Finite Group Databasebeta

← C3×D3×#462 #11865619

Subgroups — C3×D3×#462 #11865619

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C212yesmaximal
2C3×D3×C4⋊Q8C211yesmaximal, characteristic
3C3×C4×D3×Q8C211yesmaximal, characteristic
4C32×#462C211yesmaximal, characteristic, complemented
5C3×#5182C212yesmaximal, complemented
6C3×#5090C211yesmaximal, characteristic, complemented
7C3×#5031C211yesmaximal, characteristic, complemented
8C3×#4849C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic
10C3×D3×#103C212yesmaximal
11C3×#4795C212yesmaximal, complemented
12C2×C3×#462—31nomaximal
13D3×#462C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C2×C3×D3×Q8C2211yescharacteristic
16C2×C32×Q16C2212yes—
17C32×C4⋊Q8C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic
19C3×Q8×Dic3C2211yescharacteristic
20C3×#944C2212yes—
21C2×C3×#216C2212yes—
22C2×C3×#216C2212yes—
23C3×D3×Q16—28no—
24C2×C3×Dic12C2212yes—
25C2×C3×D3×C8C2212yes—
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4—21no—
28C3×D3×C4⋊C4—21no—
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#888—21no—
31C3×#888—21no—
32C3×#887—21no—
33C3×#887C2211yescharacteristic
34C3×C42×D3—21no—
35C3×C42×D3C2211yescharacteristic
36C3×#869C2211yescharacteristic
37C3×C4×Dic6—21no—
38C3×C4×Dic6C2211yescharacteristic
39C32×C4⋊C8C2211yescharacteristic
40C32×#103C2212yes—
41C3×#835C2212yes—
42C3×#816C2212yes—
43C3×Dic3⋊C8C2212yes—
44C3×#810C2212yes—
45C3×C4⋊(C3⋊C8)C2211yescharacteristic
46C22×C3×Q16—32no—
47C2×C3×C4⋊Q8—31no—
48C2×C3×C4×Q8—31no—
49C2×D3×Q16C2×C312yes—
50D3×C4⋊Q8C2×C311yescharacteristic
51C4×D3×Q8C2×C311yescharacteristic
52C3×#462—21no—
53C3×#462—32no—
54C3×#462—31no—
55C3×#462—31no—
56C3×#462—31no—
57C3×#462—32no—
58C3×#462D311yescharacteristic, direct product factor
59C3×#462C2×C311yescharacteristic, complemented
60C2×C3×C4⋊C8—31no—
61C2×C3×#103—32no—
62#5182C2×C312yescomplemented
63#5090C2×C311yescharacteristic, complemented
64#5031C2×C311yescharacteristic, complemented
65#4849C2×C311yescharacteristic, complemented
66D3×C4⋊C8C2×C311yescharacteristic
67D3×#103C2×C312yes—
68#4795C2×C312yescomplemented
69C2×C32×Q8C2312yes—
70C2×C32×Q8C2311yescharacteristic
71C3×D3×Q8—22no—
72C3×D3×Q8—24no—
73C3×D3×Q8—24no—
74C3×D3×Q8D414yes—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—21no—
82C2×C3×Dic6—22no—
83C2×C3×Dic6C2312yes—
84C2×C3×Dic6C2311yescharacteristic
85C32×Q16—24no—
86C2×C32×C8C2312yes—
87C32×C4⋊C4—21no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C42—21no—
92C32×C42C2311yescharacteristic
93C3×#216—24no—
94C3×#216—24no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—22no—
103C3×Dic3⋊C4—22no—
104C3×C4×Dic3—21no—
105C3×C4×Dic3—21no—
106C3×C4×Dic3—21no—
