Finite Group Databasebeta

← A4×#824 #11921328

Subgroups — A4×#824 #11921328

Order 1152.

392 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 57 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×A4×Dic6C211yesmaximal, characteristic
2C3×A4×M16C211yesmaximal, characteristic
3A4×#208C211yesmaximal, characteristic
4C22×#824C311yesmaximal, characteristic, complemented
5A4×#101—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×Dic3×A4C412yes—
8A4×Dic6—21no—
9A4×Dic6—21no—
10C3×C8×A4—21no—
11A4×C3⋊C8—21no—
12C3×#824—41nomaximal
13C23×Dic6C2×C311yescharacteristic
14C2×Q8×A4—31no—
15C22×C3×M16C2×C311yescharacteristic
16C22×#208C2×C311yescharacteristic
17A4×M16—21no—
18A4×M16—31no—
19A4×M16D311yescharacteristic
20C2×#824—31no—
21C2×#824—31no—
22C2×#824—31no—
23C2×#824—31no—
24C22×C3×A4C2×C411yescharacteristic
25C2×C3×Dic6—41no—
26C3×C4×A4D411yescharacteristic
27C3×C4×A4D411yescharacteristic
28Dic3×A4—22no—
29C32×M16—41no—
30C3×#208—41no—
31C22×#101—31noSylow
32C23×C3×C4C22×C311yescharacteristic
33C23×Dic3C3×C412yes—
34C22×Dic6—21no—
35C22×Dic6—21no—
36C22×Dic6—31no—
37C22×Dic6—31no—
38C22×Dic6—32no—
39C22×Dic6—61no—
40C22×Dic6—61no—
41Q8×A4—61no—
42Q8×A4—61no—
43C2×C4×A4—21no—
44C2×C4×A4—32no—
45C2×C4×A4C2×D311yescharacteristic
46C2×C3×M16—31no—
47C2×C3×M16—31no—
48C2×C3×M16—61no—
49C22×C3×C8—21no—
50C2×#208—31no—
51C2×#208—31no—
52C2×#208—61no—
53C22×C3⋊C8—21no—
54C8×A4—22no—
55C8×A4—21no—
56C8×A4—61no—
57C3×#101—121no—
58#824—32no—
59#824—31no—
60#824—31no—
61#824—31no—
62#824A411yescharacteristic, direct product factor
63C2×C3×A4—21no—
64C2×C3×A4C22⋊C411yescharacteristic
65C2×C32×C4—41no—
66C2×C3×Dic3—42no—
67C3×Dic6—81no—
68C3×Dic6—81no—
69C32×C8—81no—
70C3×C3⋊C8—81no—
71C23×Q8—31no—
72C22×M16—31no—
73C22×M16C3×D311yescharacteristic
74C2×#101—91no—
75C2×#101—91no—
76C2×#101—91no—
77C2×#101—91no—
78C24×C3C2×C3×C411yescharacteristic
79C22×A4—21no—
80C22×A4C4×D311yescharacteristic
81C2×C3×Q8—121no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4C3×D411yescharacteristic
87C22×C3×C4C3×D411yescharacteristic
88C22×Dic3—22no—
89C22×Dic3—32no—
90C22×Dic3—32no—
91C22×Dic3—62no—
92C2×Dic6—32no—
93C2×Dic6—31no—
94C2×Dic6—32no—
95C2×Dic6—61no—
96C2×Dic6—61no—
97C2×Dic6—61no—
98C2×Dic6—61no—
99C2×Dic6—64no—
100C2×Dic6—62no—
101C2×Dic6—62no—
102C2×Dic6—61no—
103C2×Dic6—61no—
104C2×Dic6—61no—
105C2×Dic6—61no—
106C2×Dic6C2×A411yescharacteristic
107C4×A4—21no—
108C4×A4—21no—
109C4×A4—62no—
110C4×A4D1211yescharacteristic
111C4×A4#6711yescharacteristic
112C3×M16—31no—
113C3×M16—41no—
114C3×M16—61no—
115C3×M16—61no—
116C3×M16—81no—
117C3×M16—121no—
118C3×M16C2×A411yescharacteristic
119C2×C3×C8—61no—
120C2×C3×C8—61no—
121#208—31no—
122#208—61no—
123#208—61no—
124#208C2×A411yescharacteristic
125C2×C3⋊C8—61no—
126C2×C3⋊C8—61no—
127C22×C32—41no—
128C3×A4#10111yescharacteristic, complemented
129C32×C4—41no—
130C32×C4—41no—
131C3×Dic3—82no—
132C22×Q8—61no—
133C22×Q8—61no—
134C22×Q8—91no—
135C22×Q8—91no—
136C22×Q8—92no—
137C22×Q8—181no—
138C22×Q8—181no—
139C23×C4—32no—
140C23×C4C2×C3×D311yescharacteristic
141C2×M16—31no—
142C2×M16—31no—
143C2×M16—61no—
144C2×M16—91no—
145C2×M16—91no—
146C2×M16—181no—
147C22×C8—21no—
148C22×C8—61no—
149#101—31no—
150#101—91no—
151#101—91no—
152#101—92no—
153#101—91no—
154C23×C3—21no—
155C23×C3—31no—
156C23×C3—31no—
157C23×C3—61no—
158C23×C3C3×C22⋊C411yescharacteristic
159C2×A4—21no—
160C2×A4—21no—
161C2×A4—41no—
162C2×A4(C2×D3)⋊C411yescharacteristic
163C3×Q8—241no—
164C3×Q8—241no—
