Finite Group Databasebeta

← #21435115

Subgroups — #21435115

Order 7552.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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#127×D59C211yesmaximal, characteristic, complemented
2#16837937C211yesmaximal, characteristic, complemented
3#16837791C211yesmaximal, characteristic, complemented
4#16837789C211yesmaximal, characteristic, complemented
5#16837768C211yesmaximal, characteristic, complemented
6#16837601C212yesmaximal, complemented
7#16837596C212yesmaximal, complemented
8#16837554C212yesmaximal, complemented
9#16837537C212yesmaximal, complemented
10#16837457C211yesmaximal, characteristic, complemented
11C59×#490C211yesmaximal, characteristic, complemented
12C2×D4×D59—21no—
13C2×D4×D59—21no—
14C2×D4×D59C2212yes—
15C2×#11745660C2212yescomplemented
16C2×#11745670C2212yescomplemented
17C2×D472C2212yescomplemented
18C2×#11745669C2212yescomplemented
19#14273724C2211yescharacteristic
20#14273723—21no—
21#14273723—21no—
22#14273723C2212yes—
23#14273722—21no—
24#14273715C2211yescharacteristic, complemented
25#14273712—21no—
26#14273707C2211yescharacteristic
27#14273702C2211yescharacteristic
28#14273692C2211yescharacteristic, complemented
29#14273689—21no—
30#14273689C2211yescharacteristic, complemented
31#14273685—21no—
32C42×D59C2211yescharacteristic
33Dic59⋊C8C2212yescomplemented
34#14273647C2212yescomplemented
35#14273647C2212yescomplemented
36(C2×D59)⋊C8C2212yes—
37#14273638C2211yescharacteristic, complemented
38#127×C59C2211yescharacteristic
39#125×C59C2211yescharacteristic, complemented
40#102×C59C2212yescomplemented
41#102×C59C2212yescomplemented
42#97×C59C2211yescharacteristic, complemented
43C23×D59—22no—
44C2×D4×C59—21no—
45C2×D4×C59—21no—
46C2×D4×C59C2312yes—
47C2×C22⋊D59—22no—
48C2×C22⋊D59—22no—
49C2×C22⋊D59—22no—
50D4×D59—42no—
51D4×D59—42no—
52D4×D59—44no—
53D4×D59—44no—
54C2×D236—21no—
55C2×D236—21no—
56C2×D236—21no—
57C2×D236C2312yes—
58C2×D236C2311yescharacteristic
59C2×C4×D59—21no—
60C2×C4×D59D411yescharacteristic
61C2×C4×D59D411yescharacteristic
62C2×C4×D59C2311yescharacteristic
63C2×Dic118C2311yescharacteristic
64C2×C8×C59C2312yes—
65C4⋊C4×C59—21no—
66C4⋊C4×C59—21no—
67C4⋊C4×C59C2311yescharacteristic
68C4⋊C4×C59C2311yescharacteristic
69C42×C59C2311yescharacteristic
70#11745670—42no—
71#11745669—42no—
72(C2×D59)⋊C4—21no—
73(C2×D59)⋊C4—21no—
74(C2×D59)⋊C4—21no—
75(C2×D59)⋊C4—21no—
76(C2×D59)⋊C4—21no—
77C4⋊Dic59—21no—
78Dic59⋊C4—21no—
79C4×Dic59—21no—
80C4×Dic59D411yescharacteristic
81C4×Dic59D411yescharacteristic
82C4×Dic59C2311yescharacteristic
83C2×C59⋊C8C2312yes—
84D472—42no—
85#11745660—42no—
86C23×C59—22no—
87C22×D59—21no—
88C22×D59—22no—
89C22×D59—44no—
90C22×D59—44no—
91C22×D59—44no—
92C22×D59C2×D411yescharacteristic
93D4×C59—22no—
94D4×C59—22no—
95D4×C59—42no—
96D4×C59—42no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59C2×D411yescharacteristic
100C2×C4×C59C2×D411yescharacteristic
101C2×C4×C59C2411yescharacteristic
102C22⋊D59—44no—
103C22⋊D59—44no—
104C22⋊D59—44no—
105C2×Dic59—21no—
106C2×Dic59C2×D411yescharacteristic
107C2×Dic59C2×D411yescharacteristic
108C2×Dic59C2×D411yescharacteristic
109D236—22no—
110D236—22no—
111D236—22no—
112D236—42no—
113D236—42no—
114D236—42no—
115C4×D59—22no—
116C4×D59—22no—
117C4×D59—22no—
118C4×D59—42no—
119Dic118—22no—
120C8×C59—22no—
121C59⋊C8—22no—
122C22×C59—42no—
123C22×C59—42no—
124C22×C59—42no—
125C22×C59C22×D411yescharacteristic
126C2×D59—21no—
127C2×D59—21no—
128C2×D59—42no—
129C2×D59—41no—
130C2×D59—41no—
131C2×D59—42no—
132C2×D59—42no—
133C2×D59—41no—
134C2×D59—88no—
135C2×D59AGL(1,ℤ/8)12yes—
136C4×C59—21no—
137C4×C59—21no—
138C4×C59—41no—
139C4×C59—41no—
140C4×C59H(5,𝔽2)12yes—
141Dic59—21no—
142Dic59—21no—
143Dic59—41no—
144Dic59AGL(1,ℤ/8)12yes—
145#3217—591nomaximal, Sylow
146C2×C59—82no—
147C2×C59#53511yescharacteristic
