Finite Group Databasebeta

← C3×D3×#475 #11868380

Subgroups — C3×D3×#475 #11868380

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2C3×C4×D3×Q8C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5020C211yesmaximal, characteristic, complemented
6C3×D3×#106C212yesmaximal
7C3×#4854C212yesmaximal, complemented
8C3×#4851C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic
10C3×D3×#103C212yesmaximal
11C3×#4791C212yesmaximal, complemented
12C2×C3×#475—31nomaximal
13D3×#475C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C2×C3×D3×Q8C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×Q8×Dic3C2211yescharacteristic
19C3×#944—21no—
20C2×C3×D3×C8C2212yes—
21C3×D3×C4⋊C4—21no—
22C3×D3×C4⋊C4—21no—
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×D3×C4⋊C4C2212yes—
25C3×#888—21no—
26C3×#888C2212yes—
27C3×#887—21no—
28C3×#887C2211yescharacteristic
29C3×C42×D3—21no—
30C3×C42×D3C2211yescharacteristic
31C3×#869C2211yescharacteristic
32C3×C4×Dic6—21no—
33C3×C4×Dic6C2211yescharacteristic
34C32×#106C2212yes—
35C32×C4⋊C8C2211yescharacteristic
36C32×#103C2212yes—
37C3×#835C2212yes—
38C3×#817C2212yes—
39C3×#816C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#810C2212yes—
42C3×#808C2212yes—
43C3×#808C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C2×C3×C4⋊Q8—31no—
46C2×C3×C4×Q8—31no—
47D3×C4⋊Q8C2×C311yescharacteristic
48C4×D3×Q8C2×C311yescharacteristic
49C3×#475—21no—
50C3×#475—31no—
51C3×#475—31no—
52C3×#475—32no—
53C3×#475—31no—
54C3×#475—32no—
55C3×#475D311yescharacteristic, direct product factor
56C3×#475C2×C311yescharacteristic, complemented
57C2×C3×#106—32no—
58C2×C3×C4⋊C8—31no—
59C2×C3×#103—32no—
60#5094C2×C311yescharacteristic, complemented
61#5020C2×C311yescharacteristic, complemented
62D3×#106C2×C312yes—
63#4854C2×C312yescomplemented
64#4851C2×C311yescharacteristic, complemented
65D3×C4⋊C8C2×C311yescharacteristic
66D3×#103C2×C312yes—
67#4791C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×Q8C2311yescharacteristic
70C3×D3×Q8—22no—
71C3×D3×Q8—44no—
72C3×D3×Q8Q814yescomplemented
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6C2311yescharacteristic
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2311yescharacteristic
87C32×C4⋊C4C2312yes—
88C32×C42—21no—
89C32×C42C2311yescharacteristic
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—22no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×D3×C8—24no—
107C2×#475—31noSylow
108C22×C3×Q8—31no—
109C22×C3×Q8—61no—
110C2×D3×Q8—21no—
111C2×D3×Q8C22×C311yescharacteristic
112C22×C3×C8—32no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—32no—
115C3×C4⋊Q8—31no—
116C3×C4⋊Q8—61no—
117C3×C4⋊Q8—61no—
118C3×C4⋊Q8C2×D311yescharacteristic
119C3×C4⋊Q8C22×C311yescharacteristic
120C3×C4×Q8—21no—
121C3×C4×Q8—31no—
122C3×C4×Q8—31no—
123C3×C4×Q8—31no—
124C3×C4×Q8—61no—
125C3×C4×Q8—61no—
126C3×C4×Q8C2×D311yescharacteristic
127C3×C4×Q8C22×C311yescharacteristic
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—61no—
131C2×C3×C4⋊C4—61no—
132C2×C3×C42—31no—
133C2×C3×C42—61no—
134Q8×Dic3C22×C311yescharacteristic
135#944—21no—
136C2×D3×C8C22×C312yes—
137D3×C4⋊C4—21no—
138D3×C4⋊C4—21no—
