Finite Group Databasebeta

← #20247850

Subgroups — #20247850

Order 6016.

568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13093998C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic, complemented
3#15689039C214yesmaximal, complemented
4#15689025C211yesmaximal, characteristic, complemented
5#15689025C211yesmaximal, characteristic, complemented
6#15689015C214yesmaximal, complemented
7#15688993C211yesmaximal, characteristic, complemented
8#15688989C211yesmaximal, characteristic, complemented
9C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47C2212yes—
12#13093998—24no—
13#13093983—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2214yes—
18C2×C22⋊Dic47C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2214yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×C4×Dic47C2212yes—
23C47⋊#95C2214yes—
24C23×C4×C47C2211yescharacteristic
25C2×C22⋊C4×C47C2212yes—
26C2×C42×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#95×C47C2212yes—
29C24×C47C2311yescharacteristic
30C23×D47C2312yes—
31C22×C4×C47—22no—
32C22×C4×C47—22no—
33C22×C4×C47D414yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—24no—
39C2×C22⋊D47—44no—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C2×D188—22no—
44C2×D188—22no—
45C2×D188—22no—
46C22⋊C4×C47—24no—
47C42×C47—22no—
48C42×C47—22no—
49C22⋊Dic47—24no—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—28no—
52(C2×D47)⋊C4—44no—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56C4⋊Dic47—44no—
57C4×Dic47—24no—
58C23×C47—22no—
59C23×C47—21no—
60C23×C47—21no—
61C23×C47—22no—
62C23×C47C2×D412yes—
63C23×C47C2411yescharacteristic
64C22×D47—22no—
65C22×D47—24no—
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—24no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—28no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D412yes—
79C2×C4×C47#4114yes—
80C2×C4×C47#4112yes—
81C2×C4×C47#4112yes—
82C22⋊D47—48no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—24no—
87C2×Dic47—24no—
88C2×Dic47—24no—
89D188—44no—
90C22×C47—22no—
91C22×C47—22no—
92C22×C47—22no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47C22×D411yescharacteristic
96C22×C47C2×#4111yescharacteristic
97C22×C47C2×#4111yescharacteristic
98C22×C47C2×#4112yes—
99C22×C47H(5,𝔽2)12yes—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—44no—
104C2×D47—44no—
105C4×C47—22no—
106C4×C47—24no—
107C4×C47—42no—
108C4×C47#12314yes—
109Dic47—42no—
110Dic47—42no—
111Dic47—42no—
112#2500—471nomaximal, Sylow
113C2×C47—42no—
114C2×C47C2×#12311yescharacteristic
115C2×C47#53211yescharacteristic
116C2×C47#53511yescharacteristic
117C2×C47#55312yes—
118C2×C47#55512yes—
119D47—82no—
120C2×#121—471no—
121C2×#117—471no—
122#394—474no—
123#390—471no—
124#390—471no—
125#388—474no—
126#384—471no—
127#382—471no—
128C4×C22⋊C4D4711yescharacteristic, complemented
129C47#250011yescharacteristic, complemented, Sylow
130C22×D4—472no—
131C22×D4—471no—
132C23×C4C2×D4711yescharacteristic
133#121—944no—
134#117—944no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—471no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—474no—
139C2×C22⋊C4—472no—
140C2×C22⋊C4—472no—
141C2×C22⋊C4—474no—
142C2×C22⋊C4—474no—
143C2×C22⋊C4C2×D4712yes—
144C2×C42—472no—
145C2×C42C2×D4711yescharacteristic
146C2×C42C2×D4711yescharacteristic
147#95—474no—
148#95C2×D4712yes—
149C24—472no—
150C24C22×D4711yescharacteristic
151C2×D4—944no—
152C2×D4—942no—
153C2×D4—942no—
154C2×D4—942no—
155C2×D4—1884no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—472no—
159C22×C4—472no—
160C22×C4—472no—
161C22×C4D18814yes—
162C22×C4C22×D4712yes—
163C22×C4C22×D4711yescharacteristic
164C22×C4C22×D4712yes—
165C22×C4C22×D4711yescharacteristic
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—1884no—
170C22⋊C4—24no—
171C22⋊C4—944no—
172C22⋊C4—944no—
173C22⋊C4—948no—
174C22⋊C4—1884no—
175C42—22no—
176C42—22no—
177C42—944no—
178C23—21no—
179C23—21no—
180C23—22no—
181C23—22no—
182C23—942no—
183C23—942no—
184C23—942no—
185C23—944no—
186C23—944no—
187C23C2×D18812yes—
188C23C23×D4711yescharacteristic
189D4—1888no—
190D4—1884no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—28no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—944no—
203C2×C4—944no—
204C2×C4—944no—
205C2×C4C2×D18812yes—
206C2×C4C2×D18812yes—
207C2×C4#1062535014yes—
208C2×C4#1062535212yes—
209C2×C4#1062535212yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—1884no—
216C22—1884no—
217C22—1882no—
218C22—1882no—
219C22—1882no—
220C22C22×D18811yescharacteristic
221C22C2×#1062535211yescharacteristic
222C22C2×#1062535211yescharacteristic
223C22C2×#1062535012yes—
224C22#1309407012yes—
225C4—24no—
226C4—22no—
227C4—42no—
228C4—1882no—
229C4—1882no—
230C4—1882no—
231C4#1309400814yes—
232C2—42no—
233C2—3762no—
234C2C2×#1309400811yescharacteristic
235C2#1568967311yescharacteristic
236C2#1568969211yescharacteristic
237C2#1568981912yes—
238C2#1568983812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C22⋊C4×C47C2
hypercenterC4×C22⋊C4D47
hypocenterC47#2500
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#13093983C2semidirect
3. #15689039C2semidirect
4. #15689025C2semidirect
5. #15689025C2semidirect
6. #15689015C2semidirect
7. #15688993C2semidirect
8. #15688989C2semidirect
9. C4×C22⋊C4×C47C2semidirect
128. C4×C22⋊C4D47semidirect
129. C47#2500semidirect