Finite Group Databasebeta

← #11885792

Subgroups — #11885792

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#546C211yesmaximal, characteristic, complemented
2C2×#63513C211yesmaximal, characteristic, complemented
3C22×#3673C211yesmaximal, characteristic, complemented
4#10589652C211yesmaximal, characteristic, complemented
5#10588919C211yesmaximal, characteristic, complemented
6#10588897C211yesmaximal, characteristic, complemented
7#10588740C211yesmaximal, characteristic, complemented
8#10588738C211yesmaximal, characteristic, complemented
9#10588729C211yesmaximal, characteristic, complemented
10#10588727C211yesmaximal, characteristic, complemented
11#10588721C211yesmaximal, characteristic, complemented
12#10588720C211yesmaximal, characteristic, complemented
13#10588699C211yesmaximal, characteristic, complemented
14C4×#3673C211yesmaximal, characteristic, complemented
15D4×C9⋊C8C211yesmaximal, characteristic, complemented
16#83505—31nomaximal
17C2×C9×#41C2211yescharacteristic, complemented
18C22×D4×C9C2211yescharacteristic
19C2×#3697C2211yescharacteristic, complemented
20C22×D36C2211yescharacteristic
21C9×#124C2211yescharacteristic, complemented
22C9×#123—21no—
23C9×C22⋊Q8C2211yescharacteristic
24C9×#121—21no—
25C9×#121C2211yescharacteristic, complemented
26C9×#120—21no—
27C4×D4×C9C2211yescharacteristic
28C4×D4×C9C2211yescharacteristic, complemented
29C2×C9×C22⋊C4—21no—
30#63513—24no—
31C2×#3675C2211yescharacteristic, complemented
32C2×#3675C2211yescharacteristic, complemented
33C2×#3674C2211yescharacteristic, complemented
34#63499—21no—
35C2×#3673—24no—
36C2×#3673C2211yescharacteristic
37C2×#3673C2211yescharacteristic
38C2×#3673C2211yescharacteristic
39C2×#3673C2211yescharacteristic
40C2×#3672C2211yescharacteristic, complemented
41C2×#3672C2211yescharacteristic, complemented
42#63492C2211yescharacteristic, complemented
43#63486C2211yescharacteristic
44C22×C9⋊C8C2211yescharacteristic
45C22×C9⋊C8C2211yescharacteristic, complemented
46#63456—21no—
47#63446—21no—
48C22⋊C4×D9—21no—
49#63437C2211yescharacteristic, complemented
50C4×D36C2211yescharacteristic, complemented
51#63395C2211yescharacteristic, complemented
52#63392C2211yescharacteristic, complemented
53#63392C2211yescharacteristic, complemented
54#63389C2211yescharacteristic
55#63389C2211yescharacteristic, complemented
56#63369C2211yescharacteristic, complemented
57#63369C2211yescharacteristic, complemented
58#63368C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60C4⋊(C9⋊C8)C2211yescharacteristic, complemented
61C4×C9⋊C8C2211yescharacteristic, complemented
62C3×#546D311yescharacteristic
63C2×#950—31no—
64C22×#213—31no—
65#5550—31no—
66#5238—31no—
67#5218—31no—
68#5059—31no—
69#5057—31no—
70#5051—31no—
71#5046—31no—
72#5038—31no—
73#5037—31no—
74#5016—31no—
75C4×#213—31no—
76D4×C3⋊C8—31no—
77C24×C9—21no—
78C23×D9—21no—
79C9×#41—22no—
80C9×#41—41no—
81C2×Q8×C9C2311yescharacteristic
82C2×D4×C9—22no—
83C2×D4×C9—21no—
