Finite Group Databasebeta

← C42×C3⋊S4 #11922835

Subgroups — C42×C3⋊S4 #11922835

Order 1152.

1210 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 159 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×C4×C3⋊S4C213yesmaximal
2C3×C42×A4C211yesmaximal, characteristic, complemented
3C4×C3⋊SL(2,ℤ/4)C213yesmaximal, complemented
4C42×S4—33nomaximal
5C42×#67—31nomaximal
6C22×C3⋊S4C2211yescharacteristic
7C2×C3×C4×A4C2213yes—
8C2×C3⋊SL(2,ℤ/4)C2213yes—
9C4×C3⋊S4C4112yesdirect product factor
10C42×C3⋊D3—41nomaximal
11C2×C4×S4—39no—
12C22×C3×C42D311yescharacteristic, complemented
13C2×C4×#67—33no—
14C2×C42×D3—31no—
15C42×A4D313yescomplemented
16C4×SL(2,ℤ/4)—39no—
17C4×#217—33no—
18C4×(C2×D3)⋊C4—33no—
19C4×Dic3⋊C4—33no—
20C42×Dic3—31no—
21C22×C3×A4C2311yescharacteristic
22C2×C3⋊S4C2×C416yes—
23C2×C4×C3⋊D3—43no—
24C3×C4×A4C2×C416yescomplemented
25C3⋊SL(2,ℤ/4)C2×C416yescomplemented
26C32×C42—41no—
27C4×C3⋊Dic3—43no—
28C42×D4—91noSylow
29C22×S4—33no—
30C23×C3×C4C2×D313yes—
31C22×#67—31no—
32C22×C4×D3—33no—
33C2×C4×A4C2×D319yes—
34C2×SL(2,ℤ/4)—39no—
35C4×S4—336no—
36C2×C3×C42—31no—
37C2×C3×C42—33no—
38C2×#217—33no—
39C4×#67—312no—
40C4×#67—312no—
41C2×(C2×D3)⋊C4—33no—
42C2×Dic3⋊C4—33no—
43C2×C4×Dic3—33no—
44C2×C4×Dic3—33no—
45C2×C4×Dic3—33no—
46C42×D3—63no—
47C42×D3—61no—
48C42×D3—123no—
49C3⋊#95—36no—
50C22×C3⋊D3—41no—
51C2×C3×A4C22×C413yes—
52C3⋊S4C4214yesdirect product factor
53C2×C32×C4—43no—
54C2×C3⋊Dic3—43no—
55C4×C3⋊D3—412no—
56C2×C4×D4—93no—
57C22×C42—91no—
58C22×C42C3⋊D311yescharacteristic, complemented
59C4×C4⋊C4—93no—
60C4×C22⋊C4—93no—
61C4×C22⋊C4—93no—
62C43—91no—
63C24×C3C22×D311yescharacteristic
64C23×D3—31no—
65C22×A4C22×D313yes—
66C2×S4—318no—
67C22×C3×C4—33no—
68C22×C3×C4—33no—
69C22×C3×C4—36no—
70C22×C3×C4C4×D316yescomplemented
71C2×#67—36no—
72C2×#67—36no—
73C22×Dic3—31no—
74C22×Dic3—33no—
75C22×Dic3—33no—
76C2×C4×D3—312no—
77C2×C4×D3—63no—
78C2×C4×D3—66no—
79C2×C4×D3—63no—
80C2×C4×D3—129no—
81C4×A4C4×D3118yescomplemented
82SL(2,ℤ/4)—318no—
83C3×C42—33no—
84C3×C42—43no—
85C3×C42—61no—
86C3×C42S411yescharacteristic, complemented
87#217—36no—
88#217—36no—
89(C2×D3)⋊C4—312no—
90Dic3⋊C4—312no—
91C4×Dic3—312no—
92C4×Dic3—63no—
93C4×Dic3—66no—
94C4×Dic3—63no—
95C4×Dic3—129no—
96C22×C32—41no—
97C2×C3⋊D3—46no—
98C3×A4C2×C4211yescharacteristic, complemented
99C32×C4—46no—
100C3⋊Dic3—46no—
101C22×D4—91no—
102C23×C4—93no—
103C23×C4C2×C3⋊D313yes—
104C4×D4—912no—
105C4×D4—912no—
106C2×C4⋊C4—93no—
107C2×C22⋊C4—93no—
108C2×C22⋊C4—93no—
109C2×C42—31no—
110C2×C42—33no—
111C2×C42—93no—
112C2×C42—93no—
113C2×C42—93no—
114C2×C42—183no—
115C2×C42—181no—
116#95—96no—
117C23×C3—31no—
118C23×C3—33no—
119C23×C3C2×C4×D313yes—
120C22×D3—36no—
121C22×D3—63no—
122C22×D3—61no—
123C22×D3—123no—
124C2×A4C2×C4×D319yes—
125S4—312no—
126C2×C3×C4—33no—
127C2×C3×C4—36no—
128C2×C3×C4—36no—
129C2×C3×C4—36no—
130C2×C3×C4—49no—
131C2×C3×C4—63no—
