Finite Group Databasebeta

← D3×#4880 #11858442

Subgroups — D3×#4880 #11858442

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×C8C211yesmaximal, characteristic
2D3×#892C212yesmaximal
3#10592579C211yesmaximal, characteristic, complemented
4C3×#4880C211yesmaximal, characteristic, complemented
5C3×D3×#107C211yesmaximal, characteristic, complemented
6#10590714C211yesmaximal, characteristic, complemented
7#10590707C211yesmaximal, characteristic, complemented
8D3×#818C211yesmaximal, characteristic, complemented
9#10590574C212yesmaximal, complemented
10#10590571C212yesmaximal, complemented
11D3×#808C212yesmaximal, complemented
12D3×#427—31nomaximal
13C2×#4880—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×#107C2211yescharacteristic, complemented
33#63645C2211yescharacteristic, complemented
34#63635C2212yescomplemented
35C3×#818C2211yescharacteristic, complemented
36C3×#818C2211yescharacteristic, complemented
37C3×#808C2212yescomplemented
38C3×#807C2212yescomplemented
39#63575C2212yescomplemented
40#63574C2212yescomplemented
41#63573C2212yescomplemented
42C22×D3×C8—31no—
43C22×D3×C8—31no—
44D3×#117—32no—
45C2×#892—32no—
46C3×#427—31no—
47C2×C3×#107—31no—
48#5106—31no—
49C2×#818—31no—
50#4998—32no—
51C2×#808—32no—
52#4880—31no—
53#4880—32no—
54#4880—31no—
55#4880—31no—
56#4880—31no—
57#4880—31no—
58#4880—32no—
59#4880—61no—
60#4880D311yescharacteristic, direct product factor
61D3×#107—31no—
62D3×#107D311yescharacteristic, complemented
63#4860—32no—
64D3×#106—32no—
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—21no—
140C3×#107—31no—
141C3×#107—31no—
142C3×#107—32no—
143C3×#107C2×D311yescharacteristic, complemented
144C3×#107C2×D311yescharacteristic, complemented
145C3×#106—32no—
146#818—31no—
147#818—31no—
148#818—32no—
149#818—61no—
150#818C2×D311yescharacteristic, complemented
151#818C2×D311yescharacteristic, complemented
152#817—32no—
153#808—32no—
154#808—32no—
155#808—32no—
156#808—32no—
157#808—32no—
158#808—62no—
159#808C2×D312yescomplemented
160#807—32no—
161#807C2×D312yescomplemented
162C22×C3⋊D3C2×D411yescharacteristic
163C22×C3×D3C2×D411yescharacteristic
164C22×C3×D3C2×D411yescharacteristic
165C2×D32—22no—
166C2×D32—22no—
167C2×D32C4⋊C414yes—
168C2×C32×C4—22no—
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C2×D411yescharacteristic
172C4×C3⋊D3C22×C412yes—
173C4×C3⋊D3C2×Q812yes—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3C2×D411yescharacteristic
177C2×C3×Dic3C2×D411yescharacteristic
178C3×C4×D3—44no—
179C3×C4×D3C22×C412yes—
180C3×C4×D3C22×C412yes—
181C3×C4×D3C2×Q812yes—
182C3×C4×D3C2×Q812yes—
183#624C4⋊C414yes—
184D3×Dic3—44no—
185D3×Dic3C4⋊C414yes—
186D3×Dic3C4⋊C414yes—
187C32×C8C22×C412yes—
188C3⋊(C3⋊C8)C22×C412yes—
189C3×C3⋊C8C22×C412yes—
190C3×C3⋊C8C22×C412yes—
191C23×C8—91no—
192C2×#117—92no—
193#427—31no—
194#427—92no—
195#427—91no—
196#427—92no—
197#427—91no—
198#427—91no—
199C2×#107—31no—
200C2×#107—91no—
201C2×#106—92no—
202C23×D3—31no—
203C23×D3—31no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—62no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—62no—
210C2×C4×D3—22no—
211C2×C4×D3—31no—
212C2×C4×D3—31no—
213C2×C4×D3—31no—
214C2×C4×D3—31no—
215C2×C4×D3—31no—
216C2×C4×D3—31no—
217C2×C4×D3—34no—
218C2×C4×D3—34no—
219C2×C4×D3—34no—
220C2×C4×D3—34no—
221C2×C4×D3—61no—
222C2×C4×D3—62no—
223C2×C4×D3C22×D311yescharacteristic
224C2×C4×D3C22×D311yescharacteristic
225C2×C3×C8—21no—
226C2×C3×C8—31no—
227C2×C3×C8—31no—
228C2×C3×C8—34no—
229C2×C3×C8—34no—
