Finite Group Databasebeta

← #11887084

Subgroups — #11887084

Order 1152.

1386 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#638C211yesmaximal, characteristic
2#10595982C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4#10592917C211yesmaximal, characteristic, complemented
5#10592813C211yesmaximal, characteristic, complemented
6C8×#638C211yesmaximal, characteristic, complemented
7#10592667C211yesmaximal, characteristic, complemented
8#10592477C211yesmaximal, characteristic, complemented
9#10592476C211yesmaximal, characteristic, complemented
10#10592475C211yesmaximal, characteristic, complemented
11C3⋊D3×#102C211yesmaximal, characteristic, complemented
12#10592461C211yesmaximal, characteristic, complemented
13#10592460C211yesmaximal, characteristic, complemented
14#10592459C211yesmaximal, characteristic, complemented
15#10592457C211yesmaximal, characteristic, complemented
16#78758—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C22×#638—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22#64162—21no—
23#64149C2211yescharacteristic
24#64148—21no—
25#64147C2211yescharacteristic
26#64146—21no—
27D4×C3⋊Dic3C2211yescharacteristic
28C2×#3754C2211yescharacteristic
29C2×#3754C2211yescharacteristic, complemented
30#64139C2211yescharacteristic
31C4×#638—21no—
32C4×#638C2211yescharacteristic
33#64133—21no—
34#64133C2211yescharacteristic, complemented
35C2×#3744C2211yescharacteristic, complemented
36C2×C8×C3⋊D3C2211yescharacteristic, complemented
37#64106C2211yescharacteristic, complemented
38#64105—21no—
39C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
40#64098—21no—
41#64097C2211yescharacteristic, complemented
42#64096C2211yescharacteristic, complemented
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63659C2211yescharacteristic, complemented
49#63657C2211yescharacteristic, complemented
50#63648C2211yescharacteristic, complemented
51#63647C2211yescharacteristic, complemented
52#63644C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C8×C3⋊Dic3C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57#63636C2211yescharacteristic, complemented
58#63635C2211yescharacteristic, complemented
59#63635C2211yescharacteristic, complemented
60D4×#67—34no—
61#5511—34no—
62C2×C3×#102D314yescomplemented
63#5218—34no—
64#5114—34no—
65C8×#67—34no—
66#4968—34no—
67#4778—34no—
68#4777—34no—
69#4776—34no—
70D3×#102—34no—
71#4762—34no—
72#4761—34no—
73#4760—34no—
74#4758—34no—
75C24×C32—21no—
76C23×C3⋊D3—21no—
77C2×C32×D4—22no—
78C2×C32×D4—21no—
79C2×C32×D4—41no—
80C2×C32×D4C2311yescharacteristic
81C2×C32×D4C2311yescharacteristic
82C22×C32×C4—21no—
83C22×C32×C4C2311yescharacteristic
84C2×#638—21no—
85C2×#638—21no—
86C2×#638—21no—
87C2×#638—21no—
88C2×#638—21no—
89C2×#638—44no—
90C2×#638D411yescharacteristic
91C22×C3⋊Dic3—21no—
92D4×C3⋊D3—22no—
93D4×C3⋊D3—41no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634—21no—
98C2×#634C2311yescharacteristic
99C2×C32×C8—41no—
100C2×C32×C8C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3757—21no—
106#3757—21no—
107#3757—21no—
108#3757D411yescharacteristic
109#3754—22no—
110#3754—41no—
111#3752—21no—
112#3752—21no—
113#3752D411yescharacteristic
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750—21no—
121#3750D411yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—41no—
127C8×C3⋊D3—41no—
