Finite Group Databasebeta

← #20251463

Subgroups — #20251463

Order 6016.

456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13094019C212yesmaximal, complemented
2#15689057C212yesmaximal, complemented
3#15689047C212yesmaximal, complemented
4#15689045C212yesmaximal, complemented
5#15689045C212yesmaximal, complemented
6#15689041C212yesmaximal
7#15689040C211yesmaximal, characteristic
8#15688992C211yesmaximal, characteristic, complemented
9C47×#398C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11#13094019—28no—
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30#95×C47C2212yes—
31#95×C47C2211yescharacteristic
32C23×D47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C2×D188—42no—
42C2×D188—41no—
43C4⋊C4×C47—24no—
44C4⋊C4×C47—41no—
45C4⋊C4×C47—41no—
46(C2×D47)⋊C4—24no—
47(C2×D47)⋊C4—24no—
48(C2×D47)⋊C4—24no—
49(C2×D47)⋊C4—42no—
50(C2×D47)⋊C4—42no—
51(C2×D47)⋊C4—42no—
52C4⋊Dic47—24no—
53C4⋊Dic47—41no—
54Dic47⋊C4—24no—
55Dic47⋊C4—42no—
56Dic47⋊C4—42no—
57Dic47⋊C4—42no—
58C4×Dic47D414yescomplemented
59C23×C47C2411yescharacteristic
60C22×D47—22no—
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D412yes—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47C2×D414yes—
89D188—44no—
90C22×C47C22×D411yescharacteristic
91C22×C47H(5,𝔽2)11yescharacteristic
92C22×C47H(5,𝔽2)12yes—
93C22×C472−1+411yescharacteristic
94C22×C472−1+412yes—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C4×C47—22no—
103C4×C47—42no—
104C4×C47—42no—
105C4×C47—41no—
106C4×C47—41no—
107Dic47—24no—
108Dic47—42no—
109Dic47—42no—
110#2823—471nomaximal, Sylow
111C2×C47#53711yescharacteristic
112C2×C47#53712yes—
113C2×C47#56011yescharacteristic
114C2×C47#56311yescharacteristic
115C2×C47#56312yes—
116D47—82no—
117C2×#126—472no—
118#398—472no—
119#398D4711yescharacteristic, complemented
120#396—472no—
121#396—472no—
122#396—472no—
123#394—471no—
124#394—472no—
125#384—471no—
126C47#282311yescharacteristic, complemented, Sylow
127C22×D4—471no—
128#126—948no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—472no—
131C2×C4⋊C4—472no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4C2×D4712yes—
136C2×C4⋊C4C2×D4711yescharacteristic
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C22⋊C4—472no—
139C2×C22⋊C4—472no—
140C2×C22⋊C4—472no—
141C2×C22⋊C4—472no—
142C2×C22⋊C4—472no—
143C2×C22⋊C4—472no—
144C2×C42—471no—
145#95—471no—
146#95—472no—
147#95C2×D4712yes—
148#95C2×D4711yescharacteristic
149C24—472no—
150C2×D4—1881no—
151C2×D4—1882no—
152C22×C4—472no—
153C22×C4—472no—
154C22×C4—472no—
155C22×C4C22×D4711yescharacteristic
156C22×C4C22×D4712yes—
157C22×C4C22×D4712yes—
158C22×C4C22×D4711yescharacteristic
159C22×C4C22×D4711yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—944no—
164C4⋊C4—944no—
165C4⋊C4—1882no—
166C4⋊C4—1882no—
167C4⋊C4—1882no—
168C4⋊C4—1881no—
169C22⋊C4—944no—
170C22⋊C4—944no—
171C22⋊C4—944no—
172C22⋊C4—1882no—
173C22⋊C4—1882no—
174C22⋊C4—1882no—
175C42—474no—
176C23—942no—
177C23—942no—
178C23—942no—
179C23—942no—
180C23—942no—
181C23—942no—
182C23—942no—
183C23C23×D4711yescharacteristic
184D4—1884no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—474no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4D4×D4712yes—
207C22—1882no—
208C22—1882no—
209C22—1882no—
210C22—1882no—
211C22—1882no—
212C22—1882no—
213C22—1882no—
214C22C2×D4×D4711yescharacteristic
215C22#1309406911yescharacteristic
216C22#1309407012yes—
217C22#1309407111yescharacteristic
218C22#1309407212yes—
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—42no—
224C4—944no—
225C4—1882no—
226C4—1882no—
227C2—3762no—
228C2#1568970011yescharacteristic
229C2#1568970312yes—
230C2#1568986311yescharacteristic
231C2#1568987211yescharacteristic
232C2#1568987712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2823
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
2. #15689057C2semidirect
3. #15689047C2semidirect
4. #15689045C2semidirect
5. #15689045C2semidirect
8. #15688992C2semidirect
9. C47×#398C2semidirect
58. C4×Dic47D4semidirect
119. #398D47semidirect
126. C47#2823semidirect