Finite Group Databasebeta

← #21435084

Subgroups — #21435084

Order 7552.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837953C211yesmaximal, characteristic, complemented
2#124×D59C211yesmaximal, characteristic, complemented
3#16837792C211yesmaximal, characteristic, complemented
4#16837791C211yesmaximal, characteristic, complemented
5#16837764C211yesmaximal, characteristic, complemented
6#16837620C212yesmaximal, complemented
7#16837616C212yesmaximal, complemented
8#16837542C212yesmaximal, complemented
9#16837537C212yesmaximal, complemented
10#16837457C211yesmaximal, characteristic, complemented
11C59×#489C211yesmaximal, characteristic, complemented
12C2×#11745689—21no—
13C2×Q8×D59C2211yescharacteristic
14C2×D4×D59C2211yescharacteristic
15C2×#11745660C2212yescomplemented
16C2×#11745671C2212yescomplemented
17C2×D472C2212yes—
18C2×#11745669C2212yes—
19#14273724C2211yescharacteristic, complemented
20#14273716—21no—
21#14273716C2211yescharacteristic
22#14273715C2211yescharacteristic
23#14273714C2211yescharacteristic
24#14273713—21no—
25#14273713—21no—
26#14273702—21no—
27#14273702C2212yes—
28#14273689—21no—
29#14273689C2212yescomplemented
30C22⋊C4×D59—21no—
31C22⋊C4×D59—21no—
32C42×D59C2211yescharacteristic
33Dic59⋊C8C2212yescomplemented
34#14273650C2212yescomplemented
35#14273647C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic, complemented
38C4⋊Q8×C59C2211yescharacteristic, complemented
39#124×C59C2211yescharacteristic
40#103×C59C2212yescomplemented
41#102×C59C2212yes—
42#97×C59C2211yescharacteristic, complemented
43C23×D59—21no—
44C2×Q8×C59—21no—
45C2×Q8×C59C2311yescharacteristic
46C2×D4×C59C2311yescharacteristic
47C2×C22⋊D59—21no—
48#11745689—44no—
49Q8×D59—42no—
50D4×D59—42no—
51C2×D236—22no—
52C2×D236—21no—
53C2×D236—21no—
54C2×D236C2311yescharacteristic
55C2×D236C2312yes—
56C2×C4×D59—21no—
57C2×C4×D59—22no—
58C2×C4×D59D411yescharacteristic
59C2×C4×D59D411yescharacteristic
60C2×C4×D59C2311yescharacteristic
61C2×Dic118—21no—
62C2×Dic118C2311yescharacteristic
63C2×C8×C59C2312yes—
64C4⋊C4×C59—21no—
65C4⋊C4×C59C2312yes—
66C22⋊C4×C59—21no—
67C22⋊C4×C59—21no—
68C42×C59C2311yescharacteristic
69C22⋊Dic59—21no—
70C22⋊Dic59—21no—
71#11745671—42no—
72#11745669—42no—
73(C2×D59)⋊C4—21no—
74(C2×D59)⋊C4—21no—
75(C2×D59)⋊C4—21no—
76(C2×D59)⋊C4—21no—
77(C2×D59)⋊C4—22no—
78(C2×D59)⋊C4—22no—
79C4×Dic59D411yescharacteristic
80C4×Dic59D411yescharacteristic
81C4×Dic59C2311yescharacteristic
82C2×C59⋊C8C2312yes—
83D472—42no—
84#11745660—42no—
85C23×C59—21no—
86C22×D59—21no—
87C22×D59—22no—
88C22×D59—42no—
89C22×D59—42no—
90C22×D59—42no—
91C22×D59C2×D411yescharacteristic
92Q8×C59—22no—
93Q8×C59—42no—
94D4×C59—22no—
95C2×C4×C59—21no—
96C2×C4×C59—22no—
97C2×C4×C59C2×D411yescharacteristic
98C2×C4×C59C2×D411yescharacteristic
99C2×C4×C59C2411yescharacteristic
100C22⋊D59—42no—
101C2×Dic59—21no—
102C2×Dic59C2×D411yescharacteristic
103C2×Dic59C2×D411yescharacteristic
104C2×Dic59C2×D411yescharacteristic
105D236—22no—
106D236—22no—
107D236—22no—
108D236—42no—
109D236—42no—
110D236—44no—
111C4×D59—22no—
112C4×D59—22no—
113C4×D59—41no—
114C4×D59—44no—
115C4×D59—42no—
116Dic118—22no—
117Dic118—42no—
118C8×C59—22no—
119C59⋊C8—22no—
120C22×C59—41no—
121C22×C59—41no—
122C22×C59—41no—
123C22×C59C22×D411yescharacteristic
124C2×D59—21no—
125C2×D59—21no—
126C2×D59—41no—
127C2×D59—42no—
128C2×D59—42no—
129C2×D59—41no—
130C2×D59—42no—
131C2×D59—41no—
132C2×D59—84no—
133C2×D59AGL(1,ℤ/8)12yes—
134C4×C59—21no—
135C4×C59—21no—
136C4×C59—41no—
137C4×C59—42no—
138C4×C59H(5,𝔽2)12yes—
139Dic59—21no—
140Dic59—21no—
141Dic59—21no—
142Dic59—41no—
143#3213—591nomaximal, Sylow
144C2×C59—81no—
145C2×C59#53511yescharacteristic
