Finite Group Databasebeta

← D3×#64138 #13177319

Subgroups — D3×#64138 #13177319

Order 1728.

2364 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
1C22×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×D3×#638C211yesmaximal, characteristic
3#11723970C211yesmaximal, characteristic, complemented
4C3×#64138C211yesmaximal, characteristic, complemented
5D3×#3757C211yesmaximal, characteristic, complemented
6#11723612C211yesmaximal, characteristic, complemented
7#11723605C211yesmaximal, characteristic, complemented
8D3×#3752C212yesmaximal, complemented
9#11723513C212yesmaximal, complemented
10D3×#3750C212yesmaximal, complemented
11#11723414C212yesmaximal, complemented
12C2×#64138—31nomaximal
13D3×#929—34nomaximal
14C23×C32×D3C2211yescharacteristic
15C22×D3×C3⋊D3C2211yescharacteristic
16C22×C33×C4C2211yescharacteristic, complemented
17C2×#6312C2211yescharacteristic
18C2×C3×#638C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic, complemented
20C2×C32×C4×D3—24no—
21C2×C32×C4×D3C2212yes—
22C2×C32×C4×D3C2212yescomplemented
23D3×#638—24no—
24C2×#6291C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×D3×C3⋊Dic3C2212yes—
27C2×D3×C3⋊Dic3C2211yescharacteristic
28#88864C2211yescharacteristic, complemented
29#88859C2212yescomplemented
30#88857C2212yescomplemented
31C3×#3757C2211yescharacteristic, complemented
32C3×#3752C2212yescomplemented
33C3×#3750C2212yescomplemented
34#88807C2212yescomplemented
35#88806C2212yescomplemented
36#88804C2212yescomplemented
37#88803C2212yescomplemented
38(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
39C23×C32×C4—31no—
40C22×#638—31no—
41C22×C3×C4×D3D314yescomplemented
42C2×D3×#67—34no—
43C2×#3757—31no—
44#64138—31no—
45#64138—31no—
46#64138—31no—
47#64138—32no—
48#64138—32no—
49#64138—34no—
50#64138—64no—
51#64138D311yescharacteristic, direct product factor
52C2×#3752—32no—
53C2×#3750—32no—
54C3×#929—34no—
55D3×#217—34no—
56#63966—34no—
57#63961—34no—
58D3×(C2×D3)⋊C4—38no—
59#63905—38no—
60D3×Dic3⋊C4—38no—
61#63850—38no—
62C23×C33C2311yescharacteristic
63C22×C3⋊(C3⋊D3)C2311yescharacteristic
64C22×C3×C3⋊D3C2311yescharacteristic
65C22×C32×D3—24no—
66C22×C32×D3D414yes—
67C22×C32×D3C2311yescharacteristic
68C22×C32×D3C2311yescharacteristic
69C2×D3×C3⋊D3—22no—
70C2×D3×C3⋊D3—24no—
71C2×C33×C4—22no—
72C2×C33×C4C2312yes—
73#6312—22no—
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3⋊(C3⋊Dic3)C2312yes—
76C3×#638—22no—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C2×C32×Dic3—22no—
80C2×C32×Dic3C2312yes—
81C32×C4×D3—24no—
82C32×C4×D3—24no—
83#6291—22no—
84#6290—22no—
85D3×C3⋊Dic3—22no—
86D3×C3⋊Dic3—24no—
87C2×#929—94no—
88D3×#123—91no—
89C24×C32—31no—
90C23×C3⋊D3—31no—
91C23×C3×D3C2×D314yes—
92C22×D32—34no—
93C22×C32×C4—24no—
