Finite Group Databasebeta

← D3×#5189 #11867007

Subgroups — D3×#5189 #11867007

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×C3×D3×Q16C211yesmaximal, characteristic, complemented
2D3×#946C212yesmaximal
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic
4#10592888C211yesmaximal, characteristic, complemented
5C3×#5189C211yesmaximal, characteristic, complemented
6#10591638C212yesmaximal, complemented
7#10591600C212yesmaximal, complemented
8D3×#835C212yesmaximal, complemented
9#10590858C211yesmaximal, characteristic, complemented
10#10590854C211yesmaximal, characteristic, complemented
11D3×#817C211yesmaximal, characteristic, complemented
12C2×#5189—31nomaximal
13D3×#470—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×C4×D32C2211yescharacteristic
16C2×C32×Q16C2211yescharacteristic, complemented
17#64155C2212yes—
18C2×#3743C2211yescharacteristic
19C3×#946C2212yes—
20C2×C3×#216C2212yescomplemented
21C3×D3×Q16—24no—
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25D3×(C2×D3)⋊C4—22no—
26D3×C4⋊Dic3C2212yes—
27#63888—22no—
28#63887—22no—
29D3×Dic3⋊C4—22no—
30#63871C2212yes—
31#63856C2212yes—
32C2×#3712C2211yescharacteristic
33C2×#3711C2211yescharacteristic
34C2×D3×C3⋊C8C2211yescharacteristic
35D3×ΓL(1,𝔽25)—24no—
36#63662C2212yescomplemented
37#63644C2211yescharacteristic, complemented
38C3×#835C2212yescomplemented
39C3×#817C2211yescharacteristic, complemented
40#63573C2212yescomplemented
41#63566C2212yescomplemented
42#63565C2212yescomplemented
43C22×C3×Q16—31no—
44C2×#946—32no—
45C2×D3×Q16D311yescharacteristic, complemented
46C2×D3×M16—31no—
47C22×ΓL(1,𝔽25)—31no—
48D3×C22⋊Q8—32no—
49C3×#470—31no—
50C2×#835—32no—
51#5189—31no—
52#5189—31no—
53#5189—32no—
54#5189—31no—
55#5189—32no—
56#5189—31no—
57#5189—61no—
58#5189D311yescharacteristic, direct product factor
59#5137—31no—
60C2×#817—31no—
61#5052—32no—
62#4867—31no—
63D3×#106—31no—
64#4816—32no—
65D3×#103—32no—
66C22×D32D411yescharacteristic
67C2×C32×Q8C2312yes—
68C2×C4×C3⋊D3C2311yescharacteristic
69C3×D3×Q8—24no—
70C3×D3×Q8—24no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6—22no—
75C2×C3×Dic6C2312yes—
76C2×#624D411yescharacteristic
77C2×D3×Dic3—22no—
78C2×D3×Dic3D411yescharacteristic
79C2×D3×Dic3D411yescharacteristic
80C4×D32—22no—
81C4×D32—22no—
82C32×Q16—22no—
83C2×C32×C8C2311yescharacteristic
84#3752—22no—
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—22no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3743—22no—
89C3×#216—24no—
90C3×(C2×D3)⋊C4—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—
98#3724—22no—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—22no—
101#3722—22no—
102(C2×D3)⋊Dic3—22no—
103#3712—22no—
104#3711—22no—
105D3×C3⋊C8—22no—
106C2×#470—91noSylow
107C22×C3×Q8—32no—
108C2×D3×Q8C2×D312yes—
109C22×C4×D3—31no—
110C22×C4×D3—31no—
111C2×C3×Q16—21no—
112C2×C3×Q16—32no—
113C2×C3×Q16—31no—
114C2×C3×Q16—64no—
115C2×C3×Q16C2×D311yescharacteristic, complemented
116C2×C3×Q16C2×D311yescharacteristic, complemented
117C2×C3×M16—31no—
118C22×C3×C8—31no—
119C3×C22⋊Q8—32no—
120#946—32no—
121#946—32no—
122#946—32no—
123#946—32no—
124#946—62no—
125#946—62no—
126#946—62no—
127#946C2×D312yes—
128C2×#216C2×D312yescomplemented
129C2×(C2×D3)⋊C4—62no—
130C2×C4⋊Dic3—32no—
131#924—32no—
132C2×Dic3⋊C4—62no—
133C2×#208—31no—
134C22×C3⋊C8—31no—
135D3×Q16—24no—
136D3×M16—64no—
137C2×Dic12C2×D311yescharacteristic, complemented
138C2×ΓL(1,𝔽25)—31no—
139C2×ΓL(1,𝔽25)—31no—
140C2×ΓL(1,𝔽25)—31no—
141C2×ΓL(1,𝔽25)—31no—
142C2×ΓL(1,𝔽25)—31no—
143C2×ΓL(1,𝔽25)—61no—
