Finite Group Databasebeta

← #11899676

Subgroups — #11899676

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594734C212yesmaximal, complemented
2C3⋊D3×D16C211yesmaximal, characteristic, complemented
3C3×#4912C211yesmaximal, characteristic, complemented
4C3×D3×D16C211yesmaximal, characteristic, complemented
5#10591036C212yesmaximal, complemented
6#10591033C212yesmaximal, complemented
7#10591024C212yesmaximal, complemented
8#10590244C211yesmaximal, characteristic, complemented
9#10590243C211yesmaximal, characteristic, complemented
10D3×D48C211yesmaximal, characteristic, complemented
11#10590227C211yesmaximal, characteristic, complemented
12#82031—31nomaximal
13#82019—31nomaximal
14#64314—22no—
15D8×C3⋊D3C2212yescomplemented
16C3×#912C2212yescomplemented
17C3×D3×D8C2212yescomplemented
18#63937—22no—
19#63934—22no—
20#63925—22no—
21#63810C2212yescomplemented
22#63808C2212yescomplemented
23#63803C2211yescharacteristic
24D3×D24C2212yescomplemented
25C32×D16C2211yescharacteristic, complemented
26#63653C2212yescomplemented
27#63626C2211yescharacteristic, complemented
28C16×C3⋊D3C2211yescharacteristic, complemented
29C3×#827C2212yescomplemented
30C3×#826C2212yescomplemented
31C3×Dic24C2211yescharacteristic, complemented
32C3×D48C2211yescharacteristic, complemented
33C3×D3×C16C2211yescharacteristic, complemented
34C3×D3×C16C2211yescharacteristic, complemented
35#63549C2212yescomplemented
36#63547C2212yescomplemented
37#63546C2212yescomplemented
38#63544C2211yescharacteristic, complemented
39#63543C2211yescharacteristic, complemented
40#63543C2211yescharacteristic, complemented
41#5769—32no—
42#5757—32no—
43C3×#508—31no—
44C2×C3×D16—31no—
45#5193—32no—
46#5147—32no—
47#4919—31no—
48#4919—31no—
49#4914—32no—
50#4914—32no—
51#4912—31no—
52#4912D311yescharacteristic, complemented
53#4911—32no—
54#4911—32no—
55D3×D16—31no—
56D3×D16—31no—
57D3×D16—31no—
58D3×D16—61no—
59D3×D16D311yescharacteristic, complemented
60#4904—31no—
61C2×D48—31no—
62#4901—31no—
63#4901—31no—
64D4×C3⋊D3—22no—
65C3×#237—22no—
66C3×D3×D4—22no—
67#3811—42no—
68D3×#67—42no—
69C2×#626—42no—
70#3804—42no—
71D3×D12—22no—
72#3799—22no—
73#3798D411yescharacteristic
74#3796—22no—
75C32×D8C2312yes—
76#3753—22no—
77#3745C2312yes—
78C8×C3⋊D3C2311yescharacteristic
79C3×#214—22no—
80C3×#213—22no—
81C3×Dic12C2312yes—
82C3×D24C2312yes—
83C3×D3×C8C2311yescharacteristic
84C3×D3×C8C2311yescharacteristic
85#3717—22no—
86#3715—22no—
87#3714—22no—
88#3712D411yescharacteristic
89#3711D411yescharacteristic
90#3711D411yescharacteristic
91C32×C16C2311yescharacteristic
92C3⋊(C3⋊C16)C2311yescharacteristic
93C3×C3⋊C16C2311yescharacteristic
94C3×C3⋊C16C2311yescharacteristic
95#3415—91noSylow
96#1009—62no—
97#1004—62no—
98C3×#135—32no—
99C2×C3×D8—32no—
100#949—62no—
101#932—62no—
102#919—32no—
103#919—32no—
104#914—62no—
105#914—62no—
106#912—32no—
