Finite Group Databasebeta

← C3⋊D3×#550 #11902689

Subgroups — C3⋊D3×#550 #11902689

Order 1152.

5208 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C212yesmaximal, complemented
2C32×#550C211yesmaximal, characteristic, complemented
3#10596305C212yesmaximal, complemented
4#10596189C213yesmaximal, complemented
5C3⋊D3×#127C213yesmaximal, complemented
6C3⋊D3×#121C216yesmaximal, complemented
7#10596070C216yesmaximal, complemented
8#10596048C211yesmaximal, characteristic, complemented
9C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
10#10596024C213yesmaximal, complemented
11C4×D4×C3⋊D3C213yesmaximal, complemented
12D3×#550—34nomaximal
13C2×C32×#41C2212yescomplemented
14#41×C3⋊D3—216no—
15C2×#3832C2212yescomplemented
16C2×Q8×C3⋊D3C2211yescharacteristic
17C2×#3830C2216yescomplemented
18C2×D4×C3⋊D3C2213yes—
19C2×D4×C3⋊D3C2216yes—
20C2×D4×C3⋊D3C2216yes—
21C2×#3828C2216yescomplemented
22C22×C4×C3⋊D3C2216yes—
23C32×#127C2213yescomplemented
24C32×#121C2216yescomplemented
25C32×C4×Q8C2211yescharacteristic, complemented
26C32×C4×D4C2213yescomplemented
27Q8×C3⋊Dic3C2211yescharacteristic, complemented
28#64149C2216yescomplemented
29#64149C2216yescomplemented
30#64149C2216yescomplemented
31#64148C22112yescomplemented
32#64147C2216yescomplemented
33D4×C3⋊Dic3C2213yescomplemented
34#64139C2216yescomplemented
35C4×#638C2216yescomplemented
36#64104C2216yescomplemented
37#64102C2213yescomplemented
38C4⋊C4×C3⋊D3C2211yescharacteristic
39C4⋊C4×C3⋊D3C2213yes—
40#64096C2213yescomplemented
41#64093C22112yescomplemented
42#64090C2216yescomplemented
43C22⋊C4×C3⋊D3C2216yes—
44#64083C2213yescomplemented
45C4×C4⋊(C3⋊D3)C2213yescomplemented
46C42×C3⋊D3C2213yes—
47C4×#634C2213yescomplemented
48C2×D3×#41—38no—
49C3×#550D314yescomplemented
50#5834—38no—
51#5718—312no—
52D3×#127—312no—
53D3×#121—324no—
54#5599—324no—
55#5577—34no—
56C4×D3×Q8—34no—
57#5553—312no—
58C4×D3×D4—312no—
59C23×C3⋊D3C2316yes—
60C32×#41—28no—
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4C2316yes—
63C2×C32×D4C2313yes—
64C2×C32×D4C2316yes—
65C22×C32×C4C2316yes—
66C2×#638C2316yes—
67C2×#638C23112yes—
68C2×#638C23112yes—
69C22×C3⋊Dic3C2316yes—
70#3832—28no—
71Q8×C3⋊D3D418yescomplemented
72#3830—224no—
73D4×C3⋊D3—224no—
74D4×C3⋊D3—212no—
75D4×C3⋊D3—412no—
76#3828—224no—
77C2×C4⋊(C3⋊D3)C2313yes—
78C2×C4⋊(C3⋊D3)C2316yes—
79C2×C4⋊(C3⋊D3)C2316yes—
80C2×C4×C3⋊D3—224no—
81C2×C4×C3⋊D3C2313yes—
82C2×C4×C3⋊D3C2316yes—
83C2×C4×C3⋊D3C2312yes—
84C2×C4×C3⋊D3C2316yes—
85C2×C4×C3⋊D3C2313yes—
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×#634C2313yes—
88C32×C4⋊C4C2313yes—
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4C2316yes—
91C32×C42C2313yes—
92#3757C2316yes—
93#3752C2316yes—
94#3752C2316yes—
95C4⋊(C3⋊Dic3)C2313yes—
96C4⋊(C3⋊Dic3)C2311yescharacteristic
97#3750C2316yes—
98#3750C2312yes—
99C4×C3⋊Dic3C2313yes—
