Finite Group Databasebeta

← #11918968

Subgroups — #11918968

Order 1152.

2136 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593139C212yesmaximal, complemented
2C9×#575C211yesmaximal, characteristic, complemented
3C2×#63513C212yesmaximal, complemented
4#10589881C214yesmaximal, complemented
5#10589880C214yesmaximal, complemented
6#10589877C214yesmaximal, complemented
7#10589876C214yesmaximal, complemented
8#10589870C214yesmaximal, complemented
9D9×#135C214yesmaximal, complemented
10#10589850C211yesmaximal, characteristic, complemented
11C2×#63469C211yesmaximal, characteristic, complemented
12#87199—31nomaximal
13C2×C9×#41C2212yescomplemented
14#63716—22no—
15#63716C2214yescomplemented
16#63715—22no—
17#63715C2214yescomplemented
18#41×D9—24no—
19#41×D9C2218yescomplemented
20#63713C2214yescomplemented
21#63710—24no—
22#63710C2214yescomplemented
23C2×#3697—24no—
24C2×#3697C2211yescharacteristic
25C2×#3697C2212yescomplemented
26C9×#137C2214yescomplemented
27C9×AGL(1,ℤ/8)C2214yescomplemented
28C9×#135C2214yescomplemented
29C2×C9×M16C2211yescharacteristic, complemented
30#63513C2214yescomplemented
31#63513C2214yescomplemented
32#63513C2214yescomplemented
33#63513C2214yescomplemented
34C2×#3675C2212yescomplemented
35C2×#3674C2212yescomplemented
36C2×#3673C2212yescomplemented
37C2×#3672C2212yescomplemented
38C22×C9⋊C8C2211yescharacteristic, complemented
39#63481C2214yescomplemented
40#63480C2218yescomplemented
41Q16×D9C2214yescomplemented
42#63478C2218yescomplemented
43#63477C2218yescomplemented
44#63476C2218yescomplemented
45SD16×D9C2218yescomplemented
46#63474C2214yescomplemented
47#63473C2218yescomplemented
48D8×D9C2214yescomplemented
49#63471C2214yescomplemented
50#63470C2214yescomplemented
51#63469C2214yescomplemented
52#63469C2214yescomplemented
53#63467C2214yescomplemented
54C2×#3663C2212yescomplemented
55C2×C8×D9C2212yescomplemented
56#5964—32no—
57C3×#575D311yescharacteristic
58C2×#950—32no—
59#5779—34no—
60#5778—34no—
61#5775—34no—
62#5774—34no—
63#5768—34no—
64D3×#135—34no—
65#5748—31no—
66C2×#907—31no—
67C9×#41—22no—
68C9×#41—22no—
69C9×#41C2314yes—
70C9×#41C2314yes—
71C2×Q8×C9C2312yes—
72C2×D4×C9—22no—
73C2×D4×C9C2312yes—
74C22×C4×C9—22no—
75C22×C4×C9C2311yescharacteristic
76C2×#611—22no—
77C2×#611—28no—
78C2×#611D412yes—
79#3701—24no—
80#3701C2318yes—
81Q8×D9—24no—
82Q8×D9C2318yes—
83#3699—28no—
84#3699—28no—
85#3699—24no—
86#3699C2318yes—
87D4×D9—28no—
88D4×D9—28no—
89D4×D9—24no—
90D4×D9C2318yes—
91#3697—22no—
92#3697—22no—
93#3697—28no—
94#3697—24no—
95#3697—28no—
96#3697—24no—
97#3697D414yes—
98#3697C2314yes—
99#3697C2314yes—
100#3697C2314yes—
101C2×D36—24no—
102C2×D36D411yescharacteristic
103C2×D36C2312yes—
104C2×C4×D9—22no—
105C2×C4×D9—28no—
106C2×C4×D9C2312yes—
107C2×Dic18—24no—
108C2×Dic18D411yescharacteristic
109C2×Dic18C2312yes—
110C9×Q16C2314yes—
111C9×SD16C2318yes—
112C9×D8C2314yes—
113C9×M16C2314yes—
114C2×C8×C9C2312yes—
115#3675C2314yes—
116#3675C2314yes—
117#3674C2314yes—
118#3674C2314yes—
119#3673C2314yes—
120#3673C2314yes—
121#3672C2314yes—
122#3672C2314yes—
123C2×C9⋊C8C2312yes—
124C2×C9⋊C8C2312yes—