139D3×C4⋊C4C22×C312yes—
140D3×C4⋊C4C22×C311yescharacteristic
141#888—21no—
142#888C22×C312yes—
143#887—21no—
144#887C22×C311yescharacteristic
145C42×D3—21no—
146C42×D3C22×C311yescharacteristic
147#869C22×C311yescharacteristic
148C4×Dic6—21no—
149C4×Dic6C22×C311yescharacteristic
150C3×#106—22no—
151C3×#106—32no—
152C3×#106—32no—
153C3×#106—32no—
154C3×#106C2×D312yes—
155C3×#106C22×C312yes—
156C3×C4⋊C8—21no—
157C3×C4⋊C8—32no—
158C3×C4⋊C8—31no—
159C3×C4⋊C8C2×D311yescharacteristic
160C3×C4⋊C8C22×C311yescharacteristic
161C3×#103—22no—
162C3×#103—32no—
163C3×#103—32no—
164C3×#103—32no—
165C3×#103C2×D312yes—
166C3×#103C22×C312yes—
167#835C22×C312yes—
168#817C22×C312yes—
169#816C22×C312yes—
170Dic3⋊C8C22×C312yes—
171#810C22×C312yes—
172#808C22×C312yes—
173#808C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C22×C3×D3C2×D411yescharacteristic
176C32×Q8—21no—
177C32×Q8—42no—
178C32×Q8C2×Q812yescomplemented
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×C4×D3—24no—
192C3×C4×D3—22no—
193C3×C4×D3—44no—
194C3×C4×D3—42no—
195C3×C4×D3SD1614yes—
196C3×C4×D3C2×Q812yes—
197C3×C4×D3#4112yes—
198C3×Dic6—21no—
199C3×Dic6—24no—
200C3×Dic6—42no—
201C3×Dic6—44no—
202C3×Dic6C2×Q812yescomplemented
203C32×C8—22no—
204C3×C3⋊C8—22no—
205C2×C4⋊Q8—31no—
206C2×C4×Q8—31no—
207#475—31no—
208#475—31no—
209#475—32no—
210#475—31no—
211#475—32no—
212#475C3×D311yescharacteristic, direct product factor
213C2×#106—32no—
214C2×C4⋊C8—31no—
215C2×#103—32no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—34no—
220C2×C3×Q8—31no—
221C2×C3×Q8—41no—
222C2×C3×Q8—61no—
223C2×C3×Q8—62no—
224C2×C3×Q8—62no—
225C2×C3×Q8—61no—
226C2×C3×Q8—124no—
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×Q8C23×C311yescharacteristic
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4—62no—
235D3×Q8—22no—
236D3×Q8—44no—
237D3×Q8C3×Q814yescomplemented
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—22no—
241C2×C4×D3C3×D411yescharacteristic
242C2×C4×D3C3×D411yescharacteristic
243C2×C4×D3C23×C311yescharacteristic
244C2×Dic6—21no—
245C2×Dic6—21no—
246C2×Dic6—22no—
247C2×Dic6C23×C311yescharacteristic
248C2×C3×C8—22no—
249C2×C3×C8—32no—
250C2×C3×C8—64no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C23×C312yes—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—32no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—41no—
262C3×C4⋊C4—41no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—62no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C22×D311yescharacteristic
272C3×C4⋊C4C23×C311yescharacteristic
273C3×C4⋊C4C23×C312yes—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—31no—
278C3×C42—31no—
279C3×C42—31no—
280C3×C42—41no—
281C3×C42—61no—
282C3×C42—61no—
283C3×C42—61no—
284C3×C42C22×D311yescharacteristic
285C3×C42C23×C311yescharacteristic
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3C23×C311yescharacteristic
289C4⋊Dic3C23×C312yes—
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—22no—
294Dic3⋊C4—22no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3C3×D411yescharacteristic
299C4×Dic3C3×D411yescharacteristic
300C4×Dic3C23×C311yescharacteristic
301C2×C3⋊C8C23×C312yes—
