Finite Group Databasebeta

← #11772870

Subgroups — #11772870

Order 1152.

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

normal subgroups only

This group has 282 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#10592770C211yesmaximal, characteristic
2C32×#353C211yesmaximal, characteristic
3#10589411C211yesmaximal, characteristic
4#67539—34nomaximal
5C32×#127C2211yescharacteristic
6#64079C411yescharacteristic, complemented
7C32×#99—21no—
8#63661—21no—
9#63659—21no—
10#63659—21no—
11#63630C411yescharacteristic, complemented
12#5071—34no—
13C3×#353D314yes—
14#4545—34no—
15C2×C32×D4—41no—
16C2×C32×D4D411yescharacteristic
17C2×C32×D4D411yescharacteristic
18C32×C22⋊C4—41no—
19C32×C42C2×C411yescharacteristic
20#3757—41no—
21C4⋊(C3⋊Dic3)—21no—
22#3750—41no—
23C2×C3⋊(C3⋊C8)—21no—
24#1412—91noSylow
25C3×#127C2×D314yes—
26#870—34no—
27C3×#99—24no—
28#834—64no—
29#832—64no—
30#832—64no—
31#803—34no—
32C23×C32—21no—
33C23×C32—21no—
34C32×D4—41no—
35C32×D4—41no—
36C32×D4—82no—
37C2×C32×C4—21no—
38C2×C32×C4—81no—
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C3⋊Dic3—41no—
41C2×C3⋊Dic3—81no—
42C3⋊(C3⋊C8)—41no—
43#490—91no—
44#353—91no—
45#353C3⋊D311yescharacteristic
46C2×C3×D4—44no—
47C2×C3×D4D1214yes—
48C2×C3×D4#6714yes—
49C3×C22⋊C4—44no—
50C3×C42C4×D314yes—
51#217—124no—
52C4⋊Dic3—64no—
53Dic3⋊C4—124no—
54C2×C3⋊C8—64no—
55C22×C32—41no—
56C22×C32—41no—
57C22×C32—81no—
58C22×C32—81no—
59C22×C32#9911yescharacteristic
60C32×C4—21no—
61C32×C4—41no—
62C32×C4—161no—
63C3⋊Dic3—81no—
64C3⋊Dic3—161no—
65#127C2×C3⋊D311yescharacteristic
66#125—91no—
67#102—181no—
68#102—181no—
69#99—21no—
70#99—181no—
71#97—91no—
72C23×C3—24no—
73C23×C3—24no—
74C3×D4—44no—
75C3×D4—44no—
76C3×D4—88no—
77C2×C3×C4—24no—
78C2×C3×C4—84no—
79C2×C3×C4(C2×D3)⋊C414yes—
80C2×Dic3—124no—
81C2×Dic3—244no—
82C3⋊C8—124no—
83C2×C32—21no—
84C2×C32—81no—
85C2×C32—81no—
86C2×C32#35411yescharacteristic
87C2×D4—41no—
88C2×D4C4⋊(C3⋊D3)11yescharacteristic
89C2×D4#63811yescharacteristic
90C2×C8—181no—
91C4⋊C4—181no—
92C4⋊C4—361no—
93C22⋊C4—41no—
94C22⋊C4—361no—
95C42C4×C3⋊D311yescharacteristic
96C22×C3—44no—
97C22×C3—44no—
98C22×C3—84no—
99C22×C3—84no—
100C22×C3#80614yes—
101C3×C4—24no—
102C3×C4—44no—
103C3×C4—164no—
104Dic3—244no—
105Dic3—484no—
106C32#141211yescharacteristic, complemented, Sylow
107C23—21no—
108C23—21no—
109D4—41no—
110D4—41no—
111D4—82no—
112C2×C4—21no—
113C2×C4—81no—
114C2×C4—361no—
115C2×C4—721no—
116C2×C4#375211yescharacteristic
117C8—361no—
118C2×C3—24no—
119C2×C3—84no—
120C2×C3—84no—
121C2×C3#447314yes—
122C22—41no—
123C22—41no—
124C22—81no—
125C22—81no—
126C22#6363311yescharacteristic
127C4—21no—
128C4—41no—
129C4—161no—
130C4—721no—
131C4—1441no—
132C3#6753914yescomplemented
133C2—21no—
134C2—81no—
135C2—81no—
136C2#1058933911yescharacteristic
subgroupG/H
centerC2#10589339
commutatorC32×C42C2×C4
Frattini#127C2×C3⋊D3
FittingC32×#353C2
socleC2×C32#354
prime radical, cosocleC32×#127C22
hypercenter#353C3⋊D3
hypocenterC32#1412
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
6. #64079C4semidirect
11. #63630C4semidirect
106. C32#1412semidirect
132. C3#67539semidirect

Maximal subgroups

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

subgroupindex
#105927702
C32×#3532
#105894112
#675393