Finite Group Databasebeta

← #41×C22⋊D283 #49134746

Subgroups — #41×C22⋊D283 #49134746

Order 36224.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic, complemented
2#31827134C211yesmaximal, characteristic, complemented
3Q8×C22⋊D283C211yesmaximal, characteristic, complemented
4#31827126C211yesmaximal, characteristic, complemented
5#31827122C211yesmaximal, characteristic, complemented
6#31827114C213yesmaximal, complemented
7#31827109C213yesmaximal, complemented
8#31827103C213yesmaximal, complemented
9D4×C22⋊D283C213yesmaximal, complemented
10#31827011C213yesmaximal, complemented
11#31826976C213yesmaximal, complemented
12#31826972C213yesmaximal, complemented
13#41×Dic283C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊D283C213yesmaximal, complemented
15C22×#41×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic, complemented
17C2×#17985392C2213yescomplemented
18C2×#17985391C2213yescomplemented
19#41×D283—28no—
20C2×Q8×D283C2211yescharacteristic, complemented
21C22×C22⋊D283C2213yes—
22C2×D4×D283C2213yescomplemented
23C22×C4×D283C2213yescomplemented
24#22583608C2213yescomplemented
25#22583606C2213yescomplemented
26#22583599C2213yescomplemented
27#22583597C2213yescomplemented
28#22583593C2216yescomplemented
29#22583591C2216yescomplemented
30#22583589C2213yescomplemented
31#22583589C2213yescomplemented
32#22583586C2213yescomplemented
33#22583586C2213yescomplemented
34#22583584C2213yescomplemented
35#22583584C2213yescomplemented
36#22583582C2216yescomplemented
37#22583582C2216yescomplemented
38#22583581C2213yescomplemented
39#22583581C2213yescomplemented
40#22583579C2216yescomplemented
41#22583578C2216yescomplemented
42Q8×Dic283C2211yescharacteristic, complemented
43Q8×Dic283C2211yescharacteristic, complemented
44D4×Dic283C2213yescomplemented
45D4×Dic283C2213yescomplemented
46C4×C22⋊D283C2213yes—
47C4×C22⋊D283C2211yescharacteristic
48C4×C22⋊D283C2213yescomplemented
49C4×C22⋊D283C2216yescomplemented
50C4×C22⋊D283C2213yescomplemented
51C4×C22⋊D283C2213yescomplemented
52C4×C22⋊D283C2213yescomplemented
53C4×C22⋊D283C2213yescomplemented
54C4×C22⋊D283C2213yescomplemented
55#22583569C2213yescomplemented
56C2×Dic283⋊C4C2213yescomplemented
57C2×C22⋊Dic283C2213yescomplemented
58C2×(C2×D283)⋊C4C2213yescomplemented
59C2×C4×Dic283C2213yescomplemented
60C2×#41×C283—28no—
61C2×#41×C283C2211yescharacteristic
62C2×#41×C283C2213yescomplemented
63C2×#41×C283C2213yescomplemented
64C2×#41×C283C2211yescharacteristic, complemented
65C22×Q8×C283C2211yescharacteristic, complemented
66C22×D4×C283C2213yescomplemented
67C23×C4×C283C2213yescomplemented
68C23×D283C2313yes—
69#17985393—24no—
70#17985392—212no—
71#17985391—212no—
72C2×Dic566C2313yes—
73Q8×D283—24no—
74C2×D1132C2313yes—
75C2×C22⋊D283—212no—
76C2×C22⋊D283C2313yes—
77C2×C22⋊D283C2313yes—
78C2×C22⋊D283C2313yes—
79C2×C22⋊D283C2316yes—
80C2×C22⋊D283C2316yes—
81C2×C22⋊D283C2311yescharacteristic
82D4×D283—212no—
83C22×Dic283C2313yes—
84C22×Dic283C2313yes—
85C22×Dic283C2313yes—
86C2×C4×D283—212no—
87C2×C4×D283C2311yescharacteristic
88C2×C4×D283C2313yes—
89C2×C4×D283C2313yes—
90C2×C4×D283C2313yes—
91C4⋊Dic283C2313yes—
92C4⋊Dic283C2313yes—
93Dic283⋊C4C2311yescharacteristic
94Dic283⋊C4C2313yes—
