Finite Group Databasebeta

← D9×#548 #11902568

Subgroups — D9×#548 #11902568

Order 1152.

2430 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D9C211yesmaximal, characteristic, complemented
2C22×Q8×D9C211yesmaximal, characteristic, complemented
3C9×#548C211yesmaximal, characteristic, complemented
4#10589933C211yesmaximal, characteristic, complemented
5#10589919C211yesmaximal, characteristic, complemented
6#10589779C213yesmaximal, complemented
7D9×#124C213yesmaximal, complemented
8#10589735C213yesmaximal, complemented
9D9×C22⋊Q8C213yesmaximal, complemented
10D9×#121C213yesmaximal, complemented
11#10589700C213yesmaximal, complemented
12#10589678C211yesmaximal, characteristic, complemented
13C4×Q8×D9C211yesmaximal, characteristic, complemented
14#10589654C213yesmaximal, complemented
15C4×D4×D9C213yesmaximal, complemented
16D3×#548—31nomaximal
17C2×C9×#41C2211yescharacteristic, complemented
18C22×Q8×C9C2211yescharacteristic, complemented
19#41×D9—28no—
20C2×#3701C2211yescharacteristic, complemented
21C2×Q8×D9—28no—
22C2×Q8×D9C2213yes—
23C2×Q8×D9C2211yescharacteristic
24C2×Q8×D9C2213yescomplemented
25C2×Q8×D9C2211yescharacteristic, complemented
26C2×#3699C2213yescomplemented
27C2×D4×D9C2213yes—
28C2×D4×D9C2213yes—
29C2×#3697C2213yescomplemented
30C22×C4×D9C2213yes—
31C22×C4×D9C2213yes—
32C22×Dic18C2213yescomplemented
33C9×#124C2213yescomplemented
34C9×C22⋊Q8C2213yescomplemented
35C9×#121C2213yescomplemented
36C4×Q8×C9C2211yescharacteristic, complemented
37C4×D4×C9C2213yescomplemented
38#63509C2213yescomplemented
39#63508C2213yescomplemented
40Q8×Dic9C2211yescharacteristic, complemented
41#63501C2216yescomplemented
42#63500C2213yescomplemented
43#63498C2213yescomplemented
44D4×Dic9C2213yescomplemented
45#63492C2213yescomplemented
46C4×#611C2213yescomplemented
47C4×#611C2213yescomplemented
48#63486C2213yescomplemented
49#63459C2213yescomplemented
50#63458C2216yescomplemented
51#63457C2213yescomplemented
52#63455C2213yescomplemented
53C4⋊C4×D9C2213yes—
54C4⋊C4×D9C2213yes—
55#63449C2213yescomplemented
56#63447C2216yescomplemented
57#63447C2216yescomplemented
58#63446C2216yescomplemented
59#611⋊C4C2213yescomplemented
60#611⋊C4C2213yescomplemented
61C22⋊C4×D9C2216yes—
62C22⋊C4×D9C2213yes—
63C22⋊C4×D9C2211yescharacteristic
64#63440C2216yescomplemented
65#63437C2213yescomplemented
66C4×D36C2213yescomplemented
67C42×D9C2213yes—
68C4×Dic18C2213yescomplemented
69C2×D3×#41—31no—
70C22×D3×Q8—31no—
71C3×#548D311yescharacteristic
72#5831—31no—
73#5817—31no—
74#5677—33no—
75D3×#124—33no—
