Finite Group Databasebeta

← D3×#5152 #11860157

Subgroups — D3×#5152 #11860157

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×C3×D3×D8C211yesmaximal, characteristic
2D3×D4×Dic3C212yesmaximal, complemented
3#10592851C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5#10591436C212yesmaximal, complemented
6#10591430C212yesmaximal, complemented
7D3×#832C212yesmaximal, complemented
8#10590781C211yesmaximal, characteristic, complemented
9#10590771C211yesmaximal, characteristic, complemented
10D3×#817C211yesmaximal, characteristic, complemented
11D3×#815C211yesmaximal, characteristic, complemented
12C2×#5152—31nomaximal
13D3×#442—31nomaximal
14C2×C3×D3×D4C2212yes—
15C22×D3×Dic3—22no—
16C2×C32×D8C2211yescharacteristic
17D4×C3⋊Dic3C2212yescomplemented
18C3×D4×Dic3C2212yescomplemented
19C2×C3×#213C2212yes—
20C3×D3×D8C418yescomplemented
21C2×C3×D24C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23#67⋊Dic3—22no—
24Dic3×#67—22no—
25D3×#217—22no—
26#63898C2212yescomplemented
27Dic3×D12C2212yescomplemented
28D3×C4⋊Dic3C2212yes—
29C4×D3×Dic3C2211yescharacteristic
30C2×D3×C3⋊C8C2211yescharacteristic
31#63659C2212yescomplemented
32#63644C2211yescharacteristic, complemented
33#63642C2211yescharacteristic, complemented
34C3×#832C2212yescomplemented
35C3×#817C2211yescharacteristic, complemented
36C3×#815C2211yescharacteristic, complemented
37#63573C2212yescomplemented
38#63563C2212yescomplemented
39#63562C2212yescomplemented
40#63555C2211yescharacteristic, complemented
41#63554C2211yescharacteristic, complemented
42C22×C3×D8—31no—
43C2×D4×Dic3—32no—
44C2×D3×D8D311yescharacteristic
45C4×D3×D4—32no—
46C3×#442—31no—
47C2×#832—32no—
48#5152—31no—
49#5152—31no—
50#5152—32no—
51#5152—32no—
52#5152—31no—
53#5152—31no—
54#5152—61no—
55#5152D311yescharacteristic, direct product factor
56C2×#817—31no—
57C2×#815—31no—
58#5014—32no—
59#4869—31no—
60D3×#106—31no—
61#4785—32no—
62D3×#102—32no—
63#4711—31no—
64D3×#97—31no—
65C23×C3×D3—22no—
66C2×C32×D4C2312yes—
67C22×C3⋊Dic3—22no—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C3×D3×D4—24no—
71C3×D3×D4C2×C418yescomplemented
72C2×C3×D12C2312yes—
73C2×C3×C4×D3C2311yescharacteristic
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C2×D3×Dic3—22no—
77C2×D3×Dic3—48no—
78C2×D3×Dic3D412yes—
79C32×D8C2×C414yescomplemented
80C2×C32×C8C2311yescharacteristic
81#3757—22no—
82C4⋊(C3⋊Dic3)C2312yes—
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—22no—
86C3×#213C2×C418yescomplemented
87C3×C4⋊Dic3C2312yes—
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×D24C2×C414yescomplemented
92C3×D3×C8C2×C414yescomplemented
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32D412yes—
97D3×C3⋊C8—22no—
98C2×#442—91noSylow
99C22×C3×D4—32no—
100C23×Dic3—62no—
101C2×D3×D4C2×D312yes—
102C22×C4×D3—62no—
103C2×C3×D8—21no—
104C2×C3×D8—32no—
105C2×C3×D8—38no—
106C2×C3×D8—31no—
107C2×C3×D8C2×D311yescharacteristic
108C2×C3×D8C2×D311yescharacteristic
109C22×C3×C8—31no—
110C3×C4×D4—32no—
111C2×#217—62no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—32no—
116D4×Dic3—62no—
117D4×Dic3—62no—
118D4×Dic3—62no—
119D4×Dic3C2×D312yescomplemented
120C2×#213C2×D312yes—
121C4×#67—62no—
122C2×C4⋊Dic3—32no—
