Finite Group Databasebeta

← D3×#63560 #13155331

Subgroups — D3×#63560 #13155331

Order 1728.

748 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Dic6C211yesmaximal, characteristic
2D3×#3748C211yesmaximal, characteristic
3C3×D3×#208C211yesmaximal, characteristic
4#11722074C211yesmaximal, characteristic, complemented
5#11722029C211yesmaximal, characteristic, complemented
6#11722028C211yesmaximal, characteristic, complemented
7C3×#63560C211yesmaximal, characteristic, complemented
8D3×#836—31nomaximal
9C2×#63560—31nomaximal
10D3×#824—31nomaximal
11C2×C3×#634C2211yescharacteristic
12C2×C32×C4×D3C2211yescharacteristic
13C2×C32×Dic6C2211yescharacteristic
14C2×C3×#627C412yes—
15C2×C3×D3×Dic3C412yes—
16C3×D3×Dic6—21no—
17C3×D3×Dic6—21no—
18C3×D3×Dic6—21no—
19C3×D3×Dic6—21no—
20#88855C2211yescharacteristic
21C3×#3748C2211yescharacteristic
22C3×#3748C2211yescharacteristic
23C32×#208C2211yescharacteristic
24#88786—21no—
25D3×C3⋊(C3⋊C8)—21no—
26C3×#3711—21no—
27C3×D3×C3⋊C8—21no—
28C2×C3×D3×Q8—31no—
29C22×C3×Dic6—31no—
30C2×D3×Dic6D311yescharacteristic
31C2×#3748—31no—
32C2×C3×#208—31no—
33C3×D3×M16—31no—
34D3×#208—31no—
35D3×#208—31no—
36D3×#208—61no—
37D3×#208D311yescharacteristic
38#63663—31no—
39#63651—31no—
40C3×#836—31no—
41C3×#824—31no—
42#63561—31no—
43#63560—31no—
44#63560—31no—
45#63560—31no—
46#63560—31no—
47#63560—31no—
48#63560—31no—
49#63560—61no—
50#63560—61no—
51#63560D311yescharacteristic, direct product factor
52C22×C32×D3C2×C411yescharacteristic
53C2×C33×C4C2311yescharacteristic
54C2×C3×C3⋊Dic3C2×C412yes—
55C3×#634—21no—
56C3×#634—21no—
57C2×C32×Dic3C2×C412yes—
58C2×C32×Dic3C2×C411yescharacteristic
59C32×C4×D3D411yescharacteristic
60C32×C4×D3D411yescharacteristic
61C32×C4×D3D411yescharacteristic
62C32×C4×D3D411yescharacteristic
63C32×Dic6—21no—
64C32×Dic6—21no—
65C3×#627—22no—
66C3×#627—22no—
67C3×D3×Dic3—22no—
68C3×D3×Dic3—22no—
69C3⋊(C3⋊(C3⋊C8))—21no—
70C3×C3⋊(C3⋊C8)—21no—
71C3×C3⋊(C3⋊C8)—21no—
72C32×C3⋊C8—21no—
73C2×#836—91no—
74C2×#824—91no—
75D3×#101—91no—
76C2×C32×Q8—31no—
77C22×C32×C4—31no—
78C2×#634C2×D311yescharacteristic
79C22×C3×Dic3—32no—
80C3×D3×Q8—61no—
81C3×D3×Q8—61no—
82C3×D3×Q8—61no—
83C3×D3×Q8—61no—
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3—32no—
86C2×C3×C4×D3C2×D311yescharacteristic
87C2×C3×C4×D3C2×D311yescharacteristic
88C2×C3×Dic6—21no—
89C2×C3×Dic6—31no—
90C2×C3×Dic6—31no—
91C2×C3×Dic6—32no—
92C2×C3×Dic6—32no—
93C2×C3×Dic6—61no—
94C2×C3×Dic6—61no—
95C2×C3×Dic6—61no—
96C2×C3×Dic6—61no—
97C2×C3×Dic6—61no—
98C2×C3×Dic6C2×D311yescharacteristic
99C2×C3×Dic6C2×D311yescharacteristic
100C2×#627Dic312yes—
101C2×D3×Dic3Dic312yes—
102D3×Dic6—21no—
103D3×Dic6—21no—
104D3×Dic6—21no—
105D3×Dic6—21no—
