Finite Group Databasebeta

← A4×#832 #11921359

Subgroups — A4×#832 #11921359

Order 1152.

578 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 75 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×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
4C22×#832C311yesmaximal, characteristic, complemented
5A4×#102—31nomaximal
6C23×C3×A4—21no—
7C3×D4×A4—21no—
8C3×D4×A4C412yescomplemented
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4—21no—
11A4×C3⋊C8—21no—
12C3×#832—41nomaximal
13C23×C3×D4C2×C311yescharacteristic
14C2×D4×A4—21no—
15C2×D4×A4D311yescharacteristic
16C22×C4⋊Dic3C2×C311yescharacteristic, complemented
17C23×C3⋊C8C2×C311yescharacteristic, complemented
18C2×C8×A4—31no—
19A4×C4⋊C4—31no—
20C2×#832—31no—
21C2×#832—31no—
22C2×#832—31no—
23C2×#832—31no—
24C22×C3×A4—22no—
25C22×C3×A4—41no—
26C22×C3×A4—41no—
27C22×C3×A4D411yescharacteristic
28C2×C32×D4—41no—
29C3×C4×A4C2×C411yescharacteristic
30C3×C4×A4D411yescharacteristic
31Dic3×A4—41no—
32C3×C4⋊Dic3—41no—
33C2×C3×C3⋊C8—41no—
34C22×#102—31noSylow
35C25×C3—21no—
36C23×A4—22no—
37C23×A4—21no—
38C22×C3×D4—21no—
39C22×C3×D4—31no—
40C22×C3×D4—32no—
41C22×C3×D4—31no—
42C22×C3×D4—61no—
43C22×C3×D4—61no—
44C22×C3×D4C3×C412yescomplemented
45C23×C3×C4C22×C311yescharacteristic
46C23×Dic3—21no—
47D4×A4—22no—
48D4×A4—21no—
49D4×A4—22no—
50D4×A4Dic312yescomplemented
51C2×C4×A4—21no—
52C2×C4×A4—61no—
53C2×C4×A4C2×D311yescharacteristic
54C2×C4⋊Dic3—31no—
55C2×C4⋊Dic3—31no—
56C2×C4⋊Dic3—61no—
57C22×C3⋊C8—21no—
58C22×C3⋊C8—31no—
59C22×C3⋊C8—31no—
60C22×C3⋊C8—61no—
61C8×A4—61no—
62C3×#102—121no—
63#832—32no—
64#832—31no—
65#832—31no—
66#832—31no—
67#832A411yescharacteristic, direct product factor
68C23×C32—81no—
69C2×C3×A4—42no—
70C2×C3×A4C22⋊C411yescharacteristic
71C2×C3×A4D811yescharacteristic
72C2×C3×A4SD1611yescharacteristic
73C32×D4—42no—
74C32×D4—81no—
75C2×C32×C4—41no—
76C2×C3×Dic3—81no—
77C3×C3⋊C8—81no—
78C23×D4C3×D311yescharacteristic
79C23×C8—31no—
80C22×C4⋊C4—31no—
81C2×#102—91no—
82C2×#102—91no—
83C2×#102—91no—
84C2×#102—91no—
85C24×C3—22no—
86C24×C3—41no—
87C24×C3—41no—
88C24×C3—61no—
89C24×C3—62no—
90C24×C3—61no—
91C24×C3—121no—
92C24×C3—121no—
93C24×C3C3×D411yescharacteristic
94C22×A4—24no—
95C22×A4—22no—
96C22×A4—21no—
97C22×A4—42no—
98C22×A4—42no—
99C22×A4—41no—
100C22×A4—41no—
101C22×A4#6711yescharacteristic
102C2×C3×D4—32no—
103C2×C3×D4—32no—
104C2×C3×D4—32no—
105C2×C3×D4—32no—
106C2×C3×D4—31no—
107C2×C3×D4—41no—
108C2×C3×D4—61no—
109C2×C3×D4—61no—
110C2×C3×D4—61no—
111C2×C3×D4—61no—
112C2×C3×D4—64no—
113C2×C3×D4—61no—
114C2×C3×D4—62no—
115C2×C3×D4—61no—
116C2×C3×D4—62no—
117C2×C3×D4—81no—
118C2×C3×D4C2×A411yescharacteristic
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4C2×C3×C411yescharacteristic
124C22×C3×C4C3×D411yescharacteristic
125C22×Dic3—41no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—121no—
129C4×A4—21no—
130C4×A4—21no—
131C4×A4—121no—
132C4×A4C2×Dic311yescharacteristic
133C4×A4#6711yescharacteristic
134C2×C3×C8—121no—
135C3×C4⋊C4—121no—
136C4⋊Dic3—31no—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139C4⋊Dic3C2×A411yescharacteristic, complemented
140C2×C3⋊C8—31no—
141C2×C3⋊C8—61no—
142C2×C3⋊C8—61no—
