Finite Group Databasebeta

← D3×#4715 #11874393

Subgroups — D3×#4715 #11874393

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C212yesmaximal, complemented
2C2×D3×#204C212yesmaximal
3D3×#875C211yesmaximal, characteristic
4D3×#869C211yesmaximal, characteristic, complemented
5#10592414C211yesmaximal, characteristic, complemented
6C3×#4715C211yesmaximal, characteristic, complemented
7C3×D3×#97C211yesmaximal, characteristic, complemented
8#10590899C212yesmaximal, complemented
9#10590897C212yesmaximal, complemented
10#10590374C211yesmaximal, characteristic, complemented
11#10590372C211yesmaximal, characteristic, complemented
12D3×#497—31nomaximal
13C2×#4715—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×D3×Dic6C2212yes—
16C2×D3×Dic6C2211yescharacteristic
17C2×#3746C2212yescomplemented
18C2×#3744C2212yes—
19#64084C2211yescharacteristic
20#64078C2211yescharacteristic, complemented
21C2×C3×Dic12C2212yescomplemented
22C2×C3×#204C2212yes—
23C2×C3×D3×C8C2212yes—
24C3×#875C2211yescharacteristic
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—22no—
28#63918—22no—
29D3×C4⋊Dic3—22no—
30#63866C2212yescomplemented
31#63864C2211yescharacteristic
32#63860C2211yescharacteristic
33#63852—22no—
34C2×#3719C2212yescomplemented
35C2×#3719C2212yescomplemented
36C2×#3717C2212yes—
37C2×#3716C2212yes—
38D3×Dic12—28no—
39D3×#204—28no—
40C32×#97C2211yescharacteristic, complemented
41C3×#815C2212yescomplemented
42C3×#803C2211yescharacteristic, complemented
43C2×D3×Q16—32no—
44C2×D3×SD16—32no—
45C22×Dic12—32no—
46C22×#204—32no—
47D3×C4⋊Q8—31no—
48D3×#124—31no—
49C2×#875—31no—
50C2×#869—31no—
51C3×#497—31no—
52C2×C3×#97—31no—
53#5190—32no—
54#5167—32no—
55#5086—31no—
56#5060—31no—
57#4715—32no—
58#4715—32no—
59#4715—31no—
60#4715—31no—
61#4715—31no—
62#4715—31no—
63#4715—61no—
64#4715D311yescharacteristic, direct product factor
65D3×#97D311yescharacteristic, complemented
66C22×D32—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×#634C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3D412yes—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×#627—22no—
77C2×#626—21no—
78C2×D3×Dic3—22no—
79C2×D3×Dic3—21no—
80D3×D12—24no—
81D3×Dic6—24no—
82D3×Dic6—24no—
83D3×Dic6—24no—
84C2×C32×C8C2312yes—
85C32×C42C2311yescharacteristic
86#3752—22no—
87C4⋊(C3⋊Dic3)—22no—
88#3746—24no—
89#3744—24no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—22no—
92C3×C4×Dic3D412yes—
93C3×C4×Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C3×Dic12—24no—
96C3×#204—24no—
97C3×D3×C8D418yes—
98Dic3⋊Dic3—24no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3719—24no—
102#3719—24no—
103#3717—24no—
104#3716—24no—
105C2×#497—91noSylow
106C2×D3×Q8—31no—
107C2×D3×Q8—32no—
108C2×D3×D4—31no—
109C22×D12—31no—
110C22×Dic6—32no—
111C22×Dic6—31no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C22×C3×C8—32no—
115C3×C4⋊Q8—31no—
116C3×#124—31no—
117C2×C3×C42—31no—
118#947—31no—
119#944—32no—
120C2×#216—32no—
121C2×#216—32no—
122C2×#215—32no—
123#936—31no—
124C2×#214—32no—
