Finite Group Databasebeta

← A4×#822 #11921326

Subgroups — A4×#822 #11921326

Order 1152.

280 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 57 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×M16C211yesmaximal, characteristic
2A4×#208C211yesmaximal, characteristic
3C2×A4×C3⋊C8C211yesmaximal, characteristic
4C22×#822C311yesmaximal, characteristic, complemented
5A4×#108—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C3×C8×A4—21no—
8A4×C3⋊C8—21no—
9A4×C3⋊C8C412yes—
10C3×#822—41nomaximal
11C22×C3×M16C2×C311yescharacteristic
12C22×#208C2×C311yescharacteristic
13C23×C3⋊C8C2×C311yescharacteristic
14A4×M16—21no—
15A4×M16—31no—
16A4×M16D311yescharacteristic
17C2×C8×A4—31no—
18C2×#822—31no—
19C2×#822—31no—
20C2×#822—31no—
21C2×#822—31no—
22C22×C3×A4Q811yescharacteristic
23C3×C4×A4C2×C411yescharacteristic
24C3×C4×A4D411yescharacteristic
25C32×M16—41no—
26C3×#208—41no—
27C2×C3×C3⋊C8—41no—
28C22×#108—31noSylow
29C23×C3×C4C22×C311yescharacteristic
30C2×C4×A4—21no—
31C2×C4×A4C2×D311yescharacteristic
32C2×C3×M16—31no—
33C2×C3×M16—31no—
34C2×C3×M16—61no—
35C22×C3×C8—21no—
36C2×#208—31no—
37C2×#208—31no—
38C2×#208—61no—
39C22×C3⋊C8—21no—
40C22×C3⋊C8—31no—
41C22×C3⋊C8—31no—
42C22×C3⋊C8—32no—
43C22×C3⋊C8C3×C412yes—
44C8×A4—22no—
45C8×A4—21no—
46C8×A4—32no—
47C8×A4—61no—
48C3×#108—121no—
49#822—32no—
50#822—31no—
51#822—31no—
52#822—31no—
53#822A411yescharacteristic, direct product factor
54C2×C3×A4—21no—
55C2×C3×A4C4⋊C411yescharacteristic
56C2×C32×C4—41no—
57C32×C8—81no—
58C3×C3⋊C8—42no—
59C3×C3⋊C8—81no—
60C22×M16—31no—
61C22×M16C3×D311yescharacteristic
62C23×C8—31no—
63C2×#108—91no—
64C2×#108—91no—
65C2×#108—91no—
66C2×#108—91no—
67C24×C3C3×Q811yescharacteristic
68C22×A4—21no—
69C22×A4Dic611yescharacteristic
70C22×C3×C4—31no—
71C22×C3×C4—31no—
72C22×C3×C4—31no—
73C22×C3×C4—31no—
74C22×C3×C4C2×C3×C411yescharacteristic
75C22×C3×C4C3×D411yescharacteristic
76C4×A4—21no—
77C4×A4—21no—
78C4×A4C4×D311yescharacteristic
79C4×A4#6711yescharacteristic
80C3×M16—31no—
81C3×M16—41no—
82C3×M16—61no—
83C3×M16—61no—
84C3×M16—81no—
85C3×M16—121no—
86C3×M16C2×A411yescharacteristic
87C2×C3×C8—61no—
88C2×C3×C8—61no—
89C2×C3×C8—121no—
90#208—31no—
91#208—61no—
92#208—61no—
93#208C2×A411yescharacteristic
94C2×C3⋊C8—32no—
95C2×C3⋊C8—31no—
96C2×C3⋊C8—32no—
97C2×C3⋊C8—32no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—61no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8C2×A411yescharacteristic
102C22×C32—41no—
103C3×A4#10811yescharacteristic, complemented
104C32×C4—41no—
105C32×C4—41no—
106C23×C4C2×C3×D311yescharacteristic
107C2×M16—31no—
108C2×M16—31no—
109C2×M16—61no—
110C2×M16—91no—
111C2×M16—91no—
112C2×M16—181no—
113C22×C8—21no—
114C22×C8—32no—
115C22×C8—61no—
116C22×C8—91no—
117C22×C8—92no—
118C22×C8—91no—
119#108—31no—
120#108—91no—
121#108—91no—
122#108—92no—
123#108—91no—
124C23×C3—21no—
125C23×C3—31no—
