Finite Group Databasebeta

← #16777869

Subgroups — #16777869

Order 3328.

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

normal subgroups only

This group has 166 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#13129924C211yesmaximal, characteristic
2#13129771C211yesmaximal, characteristic
3#13116283C211yesmaximal, characteristic
4#11719116—21no—
5#11718794—21no—
6#11718771C2211yescharacteristic
7C2×#88057C411yescharacteristic, complemented
8#11718284—21no—
9C13×#341C411yescharacteristic, complemented
10#11718146—21no—
11C2×#6127D411yescharacteristic
12#88237—41no—
13C2×C13×M16—21no—
14C22×C8×C13C2×C411yescharacteristic
15C2×C4⋊Dic13—21no—
16C2×#6099D411yescharacteristic
17#88119—22no—
18#88107—41no—
19#88106—41no—
20#88061—41no—
21#88060—41no—
22#88057—41no—
23#88056—41no—
24#7410—131nomaximal, Sylow
25C22×C4×C13C22⋊C411yescharacteristic
26C2×C22⋊D13—21no—
27C22×Dic13—41no—
28#6127—41no—
29#6127—41no—
30C2×D52D811yescharacteristic
31C2×C4×D13—21no—
32C2×Dic26SD1611yescharacteristic
33C22⋊#261—42no—
34C4⋊#261—81no—
35C4×#261—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#1391—131no—
48#1321—131no—
49C23×C13#10411yescharacteristic
50C22×D13—21no—
51C2×#261—82no—
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13#9911yescharacteristic
55C2×C4×C13#10211yescharacteristic
56C22⋊D13—81no—
57C2×Dic13—21no—
58C2×Dic13—81no—
59C2×Dic13—161no—
60D52—41no—
61C4×D13—41no—
62C4×D13—41no—
63Dic26—41no—
64C8×C13—41no—
65C8×C13—81no—
66#1055—41no—
67C2×#106—131no—
68#417—261no—
69#410—261no—
70#408—131no—
71#349—261no—
72#343—261no—
73#341#26111yescharacteristic, complemented
74C22×C13—21no—
75C22×C13—41no—
76C22×C13#32711yescharacteristic
77C2×D13—41no—
78C2×D13—81no—
79#261—162no—
80C4×C13—21no—
81C4×C13#35211yescharacteristic
82C4×C13#35411yescharacteristic
83Dic13—41no—
84Dic13—161no—
85C2×#41—131no—
86C2×M16—21no—
87C2×M16—131no—
88C22×C8C2×#26111yescharacteristic
89#117—521no—
90C2×C4⋊C4—261no—
91M32—521no—
92#106—521no—
93#103—521no—
94#102—521no—
95#99—262no—
96#99—521no—
97C22⋊C8—521no—
98C2×C13—21no—
99C2×C13—41no—
100C2×C13#134411yescharacteristic
101D13—81no—
102#41—521no—
103#41—521no—
104C2×Q8—131no—
105C2×D4—131no—
106C2×D4—261no—
107C22×C4—261no—
108C22×C4—521no—
109C22×C4C22⋊#26111yescharacteristic
110M16—41no—
111M16—41no—
112M16—521no—
113C2×C8—21no—
114C2×C8—41no—
115C2×C8—41no—
116C2×C8—261no—
117C4⋊C4—521no—
118C4⋊C4—521no—
119C4⋊C4—1041no—
120C22⋊C4—522no—
121C42—1041no—
122C16—1041no—
123C13#741011yescharacteristic, complemented, Sylow
124C23—261no—
125C23#8811811yescharacteristic
126Q8—521no—
127D4—521no—
128D4—1041no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—261no—
132C2×C4—521no—
133C2×C4—521no—
134C2×C4—1042no—
135C2×C4—1041no—
136C2×C4—2081no—
137C2×C4#8810711yescharacteristic
138C2×C4#8811511yescharacteristic
139C8—41no—
140C8—81no—
141C8—521no—
142C22—21no—
143C22—41no—
144C22—521no—
145C22—1041no—
146C22#1171824011yescharacteristic
147C4—21no—
148C4—521no—
149C4—2081no—
150C4—2082no—
151C4#1171822611yescharacteristic
152C4#1171823711yescharacteristic
153C2—21no—
154C2—41no—
155C2—1041no—
156C2#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#7410
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
7. C2×#88057C4semidirect
9. C13×#341C4semidirect
73. #341#261semidirect
123. C13#7410semidirect

Maximal subgroups

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

subgroupindex
#131299242
#131297712
#131162832
#741013