Finite Group Databasebeta

← #16777788

Subgroups — #16777788

Order 3328.

148 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 38 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#13129782C212yesmaximal
2#13115011C211yesmaximal, characteristic
3C2×C13×#97C411yescharacteristic
4C2×#88059—22no—
5#11718585C411yescharacteristic
6#11718585C2211yescharacteristic
7#11718284—22no—
8C22×C8×C13—21no—
9C2×C42×C13C2×C411yescharacteristic
10C2×#6099—21no—
11C2×#6099D412yes—
12#88106—42no—
13C13×#97—21no—
14C13×#97C812yes—
15#88059—44no—
16C4⋊#1055—41no—
17C4⋊#1055—41no—
18#7374—131nomaximal, Sylow
19C22×C4×C13—21no—
20C22×C4×C13C22⋊C411yescharacteristic
21C2×C8×C13—22no—
22C2×C8×C13—22no—
23C2×C8×C13—22no—
24C42×C13—21no—
25C42×C13C2×C811yescharacteristic
26C42×C13M1611yescharacteristic
27#6099—42no—
28#6099—42no—
29C2×#1055—22no—
30C2×#1055—41no—
31#6092—82no—
32#1849—131no—
33#1327—132no—
34C23×C13#10111yescharacteristic
35C2×C4×C13—21no—
36C2×C4×C13—21no—
37C2×C4×C13—21no—
38C2×C4×C13—21no—
39C2×C4×C13—81no—
40C2×C4×C13C22⋊C811yescharacteristic
41C2×C4×C13#9911yescharacteristic
42C8×C13—24no—
43#1055—42no—
44#1055—81no—
45C2×#108—262no—
46#423—131no—
47#423—131no—
48C2×#97#26111yescharacteristic
49#349—262no—
50C22×C13—21no—
51C22×C13—41no—
52C22×C13#32411yescharacteristic
53C4×C13—21no—
54C4×C13—41no—
55C4×C13—41no—
56C4×C13#35311yescharacteristic
57C4×C13#35611yescharacteristic
58C2×M16—132no—
59C2×M16—261no—
60C22×C8—21no—
61C2×C42C2×#26111yescharacteristic
62M32—522no—
63#108—524no—
64C4⋊C8—521no—
65C4⋊C8—521no—
66#97—21no—
67#97#105712yes—
68C2×C13—21no—
69C2×C13—41no—
70C2×C13#132511yescharacteristic
71C22×C4—21no—
72C22×C4C22⋊#26111yescharacteristic
73M16—522no—
74M16—522no—
75C2×C8—22no—
76C2×C8—22no—
77C2×C8—22no—
78C2×C8—262no—
79C2×C8—521no—
80C42—21no—
81C42C2×#105711yescharacteristic
82C42#612211yescharacteristic
83C16—1042no—
84C13#737411yescharacteristic, complemented, Sylow
85C23#8811311yescharacteristic
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—81no—
91C2×C4#8810711yescharacteristic
92C2×C4C22⋊#105711yescharacteristic
93C8—24no—
94C8—522no—
95C8—1041no—
96C22—21no—
97C22—41no—
98C22#1171828511yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4#1171822511yescharacteristic
103C4#1171822711yescharacteristic
104C2—21no—
105C2—41no—
106C2#1312977811yescharacteristic
subgroupG/H
centerC4#11718225
commutatorC42×C13C2×C8
FrattiniC2×C42C2×#261
FittingC2×C13×#97C4
socleC2×C13#1325
prime radicalC23×C13#101
cosocle#11718585C22
hypercenterC2×#97#261
hypocenterC13#7374
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
84. C13#7374semidirect

Maximal subgroups

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

subgroupindex
#131297822
#131150112
#737413