Finite Group Databasebeta

← D3×#63866 #13168155

Subgroups — D3×#63866 #13168155

Order 1728.

1490 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#634C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic
3#11723678C211yesmaximal, characteristic, complemented
4#11723455C211yesmaximal, characteristic, complemented
5#11723443C211yesmaximal, characteristic, complemented
6C3×C4×D3×Dic3C211yesmaximal, characteristic
7C3×#63866C211yesmaximal, characteristic, complemented
8#11723033C214yesmaximal, complemented
9D3×Dic3⋊Dic3C214yesmaximal
10D3×#944—31nomaximal
11C2×#63866—31nomaximal
12D3×#869—31nomaximal
13C2×#6308C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6293C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20D3×#634—24no—
21C2×C3×#627C2212yes—
22C2×C3×D3×Dic3C2212yes—
23C2×C3×D3×Dic3C2212yes—
24C3×D3×Dic6—24no—
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×C4×Dic3C2211yescharacteristic
27#88815C2214yes—
28#88807C2214yes—
29Dic3⋊(C3⋊Dic3)C2214yes—
30C3×Dic3⋊Dic3C2214yes—
31C3×Dic32C2212yes—
32C22×#634—31no—
33C2×C3×D3×Q8—31no—
34C22×C3×Dic6—31no—
35C2×D3×Dic6—31no—
36C2×D3×Dic6—31no—
37C2×D3×Dic6—61no—
38C2×D3×Dic6D311yescharacteristic
39#64153—31no—
40#64078—31no—
41C3×#944—31no—
42C2×C3×C4×Dic3—31no—
43C3×C42×D3—31no—
44C3×#869—31no—
45C2×Dic3⋊Dic3—34no—
46#63918—34no—
47D3×C4⋊Dic3—34no—
48D3×Dic3⋊C4—34no—
49C4×D3×Dic3D311yescharacteristic
50#63873—31no—
51#63866—31no—
52#63866—31no—
53#63866—31no—
54#63866—31no—
55#63866—31no—
56#63866—31no—
57#63866—34no—
58#63866—61no—
59#63866—61no—
60#63866D311yescharacteristic, direct product factor
61#63839—34no—
62C22×C32×D3C2311yescharacteristic
63C2×C33×C4C2311yescharacteristic
64C2×C3⋊(C3⋊Dic3)C2312yes—
65#6308—22no—
66C2×C3×C3⋊Dic3C2312yes—
67C2×C3×C3⋊Dic3C2312yes—
68C2×C3×C3⋊Dic3C2312yes—
69C3×#634—22no—
70C3×#634—22no—
71C2×C32×Dic3C2312yes—
72C2×C32×Dic3C2311yescharacteristic
73C2×C32×Dic3C2312yes—
74C32×C4×D3D414yes—
75C32×Dic6—22no—
76#6293—24no—
77D3×C3⋊Dic3—24no—
78C3×#627—24no—
79C3×D3×Dic3—24no—
80C3×D3×Dic3Q818yescomplemented
81C2×#944—91no—
82D3×C4⋊Q8—91no—
83C2×#869—91no—
84C2×C32×Q8—31no—
85C22×C32×C4—31no—
86C22×C3⋊Dic3—32no—
87C2×#634—31no—
88C2×#634—31no—
89C2×#634—31no—
90C2×#634—32no—
91C2×#634—64no—
92C2×#634—61no—
93C2×#634—61no—
94C2×#634—61no—
95C2×#634—121no—
96C2×#634C2×D311yescharacteristic
97C2×#634C2×D311yescharacteristic
98C22×C3×Dic3—32no—
99C22×C3×Dic3—32no—
100C3×D3×Q8—64no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—32no—
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3C2×D311yescharacteristic
105C2×C3×C4×D3C2×D311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—32no—
112C2×C3×Dic6—32no—
113C2×C3×Dic6—64no—
114C2×C3×Dic6—61no—
115C2×C3×Dic6—61no—
116C2×C3×Dic6C2×D311yescharacteristic
117C2×C3×Dic6C2×D311yescharacteristic
