Finite Group Databasebeta

← #11870503

Subgroups — #11870503

Order 1152.

990 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic
4C3×#5218C211yesmaximal, characteristic
5#10591489C212yesmaximal, complemented
6Dic3×#214C212yesmaximal, complemented
7#10591408C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9#10591124C211yesmaximal, characteristic, complemented
10#10591101C211yesmaximal, characteristic, complemented
11#10591053C211yesmaximal, characteristic, complemented
12#82314—31nomaximal
13#80132—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3—21no—
16C2×#3754C2212yes—
17#64133C2211yescharacteristic
18C2×C3×#217—21no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27#63964—21no—
28#63955—21no—
29#63918C2211yescharacteristic, complemented
30#63867—21no—
31#63866C2211yescharacteristic, complemented
32#63844C2211yescharacteristic, complemented
33Dic3×Dic6C2211yescharacteristic, complemented
34#63837—21no—
35#63659C2212yes—
36#63657C2211yescharacteristic
37C3×#832C2212yes—
38C3×#830C2211yescharacteristic
39#63574C2212yescomplemented
40#63573C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63567C2212yescomplemented
43#63565C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×C4×D4—31no—
46C2×D4×Dic3D311yescharacteristic
47#5622—31no—
48#5470—31no—
49C3×#450—31no—
50#5218—31no—
51#5218—31no—
52#5218—61no—
53#5218D311yescharacteristic
54#5162—32no—
55Dic3×SD16—32no—
56#5043—31no—
57#5019—32no—
58C4×#214—32no—
59C4×#214—32no—
60#5008—32no—
61#4971—31no—
62#4971—31no—
63#4925—31no—
64#4761—32no—
65#4758—32no—
66#4721—31no—
67#4718—31no—
68C24×C32—21no—
69C2×C32×D4—24no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×#634C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—44no—
78C22×C3×Dic3D411yescharacteristic
79C22×C3×Dic3D411yescharacteristic
80C2×C3×Dic6C2311yescharacteristic
81C2×#627—21no—
82#3757—21no—
83#3754—24no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—21no—
88C3×#217—22no—
89C3×#217—22no—
90C3×#214—24no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic32—21no—
106Dic32—21no—
107#3101—91noSylow
108C22×C3×D4—21no—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C2×D311yescharacteristic
111C23×C3×C4—61no—
112C23×Dic3—21no—
113C2×C3×SD16—32no—
114C3×C22⋊Q8—31no—
115C3×C4×D4—32no—
116C3×C4×D4—32no—
117C3×C4×D4—61no—
118C3×C4×D4—61no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C22⋊C4—61no—
121C2×C3×C42—31no—
122C2×#217—21no—
123Q8×Dic3—31no—
124#944—31no—
125D4×Dic3—21no—
126D4×Dic3—21no—
127D4×Dic3C2×D312yes—
128D4×Dic3C2×D312yes—
129C2×#214—32no—
130C2×#214—32no—
131C2×#214—62no—
132C2×#214C2×D312yes—
133#926—61no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135#924—31no—
136#924—31no—
137#924—61no—
138#924—61no—
139#924C2×D311yescharacteristic
140C2×C4×Dic3C2×D311yescharacteristic
141#889—61no—
142#888—31no—
143#887—31no—
144#887—61no—
145#878—61no—
146#877—61no—
147#870—61no—
148#869—31no—
149#869—31no—
150C4×Dic6—31no—
151C4×Dic6—31no—
152C4×Dic6—61no—
153C3×#102—32no—
154C3×C22⋊C8—31no—
155#835—32no—
156#832—32no—
157#832—32no—
158#832—62no—
159#832C2×D312yes—
160#830—31no—
161#830—31no—
162#830—61no—
163#830C2×D311yescharacteristic
164#817—32no—
165#816—32no—
166Dic3⋊C8—32no—
167C8×Dic3—32no—
168#810—32no—
169#810—32no—
170#808—32no—
171#808—32no—
172#808—32no—
173C4⋊(C3⋊C8)—32no—
174C4×C3⋊C8—32no—
175C23×C32—24no—
176C23×C32—22no—
177C23×C32—42no—
178C23×C32—42no—
179C23×C32C2×D411yescharacteristic
180C32×D4—24no—
181C32×D4—22no—
182C32×D4#4114yes—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188#634—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3—44no—
195C2×C3×Dic3—44no—
