Finite Group Databasebeta

← C2×C3×#4783 #11863763

Subgroups — C2×C3×#4783 #11863763

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C22×C3×Dic12C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C32×#102C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4783C218yesmaximal, direct product factor
9C2×C3×#452—31nomaximal
10C2×#4783C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C23×C3×Dic3—21no—
14C2×C3×#237—24no—
15C2×C3×#237—22no—
16C2×C3×#237—24no—
17C2×C3×#237C2214yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C3×#214—24no—
24C2×C3×#214C2214yescomplemented
25C2×C3×(C2×D3)⋊C4—21no—
26C2×C3×C4⋊Dic3—21no—
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×C3×Dic12—24no—
29C2×C3×Dic12C2214yescomplemented
30C3×#897—22no—
31C3×#897C2214yescomplemented
32C32×#102C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34C3×#810C2214yescomplemented
35C22×C3×#41—31no—
36C22×#237C2×C311yescharacteristic
37C22×C3×Q16—31no—
38C22×C3×SD16—31no—
39C2×C3×C22⋊Q8—31no—
40C22×#214C2×C311yescharacteristic, complemented
41C22×Dic12C2×C311yescharacteristic, complemented
42C2×#897C2×C311yescharacteristic, complemented
43C3×#452—38no—
44C2×C3×#103—31no—
45C2×C3×#102—21no—
46C2×C3×#102D311yescharacteristic, complemented
47C2×C3×#102C2×C311yescharacteristic, complemented
48C2×C3×C22⋊C8—31no—
49C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
50C2×#810C2×C311yescharacteristic, complemented
51#4783C2×C318yesdirect product factor
52C24×C32—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4D414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—28no—
61C2×C3×#67—24no—
62C22×C3×Dic3—28no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—24no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C3×#237—216no—
68C3×#237—28no—
69C3×#237—28no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3D412yes—
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D414yes—
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2312yes—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C3×#214—28no—
87C3×(C2×D3)⋊C4—24no—
88C3×C4⋊Dic3—24no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91C3×Dic12—28no—
92C2×#452—31noSylow
93C2×C3×#41—34no—
94C2×C3×#41—62no—
95C2×C3×#41—64no—
96C2×C3×#41—64no—
97C22×C3×Q8—31no—
98C22×C3×Q8—31no—
99C22×C3×D4—21no—
100C22×C3×D4—61no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C22×C311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C22×#67—21no—
106C23×Dic3—21no—
107C2×#237—24no—
108C2×#237—22no—
109C2×#237—24no—
110C2×#237C22×C314yes—
111C22×C4×D3C22×C311yescharacteristic
112C22×Dic6C22×C311yescharacteristic
113C22×Dic6C22×C311yescharacteristic
114C2×C3×Q16—34no—
115C2×C3×Q16—64no—
116C2×C3×SD16—34no—
117C2×C3×SD16—64no—
118C22×C3×C8—21no—
119C22×C3×C8—31no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C22×C311yescharacteristic
122C3×C22⋊Q8—34no—
123C3×C22⋊Q8—62no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—61no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C22×C311yescharacteristic
128C2×C3×C22⋊C4—61no—
129C2×#214—24no—
130C2×#214C22×C314yescomplemented
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3—21no—
133C22×C3⋊C8C22×C311yescharacteristic
134C2×Dic12—24no—
135C2×Dic12C22×C314yescomplemented
