Finite Group Databasebeta

← #21435100

Subgroups — #21435100

Order 7552.

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

normal subgroups only

This group has 400 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#16837957C211yesmaximal, characteristic, complemented
2#124×D59C211yesmaximal, characteristic
3#16837797C211yesmaximal, characteristic, complemented
4#16837796C211yesmaximal, characteristic, complemented
5#16837764C211yesmaximal, characteristic, complemented
6#16837627C212yesmaximal, complemented
7#16837623C212yesmaximal, complemented
8#16837559C212yesmaximal, complemented
9#16837554C212yesmaximal
10#16837457C211yesmaximal, characteristic, complemented
11C59×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2211yescharacteristic
13C2×D4×D59C2211yescharacteristic
14C2×Dic236C2212yescomplemented
15C2×#11745672C2212yescomplemented
16C2×#11745660C2212yes—
17C2×#11745670C2212yes—
18#14273727C2211yescharacteristic, complemented
19#14273718—21no—
20#14273716C2211yescharacteristic
21#14273715C2211yescharacteristic
22#14273714C2211yescharacteristic
23#14273713—21no—
24#14273713—21no—
25#14273707C2212yes—
26#14273703—21no—
27Q8×Dic59—21no—
28#14273692C2212yescomplemented
29#14273685—21no—
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—
48Q8×D59—42no—
49D4×D59—42no—
50C2×D236C2311yescharacteristic
51C2×C4×D59—21no—
52C2×C4×D59D411yescharacteristic
53C2×C4×D59D411yescharacteristic
54C2×C4×D59C2311yescharacteristic
55C2×Dic118—21no—
56C2×Dic118C2311yescharacteristic
57C2×Dic118C2312yes—
58C2×C8×C59C2312yes—
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2312yes—
61C22⋊C4×C59—21no—
62C22⋊C4×C59—21no—
63C42×C59C2311yescharacteristic
64C22⋊Dic59—21no—
65C22⋊Dic59—21no—
66#11745672—42no—
67#11745670—42no—
68(C2×D59)⋊C4—22no—
69(C2×D59)⋊C4—21no—
70(C2×D59)⋊C4—21no—
71(C2×D59)⋊C4—21no—
72(C2×D59)⋊C4—21no—
73C4⋊Dic59—21no—
74C4⋊Dic59—21no—
75C4⋊Dic59—22no—
76Dic59⋊C4—22no—
77C4×Dic59—22no—
78C4×Dic59D411yescharacteristic
79C4×Dic59D411yescharacteristic
80C4×Dic59C2311yescharacteristic
81C2×C59⋊C8C2312yes—
82Dic236—42no—
83#11745660—42no—
84C23×C59—21no—
85C22×D59—21no—
86C22×D59—42no—
87C22×D59—42no—
88C22×D59—42no—
89C22×D59C2×D411yescharacteristic
90Q8×C59—22no—
91Q8×C59—42no—
92D4×C59—22no—
93C2×C4×C59—22no—
94C2×C4×C59—21no—
95C2×C4×C59C2×D411yescharacteristic
96C2×C4×C59C2×D411yescharacteristic
97C2×C4×C59C2411yescharacteristic
98C22⋊D59—42no—
99C2×Dic59—22no—
100C2×Dic59—21no—
101C2×Dic59C2×D411yescharacteristic
102C2×Dic59C2×D411yescharacteristic
103C2×Dic59C2×D411yescharacteristic
104D236—22no—
105C4×D59—22no—
106C4×D59—22no—
107C4×D59—41no—
108C4×D59—42no—
109Dic118—22no—
110Dic118—22no—
111Dic118—22no—
112Dic118—42no—
113C8×C59—22no—
114C59⋊C8—22no—
115C22×C59—41no—
116C22×C59—41no—
117C22×C59—41no—
118C22×C59C22×D411yescharacteristic
119C2×D59—21no—
120C2×D59—21no—
121C2×D59—41no—
122C2×D59—41no—
123C2×D59—41no—
124C2×D59—84no—
125C2×D59#13712yes—
126C4×C59—21no—
127C4×C59—21no—
128C4×C59—41no—
129C4×C59—42no—
130C4×C59H(5,𝔽2)12yes—
131Dic59—21no—
132Dic59—21no—
133Dic59—21no—
134Dic59—41no—
135Dic59—42no—
136#3215—591nomaximal, Sylow
137C2×C59—81no—
138C2×C59#53511yescharacteristic
139C2×C59C2×#13711yescharacteristic
140C2×C59#57511yescharacteristic
141D59—22no—
142D59—81no—
143#533—591no—
144C2×#124—591no—
145#497—591no—