148C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
150D59—22no—
151D59—81no—
152D59—82no—
153C2×#127—591no—
154#529—591no—
155#496—591no—
156#496—591no—
157#490—591no—
158#490D5911yescharacteristic, complemented
159#460—592no—
160#459—592no—
161#450—592no—
162#447—592no—
163#432—591no—
164C59#321711yescharacteristic, complemented, Sylow
165C22×D4—592no—
166C22×D4—1181no—
167C22×D4—1181no—
168C2×SD16—592no—
169C2×SD16—592no—
170C2×D8—592no—
171C2×D8—592no—
172#127—592no—
173#127—591no—
174#127—1181no—
175#127—1181no—
176#127C2×D5911yescharacteristic
177#126—1181no—
178#125C2×D5911yescharacteristic, complemented
179#124—591no—
180#123—1181no—
181C22⋊Q8—591no—
182#121—591no—
183C4×Q8—591no—
184C4×D4—591no—
185C4×D4—1181no—
186#117—1181no—
187C2×C42—591no—
188C4⋊C8—592no—
189#102—592no—
190#102—592no—
191#102C2×D5912yescomplemented
192#102C2×D5912yescomplemented
193C22⋊C8—592no—
194#97—591no—
195#97C2×D5911yescharacteristic, complemented
196C24—1182no—
197C2×Q8—591no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—592no—
201C2×D4—591no—
202C2×D4—1181no—
203C2×D4—1182no—
204C2×D4—1182no—
205C2×D4—1182no—
206C2×D4—1181no—
207C2×D4—1181no—
208C2×D4—2362no—
209C2×D4—2362no—
210C2×D4—2364no—
211C2×D4—2364no—
212C2×D4C22×D5912yes—
213C22×C4—591no—
214C22×C4—591no—
215C22×C4—591no—
216C22×C4—1181no—
217SD16—2362no—
218SD16—2362no—
219D8—2362no—
220D8—2362no—
221C2×C8—592no—
222C2×C8C22×D5912yes—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—1181no—
226C4⋊C4—1181no—
227C4⋊C4C22×D5911yescharacteristic
228C4⋊C4C22×D5911yescharacteristic
229C22⋊C4—1181no—
230C22⋊C4—1181no—
231C22⋊C4—1181no—
232C22⋊C4—1181no—
233C22⋊C4—1181no—
234C42—591no—
235C42—591no—
236C42—591no—
237C42—1181no—
238C42C22×D5911yescharacteristic
239C23—22no—
240C23—591no—
241C23—1181no—
242C23—1182no—
243C23—2364no—
244C23—2364no—
245C23—2364no—
246Q8—1182no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—1182no—
252D4—1182no—
253D4—1182no—
254D4—2362no—
255D4—2362no—
256D4—2362no—
257D4—2364no—
258D4—2364no—
259D4—2364no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—591no—
263C2×C4—591no—
264C2×C4—591no—
265C2×C4—1182no—
266C2×C4—1182no—
267C2×C4—1182no—
268C2×C4—1181no—
269C2×C4—2362no—
270C2×C4D4×D5911yescharacteristic
271C2×C4D4×D5911yescharacteristic
272C2×C4C23×D5911yescharacteristic
273C8—22no—
274C8—1182no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—592no—
279C22—1181no—
280C22—1181no—
281C22—4728no—
282C22—2361no—
283C22—2362no—
284C22—2362no—
285C22—2361no—
286C22—2362no—
287C22—2361no—
288C22C2×D4×D5911yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—592no—
294C4—1181no—
295C4—1181no—
296C4—2361no—
297C4#1427377312yes—
298C2—82no—
299C2—1182no—
300C2—4722no—
301C2—4721no—
302C2#1683797011yescharacteristic
303C2AGL(1,ℤ/8)×D5911yescharacteristic
304C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#490C2
socleC22×C59C22×D4
hypercenter#490D59
hypocenterC59#3217
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #127×D59C2semidirect
2. #16837937C2semidirect
3. #16837791C2semidirect
4. #16837789C2semidirect
5. #16837768C2semidirect
6. #16837601C2semidirect
7. #16837596C2semidirect
8. #16837554C2semidirect
9. #16837537C2semidirect
10. #16837457C2semidirect
11. C59×#490C2semidirect
15. C2×#11745660C22semidirect
16. C2×#11745670C22semidirect
17. C2×D472C22semidirect
18. C2×#11745669C22semidirect
24. #14273715C22semidirect
28. #14273692C22semidirect
30. #14273689C22semidirect
33. Dic59⋊C8C22semidirect
34. #14273647C22semidirect
35. #14273647C22semidirect
37. #14273638C22semidirect
39. #125×C59C22semidirect
40. #102×C59C22semidirect
41. #102×C59C22semidirect
42. #97×C59C22semidirect
158. #490D59semidirect
164. C59#3217semidirect
178. #125C2×D59semidirect
191. #102C2×D59semidirect
192. #102C2×D59semidirect
195. #97C2×D59semidirect