Finite Group Databasebeta

← D3×#4696 #11874248

Subgroups — D3×#4696 #11874248

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic, complemented
2C2×D3×D24C211yesmaximal, characteristic
3C2×D3×#204C212yesmaximal, complemented
4D3×#875C212yesmaximal, complemented
5#10592395C211yesmaximal, characteristic, complemented
6C3×#4696C211yesmaximal, characteristic, complemented
7C3×C4×D3×C8C211yesmaximal, characteristic, complemented
8#10590865C211yesmaximal, characteristic, complemented
9#10590864C211yesmaximal, characteristic, complemented
10#10590862C212yesmaximal, complemented
11#10590370C212yesmaximal, complemented
12D3×#495—31nomaximal
13C2×#4696—31nomaximal
14C2×D3×D12C2212yes—
15C2×D3×Dic6C2212yes—
16C2×#3746C2211yescharacteristic, complemented
17C2×#3745C2211yescharacteristic
18C2×#3744C2212yescomplemented
19#64084C2212yescomplemented
20C2×C3×Dic12C2211yescharacteristic, complemented
21C2×C3×D24C2211yescharacteristic
22C2×C3×#204C2212yescomplemented
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#875C2212yescomplemented
26C3×C42×D3C2211yescharacteristic
27D3×(C2×D3)⋊C4—24no—
28#63864C2212yescomplemented
29#63860C2212yescomplemented
30#63852—24no—
31C2×#3719C2212yescomplemented
32C2×#3717C2212yescomplemented
33C2×#3716C2212yescomplemented
34C2×#3714C2212yes—
35D3×Dic12—24no—
36D3×D24—24no—
37D3×#204—28no—
38C32×C4×C8C2211yescharacteristic, complemented
39C3×C8×Dic3C2211yescharacteristic, complemented
40C3×C8×Dic3C2211yescharacteristic, complemented
41C3×C4×C3⋊C8C2211yescharacteristic, complemented
42C2×D3×Q16—31no—
43C2×D3×SD16—32no—
44C2×D3×D8—31no—
45C22×Dic12—31no—
46C22×D24—31no—
47C22×#204—32no—
48D3×#124—32no—
49C2×#875—32no—
50C3×#495—31no—
51C2×C3×C4×C8—31no—
52#5191—31no—
53#5168—32no—
54#5155—31no—
55#5059—32no—
56#4696—31no—
57#4696—31no—
58#4696—32no—
59#4696—32no—
60#4696—31no—
61#4696—31no—
62#4696—61no—
63#4696D311yescharacteristic, direct product factor
64C4×D3×C8D311yescharacteristic, complemented
65C22×D32—22no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×#634C2312yes—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2311yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×#627—22no—
73C2×#626—22no—
74C2×D3×Dic3—22no—
75D3×D12—24no—
76D3×D12—24no—
77D3×Dic6—24no—
78D3×Dic6—24no—
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C32×C42C2311yescharacteristic
82#3752—24no—
83#3746—22no—
84#3745—22no—
85#3744—24no—
86C3×(C2×D3)⋊C4—24no—
87C3×C4×Dic3D412yes—
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×Dic12—22no—
92C3×D24—22no—
93C3×#204—24no—
94C3×D3×C8D414yes—
95C3×D3×C8D414yes—
96#3722—24no—
97(C2×D3)⋊Dic3—24no—
98#3719—24no—
99#3717—24no—
100#3716—24no—
101#3714—24no—
102C2×#495—91noSylow
103C2×D3×Q8—32no—
104C2×D3×D4—32no—
105C22×D12—32no—
106C22×Dic6—32no—
107C2×C3×Q16—31no—
108C2×C3×SD16—32no—
109C2×C3×D8—31no—
110C22×C3×C8—31no—
111C22×C3×C8—31no—
112C3×#124—32no—
113C2×C3×C42—31no—
114#947—32no—
115C2×#216—32no—
116C2×#215—32no—
117#936—32no—
118C2×#214—32no—
119C2×#213—32no—
120C2×(C2×D3)⋊C4—64no—
121D3×Q16—64no—
122D3×SD16—68no—
123D3×D8—64no—
