Finite Group Databasebeta

← #4179⋊A4 #14518165

Subgroups — #4179⋊A4 #14518165

Order 1944.

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

normal subgroups only

This group has 207 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#11757809C211yesmaximal, characteristic, complemented
2C3⋊(D9⋊A4)C311yesmaximal, characteristic, complemented
3A4×(C3⋊D3)⋊C3—31nomaximal
4C22×#4179C311yesmaximal, characteristic, complemented
5#10619768C312yesmaximal, complemented
6#4179⋊C3—41nomaximal
7A4×H(3,𝔽3)—21no—
8A4×H(3,𝔽3)D311yescharacteristic
9C3×C9⋊A4C2×C311yescharacteristic, complemented
10C22×#732C2×C311yescharacteristic, complemented
11C2×#4179—31no—
12C2×#4179—31no—
13#66362—21no—
14#66362—22no—
15#66358C2×C312yescomplemented
16#6911—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×#732—31no—
26#4179—31no—
27#4179—42no—
28#4179A411yescharacteristic, complemented
29C32×A4—31no—
30C32×A4—61no—
31C32×A4C3×D311yescharacteristic
32C22×H(3,𝔽3)—21no—
33C22×H(3,𝔽3)C3×D311yescharacteristic
34C22×C3×C9C2×C3211yescharacteristic, complemented
35C2×C3⋊D9—31no—
36C2×C3⋊D9—31no—
37C2×(C3⋊D3)⋊C3—91no—
38C2×(C3⋊D3)⋊C3—91no—
39C22⋊H(3,𝔽3)—22no—
40C22⋊H(3,𝔽3)—61no—
41C22⋊H(3,𝔽3)—61no—
42C22⋊H(3,𝔽3)—61no—
43C22⋊H(3,𝔽3)C3×D312yes—
44C3×C22⋊C9—21no—
45C9⋊A4—31no—
46C9⋊A4—61no—
47C3×3−1+2—41no—
48C3×H(3,𝔽3)—41no—
49C3×H(3,𝔽3)—81no—
50#732—42no—
51#732—82no—
52#732—81no—
53#732C2×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×H(3,𝔽3)—31no—
64C2×H(3,𝔽3)—61no—
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×C32—61no—
74C22×C32C32×D311yescharacteristic
75C2×C3⋊D3—91no—
76C2×C3⋊D3—91no—
77C2×C3×D3—271no—
78C2×C3×D3—271no—
79C3×A4—21no—
80C3×A4—32no—
81C3×A4—62no—
82C3×A4—91no—
83C3×A4—91no—
84C3×A4—181no—
85C3×A4—183no—
86C3×A4(C3⋊D3)⋊C311yescharacteristic
87C22×C9—31no—
88C2×D9—271no—
89C2×D9—271no—
90C22⋊C9—61no—
91C33—41no—
92C33—121no—
93C33—241no—
943−1+2—121no—
953−1+2—241no—
96H(3,𝔽3)—21no—
97H(3,𝔽3)—42no—
98H(3,𝔽3)—82no—
99H(3,𝔽3)—241no—
100H(3,𝔽3)—241no—
101H(3,𝔽3)—241no—
102H(3,𝔽3)D3×A411yescharacteristic
103C3×C9—81no—
104C3×C9C2×C3×A411yescharacteristic, complemented
105C23×C3—271no—
106C22×D3—91no—
107C22×D3—271no—
108C2×A4—271no—
109C2×A4—272no—
110C2×C32—31no—
111C2×C32—91no—
112C2×C32—181no—
113C2×C32—1081no—
114C3⋊D3—31no—
115C3⋊D3—91no—
116C3×D3—91no—
117C3×D3—271no—
118C3×D3—361no—
119C3×D3—362no—
120C3×D3—1081no—
121C2×C9—91no—
122D9—91no—
123D9—271no—
124C22×C3—31no—
125C22×C3—91no—
126C22×C3—181no—
127C22×C3—811no—
128C22×C3—811no—
129C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
130C2×D3—271no—
131C2×D3—271no—
132C2×D3—811no—
133C2×D3—811no—
134A4—31no—
135A4—61no—
136A4—92no—
137A4—182no—
138C32—31no—
139C32—41no—
140C32—61no—
141C32—81no—
142C32—122no—
143C32—242no—
144C32—361no—
145C32—361no—
146C32—721no—
147C32—723no—
148C32C3×D3×A411yescharacteristic
149C9—31no—
150C9—241no—
151C23—271noSylow
152C2×C3—31no—
153C2×C3—91no—
154C2×C3—271no—
155C2×C3—271no—
156C2×C3—541no—
157C2×C3—811no—
158C2×C3—1081no—
159C2×C3—1082no—
160D3—91no—
161D3—271no—
162D3—271no—
163D3—811no—
164C22—811no—
165C22—811no—
166C22#4179⋊C311yescharacteristic, complemented
167C3—31no—
168C3—91no—
169C3—121no—
170C3—181no—
171C3—241no—
172C3—362no—
173C3—722no—
174C3A4×(C3⋊D3)⋊C311yescharacteristic
175C2—31no—
176C2—271no—
177C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC32C3×D3×A4
FittingC22×#732C2×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. #11757809C2semidirect
2. C3⋊(D9⋊A4)C3semidirect
4. C22×#4179C3semidirect
5. #10619768C3semidirect
9. C3×C9⋊A4C2×C3semidirect
10. C22×#732C2×C3semidirect
15. #66358C2×C3semidirect
19. C22×C3⋊D9C32semidirect
28. #4179A4semidirect
34. C22×C3×C9C2×C32semidirect
53. #732C2×A4semidirect
67. C3⋊D9C3×A4semidirect
104. C3×C9C2×C3×A4semidirect
166. C22#4179⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578092
C3⋊(D9⋊A4)3
A4×(C3⋊D3)⋊C33
C22×#41793
#106197683
#4179⋊C34