Finite Group Databasebeta

← #11918969

Subgroups — #11918969

Order 1152.

4272 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#10596756C212yesmaximal, complemented
2C32×#575C211yesmaximal, characteristic, complemented
3C2×#64159C212yesmaximal, complemented
4#10596250C214yesmaximal, complemented
5#10596249C214yesmaximal, complemented
6#10596246C214yesmaximal, complemented
7#10596245C214yesmaximal, complemented
8#10596239C214yesmaximal, complemented
9C3⋊D3×#135C214yesmaximal, complemented
10#10596219C211yesmaximal, characteristic, complemented
11C2×#64116C211yesmaximal, characteristic, complemented
12#87199—34nomaximal
13C2×C32×#41C2212yescomplemented
14#64367—22no—
15#64367C2214yescomplemented
16#64366—22no—
17#64366C2214yescomplemented
18#41×C3⋊D3—24no—
19#41×C3⋊D3C2218yescomplemented
20#64364C2214yescomplemented
21#64361—24no—
22#64361C2214yescomplemented
23C2×#3828—24no—
24C2×#3828C2211yescharacteristic
25C2×#3828C2212yescomplemented
26C32×#137C2214yescomplemented
27C32×AGL(1,ℤ/8)C2214yescomplemented
28C32×#135C2214yescomplemented
29C2×C32×M16C2211yescharacteristic, complemented
30#64159C2214yescomplemented
31#64159C2214yescomplemented
32#64159C2214yescomplemented
33#64159C2214yescomplemented
34C2×#3756C2212yescomplemented
35C2×#3755C2212yescomplemented
36C2×#3754C2212yescomplemented
37C2×#3753C2212yescomplemented
38C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
39#64128C2214yescomplemented
40#64127C2218yescomplemented
41Q16×C3⋊D3C2214yescomplemented
42#64125C2218yescomplemented
43#64124C2218yescomplemented
44#64123C2218yescomplemented
45SD16×C3⋊D3C2218yescomplemented
46#64121C2214yescomplemented
47#64120C2218yescomplemented
48D8×C3⋊D3C2214yescomplemented
49#64118C2214yescomplemented
50#64117C2214yescomplemented
51#64116C2214yescomplemented
52#64116C2214yescomplemented
53#64113C2214yescomplemented
54C2×#3743C2212yescomplemented
55C2×C8×C3⋊D3C2212yescomplemented
56#5964—38no—
57C3×#575D314yescomplemented
58C2×#950—38no—
59#5779—316no—
60#5778—316no—
61#5775—316no—
62#5774—316no—
63#5768—316no—
64D3×#135—316no—
65#5748—34no—
66C2×#907—34no—
67C32×#41—22no—
68C32×#41—22no—
69C32×#41C2314yes—
70C32×#41C2314yes—
71C2×C32×Q8C2312yes—
72C2×C32×D4—22no—
73C2×C32×D4C2312yes—
74C22×C32×C4—22no—
75C22×C32×C4C2311yescharacteristic
76C2×#638—22no—
77C2×#638—28no—
78C2×#638D412yes—
79#3832—24no—
80#3832C2318yes—
81Q8×C3⋊D3—24no—
82Q8×C3⋊D3C2318yes—
83#3830—28no—
84#3830—28no—
85#3830—24no—
86#3830C2318yes—
87D4×C3⋊D3—28no—
88D4×C3⋊D3—28no—
89D4×C3⋊D3—24no—
90D4×C3⋊D3C2318yes—
91#3828—22no—
92#3828—22no—
93#3828—28no—
94#3828—24no—
95#3828—28no—
96#3828—24no—
97#3828D414yes—
98#3828C2314yes—
99#3828C2314yes—
100#3828C2314yes—
101C2×C4⋊(C3⋊D3)—24no—
102C2×C4⋊(C3⋊D3)D411yescharacteristic
103C2×C4⋊(C3⋊D3)C2312yes—
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—28no—
106C2×C4×C3⋊D3C2312yes—
107C2×#634—24no—
108C2×#634D411yescharacteristic
109C2×#634C2312yes—
110C32×Q16C2314yes—
111C32×SD16C2318yes—
112C32×D8C2314yes—
113C32×M16C2314yes—
114C2×C32×C8C2312yes—
115#3756C2314yes—
116#3756C2314yes—
117#3755C2314yes—
