Finite Group Databasebeta

← D3×#63957 #13171746

Subgroups — D3×#63957 #13171746

Order 1728.

1762 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C3⋊Dic3C211yesmaximal, characteristic
2#11723715C211yesmaximal, characteristic, complemented
3#11723598C212yesmaximal, complemented
4C3×D3×#217C212yesmaximal
5C3×#63957C211yesmaximal, characteristic, complemented
6#11722917C212yesmaximal, complemented
7#11722916C212yesmaximal, complemented
8D3×#3724C212yesmaximal, complemented
9D3×Dic32C212yesmaximal, complemented
10C2×#63957—31nomaximal
11D3×#877—32nomaximal
12C23×C32×D3C2211yescharacteristic
13C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C2×D3×C3⋊Dic3C418yescomplemented
16C2×D3×C3⋊Dic3C2211yescharacteristic
17C2×D3×C3⋊Dic3C2211yescharacteristic
18C2×D3×C3⋊Dic3C2211yescharacteristic
19C2×D3×C3⋊Dic3C2211yescharacteristic
20C2×C3×D3×Dic3C2214yes—
21C3×#3757C2212yes—
22C32×#217C2212yes—
23#88815C2212yescomplemented
24#88813C2212yescomplemented
25#88806C2214yescomplemented
26Dic3×C3⋊Dic3C2214yescomplemented
27C3×#3724C2212yescomplemented
28C3×(C2×D3)⋊Dic3C2214yes—
29C3×Dic32C2212yescomplemented
30C23×C3⋊Dic3—31no—
31C22×D3×Dic3—32no—
32C22×D3×Dic3—61no—
33#64086—32no—
34C2×C3×#217—32no—
35C3×D3×C22⋊C4—32no—
36C3×#877—32no—
37D3×#217D312yes—
38C2×#3724—32no—
39#63957—31no—
40#63957—32no—
41#63957—32no—
42#63957—32no—
43#63957—32no—
44#63957—62no—
45#63957D311yescharacteristic, direct product factor
46#63955—32no—
47C2×Dic32—32no—
48#63878—34no—
49#63877—34no—
50D3×Dic3⋊C4—34no—
51C4×D3×Dic3—34no—
52C23×C33C2311yescharacteristic
53C22×C32×D3—24no—
54C22×C32×D3C2×C414yes—
55C22×C32×D3C2311yescharacteristic
56C22×C32×D3C2311yescharacteristic
57C2×C3⋊(C3⋊Dic3)C2×C414yescomplemented
58C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
59C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
60C2×C3×C3⋊Dic3C2×C414yescomplemented
61C2×C3×C3⋊Dic3C2314yes—
62C2×C3×C3⋊Dic3C2311yescharacteristic
63C2×C3×C3⋊Dic3C2311yescharacteristic
64C2×C32×Dic3C2314yes—
65D3×C3⋊Dic3C2×C414yes—
66D3×C3⋊Dic3C2×C414yes—
67D3×C3⋊Dic3C2×C414yescomplemented
68D3×C3⋊Dic3C2×C414yescomplemented
69C3×D3×Dic3—28no—
70D3×#117—91no—
71C2×#877—92no—
72C24×C32—31no—
73C23×C3×D3—21no—
74C23×C3×D3C2×D312yes—
75C22×C3⋊Dic3—32no—
76C22×C3⋊Dic3—31no—
77C22×C3⋊Dic3—38no—
78C22×C3⋊Dic3—31no—
79C22×C3⋊Dic3—31no—
80C22×C3⋊Dic3—31no—
81C22×C3⋊Dic3—31no—
82C22×C3⋊Dic3—61no—
83C22×C3⋊Dic3—62no—
84C22×C3⋊Dic3—121no—
85C22×C3⋊Dic3C2×D311yescharacteristic
86C22×C3×Dic3—32no—
87C22×C3×Dic3—34no—
88C22×C3×Dic3—61no—
89C2×C3×C4×D3—34no—