100C4×C3⋊Dic3C2313yes—
101C4×C3⋊Dic3C2313yes—
102C2×#550—91noSylow
103C2×C3×#41C2×D318yescomplemented
104D3×#41—664no—
105C2×#239—38no—
106C2×D3×Q8—34no—
107C2×#237—324no—
108C2×D3×D4—324no—
109C2×D3×D4—312no—
110C2×D3×D4—324no—
111C2×#235—324no—
112C22×C4×D3—324no—
113C3×#127C2×D3112yescomplemented
114C3×#121C2×D3124yescomplemented
115C3×C4×Q8C2×D314yescomplemented
116C3×C4×D4C2×D3112yescomplemented
117Q8×Dic3—34no—
118#940—324no—
119#940—324no—
120#940—324no—
121#939—348no—
122#938—324no—
123D4×Dic3—312no—
124#930—324no—
125C4×#67—324no—
126#895—324no—
127#893—312no—
128D3×C4⋊C4—34no—
129D3×C4⋊C4—312no—
130#887—312no—
131#884—348no—
132#67⋊C4—324no—
133D3×C22⋊C4—324no—
134#874—312no—
135C4×D12—312no—
136C42×D3—312no—
137C4×Dic6—312no—
138C23×C32C2416yes—
139C22×C3⋊D3—212no—
140C22×C3⋊D3—212no—
141C22×C3⋊D3—212no—
142C22×C3⋊D3C2416yes—
143C22×C3⋊D3C2411yescharacteristic
144C32×Q8C2×D414yescomplemented
145C32×D4—212no—
146C32×D4—26no—
147C32×D4—46no—
148C2×C32×C4—212no—
149C2×C32×C4C2413yes—
150C2×C32×C4C2412yes—
151C2×C32×C4C2413yes—
152C2×C32×C4C2411yescharacteristic
153#638—224no—
154#638—212no—
155#638—412no—
156C2×C3⋊Dic3—212no—
157C2×C3⋊Dic3C2413yes—
158C2×C3⋊Dic3C2412yes—
159C2×C3⋊Dic3C2413yes—
160C2×C3⋊Dic3C2411yescharacteristic
161C4⋊(C3⋊D3)—212no—
162C4⋊(C3⋊D3)—26no—
163C4⋊(C3⋊D3)—46no—
164C4×C3⋊D3—24no—
165C4×C3⋊D3—26no—
166C4×C3⋊D3—212no—
167C4×C3⋊D3—212no—
168C4×C3⋊D3C2×D4112yes—
169C4×C3⋊D3#4114yescomplemented
170#634C2×D4112yescomplemented
171C22×#41—92no—
172#550—92no—
173#550—93no—
174#550—96no—
175#550—91no—
176#550—93no—
177#550C3⋊D311yescharacteristic, direct product factor
178C2×#127—93no—
179C2×#121—96no—
180C2×C4×Q8—91no—
181C2×C4×D4—93no—
182C23×D3—324no—
183C3×#41—232no—
184C2×C3×Q8C22×D314yes—
185C2×C3×D4C22×D3112yes—
186C2×C3×D4C22×D3124yes—
187C2×C3×D4C22×D3124yes—
188C22×C3×C4C22×D3124yes—
189C2×#67—324no—
190C2×#67—348no—
191C2×#67—348no—
192C22×Dic3—324no—
193#239—632no—
194D3×Q8—332no—
195#237—696no—
196D3×D4—696no—
197D3×D4—648no—
198D3×D4—1248no—
199#235—696no—
200C2×D12—312no—
201C2×D12—324no—
202C2×D12—324no—
203C2×C4×D3—34no—
204C2×C4×D3—312no—
205C2×C4×D3—312no—
206C2×C4×D3—324no—
207C2×C4×D3—38no—
208C2×C4×D3—324no—
209C2×C4×D3—696no—
210C2×Dic6—312no—
211C3×C4⋊C4C22×D3112yes—
212C3×C4⋊C4C22×D314yes—
213C3×C22⋊C4C22×D3124yes—
214C3×C42C22×D3112yes—
215#217—324no—
216(C2×D3)⋊C4—324no—
217(C2×D3)⋊C4—324no—
218C4⋊Dic3—312no—
219C4⋊Dic3—34no—
220Dic3⋊C4—324no—
221Dic3⋊C4—38no—
222C4×Dic3—312no—
223C4×Dic3—312no—
224C4×Dic3—312no—
225C22×C32—26no—
226C22×C32—26no—
227C22×C32—26no—
228C22×C32C2511yescharacteristic
229C2×C3⋊D3—26no—
230C2×C3⋊D3—26no—
231C2×C3⋊D3—26no—
232C2×C3⋊D3—424no—
233C2×C3⋊D3C22×D412yes—
234C2×C3⋊D3C2×#4112yes—
235C2×C3⋊D3H(5,𝔽2)12yes—
236C32×C4—22no—
237C32×C4—23no—
238C32×C4C22×D416yes—
239C32×C4C2×#4112yescomplemented
