Finite Group Databasebeta

← C22×C3×A4⋊C8 #11922760

Subgroups — C22×C3×A4⋊C8 #11922760

Order 1152.

860 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 860 conjugacy classes of subgroups — too many to draw. Only its 184 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⋊C8C216yesmaximal, direct product factor
3C22×A4⋊C8C311yesmaximal, characteristic, direct product factor
4C22×C3×C22⋊C8—31nomaximal
5C23×C3×A4C411yescharacteristic
6C2×C3×C4×A4C413yes—
7C2×C3×C4×A4C2213yes—
8C22×C3×C3⋊C8—41nomaximal
9C3×A4⋊C8C2214yesdirect product factor
10C24×C3×C4D311yescharacteristic
11C22×C4×A4—21no—
12C22×C4×A4C2×C311yescharacteristic
13C23×C3×C8—31no—
14C23×C3×C8—31no—
15C2×A4⋊C8C2×C316yesdirect product factor
16C2×C3×C22⋊C8—36no—
17C2×C3×C22⋊C8—36no—
18C22×C3×A4C814yescomplemented
19C22×C3×A4C2×C413yes—
20C22×C32×C4—41no—
21C3×C4×A4C2×C413yes—
22C3×C4×A4C2311yescharacteristic
23C2×C3×C3⋊C8—46no—
24C22×C22⋊C8—31noSylow
25C25×C3Dic311yescharacteristic
26C23×A4—21no—
27C23×A4C3×C411yescharacteristic
28C23×C3×C4—31no—
29C23×C3×C4—31no—
30C23×C3×C4—33no—
31C23×C3×C4—33no—
32C23×C3×C4Dic313yes—
33C23×C3×C4C2×D313yes—
34C2×C4×A4—23no—
35C2×C4×A4—23no—
36C2×C4×A4C3×C413yes—
37C2×C4×A4C22×C313yes—
38C22×C3×C8—36no—
39C22×C3×C8—36no—
40C22×C3×C8—61no—
41C22×C3×C8—63no—
42C22×C3×C8—63no—
43C22×C3×C8—61no—
44C22×C3⋊C8—41no—
45A4⋊C8C22×C314yesdirect product factor
46C3×C22⋊C8—312no—
47C3×C22⋊C8—34no—
48C23×C32—41no—
49C2×C3×A4C2×C816yescomplemented
50C2×C3×A4C22×C411yescharacteristic
51C2×C32×C4—43no—
52C2×C32×C4—43no—
53C3×C3⋊C8—44no—
54C24×C4C3×D311yescharacteristic
55C23×C8—31no—
56C23×C8—31no—
57C2×C22⋊C8—36no—
58C2×C22⋊C8—36no—
59C24×C3—31no—
60C24×C3—34no—
61C24×C3—33no—
62C24×C3C3⋊C814yescomplemented
63C24×C3C2×Dic313yes—
64C22×A4—24no—
65C22×A4—23no—
66C22×A4C3×C814yescomplemented
67C22×A4C2×C3×C413yes—
68C22×C3×C4—31no—
69C22×C3×C4—33no—
70C22×C3×C4—33no—
71C22×C3×C4—33no—
72C22×C3×C4—33no—
73C22×C3×C4—33no—
74C22×C3×C4—33no—
75C22×C3×C4—36no—
76C22×C3×C4—33no—
77C22×C3×C4—33no—
78C22×C3×C4—41no—
79C22×C3×C4—63no—
80C22×C3×C4—61no—
81C22×C3×C4—63no—
82C22×C3×C4—81no—
83C22×C3×C4C2×Dic313yes—
84C22×C3×C4S411yescharacteristic
85C22×C3×C4C22×D311yescharacteristic
86C4×A4—23no—
87C4×A4—21no—
88C4×A4C2×C3×C413yes—
89C4×A4C23×C311yescharacteristic
90C2×C3×C8—34no—
91C2×C3×C8—34no—
92C2×C3×C8—66no—
93C2×C3×C8—66no—
94C2×C3×C8—66no—
95C2×C3×C8—66no—
96C2×C3⋊C8—46no—
97C22×C32—44no—
98C22×C32—43no—
99C3×A4C22×C811yescharacteristic, complemented
100C32×C4—43no—
101C32×C4—41no—
102C25C3×Dic311yescharacteristic
103C23×C4—31no—
104C23×C4—33no—
105C23×C4—31no—
106C23×C4—33no—
107C23×C4C3×Dic313yes—
108C23×C4C2×C3×D313yes—
109C22×C8—36no—
110C22×C8—36no—
111C22×C8—61no—
112C22×C8—63no—
113C22×C8—63no—
114C22×C8—61no—
115C22⋊C8—312no—
116C22⋊C8—34no—
117C23×C3—34no—
118C23×C3—34no—
119C23×C3—33no—
120C23×C3—33no—
121C23×C3—33no—
122C23×C3—312no—
123C23×C3—36no—
124C23×C3—41no—
125C23×C3—61no—
126C23×C3—66no—
127C23×C3—81no—
128C23×C3C2×C3⋊C816yescomplemented
129C23×C3SL(2,ℤ/4)11yescharacteristic
130C23×C3C22×Dic311yescharacteristic
131C2×A4—26no—
132C2×A4—21no—
133C2×A4C2×C3×C816yescomplemented
134C2×A4C22×C3×C411yescharacteristic
135C2×C3×C4—33no—
136C2×C3×C4—33no—
137C2×C3×C4—33no—
138C2×C3×C4—33no—
139C2×C3×C4—36no—
140C2×C3×C4—31no—
141C2×C3×C4—33no—
142C2×C3×C4—33no—
143C2×C3×C4—31no—
144C2×C3×C4—43no—
145C2×C3×C4—43no—
146C2×C3×C4—63no—
