Finite Group Databasebeta

← A4×#828 #11921347

Subgroups — A4×#828 #11921347

Order 1152.

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

normal subgroups only

This group has 238 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
1C3×A4×Q16C211yesmaximal, characteristic, complemented
2A4×D24C211yesmaximal, characteristic
3A4×C3⋊C16C211yesmaximal, characteristic, complemented
4C22×#828C311yesmaximal, characteristic, complemented
5A4×SD32—31nomaximal
6C3×Q8×A4—21no—
7A4×D12—21no—
8C3×C8×A4C2211yescharacteristic
9C3×#828—41nomaximal
10C22×C3×Q16C2×C311yescharacteristic, complemented
11C22×D24C2×C311yescharacteristic
12A4×Q16—21no—
13A4×Q16D311yescharacteristic, complemented
14A4×D8—31no—
15C2×#828—31no—
16C2×#828—31no—
17C2×#828—31no—
18C2×#828—31no—
19C22×C3⋊C16C2×C311yescharacteristic, complemented
20A4×C16—31no—
21C2×D3×A4—41no—
22C3×C4×A4—41no—
23C3×C4×A4D411yescharacteristic
24C32×Q16—41no—
25C3×D24—41no—
26C3×C3⋊C16—41no—
27C22×SD32—31noSylow
28C22×C3×Q8—21no—
29C22×D12—21no—
30Q8×A4—22no—
31Q8×A4—21no—
32D4×A4—61no—
33C2×C3×Q16—31no—
34C2×C3×Q16—31no—
35C2×C3×Q16—61no—
36C22×C3×C8C22×C311yescharacteristic
37C2×D24—31no—
38C2×D24—31no—
39C2×D24—61no—
40C8×A4—21no—
41C8×A4C2×D311yescharacteristic
42C3×SD32—121no—
43#828—32no—
44#828—31no—
45#828—31no—
46#828—31no—
47#828A411yescharacteristic, direct product factor
48C2×C3⋊C16—31no—
49C2×C3⋊C16—31no—
50C2×C3×A4D811yescharacteristic
51D3×A4—81no—
52C32×Q8—81no—
53C3×D12—81no—
54C32×C8—41no—
55C22×Q16C3×D311yescharacteristic, complemented
56C22×D8—31no—
57C2×SD32—91no—
58C2×SD32—91no—
59C2×SD32—91no—
60C2×SD32—91no—
61C22×C16—31no—
62C23×D3—41no—
63C22×A4—121no—
64C2×C3×Q8—61no—
65C2×C3×Q8—61no—
66C2×C3×Q8—121no—
67C22×C3×C4—41no—
68C22×C3×C4C3×D411yescharacteristic
69C2×D12—61no—
70C2×D12—61no—
71C2×D12—121no—
72C4×A4—21no—
73C4×A4—42no—
74C4×A4—41no—
75C4×A4#6711yescharacteristic
76C3×Q16—31no—
77C3×Q16—41no—
78C3×Q16—61no—
79C3×Q16—61no—
80C3×Q16—81no—
81C3×Q16C2×A411yescharacteristic, complemented
82C3×D8—121no—
83C2×C3×C8—31no—
84C2×C3×C8—31no—
85D24—31no—
86D24—61no—
87D24—61no—
88D24C2×A411yescharacteristic
89C3×C16—121no—
90C3⋊C16—31no—
91C3⋊C16C2×A411yescharacteristic, complemented
92C2×C3×D3—161no—
93C3×A4SD3211yescharacteristic, complemented
94C32×C4—41no—
95C32×C4—161no—
96C22×Q8—21no—
97C22×D4—61no—
98C2×Q16—31no—
99C2×Q16—31no—
100C2×Q16—61no—
101C2×D8—91no—
102C2×D8—91no—
103C2×D8—181no—
104C22×C8C2×C3×D311yescharacteristic
105SD32—31no—
106SD32—91no—
107SD32—91no—
108SD32—92no—
109SD32—91no—
110C2×C16—91no—
111C2×C16—91no—
112C23×C3C3×D811yescharacteristic
113C22×D3—81no—
114C22×D3—121no—
115C22×D3—121no—
116C22×D3—241no—
117C2×A4—21no—
118C2×A4—241no—
119C2×A4#21311yescharacteristic
120C3×Q8—21no—
121C3×Q8—61no—
122C3×Q8—81no—
123C3×Q8—82no—