196C2×C3×Dic3SD1614yescomplemented
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×Dic6—22no—
202#627—42no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205#533—91no—
206C2×C4×D4—31no—
207#483—91no—
208#483—91no—
209#476—92no—
210#461—92no—
211#450—31no—
212#450—91no—
213C4×SD16—92no—
214C4×SD16—92no—
215#431—91no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—41no—
219C2×C3×Q8—31no—
220C2×C3×D4—24no—
221C2×C3×D4—24no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—41no—
226C2×C3×D4—44no—
227C2×C3×D4C22×D312yes—
228C2×C3×D4C22×D312yes—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—62no—
233C22×C3×C4—62no—
234C22×C3×C4—61no—
235C22×C3×C4—124no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×Dic3—21no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—44no—
242C22×Dic3#6711yescharacteristic
243C22×Dic3#6711yescharacteristic
244C2×Dic6—31no—
245C2×Dic6—31no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C2×Dic6—61no—
249C2×Dic6C22×D311yescharacteristic
250C3×SD16—64no—
251C2×C3×C8—32no—
252C3×C4⋊C4—32no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—61no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—31no—
263#217—21no—
264#217—22no—
265#217—22no—
266#217—61no—
267#217—61no—
268#217—121no—
269#214—24no—
270#214—64no—
271#214—64no—
272#214—124no—
273C4⋊Dic3—21no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3C22×D311yescharacteristic
282C4⋊Dic3C22×D312yes—
283Dic3⋊C4—21no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—121no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3#6711yescharacteristic
298C4×Dic3#6711yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8—32no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8C22×D312yes—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—24no—
308C22×C32—48no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32C2×SD1612yes—
312C22×C32C22×D411yescharacteristic
313C32×C4—21no—
314C32×C4C2×#4112yes—
315C3⋊Dic3—41no—
316C3⋊Dic3—41no—
317C3×Dic3—21no—
318C3×Dic3—21no—
319C3×Dic3—41no—
320C3×Dic3—42no—
321C3×Dic3—41no—
322C3×Dic3C2×SD1612yes—
323C3×Dic3C2×SD1612yes—
324C22×D4D3211yescharacteristic
325C23×C4—61no—
326C2×SD16—32no—
327C2×SD16—92no—
328C4⋊Q8—91no—
329C4⋊Q8—91no—
330#125—181no—
331C22⋊Q8—31no—
332C22⋊Q8—91no—
333C22⋊Q8—181no—
334C4×Q8—91no—
335C4×Q8—91no—
336C4×Q8—181no—
337C4×D4—32no—
338C4×D4—32no—
339C4×D4—61no—
340C4×D4—61no—
341#117—181no—
342C2×C4⋊C4—31no—
343C2×C22⋊C4—61no—
344C2×C42—31no—
345#106—92no—
346#106—92no—
347C4⋊C8—92no—
348#103—92no—
349#103—92no—
350#102—32no—
351#102—92no—
352C22⋊C8—31no—
353C22⋊C8—91no—
354C4×C8—92no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—42no—
361C23×C3—44no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—82no—
367C23×C3—82no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C3×Q8—62no—
371C3×D4—24no—
372C3×D4—24no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—24no—
376C3×D4—42no—
377C3×D4—44no—
378C3×D4#23514yes—
379C3×D4#23714yes—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—34no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—42no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—124no—
394C2×C3×C4—124no—
395C2×C3×C4—121no—
396C2×C3×C4—122no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—41no—
405C2×Dic3—42no—
406C2×Dic3—44no—
407C2×Dic3—44no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3#21414yescomplemented
415C2×Dic3C2×#6711yescharacteristic
416C2×Dic3C2×#6711yescharacteristic
417C2×Dic3C2×#6711yescharacteristic
418C2×Dic3C2×#6711yescharacteristic
419Dic6—22no—
420Dic6—62no—
421Dic6—62no—
422Dic6—122no—
423Dic6—122no—