146C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C59#57511yescharacteristic
148D59—22no—
149D59—82no—
150D59—81no—
151#532—591no—
152C2×#124—591no—
153#496—591no—
154#496—591no—
155#489—591no—
156#489D5911yescharacteristic, complemented
157#463—592no—
158#463—592no—
159#448—592no—
160#447—592no—
161#432—591no—
162C59#321311yescharacteristic, complemented, Sylow
163C2×#41—1181no—
164C22×Q8—591no—
165C22×D4—591no—
166C2×SD16—592no—
167C2×SD16—592no—
168C2×D8—592no—
169C2×D8—592no—
170C4⋊Q8C2×D5911yescharacteristic, complemented
171#127—591no—
172#124—591no—
173#124—591no—
174#124—591no—
175#124—1181no—
176#124—1181no—
177#124—1181no—
178#124C2×D5911yescharacteristic
179#121—592no—
180#121—1181no—
181C4×D4—592no—
182C4×D4—1181no—
183C2×C22⋊C4—1181no—
184C2×C22⋊C4—1181no—
185C2×C42—591no—
186C4⋊C8—592no—
187#103—592no—
188#103C2×D5912yescomplemented
189#102—592no—
190#102C2×D5912yes—
191C22⋊C8—592no—
192#97—591no—
193#97C2×D5911yescharacteristic, complemented
194C24—1181no—
195#41—2364no—
196C2×Q8—21no—
197C2×Q8—591no—
198C2×Q8—1181no—
199C2×Q8—2362no—
200C2×Q8C22×D5911yescharacteristic
201C2×D4—591no—
202C2×D4—592no—
203C2×D4—1182no—
204C2×D4—1181no—
205C2×D4—1181no—
206C2×D4—1181no—
207C2×D4—2362no—
208C2×D4C22×D5911yescharacteristic
209C22×C4—591no—
210C22×C4—591no—
211C22×C4—591no—
212C22×C4—1182no—
213C22×C4—1181no—
214SD16—2362no—
215SD16—2362no—
216D8—2362no—
217D8—2362no—
218C2×C8—592no—
219C2×C8C22×D5912yes—
220C4⋊C4—21no—
221C4⋊C4C22×D5912yes—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—1181no—
225C22⋊C4—1181no—
226C22⋊C4—1182no—
227C22⋊C4—1182no—
228C22⋊C4—1181no—
229C22⋊C4—1181no—
230C22⋊C4—1181no—
231C22⋊C4—1181no—
232C42—591no—
233C42—591no—
234C42—591no—
235C42C22×D5911yescharacteristic
236C23—21no—
237C23—591no—
238C23—1181no—
239C23—1182no—
240C23—2362no—
241C23—2362no—
242C23—2362no—
243Q8—22no—
244Q8—42no—
245Q8—1182no—
246Q8—2362no—
247D4—22no—
248D4—1182no—
249D4—1182no—
250D4—1182no—
251D4—2362no—
252D4—2362no—
253D4—2364no—
254D4—2362no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—591no—
258C2×C4—591no—
259C2×C4—591no—
260C2×C4—1182no—
261C2×C4—1182no—
262C2×C4—1181no—
263C2×C4—2361no—
264C2×C4—2364no—
265C2×C4—2362no—
266C2×C4D4×D5911yescharacteristic
267C2×C4D4×D5911yescharacteristic
268C2×C4C23×D5911yescharacteristic
269C8—22no—
270C8—1182no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—592no—
275C22—1181no—
276C22—1181no—
277C22—4724no—
278C22—2362no—
279C22—2361no—
280C22—2362no—
281C22—2361no—
282C22—2361no—
283C22—2362no—
284C22C2×D4×D5911yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—41no—
289C4—1181no—
290C4—1181no—
291C4—1181no—
292C4—2361no—
293C4#1427377312yes—
294C2—81no—
295C2—1182no—
296C2—4721no—
297C2—4722no—
298C2#1683797011yescharacteristic
299C2AGL(1,ℤ/8)×D5911yescharacteristic
300C2#1683820111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#489C2
socleC22×C59C22×D4
hypercenter#489D59
hypocenterC59#3213
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16837953C2semidirect
2. #124×D59C2semidirect
3. #16837792C2semidirect
4. #16837791C2semidirect
5. #16837764C2semidirect
6. #16837620C2semidirect
7. #16837616C2semidirect
8. #16837542C2semidirect
9. #16837537C2semidirect
10. #16837457C2semidirect
11. C59×#489C2semidirect
15. C2×#11745660C22semidirect
16. C2×#11745671C22semidirect
19. #14273724C22semidirect
29. #14273689C22semidirect
33. Dic59⋊C8C22semidirect
34. #14273650C22semidirect
37. #14273638C22semidirect
38. C4⋊Q8×C59C22semidirect
40. #103×C59C22semidirect
42. #97×C59C22semidirect
156. #489D59semidirect
162. C59#3213semidirect
170. C4⋊Q8C2×D59semidirect
188. #103C2×D59semidirect
193. #97C2×D59semidirect