76#5633—33no—
77D3×C22⋊Q8—33no—
78D3×#121—33no—
79#5598—33no—
80#5576—31no—
81C4×D3×Q8—31no—
82#5552—33no—
83C4×D3×D4—33no—
84C23×D9C2313yes—
85C23×D9C2311yescharacteristic
86C9×#41—24no—
87C2×Q8×C9—24no—
88C2×Q8×C9C2313yes—
89C2×Q8×C9C2311yescharacteristic
90C2×D4×C9C2313yes—
91C2×D4×C9C2313yes—
92C22×C4×C9C2313yes—
93C22×C4×C9C2313yes—
94C2×#611C2313yes—
95C2×#611C2313yes—
96C2×#611C2316yes—
97C22×Dic9C2313yes—
98C22×Dic9C2313yes—
99#3701—24no—
100Q8×D9—24no—
101Q8×D9—212no—
102Q8×D9—212no—
103Q8×D9D418yescomplemented
104#3699—212no—
105D4×D9—212no—
106D4×D9—212no—
107#3697—212no—
108C2×D36C2313yes—
109C2×D36C2313yes—
110C2×C4×D9—212no—
111C2×C4×D9—212no—
112C2×C4×D9C2313yes—
113C2×C4×D9C2313yes—
114C2×C4×D9C2311yescharacteristic
115C2×C4×D9C2313yes—
116C2×C4×D9C2313yes—
117C2×C4×D9C2311yescharacteristic
118C2×C4×D9C2313yes—
119C2×C4×D9C2313yes—
120C2×C4×D9C2313yes—
121C2×Dic18—212no—
122C2×Dic18C2313yes—
123C2×Dic18C2316yes—
124C2×Dic18C2313yes—
125C9×C4⋊C4C2313yes—
126C9×C4⋊C4C2313yes—
127C9×C22⋊C4C2311yescharacteristic
128C9×C22⋊C4C2313yes—
129C9×C22⋊C4C2316yes—
130C42×C9C2313yes—
131#3676C2311yescharacteristic
132#3676C2313yes—
133#3676C2316yes—
134(C2×D9)⋊C4C2311yescharacteristic
135(C2×D9)⋊C4C2313yes—
136(C2×D9)⋊C4C2316yes—
137(C2×D9)⋊C4C2316yes—
138(C2×D9)⋊C4C2311yescharacteristic
139(C2×D9)⋊C4C2313yes—
140C4⋊Dic9C2313yes—
141C4⋊Dic9C2313yes—
142Dic9⋊C4C2313yes—
143Dic9⋊C4C2313yes—
144Dic9⋊C4C2316yes—
145C4×Dic9C2313yes—
146C4×Dic9C2313yes—
147C4×Dic9C2313yes—
148C2×#548—91noSylow
149C2×C3×#41C2×D311yescharacteristic
150C22×C3×Q8C2×D311yescharacteristic
151D3×#41—68no—
152C2×#239—31no—
153C2×D3×Q8—31no—
154C2×D3×Q8—33no—
155C2×D3×Q8—33no—
156C2×D3×Q8—31no—
157C2×D3×Q8—68no—
158C2×#237—33no—
159C2×D3×D4—33no—
160C2×D3×D4—33no—
161C2×#235—33no—
162C22×C4×D3—33no—
163C22×C4×D3—33no—
164C22×Dic6—33no—
165C3×#124C2×D313yes—
166C3×C22⋊Q8C2×D313yes—
167C3×#121C2×D313yes—
168C3×C4×Q8C2×D311yescharacteristic
169C3×C4×D4C2×D313yes—
170#947—33no—
171#946—33no—
172Q8×Dic3—31no—
173#939—36no—
174#938—33no—
175#936—33no—
176D4×Dic3—33no—
177#930—33no—
178C4×#67—33no—
179C4×#67—33no—
180#924—33no—
181#897—33no—
182#896—36no—
183#895—33no—
184#893—33no—
185D3×C4⋊C4—33no—
186D3×C4⋊C4—33no—
187#887—33no—
188#885—36no—
189#885—36no—
190#884—36no—
191#67⋊C4—33no—
192#67⋊C4—33no—
193D3×C22⋊C4—33no—
194D3×C22⋊C4—36no—
195D3×C22⋊C4—31no—
196#878—36no—
197#875—33no—
198C4×D12—33no—
199C42×D3—33no—
200C4×Dic6—33no—
201C23×C9C2413yes—
202C23×C9C2411yescharacteristic
203C22×D9—22no—
