Finite Group Databasebeta

← D3×#63870 #13168207

Subgroups — D3×#63870 #13168207

Order 1728.

1154 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723679C211yesmaximal, characteristic, complemented
2C4×D3×C3⋊Dic3C211yesmaximal, characteristic
3#11723448C212yesmaximal, complemented
4C3×D3×Dic3⋊C4C212yesmaximal
5C3×#63870C211yesmaximal, characteristic, complemented
6#11723018C211yesmaximal, characteristic, complemented
7#11723016C212yesmaximal, complemented
8#11723015C211yesmaximal, characteristic, complemented
9D3×#3724C211yesmaximal, characteristic
10D3×#3724C211yesmaximal, characteristic
11D3×Dic3⋊Dic3C212yesmaximal
12C2×#63870—31nomaximal
13D3×#889—32nomaximal
14C2×C32×C4×D3C2211yescharacteristic
15C2×D3×C3⋊Dic3C2211yescharacteristic
16C2×D3×C3⋊Dic3C2211yescharacteristic
17C2×C3×D3×Dic3C2212yes—
18C2×C3×D3×Dic3C2212yes—
19C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C3×#3750C2212yes—
21C3×C4×C3⋊Dic3C2211yescharacteristic
22C32×Dic3⋊C4C2212yes—
23#88815C2211yescharacteristic
24#88815C2212yes—
25#88815C2211yescharacteristic
26#88807C2212yes—
27#88806C2212yes—
28#88806C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30Dic3×C3⋊Dic3C2211yescharacteristic
31Dic3×C3⋊Dic3C2211yescharacteristic
32C3×#3724C2211yescharacteristic
33C3×#3724C2212yes—
34C3×#3724C2211yescharacteristic
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C2×C4×C3⋊Dic3—31no—
38#64098—32no—
39C2×C3×Dic3⋊C4—32no—
40C3×D3×C4⋊C4—32no—
41C3×#889—32no—
42C2×#3724—31no—
43C2×#3724—31no—
44C2×Dic3⋊Dic3—32no—
45D3×C4⋊Dic3—32no—
46D3×Dic3⋊C4—32no—
47D3×Dic3⋊C4—32no—
48D3×Dic3⋊C4—32no—
49D3×Dic3⋊C4D312yes—
50C4×D3×Dic3—32no—
51C4×D3×Dic3—61no—
52#63870—31no—
53#63870—32no—
54#63870—32no—
55#63870—31no—
56#63870—31no—
57#63870—32no—
58#63870—62no—
59#63870D311yescharacteristic, direct product factor
60#63867—32no—
61#63847—32no—
62#63847—32no—
63#63846—32no—
64#63845—32no—
65C22×C32×D3C2311yescharacteristic
66C2×C33×C4C2311yescharacteristic
67C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
68C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
69C2×C3×C3⋊Dic3C2311yescharacteristic
70C2×C3×C3⋊Dic3C2312yes—
71C2×C3×C3⋊Dic3C2312yes—
72C2×C3×C3⋊Dic3C2311yescharacteristic
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2311yescharacteristic
76C32×C4×D3—22no—
77D3×C3⋊Dic3—22no—
78D3×C3⋊Dic3Q814yes—
79C3×D3×Dic3—24no—
80C3×D3×Dic3—24no—
81D3×#125—91no—
82C2×#889—92no—
83C22×C32×C4—31no—
84C22×C3⋊Dic3—31no—
85C22×C3⋊Dic3—31no—
86C22×C3×Dic3—32no—
87C22×C3×Dic3—32no—
88C2×C3×C4×D3—21no—
89C2×C3×C4×D3—32no—
90C2×C3×C4×D3—32no—
91C2×C3×C4×D3C2×D312yes—
92C2×D3×Dic3—32no—
