Finite Group Databasebeta

← #11910347

Subgroups — #11910347

Order 1152.

1587 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#532C211yesmaximal, characteristic, complemented
2#10589934C212yesmaximal, complemented
3#10589930C212yesmaximal, complemented
4#10589837C212yesmaximal, complemented
5#10589822C212yesmaximal, complemented
6#10589786C212yesmaximal, complemented
7#10589785C211yesmaximal, characteristic, complemented
8#10589774C211yesmaximal, characteristic, complemented
9#10589723C214yesmaximal, complemented
10#10589722C214yesmaximal, complemented
11#10589649C214yesmaximal, complemented
12#10589640C214yesmaximal, complemented
13#10589581C212yesmaximal, complemented
14#86248—31nomaximal
15C2×C9×#41C2211yescharacteristic
16C2×C9×#41C2211yescharacteristic, complemented
17C2×#3697C2212yes—
18C22×C4×D9C2212yescomplemented
19C9×C4⋊Q8C2211yescharacteristic, complemented
20C9×#127C2211yescharacteristic
21C9×#124C2211yescharacteristic
22C9×#124C2211yescharacteristic, complemented
23C9×#121C2214yescomplemented
24C4×D4×C9C2214yescomplemented
25C2×C42×C9C2211yescharacteristic, complemented
26#63509C2212yes—
27#63508C2214yescomplemented
28#63506C2212yescomplemented
29#63502C2212yes—
30#63501C2214yes—
31#63501C2214yes—
32#63501C2214yescomplemented
33#63501C2214yescomplemented
34#63500C2214yes—
35#63499C2212yes—
36#63499C2212yescomplemented
37#63499C2214yescomplemented
38#63498C2212yescomplemented
39#63497C2212yes—
40#63497C2212yescomplemented
41#63497C2214yescomplemented
42#63492C2212yes—
43#63491C2214yescomplemented
44C4×#611C2214yes—
45C4×#611C2214yescomplemented
46C4×#611C2214yescomplemented
47#63488C2212yescomplemented
48#63486C2212yescomplemented
49C2×C4×Dic9C2212yescomplemented
50#63460C2214yescomplemented
51#63458C2214yescomplemented
52#63456C2214yes—
53#63451C2214yescomplemented
54#63448C2214yescomplemented
55#63447C2214yes—
56#63446C2214yes—
57#63445C2214yescomplemented
58#63444C2214yes—
59#63441C2214yescomplemented
60#63440C2214yescomplemented
61#63440C2214yescomplemented
62#63438C2214yescomplemented
63#63437C2212yes—
64C4×D36C2212yes—
65#63434C2214yescomplemented
66#63432C2212yescomplemented
67C4×Dic18C2212yescomplemented
68C3×#532D311yescharacteristic
69#5832—32no—
70#5828—32no—
71#5735—32no—
72#5720—32no—
73#5684—32no—
74#5683—31no—
75#5672—31no—
76#5621—34no—
77#5620—34no—
78#5547—34no—
79#5538—34no—
80#5479—32no—
81C23×D9C2312yes—
82C9×#41—42no—
83C9×#41—42no—
84C2×Q8×C9C2311yescharacteristic
85C2×Q8×C9C2311yescharacteristic
86C2×D4×C9C2311yescharacteristic
87C2×D4×C9C2312yes—
88C2×D4×C9C2314yes—
89C2×D4×C9C2312yes—
90C2×D4×C9C2311yescharacteristic
91C22×C4×C9C2312yes—
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2312yes—
94C22×C4×C9C2312yes—
95C2×#611C2314yes—
96C2×#611C2314yes—
97C2×#611C2314yes—
98C2×#611C2314yes—
99C22×Dic9C2312yes—
100C22×Dic9C2314yes—
101#3697—44no—
102C2×D36C2312yes—
103C2×D36C2312yes—
104C2×C4×D9—44no—
105C2×C4×D9C2314yes—
106C2×C4×D9C2314yes—
107C2×Dic18C2312yes—
108C2×Dic18C2312yes—
109C9×C4⋊C4C2314yes—
110C9×C22⋊C4C2314yes—
111C9×C22⋊C4C2314yes—
112C42×C9C2312yes—
113C42×C9C2311yescharacteristic
114C42×C9C2311yescharacteristic
115#3676C2312yes—
116#3676C2312yes—
117#3676C2314yes—
118#3676C2314yes—
119#3676C2314yes—
120(C2×D9)⋊C4C2314yes—
