Finite Group Databasebeta

← #16777739

Subgroups — #16777739

Order 3328.

178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 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#13129768C212yesmaximal
2#13114917C211yesmaximal, characteristic
3C2×#88180C411yescharacteristic
4C13×#407C411yescharacteristic
5#11718868C2211yescharacteristic
6#11718284—22no—
7#11718146—22no—
8C23×C4×C13C2×C411yescharacteristic
9C2×C13×M16—21no—
10C2×C22⋊Dic13C812yes—
11#88180—41no—
12#88180—41no—
13C2×C4⋊Dic13—21no—
14C2×C4×Dic13—21no—
15C2×#6099D412yes—
16#88106—42no—
17C13×C22⋊C8—41no—
18C22⋊#1055—41no—
19#7351—131nomaximal, Sylow
20C24×C13C2×C811yescharacteristic
21C22×C4×C13—21no—
22C22×C4×C13—21no—
23C22×C4×C13—42no—
24C22×C4×C13C22⋊C411yescharacteristic
25C22×C4×C13M1611yescharacteristic
26C22×Dic13—22no—
27C13×M16—42no—
28C2×C8×C13—41no—
29C22⋊Dic13—42no—
30C4⋊Dic13—41no—
31C4⋊Dic13—41no—
32C4×Dic13—42no—
33#6099—42no—
34C2×#1055—22no—
35#6092—82no—
36#1822—131no—
37#1320—132no—
38C23×C13—21no—
39C23×C13—41no—
40C23×C13—81no—
41C23×C13C22⋊C811yescharacteristic
42C2×C4×C13—22no—
43C2×C4×C13—21no—
44C2×C4×C13—42no—
45C2×C4×C13—42no—
46C2×C4×C13—41no—
47C2×C4×C13#9911yescharacteristic
48C2×C4×C13#10011yescharacteristic
49C2×Dic13—42no—
50C2×Dic13—82no—
51C8×C13—81no—
52#1055—42no—
53C2×#117—131no—
54#407—131no—
55#407#26111yescharacteristic
56#349—262no—
57#343—262no—
58C22×C13—21no—
59C22×C13—41no—
60C22×C13—42no—
61C22×C13—41no—
62C22×C13—82no—
63C22×C13#32311yescharacteristic
64C4×C13—21no—
65C4×C13—41no—
66C4×C13#35212yes—
67Dic13—82no—
68C23×C4C2×#26111yescharacteristic
69C2×M16—21no—
70C2×M16—132no—
71#117—521no—
72#117—521no—
73C2×C4⋊C4—261no—
74C2×C22⋊C4—132no—
75C2×C42—261no—
76M32—522no—
77C22⋊C8—41no—
78C22⋊C8—521no—
79C2×C13—21no—
80C2×C13—41no—
81C2×C13—81no—
82C2×C13#131711yescharacteristic
83C24D13⋊C811yescharacteristic
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—42no—
87C22×C4—262no—
88C22×C4#611811yescharacteristic
89C22×C4C22⋊#26111yescharacteristic
90M16—42no—
91M16—522no—
92C2×C8—41no—
93C2×C8—262no—
94C4⋊C4—521no—
95C4⋊C4—521no—
96C22⋊C4—522no—
97C42—522no—
98C16—1042no—
99C13#735111yescharacteristic, complemented, Sylow
100C23—21no—
101C23—41no—
102C23—81no—
103C23#8811111yescharacteristic
104C2×C4—22no—
105C2×C4—21no—
106C2×C4—42no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4—522no—
110C2×C4—1042no—
111C2×C4#8810711yescharacteristic
112C2×C4#8812111yescharacteristic
113C8—81no—
114C8—522no—
115C22—21no—
116C22—41no—
117C22—42no—
118C22—41no—
119C22—82no—
120C22#1171828711yescharacteristic
121C4—21no—
122C4—41no—
123C4—1042no—
124C4#1171823712yes—
125C2—21no—
126C2—41no—
127C2—81no—
128C2#1312976311yescharacteristic
subgroupG/H
centerC2#13129763
commutator, prime radicalC24×C13C2×C8
FrattiniC23×C4C2×#261
FittingC13×#407C4
socleC2×C13#1317
cosocle#11718868C22
hypercenter#407#261
hypocenterC13#7351
LCSG ▷ C24×C13 ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
99. C13#7351semidirect

Maximal subgroups

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

subgroupindex
#131297682
#131149172
#735113