Finite Group Databasebeta

← D3×#5155 #11874263

Subgroups — D3×#5155 #11874263

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×C3×D3×D8C211yesmaximal, characteristic
2D3×#936C212yesmaximal, complemented
3C2×D3×#214C212yesmaximal, complemented
4C2×D3×Dic12C211yesmaximal, characteristic, complemented
5#10592854C211yesmaximal, characteristic, complemented
6C3×#5155C211yesmaximal, characteristic, complemented
7#10591474C212yesmaximal, complemented
8#10591470C212yesmaximal, complemented
9#10590869C211yesmaximal, characteristic, complemented
10#10590864C211yesmaximal, characteristic, complemented
11D3×C8×Dic3C211yesmaximal, characteristic, complemented
12C2×#5155—31nomaximal
13D3×#495—31nomaximal
14C2×C3×D3×D4C2212yes—
15C2×D3×Dic6C2212yes—
16C2×C32×D8C2211yescharacteristic
17#64145C2212yescomplemented
18C2×#3754C2212yescomplemented
19C2×#3746C2211yescharacteristic, complemented
20C3×#936C2212yescomplemented
21C2×C3×#214C2212yescomplemented
22C2×C3×#213C2212yes—
23C3×D3×D8—24no—
24C2×C3×Dic12C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27D3×#217—24no—
28#63959—24no—
29D3×#214—28no—
30C4×D3×Dic3C2211yescharacteristic
31#63863C2212yescomplemented
32#63860C2212yescomplemented
33C2×#3719C2212yescomplemented
34C2×#3716C2212yescomplemented
35C2×#3715C2212yescomplemented
36C2×D3×C3⋊C8C2211yescharacteristic
37D3×Dic12—24no—
38C8×C3⋊Dic3C2211yescharacteristic, complemented
39C3×C8×Dic3C2211yescharacteristic, complemented
40#63553C2211yescharacteristic, complemented
41Dic3×C3⋊C8C2211yescharacteristic, complemented
42C22×C3×D8—31no—
43C2×#936—32no—
44C22×#214—32no—
45C2×D3×Q16—31no—
46C2×D3×SD16—32no—
47C2×D3×D8D311yescharacteristic
48C22×Dic12—31no—
49D3×#124—32no—
50C3×#495—31no—
51#5191—31no—
52#5168—32no—
53#5155—31no—
54#5155—31no—
55#5155—32no—
56#5155—32no—
57#5155—31no—
58#5155—31no—
59#5155—61no—
60#5155D311yescharacteristic, direct product factor
61C2×C8×Dic3—31no—
62#5059—32no—
63#4696—31no—
64C4×D3×C8—31no—
65C23×C3×D3—22no—
66C2×C32×D4C2312yes—
67C2×#634C2312yes—
68C2×C3×#67—22no—
69C3×D3×D4—24no—
70C3×D3×D4—24no—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×#627—22no—
75C2×D3×Dic3—22no—
76C2×D3×Dic3D412yes—
77D3×Dic6—24no—
78D3×Dic6—24no—
79C32×D8—22no—
80C2×C32×C8C2311yescharacteristic
81#3757—24no—
82#3754—24no—
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3746—22no—
86C3×#217—24no—
87C3×#214—24no—
88C3×#213—24no—
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12—22no—
93C3×D24—22no—
94C3×D3×C8D414yes—
95(C2×D3)⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97Dic32D412yes—
98#3719—24no—
99#3716—24no—
100#3715—24no—
101D3×C3⋊C8D414yes—
102C2×#495—91noSylow
103C22×C3×D4—32no—
104C2×D3×Q8—32no—
105C2×D3×D4C2×D312yes—
106C22×Dic6—32no—
107C2×C3×Q16—31no—
108C2×C3×SD16—32no—
109C2×C3×D8—21no—
110C2×C3×D8—32no—
111C2×C3×D8—31no—
112C2×C3×D8—64no—
113C2×C3×D8C2×D311yescharacteristic
