Finite Group Databasebeta

← #15750088

Subgroups — #15750088

Order 3328.

196 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#11718058C212yesmaximal
2C13×#1838C211yesmaximal, characteristic
3C13×#423C411yescharacteristic
4C13×#423C411yescharacteristic
5C2×C13×#97C2211yescharacteristic
6C2×#88052—22no—
7C13×#341—22no—
8#11718058—22no—
9#11718058C414yes—
10C2×C13×M16—21no—
11C2×C13×M16—21no—
12C22×C8×C13D412yes—
13C2×C42×C13C2×C411yescharacteristic
14C13×C4⋊C8—41no—
15C13×C4⋊C8—41no—
16C13×#97C2×C412yes—
17C13×#97D411yescharacteristic
18C13×#97Q811yescharacteristic
19#88052—24no—
20#88052—24no—
21C2×#6090—24no—
22#7267—131nomaximal, Sylow
23C22×C4×C13—21no—
24C22×C4×C13C22⋊C411yescharacteristic
25C13×M16—42no—
26C13×M16—42no—
27C2×C8×C13—22no—
28C2×C8×C13—22no—
29C2×C8×C13—41no—
30C2×C8×C13—41no—
31C2×C8×C13C22⋊C412yes—
32C2×C8×C13C4⋊C412yes—
33C42×C13—21no—
34C42×C13C4211yescharacteristic
35C42×C13C4⋊C411yescharacteristic
36#6090—28no—
37C2×#347—132no—
38#1838D1311yescharacteristic
39C23×C13#10111yescharacteristic
40C2×C4×C13—21no—
41C2×C4×C13—21no—
42C2×C4×C13—81no—
43C2×C4×C13#9511yescharacteristic
44C2×C4×C13#10011yescharacteristic
45C2×C4×C13#10412yes—
46C2×C4×C13#10412yes—
47C8×C13—22no—
48C8×C13—22no—
49C8×C13—81no—
50C8×C13—81no—
51C2×M32—262no—
52#423Dic1311yescharacteristic
53#423Dic1311yescharacteristic
54C2×#97C2×D1311yescharacteristic
55#347—134no—
56#347—262no—
57#341—22no—
58C22×C13—41no—
59C22×C13#33012yes—
60C22×C13#34311yescharacteristic
61C4×C13—41no—
62C4×C13—41no—
63C4×C13#32911yescharacteristic
64C4×C13#32911yescharacteristic
65C4×C13#33912yes—
66C2×M16—21no—
67C2×M16—21no—
68C22×C8C22⋊D1312yes—
69C2×C42C2×Dic1311yescharacteristic
70M32—264no—
71M32—264no—
72C2×C16—264no—
73C4⋊C8—41no—
74C4⋊C8—41no—
75#97Dic2611yescharacteristic
76#97C4×D1312yes—
77#97D5211yescharacteristic
78C2×C13—21no—
79C2×C13—22no—
80C2×C13#129511yescharacteristic
81C22×C4—21no—
82C22×C4C22⋊Dic1311yescharacteristic
83M16—42no—
84M16—42no—
85C2×C8—22no—
86C2×C8—22no—
87C2×C8—41no—
88C2×C8—41no—
89C2×C8#610112yes—
90C2×C8#610312yes—
91C42—21no—
92C42C4×Dic1311yescharacteristic
93C42C4⋊Dic1311yescharacteristic
94C16—268no—
95C13#726711yescharacteristic, complemented, Sylow
96C23#8807611yescharacteristic
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—81no—
100C2×C4#8807111yescharacteristic
101C2×C4#8807311yescharacteristic
102C2×C4#8807712yes—
103C2×C4#8807712yes—
104C8—22no—
105C8—22no—
106C8—81no—
107C8—81no—
108C22—41no—
109C22#1171812211yescharacteristic
110C22#1171813512yes—
111C4—41no—
112C4—41no—
113C4#1171812412yes—
114C4#1171813211yescharacteristic
115C4#1171813211yescharacteristic
116C2—21no—
117C2—22no—
118C2#1311271711yescharacteristic
subgroupG/H
centerC4#11718132
commutatorC42×C13C42
FrattiniC2×#97C2×D13
FittingC13×#1838C2
socleC2×C13#1295
prime radicalC23×C13#101
cosocleC2×C13×#97C22
hypercenter#1838D13
hypocenterC13#7267
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#97 ◁ #1838

Complements

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

NH ≅ G/Ntype
95. C13#7267semidirect

Maximal subgroups

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

subgroupindex
C2×#117180582
C13×#18382
#726713