Finite Group Databasebeta

← #20247849

Subgroups — #20247849

Order 6016.

568 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13093995C211yesmaximal, characteristic
2C2×#13093982C211yesmaximal, characteristic, complemented
3#15689038C214yesmaximal, complemented
4#15689026C211yesmaximal, characteristic, complemented
5#15689017C214yesmaximal, complemented
6#15688992C211yesmaximal, characteristic, complemented
7#15688989C211yesmaximal, characteristic, complemented
8C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
9C47×#390C211yesmaximal, characteristic, complemented
10C22×C22⋊D47C2212yes—
11C22×C4×D47C2211yescharacteristic
12#13093995—24no—
13#13093982—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4C2214yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2214yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2214yes—
25C22×D4×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2214yes—
28C2×C42×C47C2211yescharacteristic
29C24×C47C2312yes—
30C23×D47C2311yescharacteristic
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—44no—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2311yescharacteristic
42C22×Dic47C2312yes—
43C2×C4×D47—22no—
44C2×C4×D47—22no—
45C2×C4×D47D414yes—
46C4⋊C4×C47—22no—
47C22⋊C4×C47—44no—
48C42×C47—22no—
49C22⋊Dic47—24no—
50C22⋊Dic47—28no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—24no—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55Dic47⋊C4—44no—
56C4×Dic47—22no—
57C4×Dic47—24no—
58C23×C47—22no—
59C23×C47—24no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—24no—
63C23×C47C2411yescharacteristic
64C22×D47—22no—
65C22×D47—21no—
66C22×D47—21no—
67C22×D47—22no—
68C22×D47C2×D412yes—
69D4×C47—44no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—24no—
74C2×C4×C47—22no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47#4112yes—
77C2×C4×C47#4112yes—
78C22⋊D47—48no—
79C2×Dic47—22no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—24no—
86C2×Dic47—24no—
87C2×Dic47C2×D412yes—
88C2×Dic47#4114yes—
89C4×D47—28no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—44no—
94C22×C47—44no—
95C22×C47C22×D411yescharacteristic
96C22×C47C2×#4112yes—
97C22×C47C2×#4111yescharacteristic
98C22×C47C2×#4111yescharacteristic
99C22×C47H(5,𝔽2)12yes—
100C2×D47—22no—
101C2×D47—22no—
102C2×D47—22no—
103C2×D47—42no—
104C2×D47—42no—
105C4×C47—42no—
106C4×C47—42no—
107C4×C47#12314yes—
108Dic47—22no—
109Dic47—24no—
110Dic47—42no—
111Dic47—42no—
112#2500—471nomaximal, Sylow
113C2×C47—82no—
114C2×C47C2×#12311yescharacteristic
115C2×C47#53211yescharacteristic
116C2×C47#53511yescharacteristic
117C2×C47#55312yes—
118C2×C47#55512yes—
119D47—42no—
120C2×#121—471no—
121C2×#117—471no—
122#394—474no—
123#390—471no—
124#390D4711yescharacteristic, complemented
125#388—474no—
126#384—471no—
127#382—471no—
128C4×C22⋊C4—471no—
129C47#250011yescharacteristic, complemented, Sylow
130C22×D4—472no—
131C22×D4C2×D4711yescharacteristic
132C23×C4—471no—
133#121—944no—
134#117—944no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—471no—
137C2×C4⋊C4—474no—
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C22⋊C4—472no—
140C2×C22⋊C4—474no—
141C2×C22⋊C4—472no—
142C2×C22⋊C4—472no—
143C2×C22⋊C4C2×D4714yes—
144C2×C42—472no—
145C2×C42—471no—
146C2×C42C2×D4711yescharacteristic
147#95—472no—
148#95—474no—
149C24—471no—
150C24C22×D4712yes—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—944no—
155C2×D4—1884no—
156C22×C4—471no—
157C22×C4—472no—
158C22×C4—474no—
159C22×C4—472no—
160C22×C4—472no—
161C22×C4—942no—
162C22×C4—942no—
163C22×C4C22×D4712yes—
164C22×C4C22×D4712yes—
165C22×C4C22×D4711yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—1884no—
170C22⋊C4—44no—
171C22⋊C4—944no—
172C22⋊C4—944no—
173C22⋊C4—948no—
174C22⋊C4—944no—
175C42—22no—
176C42—944no—
177C42—942no—
178C23—22no—
179C23—24no—
180C23—22no—
181C23—22no—
182C23—24no—
183C23—472no—
184C23—942no—
185C23—941no—
186C23—941no—
187C23—942no—
188C23C23×D4711yescharacteristic
189D4—44no—
190D4—1888no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—472no—
197C2×C4—474no—
198C2×C4—941no—
199C2×C4—942no—
200C2×C4—941no—
201C2×C4—942no—
202C2×C4—948no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—944no—
206C2×C4—944no—
207C2×C4#1062535012yes—
208C2×C4D4×D4712yes—
209C2×C4#1062535212yes—
210C22—44no—
211C22—44no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—942no—
216C22—942no—
217C22—942no—
218C22—1882no—
219C22—1882no—
220C22C2×D4×D4711yescharacteristic
221C22#41×D4712yes—
222C22C2×#1062535211yescharacteristic
223C22C2×#1062535011yescharacteristic
224C22#1309406912yes—
225C4—42no—
226C4—42no—
227C4—944no—
228C4—942no—
229C4—1882no—
230C4—1882no—
231C4#1309400614yes—
232C2—82no—
233C2—1882no—
234C2C2×#1309400611yescharacteristic
235C2#1568967211yescharacteristic
236C2#1568968611yescharacteristic
237C2#1568982312yes—
238C2#1568983712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2500
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#13093982C2semidirect
3. #15689038C2semidirect
4. #15689026C2semidirect
5. #15689017C2semidirect
6. #15688992C2semidirect
7. #15688989C2semidirect
8. C4×(C2×D47)⋊C4C2semidirect
9. C47×#390C2semidirect
124. #390D47semidirect
129. C47#2500semidirect