Finite Group Databasebeta

← D3×#4867 #11867009

Subgroups — D3×#4867 #11867009

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic, complemented
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic
3D3×#897C212yesmaximal
4#10592566C211yesmaximal, characteristic, complemented
5C3×#4867C211yesmaximal, characteristic, complemented
6C3×D3×#106C211yesmaximal, characteristic, complemented
7#10590858C211yesmaximal, characteristic, complemented
8#10590853C211yesmaximal, characteristic, complemented
9D3×#810C212yesmaximal, complemented
10#10590587C212yesmaximal, complemented
11#10590524C212yesmaximal, complemented
12D3×#470—31nomaximal
13C2×#4867—31nomaximal
14C2×C4×D32C2211yescharacteristic
15C2×D3×Dic6C2212yes—
16C2×#3746C2211yescharacteristic, complemented
17C2×#3743C2211yescharacteristic
18#64106C2212yes—
19C2×C3×Dic12C2211yescharacteristic, complemented
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C3×#897C2212yes—
23C3×D3×C4⋊C4C2212yes—
24D3×(C2×D3)⋊C4—22no—
25#63895—22no—
26#63893—22no—
27D3×C4⋊Dic3—22no—
28#63871C2212yes—
29#63857C2212yes—
30C2×#3719C2212yescomplemented
31C2×#3712C2211yescharacteristic
32C2×#3711C2211yescharacteristic
33C2×D3×C3⋊C8C2211yescharacteristic
34D3×Dic12—24no—
35D3×ΓL(1,𝔽25)—24no—
36C32×#106C2211yescharacteristic, complemented
37#63637C2212yescomplemented
38C3×#817C2211yescharacteristic, complemented
39C3×#810C2212yescomplemented
40C3×#808C2212yescomplemented
41#63567C2212yescomplemented
42#63565C2212yescomplemented
43C2×D3×Q16—31no—
44C2×D3×M16—31no—
45C22×Dic12—31no—
46C22×ΓL(1,𝔽25)—31no—
47D3×C22⋊Q8—32no—
48C2×#897—32no—
49C3×#470—31no—
50C2×C3×#106—31no—
51#5189—31no—
52#5137—31no—
53#5052—32no—
54C2×#810—32no—
55#4867—31no—
56#4867—31no—
57#4867—32no—
58#4867—31no—
59#4867—31no—
60#4867—32no—
61#4867—61no—
62#4867D311yescharacteristic, direct product factor
63D3×#106D311yescharacteristic, complemented
64#4816—32no—
65D3×#103—32no—
66C22×D32D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3C2311yescharacteristic
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×#627—22no—
74C2×#624D411yescharacteristic
75C2×D3×Dic3—22no—
76C2×D3×Dic3D411yescharacteristic
77C2×D3×Dic3D411yescharacteristic
78C4×D32—22no—
79C4×D32—22no—
80D3×Dic6—24no—
81D3×Dic6—24no—
82C2×C32×C8C2311yescharacteristic
83C32×C4⋊C4C2312yes—
84#3752—22no—
85C4⋊(C3⋊Dic3)—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87#3746—22no—
88#3743—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12—22no—
96C3×ΓL(1,𝔽25)—22no—
97C3×D3×C8D414yes—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3719—24no—
103#3712—22no—
104#3711—22no—
105D3×C3⋊C8—22no—
106C2×#470—91noSylow
107C2×D3×Q8—32no—
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×Dic6—32no—
111C2×C3×Q16—31no—
112C2×C3×M16—31no—
113C22×C3×C8—31no—
114C3×C22⋊Q8—32no—
115C2×C3×C4⋊C4—32no—
116#946—32no—
117C2×#216—32no—
118C2×(C2×D3)⋊C4—62no—
119C2×C4⋊Dic3—62no—
120#924—32no—
121C2×#208—31no—
122C22×C3⋊C8—31no—
123D3×Q16—64no—
124D3×M16—64no—
125C2×Dic12—32no—
126C2×Dic12—31no—
127C2×Dic12—31no—
128C2×Dic12—61no—
129C2×Dic12—64no—
130C2×Dic12C2×D311yescharacteristic, complemented
