Finite Group Databasebeta

← #537×D283 #49134581

Subgroups — #537×D283 #49134581

Order 36224.

1640 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C212yesmaximal, complemented
2#31827046C211yesmaximal, characteristic, complemented
3#31827045C214yesmaximal, complemented
4#31827044C214yesmaximal, complemented
5#31827043C212yesmaximal, complemented
6#31827042C214yesmaximal, complemented
7C22⋊Q8×D283C214yesmaximal, complemented
8#121×D283C214yesmaximal, complemented
9#121×D283C214yesmaximal, complemented
10C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
11#537×C283C211yesmaximal, characteristic, complemented
12C2×#17985393C2212yescomplemented
13C2×#17985392C2212yescomplemented
14C2×#17985392C2214yescomplemented
15C2×#17985391C2214yescomplemented
16C2×#17985391C2212yescomplemented
17#41×D283—216no—
18C2×Q8×D283C2212yes—
19C2×D4×D283C2212yes—
20C2×D4×D283C2214yes—
21C2×D4×D283C2214yes—
22C22×C4×D283C2214yes—
23C22×C4×D283C2212yes—
24C22×C4×D283C2211yescharacteristic
25#22583590C2214yescomplemented
26#22583589C2214yescomplemented
27#22583588C2218yescomplemented
28#22583587C2218yescomplemented
29#22583586C2214yescomplemented
30#22583585C2214yescomplemented
31#22583585C2214yescomplemented
32#22583584C2214yescomplemented
33#22583584C2214yescomplemented
34#22583583C2218yescomplemented
35#22583583C2218yescomplemented
36#22583582C2218yescomplemented
37#22583582C2218yescomplemented
38#22583581C2214yescomplemented
39#22583581C2214yescomplemented
40C2×C4⋊Dic283C2211yescharacteristic, complemented
41C2×Dic283⋊C4C2212yescomplemented
42C4⋊C4×D283C2214yes—
43C4⋊C4×D283C2214yes—
44C4⋊C4×D283C2214yescomplemented
45C22⋊C4×D283C2218yes—
46C2×#41×C283C2212yescomplemented
47C22⋊Q8×C283C2214yescomplemented
48#121×C283C2214yescomplemented
49#121×C283C2214yescomplemented
50C2×C4⋊C4×C283C2211yescharacteristic, complemented
51C23×D283C2314yes—
52C23×D283C2311yescharacteristic
53#17985393—28no—
54#17985392—216no—
55#17985392—28no—
56#17985391—216no—
57#17985391—28no—
58C2×Dic566C2314yes—
59C2×Dic566C2312yes—
60Q8×D283—28no—
61C2×D1132C2314yes—
62C2×D1132C2312yes—
63C2×D1132C2314yes—
64C2×C22⋊D283C2314yes—
65C2×C22⋊D283C2314yes—
66C2×C22⋊D283C2314yes—
67C2×C22⋊D283C2318yes—
68D4×D283—216no—
69D4×D283—28no—
70D4×D283—48no—
71C22×Dic283C2314yes—
72C22×Dic283C2312yes—
73C22×Dic283C2311yescharacteristic
74C2×C4×D283—216no—
75C2×C4×D283—44no—
76C2×C4×D283D418yescomplemented
77C2×C4×D283C2314yes—
78C2×C4×D283C2314yes—
79C2×C4×D283C2314yes—
80C2×C4×D283C2314yes—
81C2×C4×D283C2314yes—
82C2×C4×D283C2312yes—
83C2×C4×D283C2312yes—
84C4⋊Dic283C2314yes—
85C4⋊Dic283C2314yes—
86Dic283⋊C4C2318yes—
87Dic283⋊C4C2318yes—
88C22⋊Dic283C2318yes—
89(C2×D283)⋊C4C2318yes—
90(C2×D283)⋊C4C2318yes—
91#41×C283—28no—
92C2×Q8×C283C2312yes—
93C2×D4×C283C2312yes—
94C2×D4×C283C2314yes—
95C2×D4×C283C2314yes—
96C22×C4×C283C2314yes—
97C22×C4×C283C2312yes—
98C22×C4×C283C2311yescharacteristic
99C4⋊C4×C283C2314yes—
100C4⋊C4×C283C2314yes—
101C22⋊C4×C283C2318yes—
102C22×D283—22no—
103C22×D283—22no—
104C22×D283—28no—
105C22×D283—28no—
106C22×D283—28no—
107C22×D283C2×D414yes—
108C22×D283C2414yes—
109C22×D283C2411yescharacteristic
110C22×D283C2411yescharacteristic
111Dic566—24no—
112Dic566—28no—
113D1132—28no—
114D1132—24no—
