C23×D3C2×A411yescharacteristic
170C22×A4—22no—
171C22×A4—22no—
172C22×A4—21no—
173C22×A4—32no—
174C22×A4—34no—
175C22×A4—32no—
176C22×A4—42no—
177C22×A4—68no—
178C22×A4—62no—
179C22×A4C4×D312yescomplemented
180C22×A4C22×D311yescharacteristic
181C22×C3×C4—22no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—62no—
185C22×C3×C4—122no—
186C22×Dic3—22no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—62no—
190C2×C4×D3—34no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3—64no—
201C2×C4×D3—64no—
202C2×C4×D3C2×A412yescomplemented
203C4×A4—22no—
204C4×A4—42no—
205C4×A4—62no—
206C3×C22⋊C4—32no—
207C3×C22⋊C4—31no—
208C3×C22⋊C4—32no—
209C3×C22⋊C4—41no—
210C3×C22⋊C4—81no—
211C3×C22⋊C4—122no—
212C3×C22⋊C4—121no—
213C3×C22⋊C4C2×A411yescharacteristic, complemented
214#217—32no—
215#217—31no—
216#217—32no—
217#217C2×A411yescharacteristic, complemented
218(C2×D3)⋊C4—34no—
219(C2×D3)⋊C4—32no—
220(C2×D3)⋊C4—32no—
221(C2×D3)⋊C4—32no—
222(C2×D3)⋊C4C2×A412yescomplemented
223C22×C32—42no—
224C22×C32—41no—
225C22×C32—82no—
226C2×C3×D3—42no—
227C2×C3×D3—42no—
228C2×C3×D3—44no—
229C2×C3×D3—88no—
230C2×C3×D3—82no—
231C3×A4C2×C22⋊C411yescharacteristic, complemented
232C32×C4—82no—
233C3×Dic3—82no—
234C25—31no—
235C25—34no—
236C25—31no—
237C25—64no—
238C25—91no—
239C25—91no—
240C25—91no—
241C25—91no—
242C25—94no—
243C25—184no—
244C25C2×C3×D311yescharacteristic
245C23×C4—32no—
246C23×C4—64no—
247C23×C4—92no—
248C23×C4—92no—
249C23×C4—92no—
250C23×C4—92no—
251C23×C4—184no—
252C23×C4C2×C3×D312yescomplemented
253C2×C22⋊C4—31no—
254C2×C22⋊C4—31no—
255C2×C22⋊C4—31no—
256C2×C22⋊C4—32no—
257C2×C22⋊C4—91no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4—91no—
262C2×C22⋊C4—91no—
263C2×C22⋊C4—94no—
264C2×C22⋊C4—92no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C22⋊C4—94no—
268C2×C22⋊C4—91no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4—92no—
272C2×C22⋊C4—92no—
273C2×C22⋊C4—91no—
274C23×C3—22no—
275C23×C3—32no—
276C23×C3—31no—
277C23×C3—31no—
278C23×C3—32no—
279C23×C3—32no—
280C23×C3—32no—
281C23×C3—32no—
282C23×C3—31no—
283C23×C3—41no—
284C23×C3—62no—
285C23×C3—62no—
286C23×C3—62no—
287C23×C3—64no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3—64no—
291C23×C3—81no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—124no—
295C23×C3—244no—
296C23×C3C22×C3×C411yescharacteristic
297C23×C3C2×C3×D412yes—
298C23×C3C22×A411yescharacteristic
299C22×D3—24no—
300C22×D3—22no—
301C22×D3—34no—
302C22×D3—32no—
303C22×D3—38no—
304C22×D3—31no—
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—34no—
308C22×D3—34no—
309C22×D3—34no—
310C22×D3—32no—
311C22×D3—34no—
312C22×D3—38no—
313C22×D3—38no—
