Finite Group Databasebeta

← A4×#876 #11923149

Subgroups — A4×#876 #11923149

Order 1152.

670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×A4C211yesmaximal, characteristic, complemented
2A4×(C2×D3)⋊C4C213yesmaximal
3A4×Dic3⋊C4C213yesmaximal, complemented
4C22×#876C311yesmaximal, characteristic, complemented
5A4×#126—31nomaximal
6C22×D3×A4C2211yescharacteristic
7C2×C3×C4×A4C2213yes—
8C2×Dic3×A4C2213yes—
9C3×#876—41nomaximal
10C22×C3×C42C2×C311yescharacteristic, complemented
11C22×(C2×D3)⋊C4C2×C313yes—
12C22×Dic3⋊C4C2×C313yescomplemented
13C2×#876—31no—
14C2×#876—31no—
15C2×#876—33no—
16C2×#876—33no—
17A4×C4⋊C4—33no—
18A4×C22⋊C4—33no—
19C42×A4—21no—
20C42×A4D311yescharacteristic, complemented
21C22×C3×A4C2311yescharacteristic
22C2×D3×A4—23no—
23C3×C4×A4—23no—
24Dic3×A4—23no—
25C32×C42—41no—
26C3×(C2×D3)⋊C4—43no—
27C3×Dic3⋊C4—43no—
28C22×#126—31noSylow
29C24×D3C22×C311yescharacteristic
30C23×A4—31no—
31C23×C3×C4C22×C313yes—
32C23×Dic3C22×C313yes—
33C2×C4×A4—23no—
34C2×C4×A4—33no—
35C2×C4×A4C2×D313yes—
36C3×#126—121no—
37C2×C3×C42—31no—
38C2×C3×C42—33no—
39C2×(C2×D3)⋊C4—33no—
40C2×(C2×D3)⋊C4—33no—
41C2×(C2×D3)⋊C4—33no—
42C2×(C2×D3)⋊C4—33no—
43C2×Dic3⋊C4—33no—
44C2×Dic3⋊C4—33no—
45C2×Dic3⋊C4—36no—
46#876—32no—
47#876—36no—
48#876—36no—
49#876—31no—
50#876—33no—
51#876—33no—
52#876A411yescharacteristic, direct product factor
53C22×C3×D3—41no—
54C2×C3×A4#4113yes—
55D3×A4—41no—
56C2×C32×C4—43no—
57C2×C3×Dic3—43no—
58C2×#126—91no—
59C2×#126—91no—
60C2×#126—93no—
61C2×#126—93no—
62C22×C4⋊C4—33no—
63C22×C22⋊C4—33no—
64C22×C42C3×D311yescharacteristic, complemented
65C24×C3C23×C311yescharacteristic
66C23×D3—23no—
67C23×D3—31no—
68C23×D3—31no—
69C23×D3—63no—
70C22×A4—21no—
71C22×A4—63no—
72C22×A4C22×D311yescharacteristic
73C22×C3×C4—23no—
74C22×C3×C4—33no—
75C22×C3×C4—33no—
76C22×C3×C4—63no—
77C22×Dic3—23no—
78C22×Dic3—33no—
79C22×Dic3—33no—
80C22×Dic3—63no—
81C4×A4—26no—
82C4×A4—23no—
83C4×A4—63no—
84C3×C4⋊C4—123no—
85C3×C22⋊C4—123no—
86C3×C42—32no—
87C3×C42—33no—
88C3×C42—41no—
89C3×C42—81no—
90C3×C42C2×A411yescharacteristic, complemented
91(C2×D3)⋊C4—36no—
92(C2×D3)⋊C4—33no—
93(C2×D3)⋊C4—33no—
94(C2×D3)⋊C4—33no—
95(C2×D3)⋊C4C2×A413yes—
96Dic3⋊C4—36no—
97Dic3⋊C4—33no—
98Dic3⋊C4—36no—
99Dic3⋊C4C2×A413yescomplemented
100C22×C32—41no—
101C2×C3×D3—83no—
102C3×A4#12611yescharacteristic, complemented
103C32×C4—83no—
104C3×Dic3—83no—
105C25—31no—
106C23×C4—33no—
107C23×C4C2×C3×D313yes—
108#126—31no—
109#126—93no—
110#126—93no—
111#126—96no—
112#126—92no—
113#126—96no—
114#126—91no—
115C2×C4⋊C4—93no—
116C2×C4⋊C4—96no—
117C2×C4⋊C4—93no—
118C2×C22⋊C4—93no—
119C2×C22⋊C4—93no—
120C2×C22⋊C4—93no—
121C2×C22⋊C4—93no—
122C2×C42—31no—
123C2×C42—33no—
124C23×C3—33no—
125C23×C3—31no—
126C23×C3—121no—
127C23×C3C3×#4113yes—
128C22×D3—31no—
129C22×D3—41no—
130C22×D3—63no—
131C22×D3—63no—
132C22×D3—63no—
133C22×D3—63no—
134C22×D3—122no—
135C22×D3—123no—
136C22×D3C22×A411yescharacteristic