124C2×Dic12—32no—
125C2×Dic12—31no—
126C2×Dic12—31no—
127C2×Dic12—61no—
128C2×Dic12—64no—
129C2×Dic12C2×D311yescharacteristic, complemented
130C2×D24—32no—
131C2×D24—31no—
132C2×D24—31no—
133C2×D24—61no—
134C2×D24—64no—
135C2×D24C2×D311yescharacteristic
136C2×#204—32no—
137C2×#204—32no—
138C2×#204—32no—
139C2×#204—32no—
140C2×#204—62no—
141C2×#204—68no—
142C2×#204C2×D312yescomplemented
143C2×D3×C8C2×D311yescharacteristic
144C2×D3×C8C2×D311yescharacteristic
145#885—64no—
146D3×C22⋊C4—64no—
147#875—32no—
148#875—32no—
149#875—32no—
150#875—32no—
151#875—62no—
152#875—64no—
153#875C2×D312yescomplemented
154C42×D3C2×D311yescharacteristic
155C3×C4×C8—21no—
156C3×C4×C8—31no—
157C3×C4×C8—31no—
158C3×C4×C8—31no—
159C3×C4×C8C2×D311yescharacteristic, complemented
160C3×C4×C8C2×D311yescharacteristic, complemented
161C8×Dic3C2×D311yescharacteristic, complemented
162C8×Dic3C2×D311yescharacteristic, complemented
163C4×C3⋊C8C2×D311yescharacteristic, complemented
164C22×C3⋊D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3C2×D411yescharacteristic
167C2×D32—44no—
168C2×D32—48no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—22no—
174#634—22no—
175#634—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D411yescharacteristic
179C3×D12—22no—
180C3×D12—22no—
181C3×C4×D3—24no—
182C3×C4×D3C2×D412yes—
183C3×C4×D3C2×D412yes—
184C3×Dic6—22no—
185C3×Dic6—22no—
186#627—44no—
187#626—44no—
188D3×Dic3—44no—
189C32×C8C2×D412yes—
190C32×C8C2×D412yes—
191C3×C3⋊C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C22×Q16—91no—
194C22×SD16—92no—
195C22×D8—91no—
196C2×#124—92no—
197#495—31no—
198#495—92no—
199#495—91no—
200#495—92no—
201#495—91no—
202#495—91no—
203C2×C4×C8—31no—
204C23×D3—62no—
205C23×D3—62no—
206C2×C3×Q8—32no—
207C2×C3×D4—32no—
208C22×C3×C4—31no—
209C22×C3×C4—32no—
210C2×#67—62no—
211C22×Dic3—62no—
212D3×Q8—64no—
213D3×Q8—64no—
214D3×D4—64no—
215D3×D4—64no—
216C2×D12—32no—
217C2×D12—32no—
218C2×D12—62no—
219C2×D12—64no—
220C2×D12—64no—
221C2×D12—62no—
222C2×D12C22×D312yes—
223C2×C4×D3—62no—
224C2×C4×D3D1212yes—
225C2×C4×D3C22×D311yescharacteristic
226C2×Dic6—32no—
227C2×Dic6—32no—
228C2×Dic6—62no—
229C2×Dic6—64no—
230C2×Dic6—64no—
231C2×Dic6—62no—
232C2×Dic6—62no—
233C2×Dic6C22×D312yes—
234C3×Q16—62no—
235C3×SD16—64no—
236C3×D8—62no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—31no—
240C2×C3×C8—31no—
241C2×C3×C8—34no—
242C2×C3×C8—34no—
243C2×C3×C8C22×D311yescharacteristic
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C22⋊C4—64no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42—31no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#217—64no—
254#216—64no—
255#215—64no—
256#214—64no—
257#213—64no—
258(C2×D3)⋊C4—24no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—124no—
265C4×Dic3D1212yes—
266C4×Dic3C22×D311yescharacteristic
267C2×C3⋊C8C22×D311yescharacteristic
268C2×C3⋊C8C22×D311yescharacteristic
269Dic12—22no—
270Dic12—64no—
271Dic12—62no—
272Dic12—62no—
273Dic12—122no—
274D24—22no—
275D24—64no—
276D24—62no—
277D24—62no—
278D24—122no—
279#204—24no—
280#204—64no—
281#204—64no—
