Finite Group Databasebeta

← #16777828

Subgroups — #16777828

Order 3328.

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

normal subgroups only

This group has 116 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#13129948C211yesmaximal, characteristic
2#13129863C211yesmaximal, characteristic
3#13116706C211yesmaximal, characteristic
4C2×Dic104C411yescharacteristic
5#11718534—21no—
6#11718261—21no—
7#11718249—21no—
8C13×#367C411yescharacteristic
9#11718094C2211yescharacteristic
10#11718084—21no—
11C2×Dic52—21no—
12#88141—41no—
13#88106—41no—
14C2×C13×C16C2×C411yescharacteristic
15C13×#107—21no—
16C8×Dic13D411yescharacteristic
17C2×#6090D411yescharacteristic
18#88050—41no—
19Dic104—21no—
20Dic104C812yes—
21#88036—22no—
22#7391—131nomaximal, Sylow
23C2×Dic26—41no—
24C2×C8×C13C22⋊C411yescharacteristic
25C13×C4⋊C4—41no—
26#6101—81no—
27C4×Dic13—81no—
28C4×Dic13SD1611yescharacteristic
29C2×#1055D811yescharacteristic
30Dic52—22no—
31Dic52—41no—
32#6092—81no—
33C13×C16C2×C811yescharacteristic
34C13×C16M1611yescharacteristic
35#6090—21no—
36#2176—131no—
37#1398—131no—
38#1369—131no—
39C2×C4×C13—81no—
40C2×C4×C13#10211yescharacteristic
41C2×Dic13—21no—
42C2×Dic13—81no—
43Dic26—42no—
44Dic26—81no—
45C8×C13C22⋊C811yescharacteristic
46C8×C13#10411yescharacteristic
47#1055—21no—
48C2×Q32—131no—
49C4×Q16—261no—
50M64—261no—
51#367#26111yescharacteristic
52#364—261no—
53#358—261no—
54#346—131no—
55C22×C13#36111yescharacteristic
56C4×C13—161no—
57C4×C13D4⋊C811yescharacteristic
58C4×C13#36011yescharacteristic
59Dic13—41no—
60Dic13—82no—
61C2×Q16—261no—
62C4×Q8—521no—
63Q32—132no—
64Q32—261no—
65M32—521no—
66C2×C16—131no—
67C2×C16C2×#26111yescharacteristic
68#107—21no—
69#103—521no—
70C4×C8—131no—
71C32—262no—
72C2×C13—21no—
73C2×C13#133311yescharacteristic
74C2×Q8—521no—
75Q16—262no—
76Q16—521no—
77C2×C8—131no—
78C2×C8C22⋊#26111yescharacteristic
79C4⋊C4—41no—
80C4⋊C4—1041no—
81C42—131no—
82C42—1041no—
83C16—261no—
84C16—1041no—
85C16D13⋊C811yescharacteristic
86C16#611811yescharacteristic
87C13#739111yescharacteristic, complemented, Sylow
88Q8—522no—
89Q8—1041no—
90C2×C4—81no—
91C2×C4—261no—
92C2×C4—1041no—
93C2×C4#8811511yescharacteristic
94C8—261no—
95C8#8811111yescharacteristic
96C8#8811811yescharacteristic
97C22#1171827811yescharacteristic
98C4—161no—
99C4—521no—
100C4—1042no—
101C4#1171824311yescharacteristic
102C4#1171827911yescharacteristic
103C2—21no—
104C2#1312979511yescharacteristic
subgroupG/H
centerC2#13129795
commutatorC13×C16C2×C8
FrattiniC2×C16C2×#261
FittingC13×#367C4
socleC2×C13#1333
prime radicalC22×C13#361
cosocle#11718094C22
hypercenter#367#261
hypocenterC13#7391
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #367

Complements

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

NH ≅ G/Ntype
87. C13#7391semidirect

Maximal subgroups

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

subgroupindex
#131299482
#131298632
#131167062
#739113