Finite Group Databasebeta

← D3×#4529 #11783237

Subgroups — D3×#4529 #11783237

Order 1152.

1081 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
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4#10589395C211yesmaximal, characteristic, complemented
5C3×#4529C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8C2×#4529—31nomaximal
9D3×#340—31nomaximal
10C22×C3×C4×D3—21no—
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×D3×C4⋊C4—22no—
21C3×D3×C4⋊C4C414yescomplemented
22C2×Dic3⋊Dic3—21no—
23D3×C4⋊Dic3—22no—
24D3×C4⋊Dic3C414yescomplemented
25C2×D3×C3⋊C8—22no—
26C2×D3×C3⋊C8—22no—
27C2×D3×C3⋊C8C414yescomplemented
28C22×C3×C4⋊C4—31no—
29C22×C4⋊Dic3—31no—
30C23×C3⋊C8—31no—
31C22×D3×C8—31no—
32C2×D3×C4⋊C4—31no—
33C2×D3×C4⋊C4D311yescharacteristic
34C3×#340—31no—
35#4551—31no—
36#4529—31no—
37#4529—31no—
38#4529—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42#4529D311yescharacteristic, direct product factor
43C23×C3×D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—24no—
51C2×C3×C4×D3—42no—
52C2×C3×C4×D3—42no—
53C2×C3×C4×D3C2×C412yes—
54C2×C3×C4×D3C2×C412yes—
55C2×C3×C4×D3C2×C412yes—
56C2×C3×C4×D3D412yes—
57C2×C3×C4×D3D412yes—
58C2×C3×C4×D3Q812yes—
59C2×D3×Dic3—24no—
60C2×D3×Dic3—42no—
61C2×D3×Dic3—42no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2×C412yescomplemented
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2×C412yescomplemented
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)C2×C412yescomplemented
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2×C412yescomplemented
72C3×C4⋊Dic3C2×C412yescomplemented
73C3×Dic3⋊C4—24no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C412yescomplemented
77Dic3⋊Dic3—24no—
78D3×C3⋊C8—28no—
79C2×#340—91noSylow
80C23×C3×C4—31no—
81C23×C3×C4—61no—
82C23×Dic3—61no—
83C22×C4×D3—21no—
84C22×C4×D3—61no—
85C22×C4×D3C2×D311yescharacteristic
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—34no—
91C2×C3×C4⋊C4—62no—
92C2×C3×C4⋊C4—61no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—34no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—62no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×Dic3⋊C4—21no—
104C2×Dic3⋊C4—61no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—34no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8—62no—
110C22×C3⋊C8—62no—
111C22×C3⋊C8C2×D311yescharacteristic
112C2×D3×C8—34no—
113C2×D3×C8—62no—
114C2×D3×C8—62no—
115D3×C4⋊C4—22no—
116D3×C4⋊C4—34no—
117D3×C4⋊C4—62no—
118D3×C4⋊C4Dic314yescomplemented
119C23×C32C2×D411yescharacteristic
120C22×C3×D3C22⋊C412yes—
121C22×C3×D3C22⋊C412yes—
122C22×C3×D3C4⋊C412yes—
123C22×C3×D3D812yes—
124C22×C3×D3SD1612yes—
125C22×C3×D3SD1612yes—
126C22×C3×D3Q1612yes—
127C2×C32×C4—22no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×Q811yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3C22⋊C412yes—
146C2×C3×Dic3C22⋊C412yes—
147C2×C3×Dic3C4⋊C412yes—
148C3×C4×D3—48no—
149C3×C4×D3C4214yes—
150C3×C4×D3C22⋊C414yes—
151C3×C4×D3C4⋊C414yes—
152C3×C4×D3C4⋊C414yes—
153D3×Dic3—48no—
154C3⋊(C3⋊C8)—22no—
155C3×C3⋊C8—22no—
156C23×C8—91no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—91no—
159#340—31no—
160#340—91no—
161#340—91no—
162#340—91no—
163C24×C3—31no—
164C23×D3#6711yescharacteristic
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—41no—
176C22×C3×C4—64no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—122no—
180C22×C3×C4—122no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—64no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—121no—
189C22×Dic3—122no—
190C22×Dic3—122no—
191C22×Dic3#6711yescharacteristic
192C2×C4×D3—24no—
193C2×C4×D3—42no—
194C2×C4×D3—42no—
195C2×C4×D3—64no—
196C2×C4×D3—122no—
197C2×C4×D3—122no—
198C2×C4×D3Dic612yes—
199C2×C4×D3C4×D312yes—
200C2×C4×D3C4×D312yes—
201C2×C4×D3D1212yes—
202C2×C4×D3C2×Dic312yes—
203C2×C4×D3#6712yes—
204C2×C3×C8—32no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—32no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—64no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4C4×D312yescomplemented
