Finite Group Databasebeta

← #16778201

Subgroups — #16778201

Order 3328.

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

normal subgroups only

This group has 138 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#13114438C211yesmaximal, characteristic
4C13×#498C411yescharacteristic, complemented
5#11718749—21no—
6#11718742—21no—
7#11718354C2211yescharacteristic
8#11718227—21no—
9#11718225—21no—
10C8×#1055C411yescharacteristic, complemented
11C13×C4⋊Q8—21no—
12C2×#6095—41no—
13#88128D411yescharacteristic
14#88123D411yescharacteristic
15#88113—41no—
16#88107—41no—
17C13×#106—41no—
18C4×C8×C13C2×C411yescharacteristic
19#88075—42no—
20#88049—42no—
21C4×#1055—21no—
22#7536—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
33C4⋊Dic13—41no—
34C2×#1055—22no—
35#6095—82no—
36#1708—131no—
37#1410—131no—
38#1409—131no—
39C22×D13—41no—
40C2×#261—161no—
41Q8×C13—82no—
42C2×C4×C13—21no—
43C2×C4×C13—81no—
44C2×C4×C13#9911yescharacteristic
45C2×Dic13—41no—
46D52—81no—
47D52—82no—
48Dic26—81no—
49#1057—161no—
50C8×C13—22no—
51#1055—42no—
52#498#26111yescharacteristic, complemented
53#492—131no—
54#487—261no—
55#486—261no—
56#356—261no—
57#353—261no—
58C82—131no—
59C22×C13#35311yescharacteristic
60C2×D13—81no—
61C2×D13—161no—
62#261—321no—
63C4×C13—22no—
64C4×C13—21no—
65C4×C13—161no—
66Dic13—81no—
67C2×SD16—521no—
68C4⋊Q8—21no—
69C4⋊Q8—131no—
70#127—131no—
71#106—41no—
72#103—522no—
73#102—522no—
74#101—521no—
75#99—521no—
76C4×C8—261no—
77C4×C8C2×#26111yescharacteristic
78C2×C13—21no—
79C2×C13#140911yescharacteristic
80D13—161no—
81C2×Q8—41no—
82C2×Q8—261no—
83C2×D4—261no—
84C2×D4—521no—
85SD16—1042no—
86M16—1041no—
87C2×C8—21no—
88C2×C8—262no—
89C4⋊C4—41no—
90C4⋊C4—41no—
91C4⋊C4—521no—
92C22⋊C4—1041no—
93C42C22⋊#26111yescharacteristic
94C13#753611yescharacteristic, complemented, Sylow
95C23—521no—
96Q8—82no—
97Q8—1041no—
98D4—1041no—
99D4—1042no—
100C2×C4—21no—
101C2×C4—81no—
102C2×C4—521no—
103C2×C4—2081no—
104C2×C4#8811911yescharacteristic
105C8—22no—
106C8—522no—
107C8—2081no—
108C22—1041no—
109C22—2081no—
110C22#1171829411yescharacteristic
111C4—22no—
112C4—21no—
113C4—161no—
114C4—1041no—
115C4—4161no—
116C2—21no—
117C2—2081no—
118C2#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#7536
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
52. #498#261semidirect
94. C13#7536semidirect

Maximal subgroups

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

subgroupindex
#131299722
#131299702
#131144382
#753613