107C3×C4×Dic3D411yescharacteristic
108C3×C4×Dic3D411yescharacteristic
109C3×C4×Dic3C2311yescharacteristic
110C2×C3×C3⋊C8C2312yes—
111C3×Dic12—24no—
112C3×D3×C8—24no—
113C2×#462—31noSylow
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C2×D3×Q8C22×C312yes—
117C2×D3×Q8C22×C311yescharacteristic
118C2×C3×Q16—22no—
119C2×C3×Q16—32no—
120C2×C3×Q16—32no—
121C2×C3×Q16—32no—
122C2×C3×Q16—68no—
123C2×C3×Q16C2×D312yes—
124C2×C3×Q16C22×C312yes—
125C22×C3×C8—32no—
126C3×C4⋊Q8—21no—
127C3×C4⋊Q8—32no—
128C3×C4⋊Q8—31no—
129C3×C4⋊Q8—61no—
130C3×C4⋊Q8—61no—
131C3×C4⋊Q8C2×D311yescharacteristic
132C3×C4⋊Q8C22×C311yescharacteristic
133C3×C4×Q8—21no—
134C3×C4×Q8—31no—
135C3×C4×Q8—31no—
136C3×C4×Q8—31no—
137C3×C4×Q8—61no—
138C3×C4×Q8—61no—
139C3×C4×Q8C2×D311yescharacteristic
140C3×C4×Q8C22×C311yescharacteristic
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—61no—
143C2×C3×C4⋊C4—61no—
144C2×C3×C4⋊C4—61no—
145C2×C3×C42—31no—
146C2×C3×C42—61no—
147Q8×Dic3C22×C311yescharacteristic
148#944C22×C312yes—
149C2×#216C22×C312yes—
150C2×#216C22×C312yes—
151D3×Q16—28no—
152C2×Dic12C22×C312yes—
153C2×D3×C8C22×C312yes—
154D3×C4⋊C4—21no—
155D3×C4⋊C4—21no—
156D3×C4⋊C4—21no—
157D3×C4⋊C4C22×C311yescharacteristic
158#888—21no—
159#888—21no—
160#887—21no—
161#887C22×C311yescharacteristic
162C42×D3—21no—
163C42×D3C22×C311yescharacteristic
164#869C22×C311yescharacteristic
165C4×Dic6—21no—
166C4×Dic6C22×C311yescharacteristic
167C3×C4⋊C8—21no—
168C3×C4⋊C8—32no—
169C3×C4⋊C8—31no—
170C3×C4⋊C8C2×D311yescharacteristic
171C3×C4⋊C8C22×C311yescharacteristic
172C3×#103—22no—
173C3×#103—32no—
174C3×#103—32no—
175C3×#103—32no—
176C3×#103C2×D312yes—
177C3×#103C22×C312yes—
178#835C22×C312yes—
179#816C22×C312yes—
180Dic3⋊C8C22×C312yes—
181#810C22×C312yes—
182C4⋊(C3⋊C8)C22×C311yescharacteristic
183C22×C3×D3C2×D411yescharacteristic
184C32×Q8—21no—
185C32×Q8—22no—
186C32×Q8—22no—
187C32×Q8C2×D412yes—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—22no—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×C4×D3—24no—
201C3×C4×D3—22no—
202C3×C4×D3—44no—
203C3×C4×D3—42no—
204C3×C4×D3Q1614yescomplemented
205C3×C4×D3C2×D412yes—
206C3×C4×D3#4112yes—
207C3×Dic6—21no—
208C3×Dic6—24no—
209C3×Dic6—22no—
210C3×Dic6—22no—
211C3×Dic6—44no—
212C3×Dic6C2×D412yes—
213C32×C8—22no—
214C3×C3⋊C8—22no—
215C22×Q16—32no—
216C2×C4⋊Q8—31no—
217C2×C4×Q8—31no—
218#462—32no—
219#462—31no—
220#462—31no—
221#462—31no—
222#462—32no—
223#462C3×D311yescharacteristic, direct product factor
224C2×C4⋊C8—31no—
225C2×#103—32no—
226C2×C3×Q8—21no—
227C2×C3×Q8—22no—
228C2×C3×Q8—34no—
229C2×C3×Q8—31no—
230C2×C3×Q8—32no—
231C2×C3×Q8—61no—
232C2×C3×Q8—62no—
233C2×C3×Q8—62no—
234C2×C3×Q8—64no—
235C2×C3×Q8—64no—
