Finite Group Databasebeta

← Dic3×#942 #11860410

Subgroups — Dic3×#942 #11860410

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3Dic3×#235C211yesmaximal, characteristic
4#10592924C211yesmaximal, characteristic, complemented
5#10591576C212yesmaximal, complemented
6Dic3×#216C212yesmaximal, complemented
7#10591566C212yesmaximal, complemented
8Dic3×#215C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10#10591087C211yesmaximal, characteristic
11Dic3×#208C211yesmaximal, characteristic, complemented
12Dic3×#137—31nomaximal
13C4×#942—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×Q8×Dic3—21no—
19C3×Q8×Dic3—21no—
20C3×Q8×Dic3C2212yes—
21C3×Q8×Dic3C2212yes—
22C2×C3×#216C2212yes—
23C3×#942C418yescomplemented
24C2×C3×#215C2212yes—
25C2×C3×C4⋊Dic3—21no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4×Dic3—21no—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30Dic3×#67—21no—
31Dic3×#67—21no—
32Dic3×D12C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34C4×D3×Dic3—21no—
35#63855—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63662C2212yes—
39#63662C2212yes—
40#63575C2212yes—
41#63573C2212yes—
42#63565C2212yes—
43#63562C2212yes—
44#63554C2212yes—
45Dic3×C3⋊C8C2212yes—
46C2×C3×#137—31no—
47C2×C3×C4×Q8—31no—
48Dic3×#41—31no—
49C2×Q8×Dic3D311yescharacteristic, complemented
50C2×#942D311yescharacteristic
51C4×#235—31no—
52#5232—31no—
53#5225—31no—
54#5225—31no—
55#5225—61no—
56#5184—32no—
57Dic3×Q16—32no—
58#5164—32no—
59Dic3×SD16—32no—
60#5121—31no—
61Dic3×M16—31no—
62#5030—32no—
63C4×#216—32no—
64#5026—32no—
65C4×#215—32no—
66#4966—31no—
67#4964—31no—
68C4×#208—31no—
69C2×C32×Q8—21no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2×C414yescomplemented
72C2×C32×Q8C2312yes—
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C3×#235—22no—
80C3×#235C2×C414yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×Dic6C2311yescharacteristic
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86#3757—21no—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C4×C3⋊Dic3—21no—
90#3748—22no—
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×#216C2×C418yescomplemented
93C3×#215C2×C418yescomplemented
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—22no—
99C3×C4×Dic3—22no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×#208C2×C414yescomplemented
105C2×C3×C3⋊C8C2312yes—
106Dic3⋊Dic3—21no—
107Dic3⋊Dic3—21no—
108(C2×D3)⋊Dic3—21no—
109(C2×D3)⋊Dic3—21no—
110Dic32—21no—
111Dic32—21no—
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C22×C3×Q8—21no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C2×D311yescharacteristic
117C2×#235C2×D311yescharacteristic
118C3×#137—38no—
119C2×C3×Q16—32no—
120C2×C3×SD16—32no—
121C2×C3×M16—31no—
122C3×C4×Q8—32no—
123C3×C4×Q8—32no—
124C3×C4×Q8—61no—
125C3×C4×Q8—61no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—61no—
128C2×C3×C42—31no—
129C2×C3×C42—61no—
130Q8×Dic3—21no—
131Q8×Dic3—21no—
132Q8×Dic3—31no—
133Q8×Dic3—31no—
134Q8×Dic3C2×D312yes—
135Q8×Dic3C2×D312yes—
136C2×#216C2×D312yes—
137#942Dic318yesdirect product factor
138C2×#215C2×D312yes—
139D4×Dic3—31no—
140D4×Dic3—31no—
141D4×Dic3—61no—
142D4×Dic3—61no—
