Finite Group Databasebeta

← #14518151

Subgroups — #14518151

Order 1944.

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

normal subgroups only

This group has 242 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#11757801C211yesmaximal, characteristic, complemented
2A4×#272C311yesmaximal, characteristic, complemented
3D3×C22⋊H(3,𝔽3)—31nomaximal
4C22×#4174C311yesmaximal, characteristic, complemented
5#10619773C312yesmaximal, complemented
6#92281—41nomaximal
7C3×C22⋊H(3,𝔽3)D311yescharacteristic, complemented
8A4×3−1+2—21no—
9A4×H(3,𝔽3)C2×C311yescharacteristic, complemented
10C22×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
11C2×#4174—31no—
12C2×#4174—31no—
13#66368—21no—
14#66366—22no—
15#66363C2×C312yescomplemented
16#6909—41noSylow
17C22×C32×D3—31no—
18C3×D3×A4—31no—
19C3×D3×A4—32no—
20C3×D3×A4—91no—
21C22×#272C3211yescharacteristic
22C2×C22⋊H(3,𝔽3)—91no—
23C3×#272—41no—
24D3×H(3,𝔽3)—121no—
25C2×AΣL(1,𝔽27)—31no—
26#4174—31no—
27#4174—42no—
28#4174A411yescharacteristic, complemented
29C22×C33C3×D311yescharacteristic, complemented
30C2×C32×D3—91no—
31C2×C32×D3—91no—
32C32×A4—31no—
33C32×A4C3×D311yescharacteristic
34C32×A4C3×D312yescomplemented
35C22×3−1+2—21no—
36C22×H(3,𝔽3)C2×C3211yescharacteristic
37C2×#272—31no—
38C2×#272—31no—
39C22⋊H(3,𝔽3)—21no—
40C22⋊H(3,𝔽3)—31no—
41C22⋊H(3,𝔽3)—61no—
42C22⋊H(3,𝔽3)—61no—
43#1094—22no—
44C9⋊A4—61no—
45C9⋊A4—61no—
46C9×A4—61no—
47C3×3−1+2—81no—
48C3×H(3,𝔽3)—41no—
49C3×H(3,𝔽3)—41no—
50AΣL(1,𝔽27)—42no—
51AΣL(1,𝔽27)—82no—
52AΣL(1,𝔽27)—81no—
53AΣL(1,𝔽27)C2×A411yescharacteristic, complemented
54C23×C32—91no—
55C22×C3×D3—31no—
56C22×C3×D3—91no—
57C22×C3×D3—91no—
58C2×C3×A4—92no—
59C2×C3×A4—91no—
60D3×A4—91no—
61D3×A4—92no—
62D3×A4—93no—
63C2×C33—31no—
64C32×D3—31no—
65C32×D3—91no—
66C32×D3—122no—
67C32×D3—121no—
68C32×D3—361no—
69C2×3−1+2—61no—
70C2×H(3,𝔽3)—31no—
71C2×H(3,𝔽3)—361no—
72#272—31no—
73#272C3×A411yescharacteristic
74C22×C32—31no—
75C22×C32—31no—
76C22×C32—91no—
77C22×C32—271no—
78C22×C32—271no—
79C22×C32C32×D311yescharacteristic
80C2×C3×D3—91no—
81C2×C3×D3—93no—
82C2×C3×D3—93no—
83C2×C3×D3—91no—
84C2×C3×D3—271no—
85C2×C3×D3—271no—
86C3×A4—21no—
87C3×A4—32no—
88C3×A4—61no—
89C3×A4—91no—
90C3×A4—93no—
91C3×A4—92no—
92C3×A4(C3⋊D3)⋊C311yescharacteristic
93C22×C9—61no—
94C22⋊C9—62no—
95C33—41no—
96C33—42no—
97C33—121no—
98C33D3×A411yescharacteristic, complemented
993−1+2—21no—
1003−1+2—82no—
1013−1+2—241no—
1023−1+2—241no—
103H(3,𝔽3)—81no—
104H(3,𝔽3)—121no—
105H(3,𝔽3)—241no—
106H(3,𝔽3)—241no—
107H(3,𝔽3)C2×C3×A411yescharacteristic
108C3×C9—241no—
109C23×C3—91no—
110C23×C3—271no—
111C22×D3—31no—
112C22×D3—91no—
113C2×A4—271no—
114C2×A4—272no—
115C2×C32—31no—
116C2×C32—91no—
117C2×C32—91no—
118C2×C32—93no—
119C2×C32—91no—
120C2×C32—271no—
121C2×C32—361no—
122C2×C32—362no—
123C3×D3—31no—
124C3×D3—91no—
125C3×D3—91no—
126C3×D3—93no—
127C3×D3—91no—
128C3×D3—271no—
129C3×D3—361no—
130C3×D3—362no—
131C3×D3—363no—
132C2×C9—181no—
133C22×C3—31no—
134C22×C3—91no—
135C22×C3—91no—
136C22×C3—271no—
137C22×C3—271no—
138C22×C3—273no—
139C22×C3—273no—
140C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
141C2×D3—91no—
142C2×D3—91no—
143C2×D3—271no—
144C2×D3—271no—
145A4—31no—
146A4—61no—
147A4—92no—
148A4—181no—
149C32—31no—
150C32—31no—
151C32—41no—
152C32—81no—
153C32—91no—
154C32—122no—
155C32—241no—
156C32—361no—
157C32—362no—
158C32—363no—
159C32C3×D3×A411yescharacteristic
160C9—61no—
161C9—242no—
162C23—91noSylow
163C2×C3—31no—
164C2×C3—91no—
165C2×C3—93no—
166C2×C3—91no—
167C2×C3—271no—
168C2×C3—271no—
169C2×C3—273no—
170C2×C3—271no—
171C2×C3—1081no—
172C2×C3—1082no—
173D3—31no—
174D3—91no—
175D3—91no—
176D3—271no—
177C22—271no—
178C22—271no—
179C22#9228111yescharacteristic, complemented
180C3—31no—
181C3—91no—
182C3—91no—
183C3—121no—
184C3—241no—
185C3—362no—
186C3—721no—
187C3A4×(C3⋊D3)⋊C311yescharacteristic
188C2—31no—
189C2—91no—
190C2—271no—
subgroupG/H
center, hypercenterC3A4×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterC22×H(3,𝔽3)C2×C32
FrattiniC32C3×D3×A4
FittingC22×AΣL(1,𝔽27)C2×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. #11757801C2semidirect
2. A4×#272C3semidirect
4. C22×#4174C3semidirect
5. #10619773C3semidirect
7. C3×C22⋊H(3,𝔽3)D3semidirect
9. A4×H(3,𝔽3)C2×C3semidirect
10. C22×AΣL(1,𝔽27)C2×C3semidirect
15. #66363C2×C3semidirect
28. #4174A4semidirect
29. C22×C33C3×D3semidirect
34. C32×A4C3×D3semidirect
53. AΣL(1,𝔽27)C2×A4semidirect
98. C33D3×A4semidirect
179. C22#92281semidirect

Maximal subgroups

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

subgroupindex
#117578012
A4×#2723
D3×C22⋊H(3,𝔽3)3
C22×#41743
#106197733
#922814