Finite Group Databasebeta

← A4×C4⋊(C3⋊C8) #11921245

Subgroups — A4×C4⋊(C3⋊C8) #11921245

Order 1152.

370 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C3×C42×A4C211yesmaximal, characteristic
2C2×A4×C3⋊C8C212yesmaximal
3C22×C4⋊(C3⋊C8)C311yesmaximal, characteristic, complemented
4A4×C4⋊C8—31nomaximal
5C2×C3×C4×A4C411yescharacteristic
6C2×C3×C4×A4C411yescharacteristic
7C2×C3×C4×A4C2211yescharacteristic
8A4×C3⋊C8—22no—
9C3×C4⋊(C3⋊C8)—41nomaximal
10C22×C3×C42C2×C311yescharacteristic
11C23×C3⋊C8C2×C312yes—
12C2×C8×A4—32no—
13C42×A4—21no—
14C42×A4D311yescharacteristic
15C2×C4⋊(C3⋊C8)—31no—
16C2×C4⋊(C3⋊C8)—31no—
17C2×C4⋊(C3⋊C8)—32no—
18C22×C3×A4C2×C411yescharacteristic
19C3×C4×A4—21no—
20C3×C4×A4C812yescomplemented
21C3×C4×A4D411yescharacteristic
22C3×C4×A4Q811yescharacteristic
23C32×C42—41no—
24C2×C3×C3⋊C8—42no—
25C22×C4⋊C8—31noSylow
26C23×C3×C4C3×C411yescharacteristic
27C23×C3×C4C3×C411yescharacteristic
28C23×C3×C4C22×C311yescharacteristic
29C2×C4×A4—21no—
30C2×C4×A4—21no—
31C2×C4×A4—21no—
32C2×C4×A4Dic311yescharacteristic
33C2×C4×A4Dic311yescharacteristic
34C2×C4×A4C2×D311yescharacteristic
35C2×C3×C42—31no—
36C2×C3×C42—31no—
37C2×C3×C42—31no—
38C2×C3×C42—31no—
39C22×C3⋊C8—22no—
40C22×C3⋊C8—32no—
41C22×C3⋊C8—32no—
42C22×C3⋊C8—62no—
43C8×A4—62no—
44C3×C4⋊C8—121no—
45C4⋊(C3⋊C8)—32no—
46C4⋊(C3⋊C8)—31no—
47C4⋊(C3⋊C8)—32no—
48C4⋊(C3⋊C8)A411yescharacteristic, direct product factor
49C2×C3×A4C4⋊C411yescharacteristic
50C2×C3×A4C2×C811yescharacteristic
51C2×C3×A4M1611yescharacteristic
52C2×C32×C4—41no—
53C2×C32×C4—41no—
54C2×C32×C4—41no—
55C3×C3⋊C8—82no—
56C23×C8—32no—
57C22×C42C3×D311yescharacteristic
58C2×C4⋊C8—91no—
59C2×C4⋊C8—92no—
60C2×C4⋊C8—91no—
61C24×C3C2×C3×C411yescharacteristic
62C22×A4—21no—
63C22×A4C2×Dic311yescharacteristic
64C22×C3×C4—21no—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—31no—
70C22×C3×C4—32no—
71C22×C3×C4—31no—
72C22×C3×C4—31no—
73C22×C3×C4—31no—
74C22×C3×C4—61no—
75C22×C3×C4C3×C812yescomplemented
76C22×C3×C4C3×D411yescharacteristic
77C22×C3×C4C3×Q811yescharacteristic
78C4×A4—22no—
79C4×A4—21no—
80C4×A4—22no—
81C4×A4—21no—
82C4×A4—21no—
83C4×A4C3⋊C812yescomplemented
84C4×A4Dic611yescharacteristic
85C4×A4D1211yescharacteristic
86C2×C3×C8—122no—
87C3×C42—32no—
88C3×C42—31no—
89C3×C42—31no—
90C3×C42—31no—
91C3×C42—41no—
92C3×C42—81no—
93C3×C42C2×A411yescharacteristic
94C2×C3⋊C8—32no—
95C2×C3⋊C8—62no—
96C2×C3⋊C8—62no—
97C2×C3⋊C8—62no—
98C2×C3⋊C8—62no—
99C2×C3⋊C8C2×A412yes—
100C22×C32—41no—
101C3×A4C4⋊C811yescharacteristic, complemented
102C32×C4—42no—
103C32×C4—41no—
104C32×C4—41no—
105C32×C4—81no—
106C23×C4C3×Dic311yescharacteristic
107C23×C4C3×Dic311yescharacteristic
108C23×C4C2×C3×D311yescharacteristic
109C22×C8—62no—
110C22×C8—92no—
111C22×C8—92no—
112C22×C8—182no—
113C2×C42—31no—
114C2×C42—31no—
115C2×C42—31no—
116C2×C42—31no—
117C4⋊C8—31no—
118C4⋊C8—92no—
119C4⋊C8—92no—
120C4⋊C8—91no—
121C23×C3—31no—
122C23×C3—31no—
123C23×C3—31no—
124C23×C3—31no—
125C23×C3C3×C4⋊C411yescharacteristic
126C23×C3C2×C3×C811yescharacteristic
127C23×C3C3×M1611yescharacteristic
128C2×A4—21no—
129C2×A4—21no—
130C2×A4—21no—
131C2×A4C2×C3⋊C811yescharacteristic
132C2×A4#20811yescharacteristic
133C2×A4C4⋊Dic311yescharacteristic
134C2×C3×C4—32no—
135C2×C3×C4—32no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—32no—
139C2×C3×C4—32no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—31no—
143C2×C3×C4—31no—
144C2×C3×C4—32no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—41no—
149C2×C3×C4—41no—
150C2×C3×C4—41no—
151C2×C3×C4—61no—
152C2×C3×C4—61no—
153C2×C3×C4—61no—