124C3×Q8—121no—
125C3×Q8—121no—
126C3×D4—241no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—121no—
130C2×C3×C4—121no—
131D12—21no—
132D12—61no—
133D12—121no—
134D12—121no—
135C3×C8—31no—
136C3×C8—41no—
137C3×C8—81no—
138C3×C8C22×A411yescharacteristic
139C2×C32—41no—
140C3×D3—321no—
141C24—121no—
142C2×Q8—61no—
143C2×Q8—61no—
144C2×Q8—121no—
145C2×D4—181no—
146C2×D4—181no—
147C2×D4—361no—
148C22×C4—41no—
149C22×C4C3×#6711yescharacteristic
150Q16—31no—
151Q16—61no—
152Q16—61no—
153Q16D3×A411yescharacteristic, complemented
154D8—31no—
155D8—91no—
156D8—181no—
157D8—181no—
158C2×C8—31no—
159C2×C8—31no—
160C16—31no—
161C16—91no—
162C22×C3—31no—
163C22×C3—31no—
164C22×C3—481no—
165C22×C3C3×SD3211yescharacteristic, complemented
166C2×D3—41no—
167C2×D3—121no—
168C2×D3—241no—
169C2×D3—241no—
170C2×D3—241no—
171C2×D3—241no—
172A4—21no—
173A4#82811yescharacteristic, direct product factor
174C3×C4—31no—
175C3×C4—41no—
176C3×C4—41no—
177C3×C4—81no—
178C3×C4—121no—
179C3×C4—161no—
180C3×C4—162no—
181C3×C4D4×A411yescharacteristic
182C32—41noSylow
183C23—241no—
184C23—361no—
185C23—361no—
186C23—721no—
187C23C3×#21311yescharacteristic
188Q8—21no—
189Q8—61no—
190Q8—121no—
191Q8—121no—
192D4—61no—
193D4—181no—
194D4—361no—
195D4—361no—
196C2×C4—31no—
197C2×C4—31no—
198C2×C4—121no—
199C2×C4—121no—
200C8—31no—
201C8C2×D3×A411yescharacteristic
202C2×C3—31no—
203C2×C3—31no—
204C2×C3—41no—
205C2×C3—81no—
206C2×C3—961no—
207C2×C3A4×D811yescharacteristic
208D3—81no—
209D3—241no—
210C22—31no—
211C22—31no—
212C22—121no—
213C22—361no—
214C22—721no—
215C22—721no—
216C22—721no—
217C22—721no—
218C22C3×#82811yescharacteristic, complemented
219C4—31no—
220C4—41no—
221C4—121no—
222C4A4×#6711yescharacteristic
223C3—41no—
224C3—81no—
225C3A4×SD3211yescharacteristic, complemented
226C2—31no—
227C2—31no—
228C2—241no—
229C2—721no—
230C2A4×#21311yescharacteristic
subgroupG/H
centerC2A4×#213
commutator, cosocleC22×C3×C8C22×C3
FrattiniC8C2×D3×A4
FittingC22×C3×Q16C2×C3
socleC23×C3C3×D8
prime radicalA4×D24C2
hypercenterQ16D3×A4
hypocenterC22×C3C3×SD32
LCSG ▷ C22×C3×C8 ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

Complements

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

NH ≅ G/Ntype
1. C3×A4×Q16C2semidirect
3. A4×C3⋊C16C2semidirect
4. C22×#828C3semidirect
10. C22×C3×Q16C2×C3semidirect
13. A4×Q16D3semidirect
19. C22×C3⋊C16C2×C3semidirect
47. #828A4direct (N × H)
55. C22×Q16C3×D3semidirect
81. C3×Q16C2×A4semidirect
91. C3⋊C16C2×A4semidirect
93. C3×A4SD32semidirect
153. Q16D3×A4semidirect
165. C22×C3C3×SD32semidirect
173. A4#828direct (N × H)
218. C22C3×#828semidirect
225. C3A4×SD32semidirect

Maximal subgroups

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

subgroupindex
C3×A4×Q162
A4×D242
A4×C3⋊C162
C22×#8283
A4×SD323
C3×#8284