Finite Group Databasebeta

← A4×#926 #11923346

Subgroups — A4×#926 #11923346

Order 1152.

934 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2A4×#217C212yesmaximal
3A4×C4⋊Dic3C212yesmaximal, complemented
4C4×Dic3×A4C212yesmaximal, complemented
5C22×#926C311yesmaximal, characteristic, complemented
6A4×#117—31nomaximal
7C23×C3×A4C2211yescharacteristic
8C2×C3×C4×A4C414yescomplemented
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2214yes—
12C3×#926—41nomaximal
13C24×C3×C4C2×C311yescharacteristic
14C22×C4×A4—21no—
15C22×C4×A4D311yescharacteristic
16C22×#217C2×C312yes—
17C2×#926—31no—
18C2×#926—32no—
19C2×#926—32no—
20C2×#926—31no—
21C2×#926—32no—
22C22×C4⋊Dic3C2×C312yescomplemented
23C22×C4×Dic3C2×C312yescomplemented
24A4×C4⋊C4—32no—
25A4×C22⋊C4—32no—
26C42×A4—32no—
27C22×C3×A4—22no—
28C22×C3×A4C2×C412yes—
29C22×C3×A4C2311yescharacteristic
30C22×C32×C4—41no—
31C3×C4×A4C2×C412yes—
32C3×C4×A4C2×C412yes—
33Dic3×A4—24no—
34C3×#217—42no—
35C3×C4⋊Dic3—42no—
36C3×C4×Dic3—42no—
37C22×#117—31noSylow
38C25×C3C22×C311yescharacteristic
39C23×A4—21no—
40C23×A4C2×D311yescharacteristic
41C23×C3×C4—31no—
42C23×C3×C4—34no—
43C23×C3×C4—31no—
44C23×C3×C4—31no—
45C23×C3×C4—31no—
46C23×C3×C4C3×C414yescomplemented
47C23×C3×C4C22×C311yescharacteristic
48C23×C3×C4C22×C311yescharacteristic
49C23×Dic3C22×C314yes—
50C2×C4×A4—24no—
51C2×C4×A4—21no—
52C2×C4×A4—21no—
53C2×C4×A4—34no—
54C2×C4×A4Dic314yescomplemented
55C2×C4×A4C2×D311yescharacteristic
56C2×C4×A4C2×D311yescharacteristic
57C3×#117—121no—
58C2×#217—32no—
59C2×#217—32no—
60C2×#217—34no—
61#926—32no—
62#926—32no—
63#926—38no—
64#926—32no—
65#926—31no—
66#926—32no—
67#926—32no—
68#926—32no—
69#926A411yescharacteristic, direct product factor
70C2×C4⋊Dic3—32no—
71C2×C4⋊Dic3—32no—
72C2×C4⋊Dic3—34no—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—34no—
76C23×C32—41no—
77C2×C3×A4—22no—
78C2×C3×A4C22×C411yescharacteristic
79C2×C3×A4#4112yes—
80C2×C32×C4—44no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C3×Dic3—44no—
84C24×C4C3×D311yescharacteristic
85C2×#117—91no—
86C2×#117—92no—
87C2×#117—92no—
88C2×#117—92no—
89C2×#117—91no—
90C22×C4⋊C4—32no—
91C22×C22⋊C4—32no—
92C22×C42—32no—
93C24×C3—22no—
94C24×C3—31no—
95C24×C3—32no—
96C24×C3—31no—
97C24×C3—62no—
98C24×C3C2×C3×C412yes—
99C24×C3C23×C311yescharacteristic
100C22×A4—24no—
101C22×A4—22no—
102C22×A4—22no—
103C22×A4—21no—
104C22×A4C2×Dic312yes—
105C22×A4C22×D311yescharacteristic
106C22×C3×C4—32no—
107C22×C3×C4—34no—
108C22×C3×C4—34no—
109C22×C3×C4—34no—
110C22×C3×C4—31no—
111C22×C3×C4—34no—
112C22×C3×C4—34no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—31no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—34no—
120C22×C3×C4—34no—
121C22×C3×C4—34no—
122C22×C3×C4—32no—
123C22×C3×C4—32no—
124C22×C3×C4—41no—
125C22×C3×C4—81no—
126C22×C3×C4C2×C3×C412yes—
127C22×C3×C4C2×C3×C412yes—
128C22×C3×C4C2×A411yescharacteristic
129C22×Dic3—24no—
130C22×Dic3—34no—
131C22×Dic3—34no—
132C22×Dic3—64no—
133C4×A4—22no—
134C4×A4—22no—
135C4×A4—64no—
136C4×A4C2×Dic312yes—
