Finite Group Databasebeta

← A4×#818 #11921321

Subgroups — A4×#818 #11921321

Order 1152.

342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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×C4⋊Dic3C212yesmaximal
3C22×#818C311yesmaximal, characteristic, complemented
4A4×#107—31nomaximal
5C2×C3×C4×A4C2211yescharacteristic
6C2×Dic3×A4—22no—
7C3×C8×A4C412yescomplemented
8C3×#818—41nomaximal
9C23×C3×C8C2×C311yescharacteristic
10C22×C4⋊Dic3C2×C312yes—
11C2×C8×A4—21no—
12C2×C8×A4D311yescharacteristic
13A4×C4⋊C4—32no—
14C2×#818—31no—
15C2×#818—31no—
16C2×#818—32no—
17C22×C3×A4D411yescharacteristic
18C3×C4×A4C2×C411yescharacteristic
19C3×C4×A4Q811yescharacteristic
20Dic3×A4—42no—
21C2×C32×C8—41no—
22C3×C4⋊Dic3—42no—
23C22×#107—31noSylow
24C23×C3×C4C22×C311yescharacteristic
25C23×Dic3—22no—
26C2×C4×A4—21no—
27C2×C4×A4—62no—
28C2×C4×A4C2×D311yescharacteristic
29C22×C3×C8—31no—
30C22×C3×C8—32no—
31C22×C3×C8—31no—
32C22×C3×C8C3×C412yescomplemented
33C2×C4⋊Dic3—32no—
34C2×C4⋊Dic3—32no—
35C2×C4⋊Dic3—62no—
36C8×A4—22no—
37C8×A4Dic312yescomplemented
38C3×#107—121no—
39#818—32no—
40#818—31no—
41#818—32no—
42#818A411yescharacteristic, direct product factor
43C2×C3×A4C4⋊C411yescharacteristic
44C2×C3×A4D811yescharacteristic
45C2×C3×A4Q1611yescharacteristic
46C2×C32×C4—41no—
47C2×C3×Dic3—82no—
48C32×C8—42no—
49C23×C8C3×D311yescharacteristic
50C22×C4⋊C4—32no—
51C2×#107—91no—
52C2×#107—92no—
53C2×#107—91no—
54C24×C3C3×D411yescharacteristic
55C22×A4—21no—
56C22×A4D1211yescharacteristic
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4C2×C3×C411yescharacteristic
62C22×C3×C4C3×Q811yescharacteristic
63C22×Dic3—42no—
64C22×Dic3—62no—
65C22×Dic3—62no—
66C22×Dic3—122no—
67C4×A4—21no—
68C4×A4—21no—
69C4×A4—122no—
70C4×A4Dic611yescharacteristic
71C4×A4C2×Dic311yescharacteristic
72C2×C3×C8—32no—
73C2×C3×C8—31no—
74C2×C3×C8—32no—
75C2×C3×C8—32no—
76C2×C3×C8—32no—
77C2×C3×C8—41no—
78C2×C3×C8—81no—
79C2×C3×C8C2×A411yescharacteristic
80C3×C4⋊C4—122no—
81C4⋊Dic3—32no—
82C4⋊Dic3—62no—
83C4⋊Dic3—62no—
84C4⋊Dic3C2×A412yes—
85C22×C32—41no—
86C3×A4#10711yescharacteristic, complemented
87C32×C4—41no—
88C32×C4—41no—
89C3×Dic3—162no—
90C23×C4—62no—
91C23×C4C2×C3×D311yescharacteristic
92C22×C8—31no—
93C22×C8—31no—
94C22×C8—32no—
95C22×C8C3×Dic312yescomplemented
96C2×C4⋊C4—92no—
97C2×C4⋊C4—92no—
98C2×C4⋊C4—182no—
99#107—31no—
100#107—92no—
101#107—92no—
102#107—91no—
103C23×C3—31no—
104C23×C3—31no—
105C23×C3—31no—
106C23×C3—31no—
107C23×C3C3×C4⋊C411yescharacteristic
108C23×C3C3×D811yescharacteristic
109C23×C3C3×Q1611yescharacteristic
110C2×A4—21no—
111C2×A4—21no—
112C2×A4—21no—
113C2×A4D2411yescharacteristic
114C2×A4Dic1211yescharacteristic
115C2×A4C4⋊Dic311yescharacteristic
116C2×C3×C4—32no—
117C2×C3×C4—31no—
118C2×C3×C4—31no—
119C2×C3×C4—31no—
120C2×C3×C4—31no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—31no—
124C2×C3×C4—41no—
125C2×C3×C4—81no—
126C2×C3×C4—242no—
127C2×C3×C4C22×A411yescharacteristic
128C2×Dic3—22no—
129C2×Dic3—62no—
130C2×Dic3—122no—
131C2×Dic3—122no—
132C2×Dic3—122no—
133C2×Dic3—122no—
134C3×C8—32no—