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127D72C2314yes—
128#3664C2318yes—
129#3663C2318yes—
130C8×D9C2314yes—
131C8×D9C2314yes—
132Dic36C2314yes—
133#3584—91noSylow
134C2×C3×#41C2×D312yes—
135#1010—34no—
136#1010—62no—
137#1009—34no—
138#1009—62no—
139D3×#41—38no—
140D3×#41—64no—
141#1007—34no—
142#1004—34no—
143#1004—64no—
144C2×#235—31no—
145C2×#235—32no—
146C2×#235—64no—
147C3×#137C2×D314yes—
148C3×AGL(1,ℤ/8)C2×D314yes—
149C3×#135C2×D314yes—
150C2×C3×M16C2×D311yescharacteristic
151#950—34no—
152#950—34no—
153#950—34no—
154#950—34no—
155C2×#216—32no—
156C2×#215—32no—
157C2×#214—32no—
158C2×#213—32no—
159C22×C3⋊C8—31no—
160#919—34no—
161#918—38no—
162D3×Q16—34no—
163#916—38no—
164#915—38no—
165#914—38no—
166D3×SD16—38no—
167#912—34no—
168#911—38no—
169D3×D8—34no—
170#909—34no—
171#908—34no—
172#907—34no—
173#907—34no—
174#904—34no—
175C2×ΓL(1,𝔽25)—32no—
176C2×D3×C8—32no—
177C23×C9—22no—
178C23×C9C2×D411yescharacteristic
179C22×D9—22no—
180C22×D9—28no—
181C22×D9C2×D412yes—
182Q8×C9—22no—
183Q8×C9C2414yes—
184D4×C9—24no—
185D4×C9—24no—
186D4×C9—22no—
187D4×C9C2414yes—
188C2×C4×C9—22no—
189C2×C4×C9—24no—
190C2×C4×C9—24no—
191C2×C4×C9C2×D411yescharacteristic
192C2×C4×C9C2×D412yes—
193C2×C4×C9C2411yescharacteristic
194C2×C4×C9C2412yes—
195#611—24no—
196#611—24no—
197#611—28no—
198#611—28no—
199#611C2×D418yes—
200C2×Dic9—22no—
201C2×Dic9—28no—
202C2×Dic9C2×D412yes—
203D36—28no—
204D36—22no—
205D36C2×D414yes—
206D36C2414yes—
207C4×D9—28no—
208C4×D9—24no—
209C4×D9—24no—
210C4×D9—28no—
211C4×D9C2×D414yes—
212C4×D9C2414yes—
213Dic18—22no—
214Dic18—28no—
215Dic18C2×D414yes—
216Dic18C2414yes—
217C8×C9C2414yes—
218C9⋊C8C2411yescharacteristic
219C9⋊C8C2411yescharacteristic
220C9⋊C8C2412yes—
221#585—92no—
222#578—94no—
223#577—94no—
224#577—94no—
225#576—94no—
226#575—94no—
227#575—91no—
228#575D911yescharacteristic, complemented
229C2×#135—92no—
230C2×#135—94no—
231C2×#131—91no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41C22×D314yes—
235C3×#41C22×D314yes—
236C2×C3×Q8C22×D312yes—
237C2×C3×D4—22no—
238C2×C3×D4C22×D312yes—
239C22×C3×C4—22no—
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—32no—
242C2×#67—68no—
243C2×#67—62no—
244#239—38no—
245#239—64no—
246D3×Q8—38no—
247D3×Q8—64no—
248#237—38no—
249#237—64no—
250#237—68no—
251#237—68no—
252D3×D4—38no—
253D3×D4—64no—
254D3×D4—68no—
255D3×D4—68no—
256#235—34no—
257#235—34no—
258#235—34no—
259#235—34no—
260#235—64no—
261#235—68no—
262#235—64no—
263#235—68no—
264#235—62no—
265#235—62no—
266C2×D12—31no—
267C2×D12—32no—
268C2×D12—64no—
269C2×C4×D3—32no—
270C2×C4×D3—68no—
271C2×C4×D3—62no—
272C2×Dic6—31no—
273C2×Dic6—32no—
274C2×Dic6—64no—
275C3×Q16C22×D314yes—
276C3×SD16C22×D318yes—
277C3×D8C22×D314yes—
278C3×M16C22×D314yes—
279C2×C3×C8C22×D312yes—
280#216—34no—
281#216—34no—
282#215—34no—
283#215—34no—
284#214—34no—
285#214—34no—
286#213—34no—
287#213—34no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—32no—
292Dic12—34no—
293D24—34no—
294#204—38no—
295ΓL(1,𝔽25)—38no—
296D3×C8—34no—
297D3×C8—34no—
298C22×C9—24no—
299C22×C9—41no—
300C22×C9—82no—
301C22×C9C22×D412yes—
302C22×C9C22×D411yescharacteristic