107#912C2×D312yescomplemented
108#911—62no—
109#911—62no—
110D3×D8—32no—
111D3×D8—32no—
112D3×D8—32no—
113D3×D8—62no—
114D3×D8C2×D312yescomplemented
115#904—32no—
116C2×D24—32no—
117#901—31no—
118#901—31no—
119C3×Q32—31no—
120C3×SD32—32no—
121C3×D16—21no—
122C3×D16—32no—
123C3×D16—31no—
124C3×D16C2×D311yescharacteristic, complemented
125C3×D16C2×D311yescharacteristic, complemented
126C2×C3×C16—31no—
127C2×C3×C16—31no—
128#828—32no—
129#828—32no—
130#827—32no—
131#827C2×D312yescomplemented
132#826—32no—
133#826—32no—
134#826—32no—
135#826—62no—
136#826C2×D312yescomplemented
137#812—31no—
138#812—31no—
139Dic24C2×D311yescharacteristic, complemented
140#800—32no—
141D48—32no—
142D48—31no—
143D48—31no—
144D48—61no—
145D48C2×D311yescharacteristic, complemented
146#798—31no—
147#798—31no—
148#798—31no—
149#798—31no—
150D3×C16—31no—
151D3×C16—31no—
152D3×C16—61no—
153D3×C16C2×D311yescharacteristic, complemented
154D3×C16C2×D311yescharacteristic, complemented
155C22×C3⋊D3—42no—
156C22×C3×D3—42no—
157C2×D32—42no—
158C32×D4—22no—
159#638—42no—
160C4⋊(C3⋊D3)—22no—
161C4×C3⋊D3C2×D411yescharacteristic
162C3×#67—42no—
163C3×#67—42no—
164C2×C3×Dic3—42no—
165C3×D12—22no—
166C3×C4×D3C2×D411yescharacteristic
167C3×C4×D3C2×D411yescharacteristic
168C3×Dic6—22no—
169#627D811yescharacteristic
170#626—42no—
171#626—42no—
172#626—42no—
173#626D811yescharacteristic
174#626D811yescharacteristic
175#625D811yescharacteristic
176#624—42no—
177D3×Dic3—42no—
178C32×C8C2411yescharacteristic
179C3⋊(C3⋊C8)C2×D411yescharacteristic
180C3×C3⋊C8C2×D411yescharacteristic
181C3×C3⋊C8C2×D411yescharacteristic
182#576—92no—
183#509—92no—
184#509—92no—
185#509—92no—
186#508—31no—
187#508—91no—
188#508—91no—
189C2×D16—31no—
190C2×D16—91no—
191C2×D16—91no—
192#504—91no—
193C3×#41—62no—
194C2×C3×D4—62no—
195C2×#67—122no—
196C2×#67—122no—
197#239—62no—
198#239—62no—
199#237—22no—
200#237—62no—
201#237—122no—
202D3×D4—22no—
203D3×D4—62no—
204D3×D4—62no—
205D3×D4—62no—
206D3×D4—122no—
207D3×D4—122no—
208D3×D4—122no—
209D3×D4—122no—
210#235—31no—
211#235—31no—
212#235—62no—
213#235—122no—
214C2×D12—62no—
215C2×D12—122no—
216C3×Q16—32no—
217C3×SD16—62no—
218C3×D8—22no—
219C3×D8—32no—
220C3×D8—62no—
221C3×D8C22×D312yes—
222C3×D8C22×D312yes—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225#215—62no—
226#215—62no—
227#214—22no—
228#214—62no—
229#213—22no—
230#213—62no—
231#213—62no—
232#213—62no—
233#213—122no—
234#208—31no—
235#208—31no—
236Dic12C22×D312yes—
237D24—32no—
238D24—32no—
239D24—62no—
240D24—62no—
241D24C22×D312yes—
242#204—62no—
243ΓL(1,𝔽25)—31no—
244ΓL(1,𝔽25)—31no—
245ΓL(1,𝔽25)—31no—
246ΓL(1,𝔽25)—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
262C22×C32—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—162no—
265C2×C3⋊D3C2×D811yescharacteristic
266C2×C3×D3—42no—
267C2×C3×D3—162no—
268C2×C3×D3C2×D811yescharacteristic