118C2×#627—32no—
119C2×#627—32no—
120C2×#627—62no—
121C2×#627C2×D312yes—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—62no—
125C2×D3×Dic3C2×D312yes—
126C2×D3×Dic3C2×D312yes—
127D3×Dic6—24no—
128D3×Dic6—68no—
129D3×Dic6—64no—
130D3×Dic6—64no—
131C32×C42—31no—
132C4⋊(C3⋊Dic3)—34no—
133#3750—34no—
134C4×C3⋊Dic3C2×D311yescharacteristic
135C3×C4⋊Dic3—34no—
136C3×Dic3⋊C4—34no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3—32no—
141C3×C4×Dic3—32no—
142C3×C4×Dic3—61no—
143C3×C4×Dic3C2×D311yescharacteristic
144C3×C4×Dic3C2×D311yescharacteristic
145#3724—34no—
146Dic3⋊Dic3—34no—
147Dic3⋊Dic3—34no—
148Dic3⋊Dic3—34no—
149Dic3⋊Dic3—34no—
150Dic3⋊Dic3—34no—
151Dic3⋊Dic3—34no—
152Dic3⋊Dic3—64no—
153Dic3⋊Dic3—64no—
154Dic3⋊Dic3C2×D314yes—
155Dic32C2×D312yes—
156C22×C33C2411yescharacteristic
157C2×C32×D3C2×D412yes—
158C2×C32×D3C2×Q814yes—
159C33×C4C2×D412yes—
160C3⋊(C3⋊Dic3)—22no—
161C3×C3⋊Dic3—22no—
162C3×C3⋊Dic3—22no—
163C3×C3⋊Dic3C2×Q814yescomplemented
164C32×Dic3—22no—
165C32×Dic3C2×D412yes—
166C32×Dic3C2×Q814yescomplemented
167C22×C3×Q8—91no—
168C2×D3×Q8—31no—
169C2×D3×Q8—91no—
170C22×Dic6—31no—
171C22×Dic6—91no—
172C22×Dic6—91no—
173C22×Dic6—181no—
174C3×C4⋊Q8—91no—
175C2×C3×C42—91no—
176#944—31no—
177#944—94no—
178#944—91no—
179#944—91no—
180#944—91no—
181#944—91no—
182#944—91no—
183#944—181no—
184C2×C4⋊Dic3—94no—
185C2×Dic3⋊C4—94no—
186C2×C4×Dic3—31no—
187D3×C4⋊C4—94no—
188#888—94no—
189C42×D3—31no—
190#869—31no—
191#869—94no—
192#869—91no—
193#869—91no—
194#869—91no—
195#869—91no—
196#869—181no—
197C23×C32—31no—
198C22×C3×D3—21no—
199C22×C3×D3C22×D311yescharacteristic
200C22×C3×D3C22×D311yescharacteristic
201C32×Q8—62no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—31no—
206C2×C32×C4—32no—
207C2×C32×C4—34no—
208C2×C32×C4—32no—
209C2×C32×C4—41no—
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C22×D311yescharacteristic
212C2×C32×C4C22×D311yescharacteristic
213C2×C3⋊Dic3—32no—
214C2×C3⋊Dic3—32no—
215C2×C3⋊Dic3—32no—
216C2×C3⋊Dic3—62no—
217C2×C3⋊Dic3—62no—
218C2×C3⋊Dic3—62no—
219C2×C3⋊Dic3—64no—
220C2×C3⋊Dic3—122no—
221C2×C3⋊Dic3C22×D312yes—
222C2×C3⋊Dic3C22×D312yes—
223C2×C3⋊Dic3C22×D312yes—
224#634—22no—
225#634—22no—
226#634—64no—
227#634—62no—
228#634—64no—
229#634—62no—
230#634—62no—
231#634—122no—
232#634—122no—
233#634—124no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—32no—
238C2×C3×Dic3—32no—
239C2×C3×Dic3—38no—
240C2×C3×Dic3—32no—
241C2×C3×Dic3—32no—
242C2×C3×Dic3—32no—
243C2×C3×Dic3—32no—
244C2×C3×Dic3—62no—
245C2×C3×Dic3—62no—
246C2×C3×Dic3—62no—
247C2×C3×Dic3—64no—
248C2×C3×Dic3C22×D312yes—
249C2×C3×Dic3C22×D312yes—
250C2×C3×Dic3C22×D312yes—
251C2×C3×Dic3C22×D311yescharacteristic
252C2×C3×Dic3C22×D312yes—
253C2×C3×Dic3C22×D311yescharacteristic
254C3×C4×D3—24no—
255C3×C4×D3—38no—
