Finite Group Databasebeta

← #11771242

Subgroups — #11771242

Order 1152.

576 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C32×#381C211yesmaximal, characteristic
2#10592906C212yesmaximal
3#67629—34nomaximal
4C23×C32×C4C2211yescharacteristic
5C2×C32×C22⋊C4C412yes—
6C2×#3748—22no—
7C32×#95—22no—
8#63657—22no—
9#63657C414yescomplemented
10C3×#381D314yes—
11#5207—38no—
12C24×C32C2×C411yescharacteristic
13C22×C32×C4—22no—
14C22×C32×C4—42no—
15C22×C32×C4C2×C412yes—
16C22×C32×C4D412yes—
17C22×C32×C4D411yescharacteristic
18C22×C32×C4Q811yescharacteristic
19C32×C22⋊C4—42no—
20#3748—44no—
21C2×C3⋊(C3⋊C8)—24no—
22#1306—91noSylow
23C23×C3×C4C2×D314yes—
24C2×C3×C22⋊C4Dic318yes—
25C2×#208—68no—
26C3×#95—28no—
27#830—316no—
28#830—68no—
29C23×C32—22no—
30C23×C32—42no—
31C23×C32C4211yescharacteristic
32C23×C32C22⋊C411yescharacteristic
33C23×C32C4⋊C411yescharacteristic
34C2×C32×C4—24no—
35C2×C32×C4—42no—
36C2×C32×C4—41no—
37C2×C32×C4—41no—
38C2×C32×C4—44no—
39C2×C32×C4—42no—
40C2×C32×C4C22⋊C412yes—
41C2×C32×C4C4⋊C412yes—
42C3⋊(C3⋊C8)—44no—
43#407—92no—
44#381C3⋊D311yescharacteristic
45C24×C3C2×Dic314yes—
46C22×C3×C4—28no—
47C22×C3×C4—48no—
48C22×C3×C4Dic614yes—
49C22×C3×C4C4×D318yes—
50C22×C3×C4D1214yes—
51C22×C3×C4#6718yes—
52C3×C22⋊C4—48no—
53#208—1216no—
54C2×C3⋊C8—616no—
55C22×C32—22no—
56C22×C32—21no—
57C22×C32—21no—
58C22×C32—22no—
59C22×C32—22no—
60C22×C32—44no—
61C22×C32#9511yescharacteristic
62C22×C32#9912yes—
63C32×C4—22no—
64C32×C4—22no—
65C32×C4—82no—
66C23×C4C2×C3⋊D311yescharacteristic
67C2×M16—182no—
68C2×C22⋊C4C3⋊Dic312yes—
69C22⋊C8—94no—
70C22⋊C8—182no—
71#95—22no—
72C23×C3—28no—
73C23×C3—48no—
74C23×C3C4×Dic314yes—
75C23×C3C4⋊Dic314yes—
76C23×C3#21714yes—
77C2×C3×C4—216no—
78C2×C3×C4—44no—
79C2×C3×C4—48no—
80C2×C3×C4—44no—
81C2×C3×C4—416no—
82C2×C3×C4—48no—
83C2×C3×C4Dic3⋊C418yes—
84C2×C3×C4(C2×D3)⋊C418yes—
85C3⋊C8—1216no—
86C2×C32—22no—
87C2×C32—41no—
88C2×C32—41no—
89C2×C32#34211yescharacteristic
90C2×C32#34412yes—
91C24C2×C3⋊Dic311yescharacteristic
92C22×C4—22no—
93C22×C4—42no—
94C22×C4#63411yescharacteristic
95C22×C4C4×C3⋊D312yes—
96C22×C4C4⋊(C3⋊D3)11yescharacteristic
97C22×C4#63812yes—
98M16—364no—
99C2×C8—184no—
100C22⋊C4—42no—
101C22×C3—28no—
102C22×C3—24no—
103C22×C3—24no—
104C22×C3—28no—
105C22×C3—28no—
106C22×C3—416no—
107C22×C3C3⋊#9514yes—
108C22×C3#83418yes—
109C3×C4—28no—
110C3×C4—28no—
111C3×C4—88no—
112C32#130611yescharacteristic, complemented, Sylow
113C23—22no—
114C23—42no—
115C23C4×C3⋊Dic311yescharacteristic
116C23C4⋊(C3⋊Dic3)11yescharacteristic
117C23#375711yescharacteristic
118C2×C4—24no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—44no—
123C2×C4—42no—
124C2×C4#375012yes—
125C2×C4#375212yes—
126C8—364no—
127C2×C3—28no—
128C2×C3—44no—
129C2×C3—44no—
130C2×C3#452614yes—
131C2×C3#453318yes—
132C22—22no—
133C22—21no—
134C22—21no—
135C22—22no—
136C22—22no—
137C22—44no—
138C22#6365811yescharacteristic
139C22#6366112yes—
140C4—22no—
141C4—22no—
142C4—82no—
143C3#6762914yescomplemented
144C2—22no—
145C2—41no—
146C2—41no—
147C2#1058939211yescharacteristic
148C2#1058939912yes—
subgroupG/H
centerC22#63658
commutatorC23×C32C42
FrattiniC23×C4C2×C3⋊D3
FittingC32×#381C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C32×C4C22
hypercenter#381C3⋊D3
hypocenterC32#1306
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
9. #63657C4semidirect
112. C32#1306semidirect
143. C3#67629semidirect

Maximal subgroups

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

subgroupindex
C32×#3812
#105929062
#676293