Finite Group Databasebeta

← D3×#4860 #11858427

Subgroups — D3×#4860 #11858427

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×C8C211yesmaximal, characteristic
2D3×#892C212yesmaximal
3#10592559C211yesmaximal, characteristic, complemented
4C3×#4860C211yesmaximal, characteristic, complemented
5C3×D3×#106C211yesmaximal, characteristic, complemented
6#10590712C211yesmaximal, characteristic, complemented
7#10590706C211yesmaximal, characteristic, complemented
8D3×#817C211yesmaximal, characteristic, complemented
9#10590574C212yesmaximal, complemented
10#10590572C212yesmaximal, complemented
11D3×#807C212yesmaximal, complemented
12D3×#427—31nomaximal
13C2×#4860—31nomaximal
14C2×C4×D32C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16#64101C2212yes—
17C2×C3×D3×C8C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×#892C2212yes—
20C3×D3×C4⋊C4C2212yes—
21D3×(C2×D3)⋊C4—22no—
22D3×C4⋊Dic3C2212yes—
23#63878—22no—
24C4×D3×Dic3—22no—
25#63849C2212yes—
26#63841C2212yes—
27#63836—22no—
28C2×#3710C2211yescharacteristic
29C2×D3×C3⋊C8C2211yescharacteristic
30C2×D3×C3⋊C8C2211yescharacteristic
31D32×C8C418yescomplemented
32C32×#106C2211yescharacteristic, complemented
33#63644C2211yescharacteristic, complemented
34#63634C2212yescomplemented
35C3×#817C2211yescharacteristic, complemented
36C3×#817C2211yescharacteristic, complemented
37C3×#808C2212yescomplemented
38C3×#807C2212yescomplemented
39#63576C2212yescomplemented
40#63575C2212yescomplemented
41#63573C2212yescomplemented
42C22×D3×C8—31no—
43C22×D3×C8—31no—
44D3×#117—32no—
45C2×#892—32no—
46C3×#427—31no—
47C2×C3×#106—31no—
48#5106—31no—
49C2×#817—31no—
50#4998—32no—
51C2×#807—32no—
52#4880—32no—
53D3×#107—32no—
54#4860—31no—
55#4860—32no—
56#4860—31no—
57#4860—31no—
58#4860—31no—
59#4860—31no—
60#4860—32no—
61#4860—61no—
62#4860D311yescharacteristic, direct product factor
63D3×#106—31no—
64D3×#106D311yescharacteristic, complemented
65C22×D32D411yescharacteristic
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×C4×D3C2311yescharacteristic
70C2×#624D411yescharacteristic
71C2×D3×Dic3—22no—
72C2×D3×Dic3D411yescharacteristic
73C2×D3×Dic3D411yescharacteristic
74C4×D32C2×C414yes—
75C4×D32Q814yes—
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4C2312yes—
78#3752—22no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4×C3⋊Dic3—22no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C8×C3⋊D3C2×C414yescomplemented
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3—22no—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C3×D3×C8C2×C414yes—
91C3×D3×C8C2×C414yescomplemented
92Dic3⋊Dic3—22no—
93#3722—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96Dic32—22no—
97#3710C2×C414yescomplemented
98D3×C3⋊C8C2×C414yes—
99D3×C3⋊C8C2×C414yescomplemented
100C2×#427—91noSylow
101C22×C4×D3—31no—
102C22×C4×D3—31no—
103C22×C3×C8—31no—
104C22×C3×C8—31no—
105C3×#117—32no—
106C2×C3×C4⋊C4—32no—
107C2×(C2×D3)⋊C4—62no—
108#926—32no—
109C2×C4⋊Dic3—32no—
110C2×C4×Dic3—62no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C2×D3×C8—31no—
114C2×D3×C8—31no—
