Finite Group Databasebeta

← D3×#5191 #11874265

Subgroups — D3×#5191 #11874265

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×Q16C211yesmaximal, characteristic, complemented
2D3×#947C212yesmaximal, complemented
3C2×D3×#215C212yesmaximal, complemented
4C2×D3×D24C211yesmaximal, characteristic
5#10592890C211yesmaximal, characteristic, complemented
6C3×#5191C211yesmaximal, characteristic, complemented
7#10591610C212yesmaximal, complemented
8#10591609C212yesmaximal, complemented
9#10590869C211yesmaximal, characteristic, complemented
10#10590865C211yesmaximal, characteristic, complemented
11D3×C8×Dic3C211yesmaximal, characteristic, complemented
12C2×#5191—31nomaximal
13D3×#495—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×D3×D12C2212yes—
16C2×C32×Q16C2211yescharacteristic, complemented
17#64156C2212yescomplemented
18C2×#3755C2212yescomplemented
19C2×#3745C2211yescharacteristic
20C3×#947C2212yescomplemented
21C2×C3×#216C2212yescomplemented
22C2×C3×#215C2212yescomplemented
23C3×D3×Q16—24no—
24C2×C3×Dic12C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27D3×#215—28no—
28D3×(C2×D3)⋊C4—24no—
29#63907—24no—
30C4×D3×Dic3C2211yescharacteristic
31#63864C2212yescomplemented
32#63863C2212yescomplemented
33C2×#3717C2212yescomplemented
34C2×#3715C2212yescomplemented
35C2×#3714C2212yes—
36C2×D3×C3⋊C8C2211yescharacteristic
37D3×D24—24no—
38C8×C3⋊Dic3C2211yescharacteristic, complemented
39C3×C8×Dic3C2211yescharacteristic, complemented
40#63553C2211yescharacteristic, complemented
41Dic3×C3⋊C8C2211yescharacteristic, complemented
42C22×C3×Q16—31no—
43C2×#947—32no—
44C22×#215—32no—
45C2×D3×Q16D311yescharacteristic, complemented
46C2×D3×SD16—32no—
47C2×D3×D8—31no—
48C22×D24—31no—
49D3×#124—32no—
50C3×#495—31no—
51#5191—31no—
52#5191—31no—
53#5191—32no—
54#5191—32no—
55#5191—31no—
56#5191—31no—
57#5191—61no—
58#5191D311yescharacteristic, direct product factor
59#5168—32no—
60#5155—31no—
61C2×C8×Dic3—31no—
62#5059—32no—
63#4696—31no—
64C4×D3×C8—31no—
65C22×D32—22no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2312yes—
68C3×D3×Q8—24no—
69C3×D3×Q8—24no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6—22no—
74C2×C3×Dic6C2312yes—
75C2×#626—22no—
76C2×D3×Dic3D412yes—
77D3×D12—24no—
78D3×D12—24no—
79C32×Q16—22no—
80C2×C32×C8C2311yescharacteristic
81#3755—24no—
82#3752—24no—
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3745—22no—
86C3×#216—24no—
87C3×#215—24no—
88C3×(C2×D3)⋊C4—24no—
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12—22no—
93C3×D24—22no—
94C3×D3×C8D414yes—
95#3722—24no—
96(C2×D3)⋊Dic3—24no—
97Dic32D412yes—
98#3717—24no—
99#3715—24no—
100#3714—24no—
101D3×C3⋊C8D414yes—
102C2×#495—91noSylow
103C22×C3×Q8—32no—
104C2×D3×Q8C2×D312yes—
105C2×D3×D4—32no—
106C22×D12—32no—
107C2×C3×Q16—21no—
108C2×C3×Q16—32no—
109C2×C3×Q16—31no—
110C2×C3×Q16—64no—
111C2×C3×Q16C2×D311yescharacteristic, complemented
112C2×C3×Q16C2×D311yescharacteristic, complemented
113C2×C3×SD16—32no—
114C2×C3×D8—31no—
115C22×C3×C8—31no—
116C3×#124—32no—
117#947—32no—
118#947—32no—
119#947—32no—
120#947—32no—
121#947—62no—
122#947—64no—
123#947C2×D312yescomplemented
124C2×#216C2×D312yescomplemented
125C2×#215—32no—
126C2×#215—32no—
127C2×#215—32no—
128C2×#215—32no—
129C2×#215—62no—
130C2×#215—68no—
131C2×#215C2×D312yescomplemented
132#936—32no—
133C2×#214—32no—
134C2×#213—32no—
135C2×(C2×D3)⋊C4—64no—
136C2×C4×Dic3—31no—
137C22×C3⋊C8—31no—
138D3×Q16—24no—
139D3×SD16—68no—
140D3×D8—64no—
141C2×Dic12C2×D311yescharacteristic, complemented
142C2×D24—32no—
143C2×D24—31no—
144C2×D24—31no—
145C2×D24—61no—
146C2×D24—64no—
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—
