Finite Group Databasebeta

← C3×D3×#470 #11866991

Subgroups — C3×D3×#470 #11866991

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
2C2×C3×D3×M16C211yesmaximal, characteristic
3C3×D3×C22⋊Q8C212yesmaximal
4C32×#470C211yesmaximal, characteristic, complemented
5C3×#5189C211yesmaximal, characteristic, complemented
6C3×#5137C211yesmaximal, characteristic, complemented
7C3×#5052C212yesmaximal, complemented
8C3×#4867C211yesmaximal, characteristic, complemented
9C3×D3×#106C211yesmaximal, characteristic, complemented
10C3×#4816C212yesmaximal, complemented
11C3×D3×#103C212yesmaximal, complemented
12C2×C3×#470—31nomaximal
13D3×#470C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×Q16C2211yescharacteristic, complemented
17C2×C32×M16C2211yescharacteristic
18C32×C22⋊Q8C2212yes—
19C3×#946C2212yes—
20C2×C3×#216C2212yescomplemented
21C3×#924C2212yes—
22C2×C3×#208C2211yescharacteristic
23C3×D3×Q16—24no—
24C3×D3×M16—24no—
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C3×#897C2212yes—
31C3×#896—22no—
32C3×D3×C4⋊C4—22no—
33C3×D3×C4⋊C4C2212yes—
34C3×D3×C22⋊C4—22no—
35C3×#878—22no—
36C32×#106C2211yescharacteristic, complemented
37C32×#103C2212yescomplemented
38C3×#835C2212yescomplemented
39C3×#817C2211yescharacteristic, complemented
40C3×#816C2212yescomplemented
41C3×#810C2212yescomplemented
42C3×#808C2212yescomplemented
43C22×C3×Q16—31no—
44C22×C3×M16—31no—
45C2×C3×C22⋊Q8—32no—
46C2×D3×Q16C2×C311yescharacteristic, complemented
47C2×D3×M16C2×C311yescharacteristic
48D3×C22⋊Q8C2×C312yes—
49C3×#470—21no—
50C3×#470—31no—
51C3×#470—31no—
52C3×#470—32no—
53C3×#470—31no—
54C3×#470—32no—
55C3×#470D311yescharacteristic, direct product factor
56C3×#470C2×C311yescharacteristic, complemented
57C2×C3×#106—31no—
58C2×C3×#103—32no—
59#5189C2×C311yescharacteristic, complemented
60#5137C2×C311yescharacteristic, complemented
61#5052C2×C312yescomplemented
62#4867C2×C311yescharacteristic, complemented
63D3×#106C2×C311yescharacteristic, complemented
64#4816C2×C312yescomplemented
65D3×#103C2×C312yescomplemented
66C23×C3×D3D411yescharacteristic
67C2×C32×Q8C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3×Dic3D411yescharacteristic
70C3×D3×Q8—24no—
71C3×D3×Q8—24no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6—22no—
81C2×C3×Dic6C2312yes—
82C32×Q16—22no—
83C32×M16—22no—
84C2×C32×C8C2311yescharacteristic
85C2×C32×C8C2311yescharacteristic
86C32×C4⋊C4—22no—
87C32×C4⋊C4C2312yes—
88C32×C22⋊C4—22no—
89C3×#217—22no—
90C3×#216—24no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97C3×Dic3⋊C4—22no—
98C3×#208—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C3×Dic12—22no—
102C3×ΓL(1,𝔽25)—22no—
103C3×ΓL(1,𝔽25)—22no—
104C3×D3×C8—22no—
105C3×D3×C8D414yes—
106C2×#470—31noSylow
107C22×C3×Q8—32no—
108C23×C3×C4—31no—
109C2×D3×Q8C22×C312yes—
110C22×C4×D3C22×C311yescharacteristic
111C2×C3×Q16—21no—
112C2×C3×Q16—32no—
113C2×C3×Q16—31no—
114C2×C3×Q16—64no—
115C2×C3×Q16C2×D311yescharacteristic, complemented
116C2×C3×Q16C22×C311yescharacteristic, complemented
117C2×C3×M16—21no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C2×C3×M16—31no—
121C2×C3×M16—64no—
122C2×C3×M16C2×D311yescharacteristic
123C2×C3×M16C22×C311yescharacteristic
124C22×C3×C8—31no—
125C22×C3×C8—31no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—32no—
128C3×C22⋊Q8—32no—
129C3×C22⋊Q8—32no—
130C3×C22⋊Q8—62no—
131C3×C22⋊Q8—62no—
132C3×C22⋊Q8C2×D312yes—
