Finite Group Databasebeta

← #20252993

Subgroups — #20252993

Order 6016.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625324C211yesmaximal, characteristic, complemented
2#15689630C212yesmaximal, complemented
3#15689378C212yesmaximal, complemented
4#15689373C212yesmaximal, complemented
5#15689366C214yesmaximal, complemented
6#15689161C211yesmaximal, characteristic, complemented
7#15689119C212yesmaximal, complemented
8C2×#135×C47C211yesmaximal, characteristic, complemented
9C22×C4×D47C2211yescharacteristic
10C2×#10625324—24no—
11C2×#10625324C2212yes—
12C2×#10625324C2212yes—
13C22×C47⋊C8C2211yescharacteristic
14#13094005—22no—
15#13094000C2214yes—
16#13093995C2214yes—
17#13093992—22no—
18C4×C22⋊D47—24no—
19#13093983C2212yes—
20#13093958C2212yescomplemented
21#13093956C2212yescomplemented
22#13093948C2214yescomplemented
23#13093945C2214yescomplemented
24C2×#41×C47C2212yes—
25#135×C47—24no—
26C2×Q16×C47C2211yescharacteristic, complemented
27C2×SD16×C47C2212yescomplemented
28C2×D8×C47C2211yescharacteristic, complemented
29C22×C8×C47C2211yescharacteristic
30C23×D47D411yescharacteristic
31#41×C47—24no—
32#41×C47—24no—
33C2×Q8×C47C2312yes—
34C2×D4×C47—22no—
35C2×D4×C47C2312yes—
36C22×C4×C47—22no—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—24no—
39C22×Dic47D411yescharacteristic
40C2×C4×D47—22no—
41C2×C4×D47—22no—
42C2×C4×D47D412yes—
43C2×C4×D47C2312yes—
44Q16×C47—22no—
45SD16×C47—24no—
46D8×C47—22no—
47C2×C8×C47D414yescomplemented
48C2×C8×C47C2311yescharacteristic
49C2×C8×C47C2311yescharacteristic
50C22⋊Dic47—22no—
51C22⋊Dic47—24no—
52(C2×D47)⋊C4—24no—
53C4⋊Dic47C2314yes—
54Dic47⋊C4—24no—
55C4×Dic47—22no—
56C2×C47⋊C8—22no—
57C2×C47⋊C8C2312yes—
58#10625324—24no—
59#10625324—24no—
60C23×C47—22no—
61C23×C47C2×D411yescharacteristic
62C22×D47—22no—
63C22×D47—42no—
64C22×D47C2×D412yes—
65Q8×C47—22no—
66Q8×C47—22no—
67D4×C47—22no—
68D4×C47—22no—
69D4×C47—44no—
70C2×C4×C47—22no—
71C2×C4×C47—44no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D412yes—
74C2×C4×C47#4112yes—
75C2×C4×C47C2411yescharacteristic
76C22⋊D47—48no—
77C2×Dic47—22no—
78C2×Dic47—24no—
79C2×Dic47C2×D412yes—
80C4×D47—24no—
81C4×D47—22no—
82C4×D47—22no—
83C8×C47C2×D412yes—
84C8×C47C2×D412yes—
85C47⋊C8—22no—
86C22×C47—22no—
87C22×C47—42no—
88C22×C47—44no—
89C22×C47#12112yes—
90C22×C47C22×D411yescharacteristic
91C2×D47—22no—
92C2×D47—24no—
93C2×D47—44no—
94C4×C47—42no—
95C4×C47#12112yes—
96C4×C47C22×D411yescharacteristic
97C4×C47C2×#4111yescharacteristic
98Dic47—22no—
99Dic47—44no—
100#3054—471nomaximal, Sylow
101C2×C47—22no—
102C2×C47—82no—
103C2×C47C2×#12111yescharacteristic
104C2×C47#57512yes—
105D47—42no—
106C2×#135D4711yescharacteristic, complemented
107C22×M16—471no—
108#525—472no—
109#470—472no—
110#469—472no—
111#468—474no—
112#427—471no—
113#416—472no—
114C47#305411yescharacteristic, complemented, Sylow
115C2×#41C2×D4712yes—
116C23×C4—471no—
117#135—24no—
118C2×Q16C2×D4711yescharacteristic, complemented
119C2×SD16C2×D4712yescomplemented
120C2×D8C2×D4711yescharacteristic, complemented
121C2×M16—472no—
122C2×M16—472no—
123C2×M16—944no—
124C22×C8—471no—
125C22×C8C2×D4711yescharacteristic
126#123—942no—
127C22⋊Q8—474no—
128#121—474no—
129#120—942no—
130C4×D4—944no—
131#117—472no—
132#107—472no—
133#106—472no—
134#103—474no—
135#102—474no—
136C24—471no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D4712yes—
140C2×D4—22no—
141C2×D4—944no—
142C2×D4C22×D4712yes—
143C22×C4—22no—
144C22×C4—471no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4—942no—
148C22×C4—942no—
149C22×C4C22×D4711yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—944no—
154M16—944no—
155C2×C8—472no—
156C2×C8—942no—
157C2×C8C22⋊D4714yescomplemented
158C2×C8C22×D4711yescharacteristic
159C2×C8C22×D4711yescharacteristic
160C4⋊C4—474no—
161C4⋊C4—944no—
162C22⋊C4—944no—
163C22⋊C4—944no—
164C22⋊C4—942no—
165C42—942no—
166C23—22no—
167C23—472no—
168C23—942no—
169C23—1882no—
170C23D4×D4711yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—1888no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—472no—
180C2×C4—942no—
181C2×C4—944no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—944no—
185C2×C4D4×D4711yescharacteristic
186C2×C4#1062535212yes—
187C2×C4C2×C22⋊D4712yes—
188C2×C4C23×D4711yescharacteristic
189C8—942no—
190C8C2×C22⋊D4712yes—
191C8C2×C22⋊D4712yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—942no—
196C22—944no—
197C22—1884no—
198C22#1309399512yes—
199C22C2×D4×D4711yescharacteristic
200C4—42no—
201C4—942no—
202C4—1884no—
203C4#1309399512yes—
204C4C22×C22⋊D4711yescharacteristic
205C4C2×#1062535211yescharacteristic
206C2—22no—
207C2—82no—
208C2—1882no—
209C2C2×#1309399511yescharacteristic
210C2#1568992012yes—
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#135×C47C2
socleC22×C47C22×D4
hypercenterC2×#135D47
hypocenterC47#3054
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#10625324C2semidirect
2. #15689630C2semidirect
3. #15689378C2semidirect
4. #15689373C2semidirect
5. #15689366C2semidirect
6. #15689161C2semidirect
7. #15689119C2semidirect
8. C2×#135×C47C2semidirect
20. #13093958C22semidirect
21. #13093956C22semidirect
22. #13093948C22semidirect
23. #13093945C22semidirect
26. C2×Q16×C47C22semidirect
27. C2×SD16×C47C22semidirect
28. C2×D8×C47C22semidirect
47. C2×C8×C47D4semidirect
106. C2×#135D47semidirect
114. C47#3054semidirect
118. C2×Q16C2×D47semidirect
119. C2×SD16C2×D47semidirect
120. C2×D8C2×D47semidirect
157. C2×C8C22⋊D47semidirect