Finite Group Databasebeta

← #41×C4⋊(C3⋊D3) #11902765

Subgroups — #41×C4⋊(C3⋊D3) #11902765

Order 1152.

4944 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C212yesmaximal, complemented
2C32×C4×#41C211yesmaximal, characteristic, complemented
3#10596048C211yesmaximal, characteristic, complemented
4#10596047C212yesmaximal, complemented
5Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
6#10596026C213yesmaximal, complemented
7#10596025C216yesmaximal, complemented
8D4×C4⋊(C3⋊D3)C213yesmaximal, complemented
9#10595995C216yesmaximal, complemented
10#10595948C213yesmaximal, complemented
11C2×C4×C4⋊(C3⋊D3)C213yesmaximal, complemented
12#41×D12—34nomaximal
13C2×C32×#41C2211yescharacteristic
14#41×C3⋊D3—216no—
15C2×#3832C2212yescomplemented
16C2×Q8×C3⋊D3C2212yescomplemented
17C2×#3830C2216yescomplemented
18C2×D4×C3⋊D3C2216yescomplemented
19C2×#3828C2216yescomplemented
20C22×C4⋊(C3⋊D3)C2213yes—
21C22×C4×C3⋊D3C2216yescomplemented
22C32×C4×Q8C2211yescharacteristic, complemented
23C32×C4×Q8C2211yescharacteristic, complemented
24C32×C4×D4C2213yescomplemented
25C32×C4×D4C2213yescomplemented
26C32×#117C2213yescomplemented
27C2×C32×C42C2213yescomplemented
28#64139C2216yescomplemented
29#64139C2216yescomplemented
30C2×#3752C2216yescomplemented
31C2×C4⋊(C3⋊Dic3)C2213yescomplemented
32#64106C2216yescomplemented
33#64106C2216yescomplemented
34#64104C2216yescomplemented
35#64104C2216yescomplemented
36#64095C22112yescomplemented
37#64091C22112yescomplemented
38#64084C2216yescomplemented
39#64083C2213yescomplemented
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41C4×C4⋊(C3⋊D3)C2213yes—
42C4×C4⋊(C3⋊D3)C2213yescomplemented
43C4×C4⋊(C3⋊D3)C2216yescomplemented
44C4×C4⋊(C3⋊D3)C2216yescomplemented
45C4×C4⋊(C3⋊D3)C2213yescomplemented
46C4×C4⋊(C3⋊D3)C2216yescomplemented
47#64078C2213yescomplemented
48C2×D3×#41—38no—
49C3×C4×#41D314yescomplemented
50#5577—34no—
51#5576—38no—
52Q8×D12—34no—
53#5555—312no—
54#5554—324no—
55D4×D12—312no—
56#5524—324no—
57#5477—312no—
58C2×C4×D12—312no—
59C23×C3⋊D3C2316yes—
60C32×#41D418yescomplemented
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4C2313yes—
63C22×C32×C4C2313yes—
64C22×C32×C4C2313yes—
65C22×C32×C4C2313yes—
66C2×#638C23112yes—
67C22×C3⋊Dic3C2316yes—
68#3832—28no—
69Q8×C3⋊D3—28no—
70#3830—224no—
71D4×C3⋊D3—224no—
72#3828—224no—
73C2×C4⋊(C3⋊D3)—212no—
74C2×C4⋊(C3⋊D3)C2313yes—
75C2×C4⋊(C3⋊D3)C2316yes—
76C2×C4⋊(C3⋊D3)C2316yes—
