Finite Group Databasebeta

← #11865019

Subgroups — #11865019

Order 1152.

2286 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C32×#575C211yesmaximal, characteristic, complemented
3#10596301C211yesmaximal, characteristic, complemented
4#10596293C211yesmaximal, characteristic, complemented
5#10592935C211yesmaximal, characteristic, complemented
6#10592901C214yesmaximal, complemented
7#10592897C214yesmaximal, complemented
8#10592838C211yesmaximal, characteristic, complemented
9C2×#63650C211yesmaximal, characteristic, complemented
10#84005—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×C32×#41C2211yescharacteristic, complemented
13#64366—22no—
14#64366—22no—
15#64366—22no—
16#64366C2214yes—
17C2×#3832—21no—
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3—22no—
20C2×#3828—21no—
21C2×#3828C2211yescharacteristic
22C22×C4⋊(C3⋊D3)—21no—
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C32×#137—21no—
25C32×#137C2212yescomplemented
26C32×AGL(1,ℤ/8)—21no—
27C32×AGL(1,ℤ/8)C2212yescomplemented
28C32×#135—22no—
29C2×C32×M16C2211yescharacteristic, complemented
30#64160—21no—
31#64159—22no—
32#64158—21no—
33#64156C2212yescomplemented
34#64151C2212yescomplemented
35#64149C2212yescomplemented
36#64146—22no—
37#64141C2212yescomplemented
38#64139—22no—
39#64135C2211yescharacteristic, complemented
40C2×#3748C2211yescharacteristic, complemented
41#63664C2214yescomplemented
42#63652C2214yescomplemented
43#63650C2214yescomplemented
44C2×#1009—34no—
45C3×#575D314yescomplemented
46#5830—34no—
47#5822—34no—
48#5236—34no—
49#5202—316no—
50#5198—316no—
51#5139—34no—
52C2×#823—34no—
53C23×C3⋊D3—22no—
54C23×C3⋊D3D412yes—
55C32×#41—21no—
56C32×#41—21no—
57C32×#41—21no—
58C32×#41—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41D412yescomplemented
62C32×#41C2312yes—
63C2×C32×Q8D411yescharacteristic, complemented
64C2×C32×Q8C2311yescharacteristic, complemented
65C2×C32×D4—21no—
66C2×C32×D4—21no—
67C2×C32×D4D411yescharacteristic, complemented
68C2×C32×D4C2311yescharacteristic, complemented
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C2×#638—22no—
73C2×#638—21no—
74C2×#638—24no—
75#3832—24no—
76#3832—24no—
77D4×C3⋊D3—28no—
78D4×C3⋊D3—24no—
79D4×C3⋊D3—28no—
80D4×C3⋊D3—24no—
81#3828—24no—
82#3828—21no—
83#3828—21no—
84#3828—24no—
85#3828D412yescomplemented
86#3828C2312yes—
87C2×C4⋊(C3⋊D3)—22no—
88C2×C4⋊(C3⋊D3)—24no—
89C2×C4⋊(C3⋊D3)—21no—
90C2×C4⋊(C3⋊D3)—21no—
91C2×C4⋊(C3⋊D3)—21no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)—24no—
94C2×C4⋊(C3⋊D3)D412yes—
95C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
96C2×C4⋊(C3⋊D3)C2312yes—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—21no—
99C2×#634D411yescharacteristic, complemented
100C32×Q16—22no—
101C32×SD16—22no—
102C32×SD16—22no—
103C32×D8—22no—
104C32×M16—21no—
105C32×M16C2312yescomplemented
106C2×C32×C8—21no—
107#3757—21no—
108#3756—22no—
109#3755—22no—
110#3754—22no—
111#3753—22no—
112#3752—24no—
113C4⋊(C3⋊Dic3)—21no—
114C4×C3⋊Dic3C2312yescomplemented
115#3748—21no—
116#3748C2312yescomplemented
117C2×C3⋊(C3⋊C8)—21no—
118#3019—91noSylow
119C2×C3×#41C2×D314yes—
120C2×C3×#41C2×D314yescomplemented
121#1009—316no—
122#1009—68no—
123#1009—68no—
124#1009—68no—
125C2×#239—64no—
126C2×D3×D4—68no—
127C2×D3×D4—64no—
128C2×#235—34no—
129C2×#235—64no—
130C22×D12—34no—
131C22×D12—64no—
132C3×#137—24no—