164C22×C3⋊D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3C2×D411yescharacteristic
167C2×D32—44no—
168C2×D32—48no—
169C32×Q8—22no—
170C32×Q8—22no—
171C2×C32×C4—22no—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3C2×D412yes—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D411yescharacteristic
179C3×D12—22no—
180C3×D12—22no—
181C3×C4×D3—44no—
182C3×C4×D3C2×D412yes—
183C3×C4×D3C2×D412yes—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—44no—
187#626—44no—
188D3×Dic3—24no—
189C32×C8C2×D412yes—
190C3⋊(C3⋊C8)C2×D412yes—
191C3×C3⋊C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C22×Q16—31no—
194C22×SD16—92no—
195C22×D8—91no—
196C2×#124—92no—
197#495—31no—
198#495—91no—
199#495—92no—
200#495—91no—
201#495—92no—
202#495—91no—
203C2×C4×C8—91no—
204C23×D3—62no—
205C23×D3—62no—
206C2×C3×Q8—22no—
207C2×C3×Q8—32no—
208C2×C3×Q8—62no—
209C2×C3×Q8—64no—
210C2×C3×Q8—64no—
211C2×C3×Q8C22×D312yes—
212C2×C3×Q8C22×D312yes—
213C2×C3×D4—32no—
214C22×C3×C4—31no—
215C22×C3×C4—62no—
216C2×#67—62no—
217C22×Dic3—32no—
218D3×Q8—24no—
219D3×Q8—24no—
220D3×D4—64no—
221D3×D4—64no—
222C2×D12—32no—
223C2×D12—32no—
224C2×D12—62no—
225C2×D12—64no—
226C2×D12—64no—
227C2×D12—62no—
228C2×D12C22×D312yes—
229C2×C4×D3—22no—
230C2×C4×D3—32no—
231C2×C4×D3C22×D311yescharacteristic
232C2×Dic6—22no—
233C2×Dic6C22×D312yes—
234C3×Q16—22no—
235C3×Q16—22no—
236C3×Q16—42no—
237C3×Q16—64no—
238C3×Q16—62no—
239C3×SD16—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—64no—
250#216—24no—
251#215—24no—
252#215—64no—
253#215—64no—
254#215—64no—
255#215—64no—
256#215—124no—
257#214—64no—
258#213—64no—
259(C2×D3)⋊C4—24no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—124no—
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—
279D24—22no—
280D24—64no—
281D24—62no—
282D24—62no—
283D24—122no—
284#204—64no—
285D3×C8—34no—
286D3×C8#6714yes—
287C22×C32C22×D411yescharacteristic
288C2×C3⋊D3—42no—
289C2×C3⋊D3—44no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3#12712yes—
293C2×C3×D3#13514yes—
294D32—88no—
295C32×C4—42no—
296C32×C4C22×D411yescharacteristic
297C32×C4C22×D411yescharacteristic
298C3⋊Dic3—22no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3#12712yes—
302C22×Q8—32no—
303C22×D4—92no—
304C2×Q16—32no—
305C2×Q16—31no—
306C2×Q16—64no—
307C2×Q16D3211yescharacteristic, complemented
308C2×SD16—32no—
309C2×SD16—92no—
310C2×SD16—92no—
311C2×SD16—92no—
312C2×SD16—188no—
313C2×D8—31no—
314C2×D8—92no—
315C2×D8—91no—
316C2×D8—184no—
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—31no—
331C23×C3—62no—
332C22×D3—22no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—122no—
336C22×D3—124no—
337C22×D3—128no—
338C22×D3—128no—
339C22×D3—124no—
340C22×D3D3×D411yescharacteristic
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—22no—
344C3×Q8—22no—
345C3×Q8—42no—
346C3×Q8—42no—
347C3×Q8—62no—
348C3×Q8—62no—
349C3×Q8—124no—
350C3×D4—62no—
351C3×D4—62no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—31no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—42no—
360C2×C3×C4—62no—
361C2×C3×C4—124no—
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364#67—124no—
365C2×Dic3—22no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—62no—
369C2×Dic3—64no—
370C2×Dic3D3×D412yes—
371C2×Dic3D3×D411yescharacteristic
372D12—22no—
373D12—22no—
374D12—62no—
375D12—62no—
376D12—62no—
377D12—62no—
378D12—122no—
379D12—122no—
380D12—124no—
381C4×D3—44no—
382C4×D3—64no—
383C4×D3D3×D412yes—
384C4×D3C2×#6712yes—
385Dic6—22no—
386Dic6—22no—
387Dic6—44no—
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×C32C2×#12711yescharacteristic
399C2×C32C2×#13512yes—
400C3⋊D3—82no—
401C3×D3—82no—
