Finite Group Databasebeta

← #11887200

Subgroups — #11887200

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589931C211yesmaximal, characteristic
2#10589631C211yesmaximal, characteristic, complemented
3C9×#416C211yesmaximal, characteristic, complemented
4#10588918C211yesmaximal, characteristic, complemented
5#10588795C211yesmaximal, characteristic, complemented
6C8×#611C211yesmaximal, characteristic, complemented
7#10588684C211yesmaximal, characteristic, complemented
8#10588493C211yesmaximal, characteristic, complemented
9#10588485C211yesmaximal, characteristic, complemented
10#10588480C211yesmaximal, characteristic, complemented
11#10588478C211yesmaximal, characteristic, complemented
12#10588456C211yesmaximal, characteristic, complemented
13D9×#102C211yesmaximal, characteristic, complemented
14#10588443C211yesmaximal, characteristic, complemented
15#10588438C211yesmaximal, characteristic, complemented
16#78845—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×D4×D9C2211yescharacteristic
19C22×C8×C9C2211yescharacteristic, complemented
20C9×#117C2211yescharacteristic, complemented
21#63509C2211yescharacteristic
22#63508C2211yescharacteristic
23C2×#3674C2211yescharacteristic, complemented
24#63501—21no—
25#63499—21no—
26D4×Dic9C2211yescharacteristic
27C2×#3672C2211yescharacteristic
28#63492C2211yescharacteristic
29#63491—21no—
30C4×#611C2211yescharacteristic
31C2×(C2×D9)⋊C4—21no—
32#63486C2211yescharacteristic, complemented
33C2×#3664C2211yescharacteristic
34C2×C8×D9C2211yescharacteristic
35#63459C2211yescharacteristic
36C4⋊C4×D9C2211yescharacteristic
37#63452C2211yescharacteristic, complemented
38#63449C2211yescharacteristic, complemented
39#63445—21no—
40#63441—21no—
41#63434—21no—
42#63432—21no—
43C9×#103C2211yescharacteristic, complemented
44C9×#103C2211yescharacteristic, complemented
45C9×#102C2211yescharacteristic
46C9×#102C2211yescharacteristic
47#63395C2211yescharacteristic, complemented
48#63392C2211yescharacteristic
49#63389C2211yescharacteristic, complemented
50#63380C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52#63377C2211yescharacteristic, complemented
53#63376C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55C8×Dic9C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63369C2211yescharacteristic
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5829—31no—
61#5529—31no—
62C3×#416D311yescharacteristic
63#5239—31no—
64#5114—31no—
65C8×#67—31no—
66#5003—31no—
67#4813—31no—
68#4805—31no—
69#4800—31no—
70#4798—31no—
71#4776—31no—
72D3×#102—31no—
73#4763—31no—
74#4758—31no—
75C23×D9—21no—
76C9×#41—22no—
77C9×#41—41no—
78C2×Q8×C9C2311yescharacteristic
79C2×D4×C9—21no—
80C2×D4×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9C2311yescharacteristic
83C2×#611—21no—
84C2×#611—21no—
85C2×#611D411yescharacteristic
86C22×Dic9—21no—
87D4×D9—22no—
88D4×D9—41no—
89C2×D36C2311yescharacteristic
90C2×C4×D9—21no—
91C2×C4×D9C2311yescharacteristic
92C2×Dic18C2311yescharacteristic
93C2×C8×C9—41no—
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C9×C4⋊C4C2311yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C22⋊C4—21no—
99C42×C9—21no—
100#3676—21no—
101#3676—21no—
102#3676D411yescharacteristic
103#3674—41no—
104#3672—22no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4D411yescharacteristic
111C4⋊Dic9—21no—
112C4⋊Dic9—21no—
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120Dic9⋊C4D411yescharacteristic
121C4×Dic9—21no—
122C4×Dic9C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125#3664—41no—
126C8×D9—41no—
127#3296—91noSylow
128C2×C3×#41C2×D311yescharacteristic
129C2×D3×D4—31no—
130C22×C3×C8C2×D311yescharacteristic
131C3×#117C2×D311yescharacteristic
132#947—31no—
133#946—31no—
134C2×#216—31no—
135#939—61no—
136#937—61no—
137D4×Dic3—31no—
138C2×#214—31no—
139#930—31no—
140#929—61no—
141C4×#67—31no—
142C2×(C2×D3)⋊C4—61no—
143#924—31no—
144C2×#204—31no—
145C2×D3×C8—31no—
146#897—31no—
