Finite Group Databasebeta

← C3⋊D3×#578 #11918903

Subgroups — C3⋊D3×#578 #11918903

Order 1152.

4224 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×2−1+4C212yesmaximal, complemented
2C32×#578C211yesmaximal, characteristic, complemented
3#10596309C212yesmaximal, complemented
4#10596250C216yesmaximal, complemented
5C3⋊D3×#137C216yesmaximal, complemented
6#10596242C213yesmaximal, complemented
7C3⋊D3×#135C213yesmaximal, complemented
8#10596237C213yesmaximal, complemented
9C2×Q16×C3⋊D3C213yesmaximal, complemented
10#10596224C211yesmaximal, characteristic, complemented
11C3⋊D3×#131C211yesmaximal, characteristic, complemented
12D3×#578—34nomaximal
13C32×2−1+4C2212yescomplemented
14#64367—26no—
15#64367C2216yescomplemented
16#64367C2212yescomplemented
17#41×C3⋊D3—26no—
18#41×C3⋊D3C2216yes—
19#41×C3⋊D3C2211yescharacteristic
20#64364—22no—
21#64364C2216yescomplemented
22C2×Q8×C3⋊D3—22no—
23C2×Q8×C3⋊D3C2216yes—
24C32×#137C2216yescomplemented
25C32×#135C2213yescomplemented
26C2×C32×Q16C2213yescomplemented
27C32×#131C2211yescharacteristic, complemented
28#64160C2216yescomplemented
29#64159C2216yescomplemented
30#64157C2211yescharacteristic, complemented
31C2×#3756C2216yescomplemented
32#64151C2216yescomplemented
33#64128C2213yescomplemented
34#64127C22112yescomplemented
35Q16×C3⋊D3C2213yes—
36Q16×C3⋊D3C2216yes—
37Q16×C3⋊D3C2216yescomplemented
38Q16×C3⋊D3C2216yescomplemented
39#64125C2216yescomplemented
40#64124C22112yescomplemented
41SD16×C3⋊D3C2216yes—
42#64121C2213yescomplemented
43D8×C3⋊D3C2211yescharacteristic
44#64118C2216yescomplemented
45#64116C2213yescomplemented
46M16×C3⋊D3C2213yes—
47C2×#3746C2213yescomplemented
48#64113C2213yescomplemented
49#64110C2213yescomplemented
50C2×C8×C3⋊D3C2213yes—
51D3×2−1+4—38no—
52C3×#578D314yescomplemented
53#5838—38no—
54#5779—324no—
55D3×#137—324no—
56#5771—312no—
57D3×#135—312no—
58#5766—312no—
59C2×D3×Q16—312no—
60#5753—34no—
61D3×#131—34no—
62C32×#41—26no—
63C32×#41C2316yes—
64C32×#41C2311yescharacteristic
65C2×C32×Q8—22no—
66C2×C32×Q8C2316yes—
67#3832—26no—
68#3832D411yescharacteristic
69#3832C2316yes—
70Q8×C3⋊D3—22no—
71Q8×C3⋊D3—26no—
72Q8×C3⋊D3—26no—
73Q8×C3⋊D3—26no—
74Q8×C3⋊D3D411yescharacteristic
75Q8×C3⋊D3C2316yes—
76Q8×C3⋊D3C23112yes—
77#3830—26no—
78#3830—212no—
79#3830—26no—
80#3830D413yes—
81#3830C2316yes—
82D4×C3⋊D3—26no—
83D4×C3⋊D3D413yes—
84D4×C3⋊D3C2312yes—
85#3828—212no—
86#3828—26no—
87#3828—26no—
88#3828C2313yes—
89#3828C2316yes—
90C2×C4×C3⋊D3—26no—
91C2×C4×C3⋊D3—26no—
92C2×C4×C3⋊D3C2313yes—
93C2×#634—26no—
94C2×#634—26no—
95C2×#634C2316yes—
96C32×Q16C2313yes—
97C32×Q16C2316yes—
98C32×SD16C2316yes—
99C32×D8C2311yescharacteristic
100C32×M16C2313yes—
101C2×C32×C8C2313yes—
102#3756C23112yes—
103#3756C2316yes—
104#3755C2316yes—
105#3754C2316yes—
106#3753C2312yes—
107#3748C2313yes—
108C2×C3⋊(C3⋊C8)C2313yes—
109#3746C2313yes—
110#3746C2316yes—
111#3745C2311yescharacteristic
