Finite Group Databasebeta

← #15750367

Subgroups — #15750367

Order 3328.

118 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 49 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#13116674C211yesmaximal, characteristic
2#13113034C211yesmaximal, characteristic, complemented
3C13×#1397C211yesmaximal, characteristic, complemented
4#11718562—21no—
5#11718361C411yescharacteristic
6C2×C13×C32—21no—
7C4×C13×C16C2211yescharacteristic
8#11718100—21no—
9#11718091—21no—
10#11718055C411yescharacteristic
11#88158C811yescharacteristic
12#88155—21no—
13C2×C13×C16D411yescharacteristic
14C2×C13×C16D411yescharacteristic
15C4×C8×C13C2×C411yescharacteristic
16#88059C811yescharacteristic
17#88052—21no—
18#88045—21no—
19#88038—41no—
20C16×D13—41no—
21C13×C32—22no—
22#88034—41no—
23#7382—131nomaximal, Sylow
24#6127—21no—
25C2×C8×C13C22⋊C411yescharacteristic
26C2×C8×C13C2×C811yescharacteristic
27C42×C13M1611yescharacteristic
28#6099—21no—
29Dic52C1611yescharacteristic
30D104C1611yescharacteristic
31#6095—21no—
32#6094—41no—
33C8×D13—41no—
34C13×C16—21no—
35C13×C16D811yescharacteristic
36C13×C16SD1611yescharacteristic
37#6090—41no—
38#2170—131no—
39#1422—131no—
40#1397D1311yescharacteristic, complemented
41C2×C4×C13—21no—
42C2×C4×C13C22⋊C811yescharacteristic
43C22⋊D13—41no—
44D52—21no—
45C4×D13—41no—
46Dic26—21no—
47C8×C13#10211yescharacteristic
48C8×C13#10411yescharacteristic
49C8×C13C2×C1611yescharacteristic
50C8×C13M3211yescharacteristic
51#1055—41no—
52#504—261no—
53#443—131no—
54M64—261no—
55C2×C32—21no—
56#364—131no—
57#350—261no—
58C4×C16C2×D1311yescharacteristic
59C22×C13#35011yescharacteristic
60C2×D13—41no—
61C4×C13—41no—
62C4×C13D4⋊C811yescharacteristic
63C4×C13C22⋊C1611yescharacteristic
64Dic13—41no—
65#135—131no—
66#131—261no—
67M32—261no—
68M32—521no—
69C2×C16—521no—
70C2×C16D5211yescharacteristic
71C2×C16C22⋊D1311yescharacteristic
72#108—131no—
73#104—261no—
74C4×C8C4×D1311yescharacteristic
75C32—22no—
76C32—521no—
77C2×C13—21no—
78C2×C13D4⋊C1611yescharacteristic
79D13—81no—
80#41—261no—
81Q16—131no—
82SD16—261no—
83D8—131no—
84M16—261no—
85M16—521no—
86C2×C8—521no—
87C2×C8C8×D1311yescharacteristic
88C2×C8#610311yescharacteristic
89C42#609411yescharacteristic
90C16—21no—
91C16—521no—
92C16#609511yescharacteristic
93C16D10411yescharacteristic
94C13#738211yescharacteristic, complemented, Sylow
95Q8—261no—
96D4—261no—
97D4—521no—
98C2×C4—21no—
99C2×C4—521no—
100C2×C4#8806011yescharacteristic
101C8—521no—
102C8C16×D1311yescharacteristic
103C8#8803811yescharacteristic
104C8#8804511yescharacteristic
105C8#8806111yescharacteristic
106C22—521no—
107C22#1171810011yescharacteristic
108C4—41no—
109C4—521no—
110C4#1171805111yescharacteristic
111C4#1171809911yescharacteristic
112C2—21no—
113C2—1041no—
114C2#1311279211yescharacteristic
subgroupG/H
centerC8#88061
commutatorC8×C13C2×C16
FrattiniC4×C16C2×D13
FittingC13×#1397C2
socleC2×C13D4⋊C16
prime radical#88158C8
cosocleC4×C13×C16C22
hypercenter#1397D13
hypocenterC13#7382
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C16 ◁ C4×C16 ◁ #1397

Complements

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

NH ≅ G/Ntype
2. #13113034C2semidirect
3. C13×#1397C2semidirect
40. #1397D13semidirect
94. C13#7382semidirect

Maximal subgroups

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

subgroupindex
#131166742
#131130342
C13×#13972
#738213