Finite Group Databasebeta

← #11904942

Subgroups — #11904942

Order 1152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#518C211yesmaximal, characteristic, complemented
2#10589906C211yesmaximal, characteristic
3C2×#63497C211yesmaximal, characteristic, complemented
4#10589666C214yesmaximal, complemented
5#10589658C214yesmaximal, complemented
6#10589643C214yesmaximal, complemented
7#10589640C214yesmaximal, complemented
8#10589633C214yesmaximal, complemented
9#10589597C214yesmaximal, complemented
10C2×#63448C211yesmaximal, characteristic, complemented
11#10589588C211yesmaximal, characteristic, complemented
12#10589585C211yesmaximal, characteristic, complemented
13C2×#63439C211yesmaximal, characteristic, complemented
14#85859—31nomaximal
15C22×D4×C9C2211yescharacteristic
16C22×#611C2211yescharacteristic
17C23×Dic9C2211yescharacteristic
18C4×D4×C9C2214yes—
19C4×D4×C9C2214yescomplemented
20C9×#117C2212yescomplemented
21C2×C9×C22⋊C4C2211yescharacteristic
22C2×C9×C22⋊C4C2211yescharacteristic
23C2×C9×C22⋊C4C2212yescomplemented
24#63515C2212yes—
25C2×#3676C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×#3676C2212yescomplemented
28#63501C2214yes—
29#63499C2212yes—
30#63497C2214yes—
31#63497C2212yes—
32#63497C2212yescomplemented
33#63497C2212yescomplemented
34#63491C2212yes—
35#63491C2214yescomplemented
36C4×#611C2214yescomplemented
37C4×#611C2214yescomplemented
38C2×(C2×D9)⋊C4C2212yescomplemented
39#63488C2214yescomplemented
40C2×C4⋊Dic9C2212yescomplemented
41#63486C2214yescomplemented
42#63486C2214yescomplemented
43C2×Dic9⋊C4C2212yescomplemented
44C2×Dic9⋊C4C2212yescomplemented
45C2×C4×Dic9C2212yescomplemented
46#63460C2214yescomplemented
47#63458C2214yescomplemented
48#63451C2214yescomplemented
49#63451C2214yescomplemented
50#63448C2214yes—
51#63448C2212yescomplemented
52#63448C2212yescomplemented
53#63447C2214yescomplemented
54#63445C2214yescomplemented
55#611⋊C4C2214yes—
56C22⋊C4×D9C2212yescomplemented
57#63441C2214yescomplemented
58#63441C2214yescomplemented
59#63440C2214yescomplemented
60#63440C2214yescomplemented
61#63439C2214yescomplemented
62#63439C2214yescomplemented
63#63439C2212yescomplemented
64#63438C2214yescomplemented
65#63434C2214yescomplemented
66#63432C2214yescomplemented
67C4×Dic18C2214yescomplemented
68C3×#518D311yescharacteristic
69#5804—31no—
70C2×#935—31no—
71#5564—34no—
72#5556—34no—
73#5541—34no—
74#5538—34no—
75#5531—34no—
76#5495—34no—
77C2×#886—31no—
78#5486—31no—
79#5483—31no—
80C2×#877—31no—
81C24×C9C2311yescharacteristic
82C24×C9C2311yescharacteristic
83C23×D9C2311yescharacteristic
84C2×D4×C9—24no—
85C2×D4×C9C2312yes—
86C2×D4×C9C2312yes—
87C22×C4×C9C2311yescharacteristic
88C22×C4×C9C2314yes—
89C22×C4×C9C2312yes—
90C22×C4×C9C2312yes—
91C2×#611—24no—
92C2×#611C2312yes—
93C2×#611C2312yes—
94C2×#611C2314yes—
95C22×Dic9—24no—
96C22×Dic9C2312yes—
97C22×Dic9C2311yescharacteristic
98C22×Dic9C2311yescharacteristic
99C22×Dic9C2311yescharacteristic
100C22×Dic9C2312yes—
101C22×Dic9C2312yes—
102C22×Dic9C2312yes—
103C2×C4×D9C2314yes—
104C2×Dic18C2314yes—
105C9×C4⋊C4C2314yes—
106C9×C22⋊C4C2312yes—
107C9×C22⋊C4C2312yes—
108C9×C22⋊C4C2312yes—
109C9×C22⋊C4C2312yes—
110C9×C22⋊C4C2314yes—
111C42×C9C2314yes—
112#3676C2314yes—
113#3676C2314yes—
