Finite Group Databasebeta

← #16845791

Subgroups — #16845791

Order 3968.

316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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#14521013C212yesmaximal
2#14520818C214yesmaximal, complemented
3C22×C4⋊C4×C31C211yesmaximal, characteristic
4C23×C4×C31C412yes—
5C23×C4×C31C2211yescharacteristic
6C2×C4⋊C4×C31—22no—
7C2×C4⋊C4×C31—22no—
8C2×C4⋊C4×C31C412yes—
9C2×C4⋊C4×C31C2212yes—
10C2×#92474C2214yes—
11C22⋊(C31⋊C8)—22no—
12C22⋊(C31⋊C8)—22no—
13C24×C31C2×C411yescharacteristic
14C22×C4×C31—24no—
15C22×C4×C31—22no—
16C22×C4×C31—22no—
17C22×C4×C31—44no—
18C22×C4×C31C2×C411yescharacteristic
19C22×C4×C31C2×C414yes—
20C22×C4×C31D412yes—
21C22×C4×C31D412yes—
22C22×C4×C31C2311yescharacteristic
23C4⋊C4×C31—24no—
24C4⋊C4×C31—24no—
25#92474—28no—
26C2×C31⋊C8—24no—
27C23×C31—22no—
28C23×C31—22no—
29C23×C31—22no—
30C23×C31C22⋊C411yescharacteristic
31C23×C31C22⋊C411yescharacteristic
32C23×C31C22×C411yescharacteristic
33C2×C4×C31—22no—
34C2×C4×C31—24no—
35C2×C4×C31—24no—
36C2×C4×C31—24no—
37C2×C4×C31—44no—
38C2×C4×C31—44no—
39C2×C4×C31—44no—
40C2×C4×C31C22⋊C412yes—
41C2×C4×C31C2×D412yes—
42C2×C4×C31#4114yes—
43C31⋊C8—44no—
44#1821—311nomaximal, Sylow
45C22×C31—28no—
46C22×C31—21no—
47C22×C31—21no—
48C22×C31—21no—
49C22×C31—21no—
50C22×C31—21no—
51C22×C31—21no—
52C22×C31#10012yes—
53C22×C31#10112yes—
54C22×C31C2×C22⋊C411yescharacteristic
55C22×C31#11712yes—
56C4×C31—22no—
57C4×C31—44no—
58C4×C31#12314yes—
59C22×C4⋊C4D3111yescharacteristic
60#407—312no—
61#343—314no—
62C2×C31—22no—
63C2×C31—22no—
64C2×C31—22no—
65C2×C31#38111yescharacteristic
66C2×C31C2×#10011yescharacteristic
67C2×C31C2×#10111yescharacteristic
68C23×C4Dic3112yes—
69C23×C4C2×D3111yescharacteristic
70C2×M16—314no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4Dic3112yes—
74C2×C4⋊C4C2×D3112yes—
75C22⋊C8—622no—
76C22⋊C8—622no—
77C31#182111yescharacteristic, complemented, Sylow
78C24C2×Dic3111yescharacteristic
79C22×C4—24no—
80C22×C4—22no—
81C22×C4—22no—
82C22×C4—44no—
83C22×C4C2×Dic3111yescharacteristic
84C22×C4C2×Dic3114yes—
85C22×C4C22⋊D3112yes—
86C22×C4C22⋊D3112yes—
87C22×C4C22×D3111yescharacteristic
88M16—628no—
89C2×C8—624no—
90C4⋊C4—24no—
91C4⋊C4—24no—
92C23—22no—
93C23—22no—
94C23—22no—
95C23C22⋊Dic3111yescharacteristic
96C23C22⋊Dic3111yescharacteristic
97C23C22×Dic3111yescharacteristic
98C2×C4—22no—
99C2×C4—24no—
100C2×C4—24no—
101C2×C4—24no—
102C2×C4—44no—
103C2×C4—44no—
104C2×C4—44no—
105C2×C4C22⋊Dic3112yes—
106C2×C4#9249514yes—
107C2×C4C2×C22⋊D3112yes—
108C8—1244no—
109C22—28no—
110C22—21no—
111C22—21no—
112C22—21no—
113C22—21no—
114C22—21no—
115C22—21no—
116C22#1175842112yes—
117C22#1175842412yes—
118C22#1175850312yes—
119C22C2×C22⋊Dic3111yescharacteristic
120C4—22no—
121C4—44no—
122C4#1175850614yes—
123C2—22no—
124C2—22no—
125C2—22no—
126C2#1452091211yescharacteristic
127C2C2×#1175842111yescharacteristic
128C2C2×#1175842411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic31
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC22×C4⋊C4×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC24×C31C2×C4
cosocleC22×C4×C31C23
hypercenterC22×C4⋊C4D31
hypocenterC31#1821
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14520818C2semidirect
77. C31#1821semidirect

Maximal subgroups

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

subgroupindex
#145210132
#145208182
C22×C4⋊C4×C312
#182131