Finite Group Databasebeta

← #21431025

Subgroups — #21431025

Order 7552.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273712C212yesmaximal
2#16837335C212yesmaximal, complemented
3#16837329C212yesmaximal, complemented
4#16837328C212yesmaximal, complemented
5#16837304C211yesmaximal, characteristic
6#16837300C211yesmaximal, characteristic, complemented
7#16837276C212yesmaximal, complemented
8#16837273C212yesmaximal, complemented
9C59×#389C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C22×C4×D59C2212yes—
12#14273712—28no—
13C2×C4⋊Dic59C2211yescharacteristic
14C2×C4⋊Dic59C2211yescharacteristic
15C2×C4⋊Dic59C2211yescharacteristic
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—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C59⋊#95C2212yes—
27C2×C4⋊C4×C59C2212yes—
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2211yescharacteristic
30C2×C42×C59C2211yescharacteristic
31#95×C59C2212yes—
32C23×D59C2312yes—
33C22×C4×C59C2312yes—
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C22×Dic59C2312yes—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C2×D236—41no—
42C2×D236—41no—
43C2×D236D414yes—
44C2×C4×D59—24no—
45C2×C4×D59—42no—
46C2×C4×D59—42no—
47C4⋊C4×C59—24no—
48C4⋊C4×C59—22no—
49C4⋊C4×C59—41no—
50C42×C59—41no—
51(C2×D59)⋊C4—24no—
52(C2×D59)⋊C4—24no—
53(C2×D59)⋊C4—24no—
54(C2×D59)⋊C4—24no—
55(C2×D59)⋊C4—24no—
56C4⋊Dic59—22no—
57C4⋊Dic59—41no—
58C4⋊Dic59—41no—
59Dic59⋊C4—24no—
60Dic59⋊C4—42no—
61C23×C59C2411yescharacteristic
62C22×D59—22no—
63C22×D59—22no—
64C22×D59—22no—
65C22×D59—22no—
66C22×D59—22no—
67C22×D59—22no—
68C22×D59C2×D414yes—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—21no—
72C2×C4×C59—21no—
73C2×C4×C59—21no—
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59C2×D412yes—
82C2×C4×C59#4112yes—
83C2×C4×C59#4112yes—
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—
94C4×D59—48no—
95C22×C59C22×D411yescharacteristic
96C22×C59C2×#4111yescharacteristic
97C22×C59C2×#4111yescharacteristic
98C22×C59H(5,𝔽2)11yescharacteristic
99C22×C59H(5,𝔽2)11yescharacteristic
100C22×C592−1+411yescharacteristic
101C22×C592−1+411yescharacteristic
102C2×D59—24no—
103C2×D59—24no—
104C2×D59—24no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—42no—
108C2×D59—42no—
109C4×C59—22no—
110C4×C59—22no—
111C4×C59—22no—
112C4×C59—42no—
113C4×C59—42no—
114Dic59—42no—
115Dic59—42no—
116Dic59—42no—
117#2724—591nomaximal, Sylow
118C2×C59#53411yescharacteristic
119C2×C59#53911yescharacteristic
120C2×C59#53911yescharacteristic
121C2×C59#54711yescharacteristic
122C2×C59#54711yescharacteristic
123C2×C59#55911yescharacteristic
124C2×C59#56311yescharacteristic
125D59—44no—
126C2×#123—592no—
127#398—592no—
128#397—592no—
129#397—592no—
130#390—591no—
131#389—591no—
132#389D5911yescharacteristic, complemented
133#385—592no—
134#385—592no—
135C59#272411yescharacteristic, complemented, Sylow
136C22×D4—591no—
137C23×C4—592no—
138#123—1188no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4—591no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4—592no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4C2×D5912yes—
145C2×C4⋊C4C2×D5911yescharacteristic
146C2×C4⋊C4C2×D5911yescharacteristic
147C2×C22⋊C4—592no—
148C2×C22⋊C4—592no—
149C2×C22⋊C4—592no—
150C2×C22⋊C4—592no—
151C2×C22⋊C4—592no—
152C2×C42C2×D5911yescharacteristic
153#95—592no—
154#95—592no—
155#95—592no—
156#95—592no—
157#95C2×D5912yes—
158C24—592no—
159C2×D4—594no—
160C2×D4—2361no—
161C2×D4—2361no—
162C22×C4—592no—
163C22×C4—592no—
164C22×C4—592no—
165C22×C4—1184no—
166C22×C4—2362no—
167C22×C4—2362no—
168C22×C4C22×D5912yes—
169C22×C4C22×D5912yes—
170C22×C4C22×D5911yescharacteristic
171C22×C4C22×D5911yescharacteristic
172C22×C4C22×D5911yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—24no—
175C4⋊C4—41no—
176C4⋊C4—1184no—
177C4⋊C4—1182no—
178C4⋊C4—2362no—
179C4⋊C4—2361no—
180C4⋊C4—2361no—
181C22⋊C4—1184no—
182C22⋊C4—1184no—
183C22⋊C4—1184no—
184C22⋊C4—1184no—
185C22⋊C4—1184no—
186C42—41no—
187C23—594no—
188C23—1182no—
189C23—1182no—
190C23—1182no—
191C23—1182no—
192C23—1182no—
193C23—1182no—
194C23C23×D5911yescharacteristic
195D4—2364no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1182no—
216C2×C4—1182no—
217C2×C4—2368no—
218C2×C4#1174568512yes—
219C2×C4D4×D5912yes—
220C2×C4#1174568912yes—
221C22—1184no—
222C22—1184no—
223C22—1184no—
224C22—2362no—
225C22—2362no—
226C22—2362no—
227C22—2362no—
228C22C2×D4×D5911yescharacteristic
229C22C2×#1174568511yescharacteristic
230C22C2×#1174568911yescharacteristic
231C22#1427377211yescharacteristic
232C22#1427377311yescharacteristic
233C22#1427377411yescharacteristic
234C22#1427377511yescharacteristic
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—2362no—
241C4—2362no—
242C4—2362no—
243C2—2364no—
244C2#1683796011yescharacteristic
245C2#1683799911yescharacteristic
246C2#1683800111yescharacteristic
247C2#1683805511yescharacteristic
248C2#1683805711yescharacteristic
249C2#1683813711yescharacteristic
250C2#1683815611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#389C2
hypercenter#389D59
hypocenterC59#2724
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #16837335C2semidirect
3. #16837329C2semidirect
4. #16837328C2semidirect
6. #16837300C2semidirect
7. #16837276C2semidirect
8. #16837273C2semidirect
9. C59×#389C2semidirect
132. #389D59semidirect
135. C59#2724semidirect