Finite Group Databasebeta

← A4×#936 #11923355

Subgroups — A4×#936 #11923355

Order 1152.

934 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 99 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
2C2×A4×Dic6C211yesmaximal, characteristic, complemented
3A4×#217C214yesmaximal, complemented
4C4×Dic3×A4C211yesmaximal, characteristic, complemented
5C22×#936C311yesmaximal, characteristic, complemented
6A4×#124—31nomaximal
7C23×C3×A4C2212yes—
8C3×D4×A4—22no—
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C2212yes—
11C2×Dic3×A4C2212yes—
12A4×Dic6—22no—
13C3×#936—41nomaximal
14C23×C3×D4C2×C311yescharacteristic
15C23×Dic6C2×C311yescharacteristic, complemented
16C2×Q8×A4—31no—
17C2×D4×A4—21no—
18C2×D4×A4D311yescharacteristic
19C22×#217C2×C314yescomplemented
20C2×#936—31no—
21C2×#936—31no—
22C2×#936—31no—
23C2×#936—31no—
24C2×#936—34no—
25C22×C4×Dic3C2×C311yescharacteristic, complemented
26A4×C22⋊C4—34no—
27C42×A4—31no—
28C22×C3×A4—22no—
29C22×C3×A4—24no—
30C22×C3×A4C2311yescharacteristic
31C2×C32×D4—41no—
32C2×C3×Dic6—41no—
33C3×C4×A4D412yes—
34Dic3×A4—22no—
35Dic3×A4—22no—
36C3×#217—44no—
37C3×C4×Dic3—41no—
38C22×#124—31noSylow
39C25×C3C22×C312yes—
40C23×A4—22no—
41C23×A4C2×D312yes—
42C22×C3×D4—22no—
43C22×C3×D4—31no—
44C22×C3×D4—31no—
45C22×C3×D4—32no—
46C22×C3×D4—62no—
47C23×C3×C4C22×C311yescharacteristic
48C23×Dic3C22×C312yes—
49C23×Dic3C22×C312yes—
50C22×Dic6—22no—
51C22×Dic6—31no—
52C22×Dic6—31no—
53C22×Dic6—32no—
54C22×Dic6—62no—
55Q8×A4—62no—
56D4×A4—24no—
57D4×A4—22no—
58C2×C4×A4—21no—
59C2×C4×A4—32no—
60C2×C4×A4—32no—
61C2×C4×A4C2×D311yescharacteristic
62C3×#124—121no—
63C2×#217—34no—
64C2×#217—34no—
65C2×#217—34no—
66C2×#217—34no—
67#936—34no—
68#936—34no—
69#936—32no—
70#936—34no—
71#936—31no—
72#936—31no—
73#936—34no—
74#936—31no—
75#936A411yescharacteristic, direct product factor
76C2×C4×Dic3—31no—
77C2×C4×Dic3—31no—
78C2×C4×Dic3—32no—
79C23×C32—42no—
80C2×C3×A4—42no—
81C2×C3×A4C2×D411yescharacteristic
82C2×C3×A4#4112yes—
83C32×D4—82no—
84C2×C32×C4—41no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87C3×Dic6—82no—
88C23×Q8—31no—
89C23×D4C3×D311yescharacteristic
90C2×#124—91no—
91C2×#124—91no—
92C2×#124—94no—
93C2×#124—91no—
94C2×#124—91no—
95C22×C22⋊C4—34no—
96C22×C42—31no—
97C24×C3—22no—
98C24×C3—24no—
99C24×C3—32no—
100C24×C3—32no—
101C24×C3—64no—
102C24×C3—62no—
103C24×C3C23×C311yescharacteristic
104C22×A4—24no—
105C22×A4—24no—
106C22×A4—22no—
107C22×A4—21no—
108C22×A4—44no—
109C22×A4C22×D311yescharacteristic
110C2×C3×Q8—121no—
111C2×C3×D4—32no—
112C2×C3×D4—32no—
113C2×C3×D4—31no—
114C2×C3×D4—41no—
115C2×C3×D4—62no—
116C2×C3×D4—62no—
117C2×C3×D4—64no—
118C2×C3×D4—62no—
119C2×C3×D4—64no—
120C2×C3×D4—62no—
121C2×C3×D4—81no—
122C2×C3×D4C2×A411yescharacteristic
123C22×C3×C4—31no—
124C22×C3×C4—31no—
125C22×C3×C4—32no—
126C22×C3×C4C3×D412yes—
127C22×Dic3—22no—
128C22×Dic3—22no—
129C22×Dic3—32no—
130C22×Dic3—32no—