154C2×C3×C4—61no—
155C2×C3×C4—81no—
156C2×C3×C4—81no—
157C2×C3×C4—81no—
158C2×C3×C4C4×A411yescharacteristic
159C2×C3×C4C4×A411yescharacteristic
160C2×C3×C4C22×A411yescharacteristic
161C3×C8—242no—
162C3⋊C8—22no—
163C3⋊C8—62no—
164C2×C32—41no—
165C2×C32—41no—
166C2×C32—41no—
167C24C2×C3×Dic311yescharacteristic
168C22×C4—21no—
169C22×C4—31no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—31no—
173C22×C4—31no—
174C22×C4—32no—
175C22×C4—31no—
176C22×C4—31no—
177C22×C4—31no—
178C22×C4—61no—
179C22×C4C3×C3⋊C812yescomplemented
180C22×C4C3×Dic611yescharacteristic
181C22×C4C3×D1211yescharacteristic
182C2×C8—32no—
183C2×C8—92no—
184C2×C8—182no—
185C2×C8—182no—
186C2×C8—182no—
187C2×C8—182no—
188C42—32no—
189C42—31no—
190C42—31no—
191C42—31no—
192C42D3×A411yescharacteristic
193C22×C3—31no—
194C22×C3—31no—
195C22×C3—31no—
196C22×C3—32no—
197C22×C3—31no—
198C22×C3—31no—
199C22×C3—31no—
200C22×C3—31no—
201C22×C3—31no—
202C22×C3—31no—
203C22×C3—41no—
204C22×C3—81no—
205C22×C3C3×C4⋊C811yescharacteristic, complemented
206C22×C3C2×C4×A411yescharacteristic
207A4—21no—
208A4C4⋊(C3⋊C8)11yescharacteristic, direct product factor
209C3×C4—21no—
210C3×C4—31no—
211C3×C4—31no—
212C3×C4—32no—
213C3×C4—41no—
214C3×C4—42no—
215C3×C4—41no—
216C3×C4—61no—
217C3×C4—81no—
218C3×C4—82no—
219C3×C4—81no—
220C3×C4—82no—
221C3×C4—81no—
222C3×C4C8×A412yescomplemented
223C3×C4D4×A411yescharacteristic
224C3×C4Q8×A411yescharacteristic
225C32—41noSylow
226C23—31no—
227C23—31no—
228C23—31no—
229C23—31no—
230C23C2×C3×C3⋊C811yescharacteristic
231C23C3×#20811yescharacteristic
232C23C3×C4⋊Dic311yescharacteristic
233C2×C4—32no—
234C2×C4—32no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—31no—
242C2×C4—31no—
243C2×C4—32no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—31no—
247C2×C4—61no—
248C2×C4—61no—
249C2×C4—61no—
250C2×C4—61no—
251C2×C4Dic3×A411yescharacteristic
252C2×C4Dic3×A411yescharacteristic
253C2×C4C2×D3×A411yescharacteristic
254C8—62no—
255C8—182no—
256C2×C3—31no—
257C2×C3—31no—
258C2×C3—31no—
259C2×C3—31no—
260C2×C3—41no—
261C2×C3—41no—
262C2×C3—41no—
263C2×C3—81no—
264C2×C3—81no—
265C2×C3—81no—
266C2×C3A4×C4⋊C411yescharacteristic
267C2×C3C2×C8×A411yescharacteristic
268C2×C3A4×M1611yescharacteristic
269C22—31no—
270C22—31no—
271C22—31no—
272C22—32no—
273C22—31no—
274C22—31no—
275C22—31no—
276C22—31no—
277C22—31no—
278C22—31no—
279C22C3×C4⋊(C3⋊C8)11yescharacteristic, complemented
280C22C2×Dic3×A411yescharacteristic
281C4—21no—
282C4—32no—
283C4—31no—
284C4—31no—
285C4—61no—
286C4A4×C3⋊C812yescomplemented
287C4A4×Dic611yescharacteristic
288C4A4×D1211yescharacteristic
289C3—41no—
290C3—81no—
291C3A4×C4⋊C811yescharacteristic, complemented
292C2—31no—
293C2—31no—
294C2—31no—
295C2—31no—
296C2C2×A4×C3⋊C811yescharacteristic
297C2A4×#20811yescharacteristic
298C2A4×C4⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×A4
commutatorC23×C3C2×C3×C8
FittingC22×C3×C42C2×C3
socleC24×C3C2×C3×C4
prime radicalC22×C3×A4C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC42D3×A4
hypocenterC22×C3C3×C4⋊C8
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊(C3⋊C8)C3semidirect
20. C3×C4×A4C8semidirect
48. C4⋊(C3⋊C8)A4direct (N × H)
75. C22×C3×C4C3×C8semidirect
83. C4×A4C3⋊C8semidirect
101. C3×A4C4⋊C8semidirect
179. C22×C4C3×C3⋊C8semidirect
205. C22×C3C3×C4⋊C8semidirect
208. A4C4⋊(C3⋊C8)direct (N × H)
222. C3×C4C8×A4semidirect
279. C22C3×C4⋊(C3⋊C8)semidirect
286. C4A4×C3⋊C8semidirect
291. C3A4×C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C3×C42×A42
C2×A4×C3⋊C82
C22×C4⋊(C3⋊C8)3
A4×C4⋊C83
C3×C4⋊(C3⋊C8)4