Finite Group Databasebeta

← D9×#468 #11866881

Subgroups — D9×#468 #11866881

Order 1152.

816 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D9C211yesmaximal, characteristic, complemented
2C2×M16×D9C211yesmaximal, characteristic, complemented
3D9×C22⋊Q8C211yesmaximal, characteristic, complemented
4D9×#121C211yesmaximal, characteristic
5C9×#468C211yesmaximal, characteristic, complemented
6#10588854C211yesmaximal, characteristic, complemented
7#10588816C211yesmaximal, characteristic, complemented
8#10588732C211yesmaximal, characteristic, complemented
9#10588718C211yesmaximal, characteristic, complemented
10#10588566C211yesmaximal, characteristic, complemented
11D9×#107C211yesmaximal, characteristic, complemented
12#10588492C211yesmaximal, characteristic, complemented
13D9×#103C211yesmaximal, characteristic, complemented
14#10588460C211yesmaximal, characteristic, complemented
15D9×#102C211yesmaximal, characteristic, complemented
16D3×#468—31nomaximal
17C2×Q8×D9C2211yescharacteristic
18C2×D4×D9—21no—
19C2×D4×D9C2211yescharacteristic
20C22×C4×D9C2211yescharacteristic
21C2×C9×SD16C2211yescharacteristic, complemented
22C2×C9×M16C2211yescharacteristic, complemented
23C9×C22⋊Q8C2211yescharacteristic, complemented
24C9×#121C2211yescharacteristic
25#63508C2211yescharacteristic, complemented
26C2×#3675C2211yescharacteristic, complemented
27#63501—21no—
28#63500C2211yescharacteristic
29C2×#3672C2211yescharacteristic, complemented
30#63492C2211yescharacteristic
31#63486C2211yescharacteristic, complemented
32C2×#3667C2211yescharacteristic, complemented
33SD16×D9—24no—
34M16×D9—24no—
35C2×#3664C2211yescharacteristic, complemented
36C2×#3663C2211yescharacteristic, complemented
37C2×#3663C2211yescharacteristic, complemented
38C2×C8×D9C2211yescharacteristic
39C2×C8×D9C2211yescharacteristic
40#63459C2211yescharacteristic, complemented
41#63458—21no—
42#63457C2211yescharacteristic
43C4⋊C4×D9—21no—
44C4⋊C4×D9C2211yescharacteristic
45C4⋊C4×D9C2211yescharacteristic
46#63446—21no—
47C22⋊C4×D9—21no—
48C22⋊C4×D9—21no—
49#63440—21no—
50C9×#107C2211yescharacteristic, complemented
51C9×#103C2211yescharacteristic, complemented
52C9×#102C2211yescharacteristic, complemented
53#63395C2211yescharacteristic, complemented
54#63392C2211yescharacteristic, complemented
55#63380C2211yescharacteristic, complemented
56#63378C2211yescharacteristic, complemented
57#63376C2211yescharacteristic, complemented
58#63369C2211yescharacteristic, complemented
59#63368C2211yescharacteristic, complemented
60#63366C2211yescharacteristic, complemented
61#63366C2211yescharacteristic, complemented
62C2×D3×SD16—31no—
63C2×D3×M16—31no—
64D3×C22⋊Q8—31no—
65D3×#121—31no—
66C3×#468D311yescharacteristic
67#5174—31no—
68#5134—31no—
69#5049—31no—
70#5042—31no—
71#4886—31no—
72D3×#107—31no—
73#4812—31no—
74D3×#103—31no—
75#4780—31no—
76D3×#102—31no—
77C23×D9—21no—
78C23×D9D411yescharacteristic