114#3676C2312yes—
115#3676C2312yes—
116#3676C2314yes—
117#3676C2312yes—
118#3676C2312yes—
119(C2×D9)⋊C4C2314yes—
120(C2×D9)⋊C4C2314yes—
121(C2×D9)⋊C4C2314yes—
122(C2×D9)⋊C4C2314yes—
123C4⋊Dic9C2314yes—
124C4⋊Dic9C2314yes—
125C4⋊Dic9C2314yes—
126Dic9⋊C4C2314yes—
127Dic9⋊C4C2314yes—
128Dic9⋊C4C2314yes—
129Dic9⋊C4C2314yes—
130Dic9⋊C4C2314yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134C4×Dic9C2314yes—
135C4×Dic9C2314yes—
136C4×Dic9C2314yes—
137#3491—91noSylow
138C22×C3×D4C2×D311yescharacteristic
139C22×#67—31no—
140C23×Dic3—31no—
141C3×C4×D4C2×D314yes—
142C3×C4×D4C2×D314yes—
143C3×#117C2×D312yes—
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4C2×D312yes—
147#953—32no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—32no—
151#939—34no—
152#937—32no—
153#935—34no—
154#935—32no—
155#935—32no—
156#935—32no—
157#929—32no—
158#929—34no—
159C4×#67—34no—
160C4×#67—34no—
161C2×(C2×D3)⋊C4—32no—
162#926—34no—
163C2×C4⋊Dic3—32no—
164#924—34no—
165#924—34no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—32no—
168C2×C4×Dic3—32no—
169#898—34no—
170#896—34no—
171#889—34no—
172#889—34no—
173#886—34no—
174#886—32no—
175#886—32no—
176#885—34no—
177#883—34no—
178#67⋊C4—34no—
179D3×C22⋊C4—32no—
180#879—34no—
181#879—34no—
182#878—34no—
183#878—34no—
184#877—34no—
185#877—34no—
186#877—32no—
187#876—34no—
188#872—34no—
189#870—34no—
190C4×Dic6—34no—
191C23×C9—22no—
192C23×C9—42no—
193C23×C9—42no—
194C23×C9#4114yes—
195C23×C9C2412yes—
196C23×C9C2411yescharacteristic
197C23×C9C2411yescharacteristic
198C23×C9C2411yescharacteristic
199C22×D9—22no—
200C22×D9—42no—
201C22×D9C2412yes—
202D4×C9—24no—
203D4×C9—24no—
204C2×C4×C9—22no—
205C2×C4×C9—42no—
206C2×C4×C9—44no—
207C2×C4×C9—42no—
208C2×C4×C9C2414yes—
209C2×C4×C9C2412yes—
210C2×C4×C9C2414yes—
211#611—24no—
212#611—24no—
213#611—44no—
214C2×Dic9—24no—
215C2×Dic9—24no—
216C2×Dic9—22no—
217C2×Dic9—22no—
218C2×Dic9—22no—
219C2×Dic9—42no—
220C2×Dic9—42no—
221C2×Dic9C2412yes—
222C2×Dic9C2414yes—
223C2×Dic9C2412yes—
224C2×Dic9C2414yes—
225C2×Dic9C2412yes—
226C4×D9—44no—
227Dic18—44no—
228#552—94no—
229#552—94no—
230#551—94no—
231#551—94no—
232#543—91no—
233#539—94no—
234#534—91no—
235#529—94no—
236C2×#123—91no—
237C2×#123—91no—
238#518—91no—
239#518D911yescharacteristic, complemented
240C2×#117—91no—
241C24×C3C22×D311yescharacteristic
242C24×C3C22×D311yescharacteristic
243C23×D3—31no—
244C2×C3×D4—24no—
245C2×C3×D4C22×D312yes—
246C2×C3×D4C22×D312yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D314yes—
251C2×#67—32no—
252C2×#67—32no—
253C2×#67—34no—
254C2×#67—64no—
255C22×Dic3—32no—
256C22×Dic3—31no—
257C22×Dic3—32no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—64no—
263C2×C4×D3—34no—
264C2×Dic6—34no—
265C3×C4⋊C4C22×D314yes—
266C3×C22⋊C4C22×D312yes—
267C3×C22⋊C4C22×D312yes—
268C3×C22⋊C4C22×D312yes—
269C3×C22⋊C4C22×D312yes—
270C3×C22⋊C4C22×D314yes—
271C3×C42C22×D314yes—
272#217—32no—
273#217—32no—
274#217—32no—
275#217—32no—
276#217—34no—
277#217—34no—
278#217—34no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—34no—
282(C2×D3)⋊C4—34no—
283C4⋊Dic3—34no—
284C4⋊Dic3—34no—
285C4⋊Dic3—34no—
286Dic3⋊C4—34no—
287Dic3⋊C4—34no—
288Dic3⋊C4—34no—
289Dic3⋊C4—34no—
290Dic3⋊C4—34no—
291Dic3⋊C4—34no—
292Dic3⋊C4—34no—