118#3755C2314yes—
119#3754C2314yes—
120#3754C2314yes—
121#3753C2314yes—
122#3753C2314yes—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2312yes—
126C2×C3⋊(C3⋊C8)C2312yes—
127#3746C2314yes—
128#3745C2314yes—
129#3744C2318yes—
130#3743C2318yes—
131C8×C3⋊D3C2314yes—
132C8×C3⋊D3C2314yes—
133#3584—91noSylow
134C2×C3×#41C2×D318yescomplemented
135#1010—316no—
136#1010—68no—
137#1009—316no—
138#1009—68no—
139D3×#41—332no—
140D3×#41—616no—
141#1007—316no—
142#1004—316no—
143#1004—616no—
144C2×#235—34no—
145C2×#235—38no—
146C2×#235—616no—
147C3×#137C2×D3116yescomplemented
148C3×AGL(1,ℤ/8)C2×D3116yescomplemented
149C3×#135C2×D3116yescomplemented
150C2×C3×M16C2×D314yescomplemented
151#950—316no—
152#950—316no—
153#950—316no—
154#950—316no—
155C2×#216—38no—
156C2×#215—38no—
157C2×#214—38no—
158C2×#213—38no—
159C22×C3⋊C8—34no—
160#919—316no—
161#918—332no—
162D3×Q16—316no—
163#916—332no—
164#915—332no—
165#914—332no—
166D3×SD16—332no—
167#912—316no—
168#911—332no—
169D3×D8—316no—
170#909—316no—
171#908—316no—
172#907—316no—
173#907—316no—
174#904—316no—
175C2×ΓL(1,𝔽25)—38no—
176C2×D3×C8—38no—
177C23×C32—22no—
178C23×C32C2×D411yescharacteristic
179C22×C3⋊D3—22no—
180C22×C3⋊D3—28no—
181C22×C3⋊D3C2×D412yes—
182C32×Q8—22no—
183C32×Q8C2414yes—
184C32×D4—24no—
185C32×D4—24no—
186C32×D4—22no—
187C32×D4C2414yes—
188C2×C32×C4—22no—
189C2×C32×C4—24no—
190C2×C32×C4—24no—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2411yescharacteristic
194C2×C32×C4C2412yes—
195#638—24no—
196#638—24no—
197#638—28no—
198#638—28no—
199#638C2×D418yes—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—28no—
202C2×C3⋊Dic3C2×D412yes—
203C4⋊(C3⋊D3)—28no—
204C4⋊(C3⋊D3)—22no—
205C4⋊(C3⋊D3)C2×D414yes—
206C4⋊(C3⋊D3)C2414yes—
207C4×C3⋊D3—28no—
208C4×C3⋊D3—24no—
209C4×C3⋊D3—24no—
210C4×C3⋊D3—28no—
211C4×C3⋊D3C2×D414yes—
212C4×C3⋊D3C2414yes—
213#634—22no—
214#634—28no—
215#634C2×D414yes—
216#634C2414yes—
217C32×C8C2414yes—
218C3⋊(C3⋊C8)C2411yescharacteristic
219C3⋊(C3⋊C8)C2411yescharacteristic
220C3⋊(C3⋊C8)C2412yes—
221#585—92no—
222#578—94no—
223#577—94no—
224#577—94no—
225#576—94no—
226#575—94no—
227#575—91no—
228#575C3⋊D311yescharacteristic, complemented
229C2×#135—92no—
230C2×#135—94no—
231C2×#131—91no—
232C3×#41—28no—
233C3×#41—28no—
234C3×#41C22×D3116yes—
235C3×#41C22×D3116yes—
236C2×C3×Q8C22×D318yes—
237C2×C3×D4—28no—
238C2×C3×D4C22×D318yes—
239C22×C3×C4—28no—
240C22×C3×C4C22×D314yes—
241C2×#67—38no—
242C2×#67—632no—
243C2×#67—68no—
244#239—332no—
245#239—616no—
246D3×Q8—332no—
247D3×Q8—616no—
248#237—332no—
249#237—616no—
250#237—632no—
251#237—632no—
252D3×D4—332no—
253D3×D4—616no—
254D3×D4—632no—
255D3×D4—632no—
256#235—316no—
257#235—316no—
258#235—316no—
259#235—316no—
260#235—616no—
261#235—632no—
262#235—616no—
263#235—632no—
264#235—68no—
265#235—68no—
266C2×D12—34no—
267C2×D12—38no—
268C2×D12—616no—
269C2×C4×D3—38no—
270C2×C4×D3—632no—
271C2×C4×D3—68no—
272C2×Dic6—34no—
273C2×Dic6—38no—
274C2×Dic6—616no—
275C3×Q16C22×D3116yes—
276C3×SD16C22×D3132yes—
277C3×D8C22×D3116yes—
278C3×M16C22×D3116yes—
279C2×C3×C8C22×D318yes—
280#216—316no—
