Finite Group Databasebeta

← #20243285

Subgroups — #20243285

Order 6016.

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

normal subgroups only

This group has 272 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
1C2×#13093958C211yesmaximal, characteristic
2C2×#13093956C211yesmaximal, characteristic
3C4×C4⋊Dic47C212yesmaximal
4#15688886C212yesmaximal
5C2×#97×C47C211yesmaximal, characteristic
6C2×C4⋊Dic47C2212yes—
7C2×C4⋊Dic47C2212yes—
8C2×C4×Dic47—22no—
9#13093958C414yescomplemented
10#13093956C414yescomplemented
11C47⋊#95—22no—
12C22×C8×C47C2211yescharacteristic
13C22×C8×C47C2211yescharacteristic
14C2×C42×C47C2211yescharacteristic
15#97×C47C414yescomplemented
16C22×C4×C47D412yes—
17C22×C4×C47C2311yescharacteristic
18C22×Dic47—22no—
19C22×Dic47—22no—
20C2×C8×C47—21no—
21C2×C8×C47—21no—
22C2×C8×C47C2×C412yes—
23C2×C8×C47C2×C412yes—
24C2×C8×C47C2×C412yes—
25C2×C8×C47C2×C412yes—
26C42×C47C2×C412yes—
27C42×C47Q812yes—
28C4⋊Dic47—22no—
29C4⋊Dic47—22no—
30C4⋊Dic47C2×C414yes—
31C4⋊Dic47C2×C414yes—
32C4×Dic47—44no—
33C23×C47C2×D411yescharacteristic
34C2×C4×C47—22no—
35C2×C4×C47—22no—
36C2×C4×C47C4⋊C414yes—
37C2×C4×C47C22×C411yescharacteristic
38C2×C4×C47C22×C411yescharacteristic
39C2×C4×C47C22×C411yescharacteristic
40C2×C4×C47C2×Q811yescharacteristic
41C2×C4×C47#4111yescharacteristic
42C2×C4×C47#4111yescharacteristic
43C2×Dic47—24no—
44C2×Dic47—24no—
45C2×Dic47—42no—
46C2×Dic47—42no—
47C2×Dic47—42no—
48C2×Dic47—42no—
49C8×C47—22no—
50C8×C47C4214yescomplemented
51C22×C47C2×C4⋊C411yescharacteristic
52C22×C47C4×D411yescharacteristic
53C22×C47C4×D411yescharacteristic
54C22×C47AGL(1,ℤ/8)12yes—
55C22×C47#13712yes—
56C4×C47—24no—
57C4×C47C2×C4211yescharacteristic
58C4×C47#11711yescharacteristic
59C4×C47C4×Q811yescharacteristic
60C4×C47C4×Q811yescharacteristic
61Dic47—44no—
62Dic47—44no—
63#1776—471nomaximal, Sylow
64C2×C47C4×C4⋊C411yescharacteristic
65C2×C47#42812yes—
66C2×C47#44012yes—
67C2×C47#44111yescharacteristic
68C2×C47#44211yescharacteristic
69C2×#107—471no—
70C2×#106—471no—
71C2×#97D4711yescharacteristic
72C4×C4⋊C4—472no—
73#340—472no—
74C47#177611yescharacteristic, complemented, Sylow
75C22×C8C2×D4711yescharacteristic
76C22×C8C2×D4711yescharacteristic
77C2×C4⋊C4—472no—
78C2×C4⋊C4—472no—
79C2×C42—942no—
80C2×C42C2×D4711yescharacteristic
81#107—474no—
82#106—474no—
83#97Dic4714yescomplemented
84#95—942no—
85C22×C4—942no—
86C22×C4—942no—
87C22×C4D18812yes—
88C22×C4C22×D4711yescharacteristic
89C2×C8—21no—
90C2×C8—21no—
91C2×C8C4×D4712yes—
92C2×C8C4×D4712yes—
93C2×C8C2×Dic4712yes—
94C2×C8C2×Dic4712yes—
95C4⋊C4—474no—
96C4⋊C4—474no—
97C4⋊C4—942no—
98C4⋊C4—942no—
99C42—1884no—
100C42Dic9412yes—
101C42C2×Dic4712yes—
102C23C2×D18811yescharacteristic
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—944no—
106C2×C4—944no—
107C2×C4—1882no—
108C2×C4—1882no—
109C2×C4—1882no—
110C2×C4—1882no—
111C2×C4C4⋊Dic4714yes—
112C2×C4C2×Dic9411yescharacteristic
113C2×C4C2×C4×D4711yescharacteristic
114C2×C4C2×C4×D4711yescharacteristic
115C2×C4#1062535011yescharacteristic
116C2×C4#1062535011yescharacteristic
117C2×C4C22×Dic4711yescharacteristic
118C8—22no—
119C8C4×Dic4714yescomplemented
120C22C2×C4⋊Dic4711yescharacteristic
121C22C4×D18811yescharacteristic
122C22C4×D18811yescharacteristic
123C22#1309405212yes—
124C22#1309405712yes—
125C4—24no—
126C4—1884no—
127C4—1884no—
128C4C2×C4×Dic4711yescharacteristic
129C4#1309398311yescharacteristic
130C4C4×Dic9411yescharacteristic
131C4C4×Dic9411yescharacteristic
132C2C4×C4⋊Dic4711yescharacteristic
133C2#1568916512yes—
134C2#1568922512yes—
135C2#1568923111yescharacteristic
136C2#1568923611yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC2×#97×C47C2
socleC23×C47C2×D4
hypercenterC2×#97D47
hypocenterC47#1776
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
9. #13093958C4semidirect
10. #13093956C4semidirect
15. #97×C47C4semidirect
50. C8×C47C42semidirect
74. C47#1776semidirect
83. #97Dic47semidirect
119. C8C4×Dic47semidirect