Finite Group Databasebeta

← C3⋊D3×#472 #11867905

Subgroups — C3⋊D3×#472 #11867905

Order 1152.

1464 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×AGL(1,ℤ/8)C212yesmaximal, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3C3⋊D3×#131C211yesmaximal, characteristic, complemented
4C32×#472C211yesmaximal, characteristic, complemented
5#10592898C212yesmaximal, complemented
6#10592859C211yesmaximal, characteristic, complemented
7#10592841C211yesmaximal, characteristic, complemented
8#10592596C211yesmaximal, characteristic, complemented
9C3⋊D3×#108C211yesmaximal, characteristic, complemented
10#10592448C212yesmaximal, complemented
11C3⋊D3×#100C212yesmaximal, complemented
12D3×#472—34nomaximal
13#41×C3⋊D3C2211yescharacteristic
14C2×D4×C3⋊D3C2212yes—
15C32×AGL(1,ℤ/8)C2212yescomplemented
16C2×C32×D8C2211yescharacteristic, complemented
17C32×#131C2211yescharacteristic, complemented
18#64158C2212yescomplemented
19#64157C2211yescharacteristic, complemented
20#64141C2212yescomplemented
21C2×#3753C2212yescomplemented
22#64123—22no—
23SD16×C3⋊D3—22no—
24#64120—22no—
25D8×C3⋊D3—22no—
26D8×C3⋊D3—21no—
27D8×C3⋊D3—21no—
28D8×C3⋊D3—21no—
29D8×C3⋊D3—21no—
30#64117C2212yescomplemented
31#64116—21no—
32#64116C2211yescharacteristic, complemented
33M16×C3⋊D3—21no—
34M16×C3⋊D3C2212yes—
35M16×C3⋊D3C2211yescharacteristic
36C2×#3745C2211yescharacteristic, complemented
37#64110—21no—
38#64110C2211yescharacteristic, complemented
39C2×C8×C3⋊D3—21no—
40C2×C8×C3⋊D3C2211yescharacteristic
41C32×#108C2211yescharacteristic, complemented
42C32×#100C2212yescomplemented
43#63660C2212yescomplemented
44#63650C2212yescomplemented
45#63650C2212yescomplemented
46#63649C2212yescomplemented
47#63646C2211yescharacteristic, complemented
48D3×AGL(1,ℤ/8)—38no—
49C2×D3×D8—34no—
50D3×#131—34no—
51C3×#472D314yescomplemented
52#5199—38no—
53#5160—34no—
54#5142—34no—
55#4897—34no—
56D3×#108—34no—
57#4749—38no—
58D3×#100—38no—
59C23×C3⋊D3—22no—
60C32×#41C2311yescharacteristic
61C2×C32×D4C2312yes—
62C2×#638—22no—
63#3832D411yescharacteristic
64Q8×C3⋊D3D411yescharacteristic
65#3830—21no—
66#3830D411yescharacteristic
67D4×C3⋊D3—21no—
68D4×C3⋊D3—22no—
69D4×C3⋊D3—22no—
70D4×C3⋊D3—22no—
71D4×C3⋊D3—22no—
72D4×C3⋊D3D411yescharacteristic
73#3828—21no—
74#3828C2311yescharacteristic
75C2×C4⋊(C3⋊D3)C2312yes—
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3C2311yescharacteristic
78C32×SD16—22no—
79C32×D8—22no—
80C32×D8—21no—
81C32×D8—21no—
82C32×M16—21no—
83C32×M16C2311yescharacteristic
84C32×M16C2312yes—
85C2×C32×C8—21no—
86C2×C32×C8C2311yescharacteristic
87#3755—22no—
88#3754—22no—
89#3753—22no—
90#3753—22no—
91#3753—22no—
92#3753—22no—
93#3748—21no—
94#3748C2311yescharacteristic
95#3748C2312yes—
96C2×C3⋊(C3⋊C8)—21no—
97C2×C3⋊(C3⋊C8)C2311yescharacteristic
98#3745—22no—
99#3745—21no—
100#3745—21no—
101#3744—22no—
102#3743—21no—
103#3743—22no—
104#3743—21no—
105#3743—21no—
106C8×C3⋊D3—21no—
107C8×C3⋊D3—22no—
108C8×C3⋊D3—21no—
109C8×C3⋊D3—21no—