131C22×Dic3—32no—
132C22×Dic3—32no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C2×Dic6—32no—
136C2×Dic6—31no—
137C2×Dic6—32no—
138C2×Dic6—62no—
139C2×Dic6—62no—
140C2×Dic6—64no—
141C2×Dic6—64no—
142C2×Dic6—62no—
143C2×Dic6—62no—
144C2×Dic6C2×A411yescharacteristic, complemented
145C4×A4—22no—
146C4×A4—62no—
147C4×A4—62no—
148C4×A4#6712yes—
149C3×C22⋊C4—124no—
150C3×C42—121no—
151#217—38no—
152#217—34no—
153#217—34no—
154#217—34no—
155#217C2×A414yescomplemented
156C4×Dic3—32no—
157C4×Dic3—31no—
158C4×Dic3—32no—
159C4×Dic3C2×A411yescharacteristic, complemented
160C22×C32—41no—
161C22×C32—82no—
162C22×C32—84no—
163C3×A4#12411yescharacteristic, complemented
164C32×C4—42no—
165C3×Dic3—82no—
166C3×Dic3—82no—
167C25C2×C3×D312yes—
168C22×Q8—62no—
169C22×Q8—91no—
170C22×Q8—91no—
171C22×Q8—92no—
172C22×Q8—182no—
173C22×D4—22no—
174C22×D4—31no—
175C22×D4—31no—
176C22×D4—32no—
177C22×D4—62no—
178C23×C4—32no—
179C23×C4—32no—
180C23×C4C2×C3×D311yescharacteristic
181#124—31no—
182#124—91no—
183#124—94no—
184#124—91no—
185#124—94no—
186#124—94no—
187#124—94no—
188#124—92no—
189#124—91no—
190C2×C22⋊C4—94no—
191C2×C22⋊C4—94no—
192C2×C22⋊C4—94no—
193C2×C22⋊C4—94no—
194C2×C42—91no—
195C2×C42—92no—
196C2×C42—91no—
197C23×C3—31no—
198C23×C3—32no—
199C23×C3—31no—
200C23×C3—32no—
201C23×C3—42no—
202C23×C3—42no—
203C23×C3—62no—
204C23×C3—62no—
205C23×C3—64no—
206C23×C3—64no—
207C23×C3—62no—
208C23×C3—62no—
209C23×C3—64no—
210C23×C3—64no—
211C23×C3—82no—
212C23×C3—122no—
213C23×C3—124no—
214C23×C3—124no—
215C23×C3C2×C3×D411yescharacteristic
216C23×C3C3×#4112yes—
217C23×C3C22×A412yes—
218C2×A4—22no—
219C2×A4—21no—
220C2×A4—44no—
221C2×A4—42no—
222C2×A4#23712yes—
223C2×A4C2×#6711yescharacteristic
224C3×Q8—242no—
225C3×D4—22no—
226C3×D4—64no—
227C3×D4—64no—
228C3×D4—62no—
229C3×D4—82no—
230C3×D4—84no—
231C2×C3×C4—32no—
232C2×C3×C4—31no—
233C2×C3×C4—32no—
234C2×C3×C4—32no—
235C2×C3×C4—32no—
236C2×C3×C4—41no—
237C2×C3×C4—81no—
238C2×C3×C4—122no—
239C2×C3×C4—122no—
240C2×C3×C4C22×A411yescharacteristic
241C2×Dic3—32no—
242C2×Dic3—32no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3C22×A412yes—
252C2×Dic3C22×A412yes—
253Dic6—22no—
254Dic6—64no—
255Dic6—64no—
256Dic6—62no—
257C2×C32—41no—
258C2×C32—42no—
259C2×C32—162no—
260C24—24no—
261C24—22no—
262C24—32no—
263C24—32no—
264C24—62no—
265C24—64no—
266C24C22×C3×D311yescharacteristic
267C2×Q8—31no—
268C2×Q8—92no—
269C2×Q8—92no—
270C2×Q8—91no—
271C2×Q8—182no—
272C2×Q8—182no—
273C2×Q8—182no—
274C2×Q8—184no—
275C2×Q8—182no—
276C2×Q8—184no—
277C2×D4—32no—
278C2×D4—32no—
279C2×D4—31no—
280C2×D4—62no—
281C2×D4—62no—
282C2×D4—64no—
283C2×D4—62no—
284C2×D4—64no—
285C2×D4—62no—
286C2×D4D3×A411yescharacteristic
287C22×C4—31no—
288C22×C4—31no—
289C22×C4—32no—
290C22×C4—62no—
291C22×C4—62no—
292C22×C4—92no—
293C22×C4—92no—
294C22×C4—92no—
295C22×C4—92no—
296C22×C4—182no—
297C22×C4—182no—
298C22×C4C3×#6712yes—
299C22⋊C4—34no—
300C22⋊C4—94no—
