Finite Group Databasebeta

← A4×#823 #11921327

Subgroups — A4×#823 #11921327

Order 1152.

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

normal subgroups only

This group has 504 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×D12C211yesmaximal, characteristic
2C3×A4×M16C211yesmaximal, characteristic, complemented
3A4×#208C211yesmaximal, characteristic, complemented
4C22×#823C311yesmaximal, characteristic, complemented
5A4×#100—31nomaximal
6C22×D3×A4C412yes—
7C2×C3×C4×A4C2211yescharacteristic
8A4×D12—21no—
9A4×D12—21no—
10C3×C8×A4—21no—
11A4×C3⋊C8—21no—
12C3×#823—41nomaximal
13C23×D12C2×C311yescharacteristic
14C2×D4×A4—31no—
15C22×C3×M16C2×C311yescharacteristic, complemented
16C22×#208C2×C311yescharacteristic, complemented
17A4×M16—21no—
18A4×M16—31no—
19A4×M16D311yescharacteristic, complemented
20C2×#823—31no—
21C2×#823—31no—
22C2×#823—31no—
23C2×#823—31no—
24C22×C3×A4C2×C411yescharacteristic
25C2×D3×A4—22no—
26C2×D3×A4—42no—
27C2×C3×D12—41no—
28C3×C4×A4D411yescharacteristic
29C3×C4×A4D411yescharacteristic
30C32×M16—41no—
31C3×#208—41no—
32C22×#100—31noSylow
33C24×D3C3×C412yes—
34C23×A4—32no—
35C23×C3×C4C22×C311yescharacteristic
36C22×D12—21no—
37C22×D12—21no—
38C22×D12—31no—
39C22×D12—31no—
40C22×D12—32no—
41C22×D12—61no—
42C22×D12—61no—
43D4×A4—61no—
44D4×A4—61no—
45C2×C4×A4—21no—
46C2×C4×A4C2×D311yescharacteristic
47C2×C3×M16—31no—
48C2×C3×M16—31no—
49C2×C3×M16—61no—
50C22×C3×C8—21no—
51C2×#208—31no—
52C2×#208—31no—
53C2×#208—61no—
54C22×C3⋊C8—21no—
55C8×A4—22no—
56C8×A4—21no—
57C8×A4—61no—
58C3×#100—121no—
59#823—32no—
60#823—31no—
61#823—31no—
62#823—31no—
63#823A411yescharacteristic, direct product factor
64C22×C3×D3—42no—
65C2×C3×A4—21no—
66C2×C3×A4C22⋊C411yescharacteristic
67D3×A4—42no—
68C2×C32×C4—41no—
69C3×D12—81no—
70C3×D12—81no—
71C32×C8—81no—
72C3×C3⋊C8—81no—
73C23×D4—31no—
74C22×M16—31no—
75C22×M16C3×D311yescharacteristic, complemented
76C2×#100—91no—
77C2×#100—91no—
78C2×#100—91no—
79C2×#100—91no—
80C24×C3C2×C3×C411yescharacteristic
81C23×D3—22no—
82C23×D3—32no—
83C23×D3—32no—
84C23×D3—42no—
85C23×D3—62no—
86C23×D3—122no—
87C22×A4—21no—
88C22×A4—62no—
89C22×A4—122no—
90C22×A4C4×D311yescharacteristic
91C2×C3×D4—121no—
92C22×C3×C4—31no—
93C22×C3×C4—31no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C22×C3×C4C3×D411yescharacteristic
97C22×C3×C4C3×D411yescharacteristic
98C2×D12—32no—
99C2×D12—32no—
100C2×D12—31no—
101C2×D12—61no—
102C2×D12—61no—
103C2×D12—61no—
104C2×D12—61no—
105C2×D12—64no—
106C2×D12—62no—
107C2×D12—62no—
108C2×D12—61no—
109C2×D12—61no—
110C2×D12—61no—
111C2×D12—61no—
112C2×D12C2×A411yescharacteristic
