Finite Group Databasebeta

← #11771737

Subgroups — #11771737

Order 1152.

214 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 26 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#10592888C211yesmaximal, characteristic
2#10590184C211yesmaximal, characteristic
3#10590180C211yesmaximal, characteristic
4#64286—21no—
5C2×C32×Q16C411yescharacteristic, complemented
6#64155—21no—
7C2×#3743C2211yescharacteristic
8#63773—21no—
9#63662—21no—
10#63644C411yescharacteristic, complemented
11#5189—62no—
12C2×C32×Q8—21no—
13C2×C4×C3⋊D3D411yescharacteristic
14C22⋊#157—41no—
15C4⋊#157—41no—
16C4×#157—22no—
17C32×Q16—41no—
18C2×C32×C8C2×C411yescharacteristic
19#3752—41no—
20C4⋊(C3⋊Dic3)—21no—
21#3750—41no—
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23#3743—41no—
24#3708—41no—
25#1340—91nomaximal, Sylow
26C2×C3×Q16—22no—
27#946—64no—
28C2×ΓL(1,𝔽25)—62no—
29#835—64no—
30#817—62no—
31C22×C3⋊D3D811yescharacteristic
32C2×#157—42no—
33C32×Q8—41no—
34C32×Q8—41no—
35C2×C32×C4—41no—
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C3⋊Dic3—41no—
38C2×C3⋊Dic3SD1611yescharacteristic
39C4×C3⋊D3—21no—
40C4×C3⋊D3—21no—
41C32×C8—21no—
42C3⋊(C3⋊C8)—21no—
43#470—91no—
44#349—91no—
45H(3,ℤ/4)—91no—
46C2×C3×Q8—24no—
47C2×C4×D3—62no—
48C3×Q16—44no—
49C2×C3×C8—22no—
50(C2×D3)⋊C4—124no—
51C4⋊Dic3—64no—
52Dic3⋊C4—124no—
53C2×C3⋊C8—62no—
54ΓL(1,𝔽25)—124no—
55C22×C32#10211yescharacteristic
56C2×C3⋊D3—21no—
57C2×C3⋊D3—41no—
58#157—82no—
59C32×C4—81no—
60C32×C4#9911yescharacteristic
61C32×C4#10411yescharacteristic
62C3⋊Dic3—21no—
63C3⋊Dic3—81no—
64C2×Q16#15711yescharacteristic, complemented
65C2×M16—91no—
66C22⋊Q8—181no—
67#117—181no—
68M32—181no—
69#106—91no—
70#103—181no—
71C22×D3—62no—
72C3×Q8—44no—
73C3×Q8—44no—
74C2×C3×C4—22no—
75C2×C3×C4—44no—
76C2×Dic3—62no—
77C2×Dic3—124no—
78C4×D3—122no—
79C4×D3—122no—
80C3×C8—24no—
81C3⋊C8—122no—
82C2×C32—21no—
83C2×C32#32711yescharacteristic
84C3⋊D3—41no—
85C2×Q8—21no—
86C22×C4—91no—
87Q16—41no—
88M16—361no—
89C2×C8—91no—
90C2×C8C2×#15711yescharacteristic
91C4⋊C4—181no—
92C4⋊C4—361no—
93C4⋊C4—361no—
94C22⋊C4—361no—
95C22⋊C4—361no—
96C42—182no—
97C16—361no—
98C22×C3—22no—
99C2×D3—122no—
100C2×D3—124no—
101C3×C4—22no—
102C3×C4—22no—
103C3×C4—84no—
104Dic3—122no—
105Dic3—244no—
106C32#134011yescharacteristic, complemented, Sylow
107C23—91no—
108Q8—41no—
109Q8—41no—
110C2×C4—41no—
111C2×C4—91no—
112C2×C4—181no—
113C2×C4—181no—
114C2×C4—362no—
115C2×C4—361no—
116C2×C4C22⋊#15711yescharacteristic
117C8—21no—
118C8—181no—
119C2×C3—24no—
120C2×C3—22no—
121D3—242no—
122C22—181no—
123C22—361no—
124C22#6378211yescharacteristic
125C4—81no—
126C4—181no—
127C4—721no—
128C4—722no—
129C4#6378311yescharacteristic
130C4#6378611yescharacteristic
131C3—22no—
132C2—21no—
133C2—361no—
134C2#1059020911yescharacteristic
subgroupG/H
centerC2#10590209
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC2×C32×Q16C4
socleC2×C32#327
prime radicalC22×C3⋊D3D8
cosocleC2×#3743C22
hypercenterC2×Q16#157
hypocenterC32#1340
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
5. C2×C32×Q16C4semidirect
10. #63644C4semidirect
64. C2×Q16#157semidirect
106. C32#1340semidirect

Maximal subgroups

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

subgroupindex
#105928882
#105901842
#105901802
#13409