Finite Group Databasebeta

← #16777378

Subgroups — #16777378

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#13131208C211yesmaximal, characteristic
2#13130766C211yesmaximal, characteristic
3#13113140C211yesmaximal, characteristic
4C4×#6094—21no—
5C4×#6094C2211yescharacteristic
6#11718269C411yescharacteristic
7#11718267C411yescharacteristic
8#11718266—21no—
9#11718263—21no—
10#11718262C412yescomplemented
11#11718234—21no—
12#11718233—21no—
13C13×#322C411yescharacteristic, complemented
14#11718046—21no—
15C8×#1055C411yescharacteristic, complemented
16#88237—21no—
17D13⋊M16—21no—
18C2×#6094—22no—
19C2×#6094C2×C411yescharacteristic
20C2×#6094D411yescharacteristic
21C42×D13D411yescharacteristic
22#88106—22no—
23C4×C8×C13—21no—
24C4×C8×C13C2×C411yescharacteristic
25#88055—22no—
26#88055C2×C411yescharacteristic
27#88055Q811yescharacteristic
28C4×#1055—21no—
29C4×#1055D411yescharacteristic
30#7225—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#6094—44no—
51#6092—42no—
52#2165—131no—
53#1841—131no—
54#1455—131no—
55C22×D13#10411yescharacteristic
56C2×#261—81no—
57C2×C4×C13—21no—
58C2×C4×C13#9511yescharacteristic
59C2×Dic13—21no—
60C2×Dic13#10411yescharacteristic
61C4×D13—21no—
62C4×D13—21no—
63C4×D13—42no—
64#1057—81no—
65C8×C13—21no—
66C8×C13—21no—
67C8×C13—42no—
68#1055—24no—
69#1055—21no—
70#1055—21no—
71C4×M16—131no—
72C4×M16—261no—
73#364—261no—
74#349—261no—
75#347—132no—
76#344—261no—
77#339—261no—
78#338—131no—
79H(3,ℤ/4)—131no—
80#322—261no—
81#322#26111yescharacteristic, complemented
82C82—131no—
83C22×C13#33911yescharacteristic
84C2×D13—21no—
85C2×D13—41no—
86#261—161no—
87C4×C13—22no—
88C4×C13H(3,ℤ/4)11yescharacteristic
89C4×C13#34411yescharacteristic
90Dic13—21no—
91Dic13—41no—
92C2×M16—131no—
93C2×M16—131no—
94C2×M16—262no—
95C2×M16—261no—
96#117—261no—
97C2×C42—131no—
98M32—262no—
99#97—131no—
100#97—131no—
101#97—262no—
102C4×C8—21no—
103C4×C8—131no—
104C4×C8—261no—
105C4×C8C2×#26111yescharacteristic
106C2×C13—21no—
107C2×C13#128811yescharacteristic
108D13—41no—
109C22×C4—131no—
110C22×C4—261no—
111M16—521no—
112M16—521no—
113M16—524no—
114M16—521no—
115M16—521no—
116C2×C8—22no—
117C2×C8—131no—
118C2×C8—131no—
119C2×C8—262no—
120C2×C8—521no—
121C2×C8C4×#26111yescharacteristic
122C2×C8C4⋊#26111yescharacteristic
123C4⋊C4—521no—
124C22⋊C4—521no—
125C42—131no—
126C42—261no—
127C42—521no—
128C42C22⋊#26111yescharacteristic
129C16—522no—
130C13#722511yescharacteristic, complemented, Sylow
131C23—131no—
132C2×C4—21no—
133C2×C4—131no—
134C2×C4—261no—
135C2×C4—261no—
136C2×C4—261no—
137C2×C4—522no—
138C2×C4—1041no—
139C2×C4(C2×#261)⋊C411yescharacteristic
140C8—21no—
141C8—21no—
142C8—42no—
143C8—264no—
144C8—261no—
145C8—261no—
146C8—1041no—
147C22—261no—
148C22—521no—
149C22#1171823411yescharacteristic
150C4—22no—
151C4—261no—
152C4—521no—
153C4—2081no—
154C4#1171826611yescharacteristic
155C4#1171826711yescharacteristic
156C2—21no—
157C2—521no—
158C2#1312969611yescharacteristic
subgroupG/H
centerC4#11718267
commutatorC2×C8×C13C42
FrattiniC4×C8C2×#261
FittingC13×#322C4
socleC2×C13#1288
prime radicalC22×D13#104
cosocleC4×#6094C22
hypercenter#322#261
hypocenterC13#7225
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
10. #11718262C4semidirect
13. C13×#322C4semidirect
15. C8×#1055C4semidirect
81. #322#261semidirect
130. C13#7225semidirect

Maximal subgroups

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

subgroupindex
#131312082
#131307662
#131131402
#722513