Finite Group Databasebeta

← #21433323

Subgroups — #21433323

Order 7552.

994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#14273753C212yesmaximal, complemented
2#16837913C211yesmaximal, characteristic, complemented
3#16837553C214yesmaximal, complemented
4#16837536C214yesmaximal, complemented
5#16837407C212yesmaximal, complemented
6#16837366C211yesmaximal, characteristic, complemented
7C23×D4×C59C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic, complemented
9#14273753—28no—
10C2×#11745670C2214yescomplemented
11C2×#11745669C2214yescomplemented
12C2×#11745664C2212yescomplemented
13#14273710—21no—
14#14273706C2212yescomplemented
15#14273701C2212yescomplemented
16#14273696—21no—
17C4×C22⋊D59—22no—
18#14273686C2211yescharacteristic, complemented
19#14273648C2218yescomplemented
20C22⋊(C59⋊C8)C2214yescomplemented
21C25×C59—21no—
22C22×D4×C59—28no—
23C22×D4×C59—22no—
24C22×D4×C59—21no—
25C22×D4×C59C2214yes—
26C22×D4×C59C2212yes—
27C23×C4×C59C2211yescharacteristic
28C24×C59—28no—
29C24×C59—24no—
30C24×C59—22no—
31C24×C59—48no—
32C24×C59D411yescharacteristic
33C2×D4×C59—28no—
34C2×D4×C59—216no—
35C2×D4×C59—216no—
36C2×D4×C59—24no—
37C2×D4×C59—22no—
38C2×D4×C59—24no—
39C2×D4×C59D418yescomplemented
40C2×D4×C59C2314yes—
41C22×C4×C59—24no—
42C22×C4×C59D412yes—
43C22×C4×C59D411yescharacteristic
44C22×C4×C59C2312yes—
45C22×C4×C59C2311yescharacteristic
46C2×C22⋊D59—22no—
47C2×C22⋊D59—21no—
48#11745685—24no—
49C2×D236C2311yescharacteristic, complemented
50C2×C4×D59—21no—
51C2×Dic118C2311yescharacteristic, complemented
52C22⋊Dic59—21no—
53C22⋊Dic59—22no—
54#11745670—28no—
55#11745669—28no—
56(C2×D59)⋊C4—22no—
57C4⋊Dic59C2312yescomplemented
58Dic59⋊C4—22no—
59C4×Dic59—21no—
60#11745664—24no—
61C2×C59⋊C8C2314yescomplemented
62C23×C59—22no—
63C23×C59—24no—
64C23×C59—216no—
65C23×C59—28no—
66C23×C59—24no—
67C23×C59—432no—
68C23×C59—48no—
69C23×C59—48no—
70C23×C59—48no—
71C23×C59C2×D411yescharacteristic
72C23×C59C2×D412yes—
73C22×D59—21no—
74D4×C59—216no—
75D4×C59—28no—
76D4×C59—24no—
77D4×C59C2×D418yes—
78C2×C4×C59—22no—
79C2×C4×C59—24no—
80C2×C4×C59—24no—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D414yes—
84C2×C4×C59C2411yescharacteristic
85C22⋊D59—42no—
86C22⋊D59—44no—
87C2×Dic59—22no—
88C2×Dic59—21no—
89D236—22no—
90C4×D59—42no—
91Dic118—22no—
92C59⋊C8—24no—
93C22×C59—28no—
94C22×C59—22no—
95C22×C59—22no—
96C22×C59—22no—
97C22×C59—28no—
98C22×C59—416no—
99C22×C59—432no—
100C22×C59—48no—
101C22×C59#12012yes—
102C22×C59AGL(1,ℤ/8)14yescomplemented
103C22×C59C22×D411yescharacteristic
104C2×D59—41no—
105C2×D59—42no—
106C4×C59—22no—
107C4×C59#12012yes—
108C4×C59C22×D412yes—
109Dic59—41no—
110Dic59—42no—
111#3003—591nomaximal, Sylow
112C2×C59—22no—
113C2×C59—24no—
114C2×C59—48no—
115C2×C59C2×#12011yescharacteristic
116C2×C59C2×AGL(1,ℤ/8)12yes—
117D59—81no—
118C23×D4D5911yescharacteristic, complemented
119C2×AGL(1,ℤ/8)—592no—
120#525—591no—
121#450—594no—