94C22×C32×C4—31no—
95C22×C32×C4—32no—
96C22×C32×C4—32no—
97C22×C32×C4—64no—
98C22×C32×C4C2×D314yescomplemented
99C22×C32×C4C2×D311yescharacteristic, complemented
100C2×#638—31no—
101C2×#638—34no—
102C2×#638—31no—
103C2×#638—31no—
104C2×#638—64no—
105C2×#638—64no—
106C2×#638C2×D311yescharacteristic
107C22×C3⋊Dic3—31no—
108C22×C3⋊Dic3—32no—
109C2×C3×#67—34no—
110C22×C3×Dic3C2×D314yescomplemented
111C2×C3×C4×D3—216no—
112C2×C3×C4×D3C2×D318yes—
113C2×C3×C4×D3C2×D318yescomplemented
114D3×#67—616no—
115C2×#626—34no—
116C2×#625—34no—
117C2×D3×Dic3—34no—
118C2×D3×Dic3—38no—
119#3757—31no—
120#3757—34no—
121#3757—32no—
122#3757—64no—
123#3757C2×D311yescharacteristic, complemented
124#3752—32no—
125#3752—32no—
126#3752—38no—
127#3752—32no—
128#3752—68no—
129#3752C2×D312yescomplemented
130#3750—32no—
131#3750—38no—
132#3750—32no—
133#3750—32no—
134#3750—68no—
135#3750C2×D312yescomplemented
136C3×#217—34no—
137C3×(C2×D3)⋊C4—38no—
138C3×Dic3⋊C4—38no—
139#3724—38no—
140Dic3⋊Dic3—38no—
141#3722—38no—
142(C2×D3)⋊Dic3—38no—
143(C2×D3)⋊Dic3—38no—
144C22×C33—22no—
145C22×C33C2×D412yes—
146C22×C33C2411yescharacteristic
147C2×C3⋊(C3⋊D3)—21no—
148C2×C3⋊(C3⋊D3)—22no—
149C2×C3×C3⋊D3—21no—
150C2×C3×C3⋊D3—22no—
151C2×C32×D3—22no—
152C2×C32×D3—28no—
153C2×C32×D3C2×D412yes—
154C2×C32×D3C2×D412yes—
155C2×C32×D3#4114yes—
156D3×C3⋊D3—44no—
157C33×C4—22no—
158C3⋊(C3⋊Dic3)—21no—
159C3⋊(C3⋊Dic3)—22no—
160C3×C3⋊Dic3—21no—
161C3×C3⋊Dic3—22no—
162C32×Dic3—22no—
163C23×C3×C4—34no—
164C22×#67—94no—
165C2×D3×D4—91no—
166C22×C4×D3C3⋊D311yescharacteristic, complemented
167C3×#123—91no—
168C2×#217—94no—
169#935—91no—
170#929—34no—
171#929—98no—
172#929—98no—
173#929—94no—
174#929—94no—
175#929—94no—
176#929—91no—
177#929—184no—
178C2×(C2×D3)⋊C4—98no—
179C2×Dic3⋊C4—98no—
180#894—92no—
181D3×C4⋊C4—92no—
182#886—91no—
183#883—92no—
184D3×C22⋊C4—91no—
185D3×C22⋊C4—92no—
186C23×C32—24no—
187C23×C32—31no—
188C23×C32—34no—
189C23×C32—31no—
190C23×C32—64no—
191C23×C32C22×D314yes—
192C23×C32C22×D311yescharacteristic
193C22×C3⋊D3—31no—
194C22×C3⋊D3—34no—
195C22×C3⋊D3—64no—
196C22×C3⋊D3—64no—
197C22×C3⋊D3—62no—
198C22×C3⋊D3C22×D311yescharacteristic
199C22×C3×D3—216no—
200C22×C3×D3—34no—
201C22×C3×D3#67116yes—
202C22×C3×D3C22×D314yes—
203C22×C3×D3C22×D314yes—
204C2×D32—616no—
205C2×D32—68no—
206C2×C32×C4—22no—
207C2×C32×C4—28no—
208C2×C32×C4—28no—
209C2×C32×C4—32no—
210C2×C32×C4—48no—
211C2×C32×C4—64no—
212C2×C32×C4—64no—
213C2×C32×C4—62no—
214C2×C32×C4C22×D318yes—
215C2×C32×C4C22×D312yes—
216#638—22no—
217#638—62no—
218#638—62no—
219#638—62no—
220#638—68no—
221#638—128no—
222C2×C3⋊Dic3—31no—
223C2×C3⋊Dic3—32no—
224C2×C3⋊Dic3—38no—
225C2×C3⋊Dic3—34no—
226C2×C3⋊Dic3—64no—
227C2×C3⋊Dic3—68no—
228C2×C3⋊Dic3—64no—