121(C2×D9)⋊C4C2314yes—
122(C2×D9)⋊C4C2314yes—
123(C2×D9)⋊C4C2314yes—
124(C2×D9)⋊C4C2314yes—
125(C2×D9)⋊C4C2314yes—
126C4⋊Dic9C2314yes—
127C4⋊Dic9C2312yes—
128C4⋊Dic9C2312yes—
129Dic9⋊C4C2314yes—
130Dic9⋊C4C2314yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134Dic9⋊C4C2314yes—
135C4×Dic9C2314yes—
136C4×Dic9C2312yes—
137C4×Dic9C2312yes—
138#3529—91noSylow
139C2×C3×#41C2×D311yescharacteristic
140C2×C3×#41C2×D311yescharacteristic
141C2×#235—32no—
142C22×C4×D3—32no—
143C3×C4⋊Q8C2×D311yescharacteristic
144C3×#127C2×D311yescharacteristic
145C3×#124C2×D311yescharacteristic
146C3×#124C2×D311yescharacteristic
147C3×#121C2×D314yes—
148C3×C4×D4C2×D314yes—
149C2×C3×C42C2×D311yescharacteristic
150#947—32no—
151#946—34no—
152#944—32no—
153#940—32no—
154#939—34no—
155#939—34no—
156#939—34no—
157#939—34no—
158#938—34no—
159#937—32no—
160#937—34no—
161#937—32no—
162#936—32no—
163#935—32no—
164#935—34no—
165#935—32no—
166#930—32no—
167#929—34no—
168C4×#67—34no—
169C4×#67—34no—
170C4×#67—34no—
171#926—32no—
172#924—32no—
173C2×C4×Dic3—32no—
174#898—34no—
175#896—34no—
176#894—34no—
177#889—34no—
178#886—34no—
179#885—34no—
180#884—34no—
181#883—34no—
182#882—34no—
183#879—34no—
184#878—34no—
185#878—34no—
186#876—34no—
187#875—32no—
188C4×D12—32no—
189#872—34no—
190#870—32no—
191C4×Dic6—32no—
192C23×C9C2412yes—
193C23×C9C2411yescharacteristic
194C23×C9C2412yes—
195C22×D9—42no—
196C22×D9—44no—
197C22×D9C2414yes—
198Q8×C9—41no—
199Q8×C9—41no—
200D4×C9—44no—
201D4×C9—42no—
202D4×C9—42no—
203D4×C9—41no—
204D4×C9—41no—
205C2×C4×C9—24no—
206C2×C4×C9—24no—
207C2×C4×C9—22no—
208C2×C4×C9—42no—
209C2×C4×C9C2412yes—
210C2×C4×C9C2412yes—
211C2×C4×C9C2411yescharacteristic
212C2×C4×C9C2412yes—
213C2×C4×C9C2412yes—
214C2×C4×C9C2411yescharacteristic
215#611—44no—
216#611—44no—
217#611—44no—
218#611—44no—
219C2×Dic9—42no—
220C2×Dic9—44no—
221C2×Dic9C2414yes—
222C2×Dic9C2414yes—
223C2×Dic9C2414yes—
224D36—42no—
225D36—42no—
226C4×D9—28no—
227C4×D9—44no—
228Dic18—42no—
229Dic18—42no—
230#563—92no—
231#563—91no—
232#562—92no—
233#562—94no—
234H(3,𝔽4)—91no—
235#560—92no—
236#560—94no—
237#532—92no—
238#532D911yescharacteristic, complemented
239#529—94no—
240#529—92no—
241#525—92no—
242#525—94no—
243C23×D3—32no—
244C3×#41—42no—
245C3×#41—42no—
246C2×C3×Q8C22×D311yescharacteristic
247C2×C3×Q8C22×D311yescharacteristic
248C2×C3×D4C22×D311yescharacteristic
249C2×C3×D4C22×D312yes—
250C2×C3×D4C22×D314yes—
251C2×C3×D4C22×D312yes—
252C2×C3×D4C22×D311yescharacteristic
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D312yes—
257C2×#67—34no—
258C2×#67—34no—
259C2×#67—34no—
260C2×#67—34no—
261C22×Dic3—32no—
262C22×Dic3—34no—
263#235—124no—
264C2×D12—32no—
265C2×D12—32no—
266C2×C4×D3—34no—
267C2×C4×D3—34no—
268C2×C4×D3—124no—
269C2×Dic6—32no—
270C2×Dic6—32no—
271C3×C4⋊C4C22×D314yes—
272C3×C22⋊C4C22×D314yes—
273C3×C22⋊C4C22×D314yes—
274C3×C42C22×D312yes—
275C3×C42C22×D311yescharacteristic
276C3×C42C22×D311yescharacteristic
277#217—34no—
278#217—34no—
279#217—32no—
280#217—32no—
281#217—34no—
282(C2×D3)⋊C4—34no—
283(C2×D3)⋊C4—34no—
284(C2×D3)⋊C4—34no—
285(C2×D3)⋊C4—34no—
286(C2×D3)⋊C4—34no—
287(C2×D3)⋊C4—34no—
288C4⋊Dic3—32no—
289C4⋊Dic3—32no—
290C4⋊Dic3—34no—
291Dic3⋊C4—34no—
292Dic3⋊C4—34no—
293Dic3⋊C4—34no—
294Dic3⋊C4—34no—