133C3×C22⋊Q8C22×C312yes—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4—62no—
136C2×C3×C22⋊C4—62no—
137#946C22×C312yes—
138C2×#216C22×C312yescomplemented
139#924C22×C312yes—
140C2×#208C22×C311yescharacteristic
141D3×Q16—24no—
142D3×M16—24no—
143C2×Dic12C22×C311yescharacteristic, complemented
144C2×ΓL(1,𝔽25)C22×C311yescharacteristic
145C2×ΓL(1,𝔽25)C22×C311yescharacteristic
146C2×D3×C8C22×C311yescharacteristic
147C2×D3×C8C22×C311yescharacteristic
148#897C22×C312yes—
149#896—22no—
150D3×C4⋊C4—22no—
151D3×C4⋊C4C22×C312yes—
152D3×C22⋊C4—22no—
153#878—22no—
154C3×#106—21no—
155C3×#106—31no—
156C3×#106—32no—
157C3×#106C2×D311yescharacteristic, complemented
158C3×#106C22×C311yescharacteristic, complemented
159C3×#103—22no—
160C3×#103—32no—
161C3×#103—32no—
162C3×#103—32no—
163C3×#103C2×D312yescomplemented
164C3×#103C22×C312yescomplemented
165#835C22×C312yescomplemented
166#817C22×C311yescharacteristic, complemented
167#816C22×C312yescomplemented
168#810C22×C312yescomplemented
169#808C22×C312yescomplemented
170C23×C32C2×D411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3—24no—
173C22×C3×D3C2×D411yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C32×Q8—22no—
176C32×Q8—22no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×D411yescharacteristic
187C2×C3×Dic3C2×D411yescharacteristic
188C3×C4×D3—22no—
189C3×C4×D3—21no—
190C3×C4×D3—21no—
191C3×C4×D3—22no—
192C3×C4×D3—44no—
193C3×C4×D3—44no—
194C3×C4×D3C2×D412yes—
195C3×C4×D3#4112yes—
196C3×Dic6—22no—
197C3×Dic6—22no—
198C3×Dic6—44no—
199C32×C8—21no—
200C32×C8C2×D412yes—
201C3×C3⋊C8—21no—
202C3×C3⋊C8C2×D412yes—
203C22×Q16—31no—
204C22×M16—31no—
205C2×C22⋊Q8—32no—
206#470—31no—
207#470—31no—
208#470—32no—
209#470—31no—
210#470—32no—
211#470C3×D311yescharacteristic, direct product factor
212C2×#106—31no—
213C2×#103—32no—
214C24×C3—31no—
215C23×D3C3×D411yescharacteristic
216C2×C3×Q8—22no—
217C2×C3×Q8—32no—
218C2×C3×Q8—62no—
219C2×C3×Q8—64no—
220C2×C3×Q8—64no—
221C2×C3×Q8C22×D312yes—
222C2×C3×Q8C23×C312yes—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—62no—
230C22×C3×C4—62no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C23×C311yescharacteristic
235C22×Dic3C3×D411yescharacteristic
236D3×Q8—24no—
237D3×Q8—24no—
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—22no—
241C2×C4×D3—22no—
242C2×C4×D3C3×D411yescharacteristic
243C2×C4×D3C3×D411yescharacteristic
244C2×C4×D3C23×C311yescharacteristic
245C2×C4×D3C23×C311yescharacteristic
246C2×Dic6—22no—
247C2×Dic6C23×C312yes—
248C3×Q16—22no—
249C3×Q16—22no—
250C3×Q16—42no—
251C3×Q16—64no—
252C3×Q16—62no—
253C3×M16—22no—
254C3×M16—22no—
255C3×M16—42no—
256C3×M16—62no—
257C3×M16—62no—
258C3×M16—62no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—31no—
262C2×C3×C8—34no—
263C2×C3×C8—31no—
264C2×C3×C8—62no—
265C2×C3×C8C22×D311yescharacteristic
266C2×C3×C8C22×D311yescharacteristic
267C2×C3×C8C23×C311yescharacteristic
268C2×C3×C8C23×C311yescharacteristic
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—32no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—62no—
277C3×C4⋊C4—62no—
278C3×C4⋊C4C22×D312yes—
279C3×C4⋊C4C23×C312yes—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—62no—
284C3×C22⋊C4—62no—
285C3×C22⋊C4—62no—
286#217—22no—
287#216—24no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—22no—
290C4⋊Dic3—22no—
291C4⋊Dic3C23×C312yes—
292Dic3⋊C4—22no—
293Dic3⋊C4—22no—
294Dic3⋊C4—22no—
295#208—22no—
296C2×C3⋊C8C23×C311yescharacteristic