269C2×C3×D3C2×D811yescharacteristic
270D32—162no—
271C32×C4C22×D411yescharacteristic
272C3⋊Dic3C2×D811yescharacteristic
273C3×Dic3—42no—
274C3×Dic3C2×D811yescharacteristic
275C3×Dic3C2×D811yescharacteristic
276H(5,𝔽2)—182no—
277AGL(1,ℤ/8)—182no—
278AGL(1,ℤ/8)—182no—
279AGL(1,ℤ/8)—182no—
280#135—32no—
281#135—92no—
282#135—92no—
283C2×D8—32no—
284C2×D8—92no—
285C2×D8—92no—
286#131—91no—
287Q32—31no—
288SD32—32no—
289SD32—92no—
290SD32—92no—
291D16—32no—
292D16—31no—
293D16—92no—
294D16—92no—
295D16—91no—
296D16D3211yescharacteristic, complemented
297M32—91no—
298M32—91no—
299M32—91no—
300C2×C16—31no—
301C2×C16—31no—
302C2×C16—91no—
303C23×C3—122no—
304C22×D3—42no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—122no—
309C22×D3—242no—
310C3×Q8—62no—
311C3×D4—22no—
312C3×D4—22no—
313C3×D4—42no—
314C3×D4—62no—
315C3×D4—122no—
316C3×D4—122no—
317C2×C3×C4—31no—
318C2×C3×C4—31no—
319C2×C3×C4—122no—
320#67—31no—
321#67—31no—
322#67—31no—
323#67—31no—
324#67—42no—
325#67—42no—
326#67—122no—
327#67—122no—
328#67—122no—
329#67—122no—
330#67—122no—
331#67—242no—
332C2×Dic3—42no—
333C2×Dic3—122no—
334D12—22no—
335D12—31no—
336D12—31no—
337D12—62no—
338D12—62no—
339D12—122no—
340D12—122no—
341D12—122no—
342D12—122no—
343C4×D3—31no—
344C4×D3—31no—
345C4×D3—61no—
346C4×D3—122no—
347C4×D3—122no—
348C4×D3—122no—
349C4×D3D3×D411yescharacteristic
350C4×D3D3×D411yescharacteristic
351Dic6—22no—
352Dic6—31no—
353Dic6—31no—
354C3×C8—21no—
355C3×C8—31no—
356C3×C8—31no—
357C3×C8C23×D311yescharacteristic
358C3×C8C23×D311yescharacteristic
359C3⋊C8—31no—
360C3⋊C8—31no—
361C3⋊C8—61no—
362C3⋊C8D3×D411yescharacteristic
363C3⋊C8D3×D411yescharacteristic
364C2×C32—82no—
365C2×C32C22×D811yescharacteristic
366C3⋊D3—21no—
367C3⋊D3—82no—
368C3×D3—21no—
369C3×D3—21no—
370C3×D3—82no—
371#41—62no—
372#41—91no—
373#41—182no—
374#41—182no—
375#41—362no—
376C2×D4—62no—
377C2×D4—182no—
378C2×D4—182no—
379C2×D4—362no—
380C2×D4—362no—
381C2×D4—362no—
382Q16—32no—
383SD16—62no—
384SD16—182no—
385SD16—182no—
386D8—32no—
387D8—62no—
388D8—92no—
389D8—182no—
390D8—182no—
391D8C2×D3212yes—
392M16—91no—
393M16—91no—
394M16—91no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—91no—
398C16—31no—
399C16—31no—
400C16—91no—
401C16C2×D3211yescharacteristic
402C22×C3—31no—
403C22×C3—31no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—82no—
407C22×C3—122no—
408C22×C3—482no—
409C2×D3—31no—
410C2×D3—31no—
411C2×D3—42no—
412C2×D3—61no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—162no—
416C2×D3—242no—
417C2×D3—482no—
418C2×D3—482no—
419C2×D3—482no—
420C2×D3—484no—
421C2×D3—482no—
422C2×D3D3×D811yescharacteristic
423C2×D3D3×D811yescharacteristic
424C3×C4—21no—
425C3×C4—31no—
426C3×C4—31no—
427C3×C4—122no—
428C3×C4C2×D3×D411yescharacteristic
429C3×C4C2×D3×D411yescharacteristic
430Dic3—31no—
431Dic3—31no—
432Dic3—42no—
433Dic3—61no—
