Finite Group Databasebeta

← D3×#5056 #11873456

Subgroups — D3×#5056 #11873456

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#124C211yesmaximal, characteristic
2D3×#870C211yesmaximal, characteristic, complemented
3#10592755C211yesmaximal, characteristic, complemented
4C3×#5056C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6D3×#835C212yesmaximal, complemented
7#10591478C212yesmaximal, complemented
8D3×#832C212yesmaximal
9C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
10#10590278C211yesmaximal, characteristic, complemented
11#10590274C211yesmaximal, characteristic, complemented
12C2×#5056—31nomaximal
13D3×#488—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C2×C3×D3×D4C2211yescharacteristic
16C32×#124C2211yescharacteristic
17#64079C2211yescharacteristic, complemented
18C3×#947C2211yescharacteristic
19C3×#936C2211yescharacteristic
20C3×#885—22no—
21C3×D3×C22⋊C4—22no—
22C3×#875C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24C3×#870C2211yescharacteristic, complemented
25D3×C4⋊Dic3C2212yes—
26D3×Dic3⋊C4—22no—
27#63869C2212yescomplemented
28#63867—22no—
29C2×D3×C3⋊C8C2212yes—
30#63662C2212yescomplemented
31#63659C2212yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
33C3×#835C2212yescomplemented
34C3×#832C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic, complemented
36#63566C2212yescomplemented
37#63565C2212yescomplemented
38#63563C2212yes—
39#63562C2212yes—
40Dic3×C3⋊C8C2212yescomplemented
41C2×C3×#124—31no—
42D3×#125—31no—
43D3×#124D311yescharacteristic
44C2×#870—31no—
45C3×#488—31no—
46C2×#835—32no—
47C2×#832—32no—
48#5068—31no—
49#5056—31no—
50#5056—31no—
51#5056—31no—
52#5056—32no—
53#5056—32no—
54#5056—31no—
55#5056—61no—
56#5056D311yescharacteristic, direct product factor
57C2×C4×C3⋊C8—31no—
58D3×#103—32no—
59#4800—32no—
60D3×#102—32no—
61#4768—32no—
62#4697—31no—
63C4×D3×C8—31no—
64C23×C3×D3—21no—
65C2×C32×Q8C2311yescharacteristic
66C2×C32×D4C2311yescharacteristic
67C2×C3×#67—21no—
68C3×D3×Q8—24no—
69C3×D3×D4—24no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3D412yes—
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×D3×Dic3—22no—
77C32×C22⋊C4—22no—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80#3750—22no—
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×#217—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3D412yes—
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2312yes—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93D3×C3⋊C8—24no—
94C2×#488—91noSylow
95C22×C3×Q8—31no—
96C22×C3×D4—31no—
97C2×D3×Q8C2×D311yescharacteristic
98C2×D3×D4C2×D311yescharacteristic
99C3×#125—31no—
100C3×#124—21no—
101C3×#124—31no—
102C3×#124—31no—
103C3×#124—31no—
104C3×#124—62no—
105C3×#124C2×D311yescharacteristic
106C3×#124C2×D311yescharacteristic
107C2×C3×C22⋊C4—62no—
108C2×C3×C42—31no—
109#947C2×D311yescharacteristic
110#936C2×D311yescharacteristic
111C2×C4⋊Dic3—32no—
112C2×Dic3⋊C4—62no—
113C22×C3⋊C8—32no—
114C2×D3×C8—32no—
115D3×C4⋊C4—32no—
116D3×C4⋊C4—62no—
117#890—32no—
118#889—62no—
119#885—22no—
120D3×C22⋊C4—22no—
121#875C2×D311yescharacteristic
122C42×D3C2×D311yescharacteristic
123#870—31no—
124#870—31no—
125#870—32no—
126#870—61no—
127#870—62no—
128#870C2×D311yescharacteristic, complemented
129C3×#103—32no—
130C3×#102—32no—
131C3×C4×C8—31no—
132#835—32no—
133#835—32no—
134#835—32no—
135#835—32no—
136#835—62no—
137#835C2×D312yescomplemented
138#832—32no—
139#832—32no—
140#832—32no—
141#832—32no—
142#832—62no—
143#832C2×D312yes—
144#821—32no—
145#816—32no—
146C8×Dic3—32no—
147#810—32no—
148#809—32no—
149C4×C3⋊C8—31no—
150C4×C3⋊C8—31no—
151C4×C3⋊C8—32no—
