Finite Group Databasebeta

← D3×#5137 #11867013

Subgroups — D3×#5137 #11867013

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2D3×#924C212yesmaximal
3C2×D3×Dic12C211yesmaximal, characteristic, complemented
4#10592836C211yesmaximal, characteristic, complemented
5C3×#5137C211yesmaximal, characteristic, complemented
6#10591121C212yesmaximal, complemented
7#10590854C211yesmaximal, characteristic, complemented
8#10590853C211yesmaximal, characteristic, complemented
9#10590849C212yesmaximal, complemented
10D3×#817C211yesmaximal, characteristic, complemented
11D3×#816C212yesmaximal, complemented
12C2×#5137—31nomaximal
13D3×#470—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×D3×Dic6C2212yes—
16C2×C32×M16C2211yescharacteristic
17#64133C2212yes—
18C2×#3746C2211yescharacteristic, complemented
19C3×#924C2212yes—
20C2×C3×#208C2211yescharacteristic
21C3×D3×M16—24no—
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27D3×#217—22no—
28#63964—22no—
29D3×C4⋊Dic3C2212yes—
30D3×Dic3⋊C4—22no—
31#63857C2212yes—
32#63856C2212yes—
33#63851—22no—
34C2×#3719C2212yescomplemented
35D3×Dic12—24no—
36#63644C2211yescharacteristic, complemented
37#63643C2212yescomplemented
38C3×#817C2211yescharacteristic, complemented
39C3×#816C2212yescomplemented
40#63573C2212yescomplemented
41#63567C2212yescomplemented
42#63566C2212yescomplemented
43C22×C3×M16—31no—
44C2×#924—32no—
45C2×D3×Q16—31no—
46C2×D3×M16D311yescharacteristic
47C22×Dic12—31no—
48D3×C22⋊Q8—32no—
49C3×#470—31no—
50#5189—31no—
51#5137—31no—
52#5137—31no—
53#5137—32no—
54#5137—31no—
55#5137—31no—
56#5137—32no—
57#5137—61no—
58#5137D311yescharacteristic, direct product factor
59C2×#817—31no—
60C2×#816—32no—
61#5052—32no—
62#4867—31no—
63D3×#106—31no—
64#4816—32no—
65D3×#103—32no—
66C23×C3×D3D411yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C2×#634C2312yes—
69C22×C3×Dic3D411yescharacteristic
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×#627—22no—
78C2×D3×Dic3—22no—
79C2×D3×Dic3—22no—
80D3×Dic6—24no—
81D3×Dic6—24no—
82C32×M16—22no—
83C2×C32×C8C2311yescharacteristic
84C2×C32×C8C2311yescharacteristic
85#3757—22no—
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—22no—
88#3746—22no—
89C3×#217—22no—
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×#208—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12—22no—
96C3×ΓL(1,𝔽25)—22no—
97C3×ΓL(1,𝔽25)—22no—
98C3×D3×C8—22no—
99C3×D3×C8D414yes—
100#3724—22no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105#3719—24no—
106C2×#470—91noSylow
107C23×C3×C4—31no—
108C2×D3×Q8—32no—
109C22×C4×D3C2×D311yescharacteristic
110C22×Dic6—32no—
111C2×C3×Q16—31no—
112C2×C3×M16—21no—
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C2×C3×M16—31no—
116C2×C3×M16—64no—
117C2×C3×M16C2×D311yescharacteristic
118C2×C3×M16C2×D311yescharacteristic
119C22×C3×C8—31no—
120C22×C3×C8—31no—
121C3×C22⋊Q8—32no—
122C2×#217—62no—
123#946—32no—
124C2×#216—32no—
125C2×C4⋊Dic3—32no—