93C2×D3×Dic3—32no—
94C2×D3×Dic3—61no—
95C2×D3×Dic3—61no—
96C2×D3×Dic3C2×D312yes—
97C2×D3×Dic3C2×D312yes—
98C32×C4⋊C4—32no—
99C4⋊(C3⋊Dic3)—32no—
100#3750—32no—
101#3750—32no—
102#3750—32no—
103#3750C2×D312yes—
104C4×C3⋊Dic3—32no—
105C4×C3⋊Dic3—31no—
106C4×C3⋊Dic3—31no—
107C4×C3⋊Dic3—31no—
108C4×C3⋊Dic3—62no—
109C4×C3⋊Dic3—61no—
110C4×C3⋊Dic3—121no—
111C4×C3⋊Dic3C2×D311yescharacteristic
112C3×C4⋊Dic3—32no—
113C3×C4⋊Dic3—32no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—32no—
116C3×Dic3⋊C4—32no—
117C3×Dic3⋊C4—32no—
118C3×Dic3⋊C4—32no—
119C3×Dic3⋊C4—32no—
120C3×Dic3⋊C4—32no—
121C3×Dic3⋊C4—32no—
122C3×Dic3⋊C4—32no—
123C3×Dic3⋊C4—62no—
124C3×Dic3⋊C4C2×D312yes—
125C3×Dic3⋊C4C2×D312yes—
126C3×C4×Dic3—32no—
127C3×C4×Dic3—61no—
128#3724—32no—
129#3724—31no—
130#3724—31no—
131#3724—32no—
132#3724—32no—
133#3724—32no—
134#3724—32no—
135#3724—62no—
136#3724—62no—
137#3724C2×D312yes—
138#3724C2×D311yescharacteristic
139#3724C2×D311yescharacteristic
140Dic3⋊Dic3—32no—
141Dic3⋊Dic3—32no—
142Dic3⋊Dic3—32no—
143Dic3⋊Dic3—32no—
144Dic3⋊Dic3—32no—
145Dic3⋊Dic3—32no—
146Dic3⋊Dic3—32no—
147Dic3⋊Dic3—32no—
148Dic3⋊Dic3—62no—
149Dic3⋊Dic3—62no—
150Dic3⋊Dic3C2×D312yes—
151Dic3⋊Dic3C2×D312yes—
152Dic32—32no—
153Dic32—32no—
154Dic32—61no—
155Dic32—61no—
156C22×C33C2411yescharacteristic
157C2×C32×D3C2×Q812yes—
158C2×C32×D3#4112yes—
159C2×C32×D3#4112yes—
160C33×C4—21no—
161C3⋊(C3⋊Dic3)—21no—
162C3⋊(C3⋊Dic3)C2×Q812yes—
163C3×C3⋊Dic3—21no—
164C3×C3⋊Dic3—22no—
165C3×C3⋊Dic3—22no—
166C3×C3⋊Dic3C2×Q812yes—
167C32×Dic3—21no—
168C32×Dic3—22no—
169C32×Dic3—22no—
170C3×#125—91no—
171C2×C3×C4⋊C4—92no—
172C2×C4⋊Dic3—92no—
173C2×Dic3⋊C4—32no—
174C2×Dic3⋊C4—92no—
175C2×Dic3⋊C4—92no—
176C2×Dic3⋊C4—92no—
177C2×C4×Dic3—92no—
178C2×C4×Dic3—181no—
179D3×C4⋊C4—32no—
180D3×C4⋊C4—91no—
181D3×C4⋊C4—91no—
182D3×C4⋊C4—92no—
183#890—91no—
184#890—91no—
185#889—32no—
186#889—92no—
187#889—92no—
188#889—92no—
189#889—92no—
190#889—92no—
191#889—92no—
192#889—92no—
193#889—92no—
194#889—92no—
195#889—182no—
196C42×D3—91no—
197#870—91no—
198C23×C32—31no—
199C22×C3×D3—21no—
200C22×C3×D3C22×D312yes—
201C2×C32×C4—21no—
202C2×C32×C4—22no—
203C2×C32×C4—31no—
204C2×C32×C4—32no—
205C2×C32×C4—32no—
206C2×C32×C4—41no—
207C2×C32×C4—62no—
208C2×C32×C4C22×D312yes—
209C2×C32×C4C22×D311yescharacteristic
210C2×C3⋊Dic3—32no—
211C2×C3⋊Dic3—31no—
212C2×C3⋊Dic3—34no—
213C2×C3⋊Dic3—32no—
214C2×C3⋊Dic3—31no—
215C2×C3⋊Dic3—61no—
216C2×C3⋊Dic3—61no—
217C2×C3⋊Dic3—62no—
218C2×C3⋊Dic3—62no—
219C2×C3⋊Dic3—62no—
220C2×C3⋊Dic3—121no—
221C2×C3⋊Dic3—121no—
222C2×C3⋊Dic3C22×D311yescharacteristic
223C2×C3⋊Dic3C22×D312yes—
224C2×C3⋊Dic3C22×D312yes—