110C8×C3⋊D3D411yescharacteristic
111C8×C3⋊D3D411yescharacteristic
112C8×C3⋊D3D411yescharacteristic
113C8×C3⋊D3D411yescharacteristic
114C2×#472—91noSylow
115D3×#41—34no—
116C2×D3×D4—38no—
117C3×AGL(1,ℤ/8)C2×D318yescomplemented
118C2×C3×D8C2×D314yescomplemented
119C3×#131C2×D314yescomplemented
120#949—38no—
121#948—34no—
122#932—38no—
123C2×#213—38no—
124#914—68no—
125D3×SD16—68no—
126#911—68no—
127D3×D8—64no—
128D3×D8—64no—
129D3×D8—64no—
130D3×D8—64no—
131D3×D8—68no—
132#908—38no—
133#907—34no—
134#907—64no—
135D3×M16—38no—
136D3×M16—34no—
137D3×M16—64no—
138C2×D24—34no—
139#901—34no—
140#901—64no—
141C2×D3×C8—34no—
142C2×D3×C8—64no—
143C3×#108C2×D314yescomplemented
144C3×#100C2×D318yescomplemented
145#833—38no—
146#823—38no—
147#823—38no—
148#822—38no—
149#819—34no—
150C23×C32—22no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—42no—
154C22×C3⋊D3—42no—
155C22×C3⋊D3—84no—
156C22×C3⋊D3#4111yescharacteristic
157C32×Q8C2×D411yescharacteristic
158C32×D4—21no—
159C32×D4—22no—
160C32×D4—22no—
161C32×D4C2×D411yescharacteristic
162C2×C32×C4—21no—
163C2×C32×C4C2411yescharacteristic
164#638—21no—
165#638—21no—
166#638—21no—
167#638—42no—
168#638—42no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3#4111yescharacteristic
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)C2×D411yescharacteristic
175C4×C3⋊D3—21no—
176C4×C3⋊D3—21no—
177C4×C3⋊D3—21no—
178C4×C3⋊D3C2×D411yescharacteristic
179C4×C3⋊D3C2×D411yescharacteristic
180C4×C3⋊D3C2×D411yescharacteristic
181C4×C3⋊D3C2×D411yescharacteristic
182#634—21no—
183#634C2×D411yescharacteristic
184C32×C8—21no—
185C32×C8—22no—
186C32×C8C2×D411yescharacteristic
187C32×C8C2×D411yescharacteristic
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—22no—
190C3⋊(C3⋊C8)C2×D411yescharacteristic
191C3⋊(C3⋊C8)C2×D411yescharacteristic
192C2×AGL(1,ℤ/8)—92no—
193C22×D8—91no—
194C2×#131—91no—
195#472—92no—
196#472—91no—
197#472—91no—
198#472—91no—
199#472—92no—
200#472C3⋊D311yescharacteristic, direct product factor
201C2×#108—91no—
202C2×#100—92no—
203C23×D3—68no—
204C3×#41C22×D314yes—
205C2×C3×D4C22×D318yes—
206C2×#67—68no—
207#239—34no—
208D3×Q8—34no—
209#237—34no—
210#237—64no—
211D3×D4—34no—
212D3×D4—68no—
213D3×D4—68no—
214D3×D4—68no—
215D3×D4—68no—
216D3×D4—64no—
217#235—34no—
218#235—64no—
219C2×D12—38no—
220C2×C4×D3—34no—
221C2×C4×D3—64no—
222C3×SD16—28no—
223C3×D8—28no—
224C3×D8—24no—
225C3×D8—24no—
226C3×M16—24no—
227C3×M16C22×D318yes—
228C3×M16C22×D314yes—
229C2×C3×C8—24no—
230C2×C3×C8C22×D314yes—
231#215—68no—
232#214—68no—
233#213—68no—
234#213—68no—
235#213—68no—
236#213—68no—
237#208—38no—
238#208—34no—
239#208—64no—
240C2×C3⋊C8—34no—
241C2×C3⋊C8—64no—
242D24—68no—
243D24—64no—
244D24—64no—
245#204—68no—
246ΓL(1,𝔽25)—64no—
247ΓL(1,𝔽25)—64no—
248ΓL(1,𝔽25)—68no—
249ΓL(1,𝔽25)—64no—
250D3×C8—34no—
251D3×C8—34no—
252D3×C8—34no—
253D3×C8—34no—
254D3×C8—64no—
255D3×C8—64no—
256D3×C8—68no—
257D3×C8—64no—
258C22×C32—21no—
259C22×C32—42no—
260C22×C32—82no—
