Finite Group Databasebeta

← D3×D4×C22⋊C9 #13164611

Subgroups — D3×D4×C22⋊C9 #13164611

Order 1728.

1226 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 1226 conjugacy classes of subgroups — too many to draw. Only its 125 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×D3×C22⋊C9C212yesmaximal, complemented
2C3×D4×C22⋊C9C211yesmaximal, characteristic, complemented
3#67×C22⋊C9C212yesmaximal, complemented
4D12×C22⋊C9C211yesmaximal, characteristic, complemented
5C4×D3×C22⋊C9C211yesmaximal, characteristic, complemented
6C22×C3×D3×D4C311yesmaximal, characteristic
7C2×D4×C22⋊C9—31nomaximal
8C22×C3×C22⋊C9C2212yescomplemented
9C2×D3×C22⋊C9—24no—
10C2×D3×C22⋊C9C2211yescharacteristic
11C2×D3×C22⋊C9C2212yescomplemented
12D3×D4×C9—41nomaximal
13C3×C4×C22⋊C9C2211yescharacteristic, complemented
14Dic3×C22⋊C9C2211yescharacteristic, complemented
15C24×C3×D3C2×C312yes—
16C22×C32×D4C2×C311yescharacteristic
17C22×C3×#67C2×C312yes—
18C2×C3×D3×D4—31no—
19C2×C3×D3×D4—32no—
20C2×C3×D3×D4—31no—
21C2×C3×D3×D4—31no—
22C2×C3×D3×D4—31no—
23C2×C3×D3×D4—32no—
24C22×C3×D12C2×C311yescharacteristic
25C22×C3×C4×D3C2×C311yescharacteristic
26C23×C22⋊C9—32no—
27D4×C22⋊C9—21no—
28D4×C22⋊C9—32no—
29D4×C22⋊C9—31no—
30D4×C22⋊C9D311yescharacteristic, direct product factor
31C2×C4×C22⋊C9—31no—
32C22×D3×C9—42no—
33C2×C3×C22⋊C9—22no—
34C2×C3×C22⋊C9C2311yescharacteristic
35D3×C22⋊C9—22no—
36D3×C22⋊C9D412yesdirect product factor
37C3×D4×C9—41no—
38C9×#67—42no—
39C9×D12—41no—
40C4×D3×C9—41no—
41C23×C3×D4—31no—
42C22×D3×D4C911yescharacteristic, complemented
43C24×C32C22×C312yes—
44C23×C3×D3—24no—
45C23×C3×D3—32no—
46C23×C3×D3—32no—
47C23×C3×D3—32no—
48C23×C3×D3—32no—
49C23×C3×D3—64no—
50C23×C3×D3C22×C312yes—
51C23×C3×D3C22×C311yescharacteristic
52C2×C32×D4—31no—
53C2×C32×D4—31no—
54C2×C32×D4—32no—
55C22×C32×C4C22×C311yescharacteristic
56C2×C3×#67—32no—
57C2×C3×#67—32no—
58C2×C3×#67—32no—
59C2×C3×#67—32no—
60C22×C3×Dic3C22×C311yescharacteristic
61C3×D3×D4—34no—
62C3×D3×D4—34no—
63C3×D3×D4—32no—
64C3×D3×D4—32no—
65C3×D3×D4—32no—
66C3×D3×D4—32no—
67C3×D3×D4—31no—
68C3×D3×D4—32no—
69C3×D3×D4—31no—
70C3×D3×D4—31no—
71C3×D3×D4A411yescharacteristic
72C2×C3×D12—31no—
73C2×C3×D12—32no—
74C2×C3×D12—31no—
75C2×C3×C4×D3—31no—
76C2×C3×C4×D3—31no—
77C2×C3×C4×D3—31no—
78C2×C3×C4×D3—31no—
79C22×C22⋊C9—22no—
80C22×C22⋊C9—31no—
81C22×C22⋊C9—32no—
82C22×C22⋊C9—64no—
83C22×C22⋊C9C2×D312yescomplemented
84C2×D4×C9—121no—
85C4×C22⋊C9—21no—
86C4×C22⋊C9—31no—