144C2×ΓL(1,𝔽25)—64no—
145C2×ΓL(1,𝔽25)C2×D311yescharacteristic
146C2×D3×C8—31no—
147C2×D3×C8C2×D311yescharacteristic
148#897—32no—
149#896—62no—
150D3×C4⋊C4—32no—
151D3×C4⋊C4—62no—
152D3×C22⋊C4—62no—
153#878—62no—
154C3×#106—31no—
155C3×#103—32no—
156#835—32no—
157#835—32no—
158#835—32no—
159#835—32no—
160#835—62no—
161#835C2×D312yescomplemented
162#817—31no—
163#817—31no—
164#817—32no—
165#817—61no—
166#817C2×D311yescharacteristic, complemented
167#816—32no—
168#810—32no—
169#808—32no—
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3×D3C2×D411yescharacteristic
172C22×C3×D3C2×D411yescharacteristic
173C2×D32—22no—
174C2×D32—24no—
175C32×Q8—22no—
176C32×Q8—22no—
177C2×C32×C4—22no—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3C2×D411yescharacteristic
181C4×C3⋊D3—21no—
182C4×C3⋊D3—21no—
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—
194C3×Dic6—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—31no—
204C22×M16—91no—
205C2×C22⋊Q8—92no—
206#470—31no—
207#470—92no—
208#470—91no—
209#470—92no—
210#470—91no—
211#470—91no—
212C2×#106—91no—
213C2×#103—92no—
214C23×D3—31no—
215C23×D3—31no—
216C2×C3×Q8—22no—
217C2×C3×Q8—32no—
218C2×C3×Q8—62no—
219C2×C3×Q8—64no—
220C2×C3×Q8—64no—
221C2×C3×Q8C22×D312yes—
222C2×C3×Q8C22×D312yes—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—62no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—62no—
229D3×Q8—24no—
230D3×Q8—24no—
231C2×C4×D3—22no—
232C2×C4×D3—31no—
233C2×C4×D3—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—61no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3C22×D311yescharacteristic
245C2×C4×D3C22×D311yescharacteristic
246C2×Dic6—22no—
247C2×Dic6C22×D312yes—
248C3×Q16—22no—
249C3×Q16—22no—
250C3×Q16—42no—
251C3×Q16—64no—
252C3×Q16—62no—
253C3×M16—62no—
254C2×C3×C8—21no—
255C2×C3×C8—31no—
256C2×C3×C8—34no—
257C2×C3×C8—31no—
258C2×C3×C8C22×D311yescharacteristic
259C2×C3×C8C22×D311yescharacteristic
260C3×C4⋊C4—32no—
261C3×C4⋊C4—62no—
262C3×C22⋊C4—62no—
263#217—62no—
264#216—24no—
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—32no—
273C4⋊Dic3—32no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—62no—
277C4⋊Dic3C22×D312yes—
278Dic3⋊C4—22no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—122no—
286#208—62no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8C22×D311yescharacteristic
292C2×C3⋊C8C22×D311yescharacteristic
293Dic12—22no—
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×C8#6714yes—
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—32no—
321C23×C4—91no—
322C2×Q16—32no—
323C2×Q16—31no—
324C2×Q16—64no—
325C2×Q16D3211yescharacteristic, complemented
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—92no—
340C2×C4⋊C4—182no—
341C2×C22⋊C4—182no—
342#106—31no—
343#106—92no—
344#106—91no—
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—64no—
357C22×D3—62no—
358C22×D3D3×D411yescharacteristic
359C22×D3D3×D411yescharacteristic
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—42no—
365C3×Q8—42no—
366C3×Q8—62no—
367C3×Q8—62no—
368C3×Q8—124no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—31no—
373C2×C3×C4—32no—
374C2×C3×C4—32no—
375C2×C3×C4—31no—
376C2×C3×C4—42no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—124no—
382C2×C3×C4C23×D311yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—31no—
387C2×Dic3—31no—
388C2×Dic3—61no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—122no—
394C2×Dic3—124no—
395C2×Dic3D3×D411yescharacteristic
396C2×Dic3D3×D411yescharacteristic
397C4×D3—21no—
398C4×D3—21no—