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C3×C4⋊C4—22no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4C22×D312yes—
237C3×C4⋊C4C22×D312yes—
238C3×C22⋊C4—62no—
239C3×C42—62no—
240#217—62no—
241(C2×D3)⋊C4—22no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—122no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3C22×D312yes—
253C4⋊Dic3C22×D312yes—
254Dic3⋊C4—22no—
255Dic3⋊C4—62no—
256C4×Dic3—22no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—122no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—34no—
267C2×C3⋊C8—34no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271D3×C8—34no—
272D3×C8—34no—
273D3×C8—34no—
274D3×C8—34no—
275D3×C8—34no—
276D3×C8—34no—
277D3×C8—64no—
278D3×C8C4×D314yes—
279D3×C8C4×D314yescomplemented
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3C2×C4⋊C412yes—
284C2×C3×D3—21no—
285C2×C3×D3—21no—
286C2×C3×D3C2×C4⋊C412yes—
287C2×C3×D3C2×C4⋊C412yes—
288C2×C3×D3#13512yes—
289C2×C3×D3#13512yes—
290D32—28no—
291C32×C4—42no—
292C32×C4C23×C411yescharacteristic
293C32×C4C22×Q811yescharacteristic
294C3⋊Dic3—42no—
295C3⋊Dic3C2×C4⋊C412yes—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C3×Dic3C2×C4⋊C412yes—
299C3×Dic3C2×C4⋊C412yes—
300C23×C4—91no—
301C22×C8—31no—
302C22×C8—31no—
303C22×C8—98no—
304C22×C8—91no—
305C22×C8—91no—
306C22×C8—91no—
307C22×C8—91no—
308#117—32no—
309#117—92no—
310#117—92no—
311#117—92no—
312#117—182no—
313#117—182no—
314C2×C4⋊C4—32no—
315C2×C4⋊C4—92no—
316C2×C22⋊C4—182no—
317C2×C42—182no—
318#107—31no—
319#107—31no—
320#107—32no—
321#107—92no—
322#107—91no—
323#107D3211yescharacteristic, complemented
324#106—32no—
325#106—92no—
326#106—92no—
327#106—92no—
328C23×C3—31no—
329C23×C3—31no—
330C22×D3—31no—
331C22×D3—31no—
332C22×D3—34no—
333C22×D3—34no—
334C22×D3—61no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3D3×D411yescharacteristic
340C22×D3D3×D411yescharacteristic
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—31no—
345C2×C3×C4—31no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—42no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—124no—
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—61no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366C2×Dic3—124no—
367C2×Dic3D3×D411yescharacteristic
368C2×Dic3D3×D411yescharacteristic
369C4×D3—34no—
370C4×D3—34no—
371C4×D3—32no—
372C4×D3—32no—
373C4×D3—32no—
374C4×D3—32no—
375C4×D3—34no—
376C4×D3—34no—
377C4×D3—44no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—124no—
381C4×D3C2×C4×D312yes—
382C4×D3C2×C4×D312yes—
383C4×D3D3×Q812yes—
384C4×D3D3×Q812yes—
385C3×C8—22no—
386C3×C8—32no—
387C3×C8—32no—
388C3×C8C2×C4×D312yes—
389C3×C8C2×C4×D312yes—
390C3⋊C8—32no—
391C3⋊C8—32no—
392C3⋊C8—62no—
393C3⋊C8C2×C4×D312yes—
394C3⋊C8C2×C4×D312yes—
395C2×C32C22×C4⋊C411yescharacteristic
396C2×C32C2×#13511yescharacteristic
397C2×C32C2×#13511yescharacteristic
398C3⋊D3—22no—
399C3×D3—22no—
400C3×D3#42714yescomplemented
401C24—91no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—62no—
405C22×C4—91no—
406C22×C4—94no—
407C22×C4—94no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—182no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8—34no—
415C2×C8—34no—
416C2×C8—94no—
417C2×C8—94no—
418C2×C8—94no—
419C2×C8—91no—
420C2×C8—94no—
421C2×C8C2×D3211yescharacteristic
422C4⋊C4—32no—
423C4⋊C4—32no—
424C4⋊C4—62no—
425C4⋊C4—92no—
426C4⋊C4—182no—
427C4⋊C4C2×D3212yes—
428C22⋊C4—62no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C22⋊C4—182no—
432C42—62no—
433C42—182no—
434C42—182no—
435C42—182no—
