Finite Group Databasebeta

← D3×#4869 #11860176

Subgroups — D3×#4869 #11860176

Order 1152.

1282 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D24C211yesmaximal, characteristic
2D3×#893C212yesmaximal, complemented
3#10592568C211yesmaximal, characteristic, complemented
4C3×#4869C211yesmaximal, characteristic, complemented
5C3×D3×#106C211yesmaximal, characteristic, complemented
6#10590781C211yesmaximal, characteristic, complemented
7#10590768C211yesmaximal, characteristic, complemented
8D3×#815C211yesmaximal, characteristic, complemented
9D3×#809C212yesmaximal, complemented
10#10590589C212yesmaximal, complemented
11#10590462C212yesmaximal, complemented
12D3×#442—31nomaximal
13C2×#4869—31nomaximal
14C2×D3×D12C2212yes—
15C2×C4×D32—22no—
16C2×#3745C2211yescharacteristic
17#64102C2212yescomplemented
18C2×C3×D24C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×#893C2212yescomplemented
21C3×D3×C4⋊C4C2212yes—
22D3×(C2×D3)⋊C4—22no—
23#63904—22no—
24#63898C2212yescomplemented
25#63894C2212yescomplemented
26#63881—22no—
27C4×D3×Dic3C2211yescharacteristic
28C2×#3714C2212yes—
29C2×D3×C3⋊C8C2211yescharacteristic
30D3×D24C418yescomplemented
31C32×#106C2211yescharacteristic, complemented
32#63642C2211yescharacteristic, complemented
33#63636C2212yescomplemented
34C3×#817C2211yescharacteristic, complemented
35C3×#815C2211yescharacteristic, complemented
36C3×#809C2212yescomplemented
37C3×#808C2212yescomplemented
38#63564C2212yescomplemented
39#63562C2212yescomplemented
40#63555C2211yescharacteristic, complemented
41#63554C2211yescharacteristic, complemented
42C2×D3×D8—31no—
43C22×D24—31no—
44C4×D3×D4—32no—
45C2×#893—32no—
46C3×#442—31no—
47C2×C3×#106—31no—
48#5152—31no—
49C2×#815—31no—
50#5014—32no—
51C2×#809—32no—
52#4869—31no—
53#4869—32no—
54#4869—31no—
55#4869—31no—
56#4869—31no—
57#4869—32no—
58#4869—61no—
59#4869D311yescharacteristic, direct product factor
60D3×#106D311yescharacteristic, complemented
61#4785—32no—
62D3×#102—32no—
63#4711—31no—
64D3×#97—31no—
65C22×D32—22no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C4×C3⋊D3—22no—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3C2311yescharacteristic
72C2×#626—22no—
73C2×#624—22no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3D412yes—
76D3×D12—24no—
77D3×D12C2×C418yescomplemented
78C4×D32—48no—
79C2×C32×C8C2311yescharacteristic
80C32×C4⋊C4C2312yes—
81#3752—22no—
82C4×C3⋊Dic3C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3745C2×C414yescomplemented
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—22no—
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×D24C2×C414yescomplemented
92C3×D3×C8C2×C414yescomplemented
93#3722—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32D412yes—
96#3714C2×C418yescomplemented
97D3×C3⋊C8—22no—
98C2×#442—91noSylow
99C2×D3×D4—32no—
100C22×D12—32no—
101C22×C4×D3—62no—
102C22×C4×D3—62no—
103C2×C3×D8—31no—
104C22×C3×C8—31no—
105C3×C4×D4—32no—
106C2×C3×C4⋊C4—32no—
107D4×Dic3—32no—
108C2×#213—32no—
109C4×#67—62no—
110C2×(C2×D3)⋊C4—62no—
111C2×C4×Dic3—31no—
112C22×C3⋊C8—31no—
113D3×D8—38no—
114C2×D24—32no—
115C2×D24—31no—
116C2×D24—31no—
117C2×D24—38no—
118C2×D24—61no—
