Finite Group Databasebeta

← #15750557

Subgroups — #15750557

Order 3328.

136 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 49 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#13117097C211yesmaximal, characteristic
2C4⋊#88034C211yesmaximal, characteristic, complemented
3C13×#1372C211yesmaximal, characteristic, complemented
4C2×Dic104C411yescharacteristic
5C2×#88040—21no—
6C2×D208C411yescharacteristic
7#11718357—21no—
8C4×C13×C16C2211yescharacteristic
9C13×#335—21no—
10C2×#88034—21no—
11C2×Dic52—21no—
12C2×D104—21no—
13C2×#6095—41no—
14#88129—41no—
15C2×C13×C16C2×C411yescharacteristic
16C2×C13×C16D411yescharacteristic
17C13×C4⋊C8—41no—
18C4×C8×C13D411yescharacteristic
19Dic104—41no—
20#88040—41no—
21#88040—41no—
22D208—41no—
23#88034—41no—
24#7446—131nomaximal, Sylow
25C2×D52—41no—
26C2×Dic26—41no—
27C2×C8×C13—81no—
28C2×C8×C13C22⋊C411yescharacteristic
29C2×C8×C13SD1611yescharacteristic
30C42×C13D811yescharacteristic
31#6103—81no—
32#6103—81no—
33Dic52—41no—
34Dic52—41no—
35D104—41no—
36D104—41no—
37#6095—82no—
38C13×C16—21no—
39C13×C16D811yescharacteristic
40C13×C16SD1611yescharacteristic
41#2249—131no—
42C4⋊C32—131no—
43#1372D1311yescharacteristic, complemented
44C22×D13—81no—
45C2×C4×C13#10211yescharacteristic
46C2×C4×C13D1611yescharacteristic
47C2×C4×C13SD3211yescharacteristic
48C2×Dic13—81no—
49D52—81no—
50D52—81no—
51Dic26—81no—
52Dic26—81no—
53C8×C13—21no—
54C8×C13—161no—
55C8×C13#10011yescharacteristic
56C8×C13#10211yescharacteristic
57C2×Q32—131no—
58C2×SD32—261no—
59C2×D16—131no—
60#495—261no—
61C2×C32—261no—
62C4×C16C2×D1311yescharacteristic
63#335—21no—
64C22×C13#35711yescharacteristic
65C2×D13—161no—
66C2×D13—161no—
67C2×D13—161no—
68C4×C13—21no—
69C4×C13—21no—
70C4×C13#33111yescharacteristic
71C4×C13#36111yescharacteristic
72Dic13—161no—
73C2×Q16—261no—
74C2×SD16—521no—
75C2×D8—261no—
76#124—521no—
77Q32—521no—
78SD32—521no—
79SD32—521no—
80D16—521no—
81C2×C16C4×D1311yescharacteristic
82C2×C16D5211yescharacteristic
83C4⋊C8—41no—
84C4×C8C22⋊D1311yescharacteristic
85C32—521no—
86C2×C13#136111yescharacteristic
87C2×C13#141711yescharacteristic
88C2×C13#141811yescharacteristic
89D13—321no—
90C2×Q8—521no—
91C2×D4—521no—
92Q16—521no—
93Q16—521no—
94SD16—1042no—
95D8—521no—
96D8—521no—
97C2×C8—81no—
98C2×C8#610311yescharacteristic
99C2×C8#610611yescharacteristic
100C22⋊C4—1041no—
101C22⋊C4—1041no—
102C42#610411yescharacteristic
103C16—21no—
104C16#609511yescharacteristic
105C16D10411yescharacteristic
106C13#744611yescharacteristic, complemented, Sylow
107C23—1041no—
108Q8—1041no—
109Q8—1041no—
110D4—1041no—
111D4—1041no—
112C2×C4—1041no—
113C2×C4#8804911yescharacteristic
114C2×C4#8806611yescharacteristic
115C2×C4#8806811yescharacteristic
116C8—21no—
117C8—161no—
118C8#8806111yescharacteristic
119C8#8806311yescharacteristic
120C22—2081no—
121C22—2081no—
122C22—2081no—
123C22#1171808311yescharacteristic
124C4—21no—
125C4—21no—
126C4—2081no—
127C4#1171807711yescharacteristic
128C4#1171808711yescharacteristic
129C2—4161no—
130C2#1311288111yescharacteristic
131C2#1311301911yescharacteristic
132C2#1311302211yescharacteristic
subgroupG/H
centerC22#11718083
commutatorC2×C13×C16C2×C4
FrattiniC4×C16C2×D13
FittingC13×#1372C2
socleC22×C13#357
prime radicalC2×D208C4
cosocleC4×C13×C16C22
hypercenter#1372D13
hypocenterC13#7446
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×C16 ◁ #1372

Complements

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

NH ≅ G/Ntype
2. C4⋊#88034C2semidirect
3. C13×#1372C2semidirect
43. #1372D13semidirect
106. C13#7446semidirect

Maximal subgroups

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

subgroupindex
#131170972
C4⋊#880342
C13×#13722
#744613