125C2×(C2×D3)⋊C4—62no—
126C2×C4⋊Dic3—62no—
127D3×Q16—68no—
128D3×SD16—68no—
129C2×Dic12—32no—
130C2×Dic12—32no—
131C2×Dic12—32no—
132C2×Dic12—32no—
133C2×Dic12—62no—
134C2×Dic12—68no—
135C2×Dic12C2×D312yescomplemented
136C2×#204—32no—
137C2×#204—32no—
138C2×#204—32no—
139C2×#204—32no—
140C2×#204—62no—
141C2×#204—68no—
142C2×#204C2×D312yes—
143C2×D3×C8C2×D312yes—
144D3×C4⋊C4—62no—
145#888—62no—
146#885—62no—
147D3×C22⋊C4—62no—
148#875—31no—
149#875—31no—
150#875—31no—
151#875—31no—
152#875—61no—
153#875—62no—
154#875C2×D311yescharacteristic
155C42×D3C2×D311yescharacteristic
156#869—32no—
157#869—31no—
158#869—31no—
159#869—61no—
160#869—62no—
161#869C2×D311yescharacteristic, complemented
162C3×#97—21no—
163C3×#97—32no—
164C3×#97—31no—
165C3×#97C2×D311yescharacteristic, complemented
166C3×#97C2×D311yescharacteristic, complemented
167#815C2×D312yescomplemented
168#803C2×D311yescharacteristic, complemented
169C22×C3⋊D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3C2×D411yescharacteristic
172C2×D32—42no—
173C2×D32—44no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C4⋊(C3⋊D3)—22no—
179#634—22no—
180#634—22no—
181#634—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D411yescharacteristic
186C3×D12—22no—
187C3×C4×D3—24no—
188C3×C4×D3C2×D414yes—
189C3×Dic6—22no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192#627—44no—
193#627—42no—
194#626—42no—
195D3×Dic3—44no—
196D3×Dic3—42no—
197C32×C8C2×D414yes—
198C3×C3⋊C8C2×D414yes—
199C22×Q16—92no—
200C22×SD16—92no—
201C2×C4⋊Q8—91no—
202C2×#124—91no—
203#497—31no—
204#497—91no—
205#497—91no—
206#497—92no—
207#497—92no—
208#497—91no—
209C2×#97—31no—
210C23×D3—61no—
211C23×D3—61no—
212C2×C3×Q8—32no—
213C2×C3×Q8—31no—
214C2×C3×D4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C2×#67—61no—
218C22×Dic3—62no—
219C22×Dic3—61no—
220D3×Q8—64no—
221D3×Q8—64no—
222D3×Q8—64no—
223D3×D4—64no—
224C2×D12—31no—
225C2×D12—31no—
226C2×D12—61no—
227C2×D12—64no—
228C2×D12—61no—
229C2×D12C22×D311yescharacteristic
230C2×C4×D3—61no—
231C2×C4×D3—62no—
232C2×C4×D3D1212yes—
233C2×C4×D3C22×D311yescharacteristic
234C2×Dic6—32no—
235C2×Dic6—32no—
236C2×Dic6—31no—
237C2×Dic6—31no—
238C2×Dic6—62no—
239C2×Dic6—61no—
240C2×Dic6—64no—
241C2×Dic6—64no—
242C2×Dic6—64no—
243C2×Dic6—62no—
244C2×Dic6—61no—
245C2×Dic6—61no—
246C2×Dic6—62no—
247C2×Dic6C22×D312yes—
248C2×Dic6C22×D311yescharacteristic
249C3×Q16—64no—
250C3×SD16—64no—
251C2×C3×C8—22no—
252C2×C3×C8—32no—
253C2×C3×C8—38no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C22×D312yes—
256C3×C4⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C42—21no—
259C3×C42—32no—
260C3×C42—31no—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D311yescharacteristic
263#217—62no—
264#216—64no—
265#216—64no—
266#215—64no—
267#214—64no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—122no—
275C4⋊Dic3—22no—
276C4⋊Dic3—64no—
277C4⋊Dic3—62no—
278C4⋊Dic3—62no—
279C4⋊Dic3—122no—
280Dic3⋊C4—64no—
281C4×Dic3D1212yes—
282C4×Dic3C22×D311yescharacteristic