302D3×C8—24no—
303C22×C32C22×D411yescharacteristic
304C2×C3×D3C22⋊Q812yes—
305C2×C3×D3C2×SD1612yes—
306C2×C3×D3#13712yes—
307C32×C4—22no—
308C32×C4—21no—
309C32×C4—42no—
310C32×C4—41no—
311C32×C4C2×SD1612yes—
312C32×C4C22×Q811yescharacteristic
313C32×C4C2×#4111yescharacteristic
314C3×Dic3—22no—
315C3×Dic3—21no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3C22⋊Q812yes—
319C3×Dic3C2×SD1612yes—
320C22×Q8—31no—
321C22×Q8—61no—
322C22×C8—32no—
323C4⋊Q8—32no—
324C4⋊Q8—31no—
325C4⋊Q8—61no—
326C4⋊Q8—61no—
327C4⋊Q8C2×C3×D311yescharacteristic
328C4×Q8—31no—
329C4×Q8—31no—
330C4×Q8—31no—
331C4×Q8—61no—
332C4×Q8—61no—
333C4×Q8C2×C3×D311yescharacteristic
334C2×C4⋊C4—31no—
335C2×C4⋊C4—32no—
336C2×C4⋊C4—61no—
337C2×C4⋊C4—61no—
338C2×C42—31no—
339C2×C42—61no—
340#106—32no—
341#106—32no—
342#106—32no—
343#106C2×C3×D312yes—
344C4⋊C8—32no—
345C4⋊C8—31no—
346C4⋊C8C2×C3×D311yescharacteristic
347#103—32no—
348#103—32no—
349#103—32no—
350#103C2×C3×D312yes—
351C23×C3—31no—
352C22×D3C2×C3×D411yescharacteristic
353C3×Q8—21no—
354C3×Q8—21no—
355C3×Q8—22no—
356C3×Q8—32no—
357C3×Q8—41no—
358C3×Q8—42no—
359C3×Q8—42no—
360C3×Q8—64no—
361C3×Q8—61no—
362C3×Q8—82no—
363C3×Q8—124no—
364C3×Q8—122no—
365C3×Q8D3×Q812yescomplemented
366C3×Q8C2×C3×Q812yescomplemented
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—31no—
377C2×C3×C4—31no—
378C2×C3×C4—34no—
379C2×C3×C4—32no—
380C2×C3×C4—32no—
381C2×C3×C4—31no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—62no—
386C2×C3×C4—64no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—62no—
390C2×C3×C4—122no—
391C2×C3×C4—124no—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4C2×C3×D411yescharacteristic
395C2×C3×C4C2×C3×D411yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C24×C311yescharacteristic
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3C2×C3×D411yescharacteristic
402C2×Dic3C2×C3×D411yescharacteristic
403C2×Dic3C2×C3×D411yescharacteristic
404C4×D3—24no—
405C4×D3—22no—
406C4×D3—44no—
407C4×D3—42no—
408C4×D3C3×SD1614yes—
409C4×D3C2×C3×Q812yes—
410C4×D3C3×#4112yes—
411Dic6—21no—
412Dic6—24no—
413Dic6—42no—
414Dic6—44no—
415Dic6C2×C3×Q812yescomplemented
416C3×C8—22no—
417C3×C8—22no—
418C3×C8—42no—
419C3×C8—62no—
420C3⋊C8—22no—
421C2×C32C2×C22⋊Q811yescharacteristic
422C2×C32C22×SD1611yescharacteristic
423C2×C32C2×#13711yescharacteristic
424C3×D3#47514yesdirect product factor
425C2×Q8—21no—
426C2×Q8—34no—
427C2×Q8—31no—
428C2×Q8—61no—
429C2×Q8—62no—
430C2×Q8—62no—
431C2×Q8—61no—
432C2×Q8—124no—
433C2×Q8C22×C3×D311yescharacteristic
434C22×C4—31no—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—62no—
440C2×C8—32no—
441C2×C8—64no—
442C2×C8C22×C3×D312yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—32no—
446C4⋊C4—31no—
447C4⋊C4—61no—
448C4⋊C4—62no—
449C4⋊C4—61no—
450C4⋊C4—61no—
451C4⋊C4—62no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4C22×C3×D312yes—
455C4⋊C4C22×C3×D311yescharacteristic
456C42—21no—
457C42—31no—
458C42—31no—
459C42—31no—
460C42—61no—
461C42—61no—
462C42—61no—
463C42C22×C3×D311yescharacteristic
464C22×C3—21no—
465C22×C3—32no—
466C22×C3—32no—