204C22×D9—22no—
205C22×D9—26no—
206C22×D9—26no—
207C22×D9—26no—
208C22×D9#4114yescomplemented
209C22×D9C2413yes—
210C22×D9C2411yescharacteristic
211C22×D9C2411yescharacteristic
212Q8×C9—26no—
213Q8×C9C2×D414yescomplemented
214D4×C9—26no—
215D4×C9—26no—
216C2×C4×C9—26no—
217C2×C4×C9—26no—
218C2×C4×C9C2411yescharacteristic
219C2×C4×C9C2413yes—
220C2×C4×C9C2411yescharacteristic
221C2×C4×C9C2413yes—
222C2×C4×C9C2413yes—
223#611—26no—
224#611—26no—
225#611—212no—
226C2×Dic9—26no—
227C2×Dic9—26no—
228C2×Dic9C2411yescharacteristic
229C2×Dic9C2413yes—
230C2×Dic9C2411yescharacteristic
231C2×Dic9C2413yes—
232C2×Dic9C2413yes—
233D36—26no—
234D36—26no—
235C4×D9—22no—
236C4×D9—26no—
237C4×D9—26no—
238C4×D9—22no—
239C4×D9—26no—
240C4×D9—26no—
241C4×D9—26no—
242C4×D9—26no—
243C4×D9C2×D4112yes—
244Dic18—26no—
245Dic18—212no—
246Dic18C2×D4112yescomplemented
247C22×#41—91no—
248C23×Q8—91no—
249#548—91no—
250#548—91no—
251#548—93no—
252#548—93no—
253#548—93no—
254#548—91no—
255#548—93no—
256#548D911yescharacteristic, direct product factor
257C2×#124—93no—
258C2×C22⋊Q8—93no—
259C2×#121—93no—
260C2×C4×Q8—91no—
261C2×C4×D4—93no—
262C23×D3—31no—
263C23×D3—33no—
264C3×#41—24no—
265C2×C3×Q8—24no—
266C2×C3×Q8C22×D313yes—
267C2×C3×Q8C22×D311yescharacteristic
268C2×C3×D4C22×D313yes—
269C2×C3×D4C22×D313yes—
270C22×C3×C4C22×D313yes—
271C22×C3×C4C22×D313yes—
272C2×#67—33no—
273C2×#67—33no—
274C2×#67—36no—
275C22×Dic3—33no—
276C22×Dic3—33no—
277#239—64no—
278D3×Q8—38no—
279D3×Q8—612no—
280D3×Q8—612no—
281D3×Q8—64no—
282#237—612no—
283D3×D4—612no—
284D3×D4—612no—
285#235—612no—
286C2×D12—33no—
287C2×D12—33no—
288C2×C4×D3—33no—
289C2×C4×D3—31no—
290C2×C4×D3—33no—
291C2×C4×D3—33no—
292C2×C4×D3—33no—
293C2×C4×D3—33no—
294C2×C4×D3—31no—
295C2×C4×D3—33no—
296C2×C4×D3—33no—
297C2×C4×D3—612no—
298C2×C4×D3—612no—
299C2×Dic6—33no—
300C2×Dic6—33no—
301C2×Dic6—36no—
302C2×Dic6—612no—
303C3×C4⋊C4C22×D313yes—
304C3×C4⋊C4C22×D313yes—
305C3×C22⋊C4C22×D316yes—
306C3×C22⋊C4C22×D311yescharacteristic
307C3×C22⋊C4C22×D313yes—
308C3×C42C22×D313yes—
309#217—36no—
310#217—33no—
311#217—31no—
312(C2×D3)⋊C4—31no—
313(C2×D3)⋊C4—33no—
314(C2×D3)⋊C4—36no—
315(C2×D3)⋊C4—36no—
316(C2×D3)⋊C4—33no—
317(C2×D3)⋊C4—31no—
318C4⋊Dic3—33no—
319C4⋊Dic3—33no—
320Dic3⋊C4—36no—
321Dic3⋊C4—33no—
322Dic3⋊C4—33no—
323C4×Dic3—33no—
324C4×Dic3—33no—
325C4×Dic3—33no—
326C22×C9—21no—
327C22×C9—21no—
328C22×C9—23no—
329C22×C9—23no—
330C22×C9—23no—
331C22×C9C2×#4112yescomplemented
332C22×C9C2511yescharacteristic
333C2×D9—21no—
334C2×D9—21no—
335C2×D9—28no—
