Finite Group Databasebeta

← #21430439

Subgroups — #21430439

Order 7552.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273708C212yesmaximal
2C2×#14273704C212yesmaximal, complemented
3#16837336C212yesmaximal, complemented
4#16837330C212yesmaximal, complemented
5#16837322C211yesmaximal, characteristic, complemented
6#16837290C212yesmaximal, complemented
7#16837277C212yesmaximal, complemented
8#16837271C211yesmaximal, characteristic, complemented
9C59×#394C211yesmaximal, characteristic
10C22×Dic118C2211yescharacteristic
11C23×Dic59C2212yes—
12#14273708—28no—
13#14273704—28no—
14C2×C4⋊Dic59C2212yes—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×C22⋊Dic59C2212yes—
21C2×C22⋊Dic59C2212yes—
22C2×C22⋊Dic59C2212yes—
23C2×C4×Dic59C2211yescharacteristic
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C59⋊#95C2212yes—
27C59⋊#95C2211yescharacteristic
28C22×D4×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2211yescharacteristic
30C2×C22⋊C4×C59C2212yes—
31C2×C22⋊C4×C59C2212yes—
32#95×C59C2211yescharacteristic
33C24×C59C2312yes—
34C2×D4×C59—24no—
35C2×D4×C59—41no—
36C22×C4×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C22×Dic59—24no—
41C22×Dic59—24no—
42C22×Dic59—42no—
43C22×Dic59C2312yes—
44C22×Dic59C2312yes—
45C22×Dic59C2312yes—
46C22×Dic59C2312yes—
47C2×Dic118—24no—
48C2×Dic118—41no—
49C4⋊C4×C59—41no—
50C22⋊C4×C59—24no—
51C22⋊C4×C59—24no—
52C22⋊Dic59—24no—
53C22⋊Dic59—24no—
54C22⋊Dic59D418yes—
55C4⋊Dic59—24no—
56C4⋊Dic59—41no—
57Dic59⋊C4—24no—
58Dic59⋊C4—24no—
59Dic59⋊C4—24no—
60Dic59⋊C4—24no—
61C4×Dic59—22no—
62C23×C59—22no—
63C23×C59—22no—
64C23×C59—22no—
65C23×C59—22no—
66C23×C59—22no—
67C23×C59—22no—
68C23×C59C2×D414yes—
69C23×C59C2411yescharacteristic
70D4×C59—44no—
71C2×C4×C59—21no—
72C2×C4×C59—21no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59#4112yes—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—48no—
92C2×Dic59C2×D414yes—
93C2×Dic59C2×D414yes—
94Dic118—44no—
95C22×C59—24no—
96C22×C59—24no—
97C22×C59—24no—
98C22×C59—42no—
99C22×C59—42no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59C22×D412yes—
103C22×C59C2×#4111yescharacteristic
104C22×C59H(5,𝔽2)11yescharacteristic
105C22×C592−1+411yescharacteristic
106C22×C592−1+412yes—
107C4×C59—22no—
108C4×C59—41no—
109C4×C59—41no—
110C4×C59—42no—
111Dic59—24no—
112Dic59—24no—
113Dic59—42no—
114Dic59—42no—
115#2680—591nomaximal, Sylow
116C2×C59—44no—
117C2×C59#53612yes—
118C2×C59#53911yescharacteristic
119C2×C59D4211yescharacteristic
120C2×C59#54712yes—
121C2×C59#56311yescharacteristic
122C2×#123—592no—
123C2×C22⋊Q8—592no—
124#398—592no—
125#397—592no—
126#395—591no—
127#394D5911yescharacteristic
128#388—592no—
129#385—592no—
130#384—591no—
131C59#268011yescharacteristic, complemented, Sylow
132C22×Q8—591no—
133C22×D4C2×D5911yescharacteristic
134C23×C4—592no—
135#123—1188no—
136C22⋊Q8—1188no—
137C2×C4⋊C4—592no—
138C2×C4⋊C4—592no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4—592no—
141C2×C4⋊C4—592no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4C2×D5911yescharacteristic
144C2×C22⋊C4—592no—
145C2×C22⋊C4—592no—
146C2×C22⋊C4—592no—
147C2×C22⋊C4C2×D5912yes—
148C2×C22⋊C4C2×D5912yes—
149C2×C42—591no—
150#95—592no—
151#95—592no—
152#95—592no—
153#95—591no—
154#95C2×D5911yescharacteristic
155C24C22×D5912yes—
156C2×Q8—1184no—
157C2×Q8—2361no—
158C2×D4—24no—
159C2×D4—41no—
160C22×C4—592no—
161C22×C4—592no—
162C22×C4—592no—
163C22×C4—592no—
164C22×C4—1184no—
165C22×C4—1184no—
166C22×C4—2362no—
167C22×C4C22×D5912yes—
168C22×C4C22×D5911yescharacteristic
169C22×C4C22×D5911yescharacteristic
170C22×C4C22×D5911yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—1184no—
173C4⋊C4—1184no—
174C4⋊C4—1184no—
175C4⋊C4—1184no—
176C4⋊C4—1184no—
177C4⋊C4—2361no—
178C22⋊C4—24no—
179C22⋊C4—24no—
180C22⋊C4—598no—
181C22⋊C4—1184no—
182C22⋊C4—1184no—
183C42—1182no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23D4×D5914yes—
191C23C23×D5911yescharacteristic
192Q8—2364no—
193D4—44no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—594no—
204C2×C4—594no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—1182no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—2368no—
216C2×C4#1174568712yes—
217C22—24no—
218C22—24no—
219C22—24no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×D4×D5912yes—
225C22C2×#1174568711yescharacteristic
226C22#1427377211yescharacteristic
227C22#1427377412yes—
228C22#1427377411yescharacteristic
229C4—22no—
230C4—41no—
231C4—41no—
232C4—42no—
233C4—1184no—
234C4—1184no—
235C4—2362no—
236C4—2362no—
237C2—44no—
238C2#1683797412yes—
239C2#1683799711yescharacteristic
240C2#1683803411yescharacteristic
241C2#1683805212yes—
242C2#1683815211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2680
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14273704C2semidirect
3. #16837336C2semidirect
4. #16837330C2semidirect
5. #16837322C2semidirect
6. #16837290C2semidirect
7. #16837277C2semidirect
8. #16837271C2semidirect
131. C59#2680semidirect