165C2×C3×C4—32no—
166C2×C3×C4—31no—
167C2×C3×C4—31no—
168C2×C3×C4—31no—
169C2×C3×C4—31no—
170C2×C3×C4—31no—
171C2×C3×C4—31no—
172C2×C3×C4—31no—
173C2×C3×C4—41no—
174C2×C3×C4—81no—
175C2×C3×C4—122no—
176C2×C3×C4C22×A411yescharacteristic
177C2×Dic3—32no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—62no—
182C2×Dic3C4×A412yes—
183Dic6—21no—
184Dic6—21no—
185Dic6—62no—
186Dic6—62no—
187Dic6—62no—
188Dic6—62no—
189Dic6—61no—
190Dic6—61no—
191C3×C8—21no—
192C3×C8—61no—
193C3×C8—81no—
194C3×C8—82no—
195C3×C8—241no—
196C3⋊C8—21no—
197C3⋊C8—61no—
198C2×C32—41no—
199C2×C32—81no—
200C24C3×C4×D311yescharacteristic
201C2×Q8—31no—
202C2×Q8—92no—
203C2×Q8—92no—
204C2×Q8—91no—
205C2×Q8—181no—
206C2×Q8—181no—
207C2×Q8—181no—
208C2×Q8—181no—
209C2×Q8—181no—
210C2×Q8—181no—
211C2×Q8—182no—
212C2×Q8—182no—
213C2×Q8—181no—
214C2×Q8—181no—
215C2×Q8—184no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—31no—
219C22×C4—31no—
220C22×C4—62no—
221C22×C4—92no—
222C22×C4—92no—
223C22×C4—182no—
224C22×C4C3×D1211yescharacteristic
225C22×C4C3×#6711yescharacteristic
226M16—31no—
227M16—31no—
228M16—61no—
229M16—61no—
230M16—91no—
231M16—181no—
232M16—181no—
233M16D3×A411yescharacteristic
234C2×C8—61no—
235C2×C8—61no—
236C2×C8—181no—
237C2×C8—181no—
238C22×C3—31no—
239C22×C3—31no—
240C22×C3—31no—
241C22×C3—41no—
242C22×C3—61no—
243C22×C3—61no—
244C22×C3—61no—
245C22×C3—61no—
246C22×C3—81no—
247C22×C3C3×#10111yescharacteristic, complemented
248C22×C3C2×C4×A411yescharacteristic
249A4—21no—
250A4#82411yescharacteristic, direct product factor
251C3×C4—31no—
252C3×C4—31no—
253C3×C4—41no—
254C3×C4—41no—
255C3×C4—81no—
256C3×C4—81no—
257C3×C4—242no—
258C3×C4D4×A411yescharacteristic
259C3×C4D4×A411yescharacteristic
260Dic3—22no—
261Dic3—62no—
262C32—41noSylow
263C23—21no—
264C23—31no—
265C23—31no—
266C23—61no—
267C23C3×(C2×D3)⋊C411yescharacteristic
268Q8—61no—
269Q8—61no—
270Q8—182no—
271Q8—182no—
272Q8—182no—
273Q8—182no—
274Q8—181no—
275Q8—181no—
276C2×C4—32no—
277C2×C4—31no—
278C2×C4—31no—
279C2×C4—31no—
280C2×C4—31no—
281C2×C4—31no—
282C2×C4—31no—
283C2×C4—31no—
284C2×C4—32no—
285C2×C4—92no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4C2×D3×A411yescharacteristic
291C8—21no—
292C8—61no—
293C8—61no—
294C8—181no—
295C2×C3—21no—
296C2×C3—31no—
297C2×C3—31no—
298C2×C3—41no—
299C2×C3—61no—
300C2×C3—81no—
301C2×C3—81no—
302C2×C3—161no—
303C2×C3A4×C22⋊C411yescharacteristic
304C22—31no—
305C22—31no—
306C22—31no—
307C22—61no—
308C22—61no—
309C22—61no—
310C22—61no—
311C22C3×#82411yescharacteristic, complemented
312C22C4×D3×A411yescharacteristic
313C4—31no—
314C4—31no—
315C4—62no—
316C4—182no—
317C4A4×D1211yescharacteristic
318C4A4×#6711yescharacteristic
319C3—41no—
320C3—81no—
321C3A4×#10111yescharacteristic, complemented
322C2—21no—
323C2—31no—
324C2—31no—
325C2—61no—
326C2A4×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2A4×(C2×D3)⋊C4
commutatorC24×C3C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC22×C3×M16C2×C3
socleC23×C3C3×C22⋊C4
prime radicalC22×C3×A4C2×C4
cosocleC23×C3×C4C22×C3
hypercenterM16D3×A4
hypocenterC22×C3C3×#101
LCSG ▷ C24×C3 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
4. C22×#824C3semidirect
62. #824A4direct (N × H)
128. C3×A4#101semidirect
247. C22×C3C3×#101semidirect
250. A4#824direct (N × H)
311. C22C3×#824semidirect
321. C3A4×#101semidirect

Maximal subgroups

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

subgroupindex
C2×A4×Dic62
C3×A4×M162
A4×#2082
C22×#8243
A4×#1013
C3×#8244