Finite Group Databasebeta

← #16778176

Subgroups — #16778176

Order 3328.

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

normal subgroups only

This group has 138 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, complemented
2#13129843C211yesmaximal, characteristic, complemented
3#13114159C211yesmaximal, characteristic
4C13×#562C411yescharacteristic
5#11718730C2211yescharacteristic
6#11718716—21no—
7#11718232—21no—
8#11718227—21no—
9#11718135C411yescharacteristic
10#11718132—21no—
11C13×#125C2×C411yescharacteristic
12C13×#124—21no—
13C13×#123—41no—
14C13×C22⋊Q8—41no—
15C13×#121—41no—
16#88123D411yescharacteristic
17#88113—41no—
18#88106—41no—
19#88075—41no—
20#88072—41no—
21#88050—41no—
22#88043—21no—
23#88043D411yescharacteristic
24#7525—131nomaximal, Sylow
25C2×Q8×C13—21no—
26C2×D4×C13—21no—
27C2×D4×C13—41no—
28C22×C4×C13—41no—
29C2×Dic26—21no—
30#6122—81no—
31C13×C4⋊C4—21no—
32C13×C4⋊C4—41no—
33C13×C4⋊C4—41no—
34C13×C22⋊C4—41no—
35C13×C22⋊C4—41no—
36C13×C22⋊C4—41no—
37C42×C13C22⋊C411yescharacteristic
38C4⋊Dic13—41no—
39C2×#1055—21no—
40C2×#1055—41no—
41#6092—42no—
42#1662—131no—
43#1413—131no—
44#1356—131no—
45C23×C13—41no—
46Q8×C13—81no—
47D4×C13—81no—
48D4×C13—161no—
49C2×C4×C13—21no—
50C2×C4×C13—41no—
51C2×C4×C13—41no—
52C2×C4×C13—161no—
53C2×C4×C13#9911yescharacteristic
54C2×Dic13—41no—
55Dic26—81no—
56#1057—161no—
57#1055—41no—
58#1055—81no—
59#562#26111yescharacteristic
60#491—131no—
61#489—261no—
62#356—261no—
63#347—261no—
64#330—131no—
65#329—261no—
66C22×C13—81no—
67C22×C13—81no—
68C22×C13—81no—
69C22×C13AΣL(1,𝔽16)11yescharacteristic
70C4×C13—21no—
71C4×C13—41no—
72C4×C13—81no—
73C4×C13—81no—
74Dic13—81no—
75C4⋊Q8—131no—
76#125C2×#26111yescharacteristic
77#124—21no—
78#123—41no—
79C22⋊Q8—41no—
80#121—41no—
81M32—521no—
82#103—521no—
83#103—521no—
84#102—521no—
85#101—521no—
86#97—131no—
87#97—261no—
88C2×C13—21no—
89C2×C13—161no—
90C2×C13#140411yescharacteristic
91C2×Q8—21no—
92C2×Q8—261no—
93C2×D4—21no—
94C2×D4—41no—
95C22×C4—41no—
96M16—1041no—
97C2×C8—261no—
98C2×C8—521no—
99C4⋊C4—21no—
100C4⋊C4—41no—
101C4⋊C4—41no—
102C4⋊C4—521no—
103C22⋊C4—41no—
104C22⋊C4—41no—
105C22⋊C4—41no—
106C42C22⋊#26111yescharacteristic
107C16—522no—
108C13#752511yescharacteristic, complemented, Sylow
109C23—41no—
110Q8—81no—
111Q8—1041no—
112D4—81no—
113D4—161no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—161no—
118C2×C4—521no—
119C2×C4#8811911yescharacteristic
120C8—521no—
121C8—1041no—
122C8—2081no—
123C22—81no—
124C22—81no—
125C22—81no—
126C22#1171830611yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—1041no—
132C2—21no—
133C2—161no—
134C2#1312995911yescharacteristic
subgroupG/H
centerC2#13129959
commutatorC13×#125C2×C4
Frattini#125C2×#261
Fitting, prime radicalC13×#562C4
socleC2×C13#1404
cosocle#11718730C22
hypercenter#562#261
hypocenterC13#7525
LCSG ▷ C13×#125 ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #13129979C2semidirect
2. #13129843C2semidirect
108. C13#7525semidirect

Maximal subgroups

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

subgroupindex
#131299792
#131298432
#131141592
#752513