Finite Group Databasebeta

← A4×#803 #11921244

Subgroups — A4×#803 #11921244

Order 1152.

390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C3×C42×A4C211yesmaximal, characteristic
2C2×A4×C3⋊C8C212yesmaximal
3C22×#803C311yesmaximal, characteristic, complemented
4A4×#97—31nomaximal
5C2×C3×C4×A4C412yes—
6C2×C3×C4×A4C2211yescharacteristic
7A4×C3⋊C8C414yescomplemented
8C3×#803—41nomaximal
9C22×C3×C42C2×C311yescharacteristic
10C23×C3⋊C8C2×C312yes—
11C2×C8×A4—32no—
12C42×A4—21no—
13C42×A4D311yescharacteristic
14C2×#803—31no—
15C2×#803—31no—
16C2×#803—32no—
17C22×C3×A4C2×C411yescharacteristic
18C3×C4×A4—22no—
19C3×C4×A4C2×C412yes—
20C32×C42—41no—
21C2×C3×C3⋊C8—42no—
22C22×#97—31noSylow
23C23×C3×C4C3×C412yes—
24C23×C3×C4C22×C311yescharacteristic
25C2×C4×A4—22no—
26C2×C4×A4—21no—
27C2×C4×A4Dic312yes—
28C2×C4×A4C2×D311yescharacteristic
29C2×C3×C42—31no—
30C2×C3×C42—31no—
31C2×C3×C42—32no—
32C22×C3⋊C8—32no—
33C22×C3⋊C8—32no—
34C22×C3⋊C8—34no—
35C22×C3⋊C8C3×C414yescomplemented
36C8×A4—34no—
37C3×#97—121no—
38#803—32no—
39#803—31no—
40#803—32no—
41#803A411yescharacteristic, direct product factor
42C2×C3×A4C4211yescharacteristic
43C2×C3×A4M1612yes—
44C2×C32×C4—42no—
45C2×C32×C4—41no—
46C3×C3⋊C8—44no—
47C23×C8—32no—
48C22×C42C3×D311yescharacteristic
49C2×#97—91no—
50C2×#97—92no—
51C2×#97—91no—
52C24×C3C2×C3×C411yescharacteristic
53C22×A4—21no—
54C22×A4C2×Dic311yescharacteristic
55C22×C3×C4—22no—
56C22×C3×C4—31no—
57C22×C3×C4—32no—
58C22×C3×C4—31no—
59C22×C3×C4—32no—
60C22×C3×C4—32no—
61C22×C3×C4—62no—
62C22×C3×C4C2×C3×C412yes—
63C4×A4—24no—
64C4×A4—22no—
65C4×A4—22no—
66C4×A4C4×D312yes—
67C2×C3×C8—122no—
68C3×C42—32no—
69C3×C42—32no—
70C3×C42—31no—
71C3×C42—41no—
72C3×C42—81no—
73C3×C42C2×A411yescharacteristic
74C2×C3⋊C8—34no—
75C2×C3⋊C8—32no—
76C2×C3⋊C8—34no—
77C2×C3⋊C8—34no—
78C2×C3⋊C8—34no—
79C2×C3⋊C8C2×A412yes—
80C22×C32—41no—
81C3×A4#9711yescharacteristic, complemented
82C32×C4—42no—
83C32×C4—82no—
84C23×C4C3×Dic312yes—
85C23×C4C2×C3×D311yescharacteristic
86C22×C8—34no—
87C22×C8—92no—
88C22×C8—92no—
89C22×C8—94no—
90C2×C42—31no—
91C2×C42—31no—
92C2×C42—32no—
93#97—31no—
94#97—92no—
95#97—92no—
96#97—91no—
97C23×C3—31no—
98C23×C3—32no—
99C23×C3—31no—
100C23×C3C3×C4211yescharacteristic
101C23×C3C3×M1612yes—
102C2×A4—22no—
103C2×A4—21no—
104C2×A4#20812yes—
105C2×A4C4×Dic311yescharacteristic
106C2×C3×C4—32no—
107C2×C3×C4—31no—
108C2×C3×C4—32no—
109C2×C3×C4—32no—
110C2×C3×C4—32no—
111C2×C3×C4—32no—
112C2×C3×C4—41no—
113C2×C3×C4—42no—
114C2×C3×C4—62no—
115C2×C3×C4—62no—
116C2×C3×C4—62no—
