Finite Group Databasebeta

← #20251470

Subgroups — #20251470

Order 6016.

472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689064C212yesmaximal, complemented
2#15689051C212yesmaximal, complemented
3#15689037C212yesmaximal, complemented
4#15689037C212yesmaximal, complemented
5#15689035C211yesmaximal, characteristic, complemented
6#15689035C212yesmaximal, complemented
7#15689003C212yesmaximal, complemented
8#15688995C211yesmaximal, characteristic, complemented
9C47×#392C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×C22⋊Dic47C2211yescharacteristic
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C22×D4×C47C2212yes—
27C22×D4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2212yes—
30#95×C47C2211yescharacteristic
31C24×C47C2312yes—
32C24×C47C2311yescharacteristic
33C2×D4×C47—24no—
34C2×D4×C47—42no—
35C2×D4×C47—42no—
36C2×D4×C47—42no—
37C2×D4×C47—41no—
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—42no—
42C22×Dic47—41no—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C2×Dic94—42no—
48C2×Dic94—41no—
49C22⋊C4×C47—41no—
50C22⋊C4×C47—42no—
51C22⋊Dic47—22no—
52C22⋊Dic47—42no—
53C22⋊Dic47—42no—
54C22⋊Dic47—42no—
55C22⋊Dic47—42no—
56C22⋊Dic47—42no—
57Dic47⋊C4—42no—
58Dic47⋊C4—42no—
59C23×C47—22no—
60C23×C47—21no—
61C23×C47—22no—
62C23×C47—21no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47#4112yes—
71C23×C47C2411yescharacteristic
72D4×C47—48no—
73D4×C47—44no—
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—21no—
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—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—44no—
94Dic94—44no—
95C22×C47—24no—
96C22×C47—22no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47C2×#4111yescharacteristic
108C22×C47H(5,𝔽2)12yes—
109C22×C47H(5,𝔽2)12yes—
110C22×C47H(5,𝔽2)11yescharacteristic
111C22×C472−1+411yescharacteristic
112C4×C47—42no—
113C4×C47—41no—
114C4×C47—41no—
115Dic47—42no—
116Dic47—42no—
117Dic47—42no—
118Dic47—42no—
119#2824—471nomaximal, Sylow
120C2×C47—42no—
121C2×C47—82no—
122C2×C47#53812yes—
123C2×C47#53911yescharacteristic
124C2×C47#56011yescharacteristic
125C2×C47H(3,𝔽4)11yescharacteristic
126C2×C47#56212yes—
127#400—472no—
128#397—472no—
129#394—472no—
130#394—472no—
131#393—472no—
132#393—471no—
133#392D4711yescharacteristic
134#386—472no—
135#385—471no—
136C47#282411yescharacteristic, complemented, Sylow
137C22×Q8—471no—
138C22×D4C2×D4712yes—
139C22×D4C2×D4711yescharacteristic
140C23×C4—471no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—472no—
143C2×C22⋊C4—471no—
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×D4712yes—
151#95—472no—
152#95—472no—
153#95—472no—
154#95—472no—
155#95—472no—
156#95—471no—
157#95C2×D4711yescharacteristic
158C24C22×D4712yes—
159C24C22×D4711yescharacteristic
160C2×Q8—1881no—
161C2×Q8—1882no—
162C2×D4—24no—
163C2×D4—42no—
164C2×D4—41no—
165C2×D4—42no—
166C2×D4—42no—
167C22×C4—472no—
168C22×C4—472no—
169C22×C4—472no—
170C22×C4—472no—
171C22×C4—1881no—
172C22×C4—1882no—
173C22×C4C22×D4712yes—
174C22×C4C22×D4711yescharacteristic
175C22×C4C22×D4711yescharacteristic
176C4⋊C4—1882no—
177C4⋊C4—1882no—
178C22⋊C4—41no—
179C22⋊C4—42no—
180C22⋊C4—942no—
181C22⋊C4—1882no—
182C22⋊C4—1882no—
183C22⋊C4—1882no—
184C22⋊C4—1882no—
185C22⋊C4—1882no—
186C23—21no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23#1062535212yes—
198C23C23×D4711yescharacteristic
199Q8—1884no—
200D4—48no—
201D4—44no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—1884no—
222C22—24no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22C2×#1062535211yescharacteristic
235C22#1309406911yescharacteristic
236C22#1309406912yes—
237C22#1309406912yes—
238C22#1309407111yescharacteristic
239C4—41no—
240C4—41no—
241C4—42no—
242C4—1882no—
243C4—1882no—
244C4—1882no—
245C4—1882no—
246C2—42no—
247C2—82no—
248C2#1568970812yes—
249C2#1568971811yescharacteristic
250C2#1568986011yescharacteristic
251C2#1568986611yescharacteristic
252C2#1568986812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2824
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #15689064C2semidirect
2. #15689051C2semidirect
3. #15689037C2semidirect
4. #15689037C2semidirect
5. #15689035C2semidirect
6. #15689035C2semidirect
7. #15689003C2semidirect
8. #15688995C2semidirect
136. C47#2824semidirect