Finite Group Databasebeta

← #16777730

Subgroups — #16777730

Order 3328.

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

normal subgroups only

This group has 200 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#13129762C212yesmaximal
2#13114913C211yesmaximal, characteristic
3C2×C13×#117C411yescharacteristic
4#11718872C411yescharacteristic
5#11718872C2211yescharacteristic
6#11718305—22no—
7#11718118—22no—
8C23×C4×C13C2×C411yescharacteristic
9C13×#117—41no—
10C13×#117—41no—
11C2×C13×C4⋊C4—21no—
12C2×C13×C22⋊C4—21no—
13C2×C42×C13C812yescomplemented
14C2×C22⋊Dic13—21no—
15C2×C22⋊Dic13D412yes—
16C22⋊#1057—42no—
17#88071—41no—
18#88071—41no—
19#7348—131nomaximal, Sylow
20C24×C13C22⋊C411yescharacteristic
21C22×C4×C13—21no—
22C22×C4×C13—21no—
23C22×C4×C13—22no—
24C22×C4×C13—42no—
25C22×C4×C13C2×C811yescharacteristic
26C22×C4×C13M1611yescharacteristic
27C22×Dic13—22no—
28C22×Dic13—41no—
29C2×#1057—82no—
30C13×C4⋊C4—42no—
31C13×C22⋊C4—41no—
32C13×C22⋊C4—41no—
33C42×C13—42no—
34C22⋊Dic13—42no—
35C22⋊Dic13—42no—
36#1820—131no—
37#1317—132no—
38C23×C13—22no—
39C23×C13—81no—
40C23×C13C22⋊C811yescharacteristic
41C23×C13#9911yescharacteristic
42C23×C13#10011yescharacteristic
43C2×C4×C13—21no—
44C2×C4×C13—21no—
45C2×C4×C13—42no—
46C2×C4×C13—42no—
47C2×C4×C13—41no—
48C2×C4×C13—41no—
49C2×C4×C13—42no—
50C2×C4×C13—82no—
51C2×Dic13—42no—
52C2×Dic13—82no—
53C2×Dic13—81no—
54C2×Dic13—82no—
55#1057—162no—
56C2×#117#26111yescharacteristic
57#381—131no—
58#381—131no—
59#342—262no—
60#323—262no—
61C22×C13—21no—
62C22×C13—21no—
63C22×C13—41no—
64C22×C13—41no—
65C22×C13—41no—
66C22×C13—82no—
67C22×C13#32311yescharacteristic
68C22×C13#35212yes—
69C4×C13—41no—
70C4×C13—41no—
71C4×C13—82no—
72Dic13—82no—
73Dic13—161no—
74C23×C4C2×#26111yescharacteristic
75#117—41no—
76#117—41no—
77C2×C4⋊C4—21no—
78C2×C22⋊C4—21no—
79C2×C22⋊C4—132no—
80C2×C22⋊C4—261no—
81C2×C42#105712yescomplemented
82C22⋊C8—522no—
83#95—521no—
84#95—521no—
85C2×C13—22no—
86C2×C13—21no—
87C2×C13—41no—
88C2×C13—41no—
89C2×C13#131711yescharacteristic
90C24C22⋊#26111yescharacteristic
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—22no—
94C22×C4—42no—
95C22×C4—262no—
96C22×C4—521no—
97C22×C4C2×#105711yescharacteristic
98C22×C4#612211yescharacteristic
99C2×C8—1042no—
100C4⋊C4—42no—
101C22⋊C4—41no—
102C22⋊C4—41no—
103C22⋊C4—522no—
104C22⋊C4—522no—
105C42—42no—
106C13#734811yescharacteristic, complemented, Sylow
107C23—22no—
108C23—81no—
109C23#8811911yescharacteristic
110C23C22⋊#105711yescharacteristic
111C23#8812111yescharacteristic
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4—82no—
120C2×C4—522no—
121C2×C4—1042no—
122C2×C4—1041no—
123C2×C4—1042no—
124C8—2082no—
125C22—21no—
126C22—21no—
127C22—41no—
128C22—41no—
129C22—41no—
130C22—82no—
131C22#1171828812yes—
132C22#1171830511yescharacteristic
133C4—41no—
134C4—41no—
135C4—82no—
136C4—1042no—
137C4—2081no—
138C2—21no—
139C2—22no—
140C2—41no—
141C2—41no—
142C2#1312976211yescharacteristic
subgroupG/H
centerC2#13129762
commutatorC22×C4×C13C2×C8
FrattiniC23×C4C2×#261
FittingC2×C13×#117C4
socleC2×C13#1317
prime radicalC24×C13C22⋊C4
cosocle#11718872C22
hypercenterC2×#117#261
hypocenterC13#7348
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
13. C2×C42×C13C8semidirect
81. C2×C42#1057semidirect
106. C13#7348semidirect

Maximal subgroups

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

subgroupindex
#131297622
#131149132
#734813