Finite Group Databasebeta

← #11772892

Subgroups — #11772892

Order 1152.

252 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 59 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#10592755C211yesmaximal, characteristic
2C32×#354C211yesmaximal, characteristic
3#10589408C211yesmaximal, characteristic
4#67543—34nomaximal
5C32×#124C2211yescharacteristic
6#64079C411yescharacteristic, complemented
7C32×#99—21no—
8#63663—21no—
9#63662—21no—
10#63659—21no—
11C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
12#5056—34no—
13C3×#354D314yes—
14#4542—34no—
15C2×C32×Q8D411yescharacteristic
16C2×C32×D4D411yescharacteristic
17C32×C22⋊C4—41no—
18C32×C22⋊C4—41no—
19C32×C42C2×C411yescharacteristic
20C4⋊(C3⋊Dic3)—21no—
21#3750—41no—
22#3748—41no—
23C2×C3⋊(C3⋊C8)—21no—
24#1414—91noSylow
25C3×#124C2×D314yes—
26#870—34no—
27C3×#99—24no—
28#836—64no—
29#835—64no—
30#832—64no—
31C4×C3⋊C8—34no—
32C23×C32—21no—
33C32×Q8—41no—
34C32×D4—41no—
35C2×C32×C4—21no—
36C2×C32×C4—21no—
37C2×C32×C4—81no—
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C3⋊Dic3—41no—
40C3⋊(C3⋊C8)—41no—
41C3⋊(C3⋊C8)—81no—
42#488—91no—
43#355—91no—
44#354C3⋊D311yescharacteristic
45C2×C3×Q8D1214yes—
46C2×C3×D4#6714yes—
47C3×C22⋊C4—44no—
48C3×C22⋊C4—44no—
49C3×C42C4×D314yes—
50C4⋊Dic3—64no—
51Dic3⋊C4—124no—
52#208—124no—
53C2×C3⋊C8—64no—
54C22×C32—41no—
55C22×C32—81no—
56C22×C32#9911yescharacteristic
57C32×C4—21no—
58C32×C4—41no—
59C32×C4—41no—
60C32×C4—161no—
61C3⋊Dic3—81no—
62#125—91no—
63#124C2×C3⋊D311yescharacteristic
64#103—181no—
65#102—181no—
66#101—181no—
67#99—21no—
68C4×C8—91no—
69C23×C3—24no—
70C3×Q8—44no—
71C3×D4—44no—
72C2×C3×C4—24no—
73C2×C3×C4—24no—
74C2×C3×C4—84no—
75C2×C3×C4(C2×D3)⋊C414yes—
76C2×Dic3—124no—
77C3⋊C8—124no—
78C3⋊C8—244no—
79C2×C32—21no—
80C2×C32—81no—
81C2×C32#35411yescharacteristic
82C2×Q8C4⋊(C3⋊D3)11yescharacteristic
83C2×D4#63811yescharacteristic
84M16—361no—
85C2×C8—181no—
86C4⋊C4—181no—
87C4⋊C4—361no—
88C22⋊C4—41no—
89C22⋊C4—41no—
90C42C4×C3⋊D311yescharacteristic
91C22×C3—44no—
92C22×C3—84no—
93C22×C3#80614yes—
94C3×C4—24no—
95C3×C4—44no—
96C3×C4—44no—
97C3×C4—164no—
98Dic3—244no—
99C32#141411yescharacteristic, complemented, Sylow
100C23—21no—
101Q8—41no—
102D4—41no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—81no—
106C2×C4—361no—
107C2×C4#375211yescharacteristic
108C8—361no—
109C8—721no—
110C2×C3—24no—
111C2×C3—84no—
112C2×C3#447314yes—
113C22—41no—
114C22—81no—
115C22#6363311yescharacteristic
116C4—21no—
117C4—41no—
118C4—41no—
119C4—161no—
120C4—721no—
121C3#6754314yescomplemented
122C2—21no—
123C2—81no—
124C2#1058933911yescharacteristic
subgroupG/H
centerC2#10589339
commutatorC32×C42C2×C4
Frattini#124C2×C3⋊D3
FittingC32×#354C2
socleC2×C32#354
prime radicalC2×C32×D4D4
cosocleC32×#124C22
hypercenter#354C3⋊D3
hypocenterC32#1414
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #354

Complements

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

NH ≅ G/Ntype
6. #64079C4semidirect
11. C4×C3⋊(C3⋊C8)C4semidirect
99. C32#1414semidirect
121. C3#67543semidirect

Maximal subgroups

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

subgroupindex
#105927552
C32×#3542
#105894082
#675433