Finite Group Databasebeta

← #15750490

Subgroups — #15750490

Order 3328.

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

normal subgroups only

This group has 140 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#13112938C211yesmaximal, characteristic
3C13×#1400C211yesmaximal, characteristic
4C2×C13×M32C2211yescharacteristic
5#11718777—21no—
6#11718767—21no—
7C2×Dic104C411yescharacteristic, complemented
8C13×M64—21no—
9#11718097C411yescharacteristic, complemented
10#11718095—21no—
11C22×C8×C13D411yescharacteristic
12#88180—41no—
13#88178—41no—
14C2×Dic52—21no—
15C13×M32—41no—
16C2×C13×C16C2×C411yescharacteristic
17C2×C13×C16D411yescharacteristic
18#88058—21no—
19#88058—41no—
20#88057—22no—
21#88056—41no—
22Dic104—41no—
23C13×C32—41no—
24#7423—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—
32C22⋊Dic13—81no—
33C4⋊Dic13—42no—
34C4⋊Dic13—41no—
35#6101—81no—
36C4×Dic13—81no—
37Dic52—41no—
38Dic52—41no—
39C13×C16—21no—
40C13×C16—21no—
41#2219—131no—
42#1400D1311yescharacteristic
43#1384—131no—
44C23×C13D1611yescharacteristic
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13#10211yescharacteristic
48C2×C4×C13SD3211yescharacteristic
49C2×Dic13—82no—
50C2×Dic13—81no—
51C2×Dic13—81no—
52Dic26—81no—
53Dic26—81no—
54C8×C13—21no—
55C8×C13#9911yescharacteristic
56C8×C13#10411yescharacteristic
57C2×Q32—131no—
58C2×M32C2×D1311yescharacteristic
59#467—261no—
60#427—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—162no—
72Dic13—161no—
73C2×Q16—261no—
74C22×C8D5211yescharacteristic
75C22⋊Q8—521no—
76#117—521no—
77Q32—521no—
78M32—41no—
79C2×C16C4×D1311yescharacteristic
80C2×C16C22⋊D1311yescharacteristic
81#107—261no—
82#107—521no—
83#106—262no—
84#103—521no—
85C32—41no—
86C2×C13—21no—
87C2×C13—41no—
88C2×C13#134711yescharacteristic
89C2×Q8—521no—
90C22×C4D10411yescharacteristic
91Q16—521no—
92Q16—521no—
93C2×C8—21no—
94C2×C8—21no—
95C2×C8#609511yescharacteristic
96C2×C8#610311yescharacteristic
97C4⋊C4—522no—
98C4⋊C4—521no—
99C4⋊C4—1041no—
100C22⋊C4—1041no—
101C22⋊C4—1041no—
102C42—1041no—
103C16—21no—
104C16—21no—
105C13#742311yescharacteristic, complemented, Sylow
106C23D20811yescharacteristic
107Q8—1041no—
108Q8—1041no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—1042no—
112C2×C4—1041no—
113C2×C4—1041no—
114C2×C4#8804011yescharacteristic
115C2×C4#8806111yescharacteristic
116C8—21no—
117C8#8804611yescharacteristic
118C8#8806511yescharacteristic
119C22—21no—
120C22—41no—
121C22#1171810111yescharacteristic
122C4—21no—
123C4—2081no—
124C4—2082no—
125C4—2081no—
126C4#1171806211yescharacteristic
127C4#1171811011yescharacteristic
128C2—21no—
129C2—41no—
130C2#1311284611yescharacteristic
subgroupG/H
centerC2#13112846
commutatorC2×C13×C16C2×C4
FrattiniC2×M32C2×D13
FittingC13×#1400C2
socleC2×C13#1347
prime radicalC23×C13D16
cosocleC2×C13×M32C22
hypercenter#1400D13
hypocenterC13#7423
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
7. C2×Dic104C4semidirect
9. #11718097C4semidirect
105. C13#7423semidirect

Maximal subgroups

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

subgroupindex
#131169442
#131129382
C13×#14002
#742313