295Dic3⋊C4—34no—
296Dic3⋊C4—34no—
297C4×Dic3—34no—
298C4×Dic3—32no—
299C4×Dic3—32no—
300C22×C9—22no—
301C22×C9—22no—
302C22×C9—21no—
303C22×C9—24no—
304C22×C9—22no—
305C22×C9—24no—
306C22×C9C2511yescharacteristic
307C2×D9—24no—
308C2×D9—24no—
309C2×D9—24no—
310C2×D9—48no—
311C4×C9—22no—
312C4×C9—22no—
313C4×C9—21no—
314C4×C9—22no—
315C4×C9—22no—
316C4×C9H(5,𝔽2)12yes—
317Dic9—24no—
318Dic9—24no—
319Dic9—24no—
320C2×#41—92no—
321C2×#41C2×D911yescharacteristic
322C2×#41C2×D911yescharacteristic, complemented
323C23×C4—92no—
324C4⋊Q8—92no—
325C4⋊Q8C2×D911yescharacteristic, complemented
326#127—92no—
327#127C2×D911yescharacteristic
328#126—94no—
329#126—94no—
330#126—94no—
331#125—94no—
332#125—92no—
333#124—92no—
334#124—92no—
335#124—94no—
336#124—92no—
337#124C2×D911yescharacteristic
338#124C2×D911yescharacteristic, complemented
339#123—92no—
340#123—92no—
341#123—94no—
342#123—94no—
343#123—94no—
344#123—94no—
345#123—94no—
346C22⋊Q8—94no—
347C22⋊Q8—92no—
348C22⋊Q8—94no—
349C22⋊Q8—94no—
350C22⋊Q8—94no—
351#121—94no—
352#121—94no—
353#121—94no—
354#121—94no—
355#121—94no—
356#121—92no—
357#121—94no—
358#121C2×D914yescomplemented
359#120—92no—
360#120—94no—
361#120—92no—
362#120—94no—
363C4×Q8—92no—
364C4×D4—94no—
365C4×D4—94no—
366C4×D4—94no—
367C4×D4—92no—
368C4×D4C2×D914yescomplemented
369#117—92no—
370#117—94no—
371C2×C42—92no—
372C2×C42C2×D911yescharacteristic, complemented
373C23×C3C23×D312yes—
374C23×C3C23×D311yescharacteristic
375C23×C3C23×D312yes—
376C22×D3—34no—
377C22×D3—122no—
378C22×D3—124no—
379C3×Q8—41no—
380C3×Q8—41no—
381C3×D4—44no—
382C3×D4—42no—
383C3×D4—42no—
384C3×D4—41no—
385C3×D4—41no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—22no—
389C2×C3×C4—42no—
390C2×C3×C4C23×D312yes—
391C2×C3×C4C23×D312yes—
392C2×C3×C4C23×D311yescharacteristic
393C2×C3×C4C23×D312yes—
394C2×C3×C4C23×D312yes—
395C2×C3×C4C23×D311yescharacteristic
396#67—124no—
397#67—124no—
398#67—124no—
399#67—124no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—122no—
404C2×Dic3—124no—
405D12—122no—
406D12—122no—
407C4×D3—68no—
408C4×D3—124no—
409Dic6—122no—
410Dic6—122no—
411C2×C9—42no—
412C2×C9—42no—
413C2×C9—41no—
414C2×C9C2×H(5,𝔽2)11yescharacteristic
415C2×C9#58512yes—
416D9—44no—
417C24—92no—
418#41—42no—
419#41—42no—
420#41—364no—
421C2×Q8—92no—
422C2×Q8—92no—
423C2×Q8C22×D911yescharacteristic
424C2×Q8C22×D911yescharacteristic
425C2×D4—94no—
426C2×D4—94no—
427C2×D4—94no—
428C2×D4—94no—
429C2×D4—92no—
430C2×D4—92no—
431C2×D4C22×D914yes—
432C2×D4C22×D911yescharacteristic
433C2×D4C22×D912yes—
434C2×D4C22×D911yescharacteristic
435C2×D4C22×D912yes—
436C22×C4—94no—
437C22×C4—92no—
438C22×C4—94no—
439C22×C4—94no—
440C22×C4—364no—
441C22×C4C22×D912yes—
442C22×C4C22×D911yescharacteristic
443C22×C4C22×D912yes—
444C22×C4C22×D912yes—
445C4⋊C4—94no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—94no—
449C4⋊C4—94no—
450C4⋊C4—94no—
451C4⋊C4—92no—
452C4⋊C4—94no—
453C4⋊C4—92no—
454C4⋊C4C22×D914yes—
455C22⋊C4—92no—
456C22⋊C4—92no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4C22×D914yes—
467C22⋊C4C22×D914yes—
468C42—92no—
469C42—92no—
470C42—94no—
471C42C22×D911yescharacteristic
472C42C22×D911yescharacteristic
473C42C22×D912yes—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—24no—
478C22×C3—22no—