119C2×D24C2×D311yescharacteristic
120C2×D3×C8—31no—
121C2×D3×C8C2×D311yescharacteristic
122#893—32no—
123#893—32no—
124#893—32no—
125#893—32no—
126#893—62no—
127#893—62no—
128#893—62no—
129#893C2×D312yescomplemented
130D3×C4⋊C4C2×D312yes—
131#67⋊C4—62no—
132D3×C22⋊C4—62no—
133C4×D12—32no—
134C42×D3—31no—
135C3×#106—21no—
136C3×#106—31no—
137C3×#106—32no—
138C3×#106C2×D311yescharacteristic, complemented
139C3×#106C2×D311yescharacteristic, complemented
140C3×#102—32no—
141C3×#97—31no—
142#832—32no—
143#821—32no—
144#817C2×D311yescharacteristic, complemented
145#815—31no—
146#815—31no—
147#815—31no—
148#815—31no—
149#815—31no—
150#815—61no—
151#815C2×D311yescharacteristic, complemented
152#809—32no—
153#809—32no—
154#809—32no—
155#809—32no—
156#809—62no—
157#809C2×D312yescomplemented
158#808C2×D312yescomplemented
159#803—31no—
160C22×C3⋊D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3C2×D411yescharacteristic
163C2×D32—28no—
164C2×D32—44no—
165C2×D32—44no—
166C2×C32×C4—22no—
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3C2×D412yes—
169C4⋊(C3⋊D3)—22no—
170C4⋊(C3⋊D3)C22×C414yescomplemented
171C4×C3⋊D3—44no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D411yescharacteristic
175C3×D12—22no—
176C3×D12C22×C414yescomplemented
177C3×C4×D3—44no—
178C3×C4×D3—44no—
179C3×C4×D3C22×C412yes—
180C3×C4×D3#4112yes—
181#626—28no—
182#624—44no—
183D3×Dic3—24no—
184D3×Dic3—44no—
185C32×C8C22×C412yescomplemented
186C3⋊(C3⋊C8)—21no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8C22×C412yescomplemented
189C22×D8—91no—
190C2×C4×D4—92no—
191#442—31no—
192#442—91no—
193#442—92no—
194#442—92no—
195#442—91no—
196#442—91no—
197C2×#106—31no—
198C2×#102—92no—
199C2×#97—91no—
200C23×D3—62no—
201C23×D3—62no—
202C2×C3×D4—32no—
203C22×C3×C4—31no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C2×#67—62no—
207C22×Dic3—32no—
208C22×Dic3—62no—
209D3×D4—38no—
210D3×D4—64no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—38no—
214C2×D12—62no—
215C2×D12—64no—
216C2×D12—62no—
217C2×D12C22×D312yes—
218C2×C4×D3—22no—
219C2×C4×D3—22no—
220C2×C4×D3—32no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—122no—
227C2×C4×D3—128no—
228C2×C4×D3—128no—
229C2×C4×D3C22×D311yescharacteristic
230C3×D8—34no—
231C2×C3×C8—21no—
232C2×C3×C8—31no—
233C2×C3×C8—34no—
234C2×C3×C8—31no—
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C3×C4⋊C4—22no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C22×D312yes—
242C3×C22⋊C4—62no—
243C3×C42—31no—
244#217—62no—
245#213—38no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—122no—
253C4⋊Dic3C22×D312yes—
254Dic3⋊C4—22no—
255C4×Dic3—31no—
256C4×Dic3—31no—
257C4×Dic3—32no—
258C4×Dic3—32no—
259C4×Dic3—61no—
260C4×Dic3C22×D311yescharacteristic
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267D24—38no—
268D24—34no—
269D24—34no—
270D24—64no—
271D24C4×D314yescomplemented
272D3×C8—62no—
273D3×C8C4×D314yescomplemented
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—24no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—42no—
278C2×C3×D3—24no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3C4×D412yes—
282C2×C3×D3AGL(1,ℤ/8)14yes—
283D32—416no—
284C32×C4—42no—