131C2×ΓL(1,𝔽25)—31no—
132C2×ΓL(1,𝔽25)—31no—
133C2×ΓL(1,𝔽25)—31no—
134C2×ΓL(1,𝔽25)—31no—
135C2×ΓL(1,𝔽25)—31no—
136C2×ΓL(1,𝔽25)—61no—
137C2×ΓL(1,𝔽25)—64no—
138C2×ΓL(1,𝔽25)C2×D311yescharacteristic
139C2×D3×C8—31no—
140C2×D3×C8C2×D311yescharacteristic
141#897—32no—
142#897—32no—
143#897—32no—
144#897—32no—
145#897—62no—
146#897—62no—
147#897—62no—
148#897C2×D312yes—
149#896—62no—
150D3×C4⋊C4—62no—
151D3×C4⋊C4C2×D312yes—
152D3×C22⋊C4—62no—
153#878—62no—
154C3×#106—21no—
155C3×#106—31no—
156C3×#106—32no—
157C3×#106C2×D311yescharacteristic, complemented
158C3×#106C2×D311yescharacteristic, complemented
159C3×#103—32no—
160#835—32no—
161#817C2×D311yescharacteristic, complemented
162#816—32no—
163#810—32no—
164#810—32no—
165#810—32no—
166#810—32no—
167#810—62no—
168#810C2×D312yescomplemented
169#808C2×D312yescomplemented
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3×D3C2×D411yescharacteristic
172C22×C3×D3C2×D411yescharacteristic
173C2×D32—22no—
174C2×D32—24no—
175C2×C32×C4—22no—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C2×D411yescharacteristic
179C4×C3⋊D3—21no—
180C4×C3⋊D3—21no—
181#634—22no—
182#634—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C2×D411yescharacteristic
186C2×C3×Dic3C2×D411yescharacteristic
187C3×C4×D3—21no—
188C3×C4×D3—21no—
189C3×C4×D3—44no—
190C3×C4×D3C2×D412yes—
191C3×C4×D3#4112yes—
192C3×Dic6—22no—
193C3×Dic6—22no—
194#627—44no—
195#624—22no—
196D3×Dic3—22no—
197D3×Dic3—22no—
198D3×Dic3—44no—
199C32×C8C2×D412yes—
200C3⋊(C3⋊C8)—21no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8C2×D412yes—
203C22×Q16—91no—
204C22×M16—91no—
205C2×C22⋊Q8—92no—
206#470—31no—
207#470—92no—
208#470—92no—
209#470—91no—
210#470—91no—
211#470—91no—
212C2×#106—31no—
213C2×#103—92no—
214C23×D3—31no—
215C23×D3—31no—
216C2×C3×Q8—32no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—62no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—62no—
223D3×Q8—64no—
224D3×Q8—64no—
225C2×C4×D3—22no—
226C2×C4×D3—31no—
227C2×C4×D3—31no—
228C2×C4×D3—31no—
229C2×C4×D3—31no—
230C2×C4×D3—31no—
231C2×C4×D3—31no—
232C2×C4×D3—61no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3C22×D311yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—32no—
241C2×Dic6—32no—
242C2×Dic6—62no—
243C2×Dic6—64no—
244C2×Dic6—64no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6C22×D312yes—
248C3×Q16—62no—
249C3×M16—62no—
250C2×C3×C8—21no—
251C2×C3×C8—31no—
252C2×C3×C8—34no—
253C2×C3×C8—31no—
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C3×C4⋊C4—22no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4C22×D312yes—
261C3×C4⋊C4C22×D312yes—
262C3×C22⋊C4—62no—
263#217—62no—
264#216—64no—
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—122no—
272C4⋊Dic3—22no—
273C4⋊Dic3—62no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—62no—
277C4⋊Dic3—122no—
278C4⋊Dic3C22×D312yes—
279Dic3⋊C4—22no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282#208—62no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—61no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8C22×D311yescharacteristic
288C2×C3⋊C8C22×D311yescharacteristic
289Dic12—22no—