123C2×C4×Dic3—31no—
124C22×C3⋊C8—31no—
125D3×D8Dic318yescomplemented
126C2×D24C2×D311yescharacteristic
127C2×D3×C8—31no—
128C2×D3×C8C2×D311yescharacteristic
129#893—32no—
130D3×C4⋊C4—32no—
131#67⋊C4—62no—
132D3×C22⋊C4—62no—
133C4×D12—32no—
134C42×D3—31no—
135C3×#106—31no—
136C3×#102—32no—
137C3×#97—31no—
138#832—32no—
139#832—32no—
140#832—32no—
141#832—32no—
142#832—62no—
143#832C2×D312yescomplemented
144#821—32no—
145#817—31no—
146#817—31no—
147#817—32no—
148#817—61no—
149#817C2×D311yescharacteristic, complemented
150#815—31no—
151#815—31no—
152#815—31no—
153#815—31no—
154#815—31no—
155#815—61no—
156#815C2×D311yescharacteristic, complemented
157#809—32no—
158#808—32no—
159#803—31no—
160C23×C32—22no—
161C22×C3×D3—22no—
162C22×C3×D3—28no—
163C22×C3×D3—44no—
164C22×C3×D3—44no—
165C22×C3×D3C2×D411yescharacteristic
166C32×D4—22no—
167C32×D4C22×C414yescomplemented
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—44no—
171C2×C3⋊Dic3C2×D412yes—
172C3×#67—28no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—44no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D411yescharacteristic
177C3×D12—22no—
178C3×D12C22×C414yescomplemented
179C3×C4×D3C22×C412yes—
180C3×C4×D3#4112yes—
181D3×Dic3—24no—
182D3×Dic3—44no—
183D3×Dic3—44no—
184D3×Dic3—44no—
185C32×C8C22×C412yescomplemented
186C3⋊(C3⋊C8)—21no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8C22×C412yescomplemented
189C22×D8—31no—
190C2×C4×D4—92no—
191#442—31no—
192#442—91no—
193#442—92no—
194#442—91no—
195#442—92no—
196#442—91no—
197C2×#106—91no—
198C2×#102—92no—
199C2×#97—91no—
200C24×C3—62no—
201C23×D3—22no—
202C2×C3×D4—22no—
203C2×C3×D4—38no—
204C2×C3×D4—32no—
205C2×C3×D4—64no—
206C2×C3×D4—62no—
207C2×C3×D4C22×D312yes—
208C2×C3×D4C22×D312yes—
209C22×C3×C4—31no—
210C22×C3×C4—62no—
211C2×#67—22no—
212C22×Dic3—22no—
213C22×Dic3—32no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C22×Dic3—62no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3—122no—
220C22×Dic3—128no—
221D3×D4—24no—
222D3×D4C2×Dic318yescomplemented
223C2×D12C22×D312yes—
224C2×C4×D3—32no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—128no—
229C2×C4×D3C22×D311yescharacteristic
230C3×D8—24no—
231C3×D8—38no—
232C3×D8—34no—
233C3×D8C4×D314yescomplemented
234C3×D8C2×Dic314yescomplemented
235C2×C3×C8—21no—
236C2×C3×C8—31no—
237C2×C3×C8—34no—
238C2×C3×C8—31no—
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D311yescharacteristic
241C3×C4⋊C4—32no—
242C3×C22⋊C4—62no—
243C3×C42—31no—
244#217—22no—
245#217—62no—
246#217—62no—
247#217—62no—
248#217—62no—
249#217—122no—
250#213C2×Dic318yescomplemented
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3C22×D312yes—
258Dic3⋊C4—62no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—61no—
264C4×Dic3C22×D311yescharacteristic
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271D24C2×Dic314yescomplemented
272D3×C8—62no—
273D3×C8C2×Dic314yescomplemented
274C22×C32—24no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32C22×D411yescharacteristic
278C2×C3×D3—24no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—416no—
282C2×C3×D3C4×D412yes—
283C2×C3×D3AGL(1,ℤ/8)14yes—
284C32×C4C23×C411yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3⋊Dic3—22no—