87C4×C22⋊C9C2×D311yescharacteristic, complemented
88C22×C3×C9—42no—
89C2×D3×C9—41no—
90C2×D3×C9—42no—
91C2×D3×C9—84no—
92C3×C22⋊C9C2×D411yescharacteristic, complemented
93C3×C4×C9—41no—
94C9×Dic3—41no—
95C25×C3—32no—
96C24×D3C2×C912yescomplemented
97C22×C3×D4—21no—
98C22×C3×D4—32no—
99C22×C3×D4—31no—
100C22×C3×D4—91no—
101C22×C3×D4—91no—
102C22×C3×D4—91no—
103C22×C3×D4—91no—
104C22×C3×D4—92no—
105C22×C3×D4—92no—
106C22×C3×D4C2×C911yescharacteristic, complemented
107C22×C3×D4C3×D311yescharacteristic
108C23×C3×C4—31no—
109C22×#67C2×C912yescomplemented
110C2×D3×D4—31no—
111C2×D3×D4—31no—
112C2×D3×D4—31no—
113C2×D3×D4—32no—
114C2×D3×D4—31no—
115C2×D3×D4—32no—
116C22×D12C2×C911yescharacteristic, complemented
117C22×C4×D3C2×C911yescharacteristic, complemented
118C23×C32—22no—
119C23×C32—32no—
120C23×C32—32no—
121C23×C32—62no—
122C23×C32C23×C311yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—31no—
125C22×C3×D3—31no—
126C22×C3×D3—32no—
127C22×C3×D3—34no—
128C22×C3×D3—32no—
129C22×C3×D3—32no—
130C22×C3×D3—32no—
131C22×C3×D3—32no—
132C22×C3×D3—32no—
133C22×C3×D3—64no—
134C22×C3×D3—64no—
135C22×C3×D3—64no—
136C22×C3×D3—64no—
137C22×C3×D3—64no—
138C22×C3×D3—64no—
139C22×C3×D3—64no—
140C22×C3×D3—64no—
141C22×C3×D3—62no—
142C22×C3×D3C3×D412yes—
143C22×C3×D3C2×A412yes—
144C32×D4—32no—
145C32×D4—32no—
146C32×D4—31no—
147C32×D4C2×A411yescharacteristic
148C2×C32×C4—31no—
149C2×C32×C4—31no—
150C3×#67—34no—
151C3×#67—32no—
152C3×#67—32no—
153C3×#67—32no—
154C3×#67C2×A412yes—
155C2×C3×Dic3—31no—
156C2×C3×Dic3—31no—
157C3×D12—32no—
158C3×D12—32no—
159C3×D12—31no—
160C3×D12C2×A411yescharacteristic
161C3×C4×D3—32no—
162C3×C4×D3—31no—
163C3×C4×D3—31no—
164C3×C4×D3—31no—
165C3×C4×D3C2×A411yescharacteristic
166C23×C9—122no—
167C2×C22⋊C9—22no—
168C2×C22⋊C9—21no—
169C2×C22⋊C9—32no—
170C2×C22⋊C9—42no—
171C2×C22⋊C9—62no—
172C2×C22⋊C9C22×D311yescharacteristic
173D4×C9—41no—
174D4×C9—81no—
175D4×C9—121no—
176D4×C9—122no—
177C2×C4×C9—121no—
178C23×D4—31noSylow
179C2×C3×C9—41no—
180C2×C3×C9—82no—
181D3×C9—42no—
182D3×C9—82no—
183C24×C3—22no—
184C24×C3—31no—
185C24×C3—32no—
186C24×C3—64no—
187C24×C3—92no—
188C24×C3—92no—
189C24×C3—92no—
190C24×C3—92no—
191C24×C3—184no—
192C24×C3C22×C912yescomplemented
193C24×C3C2×C3×D312yes—
194C23×D3—24no—
195C23×D3—32no—
196C23×D3—32no—
197C23×D3—32no—
198C23×D3—32no—
199C23×D3—64no—
200C23×D3C22×C911yescharacteristic
201C23×D3C22×C912yescomplemented
202C2×C3×D4—31no—
203C2×C3×D4—31no—
