Finite Group Databasebeta

← A4×#837 #11921367

Subgroups — A4×#837 #11921367

Order 1152.

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

normal subgroups only

This group has 472 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
1C3×A4×#41C211yesmaximal, characteristic
2C4×Dic3×A4C211yesmaximal, characteristic, complemented
3A4×#208C211yesmaximal, characteristic, complemented
4C22×#837C311yesmaximal, characteristic, complemented
5A4×#104—31nomaximal
6C3×Q8×A4C411yescharacteristic, complemented
7C3×D4×A4—21no—
8C3×D4×A4C411yescharacteristic, complemented
9C2×C3×C4×A4—21no—
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4—21no—
12A4×C3⋊C8—21no—
13C3×#837—41nomaximal
14C22×C3×#41C2×C311yescharacteristic
15A4×#41—21no—
16A4×#41D311yescharacteristic
17C22×C4×Dic3C2×C311yescharacteristic, complemented
18C22×#208C2×C311yescharacteristic, complemented
19A4×M16—31no—
20C42×A4—31no—
21C2×#837—31no—
22C2×#837—31no—
23C2×#837—31no—
24C2×#837—31no—
25C22×C3×A4—21no—
26C22×C3×A4D411yescharacteristic
27C32×#41—41no—
28C3×C4×A4—21no—
29C3×C4×A4C2×C411yescharacteristic
30C3×C4×A4D411yescharacteristic
31Dic3×A4—22no—
32C3×C4×Dic3—41no—
33C3×#208—41no—
34C22×#104—31noSylow
35C2×C3×#41—31no—
36C2×C3×#41—31no—
37C2×C3×#41—31no—
38C2×C3×#41—31no—
39C2×C3×#41—61no—
40C2×C3×#41—61no—
41C22×C3×Q8C3×C411yescharacteristic, complemented
42C22×C3×D4—21no—
43C22×C3×D4C3×C411yescharacteristic, complemented
44C23×C3×C4—21no—
45C23×C3×C4C22×C311yescharacteristic
46C23×Dic3—21no—
47Q8×A4—21no—
48Q8×A4Dic311yescharacteristic, complemented
49D4×A4—22no—
50D4×A4—21no—
51D4×A4—21no—
52D4×A4Dic311yescharacteristic, complemented
53C2×C4×A4—22no—
54C2×C4×A4—21no—
55C2×C4×A4—21no—
56C2×C4×A4—61no—
57C2×C4×A4C2×D311yescharacteristic
58C2×C4×Dic3—31no—
59C2×C4×Dic3—31no—
60C2×C4×Dic3—61no—
61C2×#208—31no—
62C2×#208—31no—
63C2×#208—61no—
64C22×C3⋊C8—21no—
65C8×A4—61no—
66C3×#104—121no—
67#837—32no—
68#837—31no—
69#837—31no—
70#837—31no—
71#837A411yescharacteristic, direct product factor
72C2×C3×A4—21no—
73C2×C3×A4—41no—
74C2×C3×A4C22⋊C411yescharacteristic
75C32×Q8—41no—
76C32×D4—41no—
77C32×D4—81no—
78C2×C32×C4—41no—
79C2×C32×C4—81no—
80C2×C3×Dic3—81no—
81C3×C3⋊C8—81no—
82C22×#41C3×D311yescharacteristic
83C22×M16—31no—
84C22×C42—31no—
85C2×#104—91no—
86C2×#104—91no—
87C2×#104—91no—
88C2×#104—91no—
89C24×C3—21no—
90C24×C3C3×D411yescharacteristic
91C22×A4—22no—
92C22×A4—21no—
93C22×A4—21no—
94C22×A4#6711yescharacteristic
95C3×#41—32no—
96C3×#41—31no—
97C3×#41—31no—
98C3×#41—31no—
99C3×#41—41no—
100C3×#41—61no—
101C3×#41—61no—
102C3×#41—62no—
103C3×#41—62no—
104C3×#41—61no—
105C3×#41—61no—
106C3×#41—81no—
107C3×#41C2×A411yescharacteristic
108C2×C3×Q8—31no—
109C2×C3×Q8—31no—
110C2×C3×Q8—61no—
111C2×C3×D4—31no—
112C2×C3×D4—31no—
113C2×C3×D4—61no—
114C2×C3×D4—61no—
115C2×C3×D4—61no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C22×C3×C4—21no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C22×C3×C4—61no—
127C22×C3×C4C2×C3×C411yescharacteristic
128C22×C3×C4C3×D411yescharacteristic