147D3×C4⋊C4—31no—
148#890—31no—
149#887—31no—
150#883—61no—
151#879—61no—
152#872—61no—
153#870—61no—
154C3×#103C2×D311yescharacteristic
155C3×#103C2×D311yescharacteristic
156C3×#102C2×D311yescharacteristic
157C3×#102C2×D311yescharacteristic
158#835—31no—
159#832—31no—
160#830—31no—
161#821—31no—
162(C2×D3)⋊C8—31no—
163#817—31no—
164#816—31no—
165Dic3⋊C8—31no—
166C8×Dic3—31no—
167#809—31no—
168#809—31no—
169#808—31no—
170#807—31no—
171C23×C9—21no—
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174C22×D9—42no—
175C22×D9—42no—
176C22×D9—81no—
177C22×D9C2×D411yescharacteristic
178Q8×C9—21no—
179Q8×C9—21no—
180D4×C9—21no—
181D4×C9—42no—
182D4×C9#4112yes—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—42no—
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2411yescharacteristic
191#611—22no—
192#611—42no—
193#611—81no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—81no—
198C2×Dic9C2×D411yescharacteristic
199C2×Dic9C2×D411yescharacteristic
200C2×Dic9C2×D411yescharacteristic
201D36—21no—
202D36—21no—
203C4×D9—21no—
204C4×D9—21no—
205C4×D9—42no—
206Dic18—21no—
207Dic18—21no—
208C8×C9—21no—
209C8×C9—21no—
210C9⋊C8—21no—
211C9⋊C8—21no—
212#552—91no—
213#546—91no—
214#488—91no—
215#483—91no—
216#482—91no—
217#478—91no—
218#467—91no—
219#465—91no—
220#464—91no—
221#452—91no—
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416D911yescharacteristic, complemented
226C2×#102—91no—
227C23×D3—61no—
228C3×#41—22no—
229C3×#41—41no—
230C2×C3×Q8C22×D311yescharacteristic
231C2×C3×D4—21no—
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—31no—
236C2×#67—61no—
237C2×#67—61no—
238C22×Dic3—61no—
239D3×D4—62no—
240D3×D4—121no—
241C2×D12—31no—
242C2×C4×D3—31no—
243C2×C4×D3—61no—
244C2×Dic6—31no—
245C2×C3×C8—41no—
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C22⋊C4—21no—
251C3×C42—21no—
252#217—31no—
253#217—61no—
254#217—61no—
255#216—121no—
256#214—62no—
257(C2×D3)⋊C4—31no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267Dic3⋊C4—31no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273C4×Dic3—31no—
274C4×Dic3—61no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277#204—121no—
278D3×C8—121no—
279C22×C9—22no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—21no—
283C22×C9—41no—
284C22×C9—41no—
285C22×C9C22×D411yescharacteristic
286C2×D9—21no—
287C2×D9—21no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—84no—
292C2×D9#13512yes—
293C4×C9—21no—
294C4×C9—41no—
295C4×C9—41no—
296C4×C9—41no—
297C4×C9C2×#4111yescharacteristic
298C4×C9H(5,𝔽2)11yescharacteristic
299Dic9—21no—
300Dic9—21no—
301Dic9—21no—
302Dic9—41no—
303Dic9—41no—
304Dic9—41no—
305C2×#41C2×D911yescharacteristic
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C22×C8—91no—
311C22×C8C2×D911yescharacteristic, complemented
312#126—181no—
313#125—91no—
314#125—181no—
315#124—91no—
316#123—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8—91no—
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8—91no—
325C4×D4—91no—
326C4×D4—91no—
327#117—181no—
328#117C2×D911yescharacteristic, complemented
329C2×C4⋊C4—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106—91no—
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103C2×D911yescharacteristic, complemented
338#103C2×D911yescharacteristic, complemented
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×D911yescharacteristic
344#102C2×D911yescharacteristic
345C22⋊C8—91no—
346C22⋊C8—91no—
347C4×C8—91no—
348C23×C3—21no—
349C23×C3D3×D411yescharacteristic
350C22×D3—31no—
351C22×D3—61no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—241no—
355C3×Q8—21no—
356C3×Q8—21no—
357C3×D4—21no—
358C3×D4—42no—
359C3×D4#23512yes—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—42no—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368#67—62no—
369#67—122no—
370#67—241no—
371C2×Dic3—31no—
372C2×Dic3—31no—
373C2×Dic3—31no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—241no—
378D12—61no—
