Finite Group Databasebeta

← C2×A4×C42⋊C3 #11922553

Subgroups — C2×A4×C42⋊C3 #11922553

Order 1152.

324 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 28 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
1A4×C42⋊C3C211yesmaximal, characteristic, direct product factor
2C2×C22⋊(C42⋊C3)C312yesmaximal, complemented
3C2×C42×A4C311yesmaximal, characteristic, complemented
4C23×C42⋊C3C311yesmaximal, characteristic, complemented
5C2×A42—41nomaximal
6C2×C3×C42⋊C3—41nomaximal
7C22×C4×A4—31no—
8C22⋊(C42⋊C3)C2×C312yescomplemented
9C42×A4—31no—
10C42×A4C2×C311yescharacteristic, complemented
11C22×C42⋊C3—31no—
12C22×C42⋊C3—31no—
13C22×C42⋊C3C2×C311yescharacteristic, complemented
14A42—41no—
15C3×C42⋊C3—41no—
16C23×C42C3211yescharacteristic, complemented, Sylow
17C2×C22⋊A4—42no—
18C23×A4—41no—
19C23×A4A411yescharacteristic
20C2×C4×A4—32no—
21C2×C4×A4—32no—
22C2×C4×A4—31no—
23C2×C4×A4—31no—
24C2×C3×C42—41no—
25C2×C42⋊C3—31no—
26C2×C42⋊C3—31no—
27C2×C42⋊C3—42no—
28C2×C42⋊C3—122no—
29C2×C42⋊C3A411yescharacteristic, direct product factor
30C2×C3×A4—161no—
31C2×C3×A4—161no—
32C24×C4—31no—
33C22×C42—31no—
34C22×C42—31no—
35C22×C42—31no—
36C22×C42—91no—
37C22×C42—91no—
38C22×C42C2×C3211yescharacteristic, complemented
39C22⋊A4—42no—
40C22×A4—31no—
41C22×A4—31no—
42C22×A4—41no—
43C22×A4—121no—
44C22×A4—121no—
45C22×A4C2×A411yescharacteristic
46C22×C3×C4—121no—
47C4×A4—32no—
48C4×A4—32no—
49C3×C42—41no—
50C3×C42—121no—
51C42⋊C3—42no—
52C42⋊C3—122no—
53C42⋊C3C2×A411yescharacteristic, direct product factor
54C3×A4—161no—
55C3×A4—161no—
56C25C3×A411yescharacteristic
57C23×C4—32no—
58C23×C4—32no—
59C23×C4—31no—
60C23×C4—31no—
61C23×C4—91no—
62C23×C4—91no—
63C23×C4—91no—
64C23×C4—91no—
65C23×C4—92no—
66C23×C4—92no—
67C2×C42—32no—
68C2×C42—31no—
69C2×C42—31no—
70C2×C42—91no—
71C2×C42—91no—
72C2×C42—91no—
73C2×C42—92no—
74C2×C42—91no—
75C2×C42—92no—
76C2×C42—91no—
77C2×C42—92no—
78C2×C42C3×A411yescharacteristic, complemented
79C23×C3—41no—
80C23×C3—161no—
81C2×A4—31no—
82C2×A4—31no—
83C2×A4—41no—
84C2×A4—121no—
85C2×A4—121no—
86C2×A4—162no—
87C2×A4—162no—
88C2×A4—482no—
89C2×A4C42⋊C311yescharacteristic, direct product factor
90C2×C3×C4—121no—
91C2×C3×C4—121no—
92C2×C3×C4—122no—
93C2×C3×C4—122no—
94C2×C32—641no—
95C24—31no—
96C24—31no—
97C24—31no—
98C24—31no—
99C24—91no—
100C24—91no—
101C24C2×C3×A411yescharacteristic
102C22×C4—31no—
103C22×C4—32no—
104C22×C4—32no—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4—91no—
108C22×C4—91no—
109C22×C4—92no—
110C22×C4—92no—
111C22×C4—92no—
112C22×C4—92no—
113C22×C4—92no—
114C22×C4—94no—
115C22×C4—94no—
116C22×C4—92no—
117C22×C4—92no—