143C4×#67—61no—
144C4×#67—61no—
145#926—31no—
146#926—31no—
147#926—61no—
148#926—61no—
149C2×C4⋊Dic3—21no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×C4×Dic3—21no—
152C2×C4×Dic3—61no—
153C2×C4×Dic3C2×D311yescharacteristic
154C2×#208—31no—
155C2×#208—31no—
156C2×#208—61no—
157C2×#208C2×D311yescharacteristic
158C4×D12—31no—
159C4×D12—31no—
160#872—61no—
161C42×D3—61no—
162C4×Dic6—31no—
163C4×Dic6—31no—
164#835—32no—
165#835—32no—
166#835—32no—
167#835—32no—
168#835—32no—
169#835—62no—
170#835—62no—
171#832—32no—
172#818—32no—
173#817—32no—
174#815—32no—
175C8×Dic3—32no—
176#810—32no—
177#809—32no—
178#808—32no—
179#807—32no—
180#803—32no—
181C4×C3⋊C8—32no—
182C23×C32C2×D411yescharacteristic
183C22×C3×D3—21no—
184C32×Q8—24no—
185C32×Q8—22no—
186C32×Q8C22×C414yes—
187C2×C32×C4—24no—
188C2×C32×C4—22no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4#4112yes—
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—41no—
200C2×C3×Dic3—42no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—21no—
206C3×D12C22×C412yes—
207C3×C4×D3—24no—
208C3×Dic6—21no—
209C3×Dic6C22×C412yes—
210D3×Dic3—42no—
211D3×Dic3—42no—
212C3⋊(C3⋊C8)—22no—
213C3×C3⋊C8C22×C414yes—
214C2×#137—31no—
215C4×#41—91no—
216C2×C4×Q8—31no—
217#441—92no—
218#440—92no—
219C4×Q16—92no—
220C4×SD16—92no—
221#428—91no—
222#419—91no—
223#417—91no—
224C4×M16—91no—
225C3×#41—34no—
226C3×#41—62no—
227C2×C3×Q8—22no—
228C2×C3×Q8—21no—
229C2×C3×Q8—22no—
230C2×C3×Q8—21no—
231C2×C3×Q8—24no—
232C2×C3×Q8—22no—
233C2×C3×Q8—31no—
234C2×C3×Q8—42no—
235C2×C3×Q8—41no—
236C2×C3×Q8C4×D314yescomplemented
237C2×C3×Q8C2×Dic314yescomplemented
238C2×C3×Q8C22×D312yes—
239C2×C3×Q8C22×D312yes—
240C2×C3×D4—31no—
241C2×C3×D4—61no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—41no—
248C22×C3×C4—61no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—21no—
253C22×Dic3—21no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256C22×Dic3#6711yescharacteristic
257C22×Dic3#6711yescharacteristic
258#235—22no—
259#235C2×Dic314yes—
260C2×D12C22×D311yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×Dic6C22×D311yescharacteristic
265C3×Q16—38no—
266C3×SD16—38no—
267C3×M16—34no—
268C2×C3×C8—32no—
269C3×C4⋊C4—32no—
270C3×C4⋊C4—62no—
271C3×C4⋊C4—62no—
272C3×C4⋊C4—61no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—62no—
278C3×C42—62no—
279#217—61no—
280#217—61no—
281#217—61no—
282#217—61no—
283#217—121no—
284#216C2×Dic318yescomplemented
285#215C2×Dic318yescomplemented
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288C4⋊Dic3—21no—
289C4⋊Dic3—22no—
290C4⋊Dic3—22no—
291C4⋊Dic3—31no—
292C4⋊Dic3—31no—
293C4⋊Dic3—31no—
294C4⋊Dic3—31no—
295C4⋊Dic3—61no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3C22×D312yes—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302C4×Dic3—22no—
303C4×Dic3—22no—
304C4×Dic3—61no—
305C4×Dic3—61no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—121no—
311C4×Dic3#6711yescharacteristic
312C4×Dic3#6711yescharacteristic
313C4×Dic3C22×D311yescharacteristic
314C4×Dic3C22×D311yescharacteristic
315#208—62no—
316#208—62no—
317#208—122no—
318#208C2×Dic314yescomplemented