303C2×D9—24no—
304C2×D9—42no—
305C2×D9—88no—
306C2×D9—82no—
307C2×D9C22×D414yes—
308C4×C9—24no—
309C4×C9C22×D412yes—
310C4×C9C22×D411yescharacteristic
311C4×C9C2511yescharacteristic
312Dic9—24no—
313Dic9C22×D414yes—
3142−1+4—94no—
3152−1+4—94no—
3162−1+4—182no—
317H(5,𝔽2)—94no—
318H(5,𝔽2)—94no—
319H(5,𝔽2)—184no—
320H(5,𝔽2)—182no—
321C2×#41—91no—
322C2×#41—98no—
323C2×#41—92no—
324C2×#41—184no—
325C2×#41—184no—
326C2×#41C2×D912yescomplemented
327#137—98no—
328#137—98no—
329#137—94no—
330#137C2×D914yescomplemented
331AGL(1,ℤ/8)—98no—
332AGL(1,ℤ/8)—98no—
333AGL(1,ℤ/8)—94no—
334AGL(1,ℤ/8)C2×D914yescomplemented
335#135—94no—
336#135—94no—
337#135—94no—
338#135—94no—
339#135—94no—
340#135—98no—
341#135—94no—
342#135—94no—
343#135C2×D914yescomplemented
344C2×Q16—92no—
345C2×Q16—94no—
346C2×SD16—92no—
347C2×SD16—92no—
348C2×SD16—98no—
349C2×D8—92no—
350C2×D8—94no—
351#131—94no—
352#131—94no—
353C2×M16—92no—
354C2×M16C2×D911yescharacteristic, complemented
355C22×C8—91no—
356C22×C8—92no—
357C23×C3—22no—
358C23×C3D3×D411yescharacteristic
359C22×D3—32no—
360C22×D3—68no—
361C22×D3—62no—
362C3×Q8—22no—
363C3×Q8C23×D314yes—
364C3×D4—24no—
365C3×D4—24no—
366C3×D4—22no—
367C3×D4C23×D314yes—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D412yes—
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D312yes—
375#67—38no—
376#67—68no—
377#67—68no—
378#67—64no—
379#67—64no—
380C2×Dic3—32no—
381C2×Dic3—68no—
382C2×Dic3—62no—
383D12—34no—
384D12—34no—
385D12—68no—
386D12—62no—
387C4×D3—34no—
388C4×D3—34no—
389C4×D3—68no—
390C4×D3—68no—
391C4×D3—64no—
392C4×D3—64no—
393Dic6—34no—
394Dic6—34no—
395Dic6—68no—
396Dic6—62no—
397C3×C8C23×D314yes—
398C3⋊C8—31no—
399C3⋊C8—31no—
400C3⋊C8—32no—
401C2×C9—21no—
402C2×C9—22no—
403C2×C9—44no—
404C2×C9C23×D411yescharacteristic
405D9—24no—
406D9—44no—
407#41—22no—
408#41—22no—
409#41—94no—
410#41—94no—
411#41—98no—
412#41—98no—
413#41—94no—
414#41—94no—
415#41—188no—
416#41—188no—
417#41—184no—
418#41—184no—
419#41—188no—
420#41—188no—
421#41—184no—
422#41—184no—
423#41—182no—
424#41—182no—
425#41C22×D914yes—
426#41C22×D914yes—
427C2×Q8—91no—
428C2×Q8—98no—
429C2×Q8—92no—
430C2×Q8—184no—
431C2×Q8—184no—
432C2×Q8C22×D912yes—
433C2×D4—22no—
434C2×D4—92no—
435C2×D4—98no—
436C2×D4—91no—
437C2×D4—92no—
438C2×D4—184no—
439C2×D4—188no—
440C2×D4—184no—
441C2×D4—188no—
442C2×D4—188no—
443C2×D4—182no—
444C2×D4C22×D912yes—
445C22×C4—22no—
446C22×C4—92no—
447C22×C4—188no—
448C22×C4—182no—
449C22×C4C22×D911yescharacteristic
450Q16—94no—
451Q16—94no—
452Q16—94no—
453Q16C22×D914yes—
454SD16—94no—
455SD16—94no—
456SD16—94no—
457SD16—94no—
458SD16—98no—
459SD16C22×D918yes—
460D8—94no—
461D8—94no—
462D8—94no—
463D8C22×D914yes—
464M16—98no—
465M16C22×D914yes—
466C2×C8—91no—
467C2×C8—91no—
468C2×C8—92no—
469C2×C8—92no—
470C2×C8—94no—
471C2×C8—94no—
472C2×C8C22×D912yes—
473C22×C3—24no—
474C22×C3—41no—
475C22×C3—82no—
476C22×C3C2×D3×D411yescharacteristic
477C22×C3C2×D3×D412yes—
478C2×D3—34no—
479C2×D3—64no—
480C2×D3—122no—
481C2×D3—248no—
482C2×D3—242no—
483C3×C4—24no—
484C3×C4C2×D3×D412yes—
485C3×C4C2×D3×D411yescharacteristic
