Finite Group Databasebeta

← #11902762

Subgroups — #11902762

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×#550C211yesmaximal, characteristic, complemented
3#10596302C212yesmaximal, complemented
4#10596188C213yesmaximal, complemented
5#10596187C213yesmaximal, complemented
6#10596083C216yesmaximal, complemented
7#10596077C216yesmaximal, complemented
8Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
9C4×#3832C211yesmaximal, characteristic, complemented
10#10596022C213yesmaximal, complemented
11C4×D4×C3⋊D3C213yesmaximal, complemented
12#86766—34nomaximal
13C2×C32×#41C2212yescomplemented
14#41×C3⋊D3—216no—
15C2×#3832C2211yescharacteristic
16C2×Q8×C3⋊D3C2212yescomplemented
17C2×#3830C2216yescomplemented
18C2×D4×C3⋊D3C2213yes—
19C2×D4×C3⋊D3C2216yescomplemented
20C2×#3828C2216yescomplemented
21C22×C4×C3⋊D3C2216yescomplemented
22C32×#127C2213yescomplemented
23C32×#121C2216yescomplemented
24C32×C4×Q8C2211yescharacteristic, complemented
25C32×C4×D4C2213yescomplemented
26Q8×C3⋊Dic3C2211yescharacteristic, complemented
27#64147C2216yescomplemented
28#64147C2216yescomplemented
29#64147C2216yescomplemented
30#64146C22112yescomplemented
31#64145C2216yescomplemented
32D4×C3⋊Dic3C2213yescomplemented
33D4×C3⋊Dic3C2216yescomplemented
34C4×#638C2216yescomplemented
35#64133C2216yescomplemented
36#64106C2216yescomplemented
37#64102C2211yescharacteristic
38#64102C2213yescomplemented
39#64101C2213yescomplemented
40C4⋊C4×C3⋊D3C2213yescomplemented
41#64092C22112yescomplemented
42#64090C2216yescomplemented
43C22⋊C4×C3⋊D3C2216yescomplemented
44C4×C4⋊(C3⋊D3)C2213yes—
45C4×C4⋊(C3⋊D3)C2213yescomplemented
46C42×C3⋊D3C2213yescomplemented
47#64078C2213yescomplemented
48C2×D3×#41—38no—
49C3×#550D314yescomplemented
50#5831—38no—
51#5717—312no—
52#5716—312no—
53#5612—324no—
54#5606—324no—
55Q8×D12—34no—
56C4×#239—34no—
57#5551—312no—
58C4×D3×D4—312no—
59C23×C3⋊D3C2316yes—
60C32×#41—28no—
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4C2313yes—
63C2×C32×D4C2316yes—
64C2×C32×D4C2316yes—
65C22×C32×C4C2316yes—
66C2×#638C2316yes—
67C2×#638C23112yes—
68C22×C3⋊Dic3C2316yes—
69#3832D418yescomplemented
70Q8×C3⋊D3—28no—
71#3830—224no—
72D4×C3⋊D3—224no—
73D4×C3⋊D3—212no—
74#3828—224no—
75C2×C4⋊(C3⋊D3)C2313yes—
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4×C3⋊D3—224no—
78C2×C4×C3⋊D3C2313yes—
79C2×C4×C3⋊D3C2316yes—
80C2×C4×C3⋊D3C2316yes—
81C2×C4×C3⋊D3C2312yes—
82C2×C4×C3⋊D3C2313yes—
83C2×C4×C3⋊D3C2313yes—
84C2×#634C2316yes—
85C32×C4⋊C4C2311yescharacteristic
86C32×C4⋊C4C2313yes—
87C32×C22⋊C4C2316yes—
88C32×C42C2313yes—
89#3757C2316yes—
90#3757C23112yes—
91#3752C2316yes—
92#3752C2316yes—
93#3752C2312yes—
94C4⋊(C3⋊Dic3)C2313yes—
95C4⋊(C3⋊Dic3)C2316yes—
96C4⋊(C3⋊Dic3)C2313yes—
97#3750C2316yes—
98C4×C3⋊Dic3C2311yescharacteristic
99C4×C3⋊Dic3C2313yes—
100C4×C3⋊Dic3C2313yes—
