Finite Group Databasebeta

← A4×#805 #11921249

Subgroups — A4×#805 #11921249

Order 1152.

462 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 57 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
1A4×#235C211yesmaximal, characteristic
2C3×C42×A4C211yesmaximal, characteristic, complemented
3A4×#208C211yesmaximal, characteristic, complemented
4C22×#805C311yesmaximal, characteristic, complemented
5A4×#104—31nomaximal
6C2×C3×C4×A4—21no—
7C2×C3×C4×A4C2211yescharacteristic
8A4×#67—21no—
9A4×D12C411yescharacteristic, complemented
10C4×D3×A4—21no—
11A4×Dic6C411yescharacteristic, complemented
12A4×C3⋊C8—21no—
13C3×#805—41nomaximal
14C22×#235C2×C311yescharacteristic
15A4×#41—31no—
16C22×C3×C42C2×C311yescharacteristic, complemented
17C22×#208C2×C311yescharacteristic, complemented
18A4×M16—31no—
19C42×A4—21no—
20C42×A4D311yescharacteristic, complemented
21C2×#805—31no—
22C2×#805—31no—
23C2×#805—31no—
24C2×#805—31no—
25C22×C3×A4D411yescharacteristic
26C2×D3×A4—21no—
27C3×#235—41no—
28C3×C4×A4—22no—
29C3×C4×A4C2×C411yescharacteristic
30C3×C4×A4D411yescharacteristic
31Dic3×A4—21no—
32C32×C42—41no—
33C3×#208—41no—
34C22×#104—31noSylow
35C23×C3×C4—21no—
36C23×C3×C4C22×C311yescharacteristic
37C22×#67—21no—
38C2×#235—31no—
39C2×#235—31no—
40C2×#235—31no—
41C2×#235—31no—
42C2×#235—61no—
43C2×#235—61no—
44C22×D12C3×C411yescharacteristic, complemented
45C22×C4×D3—21no—
46C22×Dic6C3×C411yescharacteristic, complemented
47Q8×A4—31no—
48D4×A4—31no—
49D4×A4—61no—
50C2×C4×A4—22no—
51C2×C4×A4—21no—
52C2×C4×A4—21no—
53C2×C4×A4—61no—
54C2×C4×A4C2×D311yescharacteristic
55C2×C3×C42—31no—
56C2×C3×C42—31no—
57C2×C3×C42—61no—
58C2×#208—31no—
59C2×#208—31no—
60C2×#208—61no—
61C22×C3⋊C8—21no—
62C8×A4—61no—
63C3×#104—121no—
64#805—32no—
65#805—31no—
66#805—31no—
67#805—31no—
68#805A411yescharacteristic, direct product factor
69C2×C3×A4—21no—
70C2×C3×A4C22⋊C411yescharacteristic
71D3×A4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—81no—
74C3×#67—81no—
75C3×D12—41no—
76C3×C4×D3—81no—
77C3×Dic6—41no—
78C3×C3⋊C8—81no—
79C22×#41—31no—
80C22×M16—31no—
81C22×C42C3×D311yescharacteristic, complemented
82C2×#104—91no—
83C2×#104—91no—
84C2×#104—91no—
85C2×#104—91no—
86C24×C3C3×D411yescharacteristic
87C23×D3—21no—
88C22×A4—21no—
89C22×A4—61no—
90C22×A4#6711yescharacteristic
91C3×#41—121no—
92C22×C3×C4—22no—
93C22×C3×C4—31no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—31no—
97C22×C3×C4—61no—
98C22×C3×C4—61no—
99C22×C3×C4—62no—
100C22×C3×C4C2×C3×C411yescharacteristic
101C22×C3×C4C3×D411yescharacteristic
102C2×#67—61no—
103C2×#67—61no—
104C2×#67—61no—
105C2×#67—61no—
106C22×Dic3—21no—
107#235—32no—
108#235—31no—
109#235—31no—
110#235—31no—
111#235—61no—
112#235—61no—
113#235—62no—
114#235—62no—
115#235—61no—
116#235—61no—
117#235C2×A411yescharacteristic
118C2×D12—31no—
119C2×D12—31no—
120C2×D12—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×Dic6—31no—
126C2×Dic6—31no—
127C2×Dic6—61no—
128C4×A4—24no—
129C4×A4—22no—
130C4×A4—21no—
131C4×A4—21no—