204C2×C3×D4—31no—
205C2×C3×D4—31no—
206C2×C3×D4—32no—
207C2×C3×D4—31no—
208C2×C3×D4—32no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×C3×D4—62no—
212C2×C3×D4—91no—
213C2×C3×D4—91no—
214C2×C3×D4—91no—
215C2×C3×D4—92no—
216C2×C3×D4—92no—
217C2×C3×D4—91no—
218C2×C3×D4—92no—
219C2×C3×D4—92no—
220C2×C3×D4—92no—
221C2×C3×D4—92no—
222C2×C3×D4—94no—
223C2×C3×D4—94no—
224C2×C3×D4—92no—
225C2×C3×D4—91no—
226C2×C3×D4—92no—
227C2×C3×D4—92no—
228C2×C3×D4—92no—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—91no—
232C22×C3×C4—91no—
233C22×C3×C4—91no—
234C22×C3×C4—91no—
235C22×C3×C4C22×C911yescharacteristic, complemented
236C22×C3×C4C2×C3×D311yescharacteristic
237C2×#67—32no—
238C2×#67—32no—
239C2×#67—32no—
240C2×#67—32no—
241C22×Dic3C22×C911yescharacteristic, complemented
242D3×D4—34no—
243D3×D4—34no—
244D3×D4—32no—
245D3×D4—32no—
246D3×D4—32no—
247D3×D4—32no—
248D3×D4—31no—
249D3×D4—32no—
250D3×D4—31no—
251D3×D4—31no—
252D3×D4C22⋊C911yescharacteristic, direct product factor
253C2×D12—31no—
254C2×D12—32no—
255C2×D12—31no—
256C2×C4×D3—31no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C22×C32—31no—
261C22×C32—31no—
262C22×C32—32no—
263C22×C32—62no—
264C22×C32—62no—
265C22×C32—62no—
266C22×C32—62no—
267C22×C32C2×C3×D411yescharacteristic
268C22×C32C22×A412yes—
269C2×C3×D3—24no—
270C2×C3×D3—32no—
271C2×C3×D3—31no—
272C2×C3×D3—32no—
273C2×C3×D3—32no—
274C2×C3×D3—32no—
275C2×C3×D3—32no—
276C2×C3×D3—64no—
277C2×C3×D3—62no—
278C2×C3×D3—62no—
279C2×C3×D3—64no—
280C2×C3×D3—68no—
281C2×C3×D3—64no—
282C2×C3×D3—62no—
283C2×C3×D3—62no—
284C2×C3×D3C22×A411yescharacteristic
285C2×C3×D3C22×A412yes—
286C32×C4—31no—
287C32×C4C22×A411yescharacteristic
288C3×Dic3—31no—
289C3×Dic3C22×A411yescharacteristic
290C22×C9—42no—
291C22×C9—82no—
292C22×C9—121no—
293C22×C9—122no—
294C22×C9—244no—
295C22⋊C9—21no—
296C22⋊C9D3×D411yescharacteristic, direct product factor
297C4×C9—41no—
298C4×C9—81no—
299C4×C9—121no—
300C25—32no—
301C22×D4—32no—
302C22×D4—31no—
303C22×D4—91no—
304C22×D4—91no—
305C22×D4—91no—
306C22×D4—91no—
307C22×D4—92no—
308C22×D4—92no—
309C22×D4D3×C911yescharacteristic, complemented
310C23×C4—31no—
311C3×C9—41noSylow
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—21no—
315C23×C3—32no—
316C23×C3—32no—
317C23×C3—32no—
318C23×C3—32no—
319C23×C3—32no—
320C23×C3—32no—
321C23×C3—42no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—62no—
327C23×C3—91no—
328C23×C3—92no—
329C23×C3—92no—