297C2×C3⋊C8C23×C311yescharacteristic
298Dic12—22no—
299ΓL(1,𝔽25)—22no—
300ΓL(1,𝔽25)—22no—
301D3×C8—22no—
302D3×C8C3×D414yes—
303C22×C32—21no—
304C22×C32—22no—
305C22×C32C22×D411yescharacteristic
306C2×C3×D3—21no—
307C2×C3×D3—22no—
308C2×C3×D3—44no—
309C2×C3×D3#12112yes—
310C2×C3×D3#13714yes—
311C32×C4—21no—
312C32×C4—42no—
313C32×C4—42no—
314C32×C4C22×D411yescharacteristic
315C32×C4C2×#4111yescharacteristic
316C3×Dic3—21no—
317C3×Dic3—42no—
318C3×Dic3—42no—
319C3×Dic3#12112yes—
320C22×Q8—32no—
321C23×C4—31no—
322C2×Q16—32no—
323C2×Q16—31no—
324C2×Q16—64no—
325C2×Q16C2×C3×D311yescharacteristic, complemented
326C2×M16—31no—
327C2×M16—31no—
328C2×M16—31no—
329C2×M16—64no—
330C2×M16C2×C3×D311yescharacteristic
331C22×C8—31no—
332C22×C8—31no—
333C22⋊Q8—32no—
334C22⋊Q8—32no—
335C22⋊Q8—32no—
336C22⋊Q8—62no—
337C22⋊Q8—62no—
338C22⋊Q8C2×C3×D312yes—
339C2×C4⋊C4—32no—
340C2×C4⋊C4—62no—
341C2×C22⋊C4—62no—
342#106—31no—
343#106—32no—
344#106C2×C3×D311yescharacteristic, complemented
345#103—32no—
346#103—32no—
347#103—32no—
348#103C2×C3×D312yescomplemented
349C23×C3—21no—
350C23×C3—31no—
351C23×C3—31no—
352C23×C3—62no—
353C23×C3—64no—
354C23×C3D3×D411yescharacteristic
355C23×C3C2×C3×D411yescharacteristic
356C22×D3—22no—
357C22×D3—24no—
358C22×D3C2×C3×D411yescharacteristic
359C22×D3C2×C3×D411yescharacteristic
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—42no—
365C3×Q8—42no—
366C3×Q8—62no—
367C3×Q8—62no—
368C3×Q8—124no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—31no—
380C2×C3×C4—32no—
381C2×C3×C4—32no—
382C2×C3×C4—31no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—124no—
395C2×C3×C4—124no—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4C2×C3×D411yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C24×C311yescharacteristic
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3C2×C3×D411yescharacteristic
404C2×Dic3C2×C3×D411yescharacteristic
405C4×D3—22no—
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—22no—
409C4×D3—44no—
410C4×D3—44no—
411C4×D3C2×C3×D412yes—
412C4×D3C3×#4112yes—
413Dic6—22no—
414Dic6—22no—
415Dic6—44no—
416C3×C8—21no—
417C3×C8—21no—
418C3×C8—22no—
419C3×C8—32no—
420C3×C8—41no—
421C3×C8—61no—
422C3×C8D3×D412yes—
423C3×C8C2×C3×D412yes—
424C3⋊C8—21no—
425C3⋊C8C2×C3×D412yes—
426C2×C32—41no—
427C2×C32C2×#12111yescharacteristic
428C2×C32C2×#13712yes—
429C3×D3—41no—
430C3×D3#47014yesdirect product factor
431C24—31no—
432C2×Q8—32no—
433C2×Q8—62no—
434C2×Q8—64no—
435C2×Q8—64no—
436C2×Q8C22×C3×D312yes—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4C22×C3×D311yescharacteristic
447Q16—22no—
448Q16—64no—
449Q16—62no—
450M16—22no—
451M16—62no—
452M16—62no—
453M16—62no—
454C2×C8—31no—
455C2×C8—34no—
456C2×C8—31no—
457C2×C8—62no—
458C2×C8C22×C3×D311yescharacteristic
459C2×C8C22×C3×D311yescharacteristic
460C4⋊C4—22no—
461C4⋊C4—32no—
462C4⋊C4—62no—
463C4⋊C4—62no—
464C4⋊C4—62no—
465C4⋊C4—62no—
466C4⋊C4C22×C3×D312yes—
467C22⋊C4—22no—
468C22⋊C4—62no—
469C22⋊C4—62no—
470C22⋊C4—62no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—34no—
477C22×C3—32no—
478C22×C3—41no—
479C22×C3—42no—
480C22×C3—62no—
481C22×C3—61no—
482C22×C3—124no—
483C22×C3C2×D3×D411yescharacteristic
484C22×C3C22×C3×D411yescharacteristic
485C2×D3—22no—
486C2×D3—21no—
487C2×D3—44no—
488C2×D3C3×#12112yes—
489C2×D3C3×#13714yes—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—32no—
495C3×C4—41no—
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—42no—