106C32×M16—31no—
107#3748—31no—
108#3748—31no—
109#3748—31no—
110#3748—61no—
111#3748—61no—
112#3748—61no—
113#3748—61no—
114#3748—121no—
115#3748C2×D311yescharacteristic
116#3748C2×D311yescharacteristic
117C2×C3⋊(C3⋊C8)—61no—
118C3×#208—21no—
119C3×#208—31no—
120C3×#208—31no—
121C3×#208—31no—
122C3×#208—31no—
123C3×#208—61no—
124C3×#208—61no—
125C3×#208—61no—
126C3×#208C2×D311yescharacteristic
127C3×#208C2×D311yescharacteristic
128C2×C3×C3⋊C8—61no—
129C3×ΓL(1,𝔽25)—61no—
130C3×D3×C8—61no—
131#3711—21no—
132#3711—62no—
133#3711—61no—
134#3711—61no—
135D3×C3⋊C8—21no—
136D3×C3⋊C8—62no—
137D3×C3⋊C8—61no—
138D3×C3⋊C8—61no—
139C22×C33C22×C411yescharacteristic
140C2×C32×D3—22no—
141C2×C32×D3C22⋊C411yescharacteristic
142C2×C32×D3C22⋊C411yescharacteristic
143C33×C4C2×D411yescharacteristic
144C33×C4C2×D411yescharacteristic
145C3×C3⋊Dic3—22no—
146C32×Dic3—22no—
147C32×Dic3C22⋊C411yescharacteristic
148C32×Dic3C22⋊C411yescharacteristic
149C22×C3×Q8—91no—
150C2×D3×Q8—31no—
151C22×Dic6—31no—
152C2×C3×M16—91no—
153C2×#208—31no—
154C2×#208—91no—
155C2×#208—91no—
156C2×#208—181no—
157D3×M16—31no—
158D3×M16—91no—
159C3×#101—91no—
160#836—31no—
161#836—91no—
162#836—91no—
163#836—91no—
164#836—91no—
165#836—181no—
166#824—31no—
167#824—91no—
168#824—91no—
169#824—91no—
170#824—91no—
171#824—91no—
172#824—181no—
173C23×C32—31no—
174C22×C3×D3—21no—
175C22×C3×D3C4×D311yescharacteristic
176C22×C3×D3C2×Dic311yescharacteristic
177C32×Q8—61no—
178C32×Q8—61no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—31no—
183C2×C32×C4—31no—
184C2×C32×C4—31no—
185C2×C32×C4—31no—
186C2×C32×C4—31no—
187C2×C32×C4—32no—
188C2×C32×C4—41no—
189C2×C32×C4C22×D311yescharacteristic
190C2×C32×C4C22×D311yescharacteristic
191C2×C32×C4C22×D311yescharacteristic
192C2×C3⋊Dic3C2×Dic312yes—
193#634—21no—
194#634—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—32no—
198C2×C3×Dic3—32no—
199C2×C3×Dic3—62no—
200C2×C3×Dic3—62no—
201C2×C3×Dic3—62no—
202C2×C3×Dic3C4×D312yes—
203C2×C3×Dic3C4×D311yescharacteristic
204C2×C3×Dic3C2×Dic312yes—
205C2×C3×Dic3C2×Dic311yescharacteristic
206C3×C4×D3—21no—
207C3×C4×D3—21no—
208C3×C4×D3—21no—
209C3×C4×D3—21no—
210C3×C4×D3—62no—
211C3×C4×D3—62no—
212C3×C4×D3D1211yescharacteristic
213C3×C4×D3D1211yescharacteristic
214C3×C4×D3#6711yescharacteristic
215C3×C4×D3#6711yescharacteristic
216C3×C4×D3#6711yescharacteristic
217C3×C4×D3#6711yescharacteristic
218C3×C4×D3#6711yescharacteristic
219C3×C4×D3#6711yescharacteristic
220C3×Dic6—21no—
221C3×Dic6—21no—
222C3×Dic6—21no—
223C3×Dic6—21no—
224C3×Dic6—41no—
225C3×Dic6—41no—
226C3×Dic6—62no—
227C3×Dic6—62no—
228C3×Dic6—61no—
229C3×Dic6—61no—
230C3×Dic6—61no—
231C3×Dic6—61no—
232C3×Dic6—62no—
233C3×Dic6—62no—
234C3×Dic6—121no—