136#897—22no—
137#897C22×C314yescomplemented
138C3×#103—34no—
139C3×#102—24no—
140C3×#102C2×D314yescomplemented
141C3×#102C22×C314yescomplemented
142C3×C22⋊C8—34no—
143(C2×D3)⋊C8C22×C314yescomplemented
144#810C22×C314yescomplemented
145C23×C32—24no—
146C23×C32—22no—
147C23×C32—42no—
148C23×C32—42no—
149C23×C32C2×D411yescharacteristic
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3C2×D412yes—
154C32×D4—24no—
155C32×D4—22no—
156C32×D4C2×D414yes—
157C2×C32×C4—22no—
158C2×C32×C4—42no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C3×#67—216no—
164C2×C3×Dic3—216no—
165C2×C3×Dic3—24no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—42no—
170C2×C3×Dic3C2×D412yes—
171C3×C4×D3—24no—
172C3×C4×D3—22no—
173C3×C4×D3—22no—
174C3×Dic6—24no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177C3×Dic6—22no—
178C3×Dic6—42no—
179C3×Dic6C2×D414yes—
180C32×C8—22no—
181C3×C3⋊C8—22no—
182C22×#41—31no—
183C22×Q16—31no—
184C22×SD16—31no—
185C2×C22⋊Q8—31no—
186#452—38no—
187C2×#103—31no—
188C2×#102C3×D311yescharacteristic, complemented
189C2×C22⋊C8—31no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—31no—
193C24×C3—41no—
194C23×D3C3×D411yescharacteristic
195C3×#41—68no—
196C3×#41—616no—
197C3×#41—68no—
198C2×C3×Q8—34no—
199C2×C3×Q8—32no—
200C2×C3×Q8—32no—
201C2×C3×Q8—62no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—62no—
205C2×C3×Q8—62no—
206C2×C3×D4—21no—
207C2×C3×D4—22no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—24no—
211C2×C3×D4—22no—
212C2×C3×D4—41no—
213C2×C3×D4—42no—
214C2×C3×D4—64no—
215C2×C3×D4—68no—
216C2×C3×D4D1214yes—
217C2×C3×D4C3×D414yes—
218C2×C3×D4C22×D312yes—
219C2×C3×D4C23×C312yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—41no—
227C22×C3×C4—64no—
228C22×C3×C4—68no—
229C22×C3×C4—61no—
230C22×C3×C4—62no—
231C22×C3×C4—62no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C23×C311yescharacteristic
235C2×#67—28no—
236C2×#67—24no—
237C22×Dic3—28no—
238C22×Dic3—21no—
239C22×Dic3—24no—
240C22×Dic3—21no—
241C22×Dic3C3×D411yescharacteristic
242#237—216no—
243#237—28no—
244#237—28no—
245C2×C4×D3—22no—
246C2×C4×D3—22no—
247C2×C4×D3C3×D412yes—
248C2×C4×D3C23×C312yes—
249C2×Dic6—22no—
250C2×Dic6—21no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6C3×D414yes—
255C2×Dic6C23×C312yes—
256C2×Dic6C23×C312yes—
257C3×Q16—68no—
258C3×SD16—68no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—22no—
262C2×C3×C8—32no—
263C2×C3×C8—42no—
264C2×C3×C8—62no—
265C2×C3×C8C22×D312yes—
266C2×C3×C8C23×C312yes—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—41no—
271C3×C4⋊C4—64no—
272C3×C4⋊C4C22×D312yes—
273C3×C4⋊C4C23×C312yes—
274C3×C22⋊C4—64no—
275#214—28no—
276(C2×D3)⋊C4—24no—
277C4⋊Dic3—24no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8C23×C312yes—
280Dic12—28no—
281C22×C32—24no—
282C22×C32—42no—
283C22×C32—42no—
284C22×C32—48no—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C2×C3×D3—44no—
293C32×C4—42no—
294C32×C4#12012yes—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3×Dic3—24no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C2×#41—34no—
301C2×#41—62no—
302C2×#41—64no—
303C2×#41—64no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×D4—61no—
307C22×D4C2×C3×D311yescharacteristic
308C23×C4—31no—
