Finite Group Databasebeta

← #11867109

Subgroups — #11867109

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63476C211yesmaximal, characteristic, complemented
2C2×M16×D9C211yesmaximal, characteristic, complemented
3#10589729C211yesmaximal, characteristic, complemented
4D9×#121C211yesmaximal, characteristic, complemented
5C9×#468C211yesmaximal, characteristic, complemented
6#10588851C211yesmaximal, characteristic, complemented
7#10588817C211yesmaximal, characteristic, complemented
8#10588732C211yesmaximal, characteristic, complemented
9#10588722C211yesmaximal, characteristic, complemented
10#10588563C211yesmaximal, characteristic, complemented
11#10588561C211yesmaximal, characteristic, complemented
12#10588487C211yesmaximal, characteristic, complemented
13#10588483C211yesmaximal, characteristic, complemented
14#10588455C211yesmaximal, characteristic, complemented
15#10588450C211yesmaximal, characteristic, complemented
16#80805—31nomaximal
17C2×#3701C2211yescharacteristic
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×#3673C2211yescharacteristic, complemented
30#63492C2211yescharacteristic
31#63492C2211yescharacteristic, complemented
32C2×#3667C2211yescharacteristic, complemented
33#63476—24no—
34M16×D9—24no—
35C2×D72C2211yescharacteristic, complemented
36C2×#3663C2211yescharacteristic
37C2×#3663C2211yescharacteristic
38C2×C8×D9C2211yescharacteristic, complemented
39C2×C8×D9C2211yescharacteristic, complemented
40#63457C2211yescharacteristic
41#63457C2211yescharacteristic, complemented
42#63456—21no—
43#63455—21no—
44#63454C2211yescharacteristic
45C4⋊C4×D9C2211yescharacteristic
46#63446—21no—
47#63444—21no—
48#611⋊C4—21no—
49C22⋊C4×D9—21no—
50C9×#107C2211yescharacteristic, complemented
51C9×#103C2211yescharacteristic, complemented
52C9×#102C2211yescharacteristic, complemented
53#63395C2211yescharacteristic, complemented
54#63392C2211yescharacteristic, complemented
55#63380C2211yescharacteristic, complemented
56#63380C2211yescharacteristic, complemented
57#63377C2211yescharacteristic, complemented
58#63369C2211yescharacteristic, complemented
59#63369C2211yescharacteristic, complemented
60#63367C2211yescharacteristic, complemented
61#63366C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×D3×M16—31no—
64#5627—31no—
65D3×#121—31no—
66C3×#468D311yescharacteristic
67#5171—31no—
68#5135—31no—
69#5049—31no—
70#5039—31no—
71#4883—31no—
72#4881—31no—
73#4807—31no—
74#4803—31no—
75#4775—31no—
76#4770—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—
86C2×#611—21no—
87C22×Dic9D411yescharacteristic
88#3701—22no—
89#3701—22no—
90D4×D9—22no—
91D4×D9—22no—
92D4×D9—44no—
93C2×D36—21no—
94C2×D36—21no—
95C2×D36—21no—
96C2×D36C2311yescharacteristic
97C2×D36C2311yescharacteristic
98C2×C4×D9—22no—
99C2×C4×D9—22no—
100C2×C4×D9—21no—
101C2×C4×D9—21no—
102C2×C4×D9D411yescharacteristic
103C2×C4×D9D411yescharacteristic
104C2×C4×D9C2311yescharacteristic
105C2×C4×D9C2311yescharacteristic
106C9×SD16—22no—
107C9×M16—22no—
108C2×C8×C9C2311yescharacteristic
109C2×C8×C9C2311yescharacteristic
110C9×C4⋊C4—21no—
111C9×C4⋊C4C2311yescharacteristic
112C9×C4⋊C4C2311yescharacteristic
113C9×C22⋊C4—21no—
114C9×C22⋊C4—21no—
115#3676—21no—
116#3675—22no—
117#3673—22no—
118(C2×D9)⋊C4—21no—
119(C2×D9)⋊C4—21no—
120(C2×D9)⋊C4—21no—
121(C2×D9)⋊C4—21no—
122(C2×D9)⋊C4—21no—
123(C2×D9)⋊C4—21no—
124C4⋊Dic9C2311yescharacteristic
125C4⋊Dic9C2311yescharacteristic
126Dic9⋊C4—21no—
127Dic9⋊C4—21no—