117C2×C3×C4—62no—
118C2×C3×C4—81no—
119C2×C3×C4—82no—
120C2×C3×C4C4×A412yes—
121C2×C3×C4C22×A411yescharacteristic
122C3×C8—124no—
123C3⋊C8—34no—
124C3⋊C8C4×A414yescomplemented
125C2×C32—41no—
126C2×C32—42no—
127C24C2×C3×Dic311yescharacteristic
128C22×C4—22no—
129C22×C4—31no—
130C22×C4—31no—
131C22×C4—32no—
132C22×C4—32no—
133C22×C4—32no—
134C22×C4—62no—
135C22×C4C3×C4×D312yes—
136C2×C8—32no—
137C2×C8—94no—
138C2×C8—94no—
139C2×C8—94no—
140C2×C8—92no—
141C2×C8—94no—
142C42—32no—
143C42—31no—
144C42—32no—
145C42D3×A411yescharacteristic
146C22×C3—31no—
147C22×C3—32no—
148C22×C3—32no—
149C22×C3—31no—
150C22×C3—31no—
151C22×C3—32no—
152C22×C3—32no—
153C22×C3—41no—
154C22×C3—81no—
155C22×C3C3×#9711yescharacteristic, complemented
156C22×C3C2×C4×A411yescharacteristic
157A4—21no—
158A4#80311yescharacteristic, direct product factor
159C3×C4—22no—
160C3×C4—32no—
161C3×C4—42no—
162C3×C4—62no—
163C3×C4—82no—
164C3×C4—84no—
165C3×C4—82no—
166C3×C4C2×C4×A412yes—
167C32—41noSylow
168C23—31no—
169C23—32no—
170C23—31no—
171C23C3×#20812yes—
172C23C3×C4×Dic311yescharacteristic
173C2×C4—32no—
174C2×C4—31no—
175C2×C4—32no—
176C2×C4—32no—
177C2×C4—32no—
178C2×C4—32no—
179C2×C4—62no—
180C2×C4—62no—
181C2×C4—62no—
182C2×C4—62no—
183C2×C4Dic3×A412yes—
184C2×C4C2×D3×A411yescharacteristic
185C8—34no—
186C8—94no—
187C2×C3—31no—
188C2×C3—32no—
189C2×C3—31no—
190C2×C3—42no—
191C2×C3—41no—
192C2×C3—82no—
193C2×C3—81no—
194C2×C3C42×A411yescharacteristic
195C2×C3A4×M1612yes—
196C22—32no—
197C22—31no—
198C22—32no—
199C22—32no—
200C22—32no—
201C22—31no—
202C22—31no—
203C22C3×#80311yescharacteristic, complemented
204C22C2×Dic3×A411yescharacteristic
205C4—22no—
206C4—32no—
207C4—62no—
208C4C4×D3×A412yes—
209C3—41no—
210C3—81no—
211C3A4×#9711yescharacteristic, complemented
212C2—31no—
213C2—32no—
214C2—31no—
215C2A4×#20812yes—
216C2C4×Dic3×A411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×A4
commutatorC23×C3C3×C42
FittingC22×C3×C42C2×C3
socleC24×C3C2×C3×C4
prime radicalC22×C3×A4C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC42D3×A4
hypocenterC22×C3C3×#97
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. C22×#803C3semidirect
7. A4×C3⋊C8C4semidirect
35. C22×C3⋊C8C3×C4semidirect
41. #803A4direct (N × H)
81. C3×A4#97semidirect
124. C3⋊C8C4×A4semidirect
155. C22×C3C3×#97semidirect
158. A4#803direct (N × H)
203. C22C3×#803semidirect
211. C3A4×#97semidirect

Maximal subgroups

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

subgroupindex
C3×C42×A42
C2×A4×C3⋊C82
C22×#8033
A4×#973
C3×#8034