Finite Group Databasebeta

← #16777382

Subgroups — #16777382

Order 3328.

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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#13131208C211yesmaximal, characteristic
2#13130766C211yesmaximal, characteristic
3#13113130C211yesmaximal, characteristic
4C4×#6094C2211yescharacteristic
5#11718346—21no—
6#11718269C411yescharacteristic
7#11718267C411yescharacteristic
8#11718266—21no—
9#11718263—21no—
10#11718262C412yescomplemented
11#11718234—21no—
12#11718233—21no—
13C82×C13C411yescharacteristic, complemented
14#11718047C411yescharacteristic, complemented
15#11718046—21no—
16#88237—21no—
17D13⋊M16—21no—
18C2×#6094C2×C411yescharacteristic
19C2×#6094D411yescharacteristic
20C42×D13D411yescharacteristic
21#88106—22no—
22C4×C8×C13—21no—
23C4×C8×C13C2×C411yescharacteristic
24#88060—22no—
25#88055C2×C411yescharacteristic
26#88055Q811yescharacteristic
27#88054—22no—
28C4×#1055—21no—
29C4×#1055D411yescharacteristic
30#7226—131nomaximal, Sylow
31C2×C4×D13—21no—
32C2×C4×D13C22⋊C411yescharacteristic
33C22⋊#261—41no—
34#6122—41no—
35C4⋊#261—41no—
36C4×#261—41no—
37#6118—41no—
38D13⋊C8—41no—
39C2×C8×C13—22no—
40C2×C8×C13C4211yescharacteristic
41C2×C8×C13C4⋊C411yescharacteristic
42C42×C13C22⋊C411yescharacteristic
43C4×Dic13—21no—
44C4×Dic13C4⋊C411yescharacteristic
45C2×#1055—22no—
46C2×#1055C22⋊C411yescharacteristic
47C2×#1055C4⋊C411yescharacteristic
48#6094—41no—
49#6094—41no—
50#6092—42no—
51#2165—131no—
52#1841—131no—
53#1453—131no—
54C22×D13#10411yescharacteristic
55C2×#261—81no—
56C2×C4×C13—21no—
57C2×C4×C13#9511yescharacteristic
58C2×Dic13—21no—
59C2×Dic13#10411yescharacteristic
60C4×D13—21no—
61C4×D13—21no—
62C4×D13—42no—
63#1057—81no—
64C8×C13—21no—
65C8×C13—21no—
66C8×C13—42no—
67#1055—21no—
68#1055—21no—
69#1055—42no—
70#431—261no—
71C4×M16—131no—
72#364—261no—
73#349—261no—
74#347—132no—
75#344—261no—
76#339—261no—
77#338—131no—
78H(3,ℤ/4)—131no—
79#322—131no—
80#322—261no—
81C82#26111yescharacteristic, complemented
82C22×C13#33911yescharacteristic
83C2×D13—21no—
84C2×D13—41no—
85#261—161no—
86C4×C13—22no—
87C4×C13H(3,ℤ/4)11yescharacteristic
88C4×C13#34411yescharacteristic
89Dic13—21no—
90Dic13—41no—
91C2×M16—131no—
92C2×M16—131no—
93C2×M16—261no—
94#117—261no—
95C2×C42—131no—
96M32—262no—
97C4⋊C8—262no—
98C22⋊C8—262no—
99#97—131no—
100#97—131no—
101C4×C8—21no—
102C4×C8—131no—
103C4×C8—261no—
104C4×C8C2×#26111yescharacteristic
105C2×C13—21no—
106C2×C13#128811yescharacteristic
107D13—41no—
108C22×C4—131no—
109C22×C4—261no—
110M16—521no—
111M16—521no—
112M16—521no—
113M16—521no—
114C2×C8—22no—
115C2×C8—131no—
116C2×C8—131no—
117C2×C8—262no—
118C2×C8—521no—
119C2×C8C4×#26111yescharacteristic
120C2×C8C4⋊#26111yescharacteristic
121C4⋊C4—521no—
122C22⋊C4—521no—
123C42—131no—
124C42—261no—
125C42—521no—
126C42C22⋊#26111yescharacteristic
127C16—522no—
128C13#722611yescharacteristic, complemented, Sylow
129C23—131no—
130C2×C4—21no—
131C2×C4—131no—
132C2×C4—261no—
133C2×C4—261no—
134C2×C4—261no—
135C2×C4—522no—
136C2×C4—1041no—
137C2×C4(C2×#261)⋊C411yescharacteristic
138C8—21no—
139C8—21no—
140C8—42no—
141C8—261no—
142C8—261no—
143C8—522no—
144C8—1041no—
145C22—261no—
146C22—521no—
147C22#1171823411yescharacteristic
148C4—22no—
149C4—261no—
150C4—521no—
151C4—2081no—
152C4#1171826611yescharacteristic
153C4#1171826711yescharacteristic
154C2—21no—
155C2—521no—
156C2#1312969611yescharacteristic
subgroupG/H
centerC4#11718267
commutatorC2×C8×C13C42
FrattiniC4×C8C2×#261
FittingC82×C13C4
socleC2×C13#1288
prime radicalC22×D13#104
cosocleC4×#6094C22
hypercenterC82#261
hypocenterC13#7226
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ C82

Complements

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

NH ≅ G/Ntype
10. #11718262C4semidirect
13. C82×C13C4semidirect
14. #11718047C4semidirect
81. C82#261semidirect
128. C13#7226semidirect

Maximal subgroups

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

subgroupindex
#131312082
#131307662
#131131302
#722613