261C22×C32C2×#4111yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3—21no—
264C2×C3⋊D3—42no—
265C2×C3⋊D3—42no—
266C2×C3⋊D3—84no—
267C2×C3⋊D3—84no—
268C2×C3⋊D3—82no—
269C2×C3⋊D3#12111yescharacteristic
270C2×C3⋊D3#12111yescharacteristic
271C32×C4—21no—
272C32×C4C22×D411yescharacteristic
273C32×C4C22×D411yescharacteristic
274C3⋊Dic3—21no—
275C3⋊Dic3#12111yescharacteristic
276C3⋊Dic3#12111yescharacteristic
277C2×#41—91no—
278C22×D4—92no—
279AGL(1,ℤ/8)—92no—
280AGL(1,ℤ/8)—92no—
281AGL(1,ℤ/8)—92no—
282AGL(1,ℤ/8)—182no—
283AGL(1,ℤ/8)—182no—
284AGL(1,ℤ/8)C2×C3⋊D312yescomplemented
285C2×SD16—182no—
286C2×D8—92no—
287C2×D8—91no—
288C2×D8—181no—
289C2×D8—181no—
290C2×D8—181no—
291C2×D8—181no—
292C2×D8—182no—
293C2×D8C2×C3⋊D311yescharacteristic, complemented
294#131—91no—
295#131—91no—
296#131—91no—
297#131—181no—
298#131—181no—
299#131C2×C3⋊D311yescharacteristic, complemented
300C2×M16—91no—
301C2×M16—92no—
302C2×M16—181no—
303C22×C8—91no—
304C22×C8—181no—
305#108—92no—
306#108—91no—
307#108C2×C3⋊D311yescharacteristic, complemented
308#100—92no—
309#100—92no—
310#100—92no—
311#100C2×C3⋊D312yescomplemented
312C23×C3—28no—
313C22×D3—34no—
314C22×D3—64no—
315C22×D3—68no—
316C22×D3—128no—
317C22×D3—128no—
318C22×D3—2416no—
319C3×Q8D3×D414yes—
320C3×D4—24no—
321C3×D4—28no—
322C3×D4—28no—
323C3×D4D3×D414yes—
324C2×C3×C4—24no—
325C2×C3×C4C23×D314yes—
326#67—64no—
327#67—64no—
328#67—64no—
329#67—128no—
330#67—128no—
331C2×Dic3—34no—
332C2×Dic3—64no—
333D12—34no—
334D12—64no—
335D12—68no—
336D12—68no—
337C4×D3—34no—
338C4×D3—34no—
339C4×D3—34no—
340C4×D3—34no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—64no—
344Dic6—34no—
345Dic6—64no—
346C3×C8—24no—
347C3×C8—28no—
348C3×C8D3×D414yes—
349C3×C8D3×D414yes—
350C3⋊C8—34no—
351C3⋊C8—34no—
352C3⋊C8—64no—
353C3⋊C8—68no—
354C2×C32—21no—
355C2×C32—41no—
356C2×C32—82no—
357C2×C32C2×#12111yescharacteristic
358C3⋊D3—21no—
359C3⋊D3—41no—
360C3⋊D3—82no—
361C3⋊D3#47212yesdirect product factor
362C24—182no—
363#41—91no—
364#41—91no—
365#41—91no—
366#41—181no—
367#41—181no—
368#41C22×C3⋊D311yescharacteristic
369C2×Q8—91no—
370C2×D4—91no—
371C2×D4—92no—
372C2×D4—182no—
373C2×D4—182no—
374C2×D4—182no—
375C2×D4—182no—
376C2×D4—182no—
377C2×D4—181no—
378C2×D4C22×C3⋊D312yes—
379C22×C4—91no—
380C22×C4—181no—
381SD16—22no—
382SD16—182no—
383SD16—182no—
384SD16—182no—
385D8—22no—
386D8—21no—
387D8—21no—
388D8—182no—
389D8—182no—
390D8—182no—
391D8—182no—
392D8—182no—
393D8—181no—
394D8—181no—
395M16—21no—
396M16—91no—
397M16—92no—
398M16—181no—
399M16—181no—
400M16—182no—
401M16—181no—
402M16—181no—
403M16C22×C3⋊D311yescharacteristic
404M16C22×C3⋊D312yes—
405C2×C8—21no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—181no—
412C2×C8—181no—
413C2×C8—182no—
414C2×C8—181no—
415C2×C8—181no—
416C2×C8C22×C3⋊D311yescharacteristic
417C22×C3—24no—
418C22×C3—48no—
419C22×C3—88no—
420C22×C3D3×#4114yes—
421C2×D3—34no—
422C2×D3—34no—
423C2×D3—68no—
424C2×D3—64no—
425C2×D3—128no—
426C2×D3—128no—
427C2×D3—2416no—
