Finite Group Databasebeta

← #20243417

Subgroups — #20243417

Order 6016.

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

normal subgroups only

This group has 336 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×#13093958C212yesmaximal, complemented
2#15688983C212yesmaximal
3#15688886C212yesmaximal, complemented
4C23×C8×C47C211yesmaximal, characteristic
5C2×C4⋊Dic47C2214yes—
6C2×C22⋊Dic47—22no—
7#13093958—24no—
8C47⋊#95—22no—
9C23×C4×C47C2211yescharacteristic
10C22×C8×C47—24no—
11C22×C8×C47C414yescomplemented
12C22×C8×C47C2211yescharacteristic
13C22×C8×C47C2211yescharacteristic
14C24×C47D411yescharacteristic
15C22×C4×C47—22no—
16C22×C4×C47—22no—
17C22×C4×C47C2×C412yes—
18C22×C4×C47D411yescharacteristic
19C22×C4×C47Q812yes—
20C22×C4×C47C2311yescharacteristic
21C22×Dic47—24no—
22C2×C8×C47—22no—
23C2×C8×C47—28no—
24C2×C8×C47C2×C412yes—
25C2×C8×C47C2×C412yes—
26C2×C8×C47D414yes—
27C22⋊Dic47—44no—
28C4⋊Dic47—24no—
29C4⋊Dic47—24no—
30C23×C47—22no—
31C23×C47—22no—
32C23×C47C4⋊C412yes—
33C23×C47D812yes—
34C23×C47Q1612yes—
35C23×C47C2×D411yescharacteristic
36C2×C4×C47—22no—
37C2×C4×C47—22no—
38C2×C4×C47—22no—
39C2×C4×C47—24no—
40C2×C4×C47C4⋊C412yes—
41C2×C4×C47C22×C411yescharacteristic
42C2×C4×C47C2×D412yes—
43C2×C4×C47C2×Q811yescharacteristic
44C2×C4×C47#4112yes—
45C2×Dic47—44no—
46C2×Dic47—44no—
47C2×Dic47—44no—
48C8×C47—22no—
49C8×C47C22⋊C414yescomplemented
50C22×C47—22no—
51C22×C47—22no—
52C22×C47—24no—
53C22×C47—24no—
54C22×C47#10714yescomplemented
55C22×C47C2×C4⋊C411yescharacteristic
56C22×C47#12112yes—
57C22×C47C2×D811yescharacteristic
58C22×C47C2×Q1611yescharacteristic
59C22×C47#13512yes—
60C4×C47—22no—
61C4×C47C2×C22⋊C411yescharacteristic
62C4×C47#11711yescharacteristic
63C4×C47C22⋊Q812yes—
64Dic47—84no—
65#1808—471nomaximal, Sylow
66C2×C47—24no—
67C2×C47#38011yescharacteristic
68C2×C47C2×#10711yescharacteristic
69C2×C47#42711yescharacteristic
70C2×C47#46612yes—
71C2×C47#46712yes—
72C23×C8D4711yescharacteristic
73C2×#107—472no—
74#380—472no—
75#340—472no—
76C47#180811yescharacteristic, complemented, Sylow
77C23×C4C2×D4711yescharacteristic
78C22×C8—24no—
79C22×C8Dic4714yescomplemented
80C22×C8C2×D4711yescharacteristic
81C22×C8C2×D4711yescharacteristic
82C2×C4⋊C4—474no—
83C2×C22⋊C4—942no—
84#107—944no—
85#95—942no—
86C24D18811yescharacteristic
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—944no—
90C22×C4Dic9412yes—
91C22×C4D18811yescharacteristic
92C22×C4C2×Dic4712yes—
93C22×C4C22×D4711yescharacteristic
94C2×C8—22no—
95C2×C8—28no—
96C2×C8C2×Dic4712yes—
97C2×C8C2×Dic4712yes—
98C2×C8C22⋊D4714yes—
99C4⋊C4—944no—
100C4⋊C4—944no—
101C22⋊C4—1884no—
102C23—22no—
103C23—22no—
104C23D37612yes—
105C23Dic18812yes—
106C23C4⋊Dic4712yes—
107C23C2×D18811yescharacteristic
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—24no—
112C2×C4—1884no—
113C2×C4—1884no—
114C2×C4—1884no—
115C2×C4C4⋊Dic4712yes—
116C2×C4C2×Dic9411yescharacteristic
117C2×C4#1062535012yes—
118C2×C4C22×Dic4711yescharacteristic
119C2×C4C2×C22⋊D4712yes—
120C8—22no—
121C8C22⋊Dic4714yescomplemented
122C22—22no—
123C22—24no—
124C22—24no—
125C22—22no—
126C22#1309395814yescomplemented
127C22C2×C4⋊Dic4711yescharacteristic
128C22#1309399812yes—
129C22C2×D37611yescharacteristic
130C22C2×Dic18811yescharacteristic
131C22#1309404612yes—
132C4—22no—
133C4—3764no—
134C4C2×C22⋊Dic4711yescharacteristic
135C4#1309398311yescharacteristic
136C4#1309400312yes—
137C2—24no—
138C2#1568898311yescharacteristic
139C2C2×#1309395811yescharacteristic
140C2#1568916111yescharacteristic
141C2#1568935912yes—
142C2#1568936412yes—
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC23×C8×C47C2
socleC23×C47C2×D4
hypercenterC23×C8D47
hypocenterC47#1808
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C2×#13093958C2semidirect
3. #15688886C2semidirect
11. C22×C8×C47C4semidirect
49. C8×C47C22⋊C4semidirect
54. C22×C47#107semidirect
76. C47#1808semidirect
79. C22×C8Dic47semidirect
121. C8C22⋊Dic47semidirect
126. C22#13093958semidirect