95Dic283⋊C4C2313yes—
96Dic283⋊C4C2313yes—
97Dic283⋊C4C2316yes—
98C22⋊Dic283C2311yescharacteristic
99C22⋊Dic283C2313yes—
100C22⋊Dic283C2313yes—
101C22⋊Dic283C2313yes—
102C22⋊Dic283C2316yes—
103C22⋊Dic283C2316yes—
104(C2×D283)⋊C4C2311yescharacteristic
105(C2×D283)⋊C4C2313yes—
106(C2×D283)⋊C4C2313yes—
107(C2×D283)⋊C4C2313yes—
108(C2×D283)⋊C4C2316yes—
109C4×Dic283C2311yescharacteristic
110C4×Dic283C2313yes—
111C4×Dic283C2313yes—
112C4×Dic283C2313yes—
113C24×C283C2313yes—
114#41×C283—24no—
115#41×C283—212no—
116#41×C283—212no—
117#41×C283D418yescomplemented
118C2×Q8×C283—24no—
119C2×Q8×C283C2313yes—
120C2×Q8×C283C2311yescharacteristic
121C2×D4×C283—212no—
122C2×D4×C283C2316yes—
123C2×D4×C283C2313yes—
124C2×D4×C283C2313yes—
125C22×C4×C283—212no—
126C22×C4×C283C2313yes—
127C22×C4×C283C2311yescharacteristic
128C22×C4×C283C2313yes—
129C22×C4×C283C2313yes—
130C22×C4×C283C2313yes—
131C22×C4×C283C2313yes—
132C22×D283—26no—
133C22×D283—26no—
134C22×D283—43no—
135C22×D283C2413yes—
136C22×D283C2411yescharacteristic
137Dic566—26no—
138D1132—26no—
139C22⋊D283—212no—
140C22⋊D283—26no—
141C22⋊D283—26no—
142C22⋊D283—26no—
143C22⋊D283—46no—
144C22⋊D283#4114yesdirect product factor
145C2×Dic283—26no—
146C2×Dic283—26no—
147C2×Dic283—43no—
148C2×Dic283C2411yescharacteristic
149C2×Dic283C2413yes—
150C2×Dic283C2413yes—
151C2×Dic283C2411yescharacteristic
152C2×Dic283C2413yes—
153C2×Dic283C2411yescharacteristic
154C4×D283—22no—
155C4×D283—26no—
156C4×D283—26no—
157C4×D283—26no—
158C23×C283—26no—
159C23×C283—26no—
160C23×C283—43no—
161C23×C283C2413yes—
162C23×C283C2413yes—
163C23×C283C2411yescharacteristic
164Q8×C283—26no—
165Q8×C283C2×D414yescomplemented
166D4×C283—212no—
167D4×C283—26no—
168D4×C283C2×D4112yescomplemented
169C2×C4×C283—26no—
170C2×C4×C283—22no—
171C2×C4×C283—26no—
172C2×C4×C283—26no—
173C2×C4×C283—26no—
174C2×C4×C283C2×D4112yescomplemented
175C2×C4×C283C2411yescharacteristic
176C2×C4×C283C2413yes—
177C2×C4×C283C2413yes—
178C2×C4×C283C2411yescharacteristic
179C22×C283—21no—
180C22×C283—23no—
181C22×C283—21no—
182C22×C283—23no—
183C22×C283—23no—
184C22×C283—23no—
185C22×C283—23no—
186C22×C283—412no—
187C22×C283C22×D416yes—
188C22×C283C2×#4112yescomplemented
189C22×C283C2511yescharacteristic
190C2×D283—21no—
191C2×D283—21no—
192C2×D283—23no—
193C2×D283—23no—
194C2×D283—23no—
195C2×D283—412no—
196C2×D283C2×#4112yescomplemented
197C4×C283—21no—
198C4×C283—23no—
199C4×C283C22×D412yes—
200C4×C283C22×D416yes—
201Dic283—21no—
202Dic283—23no—
203Dic283—23no—
204Dic283—21no—
205Dic283—23no—
206Dic283C2×#4112yescomplemented
207C2×C283—26no—
208C2×C283—22no—
209C2×C283—43no—
210C2×C283C23×D411yescharacteristic
211C2×C283C22×#4111yescharacteristic
212C2×C283#58511yescharacteristic
213D283—22no—
214D283—43no—
215C283D4×#4111yescharacteristic, complemented, Sylow
216D4×#41—2831nomaximal, Sylow
217C22×#41—2831no—
218C22×#41D28311yescharacteristic, complemented
219#550—2831no—
220D4×Q8—2831no—
221#548—2831no—
222#548—2831no—
223#547—2833no—
224#546—2833no—
225#546—2833no—
226D42—2833no—
227#532—2833no—
228#525—2833no—
229#525—2833no—
230C4×#41—2831no—
231C2×C4×D4—2833no—
232C2×#41—28no—
233C2×#41—2831no—
234C2×#41—2833no—
235C2×#41—2833no—
236C2×#41—5668no—