235C3×Dic6—121no—
236#627—22no—
237#627—22no—
238D3×Dic3—22no—
239D3×Dic3—22no—
240C32×C8—61no—
241C3⋊(C3⋊C8)—21no—
242C3⋊(C3⋊C8)—21no—
243C3⋊(C3⋊C8)—61no—
244C3⋊(C3⋊C8)—62no—
245C3⋊(C3⋊C8)—61no—
246C3⋊(C3⋊C8)—61no—
247C3⋊(C3⋊C8)—121no—
248C3⋊(C3⋊C8)—121no—
249C3⋊(C3⋊C8)—122no—
250C3×C3⋊C8—21no—
251C3×C3⋊C8—21no—
252C3×C3⋊C8—41no—
253C3×C3⋊C8—62no—
254C3×C3⋊C8—61no—
255C3×C3⋊C8—61no—
256C3×C3⋊C8—61no—
257C3×C3⋊C8—61no—
258C3×C3⋊C8—121no—
259C2×#101—271noSylow
260C2×C33—21no—
261C2×C33C2×C22⋊C411yescharacteristic
262C32×D3—21no—
263C32×D3#10112yescomplemented
264C2×C3×Q8—31no—
265C2×C3×Q8—31no—
266C2×C3×Q8—61no—
267C2×C3×Q8—92no—
268C2×C3×Q8—91no—
269C2×C3×Q8—181no—
270C2×C3×Q8—181no—
271C2×C3×Q8—181no—
272C2×C3×Q8—181no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—61no—
276C22×C3×C4—92no—
277C22×Dic3—32no—
278D3×Q8—61no—
279D3×Q8—61no—
280D3×Q8—61no—
281D3×Q8—61no—
282C2×C4×D3—32no—
283C2×C4×D3D3211yescharacteristic
284C2×Dic6—31no—
285C2×Dic6—31no—
286C2×Dic6—32no—
287C2×Dic6—32no—
288C2×Dic6—61no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6D3211yescharacteristic
294C3×M16—31no—
295C3×M16—31no—
296C3×M16—61no—
297C3×M16—91no—
298C3×M16—91no—
299C3×M16—181no—
300C2×C3×C8—181no—
301#208—31no—
302#208—31no—
303#208—31no—
304#208—31no—
305#208—61no—
306#208—61no—
307#208—61no—
308#208—91no—
309#208—91no—
310#208—91no—
311#208—181no—
312#208—181no—
313#208—181no—
314#208—181no—
315#208—181no—
316#208—182no—
317#208—361no—
318#208D3211yescharacteristic
319C2×C3⋊C8—61no—
320C2×C3⋊C8—181no—
321C2×C3⋊C8—181no—
322C2×C3⋊C8—182no—
323ΓL(1,𝔽25)—61no—
324ΓL(1,𝔽25)—181no—
325D3×C8—61no—
326D3×C8—181no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—31no—
331C22×C32—31no—
332C22×C32—41no—
333C22×C32—62no—
334C22×C32C2×C4×D311yescharacteristic
335C22×C32C2×C4×D311yescharacteristic
336C22×C32C22×Dic311yescharacteristic
337C2×C3×D3—22no—
338C2×C3×D3—22no—
339C2×C3×D3—21no—
340C2×C3×D3—21no—
341C2×C3×D3—42no—
342C2×C3×D3(C2×D3)⋊C411yescharacteristic
343C2×C3×D3(C2×D3)⋊C411yescharacteristic
344C2×C3×D3#21711yescharacteristic
345C2×C3×D3#21711yescharacteristic
346C32×C4—21no—
347C32×C4—21no—
348C32×C4—21no—
349C32×C4—21no—
350C32×C4—21no—
351C32×C4—21no—
352C32×C4—31no—
353C32×C4—31no—
354C32×C4—41no—
355C32×C4—41no—
356C32×C4—62no—
357C32×C4C2×D1211yescharacteristic
358C32×C4D3×D411yescharacteristic
359C32×C4D3×D411yescharacteristic
360C32×C4C2×#6711yescharacteristic
361C32×C4C2×#6711yescharacteristic
362C32×C4C2×#6711yescharacteristic
363C3⋊Dic3—22no—
364C3×Dic3—22no—
365C3×Dic3—22no—
366C3×Dic3—21no—
367C3×Dic3—21no—
368C3×Dic3—42no—
369C3×Dic3—62no—
370C3×Dic3—62no—
371C3×Dic3—122no—
372C3×Dic3(C2×D3)⋊C411yescharacteristic
