Finite Group Databasebeta

← A4×#131⋊C3 #11922564

Subgroups — A4×#131⋊C3 #11922564

Order 1152.

231 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 231 conjugacy classes of subgroups — too many to draw. Only its 36 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×#41⋊C3C211yesmaximal, characteristic
2#85665C312yesmaximal, complemented
3C22×#131⋊C3C311yesmaximal, characteristic, complemented
4A4×#131C311yesmaximal, characteristic, complemented
5A4×SL(2,𝔽3)C411yescharacteristic
6C3×#131⋊C3—41nomaximal
7C3×C8×A4—41nomaximal
8#5948C2×C312yes—
9A4×#41C2×C311yescharacteristic
10C22×#41⋊C3C2×C311yescharacteristic
11C2×#131⋊C3—31no—
12C2×#131⋊C3—31no—
13A4×M16—31no—
14C2×C8×A4—31no—
15C3×#41⋊C3—41no—
16C3×C4×A4—41no—
17C22×#131C3211yescharacteristic, complemented, Sylow
18C22⋊SL(2,𝔽3)C3×C412yes—
19C2×#41⋊C3—31no—
20C2×#41⋊C3—31no—
21Q8×A4C3×C411yescharacteristic
22C22×SL(2,𝔽3)C3×C411yescharacteristic
23D4×A4—31no—
24C2×C4×A4—31no—
25C3×#131—41no—
26C22×C3×C8—41no—
27#131⋊C3—31no—
28#131⋊C3—42no—
29#131⋊C3—122no—
30#131⋊C3A411yescharacteristic, direct product factor
31C8×A4—31no—
32C8×A4—42no—
33C8×A4A411yescharacteristic
34C2×C3×A4—41no—
35C3×SL(2,𝔽3)—41no—
36C32×C8—161no—
37C22×#41C2×C3211yescharacteristic
38C2×#131—31no—
39C2×#131—31no—
40C2×#131—91no—
41C2×#131—91no—
42C22×M16—31no—
43C23×C8—31no—
44C22×A4—31no—
45C3×#41—41no—
46C22×C3×C4—41no—
47#41⋊C3—31no—
48#41⋊C3—42no—
49#41⋊C3—122no—
50#41⋊C3C2×A411yescharacteristic
51C2×SL(2,𝔽3)—31no—
52C4×A4—31no—
53C4×A4—42no—
54C4×A4C2×A411yescharacteristic
55C3×M16—121no—
56C2×C3×C8—121no—
57C2×C3×C8—121no—
58C2×C3×C8—121no—
59C3×A4—41no—
60C32×C4—161no—
61C2×#41—31no—
62C2×#41—31no—
63C2×#41—91no—
64C2×#41—91no—
65C22×Q8C32×C411yescharacteristic
66C22×D4—31no—
67C23×C4—31no—
68#131—32no—
69#131—31no—
70#131—91no—
71#131—92no—
72#131—91no—
73#131—92no—
74#131C3×A411yescharacteristic, complemented
75C2×M16—92no—
76C2×M16—91no—
77C2×M16—91no—
78C22×C8—31no—
79C22×C8—91no—
80C22×C8—91no—
81C22×C8—91no—
82C22×C8—91no—
83C22×C8C3×A411yescharacteristic
84C23×C3—41no—
85C2×A4—42no—
86C2×A4—61no—
87C2×A4C4×A411yescharacteristic
88C3×Q8—41no—
89C3×D4—121no—
90C2×C3×C4—121no—
91C2×C3×C4—121no—
92C2×C3×C4—121no—
93SL(2,𝔽3)—42no—
94SL(2,𝔽3)—122no—
95SL(2,𝔽3)C4×A411yescharacteristic
96C3×C8—41no—
97C3×C8—41no—
98C3×C8—121no—
99C3×C8—121no—
100C3×C8—162no—
101C2×C32—161no—
102C24—31no—
103#41—32no—
104#41—31no—
105#41—91no—
106#41—92no—
107#41—91no—
108#41—92no—
109#41C2×C3×A411yescharacteristic
110C2×Q8—31no—
111C2×Q8—91no—
112C2×D4—91no—
113C2×D4—91no—
114C2×D4—92no—
115C22×C4—31no—
116C22×C4—91no—
117C22×C4—91no—
118C22×C4—91no—
119C22×C4—91no—
120C22×C4C2×C3×A411yescharacteristic
121M16—31no—
122M16—92no—
123M16—91no—
124M16—92no—
125C2×C8—31no—
126C2×C8—31no—
127C2×C8—31no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—92no—
132C2×C8—91no—
133C2×C8—91no—
134C22×C3—41no—
135C22×C3—121no—
136C22×C3—121no—
137C22×C3—121no—
138A4—42no—
139A4#131⋊C311yescharacteristic, direct product factor
140C3×C4—41no—
141C3×C4—41no—
142C3×C4—121no—
143C3×C4—121no—
144C3×C4—162no—
145C32—161noSylow
146C23—61no—
147C23—91no—
148C23—91no—
149C23—181no—
150C23C3×C4×A411yescharacteristic
151Q8—32no—
152Q8—91no—
153Q8C3×C4×A411yescharacteristic
154D4—31no—
155D4—91no—
156D4—92no—
157D4—92no—
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—31no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—92no—
165C2×C4—91no—
166C2×C4—91no—
167C8—31no—
168C8—31no—
169C8—91no—
170C8A4211yescharacteristic
171C2×C3—41no—
172C2×C3—41no—
173C2×C3—121no—
174C2×C3—121no—
175C2×C3—162no—
176C2×C3—241no—
177C22—31no—
178C22—31no—
179C22—31no—
180C22—91no—
181C22—181no—
182C22—181no—
183C22—181no—
184C22—181no—
185C22C3×#131⋊C311yescharacteristic, complemented
186C4—31no—
187C4—31no—
188C4—91no—
189C4C2×A4211yescharacteristic
190C3—41no—
191C3—41no—
192C3—162no—
193C2—31no—
194C2—31no—
195C2—61no—
196C2—181no—
197C2C4×A4211yescharacteristic
subgroupG/H
center, hypercenterC8A42
commutator, hypocenterC22×Q8C32×C4
FrattiniC4C2×A42
FittingC22×#131C32
socleC23C3×C4×A4
prime radicalA4×#41⋊C3C2
cosocleC22×#41C2×C32
LCSG ▷ C22×Q8
UCSC1 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #85665C3semidirect
3. C22×#131⋊C3C3semidirect
4. A4×#131C3semidirect
17. C22×#131C32semidirect
30. #131⋊C3A4direct (N × H)
74. #131C3×A4semidirect
139. A4#131⋊C3direct (N × H)
185. C22C3×#131⋊C3semidirect

Maximal subgroups

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

subgroupindex
A4×#41⋊C32
#856653
C22×#131⋊C33
A4×#1313
C3×#131⋊C34
C3×C8×A44