Finite Group Databasebeta

← #16777513

Subgroups — #16777513

Order 3328.

196 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 62 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×#11718232C212yesmaximal
2#13114976C211yesmaximal, characteristic
3C2×#88106—22no—
4C13×#423C411yescharacteristic
5#11718585C411yescharacteristic
6C2×#88043C2211yescharacteristic
7#11718232—22no—
8#11718232C414yes—
9#11718150—22no—
10C2×C13×M16—21no—
11C2×C42×C13C2×C411yescharacteristic
12C2×#6099—21no—
13C22×#1055D412yes—
14#88106—24no—
15#88106—24no—
16C2×#6092—24no—
17C13×C4⋊C8—41no—
18C4⋊#1055—41no—
19#88043C2×C412yes—
20#88043D411yescharacteristic
21#88043Q811yescharacteristic
22#7267—131nomaximal, Sylow
23C22×C4×C13—21no—
24C22×C4×C13C22⋊C411yescharacteristic
25C13×M16—42no—
26C2×C8×C13—41no—
27C42×C13—21no—
28C42×C13C4211yescharacteristic
29C42×C13C4⋊C411yescharacteristic
30#6099—42no—
31C2×#1055—22no—
32C2×#1055—22no—
33C2×#1055—41no—
34C2×#1055C22⋊C412yes—
35C2×#1055C4⋊C412yes—
36#6092—28no—
37C2×#347—132no—
38#1838—131no—
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—81no—
48#1055—22no—
49#1055—22no—
50#1055—81no—
51C2×M32—262no—
52#423—131no—
53#423#26111yescharacteristic
54C2×#97—131no—
55#347—134no—
56#347—262no—
57#341—262no—
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—261no—
68C22×C8—132no—
69C2×C42C2×#26111yescharacteristic
70M32—264no—
71M32—264no—
72C2×C16—264no—
73C4⋊C8—41no—
74C4⋊C8—521no—
75#97—132no—
76#97—131no—
77#97—131no—
78C2×C13—21no—
79C2×C13—22no—
80C2×C13#129511yescharacteristic
81C22×C4—21no—
82C22×C4C22⋊#26111yescharacteristic
83M16—42no—
84M16—522no—
85C2×C8—41no—
86C2×C8—132no—
87C2×C8—132no—
88C2×C8—262no—
89C2×C8—262no—
90C2×C8—521no—
91C42—21no—
92C42C4×#26111yescharacteristic
93C42C4⋊#26111yescharacteristic
94C16—268no—
95C13#726711yescharacteristic, complemented, Sylow
96C23#8811311yescharacteristic
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—81no—
100C2×C4(C2×#261)⋊C411yescharacteristic
101C2×C4#8811612yes—
102C2×C4#8811812yes—
103C2×C4#8812111yescharacteristic
104C8—81no—
105C8—262no—
106C8—262no—
107C8—1041no—
108C22—41no—
109C22#1171824212yes—
110C22#1171829111yescharacteristic
111C4—41no—
112C4—41no—
113C4#1171824712yes—
114C4#1171829311yescharacteristic
115C4#1171829911yescharacteristic
116C2—21no—
117C2—22no—
118C2#1312971211yescharacteristic
subgroupG/H
centerC4#11718299
commutatorC42×C13C42
FrattiniC2×C42C2×#261
FittingC13×#423C4
socleC2×C13#1295
prime radicalC23×C13#101
cosocleC2×#88043C22
hypercenter#423#261
hypocenterC13#7267
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

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×#117182322
#131149762
#726713