Finite Group Databasebeta

← #15750496

Subgroups — #15750496

Order 3328.

136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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#13116944C211yesmaximal, characteristic
2#13112940C211yesmaximal, characteristic
3C13×#1400C211yesmaximal, characteristic
4C2×C13×M32C2211yescharacteristic
5#11718777—21no—
6C2×#88059—21no—
7C2×Dic104C411yescharacteristic
8C13×M64—21no—
9#11718097C411yescharacteristic
10#11718095—21no—
11C22×C8×C13D411yescharacteristic
12#88178—41no—
13C2×#6099—41no—
14C2×Dic52—21no—
15C13×M32—41no—
16C2×C13×C16C2×C411yescharacteristic
17C2×C13×C16D411yescharacteristic
18#88059—22no—
19#88059—41no—
20#88058—21no—
21#88056—41no—
22Dic104—41no—
23C13×C32—41no—
24#7425—131nomaximal, Sylow
25C22×C4×C13D811yescharacteristic
26C2×Dic26—41no—
27C2×C8×C13—21no—
28C2×C8×C13—21no—
29C2×C8×C13C22⋊C411yescharacteristic
30C2×C8×C13SD1611yescharacteristic
31C22⋊Dic13—81no—
32C4⋊Dic13—41no—
33#6101—81no—
34#6099—42no—
35#6099—81no—
36C2×#1055—81no—
37Dic52—41no—
38Dic52—41no—
39C13×C16—21no—
40C13×C16—21no—
41#2219—131no—
42#1400D1311yescharacteristic
43#1385—131no—
44C23×C13SD3211yescharacteristic
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13#10211yescharacteristic
48C2×C4×C13D1611yescharacteristic
49C2×Dic13—81no—
50C2×Dic13—81no—
51Dic26—81no—
52Dic26—81no—
53C8×C13—21no—
54C8×C13#9911yescharacteristic
55C8×C13#10411yescharacteristic
56#1055—82no—
57C2×Q32—131no—
58C2×M32C2×D1311yescharacteristic
59#467—261no—
60C2×#108—261no—
61M64—21no—
62#367—131no—
63#358—261no—
64C22×C13—21no—
65C22×C13—41no—
66C22×C13#35711yescharacteristic
67C4×C13—21no—
68C4×C13#32711yescharacteristic
69C4×C13#36011yescharacteristic
70Dic13—161no—
71Dic13—161no—
72C2×Q16—261no—
73C2×M16—521no—
74C22×C8D5211yescharacteristic
75C22⋊Q8—521no—
76Q32—521no—
77M32—41no—
78C2×C16C4×D1311yescharacteristic
79C2×C16C22⋊D1311yescharacteristic
80#108—262no—
81#108—521no—
82#107—261no—
83#103—521no—
84C32—41no—
85C2×C13—21no—
86C2×C13—41no—
87C2×C13#134711yescharacteristic
88C2×Q8—521no—
89C22×C4D10411yescharacteristic
90Q16—521no—
91Q16—521no—
92M16—522no—
93M16—1041no—
94C2×C8—21no—
95C2×C8—21no—
96C2×C8—1041no—
97C2×C8#609511yescharacteristic
98C2×C8#610311yescharacteristic
99C4⋊C4—521no—
100C4⋊C4—1041no—
101C22⋊C4—1041no—
102C16—21no—
103C16—21no—
104C13#742511yescharacteristic, complemented, Sylow
105C23#8804011yescharacteristic
106Q8—1041no—
107Q8—1041no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—1041no—
111C2×C4—1041no—
112C2×C4D20811yescharacteristic
113C2×C4#8806111yescharacteristic
114C8—21no—
115C8—1042no—
116C8#8804611yescharacteristic
117C8#8806511yescharacteristic
118C22—21no—
119C22—41no—
120C22#1171810111yescharacteristic
121C4—21no—
122C4—2081no—
123C4—2081no—
124C4#1171806211yescharacteristic
125C4#1171811011yescharacteristic
126C2—21no—
127C2—41no—
128C2#1311284611yescharacteristic
subgroupG/H
centerC2#13112846
commutatorC2×C13×C16C2×C4
FrattiniC2×M32C2×D13
FittingC13×#1400C2
socleC2×C13#1347
prime radicalC23×C13SD32
cosocleC2×C13×M32C22
hypercenter#1400D13
hypocenterC13#7425
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #1400

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
#131169442
#131129402
C13×#14002
#742513