137C4×A4C2×Dic312yes—
138C3×C4⋊C4—122no—
139C3×C22⋊C4—122no—
140C3×C42—122no—
141#217—34no—
142#217—32no—
143#217—34no—
144#217C2×A412yes—
145C4⋊Dic3—34no—
146C4⋊Dic3—32no—
147C4⋊Dic3—34no—
148C4⋊Dic3C2×A412yescomplemented
149C4×Dic3—34no—
150C4×Dic3—32no—
151C4×Dic3—34no—
152C4×Dic3C2×A412yescomplemented
153C22×C32—42no—
154C22×C32—41no—
155C22×C32—82no—
156C3×A4#11711yescharacteristic, complemented
157C32×C4—42no—
158C32×C4—42no—
159C3×Dic3—84no—
160C25C2×C3×D311yescharacteristic
161C23×C4—31no—
162C23×C4—31no—
163C23×C4—31no—
164C23×C4—31no—
165C23×C4—34no—
166C23×C4—34no—
167C23×C4C3×Dic314yescomplemented
168C23×C4C2×C3×D311yescharacteristic
169C23×C4C2×C3×D311yescharacteristic
170#117—31no—
171#117—92no—
172#117—92no—
173#117—92no—
174#117—98no—
175#117—92no—
176#117—92no—
177#117—92no—
178#117—91no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—94no—
181C2×C4⋊C4—92no—
182C2×C22⋊C4—92no—
183C2×C22⋊C4—94no—
184C2×C22⋊C4—92no—
185C2×C42—92no—
186C2×C42—94no—
187C2×C42—92no—
188C23×C3—22no—
189C23×C3—32no—
190C23×C3—31no—
191C23×C3—31no—
192C23×C3—32no—
193C23×C3—32no—
194C23×C3—32no—
195C23×C3—32no—
196C23×C3—31no—
197C23×C3—41no—
198C23×C3—62no—
199C23×C3—62no—
200C23×C3—62no—
201C23×C3—64no—
202C23×C3—62no—
203C23×C3—62no—
204C23×C3—64no—
205C23×C3—81no—
206C23×C3C22×C3×C411yescharacteristic
207C23×C3C3×#4112yes—
208C23×C3C22×A411yescharacteristic
209C2×A4—24no—
210C2×A4—22no—
211C2×A4—22no—
212C2×A4—21no—
213C2×A4#23512yes—
214C2×A4C22×Dic311yescharacteristic
215C2×C3×C4—32no—
216C2×C3×C4—32no—
217C2×C3×C4—38no—
218C2×C3×C4—34no—
219C2×C3×C4—31no—
220C2×C3×C4—31no—
221C2×C3×C4—32no—
222C2×C3×C4—32no—
223C2×C3×C4—34no—
224C2×C3×C4—34no—
225C2×C3×C4—32no—
226C2×C3×C4—32no—
227C2×C3×C4—32no—
228C2×C3×C4—32no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—44no—
232C2×C3×C4—81no—
233C2×C3×C4—81no—
234C2×C3×C4—84no—
235C2×C3×C4—124no—
236C2×C3×C4C4×A414yescomplemented
237C2×C3×C4C22×A411yescharacteristic
238C2×C3×C4C22×A411yescharacteristic
239C2×Dic3—34no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3C22×A414yes—
245C2×C32—41no—
246C2×C32—42no—
247C2×C32—82no—
248C24—22no—
249C24—31no—
250C24—32no—
251C24—31no—
252C24—62no—
253C24C2×C3×Dic312yes—
254C24C22×C3×D311yescharacteristic
255C22×C4—32no—
256C22×C4—34no—
257C22×C4—34no—
258C22×C4—34no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—31no—
262C22×C4—31no—
263C22×C4—31no—
264C22×C4—34no—
265C22×C4—34no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—34no—
269C22×C4—34no—
270C22×C4—34no—
271C22×C4—32no—
272C22×C4—32no—
273C22×C4—64no—
274C22×C4—94no—
275C22×C4—94no—
276C22×C4—184no—
277C22×C4C2×C3×Dic312yes—
278C22×C4C2×C3×Dic312yes—
279C22×C4D3×A411yescharacteristic
280C4⋊C4—32no—
281C4⋊C4—94no—
282C4⋊C4—94no—
283C4⋊C4—92no—
284C22⋊C4—32no—
285C22⋊C4—94no—
286C22⋊C4—94no—
287C22⋊C4—92no—
288C42—32no—
289C42—94no—
290C42—94no—
291C42—92no—
292C22×C3—22no—
293C22×C3—31no—
294C22×C3—32no—
295C22×C3—32no—
296C22×C3—31no—
297C22×C3—31no—
298C22×C3—32no—
299C22×C3—32no—
