Finite Group Databasebeta

← #15750495

Subgroups — #15750495

Order 3328.

136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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#13112976C211yesmaximal, characteristic
2#13112940C211yesmaximal, characteristic
3C13×#2219C211yesmaximal, characteristic
4C2×C13×Q32C411yescharacteristic
5C2×C13×M32C2211yescharacteristic
6C13×#467—21no—
7C2×#88059—21no—
8C13×#367C411yescharacteristic
9C13×#358—21no—
10#11718091—21no—
11C2×C13×Q16—21no—
12C22×C8×C13D411yescharacteristic
13C13×C22⋊Q8—41no—
14C2×#6099—41no—
15C13×Q32—41no—
16C13×M32—41no—
17C2×C13×C16C2×C411yescharacteristic
18C2×C13×C16D411yescharacteristic
19C13×#107—21no—
20C13×#103—41no—
21#88059—22no—
22#88059—41no—
23#88034—41no—
24#7425—131nomaximal, Sylow
25C2×Q8×C13—41no—
26C22×C4×C13D811yescharacteristic
27C13×Q16—41no—
28C13×Q16—41no—
29C2×C8×C13—21no—
30C2×C8×C13—21no—
31C2×C8×C13C22⋊C411yescharacteristic
32C2×C8×C13SD1611yescharacteristic
33C13×C4⋊C4—41no—
34C13×C4⋊C4—81no—
35C13×C22⋊C4—81no—
36#6099—42no—
37#6099—81no—
38C2×#1055—81no—
39C13×C16—21no—
40C13×C16—21no—
41#2219D1311yescharacteristic
42#1400—131no—
43#1385—131no—
44C23×C13SD3211yescharacteristic
45Q8×C13—81no—
46Q8×C13—81no—
47C2×C4×C13—21no—
48C2×C4×C13—21no—
49C2×C4×C13—81no—
50C2×C4×C13—81no—
51C2×C4×C13#10211yescharacteristic
52C2×C4×C13D1611yescharacteristic
53C8×C13—21no—
54C8×C13#9911yescharacteristic
55C8×C13#10411yescharacteristic
56#1055—82no—
57C2×Q32Dic1311yescharacteristic
58C2×M32C2×D1311yescharacteristic
59#467—21no—
60C2×#108—261no—
61M64—261no—
62#367Dic1311yescharacteristic
63#358—21no—
64C22×C13—21no—
65C22×C13—41no—
66C22×C13#35711yescharacteristic
67C4×C13—21no—
68C4×C13—161no—
69C4×C13—161no—
70C4×C13#32711yescharacteristic
71C4×C13#36011yescharacteristic
72C2×Q16—21no—
73C2×M16—521no—
74C22×C8C22⋊D1311yescharacteristic
75C22⋊Q8—41no—
76Q32—41no—
77M32—41no—
78C2×C16C2×Dic1311yescharacteristic
79C2×C16C22⋊D1311yescharacteristic
80#108—262no—
81#108—521no—
82#107—21no—
83#103—41no—
84C32—521no—
85C2×C13—21no—
86C2×C13—41no—
87C2×C13#134711yescharacteristic
88C2×Q8—41no—
89C22×C4#610411yescharacteristic
90Q16—41no—
91Q16—41no—
92M16—522no—
93M16—1041no—
94C2×C8—21no—
95C2×C8—21no—
96C2×C8—1041no—
97C2×C8#610511yescharacteristic
98C2×C8C22⋊Dic1311yescharacteristic
99C4⋊C4—41no—
100C4⋊C4—81no—
101C22⋊C4—81no—
102C16—21no—
103C16—21no—
104C13#742511yescharacteristic, complemented, Sylow
105C23#8806711yescharacteristic
106Q8—81no—
107Q8—81no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—81no—
111C2×C4—81no—
112C2×C4#8806611yescharacteristic
113C2×C4#8807211yescharacteristic
114C8—21no—
115C8—1042no—
116C8#8807411yescharacteristic
117C8#8807711yescharacteristic
118C22—21no—
119C22—41no—
120C22#1171815411yescharacteristic
121C4—21no—
122C4—161no—
123C4—161no—
124C4#1171812911yescharacteristic
125C4#1171815811yescharacteristic
126C2—21no—
127C2—41no—
128C2#1311284511yescharacteristic
subgroupG/H
centerC2#13112845
commutatorC2×C13×C16C2×C4
FrattiniC2×M32C2×D13
FittingC13×#2219C2
socleC2×C13#1347
prime radicalC23×C13SD32
cosocleC2×C13×M32C22
hypercenter#2219D13
hypocenterC13#7425
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #2219

Complements

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

NH ≅ G/Ntype
104. C13#7425semidirect

Maximal subgroups

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

subgroupindex
#131129762
#131129402
C13×#22192
#742513