Finite Group Databasebeta

← #16778195

Subgroups — #16778195

Order 3328.

156 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 22 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#13129968C211yesmaximal, characteristic
2#13129968C211yesmaximal, characteristic
3#13114465C211yesmaximal, characteristic
4C13×#498C411yescharacteristic, complemented
5#11718749—21no—
6#11718746—21no—
7#11718356C2211yescharacteristic
8#11718225—21no—
9#11718225—21no—
10#11718047C411yescharacteristic, complemented
11C13×C4⋊Q8—21no—
12C2×#6106—42no—
13C2×D104—41no—
14#88128D411yescharacteristic
15#88128D411yescharacteristic
16#88107—41no—
17#88107—41no—
18C13×#106—41no—
19C4×C8×C13C2×C411yescharacteristic
20#88049—42no—
21C4×#1055—21no—
22#7533—131nomaximal, Sylow
23C2×Q8×C13—41no—
24C2×D52—21no—
25C2×D52—21no—
26C2×D52—41no—
27C2×D52—41no—
28C22⋊#261—81no—
29C22⋊#261—81no—
30C2×C8×C13—21no—
31C13×C4⋊C4—41no—
32C13×C4⋊C4—41no—
33C42×C13C22⋊C411yescharacteristic
34#6106—84no—
35C2×#1055—22no—
36D104—82no—
37#1715—131no—
38#1408—131no—
39#1408—131no—
40C22×D13—41no—
41C22×D13—41no—
42C2×#261—161no—
43C2×#261—161no—
44Q8×C13—82no—
45C2×C4×C13—21no—
46C2×C4×C13—81no—
47C2×C4×C13#9911yescharacteristic
48D52—81no—
49D52—81no—
50D52—82no—
51D52—82no—
52C8×C13—22no—
53#1055—42no—
54#498#26111yescharacteristic, complemented
55#493—131no—
56#492—261no—
57#486—261no—
58#353—261no—
59#353—261no—
60#322—131no—
61C22×C13#35311yescharacteristic
62C2×D13—81no—
63C2×D13—81no—
64C2×D13—161no—
65C2×D13—161no—
66#261—321no—
67#261—321no—
68C4×C13—22no—
69C4×C13—21no—
70C4×C13—161no—
71C2×SD16—522no—
72C2×D8—521no—
73C4⋊Q8—21no—
74#127—131no—
75#127—131no—
76#106—41no—
77#102—522no—
78#99—521no—
79#99—521no—
80C4×C8—261no—
81C4×C8C2×#26111yescharacteristic
82C2×C13—21no—
83C2×C13#140911yescharacteristic
84D13—161no—
85D13—161no—
86C2×Q8—41no—
87C2×D4—261no—
88C2×D4—261no—
89C2×D4—521no—
90C2×D4—521no—
91SD16—1044no—
92D8—1042no—
93C2×C8—21no—
94C2×C8—262no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C22⋊C4—1041no—
98C22⋊C4—1041no—
99C42C22⋊#26111yescharacteristic
100C13#753311yescharacteristic, complemented, Sylow
101C23—521no—
102C23—521no—
103Q8—82no—
104D4—1041no—
105D4—1041no—
106D4—1042no—
107D4—1042no—
108C2×C4—21no—
109C2×C4—81no—
110C2×C4—2081no—
111C2×C4—2081no—
112C2×C4#8811911yescharacteristic
113C8—22no—
114C8—522no—
115C22—1041no—
116C22—1041no—
117C22—2081no—
118C22—2081no—
119C22#1171829411yescharacteristic
120C4—22no—
121C4—21no—
122C4—161no—
123C4—4161no—
124C4—4161no—
125C2—21no—
126C2—2081no—
127C2—2081no—
128C2#1312996911yescharacteristic
subgroupG/H
centerC2#13129969
commutatorC4×C8×C13C2×C4
FrattiniC4×C8C2×#261
FittingC13×#498C4
socleC2×C13#1409
prime radical, cosocle#11718356C22
hypercenter#498#261
hypocenterC13#7533
LCSG ▷ C4×C8×C13 ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
4. C13×#498C4semidirect
10. #11718047C4semidirect
54. #498#261semidirect
100. C13#7533semidirect

Maximal subgroups

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

subgroupindex
#131299682
#131144652
#753313