281#216—316no—
282#215—316no—
283#215—316no—
284#214—316no—
285#214—316no—
286#213—316no—
287#213—316no—
288C2×C3⋊C8—34no—
289C2×C3⋊C8—34no—
290C2×C3⋊C8—38no—
291C2×C3⋊C8—38no—
292Dic12—316no—
293D24—316no—
294#204—332no—
295ΓL(1,𝔽25)—332no—
296D3×C8—316no—
297D3×C8—316no—
298C22×C32—24no—
299C22×C32—41no—
300C22×C32—82no—
301C22×C32C22×D412yes—
302C22×C32C22×D411yescharacteristic
303C2×C3⋊D3—24no—
304C2×C3⋊D3—42no—
305C2×C3⋊D3—88no—
306C2×C3⋊D3—82no—
307C2×C3⋊D3C22×D414yes—
308C32×C4—24no—
309C32×C4C22×D412yes—
310C32×C4C22×D411yescharacteristic
311C32×C4C2511yescharacteristic
312C3⋊Dic3—24no—
313C3⋊Dic3C22×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×C3⋊D312yescomplemented
327#137—98no—
328#137—98no—
329#137—94no—
330#137C2×C3⋊D314yescomplemented
331AGL(1,ℤ/8)—98no—
332AGL(1,ℤ/8)—98no—
333AGL(1,ℤ/8)—94no—
334AGL(1,ℤ/8)C2×C3⋊D314yescomplemented
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×C3⋊D314yescomplemented
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×C3⋊D311yescharacteristic, complemented
355C22×C8—91no—
356C22×C8—92no—
357C23×C3—28no—
358C23×C3D3×D414yes—
359C22×D3—38no—
360C22×D3—632no—
361C22×D3—68no—
362C3×Q8—28no—
363C3×Q8C23×D3116yes—
364C3×D4—216no—
365C3×D4—216no—
366C3×D4—28no—
367C3×D4C23×D3116yes—
368C2×C3×C4—28no—
369C2×C3×C4—216no—
370C2×C3×C4—216no—
371C2×C3×C4D3×D414yes—
372C2×C3×C4D3×D418yes—
373C2×C3×C4C23×D314yes—
374C2×C3×C4C23×D318yes—
375#67—332no—
376#67—632no—
377#67—632no—
378#67—616no—
379#67—616no—
380C2×Dic3—38no—
381C2×Dic3—632no—
382C2×Dic3—68no—
383D12—316no—
384D12—316no—
385D12—632no—
386D12—68no—
387C4×D3—316no—
388C4×D3—316no—
389C4×D3—632no—
390C4×D3—632no—
391C4×D3—616no—
392C4×D3—616no—
393Dic6—316no—
394Dic6—316no—
395Dic6—632no—
396Dic6—68no—
397C3×C8C23×D3116yes—
398C3⋊C8—34no—
399C3⋊C8—34no—
400C3⋊C8—38no—
401C2×C32—21no—
402C2×C32—22no—
403C2×C32—44no—
404C2×C32C23×D411yescharacteristic
405C3⋊D3—24no—
406C3⋊D3—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×C3⋊D314yes—
426#41C22×C3⋊D314yes—
427C2×Q8—91no—
428C2×Q8—98no—
429C2×Q8—92no—
430C2×Q8—184no—
431C2×Q8—184no—
432C2×Q8C22×C3⋊D312yes—
433C2×D4—22no—
434C2×D4—92no—
435C2×D4—98no—
436C2×D4—92no—
437C2×D4—91no—
438C2×D4—184no—
439C2×D4—188no—
440C2×D4—184no—
441C2×D4—188no—
442C2×D4—188no—
443C2×D4—182no—
444C2×D4C22×C3⋊D312yes—
445C22×C4—22no—
446C22×C4—92no—
447C22×C4—188no—
448C22×C4—182no—
449C22×C4C22×C3⋊D311yescharacteristic
450Q16—94no—
451Q16—94no—
452Q16—94no—
453Q16C22×C3⋊D314yes—
454SD16—94no—
455SD16—94no—
456SD16—94no—
457SD16—94no—
458SD16—98no—
459SD16C22×C3⋊D318yes—
460D8—94no—
461D8—94no—
462D8—94no—
463D8C22×C3⋊D314yes—
464M16—98no—
465M16C22×C3⋊D314yes—
466C2×C8—91no—
467C2×C8—91no—
468C2×C8—92no—
469C2×C8—92no—
470C2×C8—94no—
471C2×C8—94no—
472C2×C8C22×C3⋊D312yes—
473C22×C3—216no—
474C22×C3—44no—
475C22×C3—88no—
476C22×C3C2×D3×D414yes—
477C22×C3C2×D3×D418yes—
478C2×D3—316no—
479C2×D3—616no—
480C2×D3—128no—
481C2×D3—2432no—
482C2×D3—248no—
483C3×C4—216no—
484C3×C4C2×D3×D418yes—
485C3×C4C2×D3×D414yes—
486C3×C4C24×D314yes—
487Dic3—316no—
488Dic3—616no—