373C3×Dic3(C2×D3)⋊C411yescharacteristic
374C3×Dic3#21711yescharacteristic
375C3×Dic3#21711yescharacteristic
376C22×Q8—91no—
377C2×M16—91no—
378C2×M16—271no—
379#101—91no—
380#101—271no—
381#101—271no—
382#101—271no—
383C33C2×#10111yescharacteristic, complemented, Sylow
384C23×C3—31no—
385C23×C3—31no—
386C23×C3—61no—
387C22×D3D3×Dic311yescharacteristic
388C3×Q8—61no—
389C3×Q8—61no—
390C3×Q8—61no—
391C3×Q8—61no—
392C3×Q8—121no—
393C3×Q8—121no—
394C3×Q8—182no—
395C3×Q8—182no—
396C3×Q8—181no—
397C3×Q8—181no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—31no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—41no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—92no—
421C2×C3×C4—182no—
422C2×C3×C4—182no—
423C2×C3×C4C2×D3211yescharacteristic
424C2×C3×C4C2×D3211yescharacteristic
425C2×C3×C4C2×D3211yescharacteristic
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3D3×Dic312yes—
432C2×Dic3D3×Dic311yescharacteristic
433C4×D3—62no—
434C4×D3—62no—
435C4×D3#62511yescharacteristic
436C4×D3#62511yescharacteristic
437C4×D3#62611yescharacteristic
438C4×D3#62611yescharacteristic
439Dic6—21no—
440Dic6—21no—
441Dic6—62no—
442Dic6—62no—
443Dic6—61no—
444Dic6—61no—
445Dic6—61no—
446Dic6—61no—
447Dic6—62no—
448Dic6—62no—
449Dic6—121no—
450Dic6—121no—
451C3×C8—61no—
452C3×C8—61no—
453C3×C8—121no—
454C3×C8—181no—
455C3×C8—181no—
456C3⋊C8—21no—
457C3⋊C8—62no—
458C3⋊C8—61no—
459C3⋊C8—61no—
460C3⋊C8—61no—
461C3⋊C8—61no—
462C3⋊C8—121no—
463C3⋊C8—182no—
464C3⋊C8—181no—
465C3⋊C8—181no—
466C3⋊C8—181no—
467C3⋊C8—361no—
468C3⋊C8—361no—
469C3⋊C8—362no—
470C2×C32—21no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—32no—
477C2×C32—41no—
478C2×C32—41no—
479C2×C32—41no—
480C2×C32—41no—
481C2×C32—61no—
482C2×C32—81no—
483C2×C32D3×C22⋊C411yescharacteristic
484C2×C32C2×(C2×D3)⋊C411yescharacteristic
485C2×C32C2×#21711yescharacteristic
486C3×D3—21no—
487C3×D3—21no—
488C3×D3—22no—
489C3×D3—41no—
490C3×D3#82412yescomplemented
491C3×D3#83612yescomplemented
492C2×Q8—31no—
493C2×Q8—92no—
494C2×Q8—91no—
495C2×Q8—181no—
496C2×Q8—181no—
497C2×Q8—181no—
498C2×Q8—181no—
499C22×C4—31no—
500C22×C4—92no—
501M16—31no—
502M16—91no—
503M16—91no—
504M16—181no—
505M16—271no—
506M16—541no—
507C2×C8—181no—
508C2×C8—541no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—31no—
513C22×C3—31no—
514C22×C3—31no—
515C22×C3—31no—
516C22×C3—41no—
517C22×C3—61no—
518C22×C3—61no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3—122no—
522C22×C3C4×D3211yescharacteristic
523C22×C3C2×D3×Dic311yescharacteristic
524C22×C3C2×D3×Dic311yescharacteristic
525C2×D3—22no—
526C2×D3(C2×D3)⋊Dic311yescharacteristic
527C2×D3(C2×D3)⋊Dic311yescharacteristic
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—31no—