115D1132—44no—
116C22⋊D283—28no—
117C22⋊D283—28no—
118C22⋊D283—28no—
119C22⋊D283—48no—
120C2×Dic283—28no—
121C2×Dic283—42no—
122C2×Dic283C2×D414yescomplemented
123C2×Dic283C2414yes—
124C2×Dic283C2414yes—
125C2×Dic283C2412yes—
126C4×D283—28no—
127C4×D283—28no—
128C4×D283—28no—
129C4×D283—28no—
130C4×D283—44no—
131C4×D283C2×D418yes—
132C4×D283C2×D418yescomplemented
133C23×C283C2414yes—
134C23×C283C2411yescharacteristic
135Q8×C283—24no—
136D4×C283—28no—
137D4×C283—24no—
138D4×C283—44no—
139C2×C4×C283—28no—
140C2×C4×C283—42no—
141C2×C4×C283C2×D414yescomplemented
142C2×C4×C283C2414yes—
143C2×C4×C283C2414yes—
144C2×C4×C283C2412yes—
145C22×C283—21no—
146C22×C283—21no—
147C22×C283—24no—
148C22×C283—24no—
149C22×C283—24no—
150C22×C283C22×D412yes—
151C22×C283C2511yescharacteristic
152C2×D283—21no—
153C2×D283—21no—
154C2×D283—28no—
155C2×D283—24no—
156C2×D283—24no—
157C2×D283—24no—
158C2×D283—416no—
159C2×D283C22×D412yes—
160C2×D283C22×D412yes—
161C2×D283H(5,𝔽2)12yes—
162C2×D2832−1+412yes—
163C4×C283—24no—
164C4×C283—24no—
165C4×C283C22×D414yes—
166Dic283—24no—
167Dic283—24no—
168Dic283C22×D414yes—
169C2×C283—22no—
170C2×C283—44no—
171C2×C283C23×D411yescharacteristic
172C2×C283C2×H(5,𝔽2)11yescharacteristic
173C2×C283C2×2−1+411yescharacteristic
174D283—22no—
175D283—44no—
176D283#53714yesdirect product factor
177C283C2×#53711yescharacteristic, complemented, Sylow
178C2×#537—2831nomaximal, Sylow
179C22×#41—2832no—
180#537—2832no—
181#537—2834no—
182#537—2834no—
183#537—2834no—
184#537—2831no—
185#537D28311yescharacteristic, direct product factor
186C2×C22⋊Q8—2834no—
187C2×#121—2834no—
188C2×#121—2834no—
189C22×C4⋊C4—2831no—
190C2×#41—2832no—
191C2×#41—2834no—
192C2×#41—2832no—
193C2×#41—2834no—
194C2×#41—2832no—
195C2×#41—56616no—
196C2×#41C2×D28312yescomplemented
197C22×Q8—2832no—
198C22×D4—2832no—
199C22×D4—2834no—
200C22×D4—2834no—
201C23×C4—2831no—
202C23×C4—2834no—
203C23×C4—2832no—
204C22⋊Q8—2834no—
205C22⋊Q8—2834no—
206C22⋊Q8—2838no—
207C22⋊Q8—2834no—
208C22⋊Q8—2838no—
209C22⋊Q8C2×D28314yescomplemented
210#121—2834no—
211#121—2834no—
212#121—2838no—
213#121—2838no—
214#121—2834no—
215#121—2834no—
216#121—2834no—
217#121—2834no—
218#121—2838no—
219#121—2838no—
220#121C2×D28314yescomplemented
221#121C2×D28314yescomplemented
222C2×C4⋊C4—2832no—
223C2×C4⋊C4—2831no—
224C2×C4⋊C4—2834no—
225C2×C4⋊C4—2834no—
226C2×C4⋊C4—2834no—
227C2×C4⋊C4C2×D28311yescharacteristic, complemented
228C2×C22⋊C4—2838no—
229C24—2831no—
230C24—2834no—
231#41—28no—
232#41—56616no—
233#41—56616no—
234#41—5668no—
235#41—5668no—
236#41—5668no—
237C2×Q8—2834no—
238C2×Q8—2832no—
239C2×Q8—5668no—
240C2×Q8C22×D28312yes—
241C2×D4—2834no—
242C2×D4—2834no—
243C2×D4—2834no—
244C2×D4—2838no—
245C2×D4—2834no—
246C2×D4—2832no—
247C2×D4—2834no—
248C2×D4—5668no—
249C2×D4—56616no—
250C2×D4—11328no—
251C2×D4C22×D28314yes—
252C2×D4C22×D28312yes—
253C2×D4C22×D28314yes—
254C22×C4—2831no—
255C22×C4—2838no—
256C22×C4—2832no—
257C22×C4—2832no—
258C22×C4—2834no—
259C22×C4—2832no—
260C22×C4—2834no—
261C22×C4—2834no—
262C22×C4—2834no—
263C22×C4—2834no—
264C22×C4—2834no—
265C22×C4—56616no—
266C22×C4—11324no—
267C22×C4C22×D28314yes—
268C22×C4C22×D28312yes—
269C22×C4C22×D28311yescharacteristic
270C4⋊C4—2838no—
271C4⋊C4—2838no—
