Finite Group Databasebeta

← D3×#4712 #11874349

Subgroups — D3×#4712 #11874349

Order 1152.

1408 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D24C212yesmaximal, complemented
2C2×D3×#204C212yesmaximal, complemented
3D3×#875C211yesmaximal, characteristic, complemented
4D3×#874C211yesmaximal, characteristic, complemented
5#10592411C211yesmaximal, characteristic, complemented
6C3×#4712C211yesmaximal, characteristic, complemented
7C3×D3×#97C211yesmaximal, characteristic, complemented
8#10590883C212yesmaximal, complemented
9#10590881C212yesmaximal, complemented
10#10590371C211yesmaximal, characteristic, complemented
11#10590351C211yesmaximal, characteristic, complemented
12D3×#496—31nomaximal
13C2×#4712—31nomaximal
14C2×D3×D12—22no—
15C2×D3×D12C2212yes—
16C2×D3×D12C2211yescharacteristic
17C2×D3×Dic6C2211yescharacteristic
18C2×#3745C2212yescomplemented
19C2×#3744C2212yescomplemented
20#64084C2211yescharacteristic, complemented
21#64083C2211yescharacteristic, complemented
22C2×C3×D24C2212yescomplemented
23C2×C3×#204C2212yescomplemented
24C2×C3×D3×C8C2212yes—
25C3×#875C2211yescharacteristic, complemented
26C3×#874C2211yescharacteristic, complemented
27C3×C42×D3C2211yescharacteristic
28D3×(C2×D3)⋊C4—22no—
29#63911—22no—
30#63911C2212yescomplemented
31#63864C2211yescharacteristic, complemented
32#63860C2211yescharacteristic, complemented
33#63852—22no—
34C2×#3717C2212yescomplemented
35C2×#3716C2212yescomplemented
36C2×#3714C2212yescomplemented
37C2×#3714C2212yescomplemented
38D3×D24—28no—
39D3×#204—28no—
40C32×#97C2211yescharacteristic, complemented
41C3×#815C2212yescomplemented
42C3×#803C2211yescharacteristic, complemented
43C2×D3×SD16—32no—
44C2×D3×D8—32no—
45C22×D24—32no—
46C22×#204—32no—
47D3×#127—31no—
48D3×#124—31no—
49C2×#875—31no—
50C2×#874—31no—
51C3×#496—31no—
52C2×C3×#97—31no—
53#5176—32no—
54#5154—32no—
55#5074—31no—
56#5058—31no—
57#4712—32no—
58#4712—32no—
59#4712—31no—
60#4712—31no—
61#4712—31no—
62#4712—31no—
63#4712—61no—
64#4712D311yescharacteristic, direct product factor
65D3×#97D311yescharacteristic, complemented
66C22×D32—22no—
67C22×D32—21no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×#634C2311yescharacteristic
72C2×C3×D12—22no—
73C2×C3×D12C2312yes—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3D412yes—
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C2×#627—21no—
79C2×#626—24no—
80C2×#626—21no—
81C2×#626—22no—
82C2×D3×Dic3—21no—
83D3×D12—24no—
84D3×D12—24no—
85D3×D12—24no—
86D3×D12—48no—
87D3×Dic6—24no—
88C2×C32×C8C2312yes—
89C32×C42C2311yescharacteristic
90#3752—22no—
91#3745—24no—
92#3744—24no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4×Dic3D412yes—
95C3×C4×Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C3×D24—24no—
98C3×#204—24no—
99C3×D3×C8D418yescomplemented
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3717—24no—
103#3716—24no—
104#3714—24no—
105#3714—24no—
106C2×#496—91noSylow
107C2×D3×Q8—31no—
108C2×D3×D4—31no—
109C2×D3×D4—32no—
110C2×D3×D4—62no—
111C22×D12—32no—
112C22×D12—31no—
113C22×D12—62no—
114C22×Dic6—31no—
115C2×C3×SD16—32no—
116C2×C3×D8—32no—
117C22×C3×C8—32no—
118C3×#127—31no—
119C3×#124—31no—
120C2×C3×C42—31no—
121#947—31no—
122C2×#215—32no—
123#940—32no—
124#940—62no—
125#936—31no—
126C2×#214—32no—
127C2×#213—32no—
128C2×#213—32no—
129C2×(C2×D3)⋊C4—62no—
130D3×SD16—68no—
131D3×D8—68no—
132C2×D24—32no—
133C2×D24—32no—