118C22×C4—91no—
119C22×C4—91no—
120C22×C4—91no—
121C22×C4—92no—
122C22×C4—92no—
123C22×C4—92no—
124C22×C4—92no—
125C22×C4—92no—
126C22×C4—92no—
127C22×C4—92no—
128C22×C4—92no—
129C42—31no—
130C42—32no—
131C42—91no—
132C42—91no—
133C42—92no—
134C42—92no—
135C42C2×C3×A411yescharacteristic, complemented
136C22×C3—41no—
137C22×C3—121no—
138C22×C3—121no—
139C22×C3—161no—
140C22×C3—481no—
141C22×C3—481no—
142A4—41no—
143A4—162no—
144A4—162no—
145A4—482no—
146A4C2×C42⋊C311yescharacteristic, direct product factor
147C3×C4—122no—
148C3×C4—122no—
149C32—641noSylow
150C23—32no—
151C23—31no—
152C23—31no—
153C23—31no—
154C23—31no—
155C23—91no—
156C23—91no—
157C23—91no—
158C23—91no—
159C23—91no—
160C23—91no—
161C23—91no—
162C23—91no—
163C23—92no—
164C23—91no—
165C23—92no—
166C23—92no—
167C23C3×C42⋊C311yescharacteristic, complemented
168C23A4211yescharacteristic
169C2×C4—32no—
170C2×C4—32no—
171C2×C4—31no—
172C2×C4—31no—
173C2×C4—92no—
174C2×C4—92no—
175C2×C4—92no—
176C2×C4—92no—
177C2×C4—92no—
178C2×C4—92no—
179C2×C4—92no—
180C2×C4—92no—
181C2×C4—92no—
182C2×C4—92no—
183C2×C4—94no—
184C2×C4—94no—
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—92no—
190C2×C4—92no—
191C2×C3—41no—
192C2×C3—121no—
193C2×C3—121no—
194C2×C3—161no—
195C2×C3—481no—
196C2×C3—481no—
197C2×C3—642no—
198C22—31no—
199C22—31no—
200C22—31no—
201C22—31no—
202C22—32no—
203C22—91no—
204C22—91no—
205C22—91no—
206C22—91no—
207C22—91no—
208C22—91no—
209C22—91no—
210C22—91no—
211C22—92no—
212C22—92no—
213C22—92no—
214C22—91no—
215C22C2×C3×C42⋊C311yescharacteristic, complemented
216C22C2×A4211yescharacteristic
217C4—32no—
218C4—32no—
219C4—92no—
220C4—92no—
221C3—41no—
222C3—161no—
223C3—642no—
224C2—31no—
225C2—31no—
226C2—31no—
227C2—31no—
228C2—91no—
229C2—91no—
230C2A4×C42⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2A4×C42⋊C3
commutator, cosocle, hypocenterC22×C42C2×C32
FrattiniC22C2×A42
FittingC23×C42C32
socleC25C3×A4
LCSG ▷ C22×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. A4×C42⋊C3C2direct (N × H)
2. C2×C22⋊(C42⋊C3)C3semidirect
3. C2×C42×A4C3semidirect
4. C23×C42⋊C3C3semidirect
8. C22⋊(C42⋊C3)C2×C3semidirect
10. C42×A4C2×C3semidirect
13. C22×C42⋊C3C2×C3semidirect
16. C23×C42C32semidirect
29. C2×C42⋊C3A4direct (N × H)
38. C22×C42C2×C32semidirect
53. C42⋊C3C2×A4direct (N × H)
78. C2×C42C3×A4semidirect
89. C2×A4C42⋊C3direct (N × H)
135. C42C2×C3×A4semidirect
146. A4C2×C42⋊C3direct (N × H)
167. C23C3×C42⋊C3semidirect
215. C22C2×C3×C42⋊C3semidirect
230. C2A4×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
A4×C42⋊C32
C2×C22⋊(C42⋊C3)3
C2×C42×A43
C23×C42⋊C33
C2×A424
C2×C3×C42⋊C34