535C3×C4—31no—
536C3×C4—31no—
537C3×C4—31no—
538C3×C4—41no—
539C3×C4—41no—
540C3×C4—61no—
541C3×C4—61no—
542C3×C4—62no—
543C3×C4—62no—
544C3×C4—122no—
545C3×C4—182no—
546C3×C4D3×D1211yescharacteristic
547C3×C4C2×#62511yescharacteristic
548C3×C4C2×#62611yescharacteristic
549C3×C4D3×#6711yescharacteristic
550C3×C4D3×#6711yescharacteristic
551C3×C4D3×#6711yescharacteristic
552Dic3—22no—
553Dic3—62no—
554Dic3—62no—
555Dic3—122no—
556Dic3(C2×D3)⋊Dic311yescharacteristic
557Dic3(C2×D3)⋊Dic311yescharacteristic
558C32—21no—
559C32—21no—
560C32—21no—
561C32—41no—
562C32D3×#10111yescharacteristic, complemented
563C32C2×#82411yescharacteristic, complemented
564C32C2×#83611yescharacteristic, complemented
565C23—31no—
566Q8—61no—
567Q8—61no—
568Q8—182no—
569Q8—182no—
570Q8—181no—
571Q8—181no—
572C2×C4—31no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—32no—
578C2×C4—92no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4D3311yescharacteristic
582C8—61no—
583C8—181no—
584C8—181no—
585C8—541no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—32no—
593C2×C3—32no—
594C2×C3—41no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—41no—
598C2×C3—62no—
599C2×C3—61no—
600C2×C3—61no—
601C2×C3—81no—
602C2×C3—121no—
603C2×C3D3×(C2×D3)⋊C411yescharacteristic
604C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
605C2×C3D3×#21711yescharacteristic
606D3—21no—
607D3#6356012yesdirect product factor
608C22—31no—
609C22—31no—
610C22—62no—
611C22D32×Dic311yescharacteristic
612C4—31no—
613C4—31no—
614C4—62no—
615C4—182no—
616C4D3×#62511yescharacteristic
617C4D3×#62611yescharacteristic
618C3—21no—
619C3—21no—
620C3—21no—
621C3—41no—
622C3D3×#82411yescharacteristic, complemented
623C3C2×#6356011yescharacteristic, complemented
624C3D3×#83611yescharacteristic, complemented
625C2—21no—
626C2—32no—
627C2—61no—
628C2D3×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC2D3×(C2×D3)⋊Dic3
commutatorC22×C33C22×C4
Frattini, hypercenterC2×C4D33
Fitting, cosocleC2×C33×C4C23
socleC2×C33C2×C22⋊C4
prime radicalC22×C32×D3C2×C4
hypocenterC33C2×#101
LCSG ▷ C22×C33 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #11722074C2semidirect
5. #11722029C2semidirect
6. #11722028C2semidirect
7. C3×#63560C2semidirect
51. #63560D3direct (N × H)
263. C32×D3#101semidirect
383. C33C2×#101semidirect
490. C3×D3#824semidirect
491. C3×D3#836semidirect
562. C32D3×#101semidirect
563. C32C2×#824semidirect
564. C32C2×#836semidirect
607. D3#63560direct (N × H)
622. C3D3×#824semidirect
623. C3C2×#63560semidirect
624. C3D3×#836semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Dic62
D3×#37482
C3×D3×#2082
#117220742
#117220292
#117220282
C3×#635602
D3×#8363
C2×#635603
D3×#8243