290Dic12—64no—
291Dic12—62no—
292Dic12—62no—
293Dic12—122no—
294ΓL(1,𝔽25)—22no—
295ΓL(1,𝔽25)—62no—
296ΓL(1,𝔽25)—62no—
297ΓL(1,𝔽25)—62no—
298ΓL(1,𝔽25)—62no—
299ΓL(1,𝔽25)—62no—
300ΓL(1,𝔽25)—122no—
301D3×C8—62no—
302D3×C8D1214yes—
303C22×C32C22×D411yescharacteristic
304C2×C3⋊D3—21no—
305C2×C3⋊D3—22no—
306C2×C3×D3—21no—
307C2×C3×D3—22no—
308C2×C3×D3#12112yes—
309C2×C3×D3#13714yes—
310D32—44no—
311C32×C4—42no—
312C32×C4C22×D411yescharacteristic
313C32×C4C2×#4111yescharacteristic
314C3⋊Dic3—21no—
315C3⋊Dic3—42no—
316C3×Dic3—21no—
317C3×Dic3—42no—
318C3×Dic3—42no—
319C3×Dic3#12112yes—
320C22×Q8—92no—
321C23×C4—91no—
322C2×Q16—31no—
323C2×Q16—92no—
324C2×Q16—91no—
325C2×Q16—184no—
326C2×M16—31no—
327C2×M16—91no—
328C2×M16—91no—
329C2×M16—91no—
330C2×M16—184no—
331C22×C8—31no—
332C22×C8—91no—
333C22⋊Q8—32no—
334C22⋊Q8—92no—
335C22⋊Q8—92no—
336C22⋊Q8—92no—
337C22⋊Q8—182no—
338C22⋊Q8—182no—
339C2×C4⋊C4—32no—
340C2×C4⋊C4—182no—
341C2×C22⋊C4—182no—
342#106—31no—
343#106—32no—
344#106D3211yescharacteristic, complemented
345#103—32no—
346#103—92no—
347#103—92no—
348#103—92no—
349C23×C3—31no—
350C23×C3—31no—
351C22×D3—31no—
352C22×D3—31no—
353C22×D3—61no—
354C22×D3—62no—
355C22×D3—64no—
356C22×D3—62no—
357C22×D3—64no—
358C22×D3D3×D411yescharacteristic
359C22×D3D3×D411yescharacteristic
360C3×Q8—62no—
361C3×Q8—62no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—31no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—31no—
369C2×C3×C4—42no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—124no—
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—61no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—122no—
387C2×Dic3—124no—
388C2×Dic3D3×D411yescharacteristic
389C2×Dic3D3×D411yescharacteristic
390C4×D3—21no—
391C4×D3—21no—
392C4×D3—44no—
393C4×D3—62no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—61no—
397C4×D3—61no—
398C4×D3—61no—
399C4×D3—61no—
400C4×D3—62no—
401C4×D3—121no—
402C4×D3—121no—
403C4×D3—124no—
404C4×D3C2×D1212yes—
405C4×D3#23912yes—
406Dic6—22no—
407Dic6—22no—
408Dic6—62no—
409Dic6—62no—
410Dic6—62no—
411Dic6—62no—
412Dic6—122no—
413Dic6—122no—
414Dic6—124no—
415Dic6—124no—
416C3×C8—22no—
417C3×C8—32no—
418C3×C8—61no—
419C3×C8C2×D1212yes—
420C3×C8D3×D412yes—
421C3⋊C8—21no—
422C3⋊C8—61no—
423C3⋊C8—61no—
424C3⋊C8—121no—
425C3⋊C8C2×D1212yes—
426C2×C32C2×#12111yescharacteristic
427C2×C32C2×#13712yes—
428C3⋊D3—41no—
429C3×D3—41no—
430C3×D3#47014yescomplemented
431C24—91no—
432C2×Q8—32no—
433C2×Q8—92no—
434C2×Q8—182no—
435C2×Q8—184no—
436C2×Q8—184no—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—62no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—182no—
445C22×C4—182no—
446C22×C4—182no—
447Q16—62no—
448Q16—184no—
449Q16—182no—
450M16—62no—
451M16—182no—
452M16—182no—
453M16—182no—
454C2×C8—31no—
455C2×C8—34no—
456C2×C8—31no—
457C2×C8—91no—
458C2×C8—182no—
459C2×C8C2×D3211yescharacteristic
460C4⋊C4—32no—
461C4⋊C4—62no—
462C4⋊C4—62no—
463C4⋊C4—182no—
464C4⋊C4—182no—
465C4⋊C4—182no—
466C4⋊C4C2×D3212yes—
467C22⋊C4—62no—
468C22⋊C4—182no—
469C22⋊C4—182no—
470C22⋊C4—182no—
471C22×C3—21no—
472C22×C3—34no—
473C22×C3—32no—
