Finite Group Databasebeta

← #20253856

Subgroups — #20253856

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×#13094054C212yesmaximal, complemented
2C2×#13094049C212yesmaximal, complemented
3C2×#13094012C211yesmaximal, characteristic, complemented
4#15689515C212yesmaximal, complemented
5#15689510C212yesmaximal, complemented
6#15689505C214yesmaximal, complemented
7C4×#10625329C211yesmaximal, characteristic, complemented
8C47×#532C211yesmaximal, characteristic, complemented
9C22×Dic94C2211yescharacteristic
10C22×D188C2211yescharacteristic
11#13094054—28no—
12#13094049—28no—
13C2×#10625337C2214yescomplemented
14C2×#10625335C2214yescomplemented
15C2×#10625336C2214yes—
16C2×#10625334C2214yes—
17C2×#10625329C2212yes—
18#13094012—22no—
19#13094012C2212yes—
20#13094012C2212yes—
21C2×(C2×D47)⋊C4—22no—
22#13093935C2212yescomplemented
23C4×C47⋊C8C2212yescomplemented
24C2×#41×C47C2212yes—
25C4⋊Q8×C47C2211yescharacteristic, complemented
26#127×C47C2211yescharacteristic, complemented
27#124×C47C2212yescomplemented
28#121×C47—22no—
29C4×D4×C47—22no—
30C2×C42×C47C2211yescharacteristic
31C23×D47—21no—
32#41×C47—24no—
33#41×C47—24no—
34C2×Q8×C47C2312yes—
35C2×D4×C47—22no—
36C2×D4×C47—22no—
37C2×D4×C47C2312yes—
38C22×C4×C47—22no—
39C22×C4×C47D412yes—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—21no—
42C2×D188—24no—
43C2×D188—21no—
44C2×D188C2312yes—
45C2×Dic94—24no—
46C2×Dic94—21no—
47C2×Dic94C2312yes—
48C4⋊C4×C47—22no—
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—
58(C2×D47)⋊C4—24no—
59#10625329D418yescomplemented
60C2×C47⋊C8C2314yes—
61C23×C47—22no—
62C23×C47C2×D411yescharacteristic
63C22×D47—22no—
64C22×D47—44no—
65C22×D47—42no—
66Q8×C47—22no—
67Q8×C47—22no—
68D4×C47—22no—
69D4×C47—22no—
70D4×C47—44no—
71D4×C47—44no—
72C2×C4×C47—22no—
73C2×C4×C47—42no—
74C2×C4×C47—44no—
75C2×C4×C47C2×D414yes—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—22no—
81C2×Dic47—42no—
82D188—24no—
83D188—42no—
84Dic94—24no—
85Dic94—42no—
86C47⋊C8C2×D418yes—
87C22×C47—22no—
88C22×C47—42no—
89C22×C47—44no—
90C22×C47#12712yes—
91C22×C47C22×D411yescharacteristic
92C2×D47—42no—
93C2×D47—44no—
94C2×D47—84no—
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#532D4711yescharacteristic, complemented
110C2×#124—471no—
111#497—472no—
112#496—472no—
113#495—474no—
114C4×M16—471no—
115C47#315311yescharacteristic, complemented, Sylow
116C2×#41C2×D4712yes—
117C22×Q8—471no—
118C22×D4—471no—
119#137—948no—
120AGL(1,ℤ/8)—948no—
121C2×Q16—474no—
122C2×SD16—474no—
123C2×SD16—474no—
124C2×D8—474no—
125C2×M16—472no—
126C4⋊Q8C2×D4711yescharacteristic, complemented
127#127C2×D4711yescharacteristic, complemented
128#124—472no—
129#124—472no—
130#124—942no—
131#124C2×D4712yescomplemented
132#121—22no—
133C4×D4—22no—
134C2×C22⋊C4—942no—
135C2×C42C2×D4711yescharacteristic
136#97—472no—
137C4×C8—472no—
138C24—941no—
139#41—24no—
140#41—24no—
141C2×Q8—472no—
142C2×Q8—941no—
143C2×Q8—944no—
144C2×Q8C22×D4712yes—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—472no—
148C2×D4—944no—
149C2×D4—941no—
150C2×D4C22×D4712yes—
151C22×C4—22no—
152C22×C4—941no—
153C22×C4C22⋊D4712yes—
154C22×C4C22×D4711yescharacteristic
155Q16—948no—
156SD16—948no—
157SD16—948no—
158D8—948no—
159M16—478no—
160C2×C8—474no—
161C4⋊C4—22no—
162C22⋊C4—24no—
163C22⋊C4—944no—
164C22⋊C4—944no—
165C42C22⋊D4712yes—
166C42C22×D4711yescharacteristic
167C42C22×D4711yescharacteristic
168C23—22no—
169C23—942no—
170C23—1884no—
171C23—1882no—
172C23C2×C22⋊D4711yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—944no—
176Q8—1882no—
177D4—22no—
178D4—22no—
179D4—44no—
180D4—44no—
181D4—944no—
182D4—1882no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—44no—
186C2×C4—942no—
187C2×C4—1882no—
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—3764no—
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
FittingC47×#532C2
socleC22×C47C22×D4
hypercenter#532D47
hypocenterC47#3153
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. C2×#13094049C2semidirect
3. C2×#13094012C2semidirect
4. #15689515C2semidirect
5. #15689510C2semidirect
6. #15689505C2semidirect
7. C4×#10625329C2semidirect
8. C47×#532C2semidirect
13. C2×#10625337C22semidirect
14. C2×#10625335C22semidirect
22. #13093935C22semidirect
23. C4×C47⋊C8C22semidirect
25. C4⋊Q8×C47C22semidirect
26. #127×C47C22semidirect
27. #124×C47C22semidirect
59. #10625329D4semidirect
109. #532D47semidirect
115. C47#3153semidirect
126. C4⋊Q8C2×D47semidirect
127. #127C2×D47semidirect
131. #124C2×D47semidirect