Finite Group Databasebeta

← #11887164

Subgroups — #11887164

Order 1152.

988 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5717C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591460C212yesmaximal, complemented
6#10591459C212yesmaximal, complemented
7#10591415C212yesmaximal, complemented
8D3×#832C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic, complemented
10C3⋊C8×D12C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83483—31nomaximal
13#81577—31nomaximal
14C2×C3×D3×D4—21no—
15C2×C3×D3×D4C2212yes—
16C32×#127C2211yescharacteristic
17C2×#3754C2212yescomplemented
18C4×#634C2211yescharacteristic, complemented
19C3×#938—21no—
20C3×#938C2212yes—
21C3×#937—22no—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic, complemented
25#63898—21no—
26D3×C4⋊Dic3C2212yescomplemented
27#63887—22no—
28#63872—21no—
29#63857C2212yescomplemented
30C2×#3716C2211yescharacteristic
31C2×D3×C3⋊C8C2212yescomplemented
32#63659C2212yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
34C3×#832C2212yescomplemented
35C3×#832C2212yescomplemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37#63574C2212yescomplemented
38#63573C2211yescharacteristic, complemented
39#63567C2211yescharacteristic, complemented
40#63563C2211yescharacteristic
41#63562C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×D42—31no—
44#5730—31no—
45#5717D311yescharacteristic
46#5543—31no—
47C3×#486—31no—
48#5218—32no—
49C2×#832—32no—
50#5084—31no—
51#5075—31no—
52#5075—31no—
53#5075—61no—
54#5070D311yescharacteristic, complemented
55#5041—32no—
56#5034—32no—
57C4×#214—31no—
58D4×C3⋊C8—31no—
59#5008—31no—
60#4778—32no—
61#4777—32no—
62#4776—32no—
63D3×#102—32no—
64C4×#204—31no—
65C8×D12—31no—
66C23×C3×D3—22no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C2×#634C2311yescharacteristic
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C3×D3×D4—24no—
74C3×D3×D4—42no—
75C3×D3×D4—44no—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6—21no—
81C2×D3×Dic3—22no—
82C32×C42C2311yescharacteristic
83#3754—42no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C4×C3⋊Dic3—21no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—22no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4D412yes—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3D411yescharacteristic
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3716—22no—
101D3×C3⋊C8—42no—
102#3295—91noSylow
103C22×C3×D4—32no—
104C22×C3×D4—61no—
105C2×D3×D4—21no—
106C2×D3×D4C2×D312yes—
107C3×C4⋊Q8—31no—
108C3×#127—21no—
109C3×#127C2×D311yescharacteristic
110C3×#127C2×D311yescharacteristic
111C3×#121—32no—
112C3×#121—61no—
113C3×#120—62no—
114C3×C4×D4—31no—
115C3×C4×D4—31no—
116#946—62no—
117#938—21no—
118#938C2×D312yes—
119#937—22no—
120D4×Dic3—61no—
121C2×#214—32no—
122C2×#214—32no—
123C2×#214—31no—
124C2×#214—62no—
125C2×C4⋊Dic3—32no—
126#924—32no—
127C22×C3⋊C8—32no—
128C2×#204—31no—
129C2×D3×C8—32no—
130#897—32no—
131#893—61no—
132D3×C4⋊C4—32no—
133#890—61no—
134#890—61no—
135#878—62no—
136C4×D12C2×D311yescharacteristic
137C4×D12C2×D311yescharacteristic
138#869C2×D311yescharacteristic, complemented
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×#102—32no—
143C3×#102—32no—
144C3×C4×C8—31no—
145#832—32no—
146#832—32no—
147#832—32no—
148#832—31no—
149#832—62no—
150#832C2×D312yescomplemented
151#832C2×D312yescomplemented
152#830—32no—
153#821—31no—
154(C2×D3)⋊C8—32no—
155#817—31no—
156#816—31no—
157#810—31no—
158#809—32no—
159#808—32no—
160#808—32no—
161#808—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—61no—
165C4×C3⋊C8C2×D311yescharacteristic, complemented
166C23×C32—22no—
167C22×C3×D3—21no—
168C22×C3×D3—44no—
169C22×C3×D3—44no—
170C22×C3×D3—82no—
171C22×C3×D3C2×D412yes—
172C32×D4—22no—
173C32×D4—22no—
174C32×D4—42no—
175C32×D4—81no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181#634—21no—
182#634—21no—
183C3×#67—44no—
184C3×#67—44no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—21no—
189C3×D12SD1614yescomplemented
190C3×D12#4112yes—
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×C4×D3—42no—