128C4×Dic9—21no—
129#3667—22no—
130C2×C9⋊C8C2311yescharacteristic
131C2×C9⋊C8C2311yescharacteristic
132D72—22no—
133#3663—22no—
134#3663D414yescomplemented
135C8×D9—22no—
136C8×D9—22no—
137#3055—91noSylow
138C2×#239—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×#213—31no—
151#930—31no—
152#930—31no—
153C2×#208—31no—
154#914—64no—
155D3×M16—64no—
156C2×D24—31no—
157C2×ΓL(1,𝔽25)—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×D3×C8—31no—
160C2×D3×C8—31no—
161#895—31no—
162#895—31no—
163#894—61no—
164#893—61no—
165#892—31no—
166D3×C4⋊C4—31no—
167#884—61no—
168#882—61no—
169#67⋊C4—61no—
170D3×C22⋊C4—61no—
171C3×#107C2×D311yescharacteristic
172C3×#103C2×D311yescharacteristic
173C3×#102C2×D311yescharacteristic
174#835—31no—
175#832—31no—
176#821—31no—
177#821—31no—
178#817—31no—
179#809—31no—
180#809—31no—
181#808—31no—
182#807—31no—
183C23×C9—21no—
184C23×C9C2×D411yescharacteristic
185C22×D9—22no—
186C22×D9—22no—
187C22×D9—21no—
188C22×D9—21no—
189C22×D9—41no—
190C22×D9—42no—
191C22×D9—42no—
192C22×D9—42no—
193C22×D9C2×D411yescharacteristic
194C22×D9C2×D411yescharacteristic
195Q8×C9—21no—
196Q8×C9—21no—
197D4×C9—21no—
198D4×C9—21no—
199D4×C9—42no—
200C2×C4×C9—21no—
201C2×C4×C9—21no—
202C2×C4×C9—21no—
203C2×C4×C9—21no—
204C2×C4×C9—21no—
205C2×C4×C9C2×D411yescharacteristic
206C2×C4×C9C2411yescharacteristic
207#611—42no—
208#611—42no—
209#611—42no—
210#611—42no—
211C2×Dic9—22no—
212C2×Dic9—21no—
213C2×Dic9—21no—
214C2×Dic9C2×D411yescharacteristic
215C2×Dic9C2×D411yescharacteristic
216D36—21no—
217D36—21no—
218D36—21no—
219D36—21no—
220D36—42no—
221D36—42no—
222D36—42no—
223C4×D9—22no—
224C4×D9—21no—
225C4×D9—21no—
226C4×D9—22no—
227C4×D9—42no—
228C4×D9—42no—
229C4×D9C2×D412yes—
230C4×D9#4112yes—
231C8×C9—21no—
232C8×C9C2×D412yescomplemented
233C9⋊C8—21no—
234C9⋊C8C2×D412yescomplemented
235C2×AGL(1,ℤ/8)—91no—
236C22×M16—91no—
237#525—91no—
238C2×#121—91no—
239#469—91no—
240#469—91no—
241#468—91no—
242#468D911yescharacteristic, complemented
243#466—91no—
244#466—91no—
245#465—91no—
246#465—91no—
247#428—91no—
248#418—91no—
249#417—91no—
250C23×D3—31no—
251C23×D3—61no—
252C2×C3×Q8C22×D311yescharacteristic
253C2×C3×D4—21no—
254C2×C3×D4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—61no—
257C2×#67—61no—
258C2×#67—61no—
259C2×#67—61no—
260C22×Dic3—31no—
261#239—62no—
262#239—62no—
263D3×D4—62no—
264D3×D4—62no—
265D3×D4—124no—
266C2×D12—31no—
267C2×D12—31no—
268C2×D12—61no—
269C2×D12—61no—
270C2×D12—61no—
271C2×C4×D3—31no—
272C2×C4×D3—31no—
273C2×C4×D3—31no—
274C2×C4×D3—31no—
275C2×C4×D3—62no—
276C2×C4×D3—62no—
277C2×C4×D3—61no—
278C2×C4×D3—61no—
279C3×SD16—22no—
280C3×M16—22no—
281C2×C3×C8C22×D311yescharacteristic
282C2×C3×C8C22×D311yescharacteristic
283C3×C4⋊C4—21no—
284C3×C4⋊C4C22×D311yescharacteristic
285C3×C4⋊C4C22×D311yescharacteristic
286C3×C22⋊C4—21no—
287C3×C22⋊C4—21no—
288#217—61no—
289#215—62no—
290#213—62no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297C4⋊Dic3—31no—
298C4⋊Dic3—31no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301C4×Dic3—61no—
302#208—62no—
303C2×C3⋊C8—31no—
304C2×C3⋊C8—31no—
305D24—62no—
306ΓL(1,𝔽25)—34no—
307ΓL(1,𝔽25)—62no—
308D3×C8—62no—
309D3×C8—62no—
310C22×C9—21no—
311C22×C9—21no—
312C22×C9—21no—
313C22×C9—41no—
314C22×C9—41no—
315C22×C9—41no—
316C22×C9C22×D411yescharacteristic
317C2×D9—21no—
318C2×D9—21no—
319C2×D9—21no—
320C2×D9—21no—
321C2×D9—44no—
322C2×D9—41no—
323C2×D9—41no—
324C2×D9—41no—
325C2×D9—41no—