236C2×C3×Q8C22×D312yes—
237C2×C3×Q8C22×D311yescharacteristic
238C2×C3×Q8C23×C312yes—
239C2×C3×Q8C23×C311yescharacteristic
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4—62no—
246D3×Q8—22no—
247D3×Q8—24no—
248D3×Q8—24no—
249D3×Q8C3×D414yes—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—22no—
253C2×C4×D3C3×D411yescharacteristic
254C2×C4×D3C3×D411yescharacteristic
255C2×C4×D3C23×C311yescharacteristic
256C2×Dic6—21no—
257C2×Dic6—22no—
258C2×Dic6C23×C312yes—
259C2×Dic6C23×C311yescharacteristic
260C3×Q16—24no—
261C3×Q16—24no—
262C3×Q16—44no—
263C3×Q16—64no—
264C3×Q16—64no—
265C3×Q16—64no—
266C2×C3×C8—22no—
267C2×C3×C8—32no—
268C2×C3×C8—64no—
269C2×C3×C8C22×D312yes—
270C2×C3×C8C23×C312yes—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—41no—
280C3×C4⋊C4—41no—
281C3×C4⋊C4—41no—
282C3×C4⋊C4—61no—
283C3×C4⋊C4—61no—
284C3×C4⋊C4—62no—
285C3×C4⋊C4—62no—
286C3×C4⋊C4—61no—
287C3×C4⋊C4—61no—
288C3×C4⋊C4—61no—
289C3×C4⋊C4—61no—
290C3×C4⋊C4C22×D311yescharacteristic
291C3×C4⋊C4C23×C311yescharacteristic
292C3×C42—21no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42—31no—
296C3×C42—31no—
297C3×C42—31no—
298C3×C42—41no—
299C3×C42—61no—
300C3×C42—61no—
301C3×C42—61no—
302C3×C42C22×D311yescharacteristic
303C3×C42C23×C311yescharacteristic
304#216—24no—
305#216—24no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3C23×C311yescharacteristic
310Dic3⋊C4—21no—
311Dic3⋊C4—21no—
312Dic3⋊C4—21no—
313Dic3⋊C4—22no—
314Dic3⋊C4—22no—
315C4×Dic3—21no—
316C4×Dic3—21no—
317C4×Dic3—21no—
318C4×Dic3C3×D411yescharacteristic
319C4×Dic3C3×D411yescharacteristic
320C4×Dic3C23×C311yescharacteristic
321C2×C3⋊C8C23×C312yes—
322Dic12—24no—
323D3×C8—24no—
324C22×C32C22×D411yescharacteristic
325C2×C3×D3#12112yes—
326C2×C3×D3C2×Q1612yes—
327C2×C3×D3#13712yes—
328C32×C4—22no—
329C32×C4—21no—
330C32×C4—42no—
331C32×C4—41no—
332C32×C4C2×Q1612yescomplemented
333C32×C4C22×D411yescharacteristic
334C32×C4C2×#4111yescharacteristic
335C3×Dic3—22no—
336C3×Dic3—21no—
337C3×Dic3—42no—
338C3×Dic3—41no—
339C3×Dic3#12112yes—
340C3×Dic3C2×Q1612yescomplemented
341C22×Q8—31no—
342C22×Q8—32no—
343C2×Q16—32no—
344C2×Q16—32no—
345C2×Q16—32no—
346C2×Q16—68no—
347C2×Q16C2×C3×D312yes—
348C22×C8—32no—
349C4⋊Q8—32no—
350C4⋊Q8—31no—
351C4⋊Q8—61no—
352C4⋊Q8—61no—
353C4⋊Q8C2×C3×D311yescharacteristic
354C4×Q8—31no—
355C4×Q8—31no—
356C4×Q8—31no—
357C4×Q8—61no—
358C4×Q8—61no—
359C4×Q8C2×C3×D311yescharacteristic
360C2×C4⋊C4—31no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C42—31no—
365C2×C42—61no—
366C4⋊C8—32no—
367C4⋊C8—31no—
368C4⋊C8C2×C3×D311yescharacteristic
369#103—32no—
370#103—32no—
371#103—32no—
372#103C2×C3×D312yes—
373C23×C3—31no—
374C22×D3C2×C3×D411yescharacteristic
