Finite Group Databasebeta

← #11904951

Subgroups — #11904951

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
1C2×C9×#123C211yesmaximal, characteristic, complemented
2#10589906C211yesmaximal, characteristic
3#10589900C211yesmaximal, characteristic, complemented
4C2×#63491C211yesmaximal, characteristic, complemented
5C2×#63488C211yesmaximal, characteristic, complemented
6#10589767C214yesmaximal, complemented
7#10589760C214yesmaximal, complemented
8#10589752C214yesmaximal, complemented
9#10589751C214yesmaximal, complemented
10#10589615C214yesmaximal, complemented
11#10589597C214yesmaximal, complemented
12#10589588C211yesmaximal, characteristic, complemented
13#10589585C211yesmaximal, characteristic, complemented
14#86001—31nomaximal
15C22×D4×C9C2211yescharacteristic
16C23×C4×C9C2211yescharacteristic
17C22×#611C2211yescharacteristic
18C9×#123C2214yes—
19C9×#123C2212yescomplemented
20C9×#123C2212yescomplemented
21C2×C9×C4⋊C4C2212yescomplemented
22C2×C9×C22⋊C4C2211yescharacteristic
23C2×C9×C22⋊C4C2212yescomplemented
24#63515C2212yes—
25C2×#3676C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×#3676C2211yescharacteristic
28C2×#3676C2212yescomplemented
29#63501C2214yes—
30#63499C2212yes—
31#63497C2212yes—
32D4×Dic9C2214yes—
33D4×Dic9C2214yescomplemented
34#63491C2214yes—
35#63491C2212yes—
36#63491C2212yescomplemented
37#63491C2212yescomplemented
38C4×#611C2214yes—
39C2×(C2×D9)⋊C4C2212yescomplemented
40#63488C2214yescomplemented
41#63488C2214yescomplemented
42#63488C2212yescomplemented
43C2×C4⋊Dic9C2212yescomplemented
44#63486C2214yescomplemented
45C2×Dic9⋊C4C2212yescomplemented
46C2×C4×Dic9C2212yescomplemented
47#63460C2214yescomplemented
48#63460C2214yescomplemented
49#63459C2214yescomplemented
50#63454C2214yescomplemented
51#63452C2214yescomplemented
52#63451C2214yescomplemented
53#63451C2214yescomplemented
54#63449C2214yescomplemented
55#63448C2214yescomplemented
56#63447C2214yescomplemented
57#63445C2214yescomplemented
58#611⋊C4C2214yescomplemented
59#611⋊C4C2214yescomplemented
60C22⋊C4×D9C2212yescomplemented
61#63441C2214yescomplemented
62#63441C2214yescomplemented
63#63440C2214yescomplemented
64#63440C2214yescomplemented
65#63440C2214yescomplemented
66#63439C2214yescomplemented
67#63439C2212yescomplemented
68C2×C3×#123D311yescharacteristic
69#5804—31no—
70#5798—31no—
71C2×#929—31no—
72C2×#926—31no—
73#5665—34no—
74#5658—34no—
75#5650—34no—
76#5649—34no—
77#5513—34no—
78#5495—34no—
79#5486—31no—
80#5483—31no—
81C24×C9C2311yescharacteristic
82C24×C9C2311yescharacteristic
83C23×D9C2311yescharacteristic
84C2×D4×C9—24no—
85C2×D4×C9C2312yes—
86C2×D4×C9C2312yes—
87C22×C4×C9—24no—
88C22×C4×C9C2312yes—
89C22×C4×C9C2312yes—
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2312yes—
94C2×#611—24no—
95C2×#611C2312yes—
96C2×#611C2312yes—
97C2×#611C2314yes—
98C22×Dic9C2311yescharacteristic
99C22×Dic9C2312yes—
100C22×Dic9C2314yes—
101C22×Dic9C2312yes—
102C22×Dic9C2312yes—
103C2×C4×D9C2314yes—
104C2×Dic18C2314yes—
105C9×C4⋊C4C2314yes—
106C9×C4⋊C4C2314yes—
107C9×C22⋊C4C2312yes—
108C9×C22⋊C4C2312yes—
109C9×C22⋊C4C2314yes—
110C9×C22⋊C4C2314yes—
111#3676C2312yes—
112#3676C2312yes—
113#3676C2312yes—
114#3676C2312yes—
115#3676C2312yes—
116#3676C2312yes—
117#3676C2314yes—
118#3676C2314yes—
119(C2×D9)⋊C4C2314yes—
120(C2×D9)⋊C4C2314yes—
121(C2×D9)⋊C4C2314yes—
122(C2×D9)⋊C4C2314yes—
123C4⋊Dic9C2314yes—
124C4⋊Dic9C2314yes—
125C4⋊Dic9C2314yes—
126C4⋊Dic9C2314yes—
127Dic9⋊C4C2314yes—
128Dic9⋊C4C2314yes—
129Dic9⋊C4C2314yes—
130Dic9⋊C4C2314yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133C4×Dic9C2314yes—
134C4×Dic9C2314yes—
135C4×Dic9C2314yes—
136C4×Dic9C2314yes—
137#3491—91noSylow
138C22×C3×D4C2×D311yescharacteristic
139C23×C3×C4C2×D311yescharacteristic
