Finite Group Databasebeta

← D3×#63497 #13151140

Subgroups — D3×#63497 #13151140

Order 1728.

1104 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×D4×C9C211yesmaximal, characteristic
2C22×D3×Dic9C211yesmaximal, characteristic, complemented
3#11721835C211yesmaximal, characteristic, complemented
4C3×#63497C211yesmaximal, characteristic, complemented
5#11721280C212yesmaximal, complemented
6D3×#3676C212yesmaximal, complemented
7D3×#3676C211yesmaximal, characteristic, complemented
8#11721266C211yesmaximal, characteristic, complemented
9#11721265C211yesmaximal, characteristic, complemented
10#11721015C212yesmaximal, complemented
11D3×Dic9⋊C4C212yesmaximal, complemented
12D3×#935—31nomaximal
13C2×#63497—31nomaximal
14C23×D3×C9C2211yescharacteristic
15C23×D3×C9C2211yescharacteristic
16C2×C3×D4×C9C2211yescharacteristic
17C22×C3⋊Dic9C2211yescharacteristic, complemented
18C2×C9×#67C2211yescharacteristic
19C2×C9×#67C2211yescharacteristic
20C22×C3×Dic9C2211yescharacteristic, complemented
21D3×D4×C9—24no—
22C2×C9×D12C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×D3×Dic9—24no—
25C2×D3×Dic9C2212yes—
26C2×D3×Dic9C2212yes—
27C2×D3×Dic9C2212yescomplemented
28#88551C2211yescharacteristic, complemented
29#88551C2212yescomplemented
30#88534C2212yescomplemented
31C3×#3676C2211yescharacteristic, complemented
32C3×#3676C2212yescomplemented
33C3×Dic9⋊C4C2212yescomplemented
34(C2×D3)⋊Dic9C2212yescomplemented
35(C2×D3)⋊Dic9C2212yescomplemented
36(C2×D3)⋊Dic9C2212yescomplemented
37#88442C2212yescomplemented
38Dic9⋊Dic3C2212yescomplemented
39C2×C3×D3×D4D311yescharacteristic
40C22×D3×Dic3—31no—
41#64144—31no—
42C3×#935—31no—
43#63969—32no—
44D3×#217—32no—
45D3×#217—31no—
46#63962—31no—
47#63961—31no—
48#63884—32no—
49D3×Dic3⋊C4—32no—
50C22×D4×C9—31no—
51C23×Dic9—31no—
52C2×#3676—31no—
53C2×#3676—32no—
54#63497—31no—
55#63497—31no—
56#63497—31no—
57#63497—32no—
58#63497—32no—
59#63497—61no—
60#63497D311yescharacteristic, direct product factor
61C2×Dic9⋊C4—32no—
62C23×C3×C9C2311yescharacteristic
63C23×C3×C9C2311yescharacteristic
64C22×D3×C9—24no—
65C22×D3×C9—22no—
66C22×D3×C9—24no—
67C22×D3×C9D414yes—
68C22×D3×C9C2311yescharacteristic
69C22×D3×C9C2311yescharacteristic
70C22×D3×C9C2311yescharacteristic
71C3×D4×C9—22no—
72C2×C3×C4×C9C2311yescharacteristic
73C2×C3⋊Dic9—22no—
74C2×C3⋊Dic9C2312yes—
75C2×C3⋊Dic9C2312yes—
76C9×#67—22no—
77C9×#67—22no—
78C2×C9×Dic3C2311yescharacteristic
79C2×C3×Dic9—22no—
80C2×C3×Dic9C2312yes—
81C2×C3×Dic9C2312yes—
82C9×D12—22no—
83C4×D3×C9—22no—
84D3×Dic9—24no—
85D3×Dic9—24no—
86D3×Dic9—24no—
87C2×#935—91no—
88D3×#123—91no—
89C23×C3×D3C2×D311yescharacteristic