79C2×Q8×C9C2311yescharacteristic
80C2×D4×C9—21no—
81C2×D4×C9C2311yescharacteristic
82C22×C4×C9C2311yescharacteristic
83C2×#611—21no—
84C2×#611—21no—
85C2×#611—21no—
86C22×Dic9D411yescharacteristic
87Q8×D9—22no—
88Q8×D9—22no—
89D4×D9—22no—
90D4×D9—22no—
91D4×D9—44no—
92C2×D36—21no—
93C2×D36C2311yescharacteristic
94C2×C4×D9—22no—
95C2×C4×D9—22no—
96C2×C4×D9—21no—
97C2×C4×D9—21no—
98C2×C4×D9—21no—
99C2×C4×D9D411yescharacteristic
100C2×C4×D9D411yescharacteristic
101C2×C4×D9C2311yescharacteristic
102C2×C4×D9C2311yescharacteristic
103C2×Dic18—21no—
104C2×Dic18C2311yescharacteristic
105C9×SD16—22no—
106C9×M16—22no—
107C2×C8×C9C2311yescharacteristic
108C2×C8×C9C2311yescharacteristic
109C9×C4⋊C4—21no—
110C9×C4⋊C4C2311yescharacteristic
111C9×C4⋊C4C2311yescharacteristic
112C9×C22⋊C4—21no—
113C9×C22⋊C4—21no—
114#3676—21no—
115#3676—21no—
116#3675—22no—
117#3672—22no—
118(C2×D9)⋊C4—21no—
119(C2×D9)⋊C4—21no—
120(C2×D9)⋊C4—21no—
121(C2×D9)⋊C4—21no—
122C4⋊Dic9—21no—
123C4⋊Dic9C2311yescharacteristic
124C4⋊Dic9C2311yescharacteristic
125Dic9⋊C4—21no—
126Dic9⋊C4—21no—
127Dic9⋊C4—21no—
128Dic9⋊C4—21no—
129#3667—22no—
130C2×C9⋊C8C2311yescharacteristic
131C2×C9⋊C8C2311yescharacteristic
132#3664—22no—
133#3663—22no—
134#3663—22no—
135C8×D9—22no—
136C8×D9D414yescomplemented
137C2×#468—91noSylow
138C2×D3×Q8—31no—
139C2×D3×D4—31no—
140C2×D3×D4—61no—
141C22×C4×D3—31no—
142C2×C3×SD16C2×D311yescharacteristic
143C2×C3×M16C2×D311yescharacteristic
144C3×C22⋊Q8C2×D311yescharacteristic
145C3×#121C2×D311yescharacteristic
146#946—31no—
147C2×#215—31no—
148#939—61no—
149#938—31no—
150C2×#214—31no—
151#930—31no—
152#924—31no—
153C2×#208—31no—
154D3×SD16—64no—
155D3×M16—64no—
156C2×#204—31no—
157C2×ΓL(1,𝔽25)—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×D3×C8—31no—
160C2×D3×C8—31no—
161#897—31no—
162#896—61no—
163#895—31no—
164D3×C4⋊C4—31no—
165D3×C4⋊C4—31no—
166D3×C4⋊C4—61no—
167#884—61no—
168D3×C22⋊C4—61no—
169D3×C22⋊C4—61no—
170#878—61no—
171C3×#107C2×D311yescharacteristic
172C3×#103C2×D311yescharacteristic
173C3×#102C2×D311yescharacteristic
174#835—31no—
175#832—31no—
176#821—31no—
177#818—31no—
178#816—31no—
179#810—31no—
180#809—31no—
181#807—31no—
182#807—31no—
183C23×C9—21no—
184C23×C9C2×D411yescharacteristic
185C22×D9—22no—
186C22×D9—22no—
187C22×D9—22no—
188C22×D9—21no—
189C22×D9—42no—
190C22×D9—42no—
191C22×D9—42no—
192C22×D9C2×D411yescharacteristic
193C22×D9C2×D411yescharacteristic
194Q8×C9—21no—
195Q8×C9—21no—
196D4×C9—21no—
197D4×C9—21no—
198D4×C9—42no—
199C2×C4×C9—21no—
200C2×C4×C9—21no—
201C2×C4×C9—21no—
202C2×C4×C9—21no—
203C2×C4×C9—21no—
204C2×C4×C9C2×D411yescharacteristic
205C2×C4×C9C2411yescharacteristic
206#611—42no—
207#611—42no—
208#611—42no—
209C2×Dic9—22no—
210C2×Dic9—21no—
211C2×Dic9—21no—
212C2×Dic9—21no—
213C2×Dic9C2×D411yescharacteristic
214C2×Dic9C2×D411yescharacteristic
215D36—21no—
216D36—21no—
217D36—42no—
218C4×D9—22no—
219C4×D9—21no—