129C22×Dic3—22no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C22×Dic3—62no—
133C4×A4—22no—
134C4×A4—21no—
135C4×A4—21no—
136C4×A4—21no—
137C4×A4—62no—
138C4×A4C2×Dic311yescharacteristic
139C4×A4#6711yescharacteristic
140C3×M16—121no—
141C3×C42—121no—
142C4×Dic3—31no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3C2×A411yescharacteristic, complemented
146#208—31no—
147#208—61no—
148#208—61no—
149#208C2×A411yescharacteristic, complemented
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C22×C32—41no—
153C22×C32—81no—
154C3×A4#10411yescharacteristic, complemented
155C32×C4—41no—
156C32×C4—41no—
157C32×C4—81no—
158C3×Dic3—82no—
159C2×#41—31no—
160C2×#41—31no—
161C2×#41—31no—
162C2×#41—31no—
163C2×#41—61no—
164C2×#41—61no—
165C22×Q8C3×Dic311yescharacteristic, complemented
166C22×D4—21no—
167C22×D4C3×Dic311yescharacteristic, complemented
168C23×C4—21no—
169C23×C4—61no—
170C23×C4C2×C3×D311yescharacteristic
171C2×M16—91no—
172C2×M16—91no—
173C2×M16—181no—
174C22×C8—61no—
175C2×C42—91no—
176C2×C42—91no—
177C2×C42—181no—
178#104—31no—
179#104—91no—
180#104—91no—
181#104—92no—
182#104—91no—
183C23×C3—21no—
184C23×C3—31no—
185C23×C3—31no—
186C23×C3—41no—
187C23×C3—61no—
188C23×C3—61no—
189C23×C3—61no—
190C23×C3—121no—
191C23×C3C3×C22⋊C411yescharacteristic
192C2×A4—21no—
193C2×A4—21no—
194C2×A4—41no—
195C2×A4—42no—
196C2×A4—41no—
197C2×A4#21711yescharacteristic
198C3×Q8—31no—
199C3×Q8—41no—
200C3×Q8—61no—
201C3×Q8—61no—
202C3×Q8—81no—
203C3×Q8C4×A411yescharacteristic, complemented
204C3×D4—21no—
205C3×D4—31no—
206C3×D4—41no—
207C3×D4—61no—
208C3×D4—61no—
209C3×D4—61no—
210C3×D4—61no—
211C3×D4—62no—
212C3×D4—61no—
213C3×D4—81no—
214C3×D4—82no—
215C3×D4—81no—
216C3×D4C4×A411yescharacteristic, complemented
217C2×C3×C4—21no—
218C2×C3×C4—32no—
219C2×C3×C4—31no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—31no—
223C2×C3×C4—31no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—41no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—61no—
230C2×C3×C4—62no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—81no—
234C2×C3×C4—82no—
235C2×C3×C4—81no—
236C2×C3×C4—241no—
237C2×C3×C4C22×A411yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—61no—
243C2×Dic3—62no—
244C3×C8—241no—
245C3⋊C8—21no—
246C3⋊C8—61no—
247C2×C32—41no—
248C2×C32—81no—
249C2×C32—161no—
250C24—21no—
251C24C3×#6711yescharacteristic
252#41—32no—
253#41—31no—
254#41—31no—
255#41—31no—
256#41—61no—
257#41—61no—
258#41—62no—
259#41—62no—
260#41—61no—
261#41—61no—
262#41D3×A411yescharacteristic
263C2×Q8—31no—
264C2×Q8—31no—
265C2×Q8—61no—
266C2×D4—31no—
267C2×D4—31no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—61no—
271C2×D4—61no—
272C2×D4—61no—
273C22×C4—21no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—61no—
279C22×C4—61no—
280C22×C4—61no—
281C22×C4—61no—
282C22×C4—62no—
283C22×C4—181no—
284C22×C4—181no—
285C22×C4—182no—
286C22×C4C2×C3×Dic311yescharacteristic
287C22×C4C3×#6711yescharacteristic
288M16—31no—
289M16—91no—
290M16—181no—
291M16—181no—
292C2×C8—181no—
293C2×C8—181no—
294C42—31no—
295C42—91no—
296C42—181no—
297C42—181no—
298C22×C3—21no—