128#3295—91noSylow
129C22×C3×D4C2×D314yes—
130C22×#67—64no—
131C2×D3×D4—34no—
132C22×C3×C8C2×D314yescomplemented
133C2×C3×C4⋊C4C2×D314yescomplemented
134#953—64no—
135#940—34no—
136#939—64no—
137#938—34no—
138#937—64no—
139D4×Dic3—34no—
140C2×#214—34no—
141C2×#214—34no—
142#930—34no—
143C4×#67—34no—
144C4×#67—64no—
145#924—34no—
146#924—64no—
147C2×#204—34no—
148C2×D3×C8—34no—
149#897—34no—
150#896—64no—
151D3×C4⋊C4—34no—
152#889—64no—
153#888—34no—
154#887—34no—
155C3×#102C2×D314yes—
156C3×#102C2×D314yes—
157C3×#102C2×D314yescomplemented
158C3×#102C2×D314yescomplemented
159#832—34no—
160#832—34no—
161#830—34no—
162#821—34no—
163(C2×D3)⋊C8—34no—
164#817—34no—
165#816—34no—
166Dic3⋊C8—34no—
167C8×Dic3—34no—
168#809—34no—
169#809—34no—
170#808—34no—
171#808—34no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—42no—
175C23×C32—42no—
176C23×C32—81no—
177C23×C32C2×D411yescharacteristic
178C22×C3⋊D3—21no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3—42no—
181C22×C3⋊D3—81no—
182C22×C3⋊D3C2×D411yescharacteristic
183C32×D4—21no—
184C32×D4—21no—
185C32×D4—21no—
186C32×D4—42no—
187C32×D4#4112yes—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—81no—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195#638—42no—
196#638—42no—
197#638—42no—
198#638—42no—
199#638—81no—
200#638SD1614yescomplemented
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—42no—
205C2×C3⋊Dic3C2×D411yescharacteristic
206C2×C3⋊Dic3C2×D411yescharacteristic
207C2×C3⋊Dic3C2×D411yescharacteristic
208C4⋊(C3⋊D3)—21no—
209C4⋊(C3⋊D3)—21no—
210C4×C3⋊D3—21no—
211C4×C3⋊D3—21no—
212C4×C3⋊D3—81no—
213#634—21no—
214#634—21no—
215#634—81no—
216C32×C8—21no—
217C32×C8—21no—
218C3⋊(C3⋊C8)—21no—
219C3⋊(C3⋊C8)—21no—
220#554—91no—
221D42—91no—
222#486—91no—
223#481—91no—
224#481—91no—
225#476—91no—
226#465—91no—
227#465—91no—
228#460—91no—
229#450—91no—
230#450—91no—
231C4×SD16—91no—
232C8×D4—91no—
233C2×#102—91no—
234C2×#102C3⋊D311yescharacteristic, complemented
235C24×C3—24no—
236C23×D3—64no—
237C2×C3×D4—28no—
238C2×C3×D4—24no—
239C2×C3×D4—44no—
240C2×C3×D4C22×D314yes—
241C2×C3×D4C22×D314yes—
242C22×C3×C4—24no—
243C22×C3×C4C22×D314yes—
244C2×#67—34no—
245C2×#67—64no—
246C2×#67—64no—
247C2×#67—64no—
248C2×#67—64no—
249C2×#67—64no—
250C2×#67—1216no—
251C22×Dic3—64no—
252D3×D4—68no—
253D3×D4—124no—
254C2×D12—34no—
255C2×C4×D3—34no—
256C2×C4×D3—64no—
257C2×Dic6—34no—
258C2×Dic6—64no—
259C2×C3×C8—44no—
260C2×C3×C8C22×D314yes—
261C2×C3×C8C22×D314yes—
262C3×C4⋊C4—24no—
263C3×C4⋊C4C22×D314yes—
264C3×C4⋊C4C22×D314yes—
265#217—34no—
266#217—64no—
267#217—64no—
268#217—64no—
269#214—68no—
270#214—124no—
271(C2×D3)⋊C4—34no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—64no—
274C4⋊Dic3—34no—
275C4⋊Dic3—34no—
276C4⋊Dic3—64no—
277Dic3⋊C4—34no—
278Dic3⋊C4—64no—
279Dic3⋊C4—64no—
280Dic3⋊C4—64no—
281Dic3⋊C4—64no—
282C4×Dic3—34no—
283C4×Dic3—64no—
284C2×C3⋊C8—34no—
285C2×C3⋊C8—34no—
286#204—124no—
287D3×C8—124no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—22no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32—41no—
296C22×C32—84no—
297C22×C32C2×SD1612yes—
298C22×C32C22×D411yescharacteristic
299C2×C3⋊D3—21no—
300C2×C3⋊D3—21no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3—84no—
305C2×C3⋊D3C2×SD1612yes—
306C32×C4—21no—
307C32×C4—41no—
308C32×C4—41no—
309C32×C4C2×#4111yescharacteristic