474C22×C3—62no—
475C22×C3—61no—
476C22×C3C2×D3×D411yescharacteristic
477C22×C3C2×D3×D411yescharacteristic
478C2×D3—22no—
479C2×D3—21no—
480C2×D3—62no—
481C2×D3—61no—
482C2×D3—62no—
483C2×D3—61no—
484C2×D3—121no—
485C2×D3—122no—
486C2×D3—124no—
487C2×D3—124no—
488C2×D3#89512yes—
489C2×D3#91514yes—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—32no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—61no—
496C3×C4—82no—
497C3×C4—122no—
498C3×C4—122no—
499C3×C4C22×D1211yescharacteristic
500C3×C4C2×D3×D411yescharacteristic
501C3×C4C2×#23911yescharacteristic
502C3×C4D3×#4111yescharacteristic
503Dic3—21no—
504Dic3—42no—
505Dic3—42no—
506Dic3—61no—
507Dic3—61no—
508Dic3—121no—
509Dic3—122no—
510Dic3—122no—
511Dic3—242no—
512Dic3#89512yes—
513C32C2×#47011yescharacteristic, complemented, Sylow
514C23—31no—
515C23—31no—
516C23—91no—
517C23—182no—
518C23—184no—
519Q8—62no—
520Q8—62no—
521Q8—182no—
522Q8—182no—
523Q8—364no—
524C2×C4—22no—
525C2×C4—31no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—31no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—91no—
534C2×C4—124no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—182no—
541C2×C4—364no—
542C2×C4C22×D3211yescharacteristic
543C8—32no—
544C8—61no—
545C8—181no—
546C8D3×D1212yes—
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—34no—
550C2×C3—121no—
551C2×C3C2×#89511yescharacteristic
552C2×C3D3×#12111yescharacteristic
553C2×C3C2×#91512yes—
554C2×C3D3×#13712yes—
555D3—41no—
556D3—121no—
557D3—121no—
558D3—241no—
559D3#486714yesdirect product factor
560C22—32no—
561C22—34no—
562C22—61no—
563C22—62no—
564C22—181no—
565C22—182no—
566C22—364no—
567C22D32×D411yescharacteristic
568C4—32no—
569C4—42no—
570C4—61no—
571C4—122no—
572C4—122no—
573C4—181no—
574C4—362no—
575C4C2×D3×D1211yescharacteristic
576C4D3×#23911yescharacteristic
577C3—21no—
578C3C2×#486711yescharacteristic, complemented
579C3D3×#47011yescharacteristic, complemented
580C2—34no—
581C2—121no—
582C2—361no—
583C2D3×#89511yescharacteristic
584C2D3×#91512yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#106D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
4. #10592566C2semidirect
5. C3×#4867C2semidirect
6. C3×D3×#106C2semidirect
7. #10590858C2semidirect
8. #10590853C2semidirect
9. D3×#810C2semidirect
10. #10590587C2semidirect
11. #10590524C2semidirect
16. C2×#3746C22semidirect
19. C2×C3×Dic12C22semidirect
30. C2×#3719C22semidirect
36. C32×#106C22semidirect
37. #63637C22semidirect
38. C3×#817C22semidirect
39. C3×#810C22semidirect
40. C3×#808C22semidirect
41. #63567C22semidirect
42. #63565C22semidirect
62. #4867D3direct (N × H)
63. D3×#106D3semidirect
130. C2×Dic12C2×D3semidirect
157. C3×#106C2×D3semidirect
158. C3×#106C2×D3semidirect
161. #817C2×D3semidirect
168. #810C2×D3semidirect
169. #808C2×D3semidirect
344. #106D32semidirect
430. C3×D3#470semidirect
513. C32C2×#470semidirect
559. D3#4867direct (N × H)
578. C3C2×#4867semidirect
579. C3D3×#470semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×D3×ΓL(1,𝔽25)2
D3×#8972
#105925662
C3×#48672
C3×D3×#1062
#105908582
#105908532
D3×#8102
#105905872
#105905242
D3×#4703
C2×#48673