237C2×#41C2×D28311yescharacteristic
238C2×#41C2×D28313yescomplemented
239C2×#41C2×D28313yescomplemented
240C2×#41C2×D28311yescharacteristic, complemented
241C22×Q8—2831no—
242C22×Q8C2×D28311yescharacteristic, complemented
243C22×D4—2833no—
244C22×D4—2833no—
245C22×D4C2×D28313yescomplemented
246C23×C4—2833no—
247C23×C4C2×D28313yescomplemented
248C4⋊Q8—2833no—
249#127—2833no—
250#124—2833no—
251#124—2833no—
252#123—2836no—
253#123—2836no—
254C22⋊Q8—2833no—
255C22⋊Q8—2833no—
256C22⋊Q8—2833no—
257C22⋊Q8—2833no—
258#121—2833no—
259#121—2833no—
260#121—2836no—
261#121—2836no—
262#121—2833no—
263#121—2833no—
264#120—2836no—
265#120—2836no—
266C4×Q8—2831no—
267C4×Q8—2831no—
268C4×D4—2833no—
269C4×D4—2833no—
270C4×D4—2831no—
271C4×D4—2833no—
272C4×D4—2833no—
273C4×D4—2833no—
274C4×D4—2833no—
275C4×D4—2833no—
276C4×D4—2833no—
277C4×D4—2833no—
278C4×D4—2836no—
279#117—2833no—
280C2×C4⋊C4—2833no—
281C2×C22⋊C4—2833no—
282C2×C22⋊C4—2833no—
283C2×C42—2833no—
284C24—2833no—
285C24C22×D28313yes—
286#41—24no—
287#41—212no—
288#41—212no—
289#41—5664no—
290#41—56612no—
291#41—56612no—
292#41C22⋊D28318yesdirect product factor
293C2×Q8—24no—
294C2×Q8—2833no—
295C2×Q8—5664no—
296C2×Q8C22×D28313yes—
297C2×Q8C22×D28311yescharacteristic
298C2×D4—212no—
299C2×D4—2831no—
300C2×D4—2833no—
301C2×D4—2833no—
302C2×D4—2833no—
303C2×D4—2836no—
304C2×D4—2836no—
305C2×D4—2833no—
306C2×D4—56612no—
307C2×D4—56612no—
308C2×D4C22×D28316yes—
309C2×D4C22×D28313yes—
310C2×D4C22×D28313yes—
311C22×C4—212no—
312C22×C4—2833no—
313C22×C4—2833no—
314C22×C4—2833no—
315C22×C4—2833no—
316C22×C4—2833no—
317C22×C4—2831no—
318C22×C4—2833no—
319C22×C4—56612no—
320C22×C4C22×D28313yes—
321C22×C4C22×D28313yes—
322C22×C4C22×D28313yes—
323C22×C4C22×D28311yescharacteristic
324C22×C4C22×D28313yes—
325C22×C4C22×D28313yes—
326C4⋊C4—2831no—
327C4⋊C4—2833no—
328C4⋊C4—2833no—
329C4⋊C4—2833no—
330C4⋊C4—2836no—
331C4⋊C4—2833no—
332C4⋊C4—2833no—
333C22⋊C4—2831no—
334C22⋊C4—2833no—
335C22⋊C4—2833no—
336C22⋊C4—2833no—
337C22⋊C4—2836no—
338C22⋊C4—2836no—
339C22⋊C4—2831no—
340C22⋊C4—2833no—
341C22⋊C4—2833no—
342C22⋊C4—2833no—
343C22⋊C4—2836no—
344C42—2833no—
345C42—2833no—
346C42—2831no—
347C42—2833no—
348C23—26no—
349C23—26no—
350C23—43no—
351C23—2831no—
352C23—2833no—
353C23—5666no—
354C23—5666no—
355C23—11323no—
356C23C23×D28313yes—
357C23C23×D28313yes—
358C23C23×D28311yescharacteristic
359Q8—26no—
360Q8—5666no—
361Q8C2×C22⋊D28314yescomplemented
362D4—212no—
363D4—26no—
364D4—2834no—
365D4—5666no—
366D4—5666no—
367D4—56612no—
368D4—5666no—
369D4—5666no—
370D4—11326no—
371D4C2×C22⋊D283112yescomplemented
372C2×C4—26no—
373C2×C4—22no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—2831no—
378C2×C4—2831no—
379C2×C4—2833no—
380C2×C4—2833no—
381C2×C4—2831no—
382C2×C4—2833no—
383C2×C4—5666no—
384C2×C4—5666no—
385C2×C4—5662no—
386C2×C4—5666no—
387C2×C4—5666no—
388C2×C4—5666no—
389C2×C4—11323no—
390C2×C4C2×C22⋊D283112yescomplemented
391C2×C4C23×D28311yescharacteristic
392C2×C4C23×D28313yes—
393C2×C4C23×D28313yes—
394C2×C4C23×D28311yescharacteristic
395C22—21no—
396C22—23no—
397C22—23no—
398C22—21no—
399C22—23no—
400C22—23no—
401C22—23no—
402C22—412no—
403C22—2832no—
404C22—5661no—
405C22—5661no—
406C22—5663no—