77C2×C4⋊(C3⋊D3)C2316yes—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—224no—
80C2×C4×C3⋊D3C2312yes—
81C2×C4×C3⋊D3C2316yes—
82C2×C4×C3⋊D3C2316yes—
83C2×C4×C3⋊D3C2316yes—
84C2×#634C2316yes—
85C32×C4⋊C4C2313yes—
86C32×C4⋊C4C2313yes—
87C32×C22⋊C4C2316yes—
88C32×C42C2313yes—
89C32×C42C2311yescharacteristic
90C32×C42C2313yes—
91C32×C42C2313yes—
92#3752C2312yes—
93#3752C2316yes—
94#3752C2316yes—
95#3752C2316yes—
96#3752C23112yes—
97C4⋊(C3⋊Dic3)C2313yes—
98C4⋊(C3⋊Dic3)C2316yes—
99C4⋊(C3⋊Dic3)C2311yescharacteristic
100C4⋊(C3⋊Dic3)C2316yes—
101D4×#41—91noSylow
102C2×C3×#41C2×D314yes—
103D3×#41—664no—
104C2×#239—38no—
105C2×D3×Q8—38no—
106C2×#237—324no—
107C2×D3×D4—324no—
108C2×#235—324no—
109C22×D12—312no—
110C22×C4×D3—324no—
111C3×C4×Q8C2×D314yescomplemented
112C3×C4×Q8C2×D314yescomplemented
113C3×C4×D4C2×D3112yescomplemented
114C3×C4×D4C2×D3112yescomplemented
115C3×#117C2×D3112yescomplemented
116C2×C3×C42C2×D3112yescomplemented
117#930—324no—
118#930—324no—
119C2×(C2×D3)⋊C4—324no—
120C2×C4⋊Dic3—312no—
121#897—324no—
122#897—324no—
123#895—324no—
124#895—324no—
125#886—348no—
126#882—348no—
127#875—324no—
128#874—312no—
129C4×D12—34no—
130C4×D12—312no—
131C4×D12—312no—
132C4×D12—324no—
133C4×D12—324no—
134C4×D12—312no—
135C4×D12—324no—
136#869—312no—
137C23×C32C2413yes—
138C22×C3⋊D3—212no—
139C22×C3⋊D3—212no—
140C22×C3⋊D3—46no—
141C22×C3⋊D3C2416yes—
142C22×C3⋊D3C2412yes—
143C32×Q8C2×D414yescomplemented
144C32×D4C2×D4112yescomplemented
145C2×C32×C4—26no—
146C2×C32×C4—43no—
147C2×C32×C4C2×D4112yescomplemented
148C2×C32×C4C2413yes—
149C2×C32×C4C2413yes—
150C2×C32×C4C2411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C2×C32×C4C2413yes—
153C2×C32×C4C2411yescharacteristic
154#638—224no—
155C2×C3⋊Dic3—212no—
156C2×C3⋊Dic3C2416yes—
157C2×C3⋊Dic3C2412yes—
158C4⋊(C3⋊D3)—212no—
159C4⋊(C3⋊D3)—212no—
160C4⋊(C3⋊D3)—26no—
161C4⋊(C3⋊D3)—46no—
162C4⋊(C3⋊D3)#4114yesdirect product factor
163C4×C3⋊D3—24no—
164C4×C3⋊D3—212no—
165C4×C3⋊D3—212no—
166C4×C3⋊D3—212no—
167#634—212no—
168C22×#41—92no—
169#550—91no—
170D4×Q8—91no—
171#548—92no—
172#547—93no—
173#546—96no—
174D42—93no—
175#532—93no—
176#525—96no—
177C4×#41C3⋊D311yescharacteristic, complemented
178C2×C4×D4—93no—
179C23×D3—324no—
180C3×#41D12132yescomplemented
181C2×C3×Q8C22×D314yes—
182C2×C3×D4C22×D3112yes—
183C22×C3×C4C22×D3112yes—
184C22×C3×C4C22×D3112yes—
185C22×C3×C4C22×D3112yes—
186C2×#67—348no—
187C22×Dic3—324no—
188#239—632no—
189D3×Q8—632no—