114C2×C3×D8C2×D311yescharacteristic
115C22×C3×C8—31no—
116C3×#124—32no—
117C2×#217—64no—
118#947—32no—
119C2×#216—32no—
120C2×#215—32no—
121#936—32no—
122#936—32no—
123#936—32no—
124#936—32no—
125#936—62no—
126#936—64no—
127#936C2×D312yescomplemented
128C2×#214—32no—
129C2×#214—32no—
130C2×#214—32no—
131C2×#214—32no—
132C2×#214—62no—
133C2×#214—68no—
134C2×#214C2×D312yescomplemented
135C2×#213C2×D312yes—
136C2×C4×Dic3—31no—
137C22×C3⋊C8—31no—
138D3×Q16—64no—
139D3×SD16—68no—
140D3×D8—24no—
141C2×Dic12—32no—
142C2×Dic12—31no—
143C2×Dic12—31no—
144C2×Dic12—61no—
145C2×Dic12—64no—
146C2×Dic12C2×D311yescharacteristic, complemented
147C2×D24C2×D311yescharacteristic
148C2×#204—32no—
149C2×D3×C8—31no—
150C2×D3×C8C2×D311yescharacteristic
151#885—64no—
152D3×C22⋊C4—64no—
153#875—32no—
154C42×D3—31no—
155C3×C4×C8—31no—
156C8×Dic3—31no—
157C8×Dic3—31no—
158C8×Dic3—31no—
159C8×Dic3—31no—
160C8×Dic3—31no—
161C8×Dic3—61no—
162C8×Dic3C2×D311yescharacteristic, complemented
163C4×C3⋊C8—31no—
164C23×C32—22no—
165C22×C3×D3—22no—
166C22×C3×D3—44no—
167C22×C3×D3—48no—
168C22×C3×D3C2×D411yescharacteristic
169C32×D4—22no—
170C32×D4—22no—
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C2×D412yes—
174#634—22no—
175#634—22no—
176C3×#67—44no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D411yescharacteristic
180C3×D12—22no—
181C3×D12—22no—
182C3×C4×D3C2×D412yes—
183C3×C4×D3C2×D412yes—
184C3×Dic6—22no—
185C3×Dic6—22no—
186#627—44no—
187D3×Dic3—24no—
188D3×Dic3—44no—
189C32×C8C2×D412yes—
190C3⋊(C3⋊C8)C2×D412yes—
191C3×C3⋊C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C22×Q16—91no—
194C22×SD16—92no—
195C22×D8—31no—
196C2×#124—92no—
197#495—31no—
198#495—91no—
199#495—92no—
200#495—92no—
201#495—91no—
202#495—91no—
203C2×C4×C8—91no—
204C24×C3—62no—
205C23×D3—22no—
206C2×C3×Q8—32no—
207C2×C3×D4—22no—
208C2×C3×D4—32no—
209C2×C3×D4—64no—
210C2×C3×D4—64no—
211C2×C3×D4—62no—
212C2×C3×D4C22×D312yes—
213C2×C3×D4C22×D312yes—
214C22×C3×C4—31no—
215C2×#67—22no—
216C22×Dic3—32no—
217C22×Dic3—62no—
218D3×Q8—64no—
219D3×Q8—64no—
220D3×D4—24no—
221D3×D4—24no—
222C2×D12C22×D312yes—
223C2×C4×D3—32no—
224C2×C4×D3—62no—
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—22no—
237C3×D8—22no—
238C3×D8—42no—
239C3×D8—64no—
240C3×D8—62no—
241C2×C3×C8—21no—
242C2×C3×C8—31no—
243C2×C3×C8—31no—
244C2×C3×C8—34no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C22⋊C4—64no—
248C3×C42—31no—
249#217—24no—
250#217—64no—
251#217—64no—
252#217—64no—
253#217—64no—
254#217—124no—
255#216—64no—
256#215—64no—
257#214—24no—
258#214—64no—
259#214—64no—
260#214—64no—
261#214—64no—
262#214—124no—
263#213—24no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266C4×Dic3—31no—
267C4×Dic3—31no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—61no—
271C4×Dic3C22×D311yescharacteristic
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278Dic12—22no—
