Finite Group Databasebeta

← #13129937

Subgroups — #13129937

Order 1664.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#11719132C211yesmaximal, characteristic
2#11719116C211yesmaximal, characteristic
3#11718790C211yesmaximal, characteristic
4C2×#6127C2211yescharacteristic
5#88237—21no—
6D13⋊M16—21no—
7C2×C13×M16C411yescharacteristic, complemented
8C22×#1055C411yescharacteristic, complemented
9#88121—21no—
10#88119—21no—
11#88113C412yescomplemented
12#88107C412yes—
13#88060—21no—
14#88060—21no—
15C22×C4×C13C2×C411yescharacteristic
16C2×C22⋊D13D411yescharacteristic
17C2×C22⋊D13Q811yescharacteristic
18#6127—41no—
19#6127—41no—
20C2×D52C2×C411yescharacteristic
21C2×C4×D13D411yescharacteristic
22C2×C4×D13D411yescharacteristic
23C2×Dic26C2×C411yescharacteristic
24C22⋊#261—22no—
25#6122—22no—
26C4⋊#261—41no—
27C4×#261—41no—
28#6118—41no—
29D13⋊C8—41no—
30C13×M16—41no—
31C2×C8×C13—21no—
32C2×#1055—21no—
33C2×#1055—41no—
34#1395—131nomaximal, Sylow
35C23×C13C4⋊C411yescharacteristic
36C22×D13C22⋊C411yescharacteristic
37C22×D13C4⋊C411yescharacteristic
38C2×#261—42no—
39C2×C4×C13—21no—
40C2×C4×C13—21no—
41C2×C4×C13C4211yescharacteristic
42C2×C4×C13C22⋊C411yescharacteristic
43C22⋊D13—41no—
44C22⋊D13—41no—
45C2×Dic13C22⋊C411yescharacteristic
46C2×Dic13C4⋊C411yescharacteristic
47D52—41no—
48C4×D13—21no—
49C4×D13—21no—
50C4×D13—21no—
51C4×D13—21no—
52Dic26—41no—
53#1057—42no—
54C8×C13—41no—
55#1055—41no—
56#413—131no—
57#410—131no—
58#408—131no—
59C22×C13—21no—
60C22×C13—41no—
61C22×C13#9511yescharacteristic
62C2×D13—21no—
63C2×D13—21no—
64C2×D13—41no—
65C2×D13—41no—
66#261—82no—
67C4×C13—21no—
68C4×C13#9911yescharacteristic
69C4×C13#9911yescharacteristic
70Dic13—21no—
71Dic13—21no—
72C2×#41—131no—
73C2×M16—261no—
74C2×M16#26111yescharacteristic, complemented
75C22×C8—131no—
76#117—261no—
77#101—132no—
78#100—261no—
79#99—132no—
80#99—261no—
81C22⋊C8—261no—
82C22⋊C8—261no—
83C2×C13—21no—
84C2×C13—41no—
85C2×C13#34211yescharacteristic
86D13—41no—
87D13—41no—
88#41—521no—
89#41—521no—
90C2×Q8—131no—
91C2×D4—131no—
92C2×D4—131no—
93C2×D4—131no—
94C22×C4—131no—
95C22×C4—131no—
96C22×C4C2×#26111yescharacteristic
97M16—41no—
98M16—262no—
99M16—521no—
100C2×C8—21no—
101C2×C8—261no—
102C2×C8—521no—
103C2×C8—521no—
104C4⋊C4—521no—
105C22⋊C4—262no—
106C42—521no—
107C13#139511yescharacteristic, complemented, Sylow
108C23—131no—
109C23—131no—
110C23C4⋊#26111yescharacteristic
111Q8—521no—
112D4—521no—
113D4—521no—
114D4—521no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—131no—
118C2×C4—131no—
119C2×C4—261no—
120C2×C4—261no—
121C2×C4—261no—
122C2×C4—261no—
123C2×C4—522no—
124C2×C4C4×#26111yescharacteristic
125C2×C4C22⋊#26111yescharacteristic
126C8—41no—
127C8—522no—
128C8—521no—
129C22—21no—
130C22—41no—
131C22—261no—
132C22—261no—
133C22—521no—
134C22—521no—
135C22(C2×#261)⋊C411yescharacteristic
136C4—21no—
137C4—261no—
138C4—261no—
139C4—1042no—
140C4#8810711yescharacteristic
141C4#8811911yescharacteristic
142C2—21no—
143C2—41no—
144C2—521no—
145C2—521no—
146C2#1171828911yescharacteristic
subgroupG/H
centerC4#88119
commutatorC2×C4×C13C42
FrattiniC22×C4C2×#261
FittingC2×C13×M16C4
socleC2×C13#342
prime radical, cosocleC2×#6127C22
hypercenterC2×M16#261
hypocenterC13#1395
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
7. C2×C13×M16C4semidirect
8. C22×#1055C4semidirect
11. #88113C4semidirect
74. C2×M16#261semidirect
107. C13#1395semidirect

Maximal subgroups

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

subgroupindex
#117191322
#117191162
#117187902
#139513