407C22—5663no—
408C22—5663no—
409C22—113212no—
410C22C22×C22⋊D28316yes—
411C22#41×D28312yescomplemented
412C22C24×D28311yescharacteristic
413C4—21no—
414C4—23no—
415C4—2832no—
416C4—5661no—
417C4—5663no—
418C4—5663no—
419C4—5661no—
420C4—5663no—
421C4C22×C22⋊D28312yes—
422C4C22×C22⋊D28316yes—
423C2—22no—
424C2—26no—
425C2—43no—
426C2—5662no—
427C2—11323no—
428C2C23×C22⋊D28311yescharacteristic
429C2C2×#41×D28311yescharacteristic
430C2#3182730111yescharacteristic
subgroupG/H
centerC2×C4C23×D283
commutator, socle, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC22×#41×C283C2
hypercenterC22×#41D283
hypocenterC283D4×#41
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D283C2semidirect
2. #31827134C2semidirect
3. Q8×C22⋊D283C2semidirect
4. #31827126C2semidirect
5. #31827122C2semidirect
6. #31827114C2semidirect
7. #31827109C2semidirect
8. #31827103C2semidirect
9. D4×C22⋊D283C2semidirect
10. #31827011C2semidirect
11. #31826976C2semidirect
12. #31826972C2semidirect
13. #41×Dic283C2semidirect
14. C2×C4×C22⋊D283C2semidirect
15. C22×#41×C283C2semidirect
16. C2×#17985393C22semidirect
17. C2×#17985392C22semidirect
18. C2×#17985391C22semidirect
20. C2×Q8×D283C22semidirect
22. C2×D4×D283C22semidirect
23. C22×C4×D283C22semidirect
24. #22583608C22semidirect
25. #22583606C22semidirect
26. #22583599C22semidirect
27. #22583597C22semidirect
28. #22583593C22semidirect
29. #22583591C22semidirect
30. #22583589C22semidirect
31. #22583589C22semidirect
32. #22583586C22semidirect
33. #22583586C22semidirect
34. #22583584C22semidirect
35. #22583584C22semidirect
36. #22583582C22semidirect
37. #22583582C22semidirect
38. #22583581C22semidirect
39. #22583581C22semidirect
40. #22583579C22semidirect
41. #22583578C22semidirect
42. Q8×Dic283C22semidirect
43. Q8×Dic283C22semidirect
44. D4×Dic283C22semidirect
45. D4×Dic283C22semidirect
48. C4×C22⋊D283C22semidirect
49. C4×C22⋊D283C22semidirect
50. C4×C22⋊D283C22semidirect
51. C4×C22⋊D283C22semidirect
52. C4×C22⋊D283C22semidirect
53. C4×C22⋊D283C22semidirect
54. C4×C22⋊D283C22semidirect
55. #22583569C22semidirect
56. C2×Dic283⋊C4C22semidirect
57. C2×C22⋊Dic283C22semidirect
58. C2×(C2×D283)⋊C4C22semidirect
59. C2×C4×Dic283C22semidirect
62. C2×#41×C283C22semidirect
63. C2×#41×C283C22semidirect
64. C2×#41×C283C22semidirect
65. C22×Q8×C283C22semidirect
66. C22×D4×C283C22semidirect
67. C23×C4×C283C22semidirect
117. #41×C283D4semidirect
144. C22⋊D283#41direct (N × H)
165. Q8×C283C2×D4semidirect
168. D4×C283C2×D4semidirect
174. C2×C4×C283C2×D4semidirect
188. C22×C283C2×#41semidirect
196. C2×D283C2×#41semidirect
206. Dic283C2×#41semidirect
215. C283D4×#41semidirect
218. C22×#41D283semidirect
238. C2×#41C2×D283semidirect
239. C2×#41C2×D283semidirect
240. C2×#41C2×D283semidirect
242. C22×Q8C2×D283semidirect
245. C22×D4C2×D283semidirect
247. C23×C4C2×D283semidirect
292. #41C22⋊D283direct (N × H)
361. Q8C2×C22⋊D283semidirect
371. D4C2×C22⋊D283semidirect
390. C2×C4C2×C22⋊D283semidirect
411. C22#41×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2832
#318271342
Q8×C22⋊D2832
#318271262
#318271222
#318271142
#318271092
#318271032
D4×C22⋊D2832
#318270112
#318269762
#318269722
#41×Dic2832
C2×C4×C22⋊D2832
C22×#41×C2832
D4×#41283