126#924—32no—
127#924—32no—
128#924—32no—
129#924—32no—
130#924—62no—
131#924—62no—
132#924—62no—
133#924C2×D312yes—
134C2×Dic3⋊C4—62no—
135C2×#208C2×D311yescharacteristic
136D3×Q16—64no—
137D3×M16—24no—
138C2×Dic12—32no—
139C2×Dic12—31no—
140C2×Dic12—31no—
141C2×Dic12—61no—
142C2×Dic12—64no—
143C2×Dic12C2×D311yescharacteristic, complemented
144C2×ΓL(1,𝔽25)C2×D311yescharacteristic
145C2×ΓL(1,𝔽25)C2×D311yescharacteristic
146C2×D3×C8C2×D311yescharacteristic
147C2×D3×C8C2×D311yescharacteristic
148#897—32no—
149#896—62no—
150D3×C4⋊C4—32no—
151D3×C4⋊C4—62no—
152D3×C22⋊C4—62no—
153#878—62no—
154C3×#106—31no—
155C3×#103—32no—
156#835—32no—
157#817—31no—
158#817—31no—
159#817—32no—
160#817—61no—
161#817C2×D311yescharacteristic, complemented
162#816—32no—
163#816—32no—
164#816—32no—
165#816—32no—
166#816—62no—
167#816C2×D312yescomplemented
168#810—32no—
169#808—32no—
170C23×C32C2×D411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3—24no—
173C22×C3×D3C2×D411yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181#634—22no—
182#634—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×D411yescharacteristic
187C2×C3×Dic3C2×D411yescharacteristic
188C3×C4×D3—22no—
189C3×C4×D3—21no—
190C3×C4×D3—21no—
191C3×C4×D3—22no—
192C3×C4×D3C2×D412yes—
193C3×C4×D3#4112yes—
194C3×Dic6—22no—
195C3×Dic6—22no—
196#627—44no—
197D3×Dic3—44no—
198D3×Dic3—44no—
199C32×C8—21no—
200C32×C8C2×D412yes—
201C3×C3⋊C8—21no—
202C3×C3⋊C8C2×D412yes—
203C22×Q16—91no—
204C22×M16—31no—
205C2×C22⋊Q8—92no—
206#470—31no—
207#470—92no—
208#470—91no—
209#470—92no—
210#470—91no—
211#470—91no—
212C2×#106—91no—
213C2×#103—92no—
214C24×C3—31no—
215C23×D3D1211yescharacteristic
216C2×C3×Q8—32no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—62no—
224C22×C3×C4—62no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—62no—
228C22×Dic3—62no—
229C22×Dic3D1211yescharacteristic
230D3×Q8—64no—
231D3×Q8—64no—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3D1211yescharacteristic
237C2×C4×D3D1211yescharacteristic
238C2×C4×D3C22×D311yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—32no—
241C2×Dic6—32no—
242C2×Dic6—62no—
243C2×Dic6—64no—
244C2×Dic6—64no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6C22×D312yes—
248C3×Q16—62no—
249C3×M16—22no—
250C3×M16—22no—
251C3×M16—42no—
252C3×M16—62no—
253C3×M16—62no—
254C3×M16—62no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—31no—
258C2×C3×C8—34no—
259C2×C3×C8—31no—
260C2×C3×C8—62no—
261C2×C3×C8C22×D311yescharacteristic
262C2×C3×C8C22×D311yescharacteristic
263C2×C3×C8C22×D311yescharacteristic
264C2×C3×C8C22×D311yescharacteristic
265C3×C4⋊C4—32no—
266C3×C4⋊C4—62no—
267C3×C22⋊C4—62no—
268#217—22no—
269#217—62no—
270#217—62no—
271#217—62no—
272#217—62no—
273#217—122no—
274#216—64no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277C4⋊Dic3—32no—
278C4⋊Dic3—32no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3C22×D312yes—