330C23×C3—92no—
331C23×C3—91no—
332C23×C3—92no—
333C23×C3—94no—
334C23×C3—92no—
335C23×C3—92no—
336C23×C3—122no—
337C23×C3—182no—
338C23×C3—184no—
339C23×C3—184no—
340C23×C3—184no—
341C23×C3—184no—
342C23×C3—184no—
343C23×C3—184no—
344C23×C3—184no—
345C23×C3—184no—
346C23×C3C23×C911yescharacteristic
347C23×C3C22×C3×D311yescharacteristic
348C22×D3—22no—
349C22×D3—31no—
350C22×D3—31no—
351C22×D3—32no—
352C22×D3—34no—
353C22×D3—32no—
354C22×D3—32no—
355C22×D3—32no—
356C22×D3—32no—
357C22×D3—32no—
358C22×D3—64no—
359C22×D3—64no—
360C22×D3—64no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—62no—
367C22×D3D4×C912yescomplemented
368C22×D3C2×C22⋊C912yescomplemented
369C3×D4—21no—
370C3×D4—32no—
371C3×D4—32no—
372C3×D4—32no—
373C3×D4—32no—
374C3×D4—32no—
375C3×D4—31no—
376C3×D4—31no—
377C3×D4—31no—
378C3×D4—61no—
379C3×D4—62no—
380C3×D4—62no—
381C3×D4—92no—
382C3×D4—92no—
383C3×D4—92no—
384C3×D4—92no—
385C3×D4—94no—
386C3×D4—92no—
387C3×D4—91no—
388C3×D4C2×C22⋊C911yescharacteristic, complemented
389C3×D4D3×A411yescharacteristic
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—91no—
398C2×C3×C4—91no—
399C2×C3×C4—91no—
400C2×C3×C4—92no—
401C2×C3×C4—91no—
402C2×C3×C4—91no—
403#67—34no—
404#67—32no—
405#67—32no—
406#67—32no—
407#67C2×C22⋊C912yescomplemented
408C2×Dic3—31no—
409C2×Dic3—31no—
410D12—32no—
411D12—32no—
412D12—31no—
413D12C2×C22⋊C911yescharacteristic, complemented
414C4×D3—32no—
415C4×D3—31no—
416C4×D3—31no—
417C4×D3—31no—
418C4×D3C2×C22⋊C911yescharacteristic, complemented
419C2×C32—22no—
420C2×C32—31no—
421C2×C32—31no—
422C2×C32—62no—
423C2×C32C23×A411yescharacteristic
424C3×D3—22no—
425C3×D3—32no—
426C3×D3—62no—
427C3×D3D4×A412yes—
428C2×C9—41no—
429C2×C9—82no—
430C2×C9—81no—
431C2×C9—122no—
432C2×C9—162no—
433C2×C9—242no—
434C24—31no—
435C24—32no—
436C24—64no—
437C24—92no—
438C24—92no—
439C24—92no—
440C24—92no—
441C24—184no—
442C24C2×D3×C912yescomplemented
443C2×D4—31no—
444C2×D4—31no—
445C2×D4—31no—
446C2×D4—32no—
447C2×D4—91no—
448C2×D4—91no—
449C2×D4—91no—
450C2×D4—92no—
451C2×D4—92no—
452C2×D4—91no—
453C2×D4—92no—
454C2×D4—92no—
455C2×D4—92no—
456C2×D4—92no—
457C2×D4—94no—
458C2×D4—94no—
459C2×D4—92no—
460C2×D4—91no—
461C2×D4—92no—
462C2×D4—92no—
463C2×D4—92no—
464C22×C4—31no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4C2×D3×C911yescharacteristic, complemented
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—31no—
473C22×C3—31no—
474C22×C3—31no—
475C22×C3—31no—