84C2×D4×C9—21no—
85C2×D4×C9—21no—
86C2×D4×C9—41no—
87C2×D4×C9D411yescharacteristic
88C2×D4×C9C2311yescharacteristic
89C2×D4×C9C2311yescharacteristic
90C22×C4×C9—21no—
91C22×C4×C9—21no—
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2311yescharacteristic
94C2×#611—21no—
95C2×#611—21no—
96#3697—22no—
97#3697—41no—
98C2×D36—22no—
99C2×D36—21no—
100C2×D36—41no—
101C2×D36C2311yescharacteristic
102C2×D36C2311yescharacteristic
103C2×C4×D9—21no—
104C2×C4×D9—21no—
105C2×Dic18C2311yescharacteristic
106C9×C4⋊C4—21no—
107C9×C4⋊C4D411yescharacteristic
108C9×C4⋊C4C2311yescharacteristic
109C9×C22⋊C4—21no—
110C9×C22⋊C4—21no—
111C9×C22⋊C4—21no—
112C9×C22⋊C4—21no—
113C9×C22⋊C4—21no—
114C9×C22⋊C4D411yescharacteristic
115C9×C22⋊C4D411yescharacteristic
116C42×C9C2311yescharacteristic
117#3676—21no—
118#3675—22no—
119#3675—41no—
120#3674—22no—
121#3673—22no—
122#3673—22no—
123#3673—22no—
124#3673D414yescomplemented
125#3672—22no—
126#3672—41no—
127(C2×D9)⋊C4—21no—
128(C2×D9)⋊C4—21no—
129(C2×D9)⋊C4—21no—
130(C2×D9)⋊C4—21no—
131C4⋊Dic9C2311yescharacteristic
132Dic9⋊C4—21no—
133C2×C9⋊C8—22no—
134C2×C9⋊C8—22no—
135C2×C9⋊C8C2311yescharacteristic
136C2×C9⋊C8C2311yescharacteristic
137C2×C9⋊C8C2311yescharacteristic
138C2×C9⋊C8C2311yescharacteristic
139#3280—91noSylow
140C2×C3×#41C2×D311yescharacteristic
141C22×C3×D4C2×D311yescharacteristic
142C2×#235—31no—
143C22×D12—31no—
144C3×#124C2×D311yescharacteristic
145C3×#123—21no—
146C3×C22⋊Q8C2×D311yescharacteristic
147C3×#121—21no—
148C3×#121C2×D311yescharacteristic
149C3×#120—21no—
150C3×C4×D4C2×D311yescharacteristic
151C3×C4×D4C2×D311yescharacteristic
152C2×C3×C22⋊C4—21no—
153#950—64no—
154C2×#216—31no—
155C2×#215—31no—
156C2×#215—31no—
157#937—61no—
158C2×#214—31no—
159C2×#214—31no—
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—64no—
165#930—31no—
166#924—31no—
167C22×C3⋊C8—31no—
168C22×C3⋊C8—31no—
169#894—61no—
170#884—61no—
171D3×C22⋊C4—61no—
172#875—31no—
173C4×D12—31no—
174#835—31no—
175#832—31no—
176#832—31no—
177#830—31no—
178#830—31no—
179#810—31no—
180#809—31no—
181#809—31no—
182#807—31no—
183C4⋊(C3⋊C8)—31no—
184C4×C3⋊C8—31no—
185C23×C9—21no—
186C23×C9—21no—
187C23×C9—42no—
188C23×C9—42no—
189C23×C9—81no—
190C23×C9C2×D411yescharacteristic
191C23×C9C2×D411yescharacteristic
192C22×D9—21no—
193C22×D9—21no—
194C22×D9—42no—
195C22×D9—42no—
196C22×D9—81no—
197Q8×C9—21no—
198Q8×C9—21no—
199D4×C9—22no—
200D4×C9—21no—
201D4×C9—21no—
202D4×C9—21no—
203D4×C9—42no—
204D4×C9—42no—
205D4×C9—81no—
206D4×C9C2×D412yes—
207C2×C4×C9—21no—
208C2×C4×C9—21no—
209C2×C4×C9—21no—
210C2×C4×C9—21no—
211C2×C4×C9—21no—
212C2×C4×C9—21no—
213C2×C4×C9—42no—
214C2×C4×C9—81no—
215C2×C4×C9C2×D411yescharacteristic
216C2×C4×C9C2×D411yescharacteristic
217C2×C4×C9C2×D411yescharacteristic
218C2×C4×C9C2×D411yescharacteristic
219C2×C4×C9C2411yescharacteristic
220#611—42no—
221#611—81no—
222C2×Dic9—21no—
223C2×Dic9—21no—
224D36—21no—
225D36—21no—
226D36—21no—
227D36—42no—