115C2×D3×C8—31no—
116C2×D3×C8—31no—
117C2×D3×C8—31no—
118C2×D3×C8—31no—
119C2×D3×C8—38no—
120C2×D3×C8—38no—
121C2×D3×C8—61no—
122C2×D3×C8C2×D311yescharacteristic
123C2×D3×C8C2×D311yescharacteristic
124#892—32no—
125#892—32no—
126#892—32no—
127#892—32no—
128#892—32no—
129#892—62no—
130#892—62no—
131#892—62no—
132#892C2×D312yes—
133D3×C4⋊C4—32no—
134D3×C4⋊C4C2×D312yes—
135D3×C22⋊C4—62no—
136#877—62no—
137#872—62no—
138C42×D3—62no—
139C3×#107—32no—
140C3×#106—21no—
141C3×#106—31no—
142C3×#106—31no—
143C3×#106—32no—
144C3×#106C2×D311yescharacteristic, complemented
145C3×#106C2×D311yescharacteristic, complemented
146#818—32no—
147#817—31no—
148#817—31no—
149#817—32no—
150#817—61no—
151#817C2×D311yescharacteristic, complemented
152#817C2×D311yescharacteristic, complemented
153#808—32no—
154#808C2×D312yescomplemented
155#807—32no—
156#807—32no—
157#807—32no—
158#807—32no—
159#807—32no—
160#807—62no—
161#807C2×D312yescomplemented
162C22×C3⋊D3C2×D411yescharacteristic
163C22×C3×D3C2×D411yescharacteristic
164C22×C3×D3C2×D411yescharacteristic
165C2×D32—24no—
166C2×D32C4⋊C414yes—
167C2×C32×C4—22no—
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C2×D411yescharacteristic
171C4×C3⋊D3C22×C412yes—
172C4×C3⋊D3C2×Q812yes—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D411yescharacteristic
176C2×C3×Dic3C2×D411yescharacteristic
177C3×C4×D3—44no—
178C3×C4×D3C22×C412yes—
179C3×C4×D3C22×C412yes—
180C3×C4×D3C2×Q812yes—
181C3×C4×D3C2×Q812yes—
182#624C4⋊C414yes—
183D3×Dic3—44no—
184D3×Dic3C4⋊C414yes—
185D3×Dic3C4⋊C414yes—
186C32×C8C22×C412yes—
187C3⋊(C3⋊C8)C22×C412yes—
188C3×C3⋊C8C22×C412yes—
189C3×C3⋊C8C22×C412yes—
190C23×C8—91no—
191C2×#117—92no—
192#427—31no—
193#427—91no—
194#427—92no—
195#427—92no—
196#427—91no—
197#427—91no—
198C2×#107—92no—
199C2×#106—31no—
200C2×#106—91no—
201C23×D3—31no—
202C23×D3—31no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—62no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—62no—
209C2×C4×D3—22no—
210C2×C4×D3—31no—
211C2×C4×D3—31no—
212C2×C4×D3—31no—
213C2×C4×D3—31no—
214C2×C4×D3—31no—
215C2×C4×D3—31no—
216C2×C4×D3—34no—
217C2×C4×D3—34no—
218C2×C4×D3—34no—
219C2×C4×D3—34no—
220C2×C4×D3—61no—
221C2×C4×D3—62no—
222C2×C4×D3C22×D311yescharacteristic
223C2×C4×D3C22×D311yescharacteristic
224C2×C3×C8—21no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C2×C3×C8—34no—
228C2×C3×C8—34no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C3×C4⋊C4—22no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4C22×D312yes—
236C3×C4⋊C4C22×D312yes—
237C3×C22⋊C4—62no—
238C3×C42—62no—
239#217—62no—
240(C2×D3)⋊C4—22no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—122no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3C22×D312yes—
252C4⋊Dic3C22×D312yes—
253Dic3⋊C4—22no—
254Dic3⋊C4—62no—
255C4×Dic3—22no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—122no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8C22×D311yescharacteristic
269C2×C3⋊C8C22×D311yescharacteristic
270D3×C8—34no—
271D3×C8—34no—
272D3×C8—34no—
273D3×C8—34no—
274D3×C8—34no—
