Finite Group Databasebeta

← #16777526

Subgroups — #16777526

Order 3328.

208 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 78 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×#11718233C212yesmaximal
2#13115007C211yesmaximal, characteristic
3C2×#88106—22no—
4C13×#423C411yescharacteristic
5C2×#88062—22no—
6#11718585C411yescharacteristic
7C2×C4×#1055C2211yescharacteristic
8#11718233—22no—
9#11718233C414yes—
10C2×C13×M16—21no—
11C2×C42×C13C2×C411yescharacteristic
12C2×#6099—21no—
13C22×#1055D412yes—
14#88106—24no—
15#88106—42no—
16C2×#6092—42no—
17C13×C4⋊C8—41no—
18#88062—42no—
19#88062—42no—
20C4⋊#1055—41no—
21C4×#1055C2×C412yes—
22C4×#1055D411yescharacteristic
23C4×#1055Q811yescharacteristic
24#7273—131nomaximal, Sylow
25C22×C4×C13—21no—
26C22×C4×C13C22⋊C411yescharacteristic
27C13×M16—42no—
28C2×C8×C13—41no—
29C42×C13—21no—
30C42×C13C4211yescharacteristic
31C42×C13C4⋊C411yescharacteristic
32#6099—42no—
33C2×#1055—41no—
34C2×#1055C22⋊C412yes—
35C2×#1055C4⋊C412yes—
36C2×#1055D812yes—
37C2×#1055SD1612yes—
38C2×#1055SD1612yes—
39C2×#1055Q1612yes—
40#6092—44no—
41C2×#364—132no—
42#1848—131no—
43C23×C13#10111yescharacteristic
44C2×C4×C13—21no—
45C2×C4×C13—21no—
46C2×C4×C13—42no—
47C2×C4×C13#9511yescharacteristic
48C2×C4×C13#10011yescharacteristic
49C2×C4×C13#10212yes—
50C2×C4×C13#10312yes—
51C8×C13—81no—
52#1055—81no—
53#1055#10212yes—
54#1055#10312yes—
55#1055#10612yes—
56#1055#10712yes—
57C2×M32—262no—
58C2×#108—262no—
59#423—131no—
60#423#26111yescharacteristic
61C2×C4×C8—131no—
62#364—134no—
63#364—262no—
64C22×C13—41no—
65C22×C13#33212yes—
66C22×C13#34311yescharacteristic
67C4×C13—22no—
68C4×C13—41no—
69C4×C13#33111yescharacteristic
70C4×C13#33311yescharacteristic
71C4×C13#34012yes—
72C2×M16—21no—
73C2×M16—261no—
74C22×C8—132no—
75C2×C42C2×#26111yescharacteristic
76M32—264no—
77M32—522no—
78C2×C16—522no—
79#108—522no—
80#108—522no—
81C4⋊C8—41no—
82C4⋊C8—521no—
83C4×C8—132no—
84C4×C8—131no—
85C4×C8—131no—
86C2×C13—21no—
87C2×C13—22no—
88C2×C13#129611yescharacteristic
89C22×C4—21no—
90C22×C4C22⋊#26111yescharacteristic
91M16—42no—
92M16—522no—
93C2×C8—41no—
94C2×C8—132no—
95C2×C8—132no—
96C2×C8—132no—
97C2×C8—132no—
98C2×C8—132no—
99C2×C8—132no—
100C2×C8—521no—
101C42—21no—
102C42C4×#26111yescharacteristic
103C42C4⋊#26111yescharacteristic
104C16—524no—
105C13#727311yescharacteristic, complemented, Sylow
106C23#8811311yescharacteristic
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—42no—
110C2×C4(C2×#261)⋊C411yescharacteristic
111C2×C4#8811512yes—
112C2×C4#8811712yes—
113C2×C4#8812111yescharacteristic
114C8—81no—
115C8—132no—
116C8—132no—
117C8—132no—
118C8—132no—
119C8—1041no—
120C22—41no—
121C22#1171824512yes—
122C22#1171829111yescharacteristic
123C4—22no—
124C4—41no—
125C4#1171824612yes—
126C4#1171829711yescharacteristic
127C4#1171830311yescharacteristic
128C2—21no—
129C2—22no—
130C2#1312971411yescharacteristic
subgroupG/H
centerC4#11718303
commutatorC42×C13C42
FrattiniC2×C42C2×#261
FittingC13×#423C4
socleC2×C13#1296
prime radicalC23×C13#101
cosocleC2×C4×#1055C22
hypercenter#423#261
hypocenterC13#7273
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
105. C13#7273semidirect

Maximal subgroups

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

subgroupindex
C2×#117182332
#131150072
#727313