133C3×#137C2×D318yescomplemented
134C3×AGL(1,ℤ/8)—24no—
135C3×AGL(1,ℤ/8)C2×D318yescomplemented
136C3×#135—28no—
137C2×C3×M16C2×D314yescomplemented
138#951—64no—
139#950—68no—
140#949—64no—
141#947—38no—
142#942—38no—
143#940—38no—
144#937—68no—
145#932—38no—
146#930—68no—
147#926—34no—
148C2×#208—34no—
149#837—316no—
150#825—316no—
151#823—316no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32C2×D411yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—28no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3—82no—
160C22×C3⋊D3—84no—
161C22×C3⋊D3C2×D414yes—
162C32×Q8—21no—
163C32×Q8—21no—
164C32×Q8—21no—
165C32×Q8C2×D412yes—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—21no—
169C32×D4—21no—
170C32×D4—21no—
171C32×D4—41no—
172C32×D4—41no—
173C32×D4C2×D412yes—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—21no—
178C2×C32×C4—41no—
179C2×C32×C4—41no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—28no—
187#638—22no—
188#638—22no—
189#638—84no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—22no—
192C4⋊(C3⋊D3)—28no—
193C4⋊(C3⋊D3)—22no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—22no—
197C4⋊(C3⋊D3)—22no—
198C4⋊(C3⋊D3)C2×D412yes—
199C4×C3⋊D3—28no—
200C4×C3⋊D3—22no—
201C4×C3⋊D3—22no—
202#634—21no—
203#634C2×D412yes—
204C32×C8—22no—
205C3⋊(C3⋊C8)—22no—
206C2×H(5,𝔽2)—91no—
207#575—91no—
208#575C3⋊D311yescharacteristic, complemented
209#535—91no—
210#455—94no—
211#453—94no—
212#421—91no—
213#421—91no—
214C2×#100—91no—
215C23×D3—38no—
216C23×D3—68no—
217C3×#41—24no—
218C3×#41—24no—
219C3×#41—24no—
220C3×#41—24no—
221C3×#41—24no—
222C3×#41—24no—
223C3×#41#6718yescomplemented
224C3×#41C22×D318yes—
225C2×C3×Q8#6714yescomplemented
226C2×C3×Q8C22×D314yescomplemented
227C2×C3×D4—24no—
228C2×C3×D4—24no—
229C2×C3×D4#6714yescomplemented
230C2×C3×D4C22×D314yescomplemented
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4C22×D314yes—
234C2×#67—68no—
235C2×#67—64no—
236C2×#67—616no—
237#239—616no—
238#239—616no—
239D3×D4—632no—
240D3×D4—632no—
241D3×D4—616no—
242D3×D4—616no—
243#235—38no—
244#235—38no—
245#235—616no—
246#235—616no—
247#235—64no—
248#235—64no—
249C2×D12—34no—
250C2×D12—38no—
251C2×D12—38no—
252C2×D12—616no—
253C2×D12—68no—
254C2×D12—616no—
255C2×D12—64no—
256C2×D12—64no—
257C2×D12—64no—
258C2×D12—64no—
259C2×C4×D3—68no—
260C2×C4×D3—64no—
261C2×Dic6—34no—
262C3×Q16—28no—
263C3×SD16—28no—
264C3×SD16—28no—
265C3×D8—28no—
266C3×M16—24no—
267C3×M16C22×D318yescomplemented
268C2×C3×C8—24no—
269#217—64no—
270#216—68no—
271#215—68no—
272#214—68no—
273#213—68no—
274(C2×D3)⋊C4—616no—
275C4⋊Dic3—64no—
276C4×Dic3—38no—
277#208—38no—
278#208—64no—
279C2×C3⋊C8—64no—
280C22×C32—22no—
281C22×C32—41no—
282C22×C32—42no—
283C22×C32—42no—
284C22×C32—41no—
285C22×C32#12011yescharacteristic
286C22×C32#12011yescharacteristic
287C22×C32C22×D411yescharacteristic
288C2×C3⋊D3—24no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—44no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—44no—
293C2×C3⋊D3—82no—
294C2×C3⋊D3—88no—
295C32×C4—22no—
296C32×C4—41no—
297C32×C4#12011yescharacteristic
298C32×C4#12011yescharacteristic
299C32×C4C22×D411yescharacteristic
300C32×C4C22×D411yescharacteristic
301C3⋊Dic3—22no—
302C3⋊Dic3—42no—
303H(5,𝔽2)—94no—
304H(5,𝔽2)—182no—
305H(5,𝔽2)—182no—
306H(5,𝔽2)—182no—
307C2×#41—91no—
308C2×#41—181no—
309C2×#41—181no—