326C2×D9—41no—
327C2×D9—41no—
328C2×D9—84no—
329C2×D9#12112yes—
330C2×D9AGL(1,ℤ/8)12yescomplemented
331C4×C9—21no—
332C4×C9—41no—
333C4×C9—41no—
334C4×C9—41no—
335C4×C9C22×D411yescharacteristic
336C4×C9C2×#4111yescharacteristic
337Dic9—21no—
338Dic9—41no—
339Dic9—41no—
340Dic9#12112yes—
341C2×#41—91no—
342C22×D4—91no—
343C22×D4—181no—
344C23×C4—91no—
345AGL(1,ℤ/8)—184no—
346C2×SD16—91no—
347C2×SD16C2×D911yescharacteristic, complemented
348C2×D8—91no—
349C2×D8—91no—
350C2×M16—91no—
351C2×M16—91no—
352C2×M16—91no—
353C2×M16—184no—
354C2×M16C2×D911yescharacteristic, complemented
355C22×C8—91no—
356C22×C8—91no—
357#123—181no—
358C22⋊Q8—91no—
359C22⋊Q8C2×D911yescharacteristic, complemented
360#121—91no—
361#121—91no—
362#121—91no—
363#121—91no—
364#121—91no—
365#121—181no—
366#121—181no—
367#121C2×D911yescharacteristic
368#120—181no—
369C4×D4—181no—
370C4×D4—181no—
371#117—91no—
372C2×C4⋊C4—91no—
373C2×C22⋊C4—181no—
374#107—91no—
375#107C2×D911yescharacteristic, complemented
376#106—91no—
377#106—91no—
378#103—91no—
379#103C2×D911yescharacteristic, complemented
380#102—91no—
381#102—91no—
382#102—91no—
383#102—91no—
384#102—91no—
385#102C2×D911yescharacteristic, complemented
386C23×C3—21no—
387C23×C3D3×D411yescharacteristic
388C22×D3—31no—
389C22×D3—31no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—122no—
395C22×D3—121no—
396C22×D3—122no—
397C22×D3—122no—
398C3×Q8—21no—
399C3×Q8—21no—
400C3×D4—21no—
401C3×D4—21no—
402C3×D4—42no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—122no—
411#67—122no—
412#67—122no—
413#67—122no—
414C2×Dic3—31no—
415C2×Dic3—31no—
416C2×Dic3—62no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419D12—61no—
420D12—61no—
421D12—61no—
422D12—61no—
423D12—122no—
424D12—122no—
425D12—122no—
426C4×D3—32no—
427C4×D3—32no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—61no—
431C4×D3—61no—
432C4×D3—122no—
433C4×D3—122no—
434C3×C8—21no—
435C3×C8D3×D412yes—
436C3⋊C8—32no—
437C3⋊C8—61no—
438C2×C9—41no—
439C2×C9—81no—
440C2×C9C2×#12111yescharacteristic
441C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
442C2×C9#57511yescharacteristic
443D9—22no—
444D9—22no—
445D9—81no—
446D9—81no—
447C24—91no—
448C24—181no—
449#41—182no—
450#41—182no—
451C2×Q8C22×D911yescharacteristic
452C2×D4—21no—
453C2×D4—91no—
454C2×D4—91no—
455C2×D4—181no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—182no—
459C2×D4—182no—
460C2×D4—181no—
461C2×D4—181no—
462C2×D4—181no—
463C2×D4—181no—
464C2×D4—364no—
465C2×D4C22×D911yescharacteristic
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—91no—
471C22×C4—182no—
472C22×C4—182no—
473C22×C4—181no—
474C22×C4—181no—
475C22×C4C22×D911yescharacteristic
476SD16—22no—
477SD16—182no—
478D8—182no—
479D8—182no—
480M16—22no—
481M16—94no—
482M16—182no—
483M16—182no—
484C2×C8—91no—
485C2×C8—91no—
486C2×C8—182no—
487C2×C8—182no—
488C2×C8C22×D911yescharacteristic
489C2×C8C22×D911yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—91no—
492C4⋊C4—91no—
493C4⋊C4—181no—
494C4⋊C4—181no—
495C4⋊C4C22×D911yescharacteristic
496C4⋊C4C22×D911yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C22⋊C4—181no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C42—181no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3C2×D3×D411yescharacteristic
514C2×D3—32no—
515C2×D3—32no—
516C2×D3—61no—
517C2×D3—61no—
518C2×D3—61no—
519C2×D3—61no—
520C2×D3—124no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—244no—
