Finite Group Databasebeta

← A4×#819 #11921322

Subgroups — A4×#819 #11921322

Order 1152.

282 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×C3×C8×A4C211yesmaximal, characteristic
2A4×#208C212yesmaximal
3C22×#819C311yesmaximal, characteristic, complemented
4A4×#108—31nomaximal
5C2×C3×C4×A4C2211yescharacteristic
6C3×C8×A4C412yes—
7A4×C3⋊C8—22no—
8C3×#819—41nomaximal
9C23×C3×C8C2×C311yescharacteristic
10C22×#208C2×C312yes—
11A4×M16—32no—
12C2×C8×A4—21no—
13C2×C8×A4D311yescharacteristic
14C2×#819—31no—
15C2×#819—31no—
16C2×#819—32no—
17C22×C3×A4Q811yescharacteristic
18C3×C4×A4C2×C411yescharacteristic
19C3×C4×A4D411yescharacteristic
20C2×C32×C8—41no—
21C3×#208—42no—
22C22×#108—31noSylow
23C23×C3×C4C22×C311yescharacteristic
24C2×C4×A4—21no—
25C2×C4×A4C2×D311yescharacteristic
26C22×C3×C8—31no—
27C22×C3×C8—32no—
28C22×C3×C8—31no—
29C22×C3×C8C3×C412yes—
30C2×#208—32no—
31C2×#208—32no—
32C2×#208—62no—
33C22×C3⋊C8—22no—
34C8×A4—22no—
35C8×A4—62no—
36C8×A4Dic312yes—
37C3×#108—121no—
38#819—32no—
39#819—31no—
40#819—32no—
41#819A411yescharacteristic, direct product factor
42C2×C3×A4—21no—
43C2×C3×A4C4⋊C411yescharacteristic
44C2×C32×C4—41no—
45C32×C8—42no—
46C3×C3⋊C8—82no—
47C22×M16—32no—
48C23×C8C3×D311yescharacteristic
49C2×#108—91no—
50C2×#108—92no—
51C2×#108—91no—
52C24×C3C3×Q811yescharacteristic
53C22×A4—21no—
54C22×A4Dic611yescharacteristic
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4C2×C3×C411yescharacteristic
60C22×C3×C4C3×D411yescharacteristic
61C4×A4—21no—
62C4×A4—21no—
63C4×A4D1211yescharacteristic
64C4×A4C2×Dic311yescharacteristic
65C3×M16—122no—
66C2×C3×C8—32no—
67C2×C3×C8—31no—
68C2×C3×C8—32no—
69C2×C3×C8—32no—
70C2×C3×C8—32no—
71C2×C3×C8—41no—
72C2×C3×C8—81no—
73C2×C3×C8C2×A411yescharacteristic
74#208—32no—
75#208—62no—
76#208—62no—
77#208C2×A412yes—
78C2×C3⋊C8—62no—
79C2×C3⋊C8—62no—
80C22×C32—41no—
81C3×A4#10811yescharacteristic, complemented
82C32×C4—41no—
83C32×C4—41no—
84C23×C4C2×C3×D311yescharacteristic
85C2×M16—92no—
86C2×M16—92no—
87C2×M16—182no—
88C22×C8—31no—
89C22×C8—31no—
90C22×C8—32no—
91C22×C8—62no—
92C22×C8C3×Dic312yes—
93#108—31no—
94#108—92no—
95#108—92no—
96#108—91no—
97C23×C3—21no—
98C23×C3—31no—
99C23×C3—31no—
100C23×C3—61no—
101C23×C3C3×C4⋊C411yescharacteristic
102C2×A4—22no—
103C2×A4—21no—
104C2×A4—21no—
105C2×A4C4⋊Dic311yescharacteristic
106C2×C3×C4—32no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—31no—
112C2×C3×C4—31no—
113C2×C3×C4—31no—
114C2×C3×C4—41no—
115C2×C3×C4—81no—
116C2×C3×C4C22×A411yescharacteristic
117C3×C8—32no—
118C3×C8—42no—
119C3×C8—82no—
120C3×C8—242no—
121C3×C8C4×A412yes—
122C3⋊C8—22no—
123C3⋊C8—62no—
124C2×C32—41no—
125C2×C32—81no—
126C24C3×Dic611yescharacteristic
127C22×C4—31no—
128C22×C4—31no—
129C22×C4—31no—
130C22×C4—31no—
131C22×C4C3×D1211yescharacteristic
132C22×C4C2×C3×Dic311yescharacteristic
133M16—32no—
134M16—92no—
135M16—182no—
136M16—182no—
137C2×C8—32no—
138C2×C8—31no—
139C2×C8—32no—
140C2×C8—32no—
141C2×C8—32no—
142C2×C8—182no—
143C2×C8—182no—
144C2×C8D3×A411yescharacteristic
145C22×C3—31no—
146C22×C3—31no—
147C22×C3—31no—
148C22×C3—41no—
149C22×C3—61no—
150C22×C3—61no—
151C22×C3—61no—
152C22×C3—61no—
153C22×C3—81no—
154C22×C3C3×#10811yescharacteristic, complemented
155C22×C3Q8×A411yescharacteristic
156A4—21no—
157A4#81911yescharacteristic, direct product factor
158C3×C4—31no—
159C3×C4—31no—
160C3×C4—41no—
161C3×C4—41no—
162C3×C4—81no—
163C3×C4—81no—
164C3×C4C2×C4×A411yescharacteristic
165C3×C4D4×A411yescharacteristic
166C32—41noSylow
167C23—21no—
168C23—31no—
169C23—31no—
170C23—61no—
171C23C3×C4⋊Dic311yescharacteristic
172C2×C4—32no—
173C2×C4—31no—
174C2×C4—31no—
175C2×C4—31no—
176C2×C4—31no—
177C2×C4—31no—
178C2×C4—31no—
179C2×C4—31no—
180C2×C4C2×D3×A411yescharacteristic
181C8—32no—
182C8—62no—
183C8—182no—
184C8Dic3×A412yes—
185C2×C3—21no—
186C2×C3—31no—
187C2×C3—31no—
188C2×C3—41no—
189C2×C3—61no—
190C2×C3—81no—
191C2×C3—82no—
192C2×C3—81no—
193C2×C3A4×C4⋊C411yescharacteristic
194C22—31no—
195C22—31no—
196C22—31no—
197C22—61no—
198C22—61no—
199C22—61no—
200C22—61no—
201C22C3×#81911yescharacteristic, complemented
202C22A4×Dic611yescharacteristic
203C4—31no—
204C4—31no—
205C4A4×D1211yescharacteristic
206C4C2×Dic3×A411yescharacteristic
207C3—41no—
208C3—81no—
209C3A4×#10811yescharacteristic, complemented
210C2—21no—
211C2—31no—
212C2—31no—
213C2—61no—
214C2A4×C4⋊Dic311yescharacteristic
subgroupG/H
centerC4A4×D12
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC23×C3×C8C2×C3
socleC23×C3C3×C4⋊C4
prime radicalC22×C3×A4Q8
cosocleC23×C3×C4C22×C3
hypercenterC2×C8D3×A4
hypocenterC22×C3C3×#108
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. C22×#819C3semidirect
41. #819A4direct (N × H)
81. C3×A4#108semidirect
154. C22×C3C3×#108semidirect
157. A4#819direct (N × H)
201. C22C3×#819semidirect
209. C3A4×#108semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
A4×#2082
C22×#8193
A4×#1083
C3×#8194