476C22×C3—31no—
477C22×C3—32no—
478C22×C3—32no—
479C22×C3—32no—
480C22×C3—61no—
481C22×C3—62no—
482C22×C3—61no—
483C22×C3—62no—
484C22×C3—62no—
485C22×C3—62no—
486C22×C3—62no—
487C22×C3—64no—
488C22×C3—62no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3—92no—
493C22×C3—92no—
494C22×C3—92no—
495C22×C3—92no—
496C22×C3—91no—
497C22×C3—92no—
498C22×C3—122no—
499C22×C3—122no—
500C22×C3—122no—
501C22×C3—122no—
502C22×C3—184no—
503C22×C3—182no—
504C22×C3—182no—
505C22×C3—184no—
506C22×C3—182no—
507C22×C3—182no—
508C22×C3—184no—
509C22×C3—188no—
510C22×C3C2×D4×C911yescharacteristic, complemented
511C22×C3C22×C22⋊C912yescomplemented
512C22×C3C3×D3×D411yescharacteristic
513C22×C3C2×D3×A412yes—
514C2×D3—24no—
515C2×D3—32no—
516C2×D3—31no—
517C2×D3—32no—
518C2×D3—32no—
519C2×D3—32no—
520C2×D3—32no—
521C2×D3—64no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—64no—
525C2×D3—68no—
526C2×D3—64no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3C22×C22⋊C911yescharacteristic
530C2×D3C22×C22⋊C912yescomplemented
531C3×C4—21no—
532C3×C4—31no—
533C3×C4—31no—
534C3×C4—31no—
535C3×C4—61no—
536C3×C4—91no—
537C3×C4C22×C22⋊C911yescharacteristic, complemented
538C3×C4C2×D3×A411yescharacteristic
539Dic3—31no—
540Dic3C22×C22⋊C911yescharacteristic, complemented
541C32C2×D4×A411yescharacteristic
542C9—41no—
543C9—81no—
544C23—22no—
545C23—32no—
546C23—32no—
547C23—32no—
548C23—32no—
549C23—62no—
550C23—62no—
551C23—91no—
552C23—92no—
553C23—92no—
554C23—92no—
555C23—91no—
556C23—92no—
557C23—94no—
558C23—92no—
559C23—92no—
560C23—182no—
561C23—184no—
562C23—184no—
563C23—184no—
564C23—184no—
565C23—184no—
566C23—184no—
567C23—184no—
568C23—184no—
569C23C22×D3×C911yescharacteristic
570D4—32no—
571D4—32no—
572D4—32no—
573D4—31no—
574D4—31no—
575D4—92no—
576D4—92no—
577D4—92no—
578D4—92no—
579D4—94no—
580D4—92no—
581D4—91no—
582D4D3×C22⋊C911yescharacteristic, direct product factor
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—91no—
587C2×C4—91no—
588C2×C4—91no—
589C2×C4—92no—
590C2×C4—91no—
591C2×C4—91no—
592C2×C3—22no—
593C2×C3—22no—
594C2×C3—21no—
595C2×C3—31no—
596C2×C3—31no—
597C2×C3—32no—
598C2×C3—31no—
599C2×C3—31no—
600C2×C3—42no—
601C2×C3—61no—
602C2×C3—61no—
603C2×C3—62no—
604C2×C3—62no—
605C2×C3—62no—
606C2×C3—92no—
607C2×C3—122no—
608C2×C3—182no—
609C2×C3C23×C22⋊C911yescharacteristic
610C2×C3C22×D3×A411yescharacteristic
611D3—22no—
612D3—32no—
613D3—62no—
614D3D4×C22⋊C912yesdirect product factor