101D4×#41—91noSylow
102C2×C3×#41C2×D318yescomplemented
103D3×#41—664no—
104C2×#239—34no—
105C2×D3×Q8—38no—
106C2×#237—324no—
107C2×D3×D4—324no—
108C2×D3×D4—312no—
109C2×#235—324no—
110C22×C4×D3—324no—
111C3×#127C2×D3112yescomplemented
112C3×#121C2×D3124yescomplemented
113C3×C4×Q8C2×D314yescomplemented
114C3×C4×D4C2×D3112yescomplemented
115Q8×Dic3—34no—
116#938—324no—
117#938—324no—
118#938—324no—
119#937—348no—
120#936—324no—
121D4×Dic3—312no—
122D4×Dic3—324no—
123C4×#67—324no—
124#924—324no—
125#897—324no—
126#893—34no—
127#893—312no—
128#892—312no—
129D3×C4⋊C4—312no—
130#883—348no—
131#67⋊C4—324no—
132D3×C22⋊C4—324no—
133C4×D12—312no—
134C4×D12—312no—
135C42×D3—312no—
136#869—312no—
137C23×C32C2416yes—
138C22×C3⋊D3—212no—
139C22×C3⋊D3—212no—
140C22×C3⋊D3—46no—
141C22×C3⋊D3C2413yes—
142C22×C3⋊D3C2412yes—
143C32×Q8C2×D414yescomplemented
144C32×D4—212no—
145C32×D4—26no—
146C32×D4—46no—
147C2×C32×C4—212no—
148C2×C32×C4C2413yes—
149C2×C32×C4C2412yes—
150C2×C32×C4C2413yes—
151C2×C32×C4C2411yescharacteristic
152#638—224no—
153#638—212no—
154C2×C3⋊Dic3—212no—
155C2×C3⋊Dic3C2411yescharacteristic
156C2×C3⋊Dic3C2413yes—
157C2×C3⋊Dic3C2416yes—
158C2×C3⋊Dic3C2411yescharacteristic
159C4⋊(C3⋊D3)C2×D4112yescomplemented
160C4⋊(C3⋊D3)#4114yescomplemented
161C4×C3⋊D3—212no—
162C4×C3⋊D3—212no—
163C4×C3⋊D3—26no—
164C4×C3⋊D3—24no—
165C4×C3⋊D3—43no—
166C4×C3⋊D3C2×D4112yescomplemented
167#634—212no—
168C22×#41—92no—
169#550C3⋊D311yescharacteristic, complemented
170D4×Q8—91no—
171#548—92no—
172#547—93no—
173#546—96no—
174D42—93no—
175#532—93no—
176#525—96no—
177C4×#41—91no—
178C2×C4×D4—93no—
179C23×D3—324no—
180C3×#41—232no—
181C2×C3×Q8C22×D314yes—
182C2×C3×D4C22×D3112yes—
183C2×C3×D4C22×D3124yes—
184C2×C3×D4C22×D3124yes—
185C22×C3×C4C22×D3124yes—
186C2×#67—324no—
187C2×#67—348no—
188C22×Dic3—324no—
189#239—332no—
190D3×Q8—632no—
191#237—696no—
192D3×D4—696no—
193D3×D4—648no—
194#235—696no—
195C2×D12—34no—
196C2×D12—312no—
197C2×C4×D3—312no—
198C2×C4×D3—312no—
199C2×C4×D3—324no—
200C2×C4×D3—324no—
201C2×C4×D3—38no—
202C2×C4×D3—312no—
203C2×C4×D3—696no—
204C2×Dic6—324no—
205C3×C4⋊C4C22×D314yes—
206C3×C4⋊C4C22×D3112yes—
207C3×C22⋊C4C22×D3124yes—
208C3×C42C22×D3112yes—
209#217—324no—
210#217—348no—
211(C2×D3)⋊C4—324no—
212(C2×D3)⋊C4—324no—
213(C2×D3)⋊C4—38no—
214C4⋊Dic3—312no—
215C4⋊Dic3—324no—
216C4⋊Dic3—312no—
217Dic3⋊C4—324no—
218C4×Dic3—34no—
219C4×Dic3—312no—
220C4×Dic3—312no—
221C22×C32—26no—
222C22×C32—26no—
223C22×C32—26no—
224C22×C32C2511yescharacteristic
225C2×C3⋊D3—22no—
226C2×C3⋊D3—23no—
227C2×C3⋊D3—23no—
228C2×C3⋊D3—22no—
229C2×C3⋊D3—424no—
230C2×C3⋊D3C22×D416yes—
231C2×C3⋊D3C2×#4114yescomplemented
232C32×C4—22no—
233C32×C4—23no—
234C32×C4C22×D416yes—
235C32×C4C2×#4112yescomplemented
236C3⋊Dic3—26no—
237C3⋊Dic3—23no—
238C3⋊Dic3—21no—
239C3⋊Dic3C22×D412yes—
240C2×#41—91no—