309C23×C4—61no—
310C2×Q16—34no—
311C2×Q16—64no—
312C2×SD16—34no—
313C2×SD16—64no—
314C22×C8—31no—
315C22×C8C2×C3×D311yescharacteristic
316C22⋊Q8—34no—
317C22⋊Q8—62no—
318C2×C4⋊C4—61no—
319C2×C4⋊C4C2×C3×D311yescharacteristic
320C2×C22⋊C4—61no—
321#103—34no—
322#102C2×C3×D314yescomplemented
323C22⋊C8—34no—
324C23×C3—24no—
325C23×C3—24no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—44no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—82no—
340C23×C3—82no—
341C23×C3D3×D411yescharacteristic
342C23×C3C2×C3×D411yescharacteristic
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—22no—
346C22×D3C2×C3×D412yes—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—24no—
358C3×D4—44no—
359C3×D4—42no—
360C3×D4—616no—
361C3×D4C2×D1214yes—
362C3×D4C2×C3×D414yes—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—32no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—616no—
374C2×C3×C4—62no—
375C2×C3×C4—64no—
376C2×C3×C4—62no—
377C2×C3×C4—64no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—82no—
382C2×C3×C4—122no—
383C2×C3×C4C2×D1212yes—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D412yes—
386C2×C3×C4C2×C3×D412yes—
387C2×C3×C4C2×C3×D411yescharacteristic
388C2×C3×C4C2×C3×D412yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C24×C311yescharacteristic
391#67—216no—
392C2×Dic3—216no—
393C2×Dic3—24no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—42no—
398C2×Dic3C2×C3×D412yes—
399C4×D3—24no—
400C4×D3—22no—
401C4×D3—22no—
402Dic6—24no—
403Dic6—22no—
404Dic6—22no—
405Dic6—22no—
406Dic6—42no—
407Dic6C2×C3×D414yes—
408C3×C8—22no—
409C3×C8—22no—
410C3×C8—42no—
411C3×C8—62no—
412C3⋊C8—22no—
413C2×C32—44no—
414C2×C32#45214yescomplemented
415C2×C32C2×#12011yescharacteristic
416C2×C32C2×#13511yescharacteristic
417C2×C32C2×#13711yescharacteristic
418C3×D3—42no—
419C24—21no—
420C24—31no—
421#41—68no—
422#41—616no—
423#41—68no—
424C2×Q8—32no—
425C2×Q8—32no—
426C2×Q8—34no—
427C2×Q8—62no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—62no—
431C2×Q8—62no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—64no—
435C2×D4—68no—
436C2×D4C3×D1214yes—
437C2×D4C22×C3×D312yes—
438C22×C4—21no—
439C22×C4—31no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—64no—
443C22×C4—68no—
444C22×C4—61no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—61no—
448C22×C4C22×C3×D311yescharacteristic
449Q16—68no—
450SD16—68no—
451C2×C8—22no—
452C2×C8—32no—
453C2×C8—62no—
454C2×C8C22×C3×D312yes—
455C4⋊C4—21no—
456C4⋊C4—64no—
457C4⋊C4C22×C3×D312yes—
458C22⋊C4—64no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—44no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—48no—
471C22×C3—48no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—62no—
475C22×C3—82no—
476C22×C3—82no—
477C22×C3—88no—
478C22×C3—124no—
479C22×C3#88212yes—
480C22×C3#91212yes—
481C22×C3#91512yes—
482C22×C3C3×#12012yes—
483C22×C3C3×#13512yes—
484C22×C3C3×#13712yes—
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C22×C3×D411yescharacteristic
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—22no—
490C2×D3—44no—
491C3×C4—22no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—42no—
495C3×C4—42no—
496C3×C4—62no—
497C3×C4—64no—
498C3×C4—82no—
499C3×C4—122no—
500C3×C4#88212yes—