220C4×D9—21no—
221C4×D9—22no—
222C4×D9—42no—
223C4×D9—42no—
224C4×D9—42no—
225C4×D9C2×D412yes—
226C4×D9#4112yes—
227Dic18—21no—
228Dic18—21no—
229Dic18—42no—
230C8×C9—21no—
231C8×C9C2×D412yescomplemented
232C9⋊C8—21no—
233C9⋊C8C2×D412yescomplemented
234C22×SD16—91no—
235C22×M16—91no—
236C2×C22⋊Q8—91no—
237C2×#121—91no—
238#468—91no—
239#468—91no—
240#468—91no—
241#468—91no—
242#468—91no—
243#468—91no—
244#468—91no—
245#468D911yescharacteristic, direct product factor
246C2×#107—91no—
247C2×#103—91no—
248C2×#102—91no—
249C23×D3—31no—
250C23×D3—61no—
251C2×C3×Q8C22×D311yescharacteristic
252C2×C3×D4—21no—
253C2×C3×D4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C2×#67—61no—
256C2×#67—61no—
257C2×#67—61no—
258C22×Dic3—31no—
259D3×Q8—62no—
260D3×Q8—62no—
261D3×D4—62no—
262D3×D4—62no—
263D3×D4—124no—
264C2×D12—31no—
265C2×D12—61no—
266C2×C4×D3—31no—
267C2×C4×D3—31no—
268C2×C4×D3—31no—
269C2×C4×D3—31no—
270C2×C4×D3—62no—
271C2×C4×D3—62no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×Dic6—31no—
276C2×Dic6—61no—
277C3×SD16—22no—
278C3×M16—22no—
279C2×C3×C8C22×D311yescharacteristic
280C2×C3×C8C22×D311yescharacteristic
281C3×C4⋊C4—21no—
282C3×C4⋊C4C22×D311yescharacteristic
283C3×C4⋊C4C22×D311yescharacteristic
284C3×C22⋊C4—21no—
285C3×C22⋊C4—21no—
286#217—61no—
287#217—61no—
288#215—62no—
289#214—62no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294C4⋊Dic3—31no—
295C4⋊Dic3—31no—
296C4⋊Dic3—61no—
297Dic3⋊C4—61no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301#208—62no—
302C2×C3⋊C8—31no—
303C2×C3⋊C8—31no—
304#204—62no—
305ΓL(1,𝔽25)—62no—
306ΓL(1,𝔽25)—62no—
307D3×C8—34no—
308D3×C8—62no—
309C22×C9—21no—
310C22×C9—21no—
311C22×C9—21no—
312C22×C9—41no—
313C22×C9—41no—
314C22×C9—41no—
315C22×C9C22×D411yescharacteristic
316C2×D9—21no—
317C2×D9—21no—
318C2×D9—21no—
319C2×D9—44no—
320C2×D9—41no—
321C2×D9—41no—
322C2×D9—41no—
323C2×D9—84no—
324C2×D9#12112yes—
325C2×D9AGL(1,ℤ/8)12yes—
326C2×D9#13712yes—
327C4×C9—21no—
328C4×C9—41no—
329C4×C9—41no—
330C4×C9—41no—
331C4×C9C22×D411yescharacteristic
332C4×C9C2×#4111yescharacteristic
333Dic9—21no—
334Dic9—41no—
335Dic9—41no—
336Dic9—41no—
337Dic9#12112yes—
338C22×Q8—91no—
339C22×D4—91no—
340C22×D4—181no—
341C23×C4—91no—
342C2×SD16—91no—
343C2×SD16—91no—
344C2×SD16—91no—
345C2×SD16—184no—
346C2×SD16C2×D911yescharacteristic, complemented
347C2×M16—91no—
348C2×M16—91no—
349C2×M16—91no—
350C2×M16—184no—
351C2×M16C2×D911yescharacteristic, complemented
352C22×C8—91no—
353C22×C8—91no—
354C22⋊Q8—91no—
355C22⋊Q8—91no—
356C22⋊Q8—91no—
357C22⋊Q8—181no—
358C22⋊Q8—181no—
359C22⋊Q8C2×D911yescharacteristic, complemented
360#121—91no—
361#121—91no—
362#121—91no—
363#121—181no—
364#121—181no—
365#121C2×D911yescharacteristic
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—181no—
369C2×C22⋊C4—181no—
370C2×C22⋊C4—181no—
371#107—91no—
372#107—91no—
373#107—91no—
374#107C2×D911yescharacteristic, complemented