90C23×C3×D3C2×D311yescharacteristic
91C2×C32×D4C2×D311yescharacteristic
92C22×C3⋊Dic3—31no—
93C2×C3×#67C2×D311yescharacteristic
94C2×C3×#67C2×D311yescharacteristic
95C22×C3×Dic3—31no—
96C3×D3×D4—24no—
97C2×C3×D12C2×D311yescharacteristic
98C2×C3×C4×D3C2×D311yescharacteristic
99C2×D3×Dic3—32no—
100C2×D3×Dic3—32no—
101C2×D3×Dic3—32no—
102C2×D3×Dic3—64no—
103C24×C9—31no—
104C24×C9—31no—
105#3757—31no—
106#3757—32no—
107#3750—32no—
108C3×#217—31no—
109C3×#217—32no—
110C3×Dic3⋊C4—32no—
111#3724—32no—
112Dic3⋊Dic3—32no—
113(C2×D3)⋊Dic3—32no—
114(C2×D3)⋊Dic3—32no—
115(C2×D3)⋊Dic3—32no—
116C2×D4×C9—21no—
117C2×D4×C9—31no—
118C2×D4×C9—31no—
119C2×D4×C9—31no—
120C2×D4×C9—64no—
121C2×D4×C9C2×D311yescharacteristic
122C22×C4×C9—31no—
123C22×Dic9—31no—
124C22×Dic9—32no—
125C22×Dic9—32no—
126C22×Dic9—32no—
127C22×Dic9—64no—
128C22×Dic9—61no—
129C22×Dic9C2×D311yescharacteristic, complemented
130#3676—31no—
131#3676—32no—
132#3676—32no—
133#3676—32no—
134#3676—32no—
135#3676—61no—
136#3676—62no—
137#3676C2×D311yescharacteristic, complemented
138#3676C2×D312yescomplemented
139Dic9⋊C4—32no—
140Dic9⋊C4—32no—
141Dic9⋊C4—32no—
142Dic9⋊C4—62no—
143Dic9⋊C4C2×D312yescomplemented
144C22×C3×C9—22no—
145C22×C3×C9—21no—
146C22×C3×C9—22no—
147C22×C3×C9C2×D412yes—
148C22×C3×C9C2411yescharacteristic
149C2×D3×C9—22no—
150C2×D3×C9—28no—
151C2×D3×C9—21no—
152C2×D3×C9—22no—
153C2×D3×C9—44no—
154C2×D3×C9C2×D412yes—
155C2×D3×C9C2×D412yes—
156C2×D3×C9#4114yes—
157C3×C4×C9—21no—
158C3⋊Dic9—22no—
159C3⋊Dic9—22no—
160C9×Dic3—21no—
161C3×Dic9—22no—
162C3×Dic9—22no—
163C22×C3×D4—31no—
164C23×Dic3—91no—
165C2×D3×D4D911yescharacteristic
166C22×C4×D3—91no—
167C3×#123—91no—
168C2×#217—91no—
169C2×#217—92no—
170#935—31no—
171#935—92no—
172#935—91no—
173#935—92no—
174#935—91no—
175#935—91no—
176#935—91no—
177#935—181no—
178#929—91no—
179C2×Dic3⋊C4—92no—
180#894—92no—
181D3×C4⋊C4—92no—
182#886—91no—
183#883—92no—
184D3×C22⋊C4—91no—
185D3×C22⋊C4—92no—
186C23×C32C22×D311yescharacteristic
187C23×C32C22×D311yescharacteristic
188C22×C3×D3—24no—
189C22×C3×D3—24no—
190C22×C3×D3—22no—
191C22×C3×D3#6714yes—
192C22×C3×D3C22×D311yescharacteristic
193C22×C3×D3C22×D311yescharacteristic
194C22×C3×D3C22×D311yescharacteristic
195C32×D4—22no—
196C2×C32×C4C22×D311yescharacteristic
197C2×C3⋊Dic3—32no—
198C2×C3⋊Dic3—32no—
199C2×C3⋊Dic3—62no—
200C3×#67—22no—
201C3×#67—22no—
202C2×C3×Dic3—32no—
203C2×C3×Dic3—32no—
204C2×C3×Dic3—62no—
205C2×C3×Dic3C22×D311yescharacteristic
206C3×D12—22no—
207C3×C4×D3—22no—
208D3×Dic3—64no—
209D3×Dic3—64no—
210D3×Dic3—64no—
211C23×C9—21no—
212C23×C9—21no—
213C23×C9—31no—
214C23×C9—34no—
215C23×C9—31no—
216C23×C9—31no—
217C23×C9—64no—