300C22×C3—32no—
301C22×C3—42no—
302C22×C3—41no—
303C22×C3—62no—
304C22×C3—64no—
305C22×C3—62no—
306C22×C3—62no—
307C22×C3—62no—
308C22×C3—64no—
309C22×C3—62no—
310C22×C3—82no—
311C22×C3—84no—
312C22×C3—82no—
313C22×C3—81no—
314C22×C3C3×#11711yescharacteristic, complemented
315C22×C3C2×C4×A412yes—
316C22×C3C23×A411yescharacteristic
317A4—21no—
318A4#92611yescharacteristic, direct product factor
319C3×C4—32no—
320C3×C4—32no—
321C3×C4—42no—
322C3×C4—42no—
323C3×C4—82no—
324C3×C4—82no—
325C3×C4—244no—
326C3×C4C2×C4×A412yes—
327C3×C4C2×C4×A412yes—
328Dic3—24no—
329Dic3—64no—
330C32—41noSylow
331C23—22no—
332C23—31no—
333C23—32no—
334C23—31no—
335C23—32no—
336C23—32no—
337C23—32no—
338C23—32no—
339C23—31no—
340C23—62no—
341C23—62no—
342C23—62no—
343C23—64no—
344C23—62no—
345C23—62no—
346C23—64no—
347C23C3×#23512yes—
348C23C22×C3×Dic311yescharacteristic
349C23C2×D3×A411yescharacteristic
350C2×C4—32no—
351C2×C4—32no—
352C2×C4—38no—
353C2×C4—34no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—32no—
357C2×C4—32no—
358C2×C4—32no—
359C2×C4—34no—
360C2×C4—32no—
361C2×C4—34no—
362C2×C4—32no—
363C2×C4—32no—
364C2×C4—34no—
365C2×C4—94no—
366C2×C4—184no—
367C2×C4—184no—
368C2×C4—184no—
369C2×C4—184no—
370C2×C4Dic3×A414yescomplemented
371C2×C4C2×D3×A411yescharacteristic
372C2×C4C2×D3×A411yescharacteristic
373C2×C3—22no—
374C2×C3—31no—
375C2×C3—32no—
376C2×C3—31no—
377C2×C3—42no—
378C2×C3—41no—
379C2×C3—62no—
380C2×C3—82no—
381C2×C3—84no—
382C2×C3—82no—
383C2×C3—81no—
384C2×C3C22×C4×A411yescharacteristic
385C2×C3A4×#4112yes—
386C22—22no—
387C22—32no—
388C22—31no—
389C22—32no—
390C22—32no—
391C22—32no—
392C22—31no—
393C22—31no—
394C22—32no—
395C22—62no—
396C22—62no—
397C22—64no—
398C22—62no—
399C22—62no—
400C22—64no—
401C22—62no—
402C22C3×#92611yescharacteristic, complemented
403C22C2×Dic3×A412yes—
404C22C22×D3×A411yescharacteristic
405C4—32no—
406C4—32no—
407C4—64no—
408C4—184no—
409C4C2×Dic3×A412yes—
410C4C2×Dic3×A412yes—
411C3—41no—
412C3—81no—
413C3A4×#11711yescharacteristic, complemented
414C2—22no—
415C2—31no—
416C2—32no—
417C2—31no—
418C2—62no—
419C2A4×#23512yes—
420C2C22×Dic3×A411yescharacteristic
subgroupG/H
centerC2×C4C2×D3×A4
commutatorC23×C3C22×C3×C4
FrattiniC22C22×D3×A4
FittingC24×C3×C4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC23×C3×A4C22
hypercenterC22×C4D3×A4
hypocenterC22×C3C3×#117
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. A4×C4⋊Dic3C2semidirect
4. C4×Dic3×A4C2semidirect
5. C22×#926C3semidirect
8. C2×C3×C4×A4C4semidirect
22. C22×C4⋊Dic3C2×C3semidirect
23. C22×C4×Dic3C2×C3semidirect
46. C23×C3×C4C3×C4semidirect
54. C2×C4×A4Dic3semidirect
69. #926A4direct (N × H)
148. C4⋊Dic3C2×A4semidirect
152. C4×Dic3C2×A4semidirect
156. C3×A4#117semidirect
167. C23×C4C3×Dic3semidirect
236. C2×C3×C4C4×A4semidirect
314. C22×C3C3×#117semidirect
318. A4#926direct (N × H)
370. C2×C4Dic3×A4semidirect
402. C22C3×#926semidirect
413. C3A4×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
A4×#2172
A4×C4⋊Dic32
C4×Dic3×A42
C22×#9263
A4×#1173
C3×#9264