467C22×C3—32no—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C22×C3×D411yescharacteristic
470C2×D3C3×C22⋊Q812yes—
471C2×D3C2×C3×SD1612yes—
472C2×D3C3×#13712yes—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—32no—
481C3×C4—32no—
482C3×C4—41no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—41no—
486C3×C4—42no—
487C3×C4—41no—
488C3×C4—61no—
489C3×C4—62no—
490C3×C4—82no—
491C3×C4—81no—
492C3×C4—122no—
493C3×C4—121no—
494C3×C4D3×SD1612yes—
495C3×C4C2×C3×SD1612yes—
496C3×C4C2×D3×Q811yescharacteristic
497C3×C4D3×#4111yescharacteristic
498C3×C4C22×C3×Q811yescharacteristic
499C3×C4C2×C3×#4111yescharacteristic
500Dic3—21no—
501Dic3—22no—
502Dic3—42no—
503Dic3—41no—
504Dic3C3×C22⋊Q812yes—
505Dic3C2×C3×SD1612yes—
506C32C2×#47511yescharacteristic, complemented, Sylow
507C23—31no—
508Q8—21no—
509Q8—32no—
510Q8—42no—
511Q8—64no—
512Q8—61no—
513Q8—124no—
514Q8—122no—
515Q8C3×D3×Q812yescomplemented
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—34no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—31no—
525C2×C4—62no—
526C2×C4—64no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—124no—
531C2×C4—122no—
532C2×C4C3×D3×D411yescharacteristic
533C2×C4C3×D3×D411yescharacteristic
534C2×C4C23×C3×D311yescharacteristic
535C8—22no—
536C8—62no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—34no—
541C2×C3D3×C22⋊Q811yescharacteristic
542C2×C3C2×D3×SD1611yescharacteristic
543C2×C3D3×#13711yescharacteristic
544C2×C3C2×C3×C22⋊Q811yescharacteristic
545C2×C3C22×C3×SD1611yescharacteristic
546C2×C3C2×C3×#13711yescharacteristic
547D3C3×#47514yesdirect product factor
548C22—32no—
549C22—32no—
550C22—32no—
551C22C2×C3×D3×D411yescharacteristic
552C4—21no—
553C4—22no—
554C4—32no—
555C4—32no—
556C4—42no—
557C4—41no—
558C4—61no—
559C4—62no—
560C4—122no—
561C4—121no—
562C4C3×D3×SD1612yes—
563C4C2×C3×D3×Q811yescharacteristic
564C4C3×D3×#4111yescharacteristic
565C3—21no—
566C3D3×#47511yescharacteristic, direct product factor
567C3C2×C3×#47511yescharacteristic, complemented
568C2—34no—
569C2C3×D3×C22⋊Q811yescharacteristic
570C2C2×C3×D3×SD1611yescharacteristic
571C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#475D3
hypocenterC3C2×C3×#475
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
3. C32×#475C2semidirect
4. C3×#5094C2semidirect
5. C3×#5020C2semidirect
7. C3×#4854C2semidirect
8. C3×#4851C2semidirect
11. C3×#4791C2semidirect
13. D3×#475C3direct (N × H)
55. C3×#475D3direct (N × H)
56. C3×#475C2×C3semidirect
60. #5094C2×C3semidirect
61. #5020C2×C3semidirect
63. #4854C2×C3semidirect
64. #4851C2×C3semidirect
67. #4791C2×C3semidirect
72. C3×D3×Q8Q8semidirect
178. C32×Q8C2×Q8semidirect
202. C3×Dic6C2×Q8semidirect
212. #475C3×D3direct (N × H)
237. D3×Q8C3×Q8semidirect
365. C3×Q8D3×Q8semidirect
366. C3×Q8C2×C3×Q8semidirect
415. Dic6C2×C3×Q8semidirect
424. C3×D3#475direct (N × H)
506. C32C2×#475semidirect
515. Q8C3×D3×Q8semidirect
547. D3C3×#475direct (N × H)
566. C3D3×#475direct (N × H)
567. C3C2×C3×#475semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×C4×D3×Q82
C32×#4752
C3×#50942
C3×#50202
C3×D3×#1062
C3×#48542
C3×#48512
C3×D3×C4⋊C82
C3×D3×#1032
C3×#47912
C2×C3×#4753
D3×#4753