Finite Group Databasebeta

← A4×#798 #11921234

Subgroups — A4×#798 #11921234

Order 1152.

230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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
1D3×C8×A4C211yesmaximal, characteristic
2C3×A4×C16C211yesmaximal, characteristic, complemented
3A4×C3⋊C16C211yesmaximal, characteristic, complemented
4C22×#798C311yesmaximal, characteristic, complemented
5A4×M32—31nomaximal
6C4×D3×A4C411yescharacteristic
7C3×C8×A4C2211yescharacteristic
8A4×C3⋊C8C411yescharacteristic
9C3×#798—41nomaximal
10C22×D3×C8C2×C311yescharacteristic
11C2×C8×A4—31no—
12C22×C3×C16C2×C311yescharacteristic, complemented
13C22×C3⋊C16C2×C311yescharacteristic, complemented
14C2×#798—31no—
15C2×#798—31no—
16C2×#798—31no—
17C2×#798—31no—
18A4×C16—21no—
19A4×C16—31no—
20A4×C16D311yescharacteristic, complemented
21C2×D3×A4C811yescharacteristic
22C3×C4×A4C2×C411yescharacteristic
23Dic3×A4C811yescharacteristic
24C3×D3×C8—41no—
25C32×C16—41no—
26C3×C3⋊C16—41no—
27C22×M32—31noSylow
28C22×C4×D3C3×C411yescharacteristic
29C2×C4×A4—31no—
30C22×C3×C8C22×C311yescharacteristic
31C22×C3⋊C8C3×C411yescharacteristic
32C2×D3×C8—31no—
33C2×D3×C8—31no—
34C2×D3×C8—31no—
35C2×D3×C8—31no—
36C8×A4—21no—
37C8×A4—31no—
38C8×A4C2×D311yescharacteristic
39C3×M32—121no—
40C2×C3×C16—31no—
41C2×C3×C16—31no—
42C2×C3⋊C16—31no—
43C2×C3⋊C16—31no—
44#798—32no—
45#798—31no—
46#798—31no—
47#798—31no—
48#798A411yescharacteristic, direct product factor
49C2×C3×A4C2×C811yescharacteristic
50D3×A4—21no—
51C3×C4×D3—41no—
52C32×C8—41no—
53C3×C3⋊C8—41no—
54C23×C8—31no—
55C2×M32—91no—
56C2×M32—91no—
57C2×M32—91no—
58C2×M32—91no—
59C22×C16—31no—
60C22×C16C3×D311yescharacteristic, complemented
61C23×D3C3×C811yescharacteristic
62C22×A4—31no—
63C22×C3×C4C2×C3×C411yescharacteristic
64C22×Dic3C3×C811yescharacteristic
65C2×C4×D3—31no—
66C2×C4×D3—31no—
67C2×C4×D3—31no—
68C2×C4×D3—31no—
69C4×A4—21no—
70C4×A4—31no—
71C4×A4C4×D311yescharacteristic
72C2×C3×C8—31no—
73C2×C3×C8—31no—
74C2×C3×C8—121no—
75C2×C3⋊C8—31no—
76C2×C3⋊C8—31no—
77D3×C8—32no—
78D3×C8—31no—
79D3×C8—31no—
80D3×C8—31no—
81D3×C8C2×A411yescharacteristic
82C3×C16—31no—
83C3×C16—41no—
84C3×C16—81no—
85C3×C16—121no—
86C3×C16C2×A411yescharacteristic, complemented
87C3⋊C16—31no—
88C3⋊C16C2×A411yescharacteristic, complemented
89C2×C3×D3—41no—
90C3×A4M3211yescharacteristic, complemented
91C32×C4—41no—
92C3×Dic3—41no—
93C23×C4—31no—
94C22×C8—31no—
95C22×C8—91no—
96C22×C8—91no—
97C22×C8—91no—
98C22×C8—91no—
99C22×C8C2×C3×D311yescharacteristic
100M32—31no—
101M32—91no—
102M32—91no—
103M32—92no—
104M32—91no—
105C2×C16—31no—
106C2×C16—31no—
107C2×C16—91no—
108C2×C16—91no—
109C23×C3C2×C3×C811yescharacteristic
110C22×D3—21no—
111C22×D3—31no—
112C22×D3—31no—
113C22×D3—61no—
114C2×A4—21no—
115C2×A4—61no—