489C32#358411yescharacteristic, complemented, Sylow
490C23—22no—
491C23—92no—
492C23—188no—
493C23—182no—
494C23D4×C3⋊D311yescharacteristic
495Q8—22no—
496Q8—94no—
497Q8—94no—
498Q8—188no—
499Q8—182no—
500Q8C23×C3⋊D314yes—
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×C3⋊D314yes—
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×C3⋊D311yescharacteristic
527C2×C4D4×C3⋊D312yes—
528C2×C4C23×C3⋊D312yes—
529C2×C4C23×C3⋊D311yescharacteristic
530C8—91no—
531C8—91no—
532C8—92no—
533C8C23×C3⋊D314yes—
534C2×C3—24no—
535C2×C3—28no—
536C2×C3—416no—
537C2×C3C22×D3×D414yes—
538D3—616no—
539D3—1216no—
540C22—24no—
541C22—41no—
542C22—82no—
543C22—94no—
544C22—184no—
545C22—362no—
546C22—722no—
547C22—728no—
548C22C2×D4×C3⋊D312yes—
549C22C2×D4×C3⋊D311yescharacteristic
550C4—24no—
551C4—94no—
552C4—184no—
553C4C2×D4×C3⋊D312yes—
554C4C2×D4×C3⋊D311yescharacteristic
555C4C24×C3⋊D311yescharacteristic
556C3#8719914yescomplemented
557C2—22no—
558C2—21no—
559C2—44no—
560C2—184no—
561C2—364no—
562C2C22×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC4C2×D4×C3⋊D3
commutator, cosocleC32×C4C25
FrattiniC4C24×C3⋊D3
FittingC32×#575C2
socleC2×C32C23×D4
hypercenter#575C3⋊D3
hypocenterC32#3584
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #10596756C2semidirect
2. C32×#575C2semidirect
3. C2×#64159C2semidirect
4. #10596250C2semidirect
5. #10596249C2semidirect
6. #10596246C2semidirect
7. #10596245C2semidirect
8. #10596239C2semidirect
9. C3⋊D3×#135C2semidirect
10. #10596219C2semidirect
11. C2×#64116C2semidirect
13. C2×C32×#41C22semidirect
15. #64367C22semidirect
17. #64366C22semidirect
19. #41×C3⋊D3C22semidirect
20. #64364C22semidirect
22. #64361C22semidirect
25. C2×#3828C22semidirect
26. C32×#137C22semidirect
27. C32×AGL(1,ℤ/8)C22semidirect
28. C32×#135C22semidirect
29. C2×C32×M16C22semidirect
30. #64159C22semidirect
31. #64159C22semidirect
32. #64159C22semidirect
33. #64159C22semidirect
34. C2×#3756C22semidirect
35. C2×#3755C22semidirect
36. C2×#3754C22semidirect
37. C2×#3753C22semidirect
38. C22×C3⋊(C3⋊C8)C22semidirect
39. #64128C22semidirect
40. #64127C22semidirect
41. Q16×C3⋊D3C22semidirect
42. #64125C22semidirect
43. #64124C22semidirect
44. #64123C22semidirect
45. SD16×C3⋊D3C22semidirect
46. #64121C22semidirect
47. #64120C22semidirect
48. D8×C3⋊D3C22semidirect
49. #64118C22semidirect
50. #64117C22semidirect
51. #64116C22semidirect
52. #64116C22semidirect
53. #64113C22semidirect
54. C2×#3743C22semidirect
55. C2×C8×C3⋊D3C22semidirect
57. C3×#575D3semidirect
134. C2×C3×#41C2×D3semidirect
147. C3×#137C2×D3semidirect
148. C3×AGL(1,ℤ/8)C2×D3semidirect
149. C3×#135C2×D3semidirect
150. C2×C3×M16C2×D3semidirect
228. #575C3⋊D3semidirect
326. C2×#41C2×C3⋊D3semidirect
330. #137C2×C3⋊D3semidirect
334. AGL(1,ℤ/8)C2×C3⋊D3semidirect
343. #135C2×C3⋊D3semidirect
354. C2×M16C2×C3⋊D3semidirect
489. C32#3584semidirect
556. C3#87199semidirect

Maximal subgroups

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

subgroupindex
#105967562
C32×#5752
C2×#641592
#105962502
#105962492
#105962462
#105962452
#105962392
C3⋊D3×#1352
#105962192
C2×#641162
#871993