Finite Group Databasebeta

← #20249332

Subgroups — #20249332

Order 6016.

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

normal subgroups only

This group has 584 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×#13094020C211yesmaximal, characteristic
2C2×#13094015C211yesmaximal, characteristic, complemented
3#15689039C214yesmaximal, complemented
4#15689038C214yesmaximal, complemented
5#15689026C211yesmaximal, characteristic, complemented
6#15689025C211yesmaximal, characteristic, complemented
7#15689024C211yesmaximal, characteristic, complemented
8#15688969C211yesmaximal, characteristic, complemented
9C47×#390C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47C2212yes—
12C22×C22⋊D47C2212yes—
13#13094020—24no—
14#13094015—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2214yes—
19C2×(C2×D47)⋊C4C2214yes—
20C2×(C2×D47)⋊C4C2214yes—
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C22×D4×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2214yes—
28C2×C42×C47C2211yescharacteristic
29C24×C47C2312yes—
30C23×D47C2312yes—
31C2×D4×C47—22no—
32C2×D4×C47—22no—
33C2×D4×C47—22no—
34C22×C4×C47C2312yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—24no—
38C2×C22⋊D47—24no—
39C2×C22⋊D47—44no—
40C2×C22⋊D47—44no—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C2×D188—22no—
46C2×D188—22no—
47C2×D188—22no—
48C4⋊C4×C47—22no—
49C22⋊C4×C47—44no—
50C42×C47—22no—
51C22⋊Dic47—44no—
52(C2×D47)⋊C4—44no—
53(C2×D47)⋊C4—44no—
54C4⋊Dic47—22no—
55C4⋊Dic47—24no—
56Dic47⋊C4—24no—
57C4×Dic47—22no—
58C4×Dic47D414yes—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—24no—
63C23×C47—24no—
64C23×C47C2411yescharacteristic
65C22×D47—22no—
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—24no—
69C22×D47—24no—
70D4×C47—44no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—24no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47#4112yes—
78C2×C4×C47#4112yes—
79C22⋊D47—48no—
80C22⋊D47—48no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—24no—
87C2×Dic47—22no—
88C2×Dic47C2×D412yes—
89C2×Dic47C2×D412yes—
90D188—44no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47—44no—
95C22×C47—44no—
96C22×C47C22×D411yescharacteristic
97C22×C47C2×#4111yescharacteristic
98C22×C47C2×#4111yescharacteristic
99C22×C47H(5,𝔽2)12yes—
100C22×C47H(5,𝔽2)12yes—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—42no—
104C2×D47—44no—
105C2×D47—44no—
106C4×C47—42no—
107C4×C47—42no—
108C4×C47#12414yes—
109Dic47—22no—
110Dic47—22no—
111Dic47—42no—
112Dic47—42no—
113#2641—471nomaximal, Sylow
114C2×C47—82no—
115C2×C47C2×#12411yescharacteristic
116C2×C47#53511yescharacteristic
117C2×C47#53511yescharacteristic
118C2×C47#54012yes—
119C2×C47#54012yes—
120D47—82no—
121C2×#127—471no—
122C2×#125—471no—
123#394—474no—
124#394—474no—
125#390—471no—
126#390—471no—
127#390—471no—
128#390D4711yescharacteristic, complemented
129#376—471no—
130C47#264111yescharacteristic, complemented, Sylow
131C22×D4—472no—
132C22×D4—472no—
133C22×D4—471no—
134C22×D4C2×D4711yescharacteristic
135#127—944no—
136#125—944no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4C2×D4711yescharacteristic
141C2×C22⋊C4—474no—
142C2×C22⋊C4—474no—
143C2×C22⋊C4—474no—
144C2×C22⋊C4C2×D4714yes—
145C2×C42—471no—
146C2×C42—471no—
147C2×C42C2×D4711yescharacteristic
148#95—472no—
149#95—472no—
150C24—472no—
151C24C22×D4712yes—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—944no—
156C2×D4—944no—
157C2×D4—942no—
158C2×D4—942no—
159C2×D4—942no—
160C2×D4—1884no—
161C2×D4—1884no—
162C22×C4—471no—
163C22×C4—471no—
164C22×C4—472no—
165C22×C4—472no—
166C22×C4C22×D4712yes—
167C22×C4C22×D4712yes—
168C22×C4C22×D4711yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—944no—
171C4⋊C4—944no—
172C4⋊C4—942no—
173C22⋊C4—44no—
174C22⋊C4—1884no—
175C22⋊C4—1884no—
176C22⋊C4—1884no—
177C42—22no—
178C42—474no—
179C42—942no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—24no—
184C23—24no—
185C23—942no—
186C23—942no—
187C23—942no—
188C23—944no—
189C23—944no—
190C23C23×D4711yescharacteristic
191D4—44no—
192D4—1888no—
193D4—1888no—
194D4—1884no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—472no—
201C2×C4—472no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—944no—
208C2×C4—942no—
209C2×C4#1062535012yes—
210C2×C4D4×D4712yes—
211C2×C4#1062535212yes—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—44no—
216C22—44no—
217C22—1882no—
218C22—1882no—
219C22—1882no—
220C22—1884no—
221C22—1884no—
222C22C2×D4×D4711yescharacteristic
223C22C2×#1062535211yescharacteristic
224C22C2×#1062535011yescharacteristic
225C22#1309406912yes—
226C22#1309407012yes—
227C4—42no—
228C4—42no—
229C4—942no—
230C4—942no—
231C4—1882no—
232C4—1882no—
233C4#1309401014yes—
234C2—82no—
235C2—3762no—
236C2C2×#1309401011yescharacteristic
237C2#1568968611yescharacteristic
238C2#1568969111yescharacteristic
239C2#1568972412yes—
240C2#1568972612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2641
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#13094015C2semidirect
3. #15689039C2semidirect
4. #15689038C2semidirect
5. #15689026C2semidirect
6. #15689025C2semidirect
7. #15689024C2semidirect
8. #15688969C2semidirect
9. C47×#390C2semidirect
128. #390D47semidirect
130. C47#2641semidirect