140C22×#67—31no—
141C3×#123C2×D314yes—
142C3×#123C2×D312yes—
143C3×#123C2×D312yes—
144C2×C3×C4⋊C4C2×D312yes—
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4C2×D312yes—
147#953—32no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—32no—
152#939—34no—
153#937—32no—
154#935—32no—
155D4×Dic3—34no—
156D4×Dic3—34no—
157#929—34no—
158#929—32no—
159#929—32no—
160#929—32no—
161C4×#67—34no—
162C2×(C2×D3)⋊C4—32no—
163#926—34no—
164#926—34no—
165#926—32no—
166C2×C4⋊Dic3—32no—
167#924—34no—
168C2×Dic3⋊C4—32no—
169C2×C4×Dic3—32no—
170#898—34no—
171#898—34no—
172#897—34no—
173#892—34no—
174#890—34no—
175#889—34no—
176#889—34no—
177#887—34no—
178#886—34no—
179#885—34no—
180#883—34no—
181#67⋊C4—34no—
182#67⋊C4—34no—
183D3×C22⋊C4—32no—
184#879—34no—
185#879—34no—
186#878—34no—
187#878—34no—
188#878—34no—
189#877—34no—
190#877—32no—
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—24no—
205C2×C4×C9—24no—
206C2×C4×C9—22no—
207C2×C4×C9—22no—
208C2×C4×C9—22no—
209C2×C4×C9—42no—
210C2×C4×C9C2412yes—
211C2×C4×C9C2412yes—
212C2×C4×C9C2414yes—
213C2×C4×C9C2412yes—
214#611—24no—
215#611—24no—
216#611—44no—
217C2×Dic9—22no—
218C2×Dic9—42no—
219C2×Dic9—44no—
220C2×Dic9—42no—
221C2×Dic9—42no—
222C2×Dic9C2414yes—
223C2×Dic9C2412yes—
224C2×Dic9C2414yes—
225C2×Dic9C2414yes—
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×#123D911yescharacteristic, complemented
238#518—91no—
239#518—91no—
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×C4—24no—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D312yes—
254C2×#67—32no—
255C2×#67—32no—
256C2×#67—34no—
257C2×#67—64no—
258C22×Dic3—31no—
259C22×Dic3—34no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—32no—
263C2×C4×D3—34no—
264C2×Dic6—34no—
265C3×C4⋊C4C22×D314yes—
266C3×C4⋊C4C22×D314yes—
267C3×C22⋊C4C22×D312yes—
268C3×C22⋊C4C22×D314yes—
269C3×C22⋊C4C22×D312yes—
270C3×C22⋊C4C22×D314yes—
271#217—34no—
272#217—32no—
273#217—32no—
274#217—32no—
275#217—34no—
276#217—32no—
277#217—32no—
278#217—32no—
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—
286C4⋊Dic3—34no—
287Dic3⋊C4—34no—
288Dic3⋊C4—34no—
289Dic3⋊C4—34no—
290Dic3⋊C4—34no—
291Dic3⋊C4—34no—
292Dic3⋊C4—34no—
293C4×Dic3—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—22no—
313C4×C9—22no—
314C4×C9—24no—
315Dic9—22no—
316Dic9—24no—
317Dic9—24no—
318Dic9—24no—
319C22×D4—91no—
320C22×D4C2×D911yescharacteristic
321C23×C4C2×D911yescharacteristic
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—92no—
333#123—94no—
334#123—92no—
335#123—94no—
336#123—94no—
337#123C2×D914yes—
338#123C2×D912yescomplemented
339#123C2×D912yescomplemented
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×D4—94no—
353C4×D4—94no—
354#117—94no—
355#117—94no—
356#117—92no—
357#117—94no—
358#117—92no—
359#117—94no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4C2×D912yescomplemented
363C2×C22⋊C4—91no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4C2×D911yescharacteristic
370C2×C22⋊C4C2×D912yescomplemented
371C2×C42—92no—
372C23×C3—22no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3#23714yes—
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—24no—
386C2×C3×C4—24no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—42no—
391C2×C3×C4C23×D312yes—
392C2×C3×C4C23×D312yes—
393C2×C3×C4C23×D314yes—
394C2×C3×C4C23×D312yes—
395#67—64no—
396#67—64no—
397#67—124no—
398C2×Dic3—34no—
399C2×Dic3—32no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—124no—
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—24no—
428C22×C4—91no—
429C22×C4—92no—
430C22×C4—92no—
431C22×C4—92no—
432C22×C4—94no—
433C22×C4—94no—
434C22×C4C22×D911yescharacteristic
435C22×C4C22×D912yes—
436C22×C4C22×D912yes—
437C22×C4C22×D911yescharacteristic
