Finite Group Databasebeta

← #20253852

Subgroups — #20253852

Order 6016.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094055C212yesmaximal, complemented
2C2×#13094050C212yesmaximal, complemented
3#15689673C211yesmaximal, characteristic, complemented
4#15689518C212yesmaximal, complemented
5#15689513C212yesmaximal, complemented
6#15689505C214yesmaximal, complemented
7C4×#10625329C211yesmaximal, characteristic, complemented
8C2×#124×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2212yes—
10#13094055—28no—
11#13094050—28no—
12C2×#10625337C2214yescomplemented
13C2×#10625335C2214yes—
14C2×#10625336C2214yescomplemented
15C2×#10625334C2214yes—
16C2×#10625329C2212yes—
17#13094024C2211yescharacteristic, complemented
18#13094021C2211yescharacteristic, complemented
19#13094012C2212yescomplemented
20#13093998—22no—
21C4×D188—22no—
22#13093935C2212yescomplemented
23C4×C47⋊C8C2212yescomplemented
24C22×Q8×C47C2211yescharacteristic
25C22×D4×C47C2211yescharacteristic
26#124×C47—22no—
27#124×C47C2212yes—
28#124×C47C2212yes—
29C2×C22⋊C4×C47—22no—
30C2×C42×C47C2211yescharacteristic
31C24×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—24no—
34C2×Q8×C47C2312yes—
35C2×D4×C47—24no—
36C2×D4×C47—21no—
37C2×D4×C47C2312yes—
38C22×C4×C47—21no—
39C22×C4×C47D412yes—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—22no—
42#10625350—24no—
43#10625350—24no—
44C2×D188—22no—
45C2×D188C2312yes—
46C2×C4×D47—22no—
47C2×Dic94C2312yes—
48C22⋊C4×C47—24no—
49C22⋊C4×C47—24no—
50C42×C47D412yes—
51C42×C47C2311yescharacteristic
52C42×C47C2311yescharacteristic
53#10625337—28no—
54#10625336—28no—
55#10625335—28no—
56#10625334—28no—
57(C2×D47)⋊C4—24no—
58C4⋊Dic47—22no—
59#10625329D418yescomplemented
60C2×C47⋊C8C2314yes—
61C23×C47—22no—
62C23×C47—44no—
63C23×C47—42no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66Q8×C47—24no—
67Q8×C47—42no—
68D4×C47—24no—
69D4×C47—42no—
70C2×C4×C47—22no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47C2×D414yes—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—44no—
79C2×Dic47—22no—
80D188—22no—
81D188—22no—
82D188—44no—
83C4×D47—44no—
84Dic94—22no—
85Dic94—22no—
86C47⋊C8C2×D418yes—
87C22×C47—22no—
88C22×C47—42no—
89C22×C47—44no—
90C22×C47—84no—
91C22×C47#12712yes—
92C22×C47C22×D411yescharacteristic
93C2×D47—42no—
94C2×D47—44no—
95C4×C47—22no—
96C4×C47—22no—
97C4×C47—42no—
98C4×C47#12712yes—
99C4×C47C22×D412yes—
100Dic47—42no—
101#3153—471nomaximal, Sylow
102C2×C47—22no—
103C2×C47—82no—
104C2×C47C2×#12711yescharacteristic
105C2×C47#57512yes—
106D47—82no—
107C2×#137—472no—
108C2×AGL(1,ℤ/8)—472no—
109#532—471no—
110C2×#124D4711yescharacteristic, complemented
111#497—472no—
112#496—472no—
113#495—474no—
114C4×M16—471no—
115C47#315311yescharacteristic, complemented, Sylow
116C2×#41—472no—
117C22×Q8C2×D4711yescharacteristic
118C22×D4C2×D4711yescharacteristic
119#137—948no—
120AGL(1,ℤ/8)—948no—
121C2×Q16—474no—
122C2×SD16—474no—
123C2×SD16—474no—
124C2×D8—474no—
125C2×M16—472no—
126C4⋊Q8—471no—
127#127—471no—
128#124—22no—
129#124—472no—
130#124C2×D4712yes—
131#124C2×D4712yes—
132#121—942no—
133C4×D4—942no—
134C2×C22⋊C4—22no—
135C2×C42C2×D4711yescharacteristic
136#97—472no—
137C4×C8—472no—
138C24—21no—
139#41—944no—
140#41—944no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—472no—
144C2×Q8C22×D4712yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—472no—
148C2×D4—942no—
149C2×D4—942no—
150C2×D4C22×D4712yes—
151C22×C4—21no—
152C22×C4—942no—
153C22×C4C22⋊D4712yes—
154C22×C4C22×D4711yescharacteristic
155Q16—948no—
156SD16—948no—
157SD16—948no—
158D8—948no—
159M16—478no—
160C2×C8—474no—
161C4⋊C4—942no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—944no—
165C42C22⋊D4712yes—
166C42C22×D4711yescharacteristic
167C42C22×D4711yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—942no—
172C23C2×C22⋊D4711yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—942no—
176Q8—942no—
177D4—24no—
178D4—42no—
179D4—942no—
180D4—942no—
181D4—1884no—
182D4—1884no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—942no—
187C2×C4—1884no—
188C2×C4D4×D4714yes—
189C2×C4C2×C22⋊D4712yes—
190C2×C4C2×C22⋊D4712yes—
191C2×C4C2×C22⋊D4711yescharacteristic
192C2×C4C23×D4711yescharacteristic
193C8—478no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—1882no—
199C22—1884no—
200C22#1309402012yes—
201C22C22×C22⋊D4711yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—1882no—
206C4#1309402012yes—
207C4C2×D4×D4712yes—
208C2—22no—
209C2—82no—
210C2—3762no—
211C2C2×#1309402011yescharacteristic
212C2#1568992112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#124×C47C2
socleC22×C47C22×D4
hypercenterC2×#124D47
hypocenterC47#3153
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C2×#13094050C2semidirect
3. #15689673C2semidirect
4. #15689518C2semidirect
5. #15689513C2semidirect
6. #15689505C2semidirect
7. C4×#10625329C2semidirect
8. C2×#124×C47C2semidirect
12. C2×#10625337C22semidirect
14. C2×#10625336C22semidirect
17. #13094024C22semidirect
18. #13094021C22semidirect
19. #13094012C22semidirect
22. #13093935C22semidirect
23. C4×C47⋊C8C22semidirect
59. #10625329D4semidirect
110. C2×#124D47semidirect
115. C47#3153semidirect