272C4⋊C4—2834no—
273C4⋊C4—2834no—
274C4⋊C4C22×D28314yes—
275C4⋊C4C22×D28314yes—
276C22⋊C4—2838no—
277C22⋊C4—2838no—
278C22⋊C4—2838no—
279C22⋊C4C22×D28318yes—
280C23—2831no—
281C23—2834no—
282C23—2831no—
283C23—2834no—
284C23—5662no—
285C23—5662no—
286C23—5668no—
287C23—5668no—
288C23—5668no—
289C23C23×D28314yes—
290C23C23×D28311yescharacteristic
291Q8—24no—
292Q8—5668no—
293Q8—5664no—
294D4—28no—
295D4—24no—
296D4—44no—
297D4—5668no—
298D4—5668no—
299D4—5668no—
300D4—5668no—
301D4—5664no—
302D4—11324no—
303D4—11328no—
304C2×C4—28no—
305C2×C4—42no—
306C2×C4—2834no—
307C2×C4—2832no—
308C2×C4—2838no—
309C2×C4—2838no—
310C2×C4—2834no—
311C2×C4—2834no—
312C2×C4—5668no—
313C2×C4—5668no—
314C2×C4—5668no—
315C2×C4—5668no—
316C2×C4—5668no—
317C2×C4—11324no—
318C2×C4—11322no—
319C2×C4D4×D28314yescomplemented
320C2×C4C23×D28314yes—
321C2×C4C23×D28314yes—
322C2×C4C23×D28312yes—
323C22—21no—
324C22—21no—
325C22—24no—
326C22—24no—
327C22—24no—
328C22—2832no—
329C22—2832no—
330C22—2832no—
331C22—2832no—
332C22—5668no—
333C22—5661no—
334C22—5661no—
335C22—5664no—
336C22—5664no—
337C22—5664no—
338C22—113216no—
339C22C2×D4×D28312yes—
340C22C24×D28311yescharacteristic
341C4—24no—
342C4—24no—
343C4—2834no—
344C4—5664no—
345C4—5664no—
346C4C2×D4×D28314yes—
347C2—22no—
348C2—44no—
349C2—2834no—
350C2—5662no—
351C2—11324no—
352C2C22×D4×D28311yescharacteristic
353C2H(5,𝔽2)×D28311yescharacteristic
354C22−1+4×D28311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D283
commutator, socle, cosocleC22×C283C25
Fitting#537×C283C2
hypercenter#537D283
hypocenterC283C2×#537
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#41×D283C2semidirect
2. #31827046C2semidirect
3. #31827045C2semidirect
4. #31827044C2semidirect
5. #31827043C2semidirect
6. #31827042C2semidirect
7. C22⋊Q8×D283C2semidirect
8. #121×D283C2semidirect
9. #121×D283C2semidirect
10. C2×C4⋊C4×D283C2semidirect
11. #537×C283C2semidirect
12. C2×#17985393C22semidirect
13. C2×#17985392C22semidirect
14. C2×#17985392C22semidirect
15. C2×#17985391C22semidirect
16. C2×#17985391C22semidirect
25. #22583590C22semidirect
26. #22583589C22semidirect
27. #22583588C22semidirect
28. #22583587C22semidirect
29. #22583586C22semidirect
30. #22583585C22semidirect
31. #22583585C22semidirect
32. #22583584C22semidirect
33. #22583584C22semidirect
34. #22583583C22semidirect
35. #22583583C22semidirect
36. #22583582C22semidirect
37. #22583582C22semidirect
38. #22583581C22semidirect
39. #22583581C22semidirect
40. C2×C4⋊Dic283C22semidirect
41. C2×Dic283⋊C4C22semidirect
44. C4⋊C4×D283C22semidirect
46. C2×#41×C283C22semidirect
47. C22⋊Q8×C283C22semidirect
48. #121×C283C22semidirect
49. #121×C283C22semidirect
50. C2×C4⋊C4×C283C22semidirect
76. C2×C4×D283D4semidirect
122. C2×Dic283C2×D4semidirect
132. C4×D283C2×D4semidirect
141. C2×C4×C283C2×D4semidirect
176. D283#537direct (N × H)
177. C283C2×#537semidirect
185. #537D283direct (N × H)
196. C2×#41C2×D283semidirect
209. C22⋊Q8C2×D283semidirect
220. #121C2×D283semidirect
221. #121C2×D283semidirect
227. C2×C4⋊C4C2×D283semidirect
319. C2×C4D4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2832
#318270462
#318270452
#318270442
#318270432
#318270422
C22⋊Q8×D2832
#121×D2832
C2×C4⋊C4×D2832
#537×C2832
C2×#537283