190#237—696no—
191D3×D4—696no—
192#235—696no—
193C2×D12—34no—
194C2×D12—312no—
195C2×D12—324no—
196C2×D12—324no—
197C2×D12—324no—
198C2×D12—648no—
199C2×C4×D3—38no—
200C2×C4×D3—324no—
201C2×C4×D3—324no—
202C2×C4×D3—324no—
203C2×C4×D3—696no—
204C2×Dic6—324no—
205C3×C4⋊C4C22×D3112yes—
206C3×C4⋊C4C22×D3112yes—
207C3×C22⋊C4C22×D3124yes—
208C3×C42C22×D3112yes—
209C3×C42C22×D314yes—
210C3×C42C22×D3112yes—
211C3×C42C22×D3112yes—
212(C2×D3)⋊C4—38no—
213(C2×D3)⋊C4—324no—
214(C2×D3)⋊C4—324no—
215(C2×D3)⋊C4—324no—
216(C2×D3)⋊C4—348no—
217C4⋊Dic3—312no—
218C4⋊Dic3—324no—
219C4⋊Dic3—34no—
220C4⋊Dic3—324no—
221C22×C32—23no—
222C22×C32—23no—
223C22×C32C22×D416yes—
224C22×C32C2511yescharacteristic
225C2×C3⋊D3—22no—
226C2×C3⋊D3—22no—
227C2×C3⋊D3—26no—
228C2×C3⋊D3—26no—
229C2×C3⋊D3—26no—
230C2×C3⋊D3—424no—
231C2×C3⋊D3C2×#4114yescomplemented
232C32×C4—23no—
233C32×C4—23no—
234C32×C4—21no—
235C32×C4C22×D416yes—
236C32×C4C22×D412yes—
237C32×C4C2×#4112yescomplemented
238C3⋊Dic3—26no—
239C3⋊Dic3—22no—
240C2×#41—92no—
241C2×#41—96no—
242C2×#41—96no—
243C2×#41—1816no—
244C2×#41C2×C3⋊D311yescharacteristic
245C22×Q8—92no—
246C22×D4—96no—
247C22×D4—93no—
248C23×C4—96no—
249C4⋊Q8—93no—
250#127—93no—
251#124—96no—
252#123—912no—
253C22⋊Q8—96no—
254C22⋊Q8—96no—
255#121—96no—
256#121—96no—
257#121—96no—
258#121—96no—
259#120—912no—
260C4×Q8C2×C3⋊D311yescharacteristic, complemented
261C4×Q8C2×C3⋊D311yescharacteristic, complemented
262C4×D4—91no—
263C4×D4—96no—
264C4×D4—93no—
265C4×D4—93no—
266C4×D4—96no—
267C4×D4—93no—
268C4×D4—96no—
269C4×D4C2×C3⋊D313yescomplemented
270C4×D4C2×C3⋊D313yescomplemented
271#117C2×C3⋊D313yescomplemented
272C2×C4⋊C4—93no—
273C2×C22⋊C4—96no—
274C2×C42C2×C3⋊D313yescomplemented
275C23×C3C23×D3112yes—
276C22×D3—38no—
277C22×D3—324no—
278C22×D3—648no—
279C22×D3—648no—
280C22×D3—1224no—
281C3×Q8C2×D12116yescomplemented
282C3×D4C2×D12148yescomplemented
283C2×C3×C4—224no—
284C2×C3×C4—412no—
285C2×C3×C4C2×D12148yescomplemented
286C2×C3×C4C23×D3112yes—
287C2×C3×C4C23×D3112yes—
288C2×C3×C4C23×D314yes—
289C2×C3×C4C23×D3112yes—
290C2×C3×C4C23×D314yes—
291C2×C3×C4C23×D314yes—
292#67—696no—
293C2×Dic3—324no—
294C2×Dic3—38no—
295C2×Dic3—648no—
296D12—316no—
297D12—648no—
298D12—648no—
299D12—624no—
300D12—1224no—
301C4×D3—616no—
302C4×D3—648no—
303C4×D3—648no—
304C4×D3—648no—
305Dic6—648no—
306C2×C32—26no—
307C2×C32C23×D411yescharacteristic
308C2×C32C22×#4111yescharacteristic
309C2×C32#58511yescharacteristic