256C3×C4×D3—64no—
257C3×C4×D3D1214yes—
258C3×C4×D3#6714yes—
259C3×Dic6—22no—
260C3×Dic6—22no—
261C3×Dic6—42no—
262C3×Dic6—64no—
263C3×Dic6—64no—
264C3×Dic6—62no—
265C3×Dic6—62no—
266C3×Dic6—62no—
267C3×Dic6—62no—
268C3×Dic6—64no—
269C3×Dic6—122no—
270#627—24no—
271#627—68no—
272#627—64no—
273#627—64no—
274D3×Dic3—24no—
275D3×Dic3—68no—
276D3×Dic3—64no—
277D3×Dic3—64no—
278D3×Dic3Dic618yescomplemented
279C2×C4⋊Q8—271noSylow
280C2×C33C22×D411yescharacteristic
281C2×C33C22×Q812yes—
282C32×D3C4⋊Q814yescomplemented
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8—92no—
287C2×C3×Q8—91no—
288C2×C3×Q8—91no—
289C2×C3×Q8—184no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—61no—
293C22×C3×C4—92no—
294C22×C3×C4—92no—
295C22×Dic3—32no—
296C22×Dic3—32no—
297C22×Dic3—92no—
298C22×Dic3—92no—
299C22×Dic3—182no—
300D3×Q8—64no—
301D3×Q8—184no—
302C2×C4×D3—32no—
303C2×C4×D3—32no—
304C2×C4×D3—92no—
305C2×C4×D3D3211yescharacteristic
306C2×Dic6—31no—
307C2×Dic6—31no—
308C2×Dic6—31no—
309C2×Dic6—31no—
310C2×Dic6—32no—
311C2×Dic6—32no—
312C2×Dic6—61no—
313C2×Dic6—61no—
314C2×Dic6—64no—
315C2×Dic6—92no—
316C2×Dic6—92no—
317C2×Dic6—91no—
318C2×Dic6—91no—
319C2×Dic6—91no—
320C2×Dic6—92no—
321C2×Dic6—182no—
322C2×Dic6—181no—
323C2×Dic6—181no—
324C2×Dic6—181no—
325C2×Dic6—184no—
326C2×Dic6—184no—
327C2×Dic6—188no—
328C2×Dic6—361no—
329C2×Dic6D3211yescharacteristic
330C3×C4⋊C4—94no—
331C3×C42—31no—
332C3×C42—31no—
333C3×C42—61no—
334C3×C42—92no—
335C3×C42—91no—
336C4⋊Dic3—34no—
337C4⋊Dic3—94no—
338C4⋊Dic3—94no—
339C4⋊Dic3—94no—
340C4⋊Dic3—94no—
341C4⋊Dic3—184no—
342Dic3⋊C4—34no—
343Dic3⋊C4—94no—
344Dic3⋊C4—94no—
345Dic3⋊C4—94no—
346Dic3⋊C4—94no—
347Dic3⋊C4—94no—
348Dic3⋊C4—184no—
349C4×Dic3—31no—
350C4×Dic3—31no—
351C4×Dic3—32no—
352C4×Dic3—32no—
353C4×Dic3—61no—
354C4×Dic3D3211yescharacteristic
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—32no—
359C22×C32—34no—
360C22×C32—41no—
361C22×C32C23×D311yescharacteristic
362C22×C32C23×D311yescharacteristic
363C22×C32C23×D311yescharacteristic
364C2×C3×D3—24no—
365C2×C3×D3—22no—
366C2×C3×D3C2×Dic614yes—
367C2×C3×D3C2×D1212yes—
368C2×C3×D3D3×Q814yes—
369C2×C3×D3C2×#6712yes—
370C32×C4—22no—
371C32×C4—22no—
372C32×C4—22no—
373C32×C4—32no—
374C32×C4—34no—
375C32×C4—42no—
376C32×C4—62no—
377C32×C4C2×D1212yes—
378C32×C4D3×D412yes—
379C32×C4C2×#6712yes—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—62no—
383C3⋊Dic3—64no—
384C3⋊Dic3—62no—
385C3⋊Dic3—62no—
386C3⋊Dic3—122no—
387C3⋊Dic3—122no—
388C3⋊Dic3—124no—
389C3⋊Dic3C2×Dic614yescomplemented
390C3×Dic3—22no—
391C3×Dic3—22no—
392C3×Dic3—24no—
393C3×Dic3—22no—
394C3×Dic3—34no—
395C3×Dic3—34no—
396C3×Dic3—42no—
397C3×Dic3—64no—
398C3×Dic3—64no—
399C3×Dic3—62no—
400C3×Dic3—62no—
401C3×Dic3—62no—
402C3×Dic3—62no—
403C3×Dic3—122no—
404C3×Dic3C2×Dic614yescomplemented
