Finite Group Databasebeta

← D3×#4919 #11899527

Subgroups — D3×#4919 #11899527

Order 1152.

778 conjugacy classes of subgroups.

The subgroup lattice has 497 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#919C212yesmaximal, complemented
2#10592618C211yesmaximal, characteristic, complemented
3C3×#4919C211yesmaximal, characteristic, complemented
4C3×D3×Q32C211yesmaximal, characteristic, complemented
5#10591049C212yesmaximal, complemented
6#10591048C212yesmaximal, complemented
7D3×#828C212yesmaximal, complemented
8#10590244C211yesmaximal, characteristic, complemented
9#10590243C211yesmaximal, characteristic, complemented
10D3×D48C211yesmaximal, characteristic, complemented
11D32×C16C211yesmaximal, characteristic, complemented
12D3×#508—31nomaximal
13C2×#4919—31nomaximal
14D3×#239—22no—
15#64128C2212yescomplemented
16C3×#919C2212yescomplemented
17C3×D3×Q16C2212yes—
18#63950—22no—
19#63949—22no—
20D3×#215—22no—
21#63810C2212yescomplemented
22#63808C2212yescomplemented
23D3×D24C2212yes—
24D32×C8C2211yescharacteristic
25C32×Q32C2211yescharacteristic, complemented
26#63655C2212yescomplemented
27#63626C2211yescharacteristic, complemented
28C16×C3⋊D3C2211yescharacteristic, complemented
29C3×#829C2212yescomplemented
30C3×#828C2212yescomplemented
31C3×Dic24C2211yescharacteristic, complemented
32C3×D48C2211yescharacteristic, complemented
33C3×D3×C16C2211yescharacteristic
34C3×D3×C16C2211yescharacteristic, complemented
35#63549C2212yescomplemented
36#63547C2212yescomplemented
37#63546C2212yescomplemented
38#63542C2211yescharacteristic, complemented
39D3×C3⋊C16C2211yescharacteristic
40D3×C3⋊C16C2211yescharacteristic, complemented
41D3×#135—32no—
42C2×#919—32no—
43C3×#508—31no—
44C2×C3×Q32—31no—
45#5194—32no—
46C2×#828—32no—
47#4919—32no—
48#4919—31no—
49#4919—31no—
50#4919—32no—
51#4919—31no—
52#4919—31no—
53#4919—61no—
54#4919D311yescharacteristic, direct product factor
55D3×Q32D311yescharacteristic, complemented
56#4916—32no—
57D3×SD32—32no—
58#4912—31no—
59D3×D16—31no—
60#4904—31no—
61C2×D48—31no—
62C2×D3×C16—31no—
63C2×D3×C16—31no—
64#3832—22no—
65C3×#239—22no—
66C3×D3×Q8—22no—
67D3×D12—22no—
68D3×D12—42no—
69C4×D32—42no—
70C4×D32D411yescharacteristic
71#3799—22no—
72#3799—42no—
73#3796—22no—
74#3796—42no—
75C32×Q16C2312yes—
76#3755—22no—
77#3745C2312yes—
78C8×C3⋊D3C2311yescharacteristic
79C3×#216—22no—
80C3×#215—22no—
81C3×Dic12C2312yes—
82C3×D24C2312yes—
83C3×D3×C8C2311yescharacteristic
84C3×D3×C8C2311yescharacteristic
85#3717—22no—
86#3715—22no—
87#3714—22no—
88#3710D411yescharacteristic
89D3×C3⋊C8D411yescharacteristic
90D3×C3⋊C8D411yescharacteristic
91C32×C16C2311yescharacteristic
92C3⋊(C3⋊C16)C2311yescharacteristic
93C3×C3⋊C16C2311yescharacteristic
94C3×C3⋊C16C2311yescharacteristic
95C2×#508—91noSylow
96D3×#41—62no—
97C2×#239—62no—
98C3×#135—32no—
99C2×C3×Q16—32no—
100#950—62no—
101C2×#215—62no—
102#919—32no—
103#919—32no—
104#919—32no—