143C2×C3⋊C8—61no—
144C2×C3⋊C8—61no—
145C2×C3⋊C8C2×A411yescharacteristic, complemented
146C22×C32—41no—
147C22×C32—82no—
148C22×C32—161no—
149C22×C32—161no—
150C3×A4#10211yescharacteristic, complemented
151C32×C4—41no—
152C32×C4—41no—
153C3×Dic3—161no—
154C25—21no—
155C22×D4—21no—
156C22×D4—31no—
157C22×D4—31no—
158C22×D4—32no—
159C22×D4—61no—
160C22×D4—61no—
161C22×D4C3×Dic312yescomplemented
162C23×C4—61no—
163C23×C4C2×C3×D311yescharacteristic
164C22×C8—61no—
165C22×C8—91no—
166C22×C8—91no—
167C22×C8—181no—
168C2×C4⋊C4—91no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—181no—
171#102—31no—
172#102—91no—
173#102—91no—
174#102—92no—
175#102—91no—
176C23×C3—21no—
177C23×C3—31no—
178C23×C3—31no—
179C23×C3—31no—
180C23×C3—31no—
181C23×C3—42no—
182C23×C3—62no—
183C23×C3—62no—
184C23×C3—62no—
185C23×C3—62no—
186C23×C3—61no—
187C23×C3—81no—
188C23×C3—82no—
189C23×C3—121no—
190C23×C3—121no—
191C23×C3—121no—
192C23×C3—121no—
193C23×C3—122no—
194C23×C3—122no—
195C23×C3—122no—
196C23×C3—121no—
197C23×C3—121no—
198C23×C3—121no—
199C23×C3—121no—
200C23×C3—124no—
201C23×C3C3×C22⋊C411yescharacteristic
202C23×C3C3×D811yescharacteristic
203C23×C3C3×SD1611yescharacteristic
204C2×A4—21no—
205C2×A4—21no—
206C2×A4—21no—
207C2×A4—44no—
208C2×A4—42no—
209C2×A4#21311yescharacteristic
210C2×A4#21411yescharacteristic
211C2×A4#21711yescharacteristic
212C3×D4—21no—
213C3×D4—32no—
214C3×D4—42no—
215C3×D4—62no—
216C3×D4—62no—
217C3×D4—62no—
218C3×D4—62no—
219C3×D4—61no—
220C3×D4—81no—
221C3×D4—82no—
222C3×D4—82no—
223C3×D4C4×A412yescomplemented
224C2×C3×C4—32no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—41no—
233C2×C3×C4—81no—
234C2×C3×C4—241no—
235C2×C3×C4C22×A411yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—61no—
238C2×Dic3—121no—
239C2×Dic3—121no—
240C2×Dic3—121no—
241C2×Dic3—121no—
242C3×C8—241no—
243C3⋊C8—21no—
244C3⋊C8—61no—
245C2×C32—41no—
246C2×C32—41no—
247C2×C32—41no—
248C2×C32—162no—
249C24—22no—
250C24—41no—
251C24—41no—
252C24—61no—
253C24—62no—
254C24—61no—
255C24—121no—
256C24—121no—
257C24C3×#6711yescharacteristic
258C2×D4—32no—
259C2×D4—32no—
260C2×D4—32no—
261C2×D4—32no—
262C2×D4—31no—
263C2×D4—61no—
264C2×D4—61no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—64no—
268C2×D4—61no—
269C2×D4—62no—
270C2×D4—61no—
271C2×D4—62no—
272C2×D4D3×A411yescharacteristic
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—121no—
278C22×C4—181no—
279C22×C4—181no—
280C22×C4—361no—
281C22×C4C2×C3×Dic311yescharacteristic
282C22×C4C3×#6711yescharacteristic
283C2×C8—31no—
284C2×C8—91no—
285C2×C8—181no—
286C2×C8—181no—
287C2×C8—181no—
288C2×C8—181no—
289C4⋊C4—31no—
290C4⋊C4—91no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C22×C3—22no—
294C22×C3—31no—
295C22×C3—31no—
296C22×C3—31no—
297C22×C3—32no—
298C22×C3—31no—
299C22×C3—31no—
300C22×C3—31no—
301C22×C3—31no—
302C22×C3—31no—
303C22×C3—31no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—62no—
308C22×C3—82no—
309C22×C3—84no—
310C22×C3—81no—
311C22×C3—122no—
312C22×C3—122no—
313C22×C3—122no—
314C22×C3—122no—
315C22×C3—122no—
316C22×C3—122no—
317C22×C3—122no—
318C22×C3—122no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—161no—
