Finite Group Databasebeta

← A4×#948 #11923374

Subgroups — A4×#948 #11923374

Order 1152.

748 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 135 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×A4×#41C211yesmaximal, characteristic
2A4×#208C213yesmaximal, complemented
3C2×A4×C3⋊C8C213yesmaximal, complemented
4C22×#948C311yesmaximal, characteristic, complemented
5A4×#131—31nomaximal
6C3×Q8×A4C411yescharacteristic
7C3×D4×A4C413yes—
8C2×C3×C4×A4C2213yes—
9C3×#948—41nomaximal
10A4×C3⋊C8C2211yescharacteristic
11A4×C3⋊C8C2213yes—
12C22×C3×#41C2×C311yescharacteristic
13A4×#41—21no—
14A4×#41D311yescharacteristic
15C2×#948—31no—
16C2×#948—33no—
17C2×#948—33no—
18C2×#948—31no—
19C22×#208C2×C313yescomplemented
20C23×C3⋊C8C2×C313yescomplemented
21A4×M16—33no—
22C2×C8×A4—33no—
23C22×C3×A4C2×C413yes—
24C32×#41—41no—
25C3×C4×A4C2×C413yes—
26C3×C4×A4C2311yescharacteristic
27C3×#208—43no—
28C2×C3×C3⋊C8—43no—
29C22×#131—31noSylow
30C2×C3×#41—33no—
31C2×C3×#41—31no—
32C2×C3×#41—33no—
33C2×C3×#41—31no—
34C22×C3×Q8C3×C411yescharacteristic
35C22×C3×D4C3×C413yes—
36C23×C3×C4C22×C313yes—
37Q8×A4—21no—
38Q8×A4Dic311yescharacteristic
39D4×A4—23no—
40D4×A4Dic313yes—
41C2×C4×A4—23no—
42C2×C4×A4C2×D313yes—
43C3×#131—121no—
44#948—36no—
45#948—36no—
46#948—32no—
47#948—31no—
48#948—33no—
49#948—33no—
50#948A411yescharacteristic, direct product factor
51C2×#208—33no—
52C2×#208—36no—
53C2×#208—33no—
54C22×C3⋊C8—33no—
55C22×C3⋊C8—33no—
56C22×C3⋊C8—33no—
57C22×C3⋊C8—33no—
58C22×C3⋊C8C22×C311yescharacteristic
59C22×C3⋊C8C22×C313yes—
60C8×A4—31no—
61C8×A4—33no—
62C2×C3×A4—23no—
63C2×C3×A4C22×C411yescharacteristic
64C32×Q8—41no—
65C32×D4—43no—
66C2×C32×C4—43no—
67C3×C3⋊C8—41no—
68C3×C3⋊C8—43no—
69C22×#41C3×D311yescharacteristic
70C2×#131—91no—
71C2×#131—93no—
72C2×#131—93no—
73C2×#131—91no—
74C22×M16—33no—
75C23×C8—33no—
76C24×C3C2×C3×C413yes—
77C22×A4—23no—
78C22×A4C2×Dic313yes—
79C3×#41—32no—
80C3×#41—36no—
81C3×#41—36no—
82C3×#41—31no—
83C3×#41—33no—
84C3×#41—33no—
85C3×#41—41no—
86C3×#41—81no—
87C3×#41C2×A411yescharacteristic
88C2×C3×Q8—33no—
89C2×C3×Q8—31no—
90C2×C3×D4—33no—
91C2×C3×D4—33no—
92C2×C3×D4—36no—
93C22×C3×C4—33no—
94C22×C3×C4—33no—
95C22×C3×C4—33no—
96C22×C3×C4—33no—
97C22×C3×C4C2×C3×C413yes—
98C22×C3×C4C23×C311yescharacteristic
99C4×A4—23no—
100C4×A4—21no—
101C4×A4C2×Dic313yes—
102C4×A4C22×D311yescharacteristic
103C3×M16—123no—
104C2×C3×C8—123no—
105#208—36no—
106#208—33no—
107#208—36no—
108#208C2×A413yescomplemented
109C2×C3⋊C8—36no—
110C2×C3⋊C8—33no—
111C2×C3⋊C8—31no—
112C2×C3⋊C8—33no—
113C2×C3⋊C8—33no—
114C2×C3⋊C8—33no—
115C2×C3⋊C8—31no—
116C2×C3⋊C8—33no—
117C2×C3⋊C8C2×A413yescomplemented
118C22×C32—43no—
119C3×A4#13111yescharacteristic, complemented
120C32×C4—43no—
121C32×C4—41no—
122C2×#41—33no—
123C2×#41—33no—
124C2×#41—31no—
125C2×#41—31no—
126C22×Q8C3×Dic311yescharacteristic
127C22×D4C3×Dic313yes—
128C23×C4C2×C3×D313yes—
129#131—31no—
130#131—93no—
131#131—93no—
132#131—92no—
133#131—96no—
134#131—96no—
135#131—91no—
136C2×M16—93no—
137C2×M16—96no—
138C2×M16—93no—
139C22×C8—31no—
140C22×C8—33no—
141C22×C8—93no—
142C22×C8—93no—
143C22×C8—93no—
144C22×C8—93no—
145C23×C3—23no—
146C23×C3—33no—
147C23×C3—33no—
148C23×C3—63no—
149C23×C3C22×C3×C411yescharacteristic