217C3×C4⋊C4C2×Dic312yescomplemented
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—62no—
223C4⋊Dic3—64no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—121no—
227C4⋊Dic3C4×D312yescomplemented
228C4⋊Dic3C2×Dic312yescomplemented
229Dic3⋊C4—24no—
230Dic3⋊C4—64no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—68no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—121no—
242C2×C3⋊C8—121no—
243C2×C3⋊C8C4×D312yescomplemented
244D3×C8—68no—
245C22×C32C2×C22⋊C411yescharacteristic
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32C2×C4⋊C411yescharacteristic
248C22×C32C2×D811yescharacteristic
249C22×C32C2×SD1611yescharacteristic
250C22×C32C2×SD1611yescharacteristic
251C22×C32C2×Q1611yescharacteristic
252C2×C3×D3#9514yes—
253C2×C3×D3#10214yes—
254C2×C3×D3#10214yes—
255C2×C3×D3#10314yes—
256C2×C3×D3#10314yes—
257C2×C3×D3#10614yes—
258C2×C3×D3#10714yes—
259C32×C4—42no—
260C32×C4C2×C4211yescharacteristic
261C32×C4C2×C22⋊C411yescharacteristic
262C32×C4C2×C4⋊C411yescharacteristic
263C32×C4C2×C4⋊C411yescharacteristic
264C3⋊Dic3—42no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C3×Dic3#9514yes—
268C23×C4—31no—
269C23×C4—61no—
270C23×C4—181no—
271C22×C8—31no—
272C22×C8—94no—
273C22×C8—91no—
274C22×C8—182no—
275C22×C8—182no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4—34no—
279C2×C4⋊C4—62no—
280C2×C4⋊C4—61no—
281C2×C4⋊C4—94no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—182no—
284C2×C4⋊C4—181no—
285C2×C4⋊C4D3211yescharacteristic
286C23×C3—21no—
287C23×C3—32no—
288C23×C3—32no—
289C23×C3—32no—
290C23×C3—32no—
291C23×C3—32no—
292C23×C3—32no—
293C23×C3—32no—
294C23×C3D3×D411yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3Dic3⋊C412yes—
297C22×D3(C2×D3)⋊C412yes—
298C22×D3#21312yes—
299C22×D3#21412yes—
300C22×D3#21512yes—
301C22×D3#21612yes—
302C22×D3#21712yes—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—32no—
312C2×C3×C4—32no—
313C2×C3×C4—32no—
314C2×C3×C4—34no—
315C2×C3×C4—34no—
316C2×C3×C4—34no—
317C2×C3×C4—34no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—81no—
326C2×C3×C4—81no—
327C2×C3×C4—128no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4C2×Dic611yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×Q811yescharacteristic
342C2×C3×C4C22×Dic311yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—122no—
353C2×Dic3—128no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—241no—
359C2×Dic3—241no—
360C2×Dic3Dic3⋊C412yes—
361C2×Dic3(C2×D3)⋊C412yes—
362C2×Dic3#21712yes—
363C4×D3—48no—
364C4×D3—128no—
365C4×D3C4×Dic314yes—
366C4×D3Dic3⋊C414yes—
367C4×D3C4⋊Dic314yes—
368C4×D3(C2×D3)⋊C414yes—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C2×C32C2×#9511yescharacteristic
375C2×C32C2×#10211yescharacteristic
376C2×C32C2×#10211yescharacteristic
377C2×C32C2×#10311yescharacteristic
378C2×C32C2×#10311yescharacteristic
379C2×C32C2×#10611yescharacteristic
380C2×C32C2×#10711yescharacteristic
381C3×D3#34018yescomplemented
382C24—31no—
383C22×C4—21no—
384C22×C4—31no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—32no—
391C22×C4—64no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—122no—
395C22×C4—122no—
396C22×C4—184no—
397C22×C4—181no—
398C22×C4—362no—
399C22×C4—362no—
400C22×C4C2×D3211yescharacteristic
401C2×C8—32no—
402C2×C8—61no—
403C2×C8—61no—
404C2×C8—92no—
405C2×C8—188no—
406C2×C8—181no—
407C2×C8—181no—
408C4⋊C4—21no—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—64no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C4⋊C4—92no—
415C4⋊C4—184no—
416C4⋊C4—181no—
417C4⋊C4D3×Dic312yescomplemented
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—34no—
426C22×C3—34no—
427C22×C3—34no—
428C22×C3—34no—
429C22×C3—34no—
430C22×C3—34no—
431C22×C3—34no—
432C22×C3D3×C22⋊C411yescharacteristic
433C22×C3D3×C22⋊C411yescharacteristic
434C22×C3D3×C4⋊C411yescharacteristic
435C22×C3D3×D811yescharacteristic
436C22×C3D3×SD1611yescharacteristic
437C22×C3D3×SD1611yescharacteristic
438C22×C3D3×Q1611yescharacteristic
439C22×C3C2×Dic3⋊C411yescharacteristic