436C22×C3—21no—
437C22×C3—32no—
438C22×C3—32no—
439C22×C3—32no—
440C22×C3—32no—
441C22×C3—61no—
442C22×C3—61no—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—32no—
448C2×D3—32no—
449C2×D3—62no—
450C2×D3—68no—
451C2×D3—61no—
452C2×D3—61no—
453C2×D3—61no—
454C2×D3—61no—
455C2×D3—68no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3D3×C4⋊C412yes—
459C2×D3D3×C4⋊C412yes—
460C2×D3#91212yes—
461C2×D3#91912yes—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—32no—
465C3×C4—32no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—82no—
469C3×C4—122no—
470C3×C4—122no—
471C3×C4C22×C4×D311yescharacteristic
472C3×C4C22×C4×D311yescharacteristic
473C3×C4C2×D3×Q811yescharacteristic
474C3×C4C2×D3×Q811yescharacteristic
475Dic3—32no—
476Dic3—32no—
477Dic3—42no—
478Dic3—42no—
479Dic3—62no—
480Dic3—122no—
481Dic3—122no—
482Dic3—242no—
483Dic3D3×C4⋊C412yes—
484Dic3D3×C4⋊C412yes—
485C32C2×#42711yescharacteristic, complemented, Sylow
486C23—31no—
487C23—31no—
488C23—94no—
489C23—91no—
490C23—182no—
491C23—182no—
492C2×C4—22no—
493C2×C4—31no—
494C2×C4—31no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—94no—
502C2×C4—94no—
503C2×C4—94no—
504C2×C4—91no—
505C2×C4—92no—
506C2×C4—92no—
507C2×C4—124no—
508C2×C4—182no—
509C2×C4—364no—
510C2×C4C22×D3211yescharacteristic
511C8—32no—
512C8—32no—
513C8—92no—
514C8C4×D3212yes—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—34no—
519C2×C3—62no—
520C2×C3C2×D3×C4⋊C411yescharacteristic
521C2×C3C2×D3×C4⋊C411yescharacteristic
522C2×C3C2×#91211yescharacteristic
523C2×C3C2×#91911yescharacteristic
524C2×C3D3×#13511yescharacteristic
525C2×C3D3×#13511yescharacteristic
526D3—22no—
527D3—62no—
528D3—62no—
529D3—122no—
530D3#488014yesdirect product factor
531C22—32no—
532C22—32no—
533C22—32no—
534C22—32no—
535C22—61no—
536C22—61no—
537C22—92no—
538C22—188no—
539C22—181no—
540C22—181no—
541C22D32×D411yescharacteristic
542C4—32no—
543C4—32no—
544C4—42no—
545C4—92no—
546C4—122no—
547C4—122no—
548C4—362no—
549C4C2×C4×D3211yescharacteristic
550C4D32×Q811yescharacteristic
551C3—21no—
552C3C2×#488011yescharacteristic, complemented
553C3D3×#42711yescharacteristic, complemented
554C2—34no—
555C2—62no—
556C2—182no—
557C2D32×C4⋊C411yescharacteristic
558C2D3×#91211yescharacteristic
559C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32C2×#427
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #10592579C2semidirect
4. C3×#4880C2semidirect
5. C3×D3×#107C2semidirect
6. #10590714C2semidirect
7. #10590707C2semidirect
8. D3×#818C2semidirect
9. #10590574C2semidirect
10. #10590571C2semidirect
11. D3×#808C2semidirect
31. D32×C8C4semidirect
32. C32×#107C22semidirect
33. #63645C22semidirect
34. #63635C22semidirect
35. C3×#818C22semidirect
36. C3×#818C22semidirect
37. C3×#808C22semidirect
38. C3×#807C22semidirect
39. #63575C22semidirect
40. #63574C22semidirect
41. #63573C22semidirect
60. #4880D3direct (N × H)
62. D3×#107D3semidirect
82. C8×C3⋊D3C2×C4semidirect
91. C3×D3×C8C2×C4semidirect
97. #3710C2×C4semidirect
99. D3×C3⋊C8C2×C4semidirect
143. C3×#107C2×D3semidirect
144. C3×#107C2×D3semidirect
150. #818C2×D3semidirect
151. #818C2×D3semidirect
159. #808C2×D3semidirect
161. #807C2×D3semidirect
279. D3×C8C4×D3semidirect
323. #107D32semidirect
400. C3×D3#427semidirect
485. C32C2×#427semidirect
530. D3#4880direct (N × H)
552. C3C2×#4880semidirect
553. 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
#105925792
C3×#48802
C3×D3×#1072
#105907142
#105907072
D3×#8182
#105905742
#105905712
D3×#8082
D3×#4273
C2×#48803