428C2×D3—2416no—
429C2×D3—248no—
430C3×C4—24no—
431C3×C4C2×D3×D414yes—
432C3×C4C2×D3×D414yes—
433Dic3—34no—
434Dic3—34no—
435Dic3—64no—
436C32C2×#47211yescharacteristic, complemented, Sylow
437C23—22no—
438C23—91no—
439C23—181no—
440C23—182no—
441C23—362no—
442C23—362no—
443C23—724no—
444Q8—91no—
445Q8—181no—
446Q8D4×C3⋊D311yescharacteristic
447D4—21no—
448D4—22no—
449D4—22no—
450D4—91no—
451D4—181no—
452D4—181no—
453D4—181no—
454D4—181no—
455D4—182no—
456D4—182no—
457D4—362no—
458D4—362no—
459D4D4×C3⋊D311yescharacteristic
460C2×C4—21no—
461C2×C4—91no—
462C2×C4—91no—
463C2×C4—91no—
464C2×C4—91no—
465C2×C4—91no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4C23×C3⋊D311yescharacteristic
471C8—21no—
472C8—22no—
473C8—91no—
474C8—91no—
475C8—181no—
476C8—182no—
477C8D4×C3⋊D311yescharacteristic
478C8D4×C3⋊D311yescharacteristic
479C2×C3—24no—
480C2×C3—44no—
481C2×C3—88no—
482C2×C3D3×#12114yes—
483D3—38no—
484D3—64no—
485D3—124no—
486D3—248no—
487C22—21no—
488C22—42no—
489C22—82no—
490C22—91no—
491C22—91no—
492C22—182no—
493C22—181no—
494C22—362no—
495C22—362no—
496C22—722no—
497C22—724no—
498C22—724no—
499C22#41×C3⋊D311yescharacteristic
500C4—21no—
501C4—91no—
502C4—91no—
503C4—181no—
504C4C2×D4×C3⋊D311yescharacteristic
505C4C2×D4×C3⋊D311yescharacteristic
506C3D3×#47214yescomplemented
507C2—21no—
508C2—41no—
509C2—82no—
510C2—92no—
511C2—181no—
512C2—361no—
513C2—722no—
514C2C3⋊D3×#12111yescharacteristic
subgroupG/H
centerC2C3⋊D3×#121
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#472C2
socleC2×C32C2×#121
hypercenter#472C3⋊D3
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×AGL(1,ℤ/8)C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. C3⋊D3×#131C2semidirect
4. C32×#472C2semidirect
5. #10592898C2semidirect
6. #10592859C2semidirect
7. #10592841C2semidirect
8. #10592596C2semidirect
9. C3⋊D3×#108C2semidirect
10. #10592448C2semidirect
11. C3⋊D3×#100C2semidirect
15. C32×AGL(1,ℤ/8)C22semidirect
16. C2×C32×D8C22semidirect
17. C32×#131C22semidirect
18. #64158C22semidirect
19. #64157C22semidirect
20. #64141C22semidirect
21. C2×#3753C22semidirect
30. #64117C22semidirect
32. #64116C22semidirect
36. C2×#3745C22semidirect
38. #64110C22semidirect
41. C32×#108C22semidirect
42. C32×#100C22semidirect
43. #63660C22semidirect
44. #63650C22semidirect
45. #63650C22semidirect
46. #63649C22semidirect
47. #63646C22semidirect
51. C3×#472D3semidirect
117. C3×AGL(1,ℤ/8)C2×D3semidirect
118. C2×C3×D8C2×D3semidirect
119. C3×#131C2×D3semidirect
143. C3×#108C2×D3semidirect
144. C3×#100C2×D3semidirect
200. #472C3⋊D3direct (N × H)
284. AGL(1,ℤ/8)C2×C3⋊D3semidirect
293. C2×D8C2×C3⋊D3semidirect
299. #131C2×C3⋊D3semidirect
307. #108C2×C3⋊D3semidirect
311. #100C2×C3⋊D3semidirect
361. C3⋊D3#472direct (N × H)
436. C32C2×#472semidirect
506. C3D3×#472semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×AGL(1,ℤ/8)2
C2×D8×C3⋊D32
C3⋊D3×#1312
C32×#4722
#105928982
#105928592
#105928412
#105925962
C3⋊D3×#1082
#105924482
C3⋊D3×#1002
D3×#4723