90C2×D3×Dic3—316no—
91C2×D3×Dic3—32no—
92C2×D3×Dic3—32no—
93C2×D3×Dic3—32no—
94C2×D3×Dic3—32no—
95C2×D3×Dic3—68no—
96C2×D3×Dic3—61no—
97C2×D3×Dic3—61no—
98C2×D3×Dic3—61no—
99C2×D3×Dic3—61no—
100C2×D3×Dic3C2×D314yes—
101C32×C22⋊C4—32no—
102#3757C2×D312yes—
103#3750—34no—
104C4×C3⋊Dic3—34no—
105C3×#217—22no—
106C3×#217—32no—
107C3×#217—32no—
108C3×#217—34no—
109C3×#217—62no—
110C3×#217C2×D312yes—
111C3×#217C2×D312yes—
112C3×(C2×D3)⋊C4—34no—
113C3×Dic3⋊C4—34no—
114C3×C4×Dic3—34no—
115#3724—32no—
116#3724—34no—
117#3724—34no—
118#3724—64no—
119#3724C2×D312yescomplemented
120Dic3⋊Dic3—34no—
121(C2×D3)⋊Dic3C2×D314yes—
122Dic32—34no—
123Dic32—32no—
124Dic32—34no—
125Dic32—34no—
126Dic32—64no—
127Dic32C2×D312yescomplemented
128C22×C33—22no—
129C22×C33C22×C412yes—
130C22×C33C2411yescharacteristic
131C2×C32×D3—22no—
132C2×C32×D3—28no—
133C2×C32×D3C22×C412yes—
134C2×C32×D3C22×C412yes—
135C2×C32×D3#4114yes—
136C3⋊(C3⋊Dic3)C22×C412yes—
137C3⋊(C3⋊Dic3)C22×C412yes—
138C3×C3⋊Dic3—24no—
139C3×C3⋊Dic3C22×C412yes—
140C3×C3⋊Dic3C22×C412yes—
141C32×Dic3—24no—
142C23×Dic3—92no—
143C23×Dic3—181no—
144C22×C4×D3—91no—
145C3×#117—91no—
146C2×C3×C22⋊C4—92no—
147C2×#217—32no—
148#926—91no—
149C2×Dic3⋊C4—94no—
150C2×C4×Dic3—94no—
151#892—92no—
152D3×C4⋊C4—92no—
153D3×C22⋊C4—32no—
154#877—32no—
155#877—94no—
156#877—94no—
157#877—92no—
158#877—92no—
159#877—92no—
160#877—92no—
161#877—182no—
162#872—92no—
163C42×D3—92no—
164C23×C32—21no—
165C23×C32—22no—
166C23×C32—31no—
167C23×C32—34no—
168C23×C32—31no—
169C23×C32—41no—
170C23×C32—64no—
171C23×C32C22×D312yes—
172C23×C32C22×D311yescharacteristic
173C22×C3×D3—28no—
174C22×C3×D3—28no—
175C22×C3×D3—24no—
176C22×C3×D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3C4×D318yes—
179C22×C3×D3C22×D312yes—
180C22×C3×D3C22×D312yes—
181C2×C32×C4—34no—
182C2×C3⋊Dic3—38no—
183C2×C3⋊Dic3—34no—
184C2×C3⋊Dic3—31no—
185C2×C3⋊Dic3—32no—
186C2×C3⋊Dic3—31no—
187C2×C3⋊Dic3—32no—
188C2×C3⋊Dic3—34no—
189C2×C3⋊Dic3—34no—
190C2×C3⋊Dic3—34no—
191C2×C3⋊Dic3—34no—
192C2×C3⋊Dic3—62no—
193C2×C3⋊Dic3—62no—
194C2×C3⋊Dic3—64no—
195C2×C3⋊Dic3—68no—
196C2×C3⋊Dic3—61no—
197C2×C3⋊Dic3—61no—
198C2×C3⋊Dic3—124no—
199C2×C3⋊Dic3—121no—
200C2×C3⋊Dic3—121no—
201C2×C3⋊Dic3C4×D314yescomplemented
202C2×C3⋊Dic3C22×D314yes—
203C2×C3⋊Dic3C22×D311yescharacteristic
204C2×C3⋊Dic3C22×D311yescharacteristic
205C2×C3×Dic3—24no—
206C2×C3×Dic3—38no—
207C2×C3×Dic3—32no—
208C2×C3×Dic3—32no—
209C2×C3×Dic3—34no—
210C2×C3×Dic3—34no—
211C2×C3×Dic3—64no—
212C2×C3×Dic3—61no—
213C2×C3×Dic3—61no—
214C2×C3×Dic3—64no—