479C22×C3—24no—
480C22×C3C24×D311yescharacteristic
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—128no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—21no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4#100412yes—
491Dic3—64no—
492Dic3—64no—
493Dic3—64no—
494C9#352911yescharacteristic, complemented, Sylow
495C23—94no—
496C23—362no—
497C23—364no—
498C23C23×D912yes—
499C23C23×D911yescharacteristic
500C23C23×D912yes—
501Q8—41no—
502Q8—41no—
503Q8—362no—
504Q8—362no—
505D4—42no—
506D4—41no—
507D4—41no—
508D4—42no—
509D4—44no—
510D4—362no—
511D4—362no—
512D4—364no—
513D4—364no—
514D4—364no—
515D4—364no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—42no—
520C2×C4—94no—
521C2×C4—94no—
522C2×C4—94no—
523C2×C4—188no—
524C2×C4—364no—
525C2×C4—362no—
526C2×C4—364no—
527C2×C4C23×D912yes—
528C2×C4C23×D912yes—
529C2×C4C23×D911yescharacteristic
530C2×C4C23×D912yes—
531C2×C4C23×D912yes—
532C2×C4C23×D911yescharacteristic
533C2×C3—42no—
534C2×C3—42no—
535C2×C3—41no—
536C2×C3C2×#100411yescharacteristic
537C2×C3#596412yes—
538D3—124no—
539C22—22no—
540C22—21no—
541C22—22no—
542C22—22no—
543C22—24no—
544C22—24no—
545C22—184no—
546C22—184no—
547C22—184no—
548C22—368no—
549C22C24×D911yescharacteristic
550C4—22no—
551C4—21no—
552C4—22no—
553C4—22no—
554C4—22no—
555C4—184no—
556C4—184no—
557C4—184no—
558C4#6371012yes—
559C3#8624811yescharacteristic
560C2—42no—
561C2—41no—
562C2—42no—
563C2—364no—
564C2C2×#6371011yescharacteristic
565C2#1059313912yes—
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#532C2
hypercenter#532D9
hypocenterC9#3529
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C9×#532C2semidirect
2. #10589934C2semidirect
3. #10589930C2semidirect
4. #10589837C2semidirect
5. #10589822C2semidirect
6. #10589786C2semidirect
7. #10589785C2semidirect
8. #10589774C2semidirect
9. #10589723C2semidirect
10. #10589722C2semidirect
11. #10589649C2semidirect
12. #10589640C2semidirect
13. #10589581C2semidirect
16. C2×C9×#41C22semidirect
18. C22×C4×D9C22semidirect
19. C9×C4⋊Q8C22semidirect
22. C9×#124C22semidirect
23. C9×#121C22semidirect
24. C4×D4×C9C22semidirect
25. C2×C42×C9C22semidirect
27. #63508C22semidirect
28. #63506C22semidirect
32. #63501C22semidirect
33. #63501C22semidirect
36. #63499C22semidirect
37. #63499C22semidirect
38. #63498C22semidirect
40. #63497C22semidirect
41. #63497C22semidirect
43. #63491C22semidirect
45. C4×#611C22semidirect
46. C4×#611C22semidirect
47. #63488C22semidirect
48. #63486C22semidirect
49. C2×C4×Dic9C22semidirect
50. #63460C22semidirect
51. #63458C22semidirect
53. #63451C22semidirect
54. #63448C22semidirect
57. #63445C22semidirect
59. #63441C22semidirect
60. #63440C22semidirect
61. #63440C22semidirect
62. #63438C22semidirect
65. #63434C22semidirect
66. #63432C22semidirect
67. C4×Dic18C22semidirect
238. #532D9semidirect
322. C2×#41C2×D9semidirect
325. C4⋊Q8C2×D9semidirect
338. #124C2×D9semidirect
358. #121C2×D9semidirect
368. C4×D4C2×D9semidirect
372. C2×C42C2×D9semidirect
494. C9#3529semidirect

Maximal subgroups

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

subgroupindex
C9×#5322
#105899342
#105899302
#105898372
#105898222
#105897862
#105897852
#105897742
#105897232
#105897222
#105896492
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