Finite Group Databasebeta

← #20250315

Subgroups — #20250315

Order 6016.

504 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13094009C212yesmaximal
2#15689053C211yesmaximal, characteristic, complemented
3#15689052C212yesmaximal, complemented
4#15689052C212yesmaximal, complemented
5#15689024C211yesmaximal, characteristic
6#15689018C212yesmaximal, complemented
7#15688997C212yesmaximal, complemented
8#15688994C212yesmaximal, complemented
9C47×#398C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C4×D47C2212yes—
12#13094009—28no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2211yescharacteristic
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30#95×C47C2212yes—
31#95×C47C2211yescharacteristic
32C23×D47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C2×D188—41no—
42C2×D188—41no—
43C2×D188D414yes—
44C2×C4×D47—24no—
45C2×C4×D47—42no—
46C2×C4×D47—42no—
47C4⋊C4×C47—24no—
48C4⋊C4×C47—41no—
49C4⋊C4×C47—41no—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—24no—
53(C2×D47)⋊C4—24no—
54(C2×D47)⋊C4—24no—
55C4⋊Dic47—41no—
56Dic47⋊C4—24no—
57Dic47⋊C4—24no—
58Dic47⋊C4—42no—
59C4×Dic47—41no—
60C23×C47C2411yescharacteristic
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47—22no—
67C22×D47C2×D414yes—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D412yes—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47#4114yes—
90D188—44no—
91C4×D47—48no—
92C22×C47C22×D411yescharacteristic
93C22×C47C2×#4112yes—
94C22×C47H(5,𝔽2)11yescharacteristic
95C22×C47H(5,𝔽2)11yescharacteristic
96C22×C472−1+412yes—
97C2×D47—24no—
98C2×D47—24no—
99C2×D47—24no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—42no—
104C4×C47—22no—
105C4×C47—42no—
106C4×C47—42no—
107C4×C47—41no—
108C4×C47—41no—
109Dic47—24no—
110Dic47—42no—
111Dic47—42no—
112#2724—471nomaximal, Sylow
113C2×C47#53411yescharacteristic
114C2×C47#53912yes—
115C2×C47#54712yes—
116C2×C47#55911yescharacteristic
117C2×C47#56311yescharacteristic
118D47—44no—
119C2×#123—472no—
120#398—471no—
121#398D4711yescharacteristic, complemented
122#397—472no—
123#397—472no—
124#390—471no—
125#389—472no—
126#385—472no—
127#385—472no—
128C47#272411yescharacteristic, complemented, Sylow
129C22×D4—471no—
130C23×C4—472no—
131#123—948no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4C2×D4712yes—
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C4⋊C4C2×D4711yescharacteristic
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—472no—
146#95—472no—
147#95—472no—
148#95—471no—
149#95C2×D4712yes—
150#95C2×D4711yescharacteristic
151C24—472no—
152C2×D4—474no—
153C2×D4—1881no—
154C2×D4—1881no—
155C22×C4—472no—
156C22×C4—472no—
157C22×C4—472no—
158C22×C4—944no—
159C22×C4—1882no—
160C22×C4—1882no—
161C22×C4C22×D4711yescharacteristic
162C22×C4C22×D4712yes—
163C22×C4C22×D4711yescharacteristic
164C22×C4C22×D4712yes—
165C22×C4C22×D4711yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—944no—
170C4⋊C4—944no—
171C4⋊C4—1882no—
172C4⋊C4—1881no—
173C22⋊C4—944no—
174C22⋊C4—944no—
175C22⋊C4—944no—
176C22⋊C4—944no—
177C22⋊C4—944no—
178C42—1881no—
179C23—474no—
180C23—942no—
181C23—942no—
182C23—942no—
183C23—942no—
184C23—942no—
185C23—942no—
186C23C23×D4711yescharacteristic
187D4—1884no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—474no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—1888no—
210C2×C4D4×D4712yes—
211C22—944no—
212C22—944no—
213C22—944no—
214C22—1882no—
215C22—1882no—
216C22—1882no—
217C22—1882no—
218C22C2×D4×D4711yescharacteristic
219C22#41×D4712yes—
220C22#1309406911yescharacteristic
221C22#1309407011yescharacteristic
222C22#1309407212yes—
223C4—22no—
224C4—42no—
225C4—41no—
226C4—41no—
227C4—42no—
228C4—944no—
229C4—1882no—
230C4—1882no—
231C2—1884no—
232C2#1568968111yescharacteristic
233C2#1568972112yes—
234C2#1568977512yes—
235C2#1568985711yescharacteristic
236C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2724
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #15689053C2semidirect
3. #15689052C2semidirect
4. #15689052C2semidirect
6. #15689018C2semidirect
7. #15688997C2semidirect
8. #15688994C2semidirect
9. C47×#398C2semidirect
121. #398D47semidirect
128. C47#2724semidirect