218C23×C9—62no—
219C23×C9—64no—
220C23×C9C22×D311yescharacteristic
221C23×C9C22×D311yescharacteristic
222D4×C9—22no—
223D4×C9—42no—
224D4×C9—62no—
225D4×C9—62no—
226D4×C9—62no—
227C2×C4×C9—21no—
228C2×C4×C9—31no—
229C2×C4×C9—62no—
230C2×C4×C9C22×D311yescharacteristic
231C2×Dic9—22no—
232C2×Dic9—32no—
233C2×Dic9—32no—
234C2×Dic9—62no—
235C2×Dic9—62no—
236C2×Dic9—64no—
237C2×Dic9—64no—
238C2×Dic9—64no—
239C2×Dic9—62no—
240C2×Dic9—122no—
241C2×Dic9C22×D312yes—
242C2×Dic9C22×D312yes—
243C2×#123—271noSylow
244C2×C3×C9—22no—
245C2×C3×C9—41no—
246C2×C3×C9C22×D411yescharacteristic
247C2×C3×C9C2×#4112yes—
248D3×C9—22no—
249D3×C9—41no—
250D3×C9#12314yescomplemented
251C24×C3—31no—
252C24×C3—31no—
253C23×D3C2×D911yescharacteristic
254C23×D3C2×D911yescharacteristic
255C2×C3×D4—21no—
256C2×C3×D4—31no—
257C2×C3×D4—31no—
258C2×C3×D4—31no—
259C2×C3×D4—64no—
260C2×C3×D4C2×D911yescharacteristic
261C2×C3×D4D3211yescharacteristic
262C22×C3×C4—31no—
263C22×C3×C4—91no—
264C2×#67C2×D911yescharacteristic
265C2×#67C2×D911yescharacteristic
266C22×Dic3—31no—
267C22×Dic3—92no—
268C22×Dic3—92no—
269C22×Dic3—92no—
270C22×Dic3—91no—
271C22×Dic3—91no—
272C22×Dic3—181no—
273C22×Dic3—184no—
274D3×D4—24no—
275C2×D12C2×D911yescharacteristic
276C2×C4×D3—92no—
277C2×C4×D3—92no—
278C2×C4×D3—92no—
279C2×C4×D3—184no—
280C2×C4×D3C2×D911yescharacteristic
281C3×C4⋊C4—92no—
282C3×C22⋊C4—92no—
283C3×C22⋊C4—91no—
284#217—31no—
285#217—32no—
286#217—92no—
287#217—92no—
288#217—92no—
289#217—92no—
290#217—91no—
291#217—91no—
292#217—92no—
293#217—181no—
294#217—182no—
295(C2×D3)⋊C4—92no—
296(C2×D3)⋊C4—92no—
297(C2×D3)⋊C4—92no—
298C4⋊Dic3—92no—
299Dic3⋊C4—32no—
300Dic3⋊C4—92no—
301Dic3⋊C4—92no—
302Dic3⋊C4—92no—
303Dic3⋊C4—92no—
304Dic3⋊C4—92no—
305Dic3⋊C4—182no—
306C22×C32—22no—
307C22×C32—22no—
308C22×C32—21no—
309C22×C32C2×#6712yes—
310C22×C32C23×D311yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—28no—
313C2×C3×D3—22no—
314C2×C3×D3—21no—
315C2×C3×D3—44no—
316C2×C3×D3#23714yes—
317C2×C3×D3C2×#6712yes—
318C2×C3×D3C2×#6712yes—
319C32×C4—21no—
320C3⋊Dic3—62no—
321C3⋊Dic3—62no—
322C3×Dic3—21no—
323C3×Dic3—62no—
324C3×Dic3—62no—
325C22×C9—22no—
326C22×C9—21no—
327C22×C9—22no—
328C22×C9—21no—
329C22×C9—22no—
330C22×C9—32no—
331C22×C9—34no—
332C22×C9—32no—
333C22×C9—42no—
334C22×C9—41no—
335C22×C9—42no—
336C22×C9—68no—
337C22×C9—62no—
338C22×C9—61no—
339C22×C9—62no—
340C22×C9—124no—
341C22×C9D3×D412yes—
342C22×C9C23×D311yescharacteristic
343C4×C9—21no—
344C4×C9—41no—
345C4×C9—61no—
346Dic9—22no—
347Dic9—22no—
348Dic9—62no—
349Dic9—62no—
350Dic9—122no—
351Dic9—122no—
352C22×D4—31no—
353C23×C4—271no—
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—271no—
