Finite Group Databasebeta

← C22×A4×C3⋊C8 #11923340

Subgroups — C22×A4×C3⋊C8 #11923340

Order 1152.

966 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 966 conjugacy classes of subgroups — too many to draw. Only its 195 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×A4×C3⋊C8C216yesmaximal, direct product factor
3C24×C3⋊C8C311yesmaximal, characteristic, complemented
4C22×C8×A4—31nomaximal
5C23×C3×A4C411yescharacteristic
6C2×C3×C4×A4C413yes—
7C2×C3×C4×A4C2213yes—
8C22×C3×C3⋊C8—41nomaximal
9A4×C3⋊C8C2214yesdirect product factor
10C24×C3×C4C2×C311yescharacteristic
11C22×C4×A4—21no—
12C22×C4×A4D311yescharacteristic
13C23×C3⋊C8—31no—
14C23×C3⋊C8—31no—
15C23×C3⋊C8—36no—
16C23×C3⋊C8C2×C316yescomplemented
17C2×C8×A4—36no—
18C22×C3×A4C814yescomplemented
19C22×C3×A4C2×C413yes—
20C22×C32×C4—41no—
21C3×C4×A4C2×C413yes—
22C3×C4×A4C2311yescharacteristic
23C2×C3×C3⋊C8—46no—
24C24×C8—31noSylow
25C25×C3C3×C411yescharacteristic
26C23×A4—21no—
27C23×A4Dic311yescharacteristic
28C23×C3×C4—31no—
29C23×C3×C4—31no—
30C23×C3×C4—33no—
31C23×C3×C4—33no—
32C23×C3×C4C3×C413yes—
33C23×C3×C4C22×C313yes—
34C2×C4×A4—23no—
35C2×C4×A4—23no—
36C2×C4×A4Dic313yes—
37C2×C4×A4C2×D313yes—
38C22×C3×C8—121no—
39C22×C3⋊C8—36no—
40C22×C3⋊C8—38no—
41C22×C3⋊C8—31no—
42C22×C3⋊C8—36no—
43C22×C3⋊C8—36no—
44C22×C3⋊C8—36no—
45C22×C3⋊C8—312no—
46C22×C3⋊C8A411yescharacteristic, direct product factor
47C22×C3⋊C8C22×C314yescomplemented
48C8×A4—34no—
49C23×C32—41no—
50C2×C3×A4C2×C816yescomplemented
51C2×C3×A4C22×C411yescharacteristic
52C2×C32×C4—43no—
53C2×C32×C4—43no—
54C3×C3⋊C8—44no—
55C24×C4C3×D311yescharacteristic
56C23×C8—36no—
57C23×C8—91no—
58C23×C8—96no—
59C23×C8—91no—
60C24×C3—34no—
61C24×C3—33no—
62C24×C3—31no—
63C24×C3C3×C814yescomplemented
64C24×C3C2×C3×C413yes—
65C22×A4—24no—
66C22×A4—23no—
67C22×A4C3⋊C814yesdirect product factor
68C22×A4C2×Dic313yes—
69C22×C3×C4—32no—
70C22×C3×C4—36no—
71C22×C3×C4—36no—
72C22×C3×C4—31no—
73C22×C3×C4—33no—
74C22×C3×C4—33no—
75C22×C3×C4—33no—
76C22×C3×C4—33no—
77C22×C3×C4—33no—
78C22×C3×C4—33no—
79C22×C3×C4—36no—
80C22×C3×C4—33no—
81C22×C3×C4—33no—
82C22×C3×C4—41no—
83C22×C3×C4—81no—
84C22×C3×C4C2×C3×C413yes—
85C22×C3×C4C2×A411yescharacteristic
86C22×C3×C4C23×C311yescharacteristic
87C4×A4—23no—
88C4×A4—21no—
89C4×A4C2×Dic313yes—
90C4×A4C22×D311yescharacteristic
91C2×C3×C8—126no—
92C2×C3⋊C8—312no—
93C2×C3⋊C8—36no—
94C2×C3⋊C8—312no—
95C2×C3⋊C8—34no—
96C2×C3⋊C8—34no—
97C2×C3⋊C8C2×A416yesdirect product factor
98C22×C32—44no—
99C22×C32—43no—
100C3×A4C22×C811yescharacteristic, complemented
101C32×C4—43no—
102C32×C4—41no—
103C25C3×Dic311yescharacteristic
104C23×C4—31no—
105C23×C4—33no—
106C23×C4—31no—
107C23×C4—33no—
108C23×C4C3×Dic313yes—
109C23×C4C2×C3×D313yes—
110C22×C8—31no—
111C22×C8—34no—
112C22×C8—96no—
113C22×C8—96no—
114C22×C8—98no—
115C22×C8—96no—
116C22×C8—91no—
117C22×C8—912no—
118C22×C8—96no—
119C23×C3—33no—
120C23×C3—312no—
121C23×C3—36no—
122C23×C3—32no—
123C23×C3—312no—
124C23×C3—34no—
125C23×C3—34no—
126C23×C3—33no—
127C23×C3—33no—
128C23×C3—41no—
129C23×C3—81no—
130C23×C3C2×C3×C816yescomplemented
131C23×C3C4×A411yescharacteristic
132C23×C3C22×C3×C411yescharacteristic
133C2×A4—26no—
134C2×A4—21no—
135C2×A4C2×C3⋊C816yesdirect product factor
136C2×A4C22×Dic311yescharacteristic
137C2×C3×C4—36no—
138C2×C3×C4—36no—
139C2×C3×C4—33no—
140C2×C3×C4—33no—
141C2×C3×C4—33no—
142C2×C3×C4—36no—
143C2×C3×C4—33no—
144C2×C3×C4—33no—
145C2×C3×C4—31no—
146C2×C3×C4—33no—
147C2×C3×C4—31no—
148C2×C3×C4—43no—