150C2×A4—23no—
151C2×A4—21no—
152C2×A4—43no—
153C2×A4C22×Dic311yescharacteristic
154C3×Q8—32no—
155C3×Q8—33no—
156C3×Q8—41no—
157C3×Q8—81no—
158C3×Q8C4×A411yescharacteristic
159C3×D4—36no—
160C3×D4—36no—
161C3×D4—33no—
162C3×D4—43no—
163C3×D4—83no—
164C3×D4C4×A413yes—
165C2×C3×C4—36no—
166C2×C3×C4—33no—
167C2×C3×C4—33no—
168C2×C3×C4—33no—
169C2×C3×C4—31no—
170C2×C3×C4—33no—
171C2×C3×C4—31no—
172C2×C3×C4—33no—
173C2×C3×C4—43no—
174C2×C3×C4—83no—
175C2×C3×C4C22×A413yes—
176C3×C8—121no—
177C3×C8—123no—
178C3⋊C8—31no—
179C3⋊C8—33no—
180C3⋊C8C22×A411yescharacteristic
181C3⋊C8C22×A413yes—
182C2×C32—41no—
183C2×C32—83no—
184C24C2×C3×Dic313yes—
185#41—32no—
186#41—36no—
187#41—36no—
188#41—31no—
189#41—33no—
190#41—33no—
191#41D3×A411yescharacteristic
192C2×Q8—33no—
193C2×Q8—31no—
194C2×D4—33no—
195C2×D4—33no—
196C2×D4—36no—
197C22×C4—33no—
198C22×C4—33no—
199C22×C4—33no—
200C22×C4—33no—
201C22×C4C2×C3×Dic313yes—
202C22×C4C22×C3×D311yescharacteristic
203M16—33no—
204M16—96no—
205M16—96no—
206M16—93no—
207C2×C8—33no—
208C2×C8—91no—
209C2×C8—93no—
210C2×C8—93no—
211C2×C8—93no—
212C2×C8—96no—
213C2×C8—93no—
214C2×C8—91no—
215C2×C8—93no—
216C22×C3—31no—
217C22×C3—31no—
218C22×C3—33no—
219C22×C3—43no—
220C22×C3—63no—
221C22×C3—63no—
222C22×C3—63no—
223C22×C3—63no—
224C22×C3—83no—
225C22×C3C3×#13111yescharacteristic, complemented
226C22×C3C2×C4×A413yes—
227A4—21no—
228A4#94811yescharacteristic, direct product factor
229C3×C4—31no—
230C3×C4—33no—
231C3×C4—43no—
232C3×C4—41no—
233C3×C4—83no—
234C3×C4—81no—
235C3×C4C2×C4×A413yes—
236C3×C4C23×A411yescharacteristic
237C32—41noSylow
238C23—23no—
239C23—33no—
240C23—33no—
241C23—63no—
242C23C22×C3×Dic311yescharacteristic
243Q8—32no—
244Q8—33no—
245Q8Dic3×A411yescharacteristic
246D4—36no—
247D4—36no—
248D4—33no—
249D4Dic3×A413yes—
250C2×C4—36no—
251C2×C4—33no—
252C2×C4—33no—
253C2×C4—33no—
254C2×C4—31no—
255C2×C4—33no—
256C2×C4—31no—
257C2×C4—33no—
258C2×C4C2×D3×A413yes—
259C8—31no—
260C8—33no—
261C8—91no—
262C8—93no—
263C2×C3—23no—
264C2×C3—31no—
265C2×C3—31no—
266C2×C3—41no—
267C2×C3—63no—
268C2×C3—83no—
269C2×C3—81no—
270C2×C3—163no—
271C2×C3C22×C4×A411yescharacteristic
272C22—31no—
273C22—31no—
274C22—33no—
275C22—63no—
276C22—63no—
277C22—63no—
278C22—63no—
279C22C3×#94811yescharacteristic, complemented
280C22C2×Dic3×A413yes—
281C4—31no—
282C4—33no—
283C4C2×Dic3×A413yes—
284C4C22×D3×A411yescharacteristic
285C3—41no—
286C3—81no—
287C3A4×#13111yescharacteristic, complemented
288C2—23no—
289C2—31no—
290C2—31no—
291C2—63no—
292C2C22×Dic3×A411yescharacteristic
subgroupG/H
center, FrattiniC4C22×D3×A4
commutator, socleC23×C3C22×C3×C4
FittingC22×C3×#41C2×C3
prime radicalC3×A4×#41C2
cosocleC22×C3×C4C23×C3
hypercenter#41D3×A4
hypocenterC22×C3C3×#131
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. A4×#208C2semidirect
3. C2×A4×C3⋊C8C2semidirect
4. C22×#948C3semidirect
19. C22×#208C2×C3semidirect
20. C23×C3⋊C8C2×C3semidirect
50. #948A4direct (N × H)
108. #208C2×A4semidirect
117. C2×C3⋊C8C2×A4semidirect
119. C3×A4#131semidirect
225. C22×C3C3×#131semidirect
228. A4#948direct (N × H)
279. C22C3×#948semidirect
287. C3A4×#131semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
A4×#2082
C2×A4×C3⋊C82
C22×#9483
A4×#1313
C3×#9484