Finite Group Databasebeta

← #11772895

Subgroups — #11772895

Order 1152.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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×#488C211yesmaximal, characteristic
2#10589408C211yesmaximal, characteristic
3#10589407C211yesmaximal, characteristic
4#67782—34nomaximal
5C32×#125C411yescharacteristic, complemented
6C32×#124C2211yescharacteristic
7C32×#103—21no—
8C32×#102—21no—
9C32×C4×C8C411yescharacteristic, complemented
10#63663—21no—
11#63661—21no—
12C3×#488D314yes—
13#4542—34no—
14#4541—34no—
15C2×C32×Q8D411yescharacteristic
16C2×C32×D4D411yescharacteristic
17C2×C32×C8—21no—
18C32×C4⋊C4—21no—
19C32×C4⋊C4—41no—
20C32×C22⋊C4—41no—
21C32×C42C2×C411yescharacteristic
22#3757—41no—
23#3748—41no—
24#1414—91noSylow
25C3×#125Dic314yescomplemented
26C3×#124C2×D314yes—
27C3×#103—24no—
28C3×#102—24no—
29C3×C4×C8Dic314yescomplemented
30#836—64no—
31#834—64no—
32C23×C32—21no—
33C32×Q8—41no—
34C32×D4—41no—
35C2×C32×C4—21no—
36C2×C32×C4—21no—
37C2×C32×C4—41no—
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C3⋊Dic3—81no—
40C32×C8—41no—
41C3⋊(C3⋊C8)—81no—
42#488C3⋊D311yescharacteristic
43#355—91no—
44#354—91no—
45C2×C3×Q8#6714yes—
46C2×C3×D4#6714yes—
47C2×C3×C8—24no—
48C3×C4⋊C4—24no—
49C3×C4⋊C4—44no—
50C3×C22⋊C4—44no—
51C3×C42C2×Dic314yes—
52#217—124no—
53#208—124no—
54C22×C32—41no—
55C22×C32—81no—
56C22×C32#9911yescharacteristic
57C32×C4—21no—
58C32×C4—41no—
59C32×C4—41no—
60C32×C4—81no—
61C3⋊Dic3—161no—
62#125C3⋊Dic311yescharacteristic, complemented
63#124C2×C3⋊D311yescharacteristic
64#103—21no—
65#102—21no—
66#101—181no—
67#99—181no—
68C4×C8C3⋊Dic311yescharacteristic, complemented
69C23×C3—24no—
70C3×Q8—44no—
71C3×D4—44no—
72C2×C3×C4—24no—
73C2×C3×C4—24no—
74C2×C3×C4—44no—
75C2×C3×C4#21714yes—
76C2×Dic3—244no—
77C3×C8—44no—
78C3⋊C8—244no—
79C2×C32—21no—
80C2×C32—81no—
81C2×C32#35411yescharacteristic
82C2×Q8#63811yescharacteristic
83C2×D4#63811yescharacteristic
84M16—361no—
85C2×C8—21no—
86C4⋊C4—21no—
87C4⋊C4—41no—
88C22⋊C4—41no—
89C22⋊C4—361no—
90C42C2×C3⋊Dic311yescharacteristic
91C22×C3—44no—
92C22×C3—84no—
93C22×C3#83414yes—
94C3×C4—24no—
95C3×C4—44no—
96C3×C4—44no—
97C3×C4—84no—
98Dic3—484no—
99C32#141411yescharacteristic, complemented, Sylow
100C23—21no—
101Q8—41no—
102D4—41no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—41no—
106C2×C4—721no—
107C2×C4#375711yescharacteristic
108C8—41no—
109C8—721no—
110C2×C3—24no—
111C2×C3—84no—
112C2×C3#454114yes—
113C22—41no—
114C22—81no—
115C22#6366111yescharacteristic
116C4—21no—
117C4—41no—
118C4—41no—
119C4—81no—
120C4—1441no—
121C3#6778214yescomplemented
122C2—21no—
123C2—81no—
124C2#1058940711yescharacteristic
subgroupG/H
centerC2#10589407
commutatorC32×C42C2×C4
Frattini#124C2×C3⋊D3
FittingC32×#488C2
socleC2×C32#354
prime radicalC2×C32×D4D4
cosocleC32×#124C22
hypercenter#488C3⋊D3
hypocenterC32#1414
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #488

Complements

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

NH ≅ G/Ntype
5. C32×#125C4semidirect
9. C32×C4×C8C4semidirect
25. C3×#125Dic3semidirect
29. C3×C4×C8Dic3semidirect
62. #125C3⋊Dic3semidirect
68. C4×C8C3⋊Dic3semidirect
99. C32#1414semidirect
121. C3#67782semidirect

Maximal subgroups

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

subgroupindex
C32×#4882
#105894082
#105894072
#677823