Finite Group Databasebeta

← #15750560

Subgroups — #15750560

Order 3328.

130 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 45 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
2#13113034C211yesmaximal, characteristic, complemented
3C13×#1373C211yesmaximal, characteristic, complemented
4C2×Dic104C411yescharacteristic
5C2×#88040—21no—
6C2×D208C411yescharacteristic
7#11718357—21no—
8C13×#364—21no—
9C4×C13×C16C2211yescharacteristic
10#11718091—21no—
11C2×Dic52—21no—
12C2×D104—21no—
13C2×#6095—41no—
14#88129—41no—
15C13×M32—41no—
16C2×C13×C16C2×C411yescharacteristic
17C2×C13×C16D411yescharacteristic
18C4×C8×C13D411yescharacteristic
19Dic104—41no—
20#88040—41no—
21#88040—41no—
22D208—41no—
23#88034—41no—
24#7447—131nomaximal, Sylow
25C2×D52—41no—
26C2×Dic26—41no—
27C2×C8×C13C22⋊C411yescharacteristic
28C2×C8×C13D811yescharacteristic
29C42×C13SD1611yescharacteristic
30#6103—82no—
31Dic52—41no—
32Dic52—41no—
33D104—41no—
34D104—41no—
35#6095—81no—
36#6095—81no—
37C13×C16—21no—
38C13×C16—81no—
39C13×C16D811yescharacteristic
40C13×C16SD1611yescharacteristic
41#2249—131no—
42#1422—131no—
43#1373D1311yescharacteristic, complemented
44C22×D13—81no—
45C2×C4×C13—21no—
46C2×C4×C13#10211yescharacteristic
47C2×Dic13—81no—
48D52—81no—
49D52—81no—
50Dic26—81no—
51Dic26—81no—
52C8×C13#10011yescharacteristic
53C8×C13#10211yescharacteristic
54C8×C13D1611yescharacteristic
55C8×C13SD3211yescharacteristic
56C2×Q32—131no—
57C2×SD32—261no—
58C2×D16—131no—
59#495—261no—
60M64—261no—
61#364—21no—
62C4×C16C2×D1311yescharacteristic
63C22×C13#36111yescharacteristic
64C2×D13—162no—
65C2×D13—161no—
66C4×C13—41no—
67C4×C13#33111yescharacteristic
68C4×C13#35711yescharacteristic
69Dic13—161no—
70C2×Q16—261no—
71C2×SD16—521no—
72C2×D8—261no—
73#124—521no—
74Q32—521no—
75SD32—521no—
76SD32—521no—
77D16—521no—
78M32—41no—
79C2×C16C4×D1311yescharacteristic
80C2×C16D5211yescharacteristic
81C4×C8C22⋊D1311yescharacteristic
82C32—521no—
83C2×C13—21no—
84C2×C13#136111yescharacteristic
85D13—321no—
86C2×Q8—521no—
87C2×D4—521no—
88Q16—521no—
89Q16—521no—
90SD16—1041no—
91SD16—1041no—
92D8—521no—
93D8—521no—
94C2×C8#610311yescharacteristic
95C2×C8#610411yescharacteristic
96C22⋊C4—1042no—
97C42#610611yescharacteristic
98C16—21no—
99C16—81no—
100C16#609511yescharacteristic
101C16D10411yescharacteristic
102C13#744711yescharacteristic, complemented, Sylow
103C23—1041no—
104Q8—1041no—
105Q8—1041no—
106D4—1041no—
107D4—1041no—
108C2×C4—21no—
109C2×C4—1041no—
110C2×C4#8804911yescharacteristic
111C8#8806111yescharacteristic
112C8#8806311yescharacteristic
113C8#8806611yescharacteristic
114C8#8806811yescharacteristic
115C22—2082no—
116C22—2081no—
117C22#1171808711yescharacteristic
118C4—41no—
119C4—2081no—
120C4#1171807711yescharacteristic
121C4#1171808311yescharacteristic
122C2—21no—
123C2—4161no—
124C2#1311288111yescharacteristic
subgroupG/H
centerC2#13112881
commutatorC2×C13×C16C2×C4
FrattiniC4×C16C2×D13
FittingC13×#1373C2
socleC2×C13#1361
prime radicalC2×D208C4
cosocleC4×C13×C16C22
hypercenter#1373D13
hypocenterC13#7447
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ C4×C16 ◁ #1373

Complements

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

NH ≅ G/Ntype
2. #13113034C2semidirect
3. C13×#1373C2semidirect
43. #1373D13semidirect
102. C13#7447semidirect

Maximal subgroups

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

subgroupindex
#131170972
#131130342
C13×#13732
#744713