225C2×C3⋊Dic3C22×D311yescharacteristic
226C2×C3×Dic3—21no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—32no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—32no—
233C2×C3×Dic3—32no—
234C2×C3×Dic3—32no—
235C2×C3×Dic3—61no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—62no—
238C2×C3×Dic3—62no—
239C2×C3×Dic3—64no—
240C2×C3×Dic3—64no—
241C2×C3×Dic3C22×D312yes—
242C2×C3×Dic3C22×D312yes—
243C2×C3×Dic3C22×D312yes—
244C2×C3×Dic3C22×D312yes—
245C2×C3×Dic3C22×D312yes—
246C3×C4×D3—24no—
247C3×C4×D3—24no—
248C3×C4×D3—64no—
249C3×C4×D3—64no—
250D3×Dic3—24no—
251D3×Dic3—24no—
252D3×Dic3—38no—
253D3×Dic3—64no—
254D3×Dic3—64no—
255D3×Dic3—64no—
256C2×#125—271noSylow
257C2×C33C22×Q811yescharacteristic
258C2×C33C2×#4111yescharacteristic
259C2×C33C2×#4111yescharacteristic
260C32×D3#12514yescomplemented
261C22×C3×C4—32no—
262C22×C3×C4—61no—
263C22×C3×C4—92no—
264C22×C3×C4—92no—
265C22×Dic3—32no—
266C22×Dic3—32no—
267C22×Dic3—92no—
268C22×Dic3—92no—
269C22×Dic3—181no—
270C22×Dic3—181no—
271C2×C4×D3—32no—
272C2×C4×D3—32no—
273C2×C4×D3—91no—
274C2×C4×D3—91no—
275C2×C4×D3D3211yescharacteristic
276C3×C4⋊C4—32no—
277C3×C4⋊C4—32no—
278C3×C4⋊C4—62no—
279C3×C4⋊C4—92no—
280C3×C4⋊C4—92no—
281C3×C4⋊C4—92no—
282C3×C4⋊C4—91no—
283C3×C4⋊C4—91no—
284C3×C4⋊C4—92no—
285C3×C42—91no—
286C4⋊Dic3—32no—
287C4⋊Dic3—32no—
288C4⋊Dic3—91no—
289C4⋊Dic3—91no—
290C4⋊Dic3—92no—
291C4⋊Dic3—92no—
292C4⋊Dic3—92no—
293C4⋊Dic3—92no—
294C4⋊Dic3—182no—
295Dic3⋊C4—32no—
296Dic3⋊C4—32no—
297Dic3⋊C4—32no—
298Dic3⋊C4—32no—
299Dic3⋊C4—32no—
300Dic3⋊C4—32no—
301Dic3⋊C4—32no—
302Dic3⋊C4—32no—
303Dic3⋊C4—62no—
304Dic3⋊C4—92no—
305Dic3⋊C4—92no—
306Dic3⋊C4—92no—
307Dic3⋊C4—92no—
308Dic3⋊C4—92no—
309Dic3⋊C4—92no—
310Dic3⋊C4—92no—
311Dic3⋊C4—92no—
312Dic3⋊C4—92no—
313Dic3⋊C4—92no—
314Dic3⋊C4—92no—
315Dic3⋊C4—92no—
316Dic3⋊C4—92no—
317Dic3⋊C4—182no—
318Dic3⋊C4—182no—
319Dic3⋊C4—182no—
320Dic3⋊C4D3212yes—
321C4×Dic3—32no—
322C4×Dic3—61no—
323C4×Dic3—92no—
324C4×Dic3—92no—
325C4×Dic3—91no—
326C4×Dic3—92no—
327C4×Dic3—91no—
328C4×Dic3—91no—
329C4×Dic3—181no—
330C4×Dic3—181no—
331C4×Dic3—182no—
332C4×Dic3—181no—
333C4×Dic3—361no—
334C22×C32—22no—
335C22×C32—21no—
336C22×C32—32no—
337C22×C32—32no—
338C22×C32—32no—
339C22×C32—41no—
340C22×C32C23×D312yes—
341C22×C32C23×D311yescharacteristic
342C2×C3×D3—22no—
343C2×C3×D3—22no—
344C2×C3×D3—22no—
345C2×C3×D3#23514yes—
346C2×C3×D3#23714yes—
347C2×C3×D3D3×Q814yes—
348C32×C4—21no—
349C32×C4—22no—
350C32×C4—22no—
351C32×C4—42no—
352C32×C4—42no—
353C32×C4—61no—
354C32×C4—62no—
355C32×C4—62no—
356C3⋊Dic3—21no—
357C3⋊Dic3—22no—
358C3⋊Dic3—22no—
359C3⋊Dic3—34no—
360C3⋊Dic3—32no—