405C3×Dic3C2×D1212yes—
406C3×Dic3D3×Q814yescomplemented
407C3×Dic3C2×#6712yes—
408C22×Q8—91no—
409C22×Q8—271no—
410C4⋊Q8—91no—
411C4⋊Q8—271no—
412C4⋊Q8—274no—
413C4⋊Q8—271no—
414C4⋊Q8—271no—
415C2×C4⋊C4—274no—
416C2×C42—91no—
417C33C2×C4⋊Q811yescharacteristic, complemented, Sylow
418C23×C3—31no—
419C23×C3—31no—
420C23×C3—61no—
421C22×D3C2×D3211yescharacteristic
422C3×Q8—62no—
423C3×Q8—62no—
424C3×Q8—122no—
425C3×Q8—184no—
426C3×Q8—182no—
427C3×Q8—182no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—31no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—31no—
435C2×C3×C4—34no—
436C2×C3×C4—34no—
437C2×C3×C4—32no—
438C2×C3×C4—32no—
439C2×C3×C4—41no—
440C2×C3×C4—64no—
441C2×C3×C4—62no—
442C2×C3×C4—61no—
443C2×C3×C4—62no—
444C2×C3×C4—98no—
445C2×C3×C4—92no—
446C2×C3×C4—92no—
447C2×C3×C4—92no—
448C2×C3×C4—184no—
449C2×C3×C4C2×D3211yescharacteristic
450C2×C3×C4C2×D3211yescharacteristic
451C2×C3×C4C2×D3211yescharacteristic
452C2×Dic3—32no—
453C2×Dic3—32no—
454C2×Dic3—38no—
455C2×Dic3—32no—
456C2×Dic3—32no—
457C2×Dic3—32no—
458C2×Dic3—32no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—62no—
462C2×Dic3—64no—
463C2×Dic3—92no—
464C2×Dic3—92no—
465C2×Dic3—92no—
466C2×Dic3—182no—
467C2×Dic3—182no—
468C2×Dic3—182no—
469C2×Dic3—184no—
470C2×Dic3—184no—
471C2×Dic3—188no—
472C2×Dic3—362no—
473C2×Dic3C2×D3212yes—
474C2×Dic3C2×D3212yes—
475C2×Dic3C2×D3211yescharacteristic
476C4×D3—38no—
477C4×D3—64no—
478C4×D3—184no—
479C4×D3#62614yes—
480Dic6—22no—
481Dic6—64no—
482Dic6—64no—
483Dic6—62no—
484Dic6—62no—
485Dic6—62no—
486Dic6—62no—
487Dic6—64no—
488Dic6—122no—
489Dic6—184no—
490Dic6—184no—
491Dic6—188no—
492Dic6—184no—
493Dic6—182no—
494Dic6—182no—
495Dic6—182no—
496Dic6—184no—
497Dic6—362no—
498Dic6—362no—
499Dic6—364no—
500C2×C32—22no—
501C2×C32—22no—
502C2×C32—21no—
503C2×C32—22no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—34no—
507C2×C32—41no—
508C2×C32—42no—
509C2×C32C22×Dic612yes—
510C2×C32C22×D1211yescharacteristic
511C2×C32C2×D3×D411yescharacteristic
512C2×C32C2×D3×Q812yes—
513C2×C32C2×D3×Q812yes—
514C2×C32C22×#6711yescharacteristic
515C3×D3—24no—
516C3×D3#86914yescomplemented
517C3×D3#94414yescomplemented
518C2×Q8—31no—
519C2×Q8—92no—
520C2×Q8—91no—
521C2×Q8—91no—
522C2×Q8—184no—
523C2×Q8—272no—
524C2×Q8—271no—
525C2×Q8—544no—
526C22×C4—31no—
527C22×C4—92no—
528C22×C4—92no—
529C22×C4—272no—
530C4⋊C4—94no—
531C4⋊C4—274no—
532C4⋊C4—274no—
533C4⋊C4—274no—
534C42—31no—
535C42—92no—
536C42—91no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—34no—
541C22×C3—32no—
542C22×C3—34no—
543C22×C3—32no—
544C22×C3—41no—
545C22×C3—62no—
546C22×C3—64no—
547C22×C3C22×D3211yescharacteristic
548C22×C3C22×D3211yescharacteristic
549C22×C3C22×D3211yescharacteristic
550C2×D3D3×Dic614yes—
551C2×D3C2×#62612yes—
552C3×C4—22no—
553C3×C4—22no—
