Finite Group Databasebeta

← #20254253

Subgroups — #20254253

Order 6016.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#15689687C212yesmaximal, complemented
2#15689448C214yesmaximal, complemented
3#15689376C212yesmaximal, complemented
4#15689359C212yesmaximal, complemented
5#15689259C214yesmaximal, complemented
6C47×#408C211yesmaximal, characteristic, complemented
7C22×D188C2212yescomplemented
8C2×D376C2212yes—
9C2×D376C2212yes—
10#13094020—22no—
11#13094013—22no—
12#13093998C2214yes—
13#13093998C2214yescomplemented
14#13093992—22no—
15#13093992—22no—
16#13093983C2212yescomplemented
17#13093958C2212yescomplemented
18#13093956C2212yescomplemented
19#13093946C2214yescomplemented
20#13093946C2214yescomplemented
21C2×#41×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic, complemented
23C22×C8×C47C2211yescharacteristic, complemented
24C22⋊C8×C47C2214yescomplemented
25C23×D47—22no—
26#41×C47—41no—
27#41×C47—41no—
28C2×Q8×C47D411yescharacteristic
29C2×D4×C47D411yescharacteristic
30C2×D4×C47D412yes—
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2312yes—
33C2×C22⋊D47—24no—
34C2×C22⋊D47—24no—
35C2×D188—22no—
36C2×D188—42no—
37C2×D188—42no—
38C2×D188C2314yes—
39M16×C47—41no—
40C2×C8×C47—41no—
41C2×C8×C47C2312yes—
42C2×C8×C47C2312yes—
43C22⋊Dic47—22no—
44(C2×D47)⋊C4—24no—
45(C2×D47)⋊C4—24no—
46C4⋊Dic47C2314yes—
47C4×Dic47—22no—
48D376—42no—
49D376—42no—
50C23×C47C2×D412yes—
51C23×C47C2×D411yescharacteristic
52C22×D47—24no—
53C22×D47—44no—
54C22×D47—84no—
55Q8×C47—41no—
56D4×C47—42no—
57D4×C47—41no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47C2×D412yes—
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2411yescharacteristic
65C22⋊D47—84no—
66C22⋊D47—84no—
67C2×Dic47—24no—
68D188—24no—
69D188—24no—
70D188—44no—
71C8×C47—22no—
72C8×C47—22no—
73C22×C47—22no—
74C22×C47—21no—
75C22×C47—22no—
76C22×C47—24no—
77C22×C47C22×D411yescharacteristic
78C2×D47—44no—
79C2×D47—44no—
80C2×D47—44no—
81C2×D47—88no—
82C4×C47—22no—
83C4×C47—21no—
84C4×C47H(5,𝔽2)11yescharacteristic
85C4×C47H(5,𝔽2)11yescharacteristic
86Dic47—44no—
87#3199—471nomaximal, Sylow
88C2×C47—42no—
89C2×C47—41no—
90C2×C47#53411yescharacteristic
91C2×C47#57612yes—
92D47—84no—
93#535—472no—
94#482—474no—
95#469—472no—
96#466—472no—
97#447—474no—
98#408D4711yescharacteristic, complemented
99C47#319911yescharacteristic, complemented, Sylow
100C2×#41C2×D4711yescharacteristic
101C22×D4—472no—
102C2×D8—472no—
103C2×D8—472no—
104C2×M16C2×D4711yescharacteristic, complemented
105C22×C8C2×D4711yescharacteristic, complemented
106#127—942no—
107#124—942no—
108#121—474no—
109#121—474no—
110#120—942no—
111#120—942no—
112#117—472no—
113#107—472no—
114#106—472no—
115#102—474no—
116#102—474no—
117C22⋊C8C2×D4714yescomplemented
118C24—942no—
119#41—41no—
120#41—41no—
121C2×Q8D18811yescharacteristic
122C2×D4—474no—
123C2×D4—944no—
124C2×D4—944no—
125C2×D4—942no—
126C2×D4—1882no—
127C2×D4—1882no—
128C2×D4D18811yescharacteristic
129C2×D4D18812yes—
130C22×C4C22×D4712yes—
131C22×C4C22×D4711yescharacteristic
132D8—1882no—
133D8—1882no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D4712yes—
137C2×C8C22×D4712yes—
138C4⋊C4—474no—
139C22⋊C4—942no—
140C22⋊C4—944no—
141C22⋊C4—944no—
142C42—942no—
143C23—944no—
144C23—3764no—
145C23—1884no—
146C23C2×D18812yes—
147C23C2×D18811yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—944no—
152D4—944no—
153D4—3764no—
154D4—3764no—
155D4—1884no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—944no—
161C2×C4C2×D18812yes—
162C2×C4C2×D18811yescharacteristic
163C2×C4C23×D4711yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—3768no—
171C22—1884no—
172C22—1884no—
173C22—1884no—
174C22C22×D18811yescharacteristic
175C4—22no—
176C4—21no—
177C4—1884no—
178C4#1309406911yescharacteristic
179C4#1309406911yescharacteristic
180C2—42no—
181C2—41no—
182C2—3764no—
183C2#1568968511yescharacteristic
184C2#1568992812yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3199
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #15689687C2semidirect
2. #15689448C2semidirect
3. #15689376C2semidirect
4. #15689359C2semidirect
5. #15689259C2semidirect
6. C47×#408C2semidirect
7. C22×D188C22semidirect
13. #13093998C22semidirect
16. #13093983C22semidirect
17. #13093958C22semidirect
18. #13093956C22semidirect
19. #13093946C22semidirect
20. #13093946C22semidirect
22. C2×M16×C47C22semidirect
23. C22×C8×C47C22semidirect
24. C22⋊C8×C47C22semidirect
98. #408D47semidirect
99. C47#3199semidirect
104. C2×M16C2×D47semidirect
105. C22×C8C2×D47semidirect
117. C22⋊C8C2×D47semidirect