434Dic3D3×D811yescharacteristic
435Dic3D3×D811yescharacteristic
436C32#341511yescharacteristic, complemented, Sylow
437C23—122no—
438C23—362no—
439C23—362no—
440Q8—62no—
441Q8—91no—
442D4—22no—
443D4—62no—
444D4—91no—
445D4—91no—
446D4—91no—
447D4—122no—
448D4—122no—
449D4—182no—
450D4—362no—
451D4—362no—
452D4—362no—
453D4—362no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—91no—
457C2×C4—122no—
458C2×C4—362no—
459C2×C4—362no—
460C8—31no—
461C8—31no—
462C8—91no—
463C8C22×D3211yescharacteristic
464C2×C3—21no—
465C2×C3—61no—
466C2×C3—61no—
467C2×C3—82no—
468C2×C3—82no—
469C2×C3—162no—
470C2×C3—242no—
471C2×C3C2×D3×D811yescharacteristic
472C2×C3C2×D3×D811yescharacteristic
473D3—21no—
474D3—21no—
475D3—62no—
476D3—61no—
477D3—61no—
478D3—82no—
479D3—242no—
480D3—242no—
481D3—482no—
482C22—31no—
483C22—31no—
484C22—42no—
485C22—91no—
486C22—122no—
487C22—362no—
488C22—482no—
489C22—1442no—
490C22—1442no—
491C4—31no—
492C4—31no—
493C4—91no—
494C4—122no—
495C4D32×D411yescharacteristic
496C3—21no—
497C3#8201911yescharacteristic, complemented
498C3#8203111yescharacteristic, complemented
499C2—61no—
500C2—61no—
501C2—82no—
502C2—181no—
503C2—242no—
504C2—722no—
505C2D32×D811yescharacteristic
subgroupG/H
centerC2D32×D8
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×D16C22
socleC2×C32C22×D8
hypercenterD16D32
hypocenterC32#3415
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #10594734C2semidirect
2. C3⋊D3×D16C2semidirect
3. C3×#4912C2semidirect
4. C3×D3×D16C2semidirect
5. #10591036C2semidirect
6. #10591033C2semidirect
7. #10591024C2semidirect
8. #10590244C2semidirect
9. #10590243C2semidirect
10. D3×D48C2semidirect
11. #10590227C2semidirect
15. D8×C3⋊D3C22semidirect
16. C3×#912C22semidirect
17. C3×D3×D8C22semidirect
21. #63810C22semidirect
22. #63808C22semidirect
24. D3×D24C22semidirect
25. C32×D16C22semidirect
26. #63653C22semidirect
27. #63626C22semidirect
28. C16×C3⋊D3C22semidirect
29. C3×#827C22semidirect
30. C3×#826C22semidirect
31. C3×Dic24C22semidirect
32. C3×D48C22semidirect
33. C3×D3×C16C22semidirect
34. C3×D3×C16C22semidirect
35. #63549C22semidirect
36. #63547C22semidirect
37. #63546C22semidirect
38. #63544C22semidirect
39. #63543C22semidirect
40. #63543C22semidirect
52. #4912D3semidirect
59. D3×D16D3semidirect
107. #912C2×D3semidirect
114. D3×D8C2×D3semidirect
124. C3×D16C2×D3semidirect
125. C3×D16C2×D3semidirect
131. #827C2×D3semidirect
136. #826C2×D3semidirect
139. Dic24C2×D3semidirect
145. D48C2×D3semidirect
153. D3×C16C2×D3semidirect
154. D3×C16C2×D3semidirect
296. D16D32semidirect
436. C32#3415semidirect
497. C3#82019semidirect
498. C3#82031semidirect

Maximal subgroups

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

subgroupindex
#105947342
C3⋊D3×D162
C3×#49122
C3×D3×D162
#105910362
#105910332
#105910242
#105902442
#105902432
D3×D482
#105902272
#820313
#820193