Finite Group Databasebeta

← C3×D3×#487 #11873385

Subgroups — C3×D3×#487 #11873385

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2C3×D3×C4⋊Q8C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×#5079C211yesmaximal, characteristic, complemented
6C3×D3×#103C214yesmaximal
7C3×#4792C214yesmaximal, complemented
8C3×C4×D3×C8C211yesmaximal, characteristic
9C3×#4681C211yesmaximal, characteristic, complemented
10C2×C3×#487—31nomaximal
11D3×#487C311yesmaximal, characteristic, direct product factor
12C2×C3×D3×Q8—21no—
13C2×C3×D3×Q8C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C3×#944—21no—
17C3×#944C2212yes—
18C2×C3×D3×C8C2212yes—
19C3×D3×C4⋊C4—21no—
20C3×D3×C4⋊C4—21no—
21C3×D3×C4⋊C4—21no—
22C3×D3×C4⋊C4C2212yes—
23C3×#888—21no—
24C3×#888—21no—
25C3×#888—21no—
26C3×#888C2212yes—
27C3×C42×D3C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C32×#103C2214yes—
31C32×C4×C8C2211yescharacteristic
32C3×#835C2214yes—
33C3×#816C2214yes—
34C3×C8×Dic3C2212yes—
35C3×#810C2214yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C2×C3×C4⋊Q8—31no—
38C2×C3×C4⋊Q8—31no—
39D3×C4⋊Q8C2×C311yescharacteristic
40D3×C4⋊Q8C2×C311yescharacteristic
41C3×#487—21no—
42C3×#487—31no—
43C3×#487—31no—
44C3×#487—34no—
45C3×#487—31no—
46C3×#487D311yescharacteristic, direct product factor
47C3×#487C2×C311yescharacteristic, complemented
48C2×C3×#103—34no—
49C2×C3×C4×C8—31no—
50#5093C2×C311yescharacteristic, complemented
51#5079C2×C311yescharacteristic, complemented
52D3×#103C2×C314yes—
53#4792C2×C314yescomplemented
54C4×D3×C8C2×C311yescharacteristic
55#4681C2×C311yescharacteristic, complemented
56C2×C32×Q8—21no—
57C2×C32×Q8C2312yes—
58C3×D3×Q8—28no—
59C3×D3×Q8—44no—
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3D411yescharacteristic
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3C2311yescharacteristic
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2312yes—
69C2×C32×C8C2312yes—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4C2312yes—
74C32×C42C2311yescharacteristic
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2312yes—
87C3×D3×C8—24no—
88C2×#487—31noSylow
89C22×C3×Q8—32no—
90C22×C3×Q8—61no—
91C2×D3×Q8—21no—
92C2×D3×Q8C22×C312yes—
93C22×C3×C8—32no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8—21no—
96C3×C4⋊Q8—32no—
97C3×C4⋊Q8—32no—
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—61no—
101C3×C4⋊Q8—61no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—61no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C2×C3×C4⋊C4—32no—
109C2×C3×C4⋊C4—61no—
110C2×C3×C4⋊C4—61no—
111C2×C3×C4⋊C4—61no—
112C2×C3×C42—31no—
113#944—21no—
114#944C22×C312yes—
115C2×D3×C8C22×C312yes—
116D3×C4⋊C4—21no—
117D3×C4⋊C4—21no—
118D3×C4⋊C4—21no—
119D3×C4⋊C4C22×C312yes—
120#888—21no—
121#888—21no—
122#888—21no—
123#888C22×C312yes—
124C42×D3C22×C311yescharacteristic
125#869C22×C311yescharacteristic
126#869C22×C311yescharacteristic
127C3×#103—24no—
128C3×#103—34no—
129C3×#103—34no—
130C3×#103—34no—
131C3×#103C2×D314yes—
132C3×#103C22×C314yes—
133C3×C4×C8—21no—
134C3×C4×C8—32no—
135C3×C4×C8—31no—
136C3×C4×C8C2×D311yescharacteristic
137C3×C4×C8C22×C311yescharacteristic
138#835C22×C314yes—
139#816C22×C314yes—
140C8×Dic3C22×C312yes—
141#810C22×C314yes—
142C4×C3⋊C8C22×C311yescharacteristic
143C22×C3×D3C2×D411yescharacteristic
144C32×Q8—24no—
145C32×Q8—42no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C3×C4×D3—44no—