362C2×C22⋊C4—272no—
363C3×C9C2×#12311yescharacteristic, complemented, Sylow
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—31no—
367C23×C3—31no—
368C23×C3—34no—
369C23×C3—31no—
370C23×C3—64no—
371C23×C3—62no—
372C23×C3—64no—
373C23×C3C22×D911yescharacteristic
374C23×C3C22×D911yescharacteristic
375C23×C3C2×D3211yescharacteristic
376C23×C3C2×D3211yescharacteristic
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—22no—
380C22×D3#61114yes—
381C22×D3C22×D911yescharacteristic
382C22×D3C22×D911yescharacteristic
383C22×D3C22×D911yescharacteristic
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—42no—
387C3×D4—62no—
388C3×D4—62no—
389C3×D4—62no—
390C2×C3×C4—21no—
391C2×C3×C4—31no—
392C2×C3×C4—62no—
393C2×C3×C4—92no—
394C2×C3×C4—92no—
395C2×C3×C4—182no—
396C2×C3×C4C22×D911yescharacteristic
397C2×C3×C4C2×D3211yescharacteristic
398#67—22no—
399#67—22no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—62no—
403C2×Dic3—92no—
404C2×Dic3—92no—
405C2×Dic3—92no—
406C2×Dic3—92no—
407C2×Dic3—182no—
408C2×Dic3—182no—
409C2×Dic3—184no—
410C2×Dic3—184no—
411C2×Dic3—184no—
412C2×Dic3—182no—
413C2×Dic3—182no—
414C2×Dic3—362no—
415C2×Dic3C22×D911yescharacteristic
416D12—22no—
417C4×D3—22no—
418C4×D3—184no—
419C4×D3—184no—
420C4×D3—184no—
421C2×C32—22no—
422C2×C32—41no—
423C2×C32C2×#23712yes—
424C2×C32C22×#6711yescharacteristic
425C3×D3—22no—
426C3×D3—41no—
427C3×D3#93514yes—
428C2×C9—22no—
429C2×C9—22no—
430C2×C9—21no—
431C2×C9—34no—
432C2×C9—42no—
433C2×C9—41no—
434C2×C9—62no—
435C2×C9—81no—
436C2×C9—121no—
437C2×C9C2×D3×D411yescharacteristic
438C2×C9D3×#4112yes—
439C24—31no—
440C24—31no—
441C2×D4—31no—
442C2×D4—31no—
443C2×D4—31no—
444C2×D4—64no—
445C2×D4D3×D911yescharacteristic
446C22×C4—31no—
447C22×C4—91no—
448C22×C4—272no—
449C22×C4—272no—
450C22×C4—272no—
451C22×C4—271no—
452C22×C4—544no—
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—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—21no—
468C22×C3—22no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—34no—
473C22×C3—32no—
474C22×C3—32no—
475C22×C3—42no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3—68no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—61no—
482C22×C3—124no—
483C22×C3C2×#61112yes—
484C22×C3C23×D911yescharacteristic
485C22×C3D3×#6712yes—
486C22×C3C22×D3211yescharacteristic
487C2×D3—22no—
488C2×D3—28no—
489C2×D3—22no—
490C2×D3—21no—
491C2×D3—44no—
492C2×D3#369914yes—
493C2×D3C2×#61112yes—
494C2×D3C2×#61112yes—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—41no—
498C3×C4—61no—
499C3×C4—182no—
500C3×C4—182no—
501Dic3—21no—
502Dic3—62no—
503Dic3—62no—
504Dic3—182no—