194C3×Dic6—81no—
195D3×Dic3—82no—
196C3⋊(C3⋊C8)—22no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199#554—91no—
200D42—31no—
201#486—31no—
202#481—92no—
203#476—91no—
204#465—92no—
205#460—91no—
206#450—92no—
207C4×SD16—91no—
208C8×D4—91no—
209C2×#102—92no—
210C24×C3—62no—
211C23×D3—22no—
212C2×C3×Q8—61no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—22no—
218C2×C3×D4—31no—
219C2×C3×D4—31no—
220C2×C3×D4—41no—
221C2×C3×D4—41no—
222C2×C3×D4—62no—
223C2×C3×D4—64no—
224C2×C3×D4—62no—
225C2×C3×D4—122no—
226C2×C3×D4—124no—
227C2×C3×D4C22×D312yes—
228C2×C3×D4C22×D312yes—
229C22×C3×C4—32no—
230C22×C3×C4—61no—
231C2×#67—22no—
232C2×#67—22no—
233C22×Dic3—62no—
234D3×D4—24no—
235D3×D4—42no—
236D3×D4—44no—
237C2×D12#6711yescharacteristic
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—62no—
241C2×C4×D3C22×D312yes—
242C2×Dic6—21no—
243C2×Dic6—31no—
244C2×Dic6—31no—
245C2×Dic6—61no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—61no—
252C3×C22⋊C4—32no—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—61no—
255C3×C42—21no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258#217—22no—
259#217—62no—
260#214—62no—
261#214—122no—
262#214—122no—
263#214—124no—
264(C2×D3)⋊C4—21no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4#6712yes—
267C4⋊Dic3—21no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—61no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3#6711yescharacteristic
274C4⋊Dic3C22×D311yescharacteristic
275C4⋊Dic3C22×D312yes—
276Dic3⋊C4—62no—
277Dic3⋊C4—61no—
278Dic3⋊C4—61no—
279Dic3⋊C4—62no—
280Dic3⋊C4—121no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—121no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8—122no—
288C2×C3⋊C8C22×D311yescharacteristic
289C2×C3⋊C8C22×D311yescharacteristic
290#204—62no—
291D3×C8—122no—
292C22×C32—42no—
293C22×C32—42no—
294C22×C32—42no—
295C22×C32C22×D411yescharacteristic
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—41no—
300C2×C3×D3—41no—
301C2×C3×D3—88no—
302C2×C3×D3C2×SD1614yes—
303C32×C4—21no—
304C32×C4C2×SD1612yes—
305C32×C4C2×#4111yescharacteristic
306C32×C4H(5,𝔽2)11yescharacteristic
307C3⋊Dic3—41no—
308C3⋊Dic3—41no—
309C3×Dic3—22no—
310C3×Dic3—41no—
311C3×Dic3—42no—
312C22×D4—32no—
313C22×D4—61no—
314C2×SD16—91no—
315C2×SD16—92no—
316C22×C8—92no—
317C4⋊Q8—31no—
318#127D3211yescharacteristic
319#125—181no—
320C22⋊Q8—92no—
321C22⋊Q8—182no—
322#121—32no—
323#121—61no—
324#120—62no—
325C4×Q8—91no—
326C4×D4—31no—
327C4×D4—31no—
328C4×D4—181no—
329C2×C4⋊C4—92no—
330#106—92no—
331#106—91no—
332C4⋊C8—91no—
333#103—91no—
334#102—32no—
335#102—32no—
336#102—92no—
337#102—91no—
338#102—92no—
339C22⋊C8—92no—
340C4×C8—31no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—32no—
344C23×C3—42no—
345C23×C3—61no—
346C23×C3—124no—
347C23×C3—124no—
348C23×C3—242no—
349C22×D3—21no—
350C22×D3—44no—
351C22×D3—44no—
352C22×D3—82no—
353C22×D3C2×#6712yes—
354C3×Q8—241no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—34no—
360C3×D4—32no—
361C3×D4—42no—
362C3×D4—42no—
363C3×D4—42no—
364C3×D4—42no—
365C3×D4—61no—
366C3×D4—82no—
367C3×D4—81no—
368C3×D4—81no—
369C3×D4—82no—
370C3×D4—124no—
371C3×D4—124no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—32no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—122no—
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4C2×#6711yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387#67—44no—
388#67—44no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397C2×Dic3—242no—
398C2×Dic3C2×#6712yes—
399D12—21no—
400D12#21414yescomplemented
401D12#23712yes—
402C4×D3—22no—
403C4×D3—22no—
404C4×D3—42no—
405C4×D3—242no—
406Dic6—62no—
407Dic6—61no—
408Dic6—61no—
409Dic6—61no—
410Dic6—61no—
411Dic6—81no—
412Dic6—121no—
413C3×C8—61no—
414C3×C8—61no—
415C3⋊C8—21no—
416C3⋊C8—21no—
417C3⋊C8—62no—
418C3⋊C8—62no—
419C3⋊C8—122no—
420C2×C32—82no—
421C2×C32#54611yescharacteristic
422C2×C32C22×SD1611yescharacteristic
423C2×C32#57611yescharacteristic
424C3×D3—24no—
425C3×D3—42no—
426C24—62no—
427C2×Q8—61no—
