Finite Group Databasebeta

← C3×D3×#488 #11873421

Subgroups — C3×D3×#488 #11873421

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#125C211yesmaximal, characteristic, complemented
2C3×D3×#124C211yesmaximal, characteristic
3C32×#488C211yesmaximal, characteristic, complemented
4C3×#5068C211yesmaximal, characteristic, complemented
5C3×#5056C211yesmaximal, characteristic, complemented
6C3×D3×#103C212yesmaximal, complemented
7C3×#4800C212yesmaximal, complemented
8C3×D3×#102C212yesmaximal
9C3×#4768C212yesmaximal, complemented
10C3×#4697C211yesmaximal, characteristic, complemented
11C3×C4×D3×C8C211yesmaximal, characteristic, complemented
12C2×C3×#488—31nomaximal
13D3×#488C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2211yescharacteristic
15C2×C3×D3×D4C2211yescharacteristic
16C32×#125C2211yescharacteristic, complemented
17C32×#124C2211yescharacteristic
18C3×#947C2211yescharacteristic
19C3×#936C2211yescharacteristic
20C2×C3×D3×C8C2212yes—
21C3×D3×C4⋊C4—22no—
22C3×D3×C4⋊C4C2212yes—
23C3×#890C2212yescomplemented
24C3×#889—22no—
25C3×#885—22no—
26C3×D3×C22⋊C4—22no—
27C3×#875C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×#870C2211yescharacteristic, complemented
30C32×#103C2212yescomplemented
31C32×#102C2212yes—
32C32×C4×C8C2211yescharacteristic, complemented
33C3×#835C2212yescomplemented
34C3×#832C2212yes—
35C3×#821C2212yes—
36C3×#816C2212yescomplemented
37C3×C8×Dic3C2212yescomplemented
38C3×#810C2212yescomplemented
39C3×#809C2212yes—
40C3×C4×C3⋊C8C2211yescharacteristic, complemented
41C2×C3×#125—31no—
42C2×C3×#124—31no—
43D3×#125C2×C311yescharacteristic, complemented
44D3×#124C2×C311yescharacteristic
45C3×#488—21no—
46C3×#488—31no—
47C3×#488—31no—
48C3×#488—32no—
49C3×#488—32no—
50C3×#488—31no—
51C3×#488D311yescharacteristic, direct product factor
52C3×#488C2×C311yescharacteristic, complemented
53C2×C3×#103—32no—
54C2×C3×#102—32no—
55C2×C3×C4×C8—31no—
56#5068C2×C311yescharacteristic, complemented
57#5056C2×C311yescharacteristic, complemented
58D3×#103C2×C312yescomplemented
59#4800C2×C312yescomplemented
60D3×#102C2×C312yes—
61#4768C2×C312yescomplemented
62#4697C2×C311yescharacteristic, complemented
63C4×D3×C8C2×C311yescharacteristic, complemented
64C23×C3×D3—21no—
65C2×C32×Q8C2311yescharacteristic
66C2×C32×D4C2311yescharacteristic
67C2×C3×#67—21no—
68C3×D3×Q8—24no—
69C3×D3×D4—24no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D412yes—
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2311yescharacteristic
77C2×C32×C8C2312yes—
78C32×C4⋊C4—22no—
79C32×C4⋊C4C2312yes—
80C32×C22⋊C4—22no—
81C32×C42C2311yescharacteristic
82C3×#217—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×C4×Dic3D412yes—
91C3×C4×Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93C3×D3×C8—24no—
94C2×#488—31noSylow
95C22×C3×Q8—31no—
96C22×C3×D4—31no—
97C2×D3×Q8C22×C311yescharacteristic
98C2×D3×D4C22×C311yescharacteristic
99C22×C3×C8—32no—
100C3×#125—21no—
101C3×#125—32no—
102C3×#125—31no—
103C3×#125—62no—
104C3×#125C2×D311yescharacteristic, complemented
105C3×#125C22×C311yescharacteristic, complemented
106C3×#124—21no—
107C3×#124—31no—
108C3×#124—31no—
109C3×#124—31no—