279Dic12—64no—
280Dic12—62no—
281Dic12—62no—
282Dic12—122no—
283D24—22no—
284#204—64no—
285D3×C8—34no—
286D3×C8#6714yes—
287C22×C32—42no—
288C22×C32—44no—
289C22×C32C22×D411yescharacteristic
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—88no—
293C2×C3×D3#12712yes—
294C2×C3×D3#13514yes—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3⋊Dic3—22no—
298C3⋊Dic3—42no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3#12712yes—
302C22×Q8—92no—
303C22×D4—32no—
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—32no—
314C2×D8—31no—
315C2×D8—64no—
316C2×D8D3211yescharacteristic
317C22×C8—31no—
318C22×C8—91no—
319#124—32no—
320#124—92no—
321#124—92no—
322#124—92no—
323#124—184no—
324C2×C22⋊C4—184no—
325C2×C42—91no—
326C4×C8—31no—
327C4×C8—91no—
328C4×C8—91no—
329C4×C8—91no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—31no—
333C23×C3—42no—
334C23×C3—62no—
335C23×C3—124no—
336C23×C3—128no—
337C22×D3—22no—
338C22×D3—48no—
339C22×D3—44no—
340C22×D3D3×D411yescharacteristic
341C3×Q8—62no—
342C3×Q8—62no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—22no—
346C3×D4—22no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—124no—
352C2×C3×C4—21no—
353C2×C3×C4—31no—
354C2×C3×C4—32no—
355C2×C3×C4—32no—
356C2×C3×C4—32no—
357C2×C3×C4—62no—
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—44no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—62no—
365C2×Dic3—64no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—122no—
369C2×Dic3—124no—
370C2×Dic3D3×D412yes—
371C2×Dic3D3×D411yescharacteristic
372D12—22no—
373D12—22no—
374C4×D3—64no—
375C4×D3—124no—
376C4×D3D3×D412yes—
377C4×D3C2×#6712yes—
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—32no—
390C3×C8—32no—
391C3×C8D3×D412yes—
392C3×C8C2×#6712yes—
393C3⋊C8—32no—
394C3⋊C8—32no—
395C3⋊C8—62no—
396C3⋊C8D3×D412yes—
397C3⋊C8C2×#6712yes—
398C2×C32—82no—
399C2×C32C2×#12711yescharacteristic
400C2×C32C2×#13512yes—
401C3×D3—82no—
402C3×D3#49514yescomplemented
403C24—62no—
404C2×Q8—32no—
405C2×Q8—92no—
406C2×Q8—182no—
407C2×Q8—184no—
408C2×Q8—184no—
409C2×D4—32no—
410C2×D4—64no—
411C2×D4—64no—
412C2×D4—62no—
413C2×D4C2×D3212yes—
414C22×C4—31no—
415C22×C4—92no—
416C22×C4—182no—
417Q16—62no—
418Q16—184no—
419Q16—182no—
420SD16—64no—
421SD16—184no—
422SD16—184no—
423SD16—184no—
424D8—22no—
425D8—64no—
426D8—62no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—34no—
430C2×C8—94no—
431C2×C8—91no—
432C2×C8C2×D3211yescharacteristic
433C22⋊C4—64no—
434C22⋊C4—184no—
435C22⋊C4—184no—
436C22⋊C4—184no—
437C42—31no—
438C42—92no—
439C42—91no—
440C22×C3—21no—
441C22×C3—32no—
442C22×C3—34no—
443C22×C3—42no—
444C22×C3—44no—
445C22×C3—44no—
446C22×C3—42no—
447C22×C3—82no—
448C22×C3—84no—
449C22×C3—122no—
450C22×C3—124no—
451C22×C3—248no—
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C2×D3×D411yescharacteristic
454C2×D3—44no—
