Finite Group Databasebeta

← #16777380

Subgroups — #16777380

Order 3328.

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

normal subgroups only

This group has 192 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#13130060C211yesmaximal, characteristic
3#13116646C211yesmaximal, characteristic
4C4×#6118—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×#6118—22no—
20C2×#6094C2×C411yescharacteristic
21C2×#6094D411yescharacteristic
22C42×D13D411yescharacteristic
23#88110—22no—
24C4×#1057—21no—
25C4×#1057—21no—
26C13×M32—21no—
27C13×#97C2×C411yescharacteristic
28C8×Dic13C2×C411yescharacteristic
29C8×Dic13D411yescharacteristic
30#88052—21no—
31#88043Q811yescharacteristic
32#7225—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—44no—
42#6118—41no—
43D13⋊C8—41no—
44C2×C8×C13C4211yescharacteristic
45C2×C8×C13C22⋊C411yescharacteristic
46C42×C13C4⋊C411yescharacteristic
47C4×Dic13—21no—
48C4×Dic13C22⋊C411yescharacteristic
49C2×#1055C4⋊C411yescharacteristic
50C2×#1055C4⋊C411yescharacteristic
51#6094—41no—
52#6094—41no—
53C13×C16—41no—
54#6090—41no—
55#2165—131no—
56#1841—131no—
57#1455—131no—
58C22×D13#10411yescharacteristic
59C2×#261—81no—
60C2×C4×C13—21no—
61C2×C4×C13#9511yescharacteristic
62C2×Dic13—21no—
63C2×Dic13#10411yescharacteristic
64C4×D13—21no—
65C4×D13—21no—
66C4×D13—42no—
67#1057—24no—
68#1057—42no—
69#1057—81no—
70C8×C13—21no—
71C8×C13—21no—
72#1055—21no—
73#1055—21no—
74C4×M16—131no—
75C4×M16—261no—
76#364—261no—
77#349—261no—
78#347—131no—
79#347#26111yescharacteristic, complemented
80#344—261no—
81#339—261no—
82#338—131no—
83H(3,ℤ/4)—131no—
84#322—131no—
85#322—261no—
86C82—131no—
87C22×C13#33911yescharacteristic
88C2×D13—21no—
89C2×D13—41no—
90#261—161no—
91C4×C13—41no—
92C4×C13H(3,ℤ/4)11yescharacteristic
93C4×C13#34411yescharacteristic
94Dic13—22no—
95Dic13—21no—
96C2×M16—131no—
97C2×M16—131no—
98C2×M16—262no—
99C2×M16—261no—
100#117—261no—
101C2×C42—131no—
102M32—21no—
103M32—261no—
104#97—131no—
105#97—262no—
106#97C2×#26111yescharacteristic
107C4×C8—131no—
108C4×C8—131no—
109C4×C8—261no—
110C4×C8—261no—
111C2×C13—21no—
112C2×C13#128811yescharacteristic
113D13—41no—
114C22×C4—131no—
115C22×C4—261no—
116M16—521no—
117M16—521no—
118M16—524no—
119M16—521no—
120M16—521no—
121C2×C8—131no—
122C2×C8—131no—
123C2×C8—262no—
124C2×C8—262no—
125C2×C8—521no—
126C2×C8C4×#26111yescharacteristic
127C2×C8C22⋊#26111yescharacteristic
128C4⋊C4—521no—
129C22⋊C4—521no—
130C42—131no—
131C42—261no—
132C42—521no—
133C42C4⋊#26111yescharacteristic
134C16—41no—
135C16—521no—
136C13#722511yescharacteristic, complemented, Sylow
137C23—131no—
138C2×C4—21no—
139C2×C4—131no—
140C2×C4—261no—
141C2×C4—261no—
142C2×C4—261no—
143C2×C4—522no—
144C2×C4—1041no—
145C2×C4(C2×#261)⋊C411yescharacteristic
146C8—21no—
147C8—21no—
148C8—264no—
149C8—261no—
150C8—261no—
151C8—522no—
152C8—1041no—
153C22—261no—
154C22—521no—
155C22#1171827211yescharacteristic
156C4—41no—
157C4—262no—
158C4—261no—
159C4—2081no—
160C4#1171823511yescharacteristic
161C4#1171827411yescharacteristic
162C2—21no—
163C2—521no—
164C2#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#7225
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
79. #347#261semidirect
136. C13#7225semidirect

Maximal subgroups

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

subgroupindex
#131307672
#131300602
#131166462
#722513