Finite Group Databasebeta

← #20241229

Subgroups — #20241229

Order 6016.

208 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 113 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×C4⋊(C47⋊C8)C211yesmaximal, characteristic
2C2×C4×C47⋊C8C211yesmaximal, characteristic
3C4×C4⋊C4×C47C211yesmaximal, characteristic
4C22×C47⋊C8—21no—
5C22×C47⋊C8—21no—
6C4⋊(C47⋊C8)—21no—
7C4⋊(C47⋊C8)C412yescomplemented
8C4×C47⋊C8—21no—
9C4×C47⋊C8C412yescomplemented
10C2×C4⋊C4×C47C412yes—
11C2×C42×C47—21no—
12C2×C42×C47C2211yescharacteristic
13#95×C47—21no—
14C22×C4×C47—22no—
15C22×C4×C47C2×C411yescharacteristic
16C22×C4×C47D411yescharacteristic
17C22×C4×C47D411yescharacteristic
18C4⋊C4×C47—22no—
19C4⋊C4×C47C814yescomplemented
20C42×C47—41no—
21C42×C47—41no—
22C42×C47C2×C411yescharacteristic
23C42×C47C2×C411yescharacteristic
24C42×C47D411yescharacteristic
25C42×C47Q811yescharacteristic
26C2×C47⋊C8—24no—
27C2×C47⋊C8—22no—
28C2×C47⋊C8—22no—
29C2×C47⋊C8—41no—
30C2×C47⋊C8—41no—
31C23×C47C22⋊C411yescharacteristic
32C2×C4×C47—22no—
33C2×C4×C47—24no—
34C2×C4×C47—42no—
35C2×C4×C47—42no—
36C2×C4×C47C4211yescharacteristic
37C2×C4×C47C22⋊C411yescharacteristic
38C2×C4×C47C22⋊C411yescharacteristic
39C2×C4×C47C4⋊C411yescharacteristic
40C2×C4×C47C4⋊C411yescharacteristic
41C2×C4×C47C4⋊C411yescharacteristic
42C2×C4×C47C2×C812yes—
43C2×C4×C47M1612yes—
44C2×C4×C47D811yescharacteristic
45C2×C4×C47SD1611yescharacteristic
46C2×C4×C47SD1611yescharacteristic
47C2×C4×C47Q1611yescharacteristic
48C47⋊C8—24no—
49C47⋊C8—42no—
50C22×C47#9511yescharacteristic
51C22×C47C22⋊C812yes—
52C22×C47#10211yescharacteristic
53C22×C47#10311yescharacteristic
54C22×C47#10412yes—
55C4×C47—21no—
56C4×C47—21no—
57C4×C47—44no—
58C4×C47C4×C811yescharacteristic
59C4×C47#9711yescharacteristic
60C4×C47#10211yescharacteristic
61C4×C47#10311yescharacteristic
62C4×C47C4⋊C812yes—
63C4×C47#10611yescharacteristic
64C4×C47#10711yescharacteristic
65#1279—471nomaximal, Sylow
66C2×C47D4⋊C812yes—
67C2×C47Q8⋊C812yes—
68C2×C47#33611yescharacteristic
69C2×C47#33911yescharacteristic
70C2×C47#34011yescharacteristic
71C2×C4⋊C8—471no—
72C2×C4×C8—471no—
73C4×C4⋊C4D4711yescharacteristic
74C47#127911yescharacteristic, complemented, Sylow
75C22×C8—941no—
76C22×C8—941no—
77C2×C4⋊C4Dic4712yes—
78C2×C42—21no—
79C2×C42C2×D4711yescharacteristic
80C4⋊C8—472no—
81C4⋊C8—941no—
82C4×C8—472no—
83C4×C8—941no—
84#95—21no—
85C22×C4—22no—
86C22×C4C2×Dic4711yescharacteristic
87C22×C4C22⋊D4711yescharacteristic
88C22×C4C22⋊D4711yescharacteristic
89C2×C8—944no—
90C2×C8—942no—
91C2×C8—942no—
92C2×C8—1881no—
93C2×C8—1881no—
94C4⋊C4—22no—
95C4⋊C4C47⋊C814yescomplemented
96C42—41no—
97C42—41no—
98C42Dic9411yescharacteristic
99C42C4×D4711yescharacteristic
100C42C4×D4711yescharacteristic
101C42D18811yescharacteristic
102C23C22⋊Dic4711yescharacteristic
103C2×C4—22no—
104C2×C4—24no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4C2×C47⋊C812yes—
108C2×C4#1062532912yes—
109C2×C4C4×Dic4711yescharacteristic
110C2×C4Dic47⋊C411yescharacteristic
111C2×C4Dic47⋊C411yescharacteristic
112C2×C4C4⋊Dic4711yescharacteristic
113C2×C4(C2×D47)⋊C411yescharacteristic
114C2×C4(C2×D47)⋊C411yescharacteristic
115C2×C4#1062533411yescharacteristic
116C2×C4#1062533511yescharacteristic
117C2×C4#1062533611yescharacteristic
118C2×C4#1062533711yescharacteristic
119C8—944no—
120C8—1882no—
121C22C47⋊#9511yescharacteristic
122C22C22⋊(C47⋊C8)12yes—
123C22#1309394511yescharacteristic
124C22#1309394811yescharacteristic
125C22#1309395112yes—
126C4—21no—
127C4—21no—
128C4—44no—
129C4C4×C47⋊C811yescharacteristic
130C4#1309393511yescharacteristic
131C4#1309394411yescharacteristic
132C4#1309394711yescharacteristic
133C4C4⋊(C47⋊C8)12yes—
134C4#1309395511yescharacteristic
135C4#1309395711yescharacteristic
136C2D4⋊(C47⋊C8)12yes—
137C2Q8⋊(C47⋊C8)12yes—
138C2#1568887811yescharacteristic
139C2#1568888211yescharacteristic
140C2#1568888511yescharacteristic
subgroupG/H
centerC22×C4C22⋊D47
commutatorC4×C47C4×C8
FrattiniC2×C42C2×D47
FittingC4×C4⋊C4×C47C2
socleC23×C47C22⋊C4
hypercenterC4×C4⋊C4D47
hypocenterC47#1279
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. C4⋊(C47⋊C8)C4semidirect
9. C4×C47⋊C8C4semidirect
19. C4⋊C4×C47C8semidirect
74. C47#1279semidirect
95. C4⋊C4C47⋊C8semidirect