428C2×Q8—91no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—31no—
432C2×D4—31no—
433C2×D4—62no—
434C2×D4—64no—
435C2×D4—62no—
436C2×D4—122no—
437C2×D4—124no—
438C2×D4C2×D3212yes—
439C22×C4—32no—
440C22×C4—61no—
441C22×C4—182no—
442SD16—182no—
443SD16—362no—
444C2×C8—31no—
445C2×C8—31no—
446C2×C8—92no—
447C2×C8—362no—
448C4⋊C4—31no—
449C4⋊C4—32no—
450C4⋊C4—31no—
451C4⋊C4—61no—
452C4⋊C4—91no—
453C4⋊C4—182no—
454C4⋊C4—182no—
455C4⋊C4—181no—
456C22⋊C4—32no—
457C22⋊C4—62no—
458C22⋊C4—61no—
459C22⋊C4—182no—
460C42—181no—
461C42C2×D3211yescharacteristic
462C22×C3—21no—
463C22×C3—34no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—82no—
474C22×C3—82no—
475C22×C3—82no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3—248no—
479C22×C3C2×D3×D411yescharacteristic
480C22×C3C22×#6711yescharacteristic
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—41no—
485C2×D3—41no—
486C2×D3—88no—
487C2×D3C2×#21414yes—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—22no—
493C3×C4—41no—
494C3×C4—62no—
495C3×C4—121no—
496C3×C4—122no—
497C3×C4D3×SD1612yes—
498C3×C4C2×#21412yes—
499C3×C4C2×#23711yescharacteristic
500C3×C4#100411yescharacteristic
501C3×C4D3×#4111yescharacteristic
502C3×C4#100911yescharacteristic
503Dic3—22no—
504Dic3—42no—
505Dic3—41no—
506Dic3—122no—
507Dic3—121no—
508Dic3—121no—
509Dic3—121no—
510Dic3—121no—
511Dic3—241no—
512C32#329511yescharacteristic, complemented, Sylow
513C23—22no—
514C23—32no—
515C23—61no—
516C23—124no—
517C23—124no—
518C23—242no—
519Q8—181no—
520Q8—181no—
521Q8—241no—
522D4—22no—
523D4—22no—
524D4—32no—
525D4—34no—
526D4—42no—
527D4—61no—
528D4—81no—
529D4—124no—
530D4—124no—
531C2×C4—32no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—122no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—722no—
540C2×C4D3×#6711yescharacteristic
541C2×C4D3×#6711yescharacteristic
542C2×C4C22×D3211yescharacteristic
543C8—61no—
544C8—61no—
545C8—182no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—64no—
550C2×C3—82no—
551C2×C3—82no—
552C2×C3—122no—
553C2×C3—162no—
554C2×C3#567611yescharacteristic
555C2×C3#575711yescharacteristic
556C2×C3C2×D3×SD1611yescharacteristic
557C2×C3C22×#21411yescharacteristic
558C2×C3#580611yescharacteristic
559C2×C3#583511yescharacteristic
560D3—24no—
561D3—42no—
562C22—34no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—62no—
567C22—62no—
568C22—62no—
569C22—121no—
570C22—121no—
571C22—248no—
572C22C2×D3×#6711yescharacteristic
573C4—21no—
574C4—62no—
575C4—122no—
576C4—121no—
577C4—361no—
578C4—361no—
579C4D3×#21412yes—
580C4D3×#23711yescharacteristic
581C4#6431411yescharacteristic
582C3—21no—
583C3#8157711yescharacteristic, complemented
584C3#8348311yescharacteristic, complemented
585C2—64no—
586C2—82no—
587C2—122no—
588C2#1059509611yescharacteristic
589C2C2×D3×#21411yescharacteristic
590C2#1059522911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5717C2
hypercenter#127D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593956C2semidirect
3. #10592774C2semidirect
4. C3×#5070C2semidirect
5. #10591460C2semidirect
6. #10591459C2semidirect
7. #10591415C2semidirect
8. D3×#832C2semidirect
9. C4×#3716C2semidirect
10. C3⋊C8×D12C2semidirect
11. #10590266C2semidirect
17. C2×#3754C22semidirect
18. C4×#634C22semidirect
24. C3×#869C22semidirect
26. D3×C4⋊Dic3C22semidirect
29. #63857C22semidirect
31. C2×D3×C3⋊C8C22semidirect
32. #63659C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. C3×#832C22semidirect
35. C3×#832C22semidirect
36. C3×C4×C3⋊C8C22semidirect
37. #63574C22semidirect
38. #63573C22semidirect
39. #63567C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
54. #5070D3semidirect
138. #869C2×D3semidirect
150. #832C2×D3semidirect
151. #832C2×D3semidirect
165. C4×C3⋊C8C2×D3semidirect
189. C3×D12SD16semidirect
400. D12#214semidirect
512. C32#3295semidirect
583. C3#81577semidirect
584. C3#83483semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
#105939562
#105927742
C3×#50702
#105914602
#105914592
#105914152
D3×#8322
C4×#37162
C3⋊C8×D122
#105902662
#834833
#815773