282#204—64no—
283#204—64no—
284#204—124no—
285D3×C8D1214yes—
286D3×C8D1214yes—
287C22×C32C22×D411yescharacteristic
288C2×C3⋊D3—42no—
289C2×C3⋊D3—44no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3#12712yes—
293C2×C3×D3#13514yes—
294D32—88no—
295C32×C4—22no—
296C32×C4C22×D411yescharacteristic
297C32×C4C22×D411yescharacteristic
298C3⋊Dic3—42no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3#12712yes—
302C22×Q8—92no—
303C22×D4—92no—
304C2×Q16—31no—
305C2×Q16—92no—
306C2×Q16—91no—
307C2×Q16—184no—
308C2×SD16—32no—
309C2×SD16—92no—
310C2×SD16—92no—
311C2×SD16—92no—
312C2×SD16—188no—
313C2×D8—31no—
314C2×D8—92no—
315C2×D8—91no—
316C2×D8—184no—
317C22×C8—31no—
318C22×C8—31no—
319#124—32no—
320#124—92no—
321#124—92no—
322#124—92no—
323#124—184no—
324C2×C22⋊C4—184no—
325C2×C42—31no—
326C4×C8—31no—
327C4×C8—31no—
328C4×C8—31no—
329C4×C8D3211yescharacteristic, complemented
330C23×C3—31no—
331C23×C3—62no—
332C22×D3—22no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—122no—
336C22×D3—124no—
337C22×D3—128no—
338C22×D3—124no—
339C22×D3—128no—
340C22×D3C2×D1211yescharacteristic
341C3×Q8—62no—
342C3×Q8—62no—
343C3×D4—62no—
344C3×D4—62no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—31no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—64no—
352C2×C3×C4—62no—
353C2×C3×C4C2×D1212yes—
354C2×C3×C4D3×D412yes—
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—124no—
358C2×Dic3—22no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—122no—
362C2×Dic3—124no—
363C2×Dic3C2×D1212yes—
364C2×Dic3C2×D1211yescharacteristic
365D12—22no—
366D12—22no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—62no—
371D12—122no—
372D12—122no—
373D12—124no—
374C4×D3—24no—
375C4×D3—124no—
376C4×D3C2×D1212yes—
377C4×D3C2×D1212yes—
378Dic6—22no—
379Dic6—22no—
380Dic6—62no—
381Dic6—62no—
382Dic6—62no—
383Dic6—62no—
384Dic6—122no—
385Dic6—122no—
386Dic6—124no—
387Dic6—124no—
388C3×C8—22no—
389C3×C8—22no—
390C3×C8—32no—
391C3×C8—32no—
392C3×C8C2×D1212yes—
393C3×C8C2×D1212yes—
394C3×C8D3×D412yes—
395C3×C8D3×D412yes—
396C3⋊C8C2×D1212yes—
397C3⋊C8C2×D1212yes—
398C2×C32C2×#12711yescharacteristic
399C2×C32C2×#13512yes—
400C3⋊D3—82no—
401C3×D3—82no—
402C3×D3#49514yescomplemented
403C24—182no—
404C2×Q8—32no—
405C2×Q8—92no—
406C2×Q8—182no—
407C2×Q8—184no—
408C2×Q8—184no—
409C2×D4—32no—
410C2×D4—92no—
411C2×D4—184no—
412C2×D4—184no—
413C2×D4—182no—
414C22×C4—31no—
415C22×C4—32no—
416C22×C4—182no—
417Q16—62no—
418Q16—184no—
419Q16—182no—
420SD16—64no—
421SD16—184no—
422SD16—184no—
423SD16—184no—
424D8—62no—
425D8—184no—
426D8—182no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—34no—
430C2×C8—34no—
431C2×C8C2×D3211yescharacteristic
432C2×C8C2×D3211yescharacteristic
433C22⋊C4—64no—
434C22⋊C4—184no—
435C22⋊C4—184no—
436C22⋊C4—184no—
437C42—31no—
438C42—32no—
439C42C2×D3211yescharacteristic
440C22×C3—21no—
441C22×C3—32no—
442C22×C3—34no—
443C22×C3—122no—
444C22×C3—124no—
445C22×C3C22×D1211yescharacteristic
446C22×C3C2×D3×D411yescharacteristic
447C2×D3—42no—
448C2×D3—44no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—124no—