310C3⋊D3—24no—
311C3⋊D3—46no—
312C24—96no—
313#41—188no—
314#41—1824no—
315#41—1824no—
316#41C4⋊(C3⋊D3)18yesdirect product factor
317C2×Q8—96no—
318C2×Q8—188no—
319C2×Q8C22×C3⋊D311yescharacteristic
320C2×D4—912no—
321C2×D4—91no—
322C2×D4—96no—
323C2×D4—93no—
324C2×D4—96no—
325C2×D4—96no—
326C2×D4—1812no—
327C2×D4—1824no—
328C2×D4C22×C3⋊D313yes—
329C22×C4—96no—
330C22×C4—96no—
331C22×C4—96no—
332C22×C4—92no—
333C22×C4—96no—
334C22×C4—1824no—
335C22×C4C22×C3⋊D313yes—
336C22×C4C22×C3⋊D313yes—
337C22×C4C22×C3⋊D313yes—
338C4⋊C4—91no—
339C4⋊C4—93no—
340C4⋊C4—96no—
341C4⋊C4—96no—
342C4⋊C4C22×C3⋊D313yes—
343C4⋊C4C22×C3⋊D313yes—
344C22⋊C4—92no—
345C22⋊C4—96no—
346C22⋊C4—96no—
347C22⋊C4—96no—
348C22⋊C4—912no—
349C22⋊C4C22×C3⋊D316yes—
350C42C22×C3⋊D313yes—
351C42C22×C3⋊D313yes—
352C42C22×C3⋊D311yescharacteristic
353C42C22×C3⋊D313yes—
354C22×C3—212no—
355C22×C3—212no—
356C22×C3C22×D12124yes—
357C22×C3C24×D314yes—
358C2×D3—316no—
359C2×D3—68no—
360C2×D3—68no—
361C2×D3—624no—
362C2×D3—624no—
363C2×D3—624no—
364C2×D3—1296no—
365C3×C4—212no—
366C3×C4—212no—
367C3×C4—24no—
368C3×C4C22×D12124yes—
369C3×C4C22×D1218yes—
370C3×C4D3×#4118yescomplemented
371Dic3—624no—
372Dic3—68no—
373C32D4×#4111yescharacteristic, complemented, Sylow
374C23—92no—
375C23—96no—
376C23—1812no—
377C23—1812no—
378C23—366no—
379C23C23×C3⋊D313yes—
380Q8—1812no—
381Q8C2×C4⋊(C3⋊D3)14yescomplemented
382D4—94no—
383D4—1812no—
384D4—1824no—
385D4—1812no—
386D4—186no—
387D4—366no—
388D4C2×C4⋊(C3⋊D3)112yescomplemented
389C2×C4—26no—
390C2×C4—43no—
391C2×C4—92no—
392C2×C4—96no—
393C2×C4—1812no—
394C2×C4—184no—
395C2×C4—1812no—
396C2×C4—1812no—
397C2×C4—1812no—
398C2×C4C2×C4⋊(C3⋊D3)112yescomplemented
399C2×C4C23×C3⋊D311yescharacteristic
400C2×C4C23×C3⋊D313yes—
401C2×C4C23×C3⋊D313yes—
402C2×C4C23×C3⋊D313yes—
403C2×C4C23×C3⋊D311yescharacteristic
404C2×C4C23×C3⋊D311yescharacteristic
405C2×C3—224no—
406C2×C3C23×D1214yes—
407C2×C3C2×D3×#4114yes—
408C2×C3#596414yes—
409D3—616no—
410D3—1224no—
411C22—23no—
412C22—23no—
413C22—94no—
414C22—182no—
415C22—182no—
416C22—186no—
417C22—186no—
418C22—186no—
419C22—3624no—
420C22C22×C4⋊(C3⋊D3)16yes—
421C22C24×C3⋊D311yescharacteristic
422C4—23no—
423C4—21no—
424C4—23no—
425C4—182no—
426C4—186no—
427C4C22×C4⋊(C3⋊D3)12yes—
428C4C22×C4⋊(C3⋊D3)16yes—
429C4#41×C3⋊D312yescomplemented
430C3#41×D1214yescomplemented
431C2—26no—
432C2—184no—
433C2—366no—
434C2C23×C4⋊(C3⋊D3)11yescharacteristic
