Finite Group Databasebeta

← A4×#944 #11923363

Subgroups — A4×#944 #11923363

Order 1152.

806 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 111 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×Q8×A4C211yesmaximal, characteristic
2C2×A4×Dic6C211yesmaximal, characteristic
3A4×Dic3⋊C4C214yesmaximal
4C4×Dic3×A4C211yesmaximal, characteristic
5C22×#944C311yesmaximal, characteristic, complemented
6A4×C4⋊Q8—31nomaximal
7C3×Q8×A4—22no—
8C2×C3×C4×A4C2212yes—
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C2212yes—
11C2×Dic3×A4C2212yes—
12A4×Dic6—22no—
13C3×#944—41nomaximal
14C23×C3×Q8C2×C311yescharacteristic
15C23×Dic6C2×C311yescharacteristic
16C2×Q8×A4—21no—
17C2×Q8×A4—31no—
18C2×Q8×A4D311yescharacteristic
19C2×#944—31no—
20C2×#944—31no—
21C2×#944—34no—
22C2×#944—31no—
23C2×#944—31no—
24C22×Dic3⋊C4C2×C314yes—
25C22×C4×Dic3C2×C311yescharacteristic
26A4×C4⋊C4—34no—
27C42×A4—31no—
28C22×C3×A4C2311yescharacteristic
29C2×C32×Q8—41no—
30C2×C3×Dic6—41no—
31C3×C4×A4—22no—
32C3×C4×A4D412yes—
33Dic3×A4—22no—
34Dic3×A4Q814yescomplemented
35C3×Dic3⋊C4—44no—
36C3×C4×Dic3—41no—
37C22×C4⋊Q8—31noSylow
38C22×C3×Q8—22no—
39C22×C3×Q8—31no—
40C22×C3×Q8—32no—
41C22×C3×Q8—31no—
42C22×C3×Q8—62no—
43C23×C3×C4C22×C312yes—
44C23×C3×C4C22×C311yescharacteristic
45C23×Dic3C22×C312yes—
46C23×Dic3C22×C312yes—
47C22×Dic6—22no—
48C22×Dic6—31no—
49C22×Dic6—31no—
50C22×Dic6—32no—
51C22×Dic6—62no—
52Q8×A4—24no—
53Q8×A4—22no—
54Q8×A4—62no—
55C2×C4×A4—22no—
56C2×C4×A4—21no—
57C2×C4×A4—32no—
58C2×C4×A4—32no—
59C2×C4×A4C2×D312yes—
60C2×C4×A4C2×D311yescharacteristic
61C3×C4⋊Q8—121no—
62#944—34no—
63#944—34no—
64#944—32no—
65#944—34no—
66#944—31no—
67#944—31no—
68#944—34no—
69#944—31no—
70#944A411yescharacteristic, direct product factor
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—34no—
74C2×Dic3⋊C4—34no—
75C2×C4×Dic3—31no—
76C2×C4×Dic3—31no—
77C2×C4×Dic3—32no—
78C2×C3×A4C2×D411yescharacteristic
79C2×C3×A4C2×Q812yes—
80C32×Q8—82no—
81C2×C32×C4—41no—
82C2×C32×C4—42no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—42no—
85C3×Dic6—82no—
86C23×Q8—31no—
87C23×Q8C3×D311yescharacteristic
88C2×C4⋊Q8—91no—
89C2×C4⋊Q8—91no—
90C2×C4⋊Q8—94no—
91C2×C4⋊Q8—91no—
92C2×C4⋊Q8—91no—
93C22×C4⋊C4—34no—
94C22×C42—31no—
95C24×C3C23×C311yescharacteristic
96C22×A4—21no—
97C22×A4C22×D311yescharacteristic
98C2×C3×Q8—32no—
99C2×C3×Q8—32no—
100C2×C3×Q8—31no—
101C2×C3×Q8—41no—
102C2×C3×Q8—62no—
103C2×C3×Q8—62no—
104C2×C3×Q8—62no—
105C2×C3×Q8—64no—
106C2×C3×Q8—62no—
107C2×C3×Q8—64no—
108C2×C3×Q8—81no—
109C2×C3×Q8—121no—
110C2×C3×Q8C2×A411yescharacteristic
111C22×C3×C4—22no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—32no—