440C22×C3C2×(C2×D3)⋊C411yescharacteristic
441C22×C3C2×#21311yescharacteristic
442C22×C3C2×#21411yescharacteristic
443C22×C3C2×#21511yescharacteristic
444C22×C3C2×#21611yescharacteristic
445C22×C3C2×#21711yescharacteristic
446C2×D3#80714yes—
447C2×D3#80814yes—
448C2×D3#80914yes—
449C2×D3#81014yes—
450C2×D3C3⋊#9514yes—
451C2×D3#83214yes—
452C2×D3#83514yes—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—34no—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—82no—
461C3×C4—122no—
462C3×C4—122no—
463C3×C4C42×D311yescharacteristic
464C3×C4D3×C22⋊C411yescharacteristic
465C3×C4D3×C4⋊C411yescharacteristic
466C3×C4D3×C4⋊C411yescharacteristic
467C3×C4C2×C4×Dic311yescharacteristic
468C3×C4C2×Dic3⋊C411yescharacteristic
469C3×C4C2×C4⋊Dic311yescharacteristic
470C3×C4C2×(C2×D3)⋊C411yescharacteristic
471Dic3—42no—
472Dic3—42no—
473Dic3—122no—
474Dic3—122no—
475Dic3—242no—
476Dic3C3⋊#9514yes—
477C32C2×#34011yescharacteristic, complemented, Sylow
478C23—32no—
479C23—32no—
480C23—32no—
481C23—32no—
482C23—32no—
483C23—32no—
484C23—32no—
485C23D3×#6711yescharacteristic
486C2×C4—22no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—34no—
491C2×C4—34no—
492C2×C4—34no—
493C2×C4—34no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—128no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—182no—
504C2×C4—368no—
505C2×C4—361no—
506C2×C4—361no—
507C2×C4D3×Dic611yescharacteristic
508C2×C4C4×D3211yescharacteristic
509C2×C4C4×D3211yescharacteristic
510C2×C4D3×D1211yescharacteristic
511C2×C4C2×D3×Dic311yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C8—62no—
514C8—182no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—38no—
523C2×C3D3×#9511yescharacteristic
524C2×C3D3×#10211yescharacteristic
525C2×C3D3×#10211yescharacteristic
526C2×C3D3×#10311yescharacteristic
527C2×C3D3×#10311yescharacteristic
528C2×C3D3×#10611yescharacteristic
529C2×C3D3×#10711yescharacteristic
530C2×C3C2×#80711yescharacteristic
531C2×C3C2×#80811yescharacteristic
532C2×C3C2×#80911yescharacteristic
533C2×C3C2×#81011yescharacteristic
534C2×C3C2×C3⋊#9511yescharacteristic
535C2×C3C2×#83211yescharacteristic
536C2×C3C2×#83511yescharacteristic
537D3#452918yesdirect product factor
538C22—34no—
539C22—34no—
540C22—34no—
541C22—34no—
542C22—34no—
543C22—34no—
544C22—34no—
545C22D3×Dic3⋊C411yescharacteristic
546C22D3×(C2×D3)⋊C411yescharacteristic
547C22D3×#21311yescharacteristic
548C22D3×#21411yescharacteristic
549C22D3×#21511yescharacteristic
550C22D3×#21611yescharacteristic
551C22D3×#21711yescharacteristic
552C4—34no—
553C4—42no—
554C4—122no—
555C4—122no—
556C4—362no—
557C4C4×D3×Dic311yescharacteristic
558C4D3×Dic3⋊C411yescharacteristic
559C4D3×C4⋊Dic311yescharacteristic
560C4D3×(C2×D3)⋊C411yescharacteristic
561C3—21no—
562C3D3×#34011yescharacteristic, complemented
563C3C2×#452911yescharacteristic, complemented
564C2—38no—
565C2D3×#80711yescharacteristic
566C2D3×#80811yescharacteristic
567C2D3×#80911yescharacteristic
568C2D3×#81011yescharacteristic
569C2D3×C3⋊#9511yescharacteristic
570C2D3×#83211yescharacteristic
571C2D3×#83511yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#340
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10589395C2semidirect
5. C3×#4529C2semidirect
6. #10589164C2semidirect
7. #10589163C2semidirect
21. C3×D3×C4⋊C4C4semidirect
24. D3×C4⋊Dic3C4semidirect
27. C2×D3×C3⋊C8C4semidirect
42. #4529D3direct (N × H)
63. C32×C4⋊C4C2×C4semidirect
65. C4⋊(C3⋊Dic3)C2×C4semidirect
68. C2×C3⋊(C3⋊C8)C2×C4semidirect
71. C3×C4⋊Dic3C2×C4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
118. D3×C4⋊C4Dic3semidirect
216. C3×C4⋊C4C4×D3semidirect
217. C3×C4⋊C4C2×Dic3semidirect
227. C4⋊Dic3C4×D3semidirect
228. C4⋊Dic3C2×Dic3semidirect
243. C2×C3⋊C8C4×D3semidirect
381. C3×D3#340semidirect
417. C4⋊C4D3×Dic3semidirect
477. C32C2×#340semidirect
537. D3#4529direct (N × H)
562. C3D3×#340semidirect
563. C3C2×#4529semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×D3×C4⋊Dic32
C22×D3×C3⋊C82
#105893952
C3×#45292
#105891642
#105891632
C2×#45293
D3×#3403