314C22×D3—32no—
315C22×D3—34no—
316C22×D3—31no—
317C22×D3—34no—
318C22×D3—34no—
319C22×D3—32no—
320C22×D3—32no—
321C22×D3—32no—
322C22×D3—68no—
323C22×D3—64no—
324C22×D3—616no—
325C22×D3—68no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—64no—
329C22×D3—68no—
330C22×D3—616no—
331C22×D3—616no—
332C22×D3—68no—
333C22×D3—68no—
334C22×D3—616no—
335C22×D3—68no—
336C22×D3—68no—
337C22×D3—68no—
338C22×D3—68no—
339C22×D3—64no—
340C22×D3—64no—
341C22×D3—64no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3C3×C22⋊C414yescomplemented
346C22×D3C4×A414yescomplemented
347C22×D3C22×A411yescharacteristic
348C22×D3C22×A411yescharacteristic
349C2×A4—22no—
350C2×A4—21no—
351C2×A4—22no—
352C2×A4—34no—
353C2×A4—42no—
354C2×A4—62no—
355C2×A4C2×C4×D311yescharacteristic
356C2×A4D3×D412yes—
357C2×C3×C4—32no—
358C2×C3×C4—42no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—82no—
364C2×C3×C4—122no—
365C2×C3×C4—244no—
366C2×C3×C4C22×A412yescomplemented
367C2×Dic3—32no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3C22×A412yescomplemented
373C4×D3—24no—
374C4×D3—64no—
375C4×D3—64no—
376C4×D3—68no—
377C4×D3—64no—
378C2×C32—41no—
379C2×C32—42no—
380C2×C32—82no—
381C3×D3—44no—
382C3×D3—82no—
383C24—22no—
384C24—31no—
385C24—32no—
386C24—31no—
387C24—31no—
388C24—32no—
389C24—34no—
390C24—32no—
391C24—68no—
392C24—62no—
393C24—62no—
394C24—91no—
395C24—91no—
396C24—91no—
397C24—91no—
398C24—94no—
399C24—94no—
400C24—91no—
401C24—94no—
402C24—92no—
403C24—92no—
404C24—94no—
405C24—94no—
406C24—94no—
407C24—91no—
408C24—92no—
409C24—94no—
410C24—94no—
411C24—94no—
412C24—91no—
413C24—182no—
414C24—184no—
415C24—184no—
416C24—188no—
417C24—184no—
418C24—184no—
419C24—184no—
420C24—1816no—
421C24—184no—
422C24—184no—
423C24—184no—
424C24—1816no—
425C24C3×C4×D312yescomplemented
426C24C22×C3×D311yescharacteristic
427C22×C4—22no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—32no—
431C22×C4—62no—
432C22×C4—62no—
433C22×C4—92no—
434C22×C4—92no—
435C22×C4—92no—
436C22×C4—94no—
437C22×C4—92no—
438C22×C4—92no—
439C22×C4—184no—
440C22×C4—184no—
441C22×C4—184no—
442C22×C4—184no—
443C22×C4—184no—
444C22×C4—184no—
445C22×C4—184no—
446C22×C4—184no—
447C22×C4—182no—
448C22⋊C4—32no—
449C22⋊C4—31no—
450C22⋊C4—31no—
451C22⋊C4—32no—
452C22⋊C4—32no—
453C22⋊C4—92no—
454C22⋊C4—92no—
455C22⋊C4—92no—
456C22⋊C4—94no—
457C22⋊C4—92no—
458C22⋊C4—91no—
459C22⋊C4—92no—
460C22⋊C4D3×A411yescharacteristic, direct product factor
461C22×C3—22no—
462C22×C3—31no—
463C22×C3—32no—
464C22×C3—32no—
465C22×C3—31no—
466C22×C3—31no—
467C22×C3—32no—
468C22×C3—32no—
469C22×C3—32no—
470C22×C3—42no—
471C22×C3—41no—
472C22×C3—62no—