287C3⋊Dic3—42no—
288C3×Dic3—22no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C22×D4—32no—
292C23×C4—182no—
293C2×D8—32no—
294C2×D8—38no—
295C2×D8—31no—
296C2×D8D3211yescharacteristic
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—92no—
306C2×C22⋊C4—182no—
307C2×C42—91no—
308#106—31no—
309#106—92no—
310#106—91no—
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—22no—
320C23×C3—22no—
321C23×C3—31no—
322C23×C3—42no—
323C23×C3—68no—
324C23×C3—62no—
325C23×C3—124no—
326C23×C3—124no—
327C22×D3—22no—
328C22×D3—28no—
329C22×D3—44no—
330C22×D3—44no—
331C22×D3D3×D411yescharacteristic
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—24no—
335C3×D4—34no—
336C3×D4—42no—
337C3×D4—68no—
338C3×D4—62no—
339C3×D4C2×C4×D314yescomplemented
340C3×D4C22×Dic314yescomplemented
341C2×C3×C4—21no—
342C2×C3×C4—31no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—62no—
347C2×C3×C4—124no—
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350#67—28no—
351C2×Dic3—22no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—44no—
355C2×Dic3—62no—
356C2×Dic3—64no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360C2×Dic3—124no—
361C2×Dic3—124no—
362C2×Dic3—124no—
363C2×Dic3—124no—
364C2×Dic3—124no—
365C2×Dic3—244no—
366C2×Dic3D3×D412yes—
367C2×Dic3D3×D411yescharacteristic
368D12—22no—
369D12C22×Dic314yescomplemented
370C4×D3—64no—
371C4×D3—124no—
372C4×D3—124no—
373C4×D3—124no—
374C4×D3#23712yes—
375C4×D3C22×Dic312yes—
376C3×C8—22no—
377C3×C8—32no—
378C3×C8—61no—
379C3×C8C2×C4×D312yescomplemented
380C3×C8C22×Dic312yescomplemented
381C3⋊C8—21no—
382C3⋊C8—61no—
383C3⋊C8—61no—
384C3⋊C8—121no—
385C3⋊C8C22×Dic312yescomplemented
386C2×C32—44no—
387C2×C32C2×C4×D411yescharacteristic
388C2×C32C2×AGL(1,ℤ/8)12yes—
389C3×D3—44no—
390C3×D3#44214yescomplemented
391C24—62no—
392C2×D4—38no—
393C2×D4—32no—
394C2×D4—64no—
395C2×D4—62no—
396C2×D4C2×D3212yes—
397C22×C4—31no—
398C22×C4—62no—
399C22×C4—92no—
400C22×C4—182no—
401C22×C4—182no—
402C22×C4—182no—
403C22×C4—182no—
404C22×C4—368no—
405D8—38no—
406D8—34no—
407D8D3×Dic314yescomplemented
408C2×C8—31no—
409C2×C8—34no—
410C2×C8—31no—
411C2×C8—91no—
412C2×C8—182no—
413C2×C8C2×D3211yescharacteristic
414C4⋊C4—32no—
415C4⋊C4—92no—
416C4⋊C4—182no—
417C22⋊C4—62no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C42—31no—
422C42—92no—
423C42—91no—
424C22×C3—24no—
425C22×C3—24no—
426C22×C3—21no—
427C22×C3—34no—
428C22×C3—32no—
429C22×C3—44no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—64no—
435C22×C3—82no—
436C22×C3—82no—
437C22×C3—1216no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3C2×D3×D411yescharacteristic
441C22×C3C2×D3×D411yescharacteristic
442C2×D3—24no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—416no—
446C2×D3#91114yes—
447C2×D3D4×Dic312yes—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—32no—
451C3×C4—62no—
452C3×C4—122no—
453C3×C4C22×C4×D311yescharacteristic
454C3×C4C2×#23711yescharacteristic
455C3×C4D3×#4111yescharacteristic
456C3×C4C23×Dic311yescharacteristic
457Dic3—22no—
458Dic3—42no—
459Dic3—62no—
460Dic3—62no—
461Dic3—122no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465Dic3D4×Dic312yes—