215C2×C3×Dic3—68no—
216C2×C3×Dic3C22×D314yes—
217C2×C3×Dic3C22×D314yes—
218C3×C4×D3—68no—
219D3×Dic3—28no—
220D3×Dic3—38no—
221D3×Dic3—38no—
222D3×Dic3—38no—
223D3×Dic3—38no—
224D3×Dic3—64no—
225D3×Dic3—64no—
226D3×Dic3—64no—
227D3×Dic3—64no—
228C2×#117—271noSylow
229C2×C33—22no—
230C2×C33C23×C411yescharacteristic
231C2×C33C2×#4112yes—
232C32×D3—22no—
233C32×D3#11714yescomplemented
234C24×C3—32no—
235C24×C3—61no—
236C23×D3D3211yescharacteristic
237C22×C3×C4—94no—
238C22×C3×C4—91no—
239C22×Dic3—32no—
240C22×Dic3—34no—
241C22×Dic3—61no—
242C22×Dic3—92no—
243C22×Dic3—92no—
244C22×Dic3—92no—
245C22×Dic3—92no—
246C22×Dic3—916no—
247C22×Dic3—91no—
248C22×Dic3—92no—
249C22×Dic3—181no—
250C22×Dic3—181no—
251C22×Dic3—181no—
252C22×Dic3—181no—
253C22×Dic3—188no—
254C22×Dic3—182no—
255C22×Dic3—181no—
256C22×Dic3—361no—
257C2×C4×D3—34no—
258C2×C4×D3—98no—
259C2×C4×D3—91no—
260C2×C4×D3—91no—
261C2×C4×D3—91no—
262C2×C4×D3—91no—
263C3×C4⋊C4—92no—
264C3×C22⋊C4—32no—
265C3×C22⋊C4—32no—
266C3×C22⋊C4—62no—
267C3×C22⋊C4—94no—
268C3×C22⋊C4—92no—
269C3×C42—92no—
270#217—32no—
271#217—32no—
272#217—34no—
273#217—62no—
274#217D3212yes—
275(C2×D3)⋊C4—34no—
276C4⋊Dic3—92no—
277Dic3⋊C4—34no—
278Dic3⋊C4—94no—
279Dic3⋊C4—94no—
280Dic3⋊C4—94no—
281Dic3⋊C4—94no—
282Dic3⋊C4—184no—
283C4×Dic3—34no—
284C4×Dic3—92no—
285C4×Dic3—94no—
286C4×Dic3—94no—
287C4×Dic3—94no—
288C4×Dic3—94no—
289C4×Dic3—184no—
290C22×C32—22no—
291C22×C32—24no—
292C22×C32—24no—
293C22×C32—22no—
294C22×C32—21no—
295C22×C32—24no—
296C22×C32—22no—
297C22×C32—32no—
298C22×C32—34no—
299C22×C32—32no—
300C22×C32—42no—
301C22×C32—41no—
302C22×C32—44no—
303C22×C32—44no—
304C22×C32—68no—
305C22×C32—62no—
306C22×C32C2×C4×D312yes—
307C22×C32C2×C4×D314yes—
308C22×C32C23×D312yes—
309C22×C32C23×D311yescharacteristic
310C2×C3×D3—24no—
311C2×C3×D3—216no—
312C2×C3×D3—24no—
313C2×C3×D3—216no—
314C2×C3×D3—24no—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3C2×C4×D314yes—
318C2×C3×D3C2×C4×D314yes—
319C2×C3×D3#23718yes—
320C32×C4—64no—
321C3⋊Dic3—24no—
322C3⋊Dic3—34no—
323C3⋊Dic3—34no—
324C3⋊Dic3—32no—
325C3⋊Dic3—32no—
326C3⋊Dic3—62no—
327C3⋊Dic3—62no—
328C3⋊Dic3—64no—
329C3⋊Dic3—64no—
330C3⋊Dic3—122no—
331C3⋊Dic3—122no—
332C3⋊Dic3C2×C4×D312yes—
333C3⋊Dic3C2×C4×D312yes—
334C3×Dic3—24no—
335C3×Dic3—24no—
336C3×Dic3—34no—
337C3×Dic3—34no—
338C3×Dic3—44no—
339C3×Dic3—62no—
340C3×Dic3—62no—
341C3×Dic3—64no—
342C3×Dic3—64no—
343C3×Dic3—124no—
344C23×C4—271no—
345#117—91no—
346#117—272no—
347#117—272no—
348#117—272no—
349#117—271no—
350C2×C4⋊C4—272no—
351C2×C22⋊C4—92no—