112#3744C2316yes—
113#3743C2316yes—
114C8×C3⋊D3C2311yescharacteristic
115C8×C3⋊D3C2313yes—
116C8×C3⋊D3C2313yes—
117C8×C3⋊D3C2313yes—
118C2×#578—91noSylow
119C3×2−1+4C2×D318yescomplemented
120#1010—38no—
121#1010—324no—
122#1010—624no—
123D3×#41—34no—
124D3×#41—324no—
125D3×#41—624no—
126#1007—324no—
127#1007—68no—
128C2×D3×Q8—324no—
129C2×D3×Q8—68no—
130C3×#137C2×D3124yescomplemented
131C3×#135C2×D3112yescomplemented
132C2×C3×Q16C2×D3112yescomplemented
133C3×#131C2×D314yescomplemented
134#951—324no—
135#950—324no—
136#948—34no—
137C2×#216—324no—
138#942—324no—
139#919—312no—
140#918—348no—
141D3×Q16—312no—
142D3×Q16—324no—
143D3×Q16—324no—
144D3×Q16—324no—
145#916—324no—
146#915—348no—
147D3×SD16—324no—
148#912—312no—
149D3×D8—34no—
150#909—324no—
151#907—312no—
152D3×M16—312no—
153C2×Dic12—312no—
154#904—312no—
155#901—312no—
156C2×D3×C8—312no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3C2×D413yes—
159C32×Q8—26no—
160C32×Q8C2×D411yescharacteristic
161C32×Q8C2416yes—
162C32×D4—26no—
163C32×D4C2×D413yes—
164C32×D4C2412yes—
165C2×C32×C4—26no—
166C2×C32×C4—26no—
167C2×C32×C4C2413yes—
168#638—26no—
169#638—26no—
170#638—22no—
171#638C2×D416yes—
172C2×C3⋊Dic3—26no—
173C2×C3⋊Dic3—26no—
174C2×C3⋊Dic3C2×D413yes—
175C4⋊(C3⋊D3)—26no—
176C4⋊(C3⋊D3)C2×D413yes—
177C4⋊(C3⋊D3)C2412yes—
178C4×C3⋊D3—26no—
179C4×C3⋊D3—212no—
180C4×C3⋊D3—26no—
181C4×C3⋊D3—26no—
182C4×C3⋊D3C2×D413yes—
183C4×C3⋊D3C2×D413yes—
184C4×C3⋊D3C2411yescharacteristic
185C4×C3⋊D3C2413yes—
186#634—26no—
187#634—26no—
188#634—212no—
189#634C2×D413yes—
190#634C2416yes—
191C32×C8C2411yescharacteristic
192C32×C8C2413yes—
193C3⋊(C3⋊C8)C2411yescharacteristic
194C3⋊(C3⋊C8)C2413yes—
195C2×2−1+4—92no—
196#578—92no—
197#578—96no—
198#578—93no—
199#578—93no—
200#578—91no—
201#578C3⋊D311yescharacteristic, direct product factor
202C2×#137—96no—
203C2×#135—93no—
204C22×Q16—93no—
205C2×#131—91no—
206C3×#41—224no—
207C3×#41C22×D3124yes—
208C3×#41C22×D314yes—
209C2×C3×Q8—28no—
210C2×C3×Q8C22×D3124yes—
211#239—34no—
212#239—324no—
213#239—624no—
214D3×Q8—34no—
215D3×Q8—324no—
216D3×Q8—348no—
217D3×Q8—624no—
218D3×Q8—624no—
219D3×Q8—624no—
220D3×Q8—68no—
221#237—312no—
222#237—324no—
223#237—624no—
224#237—648no—
225#237—624no—
226D3×D4—312no—
227D3×D4—38no—
228D3×D4—624no—
229#235—312no—
230#235—324no—
231#235—624no—
232#235—624no—
233#235—648no—
234C2×C4×D3—312no—
235C2×C4×D3—624no—
236C2×C4×D3—624no—
237C2×Dic6—324no—
238C2×Dic6—624no—
239C2×Dic6—624no—
240C3×Q16C22×D3112yes—
241C3×Q16C22×D3124yes—
242C3×SD16C22×D3124yes—
243C3×D8C22×D314yes—
244C3×M16C22×D3112yes—
245C2×C3×C8C22×D3112yes—
246#216—348no—
247#216—324no—
248#215—324no—
249#214—324no—
250#213—38no—
251#208—312no—
252C2×C3⋊C8—312no—
253Dic12—312no—
254Dic12—324no—
255D24—34no—
256#204—324no—
257ΓL(1,𝔽25)—324no—
258D3×C8—34no—
259D3×C8—312no—
260D3×C8—312no—
261D3×C8—312no—
262C22×C32—22no—