361C3⋊Dic3—62no—
362C3⋊Dic3—64no—
363C3⋊Dic3—61no—
364C3⋊Dic3—62no—
365C3⋊Dic3—62no—
366C3⋊Dic3—122no—
367C3⋊Dic3—122no—
368C3⋊Dic3—122no—
369C3⋊Dic3D3×Q812yes—
370C3×Dic3—22no—
371C3×Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3—22no—
375C3×Dic3—22no—
376C3×Dic3—34no—
377C3×Dic3—42no—
378C3×Dic3—42no—
379C3×Dic3—62no—
380C3×Dic3—62no—
381C3×Dic3—62no—
382C3×Dic3—62no—
383C3×Dic3—62no—
384C3×Dic3—62no—
385C3×Dic3—62no—
386C3×Dic3—122no—
387C3×Dic3—122no—
388#125—91no—
389#125—271no—
390#125—272no—
391#125—272no—
392#125—271no—
393#125—271no—
394C2×C4⋊C4—92no—
395C2×C4⋊C4—271no—
396C2×C4⋊C4—271no—
397C2×C4⋊C4—272no—
398C2×C42—271no—
399C33C2×#12511yescharacteristic, complemented, Sylow
400C23×C3—32no—
401C23×C3—61no—
402C22×D3C2×D3211yescharacteristic
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—32no—
409C2×C3×C4—32no—
410C2×C3×C4—41no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—64no—
415C2×C3×C4—64no—
416C2×C3×C4—91no—
417C2×C3×C4—91no—
418C2×C3×C4—92no—
419C2×C3×C4—92no—
420C2×C3×C4—184no—
421C2×C3×C4—184no—
422C2×C3×C4C2×D3212yes—
423C2×C3×C4C2×D3211yescharacteristic
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—32no—
429C2×Dic3—32no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—64no—
435C2×Dic3—64no—
436C2×Dic3—98no—
437C2×Dic3—91no—
438C2×Dic3—92no—
439C2×Dic3—91no—
440C2×Dic3—92no—
441C2×Dic3—184no—
442C2×Dic3—181no—
443C2×Dic3—181no—
444C2×Dic3—182no—
445C2×Dic3—182no—
446C2×Dic3—184no—
447C2×Dic3—184no—
448C2×Dic3—361no—
449C2×Dic3—361no—
450C2×Dic3C2×D3211yescharacteristic
451C2×Dic3C2×D3212yes—
452C2×Dic3C2×D3212yes—
453C4×D3—22no—
454C4×D3—64no—
455C4×D3—64no—
456C4×D3—94no—
457C4×D3—182no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—22no—
461C2×C32—22no—
462C2×C32—22no—
463C2×C32—21no—
464C2×C32—34no—
465C2×C32—41no—
466C2×C32—41no—
467C2×C32—41no—
468C2×C32C2×#23512yes—
469C2×C32C2×#23712yes—
470C2×C32C2×D3×Q812yes—
471C2×C32C2×D3×Q811yescharacteristic
472C2×C32D3×#4111yescharacteristic
473C2×C32D3×#4111yescharacteristic
474C3×D3—24no—
475C3×D3#88918yescomplemented
476C22×C4—31no—
477C22×C4—92no—
478C22×C4—92no—
479C22×C4—271no—
480C22×C4—271no—
481C4⋊C4—32no—
482C4⋊C4—92no—
483C4⋊C4—92no—
484C4⋊C4—91no—
485C4⋊C4—91no—
486C4⋊C4—92no—
487C4⋊C4—92no—
488C4⋊C4—272no—
489C4⋊C4—272no—
490C4⋊C4—272no—
491C4⋊C4—272no—
492C4⋊C4—271no—
493C4⋊C4—271no—
494C4⋊C4—272no—
495C42—91no—
496C42—271no—
497C42—271no—
498C42—271no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—34no—
502C22×C3—34no—
503C22×C3—34no—
504C22×C3—41no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—62no—
508C22×C3C22×D3211yescharacteristic