152C4×C3⋊C8—61no—
153C4×C3⋊C8C2×D311yescharacteristic, complemented
154C23×C32—21no—
155C22×C3×D3—21no—
156C22×C3×D3—42no—
157C22×C3×D3—44no—
158C22×C3×D3C2×D411yescharacteristic
159C32×Q8—22no—
160C32×D4—22no—
161C2×C32×C4—21no—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—22no—
165C3×#67—42no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×C4×D3—24no—
172C3×C4×D3—42no—
173C3×C4×D3#4114yes—
174C3×Dic6—22no—
175C3×Dic6—42no—
176D3×Dic3—44no—
177C3⋊(C3⋊C8)—22no—
178C3×C3⋊C8—22no—
179C2×#125—91no—
180C2×#124—31no—
181#488—31no—
182#488—91no—
183#488—92no—
184#488—92no—
185#488—91no—
186#488—91no—
187C2×#103—92no—
188C2×#102—92no—
189C2×C4×C8—91no—
190C24×C3—61no—
191C23×D3—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—31no—
194C2×C3×Q8—61no—
195C2×C3×Q8—64no—
196C2×C3×Q8C22×D311yescharacteristic
197C2×C3×Q8C22×D311yescharacteristic
198C2×C3×D4—21no—
199C2×C3×D4—31no—
200C2×C3×D4—64no—
201C2×C3×D4—61no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C22×D311yescharacteristic
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—61no—
207C2×#67—21no—
208C22×Dic3—62no—
209D3×Q8—24no—
210D3×D4—24no—
211C2×D12C22×D311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—62no—
214C2×C4×D3#6712yes—
215C2×C4×D3C22×D311yescharacteristic
216C2×Dic6—21no—
217C2×Dic6C22×D311yescharacteristic
218C2×C3×C8—32no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—62no—
221C3×C22⋊C4—22no—
222C3×C22⋊C4—22no—
223C3×C22⋊C4—42no—
224C3×C22⋊C4—62no—
225C3×C22⋊C4—62no—
226C3×C22⋊C4—62no—
227C3×C42—21no—
228C3×C42—32no—
229C3×C42—31no—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232#217—22no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—22no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3C22×D312yes—
241Dic3⋊C4—22no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—122no—
249C4×Dic3#6712yes—
250C4×Dic3C22×D311yescharacteristic
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—64no—
255C2×C3⋊C8C22×D312yes—
256D3×C8—64no—
257C22×C32—41no—
258C22×C32—42no—
259C22×C32C22×D411yescharacteristic
260C2×C3×D3—41no—
261C2×C3×D3—42no—
262C2×C3×D3—84no—
263C2×C3×D3#12412yes—
264C2×C3×D3#13514yes—
265C32×C4—22no—
266C32×C4—41no—
267C32×C4C2×#4112yes—
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—41no—
271C3×Dic3—42no—
272C3×Dic3#12412yes—
273C22×Q8—31no—
274C22×D4—31no—
275C22×C8—92no—
276#125—31no—
277#125—92no—
278#125—91no—
279#125—182no—
280#124—31no—
281#124—31no—
282#124—31no—
283#124—62no—
284#124D3211yescharacteristic
285C2×C4⋊C4—92no—
286C2×C4⋊C4—182no—
287C2×C22⋊C4—62no—
288C2×C42—31no—
289#103—32no—
290#103—92no—
291#103—92no—
292#103—92no—
293#102—32no—
294#102—92no—
295#102—92no—
296#102—92no—
297C4×C8—31no—
298C4×C8—92no—
299C4×C8—91no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—31no—
303C23×C3—41no—
304C23×C3—61no—
305C23×C3—122no—
306C23×C3—124no—
307C22×D3—21no—
308C22×D3—42no—
309C22×D3—44no—
310C22×D3C2×#6711yescharacteristic
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—42no—
314C3×Q8—62no—
315C3×Q8—122no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—42no—
319C3×D4—62no—
320C3×D4—122no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—31no—
326C2×C3×C4—34no—
327C2×C3×C4—32no—
328C2×C3×C4—41no—
329C2×C3×C4—64no—
330C2×C3×C4—61no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4D3×D412yes—
334C2×C3×C4C2×#6712yes—
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337#67—42no—
338C2×Dic3—22no—
339C2×Dic3—21no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—122no—
343C2×Dic3—124no—
344C2×Dic3C2×#6712yes—
345C2×Dic3C2×#6711yescharacteristic
346D12—22no—