452C2×D3—124no—
453C2×D3—242no—
454C2×D3—244no—
455C2×D3—248no—
456C2×D3—248no—
457C2×D3#87412yes—
458C2×D3#90414yes—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—32no—
464C3×C4—42no—
465C3×C4—62no—
466C3×C4—122no—
467C3×C4C22×D1211yescharacteristic
468C3×C4C22×D1211yescharacteristic
469C3×C4C2×D3×D411yescharacteristic
470C3×C4C2×D3×D411yescharacteristic
471Dic3—22no—
472Dic3—42no—
473Dic3—122no—
474Dic3—122no—
475Dic3—242no—
476Dic3#87412yes—
477C32C2×#49511yescharacteristic, complemented, Sylow
478C23—31no—
479C23—62no—
480C23—182no—
481C23—364no—
482C23—368no—
483Q8—62no—
484Q8—62no—
485Q8—182no—
486Q8—182no—
487Q8—364no—
488D4—62no—
489D4—62no—
490D4—182no—
491D4—182no—
492D4—364no—
493C2×C4—31no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—64no—
498C2×C4—62no—
499C2×C4—182no—
500C2×C4—364no—
501C2×C4D3×D1212yes—
502C2×C4C22×D3211yescharacteristic
503C8—32no—
504C8—32no—
505C8D3×D1212yes—
506C8D3×D1212yes—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—34no—
510C2×C3—242no—
511C2×C3C2×#87411yescharacteristic
512C2×C3D3×#12711yescharacteristic
513C2×C3C2×#90412yes—
514C2×C3D3×#13512yes—
515D3—82no—
516D3—242no—
517D3—242no—
518D3—482no—
519D3#469614yesdirect product factor
520C22—34no—
521C22—32no—
522C22—124no—
523C22—122no—
524C22—364no—
525C22—362no—
526C22—728no—
527C22C2×D3×D1211yescharacteristic
528C4—22no—
529C4—32no—
530C4—62no—
531C4—122no—
532C4—362no—
533C4C2×D3×D1211yescharacteristic
534C4C2×D3×D1211yescharacteristic
535C3—21no—
536C3C2×#469611yescharacteristic, complemented
537C3D3×#49511yescharacteristic, complemented
538C2—34no—
539C2—242no—
540C2—722no—
541C2D3×#87411yescharacteristic
542C2D3×#90412yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D24C2
hypercenterC4×C8D32
hypocenterC32C2×#495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
3. C2×D3×#204C2semidirect
4. D3×#875C2semidirect
5. #10592395C2semidirect
6. C3×#4696C2semidirect
7. C3×C4×D3×C8C2semidirect
8. #10590865C2semidirect
9. #10590864C2semidirect
10. #10590862C2semidirect
11. #10590370C2semidirect
16. C2×#3746C22semidirect
18. C2×#3744C22semidirect
19. #64084C22semidirect
20. C2×C3×Dic12C22semidirect
22. C2×C3×#204C22semidirect
25. C3×#875C22semidirect
28. #63864C22semidirect
29. #63860C22semidirect
31. C2×#3719C22semidirect
32. C2×#3717C22semidirect
33. C2×#3716C22semidirect
38. C32×C4×C8C22semidirect
39. C3×C8×Dic3C22semidirect
40. C3×C8×Dic3C22semidirect
41. C3×C4×C3⋊C8C22semidirect
63. #4696D3direct (N × H)
64. C4×D3×C8D3semidirect
129. C2×Dic12C2×D3semidirect
142. C2×#204C2×D3semidirect
153. #875C2×D3semidirect
159. C3×C4×C8C2×D3semidirect
160. C3×C4×C8C2×D3semidirect
161. C8×Dic3C2×D3semidirect
162. C8×Dic3C2×D3semidirect
163. C4×C3⋊C8C2×D3semidirect
329. C4×C8D32semidirect
402. C3×D3#495semidirect
477. C32C2×#495semidirect
519. D3#4696direct (N × H)
536. C3C2×#4696semidirect
537. C3D3×#495semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×D3×D242
C2×D3×#2042
D3×#8752
#105923952
C3×#46962
C3×C4×D3×C82
#105908652
#105908642
#105908622
#105903702
D3×#4953
C2×#46963