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8C22×D312yes—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32C4×D412yes—
326C22×C32C22×D411yescharacteristic
327C2×C3×D3—22no—
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C32×C4—24no—
331C32×C4C4×D412yes—
332C32×C4C23×C411yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—41no—
335C3⋊Dic3—41no—
336C3×Dic3—22no—
337C3×Dic3—21no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—42no—
341C3×Dic3#13712yescomplemented
342C2×#41—31no—
343C22×Q8D3211yescharacteristic
344#137—38no—
345C2×Q16—32no—
346C2×SD16—32no—
347C2×M16—31no—
348C2×M16—91no—
349C4×Q8—32no—
350C4×Q8—32no—
351C4×Q8—61no—
352C4×Q8—61no—
353C4×Q8—91no—
354C4×Q8—91no—
355C4×D4—91no—
356C4×D4—91no—
357C4×D4—181no—
358C4×D4—181no—
359#117—91no—
360#117—181no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—61no—
363C2×C42—31no—
364C2×C42—61no—
365C2×C42—181no—
366#107—92no—
367#106—92no—
368#103—92no—
369#103—92no—
370#103—92no—
371#102—92no—
372#97—92no—
373C4×C8—92no—
374C23×C3—21no—
375C23×C3—61no—
376C23×C3D3×D411yescharacteristic
377C23×C3C2×#6711yescharacteristic
378C22×D3—21no—
379C3×Q8—24no—
380C3×Q8—24no—
381C3×Q8—22no—
382C3×Q8—22no—
383C3×Q8—24no—
384C3×Q8—32no—
385C3×Q8—42no—
386C3×Q8—44no—
387C3×Q8—61no—
388C3×Q8C2×C4×D314yes—
389C3×Q8C22×Dic314yes—
390C3×D4—32no—
391C3×D4—64no—
392C3×D4—61no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—31no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—42no—
406C2×C3×C4—44no—
407C2×C3×C4—62no—
408C2×C3×C4—61no—
409C2×C3×C4—64no—
410C2×C3×C4—62no—
411C2×C3×C4—121no—
412C2×C3×C4—122no—
413C2×C3×C4C2×C4×D312yes—
414C2×C3×C4#23512yes—
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4#23712yes—
417C2×C3×C4C22×Dic312yes—
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—24no—
422C2×Dic3—21no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—41no—
426C2×Dic3—42no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3—122no—
434C2×Dic3—122no—
435C2×Dic3C2×#6711yescharacteristic
436C2×Dic3C2×#6711yescharacteristic
437C2×Dic3C2×#6711yescharacteristic
438C2×Dic3C2×#6711yescharacteristic
439D12—21no—
440D12C22×Dic312yes—
441C4×D3—24no—
442C4×D3—122no—
443C4×D3—122no—
444Dic6—21no—
445Dic6C22×Dic312yes—
446C3×C8—34no—
447C3⋊C8—62no—
448C3⋊C8—62no—
449C3⋊C8—122no—
450C3⋊C8C22×Dic314yes—
451C2×C32—22no—
452C2×C32C2×C4×D411yescharacteristic
453C2×C32C2×#13711yescharacteristic
454C2×C32#57511yescharacteristic
455C3×D3—42no—
456#41—34no—
457#41—62no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—31no—
461C2×Q8D3×Dic314yescomplemented
462C2×Q8C2×D3212yes—
463C2×D4—31no—
464C2×D4—61no—
465C22×C4—21no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—181no—
471C22×C4—181no—
472C22×C4C2×D3211yescharacteristic
473Q16—38no—
474SD16—38no—
475M16—34no—
476M16—182no—
477C2×C8—32no—
478C2×C8—92no—
479C4⋊C4—32no—
480C4⋊C4—62no—
481C4⋊C4—62no—
482C4⋊C4—61no—
483C4⋊C4—91no—
484C4⋊C4—91no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C22⋊C4—181no—
488C22⋊C4—181no—
489C22⋊C4—181no—
490C42—31no—
491C42—31no—
492C42—31no—
493C42—31no—
494C42—62no—
495C42—62no—
496C42—181no—
497C42—181no—