352C2×C42—272no—
353C33C2×#11711yescharacteristic, complemented, Sylow
354C23×C3—21no—
355C23×C3—22no—
356C23×C3—32no—
357C23×C3—32no—
358C23×C3—38no—
359C23×C3—41no—
360C23×C3—61no—
361C23×C3—61no—
362C23×C3—64no—
363C23×C3—68no—
364C23×C3—68no—
365C23×C3C2×D3212yes—
366C23×C3C2×D3211yescharacteristic
367C22×D3—24no—
368C22×D3#62414yes—
369C22×D3C2×D3211yescharacteristic
370C22×D3C2×D3211yescharacteristic
371C2×C3×C4—34no—
372C2×C3×C4—34no—
373C2×C3×C4—64no—
374C2×C3×C4—91no—
375C2×C3×C4—91no—
376C2×C3×C4—94no—
377C2×C3×C4—94no—
378C2×C3×C4—188no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—38no—
382C2×Dic3—34no—
383C2×Dic3—34no—
384C2×Dic3—64no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—64no—
388C2×Dic3—68no—
389C2×Dic3—98no—
390C2×Dic3—98no—
391C2×Dic3—98no—
392C2×Dic3—98no—
393C2×Dic3—91no—
394C2×Dic3—92no—
395C2×Dic3—91no—
396C2×Dic3—92no—
397C2×Dic3—98no—
398C2×Dic3—94no—
399C2×Dic3—184no—
400C2×Dic3—184no—
401C2×Dic3—184no—
402C2×Dic3—184no—
403C2×Dic3—182no—
404C2×Dic3—182no—
405C2×Dic3—188no—
406C2×Dic3—181no—
407C2×Dic3—181no—
408C2×Dic3—184no—
409C2×Dic3—361no—
410C2×Dic3—361no—
411C2×Dic3—364no—
412C2×Dic3C2×D3214yes—
413C4×D3—68no—
414C4×D3—94no—
415C4×D3—94no—
416C4×D3—94no—
417C4×D3—94no—
418C2×C32—22no—
419C2×C32—24no—
420C2×C32—24no—
421C2×C32—22no—
422C2×C32—24no—
423C2×C32—22no—
424C2×C32—21no—
425C2×C32—34no—
426C2×C32—41no—
427C2×C32—42no—
428C2×C32—44no—
429C2×C32—44no—
430C2×C32—62no—
431C2×C32C22×C4×D311yescharacteristic
432C2×C32C22×C4×D312yes—
433C2×C32C2×#23714yes—
434C2×C32D3×#4112yes—
435C3×D3—24no—
436C3×D3—24no—
437C3×D3—24no—
438C3×D3#87718yescomplemented
439C24—31no—
440C22×C4—94no—
441C22×C4—91no—
442C22×C4—271no—
443C22×C4—271no—
444C22×C4—271no—
445C22×C4—271no—
446C22×C4—278no—
447C22×C4—271no—
448C4⋊C4—92no—
449C4⋊C4—274no—
450C4⋊C4—272no—
451C22⋊C4—32no—
452C22⋊C4—94no—
453C22⋊C4—92no—
454C42—92no—
455C42—274no—
456C42—272no—
457C22×C3—24no—
458C22×C3—24no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—24no—
464C22×C3—34no—
465C22×C3—38no—
466C22×C3—34no—
467C22×C3—44no—
468C22×C3—44no—
469C22×C3—41no—
470C22×C3—42no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—64no—
474C22×C3—616no—
475C22×C3—616no—
476C22×C3—64no—
477C22×C3—64no—
478C22×C3C4×D3214yes—
479C22×C3C2×#62412yes—
480C22×C3C22×D3212yes—
481C22×C3C22×D3211yescharacteristic
482C2×D3—22no—
483C2×D3—28no—
484C2×D3#380514yes—
485C2×D3C2×#62412yes—
486C2×D3C2×#62412yes—
487C3×C4—64no—
488C3×C4—64no—
489C3×C4—92no—
490C3×C4—92no—
491C3×C4—124no—
492C3×C4—184no—