241C2×#41—96no—
242C2×#41—96no—
243C2×#41—1816no—
244C2×#41C2×C3⋊D312yescomplemented
245C22×Q8—92no—
246C22×D4—93no—
247C22×D4—96no—
248C23×C4—96no—
249C4⋊Q8—93no—
250#127C2×C3⋊D313yescomplemented
251#124—96no—
252#123—912no—
253C22⋊Q8—96no—
254C22⋊Q8—96no—
255#121—96no—
256#121—96no—
257#121—96no—
258#121C2×C3⋊D316yescomplemented
259#120—912no—
260C4×Q8—91no—
261C4×Q8C2×C3⋊D311yescharacteristic, complemented
262C4×D4—93no—
263C4×D4—96no—
264C4×D4—96no—
265C4×D4—91no—
266C4×D4—93no—
267C4×D4—96no—
268C4×D4—93no—
269C4×D4—93no—
270C4×D4C2×C3⋊D313yescomplemented
271#117—93no—
272C2×C4⋊C4—93no—
273C2×C22⋊C4—96no—
274C2×C42—93no—
275C23×C3C23×D3124yes—
276C22×D3—38no—
277C22×D3—312no—
278C22×D3—648no—
279C22×D3—648no—
280C22×D3—1224no—
281C3×Q8D3×D4116yescomplemented
282C3×D4—248no—
283C3×D4—224no—
284C3×D4—424no—
285C2×C3×C4—248no—
286C2×C3×C4C23×D3112yes—
287C2×C3×C4C23×D318yes—
288C2×C3×C4C23×D3112yes—
289C2×C3×C4C23×D314yes—
290#67—696no—
291#67—648no—
292C2×Dic3—34no—
293C2×Dic3—34no—
294C2×Dic3—312no—
295C2×Dic3—324no—
296C2×Dic3—648no—
297D12—348no—
298D12—316no—
299C4×D3—348no—
300C4×D3—616no—
301C4×D3—648no—
302C4×D3—648no—
303C4×D3—624no—
304C4×D3—1212no—
305Dic6—648no—
306C2×C32—46no—
307C2×C32C23×D411yescharacteristic
308C2×C32C22×#4111yescharacteristic
309C2×C32#58511yescharacteristic
310C3⋊D3—24no—
311C3⋊D3—26no—
312C24—96no—
313#41—28no—
314#41—98no—
315#41—1824no—
316#41—1824no—
317C2×Q8—96no—
318C2×Q8—188no—
319C2×Q8C22×C3⋊D311yescharacteristic
320C2×D4—96no—
321C2×D4—912no—
322C2×D4—91no—
323C2×D4—93no—
324C2×D4—1824no—
325C2×D4—1812no—
326C2×D4C22×C3⋊D313yes—
327C2×D4C22×C3⋊D316yes—
328C2×D4C22×C3⋊D316yes—
329C22×C4—93no—
330C22×C4—96no—
331C22×C4—93no—
332C22×C4—96no—
333C22×C4—92no—
334C22×C4—96no—
335C22×C4—93no—
336C22×C4—1824no—
337C22×C4C22×C3⋊D316yes—
338C4⋊C4—93no—
339C4⋊C4—96no—
340C4⋊C4—93no—
341C4⋊C4—96no—
342C4⋊C4C22×C3⋊D311yescharacteristic
343C4⋊C4C22×C3⋊D313yes—
344C22⋊C4—96no—
345C22⋊C4—912no—
346C22⋊C4—92no—
347C22⋊C4—96no—
348C22⋊C4—96no—
349C22⋊C4C22×C3⋊D316yes—
350C42—91no—
351C42—93no—
352C42—93no—
353C42C22×C3⋊D313yes—
354C22×C3—224no—
355C22×C3—224no—
356C22×C3—224no—
357C22×C3C24×D314yes—
358C2×D3—324no—
359C2×D3—316no—
360C2×D3—68no—
361C2×D3—612no—
362C2×D3—612no—
363C2×D3—68no—
364C2×D3—1296no—
365C3×C4—28no—
366C3×C4—212no—
367C3×C4C2×D3×D4124yes—
368C3×C4D3×#4118yescomplemented
369Dic3—38no—
370Dic3—624no—
371Dic3—612no—
372Dic3—64no—
373C32D4×#4111yescharacteristic, complemented, Sylow
374C23—92no—
375C23—93no—
376C23—1812no—
377C23—1812no—
378C23—366no—
379C23C23×C3⋊D316yes—
380Q8—1812no—
381Q8D4×C3⋊D314yescomplemented
382D4—212no—
383D4—26no—
384D4—46no—
385D4—912no—
386D4—94no—
387D4—1824no—
388D4—1812no—
389C2×C4—212no—
390C2×C4—91no—
391C2×C4—912no—
392C2×C4—91no—
393C2×C4—93no—
394C2×C4—96no—