263C22×C32C22×D413yes—
264C2×C3⋊D3—26no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—44no—
267C2×C3⋊D3C22×D413yes—
268C2×C3⋊D3C22×D411yescharacteristic
269C32×C4—26no—
270C32×C4C22×D413yes—
271C32×C4C2511yescharacteristic
272C3⋊Dic3—26no—
273C3⋊Dic3C22×D411yescharacteristic
274C3⋊Dic3C22×D413yes—
2752−1+4—96no—
2762−1+4—92no—
2772−1+4—96no—
2782−1+4—182no—
2792−1+4—186no—
2802−1+4C2×C3⋊D312yescomplemented
281C2×#41—91no—
282C2×#41—96no—
283C2×#41—186no—
284C22×Q8—96no—
285C22×Q8—182no—
286#137—96no—
287#137—96no—
288#137—912no—
289#137—912no—
290#137—96no—
291#137C2×C3⋊D316yescomplemented
292#135—96no—
293#135—93no—
294#135—96no—
295#135—93no—
296#135—93no—
297#135C2×C3⋊D313yescomplemented
298C2×Q16—96no—
299C2×Q16—93no—
300C2×Q16—96no—
301C2×Q16—96no—
302C2×Q16—96no—
303C2×Q16—93no—
304C2×Q16C2×C3⋊D313yescomplemented
305C2×SD16—96no—
306C2×D8—91no—
307#131—91no—
308#131—93no—
309#131—93no—
310#131C2×C3⋊D311yescharacteristic, complemented
311C2×M16—93no—
312C22×C8—93no—
313C22×D3—312no—
314C22×D3—68no—
315C3×Q8—224no—
316C3×Q8D3×D414yes—
317C3×Q8C23×D3124yes—
318C3×D4—224no—
319C3×D4D3×D4112yes—
320C3×D4C23×D318yes—
321C2×C3×C4—224no—
322C2×C3×C4—224no—
323C2×C3×C4C23×D3112yes—
324#67—324no—
325#67—68no—
326#67—624no—
327#67—624no—
328C2×Dic3—312no—
329C2×Dic3—624no—
330C2×Dic3—624no—
331D12—312no—
332D12—38no—
333D12—624no—
334C4×D3—312no—
335C4×D3—312no—
336C4×D3—34no—
337C4×D3—312no—
338C4×D3—624no—
339C4×D3—624no—
340C4×D3—648no—
341C4×D3—624no—
342Dic6—312no—
343Dic6—324no—
344Dic6—648no—
345Dic6—624no—
346Dic6—624no—
347C3×C8C23×D314yes—
348C3×C8C23×D3112yes—
349C3⋊C8—34no—
350C3⋊C8—312no—
351C2×C32—23no—
352C2×C32—42no—
353C2×C32C23×D411yescharacteristic
354C3⋊D3—23no—
355C3⋊D3—42no—
356C3⋊D3#57812yesdirect product factor
357#41—26no—
358#41—91no—
359#41—93no—
360#41—93no—
361#41—96no—
362#41—96no—
363#41—96no—
364#41—186no—
365#41—1812no—
366#41—186no—
367#41—186no—
368#41—1812no—
369#41—186no—
370#41—186no—
371#41C22×C3⋊D316yes—
372#41C22×C3⋊D311yescharacteristic
373C2×Q8—22no—
374C2×Q8—91no—
375C2×Q8—96no—
376C2×Q8—912no—
377C2×Q8—96no—
378C2×Q8—186no—
379C2×Q8—186no—
380C2×Q8—186no—
381C2×Q8—186no—
382C2×Q8—186no—
383C2×Q8—182no—
384C2×Q8C22×C3⋊D316yes—
385C2×D4—93no—
386C2×D4—92no—
387C2×D4—186no—
388C22×C4—93no—
389C22×C4—186no—
390C22×C4—186no—
391Q16—96no—
392Q16—912no—
393Q16—93no—
394Q16—96no—
395Q16C22×C3⋊D313yes—
396Q16C22×C3⋊D316yes—
397SD16—96no—
398SD16—96no—
399SD16—96no—
400SD16C22×C3⋊D316yes—
401D8—92no—
402D8—91no—
403D8C22×C3⋊D311yescharacteristic
404M16—93no—
405M16—96no—
406M16C22×C3⋊D313yes—
407C2×C8—93no—
408C2×C8—91no—
409C2×C8—93no—
410C2×C8—93no—
411C2×C8—93no—
412C2×C8C22×C3⋊D313yes—
413C22×C3—28no—
414C22×C3C2×D3×D4112yes—
415C2×D3—34no—
416C2×D3—312no—
417C2×D3—624no—
418C2×D3—68no—
419C2×D3—1216no—
420C3×C4—224no—
421C3×C4C2×D3×D4112yes—
422C3×C4C24×D314yes—
423Dic3—312no—
424Dic3—34no—