275D3×C8—34no—
276D3×C8—64no—
277D3×C8C4×D314yes—
278D3×C8C4×D314yescomplemented
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—22no—
281C2×C3⋊D3C2×C4⋊C412yes—
282C2×C3×D3—22no—
283C2×C3×D3C2×C4⋊C412yes—
284C2×C3×D3C2×C4⋊C412yes—
285C2×C3×D3#13514yes—
286D32—28no—
287C32×C4—42no—
288C32×C4C23×C411yescharacteristic
289C32×C4C22×Q811yescharacteristic
290C3⋊Dic3—42no—
291C3⋊Dic3C2×C4⋊C412yes—
292C3×Dic3—42no—
293C3×Dic3—42no—
294C3×Dic3C2×C4⋊C412yes—
295C3×Dic3C2×C4⋊C412yes—
296C23×C4—91no—
297C22×C8—31no—
298C22×C8—31no—
299C22×C8—98no—
300C22×C8—91no—
301C22×C8—91no—
302C22×C8—91no—
303C22×C8—91no—
304#117—32no—
305#117—92no—
306#117—92no—
307#117—92no—
308#117—182no—
309#117—182no—
310C2×C4⋊C4—32no—
311C2×C4⋊C4—92no—
312C2×C22⋊C4—182no—
313C2×C42—182no—
314#107—32no—
315#107—92no—
316#107—92no—
317#107—92no—
318#106—31no—
319#106—31no—
320#106—32no—
321#106—92no—
322#106—91no—
323#106D3211yescharacteristic, complemented
324C23×C3—31no—
325C23×C3—31no—
326C22×D3—31no—
327C22×D3—31no—
328C22×D3—34no—
329C22×D3—34no—
330C22×D3—61no—
331C22×D3—64no—
332C22×D3—64no—
333C22×D3D3×D411yescharacteristic
334C22×D3D3×D411yescharacteristic
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—31no—
339C2×C3×C4—31no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—42no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—124no—
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—31no—
353C2×Dic3—31no—
354C2×Dic3—34no—
355C2×Dic3—34no—
356C2×Dic3—61no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360C2×Dic3—124no—
361C2×Dic3D3×D411yescharacteristic
362C2×Dic3D3×D411yescharacteristic
363C4×D3—34no—
364C4×D3—34no—
365C4×D3—32no—
366C4×D3—32no—
367C4×D3—32no—
368C4×D3—32no—
369C4×D3—34no—
370C4×D3—34no—
371C4×D3—44no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—124no—
375C4×D3C2×C4×D312yes—
376C4×D3C2×C4×D312yes—
377C4×D3D3×Q812yes—
378C4×D3D3×Q812yes—
379C3×C8—22no—
380C3×C8—32no—
381C3×C8—32no—
382C3×C8C2×C4×D312yes—
383C3×C8C2×C4×D312yes—
384C3⋊C8—32no—
385C3⋊C8—32no—
386C3⋊C8—62no—
387C3⋊C8C2×C4×D312yes—
388C3⋊C8C2×C4×D312yes—
389C2×C32C22×C4⋊C411yescharacteristic
390C2×C32C2×#13512yes—
391C3⋊D3—22no—
392C3×D3—22no—
393C3×D3#42714yescomplemented
394C24—91no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—62no—
398C22×C4—91no—
399C22×C4—94no—
400C22×C4—94no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—182no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8—34no—
408C2×C8—34no—
409C2×C8—94no—
410C2×C8—94no—
411C2×C8—94no—
412C2×C8—91no—
413C2×C8—94no—
414C2×C8C2×D3211yescharacteristic
415C4⋊C4—32no—
416C4⋊C4—32no—
417C4⋊C4—62no—
418C4⋊C4—92no—
419C4⋊C4—182no—
420C4⋊C4C2×D3212yes—
421C22⋊C4—62no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—62no—
426C42—182no—
427C42—182no—
428C42—182no—
429C22×C3—21no—
430C22×C3—32no—
431C22×C3—34no—
432C22×C3—32no—
433C22×C3—62no—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C2×D3—22no—
437C2×D3—32no—
438C2×D3—32no—
439C2×D3—62no—
440C2×D3—68no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—68no—
444C2×D3—122no—
