Finite Group Databasebeta

← #21432189

Subgroups — #21432189

Order 7552.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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#16837343C212yesmaximal, complemented
2#16837338C211yesmaximal, characteristic, complemented
3#16837328C212yesmaximal, complemented
4#16837324C212yesmaximal, complemented
5#16837320C212yesmaximal, complemented
6#16837317C212yesmaximal, complemented
7#16837311C211yesmaximal, characteristic
8#16837281C212yesmaximal, complemented
9C59×#385C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C22⋊D59C2212yes—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×Dic59⋊C4C2212yes—
14C2×Dic59⋊C4C2212yes—
15C2×C22⋊Dic59C2212yes—
16C2×(C2×D59)⋊C4C2212yes—
17C2×(C2×D59)⋊C4C2212yes—
18C2×(C2×D59)⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2211yescharacteristic
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C23×C4×C59C2211yescharacteristic
27C2×C4⋊C4×C59C2212yes—
28C2×C22⋊C4×C59C2211yescharacteristic
29C2×C22⋊C4×C59C2211yescharacteristic
30#95×C59C2212yes—
31C24×C59C2311yescharacteristic
32C23×D59C2312yes—
33C22×C4×C59—41no—
34C22×C4×C59—42no—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2312yes—
37C22×C4×C59C2312yes—
38C22×C4×C59C2311yescharacteristic
39C2×C22⋊D59—24no—
40C2×C22⋊D59—42no—
41C2×C22⋊D59—42no—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C22×Dic59C2312yes—
45C2×D236—42no—
46C2×D236—41no—
47C4⋊C4×C59—42no—
48C22⋊C4×C59—22no—
49C22⋊C4×C59—41no—
50C22⋊Dic59—42no—
51(C2×D59)⋊C4—42no—
52(C2×D59)⋊C4—42no—
53(C2×D59)⋊C4—42no—
54(C2×D59)⋊C4—42no—
55(C2×D59)⋊C4—42no—
56C4⋊Dic59—41no—
57Dic59⋊C4—42no—
58Dic59⋊C4—42no—
59C23×C59—22no—
60C23×C59—21no—
61C23×C59—22no—
62C23×C59—21no—
63C23×C59#4112yes—
64C23×C59C2411yescharacteristic
65C22×D59—22no—
66C22×D59—22no—
67C22×D59—22no—
68C22×D59—22no—
69C22×D59—22no—
70C22×D59—22no—
71C22×D59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59—44no—
83C22⋊D59—48no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59—22no—
93D236—44no—
94C22×C59—24no—
95C22×C59—22no—
96C22×C59—41no—
97C22×C59—41no—
98C22×C59—42no—
99C22×C59C2×#4111yescharacteristic
100C22×C59H(5,𝔽2)12yes—
101C22×C59H(5,𝔽2)11yescharacteristic
102C22×C59H(5,𝔽2)12yes—
103C22×C592−1+411yescharacteristic
104C2×D59—42no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—42no—
108C2×D59—42no—
109C2×D59—42no—
110C2×D59—42no—
111C4×C59—42no—
112C4×C59—41no—
113C4×C59—41no—
114C4×C59—42no—
115Dic59—42no—
116Dic59—42no—
117Dic59—42no—
118#2826—591nomaximal, Sylow
119C2×C59—42no—
120C2×C59#53812yes—
121C2×C59#53911yescharacteristic
122C2×C59#56011yescharacteristic
123C2×C59#56011yescharacteristic
124C2×C59#56212yes—
125D59—82no—
126#400—592no—
127#399—591no—
128#397—592no—
129#396—592no—
130#394—592no—
131#394—592no—
132#392—591no—
133#386—592no—
134#385D5911yescharacteristic, complemented
135C59#282611yescharacteristic, complemented, Sylow
136C22×D4—592no—
137C22×D4—591no—
138C23×C4C2×D5911yescharacteristic
139C2×C4⋊C4—592no—
140C2×C4⋊C4—592no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4C2×D5912yes—
143C2×C22⋊C4—592no—
144C2×C22⋊C4—592no—
145C2×C22⋊C4—592no—
146C2×C22⋊C4—592no—
147C2×C22⋊C4—592no—
148C2×C22⋊C4—592no—
149C2×C22⋊C4C2×D5911yescharacteristic
150C2×C22⋊C4C2×D5911yescharacteristic
151#95—592no—
152#95—592no—
153#95—591no—
154#95—592no—
155#95—591no—
156#95C2×D5912yes—
157C24—592no—
158C24C22×D5911yescharacteristic
159C2×D4—1184no—
160C2×D4—2361no—
161C2×D4—2362no—
162C2×D4—2362no—
163C2×D4—2362no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4—592no—
167C22×C4—592no—
168C22×C4—592no—
169C22×C4C22×D5912yes—
170C22×C4C22×D5911yescharacteristic
171C22×C4C22×D5912yes—
172C22×C4C22×D5911yescharacteristic
173C4⋊C4—42no—
174C4⋊C4—2362no—
175C4⋊C4—2362no—
176C4⋊C4—2361no—
177C22⋊C4—22no—
178C22⋊C4—41no—
179C22⋊C4—2362no—
180C22⋊C4—2362no—
181C22⋊C4—2362no—
182C22⋊C4—2362no—
183C22⋊C4—2362no—
184C22⋊C4—2362no—
185C23—21no—
186C23—22no—
187C23—22no—
188C23—21no—
189C23—1182no—
190C23—1182no—
191C23—1182no—
192C23—1182no—
193C23—1182no—
194C23—1182no—
195C23—1182no—
196C23#1174568512yes—
197C23C23×D5911yescharacteristic
198D4—2364no—
199D4—2368no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—1182no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1182no—
220C22—24no—
221C22—22no—
222C22—42no—
223C22—41no—
224C22—41no—
225C22—2362no—
226C22—2362no—
227C22—2362no—
228C22—2362no—
229C22—2362no—
230C22—2362no—
231C22—2362no—
232C22C2×#1174568511yescharacteristic
233C22#1427377212yes—
234C22#1427377211yescharacteristic
235C22#1427377312yes—
236C22#1427377511yescharacteristic
237C4—42no—
238C4—42no—
239C4—41no—
240C4—41no—
241C4—2362no—
242C4—2362no—
243C4—2362no—
244C2—42no—
245C2—4722no—
246C2#1683798512yes—
247C2#1683799911yescharacteristic
248C2#1683814111yescharacteristic
249C2#1683814211yescharacteristic
250C2#1683814812yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#385C2
hypercenter#385D59
hypocenterC59#2826
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #16837343C2semidirect
2. #16837338C2semidirect
3. #16837328C2semidirect
4. #16837324C2semidirect
5. #16837320C2semidirect
6. #16837317C2semidirect
8. #16837281C2semidirect
9. C59×#385C2semidirect
134. #385D59semidirect
135. C59#2826semidirect