Finite Group Databasebeta

← #20247666

Subgroups — #20247666

Order 6016.

700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C22⋊Dic47C211yesmaximal, characteristic
2#15689051C214yesmaximal, complemented
3#15688996C212yesmaximal, complemented
4#15688995C212yesmaximal, complemented
5#15688986C212yesmaximal, complemented
6#15688984C212yesmaximal, complemented
7#15688979C211yesmaximal, characteristic
8C22×C22⋊C4×C47C211yesmaximal, characteristic
9C23×Dic47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11C2×Dic47⋊C4C2214yescomplemented
12C2×C22⋊Dic47—24no—
13C2×C22⋊Dic47C2212yes—
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C47⋊#95C2214yescomplemented
19C47⋊#95C2214yescomplemented
20C47⋊#95C2214yescomplemented
21C25×C47C2211yescharacteristic
22C23×C4×C47C2211yescharacteristic
23C23×C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47—24no—
25C2×C22⋊C4×C47C2212yes—
26C2×C22⋊C4×C47C2212yes—
27C24×C47—24no—
28C24×C47—24no—
29C24×C47—42no—
30C24×C47D414yes—
31C24×C47C2311yescharacteristic
32C24×C47C2311yescharacteristic
33C24×C47C2311yescharacteristic
34C22×C4×C47—22no—
35C22×C4×C47—22no—
36C22×C4×C47—24no—
37C22×C4×C47—42no—
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×Dic47—22no—
41C22×Dic47—22no—
42C22×Dic47—24no—
43C22×Dic47—42no—
44C22×Dic47C2312yes—
45C22×Dic47C2314yes—
46C22×Dic47C2312yes—
47C22⋊C4×C47—24no—
48C22⋊C4×C47—24no—
49C22⋊Dic47—24no—
50C22⋊Dic47—24no—
51C22⋊Dic47—24no—
52C22⋊Dic47—24no—
53C22⋊Dic47—42no—
54Dic47⋊C4—44no—
55C23×C47—22no—
56C23×C47—22no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47—28no—
60C23×C47—28no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—44no—
65C23×C47—416no—
66C23×C47C2×D412yes—
67C23×C47C2×D412yes—
68C23×C47C2×D412yes—
69C23×C47#4114yes—
70C23×C47#4114yes—
71C23×C47C2411yescharacteristic
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—24no—
75C2×C4×C47—24no—
76C2×C4×C47—44no—
77C2×C4×C47—44no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—24no—
81C2×Dic47—24no—
82C2×Dic47—24no—
83C2×Dic47—24no—
84C2×Dic47—24no—
85C2×Dic47—44no—
86C2×Dic47—44no—
87C22×C47—22no—
88C22×C47—22no—
89C22×C47—22no—
90C22×C47—22no—
91C22×C47—28no—
92C22×C47—28no—
93C22×C47—22no—
94C22×C47—22no—
95C22×C47—22no—
96C22×C47—416no—
97C22×C47—44no—
98C22×C47#12314yes—
99C22×C47#12314yes—
100C22×C47C22×D411yescharacteristic
101C22×C47C2×#4112yes—
102C22×C47C2×#4112yes—
103C22×C47H(5,𝔽2)12yes—
104C4×C47—42no—
105C4×C47—42no—
106Dic47—42no—
107Dic47—42no—
108Dic47—44no—
109#2483—471nomaximal, Sylow
110C2×C47—24no—
111C2×C47—24no—
112C2×C47—42no—
113C2×C47C2×#12311yescharacteristic
114C2×C47C2×#12311yescharacteristic
115C2×C47#53411yescharacteristic
116C2×C47#55114yes—
117C22×C22⋊C4—471no—
118C22×C22⋊C4D4711yescharacteristic
119#397—474no—
120#385—472no—
121#385—472no—
122#381—472no—
123#381—472no—
124#379—471no—
125C47#248311yescharacteristic, complemented, Sylow
126C25C2×D4711yescharacteristic
127C23×C4—471no—
128C23×C4—471no—
129C23×C4C2×D4711yescharacteristic
130C23×C4C2×D4711yescharacteristic
131C2×C4⋊C4—474no—
132C2×C22⋊C4—24no—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C22⋊C4—472no—
136C2×C22⋊C4—472no—
137C2×C22⋊C4—472no—
138C2×C22⋊C4—944no—
139C2×C22⋊C4C2×D4712yes—
140C2×C22⋊C4C2×D4712yes—
141#95—474no—
142#95—474no—
143#95—474no—
144C24—24no—
145C24—24no—
146C24—42no—
147C24C22⋊D4714yes—
148C24C22×D4711yescharacteristic
149C24C22×D4711yescharacteristic
150C24C22×D4711yescharacteristic
151C22×C4—24no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4—472no—
156C22×C4—474no—
157C22×C4—472no—
158C22×C4—944no—
159C22×C4—942no—
160C22×C4—942no—
161C22×C4—1882no—
162C22×C4C22×D4712yes—
163C22×C4C22×D4712yes—
164C4⋊C4—1884no—
165C22⋊C4—24no—
166C22⋊C4—24no—
167C22⋊C4—944no—
168C22⋊C4—944no—
169C22⋊C4—944no—
170C22⋊C4—944no—
171C22⋊C4—1882no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—28no—
177C23—28no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—44no—
182C23—416no—
183C23#1062535014yes—
184C23#1062535214yes—
185C23C2×C22⋊D4712yes—
186C23C2×C22⋊D4712yes—
187C23C2×C22⋊D4712yes—
188C23C23×D4711yescharacteristic
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—44no—
194C2×C4—44no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—944no—
198C2×C4—944no—
199C2×C4—944no—
200C2×C4—944no—
201C2×C4—944no—
202C2×C4—1884no—
203C2×C4—1884no—
204C22—28no—
205C22—28no—
206C22—22no—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—416no—
214C22—44no—
215C22#1309400514yes—
216C22#1309400714yes—
217C22C22×C22⋊D4711yescharacteristic
218C22C2×#1062535212yes—
219C22C2×#1062535012yes—
220C22#1309406912yes—
221C4—42no—
222C4—42no—
223C4—1884no—
224C4—1882no—
225C4—1882no—
226C2—24no—
227C2—24no—
228C2—42no—
229C2C2×#1309400511yescharacteristic
230C2C2×#1309400711yescharacteristic
231C2#1568968211yescharacteristic
232C2#1568979914yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C22⋊C4×C47C2
hypercenterC22×C22⋊C4D47
hypocenterC47#2483
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #15689051C2semidirect
3. #15688996C2semidirect
4. #15688995C2semidirect
5. #15688986C2semidirect
6. #15688984C2semidirect
11. C2×Dic47⋊C4C22semidirect
18. C47⋊#95C22semidirect
19. C47⋊#95C22semidirect
20. C47⋊#95C22semidirect
125. C47#2483semidirect