Finite Group Databasebeta

← #16777873

Subgroups — #16777873

Order 3328.

162 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 32 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#13129927C211yesmaximal, characteristic
2#13129771C211yesmaximal, characteristic
3#13116283C211yesmaximal, characteristic
4#11719132—21no—
5#11718794—21no—
6#11718771C2211yescharacteristic
7C2×#88057C411yescharacteristic
8#11718284—21no—
9C13×#341C411yescharacteristic
10#11718146—21no—
11C2×#6127D411yescharacteristic
12D13⋊M16—41no—
13C2×C13×M16—21no—
14C22×C8×C13C2×C411yescharacteristic
15C2×C4⋊Dic13—21no—
16C2×#6099D411yescharacteristic
17#88121—22no—
18#88113—41no—
19#88106—41no—
20#88061—41no—
21#88060—41no—
22#88057—41no—
23#88056—41no—
24#7411—131nomaximal, Sylow
25C22×C4×C13C22⋊C411yescharacteristic
26C2×C22⋊D13—21no—
27C22×Dic13—41no—
28#6127—41no—
29#6127—41no—
30C2×D52SD1611yescharacteristic
31C2×C4×D13—21no—
32C2×Dic26D811yescharacteristic
33#6122—42no—
34#6118—81no—
35D13⋊C8—81no—
36C13×M16—41no—
37C13×M16—41no—
38C2×C8×C13—21no—
39C2×C8×C13—41no—
40C2×C8×C13—41no—
41C4⋊Dic13—41no—
42C4⋊Dic13—41no—
43#6099—41no—
44C2×#1055—21no—
45#6092—81no—
46#2079—131no—
47#1392—131no—
48#1321—131no—
49C23×C13#10411yescharacteristic
50C22×D13—21no—
51C2×C4×C13—21no—
52C2×C4×C13—21no—
53C2×C4×C13#9911yescharacteristic
54C2×C4×C13#10211yescharacteristic
55C22⋊D13—81no—
56C2×Dic13—21no—
57C2×Dic13—81no—
58C2×Dic13—161no—
59D52—41no—
60C4×D13—41no—
61C4×D13—41no—
62Dic26—41no—
63#1057—82no—
64C8×C13—41no—
65C8×C13—81no—
66#1055—41no—
67C2×#106—131no—
68#417—261no—
69#413—261no—
70#408—131no—
71#349—261no—
72#343—261no—
73#341#26111yescharacteristic
74C22×C13—21no—
75C22×C13—41no—
76C22×C13#32711yescharacteristic
77C2×D13—41no—
78C2×D13—81no—
79C4×C13—21no—
80C4×C13#35211yescharacteristic
81C4×C13#35411yescharacteristic
82Dic13—41no—
83Dic13—161no—
84C2×#41—131no—
85C2×M16—21no—
86C2×M16—131no—
87C2×M16—521no—
88C22×C8C2×#26111yescharacteristic
89C2×C4⋊C4—261no—
90M32—521no—
91#106—521no—
92#103—521no—
93#102—521no—
94#101—521no—
95#100—262no—
96C22⋊C8—521no—
97C2×C13—21no—
98C2×C13—41no—
99C2×C13#134411yescharacteristic
100D13—81no—
101#41—521no—
102#41—521no—
103C2×Q8—131no—
104C2×D4—131no—
105C2×D4—261no—
106C22×C4—261no—
107C22×C4—521no—
108C22×C4C22⋊#26111yescharacteristic
109M16—41no—
110M16—41no—
111M16—521no—
112M16—522no—
113M16—1041no—
114C2×C8—21no—
115C2×C8—41no—
116C2×C8—41no—
117C2×C8—261no—
118C2×C8—1041no—
119C4⋊C4—521no—
120C4⋊C4—521no—
121C16—1041no—
122C13#741111yescharacteristic, complemented, Sylow
123C23—261no—
124C23#8811811yescharacteristic
125Q8—521no—
126D4—521no—
127D4—1041no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—261no—
131C2×C4—521no—
132C2×C4—521no—
133C2×C4—1041no—
134C2×C4—2081no—
135C2×C4#8810711yescharacteristic
136C2×C4#8811511yescharacteristic
137C8—41no—
138C8—81no—
139C8—521no—
140C8—1042no—
141C22—21no—
142C22—41no—
143C22—521no—
144C22—1041no—
145C22#1171824011yescharacteristic
146C4—21no—
147C4—521no—
148C4—2081no—
149C4#1171822611yescharacteristic
150C4#1171823711yescharacteristic
151C2—21no—
152C2—41no—
153C2—1041no—
154C2#1312981711yescharacteristic
subgroupG/H
centerC2#13129817
commutatorC22×C8×C13C2×C4
FrattiniC22×C8C2×#261
FittingC13×#341C4
socleC2×C13#1344
prime radicalC2×#6127D4
cosocle#11718771C22
hypercenter#341#261
hypocenterC13#7411
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
122. C13#7411semidirect

Maximal subgroups

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

subgroupindex
#131299272
#131297712
#131162832
#741113