Finite Group Databasebeta

← #11887155

Subgroups — #11887155

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
1D122C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic, complemented
6#10590946C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590830C212yesmaximal, complemented
9#10590677C212yesmaximal, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#81075—31nomaximal
13#79439—31nomaximal
14C2×D3×D12—21no—
15C2×D3×D12C2212yes—
16C2×#3744C2212yescomplemented
17#64083C2211yescharacteristic
18C4×#634C2211yescharacteristic, complemented
19C2×C3×D3×C8C2212yescomplemented
20C3×C4×D12C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×#869C2211yescharacteristic, complemented
23#63923—22no—
24#63909—21no—
25#63909C2212yes—
26#63898—21no—
27D3×C4⋊Dic3C2212yescomplemented
28#63887—22no—
29#63872—21no—
30#63857C2212yescomplemented
31C2×#3716C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic, complemented
33#63648C2212yescomplemented
34C3×#821C2212yes—
35C3×(C2×D3)⋊C8C2212yescomplemented
36C3×#817C2212yescomplemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63573C2211yescharacteristic, complemented
39#63567C2211yescharacteristic, complemented
40#63564C2212yescomplemented
41#63564C2212yescomplemented
42#63563C2211yescharacteristic
43#5730—31no—
44D4×D12—31no—
45D4×D12—31no—
46#5543—31no—
47C3×#476—31no—
48C3×C8×D4—31no—
49#5114—32no—
50C2×#821—32no—
51#5088—31no—
52C4×#214—31no—
53#4864—32no—
54#4863—32no—
55#4848—31no—
56#4848—31no—
57#4848—61no—
58#4842D311yescharacteristic, complemented
59#4834D311yescharacteristic, complemented
60#4776—32no—
61D3×#102—32no—
62#4735—32no—
63#4731—32no—
64#4694—31no—
65C4×#204—31no—
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×#634C2311yescharacteristic
71C2×C3×D12D411yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6—21no—
76C2×#626—22no—
77C2×#626—22no—
78C2×D3×Dic3—22no—
79D3×D12—24no—
80D3×D12—42no—
81D3×D12—44no—
82C2×C32×C8C2312yes—
83C32×C42C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C4×C3⋊Dic3—21no—
87#3744—42no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4D412yes—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×D3×C8—42no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3716—22no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—61no—
105C22×D12—32no—
106C22×D12—61no—
107C22×C3×C8—32no—
108C3×C4⋊Q8—31no—
109C3×C4×D4—31no—
110C3×C4×D4—31no—
111#946—62no—
112D4×Dic3—61no—
113C2×#214—31no—
114#930—32no—
115#930—61no—
116C2×C4⋊Dic3—32no—
117#924—32no—
118C2×#204—31no—
119C2×#204—32no—
120C2×#204—32no—
121C2×#204—62no—
122C2×D3×C8C2×D312yescomplemented
123#897—32no—
124#895—32no—
125#895—61no—
126#893—61no—
127D3×C4⋊C4—32no—
128#890—61no—
129#890—61no—
130#882—62no—
131#882—62no—
132#878—62no—
133#874—31no—
134#874—31no—
135#874—61no—
136C4×D12C2×D311yescharacteristic
137C4×D12C2×D311yescharacteristic
138#869C2×D311yescharacteristic, complemented
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×#106—32no—
143C3×C4⋊C8—21no—
144C3×C4⋊C8C2×D311yescharacteristic, complemented
145C3×C4⋊C8C2×D311yescharacteristic, complemented
146C3×#102—32no—
147C3×C22⋊C8—32no—
148C3×C4×C8—31no—
149#832—31no—
150#821—31no—
151#821—32no—
152#821—32no—
153#821—32no—
154#821—32no—
155#821—62no—
156#821C2×D312yes—
157(C2×D3)⋊C8C2×D312yescomplemented
158#817—31no—
159#817C2×D312yescomplemented
160#816—31no—
161#810—31no—
162#809—32no—
163#809—32no—
164#808—31no—
165C4×C3⋊C8C2×D311yescharacteristic, complemented
166C22×C3⋊D3—22no—
167C22×C3×D3—21no—
168C22×C3×D3C2×D412yes—
169C2×D32—44no—
170C2×D32—44no—
171C2×D32—82no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—42no—
180C4⋊(C3⋊D3)—81no—
181#634—21no—
182#634—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12SD1614yescomplemented
188C3×D12#4112yes—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×C4×D3—42no—