146#497—591no—
147#489—591no—
148#489D5911yescharacteristic, complemented
149#464—592no—
150#464—592no—
151#451—592no—
152#450—592no—
153#432—591no—
154C59#321511yescharacteristic, complemented, Sylow
155C22×Q8—591no—
156C22×D4—591no—
157C2×Q16—592no—
158C2×Q16—592no—
159C2×SD16—592no—
160C2×SD16—592no—
161C4⋊Q8—591no—
162C4⋊Q8C2×D5911yescharacteristic, complemented
163#125—1181no—
164#124—591no—
165#124—591no—
166#124—591no—
167#124—1181no—
168#124—1181no—
169#124C2×D5911yescharacteristic
170C22⋊Q8—592no—
171C22⋊Q8—1181no—
172C4×Q8—592no—
173C4×Q8—1181no—
174#117—1181no—
175C2×C22⋊C4—1181no—
176C2×C22⋊C4—1181no—
177C2×C42—591no—
178C4⋊C8—592no—
179#103—592no—
180#103C2×D5912yescomplemented
181#102—592no—
182#102C2×D5912yes—
183C22⋊C8—592no—
184#97—591no—
185#97C2×D5911yescharacteristic, complemented
186C24—1181no—
187C2×Q8—21no—
188C2×Q8—591no—
189C2×Q8—592no—
190C2×Q8—1181no—
191C2×Q8—2362no—
192C2×Q8C22×D5911yescharacteristic
193C2×D4—591no—
194C2×D4—1181no—
195C2×D4—2362no—
196C2×D4C22×D5911yescharacteristic
197C22×C4—591no—
198C22×C4—591no—
199C22×C4—591no—
200C22×C4—1181no—
201Q16—2362no—
202Q16—2362no—
203SD16—2362no—
204SD16—2362no—
205C2×C8—592no—
206C2×C8C22×D5912yes—
207C4⋊C4—21no—
208C4⋊C4—1182no—
209C4⋊C4—1182no—
210C4⋊C4—1181no—
211C4⋊C4—1181no—
212C4⋊C4C22×D5912yes—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—1181no—
216C22⋊C4—1181no—
217C22⋊C4—1182no—
218C22⋊C4—1181no—
219C22⋊C4—1181no—
220C22⋊C4—1181no—
221C22⋊C4—1181no—
222C42—591no—
223C42—591no—
224C42—591no—
225C42—1182no—
226C42C22×D5911yescharacteristic
227C23—21no—
228C23—591no—
229C23—1181no—
230C23—2362no—
231C23—2362no—
232C23—2362no—
233Q8—22no—
234Q8—42no—
235Q8—1182no—
236Q8—1182no—
237Q8—1182no—
238Q8—2362no—
239D4—22no—
240D4—1182no—
241D4—2362no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—591no—
245C2×C4—591no—
246C2×C4—591no—
247C2×C4—1182no—
248C2×C4—1182no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4—2361no—
252C2×C4—2362no—
253C2×C4D4×D5911yescharacteristic
254C2×C4D4×D5911yescharacteristic
255C2×C4C23×D5911yescharacteristic
256C8—22no—
257C8—1182no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—592no—
262C22—1181no—
263C22—1181no—
264C22—4724no—
265C22—2361no—
266C22—2361no—
267C22—2361no—
268C22C2×D4×D5911yescharacteristic
269C4—21no—
270C4—21no—
271C4—42no—
272C4—41no—
273C4—1181no—
274C4—1181no—
275C4—1181no—
276C4—2361no—
277C4—2362no—
278C4#1427377312yes—
279C2—81no—
280C2—1182no—
281C2—4721no—
282C2#1683797011yescharacteristic
283C2#137×D5911yescharacteristic
284C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#489C2
socleC22×C59C22×D4
hypercenter#489D59
hypocenterC59#3215
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. #16837957C2semidirect
3. #16837797C2semidirect
4. #16837796C2semidirect
5. #16837764C2semidirect
6. #16837627C2semidirect
7. #16837623C2semidirect
8. #16837559C2semidirect
10. #16837457C2semidirect
11. C59×#489C2semidirect
14. C2×Dic236C22semidirect
15. C2×#11745672C22semidirect
18. #14273727C22semidirect
28. #14273692C22semidirect
33. Dic59⋊C8C22semidirect
34. #14273650C22semidirect
37. #14273638C22semidirect
38. C4⋊Q8×C59C22semidirect
40. #103×C59C22semidirect
42. #97×C59C22semidirect
148. #489D59semidirect
154. C59#3215semidirect
162. C4⋊Q8C2×D59semidirect
180. #103C2×D59semidirect
185. #97C2×D59semidirect