Finite Group Databasebeta

← #21432171

Subgroups — #21432171

Order 7552.

456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14273722C212yesmaximal, complemented
2#16837336C212yesmaximal, complemented
3#16837326C212yesmaximal, complemented
4#16837324C212yesmaximal, complemented
5#16837324C212yesmaximal, complemented
6#16837320C212yesmaximal
7#16837319C211yesmaximal, characteristic
8#16837271C211yesmaximal, characteristic, complemented
9C59×#398C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11#14273722—28no—
12C2×C4⋊Dic59C2212yes—
13C2×C4⋊Dic59C2211yescharacteristic
14C2×Dic59⋊C4C2212yes—
15C2×Dic59⋊C4C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×(C2×D59)⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×C4×Dic59C2211yescharacteristic
25C59⋊#95C2211yescharacteristic
26C59⋊#95C2212yes—
27C2×C4⋊C4×C59C2212yes—
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2211yescharacteristic
30#95×C59C2212yes—
31#95×C59C2211yescharacteristic
32C23×D59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2312yes—
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C2×D236—42no—
42C2×D236—41no—
43C4⋊C4×C59—24no—
44C4⋊C4×C59—41no—
45C4⋊C4×C59—41no—
46(C2×D59)⋊C4—24no—
47(C2×D59)⋊C4—24no—
48(C2×D59)⋊C4—24no—
49(C2×D59)⋊C4—42no—
50(C2×D59)⋊C4—42no—
51(C2×D59)⋊C4—42no—
52C4⋊Dic59—24no—
53C4⋊Dic59—41no—
54Dic59⋊C4—24no—
55Dic59⋊C4—42no—
56Dic59⋊C4—42no—
57Dic59⋊C4—42no—
58C4×Dic59D414yescomplemented
59C23×C59C2411yescharacteristic
60C22×D59—22no—
61C22×D59—22no—
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C22×D59—22no—
66C22×D59—22no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59C2×D412yes—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59C2×D414yes—
89D236—44no—
90C22×C59C22×D411yescharacteristic
91C22×C59H(5,𝔽2)11yescharacteristic
92C22×C59H(5,𝔽2)12yes—
93C22×C592−1+411yescharacteristic
94C22×C592−1+412yes—
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—42no—
98C2×D59—42no—
99C2×D59—42no—
100C2×D59—42no—
101C2×D59—42no—
102C4×C59—22no—
103C4×C59—42no—
104C4×C59—42no—
105C4×C59—41no—
106C4×C59—41no—
107Dic59—24no—
108Dic59—42no—
109Dic59—42no—
110#2823—591nomaximal, Sylow
111C2×C59#53711yescharacteristic
112C2×C59#53712yes—
113C2×C59#56011yescharacteristic
114C2×C59#56311yescharacteristic
115C2×C59#56312yes—
116D59—82no—
117C2×#126—592no—
118#398—592no—
119#398D5911yescharacteristic, complemented
120#396—592no—
121#396—592no—
122#396—592no—
123#394—591no—
124#394—592no—
125#384—591no—
126C59#282311yescharacteristic, complemented, Sylow
127C22×D4—591no—
128#126—1188no—
129C2×C4⋊C4—592no—
130C2×C4⋊C4—592no—
131C2×C4⋊C4—592no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—591no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4C2×D5912yes—
136C2×C4⋊C4C2×D5911yescharacteristic
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C22⋊C4—592no—
139C2×C22⋊C4—592no—
140C2×C22⋊C4—592no—
141C2×C22⋊C4—592no—
142C2×C22⋊C4—592no—
143C2×C22⋊C4—592no—
144C2×C42—591no—
145#95—591no—
146#95—592no—
147#95C2×D5912yes—
148#95C2×D5911yescharacteristic
149C24—592no—
150C2×D4—2361no—
151C2×D4—2362no—
152C22×C4—592no—
153C22×C4—592no—
154C22×C4—592no—
155C22×C4C22×D5911yescharacteristic
156C22×C4C22×D5912yes—
157C22×C4C22×D5912yes—
158C22×C4C22×D5911yescharacteristic
159C22×C4C22×D5911yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—1184no—
164C4⋊C4—1184no—
165C4⋊C4—2362no—
166C4⋊C4—2362no—
167C4⋊C4—2362no—
168C4⋊C4—2361no—
169C22⋊C4—1184no—
170C22⋊C4—1184no—
171C22⋊C4—1184no—
172C22⋊C4—2362no—
173C22⋊C4—2362no—
174C22⋊C4—2362no—
175C42—594no—
176C23—1182no—
177C23—1182no—
178C23—1182no—
179C23—1182no—
180C23—1182no—
181C23—1182no—
182C23—1182no—
183C23C23×D5911yescharacteristic
184D4—2364no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—594no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1182no—
206C2×C4D4×D5912yes—
207C22—2362no—
208C22—2362no—
209C22—2362no—
210C22—2362no—
211C22—2362no—
212C22—2362no—
213C22—2362no—
214C22C2×D4×D5911yescharacteristic
215C22#1427377211yescharacteristic
216C22#1427377312yes—
217C22#1427377411yescharacteristic
218C22#1427377512yes—
219C4—22no—
220C4—42no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—1184no—
225C4—2362no—
226C4—2362no—
227C2—4722no—
228C2#1683797911yescharacteristic
229C2#1683798212yes—
230C2#1683814211yescharacteristic
231C2#1683815111yescharacteristic
232C2#1683815612yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2823
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14273722C2semidirect
2. #16837336C2semidirect
3. #16837326C2semidirect
4. #16837324C2semidirect
5. #16837324C2semidirect
8. #16837271C2semidirect
9. C59×#398C2semidirect
58. C4×Dic59D4semidirect
119. #398D59semidirect
126. C59#2823semidirect