425Dic3—624no—
426C32C2×#57811yescharacteristic, complemented, Sylow
427C23—93no—
428C23—182no—
429Q8—26no—
430Q8—93no—
431Q8—96no—
432Q8—186no—
433Q8—1812no—
434Q8—186no—
435Q8D4×C3⋊D311yescharacteristic
436Q8C23×C3⋊D316yes—
437D4—26no—
438D4—96no—
439D4—93no—
440D4—92no—
441D4—186no—
442D4—182no—
443D4—186no—
444D4—186no—
445D4D4×C3⋊D313yes—
446D4C23×C3⋊D312yes—
447C2×C4—26no—
448C2×C4—26no—
449C2×C4—93no—
450C2×C4—93no—
451C2×C4—93no—
452C2×C4—91no—
453C2×C4—93no—
454C2×C4—186no—
455C2×C4—186no—
456C2×C4—1812no—
457C2×C4—186no—
458C2×C4—186no—
459C2×C4—186no—
460C2×C4C23×C3⋊D313yes—
461C8—91no—
462C8—93no—
463C8C23×C3⋊D311yescharacteristic
464C8C23×C3⋊D313yes—
465C2×C3—212no—
466C2×C3—48no—
467C2×C3C22×D3×D414yes—
468D3—38no—
469D3—612no—
470D3—128no—
471C22—22no—
472C22—91no—
473C22—93no—
474C22—186no—
475C22—182no—
476C22—364no—
477C22C2×D4×C3⋊D313yes—
478C4—26no—
479C4—91no—
480C4—93no—
481C4—186no—
482C4C2×D4×C3⋊D313yes—
483C4C24×C3⋊D311yescharacteristic
484C3D3×#57814yescomplemented
485C2—23no—
486C2—42no—
487C2—92no—
488C2—183no—
489C2—362no—
490C2C22×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2C22×D4×C3⋊D3
commutator, cosocleC32×C4C25
FrattiniC4C24×C3⋊D3
FittingC32×#578C2
socleC2×C32C23×D4
hypercenter#578C3⋊D3
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ #41 ◁ #578

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×2−1+4C2semidirect
2. C32×#578C2semidirect
3. #10596309C2semidirect
4. #10596250C2semidirect
5. C3⋊D3×#137C2semidirect
6. #10596242C2semidirect
7. C3⋊D3×#135C2semidirect
8. #10596237C2semidirect
9. C2×Q16×C3⋊D3C2semidirect
10. #10596224C2semidirect
11. C3⋊D3×#131C2semidirect
13. C32×2−1+4C22semidirect
15. #64367C22semidirect
16. #64367C22semidirect
21. #64364C22semidirect
24. C32×#137C22semidirect
25. C32×#135C22semidirect
26. C2×C32×Q16C22semidirect
27. C32×#131C22semidirect
28. #64160C22semidirect
29. #64159C22semidirect
30. #64157C22semidirect
31. C2×#3756C22semidirect
32. #64151C22semidirect
33. #64128C22semidirect
34. #64127C22semidirect
37. Q16×C3⋊D3C22semidirect
38. Q16×C3⋊D3C22semidirect
39. #64125C22semidirect
40. #64124C22semidirect
42. #64121C22semidirect
44. #64118C22semidirect
45. #64116C22semidirect
47. C2×#3746C22semidirect
48. #64113C22semidirect
49. #64110C22semidirect
52. C3×#578D3semidirect
119. C3×2−1+4C2×D3semidirect
130. C3×#137C2×D3semidirect
131. C3×#135C2×D3semidirect
132. C2×C3×Q16C2×D3semidirect
133. C3×#131C2×D3semidirect
201. #578C3⋊D3direct (N × H)
280. 2−1+4C2×C3⋊D3semidirect
291. #137C2×C3⋊D3semidirect
297. #135C2×C3⋊D3semidirect
304. C2×Q16C2×C3⋊D3semidirect
310. #131C2×C3⋊D3semidirect
356. C3⋊D3#578direct (N × H)
426. C32C2×#578semidirect
484. C3D3×#578semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×2−1+42
C32×#5782
#105963092
#105962502
C3⋊D3×#1372
#105962422
C3⋊D3×#1352
#105962372
C2×Q16×C3⋊D32
#105962242
C3⋊D3×#1312
D3×#5783