528C3×C4—21no—
529C3×C4—41no—
530C3×C4—41no—
531C3×C4—41no—
532C3×C4C2×D3×D411yescharacteristic
533C3×C4D3×#4111yescharacteristic
534Dic3—32no—
535Dic3—61no—
536Dic3—121no—
537Dic3—121no—
538C9#305511yescharacteristic, complemented, Sylow
539C23—21no—
540C23—91no—
541C23—91no—
542C23—182no—
543C23—182no—
544C23—181no—
545C23—181no—
546C23—361no—
547C23—362no—
548C23—362no—
549C23—362no—
550C23D4×D911yescharacteristic
551Q8—21no—
552Q8—21no—
553D4—21no—
554D4—21no—
555D4—42no—
556D4—181no—
557D4—181no—
558D4—181no—
559D4—181no—
560D4—362no—
561D4—362no—
562D4—362no—
563D4—362no—
564D4—362no—
565D4—362no—
566D4—362no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—91no—
573C2×C4—92no—
574C2×C4—92no—
575C2×C4—91no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—362no—
584C2×C4—362no—
585C2×C4D4×D911yescharacteristic
586C2×C4C23×D911yescharacteristic
587C8—21no—
588C8—92no—
589C8—181no—
590C8D4×D912yescomplemented
591C2×C3—41no—
592C2×C3—81no—
593C2×C3D3×#12111yescharacteristic
594C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
595C2×C3#577711yescharacteristic
596D3—62no—
597D3—62no—
598D3—241no—
599D3—241no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—92no—
607C22—92no—
608C22—181no—
609C22—181no—
610C22—181no—
611C22—181no—
612C22—364no—
613C22—361no—
614C22—361no—
615C22—361no—
616C22—361no—
617C22—361no—
618C22—361no—
619C22—724no—
620C22C2×D4×D911yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—92no—
626C4—181no—
627C4—361no—
628C4—361no—
629C4C2×D4×D911yescharacteristic
630C4#41×D911yescharacteristic
631C3#8080511yescharacteristic
632C2—41no—
633C2—81no—
634C2—182no—
635C2—182no—
636C2—721no—
637C2—721no—
638C2D9×#12111yescharacteristic
639C2D9×AGL(1,ℤ/8)11yescharacteristic
640C2#1058987911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#468C2
socleC22×C3C2×D3×D4
hypercenter#468D9
hypocenterC9#3055
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×#63476C2semidirect
2. C2×M16×D9C2semidirect
3. #10589729C2semidirect
4. D9×#121C2semidirect
5. C9×#468C2semidirect
6. #10588851C2semidirect
7. #10588817C2semidirect
8. #10588732C2semidirect
9. #10588722C2semidirect
10. #10588563C2semidirect
11. #10588561C2semidirect
12. #10588487C2semidirect
13. #10588483C2semidirect
14. #10588455C2semidirect
15. #10588450C2semidirect
21. C2×C9×SD16C22semidirect
22. C2×C9×M16C22semidirect
23. C9×C22⋊Q8C22semidirect
25. #63508C22semidirect
26. C2×#3675C22semidirect
29. C2×#3673C22semidirect
31. #63492C22semidirect
32. C2×#3667C22semidirect
35. C2×D72C22semidirect
38. C2×C8×D9C22semidirect
39. C2×C8×D9C22semidirect
41. #63457C22semidirect
50. C9×#107C22semidirect
51. C9×#103C22semidirect
52. C9×#102C22semidirect
53. #63395C22semidirect
54. #63392C22semidirect
55. #63380C22semidirect
56. #63380C22semidirect
57. #63377C22semidirect
58. #63369C22semidirect
59. #63369C22semidirect
60. #63367C22semidirect
61. #63366C22semidirect
134. #3663D4semidirect
232. C8×C9C2×D4semidirect
234. C9⋊C8C2×D4semidirect
242. #468D9semidirect
330. C2×D9AGL(1,ℤ/8)semidirect
347. C2×SD16C2×D9semidirect
354. C2×M16C2×D9semidirect
359. C22⋊Q8C2×D9semidirect
375. #107C2×D9semidirect
379. #103C2×D9semidirect
385. #102C2×D9semidirect
538. C9#3055semidirect
590. C8D4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#634762
C2×M16×D92
#105897292
D9×#1212
C9×#4682
#105888512
#105888172
#105887322
#105887222
#105885632
#105885612
#105884872
#105884832
#105884552
#105884502
#808053