Finite Group Databasebeta

← #106×Dic47 #20243279

Subgroups — #106×Dic47 #20243279

Order 6016.

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

normal subgroups only

This group has 280 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×#13093956C211yesmaximal, characteristic
2C2×C8×Dic47C211yesmaximal, characteristic
3C4⋊C4×Dic47C212yesmaximal
4#15688885C212yesmaximal
5C2×#106×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2211yescharacteristic
7C2×C4⋊Dic47C2212yes—
8C2×C4×Dic47—22no—
9C2×C4×Dic47C2211yescharacteristic
10#13093956C414yescomplemented
11C8×Dic47C414yescomplemented
12C47⋊#95—22no—
13C22×C8×C47C2211yescharacteristic
14C2×C4⋊C4×C47C2212yes—
15#106×C47C414yescomplemented
16C22×C4×C47—22no—
17C22×C4×C47C2311yescharacteristic
18C22×Dic47—22no—
19C22×Dic47D411yescharacteristic
20C22×Dic47D411yescharacteristic
21C2×C8×C47C2×C412yes—
22C2×C8×C47C2×C412yes—
23C2×C8×C47C2×C412yes—
24C4⋊C4×C47—22no—
25C4⋊C4×C47C2×C414yes—
26C4⋊Dic47—22no—
27C4⋊Dic47C2×C414yes—
28C4×Dic47—44no—
29C4×Dic47C2×C412yes—
30C4×Dic47Q812yes—
31C2×C47⋊C8—21no—
32C2×C47⋊C8—21no—
33C2×C47⋊C8C2×C412yes—
34C23×C47C2×D411yescharacteristic
35C2×C4×C47—24no—
36C2×C4×C47—42no—
37C2×C4×C47—42no—
38C2×C4×C47C22×C411yescharacteristic
39C2×C4×C47C22×C411yescharacteristic
40C2×C4×C47C22×C411yescharacteristic
41C2×C4×C47C2×Q811yescharacteristic
42C2×C4×C47#4111yescharacteristic
43C2×C4×C47#4111yescharacteristic
44C2×Dic47—22no—
45C2×Dic47—24no—
46C2×Dic47—42no—
47C2×Dic47—42no—
48C2×Dic47C4⋊C412yes—
49C2×Dic47C4⋊C412yes—
50C2×Dic47SD1614yes—
51C8×C47C4214yescomplemented
52C47⋊C8—22no—
53C22×C47C2×C4⋊C411yescharacteristic
54C22×C47C4×D411yescharacteristic
55C22×C47C4×D411yescharacteristic
56C22×C47C2×SD1612yes—
57C22×C47#13512yes—
58C4×C47—44no—
59C4×C47C2×C4211yescharacteristic
60C4×C47#11711yescharacteristic
61C4×C47C4×Q811yescharacteristic
62C4×C47C4×Q811yescharacteristic
63Dic47—22no—
64Dic47—44no—
65Dic47#10614yesdirect product factor
66C4×#106—471nomaximal, Sylow
67C2×C47C4×C4⋊C411yescharacteristic
68C2×C47C2×#10611yescharacteristic
69C2×C47#42711yescharacteristic
70C2×C47C4×SD1612yes—
71C2×C47C4×SD1612yes—
72C2×#106—471no—
73C2×#106D4711yescharacteristic
74C2×C4×C8—471no—
75C4×C4⋊C4—472no—
76#340—472no—
77C47C4×#10611yescharacteristic, complemented, Sylow
78C22×C8—471no—
79C22×C8C2×D4711yescharacteristic
80C2×C4⋊C4—472no—
81C2×C4⋊C4C2×D4712yes—
82C2×C42—471no—
83C2×C42—942no—
84#106—474no—
85#106Dic4714yesdirect product factor
86C4×C8—474no—
87#95—942no—
88C22×C4—22no—
89C22×C4—471no—
90C22×C4—471no—
91C22×C4—942no—
92C22×C4C22×D4711yescharacteristic
93C2×C8—472no—
94C2×C8—941no—
95C2×C8—941no—
96C2×C8C4×D4712yes—
97C2×C8C4×D4712yes—
98C2×C8C2×Dic4712yes—
99C4⋊C4—22no—
100C4⋊C4—474no—
101C4⋊C4—942no—
102C4⋊C4C2×Dic4714yes—
103C42—472no—
104C42—472no—
105C42—1884no—
106C23D4×D4711yescharacteristic
107C2×C4—24no—
108C2×C4—42no—
109C2×C4—42no—
110C2×C4—472no—
111C2×C4—474no—
112C2×C4—472no—
113C2×C4—942no—
114C2×C4—944no—
115C2×C4—1882no—
116C2×C4—1882no—
117C2×C4C2×C4×D4711yescharacteristic
118C2×C4C2×C4×D4711yescharacteristic
119C2×C4#1062535211yescharacteristic
120C2×C4Q8×D4711yescharacteristic
121C2×C4#1062535411yescharacteristic
122C2×C4C22×Dic4711yescharacteristic
123C8—942no—
124C8C4×Dic4714yescomplemented
125C22C4⋊C4×D4711yescharacteristic
126C22#1309398611yescharacteristic
127C22D4×Dic4711yescharacteristic
128C22SD16×D4712yes—
129C22#1309404512yes—
130C4—44no—
131C4—474no—
132C4—942no—
133C4—1884no—
134C4C2×C4×Dic4711yescharacteristic
135C4#1309398211yescharacteristic
136C4#1309398911yescharacteristic
137C4Q8×Dic4711yescharacteristic
138C2C4⋊C4×Dic4711yescharacteristic
139C2#106×D4711yescharacteristic
140C2#1568915811yescharacteristic
141C2#1568921012yes—
142C2SD16×Dic4712yes—
subgroupG/H
centerC23D4×D47
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC2×#106×C47C2
socleC23×C47C2×D4
hypercenterC2×#106D47
hypocenterC47C4×#106
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
10. #13093956C4semidirect
11. C8×Dic47C4semidirect
15. #106×C47C4semidirect
51. C8×C47C42semidirect
65. Dic47#106direct (N × H)
77. C47C4×#106semidirect
85. #106Dic47direct (N × H)
124. C8C4×Dic47semidirect