240C3⋊Dic3—22no—
241C3⋊Dic3—23no—
242C3⋊Dic3C22×D416yes—
243C3⋊Dic3C2×#4112yescomplemented
244C2×#41—92no—
245C2×#41—96no—
246C2×#41—96no—
247C2×#41—1816no—
248C2×#41C2×C3⋊D312yescomplemented
249C22×Q8—91no—
250C22×D4—93no—
251C22×D4—96no—
252C22×D4—96no—
253C23×C4—96no—
254#127—96no—
255#127—96no—
256#127—96no—
257#127—93no—
258#127C2×C3⋊D313yescomplemented
259#121—96no—
260#121—912no—
261#121—96no—
262#121—96no—
263#121—912no—
264#121C2×C3⋊D316yescomplemented
265C4×Q8—91no—
266C4×Q8—93no—
267C4×Q8—93no—
268C4×Q8C2×C3⋊D311yescharacteristic, complemented
269C4×D4—93no—
270C4×D4—96no—
271C4×D4—93no—
272C4×D4—96no—
273C4×D4—93no—
274C4×D4C2×C3⋊D313yescomplemented
275C2×C4⋊C4—91no—
276C2×C4⋊C4—93no—
277C2×C22⋊C4—96no—
278C2×C42—93no—
279C23×C3C23×D3124yes—
280C22×D3—34no—
281C22×D3—324no—
282C22×D3—648no—
283C22×D3—648no—
284C22×D3—648no—
285C3×Q8D3×D4116yescomplemented
286C3×D4—248no—
287C3×D4—224no—
288C3×D4—424no—
289C2×C3×C4—248no—
290C2×C3×C4C23×D3112yes—
291C2×C3×C4C23×D318yes—
292C2×C3×C4C23×D3112yes—
293C2×C3×C4C23×D314yes—
294#67—696no—
295#67—648no—
296#67—1248no—
297C2×Dic3—34no—
298C2×Dic3—312no—
299C2×Dic3—312no—
300C2×Dic3—38no—
301C2×Dic3—648no—
302D12—648no—
303D12—624no—
304D12—1224no—
305C4×D3—348no—
306C4×D3—316no—
307C4×D3—648no—
308C4×D3—616no—
309C4×D3—624no—
310C4×D3—648no—
311Dic6—348no—
312C2×C32—46no—
313C2×C32C23×D411yescharacteristic
314C2×C32C22×#4111yescharacteristic
315C2×C32C2×H(5,𝔽2)11yescharacteristic
316C3⋊D3—46no—
317C3⋊D3#55014yesdirect product factor
318C24—96no—
319#41—28no—
320#41—1824no—
321#41—1824no—
322#41—188no—
323C2×Q8—98no—
324C2×Q8—93no—
325C2×Q8C22×C3⋊D311yescharacteristic
326C2×D4—96no—
327C2×D4—912no—
328C2×D4—912no—
329C2×D4—93no—
330C2×D4—96no—
331C2×D4—96no—
332C2×D4—1824no—
333C2×D4—1812no—
334C2×D4—3612no—
335C2×D4C22×C3⋊D313yes—
336C2×D4C22×C3⋊D316yes—
337C2×D4C22×C3⋊D316yes—
338C22×C4—91no—
339C22×C4—93no—
340C22×C4—96no—
341C22×C4—93no—
342C22×C4—92no—
343C22×C4—96no—
344C22×C4—96no—
345C22×C4—1824no—
346C22×C4C22×C3⋊D316yes—
347C4⋊C4—92no—
348C4⋊C4—91no—
349C4⋊C4—96no—
350C4⋊C4—93no—
351C4⋊C4C22×C3⋊D311yescharacteristic
352C4⋊C4C22×C3⋊D313yes—
353C22⋊C4—96no—
354C22⋊C4—96no—
355C22⋊C4—96no—
356C22⋊C4C22×C3⋊D316yes—
357C42—93no—
358C42—93no—
359C42—93no—
360C42C22×C3⋊D313yes—
361C22×C3—224no—
362C22×C3—224no—
363C22×C3—224no—
364C22×C3C24×D314yes—
365C2×D3—38no—
366C2×D3—38no—
367C2×D3—38no—
368C2×D3—624no—
369C2×D3—624no—
370C2×D3—624no—
371C2×D3—1296no—
372C3×C4—28no—
373C3×C4—212no—
374C3×C4C2×D3×D4124yes—
375C3×C4D3×#4118yescomplemented
376Dic3—324no—
377Dic3—38no—
378Dic3—68no—
379Dic3—612no—
380C32C2×#55011yescharacteristic, complemented, Sylow
381C23—91no—
382C23—96no—
383C23—1812no—
384C23—1812no—
385C23—1812no—
386C23C23×C3⋊D316yes—
387Q8—912no—
388Q8D4×C3⋊D314yescomplemented
389D4—212no—
390D4—26no—
391D4—46no—