438C22×C4C22×D911yescharacteristic
439C22×C4C22×D912yes—
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⋊C4C22×D914yes—
451C4⋊C4C22×D914yes—
452C22⋊C4—92no—
453C22⋊C4—92no—
454C22⋊C4—92no—
455C22⋊C4—92no—
456C22⋊C4—92no—
457C22⋊C4—92no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4C22×D912yes—
465C22⋊C4C22×D912yes—
466C22⋊C4C22×D914yes—
467C22⋊C4C22×D914yes—
468C42—94no—
469C42—94no—
470C42—94no—
471C42—94no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—24no—
477C22×C3—44no—
478C22×C3—82no—
479C22×C3C2×#23712yes—
480C22×C3C2×#23712yes—
481C22×C3C2×#23712yes—
482C22×C3C24×D311yescharacteristic
483C2×D3—62no—
484C2×D3—64no—
485C2×D3—242no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—24no—
490Dic3—62no—
491Dic3—64no—
492Dic3—64no—
493Dic3—64no—
494C9#349111yescharacteristic, complemented, Sylow
495C23—22no—
496C23—42no—
497C23—42no—
498C23—92no—
499C23—182no—
500C23—362no—
501C23#369914yes—
502C23C23×D912yes—
503C23C23×D911yescharacteristic
504C23C23×D911yescharacteristic
505C23C23×D911yescharacteristic
506Q8—364no—
507D4—24no—
508D4—24no—
509D4—184no—
510D4—184no—
511D4—364no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—94no—
519C2×C4—94no—
520C2×C4—92no—
521C2×C4—94no—
522C2×C4—182no—
523C2×C4—364no—
524C2×C4—362no—
525C2×C4—364no—
526C2×C4—362no—
527C2×C4—362no—
528C2×C4C23×D912yes—
529C2×C4C23×D912yes—
530C2×C4C23×D914yes—
531C2×C4C23×D912yes—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—42no—
536C2×C3C22×#23711yescharacteristic
537C2×C3#596412yes—
538D3—122no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—24no—
544C22—44no—
545C22—82no—
546C22—182no—
547C22—184no—
548C22—722no—
549C22C2×#369912yes—
550C22C2×#369912yes—
551C22C2×#369912yes—
552C22C24×D911yescharacteristic
553C4—22no—
554C4—22no—
555C4—22no—
556C4—24no—
557C4—182no—
558C4—184no—
559C4—184no—
560C4—184no—
561C3#8600111yescharacteristic
562C2—22no—
563C2—22no—
564C2—22no—
565C2—42no—
566C2—362no—
567C2C22×#369911yescharacteristic
568C2#1059313912yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC2×C9×#123C2
prime radical#10589906C2
hypercenterC2×#123D9
hypocenterC9#3491
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C9×#123C2semidirect
3. #10589900C2semidirect
4. C2×#63491C2semidirect
5. C2×#63488C2semidirect
6. #10589767C2semidirect
7. #10589760C2semidirect
8. #10589752C2semidirect
9. #10589751C2semidirect
10. #10589615C2semidirect
11. #10589597C2semidirect
12. #10589588C2semidirect
13. #10589585C2semidirect
19. C9×#123C22semidirect
20. C9×#123C22semidirect
21. C2×C9×C4⋊C4C22semidirect
23. C2×C9×C22⋊C4C22semidirect
28. C2×#3676C22semidirect
33. D4×Dic9C22semidirect
36. #63491C22semidirect
37. #63491C22semidirect
39. C2×(C2×D9)⋊C4C22semidirect
40. #63488C22semidirect
41. #63488C22semidirect
42. #63488C22semidirect
43. C2×C4⋊Dic9C22semidirect
44. #63486C22semidirect
45. C2×Dic9⋊C4C22semidirect
46. C2×C4×Dic9C22semidirect
47. #63460C22semidirect
48. #63460C22semidirect
49. #63459C22semidirect
50. #63454C22semidirect
51. #63452C22semidirect
52. #63451C22semidirect
53. #63451C22semidirect
54. #63449C22semidirect
55. #63448C22semidirect
56. #63447C22semidirect
57. #63445C22semidirect
58. #611⋊C4C22semidirect
59. #611⋊C4C22semidirect
60. C22⋊C4×D9C22semidirect
61. #63441C22semidirect
62. #63441C22semidirect
63. #63440C22semidirect
64. #63440C22semidirect
65. #63440C22semidirect
66. #63439C22semidirect
67. #63439C22semidirect
237. C2×#123D9semidirect
338. #123C2×D9semidirect
339. #123C2×D9semidirect
362. C2×C4⋊C4C2×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
C2×C9×#1232
#105899062
#105899002
C2×#634912
C2×#634882
#105897672
#105897602
#105897522
#105897512
#105896152
#105895972
#105895882
#105895852
#860013