Finite Group Databasebeta

← #21435085

Subgroups — #21435085

Order 7552.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837952C211yesmaximal, characteristic, complemented
2C2×#14273715C211yesmaximal, characteristic, complemented
3#16837791C212yesmaximal, complemented
4#16837762C212yesmaximal, complemented
5#16837618C214yesmaximal, complemented
6#16837543C212yesmaximal, complemented
7#16837538C212yesmaximal, complemented
8C59×#432C211yesmaximal, characteristic, complemented
9C2×#11745685—21no—
10C22×Dic118C2211yescharacteristic
11C22×D236C2211yescharacteristic
12C2×#11745660C2214yescomplemented
13C2×D472C2214yes—
14#14273727C2211yescharacteristic, complemented
15#14273724C2211yescharacteristic, complemented
16#14273715—21no—
17#14273715—21no—
18#14273715—21no—
19#14273715C2212yes—
20#14273715C2212yes—
21#14273701—21no—
22#14273701C2212yes—
23C4×D236—21no—
24C4×D236C2212yescomplemented
25C2×(C2×D59)⋊C4—21no—
26C2×(C2×D59)⋊C4—21no—
27#14273652C2214yescomplemented
28#14273649C2214yes—
29C2×C42×C59C2211yescharacteristic
30C4⋊C8×C59C2212yescomplemented
31C22⋊C8×C59C2212yes—
32#97×C59C2212yescomplemented
33C23×D59—21no—
34C22×C4×C59D411yescharacteristic
35C22×C4×C59D411yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C2×C22⋊D59—22no—
38C22×Dic59—21no—
39#11745685—44no—
40C2×D236—21no—
41C2×D236—21no—
42C2×D236—21no—
43C2×D236—42no—
44C2×D236C2312yes—
45C2×D236C2312yes—
46C2×C4×D59—22no—
47C2×Dic118—21no—
48C2×Dic118—21no—
49C2×Dic118—42no—
50C2×Dic118C2312yes—
51C2×C8×C59C2314yes—
52C42×C59D411yescharacteristic
53C42×C59D411yescharacteristic
54C42×C59C2311yescharacteristic
55C42×C59C2311yescharacteristic
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62C4⋊Dic59—21no—
63C4⋊Dic59C2312yes—
64D472—44no—
65#11745660—44no—
66C23×C59C2×D411yescharacteristic
67C22×D59—22no—
68C22×D59—22no—
69C22×D59—42no—
70C22×D59—42no—
71C22×D59—42no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—41no—
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2411yescharacteristic
81C22⋊D59—44no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—42no—
85D236—24no—
86D236—24no—
87D236—42no—
88D236—42no—
89D236—42no—
90C4×D59—44no—
91Dic118—24no—
92Dic118—42no—
93Dic118—42no—
94C8×C59—24no—
95C22×C59—21no—
96C22×C59—21no—
97C22×C59AGL(1,ℤ/8)12yes—
98C22×C59C22×D411yescharacteristic
99C2×D59—42no—
100C2×D59—42no—
101C2×D59—42no—
102C2×D59—42no—
103C2×D59—42no—
104C2×D59—42no—
105C2×D59—84no—
106C4×C59—21no—
107C4×C59—21no—
108C4×C59—21no—
109C4×C59—21no—
110C4×C59—21no—
111C4×C59H(5,𝔽2)12yes—
112Dic59—42no—
113Dic59—42no—
114#3213—591nomaximal, Sylow
115C2×C59—22no—
116C2×C59#53511yescharacteristic
117C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
118C2×C59#57511yescharacteristic
119D59—82no—
120D59—82no—
121#532—591no—
122C2×#124—591no—
123#496—592no—
124#489—592no—
125#463—594no—
126#448—592no—
127#447—592no—
128#432D5911yescharacteristic, complemented
129C59#321311yescharacteristic, complemented, Sylow
130C2×#41—1181no—
131C22×Q8—591no—
132C22×D4—591no—
133C2×SD16—594no—
134C2×D8—594no—
135C4⋊Q8—591no—
136#127—591no—
137#124—592no—
138#124—592no—
139#124—1181no—
140#124—1181no—
141#124—1181no—
142#121—592no—
143#121—1181no—
144C4×D4—592no—
145C4×D4—1181no—
146C2×C22⋊C4—1181no—
147C2×C22⋊C4—1181no—
148C2×C42C2×D5911yescharacteristic
149C4⋊C8C2×D5912yescomplemented
150#103—594no—
151#102—594no—
152C22⋊C8C2×D5912yes—
153#97C2×D5912yescomplemented
154C24—1181no—
155#41—2364no—
156C2×Q8—592no—
157C2×Q8—1181no—
158C2×Q8—1181no—
159C2×Q8—2362no—
160C2×D4—592no—
161C2×D4—592no—
162C2×D4—1182no—
163C2×D4—1181no—
164C2×D4—1181no—
165C2×D4—1181no—
166C2×D4—2362no—
167C22×C4—1181no—
168C22×C4—1182no—
169C22×C4D23611yescharacteristic
170C22×C4D23611yescharacteristic
171C22×C4C22×D5911yescharacteristic
172SD16—2364no—
173D8—2364no—
174C2×C8C22×D5914yes—
175C4⋊C4—592no—
176C4⋊C4—1181no—
177C22⋊C4—1182no—
178C22⋊C4—1182no—
179C22⋊C4—1182no—
180C22⋊C4—1182no—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C42D23611yescharacteristic
184C42D23611yescharacteristic
185C42C22×D5911yescharacteristic
186C42C22×D5911yescharacteristic
187C23—1182no—
188C23—1182no—
189C23—2362no—
190C23—2362no—
191C23—2362no—
192C23C2×D23611yescharacteristic
193Q8—1184no—
194Q8—2362no—
195Q8—2362no—
196D4—1184no—
197D4—1184no—
198D4—2362no—
199D4—2362no—
200D4—2362no—
201D4—2364no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—2364no—
208C2×C4—2362no—
209C2×C4C2×D23611yescharacteristic
210C2×C4C2×D23611yescharacteristic
211C2×C4C2×D23611yescharacteristic
212C2×C4C2×D23611yescharacteristic
213C2×C4C2×D23611yescharacteristic
214C2×C4C23×D5911yescharacteristic
215C8—24no—
216C22—21no—
217C22—21no—
218C22—4724no—
219C22—2362no—
220C22—2362no—
221C22—2362no—
222C22—2362no—
223C22—2362no—
224C22—2362no—
225C22#1427375512yes—
226C22C22×D23611yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—2362no—
233C4—2362no—
234C4#1427377312yes—
235C2—22no—
236C2—4722no—
237C2—4722no—
238C2#1683797111yescharacteristic
239C2C2×#1427375511yescharacteristic
240C2#1683820211yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#432C2
socleC22×C59C22×D4
hypercenter#432D59
hypocenterC59#3213
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16837952C2semidirect
2. C2×#14273715C2semidirect
3. #16837791C2semidirect
4. #16837762C2semidirect
5. #16837618C2semidirect
6. #16837543C2semidirect
7. #16837538C2semidirect
8. C59×#432C2semidirect
12. C2×#11745660C22semidirect
14. #14273727C22semidirect
15. #14273724C22semidirect
24. C4×D236C22semidirect
27. #14273652C22semidirect
30. C4⋊C8×C59C22semidirect
32. #97×C59C22semidirect
128. #432D59semidirect
129. C59#3213semidirect
149. C4⋊C8C2×D59semidirect
153. #97C2×D59semidirect