299C22×C3—31no—
300C22×C3—31no—
301C22×C3—31no—
302C22×C3—41no—
303C22×C3—61no—
304C22×C3—61no—
305C22×C3—61no—
306C22×C3—61no—
307C22×C3—61no—
308C22×C3—81no—
309C22×C3—82no—
310C22×C3—81no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3—121no—
315C22×C3C3×#10411yescharacteristic, complemented
316C22×C3D4×A411yescharacteristic
317A4—21no—
318A4#83711yescharacteristic, direct product factor
319C3×C4—21no—
320C3×C4—31no—
321C3×C4—31no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—61no—
325C3×C4—81no—
326C3×C4—82no—
327C3×C4—81no—
328C3×C4—81no—
329C3×C4—242no—
330C3×C4C2×C4×A411yescharacteristic
331C3×C4D4×A411yescharacteristic
332Dic3—22no—
333Dic3—62no—
334C32—41noSylow
335C23—21no—
336C23—31no—
337C23—31no—
338C23—41no—
339C23—61no—
340C23—61no—
341C23—61no—
342C23—121no—
343C23C3×#21711yescharacteristic
344Q8—31no—
345Q8—61no—
346Q8—61no—
347Q8Dic3×A411yescharacteristic, complemented
348D4—21no—
349D4—31no—
350D4—61no—
351D4—61no—
352D4—61no—
353D4—61no—
354D4—62no—
355D4—61no—
356D4Dic3×A411yescharacteristic, complemented
357C2×C4—21no—
358C2×C4—32no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—62no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4—181no—
377C2×C4—182no—
378C2×C4C2×D3×A411yescharacteristic
379C8—61no—
380C8—181no—
381C2×C3—21no—
382C2×C3—31no—
383C2×C3—31no—
384C2×C3—41no—
385C2×C3—41no—
386C2×C3—61no—
387C2×C3—81no—
388C2×C3—81no—
389C2×C3—121no—
390C2×C3—161no—
391C2×C3—161no—
392C2×C3—162no—
393C2×C3A4×C22⋊C411yescharacteristic
394C22—21no—
395C22—31no—
396C22—31no—
397C22—31no—
398C22—61no—
399C22—61no—
400C22—61no—
401C22—61no—
402C22—61no—
403C22—121no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22C3×#83711yescharacteristic, complemented
408C22A4×#6711yescharacteristic
409C4—21no—
410C4—31no—
411C4—31no—
412C4—62no—
413C4—61no—
414C4—182no—
415C4C2×Dic3×A411yescharacteristic
416C4A4×#6711yescharacteristic
417C3—41no—
418C3—81no—
419C3A4×#10411yescharacteristic, complemented
420C2—21no—
421C2—31no—
422C2—31no—
423C2—41no—
424C2—61no—
425C2—121no—
426C2A4×#21711yescharacteristic
subgroupG/H
centerC4A4×#67
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C3×C22⋊C4
prime radicalC3×A4×#41C2
cosocleC23×C3×C4C22×C3
hypercenter#41D3×A4
hypocenterC22×C3C3×#104
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C4×Dic3×A4C2semidirect
3. A4×#208C2semidirect
4. C22×#837C3semidirect
6. C3×Q8×A4C4semidirect
8. C3×D4×A4C4semidirect
17. C22×C4×Dic3C2×C3semidirect
18. C22×#208C2×C3semidirect
41. C22×C3×Q8C3×C4semidirect
43. C22×C3×D4C3×C4semidirect
48. Q8×A4Dic3semidirect
52. D4×A4Dic3semidirect
71. #837A4direct (N × H)
145. C4×Dic3C2×A4semidirect
149. #208C2×A4semidirect
154. C3×A4#104semidirect
165. C22×Q8C3×Dic3semidirect
167. C22×D4C3×Dic3semidirect
203. C3×Q8C4×A4semidirect
216. C3×D4C4×A4semidirect
315. C22×C3C3×#104semidirect
318. A4#837direct (N × H)
347. Q8Dic3×A4semidirect
356. D4Dic3×A4semidirect
407. C22C3×#837semidirect
419. C3A4×#104semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
C4×Dic3×A42
A4×#2082
C22×#8373
A4×#1043
C3×#8374