Finite Group Databasebeta

← #16777758

Subgroups — #16777758

Order 3328.

164 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 38 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#13129782C212yesmaximal
2#13115818C211yesmaximal, characteristic
3C13×#533C411yescharacteristic
4#11718593C411yescharacteristic
5#11718585C2211yescharacteristic
6#11718284—22no—
7#11718124—22no—
8C13×C4⋊Q8—21no—
9C13×#125C812yes—
10C13×C22⋊Q8—41no—
11C4×Q8×C13—41no—
12C13×#117—21no—
13C2×C42×C13C2×C411yescharacteristic
14C2×C4×Dic13—21no—
15C2×#6099D412yes—
16#88106—42no—
17#88071—41no—
18C4⋊#1055—41no—
19#7360—131nomaximal, Sylow
20C2×Q8×C13—41no—
21C22×C4×C13—21no—
22C22×C4×C13C22⋊C411yescharacteristic
23C22×Dic13—41no—
24C13×C4⋊C4—22no—
25C13×C4⋊C4—42no—
26C13×C4⋊C4—41no—
27C13×C22⋊C4—41no—
28C42×C13—21no—
29C42×C13—41no—
30C42×C13C2×C811yescharacteristic
31C42×C13M1611yescharacteristic
32C4×Dic13—22no—
33C4×Dic13—41no—
34#6099—42no—
35C2×#1055—22no—
36#6092—82no—
37#1995—131no—
38#1327—132no—
39C23×C13#10011yescharacteristic
40Q8×C13—82no—
41C2×C4×C13—21no—
42C2×C4×C13—21no—
43C2×C4×C13—21no—
44C2×C4×C13—21no—
45C2×C4×C13—42no—
46C2×C4×C13—81no—
47C2×C4×C13C22⋊C811yescharacteristic
48C2×C4×C13#9911yescharacteristic
49C2×Dic13—42no—
50C2×Dic13—82no—
51#1055—42no—
52#533#26111yescharacteristic
53#423—131no—
54#376—131no—
55#349—262no—
56#339—262no—
57C22×C13—21no—
58C22×C13—41no—
59C22×C13#32311yescharacteristic
60C4×C13—21no—
61C4×C13—41no—
62C4×C13—41no—
63C4×C13—82no—
64C4×C13#35411yescharacteristic
65C4×C13#35611yescharacteristic
66Dic13—82no—
67C2×M16—132no—
68C4⋊Q8—21no—
69#125#105712yes—
70C22⋊Q8—41no—
71C4×Q8—41no—
72#117—21no—
73C2×C42—261no—
74C2×C42C2×#26111yescharacteristic
75M32—522no—
76C4⋊C8—521no—
77#95—521no—
78C2×C13—21no—
79C2×C13—41no—
80C2×C13#131911yescharacteristic
81C2×Q8—41no—
82C22×C4—21no—
83C22×C4—521no—
84C22×C4C22⋊#26111yescharacteristic
85M16—522no—
86C2×C8—262no—
87C4⋊C4—22no—
88C4⋊C4—42no—
89C4⋊C4—41no—
90C22⋊C4—41no—
91C42—21no—
92C42—41no—
93C42—262no—
94C42—521no—
95C42C2×#105711yescharacteristic
96C42#612211yescharacteristic
97C16—1042no—
98C13#736011yescharacteristic, complemented, Sylow
99C23#8812111yescharacteristic
100Q8—82no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—42no—
106C2×C4—81no—
107C2×C4—522no—
108C2×C4—1042no—
109C2×C4#8811911yescharacteristic
110C2×C4C22⋊#105711yescharacteristic
111C8—522no—
112C22—21no—
113C22—41no—
114C22#1171830511yescharacteristic
115C4—21no—
116C4—41no—
117C4—41no—
118C4—82no—
119C4—1042no—
120C4#1171830011yescharacteristic
121C4#1171830111yescharacteristic
122C2—21no—
123C2—41no—
124C2#1312976611yescharacteristic
subgroupG/H
centerC4#11718300
commutatorC42×C13C2×C8
FrattiniC2×C42C2×#261
FittingC13×#533C4
socleC2×C13#1319
prime radicalC23×C13#100
cosocle#11718585C22
hypercenter#533#261
hypocenterC13#7360
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
98. C13#7360semidirect

Maximal subgroups

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

subgroupindex
#131297822
#131158182
#736013