Finite Group Databasebeta

← #15750385

Subgroups — #15750385

Order 3328.

118 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 47 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#13116718C211yesmaximal, characteristic
2#13112912C211yesmaximal, characteristic, complemented
3C13×#1397C211yesmaximal, characteristic, complemented
4#11718565C411yescharacteristic
5#11718361—21no—
6C2×C13×C32—21no—
7C4×C13×C16C2211yescharacteristic
8#11718102—21no—
9#11718098C411yescharacteristic
10#11718055—21no—
11#88158—21no—
12#88155—41no—
13C2×C13×C16C2×C411yescharacteristic
14C2×C13×C16D411yescharacteristic
15C4×C8×C13D411yescharacteristic
16#88059—21no—
17#88052—41no—
18#88045—41no—
19Dic104C811yescharacteristic
20#88040—21no—
21D208C811yescharacteristic
22C13×C32—22no—
23#7388—131nomaximal, Sylow
24#6127—41no—
25C2×C8×C13C22⋊C411yescharacteristic
26C2×C8×C13D811yescharacteristic
27C42×C13SD1611yescharacteristic
28#6099—41no—
29Dic52—21no—
30D104—21no—
31#6095—41no—
32#6094—81no—
33C8×D13—81no—
34C13×C16—21no—
35C13×C16C2×C811yescharacteristic
36C13×C16M1611yescharacteristic
37#6090—81no—
38#2178—131no—
39#1397D1311yescharacteristic, complemented
40#1373—131no—
41C2×C4×C13—21no—
42C2×C4×C13#10211yescharacteristic
43C22⋊D13—81no—
44D52—41no—
45C4×D13—81no—
46Dic26—41no—
47C8×C13C22⋊C811yescharacteristic
48C8×C13#10411yescharacteristic
49C8×C13D1611yescharacteristic
50C8×C13SD3211yescharacteristic
51#1055—81no—
52#508—131no—
53#443—261no—
54C2×C32—21no—
55#368—131no—
56#364—261no—
57#359—261no—
58C4×C16C2×D1311yescharacteristic
59C22×C13#35911yescharacteristic
60C2×D13—81no—
61C4×C13—41no—
62C4×C13D4⋊C811yescharacteristic
63C4×C13#35711yescharacteristic
64Dic13—81no—
65#135—261no—
66#131—521no—
67Q32—131no—
68SD32—261no—
69D16—131no—
70M32—521no—
71C2×C16C4×D1311yescharacteristic
72C2×C16C22⋊D1311yescharacteristic
73#108—261no—
74#104—521no—
75C4×C8D5211yescharacteristic
76C32—22no—
77C2×C13—21no—
78C2×C13#133111yescharacteristic
79D13—161no—
80#41—521no—
81Q16—261no—
82SD16—521no—
83D8—261no—
84M16—521no—
85M16—1041no—
86C2×C8—1041no—
87C2×C8D10411yescharacteristic
88C2×C8#610311yescharacteristic
89C42#609511yescharacteristic
90C16—21no—
91C16—1041no—
92C16C8×D1311yescharacteristic
93C16#609411yescharacteristic
94C13#738811yescharacteristic, complemented, Sylow
95Q8—521no—
96D4—521no—
97D4—1041no—
98C2×C4—21no—
99C2×C4—1041no—
100C2×C4#8806111yescharacteristic
101C8—1041no—
102C8D20811yescharacteristic
103C8#8804011yescharacteristic
104C8#8804511yescharacteristic
105C8#8806011yescharacteristic
106C22—1041no—
107C22#1171810211yescharacteristic
108C4—41no—
109C4—1041no—
110C4#1171805111yescharacteristic
111C4#1171810111yescharacteristic
112C2—21no—
113C2—2081no—
114C2#1311279811yescharacteristic
subgroupG/H
centerC4#11718101
commutatorC13×C16C2×C8
FrattiniC4×C16C2×D13
FittingC13×#1397C2
socleC2×C13#1331
prime radical#11718565C4
cosocleC4×C13×C16C22
hypercenter#1397D13
hypocenterC13#7388
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ C4×C16 ◁ #1397

Complements

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

NH ≅ G/Ntype
2. #13112912C2semidirect
3. C13×#1397C2semidirect
39. #1397D13semidirect
94. C13#7388semidirect

Maximal subgroups

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

subgroupindex
#131167182
#131129122
C13×#13972
#738813