126C23×C3—31no—
127C23×C3—61no—
128C23×C3C3×C4⋊C411yescharacteristic
129C2×A4—21no—
130C2×A4—21no—
131C2×A4—41no—
132C2×A4Dic3⋊C411yescharacteristic
133C2×C3×C4—32no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—41no—
142C2×C3×C4—81no—
143C2×C3×C4C22×A411yescharacteristic
144C3×C8—21no—
145C3×C8—61no—
146C3×C8—81no—
147C3×C8—82no—
148C3×C8—122no—
149C3×C8—241no—
150C3⋊C8—21no—
151C3⋊C8—32no—
152C3⋊C8—61no—
153C3⋊C8C4×A412yes—
154C2×C32—41no—
155C2×C32—81no—
156C24C3×Dic611yescharacteristic
157C22×C4—31no—
158C22×C4—31no—
159C22×C4—31no—
160C22×C4—31no—
161C22×C4C3×C4×D311yescharacteristic
162C22×C4C3×#6711yescharacteristic
163M16—31no—
164M16—31no—
165M16—61no—
166M16—61no—
167M16—91no—
168M16—181no—
169M16—181no—
170M16D3×A411yescharacteristic
171C2×C8—31no—
172C2×C8—61no—
173C2×C8—61no—
174C2×C8—92no—
175C2×C8—92no—
176C2×C8—92no—
177C2×C8—91no—
178C2×C8—92no—
179C2×C8—181no—
180C2×C8—181no—
181C22×C3—31no—
182C22×C3—31no—
183C22×C3—31no—
184C22×C3—41no—
185C22×C3—61no—
186C22×C3—61no—
187C22×C3—61no—
188C22×C3—61no—
189C22×C3—81no—
190C22×C3C3×#10811yescharacteristic, complemented
191C22×C3Q8×A411yescharacteristic
192A4—21no—
193A4#82211yescharacteristic, direct product factor
194C3×C4—31no—
195C3×C4—31no—
196C3×C4—41no—
197C3×C4—41no—
198C3×C4—81no—
199C3×C4—81no—
200C3×C4C2×C4×A411yescharacteristic
201C3×C4D4×A411yescharacteristic
202C32—41noSylow
203C23—21no—
204C23—31no—
205C23—31no—
206C23—61no—
207C23C3×Dic3⋊C411yescharacteristic
208C2×C4—32no—
209C2×C4—31no—
210C2×C4—31no—
211C2×C4—31no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4C2×D3×A411yescharacteristic
217C8—21no—
218C8—32no—
219C8—61no—
220C8—61no—
221C8—92no—
222C8—181no—
223C2×C3—21no—
224C2×C3—31no—
225C2×C3—31no—
226C2×C3—41no—
227C2×C3—61no—
228C2×C3—81no—
229C2×C3—81no—
230C2×C3—161no—
231C2×C3A4×C4⋊C411yescharacteristic
232C22—31no—
233C22—31no—
234C22—31no—
235C22—61no—
236C22—61no—
237C22—61no—
238C22—61no—
239C22C3×#82211yescharacteristic, complemented
240C22A4×Dic611yescharacteristic
241C4—31no—
242C4—31no—
243C4C4×D3×A411yescharacteristic
244C4A4×#6711yescharacteristic
245C3—41no—
246C3—81no—
247C3A4×#10811yescharacteristic, complemented
248C2—21no—
249C2—31no—
250C2—31no—
251C2—61no—
252C2A4×Dic3⋊C411yescharacteristic
subgroupG/H
centerC4A4×#67
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC22×C3×M16C2×C3
socleC23×C3C3×C4⋊C4
prime radicalC22×C3×A4Q8
cosocleC23×C3×C4C22×C3
hypercenterM16D3×A4
hypocenterC22×C3C3×#108
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
4. C22×#822C3semidirect
53. #822A4direct (N × H)
103. C3×A4#108semidirect
190. C22×C3C3×#108semidirect
193. A4#822direct (N × H)
239. C22C3×#822semidirect
247. C3A4×#108semidirect

Maximal subgroups

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

subgroupindex
C3×A4×M162
A4×#2082
C2×A4×C3⋊C82
C22×#8223
A4×#1083
C3×#8224