132C4×A4—61no—
133C4×A4C4×D311yescharacteristic
134C4×A4D1211yescharacteristic
135C3×M16—121no—
136C3×C42—31no—
137C3×C42—41no—
138C3×C42—61no—
139C3×C42—61no—
140C3×C42—81no—
141C3×C42C2×A411yescharacteristic, complemented
142#208—31no—
143#208—61no—
144#208—61no—
145#208C2×A411yescharacteristic, complemented
146C2×C3⋊C8—61no—
147C2×C3⋊C8—61no—
148C22×C32—41no—
149C2×C3×D3—81no—
150C3×A4#10411yescharacteristic, complemented
151C32×C4—41no—
152C32×C4—41no—
153C32×C4—82no—
154C3×Dic3—81no—
155C2×#41—91no—
156C2×#41—91no—
157C2×#41—91no—
158C2×#41—91no—
159C2×#41—181no—
160C2×#41—181no—
161C22×Q8—31no—
162C22×D4—31no—
163C22×D4—61no—
164C23×C4—21no—
165C23×C4—61no—
166C23×C4C2×C3×D311yescharacteristic
167C2×M16—91no—
168C2×M16—91no—
169C2×M16—181no—
170C22×C8—61no—
171C2×C42—31no—
172C2×C42—31no—
173C2×C42—61no—
174#104—31no—
175#104—91no—
176#104—91no—
177#104—92no—
178#104—91no—
179C23×C3—21no—
180C23×C3—31no—
181C23×C3—31no—
182C23×C3—61no—
183C23×C3C3×C22⋊C411yescharacteristic
184C22×D3—41no—
185C22×D3—61no—
186C22×D3—61no—
187C22×D3—121no—
188C2×A4—22no—
189C2×A4—21no—
190C2×A4—21no—
191C2×A4—121no—
192C2×A4(C2×D3)⋊C411yescharacteristic
193C3×Q8—121no—
194C3×D4—121no—
195C3×D4—241no—
196C2×C3×C4—21no—
197C2×C3×C4—32no—
198C2×C3×C4—31no—
199C2×C3×C4—31no—
200C2×C3×C4—31no—
201C2×C3×C4—31no—
202C2×C3×C4—31no—
203C2×C3×C4—31no—
204C2×C3×C4—31no—
205C2×C3×C4—41no—
206C2×C3×C4—62no—
207C2×C3×C4—62no—
208C2×C3×C4—62no—
209C2×C3×C4—61no—
210C2×C3×C4—62no—
211C2×C3×C4—81no—
212C2×C3×C4—82no—
213C2×C3×C4—81no—
214C2×C3×C4—241no—
215C2×C3×C4C22×A411yescharacteristic
216#67—21no—
217#67—61no—
218#67—61no—
219#67—62no—
220#67—61no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223D12—31no—
224D12—61no—
225D12—61no—
226D12C4×A411yescharacteristic, complemented
227C4×D3—21no—
228C4×D3—61no—
229C4×D3—61no—
230C4×D3—62no—
231C4×D3—61no—
232Dic6—31no—
233Dic6—61no—
234Dic6—61no—
235Dic6C4×A411yescharacteristic, complemented
236C3×C8—241no—
237C3⋊C8—21no—
238C3⋊C8—61no—
239C2×C32—41no—
240C2×C32—81no—
241C3×D3—161no—
242C24—61no—
243C24C3×#6711yescharacteristic
244#41—31no—
245#41—91no—
246#41—91no—
247#41—92no—
248#41—91no—
249#41—181no—
250#41—181no—
251#41—182no—
252#41—182no—
253#41—181no—
254#41—181no—
255C2×Q8—91no—
256C2×Q8—91no—
257C2×Q8—181no—
258C2×D4—91no—
259C2×D4—91no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263C2×D4—181no—
264C2×D4—181no—
265C22×C4—22no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—61no—
271C22×C4—61no—
272C22×C4—62no—
273C22×C4—61no—
274C22×C4—181no—
275C22×C4—181no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4C3×C4×D311yescharacteristic
279C22×C4C3×D1211yescharacteristic
280M16—31no—
281M16—91no—
282M16—181no—
283M16—181no—
284C2×C8—181no—
285C2×C8—181no—
286C42—31no—
287C42—61no—
288C42—61no—
289C42D3×A411yescharacteristic, complemented
290C22×C3—31no—
291C22×C3—31no—
292C22×C3—31no—
293C22×C3—41no—
294C22×C3—61no—
295C22×C3—61no—
296C22×C3—61no—
297C22×C3—61no—