110C3×#124—62no—
111C3×#124C2×D311yescharacteristic
112C3×#124C22×C311yescharacteristic
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4—62no—
115C2×C3×C22⋊C4—62no—
116C2×C3×C42—31no—
117#947C22×C311yescharacteristic
118#936C22×C311yescharacteristic
119C2×D3×C8C22×C312yes—
120D3×C4⋊C4—22no—
121D3×C4⋊C4C22×C312yes—
122#890C22×C312yescomplemented
123#889—22no—
124#885—22no—
125D3×C22⋊C4—22no—
126#875C22×C311yescharacteristic
127C42×D3C22×C311yescharacteristic
128#870C22×C311yescharacteristic, complemented
129C3×#103—22no—
130C3×#103—32no—
131C3×#103—32no—
132C3×#103—32no—
133C3×#103C2×D312yescomplemented
134C3×#103C22×C312yescomplemented
135C3×#102—22no—
136C3×#102—32no—
137C3×#102—32no—
138C3×#102—32no—
139C3×#102C2×D312yes—
140C3×#102C22×C312yes—
141C3×C4×C8—21no—
142C3×C4×C8—32no—
143C3×C4×C8—31no—
144C3×C4×C8C2×D311yescharacteristic, complemented
145C3×C4×C8C22×C311yescharacteristic, complemented
146#835C22×C312yescomplemented
147#832C22×C312yes—
148#821C22×C312yes—
149#816C22×C312yescomplemented
150C8×Dic3C22×C312yescomplemented
151#810C22×C312yescomplemented
152#809C22×C312yes—
153C4×C3⋊C8C22×C311yescharacteristic, complemented
154C23×C32—21no—
155C22×C3×D3—21no—
156C22×C3×D3—42no—
157C22×C3×D3—44no—
158C22×C3×D3C2×D411yescharacteristic
159C32×Q8—22no—
160C32×D4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—21no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2411yescharacteristic
165C3×#67—42no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×C4×D3—24no—
172C3×C4×D3—42no—
173C3×C4×D3—44no—
174C3×C4×D3#4114yes—
175C3×Dic6—22no—
176C3×Dic6—42no—
177C32×C8—22no—
178C3×C3⋊C8—22no—
179C2×#125—31no—
180C2×#124—31no—
181#488—31no—
182#488—31no—
183#488—32no—
184#488—32no—
185#488—31no—
186#488C3×D311yescharacteristic, direct product factor
187C2×#103—32no—
188C2×#102—32no—
189C2×C4×C8—31no—
190C24×C3—61no—
191C23×D3—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—31no—
194C2×C3×Q8—61no—
195C2×C3×Q8—64no—
196C2×C3×Q8C22×D311yescharacteristic
197C2×C3×Q8C23×C311yescharacteristic
198C2×C3×D4—21no—
199C2×C3×D4—31no—
200C2×C3×D4—64no—
201C2×C3×D4—61no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C23×C311yescharacteristic
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—61no—
207C22×C3×C4—62no—
208C2×#67—21no—
209D3×Q8—24no—
210D3×D4—24no—
211C2×D12C23×C311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—22no—
214C2×C4×D3C3×D412yes—
215C2×C4×D3C23×C311yescharacteristic
216C2×Dic6—21no—
217C2×Dic6C23×C311yescharacteristic
218C2×C3×C8—22no—
219C2×C3×C8—32no—
220C2×C3×C8—64no—
221C2×C3×C8C22×D312yes—
222C2×C3×C8C23×C312yes—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—42no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4C22×D312yes—
233C3×C4⋊C4C23×C312yes—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—42no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42—31no—
243C3×C42C22×D311yescharacteristic
244C3×C42C23×C311yescharacteristic
245#217—22no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—22no—
248C4⋊Dic3—22no—
249C4⋊Dic3C23×C312yes—
250Dic3⋊C4—22no—
251Dic3⋊C4—22no—
252Dic3⋊C4—22no—
253C4×Dic3C3×D412yes—