132C2×C3×C4C2×S413yes—
133#67—312no—
134#67—34no—
135C2×Dic3—36no—
136C2×Dic3—36no—
137C2×Dic3—36no—
138C2×Dic3—66no—
139C2×Dic3—63no—
140C2×Dic3—63no—
141C2×Dic3—129no—
142C4×D3—612no—
143C4×D3—612no—
144C4×D3—1236no—
145C2×C32—43no—
146C3⋊D3—44no—
147C24—91no—
148C24C22×C3⋊D311yescharacteristic
149C2×D4—96no—
150C2×D4—96no—
151C22×C4—33no—
152C22×C4—33no—
153C22×C4—36no—
154C22×C4—912no—
155C22×C4—91no—
156C22×C4—93no—
157C22×C4—93no—
158C22×C4—183no—
159C22×C4—186no—
160C22×C4—183no—
161C22×C4C4×C3⋊D316yescomplemented
162C4⋊C4—912no—
163C22⋊C4—912no—
164C22⋊C4—96no—
165C22⋊C4—96no—
166C42—33no—
167C42—61no—
168C42—912no—
169C42—183no—
170C42—186no—
171C42—183no—
172C42C3⋊S411yescharacteristic, direct product factor
173C22×C3—33no—
174C22×C3—33no—
175C22×C3—33no—
176C22×C3—43no—
177C22×C3—61no—
178C22×C3C42×D311yescharacteristic, complemented
179C22×C3C22×S411yescharacteristic
180C2×D3—34no—
181C2×D3—66no—
182C2×D3—66no—
183C2×D3—1218no—
184A4C42×D313yescomplemented
185C3×C4—36no—
186C3×C4—418no—
187C3×C4C4×S416yescomplemented
188Dic3—34no—
189Dic3—66no—
190Dic3—66no—
191Dic3—1218no—
192C32—41noSylow
193C23—31no—
194C23—33no—
195C23—96no—
196C23—183no—
197C23—181no—
198C23C2×C4×C3⋊D313yes—
199D4—912no—
200D4—94no—
201C2×C4—33no—
202C2×C4—36no—
203C2×C4—36no—
204C2×C4—36no—
205C2×C4—63no—
206C2×C4—96no—
207C2×C4—96no—
208C2×C4—96no—
209C2×C4—1812no—
210C2×C4—186no—
211C2×C4—183no—
212C2×C4—183no—
213C2×C4—1812no—
214C2×C4C2×C3⋊S413yes—
215C2×C3—31no—
216C2×C3—33no—
217C2×C3—49no—
218C2×C3C2×C4×S413yes—
219D3—64no—
220D3—1212no—
221C22—33no—
222C22—33no—
223C22—33no—
224C22—61no—
225C22—94no—
226C22—186no—
227C22—186no—
228C22C42×C3⋊D311yescharacteristic, complemented
229C22C22×C3⋊S411yescharacteristic
230C4—36no—
231C4—94no—
232C4—186no—
233C4—186no—
234C4C4×C3⋊S416yesdirect product factor
235C3—43no—
236C3C42×S411yescharacteristic, complemented
237C2—31no—
238C2—33no—
239C2—184no—
240C2C2×C4×C3⋊S413yes—
subgroupG/H
center, hypercenterC42C3⋊S4
commutator, hypocenterC3×A4C2×C42
FrattiniC22C22×C3⋊S4
FittingC22×C3×C42D3
socleC24×C3C22×D3
prime radicalC22×C3⋊S4C22
cosocleC22×C3×A4C23
LCSG ▷ C3×A4
UCSC1 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C42×A4C2semidirect
3. C4×C3⋊SL(2,ℤ/4)C2semidirect
9. C4×C3⋊S4C4direct (N × H)
12. C22×C3×C42D3semidirect
15. C42×A4D3semidirect
24. C3×C4×A4C2×C4semidirect
25. C3⋊SL(2,ℤ/4)C2×C4semidirect
52. C3⋊S4C42direct (N × H)
58. C22×C42C3⋊D3semidirect
70. C22×C3×C4C4×D3semidirect
81. C4×A4C4×D3semidirect
86. C3×C42S4semidirect
98. C3×A4C2×C42semidirect
161. C22×C4C4×C3⋊D3semidirect
172. C42C3⋊S4direct (N × H)
178. C22×C3C42×D3semidirect
184. A4C42×D3semidirect
187. C3×C4C4×S4semidirect
228. C22C42×C3⋊D3semidirect
234. C4C4×C3⋊S4direct (N × H)
236. C3C42×S4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊S42
C3×C42×A42
C4×C3⋊SL(2,ℤ/4)2
C42×S43
C42×#673
C42×C3⋊D34