Finite Group Databasebeta

← #16777385

Subgroups — #16777385

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#13130767C211yesmaximal, characteristic
2#13130056C211yesmaximal, characteristic
3#13116646C211yesmaximal, characteristic
4#11719051—21no—
5#11718368C2211yescharacteristic
6#11718269C411yescharacteristic
7#11718267C411yescharacteristic
8#11718266—21no—
9#1057⋊C8—21no—
10#11718251C411yescharacteristic, complemented
11C8×#1057C411yescharacteristic, complemented
12#11718234—21no—
13C13×#347C411yescharacteristic, complemented
14#11718106—21no—
15#11718103—21no—
16#11718058C411yescharacteristic, complemented
17#88237—21no—
18D13⋊M16—21no—
19C2×#6094C2×C411yescharacteristic
20C2×#6094D411yescharacteristic
21C42×D13D411yescharacteristic
22#88111—22no—
23C4⋊#1057—22no—
24C4×#1057—21no—
25C4×#1057—21no—
26C13×M32—21no—
27C13×#97C2×C411yescharacteristic
28C8×Dic13C2×C411yescharacteristic
29C8×Dic13D411yescharacteristic
30#88052—21no—
31#88043Q811yescharacteristic
32#7226—131nomaximal, Sylow
33C2×C4×D13—21no—
34C2×C4×D13C22⋊C411yescharacteristic
35C22⋊#261—41no—
36#6122—41no—
37C2×#1057—22no—
38C2×#1057—22no—
39C4⋊#261—41no—
40C4×#261—41no—
41#6118—41no—
42D13⋊C8—41no—
43C2×C8×C13C4211yescharacteristic
44C2×C8×C13C22⋊C411yescharacteristic
45C42×C13C4⋊C411yescharacteristic
46C4×Dic13—21no—
47C4×Dic13C22⋊C411yescharacteristic
48C2×#1055C4⋊C411yescharacteristic
49C2×#1055C4⋊C411yescharacteristic
50#6094—41no—
51#6094—41no—
52C13×C16—41no—
53#6090—41no—
54#2165—131no—
55#1841—131no—
56#1453—131no—
57C22×D13#10411yescharacteristic
58C2×#261—81no—
59C2×C4×C13—21no—
60C2×C4×C13#9511yescharacteristic
61C2×Dic13—21no—
62C2×Dic13#10411yescharacteristic
63C4×D13—21no—
64C4×D13—21no—
65C4×D13—42no—
66#1057—42no—
67#1057—42no—
68#1057—81no—
69C8×C13—21no—
70C8×C13—21no—
71#1055—21no—
72#1055—21no—
73#431—261no—
74C4×M16—131no—
75#364—261no—
76#349—261no—
77#347—131no—
78#347#26111yescharacteristic, complemented
79#344—261no—
80#339—261no—
81#338—131no—
82H(3,ℤ/4)—131no—
83#322—131no—
84#322—261no—
85C82—131no—
86C22×C13#33911yescharacteristic
87C2×D13—21no—
88C2×D13—41no—
89#261—161no—
90C4×C13—41no—
91C4×C13H(3,ℤ/4)11yescharacteristic
92C4×C13#34411yescharacteristic
93Dic13—22no—
94Dic13—21no—
95C2×M16—131no—
96C2×M16—131no—
97C2×M16—261no—
98#117—261no—
99C2×C42—131no—
100M32—21no—
101M32—261no—
102C4⋊C8—262no—
103C22⋊C8—262no—
104#97—131no—
105#97C2×#26111yescharacteristic
106C4×C8—131no—
107C4×C8—131no—
108C4×C8—261no—
109C4×C8—261no—
110C2×C13—21no—
111C2×C13#128811yescharacteristic
112D13—41no—
113C22×C4—131no—
114C22×C4—261no—
115M16—521no—
116M16—521no—
117M16—521no—
118M16—521no—
119C2×C8—131no—
120C2×C8—131no—
121C2×C8—262no—
122C2×C8—262no—
123C2×C8—521no—
124C2×C8C4×#26111yescharacteristic
125C2×C8C22⋊#26111yescharacteristic
126C4⋊C4—521no—
127C22⋊C4—521no—
128C42—131no—
129C42—261no—
130C42—521no—
131C42C4⋊#26111yescharacteristic
132C16—41no—
133C16—521no—
134C13#722611yescharacteristic, complemented, Sylow
135C23—131no—
136C2×C4—21no—
137C2×C4—131no—
138C2×C4—261no—
139C2×C4—261no—
140C2×C4—261no—
141C2×C4—522no—
142C2×C4—1041no—
143C2×C4(C2×#261)⋊C411yescharacteristic
144C8—21no—
145C8—21no—
146C8—261no—
147C8—261no—
148C8—522no—
149C8—522no—
150C8—1041no—
151C22—261no—
152C22—521no—
153C22#1171827211yescharacteristic
154C4—41no—
155C4—262no—
156C4—261no—
157C4—2081no—
158C4#1171823511yescharacteristic
159C4#1171827411yescharacteristic
160C2—21no—
161C2—521no—
162C2#1312969711yescharacteristic
subgroupG/H
centerC4#11718235
commutatorC2×C8×C13C42
Frattini#97C2×#261
FittingC13×#347C4
socleC2×C13#1288
prime radicalC22×D13#104
cosocle#11718368C22
hypercenter#347#261
hypocenterC13#7226
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #347

Complements

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

NH ≅ G/Ntype
10. #11718251C4semidirect
11. C8×#1057C4semidirect
13. C13×#347C4semidirect
16. #11718058C4semidirect
78. #347#261semidirect
134. C13#7226semidirect

Maximal subgroups

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

subgroupindex
#131307672
#131300562
#131166462
#722613