445C2×D3D3×C4⋊C412yes—
446C2×D3D3×C4⋊C412yes—
447C2×D3#91614yes—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—32no—
451C3×C4—32no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—82no—
455C3×C4—122no—
456C3×C4—122no—
457C3×C4C22×C4×D311yescharacteristic
458C3×C4C22×C4×D311yescharacteristic
459C3×C4C2×D3×Q811yescharacteristic
460C3×C4C2×D3×Q811yescharacteristic
461Dic3—32no—
462Dic3—32no—
463Dic3—42no—
464Dic3—42no—
465Dic3—62no—
466Dic3—122no—
467Dic3—122no—
468Dic3—242no—
469Dic3D3×C4⋊C412yes—
470Dic3D3×C4⋊C412yes—
471C32C2×#42711yescharacteristic, complemented, Sylow
472C23—31no—
473C23—31no—
474C23—94no—
475C23—91no—
476C23—184no—
477C2×C4—22no—
478C2×C4—31no—
479C2×C4—31no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—94no—
487C2×C4—94no—
488C2×C4—94no—
489C2×C4—91no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—124no—
493C2×C4—182no—
494C2×C4—364no—
495C2×C4C22×D3211yescharacteristic
496C8—32no—
497C8—32no—
498C8—92no—
499C8C4×D3212yes—
500C2×C3—21no—
501C2×C3—22no—
502C2×C3—34no—
503C2×C3—62no—
504C2×C3C2×D3×C4⋊C411yescharacteristic
505C2×C3C2×D3×C4⋊C411yescharacteristic
506C2×C3C2×#91612yes—
507C2×C3D3×#13512yes—
508D3—22no—
509D3—62no—
510D3—62no—
511D3—122no—
512D3#486014yesdirect product factor
513C22—32no—
514C22—34no—
515C22—32no—
516C22—62no—
517C22—92no—
518C22—188no—
519C22—182no—
520C22D32×D411yescharacteristic
521C4—32no—
522C4—32no—
523C4—42no—
524C4—92no—
525C4—122no—
526C4—122no—
527C4—362no—
528C4C2×C4×D3211yescharacteristic
529C4D32×Q811yescharacteristic
530C3—21no—
531C3C2×#486011yescharacteristic, complemented
532C3D3×#42711yescharacteristic, complemented
533C2—34no—
534C2—62no—
535C2—182no—
536C2D32×C4⋊C411yescharacteristic
537C2D3×#91612yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×#427
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10592559C2semidirect
4. C3×#4860C2semidirect
5. C3×D3×#106C2semidirect
6. #10590712C2semidirect
7. #10590706C2semidirect
8. D3×#817C2semidirect
9. #10590574C2semidirect
10. #10590572C2semidirect
11. D3×#807C2semidirect
31. D32×C8C4semidirect
32. C32×#106C22semidirect
33. #63644C22semidirect
34. #63634C22semidirect
35. C3×#817C22semidirect
36. C3×#817C22semidirect
37. C3×#808C22semidirect
38. C3×#807C22semidirect
39. #63576C22semidirect
40. #63575C22semidirect
41. #63573C22semidirect
62. #4860D3direct (N × H)
64. D3×#106D3semidirect
82. C8×C3⋊D3C2×C4semidirect
91. C3×D3×C8C2×C4semidirect
97. #3710C2×C4semidirect
99. D3×C3⋊C8C2×C4semidirect
144. C3×#106C2×D3semidirect
145. C3×#106C2×D3semidirect
151. #817C2×D3semidirect
152. #817C2×D3semidirect
154. #808C2×D3semidirect
161. #807C2×D3semidirect
278. D3×C8C4×D3semidirect
323. #106D32semidirect
393. C3×D3#427semidirect
471. C32C2×#427semidirect
512. D3#4860direct (N × H)
531. C3C2×#4860semidirect
532. C3D3×#427semidirect

Maximal subgroups

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

subgroupindex
C2×D32×C82
D3×#8922
#105925592
C3×#48602
C3×D3×#1062
#105907122
#105907062
D3×#8172
#105905742
#105905722
D3×#8072
D3×#4273
C2×#48603