228D36C2×D412yes—
229C4×D9—42no—
230C4×D9—81no—
231Dic18—21no—
232Dic18—21no—
233C9⋊C8—21no—
234C9⋊C8—21no—
235C9⋊C8—21no—
236C9⋊C8C2×D412yes—
237C2×#135—91no—
238C22×D8—91no—
239#546—91no—
240#546D911yescharacteristic, complemented
241#495—91no—
242#467—91no—
243#466—91no—
244#463—91no—
245#463—91no—
246#450—91no—
247#450—91no—
248#449—91no—
249#449—91no—
250C4×D8—91no—
251C8×D4—91no—
252C24×C3—21no—
253C23×D3—61no—
254C3×#41—22no—
255C3×#41—41no—
256C2×C3×Q8C22×D311yescharacteristic
257C2×C3×D4—22no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—41no—
262C2×C3×D4#6711yescharacteristic
263C2×C3×D4C22×D311yescharacteristic
264C2×C3×D4C22×D311yescharacteristic
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C22×D311yescharacteristic
269C2×#67—61no—
270C2×#67—61no—
271#235—62no—
272#235—121no—
273C2×D12—31no—
274C2×D12—31no—
275C2×D12—62no—
276C2×D12—61no—
277C2×D12—121no—
278C2×C4×D3—61no—
279C2×C4×D3—61no—
280C2×Dic6—31no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4#6711yescharacteristic
283C3×C4⋊C4C22×D311yescharacteristic
284C3×C22⋊C4—21no—
285C3×C22⋊C4—21no—
286C3×C22⋊C4—21no—
287C3×C22⋊C4—21no—
288C3×C22⋊C4—21no—
289C3×C22⋊C4#6711yescharacteristic
290C3×C22⋊C4#6711yescharacteristic
291C3×C42C22×D311yescharacteristic
292#217—61no—
293#216—62no—
294#215—62no—
295#215—121no—
296#214—62no—
297#214—121no—
298#213—34no—
299#213—62no—
300#213—62no—
301#213—62no—
302(C2×D3)⋊C4—61no—
303(C2×D3)⋊C4—61no—
304(C2×D3)⋊C4—61no—
305(C2×D3)⋊C4—61no—
306C4⋊Dic3—31no—
307Dic3⋊C4—61no—
308C2×C3⋊C8—31no—
309C2×C3⋊C8—31no—
310C2×C3⋊C8—31no—
311C2×C3⋊C8—31no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8—62no—
314C22×C9—21no—
315C22×C9—21no—
316C22×C9—21no—
317C22×C9—22no—
318C22×C9—21no—
319C22×C9—21no—
320C22×C9—41no—
321C22×C9—41no—
322C22×C9—41no—
323C22×C9—41no—
324C22×C9—41no—
325C22×C9—84no—
326C22×C9#13512yescomplemented
327C22×C9C22×D411yescharacteristic
328C2×D9—22no—
329C2×D9—41no—
330C2×D9—41no—
331C2×D9—41no—
332C2×D9—41no—
333C2×D9—41no—
334C2×D9—84no—
335C4×C9—21no—
336C4×C9—21no—
337C4×C9—21no—
338C4×C9—21no—
339C4×C9—41no—
340C4×C9—41no—
341C4×C9C22×D411yescharacteristic
342C4×C9H(5,𝔽2)11yescharacteristic
343Dic9—41no—
344Dic9—41no—
345C2×#41—91no—
346C2×#41C2×D911yescharacteristic, complemented
347C22×D4—91no—
348C22×D4C2×D911yescharacteristic
349#135—184no—
350C2×Q16—91no—
351C2×SD16—91no—
352C2×SD16—91no—
353C2×SD16—91no—
354C2×SD16—91no—
355C2×D8—91no—
356C2×D8—91no—
357C2×D8—91no—
358C2×D8—91no—
359C2×D8—184no—
360C22×C8—91no—
361C22×C8—91no—
362#124—91no—
363#124C2×D911yescharacteristic, complemented
364#123—21no—
365#123—181no—
366C22⋊Q8—91no—
367C22⋊Q8C2×D911yescharacteristic
368#121—21no—
369#121—91no—
370#121—181no—
371#121C2×D911yescharacteristic, complemented
372#120—21no—
373#120—181no—
374C4×D4—91no—
375C4×D4C2×D911yescharacteristic
376C4×D4C2×D911yescharacteristic, complemented
377C2×C22⋊C4—21no—
378C2×C22⋊C4—181no—
379#107—91no—