392D4—1824no—
393D4—1812no—
394D4—1812no—
395D4—186no—
396D4—366no—
397D4—3612no—
398C2×C4—212no—
399C2×C4—91no—
400C2×C4—93no—
401C2×C4—912no—
402C2×C4—94no—
403C2×C4—93no—
404C2×C4—92no—
405C2×C4—1812no—
406C2×C4—184no—
407C2×C4—186no—
408C2×C4—1812no—
409C2×C4—1812no—
410C2×C4C23×C3⋊D313yes—
411C2×C4C23×C3⋊D312yes—
412C2×C4C23×C3⋊D313yes—
413C2×C4C23×C3⋊D311yescharacteristic
414C2×C3—424no—
415C2×C3C22×D3×D414yes—
416C2×C3C2×D3×#4114yes—
417C2×C3D3×H(5,𝔽2)14yes—
418D3—316no—
419D3—1224no—
420C22—26no—
421C22—26no—
422C22—26no—
423C22—92no—
424C22—92no—
425C22—92no—
426C22—186no—
427C22—186no—
428C22—186no—
429C22—3624no—
430C22C24×C3⋊D311yescharacteristic
431C4—22no—
432C4—23no—
433C4—96no—
434C4—92no—
435C4—182no—
436C4—183no—
437C4C2×D4×C3⋊D316yes—
438C4#41×C3⋊D312yescomplemented
439C3D3×#55014yescomplemented
440C2—46no—
441C2—94no—
442C2—366no—
443C2C22×D4×C3⋊D311yescharacteristic
444C2C2×#41×C3⋊D311yescharacteristic
445C2C3⋊D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#550C2
hypercenter#550C3⋊D3
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C32×#550C2semidirect
3. #10596305C2semidirect
4. #10596189C2semidirect
5. C3⋊D3×#127C2semidirect
6. C3⋊D3×#121C2semidirect
7. #10596070C2semidirect
8. #10596048C2semidirect
9. C4×Q8×C3⋊D3C2semidirect
10. #10596024C2semidirect
11. C4×D4×C3⋊D3C2semidirect
13. C2×C32×#41C22semidirect
15. C2×#3832C22semidirect
17. C2×#3830C22semidirect
21. C2×#3828C22semidirect
23. C32×#127C22semidirect
24. C32×#121C22semidirect
25. C32×C4×Q8C22semidirect
26. C32×C4×D4C22semidirect
27. Q8×C3⋊Dic3C22semidirect
28. #64149C22semidirect
29. #64149C22semidirect
30. #64149C22semidirect
31. #64148C22semidirect
32. #64147C22semidirect
33. D4×C3⋊Dic3C22semidirect
34. #64139C22semidirect
35. C4×#638C22semidirect
36. #64104C22semidirect
37. #64102C22semidirect
40. #64096C22semidirect
41. #64093C22semidirect
42. #64090C22semidirect
44. #64083C22semidirect
45. C4×C4⋊(C3⋊D3)C22semidirect
47. C4×#634C22semidirect
49. C3×#550D3semidirect
71. Q8×C3⋊D3D4semidirect
103. C2×C3×#41C2×D3semidirect
113. C3×#127C2×D3semidirect
114. C3×#121C2×D3semidirect
115. C3×C4×Q8C2×D3semidirect
116. C3×C4×D4C2×D3semidirect
144. C32×Q8C2×D4semidirect
169. C4×C3⋊D3#41semidirect
170. #634C2×D4semidirect
177. #550C3⋊D3direct (N × H)
239. C32×C4C2×#41semidirect
243. C3⋊Dic3C2×#41semidirect
248. C2×#41C2×C3⋊D3semidirect
258. #127C2×C3⋊D3semidirect
264. #121C2×C3⋊D3semidirect
268. C4×Q8C2×C3⋊D3semidirect
274. C4×D4C2×C3⋊D3semidirect
285. C3×Q8D3×D4semidirect
317. C3⋊D3#550direct (N × H)
375. C3×C4D3×#41semidirect
380. C32C2×#550semidirect
388. Q8D4×C3⋊D3semidirect
438. C4#41×C3⋊D3semidirect
439. C3D3×#550semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C32×#5502
#105963052
#105961892
C3⋊D3×#1272
C3⋊D3×#1212
#105960702
#105960482
C4×Q8×C3⋊D32
#105960242
C4×D4×C3⋊D32
D3×#5503