Finite Group Databasebeta

← #16778199

Subgroups — #16778199

Order 3328.

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

normal subgroups only

This group has 150 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#13129972C211yesmaximal, characteristic
2#13129970C211yesmaximal, characteristic
3#13114424C211yesmaximal, characteristic
4C13×#498C411yescharacteristic, complemented
5#11718746—21no—
6#11718740—21no—
7#11718354C2211yescharacteristic
8#11718227—21no—
9#11718225—21no—
10C8×#1055C411yescharacteristic, complemented
11C13×C4⋊Q8—21no—
12C2×#6106—42no—
13C2×#6095—41no—
14#88128D411yescharacteristic
15#88123D411yescharacteristic
16#88113—41no—
17#88107—41no—
18C13×#106—41no—
19C4×C8×C13C2×C411yescharacteristic
20#88048—42no—
21C4×#1055—21no—
22#7535—131nomaximal, Sylow
23C2×Q8×C13—41no—
24C2×D52—21no—
25C2×D52—41no—
26C2×Dic26—21no—
27C22⋊#261—81no—
28#6122—81no—
29C2×C8×C13—21no—
30C13×C4⋊C4—41no—
31C13×C4⋊C4—41no—
32C42×C13C22⋊C411yescharacteristic
33#6106—84no—
34C4⋊Dic13—41no—
35C2×#1055—22no—
36#6095—82no—
37#1705—131no—
38#1410—131no—
39#1409—131no—
40C22×D13—41no—
41C2×#261—161no—
42Q8×C13—82no—
43C2×C4×C13—21no—
44C2×C4×C13—81no—
45C2×C4×C13#9911yescharacteristic
46C2×Dic13—41no—
47D52—81no—
48D52—82no—
49Dic26—81no—
50#1057—161no—
51C8×C13—22no—
52#1055—24no—
53#498—261no—
54#498#26111yescharacteristic, complemented
55#492—131no—
56#492—261no—
57#356—261no—
58#353—261no—
59C82—131no—
60C22×C13#35311yescharacteristic
61C2×D13—81no—
62C2×D13—161no—
63#261—321no—
64C4×C13—22no—
65C4×C13—21no—
66C4×C13—161no—
67Dic13—81no—
68C2×SD16—521no—
69C2×SD16—522no—
70C4⋊Q8—21no—
71C4⋊Q8—131no—
72#127—131no—
73#106—41no—
74#106—522no—
75#101—521no—
76#99—521no—
77C4×C8—261no—
78C4×C8C2×#26111yescharacteristic
79C2×C13—21no—
80C2×C13#140911yescharacteristic
81D13—161no—
82C2×Q8—41no—
83C2×Q8—261no—
84C2×D4—261no—
85C2×D4—521no—
86SD16—1042no—
87SD16—1044no—
88M16—1041no—
89C2×C8—21no—
90C2×C8—262no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—521no—
94C22⋊C4—1041no—
95C42C22⋊#26111yescharacteristic
96C13#753511yescharacteristic, complemented, Sylow
97C23—521no—
98Q8—82no—
99Q8—1041no—
100D4—1041no—
101D4—1042no—
102C2×C4—21no—
103C2×C4—81no—
104C2×C4—521no—
105C2×C4—2081no—
106C2×C4#8811911yescharacteristic
107C8—22no—
108C8—264no—
109C8—2081no—
110C22—1041no—
111C22—2081no—
112C22#1171829411yescharacteristic
113C4—22no—
114C4—21no—
115C4—161no—
116C4—1041no—
117C4—4161no—
118C2—21no—
119C2—2081no—
120C2#1312996911yescharacteristic
subgroupG/H
centerC2#13129969
commutatorC4×C8×C13C2×C4
FrattiniC4×C8C2×#261
FittingC13×#498C4
socleC2×C13#1409
prime radical#88128D4
cosocle#11718354C22
hypercenter#498#261
hypocenterC13#7535
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. C8×#1055C4semidirect
54. #498#261semidirect
96. C13#7535semidirect

Maximal subgroups

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

subgroupindex
#131299722
#131299702
#131144242
#753513