301C22⋊C4—94no—
302C22⋊C4—98no—
303C22⋊C4—94no—
304C42—31no—
305C42—92no—
306C42—92no—
307C42—91no—
308C22×C3—22no—
309C22×C3—24no—
310C22×C3—31no—
311C22×C3—32no—
312C22×C3—32no—
313C22×C3—31no—
314C22×C3—31no—
315C22×C3—32no—
316C22×C3—32no—
317C22×C3—41no—
318C22×C3—62no—
319C22×C3—64no—
320C22×C3—82no—
321C22×C3—84no—
322C22×C3—84no—
323C22×C3—81no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3—124no—
327C22×C3—122no—
328C22×C3—122no—
329C22×C3—124no—
330C22×C3—164no—
331C22×C3C3×#12411yescharacteristic, complemented
332C22×C3C23×A411yescharacteristic
333A4—21no—
334A4#93611yescharacteristic, direct product factor
335C3×C4—32no—
336C3×C4—42no—
337C3×C4—82no—
338C3×C4—242no—
339C3×C4—242no—
340C3×C4D4×A412yes—
341Dic3—22no—
342Dic3—22no—
343Dic3—62no—
344Dic3—62no—
345C32—41noSylow
346C23—31no—
347C23—32no—
348C23—31no—
349C23—32no—
350C23—42no—
351C23—62no—
352C23—62no—
353C23—64no—
354C23—64no—
355C23—62no—
356C23—62no—
357C23—64no—
358C23—64no—
359C23—124no—
360C23—122no—
361C23—124no—
362C23C3×#23712yes—
363C23C2×C3×#6711yescharacteristic
364C23C2×D3×A412yes—
365Q8—62no—
366Q8—184no—
367Q8—184no—
368Q8—182no—
369D4—22no—
370D4—64no—
371D4—64no—
372D4—62no—
373C2×C4—32no—
374C2×C4—31no—
375C2×C4—32no—
376C2×C4—32no—
377C2×C4—32no—
378C2×C4—32no—
379C2×C4—32no—
380C2×C4—92no—
381C2×C4—92no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4C2×D3×A411yescharacteristic
391C2×C3—31no—
392C2×C3—32no—
393C2×C3—31no—
394C2×C3—42no—
395C2×C3—42no—
396C2×C3—41no—
397C2×C3—82no—
398C2×C3—81no—
399C2×C3—122no—
400C2×C3—162no—
401C2×C3—164no—
402C2×C3C2×D4×A411yescharacteristic
403C2×C3A4×#4112yes—
404C22—24no—
405C22—22no—
406C22—32no—
407C22—31no—
408C22—32no—
409C22—32no—
410C22—32no—
411C22—31no—
412C22—31no—
413C22—64no—
414C22—62no—
415C22—122no—
416C22—122no—
417C22—124no—
418C22—122no—
419C22—122no—
420C22—124no—
421C22C3×#93611yescharacteristic, complemented
422C22C22×D3×A411yescharacteristic
423C4—32no—
424C4—62no—
425C4—62no—
426C4—182no—
427C4—182no—
428C4A4×#6712yes—
429C3—41no—
430C3—81no—
431C3A4×#12411yescharacteristic, complemented
432C2—31no—
433C2—32no—
434C2—31no—
435C2—42no—
436C2—122no—
437C2A4×#23712yes—
438C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×D4C2×C3
prime radicalC2×C3×D4×A4C2
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×#124
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic6C2semidirect
3. A4×#217C2semidirect
4. C4×Dic3×A4C2semidirect
5. C22×#936C3semidirect
15. C23×Dic6C2×C3semidirect
19. C22×#217C2×C3semidirect
25. C22×C4×Dic3C2×C3semidirect
75. #936A4direct (N × H)
144. C2×Dic6C2×A4semidirect
155. #217C2×A4semidirect
159. C4×Dic3C2×A4semidirect
163. C3×A4#124semidirect
331. C22×C3C3×#124semidirect
334. A4#936direct (N × H)
421. C22C3×#936semidirect
431. C3A4×#124semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×A4×Dic62
A4×#2172
C4×Dic3×A42
C22×#9363
A4×#1243
C3×#9364