505Dic3—182no—
506Dic3—182no—
507Dic3—182no—
508Dic3—362no—
509Dic3—362no—
510C32C2×#93511yescharacteristic
511C9—21no—
512C9D3×#12311yescharacteristic, complemented
513C23—31no—
514C23—31no—
515C23—34no—
516C23—31no—
517C23—64no—
518C23—62no—
519C23—64no—
520C23C2×D3×D911yescharacteristic
521C23C2×D3×D911yescharacteristic
522D4—22no—
523D4—62no—
524D4—62no—
525D4—62no—
526C2×C4—31no—
527C2×C4—62no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—182no—
531C2×C4—272no—
532C2×C4—272no—
533C2×C4—544no—
534C2×C4—544no—
535C2×C4—544no—
536C2×C4—542no—
537C2×C4C2×D3×D911yescharacteristic
538C2×C3—22no—
539C2×C3—22no—
540C2×C3—22no—
541C2×C3—21no—
542C2×C3—34no—
543C2×C3—42no—
544C2×C3—41no—
545C2×C3—41no—
546C2×C3—62no—
547C2×C3—81no—
548C2×C3—121no—
549C2×C3C2×#369912yes—
550C2×C3C22×#61111yescharacteristic
551C2×C3D3×#23712yes—
552C2×C3C2×D3×#6711yescharacteristic
553D3—22no—
554D3—41no—
555D3#6349714yesdirect product factor
556C22—22no—
557C22—22no—
558C22—21no—
559C22—34no—
560C22—32no—
561C22—32no—
562C22—68no—
563C22—62no—
564C22—62no—
565C22—61no—
566C22—124no—
567C22D3×#61112yes—
568C22C22×D3×D911yescharacteristic
569C4—21no—
570C4—61no—
571C4—182no—
572C4—182no—
573C4—542no—
574C4—542no—
575C3—21no—
576C3C2×#6349711yescharacteristic, complemented
577C3D3×#93511yescharacteristic
578C2—22no—
579C2—34no—
580C2—41no—
581C2—62no—
582C2—121no—
583C2D3×#369912yes—
584C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
prime radicalC2×C3×D3×D4D3
hypercenterC2×D4D3×D9
hypocenterC3×C9C2×#123
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic9C2semidirect
3. #11721835C2semidirect
4. C3×#63497C2semidirect
5. #11721280C2semidirect
6. D3×#3676C2semidirect
7. D3×#3676C2semidirect
8. #11721266C2semidirect
9. #11721265C2semidirect
10. #11721015C2semidirect
11. D3×Dic9⋊C4C2semidirect
17. C22×C3⋊Dic9C22semidirect
20. C22×C3×Dic9C22semidirect
27. C2×D3×Dic9C22semidirect
28. #88551C22semidirect
29. #88551C22semidirect
30. #88534C22semidirect
31. C3×#3676C22semidirect
32. C3×#3676C22semidirect
33. C3×Dic9⋊C4C22semidirect
34. (C2×D3)⋊Dic9C22semidirect
35. (C2×D3)⋊Dic9C22semidirect
36. (C2×D3)⋊Dic9C22semidirect
37. #88442C22semidirect
38. Dic9⋊Dic3C22semidirect
60. #63497D3direct (N × H)
129. C22×Dic9C2×D3semidirect
137. #3676C2×D3semidirect
138. #3676C2×D3semidirect
143. Dic9⋊C4C2×D3semidirect
250. D3×C9#123semidirect
363. C3×C9C2×#123semidirect
512. C9D3×#123semidirect
555. D3#63497direct (N × H)
576. C3C2×#63497semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D4×C92
C22×D3×Dic92
#117218352
C3×#634972
#117212802
D3×#36762
#117212662
#117212652
#117210152
D3×Dic9⋊C42
D3×#9353
C2×#634973