285C32×C4C23×C411yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3⋊Dic3—22no—
288C3×Dic3—22no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C22×D4—92no—
292C23×C4—182no—
293C2×D8—31no—
294C2×D8—98no—
295C2×D8—92no—
296C2×D8—91no—
297C22×C8—31no—
298C22×C8—91no—
299C4×D4—32no—
300C4×D4—92no—
301C4×D4—92no—
302C4×D4—92no—
303C4×D4—182no—
304C4×D4—182no—
305C2×C4⋊C4—32no—
306C2×C22⋊C4—182no—
307C2×C42—91no—
308#106—31no—
309#106—32no—
310#106D3211yescharacteristic, complemented
311#102—32no—
312#102—92no—
313#102—92no—
314#102—92no—
315#97—31no—
316#97—91no—
317#97—91no—
318#97—91no—
319C23×C3—31no—
320C23×C3—62no—
321C22×D3—22no—
322C22×D3—68no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—68no—
326C22×D3—122no—
327C22×D3—124no—
328C22×D3—124no—
329C22×D3—124no—
330C22×D3—124no—
331C22×D3D3×D411yescharacteristic
332C3×D4—34no—
333C3×D4—62no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—31no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—42no—
342C2×C3×C4—62no—
343C2×C3×C4—124no—
344C2×C3×C4—124no—
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347#67—68no—
348C2×Dic3—22no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—62no—
352C2×Dic3—64no—
353C2×Dic3—124no—
354C2×Dic3D3×D412yes—
355C2×Dic3D3×D411yescharacteristic
356D12—22no—
357D12—34no—
358D12—34no—
359D12—64no—
360D12—68no—
361D12—62no—
362D12—62no—
363D12—122no—
364D12C2×C4×D314yescomplemented
365C4×D3—44no—
366C4×D3—44no—
367C4×D3—64no—
368C4×D3—124no—
369C4×D3—124no—
370C4×D3—124no—
371C4×D3—124no—
372C4×D3—124no—
373C4×D3—244no—
374C4×D3C2×C4×D312yes—
375C4×D3#23912yes—
376C3×C8—22no—
377C3×C8—32no—
378C3×C8—61no—
379C3×C8C2×C4×D312yescomplemented
380C3×C8C2×C4×D312yescomplemented
381C3⋊C8—21no—
382C3⋊C8—61no—
383C3⋊C8—61no—
384C3⋊C8—121no—
385C3⋊C8C2×C4×D312yescomplemented
386C2×C32C2×C4×D411yescharacteristic
387C2×C32C2×AGL(1,ℤ/8)12yes—
388C3⋊D3—44no—
389C3×D3—44no—
390C3×D3#44214yescomplemented
391C24—182no—
392C2×D4—32no—
393C2×D4—98no—
394C2×D4—92no—
395C2×D4—184no—
396C2×D4—182no—
397C22×C4—31no—
398C22×C4—62no—
399C22×C4—62no—
400C22×C4—92no—
401C22×C4—182no—
402C22×C4—182no—
403C22×C4—182no—
404C22×C4—368no—
405D8—34no—
406D8—98no—
407D8—94no—
408C2×C8—31no—
409C2×C8—34no—
410C2×C8—31no—
411C2×C8—91no—
412C2×C8—182no—
413C2×C8C2×D3211yescharacteristic
414C4⋊C4—32no—
415C4⋊C4—62no—
416C4⋊C4C2×D3212yes—
417C22⋊C4—62no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C42—31no—
422C42—92no—
423C42—91no—
424C22×C3—21no—
425C22×C3—34no—
426C22×C3—32no—
427C22×C3—64no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C2×D3×D411yescharacteristic
432C2×D3—24no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—64no—
436C2×D3—64no—
437C2×D3—124no—
438C2×D3—1216no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—1216no—
444C2×D3—242no—
445C2×D3—242no—
446C2×D3#89312yes—
447C2×D3#91414yes—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—32no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—62no—
454C3×C4—82no—
455C3×C4—122no—
456C3×C4C22×C4×D311yescharacteristic
457C3×C4C22×C4×D311yescharacteristic
458C3×C4C2×#23911yescharacteristic
459C3×C4D3×#4111yescharacteristic
