Finite Group Databasebeta

← #11771134

Subgroups — #11771134

Order 1152.

204 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 47 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#10593805C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3#10593795C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×#3792C412yes—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C22⋊#622—21no—
8#63779—21no—
9#63777C412yes—
10C4⋊#622—21no—
11C4⋊#622C412yes—
12C4×#622—21no—
13C4×#622—21no—
14C22×C32×C4Q811yescharacteristic
15C22×C3⋊Dic3C2×C411yescharacteristic
16C22×C3⋊Dic3D411yescharacteristic
17#3792—24no—
18#3792—42no—
19C2×#622—22no—
20C2×#622—22no—
21C2×#622—22no—
22C4×C3⋊Dic3C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26#1299—91nomaximal, Sylow
27C2×C4×Dic3—121no—
28C23×C32C4⋊C411yescharacteristic
29C2×C32×C4—22no—
30C2×C32×C4C4⋊C411yescharacteristic
31C2×C32×C4C4⋊C411yescharacteristic
32C2×C3⋊Dic3—21no—
33C2×C3⋊Dic3—21no—
34C2×C3⋊Dic3—22no—
35C2×C3⋊Dic3C4211yescharacteristic
36C2×C3⋊Dic3C22⋊C411yescharacteristic
37C2×C3⋊Dic3C22⋊C411yescharacteristic
38C2×C3⋊Dic3C22⋊C411yescharacteristic
39#622—24no—
40#622—42no—
41#622—42no—
42#431—91no—
43#423—91no—
44C4×M16—91no—
45C22×C3×C4—41no—
46C22×Dic3—121no—
47C22×Dic3—121no—
48C4×Dic3—121no—
49C4×Dic3—121no—
50C4×Dic3—121no—
51C4×Dic3—121no—
52C22×C32—21no—
53C22×C32—21no—
54C22×C32—21no—
55C22×C32#9511yescharacteristic
56C32×C4—21no—
57C32×C4#10812yes—
58C3⋊Dic3—21no—
59C3⋊Dic3—21no—
60C3⋊Dic3#10011yescharacteristic
61C3⋊Dic3#10111yescharacteristic
62C3⋊Dic3#10412yes—
63C2×M16—92no—
64C2×M16—181no—
65C2×C42—91no—
66C4⋊C8—92no—
67C4⋊C8—181no—
68C4⋊C8—181no—
69C22⋊C8—181no—
70#97—92no—
71C4×C8—181no—
72C4×C8—181no—
73C23×C3—41no—
74C2×C3×C4—44no—
75C2×C3×C4—41no—
76C2×C3×C4—41no—
77C2×Dic3—121no—
78C2×Dic3—121no—
79C2×Dic3—121no—
80C2×Dic3—121no—
81C2×Dic3—124no—
82C2×Dic3—122no—
83C2×Dic3—122no—
84C2×C32—41no—
85C2×C32#33911yescharacteristic
86C2×C32#34111yescharacteristic
87C2×C32#34311yescharacteristic
88C22×C4—91no—
89C22×C4—91no—
90C22×C4PSU(3,𝔽2)11yescharacteristic
91M16—184no—
92M16—362no—
93C2×C8—182no—
94C2×C8—182no—
95C2×C8—182no—
96C42—91no—
97C42—91no—
98C42—91no—
99C42—91no—
100C22×C3—42no—
101C22×C3—42no—
102C22×C3—42no—
103C22×C3—41no—
104C3×C4—42no—
105C3×C4—42no—
106Dic3—121no—
107Dic3—121no—
108Dic3—122no—
109Dic3—122no—
110Dic3—122no—
111C32#129911yescharacteristic, complemented, Sylow
112C23#377711yescharacteristic
113C2×C4—22no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4—91no—
117C2×C4—91no—
118C2×C4—182no—
119C2×C4—181no—
120C2×C4—181no—
121C2×C4#377711yescharacteristic
122C2×C4#377711yescharacteristic
123C8—184no—
124C8—362no—
125C8—362no—
126C2×C3—44no—
127C2×C3—41no—
128C2×C3—41no—
129C2×C3—41no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22#6374711yescharacteristic
134C4—21no—
135C4—92no—
136C4—91no—
137C4—91no—
138C4—181no—
139C4—181no—
140C4#6374812yes—
141C3—41no—
142C2—41no—
143C2#1059009211yescharacteristic
144C2#1059009411yescharacteristic
145C2#1059009711yescharacteristic
subgroupG/H
centerC22#63747
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32#95
prime radicalC23×C32C4⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypocenterC32#1299
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
111. C32#1299semidirect

Maximal subgroups

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

subgroupindex
#105938052
C4×#37922
#105937952
#12999