105#919—32no—
106#919—62no—
107#919—62no—
108#919—62no—
109#919C2×D312yescomplemented
110D3×Q16C2×D312yes—
111#916—62no—
112D3×SD16—62no—
113#912—32no—
114D3×D8—32no—
115#904—32no—
116C2×D24—32no—
117C2×D3×C8—31no—
118C2×D3×C8—31no—
119C3×Q32—21no—
120C3×Q32—32no—
121C3×Q32—31no—
122C3×Q32C2×D311yescharacteristic, complemented
123C3×Q32C2×D311yescharacteristic, complemented
124C3×SD32—32no—
125C3×D16—31no—
126C2×C3×C16—31no—
127C2×C3×C16—31no—
128#829C2×D312yescomplemented
129#828—32no—
130#828—32no—
131#828—32no—
132#828—32no—
133#828—62no—
134#828C2×D312yescomplemented
135#827—32no—
136#826—32no—
137C2×C3⋊C16—31no—
138C2×C3⋊C16—31no—
139Dic24C2×D311yescharacteristic, complemented
140#800—32no—
141D48—32no—
142D48—31no—
143D48—31no—
144D48—61no—
145D48C2×D311yescharacteristic, complemented
146D3×C16—31no—
147D3×C16—31no—
148D3×C16—31no—
149D3×C16—31no—
150D3×C16—31no—
151D3×C16—31no—
152D3×C16—61no—
153D3×C16C2×D311yescharacteristic
154D3×C16C2×D311yescharacteristic, complemented
155C2×D32—42no—
156C2×D32D811yescharacteristic
157C32×Q8—22no—
158C4⋊(C3⋊D3)—22no—
159C4⋊(C3⋊D3)—42no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3C2×D411yescharacteristic
162C3×D12—22no—
163C3×D12—42no—
164C3×C4×D3—42no—
165C3×C4×D3—42no—
166C3×C4×D3C2×D411yescharacteristic
167C3×C4×D3C2×D411yescharacteristic
168C3×Dic6—22no—
169C3×Dic6—42no—
170#626—42no—
171#626—42no—
172#626—42no—
173#624—42no—
174#624D811yescharacteristic
175D3×Dic3—42no—
176D3×Dic3D811yescharacteristic
177D3×Dic3D811yescharacteristic
178C32×C8C2411yescharacteristic
179C3⋊(C3⋊C8)C2×D411yescharacteristic
180C3×C3⋊C8C2×D411yescharacteristic
181C3×C3⋊C8C2×D411yescharacteristic
182C2×#135—92no—
183#508—31no—
184#508—91no—
185#508—91no—
186#508—92no—
187#508—92no—
188#508—91no—
189C2×Q32—31no—
190C2×SD32—92no—
191C2×D16—91no—
192C22×C16—91no—
193C3×#41—62no—
194C2×C3×Q8—62no—
195#239—22no—
196#239—62no—
197#239—62no—
198#239—62no—
199#239—62no—
200#239—122no—
201#239—122no—
202#239—122no—
203D3×Q8—22no—
204#237—62no—
205#237—122no—
206D3×D4—62no—
207D3×D4—122no—
208#235—62no—
209#235—122no—
210C2×D12—62no—
211C2×D12—122no—
212C2×C4×D3—31no—
213C2×C4×D3—31no—
214C2×C4×D3—122no—
215C2×C4×D3—122no—
216C3×Q16—22no—
217C3×Q16—32no—
218C3×Q16—62no—
219C3×Q16C22×D312yes—
220C3×Q16C22×D312yes—
221C3×SD16—62no—
222C3×D8—32no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225#216—22no—
226#215—22no—
227#215—62no—
228#215—62no—
229#215—62no—
230#215—62no—
231#215—122no—
232#214—62no—
233#213—62no—
234C2×C3⋊C8—31no—
235C2×C3⋊C8—31no—
236Dic12C22×D312yes—
237D24—32no—
238D24—32no—
239D24—62no—
240D24—62no—
241D24C22×D312yes—
242#204—62no—
243D3×C8—31no—
244D3×C8—31no—
245D3×C8—31no—
246D3×C8—31no—
247D3×C8—31no—
248D3×C8—31no—
249D3×C8—61no—
250D3×C8C22×D311yescharacteristic
251D3×C8C22×D311yescharacteristic
252C3×C16—21no—
253C3×C16—31no—
254C3×C16—31no—
255C3×C16C22×D311yescharacteristic