229C2×C3⋊Dic3—62no—
230C2×C3⋊Dic3C22×D311yescharacteristic
231C2×C3⋊Dic3C22×D312yes—
232C3×#67—68no—
233C2×C3×Dic3—28no—
234C2×C3×Dic3—38no—
235C2×C3×Dic3—34no—
236C2×C3×Dic3C22×D318yes—
237C3×C4×D3—216no—
238C3×C4×D3—216no—
239#626—68no—
240#625—68no—
241D3×Dic3—616no—
242D3×Dic3—68no—
243C2×#123—271noSylow
244C2×C33—22no—
245C2×C33C22×D411yescharacteristic
246C2×C33C2×#4112yes—
247C3⋊(C3⋊D3)—41no—
248C3×C3⋊D3—41no—
249C32×D3—22no—
250C32×D3#12314yescomplemented
251C24×C3—34no—
252C23×D3—94no—
253C23×D3—91no—
254C23×D3C2×C3⋊D311yescharacteristic
255C2×C3×D4—91no—
256C22×C3×C4—24no—
257C22×C3×C4—34no—
258C22×C3×C4—38no—
259C22×C3×C4—38no—
260C22×C3×C4—616no—
261C22×C3×C4D3214yescomplemented
262C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
263C2×#67—34no—
264C2×#67—94no—
265C2×#67—94no—
266C2×#67—94no—
267C2×#67—91no—
268C2×#67—91no—
269C2×#67—184no—
270C2×#67—1816no—
271C22×Dic3—94no—
272C22×Dic3—98no—
273C22×Dic3C2×C3⋊D311yescharacteristic, complemented
274D3×D4—184no—
275C2×D12—91no—
276C2×C4×D3—24no—
277C2×C4×D3—92no—
278C2×C4×D3—91no—
279C2×C4×D3C2×C3⋊D312yes—
280C2×C4×D3C2×C3⋊D312yescomplemented
281C3×C4⋊C4—92no—
282C3×C22⋊C4—91no—
283C3×C22⋊C4—92no—
284#217—34no—
285#217—98no—
286#217—94no—
287#217—91no—
288#217—92no—
289#217—184no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—98no—
292(C2×D3)⋊C4—98no—
293(C2×D3)⋊C4—92no—
294(C2×D3)⋊C4—98no—
295(C2×D3)⋊C4—92no—
296(C2×D3)⋊C4—92no—
297(C2×D3)⋊C4—188no—
298C4⋊Dic3—92no—
299Dic3⋊C4—38no—
300Dic3⋊C4—98no—
301Dic3⋊C4—98no—
302Dic3⋊C4—98no—
303Dic3⋊C4—92no—
304Dic3⋊C4—92no—
305Dic3⋊C4—188no—
306C22×C32—22no—
307C22×C32—24no—
308C22×C32—28no—
309C22×C32—28no—
310C22×C32—32no—
311C22×C32—34no—
312C22×C32—32no—
313C22×C32—48no—
314C22×C32—68no—
315C22×C32—62no—
316C22×C32D3×D412yes—
317C22×C32C2×#6718yes—
318C22×C32C23×D314yes—
319C22×C32C23×D311yescharacteristic
320C2×C3⋊D3—21no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—61no—
323C2×C3⋊D3—62no—
324C2×C3⋊D3—68no—
325C2×C3⋊D3—64no—
326C2×C3⋊D3—124no—
327C2×C3⋊D3—128no—
328C2×C3⋊D3—124no—
329C2×C3×D3—28no—
330C2×C3×D3—232no—
331C2×C3×D3—68no—
332C2×C3×D3—64no—
333C2×C3×D3#235116yes—
334C2×C3×D3C2×#6718yes—
335C2×C3×D3C2×#6718yes—
336D32—1216no—
337C32×C4—22no—
338C32×C4—28no—
339C32×C4—48no—
340C32×C4—62no—
341C3⋊Dic3—21no—
342C3⋊Dic3—22no—
343C3⋊Dic3—61no—
344C3⋊Dic3—62no—
345C3⋊Dic3—68no—
346C3⋊Dic3—64no—
347C3⋊Dic3—128no—
348C3⋊Dic3—124no—
349C3×Dic3—28no—
350C3×Dic3—68no—
351C3×Dic3—64no—
352C22×D4—271no—
353C23×C4—31no—
354#123—91no—
355#123—272no—
356#123—271no—
357#123—272no—
358#123—271no—
359#123—271no—
360C2×C4⋊C4—272no—
361C2×C22⋊C4—272no—
362C2×C22⋊C4—271no—
363C33C2×#12311yescharacteristic, complemented, Sylow
364C23×C3—24no—