466C32C2×#44211yescharacteristic, complemented, Sylow
467C23—22no—
468C23—31no—
469C23—68no—
470C23—62no—
471C23—124no—
472C23—124no—
473D4—22no—
474D4—34no—
475D4—68no—
476D4—62no—
477D4C2×D3×Dic314yescomplemented
478C2×C4—31no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—62no—
483C2×C4—92no—
484C2×C4—124no—
485C2×C4—184no—
486C2×C4—182no—
487C2×C4—364no—
488C2×C4—364no—
489C2×C4—364no—
490C2×C4—364no—
491C2×C4C22×D3211yescharacteristic
492C8—32no—
493C8—61no—
494C8—181no—
495C8C2×D3×Dic312yescomplemented
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—34no—
499C2×C3—44no—
500C2×C3—44no—
501C2×C3—84no—
502C2×C3—124no—
503C2×C3C4×D3×D411yescharacteristic
504C2×C3C2×#91112yes—
505C2×C3D3×AGL(1,ℤ/8)12yes—
506C2×C3C2×D4×Dic311yescharacteristic
507D3—44no—
508D3#515214yesdirect product factor
509C22—24no—
510C22—32no—
511C22—34no—
512C22—42no—
513C22—42no—
514C22—64no—
515C22—1216no—
516C22—122no—
517C22—122no—
518C22D32×D411yescharacteristic
519C4—32no—
520C4—62no—
521C4—122no—
522C4—182no—
523C4—362no—
524C4D3×#23711yescharacteristic
525C4C22×D3×Dic311yescharacteristic
526C3—21no—
527C3D3×#44211yescharacteristic, complemented
528C3C2×#515211yescharacteristic, complemented
529C2—34no—
530C2—44no—
531C2—124no—
532C2D3×#91112yes—
533C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D8C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32C2×#442
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. D3×D4×Dic3C2semidirect
3. #10592851C2semidirect
4. C3×#5152C2semidirect
5. #10591436C2semidirect
6. #10591430C2semidirect
7. D3×#832C2semidirect
8. #10590781C2semidirect
9. #10590771C2semidirect
10. D3×#817C2semidirect
11. D3×#815C2semidirect
17. D4×C3⋊Dic3C22semidirect
18. C3×D4×Dic3C22semidirect
20. C3×D3×D8C4semidirect
26. #63898C22semidirect
27. Dic3×D12C22semidirect
31. #63659C22semidirect
32. #63644C22semidirect
33. #63642C22semidirect
34. C3×#832C22semidirect
35. C3×#817C22semidirect
36. C3×#815C22semidirect
37. #63573C22semidirect
38. #63563C22semidirect
39. #63562C22semidirect
40. #63555C22semidirect
41. #63554C22semidirect
55. #5152D3direct (N × H)
71. C3×D3×D4C2×C4semidirect
79. C32×D8C2×C4semidirect
86. C3×#213C2×C4semidirect
91. C3×D24C2×C4semidirect
92. C3×D3×C8C2×C4semidirect
119. D4×Dic3C2×D3semidirect
125. D3×D8Dic3semidirect
143. #832C2×D3semidirect
149. #817C2×D3semidirect
156. #815C2×D3semidirect
167. C32×D4C22×C4semidirect
178. C3×D12C22×C4semidirect
185. C32×C8C22×C4semidirect
188. C3×C3⋊C8C22×C4semidirect
222. D3×D4C2×Dic3semidirect
233. C3×D8C4×D3semidirect
234. C3×D8C2×Dic3semidirect
250. #213C2×Dic3semidirect
271. D24C2×Dic3semidirect
273. D3×C8C2×Dic3semidirect
339. C3×D4C2×C4×D3semidirect
340. C3×D4C22×Dic3semidirect
369. D12C22×Dic3semidirect
379. C3×C8C2×C4×D3semidirect
380. C3×C8C22×Dic3semidirect
385. C3⋊C8C22×Dic3semidirect
390. C3×D3#442semidirect
407. D8D3×Dic3semidirect
466. C32C2×#442semidirect
477. D4C2×D3×Dic3semidirect
495. C8C2×D3×Dic3semidirect
508. D3#5152direct (N × H)
527. C3D3×#442semidirect
528. C3C2×#5152semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
D3×D4×Dic32
#105928512
C3×#51522
#105914362
#105914302
D3×#8322
#105907812
#105907712
D3×#8172
D3×#8152
C2×#51523
D3×#4423