380C4⋊C8—91no—
381#103—91no—
382#103—91no—
383#102—91no—
384#102—91no—
385#102—91no—
386#102—91no—
387C22⋊C8—91no—
388C22⋊C8—91no—
389C4×C8—91no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—81no—
395C23×C3C2×#6711yescharacteristic
396C23×C3C2×#6711yescharacteristic
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—122no—
400C22×D3—122no—
401C22×D3—241no—
402C3×Q8—21no—
403C3×Q8—21no—
404C3×D4—22no—
405C3×D4—21no—
406C3×D4—21no—
407C3×D4—21no—
408C3×D4—42no—
409C3×D4—42no—
410C3×D4—81no—
411C3×D4D3×D412yes—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—42no—
419C2×C3×C4—81no—
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—122no—
426#67—241no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429D12—32no—
430D12—61no—
431D12—61no—
432D12—61no—
433D12—122no—
434C4×D3—122no—
435C4×D3—241no—
436Dic6—61no—
437Dic6—61no—
438C3⋊C8—32no—
439C3⋊C8—61no—
440C3⋊C8—61no—
441C3⋊C8—61no—
442C2×C9—22no—
443C2×C9—41no—
444C2×C9—42no—
445C2×C9—81no—
446C2×C9D4211yescharacteristic
447C2×C9C2×#13511yescharacteristic
448C2×C9#57611yescharacteristic
449D9—42no—
450D9—81no—
451C24—21no—
452C24—181no—
453#41—22no—
454#41—41no—
455#41—182no—
456#41—361no—
457C2×Q8—91no—
458C2×Q8C22×D911yescharacteristic
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—91no—
465C2×D4—91no—
466C2×D4—182no—
467C2×D4—181no—
468C2×D4—181no—
469C2×D4—181no—
470C2×D4—361no—
471C2×D4#61111yescharacteristic
472C2×D4C22×D911yescharacteristic
473C2×D4C22×D911yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—181no—
477C22×C4—181no—
478C22×C4C22×D911yescharacteristic
479C22×C4C22×D911yescharacteristic
480Q16—182no—
481SD16—182no—
482SD16—182no—
483SD16—361no—
484SD16—361no—
485D8—94no—
486D8—182no—
487D8—182no—
488D8—182no—
489C2×C8—91no—
490C2×C8—91no—
491C2×C8—91no—
492C2×C8—91no—
493C2×C8—182no—
494C2×C8—182no—
495C4⋊C4—21no—
496C4⋊C4—91no—
497C4⋊C4—181no—
498C4⋊C4#61111yescharacteristic
499C4⋊C4C22×D911yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—181no—
506C22⋊C4—181no—
507C22⋊C4—181no—
508C22⋊C4—181no—
509C22⋊C4—181no—
510C22⋊C4#61111yescharacteristic
511C22⋊C4#61111yescharacteristic
512C42C22×D911yescharacteristic
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—84no—
525C22×C3#95012yes—
526C22×C3C22×#6711yescharacteristic
527C2×D3—62no—
528C2×D3—121no—
529C2×D3—121no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—244no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—41no—
539C3×C4—41no—
540C3×C4C2×D3×D411yescharacteristic
541C3×C4#100411yescharacteristic
542Dic3—121no—
543Dic3—121no—
544C9#328011yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—42no—
548C23—42no—
549C23—81no—
550C23—181no—
551C23—181no—
552C23—362no—
553C23—362no—
554C23—721no—
555C23C2×#61111yescharacteristic
556C23C2×#61111yescharacteristic
557Q8—21no—
558Q8—21no—
559Q8—181no—
560Q8—181no—
561D4—22no—
562D4—21no—
563D4—21no—
564D4—21no—
565D4—42no—
566D4—42no—
567D4—81no—
568D4—92no—