500C3×C4—61no—
501C3×C4—82no—
502C3×C4—82no—
503C3×C4—122no—
504C3×C4—122no—
505C3×C4C2×D3×D411yescharacteristic
506C3×C4D3×#4111yescharacteristic
507C3×C4C22×C3×D411yescharacteristic
508C3×C4C2×C3×#4111yescharacteristic
509Dic3—21no—
510Dic3—42no—
511Dic3—42no—
512Dic3C3×#12112yes—
513C32C2×#47011yescharacteristic, complemented, Sylow
514C23—31no—
515C23—31no—
516C23—62no—
517C23—64no—
518C23C3×D3×D411yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—62no—
522Q8—62no—
523Q8—124no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—31no—
529C2×C4—32no—
530C2×C4—32no—
531C2×C4—31no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—124no—
540C2×C4—124no—
541C2×C4C3×D3×D411yescharacteristic
542C2×C4C23×C3×D311yescharacteristic
543C8—21no—
544C8—32no—
545C8—61no—
546C8C3×D3×D412yes—
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—34no—
550C2×C3—41no—
551C2×C3—41no—
552C2×C3—81no—
553C2×C3—121no—
554C2×C3D3×#12111yescharacteristic
555C2×C3D3×#13712yes—
556C2×C3C2×C3×#12111yescharacteristic
557C2×C3C2×C3×#13712yes—
558D3—41no—
559D3C3×#47014yesdirect product factor
560C22—22no—
561C22—21no—
562C22—34no—
563C22—32no—
564C22—62no—
565C22—61no—
566C22—124no—
567C22C2×C3×D3×D411yescharacteristic
568C4—21no—
569C4—32no—
570C4—42no—
571C4—42no—
572C4—61no—
573C4—122no—
574C4—122no—
575C4C2×C3×D3×D411yescharacteristic
576C4C3×D3×#4111yescharacteristic
577C3—21no—
578C3D3×#47011yescharacteristic, direct product factor
579C3C2×C3×#47011yescharacteristic, complemented
580C2—34no—
581C2—41no—
582C2—121no—
583C2C3×D3×#12111yescharacteristic
584C2C3×D3×#13712yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#470C2
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC3×#470D3
hypocenterC3C2×C3×#470
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#470

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
4. C32×#470C2semidirect
5. C3×#5189C2semidirect
6. C3×#5137C2semidirect
7. C3×#5052C2semidirect
8. C3×#4867C2semidirect
9. C3×D3×#106C2semidirect
10. C3×#4816C2semidirect
11. C3×D3×#103C2semidirect
13. D3×#470C3direct (N × H)
16. C2×C32×Q16C22semidirect
20. C2×C3×#216C22semidirect
25. C2×C3×Dic12C22semidirect
36. C32×#106C22semidirect
37. C32×#103C22semidirect
38. C3×#835C22semidirect
39. C3×#817C22semidirect
40. C3×#816C22semidirect
41. C3×#810C22semidirect
42. C3×#808C22semidirect
46. C2×D3×Q16C2×C3semidirect
55. C3×#470D3direct (N × H)
56. C3×#470C2×C3semidirect
59. #5189C2×C3semidirect
60. #5137C2×C3semidirect
61. #5052C2×C3semidirect
62. #4867C2×C3semidirect
63. D3×#106C2×C3semidirect
64. #4816C2×C3semidirect
65. D3×#103C2×C3semidirect
115. C2×C3×Q16C2×D3semidirect
116. C2×C3×Q16C22×C3semidirect
138. C2×#216C22×C3semidirect
143. C2×Dic12C22×C3semidirect
157. C3×#106C2×D3semidirect
158. C3×#106C22×C3semidirect
163. C3×#103C2×D3semidirect
164. C3×#103C22×C3semidirect
165. #835C22×C3semidirect
166. #817C22×C3semidirect
167. #816C22×C3semidirect
168. #810C22×C3semidirect
169. #808C22×C3semidirect
211. #470C3×D3direct (N × H)
325. C2×Q16C2×C3×D3semidirect
344. #106C2×C3×D3semidirect
348. #103C2×C3×D3semidirect
430. C3×D3#470direct (N × H)
513. C32C2×#470semidirect
559. D3C3×#470direct (N × H)
578. C3D3×#470direct (N × H)
579. C3C2×C3×#470semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
C2×C3×D3×M162
C3×D3×C22⋊Q82
C32×#4702
C3×#51892
C3×#51372
C3×#50522
C3×#48672
C3×D3×#1062
C3×#48162
C3×D3×#1032
C2×C3×#4703
D3×#4703