473C22×C3—64no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—64no—
478C22×C3—62no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—81no—
482C22×C3—124no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3—162no—
486C22×C3—242no—
487C22×C3—248no—
488C22×C3C2×C3×C22⋊C411yescharacteristic, complemented
489C22×C3C2×C4×A412yescomplemented
490C22×C3C23×A411yescharacteristic
491C2×D3—22no—
492C2×D3—28no—
493C2×D3—34no—
494C2×D3—38no—
495C2×D3—32no—
496C2×D3—34no—
497C2×D3—38no—
498C2×D3—34no—
499C2×D3—34no—
500C2×D3—34no—
501C2×D3—32no—
502C2×D3—68no—
503C2×D3—62no—
504C2×D3—64no—
505C2×D3—62no—
506C2×D3—68no—
507C2×D3—616no—
508C2×D3—64no—
509C2×D3—62no—
510C2×D3—68no—
511C2×D3—62no—
512C2×D3—62no—
513C2×D3C2×C4×A412yes—
514C2×D3C2×C4×A412yescomplemented
515C2×D3D4×A414yes—
516A4—21no—
517A4D3×C22⋊C411yescharacteristic, direct product factor
518C3×C4—22no—
519C3×C4—62no—
520C3×C4—82no—
521C3×C4—162no—
522C3×C4—242no—
523Dic3—22no—
524Dic3—62no—
525C32—41noSylow
526C23—22no—
527C23—32no—
528C23—31no—
529C23—31no—
530C23—31no—
531C23—32no—
532C23—32no—
533C23—32no—
534C23—32no—
535C23—34no—
536C23—31no—
537C23—31no—
538C23—34no—
539C23—62no—
540C23—62no—
541C23—64no—
542C23—62no—
543C23—64no—
544C23—62no—
545C23—62no—
546C23—64no—
547C23—62no—
548C23—94no—
549C23—94no—
550C23—92no—
551C23—92no—
552C23—92no—
553C23—92no—
554C23—94no—
555C23—94no—
556C23—94no—
557C23—92no—
558C23—94no—
559C23—98no—
560C23—94no—
561C23—92no—
562C23—98no—
563C23—92no—
564C23—98no—
565C23—92no—
566C23—91no—
567C23—94no—
568C23—91no—
569C23—184no—
570C23—182no—
571C23—182no—
572C23—184no—
573C23—182no—
574C23—184no—
575C23—182no—
576C23—182no—
577C23—184no—
578C23—188no—
579C23—188no—
580C23—1816no—
581C23—184no—
582C23—188no—
583C23—188no—
584C23—188no—
585C23—188no—
586C23—188no—
587C23—1816no—
588C23—188no—
589C23—1816no—
590C23—1816no—
591C23—188no—
592C23C2×C3×C4×D311yescharacteristic
593C23C3×D3×D412yes—
594C23C2×D3×A411yescharacteristic
595C2×C4—32no—
596C2×C4—32no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—64no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—92no—
603C2×C4—184no—
604C2×C4—184no—
605C2×C4—182no—
606C2×C4—182no—
607C2×C4—184no—
608C2×C4—188no—
609C2×C4—182no—
610C2×C4—182no—
611C2×C4C2×D3×A412yescomplemented
612C2×C3—22no—
613C2×C3—32no—
614C2×C3—31no—
615C2×C3—31no—
616C2×C3—41no—
617C2×C3—42no—
618C2×C3—62no—
619C2×C3—82no—
620C2×C3—81no—
621C2×C3—82no—
622C2×C3—124no—
623C2×C3—162no—
624C2×C3—242no—
625C2×C3C22×C4×A411yescharacteristic
626C2×C3C2×D4×A412yes—
627D3—22no—
628D3—34no—
629D3—62no—
630D3A4×C22⋊C414yesdirect product factor
631C22—22no—
632C22—31no—
633C22—32no—