115C22×C3×C4—32no—
116C22×C3×C4—32no—
117C22×C3×C4—62no—
118C22×C3×C4C3×D412yes—
119C22×Dic3—22no—
120C22×Dic3—32no—
121C22×Dic3—32no—
122C22×Dic3—34no—
123C22×Dic3—32no—
124C22×Dic3—32no—
125C22×Dic3—62no—
126C22×Dic3C3×Q814yescomplemented
127C2×Dic6—32no—
128C2×Dic6—31no—
129C2×Dic6—32no—
130C2×Dic6—62no—
131C2×Dic6—62no—
132C2×Dic6—64no—
133C2×Dic6—64no—
134C2×Dic6—62no—
135C2×Dic6—62no—
136C2×Dic6C2×A411yescharacteristic
137C4×A4—24no—
138C4×A4—22no—
139C4×A4—22no—
140C4×A4—34no—
141C4×A4—62no—
142C4×A4#6712yes—
143C3×C4⋊C4—124no—
144C3×C42—121no—
145Dic3⋊C4—38no—
146Dic3⋊C4—34no—
147Dic3⋊C4—34no—
148Dic3⋊C4—34no—
149Dic3⋊C4C2×A414yes—
150C4×Dic3—32no—
151C4×Dic3—31no—
152C4×Dic3—32no—
153C4×Dic3C2×A411yescharacteristic
154C22×C32—41no—
155C3×A4C4⋊Q811yescharacteristic, complemented
156C32×C4—42no—
157C32×C4—82no—
158C3×Dic3—44no—
159C3×Dic3—82no—
160C22×Q8—22no—
161C22×Q8—31no—
162C22×Q8—32no—
163C22×Q8—31no—
164C22×Q8—62no—
165C22×Q8—62no—
166C22×Q8—91no—
167C22×Q8—91no—
168C22×Q8—92no—
169C22×Q8—182no—
170C23×C4—32no—
171C23×C4—32no—
172C23×C4C2×C3×D312yes—
173C23×C4C2×C3×D311yescharacteristic
174C4⋊Q8—31no—
175C4⋊Q8—91no—
176C4⋊Q8—94no—
177C4⋊Q8—91no—
178C4⋊Q8—94no—
179C4⋊Q8—94no—
180C4⋊Q8—94no—
181C4⋊Q8—92no—
182C4⋊Q8—91no—
183C2×C4⋊C4—94no—
184C2×C4⋊C4—94no—
185C2×C4⋊C4—94no—
186C2×C4⋊C4—94no—
187C2×C42—91no—
188C2×C42—92no—
189C2×C42—91no—
190C23×C3—32no—
191C23×C3—31no—
192C23×C3—31no—
193C23×C3C2×C3×D411yescharacteristic
194C23×C3C2×C3×Q812yes—
195C2×A4—22no—
196C2×A4—21no—
197C2×A4D3×Q812yes—
198C2×A4C2×#6711yescharacteristic
199C3×Q8—22no—
200C3×Q8—64no—
201C3×Q8—64no—
202C3×Q8—62no—
203C3×Q8—82no—
204C3×Q8—84no—
205C3×Q8—242no—
206C2×C3×C4—32no—
207C2×C3×C4—31no—
208C2×C3×C4—32no—
209C2×C3×C4—32no—
210C2×C3×C4—32no—
211C2×C3×C4—32no—
212C2×C3×C4—41no—
213C2×C3×C4—42no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—62no—
218C2×C3×C4—82no—
219C2×C3×C4—81no—
220C2×C3×C4—122no—
221C2×C3×C4—122no—
222C2×C3×C4C22×A412yes—
223C2×C3×C4C22×A411yescharacteristic
224C2×Dic3—34no—
225C2×Dic3—32no—
226C2×Dic3—34no—
227C2×Dic3—34no—
228C2×Dic3—34no—
229C2×Dic3—32no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3C22×A412yes—
235C2×Dic3C22×A412yes—
236Dic6—22no—
237Dic6—64no—
238Dic6—64no—
239Dic6—62no—
240C2×C32—41no—
241C2×C32—42no—
242C24C22×C3×D311yescharacteristic
243C2×Q8—32no—
244C2×Q8—31no—
245C2×Q8—32no—
246C2×Q8—31no—
247C2×Q8—62no—
248C2×Q8—62no—
249C2×Q8—62no—
250C2×Q8—64no—
251C2×Q8—62no—
252C2×Q8—64no—
253C2×Q8—92no—
254C2×Q8—92no—
255C2×Q8—91no—
256C2×Q8—182no—
257C2×Q8—182no—
258C2×Q8—182no—
259C2×Q8—184no—
