Finite Group Databasebeta

← #16777000

Subgroups — #16777000

Order 3328.

136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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#13129866C211yesmaximal, characteristic
2#13129859C211yesmaximal, characteristic
3#13114434C211yesmaximal, characteristic
4C13×#500C411yescharacteristic
5#11718742—21no—
6#11718740—21no—
7#11718360C411yescharacteristic
8C4⋊#6092—21no—
9C4⋊#6092—21no—
10C8×#1055C2211yescharacteristic
11C13×C4⋊Q8—21no—
12C2×Dic52—41no—
13#88123—21no—
14C2×#6092—41no—
15C2×#6092—41no—
16C13×#107—41no—
17C4×C8×C13C2×C411yescharacteristic
18#88075—41no—
19#88075—41no—
20#88048—41no—
21#88048—41no—
22C4×#1055D411yescharacteristic
23C4×#1055D411yescharacteristic
24#7095—131nomaximal, Sylow
25C2×Q8×C13—41no—
26C2×Dic26—41no—
27C2×C8×C13—21no—
28C13×C4⋊C4—41no—
29C13×C4⋊C4—41no—
30C42×C13C22⋊C411yescharacteristic
31C4⋊Dic13—41no—
32C4⋊Dic13—41no—
33C2×#1055D811yescharacteristic
34C2×#1055D811yescharacteristic
35C2×#1055SD1611yescharacteristic
36C2×#1055SD1611yescharacteristic
37Dic52—82no—
38#6092—81no—
39#6092—81no—
40#1707—131no—
41#1370—131no—
42#1367—131no—
43Q8×C13—81no—
44Q8×C13—81no—
45C2×C4×C13—81no—
46C2×C4×C13#10011yescharacteristic
47C2×C4×C13#10211yescharacteristic
48C2×C4×C13#10211yescharacteristic
49C2×Dic13—81no—
50Dic26—82no—
51C8×C13—22no—
52#1055—21no—
53#1055—21no—
54#1055—21no—
55#1055SD3211yescharacteristic
56#1055Q3211yescharacteristic
57#500#26111yescharacteristic
58#498—261no—
59#494—131no—
60#487—261no—
61C4⋊C16—261no—
62C4⋊C16—261no—
63C82—131no—
64C22×C13#33111yescharacteristic
65C4×C13—21no—
66C4×C13—161no—
67C4×C13#35811yescharacteristic
68C4×C13#35911yescharacteristic
69C4×C13#36011yescharacteristic
70C4×C13#36211yescharacteristic
71Dic13—161no—
72C2×Q16—521no—
73C4⋊Q8—21no—
74C4⋊Q8—261no—
75C2×C16—521no—
76C2×C16—521no—
77#107—41no—
78#106—521no—
79#106—521no—
80#103—521no—
81#103—521no—
82C4×C8—131no—
83C4×C8—131no—
84C4×C8C2×#26111yescharacteristic
85C2×C13#135911yescharacteristic
86C2×C13#136011yescharacteristic
87C2×C13#136211yescharacteristic
88C2×Q8—41no—
89C2×Q8—521no—
90Q16—1042no—
91C2×C8—21no—
92C2×C8—131no—
93C2×C8—131no—
94C2×C8—131no—
95C2×C8—131no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—521no—
99C4⋊C4—521no—
100C42C22⋊#26111yescharacteristic
101C16—1041no—
102C16—1041no—
103C13#709511yescharacteristic, complemented, Sylow
104Q8—81no—
105Q8—81no—
106Q8—1042no—
107C2×C4—81no—
108C2×C4—1041no—
109C2×C4#8811511yescharacteristic
110C2×C4#8811511yescharacteristic
111C2×C4#8812111yescharacteristic
112C8—22no—
113C8—131no—
114C8—131no—
115C8—261no—
116C8—261no—
117C8—261no—
118C22#1171829711yescharacteristic
119C4—21no—
120C4—161no—
121C4—2081no—
122C4#1171827511yescharacteristic
123C4#1171827711yescharacteristic
124C4#1171828011yescharacteristic
125C4#1171828211yescharacteristic
126C2#1312984711yescharacteristic
127C2#1312984811yescharacteristic
128C2#1312985111yescharacteristic
subgroupG/H
centerC22#11718297
commutatorC4×C8×C13C2×C4
FrattiniC4×C8C2×#261
FittingC13×#500C4
socle, prime radicalC22×C13#331
cosocleC8×#1055C22
hypercenter#500#261
hypocenterC13#7095
LCSG ▷ C4×C8×C13 ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
103. C13#7095semidirect

Maximal subgroups

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

subgroupindex
#131298662
#131298592
#131144342
#709513