116C2×A4D3×C811yescharacteristic
117C2×C3×C4—31no—
118C2×C3×C4—31no—
119C2×C3×C4—121no—
120C2×Dic3—31no—
121C2×Dic3—31no—
122C4×D3—32no—
123C4×D3—31no—
124C4×D3—31no—
125C4×D3—31no—
126C4×D3C4×A411yescharacteristic
127C3×C8—31no—
128C3×C8—41no—
129C3×C8—81no—
130C3×C8—121no—
131C3×C8C22×A411yescharacteristic
132C3⋊C8—31no—
133C3⋊C8C4×A411yescharacteristic
134C2×C32—41no—
135C3×D3—81no—
136C24—31no—
137C22×C4—31no—
138C22×C4—91no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—91no—
142C22×C4C3×C4×D311yescharacteristic
143C2×C8—31no—
144C2×C8—31no—
145C2×C8—31no—
146C2×C8—91no—
147C2×C8—91no—
148C2×C8—91no—
149C2×C8—92no—
150C2×C8—91no—
151C2×C8—91no—
152C16—31no—
153C16—31no—
154C16—91no—
155C16D3×A411yescharacteristic, complemented
156C22×C3—31no—
157C22×C3—31no—
158C22×C3—121no—
159C22×C3C3×M3211yescharacteristic, complemented
160C2×D3—31no—
161C2×D3—61no—
162C2×D3—61no—
163C2×D3—61no—
164C2×D3—61no—
165C2×D3C8×A411yescharacteristic
166A4—21no—
167A4#79811yescharacteristic, direct product factor
168C3×C4—31no—
169C3×C4—41no—
170C3×C4—81no—
171C3×C4—121no—
172C3×C4C2×C4×A411yescharacteristic
173Dic3—31no—
174Dic3C8×A411yescharacteristic
175C32—41noSylow
176C23—61no—
177C23—91no—
178C23—91no—
179C23—181no—
180C23C3×D3×C811yescharacteristic
181C2×C4—31no—
182C2×C4—31no—
183C2×C4—31no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—91no—
189C2×C4—91no—
190C8—31no—
191C8—31no—
192C8—91no—
193C8C2×D3×A411yescharacteristic
194C2×C3—31no—
195C2×C3—31no—
196C2×C3—41no—
197C2×C3—81no—
198C2×C3—241no—
199C2×C3C2×C8×A411yescharacteristic
200D3—21no—
201D3—61no—
202C22—31no—
203C22—31no—
204C22—31no—
205C22—91no—
206C22—181no—
207C22—181no—
208C22—181no—
209C22—181no—
210C22C3×#79811yescharacteristic, complemented
211C4—31no—
212C4—31no—
213C4—91no—
214C4C4×D3×A411yescharacteristic
215C3—41no—
216C3—81no—
217C3A4×M3211yescharacteristic, complemented
218C2—31no—
219C2—31no—
220C2—61no—
221C2—181no—
222C2D3×C8×A411yescharacteristic
subgroupG/H
center, FrattiniC8C2×D3×A4
commutator, socleC23×C3C2×C3×C8
FittingC22×C3×C16C2×C3
prime radicalC2×D3×A4C8
cosocleC22×C3×C8C22×C3
hypercenterC16D3×A4
hypocenterC22×C3C3×M32
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
2. C3×A4×C16C2semidirect
3. A4×C3⋊C16C2semidirect
4. C22×#798C3semidirect
12. C22×C3×C16C2×C3semidirect
13. C22×C3⋊C16C2×C3semidirect
20. A4×C16D3semidirect
48. #798A4direct (N × H)
60. C22×C16C3×D3semidirect
86. C3×C16C2×A4semidirect
88. C3⋊C16C2×A4semidirect
90. C3×A4M32semidirect
155. C16D3×A4semidirect
159. C22×C3C3×M32semidirect
167. A4#798direct (N × H)
210. C22C3×#798semidirect
217. C3A4×M32semidirect

Maximal subgroups

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

subgroupindex
D3×C8×A42
C3×A4×C162
A4×C3⋊C162
C22×#7983
A4×M323
C3×#7984