134C2×D24—32no—
135C2×D24—32no—
136C2×D24—62no—
137C2×D24—68no—
138C2×D24C2×D312yescomplemented
139C2×#204—32no—
140C2×#204—32no—
141C2×#204—32no—
142C2×#204—32no—
143C2×#204—62no—
144C2×#204—68no—
145C2×#204C2×D312yescomplemented
146C2×D3×C8C2×D312yes—
147#885—62no—
148D3×C22⋊C4—62no—
149#875—31no—
150#875—31no—
151#875—31no—
152#875—31no—
153#875—61no—
154#875—62no—
155#875C2×D311yescharacteristic, complemented
156#874—32no—
157#874—31no—
158#874—31no—
159#874—61no—
160#874—62no—
161#874C2×D311yescharacteristic, complemented
162C42×D3C2×D311yescharacteristic
163C3×#97—21no—
164C3×#97—32no—
165C3×#97—31no—
166C3×#97C2×D311yescharacteristic, complemented
167C3×#97C2×D311yescharacteristic, complemented
168#815C2×D312yescomplemented
169#803C2×D311yescharacteristic, complemented
170C22×C3⋊D3—21no—
171C22×C3⋊D3—22no—
172C22×C3×D3—21no—
173C22×C3×D3—22no—
174C22×C3×D3C2×D411yescharacteristic
175C2×D32—44no—
176C2×D32—42no—
177C2×D32—44no—
178C2×D32—48no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—21no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—22no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—44no—
186#634—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D412yes—
189C2×C3×Dic3C2×D411yescharacteristic
190C3×D12—22no—
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—44no—
194C3×C4×D3—24no—
195C3×C4×D3C2×D414yes—
196C3×Dic6—22no—
197#627—42no—
198#626—48no—
199#626—44no—
200#626—42no—
201D3×Dic3—42no—
202C32×C8C2×D414yescomplemented
203C3×C3⋊C8C2×D414yescomplemented
204C22×SD16—92no—
205C22×D8—92no—
206C2×#127—91no—
207C2×#124—91no—
208#496—31no—
209#496—91no—
210#496—91no—
211#496—92no—
212#496—92no—
213#496—91no—
214C2×#97—31no—
215C23×D3—61no—
216C23×D3—62no—
217C23×D3—61no—
218C23×D3—62no—
219C2×C3×Q8—31no—
220C2×C3×D4—31no—
221C2×C3×D4—32no—
222C2×C3×D4—62no—
223C22×C3×C4—31no—
224C22×C3×C4—32no—
225C2×#67—61no—
226C2×#67—64no—
227C2×#67—62no—
228C22×Dic3—61no—
229D3×Q8—64no—
230D3×D4—64no—
231D3×D4—64no—
232D3×D4—64no—
233D3×D4—128no—
234C2×D12—22no—
235C2×D12—32no—
236C2×D12—32no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—62no—
240C2×D12—61no—
241C2×D12—64no—
242C2×D12—64no—
243C2×D12—64no—
244C2×D12—64no—
245C2×D12—62no—
246C2×D12—61no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—122no—
250C2×D12—128no—
251C2×D12C22×D312yes—
252C2×D12C22×D311yescharacteristic
253C2×C4×D3—61no—
254C2×C4×D3D1212yes—
255C2×C4×D3C22×D311yescharacteristic
256C2×Dic6—31no—
257C2×Dic6—31no—
258C2×Dic6—61no—
259C2×Dic6—64no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C2×Dic6C22×D311yescharacteristic
263C3×SD16—64no—
264C3×D8—64no—
265C2×C3×C8—22no—
266C2×C3×C8—32no—
267C2×C3×C8—38no—
268C2×C3×C8C22×D312yes—
269C2×C3×C8C22×D312yes—
270C3×C22⋊C4—62no—
271C3×C42—21no—
272C3×C42—32no—
273C3×C42—31no—
274C3×C42C22×D311yescharacteristic
275C3×C42C22×D311yescharacteristic
276#217—62no—
277#215—64no—
278#214—64no—
279#213—64no—
280#213—64no—
281(C2×D3)⋊C4—22no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—122no—
288C4×Dic3D1212yes—
289C4×Dic3C22×D311yescharacteristic
290C2×C3⋊C8C22×D312yes—
291D24—24no—
292D24—64no—
293D24—64no—
294D24—64no—
295D24—64no—
296D24—124no—
297#204—24no—
298#204—64no—
299#204—64no—
300#204—64no—
301#204—64no—
302#204—124no—
303D3×C8D1218yescomplemented
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—41no—
306C2×C3⋊D3—42no—