122#447—594no—
123#418—592no—
124#407—591no—
125C59#300311yescharacteristic, complemented, Sylow
126C25—21no—
127C2×#41—591no—
128C22×D4—28no—
129C22×D4—22no—
130C22×D4—21no—
131C22×D4C2×D5914yes—
132C22×D4C2×D5912yes—
133C23×C4C2×D5911yescharacteristic
134AGL(1,ℤ/8)—1188no—
135C2×SD16—594no—
136C2×D8—594no—
137C2×M16—592no—
138#123—1181no—
139C22⋊Q8—592no—
140#121—592no—
141#120—1181no—
142C4×D4—1182no—
143#117—591no—
144#102—598no—
145C22⋊C8—594no—
146C24—28no—
147C24—24no—
148C24—22no—
149C24—48no—
150C24C22⋊D5911yescharacteristic
151#41—1184no—
152C2×Q8—591no—
153C2×D4—28no—
154C2×D4—216no—
155C2×D4—216no—
156C2×D4—24no—
157C2×D4—22no—
158C2×D4—24no—
159C2×D4—591no—
160C2×D4—1182no—
161C2×D4—1181no—
162C2×D4C22⋊D5918yescomplemented
163C2×D4C22×D5914yes—
164C22×C4—24no—
165C22×C4—1181no—
166C22×C4C22⋊D5912yes—
167C22×C4C22⋊D5911yescharacteristic
168C22×C4C22×D5912yes—
169C22×C4C22×D5911yescharacteristic
170SD16—1188no—
171D8—1188no—
172M16—1184no—
173C2×C8—594no—
174C4⋊C4—592no—
175C4⋊C4—1182no—
176C22⋊C4—1181no—
177C22⋊C4—1182no—
178C22⋊C4—1182no—
179C42—1181no—
180C23—22no—
181C23—24no—
182C23—216no—
183C23—28no—
184C23—24no—
185C23—432no—
186C23—48no—
187C23—48no—
188C23—48no—
189C23—1181no—
190C23C2×C22⋊D5911yescharacteristic
191C23C2×C22⋊D5912yes—
192Q8—1182no—
193D4—216no—
194D4—28no—
195D4—24no—
196D4—1182no—
197D4—2362no—
198D4—2364no—
199D4C2×C22⋊D5918yes—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—1182no—
204C2×C4—1181no—
205C2×C4—2362no—
206C2×C4C2×C22⋊D5912yes—
207C2×C4C2×C22⋊D5911yescharacteristic
208C2×C4C2×C22⋊D5914yes—
209C2×C4C23×D5911yescharacteristic
210C8—1184no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—28no—
216C22—416no—
217C22—432no—
218C22—48no—
219C22—2361no—
220C22—2362no—
221C22#1427369612yes—
222C22#1427375314yescomplemented
223C22C22×C22⋊D5911yescharacteristic
224C4—22no—
225C4—2361no—
226C4—2362no—
227C4#1427369612yes—
228C4C22×C22⋊D5912yes—
229C2—22no—
230C2—24no—
231C2—48no—
232C2—4721no—
233C2C2×#1427369611yescharacteristic
234C2C2×#1427375312yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC23×D4×C59C2
socleC22×C59C22×D4
hypercenterC23×D4D59
hypocenterC59#3003
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14273753C2semidirect
2. #16837913C2semidirect
3. #16837553C2semidirect
4. #16837536C2semidirect
5. #16837407C2semidirect
6. #16837366C2semidirect
7. C23×D4×C59C2semidirect
8. C2×#11745685C22semidirect
10. C2×#11745670C22semidirect
11. C2×#11745669C22semidirect
12. C2×#11745664C22semidirect
14. #14273706C22semidirect
15. #14273701C22semidirect
18. #14273686C22semidirect
19. #14273648C22semidirect
20. C22⋊(C59⋊C8)C22semidirect
39. C2×D4×C59D4semidirect
49. C2×D236C23semidirect
51. C2×Dic118C23semidirect
57. C4⋊Dic59C23semidirect
61. C2×C59⋊C8C23semidirect
102. C22×C59AGL(1,ℤ/8)semidirect
118. C23×D4D59semidirect
125. C59#3003semidirect
162. C2×D4C22⋊D59semidirect
222. C22#14273753semidirect