293Dic3⋊C4—34no—
294C4×Dic3—34no—
295C4×Dic3—34no—
296C4×Dic3—34no—
297C22×C9—22no—
298C22×C9—22no—
299C22×C9—22no—
300C22×C9—22no—
301C22×C9—24no—
302C22×C9—44no—
303C22×C9—82no—
304C22×C9C2×#4112yes—
305C22×C9C2×#4112yes—
306C22×C9C2×#4112yes—
307C22×C9C2511yescharacteristic
308C2×D9—22no—
309C2×D9—24no—
310C2×D9—82no—
311C4×C9—22no—
312C4×C9—24no—
313C4×C9—24no—
314Dic9—22no—
315Dic9—22no—
316Dic9—22no—
317Dic9—24no—
318Dic9—24no—
319C22×D4—91no—
320C22×D4C2×D911yescharacteristic
321C23×C4—91no—
322#126—94no—
323#126—94no—
324#126—94no—
325#126—94no—
326#125—94no—
327#125—94no—
328#125—94no—
329#124—94no—
330#123—92no—
331#123—92no—
332#123—94no—
333#123—92no—
334#123—92no—
335#123—94no—
336#123—92no—
337#123—92no—
338#123—94no—
339#123—94no—
340C22⋊Q8—94no—
341C22⋊Q8—94no—
342C22⋊Q8—94no—
343C22⋊Q8—94no—
344C22⋊Q8—94no—
345#121—94no—
346#120—92no—
347#120—92no—
348C4×Q8—94no—
349C4×D4—94no—
350C4×D4—94no—
351C4×D4—94no—
352C4×D4C2×D914yes—
353C4×D4C2×D914yescomplemented
354#117—94no—
355#117—94no—
356#117—94no—
357#117—92no—
358#117—94no—
359#117C2×D912yescomplemented
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C22⋊C4—91no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4C2×D911yescharacteristic
369C2×C22⋊C4C2×D911yescharacteristic
370C2×C22⋊C4C2×D912yescomplemented
371C2×C42—92no—
372C23×C3—22no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3#23514yes—
376C23×C3C23×D312yes—
377C23×C3C23×D311yescharacteristic
378C23×C3C23×D311yescharacteristic
379C23×C3C23×D311yescharacteristic
380C22×D3—32no—
381C22×D3—62no—
382C22×D3—122no—
383C3×D4—24no—
384C3×D4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—42no—
387C2×C3×C4—44no—
388C2×C3×C4—42no—
389C2×C3×C4C23×D314yes—
390C2×C3×C4C23×D312yes—
391C2×C3×C4C23×D314yes—
392#67—64no—
393#67—64no—
394#67—124no—
395C2×Dic3—32no—
396C2×Dic3—34no—
397C2×Dic3—32no—
398C2×Dic3—34no—
399C2×Dic3—32no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C4×D3—124no—
408Dic6—124no—
409C2×C9—22no—
410C2×C9—22no—
411C2×C9—22no—
412C2×C9—42no—
413C2×C9C22×#4111yescharacteristic
414C2×C9#58512yes—
415D9—42no—
416C24—91no—
417C24C22×D911yescharacteristic
418C24C22×D911yescharacteristic
419C2×Q8—94no—
420C2×D4—24no—
421C2×D4—92no—
422C2×D4—92no—
423C2×D4—94no—
424C2×D4—184no—
425C2×D4C22×D912yes—
426C2×D4C22×D912yes—
427C22×C4—91no—
428C22×C4—92no—
429C22×C4—92no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—92no—
433C22×C4—92no—
434C22×C4—94no—
435C22×C4—184no—
436C22×C4C22×D911yescharacteristic
437C22×C4C22×D912yes—
438C22×C4C22×D912yes—
439C22×C4C22×D914yes—
440C4⋊C4—94no—
441C4⋊C4—94no—
442C4⋊C4—94no—
443C4⋊C4—94no—
444C4⋊C4—94no—
445C4⋊C4—94no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—94no—
449C4⋊C4—94no—
450C4⋊C4—94no—
451C4⋊C4C22×D914yes—
452C22⋊C4—92no—
453C22⋊C4—92no—
454C22⋊C4—92no—
455C22⋊C4—94no—
456C22⋊C4—92no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4C22×D912yes—
464C22⋊C4C22×D912yes—
465C22⋊C4C22×D912yes—
466C22⋊C4C22×D912yes—
467C22⋊C4C22×D914yes—
468C42—94no—
469C42—94no—
470C42—94no—
471C42C22×D914yes—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—24no—
477C22×C3—44no—
478C22×C3—82no—
479C22×C3C2×#23512yes—
480C22×C3C2×#23512yes—
481C22×C3C2×#23512yes—