509C22×C3C22×D3212yes—
510C2×D3#379712yes—
511C2×D3#379812yes—
512C2×D3#380512yes—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—21no—
516C3×C4—42no—
517C3×C4—42no—
518C3×C4—62no—
519C3×C4—62no—
520C3×C4—62no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—62no—
524C3×C4—92no—
525C3×C4—122no—
526C3×C4—122no—
527C3×C4—181no—
528C3×C4—182no—
529C3×C4—182no—
530Dic3—22no—
531Dic3—22no—
532Dic3—21no—
533Dic3—34no—
534Dic3—62no—
535Dic3—62no—
536Dic3—62no—
537Dic3—62no—
538Dic3—62no—
539Dic3—62no—
540Dic3—62no—
541Dic3—92no—
542Dic3—94no—
543Dic3—122no—
544Dic3—122no—
545Dic3—182no—
546Dic3—184no—
547Dic3—182no—
548Dic3—181no—
549Dic3—182no—
550Dic3—362no—
551Dic3—362no—
552Dic3—362no—
553C32—21no—
554C32—22no—
555C32—41no—
556C32C2×#88912yescomplemented
557C32D3×#12511yescharacteristic, complemented
558C23—31no—
559C2×C4—31no—
560C2×C4—32no—
561C2×C4—32no—
562C2×C4—62no—
563C2×C4—91no—
564C2×C4—91no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—184no—
568C2×C4—184no—
569C2×C4—274no—
570C2×C4—271no—
571C2×C4—271no—
572C2×C4—542no—
573C2×C4D3311yescharacteristic
574C2×C3—21no—
575C2×C3—22no—
576C2×C3—21no—
577C2×C3—22no—
578C2×C3—22no—
579C2×C3—21no—
580C2×C3—38no—
581C2×C3—41no—
582C2×C3—41no—
583C2×C3—41no—
584C2×C3—64no—
585C2×C3C2×#379711yescharacteristic
586C2×C3C2×#379811yescharacteristic
587C2×C3D3×#23512yes—
588C2×C3D3×#23712yes—
589C2×C3D32×Q812yes—
590C2×C3C2×#380511yescharacteristic
591D3#6387014yesdirect product factor
592C22—32no—
593C22—32no—
594C22—32no—
595C22C2×D3311yescharacteristic
596C4—21no—
597C4—62no—
598C4—61no—
599C4—62no—
600C4—92no—
601C4—182no—
602C4—181no—
603C4—182no—
604C4—272no—
605C4—541no—
606C3—21no—
607C3—22no—
608C3—41no—
609C3D3×#88912yescomplemented
610C3C2×#6387011yescharacteristic, complemented
611C2—34no—
612C2D3×#379711yescharacteristic
613C2D3×#379811yescharacteristic
614C2D3×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33C2×#125
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723679C2semidirect
3. #11723448C2semidirect
5. C3×#63870C2semidirect
6. #11723018C2semidirect
7. #11723016C2semidirect
8. #11723015C2semidirect
59. #63870D3direct (N × H)
260. C32×D3#125semidirect
399. C33C2×#125semidirect
475. C3×D3#889semidirect
556. C32C2×#889semidirect
557. C32D3×#125semidirect
591. D3#63870direct (N × H)
609. C3D3×#889semidirect
610. C3C2×#63870semidirect

Maximal subgroups

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

subgroupindex
#117236792
C4×D3×C3⋊Dic32
#117234482
C3×D3×Dic3⋊C42
C3×#638702
#117230182
#117230162
#117230152
D3×#37242
D3×Dic3⋊Dic32
C2×#638703
D3×#8893