Finite Group Databasebeta

← #16778182

Subgroups — #16778182

Order 3328.

126 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 22 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#13129979C211yesmaximal, characteristic
2#13129842C211yesmaximal, characteristic
3#13114165C211yesmaximal, characteristic
4C13⋊#564C411yescharacteristic
5#11718730C2211yescharacteristic
6#11718363—21no—
7#11718232—21no—
8#11718227—21no—
9C13×#330C411yescharacteristic
10#11718057—21no—
11C13×#125C2×C411yescharacteristic
12#88144—41no—
13#88143—41no—
14#88143—41no—
15#88124—21no—
16#88123D411yescharacteristic
17#88113—41no—
18#88106—41no—
19C13×#97—21no—
20#88058—41no—
21#88057—41no—
22#88050—41no—
23#88043D411yescharacteristic
24#7526—131nomaximal, Sylow
25C2×Dic26—21no—
26#6122—81no—
27C2×C8×C13—41no—
28C13×C4⋊C4—21no—
29C13×C4⋊C4—41no—
30C42×C13C22⋊C411yescharacteristic
31C4⋊Dic13—21no—
32C4⋊Dic13—21no—
33C4⋊Dic13—41no—
34C4⋊Dic13—41no—
35#6101—41no—
36#6101—41no—
37#6101—41no—
38#6101—41no—
39C4×Dic13—41no—
40C2×#1055—21no—
41#6092—42no—
42#1663—131no—
43#1413—131no—
44#1356—131no—
45C2×C4×C13—21no—
46C2×C4×C13—41no—
47C2×C4×C13#9911yescharacteristic
48C2×Dic13—41no—
49C2×Dic13—41no—
50C2×Dic13—41no—
51Dic26—81no—
52#1057—161no—
53C8×C13—42no—
54#1055—41no—
55#564—131no—
56#501—261no—
57#491—131no—
58#356—261no—
59#347—261no—
60#330—261no—
61#330#26111yescharacteristic
62C22×C13AΣL(1,𝔽16)11yescharacteristic
63C4×C13—21no—
64C4×C13—41no—
65C4×C13—81no—
66Dic13—81no—
67Dic13—81no—
68Dic13—81no—
69C4⋊Q8—131no—
70#125—261no—
71#125—521no—
72#125—521no—
73#125—521no—
74#125C2×#26111yescharacteristic
75M32—521no—
76#107—521no—
77#106—521no—
78#103—521no—
79#101—521no—
80#97—21no—
81#97—131no—
82C2×C13—21no—
83C2×C13#140411yescharacteristic
84C2×Q8—261no—
85M16—1041no—
86C2×C8—41no—
87C2×C8—261no—
88C4⋊C4—21no—
89C4⋊C4—41no—
90C4⋊C4—261no—
91C4⋊C4—261no—
92C4⋊C4—521no—
93C4⋊C4—521no—
94C4⋊C4—521no—
95C4⋊C4—521no—
96C4⋊C4—521no—
97C4⋊C4—521no—
98C42—521no—
99C42C22⋊#26111yescharacteristic
100C16—522no—
101C13#752611yescharacteristic, complemented, Sylow
102Q8—1041no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—521no—
106C2×C4—521no—
107C2×C4—521no—
108C2×C4#8810711yescharacteristic
109C8—42no—
110C8—521no—
111C8—2081no—
112C22#1171823611yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—1041no—
117C4—1041no—
118C4—1041no—
119C2—21no—
120C2#1312996011yescharacteristic
subgroupG/H
centerC2#13129960
commutatorC13×#125C2×C4
Frattini#125C2×#261
FittingC13×#330C4
socleC2×C13#1404
prime radicalC22×C13AΣL(1,𝔽16)
cosocle#11718730C22
hypercenter#330#261
hypocenterC13#7526
LCSG ▷ C13×#125 ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #330

Complements

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

NH ≅ G/Ntype
101. C13#7526semidirect

Maximal subgroups

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

subgroupindex
#131299792
#131298422
#131141652
#752613