310C2×#41C2×C3⋊D311yescharacteristic
311C2×#41C2×C3⋊D311yescharacteristic, complemented
312C22×D4—91no—
313C22×D4—181no—
314C22×D4—182no—
315C22×D4—181no—
316#137—21no—
317#137—92no—
318#137—181no—
319#137C2×C3⋊D312yescomplemented
320AGL(1,ℤ/8)—21no—
321AGL(1,ℤ/8)—92no—
322AGL(1,ℤ/8)—181no—
323AGL(1,ℤ/8)C2×C3⋊D312yescomplemented
324#135—22no—
325#135—182no—
326C2×M16—91no—
327C2×M16C2×C3⋊D311yescharacteristic, complemented
328#127—92no—
329#124—92no—
330#121—182no—
331#120—182no—
332#117—91no—
333#104—94no—
334#104—94no—
335#100—94no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3D3×D414yes—
339C22×D3—316no—
340C22×D3—64no—
341C22×D3—68no—
342C22×D3—632no—
343C22×D3—68no—
344C22×D3—248no—
345C22×D3—2416no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—24no—
349C3×Q8C2×#6718yes—
350C3×D4—28no—
351C3×D4—28no—
352C3×D4—24no—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4—44no—
356C3×D4—44no—
357C3×D4C2×#6718yes—
358C2×C3×C4—24no—
359C2×C3×C4—28no—
360C2×C3×C4—28no—
361C2×C3×C4—24no—
362C2×C3×C4—44no—
363C2×C3×C4—44no—
364C2×C3×C4D3×D414yes—
365C2×C3×C4D3×D414yes—
366C2×C3×C4D3×D414yes—
367C2×C3×C4C2×#6714yes—
368C2×C3×C4C2×#6714yes—
369C2×C3×C4C23×D314yes—
370#67—632no—
371#67—68no—
372#67—68no—
373#67—2416no—
374C2×Dic3—64no—
375C2×Dic3—68no—
376D12—38no—
377D12—632no—
378D12—64no—
379D12—68no—
380D12—68no—
381D12—68no—
382D12—68no—
383C4×D3—632no—
384C4×D3—68no—
385C4×D3—68no—
386Dic6—38no—
387Dic6—64no—
388C3×C8—28no—
389C3⋊C8—68no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—42no—
394C2×C32—81no—
395C2×C32C2×#12011yescharacteristic
396C3⋊D3—44no—
397C3⋊D3—42no—
398C24—92no—
399C24—182no—
400#41—21no—
401#41—21no—
402#41—21no—
403#41—21no—
404#41—21no—
405#41—21no—
406#41—92no—
407#41—92no—
408#41—184no—
409#41—184no—
410#41—184no—
411#41—184no—
412#41—181no—
413#41—181no—
414#41#63812yescomplemented
415#41C22×C3⋊D312yes—
416C2×Q8—91no—
417C2×Q8#63811yescharacteristic, complemented
418C2×Q8C22×C3⋊D311yescharacteristic, complemented
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—92no—
422C2×D4—91no—
423C2×D4—92no—
424C2×D4—184no—
425C2×D4—182no—
426C2×D4—184no—
427C2×D4—188no—
428C2×D4—188no—
429C2×D4—184no—
430C2×D4—182no—
431C2×D4—181no—
432C2×D4—184no—
433C2×D4—184no—
434C2×D4—181no—
435C2×D4—181no—
436C2×D4—181no—
437C2×D4—181no—
438C2×D4#63811yescharacteristic, complemented
439C2×D4C22×C3⋊D311yescharacteristic, complemented
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—182no—
443C22×C4—181no—
444C22×C4C22×C3⋊D311yescharacteristic
445Q16—22no—
446Q16—182no—
447SD16—22no—
448SD16—22no—
449SD16—182no—
450SD16—182no—
451D8—22no—
452D8—182no—
453M16—21no—
454M16—92no—
455M16—181no—
456M16C22×C3⋊D312yescomplemented
457C2×C8—21no—
458C2×C8—181no—
459C4⋊C4—181no—
460C22⋊C4—184no—
461C22⋊C4—181no—
462C42—92no—
463C22×C3—28no—
464C22×C3—44no—
465C22×C3—48no—
466C22×C3—48no—
467C22×C3—44no—
468C22×C3#93714yes—
469C22×C3#93714yes—
470C22×C3C2×D3×D414yes—
471C2×D3—68no—
472C2×D3—616no—
473C2×D3—1216no—
474C2×D3—128no—
475C2×D3—1216no—
476C2×D3—248no—
477C2×D3—2432no—
478C3×C4—28no—
479C3×C4—44no—
480C3×C4#93714yes—
481C3×C4#93714yes—
482C3×C4C2×D3×D414yes—
483C3×C4C22×#6714yes—
484Dic3—68no—
485Dic3—128no—
486C32#301911yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—94no—
490C23—188no—
491C23—181no—
492C23—182no—