307C2×C3⋊D3—44no—
308C2×C3⋊D3—42no—
309C2×C3×D3—41no—
310C2×C3×D3—42no—
311C2×C3×D3—44no—
312C2×C3×D3—42no—
313C2×C3×D3#12712yes—
314C2×C3×D3AGL(1,ℤ/8)14yes—
315D32—84no—
316D32—88no—
317C32×C4—22no—
318C32×C4C22×D412yes—
319C3⋊Dic3—41no—
320C3×Dic3—22no—
321C3×Dic3—41no—
322C3×Dic3#12712yes—
323C22×Q8—91no—
324C22×D4—91no—
325C22×D4—92no—
326C22×D4—182no—
327C2×SD16—32no—
328C2×SD16—92no—
329C2×SD16—92no—
330C2×SD16—92no—
331C2×SD16—188no—
332C2×D8—32no—
333C2×D8—92no—
334C2×D8—92no—
335C2×D8—92no—
336C2×D8—188no—
337C22×C8—32no—
338#127—31no—
339#127—92no—
340#127—91no—
341#127—182no—
342#124—31no—
343#124—91no—
344#124—91no—
345#124—91no—
346#124—182no—
347C2×C22⋊C4—182no—
348C2×C42—31no—
349#97—32no—
350#97—31no—
351#97D3211yescharacteristic, complemented
352C23×C3—31no—
353C23×C3—61no—
354C23×C3—62no—
355C22×D3—21no—
356C22×D3—22no—
357C22×D3—61no—
358C22×D3—62no—
359C22×D3—61no—
360C22×D3—62no—
361C22×D3—121no—
362C22×D3—122no—
363C22×D3—124no—
364C22×D3—122no—
365C22×D3—128no—
366C22×D3—124no—
367C22×D3—122no—
368C22×D3—124no—
369C22×D3—128no—
370C22×D3—124no—
371C22×D3C2×D1211yescharacteristic
372C3×Q8—62no—
373C3×D4—62no—
374C3×D4—62no—
375C3×D4—62no—
376C3×D4—124no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—31no—
380C2×C3×C4—34no—
381C2×C3×C4—32no—
382C2×C3×C4—64no—
383C2×C3×C4—61no—
384C2×C3×C4C2×D1212yes—
385C2×C3×C4D3×D412yes—
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—128no—
389#67—122no—
390#67—124no—
391C2×Dic3—21no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—121no—
395C2×Dic3—122no—
396C2×Dic3C2×D1212yes—
397C2×Dic3C2×D1211yescharacteristic
398D12—22no—
399D12—22no—
400D12—22no—
401D12—44no—
402D12—62no—
403D12—62no—
404D12—62no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—122no—
409D12—122no—
410D12—122no—
411D12—124no—
412D12—124no—
413D12—124no—
414D12—122no—
415D12—128no—
416D12—244no—
417C4×D3—24no—
418C4×D3—122no—
419C4×D3C2×D1214yes—
420Dic6—22no—
421Dic6—62no—
422Dic6—62no—
423Dic6—122no—
424Dic6—122no—
425Dic6—122no—
426C3×C8—24no—
427C3×C8—34no—
428C3×C8C2×D1214yescomplemented
429C3×C8D3×D414yescomplemented
430C3⋊C8C2×D1214yescomplemented
431C2×C32C2×#12711yescharacteristic
432C2×C32C2×AGL(1,ℤ/8)12yes—
433C3⋊D3—82no—
434C3⋊D3—81no—
435C3×D3—82no—
436C3×D3—81no—
437C3×D3#49614yescomplemented
438C24—181no—
439C24—182no—
440C2×Q8—31no—
441C2×Q8—91no—
442C2×Q8—181no—
443C2×Q8—184no—
444C2×D4—31no—
445C2×D4—32no—
446C2×D4—62no—
447C2×D4—91no—
448C2×D4—92no—
449C2×D4—184no—
450C2×D4—184no—
451C2×D4—184no—
452C2×D4—181no—
453C2×D4—184no—
454C2×D4—182no—
455C2×D4—182no—
456C2×D4—368no—
457C22×C4—31no—
458C22×C4—32no—
459C22×C4—181no—
460SD16—64no—
461SD16—184no—
462SD16—184no—
463SD16—184no—
464D8—64no—
465D8—184no—
466D8—184no—
467D8—184no—
468C2×C8—32no—
469C2×C8—38no—
470C2×C8C2×D3212yes—
471C22⋊C4—62no—
472C22⋊C4—182no—
473C22⋊C4—182no—
474C22⋊C4—182no—
475C42—31no—
476C42—32no—
477C42C2×D3211yescharacteristic
478C22×C3—21no—
479C22×C3—32no—
480C22×C3—34no—
481C22×C3—121no—
482C22×C3—122no—
483C22×C3—124no—
484C22×C3—122no—
485C22×C3C22×D1211yescharacteristic
486C22×C3C2×D3×D411yescharacteristic
487C2×D3—42no—
488C2×D3—41no—
489C2×D3—44no—
490C2×D3—42no—
491C2×D3—122no—
492C2×D3—121no—
493C2×D3—122no—
494C2×D3—121no—
495C2×D3—124no—
496C2×D3—122no—
497C2×D3—124no—
498C2×D3—122no—
499C2×D3—242no—
500C2×D3—241no—
501C2×D3—244no—
502C2×D3—242no—