192C3×Dic6—81no—
193#626—44no—
194#626—44no—
195D3×Dic3—82no—
196C32×C8—22no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199#554—91no—
200D42—91no—
201#486—91no—
202#481—92no—
203#476—31no—
204#465—92no—
205#460—91no—
206#450—92no—
207C4×SD16—91no—
208C8×D4—31no—
209C2×#102—92no—
210C23×D3—62no—
211C23×D3—62no—
212C2×C3×Q8—61no—
213C2×C3×D4—31no—
214C2×C3×D4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—61no—
217C2×#67—62no—
218C2×#67—62no—
219C22×Dic3—62no—
220D3×D4—64no—
221D3×D4—122no—
222D3×D4—124no—
223C2×D12—32no—
224C2×D12—32no—
225C2×D12—62no—
226C2×D12—64no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—61no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—61no—
233C2×D12—121no—
234C2×D12—121no—
235C2×D12—122no—
236C2×D12—124no—
237C2×D12D1211yescharacteristic
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—22no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C2×C3×C8—122no—
250C2×C3×C8C22×D312yes—
251C2×C3×C8C22×D312yes—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—61no—
256C3×C22⋊C4—32no—
257C3×C22⋊C4—61no—
258C3×C42—21no—
259C3×C42C22×D311yescharacteristic
260C3×C42C22×D311yescharacteristic
261#217—62no—
262#214—62no—
263(C2×D3)⋊C4—21no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4D1212yes—
268C4⋊Dic3—21no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274C4⋊Dic3D1211yescharacteristic
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D312yes—
277Dic3⋊C4—62no—
278Dic3⋊C4—61no—
279Dic3⋊C4—61no—
280Dic3⋊C4—62no—
281Dic3⋊C4—121no—
282C4×Dic3—61no—
283C4×Dic3—61no—
284C4×Dic3—121no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287#204—62no—
288#204—122no—
289#204—122no—
290#204—124no—
291D3×C8—42no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—42no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—41no—
300C2×C3×D3—41no—
301C2×C3×D3C2×SD1614yes—
302D32—88no—
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—92no—
313C22×D4—181no—
314C2×SD16—91no—
315C2×SD16—92no—
316C22×C8—32no—
317C4⋊Q8—31no—
318#127—91no—
319#125—181no—
320C22⋊Q8—92no—
321C22⋊Q8—182no—
322#121—92no—
323#121—181no—
324#120—182no—
325C4×Q8—91no—
326C4×D4—31no—
327C4×D4—31no—
328C4×D4—181no—
329C2×C4⋊C4—92no—
330#106—32no—
331#106—91no—
332C4⋊C8D3211yescharacteristic, complemented
333#103—91no—
334#102—32no—
335#102—92no—
336#102—92no—
337#102—91no—
338#102—92no—
339C22⋊C8—32no—
340C4×C8—31no—
341C23×C3—32no—
342C23×C3—61no—
343C22×D3—21no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—122no—
347C22×D3—124no—
348C22×D3—124no—
349C22×D3—124no—
350C22×D3—124no—
351C22×D3—242no—
352C22×D3—242no—
353C22×D3C2×D1212yes—
354C3×Q8—241no—
355C3×D4—34no—
356C3×D4—32no—
357C3×D4—61no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—32no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4—122no—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—124no—
374#67—124no—
375C2×Dic3—22no—
376C2×Dic3—21no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—242no—
384C2×Dic3C2×D1212yes—
385D12—21no—
386D12—62no—
387D12—62no—
388D12—62no—
389D12—62no—
390D12—122no—
391D12—122no—
392D12—124no—
393D12—124no—
394D12—122no—
395D12—122no—
396D12—242no—
397D12—241no—
398D12—241no—
399D12—242no—
400D12#20414yescomplemented
401D12#23912yes—
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—22no—
414C3×C8—22no—
415C3×C8—42no—
416C3×C8—61no—
417C3×C8—61no—
418C3⋊C8—21no—
419C3⋊C8—21no—
420C2×C32#54611yescharacteristic
421C2×C32C22×SD1611yescharacteristic
422C2×C32#57611yescharacteristic
423C3⋊D3—82no—
424C3×D3—24no—
425C3×D3—42no—
426C24—182no—
427C2×Q8—61no—
428C2×Q8—91no—
429C2×D4—31no—
430C2×D4—31no—
431C2×D4—92no—
432C2×D4—182no—
433C2×D4—184no—
434C2×D4—182no—
435C2×D4—181no—
436C2×D4—181no—
437C2×D4—362no—
438C2×D4—364no—
439C22×C4—32no—