113C4×A4—21no—
114C4×A4—21no—
115C4×A4D1211yescharacteristic
116C4×A4#6711yescharacteristic
117C3×M16—31no—
118C3×M16—41no—
119C3×M16—61no—
120C3×M16—61no—
121C3×M16—81no—
122C3×M16—121no—
123C3×M16C2×A411yescharacteristic, complemented
124C2×C3×C8—61no—
125C2×C3×C8—61no—
126#208—31no—
127#208—61no—
128#208—61no—
129#208C2×A411yescharacteristic, complemented
130C2×C3⋊C8—61no—
131C2×C3⋊C8—61no—
132C22×C32—41no—
133C2×C3×D3—82no—
134C2×C3×D3—162no—
135C3×A4#10011yescharacteristic, complemented
136C32×C4—41no—
137C32×C4—41no—
138C25—32no—
139C22×D4—61no—
140C22×D4—61no—
141C22×D4—91no—
142C22×D4—91no—
143C22×D4—92no—
144C22×D4—181no—
145C22×D4—181no—
146C23×C4C2×C3×D311yescharacteristic
147C2×M16—31no—
148C2×M16—31no—
149C2×M16—61no—
150C2×M16—91no—
151C2×M16—91no—
152C2×M16—181no—
153C22×C8—21no—
154C22×C8—61no—
155#100—31no—
156#100—91no—
157#100—91no—
158#100—92no—
159#100—91no—
160C23×C3—21no—
161C23×C3—31no—
162C23×C3—31no—
163C23×C3—61no—
164C23×C3—122no—
165C23×C3C3×C22⋊C411yescharacteristic
166C22×D3—32no—
167C22×D3—42no—
168C22×D3—62no—
169C22×D3—62no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—122no—
173C22×D3—122no—
174C22×D3—124no—
175C22×D3—124no—
176C22×D3—122no—
177C22×D3—122no—
178C22×D3—122no—
179C22×D3C4×A412yes—
180C2×A4—21no—
181C2×A4—21no—
182C2×A4—41no—
183C2×A4—122no—
184C2×A4(C2×D3)⋊C411yescharacteristic
185C3×D4—241no—
186C3×D4—241no—
187C2×C3×C4—32no—
188C2×C3×C4—31no—
189C2×C3×C4—31no—
190C2×C3×C4—31no—
191C2×C3×C4—31no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—41no—
196C2×C3×C4—81no—
197C2×C3×C4C22×A411yescharacteristic
198D12—21no—
199D12—21no—
200D12—62no—
201D12—62no—
202D12—62no—
203D12—62no—
204D12—61no—
205D12—61no—
206C3×C8—21no—
207C3×C8—61no—
208C3×C8—81no—
209C3×C8—82no—
210C3×C8—241no—
211C3⋊C8—21no—
212C3⋊C8—61no—
213C2×C32—41no—
214C2×C32—81no—
215C3×D3—162no—
216C24—62no—
217C24—92no—
218C24—92no—
219C24—122no—
220C24—182no—
221C24—362no—
222C24C3×C4×D311yescharacteristic
223C2×D4—31no—
224C2×D4—92no—
225C2×D4—92no—
226C2×D4—91no—
227C2×D4—181no—
228C2×D4—181no—
229C2×D4—181no—
230C2×D4—181no—
231C2×D4—184no—
232C2×D4—181no—
233C2×D4—181no—
234C2×D4—182no—
235C2×D4—182no—
236C2×D4—181no—
237C2×D4—181no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4C3×D1211yescharacteristic
243C22×C4C3×#6711yescharacteristic
244M16—31no—
245M16—31no—
246M16—61no—
247M16—61no—
248M16—91no—
249M16—181no—
250M16—181no—
251M16D3×A411yescharacteristic, complemented
252C2×C8—61no—
253C2×C8—61no—
254C2×C8—181no—
255C2×C8—181no—
256C22×C3—31no—
257C22×C3—31no—
258C22×C3—31no—
259C22×C3—41no—
260C22×C3—61no—