395C2×C4—184no—
396C2×C4—1812no—
397C2×C4—1812no—
398C2×C4—1812no—
399C2×C4—186no—
400C2×C4—363no—
401C2×C4C23×C3⋊D313yes—
402C2×C4C23×C3⋊D312yes—
403C2×C4C23×C3⋊D313yes—
404C2×C4C23×C3⋊D311yescharacteristic
405C2×C3—424no—
406C2×C3C22×D3×D414yes—
407C2×C3C2×D3×#4114yes—
408C2×C3#596614yes—
409D3—616no—
410D3—624no—
411C22—26no—
412C22—26no—
413C22—26no—
414C22—96no—
415C22—94no—
416C22—182no—
417C22—183no—
418C22—183no—
419C22—182no—
420C22—3624no—
421C22C24×C3⋊D311yescharacteristic
422C4—22no—
423C4—23no—
424C4—92no—
425C4—186no—
426C4—183no—
427C4—181no—
428C4C2×D4×C3⋊D316yes—
429C4#41×C3⋊D312yescomplemented
430C3#8676614yescomplemented
431C2—46no—
432C2—184no—
433C2—186no—
434C2C22×D4×C3⋊D311yescharacteristic
435C2C2×#41×C3⋊D311yescharacteristic
436C2#1059675811yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#550C2
hypercenter#550C3⋊D3
hypocenterC32D4×#41
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. #10596302C2semidirect
4. #10596188C2semidirect
5. #10596187C2semidirect
6. #10596083C2semidirect
7. #10596077C2semidirect
8. Q8×C4⋊(C3⋊D3)C2semidirect
9. C4×#3832C2semidirect
10. #10596022C2semidirect
11. C4×D4×C3⋊D3C2semidirect
13. C2×C32×#41C22semidirect
16. C2×Q8×C3⋊D3C22semidirect
17. C2×#3830C22semidirect
19. C2×D4×C3⋊D3C22semidirect
20. C2×#3828C22semidirect
21. C22×C4×C3⋊D3C22semidirect
22. C32×#127C22semidirect
23. C32×#121C22semidirect
24. C32×C4×Q8C22semidirect
25. C32×C4×D4C22semidirect
26. Q8×C3⋊Dic3C22semidirect
27. #64147C22semidirect
28. #64147C22semidirect
29. #64147C22semidirect
30. #64146C22semidirect
31. #64145C22semidirect
32. D4×C3⋊Dic3C22semidirect
33. D4×C3⋊Dic3C22semidirect
34. C4×#638C22semidirect
35. #64133C22semidirect
36. #64106C22semidirect
38. #64102C22semidirect
39. #64101C22semidirect
40. C4⋊C4×C3⋊D3C22semidirect
41. #64092C22semidirect
42. #64090C22semidirect
43. C22⋊C4×C3⋊D3C22semidirect
45. C4×C4⋊(C3⋊D3)C22semidirect
46. C42×C3⋊D3C22semidirect
47. #64078C22semidirect
49. C3×#550D3semidirect
69. #3832D4semidirect
102. C2×C3×#41C2×D3semidirect
111. C3×#127C2×D3semidirect
112. C3×#121C2×D3semidirect
113. C3×C4×Q8C2×D3semidirect
114. C3×C4×D4C2×D3semidirect
143. C32×Q8C2×D4semidirect
159. C4⋊(C3⋊D3)C2×D4semidirect
160. C4⋊(C3⋊D3)#41semidirect
166. C4×C3⋊D3C2×D4semidirect
169. #550C3⋊D3semidirect
231. C2×C3⋊D3C2×#41semidirect
235. C32×C4C2×#41semidirect
244. C2×#41C2×C3⋊D3semidirect
250. #127C2×C3⋊D3semidirect
258. #121C2×C3⋊D3semidirect
261. C4×Q8C2×C3⋊D3semidirect
270. C4×D4C2×C3⋊D3semidirect
281. C3×Q8D3×D4semidirect
368. C3×C4D3×#41semidirect
373. C32D4×#41semidirect
381. Q8D4×C3⋊D3semidirect
429. C4#41×C3⋊D3semidirect
430. C3#86766semidirect

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
#105963022
#105961882
#105961872
#105960832
#105960772
Q8×C4⋊(C3⋊D3)2
C4×#38322
#105960222
C4×D4×C3⋊D32
#867663