Finite Group Databasebeta

← #16778198

Subgroups — #16778198

Order 3328.

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

normal subgroups only

This group has 128 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#13129974C211yesmaximal, characteristic
2#13129974C211yesmaximal, characteristic
3#13114469C211yesmaximal, characteristic
4#11718360C2211yescharacteristic
5#11718342—21no—
6#11718341—21no—
7#11718341C411yescharacteristic
8#11718227—21no—
9#11718227—21no—
10C13×#322C411yescharacteristic
11C2×Dic52—41no—
12#88123—21no—
13#88123D411yescharacteristic
14#88123D411yescharacteristic
15#88113—41no—
16#88113—41no—
17C4×C8×C13—21no—
18C4×C8×C13C2×C411yescharacteristic
19#88057—42no—
20#88057—41no—
21#88056—42no—
22#7534—131nomaximal, Sylow
23C2×Dic26—21no—
24C2×Dic26—21no—
25C2×Dic26—41no—
26#6122—81no—
27#6122—81no—
28C2×C8×C13—21no—
29C2×C8×C13—22no—
30C42×C13C22⋊C411yescharacteristic
31C4⋊Dic13—41no—
32C4⋊Dic13—41no—
33C4⋊Dic13—41no—
34C4⋊Dic13—41no—
35Dic52—82no—
36#1716—131no—
37#1411—131no—
38#1411—131no—
39C2×C4×C13—21no—
40C2×C4×C13#9911yescharacteristic
41C2×Dic13—41no—
42C2×Dic13—41no—
43C2×Dic13—81no—
44Dic26—81no—
45Dic26—81no—
46Dic26—82no—
47#1057—161no—
48#1057—161no—
49C8×C13—22no—
50C8×C13—42no—
51#498—131no—
52#498—261no—
53#494—131no—
54#487—261no—
55#356—261no—
56#356—261no—
57#322#26111yescharacteristic
58C22×C13#35311yescharacteristic
59C4×C13—22no—
60C4×C13—21no—
61Dic13—81no—
62Dic13—81no—
63Dic13—161no—
64C2×Q16—521no—
65C4⋊Q8—131no—
66C4⋊Q8—131no—
67C4⋊Q8—261no—
68#106—522no—
69#106—521no—
70#103—522no—
71#101—521no—
72#101—521no—
73C4×C8—21no—
74C4×C8C2×#26111yescharacteristic
75C2×C13—21no—
76C2×C13#140911yescharacteristic
77C2×Q8—261no—
78C2×Q8—261no—
79C2×Q8—521no—
80Q16—1042no—
81M16—1041no—
82M16—1041no—
83C2×C8—21no—
84C2×C8—22no—
85C4⋊C4—521no—
86C4⋊C4—521no—
87C4⋊C4—521no—
88C4⋊C4—521no—
89C42C22⋊#26111yescharacteristic
90C13#753411yescharacteristic, complemented, Sylow
91Q8—1041no—
92Q8—1041no—
93Q8—1042no—
94C2×C4—21no—
95C2×C4—521no—
96C2×C4—521no—
97C2×C4—1041no—
98C2×C4#8810711yescharacteristic
99C8—22no—
100C8—42no—
101C8—2081no—
102C8—2081no—
103C22#1171822511yescharacteristic
104C4—22no—
105C4—21no—
106C4—1041no—
107C4—1041no—
108C4—2081no—
109C2—21no—
110C2#1312997011yescharacteristic
subgroupG/H
centerC2#13129970
commutatorC4×C8×C13C2×C4
FrattiniC4×C8C2×#261
FittingC13×#322C4
socleC2×C13#1409
prime radicalC22×C13#353
cosocle#11718360C22
hypercenter#322#261
hypocenterC13#7534
LCSG ▷ C4×C8×C13 ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
90. C13#7534semidirect

Maximal subgroups

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

subgroupindex
#131299742
#131144692
#753413