375#103—91no—
376#103—91no—
377#103—91no—
378#103C2×D911yescharacteristic, complemented
379#102—91no—
380#102—91no—
381#102—91no—
382#102C2×D911yescharacteristic, complemented
383C23×C3—21no—
384C23×C3D3×D411yescharacteristic
385C22×D3—31no—
386C22×D3—31no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—61no—
391C22×D3—122no—
392C22×D3—122no—
393C22×D3—122no—
394C3×Q8—21no—
395C3×Q8—21no—
396C3×D4—21no—
397C3×D4—21no—
398C3×D4—42no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—122no—
407#67—122no—
408#67—122no—
409C2×Dic3—31no—
410C2×Dic3—31no—
411C2×Dic3—62no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415D12—61no—
416D12—61no—
417D12—122no—
418C4×D3—32no—
419C4×D3—32no—
420C4×D3—62no—
421C4×D3—62no—
422C4×D3—61no—
423C4×D3—61no—
424C4×D3—122no—
425C4×D3—122no—
426C4×D3—122no—
427Dic6—61no—
428Dic6—61no—
429Dic6—122no—
430C3×C8—21no—
431C3×C8D3×D412yes—
432C3⋊C8—32no—
433C3⋊C8—61no—
434C2×C9—41no—
435C2×C9—81no—
436C2×C9C2×#12111yescharacteristic
437C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
438C2×C9C2×#13711yescharacteristic
439D9—41no—
440D9—81no—
441D9#46814yesdirect product factor
442C24—91no—
443C24—181no—
444C2×Q8—91no—
445C2×Q8—181no—
446C2×Q8—182no—
447C2×Q8—182no—
448C2×Q8C22×D911yescharacteristic
449C2×D4—21no—
450C2×D4—91no—
451C2×D4—181no—
452C2×D4—182no—
453C2×D4—182no—
454C2×D4—181no—
455C2×D4—181no—
456C2×D4—181no—
457C2×D4—364no—
458C2×D4C22×D911yescharacteristic
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—182no—
465C22×C4—182no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4—181no—
469C22×C4C22×D911yescharacteristic
470SD16—22no—
471SD16—182no—
472SD16—182no—
473SD16—182no—
474M16—22no—
475M16—182no—
476M16—182no—
477M16—182no—
478C2×C8—91no—
479C2×C8—94no—
480C2×C8—91no—
481C2×C8—182no—
482C2×C8C22×D911yescharacteristic
483C2×C8C22×D911yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—91no—
486C4⋊C4—91no—
487C4⋊C4—181no—
488C4⋊C4—181no—
489C4⋊C4—181no—
490C4⋊C4—181no—
491C4⋊C4—181no—
492C4⋊C4C22×D911yescharacteristic
493C4⋊C4C22×D911yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C22⋊C4—181no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3C2×D3×D411yescharacteristic
509C2×D3—32no—
510C2×D3—32no—
511C2×D3—32no—
512C2×D3—61no—
513C2×D3—61no—
514C2×D3—61no—
515C2×D3—124no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—244no—
520C3×C4—21no—
521C3×C4—41no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4C2×D3×D411yescharacteristic
525C3×C4D3×#4111yescharacteristic
526Dic3—32no—
527Dic3—61no—
528Dic3—121no—
529Dic3—121no—
530Dic3—121no—
531C9C2×#46811yescharacteristic, complemented, Sylow
532C23—21no—
533C23—91no—
534C23—91no—
535C23—182no—
536C23—182no—
537C23—182no—
538C23—181no—
539C23—362no—
540C23—362no—
541C23—362no—
542C23D4×D911yescharacteristic
543Q8—21no—
544Q8—21no—
545Q8—181no—
546Q8—181no—
547Q8—362no—
548D4—21no—
549D4—21no—