482C22×C3C24×D311yescharacteristic
483C2×D3—62no—
484C2×D3—64no—
485C2×D3—242no—
486C3×C4—22no—
487C3×C4—24no—
488C3×C4—24no—
489Dic3—62no—
490Dic3—62no—
491Dic3—62no—
492Dic3—64no—
493Dic3—64no—
494C9#349111yescharacteristic, complemented, Sylow
495C23—22no—
496C23—42no—
497C23—42no—
498C23—92no—
499C23—182no—
500C23—362no—
501C23#369714yes—
502C23C23×D912yes—
503C23C23×D911yescharacteristic
504C23C23×D911yescharacteristic
505C23C23×D911yescharacteristic
506Q8—364no—
507D4—24no—
508D4—24no—
509D4—184no—
510D4—184no—
511D4—364no—
512C2×C4—22no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—92no—
517C2×C4—94no—
518C2×C4—92no—
519C2×C4—94no—
520C2×C4—92no—
521C2×C4—184no—
522C2×C4—184no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4—364no—
527C2×C4—362no—
528C2×C4—362no—
529C2×C4C23×D914yes—
530C2×C4C23×D912yes—
531C2×C4C23×D914yes—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—42no—
536C2×C3C22×#23511yescharacteristic
537C2×C3#596612yes—
538D3—122no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—24no—
544C22—44no—
545C22—82no—
546C22—182no—
547C22—184no—
548C22—722no—
549C22C2×#369712yes—
550C22C2×#369712yes—
551C22C2×#369712yes—
552C22C24×D911yescharacteristic
553C4—22no—
554C4—24no—
555C4—24no—
556C4—182no—
557C4—182no—
558C4—182no—
559C4—184no—
560C4—184no—
561C3#8585911yescharacteristic
562C2—22no—
563C2—22no—
564C2—22no—
565C2—42no—
566C2—362no—
567C2C22×#369711yescharacteristic
568C2#1059314112yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#518C2
prime radical#10589906C2
hypercenter#518D9
hypocenterC9#3491
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C9×#518C2semidirect
3. C2×#63497C2semidirect
4. #10589666C2semidirect
5. #10589658C2semidirect
6. #10589643C2semidirect
7. #10589640C2semidirect
8. #10589633C2semidirect
9. #10589597C2semidirect
10. C2×#63448C2semidirect
11. #10589588C2semidirect
12. #10589585C2semidirect
13. C2×#63439C2semidirect
19. C4×D4×C9C22semidirect
20. C9×#117C22semidirect
23. C2×C9×C22⋊C4C22semidirect
27. C2×#3676C22semidirect
32. #63497C22semidirect
33. #63497C22semidirect
35. #63491C22semidirect
36. C4×#611C22semidirect
37. C4×#611C22semidirect
38. C2×(C2×D9)⋊C4C22semidirect
39. #63488C22semidirect
40. C2×C4⋊Dic9C22semidirect
41. #63486C22semidirect
42. #63486C22semidirect
43. C2×Dic9⋊C4C22semidirect
44. C2×Dic9⋊C4C22semidirect
45. C2×C4×Dic9C22semidirect
46. #63460C22semidirect
47. #63458C22semidirect
48. #63451C22semidirect
49. #63451C22semidirect
51. #63448C22semidirect
52. #63448C22semidirect
53. #63447C22semidirect
54. #63445C22semidirect
56. C22⋊C4×D9C22semidirect
57. #63441C22semidirect
58. #63441C22semidirect
59. #63440C22semidirect
60. #63440C22semidirect
61. #63439C22semidirect
62. #63439C22semidirect
63. #63439C22semidirect
64. #63438C22semidirect
65. #63434C22semidirect
66. #63432C22semidirect
67. C4×Dic18C22semidirect
239. #518D9semidirect
353. C4×D4C2×D9semidirect
359. #117C2×D9semidirect
370. C2×C22⋊C4C2×D9semidirect
494. C9#3491semidirect

Maximal subgroups

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

subgroupindex
C9×#5182
#105899062
C2×#634972
#105896662
#105896582
#105896432
#105896402
#105896332
#105895972
C2×#634482
#105895882
#105895852
C2×#634392
#858593