365C23×C3—34no—
366C23×C3—34no—
367C23×C3—316no—
368C23×C3—616no—
369C23×C3—91no—
370C23×C3C2×D3214yes—
371C23×C3C22×C3⋊D311yescharacteristic
372C22×D3—24no—
373C22×D3—34no—
374C22×D3—94no—
375C22×D3—91no—
376C22×D3—184no—
377C22×D3—188no—
378C22×D3—1816no—
379C22×D3—184no—
380C22×D3—182no—
381C22×D3#63814yes—
382C22×D3C22×C3⋊D311yescharacteristic
383C22×D3C22×C3⋊D311yescharacteristic
384C3×D4—182no—
385C2×C3×C4—28no—
386C2×C3×C4—22no—
387C2×C3×C4—28no—
388C2×C3×C4—38no—
389C2×C3×C4—48no—
390C2×C3×C4—616no—
391C2×C3×C4—616no—
392C2×C3×C4—68no—
393C2×C3×C4—91no—
394C2×C3×C4—92no—
395C2×C3×C4C2×D3218yes—
396C2×C3×C4C22×C3⋊D312yes—
397#67—68no—
398#67—188no—
399#67—188no—
400#67—188no—
401#67—182no—
402#67—182no—
403#67—368no—
404C2×Dic3—22no—
405C2×Dic3—34no—
406C2×Dic3—38no—
407C2×Dic3—94no—
408C2×Dic3—98no—
409C2×Dic3—91no—
410C2×Dic3—92no—
411C2×Dic3—184no—
412C2×Dic3—188no—
413C2×Dic3—1816no—
414C2×Dic3—188no—
415C2×Dic3C22×C3⋊D312yes—
416D12—182no—
417C4×D3—24no—
418C4×D3—24no—
419C4×D3—184no—
420C4×D3—182no—
421C2×C32—22no—
422C2×C32—28no—
423C2×C32—24no—
424C2×C32—28no—
425C2×C32—34no—
426C2×C32—48no—
427C2×C32—62no—
428C2×C32C2×#23518yes—
429C2×C32C2×D3×D411yescharacteristic
430C2×C32D3×#4112yes—
431C2×C32C22×#6714yes—
432C3⋊D3—41no—
433C3⋊D3—121no—
434C3⋊D3—124no—
435C3⋊D3—244no—
436C3×D3—28no—
437C3×D3—124no—
438C3×D3#929116yescomplemented
439C24—31no—
440C24—271no—
441C2×D4—91no—
442C2×D4—271no—
443C2×D4—271no—
444C2×D4—271no—
445C2×D4—544no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—32no—
449C22×C4—64no—
450C22×C4—272no—
451C22×C4—271no—
452C22×C4D3×C3⋊D311yescharacteristic, complemented
453C4⋊C4—92no—
454C4⋊C4—272no—
455C4⋊C4—272no—
456C4⋊C4—272no—
457C22⋊C4—91no—
458C22⋊C4—92no—
459C22⋊C4—272no—
460C22⋊C4—272no—
461C22⋊C4—272no—
462C22⋊C4—271no—
463C22⋊C4—272no—
464C22×C3—28no—
465C22×C3—22no—
466C22×C3—24no—
467C22×C3—28no—
468C22×C3—316no—
469C22×C3—38no—
470C22×C3—38no—
471C22×C3—48no—
472C22×C3—632no—
473C22×C3—68no—
474C22×C3—182no—
475C22×C3—181no—
476C22×C3D3×#6718yes—
477C22×C3C2×#63812yes—
478C22×C3C22×D3214yes—
479C22×C3C23×C3⋊D311yescharacteristic
480C2×D3—22no—
481C2×D3—28no—
482C2×D3—68no—
483C2×D3—64no—
484C2×D3—188no—
485C2×D3—184no—
486C2×D3—182no—
487C2×D3—181no—
488C2×D3—364no—
489C2×D3—368no—
490C2×D3—3616no—
491C2×D3—364no—
492C2×D3#382814yes—
493C2×D3C2×#63812yes—
494C2×D3C2×#63812yes—
495C3×C4—28no—
496C3×C4—22no—
497C3×C4—48no—
498C3×C4—68no—
499C3×C4—182no—
500C3×C4—181no—
501Dic3—22no—
502Dic3—68no—
503Dic3—64no—
504Dic3—188no—
505Dic3—184no—
506Dic3—182no—
507Dic3—181no—
508Dic3—364no—
509Dic3—368no—
510C32—24no—
511C32D3×#12311yescharacteristic, complemented
512C32C2×#92914yescomplemented
513C23—31no—
514C23—31no—