261C22×C3—61no—
262C22×C3—61no—
263C22×C3—61no—
264C22×C3—81no—
265C22×C3—242no—
266C22×C3—482no—
267C22×C3C3×#10011yescharacteristic, complemented
268C22×C3C2×C4×A411yescharacteristic
269C2×D3—22no—
270C2×D3—42no—
271C2×D3—62no—
272C2×D3—122no—
273C2×D3—122no—
274C2×D3—124no—
275C2×D3—122no—
276C2×D3—122no—
277C2×D3—122no—
278C2×D3—124no—
279A4—21no—
280A4#82311yescharacteristic, direct product factor
281C3×C4—31no—
282C3×C4—31no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—81no—
286C3×C4—81no—
287C3×C4D4×A411yescharacteristic
288C3×C4D4×A411yescharacteristic
289C32—41noSylow
290C23—21no—
291C23—31no—
292C23—31no—
293C23—32no—
294C23—61no—
295C23—92no—
296C23—122no—
297C23—182no—
298C23—182no—
299C23—182no—
300C23—182no—
301C23—362no—
302C23—362no—
303C23—362no—
304C23—362no—
305C23—362no—
306C23—364no—
307C23—364no—
308C23C3×(C2×D3)⋊C411yescharacteristic
309D4—61no—
310D4—61no—
311D4—182no—
312D4—182no—
313D4—182no—
314D4—182no—
315D4—181no—
316D4—181no—
317C2×C4—32no—
318C2×C4—31no—
319C2×C4—31no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4C2×D3×A411yescharacteristic
326C8—21no—
327C8—61no—
328C8—61no—
329C8—181no—
330C2×C3—21no—
331C2×C3—31no—
332C2×C3—31no—
333C2×C3—41no—
334C2×C3—61no—
335C2×C3—81no—
336C2×C3—81no—
337C2×C3—161no—
338C2×C3—482no—
339C2×C3A4×C22⋊C411yescharacteristic
340D3—42no—
341D3—122no—
342C22—31no—
343C22—31no—
344C22—31no—
345C22—61no—
346C22—61no—
347C22—61no—
348C22—61no—
349C22—62no—
350C22—122no—
351C22—182no—
352C22—362no—
353C22—362no—
354C22—362no—
355C22—362no—
356C22—362no—
357C22—364no—
358C22—364no—
359C22C3×#82311yescharacteristic, complemented
360C22C4×D3×A411yescharacteristic
361C4—31no—
362C4—31no—
363C4A4×D1211yescharacteristic
364C4A4×#6711yescharacteristic
365C3—41no—
366C3—81no—
367C3A4×#10011yescharacteristic, complemented
368C2—21no—
369C2—31no—
370C2—31no—
371C2—61no—
372C2—122no—
373C2—362no—
374C2A4×(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 radicalC2×A4×D12C2
cosocleC23×C3×C4C22×C3
hypercenterM16D3×A4
hypocenterC22×C3C3×#100
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
2. C3×A4×M16C2semidirect
3. A4×#208C2semidirect
4. C22×#823C3semidirect
15. C22×C3×M16C2×C3semidirect
16. C22×#208C2×C3semidirect
19. A4×M16D3semidirect
63. #823A4direct (N × H)
75. C22×M16C3×D3semidirect
123. C3×M16C2×A4semidirect
129. #208C2×A4semidirect
135. C3×A4#100semidirect
251. M16D3×A4semidirect
267. C22×C3C3×#100semidirect
280. A4#823direct (N × H)
359. C22C3×#823semidirect
367. C3A4×#100semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D122
C3×A4×M162
A4×#2082
C22×#8233
A4×#1003
C3×#8234