283C2×C3⋊C8C22×D312yes—
284Dic12—24no—
285Dic12—64no—
286Dic12—64no—
287Dic12—64no—
288Dic12—64no—
289Dic12—124no—
290#204—24no—
291#204—64no—
292#204—64no—
293#204—64no—
294#204—64no—
295#204—124no—
296D3×C8D1218yes—
297C22×C32C22×D411yescharacteristic
298C2×C3⋊D3—41no—
299C2×C3⋊D3—42no—
300C2×C3×D3—41no—
301C2×C3×D3—42no—
302C2×C3×D3#12712yes—
303C2×C3×D3#13714yes—
304D32—84no—
305C32×C4—22no—
306C32×C4C22×D412yes—
307C3⋊Dic3—42no—
308C3⋊Dic3—41no—
309C3×Dic3—22no—
310C3×Dic3—42no—
311C3×Dic3—41no—
312C3×Dic3#12712yes—
313C22×Q8—91no—
314C22×Q8—92no—
315C22×D4—91no—
316C2×Q16—32no—
317C2×Q16—92no—
318C2×Q16—92no—
319C2×Q16—92no—
320C2×Q16—188no—
321C2×SD16—32no—
322C2×SD16—92no—
323C2×SD16—92no—
324C2×SD16—92no—
325C2×SD16—188no—
326C22×C8—32no—
327C4⋊Q8—31no—
328C4⋊Q8—92no—
329C4⋊Q8—91no—
330C4⋊Q8—182no—
331#124—31no—
332#124—91no—
333#124—91no—
334#124—91no—
335#124—182no—
336C2×C4⋊C4—182no—
337C2×C22⋊C4—182no—
338C2×C42—31no—
339#97—32no—
340#97—31no—
341#97D3211yescharacteristic, complemented
342C23×C3—31no—
343C23×C3—61no—
344C22×D3—21no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—121no—
348C22×D3—122no—
349C22×D3—124no—
350C22×D3—122no—
351C22×D3—124no—
352C22×D3C2×D1211yescharacteristic
353C3×Q8—62no—
354C3×Q8—62no—
355C3×Q8—62no—
356C3×D4—62no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—31no—
360C2×C3×C4—34no—
361C2×C3×C4—32no—
362C2×C3×C4—64no—
363C2×C3×C4—62no—
364C2×C3×C4—61no—
365C2×C3×C4C2×D1212yes—
366C2×C3×C4D3×D412yes—
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369#67—122no—
370C2×Dic3—22no—
371C2×Dic3—21no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—61no—
376C2×Dic3—122no—
377C2×Dic3—121no—
378C2×Dic3—124no—
379C2×Dic3—122no—
380C2×Dic3C2×D1212yes—
381C2×Dic3C2×D1211yescharacteristic
382D12—22no—
383D12—62no—
384D12—62no—
385D12—122no—
386D12—122no—
387C4×D3—24no—
388C4×D3—122no—
389C4×D3—124no—
390C4×D3C2×D1214yes—
391Dic6—22no—
392Dic6—22no—
393Dic6—22no—
394Dic6—62no—
395Dic6—62no—
396Dic6—62no—
397Dic6—62no—
398Dic6—62no—
399Dic6—62no—
400Dic6—122no—
401Dic6—122no—
402Dic6—122no—
403Dic6—124no—
404Dic6—122no—
405Dic6—122no—
406Dic6—124no—
407C3×C8—24no—
408C3×C8—34no—
409C3×C8C2×D1214yes—
410C3×C8D3×D414yes—
411C3⋊C8C2×D1214yes—
412C2×C32C2×#12711yescharacteristic
413C2×C32C2×#13712yes—
414C3⋊D3—81no—
415C3×D3—81no—
416C3×D3#49714yescomplemented
417C24—181no—
418C2×Q8—31no—
419C2×Q8—32no—
420C2×Q8—91no—
421C2×Q8—92no—
422C2×Q8—181no—
423C2×Q8—182no—
424C2×Q8—184no—
425C2×Q8—184no—
426C2×Q8—184no—
427C2×D4—31no—
428C2×D4—91no—
429C2×D4—184no—
430C2×D4—181no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—181no—
434C22×C4—182no—
435Q16—64no—
436Q16—184no—
437Q16—184no—
438Q16—184no—
439SD16—64no—
440SD16—184no—
441SD16—184no—
442SD16—184no—
443C2×C8—32no—
444C2×C8—38no—
445C2×C8C2×D3212yes—
446C4⋊C4—62no—
447C4⋊C4—184no—
448C4⋊C4—182no—
449C22⋊C4—62no—
450C22⋊C4—182no—
451C22⋊C4—182no—
452C22⋊C4—182no—
453C42—31no—
454C42—32no—
455C42C2×D3211yescharacteristic
456C22×C3—21no—