515C23—34no—
516C23—64no—
517C23—91no—
518C23—271no—
519C23—542no—
520C23—544no—
521C23C2×D3×C3⋊D311yescharacteristic
522D4—182no—
523D4—542no—
524D4—542no—
525D4—542no—
526C2×C4—22no—
527C2×C4—32no—
528C2×C4—64no—
529C2×C4—64no—
530C2×C4—62no—
531C2×C4—92no—
532C2×C4—91no—
533C2×C4—272no—
534C2×C4—271no—
535C2×C4—542no—
536C2×C4—544no—
537C2×C4C2×D3×C3⋊D312yes—
538C2×C3—22no—
539C2×C3—28no—
540C2×C3—28no—
541C2×C3—24no—
542C2×C3—316no—
543C2×C3—48no—
544C2×C3—68no—
545C2×C3—361no—
546C2×C3D3×#23518yes—
547C2×C3C2×D3×#6714yes—
548C2×C3C2×#382812yes—
549C2×C3C22×#63811yescharacteristic
550D3—22no—
551D3—124no—
552D3—361no—
553D3—364no—
554D3—724no—
555D3#6413814yesdirect product factor
556C22—22no—
557C22—34no—
558C22—32no—
559C22—32no—
560C22—68no—
561C22—62no—
562C22—182no—
563C22—181no—
564C22—542no—
565C22—541no—
566C22—1084no—
567C22D3×#63812yes—
568C22C22×D3×C3⋊D311yescharacteristic
569C4—22no—
570C4—62no—
571C4—182no—
572C4—181no—
573C4—542no—
574C4—541no—
575C3—24no—
576C3D3×#92914yescomplemented
577C3C2×#6413811yescharacteristic, complemented
578C2—22no—
579C2—34no—
580C2—62no—
581C2—361no—
582C2—1081no—
583C2D3×#382812yes—
584C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
prime radicalC2×D3×#638C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4×D3C2semidirect
3. #11723970C2semidirect
4. C3×#64138C2semidirect
5. D3×#3757C2semidirect
6. #11723612C2semidirect
7. #11723605C2semidirect
8. D3×#3752C2semidirect
9. #11723513C2semidirect
10. D3×#3750C2semidirect
11. #11723414C2semidirect
16. C22×C33×C4C22semidirect
19. C22×C32×Dic3C22semidirect
22. C2×C32×C4×D3C22semidirect
28. #88864C22semidirect
29. #88859C22semidirect
30. #88857C22semidirect
31. C3×#3757C22semidirect
32. C3×#3752C22semidirect
33. C3×#3750C22semidirect
34. #88807C22semidirect
35. #88806C22semidirect
36. #88804C22semidirect
37. #88803C22semidirect
38. (C2×D3)⋊(C3⋊Dic3)C22semidirect
41. C22×C3×C4×D3D3semidirect
51. #64138D3direct (N × H)
98. C22×C32×C4C2×D3semidirect
99. C22×C32×C4C2×D3semidirect
110. C22×C3×Dic3C2×D3semidirect
113. C2×C3×C4×D3C2×D3semidirect
123. #3757C2×D3semidirect
129. #3752C2×D3semidirect
135. #3750C2×D3semidirect
166. C22×C4×D3C3⋊D3semidirect
250. C32×D3#123semidirect
261. C22×C3×C4D32semidirect
262. C22×C3×C4C2×C3⋊D3semidirect
273. C22×Dic3C2×C3⋊D3semidirect
280. C2×C4×D3C2×C3⋊D3semidirect
363. C33C2×#123semidirect
438. C3×D3#929semidirect
452. C22×C4D3×C3⋊D3semidirect
511. C32D3×#123semidirect
512. C32C2×#929semidirect
555. D3#64138direct (N × H)
576. C3D3×#929semidirect
577. C3C2×#64138semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×D3×#6382
#117239702
C3×#641382
D3×#37572
#117236122
#117236052
D3×#37522
#117235132
D3×#37502
#117234142
C2×#641383
D3×#9293