501C3×C4C3×#12012yes—
502C3×C4C22×D1211yescharacteristic
503C3×C4C2×D3×D411yescharacteristic
504C3×C4C22×C3×D411yescharacteristic
505C3×C4C22×C3×D411yescharacteristic
506Dic3—24no—
507Dic3—22no—
508Dic3—42no—
509C32C2×#45211yescharacteristic, complemented, Sylow
510C23—24no—
511C23—22no—
512C23—32no—
513C23—42no—
514C23—42no—
515C23—62no—
516C23—62no—
517C23—62no—
518C23C3×D3×D411yescharacteristic
519Q8—34no—
520Q8—64no—
521Q8—62no—
522Q8—62no—
523Q8—62no—
524Q8—122no—
525D4—24no—
526D4—22no—
527D4—616no—
528D4C2×C3×D1214yes—
529C2×C4—22no—
530C2×C4—32no—
531C2×C4—42no—
532C2×C4—616no—
533C2×C4—62no—
534C2×C4—64no—
535C2×C4—62no—
536C2×C4—64no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—122no—
541C2×C4C2×C3×D1212yes—
542C2×C4C3×D3×D411yescharacteristic
543C2×C4C3×D3×D412yes—
544C2×C4C23×C3×D311yescharacteristic
545C8—22no—
546C8—62no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—44no—
552C2×C3—44no—
553C2×C3—84no—
554C2×C3—122no—
555C2×C3#478314yesdirect product factor
556C2×C3C3×#45214yescomplemented
557C2×C3C2×#88211yescharacteristic
558C2×C3C2×#91211yescharacteristic
559C2×C3C2×#91511yescharacteristic
560C2×C3C2×C3×#12011yescharacteristic
561C2×C3C2×C3×#13511yescharacteristic
562C2×C3C2×C3×#13711yescharacteristic
563D3—42no—
564C22—24no—
565C22—42no—
566C22—42no—
567C22—48no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—124no—
572C22C3×#88212yes—
573C22C3×#91212yes—
574C22C3×#91512yes—
575C22C2×C3×D3×D411yescharacteristic
576C4—42no—
577C4—62no—
578C4—64no—
579C4—122no—
580C4C3×#88212yes—
581C4C22×C3×D1211yescharacteristic
582C4C2×C3×D3×D411yescharacteristic
583C3—21no—
584C3C2×#478311yescharacteristic, direct product factor
585C3C2×C3×#45211yescharacteristic, complemented
586C2—44no—
587C2—122no—
588C2C3×#478314yesdirect product factor
589C2C2×C3×#88211yescharacteristic
590C2C2×C3×#91211yescharacteristic
591C2C2×C3×#91511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C3×#237C2
hypercenterC2×C3×#102D3
hypocenterC3C2×C3×#452
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C22×C3×Dic12C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C32×#102C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4783C2direct (N × H)
10. C2×#4783C3direct (N × H)
24. C2×C3×#214C22semidirect
29. C2×C3×Dic12C22semidirect
31. C3×#897C22semidirect
32. C32×#102C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. C3×#810C22semidirect
40. C22×#214C2×C3semidirect
41. C22×Dic12C2×C3semidirect
42. C2×#897C2×C3semidirect
46. C2×C3×#102D3semidirect
47. C2×C3×#102C2×C3semidirect
49. C2×(C2×D3)⋊C8C2×C3semidirect
50. C2×#810C2×C3semidirect
51. #4783C2×C3direct (N × H)
130. C2×#214C22×C3semidirect
135. C2×Dic12C22×C3semidirect
137. #897C22×C3semidirect
140. C3×#102C2×D3semidirect
141. C3×#102C22×C3semidirect
143. (C2×D3)⋊C8C22×C3semidirect
144. #810C22×C3semidirect
188. C2×#102C3×D3semidirect
322. #102C2×C3×D3semidirect
414. C2×C32#452semidirect
509. C32C2×#452semidirect
555. C2×C3#4783direct (N × H)
556. C2×C3C3×#452semidirect
584. C3C2×#4783direct (N × H)
585. C3C2×C3×#452semidirect
588. C2C3×#4783direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×C3×#2142
C22×C3×Dic122
C2×C3×#8972
C2×C32×#1022
C2×C3×(C2×D3)⋊C82
C2×C3×#8102
C3×#47832
C2×C3×#4523
C2×#47833