402C3×D3#49514yescomplemented
403C24—182no—
404C2×Q8—32no—
405C2×Q8—62no—
406C2×Q8—64no—
407C2×Q8—64no—
408C2×Q8C2×D3212yes—
409C2×D4—32no—
410C2×D4—92no—
411C2×D4—184no—
412C2×D4—184no—
413C2×D4—182no—
414C22×C4—31no—
415C22×C4—62no—
416C22×C4—92no—
417Q16—22no—
418Q16—64no—
419Q16—62no—
420SD16—64no—
421SD16—184no—
422SD16—184no—
423SD16—184no—
424D8—62no—
425D8—184no—
426D8—182no—
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—124no—
444C22×C3—122no—
445C22×C3C2×D3×D411yescharacteristic
446C22×C3C2×D3×D411yescharacteristic
447C2×D3—42no—
448C2×D3—44no—
449C2×D3—122no—
450C2×D3—124no—
451C2×D3—124no—
452C2×D3—122no—
453C2×D3—242no—
454C2×D3—244no—
455C2×D3—248no—
456C2×D3—248no—
457C2×D3#91914yes—
458C2×D3#94012yes—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—32no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—62no—
465C3×C4—82no—
466C3×C4—122no—
467C3×C4C2×D3×D411yescharacteristic
468C3×C4C2×D3×D411yescharacteristic
469C3×C4C2×D3×D411yescharacteristic
470C3×C4C22×#6711yescharacteristic
471Dic3—22no—
472Dic3—42no—
473Dic3—62no—
474Dic3—62no—
475Dic3—122no—
476Dic3#94012yes—
477C32C2×#49511yescharacteristic, complemented, Sylow
478C23—31no—
479C23—62no—
480C23—182no—
481C23—364no—
482C23—368no—
483Q8—22no—
484Q8—22no—
485Q8—62no—
486Q8—62no—
487Q8—124no—
488D4—62no—
489D4—62no—
490D4—182no—
491D4—182no—
492D4—364no—
493C2×C4—22no—
494C2×C4—31no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—92no—
500C2×C4—124no—
501C2×C4—184no—
502C2×C4C22×D3211yescharacteristic
503C8—32no—
504C8—32no—
505C8—92no—
506C8D3×#6712yes—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—34no—
510C2×C3—242no—
511C2×C3D3×#12711yescharacteristic
512C2×C3C2×#91912yes—
513C2×C3D3×#13512yes—
514C2×C3C2×#94011yescharacteristic
515D3—82no—
516D3—242no—
517D3—242no—
518D3—482no—
519D3#519114yesdirect product factor
520C22—34no—
521C22—32no—
522C22—124no—
523C22—122no—
524C22—364no—
525C22—362no—
526C22—728no—
527C22D32×D411yescharacteristic
528C4—32no—
529C4—42no—
530C4—62no—
531C4—122no—
532C4—182no—
533C4D32×D411yescharacteristic
534C4C2×D3×#6711yescharacteristic
535C3—21no—
536C3D3×#49511yescharacteristic, complemented
537C3C2×#519111yescharacteristic, complemented
538C2—34no—
539C2—242no—
540C2—722no—
541C2D3×#91912yes—
542C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×D3×D24C2
hypercenterC2×Q16D32
hypocenterC32C2×#495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
2. D3×#947C2semidirect
3. C2×D3×#215C2semidirect
5. #10592890C2semidirect
6. C3×#5191C2semidirect
7. #10591610C2semidirect
8. #10591609C2semidirect
9. #10590869C2semidirect
10. #10590865C2semidirect
11. D3×C8×Dic3C2semidirect
16. C2×C32×Q16C22semidirect
17. #64156C22semidirect
18. C2×#3755C22semidirect
20. C3×#947C22semidirect
21. C2×C3×#216C22semidirect
22. C2×C3×#215C22semidirect
24. C2×C3×Dic12C22semidirect
31. #63864C22semidirect
32. #63863C22semidirect
33. C2×#3717C22semidirect
34. C2×#3715C22semidirect
38. C8×C3⋊Dic3C22semidirect
39. C3×C8×Dic3C22semidirect
40. #63553C22semidirect
41. Dic3×C3⋊C8C22semidirect
45. C2×D3×Q16D3semidirect
58. #5191D3direct (N × H)
111. C2×C3×Q16C2×D3semidirect
112. C2×C3×Q16C2×D3semidirect
123. #947C2×D3semidirect
124. C2×#216C2×D3semidirect
131. C2×#215C2×D3semidirect
141. C2×Dic12C2×D3semidirect
162. C8×Dic3C2×D3semidirect
307. C2×Q16D32semidirect
402. C3×D3#495semidirect
477. C32C2×#495semidirect
519. D3#5191direct (N × H)
536. C3D3×#495semidirect
537. C3C2×#5191semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9472
C2×D3×#2152
C2×D3×D242
#105928902
C3×#51912
#105916102
#105916092
#105908692
#105908652
D3×C8×Dic32
C2×#51913
D3×#4953