Finite Group Databasebeta

← #16777897

Subgroups — #16777897

Order 3328.

140 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 38 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#13129950C211yesmaximal, characteristic
2#13129896C211yesmaximal, characteristic
3#13116928C211yesmaximal, characteristic
4C2×#88104—21no—
5C2×Dic104C411yescharacteristic
6C2×C16×D13C2211yescharacteristic
7#11718548—21no—
8C2×#88036—21no—
9C13×#366C411yescharacteristic
10#11718084—21no—
11C2×#6118—41no—
12C2×Dic52—21no—
13C2×C8×D13D411yescharacteristic
14#88151—41no—
15#88104—22no—
16#88104—41no—
17C2×C13×C16C2×C411yescharacteristic
18C13×#107—21no—
19C2×#6090D411yescharacteristic
20#88050—41no—
21Dic104—41no—
22C16×D13—41no—
23#88036—41no—
24#7421—131nomaximal, Sylow
25C2×C4×D13D811yescharacteristic
26C2×Dic26—41no—
27C2×#1057—81no—
28#6118—42no—
29#6118—81no—
30C2×C8×C13C22⋊C411yescharacteristic
31C13×C4⋊C4—41no—
32#6103—81no—
33C4⋊Dic13—81no—
34C2×#1055SD1611yescharacteristic
35Dic52—41no—
36Dic52—41no—
37C8×D13—21no—
38C8×D13—21no—
39C13×C16—21no—
40#6090—21no—
41#2216—131no—
42C22⋊C32—131no—
43#1381—131no—
44C22×D13SD3211yescharacteristic
45C2×C4×C13—81no—
46C2×C4×C13#10211yescharacteristic
47C2×Dic13—81no—
48C2×Dic13D1611yescharacteristic
49C4×D13—21no—
50C4×D13—21no—
51Dic26—81no—
52Dic26—81no—
53#1057—82no—
54C8×C13#9911yescharacteristic
55C8×C13#10411yescharacteristic
56#1055—21no—
57C2×Q32—131no—
58C22×C16—131no—
59#467—261no—
60C2×#108—261no—
61C2×C32—261no—
62#366#26111yescharacteristic
63#358—261no—
64C22×C13#35711yescharacteristic
65C2×D13—21no—
66C2×D13—21no—
67C2×D13—21no—
68C4×C13—161no—
69C4×C13#32711yescharacteristic
70C4×C13#36011yescharacteristic
71Dic13—21no—
72Dic13—161no—
73C2×Q16—261no—
74C2×M16—521no—
75C22×C8—131no—
76C22⋊Q8—521no—
77Q32—521no—
78C2×C16—131no—
79C2×C16—521no—
80C2×C16C2×#26111yescharacteristic
81#108—262no—
82#108—521no—
83#107—21no—
84#103—521no—
85C32—521no—
86C2×C13#134711yescharacteristic
87C2×C13#141711yescharacteristic
88C2×C13#142011yescharacteristic
89D13—41no—
90C2×Q8—521no—
91C22×C4—131no—
92Q16—521no—
93Q16—521no—
94M16—522no—
95M16—1041no—
96C2×C8—131no—
97C2×C8—261no—
98C2×C8—261no—
99C2×C8—1041no—
100C2×C8C22⋊#26111yescharacteristic
101C4⋊C4—41no—
102C4⋊C4—1041no—
103C22⋊C4—1041no—
104C16—21no—
105C16—261no—
106C13#742111yescharacteristic, complemented, Sylow
107C23—131no—
108Q8—1041no—
109Q8—1041no—
110C2×C4—81no—
111C2×C4—131no—
112C2×C4—261no—
113C2×C4—261no—
114C2×C4—1041no—
115C2×C4#8811511yescharacteristic
116C8—261no—
117C8—1042no—
118C8#8810711yescharacteristic
119C8#8811811yescharacteristic
120C22—261no—
121C22—261no—
122C22—261no—
123C22#1171827611yescharacteristic
124C4—161no—
125C4—261no—
126C4—2081no—
127C4#1171824011yescharacteristic
128C4#1171827911yescharacteristic
129C2—521no—
130C2#1312982311yescharacteristic
131C2#1312998711yescharacteristic
132C2#1312999211yescharacteristic
subgroupG/H
centerC22#11718276
commutatorC2×C13×C16C2×C4
FrattiniC2×C16C2×#261
FittingC13×#366C4
socleC22×C13#357
prime radicalC22×D13SD32
cosocleC2×C16×D13C22
hypercenter#366#261
hypocenterC13#7421
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #366

Complements

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

NH ≅ G/Ntype
106. C13#7421semidirect

Maximal subgroups

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

subgroupindex
#131299502
#131298962
#131169282
#742113