254C4×Dic3C23×C311yescharacteristic
255C2×C3⋊C8C23×C312yes—
256D3×C8—24no—
257C22×C32—41no—
258C22×C32—42no—
259C22×C32C22×D411yescharacteristic
260C2×C3×D3—41no—
261C2×C3×D3—42no—
262C2×C3×D3—84no—
263C2×C3×D3#12412yes—
264C2×C3×D3#13514yes—
265C32×C4—22no—
266C32×C4—41no—
267C32×C4—42no—
268C32×C4C2×#4112yes—
269C3×Dic3—22no—
270C3×Dic3—41no—
271C3×Dic3—42no—
272C3×Dic3#12412yes—
273C22×Q8—31no—
274C22×D4—31no—
275C22×C8—32no—
276#125—32no—
277#125—31no—
278#125—62no—
279#125C2×C3×D311yescharacteristic, complemented
280#124—31no—
281#124—31no—
282#124—31no—
283#124—62no—
284#124C2×C3×D311yescharacteristic
285C2×C4⋊C4—32no—
286C2×C4⋊C4—62no—
287C2×C22⋊C4—62no—
288C2×C42—31no—
289#103—32no—
290#103—32no—
291#103—32no—
292#103C2×C3×D312yescomplemented
293#102—32no—
294#102—32no—
295#102—32no—
296#102C2×C3×D312yes—
297C4×C8—32no—
298C4×C8—31no—
299C4×C8C2×C3×D311yescharacteristic, complemented
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—31no—
303C23×C3—41no—
304C23×C3—61no—
305C23×C3—122no—
306C23×C3—124no—
307C22×D3—21no—
308C22×D3—42no—
309C22×D3—44no—
310C22×D3C2×C3×D411yescharacteristic
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—42no—
314C3×Q8—62no—
315C3×Q8—122no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—42no—
319C3×D4—62no—
320C3×D4—122no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—31no—
328C2×C3×C4—34no—
329C2×C3×C4—32no—
330C2×C3×C4—41no—
331C2×C3×C4—42no—
332C2×C3×C4—64no—
333C2×C3×C4—61no—
334C2×C3×C4—62no—
335C2×C3×C4—124no—
336C2×C3×C4—122no—
337C2×C3×C4D3×D412yes—
338C2×C3×C4C2×C3×D412yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C24×C311yescharacteristic
341#67—42no—
342C2×Dic3—22no—
343C2×Dic3—21no—
344C2×Dic3C2×C3×D412yes—
345C2×Dic3C2×C3×D411yescharacteristic
346D12—22no—
347C4×D3—24no—
348C4×D3—42no—
349C4×D3—44no—
350C4×D3C3×#4114yes—
351Dic6—22no—
352Dic6—42no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—42no—
356C3×C8—62no—
357C3⋊C8—22no—
358C2×C32—81no—
359C2×C32C2×#12411yescharacteristic
360C2×C32C2×#13512yes—
361C3×D3—81no—
362C3×D3#48814yesdirect product factor
363C24—61no—
364C2×Q8—31no—
365C2×Q8—61no—
366C2×Q8—64no—
367C2×Q8C22×C3×D311yescharacteristic
368C2×D4—31no—
369C2×D4—64no—
370C2×D4—61no—
371C2×D4C22×C3×D311yescharacteristic
372C22×C4—31no—
373C22×C4—32no—
374C22×C4—61no—
375C22×C4—62no—
376C2×C8—32no—
377C2×C8—64no—
378C2×C8C22×C3×D312yes—
379C4⋊C4—22no—
380C4⋊C4—32no—
381C4⋊C4—62no—
382C4⋊C4—62no—
383C4⋊C4—62no—
384C4⋊C4—62no—
385C4⋊C4C22×C3×D312yes—
386C22⋊C4—22no—
387C22⋊C4—62no—
388C22⋊C4—62no—
389C22⋊C4—62no—
390C42—31no—
391C42—32no—
392C42C22×C3×D311yescharacteristic
393C22×C3—21no—
394C22×C3—32no—
395C22×C3—34no—
396C22×C3—42no—
397C22×C3—41no—
398C22×C3—42no—
399C22×C3—41no—
400C22×C3—81no—
401C22×C3—82no—
402C22×C3—121no—
403C22×C3—122no—
404C22×C3—244no—
405C22×C3C2×D3×D411yescharacteristic
406C22×C3C22×C3×D411yescharacteristic
407C2×D3—42no—
408C2×D3—41no—
409C2×D3—84no—
410C2×D3C3×#12412yes—
411C2×D3C3×#13514yes—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—32no—
416C3×C4—42no—
417C3×C4—42no—
418C3×C4—41no—
419C3×C4—42no—
420C3×C4—41no—
421C3×C4—62no—
