Finite Group Databasebeta

← (#131⋊C3)⋊A4 #11922565

Subgroups — (#131⋊C3)⋊A4 #11922565

Order 1152.

219 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 219 conjugacy classes of subgroups — too many to draw. Only its 34 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(#41⋊C3)⋊A4C211yesmaximal, characteristic
2#85666C312yesmaximal, complemented
3#85629C312yesmaximal, complemented
4Ω+(4,𝔽3)C411yescharacteristic
5C3×#131⋊C3—42nomaximal
6#5950C2×C312yes—
7#5945C2×C312yes—
8#568⋊C3—32no—
9C2×#131⋊C3—32no—
10C3×#41⋊C3—42no—
11#3573C3211yescharacteristic, complemented, Sylow
12#997C3×C412yes—
132−1+4⋊C3—32no—
14#994C3×C412yes—
15C2×#41⋊C3—32no—
16C3×#131—42no—
17#131⋊C3—32no—
18#131⋊C3—44no—
19#131⋊C3A412yescomplemented
20C8×A4—122no—
21C3×SL(2,𝔽3)—42no—
22C32×C8—161no—
23#585C2×C3211yescharacteristic
24#568—32no—
25#568—91no—
26C2×#131—32no—
27C2×#131—91no—
28C3×#41—42no—
29#41⋊C3—32no—
30#41⋊C3—44no—
31#41⋊C3C2×A412yes—
32C2×SL(2,𝔽3)—32no—
33C4×A4—122no—
34C3×M16—122no—
35C2×C3×C8—122no—
36C32×C4—161no—
372−1+4—32no—
38H(5,𝔽2)—91no—
39H(5,𝔽2)C32×C411yescharacteristic
40C2×#41—32no—
41C2×#41—91no—
42#131—32no—
43#131—92no—
44#131—94no—
45#131—92no—
46#131C3×A412yes—
47C2×M16—92no—
48C2×M16—91no—
49C2×M16—92no—
50C22×C8—32no—
51C22×C8—91no—
52C2×A4—122no—
53C3×Q8—42no—
54C3×D4—122no—
55C2×C3×C4—122no—
56SL(2,𝔽3)—44no—
57SL(2,𝔽3)C4×A412yes—
58C3×C8—42no—
59C3×C8—122no—
60C3×C8—162no—
61C2×C32—161no—
62#41—32no—
63#41—92no—
64#41—94no—
65#41—92no—
66#41C2×C3×A412yes—
67C2×Q8—32no—
68C2×Q8—91no—
69C2×D4—92no—
70C2×D4—92no—
71C2×D4—91no—
72C22×C4—32no—
73C22×C4—91no—
74M16—32no—
75M16—94no—
76M16—92no—
77C2×C8—32no—
78C2×C8—91no—
79C2×C8—92no—
80C2×C8—91no—
81C2×C8—92no—
82C22×C3—122no—
83A4—122no—
84C3×C4—42no—
85C3×C4—122no—
86C3×C4—162no—
87C32—161noSylow
88C23—32no—
89C23—91no—
90Q8—92no—
91Q8C3×C4×A412yes—
92D4—32no—
93D4—92no—
94D4—94no—
95C2×C4—32no—
96C2×C4—91no—
97C2×C4—92no—
98C2×C4—91no—
99C2×C4—92no—
100C8—32no—
101C8—91no—
102C8A4211yescharacteristic
103C2×C3—42no—
104C2×C3—162no—
105C2×C3—242no—
106C22—32no—
107C22—91no—
108C22—122no—
109C22—361no—
110C4—32no—
111C4—91no—
112C4C2×A4211yescharacteristic
113C3—42no—
114C3—162no—
115C2—62no—
116C2—181no—
117C2C4×A4211yescharacteristic
subgroupG/H
center, hypercenterC8A42
commutator, hypocenterH(5,𝔽2)C32×C4
FrattiniC4C2×A42
Fitting#3573C32
socleC2C4×A42
prime radical(#41⋊C3)⋊A4C2
cosocle#585C2×C32
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #85666C3semidirect
3. #85629C3semidirect
11. #3573C32semidirect
19. #131⋊C3A4semidirect

Maximal subgroups

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

subgroupindex
(#41⋊C3)⋊A42
#856663
#856293
C3×#131⋊C34