Finite Group Databasebeta

← #16777804

Subgroups — #16777804

Order 3328.

118 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 48 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#13129995C211yesmaximal, characteristic, complemented
2#13129943C211yesmaximal, characteristic, complemented
3#13116673C211yesmaximal, characteristic
4C13×#443C411yescharacteristic
5#11718801—21no—
6#11718249—21no—
7C2×#88036—21no—
8#11718153—21no—
9#11718055C411yescharacteristic
10C4×#6090C2211yescharacteristic
11C13×#135C811yescharacteristic
12C13×#131—21no—
13C13×#108C811yescharacteristic
14C13×#104—21no—
15C4×C8×C13C2×C411yescharacteristic
16#88052—21no—
17#88052—41no—
18C2×#6090—41no—
19C2×#6090D411yescharacteristic
20C2×#6090D411yescharacteristic
21#88036—22no—
22#88036—41no—
23#7382—131nomaximal, Sylow
24C13×#41—21no—
25C13×Q16C1611yescharacteristic
26C13×SD16—21no—
27C13×D8C1611yescharacteristic
28C13×M16—21no—
29C13×M16—41no—
30C2×C8×C13—41no—
31C2×C8×C13C22⋊C411yescharacteristic
32C2×C8×C13C2×C811yescharacteristic
33C42×C13M1611yescharacteristic
34#6090—21no—
35#6090—41no—
36#6090D811yescharacteristic
37#6090SD1611yescharacteristic
38#2170—131no—
39#1422—131no—
40#1397—131no—
41Q8×C13—21no—
42D4×C13—21no—
43D4×C13—41no—
44C2×C4×C13—21no—
45C2×C4×C13—41no—
46C2×C4×C13C22⋊C811yescharacteristic
47C8×C13—41no—
48C8×C13#10211yescharacteristic
49C8×C13#10411yescharacteristic
50C8×C13C2×C1611yescharacteristic
51C8×C13M3211yescharacteristic
52#504—261no—
53#443#26111yescharacteristic
54M64—261no—
55C2×C32—261no—
56#364—131no—
57#350—261no—
58C4×C16—131no—
59C22×C13—41no—
60C22×C13#35011yescharacteristic
61C4×C13—41no—
62C4×C13—41no—
63C4×C13D4⋊C811yescharacteristic
64C4×C13C22⋊C1611yescharacteristic
65#135#105711yescharacteristic
66#131—21no—
67M32—261no—
68M32—521no—
69C2×C16—131no—
70C2×C16—131no—
71C2×C16—521no—
72#108#105711yescharacteristic
73#104—21no—
74C4×C8C2×#26111yescharacteristic
75C32—262no—
76C32—521no—
77C2×C13—21no—
78C2×C13—81no—
79C2×C13D4⋊C1611yescharacteristic
80#41—21no—
81Q16#609211yescharacteristic
82SD16—21no—
83D8#609211yescharacteristic
84M16—21no—
85M16—41no—
86C2×C8—41no—
87C2×C8C2×#105711yescharacteristic
88C2×C8C22⋊#26111yescharacteristic
89C42#612211yescharacteristic
90C16—131no—
91C16—131no—
92C16—261no—
93C16—521no—
94C13#738211yescharacteristic, complemented, Sylow
95Q8—21no—
96D4—21no—
97D4—41no—
98C2×C4—21no—
99C2×C4—41no—
100C2×C4C22⋊#105711yescharacteristic
101C8—41no—
102C8C2×#609211yescharacteristic
103C8#8810611yescharacteristic
104C8#8811511yescharacteristic
105C8#8811611yescharacteristic
106C22—41no—
107C22#1171830411yescharacteristic
108C4—41no—
109C4—41no—
110C4C22⋊#609211yescharacteristic
111C4D4⋊#105711yescharacteristic
112C2—21no—
113C2—81no—
114C2D4⋊#609211yescharacteristic
subgroupG/H
centerC8#88115
commutatorC8×C13C2×C16
FrattiniC4×C8C2×#261
FittingC13×#443C4
socleC2×C13D4⋊C16
prime radicalC13×#135C8
cosocleC4×#6090C22
hypercenter#443#261
hypocenterC13#7382
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #13129995C2semidirect
2. #13129943C2semidirect
94. C13#7382semidirect

Maximal subgroups

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

subgroupindex
#131299952
#131299432
#131166732
#738213