440C22×C4—61no—
441C22×C4—182no—
442SD16—182no—
443SD16—362no—
444C2×C8—31no—
445C2×C8—31no—
446C2×C8—122no—
447C2×C8C2×D3212yes—
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—61no—
458C22⋊C4—182no—
459C22⋊C4—182no—
460C42—181no—
461C42C2×D3211yescharacteristic
462C22×C3—21no—
463C22×C3—34no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3C22×D1211yescharacteristic
470C22×C3C2×D3×D411yescharacteristic
471C2×D3—22no—
472C2×D3—22no—
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—242no—
483C2×D3—242no—
484C2×D3—242no—
485C2×D3—248no—
486C2×D3—248no—
487C2×D3C2×#20414yes—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—22no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—41no—
494C3×C4—62no—
495C3×C4—121no—
496C3×C4—122no—
497C3×C4C2×#20412yes—
498C3×C4D3×SD1612yes—
499C3×C4#100411yescharacteristic
500C3×C4C2×#23911yescharacteristic
501C3×C4D3×#4111yescharacteristic
502C3×C4#100911yescharacteristic
503Dic3—22no—
504Dic3—41no—
505Dic3—42no—
506Dic3—122no—
507Dic3—121no—
508Dic3—121no—
509Dic3—121no—
510Dic3—121no—
511Dic3—241no—
512C32#329511yescharacteristic, complemented, Sylow
513C23—32no—
514C23—61no—
515C23—182no—
516C23—364no—
517C23—364no—
518C23—722no—
519Q8—181no—
520Q8—181no—
521Q8—241no—
522D4—34no—
523D4—32no—
524D4—61no—
525D4—182no—
526D4—182no—
527D4—364no—
528D4—364no—
529D4—362no—
530D4—721no—
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×D1211yescharacteristic
541C2×C4D3×D1211yescharacteristic
542C2×C4C22×D3211yescharacteristic
543C8—22no—
544C8—61no—
545C8—61no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—64no—
550C2×C3—122no—
551C2×C3#555411yescharacteristic
552C2×C3#563011yescharacteristic
553C2×C3C22×#20411yescharacteristic
554C2×C3#575211yescharacteristic
555C2×C3C2×D3×SD1611yescharacteristic
556C2×C3#577411yescharacteristic
557D3—24no—
558D3—42no—
559D3—242no—
560D3—242no—
561D3—482no—
562C22—34no—
563C22—62no—
564C22—62no—
565C22—62no—
566C22—121no—
567C22—121no—
568C22—362no—
569C22—362no—
570C22—362no—
571C22—728no—
572C22C2×D3×D1211yescharacteristic
573C4—21no—
574C4—62no—
575C4—121no—
576C4—122no—
577C4—361no—
578C4—361no—
579C4D3×#20412yes—
580C4#6431411yescharacteristic
581C4D3×#23911yescharacteristic
582C3—21no—
583C3#7943911yescharacteristic, complemented
584C3#8107511yescharacteristic, complemented
585C2—64no—
586C2—122no—
587C2—722no—
588C2#1059462911yescharacteristic
589C2C2×D3×#20411yescharacteristic
590C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalD122C2
hypercenterC4⋊C8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593956C2semidirect
3. #10592547C2semidirect
4. C3×#4842C2semidirect
5. C3×#4834C2semidirect
6. #10590946C2semidirect
7. D3×#821C2semidirect
8. #10590830C2semidirect
9. #10590677C2semidirect
10. C4×#3716C2semidirect
11. #10590281C2semidirect
16. C2×#3744C22semidirect
18. C4×#634C22semidirect
19. C2×C3×D3×C8C22semidirect
22. C3×#869C22semidirect
27. D3×C4⋊Dic3C22semidirect
30. #63857C22semidirect
32. C32×C4⋊C8C22semidirect
33. #63648C22semidirect
35. C3×(C2×D3)⋊C8C22semidirect
36. C3×#817C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63573C22semidirect
39. #63567C22semidirect
40. #63564C22semidirect
41. #63564C22semidirect
58. #4842D3semidirect
59. #4834D3semidirect
122. C2×D3×C8C2×D3semidirect
138. #869C2×D3semidirect
144. C3×C4⋊C8C2×D3semidirect
145. C3×C4⋊C8C2×D3semidirect
157. (C2×D3)⋊C8C2×D3semidirect
159. #817C2×D3semidirect
165. C4×C3⋊C8C2×D3semidirect
187. C3×D12SD16semidirect
332. C4⋊C8D32semidirect
400. D12#204semidirect
512. C32#3295semidirect
583. C3#79439semidirect
584. C3#81075semidirect

Maximal subgroups

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

subgroupindex
D1222
#105939562
#105925472
C3×#48422
C3×#48342
#105909462
D3×#8212
#105908302
#105906772
C4×#37162
#105902812
#810753
#794393