424Dic6—122no—
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C2×C32—22no—
431C2×C32—44no—
432C2×C32#52511yescharacteristic
433C2×C32C22×SD1611yescharacteristic
434C2×C32#57511yescharacteristic
435C24—21no—
436C2×Q8—31no—
437C2×Q8—91no—
438C2×Q8—181no—
439C2×D4—24no—
440C2×D4—21no—
441C2×D4C2×D3212yes—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—61no—
447C22×C4—124no—
448C22×C4C2×D3211yescharacteristic
449SD16—64no—
450SD16—184no—
451C2×C8—32no—
452C2×C8—92no—
453C4⋊C4—31no—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—91no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C22⋊C4—62no—
465C22⋊C4—62no—
466C22⋊C4—61no—
467C22⋊C4—181no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—181no—
473C42—181no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—44no—
485C22×C3—48no—
486C22×C3—48no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—82no—
492C22×C3—82no—
493C22×C3—88no—
494C22×C3D3×SD1612yes—
495C22×C3C2×#21412yes—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×#6711yescharacteristic
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—22no—
501C3×C4—32no—
502C3×C4—32no—
503C3×C4—41no—
504C3×C4—61no—
505C3×C4—61no—
506C3×C4—122no—
507C3×C4—121no—
508C3×C4—121no—
509C3×C4C2×#23512yes—
510C3×C4C2×#23712yes—
511Dic3—21no—
512Dic3—21no—
513Dic3—41no—
514Dic3—42no—
515Dic3—41no—
516Dic3—121no—
517Dic3—121no—
518Dic3—121no—
519Dic3—121no—
520Dic3—241no—
521Dic3—241no—
522Dic3C2×#21412yes—
523Dic3C2×#21412yes—
524C32#310111yescharacteristic, complemented, Sylow
525C23—24no—
526C23—22no—
527C23—42no—
528C23—42no—
529C23D3×#6711yescharacteristic
530Q8—62no—
531Q8—182no—
532Q8—362no—
533D4—24no—
534D4—22no—
535D4#380414yes—
536C2×C4—22no—
537C2×C4—31no—
538C2×C4—31no—
539C2×C4—34no—
540C2×C4—31no—
541C2×C4—31no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—124no—
546C2×C4—124no—
547C2×C4—121no—
548C2×C4—122no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4D3×#6711yescharacteristic
552C2×C4C22×D3211yescharacteristic
553C8—62no—
554C8—182no—
555C2×C3—22no—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—42no—
561C2×C3—44no—
562C2×C3—44no—
563C2×C3—84no—
564C2×C3#558611yescharacteristic
565C2×C3C2×D3×SD1611yescharacteristic
566C2×C3#577311yescharacteristic
567C2×C3#579111yescharacteristic
568C2×C3C22×#21411yescharacteristic
569C2×C3#582211yescharacteristic
570C22—21no—
571C22—21no—
572C22—24no—
573C22—48no—
574C22—42no—
575C22—42no—
576C22D3×#21412yes—
577C22C2×D3×#6711yescharacteristic
578C4—21no—
579C4—32no—
580C4—32no—
581C4—61no—
582C4—61no—
583C4—121no—
584C4—122no—
585C4—121no—
586C4—361no—
587C4—361no—
588C4C2×#380412yes—
589C3—21no—
590C3#8013211yescharacteristic, complemented
591C3#8231411yescharacteristic, complemented
592C2—22no—
593C2—44no—
594C2#1059509511yescharacteristic
595C2C2×D3×#21411yescharacteristic
596C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594808C2semidirect
5. #10591489C2semidirect
6. Dic3×#214C2semidirect
7. #10591408C2semidirect
8. #10591401C2semidirect
9. #10591124C2semidirect
10. #10591101C2semidirect
11. #10591053C2semidirect
29. #63918C22semidirect
31. #63866C22semidirect
32. #63844C22semidirect
33. Dic3×Dic6C22semidirect
39. #63574C22semidirect
40. #63573C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63567C22semidirect
43. #63565C22semidirect
44. Dic3×C3⋊C8C22semidirect
196. C2×C3×Dic3SD16semidirect
414. C2×Dic3#214semidirect
524. C32#3101semidirect
590. C3#80132semidirect
591. C3#82314semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
#105948082
#105929172
C3×#52182
#105914892
Dic3×#2142
#105914082
#105914012
#105911242
#105911012
#105910532
#823143
#801323