498C42—181no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—62no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3C4×#6712yes—
511C22×C3D4×Dic312yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C22×#6711yescharacteristic
514C2×D3—22no—
515C2×D3—41no—
516C2×D3—41no—
517C3×C4—24no—
518C3×C4—24no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—22no—
522C3×C4—32no—
523C3×C4—44no—
524C3×C4—61no—
525C3×C4—61no—
526C3×C4—61no—
527C3×C4—62no—
528C3×C4—122no—
529C3×C4C4×#6712yes—
530C3×C4D4×Dic312yes—
531C3×C4C22×C4×D311yescharacteristic
532C3×C4C2×#23511yescharacteristic
533C3×C4C2×#23711yescharacteristic
534C3×C4C23×Dic311yescharacteristic
535Dic3—22no—
536Dic3—21no—
537Dic3—21no—
538Dic3—21no—
539Dic3—42no—
540Dic3—121no—
541Dic3—121no—
542Dic3—121no—
543Dic3—121no—
544Dic3—241no—
545Dic3—241no—
546Dic3#94212yesdirect product factor
547C32C4×#13711yescharacteristic, complemented, Sylow
548C23—61no—
549C23D3×#6711yescharacteristic
550Q8—22no—
551Q8—24no—
552Q8—32no—
553Q8—61no—
554Q8C2×D3×Dic314yes—
555D4—32no—
556D4—64no—
557D4—61no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—31no—
561C2×C4—31no—
562C2×C4—31no—
563C2×C4—31no—
564C2×C4—62no—
565C2×C4—61no—
566C2×C4—64no—
567C2×C4—62no—
568C2×C4—121no—
569C2×C4—122no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—362no—
573C2×C4—362no—
574C2×C4C2×D3×Dic312yes—
575C2×C4#380412yes—
576C2×C4D3×#6711yescharacteristic
577C2×C4C22×D3211yescharacteristic
578C8—34no—
579C8—182no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—42no—
586C2×C3—122no—
587C2×C3D3×#13711yescharacteristic
588C2×C3#577711yescharacteristic
589C2×C3C2×C4×#6711yescharacteristic
590C2×C3C2×D4×Dic311yescharacteristic
591C2×C3C2×#94211yescharacteristic
592C2×C3#582211yescharacteristic
593D3—42no—
594C22—21no—
595C22—21no—
596C22—62no—
597C22—121no—
598C22—121no—
599C22Dic3×#6712yes—
600C22C2×D3×#6711yescharacteristic
601C4—24no—
602C4—32no—
603C4—62no—
604C4—61no—
605C4—61no—
606C4—61no—
607C4—122no—
608C4—361no—
609C4—361no—
610C4Dic3×#6712yes—
611C4C22×D3×Dic311yescharacteristic
612C4C2×#380411yescharacteristic
613C3—21no—
614C3C4×#94211yescharacteristic, complemented
615C3Dic3×#13711yescharacteristic, complemented
616C2—22no—
617C2—122no—
618C2D3×#94211yescharacteristic
619C2#1059531711yescharacteristic
620C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
4. #10592924C2semidirect
5. #10591576C2semidirect
6. Dic3×#216C2semidirect
7. #10591566C2semidirect
8. Dic3×#215C2semidirect
9. #10591130C2semidirect
11. Dic3×#208C2semidirect
23. C3×#942C4semidirect
49. C2×Q8×Dic3D3semidirect
71. C2×C32×Q8C2×C4semidirect
92. C3×#216C2×C4semidirect
93. C3×#215C2×C4semidirect
104. C3×#208C2×C4semidirect
137. #942Dic3direct (N × H)
236. C2×C3×Q8C4×D3semidirect
237. C2×C3×Q8C2×Dic3semidirect
284. #216C2×Dic3semidirect
285. #215C2×Dic3semidirect
318. #208C2×Dic3semidirect
341. C3×Dic3#137semidirect
461. C2×Q8D3×Dic3semidirect
546. Dic3#942direct (N × H)
547. C32C4×#137semidirect
614. C3C4×#942semidirect
615. C3Dic3×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×C3×#9422
Dic3×#2352
#105929242
#105915762
Dic3×#2162
#105915662
Dic3×#2152
#105911302
#105910872
Dic3×#2082
Dic3×#1373
C4×#9423