455C2×D3—42no—
456C2×D3—88no—
457C2×D3#91214yes—
458C2×D3#94012yes—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—32no—
462C3×C4—62no—
463C3×C4—122no—
464C3×C4C2×D3×D411yescharacteristic
465C3×C4C2×D3×D411yescharacteristic
466C3×C4C2×D3×D411yescharacteristic
467C3×C4C22×#6711yescharacteristic
468Dic3—22no—
469Dic3—42no—
470Dic3—62no—
471Dic3—62no—
472Dic3—122no—
473Dic3—122no—
474Dic3—122no—
475Dic3—242no—
476Dic3#94012yes—
477C32C2×#49511yescharacteristic, complemented, Sylow
478C23—22no—
479C23—31no—
480C23—62no—
481C23—124no—
482C23—128no—
483Q8—62no—
484Q8—62no—
485Q8—182no—
486Q8—182no—
487Q8—364no—
488D4—22no—
489D4—22no—
490D4—62no—
491D4—62no—
492D4—124no—
493C2×C4—31no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—62no—
498C2×C4—92no—
499C2×C4—184no—
500C2×C4—182no—
501C2×C4—364no—
502C2×C4C22×D3211yescharacteristic
503C8—32no—
504C8—32no—
505C8—92no—
506C8D3×#6712yes—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—34no—
510C2×C3—82no—
511C2×C3—82no—
512C2×C3—162no—
513C2×C3—242no—
514C2×C3D3×#12711yescharacteristic
515C2×C3C2×#91212yes—
516C2×C3D3×#13512yes—
517C2×C3C2×#94011yescharacteristic
518D3—82no—
519D3#515514yesdirect product factor
520C22—34no—
521C22—32no—
522C22—44no—
523C22—42no—
524C22—124no—
525C22—122no—
526C22—248no—
527C22D32×D411yescharacteristic
528C4—32no—
529C4—62no—
530C4—122no—
531C4—182no—
532C4—362no—
533C4D32×D411yescharacteristic
534C4C2×D3×#6711yescharacteristic
535C3—21no—
536C3D3×#49511yescharacteristic, complemented
537C3C2×#515511yescharacteristic, complemented
538C2—34no—
539C2—82no—
540C2—242no—
541C2D3×#91212yes—
542C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D8C2
hypercenterC2×D8D32
hypocenterC32C2×#495
LCSG ▷ C2×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×#936C2semidirect
3. C2×D3×#214C2semidirect
4. C2×D3×Dic12C2semidirect
5. #10592854C2semidirect
6. C3×#5155C2semidirect
7. #10591474C2semidirect
8. #10591470C2semidirect
9. #10590869C2semidirect
10. #10590864C2semidirect
11. D3×C8×Dic3C2semidirect
17. #64145C22semidirect
18. C2×#3754C22semidirect
19. C2×#3746C22semidirect
20. C3×#936C22semidirect
21. C2×C3×#214C22semidirect
24. C2×C3×Dic12C22semidirect
31. #63863C22semidirect
32. #63860C22semidirect
33. C2×#3719C22semidirect
34. C2×#3716C22semidirect
35. C2×#3715C22semidirect
38. C8×C3⋊Dic3C22semidirect
39. C3×C8×Dic3C22semidirect
40. #63553C22semidirect
41. Dic3×C3⋊C8C22semidirect
60. #5155D3direct (N × H)
127. #936C2×D3semidirect
134. C2×#214C2×D3semidirect
146. C2×Dic12C2×D3semidirect
162. C8×Dic3C2×D3semidirect
402. C3×D3#495semidirect
477. C32C2×#495semidirect
519. D3#5155direct (N × H)
536. C3D3×#495semidirect
537. C3C2×#5155semidirect

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×#9362
C2×D3×#2142
C2×D3×Dic122
#105928542
C3×#51552
#105914742
#105914702
#105908692
#105908642
D3×C8×Dic32
C2×#51553
D3×#4953