457C22×C3—32no—
458C22×C3—34no—
459C22×C3—121no—
460C22×C3—122no—
461C22×C3C22×D1211yescharacteristic
462C22×C3C2×D3×D411yescharacteristic
463C2×D3—41no—
464C2×D3—42no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—122no—
468C2×D3—122no—
469C2×D3—241no—
470C2×D3—242no—
471C2×D3—244no—
472C2×D3—244no—
473C2×D3#87412yes—
474C2×D3#90914yes—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—32no—
479C3×C4—42no—
480C3×C4—62no—
481C3×C4—122no—
482C3×C4—121no—
483C3×C4C22×D1212yes—
484C3×C4C2×D3×D412yes—
485Dic3—22no—
486Dic3—42no—
487Dic3—41no—
488Dic3—122no—
489Dic3—121no—
490Dic3—122no—
491Dic3—121no—
492Dic3—242no—
493Dic3—241no—
494Dic3#87412yes—
495C32C2×#49711yescharacteristic, complemented, Sylow
496C23—31no—
497C23—61no—
498C23—181no—
499C23—362no—
500C23—364no—
501Q8—62no—
502Q8—62no—
503Q8—62no—
504Q8—182no—
505Q8—182no—
506Q8—182no—
507Q8—362no—
508Q8—364no—
509D4—62no—
510D4—182no—
511D4—362no—
512C2×C4—31no—
513C2×C4—34no—
514C2×C4—32no—
515C2×C4—64no—
516C2×C4—61no—
517C2×C4—62no—
518C2×C4—181no—
519C2×C4—182no—
520C2×C4—362no—
521C2×C4—364no—
522C2×C4D3×D1212yes—
523C2×C4C22×D3211yescharacteristic
524C8—34no—
525C8D3×D1214yes—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—34no—
529C2×C3—241no—
530C2×C3C2×#87411yescharacteristic
531C2×C3D3×#12711yescharacteristic
532C2×C3C2×#90912yes—
533C2×C3D3×#13712yes—
534D3—81no—
535D3—241no—
536D3—241no—
537D3—481no—
538D3#471514yesdirect product factor
539C22—34no—
540C22—32no—
541C22—122no—
542C22—121no—
543C22—362no—
544C22—361no—
545C22—724no—
546C22C2×D3×D1211yescharacteristic
547C4—22no—
548C4—32no—
549C4—62no—
550C4—121no—
551C4—122no—
552C4—361no—
553C4—362no—
554C4C2×D3×D1212yes—
555C3—21no—
556C3C2×#471511yescharacteristic, complemented
557C3D3×#49711yescharacteristic, complemented
558C2—34no—
559C2—241no—
560C2—721no—
561C2D3×#87411yescharacteristic
562C2D3×#90912yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#97D32
hypocenterC32C2×#497
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
4. D3×#869C2semidirect
5. #10592414C2semidirect
6. C3×#4715C2semidirect
7. C3×D3×#97C2semidirect
8. #10590899C2semidirect
9. #10590897C2semidirect
10. #10590374C2semidirect
11. #10590372C2semidirect
17. C2×#3746C22semidirect
20. #64078C22semidirect
21. C2×C3×Dic12C22semidirect
26. C3×#869C22semidirect
30. #63866C22semidirect
34. C2×#3719C22semidirect
35. C2×#3719C22semidirect
40. C32×#97C22semidirect
41. C3×#815C22semidirect
42. C3×#803C22semidirect
64. #4715D3direct (N × H)
65. D3×#97D3semidirect
135. C2×Dic12C2×D3semidirect
161. #869C2×D3semidirect
165. C3×#97C2×D3semidirect
166. C3×#97C2×D3semidirect
167. #815C2×D3semidirect
168. #803C2×D3semidirect
341. #97D32semidirect
416. C3×D3#497semidirect
495. C32C2×#497semidirect
538. D3#4715direct (N × H)
556. C3C2×#4715semidirect
557. C3D3×#497semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×D3×#2042
D3×#8752
D3×#8692
#105924142
C3×#47152
C3×D3×#972
#105908992
#105908972
#105903742
#105903722
D3×#4973
C2×#47153