260C2×Q8—182no—
261C2×Q8—184no—
262C2×Q8D3×A411yescharacteristic
263C22×C4—22no—
264C22×C4—31no—
265C22×C4—31no—
266C22×C4—32no—
267C22×C4—32no—
268C22×C4—32no—
269C22×C4—34no—
270C22×C4—62no—
271C22×C4—62no—
272C22×C4—92no—
273C22×C4—92no—
274C22×C4—92no—
275C22×C4—94no—
276C22×C4—92no—
277C22×C4—182no—
278C22×C4C3×#6712yes—
279C4⋊C4—34no—
280C4⋊C4—94no—
281C4⋊C4—94no—
282C4⋊C4—98no—
283C4⋊C4—94no—
284C42—31no—
285C42—92no—
286C42—92no—
287C42—91no—
288C22×C3—31no—
289C22×C3—32no—
290C22×C3—32no—
291C22×C3—31no—
292C22×C3—31no—
293C22×C3—32no—
294C22×C3—32no—
295C22×C3—41no—
296C22×C3—81no—
297C22×C3C3×C4⋊Q811yescharacteristic, complemented
298C22×C3C23×A411yescharacteristic
299A4—21no—
300A4#94411yescharacteristic, direct product factor
301C3×C4—22no—
302C3×C4—32no—
303C3×C4—42no—
304C3×C4—62no—
305C3×C4—82no—
306C3×C4—84no—
307C3×C4—82no—
308C3×C4—124no—
309C3×C4—242no—
310C3×C4D4×A412yes—
311Dic3—22no—
312Dic3—34no—
313Dic3—62no—
314Dic3Q8×A414yescomplemented
315C32—41noSylow
316C23—31no—
317C23—32no—
318C23—31no—
319C23C3×D3×Q812yes—
320C23C2×C3×#6711yescharacteristic
321Q8—22no—
322Q8—64no—
323Q8—64no—
324Q8—62no—
325Q8—62no—
326Q8—184no—
327Q8—184no—
328Q8—182no—
329C2×C4—32no—
330C2×C4—32no—
331C2×C4—31no—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—62no—
341C2×C4—94no—
342C2×C4—94no—
343C2×C4—94no—
344C2×C4—92no—
345C2×C4—94no—
346C2×C4—92no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4C2×D3×A412yes—
352C2×C4C2×D3×A411yescharacteristic
353C2×C3—31no—
354C2×C3—32no—
355C2×C3—31no—
356C2×C3—42no—
357C2×C3—41no—
358C2×C3—82no—
359C2×C3—81no—
360C2×C3C2×D4×A411yescharacteristic
361C2×C3C2×Q8×A412yes—
362C22—32no—
363C22—31no—
364C22—32no—
365C22—32no—
366C22—32no—
367C22—31no—
368C22—31no—
369C22C3×#94411yescharacteristic, complemented
370C22C22×D3×A411yescharacteristic
371C4—22no—
372C4—34no—
373C4—32no—
374C4—62no—
375C4—62no—
376C4—94no—
377C4—182no—
378C4A4×#6712yes—
379C3—41no—
380C3—81no—
381C3A4×C4⋊Q811yescharacteristic, complemented
382C2—31no—
383C2—32no—
384C2—31no—
385C2D3×Q8×A412yes—
386C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×Q8C2×C3
prime radicalC22×C3×A4C23
hypercenterC2×Q8D3×A4
hypocenterC22×C3C3×C4⋊Q8
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
5. C22×#944C3semidirect
34. Dic3×A4Q8semidirect
70. #944A4direct (N × H)
126. C22×Dic3C3×Q8semidirect
155. C3×A4C4⋊Q8semidirect
297. C22×C3C3×C4⋊Q8semidirect
300. A4#944direct (N × H)
314. Dic3Q8×A4semidirect
369. C22C3×#944semidirect
381. C3A4×C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C2×A4×Dic62
A4×Dic3⋊C42
C4×Dic3×A42
C22×#9443
A4×C4⋊Q83
C3×#9444