149C2×C3×C4—43no—
150C2×C3×C4—83no—
151C2×C3×C4—83no—
152C2×C3×C4C4×A413yes—
153C2×C3×C4C22×A413yes—
154C3×C8—124no—
155C3⋊C8—34no—
156C3⋊C8C22×A414yesdirect product factor
157C2×C32—41no—
158C2×C32—46no—
159C24—33no—
160C24—34no—
161C24—31no—
162C24C3×C3⋊C814yescomplemented
163C24C2×C3×Dic313yes—
164C22×C4—32no—
165C22×C4—36no—
166C22×C4—36no—
167C22×C4—31no—
168C22×C4—33no—
169C22×C4—33no—
170C22×C4—33no—
171C22×C4—33no—
172C22×C4—33no—
173C22×C4—33no—
174C22×C4—36no—
175C22×C4—33no—
176C22×C4—33no—
177C22×C4C2×C3×Dic313yes—
178C22×C4D3×A411yescharacteristic
179C22×C4C22×C3×D311yescharacteristic
180C2×C8—36no—
181C2×C8—94no—
182C2×C8—912no—
183C2×C8—912no—
184C2×C8—96no—
185C2×C8—94no—
186C22×C3—36no—
187C22×C3—31no—
188C22×C3—36no—
189C22×C3—38no—
190C22×C3—33no—
191C22×C3—31no—
192C22×C3—312no—
193C22×C3—36no—
194C22×C3—36no—
195C22×C3—44no—
196C22×C3—43no—
197C22×C3—84no—
198C22×C3—83no—
199C22×C3C8×A414yescomplemented
200C22×C3C22×C3×C811yescharacteristic, complemented
201C22×C3C2×C4×A413yes—
202A4—21no—
203A4C22×C3⋊C811yescharacteristic, direct product factor
204C3×C4—31no—
205C3×C4—33no—
206C3×C4—43no—
207C3×C4—41no—
208C3×C4—83no—
209C3×C4—81no—
210C3×C4C2×C4×A413yes—
211C3×C4C23×A411yescharacteristic
212C32—41noSylow
213C23—33no—
214C23—312no—
215C23—36no—
216C23—32no—
217C23—312no—
218C23—34no—
219C23—34no—
220C23—33no—
221C23—33no—
222C23C2×C3×C3⋊C816yescomplemented
223C23Dic3×A411yescharacteristic
224C23C22×C3×Dic311yescharacteristic
225C2×C4—36no—
226C2×C4—36no—
227C2×C4—33no—
228C2×C4—33no—
229C2×C4—33no—
230C2×C4—33no—
231C2×C4—36no—
232C2×C4—31no—
233C2×C4—33no—
234C2×C4—33no—
235C2×C4—31no—
236C2×C4Dic3×A413yes—
237C2×C4C2×D3×A413yes—
238C8—34no—
239C8—94no—
240C2×C3—36no—
241C2×C3—31no—
242C2×C3—31no—
243C2×C3—41no—
244C2×C3—46no—
245C2×C3—81no—
246C2×C3—86no—
247C2×C3C2×C8×A416yescomplemented
248C2×C3C22×C4×A411yescharacteristic
249C22—36no—
250C22—31no—
251C22—36no—
252C22—38no—
253C22—31no—
254C22—33no—
255C22—36no—
256C22—312no—
257C22—36no—
258C22A4×C3⋊C814yesdirect product factor
259C22C22×C3×C3⋊C811yescharacteristic, complemented
260C22C2×Dic3×A413yes—
261C4—33no—
262C4—31no—
263C4C2×Dic3×A413yes—
264C4C22×D3×A411yescharacteristic
265C3—41no—
266C3—81no—
267C3C22×C8×A411yescharacteristic, complemented
268C2—31no—
269C2—36no—
270C2—31no—
271C2C2×A4×C3⋊C816yesdirect product factor
272C2C22×Dic3×A411yescharacteristic
subgroupG/H
center, hypercenterC22×C4D3×A4
commutator, hypocenterC22×C3C22×C3×C8
FrattiniC4C22×D3×A4
FittingC24×C3×C4C2×C3
socleC25×C3C3×C4
prime radicalC23×C3×A4C4
cosocleC22×C3×C4C23×C3
LCSG ▷ C22×C3
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4×C3⋊C8C2direct (N × H)
3. C24×C3⋊C8C3semidirect
9. A4×C3⋊C8C22direct (N × H)
16. C23×C3⋊C8C2×C3semidirect
18. C22×C3×A4C8semidirect
46. C22×C3⋊C8A4direct (N × H)
47. C22×C3⋊C8C22×C3semidirect
50. C2×C3×A4C2×C8semidirect
63. C24×C3C3×C8semidirect
67. C22×A4C3⋊C8direct (N × H)
97. C2×C3⋊C8C2×A4direct (N × H)
100. C3×A4C22×C8semidirect
130. C23×C3C2×C3×C8semidirect
135. C2×A4C2×C3⋊C8direct (N × H)
156. C3⋊C8C22×A4direct (N × H)
162. C24C3×C3⋊C8semidirect
199. C22×C3C8×A4semidirect
200. C22×C3C22×C3×C8semidirect
203. A4C22×C3⋊C8direct (N × H)
222. C23C2×C3×C3⋊C8semidirect
247. C2×C3C2×C8×A4semidirect
258. C22A4×C3⋊C8direct (N × H)
259. C22C22×C3×C3⋊C8semidirect
267. C3C22×C8×A4semidirect
271. C2C2×A4×C3⋊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×A4×C3⋊C82
C24×C3⋊C83
C22×C8×A43
C22×C3×C3⋊C84