Finite Group Databasebeta

← A4×#833 #11921360

Subgroups — A4×#833 #11921360

Order 1152.

538 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×C3×D4×A4C211yesmaximal, characteristic
2A4×#208C212yesmaximal, complemented
3C22×#833C311yesmaximal, characteristic, complemented
4A4×#100—31nomaximal
5C23×C3×A4C412yes—
6C3×D4×A4—22no—
7C2×C3×C4×A4C2211yescharacteristic
8A4×C3⋊C8—22no—
9C3×#833—41nomaximal
10C23×C3×D4C2×C311yescharacteristic
11C2×D4×A4—21no—
12C2×D4×A4D311yescharacteristic
13C22×#208C2×C312yescomplemented
14A4×M16—32no—
15C2×#833—31no—
16C2×#833—31no—
17C2×#833—32no—
18C22×C3×A4—22no—
19C22×C3×A4—42no—
20C22×C3×A4C2×C411yescharacteristic
21C2×C32×D4—41no—
22C3×C4×A4D412yes—
23C3×#208—42no—
24C22×#100—31noSylow
25C25×C3C3×C412yes—
26C23×A4—22no—
27C23×A4Dic312yes—
28C22×C3×D4—22no—
29C22×C3×D4—31no—
30C22×C3×D4—32no—
31C22×C3×D4—31no—
32C22×C3×D4—62no—
33C23×C3×C4C22×C311yescharacteristic
34D4×A4—24no—
35D4×A4—22no—
36C2×C4×A4—21no—
37C2×C4×A4C2×D311yescharacteristic
38C2×#208—32no—
39C2×#208—32no—
40C2×#208—62no—
41C22×C3⋊C8—22no—
42C8×A4—62no—
43C3×#100—121no—
44#833—32no—
45#833—31no—
46#833—32no—
47#833A411yescharacteristic, direct product factor
48C23×C32—42no—
49C2×C3×A4—21no—
50C2×C3×A4—42no—
51C2×C3×A4C22⋊C411yescharacteristic
52C32×D4—82no—
53C2×C32×C4—41no—
54C3×C3⋊C8—82no—
55C23×D4C3×D311yescharacteristic
56C22×M16—32no—
57C2×#100—91no—
58C2×#100—92no—
59C2×#100—91no—
60C24×C3—22no—
61C24×C3—32no—
62C24×C3—32no—
63C24×C3—42no—
64C24×C3—62no—
65C24×C3—122no—
66C24×C3C2×C3×C411yescharacteristic
67C22×A4—24no—
68C22×A4—22no—
69C22×A4—21no—
70C22×A4—42no—
71C22×A4—44no—
72C22×A4C2×Dic311yescharacteristic
73C2×C3×D4—32no—
74C2×C3×D4—32no—
75C2×C3×D4—31no—
76C2×C3×D4—41no—
77C2×C3×D4—62no—
78C2×C3×D4—62no—
79C2×C3×D4—64no—
80C2×C3×D4—62no—
81C2×C3×D4—64no—
82C2×C3×D4—62no—
83C2×C3×D4—81no—
84C2×C3×D4C2×A411yescharacteristic
85C22×C3×C4—31no—
86C22×C3×C4—32no—
87C22×C3×C4—31no—
88C22×C3×C4C3×D412yes—
89C4×A4—22no—
90C4×A4#6712yes—
91C3×M16—122no—
92#208—32no—
93#208—62no—
94#208—62no—
95#208C2×A412yescomplemented
96C2×C3⋊C8—62no—
97C2×C3⋊C8—62no—
98C22×C32—41no—
99C22×C32—82no—
100C22×C32—162no—
101C3×A4#10011yescharacteristic, complemented
102C32×C4—42no—
103C25C3×Dic312yes—
104C22×D4—22no—
105C22×D4—31no—
106C22×D4—31no—
107C22×D4—32no—
108C22×D4—62no—
109C23×C4C2×C3×D311yescharacteristic
110C2×M16—92no—
111C2×M16—92no—
112C2×M16—182no—
113C22×C8—62no—
114#100—31no—
115#100—92no—
116#100—92no—
117#100—91no—
118C23×C3—21no—
119C23×C3—31no—
120C23×C3—31no—
121C23×C3—32no—
122C23×C3—42no—
123C23×C3—42no—
124C23×C3—62no—
125C23×C3—62no—
126C23×C3—61no—
127C23×C3—62no—
128C23×C3—62no—
129C23×C3—82no—
130C23×C3—122no—
131C23×C3—122no—
132C23×C3—122no—
133C23×C3—122no—
134C23×C3—122no—
135C23×C3—124no—
136C23×C3—124no—
137C23×C3C3×C22⋊C411yescharacteristic
138C23×C3C4×A412yes—
139C2×A4—22no—
140C2×A4—21no—
141C2×A4—21no—
142C2×A4—44no—
143C2×A4—42no—
144C2×A4#21711yescharacteristic
145C3×D4—22no—
146C3×D4—64no—
147C3×D4—64no—
148C3×D4—62no—
149C3×D4—82no—
150C3×D4—84no—
151C2×C3×C4—32no—
152C2×C3×C4—31no—
153C2×C3×C4—32no—