375C3×Q8—21no—
376C3×Q8—21no—
377C3×Q8—22no—
378C3×Q8—22no—
379C3×Q8—22no—
380C3×Q8—22no—
381C3×Q8—22no—
382C3×Q8—32no—
383C3×Q8—41no—
384C3×Q8—42no—
385C3×Q8—42no—
386C3×Q8—64no—
387C3×Q8—61no—
388C3×Q8—62no—
389C3×Q8—62no—
390C3×Q8—124no—
391C3×Q8D3×D412yes—
392C3×Q8C2×C3×D412yes—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—34no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—31no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—42no—
411C2×C3×C4—62no—
412C2×C3×C4—64no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—62no—
416C2×C3×C4—122no—
417C2×C3×C4—124no—
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4C2×C3×D411yescharacteristic
421C2×C3×C4C2×C3×D411yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423C2×C3×C4C24×C311yescharacteristic
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—22no—
427C2×Dic3C2×C3×D411yescharacteristic
428C2×Dic3C2×C3×D411yescharacteristic
429C2×Dic3C2×C3×D411yescharacteristic
430C4×D3—24no—
431C4×D3—22no—
432C4×D3—44no—
433C4×D3—42no—
434C4×D3C3×Q1614yescomplemented
435C4×D3C2×C3×D412yes—
436C4×D3C3×#4112yes—
437Dic6—21no—
438Dic6—24no—
439Dic6—22no—
440Dic6—22no—
441Dic6—44no—
442Dic6C2×C3×D412yes—
443C3×C8—22no—
444C3×C8—22no—
445C3×C8—42no—
446C3×C8—62no—
447C3⋊C8—22no—
448C2×C32C2×#12111yescharacteristic
449C2×C32C22×Q1611yescharacteristic
450C2×C32C2×#13711yescharacteristic
451C3×D3#46214yesdirect product factor
452C2×Q8—34no—
453C2×Q8—31no—
454C2×Q8—32no—
455C2×Q8—61no—
456C2×Q8—62no—
457C2×Q8—62no—
458C2×Q8—64no—
459C2×Q8—64no—
460C2×Q8C22×C3×D312yes—
461C2×Q8C22×C3×D311yescharacteristic
462C22×C4—31no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—62no—
468Q16—24no—
469Q16—64no—
470Q16—64no—
471Q16—64no—
472C2×C8—32no—
473C2×C8—64no—
474C2×C8C22×C3×D312yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—31no—
479C4⋊C4—61no—
480C4⋊C4—61no—
481C4⋊C4—61no—
482C4⋊C4—62no—
483C4⋊C4—62no—
484C4⋊C4—61no—
485C4⋊C4—61no—
486C4⋊C4—61no—
487C4⋊C4C22×C3×D311yescharacteristic
488C42—21no—
489C42—31no—
490C42—31no—
491C42—31no—
492C42—61no—
493C42—61no—
494C42—61no—
495C42C22×C3×D311yescharacteristic
496C22×C3—21no—
497C22×C3—32no—
498C22×C3—32no—
499C22×C3—32no—
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C22×C3×D411yescharacteristic
502C2×D3C3×#12112yes—
503C2×D3C2×C3×Q1612yes—
504C2×D3C3×#13712yes—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—32no—
513C3×C4—32no—
514C3×C4—41no—
515C3×C4—42no—
516C3×C4—41no—
517C3×C4—41no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—61no—
521C3×C4—62no—
522C3×C4—82no—
523C3×C4—81no—
524C3×C4—121no—
525C3×C4—122no—
526C3×C4D3×Q1612yescomplemented
527C3×C4C2×C3×Q1612yescomplemented