310C32×C4H(5,𝔽2)11yescharacteristic
311C3⋊Dic3—21no—
312C3⋊Dic3—21no—
313C3⋊Dic3—41no—
314C3⋊Dic3—41no—
315C3⋊Dic3—41no—
316C3⋊Dic3C2×SD1612yes—
317C22×D4—91no—
318C22×D4—181no—
319C22×D4C2×C3⋊D311yescharacteristic
320C2×SD16—91no—
321C2×SD16—91no—
322C2×SD16—91no—
323C22×C8—91no—
324C22×C8C2×C3⋊D311yescharacteristic, complemented
325C4⋊Q8—91no—
326#127—91no—
327#125—181no—
328C22⋊Q8—91no—
329C22⋊Q8—91no—
330C22⋊Q8—181no—
331C22⋊Q8—181no—
332#121—91no—
333#121—91no—
334#121—181no—
335#120—181no—
336#120—181no—
337C4×Q8—91no—
338C4×D4—91no—
339C4×D4—91no—
340C4×D4—181no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
343#106—91no—
344#106—91no—
345#106—91no—
346C4⋊C8—91no—
347#103—91no—
348#102—91no—
349#102—91no—
350#102—91no—
351#102—91no—
352#102—91no—
353#102C2×C3⋊D311yescharacteristic
354#102C2×C3⋊D311yescharacteristic
355#102C2×C3⋊D311yescharacteristic, complemented
356#102C2×C3⋊D311yescharacteristic, complemented
357C22⋊C8—91no—
358C22⋊C8—91no—
359C4×C8—91no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—48no—
363C23×C3—48no—
364C23×C3—84no—
365C23×C3D3×D414yes—
366C22×D3—34no—
367C22×D3—64no—
368C22×D3—128no—
369C22×D3—128no—
370C22×D3—244no—
371C3×D4—24no—
372C3×D4—24no—
373C3×D4—24no—
374C3×D4—48no—
375C3×D4#23518yes—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—84no—
381C2×C3×C4D3×D414yes—
382C2×C3×C4C23×D314yes—
383#67—316no—
384#67—128no—
385#67—128no—
386#67—128no—
387#67—128no—
388#67—244no—
389C2×Dic3—34no—
390C2×Dic3—34no—
391C2×Dic3—34no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—128no—
396D12—64no—
397D12—64no—
398C4×D3—64no—
399C4×D3—64no—
400C4×D3—244no—
401Dic6—64no—
402Dic6—64no—
403Dic6—244no—
404C3×C8—24no—
405C3×C8—24no—
406C3⋊C8—64no—
407C3⋊C8—64no—
408C2×C32—22no—
409C2×C32—42no—
410C2×C32—81no—
411C2×C32#54611yescharacteristic
412C2×C32C22×SD1611yescharacteristic
413C2×C32#57611yescharacteristic
414C3⋊D3—22no—
415C3⋊D3—81no—
416C24—21no—
417C24—181no—
418C2×Q8—91no—
419C2×Q8—181no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—91no—
424C2×D4—91no—
425C2×D4—181no—
426C2×D4—181no—
427C2×D4—181no—
428C2×D4—182no—
429C2×D4—181no—
430C2×D4—181no—
431C2×D4—361no—
432C2×D4—364no—
433C2×D4C22×C3⋊D311yescharacteristic
434C2×D4C22×C3⋊D311yescharacteristic
435C22×C4—21no—
436C22×C4—91no—
437C22×C4—181no—
438C22×C4—181no—
439C22×C4C22×C3⋊D311yescharacteristic
440SD16—182no—
441SD16—361no—
442SD16—361no—
443C2×C8—41no—
444C2×C8—91no—
445C2×C8—91no—
446C2×C8—361no—
447C2×C8C22×C3⋊D311yescharacteristic
448C2×C8C22×C3⋊D311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—91no—
451C4⋊C4—91no—
452C4⋊C4—91no—
453C4⋊C4—181no—
454C4⋊C4—181no—
455C4⋊C4—181no—
456C4⋊C4—181no—
457C4⋊C4—181no—
458C4⋊C4C22×C3⋊D311yescharacteristic
459C4⋊C4C22×C3⋊D311yescharacteristic
460C22⋊C4—91no—
461C22⋊C4—91no—
462C22⋊C4—181no—
463C22⋊C4—181no—
464C22⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C42—91no—
468C42—181no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—28no—
472C22×C3—44no—
473C22×C3—44no—
474C22×C3—44no—
475C22×C3—44no—
476C22×C3—44no—
477C22×C3—816no—
478C22×C3D3×SD1618yes—
479C22×C3C2×D3×D414yes—
480C2×D3—38no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—124no—
484C2×D3—124no—
485C2×D3—124no—
486C2×D3—2416no—
487C3×C4—24no—
488C3×C4—44no—
489C3×C4—44no—
490C3×C4C2×#23514yes—