569D4—181no—
570D4—181no—
571D4—181no—
572D4—362no—
573D4—362no—
574D4—721no—
575D4D4×D912yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—42no—
583C2×C4—81no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—362no—
587C2×C4—721no—
588C2×C4C2×#61111yescharacteristic
589C2×C4C2×#61111yescharacteristic
590C2×C4C2×#61111yescharacteristic
591C2×C4C2×#61111yescharacteristic
592C2×C4C23×D911yescharacteristic
593C8—92no—
594C8—181no—
595C8—181no—
596C8—181no—
597C2×C3—22no—
598C2×C3—41no—
599C2×C3—42no—
600C2×C3—81no—
601C2×C3D4×#6711yescharacteristic
602C2×C3C2×#95011yescharacteristic
603C2×C3#583511yescharacteristic
604D3—122no—
605D3—241no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—22no—
610C22—21no—
611C22—21no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—84no—
618C22—182no—
619C22—361no—
620C22—361no—
621C22—361no—
622C22—361no—
623C22—361no—
624C22—724no—
625C22#6351312yescomplemented
626C22C22×#61111yescharacteristic
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—41no—
632C4—41no—
633C4—361no—
634C4—361no—
635C4C2×D4×D911yescharacteristic
636C4#6371011yescharacteristic
637C3#8350511yescharacteristic
638C2—22no—
639C2—41no—
640C2—42no—
641C2—81no—
642C2—362no—
643C2—721no—
644C2D4×#61111yescharacteristic
645C2C2×#6351311yescharacteristic
646C2#1058993711yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#546C2
socleC22×C3C22×#67
hypercenter#546D9
hypocenterC9#3280
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C9×#546C2semidirect
2. C2×#63513C2semidirect
3. C22×#3673C2semidirect
4. #10589652C2semidirect
5. #10588919C2semidirect
6. #10588897C2semidirect
7. #10588740C2semidirect
8. #10588738C2semidirect
9. #10588729C2semidirect
10. #10588727C2semidirect
11. #10588721C2semidirect
12. #10588720C2semidirect
13. #10588699C2semidirect
14. C4×#3673C2semidirect
15. D4×C9⋊C8C2semidirect
17. C2×C9×#41C22semidirect
19. C2×#3697C22semidirect
21. C9×#124C22semidirect
25. C9×#121C22semidirect
28. C4×D4×C9C22semidirect
31. C2×#3675C22semidirect
32. C2×#3675C22semidirect
33. C2×#3674C22semidirect
40. C2×#3672C22semidirect
41. C2×#3672C22semidirect
42. #63492C22semidirect
45. C22×C9⋊C8C22semidirect
49. #63437C22semidirect
50. C4×D36C22semidirect
51. #63395C22semidirect
52. #63392C22semidirect
53. #63392C22semidirect
55. #63389C22semidirect
56. #63369C22semidirect
57. #63369C22semidirect
58. #63368C22semidirect
59. #63366C22semidirect
60. C4⋊(C9⋊C8)C22semidirect
61. C4×C9⋊C8C22semidirect
124. #3673D4semidirect
240. #546D9semidirect
326. C22×C9#135semidirect
346. C2×#41C2×D9semidirect
363. #124C2×D9semidirect
371. #121C2×D9semidirect
376. C4×D4C2×D9semidirect
544. C9#3280semidirect
625. C22#63513semidirect

Maximal subgroups

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

subgroupindex
C9×#5462
C2×#635132
C22×#36732
#105896522
#105889192
#105888972
#105887402
#105887382
#105887292
#105887272
#105887212
#105887202
#105886992
C4×#36732
D4×C9⋊C82
#835053