422C3×C4—81no—
423C3×C4—82no—
424C3×C4—121no—
425C3×C4—122no—
426C3×C4D3×#4112yes—
427C3×C4C2×C3×#4112yes—
428Dic3—22no—
429Dic3—42no—
430Dic3—41no—
431Dic3C3×#12412yes—
432C32C2×#48811yescharacteristic, complemented, Sylow
433C23—21no—
434C23—31no—
435C23—61no—
436C23—122no—
437C23—124no—
438Q8—22no—
439Q8—62no—
440Q8—122no—
441D4—22no—
442D4—62no—
443D4—122no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—31no—
447C2×C4—34no—
448C2×C4—32no—
449C2×C4—64no—
450C2×C4—61no—
451C2×C4—62no—
452C2×C4—122no—
453C2×C4—124no—
454C2×C4C3×D3×D412yes—
455C2×C4C23×C3×D311yescharacteristic
456C8—22no—
457C8—62no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—34no—
461C2×C3—81no—
462C2×C3—81no—
463C2×C3—161no—
464C2×C3—241no—
465C2×C3D3×#12411yescharacteristic
466C2×C3D3×#13512yes—
467C2×C3C2×C3×#12411yescharacteristic
468C2×C3C2×C3×#13512yes—
469D3—81no—
470D3C3×#48814yesdirect product factor
471C22—34no—
472C22—32no—
473C22—42no—
474C22—41no—
475C22—122no—
476C22—121no—
477C22—244no—
478C22C2×C3×D3×D411yescharacteristic
479C4—22no—
480C4—32no—
481C4—42no—
482C4—41no—
483C4—62no—
484C4—122no—
485C4—121no—
486C4C3×D3×#4112yes—
487C3—21no—
488C3D3×#48811yescharacteristic, direct product factor
489C3C2×C3×#48811yescharacteristic, complemented
490C2—34no—
491C2—81no—
492C2—241no—
493C2C3×D3×#12411yescharacteristic
494C2C3×D3×#13512yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#488C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC3×#488D3
hypocenterC3C2×C3×#488
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
1. C3×D3×#125C2semidirect
3. C32×#488C2semidirect
4. C3×#5068C2semidirect
5. C3×#5056C2semidirect
6. C3×D3×#103C2semidirect
7. C3×#4800C2semidirect
9. C3×#4768C2semidirect
10. C3×#4697C2semidirect
11. C3×C4×D3×C8C2semidirect
13. D3×#488C3direct (N × H)
16. C32×#125C22semidirect
23. C3×#890C22semidirect
29. C3×#870C22semidirect
30. C32×#103C22semidirect
32. C32×C4×C8C22semidirect
33. C3×#835C22semidirect
36. C3×#816C22semidirect
37. C3×C8×Dic3C22semidirect
38. C3×#810C22semidirect
40. C3×C4×C3⋊C8C22semidirect
43. D3×#125C2×C3semidirect
51. C3×#488D3direct (N × H)
52. C3×#488C2×C3semidirect
56. #5068C2×C3semidirect
57. #5056C2×C3semidirect
58. D3×#103C2×C3semidirect
59. #4800C2×C3semidirect
61. #4768C2×C3semidirect
62. #4697C2×C3semidirect
63. C4×D3×C8C2×C3semidirect
104. C3×#125C2×D3semidirect
105. C3×#125C22×C3semidirect
122. #890C22×C3semidirect
128. #870C22×C3semidirect
133. C3×#103C2×D3semidirect
134. C3×#103C22×C3semidirect
144. C3×C4×C8C2×D3semidirect
145. C3×C4×C8C22×C3semidirect
146. #835C22×C3semidirect
149. #816C22×C3semidirect
150. C8×Dic3C22×C3semidirect
151. #810C22×C3semidirect
153. C4×C3⋊C8C22×C3semidirect
186. #488C3×D3direct (N × H)
279. #125C2×C3×D3semidirect
292. #103C2×C3×D3semidirect
299. C4×C8C2×C3×D3semidirect
362. C3×D3#488direct (N × H)
432. C32C2×#488semidirect
470. D3C3×#488direct (N × H)
488. C3D3×#488direct (N × H)
489. C3C2×C3×#488semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1252
C3×D3×#1242
C32×#4882
C3×#50682
C3×#50562
C3×D3×#1032
C3×#48002
C3×D3×#1022
C3×#47682
C3×#46972
C3×C4×D3×C82
C2×C3×#4883
D3×#4883