503C2×D3—248no—
504C2×D3—244no—
505C2×D3—248no—
506C2×D3—244no—
507C2×D3#87412yes—
508C2×D3#90814yes—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—32no—
513C3×C4—42no—
514C3×C4—62no—
515C3×C4—121no—
516C3×C4C22×D1212yes—
517C3×C4C2×D3×D412yes—
518Dic3—22no—
519Dic3—41no—
520Dic3—121no—
521Dic3—121no—
522Dic3—241no—
523Dic3#87412yes—
524C32C2×#49611yescharacteristic, complemented, Sylow
525C23—31no—
526C23—61no—
527C23—62no—
528C23—181no—
529C23—182no—
530C23—362no—
531C23—364no—
532C23—368no—
533C23—364no—
534Q8—62no—
535Q8—182no—
536Q8—362no—
537D4—62no—
538D4—62no—
539D4—62no—
540D4—124no—
541D4—182no—
542D4—182no—
543D4—182no—
544D4—364no—
545D4—362no—
546D4—364no—
547D4—368no—
548C2×C4—31no—
549C2×C4—34no—
550C2×C4—32no—
551C2×C4—64no—
552C2×C4—61no—
553C2×C4—181no—
554C2×C4—362no—
555C2×C4D3×D1212yes—
556C2×C4C22×D3211yescharacteristic
557C8—34no—
558C8D3×D1214yescomplemented
559C2×C3—22no—
560C2×C3—21no—
561C2×C3—34no—
562C2×C3—242no—
563C2×C3—241no—
564C2×C3C2×#87411yescharacteristic
565C2×C3D3×#12711yescharacteristic
566C2×C3C2×#90812yes—
567C2×C3D3×AGL(1,ℤ/8)12yes—
568D3—82no—
569D3—81no—
570D3—242no—
571D3—241no—
572D3—242no—
573D3—241no—
574D3—482no—
575D3—481no—
576D3#471214yesdirect product factor
577C22—34no—
578C22—32no—
579C22—124no—
580C22—122no—
581C22—121no—
582C22—122no—
583C22—364no—
584C22—362no—
585C22—361no—
586C22—362no—
587C22—728no—
588C22—724no—
589C22C2×D3×D1211yescharacteristic
590C4—22no—
591C4—32no—
592C4—62no—
593C4—121no—
594C4—361no—
595C4C2×D3×D1212yes—
596C3—21no—
597C3C2×#471211yescharacteristic, complemented
598C3D3×#49611yescharacteristic, complemented
599C2—34no—
600C2—242no—
601C2—241no—
602C2—722no—
603C2—721no—
604C2D3×#87411yescharacteristic
605C2D3×#90812yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32C2×#496
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×D3×D24C2semidirect
2. C2×D3×#204C2semidirect
3. D3×#875C2semidirect
4. D3×#874C2semidirect
5. #10592411C2semidirect
6. C3×#4712C2semidirect
7. C3×D3×#97C2semidirect
8. #10590883C2semidirect
9. #10590881C2semidirect
10. #10590371C2semidirect
11. #10590351C2semidirect
18. C2×#3745C22semidirect
19. C2×#3744C22semidirect
20. #64084C22semidirect
21. #64083C22semidirect
22. C2×C3×D24C22semidirect
23. C2×C3×#204C22semidirect
25. C3×#875C22semidirect
26. C3×#874C22semidirect
30. #63911C22semidirect
31. #63864C22semidirect
32. #63860C22semidirect
34. C2×#3717C22semidirect
35. C2×#3716C22semidirect
36. C2×#3714C22semidirect
37. C2×#3714C22semidirect
40. C32×#97C22semidirect
41. C3×#815C22semidirect
42. C3×#803C22semidirect
64. #4712D3direct (N × H)
65. D3×#97D3semidirect
99. C3×D3×C8D4semidirect
138. C2×D24C2×D3semidirect
145. C2×#204C2×D3semidirect
155. #875C2×D3semidirect
161. #874C2×D3semidirect
166. C3×#97C2×D3semidirect
167. C3×#97C2×D3semidirect
168. #815C2×D3semidirect
169. #803C2×D3semidirect
202. C32×C8C2×D4semidirect
203. C3×C3⋊C8C2×D4semidirect
303. D3×C8D12semidirect
351. #97D32semidirect
428. C3×C8C2×D12semidirect
429. C3×C8D3×D4semidirect
430. C3⋊C8C2×D12semidirect
437. C3×D3#496semidirect
524. C32C2×#496semidirect
558. C8D3×D12semidirect
576. D3#4712direct (N × H)
597. C3C2×#4712semidirect
598. C3D3×#496semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
C2×D3×#2042
D3×#8752
D3×#8742
#105924112
C3×#47122
C3×D3×#972
#105908832
#105908812
#105903712
#105903512
D3×#4963
C2×#47123