135C3×C8—42no—
136C3×C8—82no—
137C3×C8C4×A412yescomplemented
138C2×C32—41no—
139C2×C32—41no—
140C2×C32—41no—
141C24C3×D1211yescharacteristic
142C22×C4—31no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—31no—
146C22×C4—122no—
147C22×C4—182no—
148C22×C4—182no—
149C22×C4—362no—
150C22×C4C3×Dic611yescharacteristic
151C22×C4C2×C3×Dic311yescharacteristic
152C2×C8—32no—
153C2×C8—31no—
154C2×C8—32no—
155C2×C8—32no—
156C2×C8—32no—
157C2×C8D3×A411yescharacteristic
158C4⋊C4—32no—
159C4⋊C4—92no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C22×C3—31no—
163C22×C3—31no—
164C22×C3—31no—
165C22×C3—32no—
166C22×C3—31no—
167C22×C3—31no—
168C22×C3—31no—
169C22×C3—31no—
170C22×C3—31no—
171C22×C3—31no—
172C22×C3—41no—
173C22×C3—81no—
174C22×C3C3×#10711yescharacteristic, complemented
175C22×C3D4×A411yescharacteristic
176A4—21no—
177A4#81811yescharacteristic, direct product factor
178C3×C4—31no—
179C3×C4—31no—
180C3×C4—41no—
181C3×C4—41no—
182C3×C4—81no—
183C3×C4—81no—
184C3×C4—482no—
185C3×C4C2×C4×A411yescharacteristic
186C3×C4Q8×A411yescharacteristic
187Dic3—42no—
188Dic3—122no—
189C32—41noSylow
190C23—31no—
191C23—31no—
192C23—31no—
193C23—31no—
194C23C3×D2411yescharacteristic
195C23C3×Dic1211yescharacteristic
196C23C3×C4⋊Dic311yescharacteristic
197C2×C4—32no—
198C2×C4—31no—
199C2×C4—31no—
200C2×C4—31no—
201C2×C4—31no—
202C2×C4—31no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—62no—
206C2×C4—182no—
207C2×C4—362no—
208C2×C4—362no—
209C2×C4—362no—
210C2×C4—362no—
211C2×C4C2×D3×A411yescharacteristic
212C8—32no—
213C8Dic3×A412yescomplemented
214C2×C3—31no—
215C2×C3—31no—
216C2×C3—31no—
217C2×C3—31no—
218C2×C3—41no—
219C2×C3—41no—
220C2×C3—41no—
221C2×C3—81no—
222C2×C3—81no—
223C2×C3—81no—
224C2×C3A4×C4⋊C411yescharacteristic
225C2×C3A4×D811yescharacteristic
226C2×C3A4×Q1611yescharacteristic
227C22—31no—
228C22—31no—
229C22—31no—
230C22—32no—
231C22—31no—
232C22—31no—
233C22—31no—
234C22—31no—
235C22—31no—
236C22—31no—
237C22C3×#81811yescharacteristic, complemented
238C22A4×D1211yescharacteristic
239C4—31no—
240C4—31no—
241C4—122no—
242C4—362no—
243C4A4×Dic611yescharacteristic
244C4C2×Dic3×A411yescharacteristic
245C3—41no—
246C3—81no—
247C3A4×#10711yescharacteristic, complemented
248C2—31no—
249C2—31no—
250C2—31no—
251C2—31no—
252C2A4×D2411yescharacteristic
253C2A4×Dic1211yescharacteristic
254C2A4×C4⋊Dic311yescharacteristic
subgroupG/H
centerC22A4×D12
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC23×C3×C8C2×C3
socleC24×C3C3×D4
prime radicalC22×C3×A4D4
cosocleC23×C3×C4C22×C3
hypercenterC2×C8D3×A4
hypocenterC22×C3C3×#107
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. C22×#818C3semidirect
7. C3×C8×A4C4semidirect
32. C22×C3×C8C3×C4semidirect
37. C8×A4Dic3semidirect
42. #818A4direct (N × H)
86. C3×A4#107semidirect
95. C22×C8C3×Dic3semidirect
137. C3×C8C4×A4semidirect
174. C22×C3C3×#107semidirect
177. A4#818direct (N × H)
213. C8Dic3×A4semidirect
237. C22C3×#818semidirect
247. C3A4×#107semidirect

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×C4⋊Dic32
C22×#8183
A4×#1073
C3×#8184