Finite Group Databasebeta

← #16844052

Subgroups — #16844052

Order 3968.

300 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 89 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#14521106C212yesmaximal, complemented
2#14520773C214yesmaximal, complemented
3C2×C4×D4×C31C211yesmaximal, characteristic
4C22×D4×C31C411yescharacteristic
5C23×C4×C31C412yes—
6C4×D4×C31—22no—
7C4×D4×C31—22no—
8C2×C4⋊C4×C31C411yescharacteristic
9C2×C22⋊C4×C31C2212yes—
10C2×C42×C31C2211yescharacteristic
11C22⋊(C31⋊C8)C2214yes—
12C4⋊(C31⋊C8)—22no—
13#11758391—22no—
14C24×C31C2×C412yes—
15C2×D4×C31—24no—
16C2×D4×C31—22no—
17C22×C4×C31—22no—
18C22×C4×C31—22no—
19C22×C4×C31—44no—
20C22×C4×C31C2×C411yescharacteristic
21C22×C4×C31C2×C411yescharacteristic
22C22×C4×C31C2×C412yes—
23C22×C4×C31C2311yescharacteristic
24C4⋊C4×C31—22no—
25C22⋊C4×C31—24no—
26C42×C31D412yes—
27C42×C31D412yes—
28C2×C31⋊C8—24no—
29C23×C31—22no—
30C23×C31—22no—
31C23×C31—42no—
32C23×C31—42no—
33C23×C31M1614yes—
34C23×C31C22×C411yescharacteristic
35D4×C31—28no—
36C2×C4×C31—22no—
37C2×C4×C31—22no—
38C2×C4×C31—22no—
39C2×C4×C31—41no—
40C2×C4×C31—44no—
41C2×C4×C31—44no—
42C2×C4×C31—42no—
43C2×C4×C31C22⋊C412yes—
44C2×C4×C31C22⋊C411yescharacteristic
45C2×C4×C31C22⋊C411yescharacteristic
46C2×C4×C31C2×D412yes—
47C31⋊C8—44no—
48#1466—311nomaximal, Sylow
49C22×C31—21no—
50C22×C31—21no—
51C22×C31—24no—
52C22×C31—44no—
53C22×C31—44no—
54C22×C31—42no—
55C22×C31—42no—
56C22×C31C2×C22⋊C411yescharacteristic
57C22×C31C2×M1612yes—
58C4×C31—22no—
59C4×C31—22no—
60C4×C31—21no—
61C4×C31—42no—
62C4×C31#10012yes—
63C2×C4×D4D3111yescharacteristic
64#432—312no—
65#323—314no—
66C2×C31—22no—
67C2×C31—44no—
68C2×C31#40711yescharacteristic
69C2×C31#41011yescharacteristic
70C2×C31C2×#10011yescharacteristic
71C22×D4Dic3111yescharacteristic
72C23×C4Dic3112yes—
73C4×D4—22no—
74C4×D4—22no—
75C2×C4⋊C4Dic3111yescharacteristic
76C2×C22⋊C4C2×D3112yes—
77C2×C42C2×D3111yescharacteristic
78C4⋊C8—622no—
79C22⋊C8—314no—
80#97—622no—
81C31#146611yescharacteristic, complemented, Sylow
82C24C2×Dic3112yes—
83C2×D4—24no—
84C2×D4—22no—
85C22×C4—22no—
86C22×C4—22no—
87C22×C4—44no—
88C22×C4C2×Dic3111yescharacteristic
89C22×C4C2×Dic3111yescharacteristic
90C22×C4C2×Dic3112yes—
91C22×C4C22×D3111yescharacteristic
92C2×C8—624no—
93C4⋊C4—22no—
94C22⋊C4—24no—
95C42C22⋊D3112yes—
96C42C22⋊D3112yes—
97C23—22no—
98C23—22no—
99C23—42no—
100C23—42no—
101C23#9247414yes—
102C23C22×Dic3111yescharacteristic
103D4—28no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—41no—
108C2×C4—44no—
109C2×C4—44no—
110C2×C4—42no—
111C2×C4C22⋊Dic3112yes—
112C2×C4C22⋊Dic3111yescharacteristic
113C2×C4C22⋊Dic3111yescharacteristic
114C2×C4C2×C22⋊D3112yes—
115C8—1244no—
116C22—21no—
117C22—21no—
118C22—24no—
119C22—44no—
120C22—44no—
121C22—42no—
122C22—42no—
123C22C2×#9247412yes—
124C22C2×C22⋊Dic3111yescharacteristic
125C4—22no—
126C4—22no—
127C4—21no—
128C4—42no—
129C4#1175842112yes—
130C2—22no—
131C2—44no—
132C2#1452101311yescharacteristic
133C2#1452102311yescharacteristic
134C2C2×#1175842111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic31
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C4×D4×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D4×C31C4
cosocleC22×C4×C31C23
hypercenterC2×C4×D4D31
hypocenterC31#1466
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14521106C2semidirect
2. #14520773C2semidirect
81. C31#1466semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145211062
#145207732
C2×C4×D4×C312
#146631