491C3×C4#100414yes—
492Dic3—38no—
493Dic3—64no—
494Dic3—64no—
495Dic3—124no—
496Dic3—124no—
497Dic3—124no—
498C32#329511yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—42no—
502C23—42no—
503C23—81no—
504C23—91no—
505C23—181no—
506C23—362no—
507C23—362no—
508C23—721no—
509C23D4×C3⋊D311yescharacteristic
510Q8—181no—
511Q8—181no—
512Q8—721no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—94no—
518D4—181no—
519D4—181no—
520D4—362no—
521D4—362no—
522D4—362no—
523D4—362no—
524D4—721no—
525D4#382812yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—81no—
531C2×C4—91no—
532C2×C4—91no—
533C2×C4—91no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—362no—
540C2×C4—721no—
541C2×C4D4×C3⋊D311yescharacteristic
542C2×C4C23×C3⋊D311yescharacteristic
543C8—21no—
544C8—21no—
545C8—181no—
546C8—181no—
547C2×C3—28no—
548C2×C3—48no—
549C2×C3—84no—
550C2×C3#549014yes—
551C2×C3#575714yes—
552C2×C3C2×D3×SD1614yes—
553D3—68no—
554D3—244no—
555C22—21no—
556C22—21no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—84no—
564C22—92no—
565C22—181no—
566C22—181no—
567C22—361no—
568C22—361no—
569C22—361no—
570C22—724no—
571C22SD16×C3⋊D312yes—
572C22C2×D4×C3⋊D311yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—92no—
577C4—181no—
578C4—181no—
579C4—361no—
580C4—361no—
581C4—361no—
582C4C2×#382811yescharacteristic
583C4#6436111yescharacteristic
584C3#7875814yescomplemented
585C2—22no—
586C2—42no—
587C2—81no—
588C2—182no—
589C2—721no—
590C2#1059596111yescharacteristic
591C2#1059622811yescharacteristic
592C2C2×SD16×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#102C2
socleC22×C32C22×D4
prime radicalD4×#638C2
hypercenterC2×#102C3⋊D3
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. #10595982C2semidirect
3. C2×C32×#102C2semidirect
4. #10592917C2semidirect
5. #10592813C2semidirect
6. C8×#638C2semidirect
7. #10592667C2semidirect
8. #10592477C2semidirect
9. #10592476C2semidirect
10. #10592475C2semidirect
11. C3⋊D3×#102C2semidirect
12. #10592461C2semidirect
13. #10592460C2semidirect
14. #10592459C2semidirect
15. #10592457C2semidirect
20. C22×C32×C8C22semidirect
21. C2×C32×C4⋊C4C22semidirect
29. C2×#3754C22semidirect
34. #64133C22semidirect
35. C2×#3744C22semidirect
36. C2×C8×C3⋊D3C22semidirect
37. #64106C22semidirect
39. C4⋊C4×C3⋊D3C22semidirect
41. #64097C22semidirect
42. #64096C22semidirect
45. C32×#102C22semidirect
46. C32×#102C22semidirect
48. #63659C22semidirect
49. #63657C22semidirect
50. #63648C22semidirect
51. #63647C22semidirect
52. #63644C22semidirect
53. #63643C22semidirect
54. #63641C22semidirect
55. C8×C3⋊Dic3C22semidirect
56. #63636C22semidirect
57. #63636C22semidirect
58. #63635C22semidirect
59. #63635C22semidirect
62. C2×C3×#102D3semidirect
132. C22×C3×C8C2×D3semidirect
133. C2×C3×C4⋊C4C2×D3semidirect
157. C3×#102C2×D3semidirect
158. C3×#102C2×D3semidirect
200. #638SD16semidirect
234. C2×#102C3⋊D3semidirect
324. C22×C8C2×C3⋊D3semidirect
342. C2×C4⋊C4C2×C3⋊D3semidirect
355. #102C2×C3⋊D3semidirect
356. #102C2×C3⋊D3semidirect
498. C32#3295semidirect
584. C3#78758semidirect

Maximal subgroups

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

subgroupindex
D4×#6382
#105959822
C2×C32×#1022
#105929172
#105928132
C8×#6382
#105926672
#105924772
#105924762
#105924752
C3⋊D3×#1022
#105924612
#105924602
#105924592
#105924572
#787583