157C3×C4×D3—44no—
158C3×C4×D3SD1614yes—
159C3×C4×D3Q1614yes—
160C3×C4×D3#4114yes—
161C3×Dic6—24no—
162C3×Dic6—42no—
163C3×Dic6—44no—
164C3×Dic6—44no—
165C32×C8—22no—
166C3×C3⋊C8—22no—
167C2×C4⋊Q8—31no—
168C2×C4⋊Q8—31no—
169#487—31no—
170#487—31no—
171#487—34no—
172#487—31no—
173#487C3×D311yescharacteristic, direct product factor
174C2×#103—34no—
175C2×C4×C8—31no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—22no—
179C2×C3×Q8—32no—
180C2×C3×Q8—41no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×Q8—68no—
184C2×C3×Q8—61no—
185C2×C3×Q8—124no—
186C2×C3×Q8C22×D312yes—
187C2×C3×Q8C23×C312yes—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193D3×Q8—28no—
194D3×Q8—44no—
195C2×C4×D3—22no—
196C2×C4×D3—22no—
197C2×C4×D3C3×D411yescharacteristic
198C2×C4×D3C3×D411yescharacteristic
199C2×C4×D3C23×C311yescharacteristic
200C2×Dic6—21no—
201C2×Dic6—22no—
202C2×Dic6—22no—
203C2×Dic6C23×C312yes—
204C2×C3×C8—22no—
205C2×C3×C8—32no—
206C2×C3×C8—64no—
207C2×C3×C8C22×D312yes—
208C2×C3×C8C23×C312yes—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—41no—
218C3×C4⋊C4—41no—
219C3×C4⋊C4—41no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C22×D312yes—
228C3×C4⋊C4C23×C312yes—
229C3×C42—21no—
230C3×C42—31no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42C22×D311yescharacteristic
234C3×C42C23×C311yescharacteristic
235C4⋊Dic3—21no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4⋊Dic3C23×C312yes—
239Dic3⋊C4—22no—
240Dic3⋊C4—22no—
241Dic3⋊C4—22no—
242Dic3⋊C4—22no—
243C4×Dic3C3×D411yescharacteristic
244C4×Dic3C3×D411yescharacteristic
245C4×Dic3C23×C311yescharacteristic
246C2×C3⋊C8C23×C312yes—
247D3×C8—24no—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3#12412yes—
250C2×C3×D3C2×SD1612yes—
251C2×C3×D3C2×Q1612yes—
252C32×C4—42no—
253C32×C4—42no—
254C32×C4C2×SD1612yes—
255C32×C4C2×Q1612yes—
256C32×C4C2×#4112yes—
257C3×Dic3—42no—
258C3×Dic3—42no—
259C3×Dic3#12412yes—
260C3×Dic3C2×SD1612yes—
261C3×Dic3C2×Q1612yes—
262C22×Q8—32no—
263C22×Q8—61no—
264C22×C8—32no—
265C4⋊Q8—32no—
266C4⋊Q8—32no—
267C4⋊Q8—31no—
268C4⋊Q8—31no—
269C4⋊Q8—61no—
270C4⋊Q8—61no—
271C4⋊Q8—61no—
272C4⋊Q8—61no—
273C4⋊Q8C2×C3×D311yescharacteristic
274C4⋊Q8C2×C3×D311yescharacteristic
275C2×C4⋊C4—32no—
276C2×C4⋊C4—61no—
277C2×C4⋊C4—61no—
278C2×C4⋊C4—61no—
279C2×C42—31no—
280#103—34no—
281#103—34no—
282#103—34no—
283#103C2×C3×D314yes—
284C4×C8—32no—
285C4×C8—31no—
286C4×C8C2×C3×D311yescharacteristic
287C23×C3—31no—
288C22×D3C2×C3×D411yescharacteristic
289C3×Q8—24no—
290C3×Q8—24no—
291C3×Q8—44no—
292C3×Q8—42no—
293C3×Q8—42no—
294C3×Q8—64no—
295C3×Q8—82no—
296C3×Q8—124no—
297C3×Q8—124no—
298C3×Q8—122no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—31no—
307C2×C3×C4—31no—
308C2×C3×C4—31no—
309C2×C3×C4—34no—
310C2×C3×C4—34no—
311C2×C3×C4—34no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—124no—
317C2×C3×C4—124no—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4C2×C3×D411yescharacteristic
321C2×C3×C4C2×C3×D411yescharacteristic
322C2×C3×C4C23×D311yescharacteristic
323C2×C3×C4C24×C311yescharacteristic
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3C2×C3×D411yescharacteristic
327C2×Dic3C2×C3×D411yescharacteristic
328C2×Dic3C2×C3×D411yescharacteristic
329C4×D3—44no—
330C4×D3—44no—
331C4×D3C3×SD1614yes—
332C4×D3C3×Q1614yes—
333C4×D3C3×#4114yes—
334Dic6—24no—
335Dic6—42no—
336Dic6—44no—
337Dic6—44no—
338C3×C8—22no—
339C3×C8—22no—
