Finite Group Databasebeta

← C22×C3⋊(A4⋊C8) #11923025

Subgroups — C22×C3⋊(A4⋊C8) #11923025

Order 1152.

958 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 227 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2C2×C3⋊(A4⋊C8)C216yesmaximal, direct product factor
3C22×A4⋊C8—33nomaximal
4C22×#830—31nomaximal
5C23×C3×A4C411yescharacteristic
6C2×C3×C4×A4C413yes—
7C2×C3×C4×A4C2213yes—
8C22×C3⋊(C3⋊C8)—41nomaximal
9C3⋊(A4⋊C8)C2214yesdirect product factor
10C24×C3×C4D311yescharacteristic
11C22×C4×A4D313yes—
12C23×C3⋊C8—31no—
13C23×C3⋊C8—31no—
14C2×A4⋊C8—318no—
15C2×#830—36no—
16C2×#830—36no—
17C22×C3×A4C814yescomplemented
18C22×C3×A4C2×C413yes—
19C22×C32×C4—41no—
20C3×C4×A4C2×C413yes—
21C3×C4×A4C2311yescharacteristic
22C2×C3⋊(C3⋊C8)—46no—
23C22×C22⋊C8—91noSylow
24C25×C3Dic311yescharacteristic
25C23×A4Dic313yes—
26C23×C3×C4—31no—
27C23×C3×C4—31no—
28C23×C3×C4—33no—
29C23×C3×C4—33no—
30C23×C3×C4Dic313yes—
31C23×C3×C4C2×D313yes—
32C2×C4×A4Dic319yes—
33C2×C4×A4C2×D319yes—
34C22×C3⋊C8—36no—
35C22×C3⋊C8—36no—
36C22×C3⋊C8—61no—
37C22×C3⋊C8—63no—
38C22×C3⋊C8—63no—
39C22×C3⋊C8—61no—
40C22×C3⋊C8—123no—
41A4⋊C8—312no—
42#830—312no—
43#830—34no—
44C23×C32—41no—
45C2×C3×A4C2×C816yescomplemented
46C2×C3×A4C22×C411yescharacteristic
47C2×C32×C4—43no—
48C2×C32×C4—43no—
49C3⋊(C3⋊C8)—44no—
50C24×C4C3⋊D311yescharacteristic
51C23×C8—91no—
52C23×C8—91no—
53C2×C22⋊C8—96no—
54C2×C22⋊C8—96no—
55C24×C3—31no—
56C24×C3—34no—
57C24×C3—33no—
58C24×C3C3⋊C814yescomplemented
59C24×C3C2×Dic313yes—
60C22×A4C3⋊C8112yescomplemented
61C22×A4C2×Dic319yes—
62C22×C3×C4—31no—
63C22×C3×C4—33no—
64C22×C3×C4—33no—
65C22×C3×C4—33no—
66C22×C3×C4—33no—
67C22×C3×C4—33no—
68C22×C3×C4—33no—
69C22×C3×C4—36no—
70C22×C3×C4—33no—
71C22×C3×C4—33no—
72C22×C3×C4—43no—
73C22×C3×C4—63no—
74C22×C3×C4—61no—
75C22×C3×C4—63no—
76C22×C3×C4C2×Dic313yes—
77C22×C3×C4S411yescharacteristic
78C22×C3×C4C22×D311yescharacteristic
79C4×A4C2×Dic319yes—
80C4×A4C22×D313yes—
81C2×C3⋊C8—34no—
82C2×C3⋊C8—34no—
83C2×C3⋊C8—66no—
84C2×C3⋊C8—66no—
85C2×C3⋊C8—66no—
86C2×C3⋊C8—66no—
87C2×C3⋊C8—1218no—
88C22×C32—44no—
89C22×C32—43no—
90C3×A4C22×C811yescharacteristic, complemented
91C32×C4—43no—
92C32×C4—41no—
93C25C3⋊Dic311yescharacteristic
94C23×C4—31no—
95C23×C4—33no—
96C23×C4—31no—
97C23×C4—33no—
98C23×C4C3⋊Dic313yes—
99C23×C4C2×C3⋊D313yes—
100C22×C8—96no—
101C22×C8—96no—
102C22×C8—181no—
103C22×C8—183no—
104C22×C8—183no—
105C22×C8—181no—
106C22⋊C8—912no—
107C22⋊C8—94no—
108C23×C3—34no—
109C23×C3—34no—
110C23×C3—33no—
111C23×C3—33no—
112C23×C3—33no—
113C23×C3—312no—
114C23×C3—36no—
115C23×C3—43no—
116C23×C3—61no—
117C23×C3—66no—
118C23×C3C2×C3⋊C816yescomplemented
119C23×C3SL(2,ℤ/4)11yescharacteristic
120C23×C3C22×Dic311yescharacteristic
121C2×A4C2×C3⋊C8118yescomplemented
122C2×A4C22×Dic313yes—
123C2×C3×C4—33no—
124C2×C3×C4—33no—
125C2×C3×C4—33no—
126C2×C3×C4—33no—
127C2×C3×C4—36no—
128C2×C3×C4—31no—
129C2×C3×C4—33no—
130C2×C3×C4—33no—
131C2×C3×C4—31no—
132C2×C3×C4—49no—
133C2×C3×C4—49no—
134C2×C3×C4—63no—
135C2×C3×C4—63no—
136C2×C3×C4SL(2,ℤ/4)13yes—
137C2×C3×C4C2×S413yes—
