Finite Group Databasebeta

← #4177⋊A4 #14518159

Subgroups — #4177⋊A4 #14518159

Order 1944.

194 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 29 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#11757805C211yesmaximal, characteristic, complemented
2C3⋊(D9⋊A4)C311yesmaximal, characteristic, complemented
3A4×(C3⋊D3)⋊C3—31nomaximal
4C22×#4177C311yesmaximal, characteristic, complemented
5#10619769C312yesmaximal, complemented
6#4177⋊C3—41nomaximal
7A4×3−1+2—21no—
8A4×H(3,𝔽3)D311yescharacteristic
9C3×C9⋊A4C2×C311yescharacteristic, complemented
10C22×#731C2×C311yescharacteristic, complemented
11C2×#4177—31no—
12C2×#4177—31no—
13#66365—22no—
14#66361—21no—
15#66357C2×C312yescomplemented
16#6910—41noSylow
17A4×C3⋊D3—31no—
18C3×D3×A4—91no—
19C22×C3⋊D9C3211yescharacteristic, complemented
20C22×(C3⋊D3)⋊C3—31no—
21(C3⋊D3)⋊A4—32no—
22D9⋊A4—91no—
23C3⋊AGL(1,ℤ/9)—41no—
24C3×(C3⋊D3)⋊C3—121no—
25C2×#731—31no—
26#4177—31no—
27#4177—42no—
28#4177A411yescharacteristic, complemented
29C32×A4—31no—
30C32×A4C3×D311yescharacteristic
31C22×3−1+2—21no—
32C22×H(3,𝔽3)C3×D311yescharacteristic
33C22×C3×C9C2×C3211yescharacteristic, complemented
34C2×C3⋊D9—31no—
35C2×C3⋊D9—31no—
36C2×(C3⋊D3)⋊C3—91no—
37C2×(C3⋊D3)⋊C3—91no—
38C22⋊H(3,𝔽3)—61no—
39C22⋊H(3,𝔽3)C3×D312yes—
40#1094—22no—
41C3×C22⋊C9—21no—
42C9⋊A4—31no—
43C9⋊A4—61no—
44C9⋊A4—61no—
45C9⋊A4—61no—
46C9×A4—61no—
47C3×3−1+2—41no—
48C3×3−1+2—81no—
49C3×H(3,𝔽3)—41no—
50#731—42no—
51#731—82no—
52#731—81no—
53#731C2×A411yescharacteristic, complemented
54C22×C3⋊D3—31no—
55C22×C3×D3—91no—
56C2×C3×A4—271no—
57D3×A4—92no—
58D3×A4—91no—
59D3×A4—271no—
60C22×D9—91no—
61C3×C3⋊D3—121no—
62C32×D3—361no—
63C2×3−1+2—61no—
64C2×H(3,𝔽3)—31no—
65C2×C3×C9—31no—
66C3⋊D9—31no—
67C3⋊D9C3×A411yescharacteristic, complemented
68AGL(1,ℤ/9)—361no—
69(C3⋊D3)⋊C3—31no—
70(C3⋊D3)⋊C3—91no—
71(C3⋊D3)⋊C3—122no—
72C22×C32—31no—
73C22×C32C32×D311yescharacteristic
74C2×C3⋊D3—91no—
75C2×C3⋊D3—91no—
76C2×C3×D3—271no—
77C2×C3×D3—271no—
78C3×A4—21no—
79C3×A4—32no—
80C3×A4—91no—
81C3×A4—91no—
82C3×A4—181no—
83C3×A4(C3⋊D3)⋊C311yescharacteristic
84C22×C9—31no—
85C22×C9—61no—
86C2×D9—271no—
87C2×D9—271no—
88C22⋊C9—62no—
89C22⋊C9—61no—
90C33—41no—
91C33—121no—
923−1+2—21no—
933−1+2—82no—
943−1+2—121no—
953−1+2—241no—
963−1+2—241no—
973−1+2—241no—
98H(3,𝔽3)—42no—
99H(3,𝔽3)—241no—
100H(3,𝔽3)D3×A411yescharacteristic
101C3×C9—81no—
102C3×C9—241no—
103C3×C9C2×C3×A411yescharacteristic, complemented
104C23×C3—271no—
105C22×D3—91no—
106C22×D3—271no—
107C2×A4—271no—
108C2×A4—272no—
109C2×C32—31no—
110C2×C32—91no—
111C2×C32—1081no—
112C3⋊D3—31no—
113C3⋊D3—91no—
114C3×D3—91no—
115C3×D3—271no—
116C3×D3—361no—
117C3×D3—362no—
118C3×D3—1081no—
119C2×C9—91no—
120C2×C9—181no—
121D9—91no—
122D9—271no—
123C22×C3—31no—
124C22×C3—91no—
125C22×C3—811no—
126C22×C3—811no—
127C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
128C2×D3—271no—
129C2×D3—271no—
130C2×D3—811no—
131C2×D3—811no—
132A4—31no—
133A4—61no—
134A4—92no—
135C32—31no—
136C32—41no—
137C32—81no—
138C32—122no—
139C32—361no—
140C32—361no—
141C32—721no—
142C32C3×D3×A411yescharacteristic
143C9—31no—
144C9—61no—
145C9—241no—
146C9—242no—
147C23—271noSylow
148C2×C3—31no—
149C2×C3—91no—
150C2×C3—271no—
151C2×C3—271no—
152C2×C3—811no—
153C2×C3—1081no—
154C2×C3—1082no—
155D3—91no—
156D3—271no—
157D3—271no—
158D3—811no—
159C22—811no—
160C22—811no—
161C22#4177⋊C311yescharacteristic, complemented
162C3—31no—
163C3—91no—
164C3—121no—
165C3—241no—
166C3—362no—
167C3A4×(C3⋊D3)⋊C311yescharacteristic
168C2—31no—
169C2—271no—
170C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC32C3×D3×A4
FittingC22×#731C2×C3
socleC22×C3C3×(C3⋊D3)⋊C3
LCSG ▷ C22×C3×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757805C2semidirect
2. C3⋊(D9⋊A4)C3semidirect
4. C22×#4177C3semidirect
5. #10619769C3semidirect
9. C3×C9⋊A4C2×C3semidirect
10. C22×#731C2×C3semidirect
15. #66357C2×C3semidirect
19. C22×C3⋊D9C32semidirect
28. #4177A4semidirect
33. C22×C3×C9C2×C32semidirect
53. #731C2×A4semidirect
67. C3⋊D9C3×A4semidirect
103. C3×C9C2×C3×A4semidirect
161. C22#4177⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578052
C3⋊(D9⋊A4)3
A4×(C3⋊D3)⋊C33
C22×#41773
#106197693
#4177⋊C34