Finite Group Databasebeta

← #16777760

Subgroups — #16777760

Order 3328.

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

normal subgroups only

This group has 184 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#13115814C211yesmaximal, characteristic
3C13×#533C411yescharacteristic
4C42×Dic13C411yescharacteristic
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×C4×Dic13—41no—
16C2×#6099D412yes—
17#88106—42no—
18C4⋊#1055—41no—
19#7361—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—
34C4×Dic13—44no—
35#6099—42no—
36C2×#1055—22no—
37#6092—82no—
38#1994—131no—
39#1327—132no—
40C23×C13#10011yescharacteristic
41Q8×C13—82no—
42C2×C4×C13—21no—
43C2×C4×C13—21no—
44C2×C4×C13—21no—
45C2×C4×C13—21no—
46C2×C4×C13—42no—
47C2×C4×C13—42no—
48C2×C4×C13C22⋊C811yescharacteristic
49C2×C4×C13#9911yescharacteristic
50C2×Dic13—42no—
51C2×Dic13—44no—
52#1055—42no—
53#533#26111yescharacteristic
54#423—131no—
55C43—131no—
56#349—262no—
57#339—262no—
58C22×C13—21no—
59C22×C13—41no—
60C22×C13#32311yescharacteristic
61C4×C13—22no—
62C4×C13—21no—
63C4×C13—41no—
64C4×C13—82no—
65C4×C13#35411yescharacteristic
66C4×C13#35611yescharacteristic
67Dic13—44no—
68C2×M16—132no—
69C4⋊Q8—21no—
70#125#105712yes—
71C22⋊Q8—41no—
72C4×Q8—41no—
73#117—21no—
74C2×C42—261no—
75C2×C42—521no—
76C2×C42C2×#26111yescharacteristic
77M32—522no—
78C4⋊C8—521no—
79C2×C13—21no—
80C2×C13—41no—
81C2×C13#131911yescharacteristic
82C2×Q8—41no—
83C22×C4—21no—
84C22×C4—521no—
85C22×C4C22⋊#26111yescharacteristic
86M16—522no—
87C2×C8—262no—
88C4⋊C4—22no—
89C4⋊C4—42no—
90C4⋊C4—41no—
91C22⋊C4—41no—
92C42—21no—
93C42—41no—
94C42—262no—
95C42—521no—
96C42—524no—
97C42C2×#105711yescharacteristic
98C42#612211yescharacteristic
99C16—1042no—
100C13#736111yescharacteristic, complemented, Sylow
101C23#8812111yescharacteristic
102Q8—82no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—522no—
110C2×C4—524no—
111C2×C4#8811911yescharacteristic
112C2×C4C22⋊#105711yescharacteristic
113C8—522no—
114C22—21no—
115C22—41no—
116C22#1171830511yescharacteristic
117C4—22no—
118C4—21no—
119C4—41no—
120C4—82no—
121C4—524no—
122C4#1171830011yescharacteristic
123C4#1171830111yescharacteristic
124C2—21no—
125C2—41no—
126C2#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#7361
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
100. C13#7361semidirect

Maximal subgroups

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

subgroupindex
#131297822
#131158142
#736113