Finite Group Databasebeta

← #20250652

Subgroups — #20250652

Order 6016.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#15689059C211yesmaximal, characteristic, complemented
2#15689052C212yesmaximal, complemented
3#15689041C212yesmaximal, complemented
4#15689032C211yesmaximal, characteristic
5#15689023C212yesmaximal, complemented
6#15689015C212yesmaximal, complemented
7#15689005C212yesmaximal, complemented
8#15689002C212yesmaximal, complemented
9C47×#381C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47C2212yes—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C22⋊Dic47C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×C4×Dic47C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2211yescharacteristic
26C23×C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2212yes—
31C24×C47C2311yescharacteristic
32C23×D47C2312yes—
33C22×C4×C47—22no—
34C22×C4×C47—41no—
35C22×C4×C47—41no—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C2×C22⋊D47—24no—
41C2×C22⋊D47—24no—
42C2×C22⋊D47—42no—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C2×D188—42no—
47C2×D188—41no—
48C22⋊C4×C47—41no—
49C22⋊C4×C47—41no—
50C22⋊Dic47—42no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—42no—
53(C2×D47)⋊C4—42no—
54(C2×D47)⋊C4—42no—
55(C2×D47)⋊C4—42no—
56C4⋊Dic47—41no—
57Dic47⋊C4—24no—
58Dic47⋊C4—42no—
59C4×Dic47—42no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—21no—
63C23×C47—21no—
64C23×C47#4112yes—
65C23×C47C2411yescharacteristic
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—22no—
70C22×D47—22no—
71C22×D47—22no—
72C22×D47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—44no—
84C22⋊D47—48no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47#4114yes—
94D188—44no—
95C22×C47—22no—
96C22×C47—24no—
97C22×C47—42no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47C2×#4112yes—
101C22×C47C2×#4111yescharacteristic
102C22×C47H(5,𝔽2)11yescharacteristic
103C22×C47H(5,𝔽2)11yescharacteristic
104C22×C47H(5,𝔽2)12yes—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—42no—
112C4×C47—42no—
113C4×C47—42no—
114C4×C47—41no—
115C4×C47—41no—
116Dic47—24no—
117Dic47—42no—
118Dic47—42no—
119#2752—471nomaximal, Sylow
120C2×C47—42no—
121C2×C47#53811yescharacteristic
122C2×C47#54012yes—
123C2×C47#55112yes—
124C2×C47#55911yescharacteristic
125C2×C47#56011yescharacteristic
126D47—82no—
127#399—471no—
128#397—472no—
129#394—472no—
130#392—471no—
131#390—472no—
132#388—472no—
133#387—472no—
134#386—472no—
135#381D4711yescharacteristic, complemented
136C47#275211yescharacteristic, complemented, Sylow
137C22×D4—472no—
138C22×D4—471no—
139C23×C4C2×D4711yescharacteristic
140C2×C4⋊C4—472no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—471no—
143C2×C22⋊C4—472no—
144C2×C22⋊C4—472no—
145C2×C22⋊C4—472no—
146C2×C22⋊C4—472no—
147C2×C22⋊C4—472no—
148C2×C22⋊C4—472no—
149C2×C22⋊C4C2×D4711yescharacteristic
150C2×C22⋊C4C2×D4711yescharacteristic
151C2×C42—472no—
152#95—472no—
153#95—472no—
154#95—471no—
155#95—471no—
156#95C2×D4712yes—
157#95C2×D4712yes—
158C24—472no—
159C24C22×D4711yescharacteristic
160C2×D4—944no—
161C2×D4—944no—
162C2×D4—1881no—
163C2×D4—1882no—
164C2×D4—1882no—
165C22×C4—22no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—472no—
169C22×C4—472no—
170C22×C4—472no—
171C22×C4C22×D4712yes—
172C22×C4C22×D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C22×C4C22×D4712yes—
175C4⋊C4—944no—
176C4⋊C4—1882no—
177C4⋊C4—1881no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—944no—
181C22⋊C4—1882no—
182C22⋊C4—1882no—
183C22⋊C4—1882no—
184C22⋊C4—1882no—
185C22⋊C4—1882no—
186C42—1882no—
187C23—22no—
188C23—21no—
189C23—21no—
190C23—22no—
191C23—942no—
192C23—942no—
193C23—942no—
194C23—942no—
195C23—942no—
196C23—942no—
197C23—942no—
198C23#1062535012yes—
199C23C23×D4711yescharacteristic
200D4—1884no—
201D4—1888no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—474no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C22—24no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—1882no—
228C22—1882no—
229C22—1882no—
230C22—1882no—
231C22—1882no—
232C22—1882no—
233C22—1882no—
234C22#41×D4712yes—
235C22C2×#1062535011yescharacteristic
236C22#1309406911yescharacteristic
237C22#1309406911yescharacteristic
238C22#1309407012yes—
239C4—41no—
240C4—41no—
241C4—42no—
242C4—42no—
243C4—944no—
244C4—1882no—
245C4—1882no—
246C2—42no—
247C2—3762no—
248C2#1568971111yescharacteristic
249C2#1568972512yes—
250C2#1568979712yes—
251C2#1568985711yescharacteristic
252C2#1568986311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#381C2
hypercenter#381D47
hypocenterC47#2752
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #15689059C2semidirect
2. #15689052C2semidirect
3. #15689041C2semidirect
5. #15689023C2semidirect
6. #15689015C2semidirect
7. #15689005C2semidirect
8. #15689002C2semidirect
9. C47×#381C2semidirect
135. #381D47semidirect
136. C47#2752semidirect