147C2×C3×C4—63no—
148C2×C3×C4—83no—
149C2×C3×C4—83no—
150C2×C3×C4SL(2,ℤ/4)13yes—
151C2×C3×C4C2×S413yes—
152C3×C8—64no—
153C3×C8—64no—
154C3⋊C8—44no—
155C2×C32—46no—
156C2×C32—41no—
157C24—31no—
158C24—33no—
159C24—34no—
160C24C3×C3⋊C814yescomplemented
161C24C2×C3×Dic313yes—
162C22×C4—31no—
163C22×C4—33no—
164C22×C4—33no—
165C22×C4—33no—
166C22×C4—33no—
167C22×C4—33no—
168C22×C4—33no—
169C22×C4—36no—
170C22×C4—33no—
171C22×C4—33no—
172C22×C4—63no—
173C22×C4—61no—
174C22×C4—63no—
175C22×C4C2×C3×Dic313yes—
176C22×C4C3×S411yescharacteristic
177C22×C4C22×C3×D311yescharacteristic
178C2×C8—34no—
179C2×C8—34no—
180C2×C8—66no—
181C2×C8—66no—
182C2×C8—66no—
183C2×C8—66no—
184C22×C3—36no—
185C22×C3—31no—
186C22×C3—36no—
187C22×C3—36no—
188C22×C3—312no—
189C22×C3—31no—
190C22×C3—33no—
191C22×C3—43no—
192C22×C3—44no—
193C22×C3—63no—
194C22×C3—64no—
195C22×C3—83no—
196C22×C3—84no—
197C22×C3A4⋊C814yesdirect product factor
198C22×C3C22×C3⋊C811yescharacteristic, complemented
199C22×C3C2×SL(2,ℤ/4)13yes—
200A4—21no—
201A4C22×C3×C811yescharacteristic, complemented
202C3×C4—31no—
203C3×C4—33no—
204C3×C4—43no—
205C3×C4—41no—
206C3×C4—83no—
207C3×C4—81no—
208C3×C4C2×SL(2,ℤ/4)13yes—
209C3×C4C22×S411yescharacteristic
210C32—41noSylow
211C23—33no—
212C23—33no—
213C23—34no—
214C23—34no—
215C23—33no—
216C23—312no—
217C23—36no—
218C23—61no—
219C23—66no—
220C23C2×C3×C3⋊C816yescomplemented
221C23C3×SL(2,ℤ/4)11yescharacteristic
222C23C22×C3×Dic311yescharacteristic
223C2×C4—33no—
224C2×C4—33no—
225C2×C4—33no—
226C2×C4—33no—
227C2×C4—36no—
228C2×C4—31no—
229C2×C4—33no—
230C2×C4—33no—
231C2×C4—31no—
232C2×C4—63no—
233C2×C4—63no—
234C2×C4C3×SL(2,ℤ/4)13yes—
235C2×C4C2×C3×S413yes—
236C8—64no—
237C8—64no—
238C2×C3—31no—
239C2×C3—36no—
240C2×C3—31no—
241C2×C3—46no—
242C2×C3—41no—
243C2×C3—86no—
244C2×C3—81no—
245C2×C3C2×A4⋊C816yesdirect product factor
246C2×C3C22×SL(2,ℤ/4)11yescharacteristic
247C22—36no—
248C22—31no—
249C22—36no—
250C22—36no—
251C22—312no—
252C22—31no—
253C22—33no—
254C22—63no—
255C22—64no—
256C22C3×A4⋊C814yesdirect product factor
257C22C22×C3×C3⋊C811yescharacteristic, complemented
258C22C2×C3×SL(2,ℤ/4)13yes—
259C4—31no—
260C4—33no—
261C4C2×C3×SL(2,ℤ/4)13yes—
262C4C22×C3×S411yescharacteristic
263C3—41no—
264C3—81no—
265C3C22×A4⋊C811yescharacteristic, direct product factor
266C2—31no—
267C2—36no—
268C2—31no—
269C2C2×C3×A4⋊C816yesdirect product factor
270C2C22×C3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC22×C3×C4S4
commutator, hypocenterA4C22×C3×C8
FrattiniC4C22×C3×S4
FittingC24×C3×C4D3
socleC25×C3Dic3
prime radicalC23×C3×A4C4
cosocleC4×A4C23×C3
LCSG ▷ A4
UCSC1 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×A4⋊C8C2direct (N × H)
3. C22×A4⋊C8C3direct (N × H)
9. C3×A4⋊C8C22direct (N × H)
15. C2×A4⋊C8C2×C3direct (N × H)
18. C22×C3×A4C8semidirect
45. A4⋊C8C22×C3direct (N × H)
49. C2×C3×A4C2×C8semidirect
62. C24×C3C3⋊C8semidirect
66. C22×A4C3×C8semidirect
99. C3×A4C22×C8semidirect
128. C23×C3C2×C3⋊C8semidirect
133. C2×A4C2×C3×C8semidirect
160. C24C3×C3⋊C8semidirect
197. C22×C3A4⋊C8direct (N × H)
198. C22×C3C22×C3⋊C8semidirect
201. A4C22×C3×C8semidirect
220. C23C2×C3×C3⋊C8semidirect
245. C2×C3C2×A4⋊C8direct (N × H)
256. C22C3×A4⋊C8direct (N × H)
257. C22C22×C3×C3⋊C8semidirect
265. C3C22×A4⋊C8direct (N × H)
269. C2C2×C3×A4⋊C8direct (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⋊C82
C22×A4⋊C83
C22×C3×C22⋊C83
C22×C3×C3⋊C84