615C22—31no—
616C22—31no—
617C22—31no—
618C22—32no—
619C22—32no—
620C22—62no—
621C22—62no—
622C22—64no—
623C22—62no—
624C22—62no—
625C22—92no—
626C22—92no—
627C22—92no—
628C22—92no—
629C22—91no—
630C22—92no—
631C22—184no—
632C22—182no—
633C22—182no—
634C22—184no—
635C22—182no—
636C22—182no—
637C22—184no—
638C22—188no—
639C22D3×D4×C911yescharacteristic, complemented
640C22C2×D3×C22⋊C912yescomplemented
641C4—31no—
642C4—31no—
643C4—91no—
644C4C2×D3×C22⋊C911yescharacteristic, complemented
645C3—21no—
646C3C2×D4×C22⋊C911yescharacteristic, complemented
647C3D3×D4×A411yescharacteristic
648C2—22no—
649C2—31no—
650C2—31no—
651C2—32no—
652C2—62no—
653C2—62no—
654C2—92no—
655C2—182no—
656C2C22×D3×C22⋊C911yescharacteristic
subgroupG/H
center, FrattiniC2×C3C22×D3×A4
commutatorC23×C3C23×C9
FittingC22×C32×D4C2×C3
socle, cosocleC23×C32C23×C3
prime radicalC22×C3×D3×D4C3
hypercenterC3×D4D3×A4
hypocenterC22×C3C2×D4×C9
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×D3×C22⋊C9C2semidirect
2. C3×D4×C22⋊C9C2semidirect
3. #67×C22⋊C9C2semidirect
4. D12×C22⋊C9C2semidirect
5. C4×D3×C22⋊C9C2semidirect
8. C22×C3×C22⋊C9C22semidirect
11. C2×D3×C22⋊C9C22semidirect
13. C3×C4×C22⋊C9C22semidirect
14. Dic3×C22⋊C9C22semidirect
30. D4×C22⋊C9D3direct (N × H)
36. D3×C22⋊C9D4direct (N × H)
42. C22×D3×D4C9semidirect
83. C22×C22⋊C9C2×D3semidirect
87. C4×C22⋊C9C2×D3semidirect
92. C3×C22⋊C9C2×D4semidirect
96. C24×D3C2×C9semidirect
106. C22×C3×D4C2×C9semidirect
109. C22×#67C2×C9semidirect
116. C22×D12C2×C9semidirect
117. C22×C4×D3C2×C9semidirect
192. C24×C3C22×C9semidirect
201. C23×D3C22×C9semidirect
235. C22×C3×C4C22×C9semidirect
241. C22×Dic3C22×C9semidirect
252. D3×D4C22⋊C9direct (N × H)
296. C22⋊C9D3×D4direct (N × H)
309. C22×D4D3×C9semidirect
367. C22×D3D4×C9semidirect
368. C22×D3C2×C22⋊C9semidirect
388. C3×D4C2×C22⋊C9semidirect
407. #67C2×C22⋊C9semidirect
413. D12C2×C22⋊C9semidirect
418. C4×D3C2×C22⋊C9semidirect
442. C24C2×D3×C9semidirect
469. C22×C4C2×D3×C9semidirect
510. C22×C3C2×D4×C9semidirect
511. C22×C3C22×C22⋊C9semidirect
530. C2×D3C22×C22⋊C9semidirect
537. C3×C4C22×C22⋊C9semidirect
540. Dic3C22×C22⋊C9semidirect
582. D4D3×C22⋊C9direct (N × H)
614. D3D4×C22⋊C9direct (N × H)
639. C22D3×D4×C9semidirect
640. C22C2×D3×C22⋊C9semidirect
644. C4C2×D3×C22⋊C9semidirect
646. C3C2×D4×C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊C92
C3×D4×C22⋊C92
#67×C22⋊C92
D12×C22⋊C92
C4×D3×C22⋊C92
C22×C3×D3×D43
C2×D4×C22⋊C93
D3×D4×C94