Finite Group Databasebeta

← #14518163

Subgroups — #14518163

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
2A4×#272C311yesmaximal, characteristic, complemented
3D3×C9⋊A4—31nomaximal
4C22×#4178C311yesmaximal, characteristic, complemented
5#10619771C312yesmaximal, complemented
6#92285—41nomaximal
7A4×H(3,𝔽3)—21no—
8A4×H(3,𝔽3)C2×C311yescharacteristic
9C3×C9⋊A4D311yescharacteristic, complemented
10C22×#732C2×C311yescharacteristic, complemented
11C2×#4178—31no—
12C2×#4178—31no—
13#66362—22no—
14#66362C2×C312yescomplemented
15#66358—21no—
16#6911—41noSylow
17C3×D3×A4—31no—
18C3×D3×A4—91no—
19C22×#272C3211yescharacteristic, complemented
20C22×D3×C9—31no—
21C2×C9⋊A4—91no—
22D3×C22⋊C9—32no—
23C3×#272—41no—
24D3×3−1+2—121no—
25C2×#732—31no—
26#4178—31no—
27#4178—42no—
28#4178A411yescharacteristic, complemented
29C32×A4—31no—
30C32×A4—61no—
31C32×A4C3×D311yescharacteristic
32C22×H(3,𝔽3)—21no—
33C22×H(3,𝔽3)C2×C3211yescharacteristic
34C22×C3×C9C3×D311yescharacteristic, complemented
35C2×#272—31no—
36C2×#272—31no—
37C2×D3×C9—91no—
38C2×D3×C9—91no—
39C22⋊H(3,𝔽3)—21no—
40C22⋊H(3,𝔽3)—22no—
41C22⋊H(3,𝔽3)—61no—
42C22⋊H(3,𝔽3)—61no—
43C22⋊H(3,𝔽3)—61no—
44C3×C22⋊C9C3×D312yescomplemented
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—91no—
57D3×A4—91no—
58D3×A4—93no—
59C23×C9—91no—
60C2×C22⋊C9—92no—
61C32×D3—121no—
62C32×D3—361no—
63C2×3−1+2—361no—
64C2×H(3,𝔽3)—31no—
65C2×H(3,𝔽3)—61no—
66C2×C3×C9—31no—
67#272—31no—
68#272C3×A411yescharacteristic, complemented
69D3×C9—31no—
70D3×C9—91no—
71D3×C9—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—62no—
81C3×A4—61no—
82C3×A4—91no—
83C3×A4—93no—
84C3×A4—183no—
85C3×A4(C3⋊D3)⋊C311yescharacteristic
86C22×C9—31no—
87C22×C9—271no—
88C22×C9—271no—
89C22⋊C9—32no—
90C33—41no—
91C33—121no—
92C33—241no—
933−1+2—121no—
943−1+2—241no—
95H(3,𝔽3)—21no—
96H(3,𝔽3)—82no—
97H(3,𝔽3)—81no—
98H(3,𝔽3)—241no—
99H(3,𝔽3)—241no—
100H(3,𝔽3)—241no—
101H(3,𝔽3)C2×C3×A411yescharacteristic
102C3×C9—42no—
103C3×C9D3×A411yescharacteristic, complemented
104C23×C3—91no—
105C22×D3—31no—
106C22×D3—91no—
107C2×A4—271no—
108C2×C32—31no—
109C2×C32—91no—
110C2×C32—181no—
111C2×C32—361no—
112C3×D3—31no—
113C3×D3—91no—
114C3×D3—91no—
115C3×D3—271no—
116C3×D3—361no—
117C3×D3—363no—
118C2×C9—91no—
119C2×C9—91no—
120C2×C9—271no—
121C2×C9—362no—
122C22×C3—31no—
123C22×C3—91no—
124C22×C3—181no—
125C22×C3—271no—
126C22×C3—271no—
127C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
128C2×D3—91no—
129C2×D3—91no—
130C2×D3—271no—
131C2×D3—271no—
132A4—31no—
133A4—61no—
134A4—181no—
135A4—182no—
136C32—31no—
137C32—41no—
138C32—61no—
139C32—81no—
140C32—242no—
141C32—241no—
142C32—361no—
143C32—363no—
144C32—723no—
145C32C3×D3×A411yescharacteristic
146C9—31no—
147C9—122no—
148C23—91noSylow
149C2×C3—31no—
150C2×C3—91no—
151C2×C3—91no—
152C2×C3—271no—
153C2×C3—271no—
154C2×C3—541no—
155C2×C3—1081no—
156D3—31no—
157D3—91no—
158D3—91no—
159D3—271no—
160C22—271no—
161C22—271no—
162C22#9228511yescharacteristic, complemented
163C3—31no—
164C3—91no—
165C3—121no—
166C3—181no—
167C3—241no—
168C3—721no—
169C3—722no—
170C3A4×(C3⋊D3)⋊C311yescharacteristic
171C2—31no—
172C2—91no—
173C2—271no—
subgroupG/H
center, hypercenterC3A4×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterC22×H(3,𝔽3)C2×C32
FrattiniC32C3×D3×A4
FittingC22×#732C2×C3
socleC22×C3C3×(C3⋊D3)⋊C3
LCSG ▷ C22×H(3,𝔽3)
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #11757809C2semidirect
2. A4×#272C3semidirect
4. C22×#4178C3semidirect
5. #10619771C3semidirect
9. C3×C9⋊A4D3semidirect
10. C22×#732C2×C3semidirect
14. #66362C2×C3semidirect
19. C22×#272C32semidirect
28. #4178A4semidirect
34. C22×C3×C9C3×D3semidirect
44. C3×C22⋊C9C3×D3semidirect
53. #732C2×A4semidirect
68. #272C3×A4semidirect
103. C3×C9D3×A4semidirect
162. C22#92285semidirect

Maximal subgroups

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

subgroupindex
#117578092
A4×#2723
D3×C9⋊A43
C22×#41783
#106197713
#922854