340C3×C8—42no—
341C3×C8—62no—
342C3⋊C8—22no—
343C2×C32C2×#12411yescharacteristic
344C2×C32C22×SD1611yescharacteristic
345C2×C32C22×Q1611yescharacteristic
346C3×D3#48714yesdirect product factor
347C2×Q8—21no—
348C2×Q8—32no—
349C2×Q8—62no—
350C2×Q8—62no—
351C2×Q8—68no—
352C2×Q8—61no—
353C2×Q8—124no—
354C2×Q8C22×C3×D312yes—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—62no—
359C22×C4—62no—
360C2×C8—32no—
361C2×C8—64no—
362C2×C8C22×C3×D312yes—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—32no—
367C4⋊C4—62no—
368C4⋊C4—62no—
369C4⋊C4—62no—
370C4⋊C4—62no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4C22×C3×D312yes—
375C42—31no—
376C42—31no—
377C42—31no—
378C42C22×C3×D311yescharacteristic
379C22×C3—21no—
380C22×C3—32no—
381C22×C3—32no—
382C22×C3—32no—
383C22×C3C2×D3×D411yescharacteristic
384C22×C3C22×C3×D411yescharacteristic
385C2×D3C3×#12412yes—
386C2×D3C2×C3×SD1612yes—
387C2×D3C2×C3×Q1612yes—
388C3×C4—22no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—32no—
392C3×C4—32no—
393C3×C4—32no—
394C3×C4—42no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—82no—
399C3×C4—82no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4D3×SD1612yes—
403C3×C4D3×Q1612yes—
404C3×C4C2×C3×SD1612yes—
405C3×C4C2×C3×Q1612yes—
406C3×C4D3×#4112yes—
407C3×C4C2×C3×#4112yes—
408Dic3—42no—
409Dic3—42no—
410Dic3C3×#12412yes—
411Dic3C2×C3×SD1612yes—
412Dic3C2×C3×Q1612yes—
413C32C2×#48711yescharacteristic, complemented, Sylow
414C23—31no—
415Q8—24no—
416Q8—42no—
417Q8—64no—
418Q8—124no—
419Q8—124no—
420Q8—122no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—31no—
426C2×C4—34no—
427C2×C4—34no—
428C2×C4—34no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—124no—
432C2×C4—124no—
433C2×C4C3×D3×D411yescharacteristic
434C2×C4C3×D3×D411yescharacteristic
435C2×C4C23×C3×D311yescharacteristic
436C8—22no—
437C8—62no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—34no—
442C2×C3D3×#12411yescharacteristic
443C2×C3C2×D3×SD1611yescharacteristic
444C2×C3C2×D3×Q1611yescharacteristic
445C2×C3C2×C3×#12411yescharacteristic
446C2×C3C22×C3×SD1611yescharacteristic
447C2×C3C22×C3×Q1611yescharacteristic
448D3C3×#48714yesdirect product factor
449C22—32no—
450C22—32no—
451C22—32no—
452C22C2×C3×D3×D411yescharacteristic
453C4—32no—
454C4—32no—
455C4—32no—
456C4—42no—
457C4—42no—
458C4—122no—
459C4—122no—
460C4C3×D3×SD1612yes—
461C4C3×D3×Q1612yes—
462C4C3×D3×#4112yes—
463C3—21no—
464C3D3×#48711yescharacteristic, direct product factor
465C3C2×C3×#48711yescharacteristic, complemented
466C2—34no—
467C2C3×D3×#12411yescharacteristic
468C2C2×C3×D3×SD1611yescharacteristic
469C2C2×C3×D3×Q1611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#487D3
hypocenterC3C2×C3×#487
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
3. C32×#487C2semidirect
4. C3×#5093C2semidirect
5. C3×#5079C2semidirect
7. C3×#4792C2semidirect
9. C3×#4681C2semidirect
11. D3×#487C3direct (N × H)
46. C3×#487D3direct (N × H)
47. C3×#487C2×C3semidirect
50. #5093C2×C3semidirect
51. #5079C2×C3semidirect
53. #4792C2×C3semidirect
55. #4681C2×C3semidirect
173. #487C3×D3direct (N × H)
346. C3×D3#487direct (N × H)
413. C32C2×#487semidirect
448. D3C3×#487direct (N × H)
464. C3D3×#487direct (N × H)
465. C3C2×C3×#487semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C32×#4872
C3×#50932
C3×#50792
C3×D3×#1032
C3×#47922
C3×C4×D3×C82
C3×#46812
C2×C3×#4873
D3×#4873