336C2×D9—23no—
337C2×D9—23no—
338C2×D9—23no—
339C2×D9—412no—
340C2×D9C22×D412yes—
341C2×D9C2×#4112yes—
342C2×D9C2×#4112yescomplemented
343C2×D92−1+412yes—
344C4×C9—23no—
345C4×C9—21no—
346C4×C9—23no—
347C4×C9—21no—
348C4×C9C22×D416yes—
349Dic9—23no—
350Dic9—21no—
351Dic9—23no—
352Dic9—21no—
353Dic9C22×D416yes—
354C2×#41—91no—
355C2×#41—93no—
356C2×#41—93no—
357C2×#41—188no—
358C2×#41C2×D911yescharacteristic, complemented
359C22×Q8—91no—
360C22×Q8—93no—
361C22×Q8—93no—
362C22×Q8—91no—
363C22×Q8—93no—
364C22×Q8—188no—
365C22×Q8C2×D911yescharacteristic, complemented
366C22×D4—93no—
367C22×D4—93no—
368C23×C4—93no—
369C23×C4—93no—
370#124—93no—
371#124—93no—
372#124—96no—
373#124—96no—
374#124—93no—
375#124C2×D913yescomplemented
376C22⋊Q8—93no—
377C22⋊Q8—93no—
378C22⋊Q8—96no—
379C22⋊Q8—93no—
380C22⋊Q8—96no—
381C22⋊Q8C2×D913yescomplemented
382#121—93no—
383#121—96no—
384#121—93no—
385#121—93no—
386#121—96no—
387#121C2×D913yescomplemented
388C4×Q8—91no—
389C4×Q8—93no—
390C4×Q8—93no—
391C4×Q8C2×D911yescharacteristic, complemented
392C4×D4—93no—
393C4×D4—93no—
394C4×D4—93no—
395C4×D4—93no—
396C4×D4—93no—
397C4×D4—93no—
398C4×D4—93no—
399C4×D4C2×D913yescomplemented
400C2×C4⋊C4—93no—
401C2×C4⋊C4—93no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—93no—
404C2×C22⋊C4—96no—
405C2×C42—93no—
406C23×C3C23×D313yes—
407C23×C3C23×D311yescharacteristic
408C22×D3—31no—
409C22×D3—34no—
410C22×D3—31no—
411C22×D3—33no—
412C22×D3—62no—
413C22×D3—62no—
414C22×D3—66no—
415C22×D3—66no—
416C22×D3—66no—
417C3×Q8—26no—
418C3×Q8D3×D414yes—
419C3×D4—26no—
420C3×D4—26no—
421C2×C3×C4—26no—
422C2×C3×C4—26no—
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D313yes—
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D313yes—
427C2×C3×C4C23×D313yes—
428#67—612no—
429#67—66no—
430#67—66no—
431C2×Dic3—33no—
432C2×Dic3—31no—
433C2×Dic3—33no—
434C2×Dic3—31no—
435C2×Dic3—33no—
436C2×Dic3—66no—
437C2×Dic3—66no—
438D12—66no—
439D12—66no—
440C4×D3—312no—
441C4×D3—66no—
442C4×D3—66no—
443C4×D3—62no—
444C4×D3—62no—
445C4×D3—66no—
446C4×D3—66no—
447C4×D3—66no—
448C4×D3—66no—
449Dic6—312no—
450Dic6—612no—
451Dic6—66no—
452C2×C9—22no—
453C2×C9—43no—
454C2×C9C23×D411yescharacteristic
455C2×C9C22×#4111yescharacteristic
456C2×C9C2×2−1+411yescharacteristic
457D9—22no—
458D9—43no—
459D9#54814yesdirect product factor
460C24—91no—
461C24—93no—
462#41—24no—
463#41—1812no—
464#41—1812no—
465#41—184no—
466C2×Q8—24no—
467C2×Q8—98no—
468C2×Q8—93no—
469C2×Q8—96no—
470C2×Q8—93no—
471C2×Q8—1812no—
472C2×Q8—1812no—
473C2×Q8—1812no—