460Dic3—22no—
461Dic3—42no—
462Dic3—62no—
463Dic3—62no—
464Dic3—122no—
465Dic3#89312yes—
466C32C2×#44211yescharacteristic, complemented, Sylow
467C23—31no—
468C23—62no—
469C23—188no—
470C23—182no—
471C23—364no—
472C23—364no—
473D4—34no—
474D4—62no—
475D4—94no—
476D4—188no—
477D4—182no—
478C2×C4—22no—
479C2×C4—31no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—62no—
484C2×C4—92no—
485C2×C4—124no—
486C2×C4—124no—
487C2×C4—184no—
488C2×C4—364no—
489C2×C4—364no—
490C2×C4—364no—
491C2×C4C22×D3211yescharacteristic
492C8—32no—
493C8—61no—
494C8—181no—
495C8C4×D3212yescomplemented
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—34no—
499C2×C3—124no—
500C2×C3C2×#89311yescharacteristic
501C2×C3C4×D3×D411yescharacteristic
502C2×C3C2×#91412yes—
503C2×C3D3×AGL(1,ℤ/8)12yes—
504D3—44no—
505D3—124no—
506D3—124no—
507D3—244no—
508D3#486914yesdirect product factor
509C22—32no—
510C22—34no—
511C22—64no—
512C22—122no—
513C22—122no—
514C22—184no—
515C22—3616no—
516C22—362no—
517C22—362no—
518C22D32×D411yescharacteristic
519C4—32no—
520C4—42no—
521C4—62no—
522C4—122no—
523C4—182no—
524C4C2×C4×D3211yescharacteristic
525C4D3×#23911yescharacteristic
526C3—21no—
527C3C2×#486911yescharacteristic, complemented
528C3D3×#44211yescharacteristic, complemented
529C2—34no—
530C2—124no—
531C2—364no—
532C2D3×#89311yescharacteristic
533C2D3×#91412yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×D3×D24C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×#442
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
2. D3×#893C2semidirect
3. #10592568C2semidirect
4. C3×#4869C2semidirect
5. C3×D3×#106C2semidirect
6. #10590781C2semidirect
7. #10590768C2semidirect
8. D3×#815C2semidirect
9. D3×#809C2semidirect
10. #10590589C2semidirect
11. #10590462C2semidirect
17. #64102C22semidirect
20. C3×#893C22semidirect
24. #63898C22semidirect
25. #63894C22semidirect
30. D3×D24C4semidirect
31. C32×#106C22semidirect
32. #63642C22semidirect
33. #63636C22semidirect
34. C3×#817C22semidirect
35. C3×#815C22semidirect
36. C3×#809C22semidirect
37. C3×#808C22semidirect
38. #63564C22semidirect
39. #63562C22semidirect
40. #63555C22semidirect
41. #63554C22semidirect
59. #4869D3direct (N × H)
60. D3×#106D3semidirect
77. D3×D12C2×C4semidirect
84. #3745C2×C4semidirect
91. C3×D24C2×C4semidirect
92. C3×D3×C8C2×C4semidirect
96. #3714C2×C4semidirect
129. #893C2×D3semidirect
138. C3×#106C2×D3semidirect
139. C3×#106C2×D3semidirect
144. #817C2×D3semidirect
151. #815C2×D3semidirect
157. #809C2×D3semidirect
158. #808C2×D3semidirect
170. C4⋊(C3⋊D3)C22×C4semidirect
176. C3×D12C22×C4semidirect
185. C32×C8C22×C4semidirect
188. C3×C3⋊C8C22×C4semidirect
271. D24C4×D3semidirect
273. D3×C8C4×D3semidirect
310. #106D32semidirect
364. D12C2×C4×D3semidirect
379. C3×C8C2×C4×D3semidirect
380. C3×C8C2×C4×D3semidirect
385. C3⋊C8C2×C4×D3semidirect
390. C3×D3#442semidirect
466. C32C2×#442semidirect
495. C8C4×D32semidirect
508. D3#4869direct (N × H)
527. C3C2×#4869semidirect
528. C3D3×#442semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
D3×#8932
#105925682
C3×#48692
C3×D3×#1062
#105907812
#105907682
D3×#8152
D3×#8092
#105905892
#105904622
D3×#4423
C2×#48693