550D4—42no—
551D4—181no—
552D4—181no—
553D4—362no—
554D4—362no—
555D4—362no—
556D4—362no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—91no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—91no—
566C2×C4—182no—
567C2×C4—182no—
568C2×C4—182no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—362no—
575C2×C4—362no—
576C2×C4—362no—
577C2×C4D4×D911yescharacteristic
578C2×C4C23×D911yescharacteristic
579C8—21no—
580C8—92no—
581C8—181no—
582C8D4×D912yescomplemented
583C2×C3—41no—
584C2×C3—81no—
585C2×C3D3×#12111yescharacteristic
586C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
587C2×C3D3×#13711yescharacteristic
588D3—34no—
589D3—121no—
590D3—241no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—92no—
598C22—92no—
599C22—92no—
600C22—181no—
601C22—181no—
602C22—181no—
603C22—364no—
604C22—361no—
605C22—361no—
606C22—361no—
607C22—724no—
608C22C2×D4×D911yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—92no—
614C4—181no—
615C4—361no—
616C4—361no—
617C4—361no—
618C4C2×D4×D911yescharacteristic
619C4#41×D911yescharacteristic
620C3D3×#46811yescharacteristic
621C2—41no—
622C2—81no—
623C2—94no—
624C2—361no—
625C2—721no—
626C2D9×#12111yescharacteristic
627C2D9×AGL(1,ℤ/8)11yescharacteristic
628C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#468C2
socleC22×C3C2×D3×D4
prime radicalD9×#121C2
hypercenter#468D9
hypocenterC9C2×#468
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D9C2semidirect
2. C2×M16×D9C2semidirect
3. D9×C22⋊Q8C2semidirect
5. C9×#468C2semidirect
6. #10588854C2semidirect
7. #10588816C2semidirect
8. #10588732C2semidirect
9. #10588718C2semidirect
10. #10588566C2semidirect
11. D9×#107C2semidirect
12. #10588492C2semidirect
13. D9×#103C2semidirect
14. #10588460C2semidirect
15. D9×#102C2semidirect
21. C2×C9×SD16C22semidirect
22. C2×C9×M16C22semidirect
23. C9×C22⋊Q8C22semidirect
25. #63508C22semidirect
26. C2×#3675C22semidirect
29. C2×#3672C22semidirect
31. #63486C22semidirect
32. C2×#3667C22semidirect
35. C2×#3664C22semidirect
36. C2×#3663C22semidirect
37. C2×#3663C22semidirect
40. #63459C22semidirect
50. C9×#107C22semidirect
51. C9×#103C22semidirect
52. C9×#102C22semidirect
53. #63395C22semidirect
54. #63392C22semidirect
55. #63380C22semidirect
56. #63378C22semidirect
57. #63376C22semidirect
58. #63369C22semidirect
59. #63368C22semidirect
60. #63366C22semidirect
61. #63366C22semidirect
136. C8×D9D4semidirect
231. C8×C9C2×D4semidirect
233. C9⋊C8C2×D4semidirect
245. #468D9direct (N × H)
346. C2×SD16C2×D9semidirect
351. C2×M16C2×D9semidirect
359. C22⋊Q8C2×D9semidirect
374. #107C2×D9semidirect
378. #103C2×D9semidirect
382. #102C2×D9semidirect
441. D9#468direct (N × H)
531. C9C2×#468semidirect
582. C8D4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D92
C2×M16×D92
D9×C22⋊Q82
D9×#1212
C9×#4682
#105888542
#105888162
#105887322
#105887182
#105885662
D9×#1072
#105884922
D9×#1032
#105884602
D9×#1022
D3×#4683