379D12—61no—
380C4×D3—61no—
381C4×D3—61no—
382C4×D3—122no—
383Dic6—61no—
384Dic6—61no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—42no—
390C2×C9—41no—
391C2×C9#54611yescharacteristic
392C2×C9C2×#13511yescharacteristic
393C2×C9#57711yescharacteristic
394D9—22no—
395D9—81no—
396C24—181no—
397#41—22no—
398#41—41no—
399C2×Q8—91no—
400C2×Q8C22×D911yescharacteristic
401C2×D4—21no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—361no—
408C2×D4C22×D911yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×D911yescharacteristic
414Q16—361no—
415SD16—182no—
416SD16—361no—
417C2×C8—41no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—361no—
421C2×C8C22×D911yescharacteristic
422C2×C8C22×D911yescharacteristic
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4C22×D911yescharacteristic
434C4⋊C4C22×D911yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—91no—
437C22⋊C4—91no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C42—21no—
446C42—91no—
447C42—181no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3C2×D3×D411yescharacteristic
455C2×D3—32no—
456C2×D3—61no—
457C2×D3—61no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—244no—
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4C2×#23511yescharacteristic
467C3×C4#100411yescharacteristic
468Dic3—61no—
469Dic3—61no—
470Dic3—61no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474C9#329611yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—181no—
478C23—362no—
479C23—362no—
480C23—721no—
481C23D4×D911yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—181no—
485Q8—181no—
486D4—21no—
487D4—42no—
488D4—182no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—721no—
493D4#369712yes—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—91no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4—721no—
510C2×C4D4×D911yescharacteristic
511C2×C4C23×D911yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—42no—
517C2×C3—41no—
518C2×C3#549011yescharacteristic
519C2×C3D3×#13511yescharacteristic
520C2×C3#577011yescharacteristic
521D3—62no—
522D3—241no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—92no—
530C22—181no—
531C22—181no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22—724no—
536C22C2×D4×D911yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—181no—
542C4—181no—
543C4—181no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4C2×#369711yescharacteristic
548C4#6371011yescharacteristic
549C3#7884511yescharacteristic
550C2—41no—
551C2—42no—
552C2—182no—
553C2—721no—
554C2#1058959211yescharacteristic
555C2D9×#13511yescharacteristic
556C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#416C2
socleC22×C3C2×D3×D4
prime radical#10589931C2
hypercenter#416D9
hypocenterC9#3296
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #10589631C2semidirect
3. C9×#416C2semidirect
4. #10588918C2semidirect
5. #10588795C2semidirect
6. C8×#611C2semidirect
7. #10588684C2semidirect
8. #10588493C2semidirect
9. #10588485C2semidirect
10. #10588480C2semidirect
11. #10588478C2semidirect
12. #10588456C2semidirect
13. D9×#102C2semidirect
14. #10588443C2semidirect
15. #10588438C2semidirect
19. C22×C8×C9C22semidirect
20. C9×#117C22semidirect
23. C2×#3674C22semidirect
32. #63486C22semidirect
37. #63452C22semidirect
38. #63449C22semidirect
43. C9×#103C22semidirect
44. C9×#103C22semidirect
47. #63395C22semidirect
49. #63389C22semidirect
52. #63377C22semidirect
53. #63376C22semidirect
54. Dic9⋊C8C22semidirect
55. C8×Dic9C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
225. #416D9semidirect
311. C22×C8C2×D9semidirect
328. #117C2×D9semidirect
337. #103C2×D9semidirect
338. #103C2×D9semidirect
474. C9#3296semidirect

Maximal subgroups

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

subgroupindex
#105899312
#105896312
C9×#4162
#105889182
#105887952
C8×#6112
#105886842
#105884932
#105884852
#105884802
#105884782
#105884562
D9×#1022
#105884432
#105884382
#788453