298C22×C3—81no—
299C22×C3—241no—
300C22×C3C3×#10411yescharacteristic, complemented
301C22×C3D4×A411yescharacteristic
302C2×D3—21no—
303C2×D3—61no—
304C2×D3—121no—
305C2×D3—121no—
306C2×D3—121no—
307C2×D3—121no—
308A4—21no—
309A4#80511yescharacteristic, direct product factor
310C3×C4—22no—
311C3×C4—31no—
312C3×C4—31no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—62no—
316C3×C4—82no—
317C3×C4—84no—
318C3×C4—81no—
319C3×C4—81no—
320C3×C4—241no—
321C3×C4C2×C4×A411yescharacteristic
322C3×C4D4×A411yescharacteristic
323Dic3—21no—
324Dic3—61no—
325C32—41noSylow
326C23—21no—
327C23—31no—
328C23—31no—
329C23—61no—
330C23—121no—
331C23—181no—
332C23—181no—
333C23—361no—
334C23C3×(C2×D3)⋊C411yescharacteristic
335Q8—31no—
336Q8—91no—
337Q8—181no—
338Q8—181no—
339D4—31no—
340D4—61no—
341D4—91no—
342D4—181no—
343D4—181no—
344D4—181no—
345D4—181no—
346D4—182no—
347D4—181no—
348C2×C4—21no—
349C2×C4—32no—
350C2×C4—31no—
351C2×C4—31no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—31no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—62no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—182no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4—181no—
369C2×C4C2×D3×A411yescharacteristic
370C8—61no—
371C8—181no—
372C2×C3—21no—
373C2×C3—31no—
374C2×C3—31no—
375C2×C3—41no—
376C2×C3—61no—
377C2×C3—81no—
378C2×C3—82no—
379C2×C3—81no—
380C2×C3—481no—
381C2×C3A4×C22⋊C411yescharacteristic
382D3—41no—
383D3—121no—
384C22—31no—
385C22—31no—
386C22—31no—
387C22—61no—
388C22—61no—
389C22—61no—
390C22—61no—
391C22—61no—
392C22—181no—
393C22—361no—
394C22—361no—
395C22—361no—
396C22—361no—
397C22C3×#80511yescharacteristic, complemented
398C22A4×#6711yescharacteristic
399C4—22no—
400C4—31no—
401C4—31no—
402C4—62no—
403C4—61no—
404C4—181no—
405C4C4×D3×A411yescharacteristic
406C4A4×D1211yescharacteristic
407C3—41no—
408C3—81no—
409C3A4×#10411yescharacteristic, complemented
410C2—21no—
411C2—31no—
412C2—31no—
413C2—61no—
414C2—121no—
415C2—361no—
416C2A4×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4A4×D12
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC22×C3×C42C2×C3
socleC23×C3C3×C22⋊C4
prime radicalA4×#235C2
cosocleC23×C3×C4C22×C3
hypercenterC42D3×A4
hypocenterC22×C3C3×#104
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C42×A4C2semidirect
3. A4×#208C2semidirect
4. C22×#805C3semidirect
9. A4×D12C4semidirect
11. A4×Dic6C4semidirect
16. C22×C3×C42C2×C3semidirect
17. C22×#208C2×C3semidirect
20. C42×A4D3semidirect
44. C22×D12C3×C4semidirect
46. C22×Dic6C3×C4semidirect
68. #805A4direct (N × H)
81. C22×C42C3×D3semidirect
141. C3×C42C2×A4semidirect
145. #208C2×A4semidirect
150. C3×A4#104semidirect
226. D12C4×A4semidirect
235. Dic6C4×A4semidirect
289. C42D3×A4semidirect
300. C22×C3C3×#104semidirect
309. A4#805direct (N × H)
397. C22C3×#805semidirect
409. C3A4×#104semidirect

Maximal subgroups

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

subgroupindex
A4×#2352
C3×C42×A42
A4×#2082
C22×#8053
A4×#1043
C3×#8054