322C22×C3—161no—
323C22×C3—162no—
324C22×C3—162no—
325C22×C3C3×#10211yescharacteristic, complemented
326C22×C3D4×A411yescharacteristic
327A4—21no—
328A4#83211yescharacteristic, direct product factor
329C3×C4—31no—
330C3×C4—31no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—81no—
334C3×C4—81no—
335C3×C4—481no—
336C3×C4C2×C4×A411yescharacteristic
337C3×C4D4×A411yescharacteristic
338Dic3—41no—
339Dic3—121no—
340C32—41noSylow
341C23—21no—
342C23—31no—
343C23—31no—
344C23—31no—
345C23—31no—
346C23—42no—
347C23—62no—
348C23—62no—
349C23—62no—
350C23—62no—
351C23—61no—
352C23—121no—
353C23—121no—
354C23—121no—
355C23—121no—
356C23—122no—
357C23—122no—
358C23—122no—
359C23—121no—
360C23—121no—
361C23—121no—
362C23—121no—
363C23—124no—
364C23C3×#21311yescharacteristic
365C23C3×#21411yescharacteristic
366C23C3×#21711yescharacteristic
367D4—21no—
368D4—32no—
369D4—62no—
370D4—62no—
371D4—62no—
372D4—62no—
373D4—61no—
374D4Dic3×A412yescomplemented
375C2×C4—32no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—61no—
384C2×C4—181no—
385C2×C4—361no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4—361no—
389C2×C4C2×D3×A411yescharacteristic
390C8—61no—
391C8—181no—
392C2×C3—31no—
393C2×C3—31no—
394C2×C3—31no—
395C2×C3—31no—
396C2×C3—42no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—81no—
401C2×C3—81no—
402C2×C3—81no—
403C2×C3—122no—
404C2×C3—162no—
405C2×C3—164no—
406C2×C3A4×C22⋊C411yescharacteristic
407C2×C3A4×D811yescharacteristic
408C2×C3A4×SD1611yescharacteristic
409C22—22no—
410C22—31no—
411C22—31no—
412C22—31no—
413C22—32no—
414C22—31no—
415C22—31no—
416C22—31no—
417C22—31no—
418C22—31no—
419C22—31no—
420C22—41no—
421C22—41no—
422C22—62no—
423C22—122no—
424C22—122no—
425C22—122no—
426C22—122no—
427C22—122no—
428C22—122no—
429C22—122no—
430C22—122no—
431C22—121no—
432C22—121no—
433C22C3×#83211yescharacteristic, complemented
434C22A4×#6711yescharacteristic
435C4—31no—
436C4—31no—
437C4—121no—
438C4—361no—
439C4C2×Dic3×A411yescharacteristic
440C4A4×#6711yescharacteristic
441C3—41no—
442C3—81no—
443C3A4×#10211yescharacteristic, complemented
444C2—31no—
445C2—31no—
446C2—31no—
447C2—31no—
448C2—42no—
449C2—122no—
450C2A4×#21311yescharacteristic
451C2A4×#21411yescharacteristic
452C2A4×#21711yescharacteristic
subgroupG/H
centerC22A4×#67
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC23×C3×D4C2×C3
socleC24×C3C3×D4
prime radicalC2×C3×D4×A4C2
cosocleC23×C3×C4C22×C3
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×#102
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. A4×C4⋊Dic3C2semidirect
3. C2×A4×C3⋊C8C2semidirect
4. C22×#832C3semidirect
8. C3×D4×A4C4semidirect
16. C22×C4⋊Dic3C2×C3semidirect
17. C23×C3⋊C8C2×C3semidirect
44. C22×C3×D4C3×C4semidirect
50. D4×A4Dic3semidirect
67. #832A4direct (N × H)
139. C4⋊Dic3C2×A4semidirect
145. C2×C3⋊C8C2×A4semidirect
150. C3×A4#102semidirect
161. C22×D4C3×Dic3semidirect
223. C3×D4C4×A4semidirect
325. C22×C3C3×#102semidirect
328. A4#832direct (N × H)
374. D4Dic3×A4semidirect
433. C22C3×#832semidirect
443. C3A4×#102semidirect

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×C4⋊Dic32
C2×A4×C3⋊C82
C22×#8323
A4×#1023
C3×#8324