493Dic3—24no—
494Dic3—34no—
495Dic3—34no—
496Dic3—62no—
497Dic3—62no—
498Dic3—64no—
499Dic3—64no—
500Dic3—94no—
501Dic3—94no—
502Dic3—92no—
503Dic3—92no—
504Dic3—124no—
505Dic3—182no—
506Dic3—182no—
507Dic3—184no—
508Dic3—184no—
509Dic3—362no—
510Dic3—362no—
511C32—21no—
512C32—22no—
513C32—41no—
514C32C2×#87712yescomplemented
515C32D3×#11711yescharacteristic, complemented
516C23—31no—
517C23—31no—
518C23—34no—
519C23—64no—
520C23D3311yescharacteristic
521C2×C4—34no—
522C2×C4—91no—
523C2×C4—91no—
524C2×C4—94no—
525C2×C4—94no—
526C2×C4—188no—
527C2×C4—274no—
528C2×C4—274no—
529C2×C4—274no—
530C2×C4—274no—
531C2×C4—271no—
532C2×C4—271no—
533C2×C4—274no—
534C2×C3—24no—
535C2×C3—22no—
536C2×C3—24no—
537C2×C3—24no—
538C2×C3—22no—
539C2×C3—21no—
540C2×C3—22no—
541C2×C3—38no—
542C2×C3—44no—
543C2×C3—44no—
544C2×C3—42no—
545C2×C3—41no—
546C2×C3—64no—
547C2×C3—64no—
548C2×C3—64no—
549C2×C3C2×C4×D3212yes—
550C2×C3D3×#23714yes—
551C2×C3C2×#380512yes—
552C2×C3C22×#62411yescharacteristic
553D3—22no—
554D3#6395714yesdirect product factor
555C22—22no—
556C22—34no—
557C22—32no—
558C22—32no—
559C22—68no—
560C22—62no—
561C22D3×#62412yes—
562C22C2×D3311yescharacteristic
563C4—64no—
564C4—92no—
565C4—92no—
566C4—184no—
567C4—272no—
568C4—272no—
569C3—21no—
570C3—22no—
571C3—41no—
572C3D3×#87712yescomplemented
573C3C2×#6395711yescharacteristic, complemented
574C2—22no—
575C2—34no—
576C2—62no—
577C2D3×#380512yes—
578C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC23×C32×D3C22
hypercenterC23D33
hypocenterC33C2×#117
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723715C2semidirect
3. #11723598C2semidirect
5. C3×#63957C2semidirect
6. #11722917C2semidirect
7. #11722916C2semidirect
8. D3×#3724C2semidirect
9. D3×Dic32C2semidirect
15. C2×D3×C3⋊Dic3C4semidirect
23. #88815C22semidirect
24. #88813C22semidirect
25. #88806C22semidirect
26. Dic3×C3⋊Dic3C22semidirect
27. C3×#3724C22semidirect
29. C3×Dic32C22semidirect
45. #63957D3direct (N × H)
57. C2×C3⋊(C3⋊Dic3)C2×C4semidirect
60. C2×C3×C3⋊Dic3C2×C4semidirect
67. D3×C3⋊Dic3C2×C4semidirect
68. D3×C3⋊Dic3C2×C4semidirect
119. #3724C2×D3semidirect
127. Dic32C2×D3semidirect
201. C2×C3⋊Dic3C4×D3semidirect
233. C32×D3#117semidirect
353. C33C2×#117semidirect
438. C3×D3#877semidirect
514. C32C2×#877semidirect
515. C32D3×#117semidirect
554. D3#63957direct (N × H)
572. C3D3×#877semidirect
573. C3C2×#63957semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C3⋊Dic32
#117237152
#117235982
C3×D3×#2172
C3×#639572
#117229172
#117229162
D3×#37242
D3×Dic322
C2×#639573
D3×#8773