399C4×D3—44no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—62no—
403C4×D3—61no—
404C4×D3—61no—
405C4×D3—61no—
406C4×D3—61no—
407C4×D3—62no—
408C4×D3—121no—
409C4×D3—121no—
410C4×D3—124no—
411C4×D3#23712yes—
412C4×D3C2×#6712yes—
413Dic6—22no—
414Dic6—22no—
415Dic6—44no—
416C3×C8—22no—
417C3×C8—32no—
418C3×C8—61no—
419C3×C8D3×D412yes—
420C3×C8C2×#6712yes—
421C3⋊C8—21no—
422C3⋊C8—61no—
423C3⋊C8—61no—
424C3⋊C8—121no—
425C3⋊C8C2×#6712yes—
426C2×C32C2×#12111yescharacteristic
427C2×C32C2×#13712yes—
428C3⋊D3—41no—
429C3×D3—41no—
430C3×D3#47014yescomplemented
431C24—91no—
432C2×Q8—32no—
433C2×Q8—62no—
434C2×Q8—64no—
435C2×Q8—64no—
436C2×Q8C2×D3212yes—
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—22no—
448Q16—64no—
449Q16—62no—
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—92no—
463C4⋊C4—182no—
464C4⋊C4—182no—
465C4⋊C4—182no—
466C4⋊C4—182no—
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—62no—
482C2×D3—61no—
483C2×D3—61no—
484C2×D3—121no—
485C2×D3—122no—
486C2×D3—124no—
487C2×D3—124no—
488C2×D3#91814yes—
489C2×D3#93812yes—
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×C4C2×D3×D411yescharacteristic
500C3×C4C2×#23711yescharacteristic
501C3×C4D3×#4111yescharacteristic
502C3×C4C22×#6711yescharacteristic
503Dic3—21no—
504Dic3—42no—
505Dic3—42no—
506Dic3—61no—
507Dic3—61no—
508Dic3—121no—
509Dic3—122no—
510Dic3—122no—
511Dic3—242no—
512Dic3#93812yes—
513C32C2×#47011yescharacteristic, complemented, Sylow
514C23—31no—
515C23—31no—
516C23—91no—
517C23—182no—
518C23—184no—
519Q8—22no—
520Q8—22no—
521Q8—62no—
522Q8—62no—
523Q8—124no—
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×#6712yes—
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—34no—
550C2×C3—121no—
551C2×C3D3×#12111yescharacteristic
552C2×C3C2×#91812yes—
553C2×C3D3×#13712yes—
554C2×C3C2×#93811yescharacteristic
555D3—41no—
556D3—121no—
557D3—121no—
558D3—241no—
559D3#518914yesdirect product factor
560C22—34no—
561C22—32no—
562C22—62no—
563C22—61no—
564C22—182no—
565C22—181no—
566C22—364no—
567C22D32×D411yescharacteristic
568C4—32no—
569C4—42no—
570C4—61no—
571C4—122no—
572C4—122no—
573C4—181no—
574C4—362no—
575C4D3×#23711yescharacteristic
576C4C2×D3×#6711yescharacteristic
577C3—21no—
578C3D3×#47011yescharacteristic, complemented
579C3C2×#518911yescharacteristic, complemented
580C2—34no—
581C2—121no—
582C2—361no—
583C2D3×#91812yes—
584C2D3×#93811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenterC2×Q16D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
4. #10592888C2semidirect
5. C3×#5189C2semidirect
6. #10591638C2semidirect
7. #10591600C2semidirect
8. D3×#835C2semidirect
9. #10590858C2semidirect
10. #10590854C2semidirect
11. D3×#817C2semidirect
16. C2×C32×Q16C22semidirect
20. C2×C3×#216C22semidirect
22. C2×C3×Dic12C22semidirect
36. #63662C22semidirect
37. #63644C22semidirect
38. C3×#835C22semidirect
39. C3×#817C22semidirect
40. #63573C22semidirect
41. #63566C22semidirect
42. #63565C22semidirect
45. C2×D3×Q16D3semidirect
58. #5189D3direct (N × H)
115. C2×C3×Q16C2×D3semidirect
116. C2×C3×Q16C2×D3semidirect
128. C2×#216C2×D3semidirect
137. C2×Dic12C2×D3semidirect
161. #835C2×D3semidirect
166. #817C2×D3semidirect
325. C2×Q16D32semidirect
430. C3×D3#470semidirect
513. C32C2×#470semidirect
559. D3#5189direct (N × H)
578. C3D3×#470semidirect
579. C3C2×#5189semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9462
C2×D3×ΓL(1,𝔽25)2
#105928882
C3×#51892
#105916382
#105916002
D3×#8352
#105908582
#105908542
D3×#8172
C2×#51893
D3×#4703