634C22—32no—
635C22—31no—
636C22—31no—
637C22—32no—
638C22—32no—
639C22—32no—
640C22—34no—
641C22—32no—
642C22—32no—
643C22—62no—
644C22—62no—
645C22—64no—
646C22—68no—
647C22—62no—
648C22—62no—
649C22—64no—
650C22—62no—
651C22—62no—
652C22—94no—
653C22—98no—
654C22—94no—
655C22—94no—
656C22—98no—
657C22—94no—
658C22—92no—
659C22—94no—
660C22—92no—
661C22—188no—
662C22—182no—
663C22—182no—
664C22—184no—
665C22—188no—
666C22—182no—
667C22—182no—
668C22—184no—
669C22—188no—
670C22—1816no—
671C22—182no—
672C22C3×D3×C22⋊C411yescharacteristic, complemented
673C22C4×D3×A412yescomplemented
674C22C22×D3×A411yescharacteristic
675C4—22no—
676C4—62no—
677C4—62no—
678C4—182no—
679C3—41no—
680C3—81no—
681C3C2×A4×C22⋊C411yescharacteristic, complemented
682C2—22no—
683C2—31no—
684C2—31no—
685C2—32no—
686C2—34no—
687C2—62no—
688C2—62no—
689C2—94no—
690C2—182no—
691C2C2×C4×D3×A411yescharacteristic
692C2D3×D4×A412yes—
subgroupG/H
center, FrattiniC22C22×D3×A4
commutatorC23×C3C22×C3×C4
FittingC22×C3×C22⋊C4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC23×D3×A4C2
hypercenterC22⋊C4D3×A4
hypocenterC22×C3C2×C3×C22⋊C4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×A4C2semidirect
3. C3×A4×C22⋊C4C2semidirect
4. A4×#217C2semidirect
5. A4×(C2×D3)⋊C4C2semidirect
6. C22×D3×C22⋊C4C3semidirect
10. C22×D3×A4C4semidirect
13. C2×C3×C4×A4C22semidirect
14. C2×Dic3×A4C22semidirect
19. C23×C4×D3C2×C3semidirect
21. C22×C3×C22⋊C4C2×C3semidirect
22. C22×#217C2×C3semidirect
23. C22×(C2×D3)⋊C4C2×C3semidirect
33. A4×C22⋊C4D3direct (N × H)
36. C22×C3×A4C2×C4semidirect
41. C2×D3×A4C2×C4semidirect
58. C24×D3C3×C4semidirect
67. C23×C3×C4C22×C3semidirect
68. C23×Dic3C22×C3semidirect
78. C2×C4×A4C2×D3semidirect
100. D3×C22⋊C4A4direct (N × H)
110. D3×A4C22⋊C4direct (N × H)
124. C22×C22⋊C4C3×D3semidirect
131. C24×C3C2×C3×C4semidirect
167. C23×D3C2×C3×C4semidirect
179. C22×A4C4×D3semidirect
202. C2×C4×D3C2×A4semidirect
213. C3×C22⋊C4C2×A4semidirect
217. #217C2×A4semidirect
222. (C2×D3)⋊C4C2×A4semidirect
231. C3×A4C2×C22⋊C4semidirect
252. C23×C4C2×C3×D3semidirect
345. C22×D3C3×C22⋊C4semidirect
346. C22×D3C4×A4semidirect
366. C2×C3×C4C22×A4semidirect
372. C2×Dic3C22×A4semidirect
425. C24C3×C4×D3semidirect
460. C22⋊C4D3×A4direct (N × H)
488. C22×C3C2×C3×C22⋊C4semidirect
489. C22×C3C2×C4×A4semidirect
514. C2×D3C2×C4×A4semidirect
517. A4D3×C22⋊C4direct (N × H)
611. C2×C4C2×D3×A4semidirect
630. D3A4×C22⋊C4direct (N × H)
672. C22C3×D3×C22⋊C4semidirect
673. C22C4×D3×A4semidirect
681. C3C2×A4×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×D3×A42
C2×C4×D3×A42
C3×A4×C22⋊C42
A4×#2172
A4×(C2×D3)⋊C42
C22×D3×C22⋊C43
C2×A4×C22⋊C43
C3×D3×C22⋊C44