474C2×Q8—184no—
475C2×Q8C22×D913yes—
476C2×Q8C22×D911yescharacteristic
477C2×D4—93no—
478C2×D4—93no—
479C2×D4—96no—
480C2×D4—93no—
481C2×D4—93no—
482C2×D4—1812no—
483C2×D4—1812no—
484C2×D4C22×D913yes—
485C2×D4C22×D913yes—
486C22×C4—93no—
487C22×C4—93no—
488C22×C4—93no—
489C22×C4—91no—
490C22×C4—93no—
491C22×C4—93no—
492C22×C4—91no—
493C22×C4—93no—
494C22×C4—93no—
495C22×C4—93no—
496C22×C4—93no—
497C22×C4—1812no—
498C22×C4—1812no—
499C22×C4C22×D913yes—
500C22×C4C22×D913yes—
501C4⋊C4—93no—
502C4⋊C4—93no—
503C4⋊C4—93no—
504C4⋊C4—96no—
505C4⋊C4—93no—
506C4⋊C4C22×D913yes—
507C4⋊C4C22×D913yes—
508C22⋊C4—91no—
509C22⋊C4—93no—
510C22⋊C4—96no—
511C22⋊C4—91no—
512C22⋊C4—91no—
513C22⋊C4—93no—
514C22⋊C4—93no—
515C22⋊C4—96no—
516C22⋊C4—96no—
517C22⋊C4C22×D911yescharacteristic
518C22⋊C4C22×D913yes—
519C22⋊C4C22×D916yes—
520C42—93no—
521C42—93no—
522C42—93no—
523C42C22×D913yes—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—23no—
527C22×C3—23no—
528C22×C3—23no—
529C22×C3D3×#4112yes—
530C22×C3C24×D311yescharacteristic
531C2×D3—32no—
532C2×D3—32no—
533C2×D3—32no—
534C2×D3—32no—
535C2×D3—68no—
536C2×D3—61no—
537C2×D3—61no—
538C2×D3—63no—
539C2×D3—63no—
540C2×D3—63no—
541C2×D3—1212no—
542C3×C4—23no—
543C3×C4—21no—
544C3×C4—23no—
545C3×C4—21no—
546C3×C4C2×D3×D416yes—
547Dic3—36no—
548Dic3—63no—
549Dic3—61no—
550Dic3—63no—
551Dic3—61no—
552C9C2×#54811yescharacteristic, complemented, Sylow
553C23—91no—
554C23—91no—
555C23—94no—
556C23—93no—
557C23—182no—
558C23—182no—
559C23—186no—
560C23—186no—
561C23—186no—
562C23C23×D913yes—
563C23C23×D911yescharacteristic
564Q8—26no—
565Q8—912no—
566Q8—1812no—
567Q8—186no—
568Q8D4×D914yescomplemented
569D4—26no—
570D4—26no—
571D4—186no—
572D4—1812no—
573D4—186no—
574D4—186no—
575D4—186no—
576C2×C4—26no—
577C2×C4—26no—
578C2×C4—93no—
579C2×C4—912no—
580C2×C4—91no—
581C2×C4—93no—
582C2×C4—93no—
583C2×C4—91no—
584C2×C4—186no—
585C2×C4—186no—
586C2×C4—182no—
587C2×C4—186no—
588C2×C4—186no—
589C2×C4—182no—
590C2×C4—186no—
591C2×C4—186no—
592C2×C4—186no—
593C2×C4—186no—
594C2×C4C23×D911yescharacteristic
595C2×C4C23×D913yes—
596C2×C4C23×D913yes—
597C2×C4C23×D911yescharacteristic
598C2×C4C23×D913yes—
599C2×C3—22no—
600C2×C3—43no—
601C2×C3C22×D3×D411yescharacteristic
602C2×C3C2×D3×#4111yescharacteristic
603C2×C3D3×2−1+411yescharacteristic
604D3—34no—
605D3—62no—
606D3—123no—
607C22—21no—
608C22—21no—
609C22—23no—
610C22—23no—
611C22—23no—
612C22—92no—
613C22—92no—
614C22—92no—
615C22—92no—
616C22—188no—
617C22—181no—
618C22—181no—
619C22—183no—
620C22—183no—
