Finite Group Databasebeta

← A4⋊#4185 #14518104

Subgroups — A4⋊#4185 #14518104

Order 1944.

348 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 43 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
1A4×#732C211yesmaximal, characteristic, complemented
2A4⋊((C3⋊D3)⋊C3)—33nomaximal
3C3×C9⋊S4—31nomaximal
4#10619755—36nomaximal
5#10619750—32nomaximal
6#10619683—31nomaximal
7C3⋊#4185—41nomaximal
8A4×H(3,𝔽3)D313yescomplemented
9C3×C9×A4D311yescharacteristic, complemented
10C22×#732D311yescharacteristic, complemented
11C2×#4185—31no—
12#66362D316yescomplemented
13#66358D312yescomplemented
14#66332—31no—
15C3×#732—41noSylow
16C3⋊(C3⋊S4)—33no—
17C3×C3⋊S4—91no—
18C9⋊S4—31no—
19(C3⋊S4)⋊C3—96no—
20C3×(C22⋊C9)⋊C2—92no—
21#638⋊C3—93no—
22C3×#611—91no—
23C3⋊((C3⋊D3)⋊C3)—123no—
24C3×C3⋊D9—121no—
25C2×#732—31no—
26#4185—61no—
27#4185—122no—
28#4185—126no—
29C32×A4—33no—
30C32×A4C3⋊D311yescharacteristic
31C22×H(3,𝔽3)C3⋊D313yescomplemented
32C22×C3×C9C3⋊D311yescharacteristic, complemented
33C2×(C3⋊D3)⋊C3—93no—
34C2×C3×D9—91no—
35C22⋊H(3,𝔽3)—63no—
36C22⋊H(3,𝔽3)C3⋊D316yescomplemented
37C3×C22⋊C9C3⋊D312yescomplemented
38C9×A4—31no—
39C9×A4—61no—
40(C3⋊Dic3)⋊C3—93no—
41C3×Dic9—91no—
42C3×H(3,𝔽3)—43no—
43C32×C9—41no—
44#732—46no—
45#732—42no—
46#732S411yescharacteristic, complemented
47C3⋊S4—91no—
48C3⋊S4—96no—
49C3⋊S4—279no—
50C3×S4—273no—
51#638—93no—
52C3×#67—271no—
53(C22⋊C9)⋊C2—92no—
54#611—91no—
55C3⋊(C3⋊D3)—123no—
56C3×C3⋊D3—361no—
57C2×H(3,𝔽3)—33no—
58C2×C3×C9—31no—
59C3⋊D9—121no—
60(C3⋊D3)⋊C3—183no—
61(C3⋊D3)⋊C3—366no—
62C3×D9—181no—
63C3×D9—362no—
64C22×C32—33no—
65C22×C32C3⋊(C3⋊D3)11yescharacteristic
66C2×C3⋊D3—93no—
67C2×C3×D3—271no—
68C3×A4—21no—
69C3×A4—33no—
70C3×A4—36no—
71C3×A4—99no—
72C3×A4#27211yescharacteristic
73C3⋊Dic3—93no—
74C3×Dic3—271no—
75C22×C9—31no—
76C2×D9—91no—
77C22⋊C9—32no—
78Dic9—91no—
79C33—41no—
80C33—123no—
81H(3,𝔽3)—46no—
82H(3,𝔽3)—243no—
83H(3,𝔽3)C3⋊S413yescomplemented
84C3×C9—42no—
85C3×C9—121no—
86C3×C9—241no—
87C3×C9C3⋊S411yescharacteristic, complemented
88S4—273no—
89S4—816no—
90C3×D4—811no—
91#67—271no—
92#67—813no—
93C2×C32—31no—
94C2×C32—93no—
95C3⋊D3—183no—
96C3⋊D3—366no—
97C3⋊D3—361no—
98C3⋊D3—1089no—
99C3×D3—541no—
100C3×D3—1083no—
101C2×C9—91no—
102D9—181no—
103D9—362no—
104C22×C3—31no—
105C22×C3—93no—
106C22×C3—811no—
107C22×C3C3⋊#27211yescharacteristic
108C2×D3—271no—
109C2×D3—813no—
110A4—61no—
111A4—96no—
112A4#418513yescomplemented
113C3×C4—811no—
114Dic3—271no—
115Dic3—813no—
116C32—33no—
117C32—41no—
118C32—81no—
119C32—123no—
120C32—126no—
121C32—369no—
122C32C3⋊(C3⋊S4)11yescharacteristic
123C9—31no—
124C9—122no—
125D4—811noSylow
126C2×C3—31no—
127C2×C3—91no—
128C2×C3—273no—
129C2×C3—1621no—
130D3—541no—
131D3—3246no—
132D3—1083no—
133D3—1623no—
134C22—811no—
135C22C3⋊#418511yescharacteristic, complemented
136C4—811no—
137C3—31no—
138C3—43no—
139C3—93no—
140C3—241no—
141C3—366no—
142C3A4⋊#27211yescharacteristic
143C2—31no—
144C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterA4×#732C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×#732D3
socleC22×C3C3⋊#272
LCSG ▷ A4×#732
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×#732C2semidirect
8. A4×H(3,𝔽3)D3semidirect
9. C3×C9×A4D3semidirect
10. C22×#732D3semidirect
12. #66362D3semidirect
13. #66358D3semidirect
31. C22×H(3,𝔽3)C3⋊D3semidirect
32. C22×C3×C9C3⋊D3semidirect
36. C22⋊H(3,𝔽3)C3⋊D3semidirect
37. C3×C22⋊C9C3⋊D3semidirect
46. #732S4semidirect
83. H(3,𝔽3)C3⋊S4semidirect
87. C3×C9C3⋊S4semidirect
112. A4#4185semidirect
135. C22C3⋊#4185semidirect

Maximal subgroups

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

subgroupindex
A4×#7322
A4⋊((C3⋊D3)⋊C3)3
C3×C9⋊S43
#106197553
#106197503
#106196833
C3⋊#41854