138C3⋊C8—64no—
139C3⋊C8—64no—
140C3⋊C8—1212no—
141C2×C32—46no—
142C2×C32—41no—
143C24—31no—
144C24—33no—
145C24—34no—
146C24C3⋊(C3⋊C8)14yescomplemented
147C24C2×C3⋊Dic313yes—
148C22×C4—31no—
149C22×C4—33no—
150C22×C4—33no—
151C22×C4—33no—
152C22×C4—33no—
153C22×C4—33no—
154C22×C4—33no—
155C22×C4—36no—
156C22×C4—33no—
157C22×C4—33no—
158C22×C4—63no—
159C22×C4—61no—
160C22×C4—63no—
161C22×C4C2×C3⋊Dic313yes—
162C22×C4C3⋊S411yescharacteristic
163C22×C4C22×C3⋊D311yescharacteristic
164C2×C8—94no—
165C2×C8—94no—
166C2×C8—186no—
167C2×C8—186no—
168C2×C8—186no—
169C2×C8—186no—
170C22×C3—36no—
171C22×C3—31no—
172C22×C3—36no—
173C22×C3—36no—
174C22×C3—312no—
175C22×C3—31no—
176C22×C3—33no—
177C22×C3—412no—
178C22×C3—49no—
179C22×C3—63no—
180C22×C3—64no—
181C22×C3A4⋊C814yescomplemented
182C22×C3C22×C3⋊C811yescharacteristic, complemented
183C22×C3C2×SL(2,ℤ/4)13yes—
184A4C22×C3⋊C813yescomplemented
185C3×C4—31no—
186C3×C4—33no—
187C3×C4—49no—
188C3×C4—43no—
189C3×C4C2×SL(2,ℤ/4)13yes—
190C3×C4C22×S411yescharacteristic
191C32—41noSylow
192C23—34no—
193C23—34no—
194C23—33no—
195C23—33no—
196C23—33no—
197C23—312no—
198C23—36no—
199C23—61no—
200C23—66no—
201C23C2×C3⋊(C3⋊C8)16yescomplemented
202C23C3⋊SL(2,ℤ/4)11yescharacteristic
203C23C22×C3⋊Dic311yescharacteristic
204C2×C4—33no—
205C2×C4—33no—
206C2×C4—33no—
207C2×C4—33no—
208C2×C4—36no—
209C2×C4—31no—
210C2×C4—33no—
211C2×C4—33no—
212C2×C4—31no—
213C2×C4—63no—
214C2×C4—63no—
215C2×C4C3⋊SL(2,ℤ/4)13yes—
216C2×C4C2×C3⋊S413yes—
217C8—184no—
218C8—184no—
219C2×C3—31no—
220C2×C3—36no—
221C2×C3—31no—
222C2×C3—418no—
223C2×C3—43no—
224C2×C3C2×A4⋊C816yescomplemented
225C2×C3C22×SL(2,ℤ/4)11yescharacteristic
226C22—36no—
227C22—31no—
228C22—36no—
229C22—312no—
230C22—36no—
231C22—31no—
232C22—33no—
233C22—63no—
234C22—64no—
235C22C3⋊(A4⋊C8)14yesdirect product factor
236C22C22×C3⋊(C3⋊C8)11yescharacteristic, complemented
237C22C2×C3⋊SL(2,ℤ/4)13yes—
238C4—31no—
239C4—33no—
240C4C2×C3⋊SL(2,ℤ/4)13yes—
241C4C22×C3⋊S411yescharacteristic
242C3—43no—
243C3C22×A4⋊C811yescharacteristic, complemented
244C2—31no—
245C2—36no—
246C2—31no—
247C2C2×C3⋊(A4⋊C8)16yesdirect product factor
248C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC22×C4C3⋊S4
commutator, hypocenterC3×A4C22×C8
FrattiniC4C22×C3⋊S4
FittingC24×C3×C4D3
socleC25×C3Dic3
prime radicalC23×C3×A4C4
cosocleC3×C4×A4C23
LCSG ▷ C3×A4
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊(A4⋊C8)C2direct (N × H)
9. C3⋊(A4⋊C8)C22direct (N × H)
17. C22×C3×A4C8semidirect
45. C2×C3×A4C2×C8semidirect
58. C24×C3C3⋊C8semidirect
60. C22×A4C3⋊C8semidirect
90. C3×A4C22×C8semidirect
118. C23×C3C2×C3⋊C8semidirect
121. C2×A4C2×C3⋊C8semidirect
146. C24C3⋊(C3⋊C8)semidirect
181. C22×C3A4⋊C8semidirect
182. C22×C3C22×C3⋊C8semidirect
184. A4C22×C3⋊C8semidirect
201. C23C2×C3⋊(C3⋊C8)semidirect
224. C2×C3C2×A4⋊C8semidirect
235. C22C3⋊(A4⋊C8)direct (N × H)
236. C22C22×C3⋊(C3⋊C8)semidirect
243. C3C22×A4⋊C8semidirect
247. C2C2×C3⋊(A4⋊C8)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C2×C3⋊(A4⋊C8)2
C22×A4⋊C83
C22×#8303
C22×C3⋊(C3⋊C8)4