493C23—182no—
494C23—722no—
495C23—724no—
496C23D4×C3⋊D311yescharacteristic
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—92no—
501Q8—181no—
502Q8C2×#63812yes—
503D4—22no—
504D4—22no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—41no—
509D4—41no—
510D4—92no—
511D4—188no—
512D4—188no—
513D4—182no—
514D4—182no—
515D4—182no—
516D4—182no—
517D4—181no—
518D4—182no—
519D4—182no—
520D4—724no—
521D4C2×#63812yes—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—188no—
529C2×C4—181no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4D4×C3⋊D311yescharacteristic
534C2×C4D4×C3⋊D311yescharacteristic
535C2×C4D4×C3⋊D311yescharacteristic
536C2×C4C2×#63811yescharacteristic
537C2×C4C2×#63811yescharacteristic
538C2×C4C23×C3⋊D311yescharacteristic
539C8—22no—
540C8—182no—
541C2×C3—24no—
542C2×C3—24no—
543C2×C3—24no—
544C2×C3—48no—
545C2×C3—84no—
546C2×C3C2×#93714yes—
547D3—1216no—
548D3—128no—
549C22—22no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—182no—
555C22—184no—
556C22—364no—
557C22—364no—
558C22—362no—
559C22—722no—
560C22—728no—
561C22#6414611yescharacteristic
562C22#6414611yescharacteristic
563C22C2×D4×C3⋊D311yescharacteristic
564C4—22no—
565C4—41no—
566C4—182no—
567C4—362no—
568C4#6414611yescharacteristic
569C4#6414611yescharacteristic
570C4C2×D4×C3⋊D311yescharacteristic
571C4C22×#63811yescharacteristic
572C3#8400514yescomplemented
573C2—21no—
574C2—21no—
575C2—21no—
576C2—42no—
577C2—81no—
578C2—364no—
579C2—362no—
580C2C2×#6414611yescharacteristic
subgroupG/H
centerC2C2×#64146
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#575C2
socleC2×C32C2×#120
hypercenter#575C3⋊D3
hypocenterC32#3019
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C32×#575C2semidirect
3. #10596301C2semidirect
4. #10596293C2semidirect
5. #10592935C2semidirect
6. #10592901C2semidirect
7. #10592897C2semidirect
8. #10592838C2semidirect
9. C2×#63650C2semidirect
12. C2×C32×#41C22semidirect
25. C32×#137C22semidirect
27. C32×AGL(1,ℤ/8)C22semidirect
29. C2×C32×M16C22semidirect
33. #64156C22semidirect
34. #64151C22semidirect
35. #64149C22semidirect
37. #64141C22semidirect
39. #64135C22semidirect
40. C2×#3748C22semidirect
41. #63664C22semidirect
42. #63652C22semidirect
43. #63650C22semidirect
45. C3×#575D3semidirect
61. C32×#41D4semidirect
63. C2×C32×Q8D4semidirect
64. C2×C32×Q8C23semidirect
67. C2×C32×D4D4semidirect
68. C2×C32×D4C23semidirect
85. #3828D4semidirect
95. C2×C4⋊(C3⋊D3)D4semidirect
99. C2×#634D4semidirect
105. C32×M16C23semidirect
114. C4×C3⋊Dic3C23semidirect
116. #3748C23semidirect
120. C2×C3×#41C2×D3semidirect
133. C3×#137C2×D3semidirect
135. C3×AGL(1,ℤ/8)C2×D3semidirect
137. C2×C3×M16C2×D3semidirect
208. #575C3⋊D3semidirect
223. C3×#41#67semidirect
225. C2×C3×Q8#67semidirect
226. C2×C3×Q8C22×D3semidirect
229. C2×C3×D4#67semidirect
230. C2×C3×D4C22×D3semidirect
267. C3×M16C22×D3semidirect
311. C2×#41C2×C3⋊D3semidirect
319. #137C2×C3⋊D3semidirect
323. AGL(1,ℤ/8)C2×C3⋊D3semidirect
327. C2×M16C2×C3⋊D3semidirect
414. #41#638semidirect
417. C2×Q8#638semidirect
418. C2×Q8C22×C3⋊D3semidirect
438. C2×D4#638semidirect
439. C2×D4C22×C3⋊D3semidirect
456. M16C22×C3⋊D3semidirect
486. C32#3019semidirect
572. C3#84005semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C32×#5752
#105963012
#105962932
#105929352
#105929012
#105928972
#105928382
C2×#636502
#840053