435C2C2×#41×C3⋊D311yescharacteristic
436C2#1059675611yescharacteristic
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×C4×#41C2
hypercenterC4×#41C3⋊D3
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C32×C4×#41C2semidirect
3. #10596048C2semidirect
4. #10596047C2semidirect
5. Q8×C4⋊(C3⋊D3)C2semidirect
6. #10596026C2semidirect
7. #10596025C2semidirect
8. D4×C4⋊(C3⋊D3)C2semidirect
9. #10595995C2semidirect
10. #10595948C2semidirect
11. C2×C4×C4⋊(C3⋊D3)C2semidirect
15. C2×#3832C22semidirect
16. C2×Q8×C3⋊D3C22semidirect
17. C2×#3830C22semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×#3828C22semidirect
21. C22×C4×C3⋊D3C22semidirect
22. C32×C4×Q8C22semidirect
23. C32×C4×Q8C22semidirect
24. C32×C4×D4C22semidirect
25. C32×C4×D4C22semidirect
26. C32×#117C22semidirect
27. C2×C32×C42C22semidirect
28. #64139C22semidirect
29. #64139C22semidirect
30. C2×#3752C22semidirect
31. C2×C4⋊(C3⋊Dic3)C22semidirect
32. #64106C22semidirect
33. #64106C22semidirect
34. #64104C22semidirect
35. #64104C22semidirect
36. #64095C22semidirect
37. #64091C22semidirect
38. #64084C22semidirect
39. #64083C22semidirect
42. C4×C4⋊(C3⋊D3)C22semidirect
43. C4×C4⋊(C3⋊D3)C22semidirect
44. C4×C4⋊(C3⋊D3)C22semidirect
45. C4×C4⋊(C3⋊D3)C22semidirect
46. C4×C4⋊(C3⋊D3)C22semidirect
47. #64078C22semidirect
49. C3×C4×#41D3semidirect
60. C32×#41D4semidirect
111. C3×C4×Q8C2×D3semidirect
112. C3×C4×Q8C2×D3semidirect
113. C3×C4×D4C2×D3semidirect
114. C3×C4×D4C2×D3semidirect
115. C3×#117C2×D3semidirect
116. C2×C3×C42C2×D3semidirect
143. C32×Q8C2×D4semidirect
144. C32×D4C2×D4semidirect
147. C2×C32×C4C2×D4semidirect
162. C4⋊(C3⋊D3)#41direct (N × H)
177. C4×#41C3⋊D3semidirect
180. C3×#41D12semidirect
231. C2×C3⋊D3C2×#41semidirect
237. C32×C4C2×#41semidirect
260. C4×Q8C2×C3⋊D3semidirect
261. C4×Q8C2×C3⋊D3semidirect
269. C4×D4C2×C3⋊D3semidirect
270. C4×D4C2×C3⋊D3semidirect
271. #117C2×C3⋊D3semidirect
274. C2×C42C2×C3⋊D3semidirect
281. C3×Q8C2×D12semidirect
282. C3×D4C2×D12semidirect
285. C2×C3×C4C2×D12semidirect
316. #41C4⋊(C3⋊D3)direct (N × H)
370. C3×C4D3×#41semidirect
373. C32D4×#41semidirect
381. Q8C2×C4⋊(C3⋊D3)semidirect
388. D4C2×C4⋊(C3⋊D3)semidirect
398. C2×C4C2×C4⋊(C3⋊D3)semidirect
429. C4#41×C3⋊D3semidirect
430. C3#41×D12semidirect

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×C4×#412
#105960482
#105960472
Q8×C4⋊(C3⋊D3)2
#105960262
#105960252
D4×C4⋊(C3⋊D3)2
#105959952
#105959482
C2×C4×C4⋊(C3⋊D3)2
#41×D123