528C3×C4C2×D3×D411yescharacteristic
529C3×C4D3×#4111yescharacteristic
530C3×C4C22×C3×D411yescharacteristic
531C3×C4C2×C3×#4111yescharacteristic
532Dic3—21no—
533Dic3—22no—
534Dic3—41no—
535Dic3—42no—
536Dic3C3×#12112yes—
537Dic3C2×C3×Q1612yescomplemented
538C32C2×#46211yescharacteristic, complemented, Sylow
539C23—31no—
540Q8—21no—
541Q8—22no—
542Q8—22no—
543Q8—32no—
544Q8—64no—
545Q8—61no—
546Q8—62no—
547Q8—62no—
548Q8—124no—
549Q8C3×D3×D412yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—34no—
556C2×C4—32no—
557C2×C4—32no—
558C2×C4—31no—
559C2×C4—62no—
560C2×C4—64no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—62no—
564C2×C4—124no—
565C2×C4—122no—
566C2×C4C3×D3×D411yescharacteristic
567C2×C4C3×D3×D411yescharacteristic
568C2×C4C23×C3×D311yescharacteristic
569C8—22no—
570C8—62no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—34no—
575C2×C3D3×#12111yescharacteristic
576C2×C3C2×D3×Q1611yescharacteristic
577C2×C3D3×#13711yescharacteristic
578C2×C3C2×C3×#12111yescharacteristic
579C2×C3C22×C3×Q1611yescharacteristic
580C2×C3C2×C3×#13711yescharacteristic
581D3C3×#46214yesdirect product factor
582C22—32no—
583C22—32no—
584C22—32no—
585C22C2×C3×D3×D411yescharacteristic
586C4—21no—
587C4—22no—
588C4—32no—
589C4—32no—
590C4—41no—
591C4—42no—
592C4—61no—
593C4—62no—
594C4—121no—
595C4—122no—
596C4C3×D3×Q1612yescomplemented
597C4C2×C3×D3×D411yescharacteristic
598C4C3×D3×#4111yescharacteristic
599C3—21no—
600C3D3×#46211yescharacteristic, direct product factor
601C3C2×C3×#46211yescharacteristic, complemented
602C2—34no—
603C2C3×D3×#12111yescharacteristic
604C2C2×C3×D3×Q1611yescharacteristic
605C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#462D3
hypocenterC3C2×C3×#462
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
4. C32×#462C2semidirect
5. C3×#5182C2semidirect
6. C3×#5090C2semidirect
7. C3×#5031C2semidirect
8. C3×#4849C2semidirect
11. C3×#4795C2semidirect
13. D3×#462C3direct (N × H)
58. C3×#462D3direct (N × H)
59. C3×#462C2×C3semidirect
62. #5182C2×C3semidirect
63. #5090C2×C3semidirect
64. #5031C2×C3semidirect
65. #4849C2×C3semidirect
68. #4795C2×C3semidirect
204. C3×C4×D3Q16semidirect
223. #462C3×D3direct (N × H)
332. C32×C4C2×Q16semidirect
340. C3×Dic3C2×Q16semidirect
434. C4×D3C3×Q16semidirect
451. C3×D3#462direct (N × H)
526. C3×C4D3×Q16semidirect
527. C3×C4C2×C3×Q16semidirect
537. Dic3C2×C3×Q16semidirect
538. C32C2×#462semidirect
581. D3C3×#462direct (N × H)
596. C4C3×D3×Q16semidirect
600. C3D3×#462direct (N × H)
601. C3C2×C3×#462semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
C3×D3×C4⋊Q82
C3×C4×D3×Q82
C32×#4622
C3×#51822
C3×#50902
C3×#50312
C3×#48492
C3×D3×C4⋊C82
C3×D3×#1032
C3×#47952
C2×C3×#4623
D3×#4623