554C3×C4—22no—
555C3×C4—34no—
556C3×C4—32no—
557C3×C4—34no—
558C3×C4—32no—
559C3×C4—42no—
560C3×C4—62no—
561C3×C4—64no—
562C3×C4—62no—
563C3×C4—62no—
564C3×C4—94no—
565C3×C4—122no—
566C3×C4—182no—
567C3×C4—182no—
568C3×C4D3×D1212yes—
569C3×C4C2×#62612yes—
570C3×C4D3×#6712yes—
571Dic3—22no—
572Dic3—34no—
573Dic3—34no—
574Dic3—64no—
575Dic3—64no—
576Dic3—62no—
577Dic3—62no—
578Dic3—62no—
579Dic3—62no—
580Dic3—122no—
581Dic3—184no—
582Dic3—182no—
583Dic3—182no—
584Dic3—182no—
585Dic3—362no—
586Dic3—362no—
587Dic3—364no—
588Dic3D3×Dic614yescomplemented
589Dic3C2×#62612yes—
590C32—21no—
591C32—21no—
592C32—21no—
593C32—41no—
594C32C2×#86911yescharacteristic, complemented
595C32D3×C4⋊Q811yescharacteristic, complemented
596C32C2×#94411yescharacteristic, complemented
597C23—31no—
598Q8—62no—
599Q8—184no—
600Q8—182no—
601Q8—182no—
602Q8—544no—
603Q8—542no—
604C2×C4—32no—
605C2×C4—31no—
606C2×C4—34no—
607C2×C4—32no—
608C2×C4—98no—
609C2×C4—92no—
610C2×C4—92no—
611C2×C4—92no—
612C2×C4—184no—
613C2×C4—272no—
614C2×C4—544no—
615C2×C4D3311yescharacteristic
616C2×C3—22no—
617C2×C3—22no—
618C2×C3—22no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—34no—
623C2×C3—34no—
624C2×C3—42no—
625C2×C3—41no—
626C2×C3—64no—
627C2×C3C2×D3×Dic612yes—
628C2×C3C2×D3×Dic612yes—
629C2×C3C2×D3×D1211yescharacteristic
630C2×C3D32×Q812yes—
631C2×C3C22×#62611yescharacteristic
632C2×C3C2×D3×#6711yescharacteristic
633D3#6386614yesdirect product factor
634C22—34no—
635C22—32no—
636C22C2×D3311yescharacteristic
637C4—34no—
638C4—32no—
639C4—62no—
640C4—94no—
641C4—182no—
642C4—182no—
643C4—542no—
644C4D3×#62612yes—
645C3—21no—
646C3—21no—
647C3—21no—
648C3—41no—
649C3D3×#86911yescharacteristic, complemented
650C3C2×#6386611yescharacteristic, complemented
651C3D3×#94411yescharacteristic, complemented
652C2—34no—
653C2D32×Dic612yes—
654C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33C2×C4⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11723678C2semidirect
4. #11723455C2semidirect
5. #11723443C2semidirect
7. C3×#63866C2semidirect
8. #11723033C2semidirect
60. #63866D3direct (N × H)
80. C3×D3×Dic3Q8semidirect
163. C3×C3⋊Dic3C2×Q8semidirect
166. C32×Dic3C2×Q8semidirect
278. D3×Dic3Dic6semidirect
282. C32×D3C4⋊Q8semidirect
389. C3⋊Dic3C2×Dic6semidirect
404. C3×Dic3C2×Dic6semidirect
406. C3×Dic3D3×Q8semidirect
417. C33C2×C4⋊Q8semidirect
516. C3×D3#869semidirect
517. C3×D3#944semidirect
588. Dic3D3×Dic6semidirect
594. C32C2×#869semidirect
595. C32D3×C4⋊Q8semidirect
596. C32C2×#944semidirect
633. D3#63866direct (N × H)
649. C3D3×#869semidirect
650. C3C2×#63866semidirect
651. C3D3×#944semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6342
C2×C3×D3×Dic62
#117236782
#117234552
#117234432
C3×C4×D3×Dic32
C3×#638662
#117230332
D3×Dic3⋊Dic32
D3×#9443
C2×#638663
D3×#8693