137C2×A4—23no—
138C2×A4—121no—
139C2×A4#23513yes—
140C2×C3×C4—33no—
141C2×C3×C4—43no—
142C2×C3×C4—63no—
143C2×C3×C4—63no—
144C2×C3×C4—63no—
145C2×C3×C4—63no—
146C2×C3×C4—83no—
147C2×C3×C4—123no—
148C2×C3×C4C22×A413yes—
149C2×Dic3—33no—
150C2×Dic3—63no—
151C2×Dic3—63no—
152C2×Dic3—63no—
153C2×Dic3—63no—
154C2×Dic3C22×A413yes—
155C2×C32—43no—
156C3×D3—161no—
157C24—63no—
158C24—91no—
159C24—91no—
160C24—183no—
161C24C22×C3×D311yescharacteristic
162C22×C4—23no—
163C22×C4—33no—
164C22×C4—33no—
165C22×C4—63no—
166C22×C4—63no—
167C22×C4—93no—
168C22×C4—93no—
169C22×C4—183no—
170C4⋊C4—33no—
171C4⋊C4—96no—
172C4⋊C4—96no—
173C4⋊C4—93no—
174C22⋊C4—33no—
175C22⋊C4—93no—
176C22⋊C4—93no—
177C22⋊C4—96no—
178C22⋊C4—93no—
179C42—32no—
180C42—33no—
181C42D3×A411yescharacteristic, complemented
182C22×C3—33no—
183C22×C3—32no—
184C22×C3—33no—
185C22×C3—33no—
186C22×C3—41no—
187C22×C3—81no—
188C22×C3—243no—
189C22×C3C3×#12611yescharacteristic, complemented
190C22×C3C23×A411yescharacteristic
191C2×D3—23no—
192C2×D3—63no—
193C2×D3—121no—
194C2×D3—123no—
195C2×D3—121no—
196C2×D3—123no—
197A4—21no—
198A4#87611yescharacteristic, direct product factor
199C3×C4—23no—
200C3×C4—63no—
201C3×C4—83no—
202C3×C4—86no—
203C3×C4—243no—
204Dic3—23no—
205Dic3—63no—
206C32—41noSylow
207C23—33no—
208C23—31no—
209C23—31no—
210C23—91no—
211C23—121no—
212C23—183no—
213C23—183no—
214C23—183no—
215C23—183no—
216C23—363no—
217C23—362no—
218C23C3×#23513yes—
219C2×C4—33no—
220C2×C4—33no—
221C2×C4—63no—
222C2×C4—63no—
223C2×C4—63no—
224C2×C4—63no—
225C2×C4—93no—
226C2×C4—183no—
227C2×C4—183no—
228C2×C4—183no—
229C2×C4—183no—
230C2×C4C2×D3×A413yes—
231C2×C3—33no—
232C2×C3—31no—
233C2×C3—43no—
234C2×C3—83no—
235C2×C3—481no—
236C2×C3A4×#4113yes—
237D3—41no—
238D3—121no—
239C22—33no—
240C22—32no—
241C22—33no—
242C22—33no—
243C22—63no—
244C22—183no—
245C22—361no—
246C22—363no—
247C22—361no—
248C22—363no—
249C22C3×#87611yescharacteristic, complemented
250C22C22×D3×A411yescharacteristic
251C4—23no—
252C4—63no—
253C4—63no—
254C4—183no—
255C3—41no—
256C3—81no—
257C3A4×#12611yescharacteristic, complemented
258C2—31no—
259C2—33no—
260C2—121no—
261C2—361no—
262C2A4×#23513yes—
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C42C2×C3
prime radicalC22×D3×A4C22
hypercenterC42D3×A4
hypocenterC22×C3C3×#126
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C3×C42×A4C2semidirect
3. A4×Dic3⋊C4C2semidirect
4. C22×#876C3semidirect
10. C22×C3×C42C2×C3semidirect
12. C22×Dic3⋊C4C2×C3semidirect
20. C42×A4D3semidirect
52. #876A4direct (N × H)
64. C22×C42C3×D3semidirect
90. C3×C42C2×A4semidirect
99. Dic3⋊C4C2×A4semidirect
102. C3×A4#126semidirect
181. C42D3×A4semidirect
189. C22×C3C3×#126semidirect
198. A4#876direct (N × H)
249. C22C3×#876semidirect
257. C3A4×#126semidirect

Maximal subgroups

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

subgroupindex
C3×C42×A42
A4×(C2×D3)⋊C42
A4×Dic3⋊C42
C22×#8763
A4×#1263
C3×#8764