Finite Group Databasebeta

← A4×#800 #11921235

Subgroups — A4×#800 #11921235

Order 1152.

230 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 39 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×Dic12C211yesmaximal, characteristic, complemented
2A4×D24C211yesmaximal, characteristic
3C3×A4×C16C211yesmaximal, characteristic, complemented
4C22×#800C311yesmaximal, characteristic, complemented
5A4×SD32—31nomaximal
6A4×D12—21no—
7A4×Dic6—21no—
8C3×C8×A4C2211yescharacteristic
9C3×#800—41nomaximal
10C22×Dic12C2×C311yescharacteristic, complemented
11C22×D24C2×C311yescharacteristic
12A4×Q16—31no—
13A4×D8—31no—
14C22×C3×C16C2×C311yescharacteristic, complemented
15C2×#800—31no—
16C2×#800—31no—
17C2×#800—31no—
18C2×#800—31no—
19A4×C16—21no—
20A4×C16D311yescharacteristic, complemented
21C2×D3×A4—41no—
22C3×C4×A4D411yescharacteristic
23Dic3×A4—41no—
24C3×Dic12—41no—
25C3×D24—41no—
26C32×C16—41no—
27C22×SD32—31noSylow
28C22×D12—21no—
29C22×Dic6—21no—
30Q8×A4—61no—
31D4×A4—61no—
32C22×C3×C8C22×C311yescharacteristic
33C2×Dic12—31no—
34C2×Dic12—31no—
35C2×Dic12—61no—
36C2×D24—31no—
37C2×D24—31no—
38C2×D24—61no—
39C8×A4—21no—
40C8×A4C2×D311yescharacteristic
41C3×SD32—121no—
42C2×C3×C16—31no—
43C2×C3×C16—31no—
44#800—32no—
45#800—31no—
46#800—31no—
47#800—31no—
48#800A411yescharacteristic, direct product factor
49C2×C3×A4D811yescharacteristic
50D3×A4—81no—
51C3×D12—81no—
52C3×Dic6—81no—
53C32×C8—41no—
54C22×Q16—31no—
55C22×D8—31no—
56C2×SD32—91no—
57C2×SD32—91no—
58C2×SD32—91no—
59C2×SD32—91no—
60C22×C16C3×D311yescharacteristic, complemented
61C23×D3—41no—
62C22×A4—121no—
63C22×C3×C4C3×D411yescharacteristic
64C22×Dic3—41no—
65C2×D12—61no—
66C2×D12—61no—
67C2×D12—121no—
68C2×Dic6—61no—
69C2×Dic6—61no—
70C2×Dic6—121no—
71C4×A4—21no—
72C4×A4—121no—
73C4×A4D1211yescharacteristic
74C3×Q16—121no—
75C3×D8—121no—
76C2×C3×C8—31no—
77C2×C3×C8—31no—
78Dic12—31no—
79Dic12—61no—
80Dic12—61no—
81Dic12C2×A411yescharacteristic, complemented
82D24—31no—
83D24—61no—
84D24—61no—
85D24C2×A411yescharacteristic
86C3×C16—31no—
87C3×C16—41no—
88C3×C16—81no—
89C3×C16C2×A411yescharacteristic, complemented
90C2×C3×D3—161no—
91C3×A4SD3211yescharacteristic, complemented
92C32×C4—41no—
93C3×Dic3—161no—
94C22×Q8—61no—
95C22×D4—61no—
96C2×Q16—91no—
97C2×Q16—91no—
98C2×Q16—181no—
99C2×D8—91no—
100C2×D8—91no—
101C2×D8—181no—
102C22×C8C2×C3×D311yescharacteristic
103SD32—31no—
104SD32—91no—
105SD32—91no—
106SD32—92no—
107SD32—91no—
108C2×C16—31no—
109C2×C16—31no—
110C23×C3C3×D811yescharacteristic
111C22×D3—81no—
112C22×D3—121no—
113C22×D3—121no—
114C22×D3—241no—
115C2×A4—21no—
116C2×A4—241no—
117C2×A4D2411yescharacteristic
118C3×Q8—241no—
119C3×D4—241no—