256C3×C16C22×D311yescharacteristic
257C3⋊C16—31no—
258C3⋊C16—31no—
259C3⋊C16—61no—
260C3⋊C16C22×D311yescharacteristic
261C3⋊C16C22×D311yescharacteristic
262C2×C3⋊D3—42no—
263C2×C3⋊D3C2×D811yescharacteristic
264C2×C3×D3—42no—
265C2×C3×D3C2×D811yescharacteristic
266C2×C3×D3C2×D811yescharacteristic
267D32—22no—
268D32—84no—
269C32×C4—42no—
270C32×C4C22×D411yescharacteristic
271C3⋊Dic3C2×D811yescharacteristic
272C3×Dic3—42no—
273C3×Dic3C2×D811yescharacteristic
274C3×Dic3C2×D811yescharacteristic
275C2×#41—182no—
276#135—32no—
277#135—92no—
278#135—92no—
279#135—92no—
280#135—182no—
281#135—182no—
282C2×Q16—32no—
283C2×SD16—182no—
284C2×D8—92no—
285C22×C8—91no—
286Q32—32no—
287Q32—31no—
288Q32D3211yescharacteristic, complemented
289SD32—32no—
290SD32—92no—
291SD32—92no—
292SD32—92no—
293D16—31no—
294D16—92no—
295D16—91no—
296C2×C16—31no—
297C2×C16—31no—
298C2×C16—91no—
299C2×C16—91no—
300C2×C16—91no—
301C2×C16—91no—
302C22×D3—31no—
303C22×D3—31no—
304C22×D3—122no—
305C22×D3—122no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—42no—
309C3×Q8—62no—
310C3×Q8—122no—
311C3×D4—62no—
312C3×D4—122no—
313C2×C3×C4—31no—
314C2×C3×C4—31no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317#67—122no—
318#67—122no—
319#67—122no—
320C2×Dic3—31no—
321C2×Dic3—31no—
322C2×Dic3—122no—
323D12—22no—
324D12—42no—
325D12—62no—
326D12—62no—
327D12—122no—
328D12—122no—
329D12—122no—
330D12—122no—
331D12—122no—
332D12—122no—
333D12—242no—
334C4×D3—31no—
335C4×D3—31no—
336C4×D3—31no—
337C4×D3—31no—
338C4×D3—31no—
339C4×D3—31no—
340C4×D3—42no—
341C4×D3—42no—
342C4×D3—61no—
343C4×D3—122no—
344C4×D3—122no—
345C4×D3—122no—
346C4×D3—122no—
347C4×D3—122no—
348C4×D3—242no—
349C4×D3D3×D411yescharacteristic
350C4×D3D3×D411yescharacteristic
351Dic6—22no—
352Dic6—42no—
353C3×C8—21no—
354C3×C8—31no—
355C3×C8—31no—
356C3×C8C23×D311yescharacteristic
357C3×C8C23×D311yescharacteristic
358C3⋊C8—31no—
359C3⋊C8—31no—
360C3⋊C8—61no—
361C3⋊C8D3×D411yescharacteristic
362C3⋊C8D3×D411yescharacteristic
363C2×C32C22×D811yescharacteristic
364C3⋊D3—21no—
365C3⋊D3—82no—
366C3×D3—21no—
367C3×D3—82no—
368C3×D3#50812yescomplemented
369#41—62no—
370#41—182no—
371#41—182no—
372#41—182no—
373#41—362no—
374#41—362no—
375C2×Q8—62no—
376C2×D4—182no—
377C2×D4—362no—
378C22×C4—91no—
379C22×C4—362no—
380Q16—32no—
381Q16—62no—
382Q16C2×D3212yes—
383SD16—62no—
384SD16—182no—
385SD16—182no—
386SD16—182no—
387D8—32no—
388D8—92no—
389D8—182no—
390C2×C8—31no—
391C2×C8—31no—
392C2×C8—91no—
393C2×C8—91no—
394C2×C8—91no—
395C2×C8—91no—
396C16—31no—
397C16—31no—
398C16—91no—
399C16C2×D3211yescharacteristic
400C22×C3—31no—
401C22×C3—31no—
402C22×C3—122no—
403C2×D3—31no—
404C2×D3—31no—
405C2×D3—42no—
406C2×D3—61no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—122no—
410C2×D3—122no—
411C2×D3—242no—
412C2×D3—244no—
413C2×D3—244no—
414C2×D3D3×D811yescharacteristic
415C2×D3D3×D811yescharacteristic
416C3×C4—21no—
417C3×C4—31no—
