Finite Group Databasebeta

← #20249193

Subgroups — #20249193

Order 6016.

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

normal subgroups only

This group has 668 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
1C2×#13094003C211yesmaximal, characteristic, complemented
2#15689059C212yesmaximal, complemented
3#15689046C214yesmaximal, complemented
4#15689035C212yesmaximal, complemented
5#15688996C212yesmaximal, complemented
6#15688983C211yesmaximal, characteristic, complemented
7#15688979C212yesmaximal
8C22×C22⋊C4×C47C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic, complemented
10#13094003—24no—
11C2×C4⋊Dic47C2211yescharacteristic, complemented
12C2×C4⋊Dic47C2212yescomplemented
13C2×Dic47⋊C4C2212yescomplemented
14C2×Dic47⋊C4C2214yescomplemented
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2214yes—
18C2×C22⋊Dic47C2214yes—
19C47⋊#95C2212yescomplemented
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—22no—
28C24×C47—22no—
29C24×C47—42no—
30C24×C47—42no—
31C24×C47Q814yescomplemented
32C24×C47C2312yes—
33C24×C47C2311yescharacteristic
34C22×C4×C47—22no—
35C22×C4×C47—42no—
36C22×C4×C47—42no—
37C22×C4×C47D414yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×Dic47C2314yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C2×Dic94—22no—
45C2×Dic94—42no—
46C22⋊C4×C47—24no—
47C22⋊C4×C47—24no—
48C22⋊Dic47—24no—
49C22⋊Dic47—24no—
50C22⋊Dic47—44no—
51C22⋊Dic47—44no—
52C4⋊Dic47—22no—
53C4⋊Dic47—42no—
54Dic47⋊C4—24no—
55Dic47⋊C4—44no—
56C23×C47—22no—
57C23×C47—22no—
58C23×C47—28no—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47—24no—
62C23×C47—24no—
63C23×C47—48no—
64C23×C47—44no—
65C23×C47—44no—
66C23×C47—48no—
67C23×C47C2×D412yes—
68C23×C47C2×Q814yes—
69C23×C47C2×Q812yes—
70C23×C47#4112yes—
71C23×C47C2411yescharacteristic
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—24no—
76C2×C4×C47—44no—
77C2×C4×C47—44no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×D412yes—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—24no—
83C2×Dic47—24no—
84C2×Dic47—24no—
85C2×Dic47—24no—
86C2×Dic47—24no—
87Dic94—44no—
88C22×C47—22no—
89C22×C47—22no—
90C22×C47—24no—
91C22×C47—24no—
92C22×C47—24no—
93C22×C47—28no—
94C22×C47—416no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47—44no—
98C22×C47C22⋊Q814yes—
99C22×C47C22×D411yescharacteristic
100C22×C47C22×Q811yescharacteristic
101C22×C47C2×#4111yescharacteristic
102C22×C47H(5,𝔽2)12yes—
103C22×C47H(5,𝔽2)12yes—
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—42no—
107Dic47—42no—
108Dic47—42no—
109Dic47—44no—
110#2626—471nomaximal, Sylow
111C2×C47—24no—
112C2×C47—44no—
113C2×C47C2×C22⋊Q811yescharacteristic
114C2×C47#53411yescharacteristic
115C2×C47#53511yescharacteristic
116C2×C47#53812yes—
117C2×C47#54312yes—
118C2×C22⋊Q8—471no—
119C22×C22⋊C4D4711yescharacteristic
120#399—472no—
121#396—474no—
122#393—472no—
123#385—472no—
124#380—471no—
125#379—472no—
126C47#262611yescharacteristic, complemented, Sylow
127C25C2×D4711yescharacteristic
128C22×Q8—471no—
129C23×C4C2×D4711yescharacteristic
130C23×C4C2×D4711yescharacteristic
131C22⋊Q8—944no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4—474no—
135C2×C4⋊C4—472no—
136C2×C22⋊C4—24no—
137C2×C22⋊C4—472no—
138C2×C22⋊C4—472no—
139C2×C22⋊C4—474no—
140C2×C22⋊C4—474no—
141C2×C22⋊C4C2×D4712yes—
142C2×C22⋊C4C2×D4712yes—
143#95—472no—
144#95—474no—
145C24—22no—
146C24—22no—
147C24—42no—
148C24—42no—
149C24Dic9414yescomplemented
150C24C22×D4712yes—
151C24C22×D4711yescharacteristic
152C2×Q8—942no—
153C2×Q8—1882no—
154C22×C4—22no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—474no—
158C22×C4—472no—
159C22×C4—472no—
160C22×C4C22⋊D4714yes—
161C22×C4C22×D4712yes—
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4711yescharacteristic
164C4⋊C4—944no—
165C4⋊C4—942no—
166C4⋊C4—1884no—
167C4⋊C4—1882no—
168C22⋊C4—24no—
169C22⋊C4—24no—
170C22⋊C4—944no—
171C22⋊C4—944no—
172C22⋊C4—1884no—
173C22⋊C4—1884no—
174C23—22no—
175C23—22no—
176C23—28no—
177C23—22no—
178C23—22no—
179C23—24no—
180C23—24no—
181C23—48no—
182C23—44no—
183C23—44no—
184C23—48no—
185C23C2×Dic9414yes—
186C23C2×Dic9412yes—
187C23#1062535012yes—
188C23C2×C22⋊D4712yes—
189C23C23×D4711yescharacteristic
190Q8—1884no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—44no—
196C2×C4—44no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—944no—
200C2×C4—944no—
201C2×C4—944no—
202C2×C4—944no—
203C2×C4—944no—
204C2×C4C2×C22⋊D4712yes—
205C2×C4C2×C22⋊D4712yes—
206C22—24no—
207C22—22no—
208C22—22no—
209C22—24no—
210C22—28no—
211C22—24no—
212C22—416no—
213C22—42no—
214C22—42no—
215C22—44no—
216C22#1309400314yes—
217C22C22×C22⋊D4711yescharacteristic
218C22C22×Dic9411yescharacteristic
219C22C2×#1062535011yescharacteristic
220C22#1309406912yes—
221C22#1309406912yes—
222C4—22no—
223C4—22no—
224C4—42no—
225C4—1882no—
226C4—1882no—
227C4—1884no—
228C2—24no—
229C2—44no—
230C2C2×#1309400311yescharacteristic
231C2#1568968211yescharacteristic
232C2#1568969011yescharacteristic
233C2#1568971112yes—
234C2#1568974912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C22⋊C4×C47C2
hypercenterC22×C22⋊C4D47
hypocenterC47#2626
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094003C2semidirect
2. #15689059C2semidirect
3. #15689046C2semidirect
4. #15689035C2semidirect
5. #15688996C2semidirect
6. #15688983C2semidirect
9. C22×Dic94C22semidirect
11. C2×C4⋊Dic47C22semidirect
12. C2×C4⋊Dic47C22semidirect
13. C2×Dic47⋊C4C22semidirect
14. C2×Dic47⋊C4C22semidirect
19. C47⋊#95C22semidirect
20. C47⋊#95C22semidirect
31. C24×C47Q8semidirect
126. C47#2626semidirect
149. C24Dic94semidirect