621C22—183no—
622C22—3612no—
623C22#41×D912yescomplemented
624C22C24×D911yescharacteristic
625C4—21no—
626C4—23no—
627C4—23no—
628C4—21no—
629C4—96no—
630C4—181no—
631C4—183no—
632C4—183no—
633C4—181no—
634C4C2×D4×D916yes—
635C3D3×#54811yescharacteristic
636C2—22no—
637C2—43no—
638C2—94no—
639C2—182no—
640C2—363no—
641C2C22×D4×D911yescharacteristic
642C2C2×#41×D911yescharacteristic
643C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#548C2
hypercenter#548D9
hypocenterC9C2×#548
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D9C2semidirect
2. C22×Q8×D9C2semidirect
3. C9×#548C2semidirect
4. #10589933C2semidirect
5. #10589919C2semidirect
6. #10589779C2semidirect
7. D9×#124C2semidirect
8. #10589735C2semidirect
9. D9×C22⋊Q8C2semidirect
10. D9×#121C2semidirect
11. #10589700C2semidirect
12. #10589678C2semidirect
13. C4×Q8×D9C2semidirect
14. #10589654C2semidirect
15. C4×D4×D9C2semidirect
17. C2×C9×#41C22semidirect
18. C22×Q8×C9C22semidirect
20. C2×#3701C22semidirect
24. C2×Q8×D9C22semidirect
25. C2×Q8×D9C22semidirect
26. C2×#3699C22semidirect
29. C2×#3697C22semidirect
32. C22×Dic18C22semidirect
33. C9×#124C22semidirect
34. C9×C22⋊Q8C22semidirect
35. C9×#121C22semidirect
36. C4×Q8×C9C22semidirect
37. C4×D4×C9C22semidirect
38. #63509C22semidirect
39. #63508C22semidirect
40. Q8×Dic9C22semidirect
41. #63501C22semidirect
42. #63500C22semidirect
43. #63498C22semidirect
44. D4×Dic9C22semidirect
45. #63492C22semidirect
46. C4×#611C22semidirect
47. C4×#611C22semidirect
48. #63486C22semidirect
49. #63459C22semidirect
50. #63458C22semidirect
51. #63457C22semidirect
52. #63455C22semidirect
55. #63449C22semidirect
56. #63447C22semidirect
57. #63447C22semidirect
58. #63446C22semidirect
59. #611⋊C4C22semidirect
60. #611⋊C4C22semidirect
64. #63440C22semidirect
65. #63437C22semidirect
66. C4×D36C22semidirect
68. C4×Dic18C22semidirect
103. Q8×D9D4semidirect
208. C22×D9#41semidirect
213. Q8×C9C2×D4semidirect
246. Dic18C2×D4semidirect
256. #548D9direct (N × H)
331. C22×C9C2×#41semidirect
342. C2×D9C2×#41semidirect
358. C2×#41C2×D9semidirect
365. C22×Q8C2×D9semidirect
375. #124C2×D9semidirect
381. C22⋊Q8C2×D9semidirect
387. #121C2×D9semidirect
391. C4×Q8C2×D9semidirect
399. C4×D4C2×D9semidirect
459. D9#548direct (N × H)
552. C9C2×#548semidirect
568. Q8D4×D9semidirect
623. C22#41×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D92
C22×Q8×D92
C9×#5482
#105899332
#105899192
#105897792
D9×#1242
#105897352
D9×C22⋊Q82
D9×#1212
#105897002
#105896782
C4×Q8×D92
#105896542
C4×D4×D92
D3×#5483