283Dic3⋊C4—22no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290Dic3⋊C4—122no—
291#208—22no—
292C2×C3⋊C8C22×D311yescharacteristic
293C2×C3⋊C8C22×D311yescharacteristic
294Dic12—22no—
295Dic12—64no—
296Dic12—62no—
297Dic12—62no—
298Dic12—122no—
299ΓL(1,𝔽25)—22no—
300ΓL(1,𝔽25)—22no—
301D3×C8—22no—
302D3×C8#6714yes—
303C22×C32—21no—
304C22×C32—22no—
305C22×C32C22×D411yescharacteristic
306C2×C3×D3—21no—
307C2×C3×D3—22no—
308C2×C3×D3—44no—
309C2×C3×D3#12112yes—
310C2×C3×D3#13714yes—
311C32×C4—21no—
312C32×C4C22×D411yescharacteristic
313C32×C4C2×#4111yescharacteristic
314C3⋊Dic3—42no—
315C3⋊Dic3—42no—
316C3×Dic3—21no—
317C3×Dic3—42no—
318C3×Dic3—42no—
319C3×Dic3#12112yes—
320C22×Q8—92no—
321C23×C4—31no—
322C2×Q16—31no—
323C2×Q16—92no—
324C2×Q16—91no—
325C2×Q16—184no—
326C2×M16—31no—
327C2×M16—31no—
328C2×M16—31no—
329C2×M16—64no—
330C2×M16D3211yescharacteristic
331C22×C8—31no—
332C22×C8—31no—
333C22⋊Q8—32no—
334C22⋊Q8—92no—
335C22⋊Q8—92no—
336C22⋊Q8—92no—
337C22⋊Q8—182no—
338C22⋊Q8—182no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—182no—
341C2×C22⋊C4—182no—
342#106—31no—
343#106—92no—
344#106—91no—
345#103—32no—
346#103—92no—
347#103—92no—
348#103—92no—
349C23×C3—21no—
350C23×C3—31no—
351C23×C3—31no—
352C23×C3—62no—
353C23×C3—64no—
354C23×C3C2×D1211yescharacteristic
355C23×C3D3×D411yescharacteristic
356C22×D3—24no—
357C22×D3—22no—
358C22×D3C2×D1211yescharacteristic
359C22×D3C2×D1211yescharacteristic
360C3×Q8—62no—
361C3×Q8—62no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—31no—
369C2×C3×C4—32no—
370C2×C3×C4—32no—
371C2×C3×C4—31no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3—124no—
395C2×Dic3—124no—
396C2×Dic3C2×D1211yescharacteristic
397C2×Dic3C2×D1211yescharacteristic
398C4×D3—22no—
399C4×D3—21no—
400C4×D3—21no—
401C4×D3—22no—
402C4×D3—124no—
403C4×D3—124no—
404C4×D3#23512yes—
405C4×D3C2×#6712yes—
406Dic6—22no—
407Dic6—22no—
408Dic6—62no—
409Dic6—62no—
410Dic6—62no—
411Dic6—62no—
412Dic6—122no—
413Dic6—122no—
414Dic6—124no—
415Dic6—124no—
416C3×C8—21no—
417C3×C8—21no—
418C3×C8—22no—
419C3×C8—32no—
420C3×C8—41no—
421C3×C8—61no—
422C3×C8D3×D412yes—
423C3×C8C2×#6712yes—
424C3⋊C8—21no—
425C3⋊C8C2×#6712yes—
426C2×C32—41no—
427C2×C32C2×#12111yescharacteristic
428C2×C32C2×#13712yes—
429C3×D3—41no—
430C3×D3#47014yescomplemented
431C24—31no—
432C2×Q8—32no—
433C2×Q8—92no—
434C2×Q8—182no—
435C2×Q8—184no—
436C2×Q8—184no—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—182no—
445C22×C4—182no—
446C22×C4C2×D3211yescharacteristic
447Q16—62no—
448Q16—184no—
449Q16—182no—
450M16—22no—
451M16—62no—
452M16—62no—
453M16—62no—
454C2×C8—31no—
455C2×C8—34no—
456C2×C8—31no—
457C2×C8—62no—
458C2×C8C2×D3211yescharacteristic
459C2×C8C2×D3211yescharacteristic
460C4⋊C4—32no—
461C4⋊C4—62no—
462C4⋊C4—92no—
463C4⋊C4—182no—
464C4⋊C4—182no—
465C4⋊C4—182no—
466C4⋊C4—182no—
467C22⋊C4—62no—
468C22⋊C4—182no—
469C22⋊C4—182no—
470C22⋊C4—182no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—34no—