418C3×C4—31no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—82no—
422C3×C4—122no—
423C3×C4C2×D3×D411yescharacteristic
424C3×C4C2×D3×D411yescharacteristic
425Dic3—31no—
426Dic3—31no—
427Dic3—42no—
428Dic3—61no—
429Dic3D3×D811yescharacteristic
430Dic3D3×D811yescharacteristic
431C32C2×#50811yescharacteristic, complemented, Sylow
432C23—91no—
433C23—362no—
434Q8—22no—
435Q8—62no—
436Q8—122no—
437D4—62no—
438D4—122no—
439D4—182no—
440D4—362no—
441D4—362no—
442D4—362no—
443D4—362no—
444C2×C4—31no—
445C2×C4—31no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—122no—
451C2×C4—122no—
452C2×C4—362no—
453C2×C4—362no—
454C2×C4—362no—
455C8—31no—
456C8—31no—
457C8—91no—
458C8C22×D3211yescharacteristic
459C2×C3—21no—
460C2×C3—32no—
461C2×C3—61no—
462C2×C3—242no—
463C2×C3C2×D3×D811yescharacteristic
464C2×C3C2×D3×D811yescharacteristic
465D3—21no—
466D3—61no—
467D3—61no—
468D3—82no—
469D3—121no—
470D3—242no—
471D3—242no—
472D3—482no—
473D3#491912yesdirect product factor
474C22—31no—
475C22—31no—
476C22—91no—
477C22—122no—
478C22—182no—
479C22—362no—
480C22—724no—
481C4—31no—
482C4—31no—
483C4—42no—
484C4—91no—
485C4—122no—
486C4D32×D411yescharacteristic
487C3—21no—
488C3C2×#491911yescharacteristic, complemented
489C3D3×#50811yescharacteristic, complemented
490C2—32no—
491C2—61no—
492C2—181no—
493C2—242no—
494C2—722no—
495C2D32×D811yescharacteristic
subgroupG/H
centerC2D32×D8
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×Q32C22
socleC2×C32C22×D8
hypercenterQ32D32
hypocenterC32C2×#508
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
1. D3×#919C2semidirect
2. #10592618C2semidirect
3. C3×#4919C2semidirect
4. C3×D3×Q32C2semidirect
5. #10591049C2semidirect
6. #10591048C2semidirect
7. D3×#828C2semidirect
8. #10590244C2semidirect
9. #10590243C2semidirect
10. D3×D48C2semidirect
11. D32×C16C2semidirect
15. #64128C22semidirect
16. C3×#919C22semidirect
21. #63810C22semidirect
22. #63808C22semidirect
25. C32×Q32C22semidirect
26. #63655C22semidirect
27. #63626C22semidirect
28. C16×C3⋊D3C22semidirect
29. C3×#829C22semidirect
30. C3×#828C22semidirect
31. C3×Dic24C22semidirect
32. C3×D48C22semidirect
34. C3×D3×C16C22semidirect
35. #63549C22semidirect
36. #63547C22semidirect
37. #63546C22semidirect
38. #63542C22semidirect
40. D3×C3⋊C16C22semidirect
54. #4919D3direct (N × H)
55. D3×Q32D3semidirect
109. #919C2×D3semidirect
122. C3×Q32C2×D3semidirect
123. C3×Q32C2×D3semidirect
128. #829C2×D3semidirect
134. #828C2×D3semidirect
139. Dic24C2×D3semidirect
145. D48C2×D3semidirect
154. D3×C16C2×D3semidirect
288. Q32D32semidirect
368. C3×D3#508semidirect
431. C32C2×#508semidirect
473. D3#4919direct (N × H)
488. C3C2×#4919semidirect
489. C3D3×#508semidirect

Maximal subgroups

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

subgroupindex
D3×#9192
#105926182
C3×#49192
C3×D3×Q322
#105910492
#105910482
D3×#8282
#105902442
#105902432
D3×D482
D32×C162
D3×#5083
C2×#49193