486C3×C4C24×D311yescharacteristic
487Dic3—34no—
488Dic3—64no—
489C9#358411yescharacteristic, complemented, Sylow
490C23—22no—
491C23—92no—
492C23—188no—
493C23—182no—
494C23D4×D911yescharacteristic
495Q8—22no—
496Q8—94no—
497Q8—94no—
498Q8—188no—
499Q8—182no—
500Q8C23×D914yes—
501D4—24no—
502D4—24no—
503D4—22no—
504D4—98no—
505D4—94no—
506D4—94no—
507D4—188no—
508D4—188no—
509D4—188no—
510D4—184no—
511D4—184no—
512D4—182no—
513D4C23×D914yes—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—92no—
518C2×C4—94no—
519C2×C4—94no—
520C2×C4—188no—
521C2×C4—188no—
522C2×C4—188no—
523C2×C4—182no—
524C2×C4—184no—
525C2×C4—184no—
526C2×C4D4×D911yescharacteristic
527C2×C4D4×D912yes—
528C2×C4C23×D912yes—
529C2×C4C23×D911yescharacteristic
530C8—91no—
531C8—91no—
532C8—92no—
533C8C23×D914yes—
534C2×C3—21no—
535C2×C3—22no—
536C2×C3—44no—
537C2×C3C22×D3×D411yescharacteristic
538D3—64no—
539D3—124no—
540C22—24no—
541C22—41no—
542C22—82no—
543C22—94no—
544C22—184no—
545C22—362no—
546C22—722no—
547C22—728no—
548C22C2×D4×D912yes—
549C22C2×D4×D911yescharacteristic
550C4—24no—
551C4—94no—
552C4—184no—
553C4C2×D4×D912yes—
554C4C2×D4×D911yescharacteristic
555C4C24×D911yescharacteristic
556C3#8719911yescharacteristic
557C2—22no—
558C2—21no—
559C2—44no—
560C2—184no—
561C2—364no—
562C2C22×D4×D911yescharacteristic
subgroupG/H
centerC4C2×D4×D9
commutator, cosocleC4×C9C25
FrattiniC3×C4C24×D3
FittingC9×#575C2
socleC2×C3C22×D3×D4
hypercenter#575D9
hypocenterC9#3584
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #10593139C2semidirect
2. C9×#575C2semidirect
3. C2×#63513C2semidirect
4. #10589881C2semidirect
5. #10589880C2semidirect
6. #10589877C2semidirect
7. #10589876C2semidirect
8. #10589870C2semidirect
9. D9×#135C2semidirect
10. #10589850C2semidirect
11. C2×#63469C2semidirect
13. C2×C9×#41C22semidirect
15. #63716C22semidirect
17. #63715C22semidirect
19. #41×D9C22semidirect
20. #63713C22semidirect
22. #63710C22semidirect
25. C2×#3697C22semidirect
26. C9×#137C22semidirect
27. C9×AGL(1,ℤ/8)C22semidirect
28. C9×#135C22semidirect
29. C2×C9×M16C22semidirect
30. #63513C22semidirect
31. #63513C22semidirect
32. #63513C22semidirect
33. #63513C22semidirect
34. C2×#3675C22semidirect
35. C2×#3674C22semidirect
36. C2×#3673C22semidirect
37. C2×#3672C22semidirect
38. C22×C9⋊C8C22semidirect
39. #63481C22semidirect
40. #63480C22semidirect
41. Q16×D9C22semidirect
42. #63478C22semidirect
43. #63477C22semidirect
44. #63476C22semidirect
45. SD16×D9C22semidirect
46. #63474C22semidirect
47. #63473C22semidirect
48. D8×D9C22semidirect
49. #63471C22semidirect
50. #63470C22semidirect
51. #63469C22semidirect
52. #63469C22semidirect
53. #63467C22semidirect
54. C2×#3663C22semidirect
55. C2×C8×D9C22semidirect
228. #575D9semidirect
326. C2×#41C2×D9semidirect
330. #137C2×D9semidirect
334. AGL(1,ℤ/8)C2×D9semidirect
343. #135C2×D9semidirect
354. C2×M16C2×D9semidirect
489. C9#3584semidirect

Maximal subgroups

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

subgroupindex
#105931392
C9×#5752
C2×#635132
#105898812
#105898802
#105898772
#105898762
#105898702
D9×#1352
#105898502
C2×#634692
#871993