477C22×C3—32no—
478C22×C3—41no—
479C22×C3—42no—
480C22×C3—62no—
481C22×C3—61no—
482C22×C3—124no—
483C22×C3C22×D1211yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C2×D3—22no—
486C2×D3—21no—
487C2×D3—44no—
488C2×D3#90914yes—
489C2×D3#93012yes—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—32no—
495C3×C4—41no—
496C3×C4—61no—
497C3×C4—122no—
498C3×C4—122no—
499C3×C4C2×#23511yescharacteristic
500C3×C4C2×D3×D411yescharacteristic
501C3×C4D3×#4111yescharacteristic
502C3×C4C22×#6711yescharacteristic
503Dic3—21no—
504Dic3—42no—
505Dic3—42no—
506Dic3—122no—
507Dic3—122no—
508Dic3—122no—
509Dic3—122no—
510Dic3—242no—
511Dic3—242no—
512Dic3#93012yes—
513C32C2×#47011yescharacteristic, complemented, Sylow
514C23—31no—
515C23—31no—
516C23—62no—
517C23—64no—
518C23D3×D1211yescharacteristic
519Q8—62no—
520Q8—62no—
521Q8—182no—
522Q8—182no—
523Q8—364no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—31no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—31no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—364no—
540C2×C4—364no—
541C2×C4D3×D1211yescharacteristic
542C2×C4C22×D3211yescharacteristic
543C8—21no—
544C8—32no—
545C8—61no—
546C8D3×#6712yes—
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—34no—
550C2×C3—41no—
551C2×C3—41no—
552C2×C3—81no—
553C2×C3—121no—
554C2×C3D3×#12111yescharacteristic
555C2×C3C2×#90912yes—
556C2×C3D3×#13712yes—
557C2×C3C2×#93011yescharacteristic
558D3—41no—
559D3#513714yesdirect product factor
560C22—22no—
561C22—21no—
562C22—34no—
563C22—32no—
564C22—62no—
565C22—61no—
566C22—124no—
567C22C2×D3×D1211yescharacteristic
568C4—21no—
569C4—32no—
570C4—61no—
571C4—122no—
572C4—122no—
573C4—362no—
574C4—362no—
575C4D3×#23511yescharacteristic
576C4C2×D3×#6711yescharacteristic
577C3—21no—
578C3D3×#47011yescharacteristic, complemented
579C3C2×#513711yescharacteristic, complemented
580C2—34no—
581C2—41no—
582C2—121no—
583C2D3×#90912yes—
584C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC2×M16D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×D3×Dic12C2semidirect
4. #10592836C2semidirect
5. C3×#5137C2semidirect
6. #10591121C2semidirect
7. #10590854C2semidirect
8. #10590853C2semidirect
9. #10590849C2semidirect
10. D3×#817C2semidirect
11. D3×#816C2semidirect
18. C2×#3746C22semidirect
22. C2×C3×Dic12C22semidirect
34. C2×#3719C22semidirect
36. #63644C22semidirect
37. #63643C22semidirect
38. C3×#817C22semidirect
39. C3×#816C22semidirect
40. #63573C22semidirect
41. #63567C22semidirect
42. #63566C22semidirect
58. #5137D3direct (N × H)
143. C2×Dic12C2×D3semidirect
161. #817C2×D3semidirect
167. #816C2×D3semidirect
430. C3×D3#470semidirect
513. C32C2×#470semidirect
559. D3#5137direct (N × H)
578. C3D3×#470semidirect
579. C3C2×#5137semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
D3×#9242
C2×D3×Dic122
#105928362
C3×#51372
#105911212
#105908542
#105908532
#105908492
D3×#8172
D3×#8162
C2×#51373
D3×#4703