120C2×C3×C4—31no—
121C2×C3×C4—31no—
122C2×Dic3—121no—
123C2×Dic3—121no—
124D12—21no—
125D12—61no—
126D12—121no—
127D12—121no—
128Dic6—21no—
129Dic6—61no—
130Dic6—121no—
131Dic6—121no—
132C3×C8—31no—
133C3×C8—41no—
134C3×C8—81no—
135C3×C8C22×A411yescharacteristic
136C2×C32—41no—
137C3×D3—321no—
138C24—121no—
139C2×Q8—181no—
140C2×Q8—181no—
141C2×Q8—361no—
142C2×D4—181no—
143C2×D4—181no—
144C2×D4—361no—
145C22×C4—121no—
146C22×C4C3×D1211yescharacteristic
147Q16—31no—
148Q16—91no—
149Q16—181no—
150Q16—181no—
151D8—31no—
152D8—91no—
153D8—181no—
154D8—181no—
155C2×C8—31no—
156C2×C8—31no—
157C16—31no—
158C16D3×A411yescharacteristic, complemented
159C22×C3—31no—
160C22×C3—31no—
161C22×C3—481no—
162C22×C3C3×SD3211yescharacteristic, complemented
163C2×D3—41no—
164C2×D3—121no—
165C2×D3—241no—
166C2×D3—241no—
167C2×D3—241no—
168C2×D3—241no—
169A4—21no—
170A4#80011yescharacteristic, direct product factor
171C3×C4—31no—
172C3×C4—41no—
173C3×C4—81no—
174C3×C4—481no—
175C3×C4D4×A411yescharacteristic
176Dic3—41no—
177Dic3—121no—
178C32—41noSylow
179C23—241no—
180C23—361no—
181C23—361no—
182C23—721no—
183C23C3×D2411yescharacteristic
184Q8—61no—
185Q8—181no—
186Q8—361no—
187Q8—361no—
188D4—61no—
189D4—181no—
190D4—361no—
191D4—361no—
192C2×C4—31no—
193C2×C4—31no—
194C2×C4—361no—
195C2×C4—361no—
196C8—31no—
197C8C2×D3×A411yescharacteristic
198C2×C3—31no—
199C2×C3—31no—
200C2×C3—41no—
201C2×C3—81no—
202C2×C3—961no—
203C2×C3A4×D811yescharacteristic
204D3—81no—
205D3—241no—
206C22—31no—
207C22—31no—
208C22—121no—
209C22—361no—
210C22—721no—
211C22—721no—
212C22—721no—
213C22—721no—
214C22C3×#80011yescharacteristic, complemented
215C4—31no—
216C4—121no—
217C4—361no—
218C4A4×D1211yescharacteristic
219C3—41no—
220C3—81no—
221C3A4×SD3211yescharacteristic, complemented
222C2—31no—
223C2—31no—
224C2—241no—
225C2—721no—
226C2A4×D2411yescharacteristic
subgroupG/H
centerC2A4×D24
commutator, cosocleC22×C3×C8C22×C3
FrattiniC8C2×D3×A4
FittingC22×C3×C16C2×C3
socleC23×C3C3×D8
prime radicalA4×D24C2
hypercenterC16D3×A4
hypocenterC22×C3C3×SD32
LCSG ▷ C22×C3×C8 ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
1. A4×Dic12C2semidirect
3. C3×A4×C16C2semidirect
4. C22×#800C3semidirect
10. C22×Dic12C2×C3semidirect
14. C22×C3×C16C2×C3semidirect
20. A4×C16D3semidirect
48. #800A4direct (N × H)
60. C22×C16C3×D3semidirect
81. Dic12C2×A4semidirect
89. C3×C16C2×A4semidirect
91. C3×A4SD32semidirect
158. C16D3×A4semidirect
162. C22×C3C3×SD32semidirect
170. A4#800direct (N × H)
214. C22C3×#800semidirect
221. C3A4×SD32semidirect

Maximal subgroups

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

subgroupindex
A4×Dic122
A4×D242
C3×A4×C162
C22×#8003
A4×SD323
C3×#8004