347C4×D3—24no—
348C4×D3—42no—
349C4×D3—124no—
350C4×D3#23714yes—
351Dic6—22no—
352Dic6—42no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C2×C32—81no—
359C2×C32C2×#12411yescharacteristic
360C2×C32C2×#13512yes—
361C3×D3—81no—
362C3×D3#48814yescomplemented
363C24—61no—
364C2×Q8—31no—
365C2×Q8—61no—
366C2×Q8—64no—
367C2×Q8C2×D3211yescharacteristic
368C2×D4—31no—
369C2×D4—64no—
370C2×D4—61no—
371C2×D4C2×D3211yescharacteristic
372C22×C4—31no—
373C22×C4—32no—
374C22×C4—61no—
375C22×C4—182no—
376C2×C8—32no—
377C2×C8—92no—
378C2×C8—184no—
379C4⋊C4—32no—
380C4⋊C4—62no—
381C4⋊C4—92no—
382C4⋊C4—182no—
383C4⋊C4—182no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C22⋊C4—22no—
387C22⋊C4—62no—
388C22⋊C4—62no—
389C22⋊C4—62no—
390C42—31no—
391C42—32no—
392C42C2×D3211yescharacteristic
393C22×C3—21no—
394C22×C3—32no—
395C22×C3—34no—
396C22×C3—41no—
397C22×C3—42no—
398C22×C3—41no—
399C22×C3—42no—
400C22×C3—81no—
401C22×C3—82no—
402C22×C3—121no—
403C22×C3—122no—
404C22×C3—244no—
405C22×C3C2×D3×D411yescharacteristic
406C22×C3C22×#6711yescharacteristic
407C2×D3—41no—
408C2×D3—42no—
409C2×D3—84no—
410C2×D3#93612yes—
411C2×D3#95014yes—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—32no—
416C3×C4—42no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—62no—
420C3×C4—81no—
421C3×C4—121no—
422C3×C4—122no—
423C3×C4C2×#23712yes—
424C3×C4D3×#4112yes—
425Dic3—22no—
426Dic3—42no—
427Dic3—41no—
428Dic3—122no—
429Dic3—122no—
430Dic3—242no—
431Dic3#93612yes—
432C32C2×#48811yescharacteristic, complemented, Sylow
433C23—21no—
434C23—31no—
435C23—61no—
436C23—122no—
437C23—124no—
438Q8—22no—
439Q8—62no—
440Q8—122no—
441D4—22no—
442D4—62no—
443D4—122no—
444C2×C4—21no—
445C2×C4—31no—
446C2×C4—34no—
447C2×C4—32no—
448C2×C4—64no—
449C2×C4—61no—
450C2×C4—62no—
451C2×C4—122no—
452C2×C4—182no—
453C2×C4—364no—
454C2×C4D3×#6712yes—
455C2×C4C22×D3211yescharacteristic
456C8—62no—
457C8—182no—
458C2×C3—21no—
459C2×C3—22no—
460C2×C3—34no—
461C2×C3—81no—
462C2×C3—81no—
463C2×C3—161no—
464C2×C3—241no—
465C2×C3D3×#12411yescharacteristic
466C2×C3D3×#13512yes—
467C2×C3C2×#93611yescharacteristic
468C2×C3C2×#95012yes—
469D3—81no—
470D3#505614yesdirect product factor
471C22—32no—
472C22—34no—
473C22—41no—
474C22—42no—
475C22—121no—
476C22—122no—
477C22—244no—
478C22C2×D3×#6711yescharacteristic
479C4—22no—
480C4—32no—
481C4—41no—
482C4—62no—
483C4—121no—
484C4—122no—
485C4—362no—
486C4D3×#23712yes—
487C3—21no—
488C3D3×#48811yescharacteristic, complemented
489C3C2×#505611yescharacteristic, complemented
490C2—34no—
491C2—81no—
492C2—241no—
493C2D3×#93611yescharacteristic
494C2D3×#95012yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenter#124D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D3×#870C2semidirect
3. #10592755C2semidirect
4. C3×#5056C2semidirect
5. #10591614C2semidirect
6. D3×#835C2semidirect
7. #10591478C2semidirect
9. C4×D3×C3⋊C8C2semidirect
10. #10590278C2semidirect
11. #10590274C2semidirect
17. #64079C22semidirect
24. C3×#870C22semidirect
27. #63869C22semidirect
30. #63662C22semidirect
32. C4×C3⋊(C3⋊C8)C22semidirect
33. C3×#835C22semidirect
35. C3×C4×C3⋊C8C22semidirect
36. #63566C22semidirect
37. #63565C22semidirect
40. Dic3×C3⋊C8C22semidirect
56. #5056D3direct (N × H)
128. #870C2×D3semidirect
137. #835C2×D3semidirect
153. C4×C3⋊C8C2×D3semidirect
362. C3×D3#488semidirect
432. C32C2×#488semidirect
470. D3#5056direct (N × H)
488. C3D3×#488semidirect
489. C3C2×#5056semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1242
D3×#8702
#105927552
C3×#50562
#105916142
D3×#8352
#105914782
D3×#8322
C4×D3×C3⋊C82
#105902782
#105902742
C2×#50563
D3×#4883