154C2×C3×C4—32no—
155C2×C3×C4—32no—
156C2×C3×C4—41no—
157C2×C3×C4—81no—
158C2×C3×C4C22×A411yescharacteristic
159C3×C8—242no—
160C3⋊C8—22no—
161C3⋊C8—62no—
162C2×C32—41no—
163C2×C32—81no—
164C2×C32—162no—
165C24—22no—
166C24—32no—
167C24—32no—
168C24—42no—
169C24—62no—
170C24—122no—
171C24C2×C3×Dic311yescharacteristic
172C2×D4—32no—
173C2×D4—32no—
174C2×D4—31no—
175C2×D4—62no—
176C2×D4—62no—
177C2×D4—64no—
178C2×D4—62no—
179C2×D4—64no—
180C2×D4—62no—
181C2×D4D3×A411yescharacteristic
182C22×C4—31no—
183C22×C4—32no—
184C22×C4—31no—
185C22×C4C3×#6712yes—
186M16—32no—
187M16—92no—
188M16—182no—
189M16—182no—
190C2×C8—182no—
191C2×C8—182no—
192C22×C3—22no—
193C22×C3—31no—
194C22×C3—31no—
195C22×C3—31no—
196C22×C3—42no—
197C22×C3—41no—
198C22×C3—61no—
199C22×C3—61no—
200C22×C3—61no—
201C22×C3—61no—
202C22×C3—62no—
203C22×C3—82no—
204C22×C3—84no—
205C22×C3—81no—
206C22×C3—122no—
207C22×C3—122no—
208C22×C3—122no—
209C22×C3—122no—
210C22×C3—122no—
211C22×C3—124no—
212C22×C3—124no—
213C22×C3—162no—
214C22×C3—164no—
215C22×C3C3×#10011yescharacteristic, complemented
216C22×C3C2×C4×A411yescharacteristic
217A4—21no—
218A4#83311yescharacteristic, direct product factor
219C3×C4—32no—
220C3×C4—42no—
221C3×C4—82no—
222C3×C4D4×A412yes—
223C32—41noSylow
224C23—21no—
225C23—31no—
226C23—31no—
227C23—32no—
228C23—42no—
229C23—62no—
230C23—62no—
231C23—61no—
232C23—62no—
233C23—62no—
234C23—122no—
235C23—122no—
236C23—122no—
237C23—122no—
238C23—122no—
239C23—124no—
240C23—124no—
241C23C3×#21711yescharacteristic
242C23Dic3×A412yes—
243D4—22no—
244D4—64no—
245D4—64no—
246D4—62no—
247C2×C4—32no—
248C2×C4—31no—
249C2×C4—32no—
250C2×C4—32no—
251C2×C4—32no—
252C2×C4C2×D3×A411yescharacteristic
253C8—62no—
254C8—182no—
255C2×C3—21no—
256C2×C3—31no—
257C2×C3—31no—
258C2×C3—42no—
259C2×C3—41no—
260C2×C3—61no—
261C2×C3—81no—
262C2×C3—82no—
263C2×C3—81no—
264C2×C3—122no—
265C2×C3—162no—
266C2×C3—164no—
267C2×C3A4×C22⋊C411yescharacteristic
268C22—22no—
269C22—31no—
270C22—31no—
271C22—31no—
272C22—42no—
273C22—61no—
274C22—61no—
275C22—61no—
276C22—61no—
277C22—62no—
278C22—122no—
279C22—122no—
280C22—122no—
281C22—122no—
282C22—122no—
283C22—124no—
284C22—124no—
285C22C3×#83311yescharacteristic, complemented
286C22C2×Dic3×A411yescharacteristic
287C4—32no—
288C4A4×#6712yes—
289C3—41no—
290C3—81no—
291C3A4×#10011yescharacteristic, complemented
292C2—21no—
293C2—31no—
294C2—31no—
295C2—42no—
296C2—61no—
297C2—122no—
298C2A4×#21711yescharacteristic
subgroupG/H
centerC2A4×#217
commutatorC24×C3C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC23×C3×D4C2×C3
socleC23×C3C3×C22⋊C4
prime radicalC2×C3×D4×A4C2
cosocleC23×C3×C4C22×C3
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×#100
LCSG ▷ C24×C3 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. A4×#208C2semidirect
3. C22×#833C3semidirect
13. C22×#208C2×C3semidirect
47. #833A4direct (N × H)
95. #208C2×A4semidirect
101. C3×A4#100semidirect
215. C22×C3C3×#100semidirect
218. A4#833direct (N × H)
285. C22C3×#833semidirect
291. C3A4×#100semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
A4×#2082
C22×#8333
A4×#1003
C3×#8334