Finite Group Databasebeta

← A4×#835 #11921361

Subgroups — A4×#835 #11921361

Order 1152.

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

normal subgroups only

This group has 450 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×Q8×A4C211yesmaximal, characteristic
2A4×C4⋊Dic3C211yesmaximal, characteristic
3C2×A4×C3⋊C8C211yesmaximal, characteristic
4C22×#835C311yesmaximal, characteristic, complemented
5A4×#103—31nomaximal
6C3×Q8×A4—21no—
7C3×Q8×A4C412yescomplemented
8C2×C3×C4×A4—21no—
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4—21no—
11A4×C3⋊C8—21no—
12C3×#835—41nomaximal
13C23×C3×Q8C2×C311yescharacteristic
14C2×Q8×A4—21no—
15C2×Q8×A4D311yescharacteristic
16C22×C4⋊Dic3C2×C311yescharacteristic
17C23×C3⋊C8C2×C311yescharacteristic
18C2×C8×A4—31no—
19A4×C4⋊C4—31no—
20C2×#835—31no—
21C2×#835—31no—
22C2×#835—31no—
23C2×#835—31no—
24C22×C3×A4D411yescharacteristic
25C2×C32×Q8—41no—
26C3×C4×A4—22no—
27C3×C4×A4C2×C411yescharacteristic
28C3×C4×A4D411yescharacteristic
29Dic3×A4—41no—
30C3×C4⋊Dic3—41no—
31C2×C3×C3⋊C8—41no—
32C22×#103—31noSylow
33C22×C3×Q8—21no—
34C22×C3×Q8—32no—
35C22×C3×Q8—31no—
36C22×C3×Q8—31no—
37C22×C3×Q8—61no—
38C22×C3×Q8—61no—
39C22×C3×Q8C3×C412yescomplemented
40C23×C3×C4—21no—
41C23×C3×C4C22×C311yescharacteristic
42C23×Dic3—21no—
43Q8×A4—22no—
44Q8×A4—21no—
45Q8×A4—22no—
46Q8×A4Dic312yescomplemented
47C2×C4×A4—22no—
48C2×C4×A4—21no—
49C2×C4×A4—21no—
50C2×C4×A4—61no—
51C2×C4×A4C2×D311yescharacteristic
52C2×C4⋊Dic3—31no—
53C2×C4⋊Dic3—31no—
54C2×C4⋊Dic3—61no—
55C22×C3⋊C8—21no—
56C22×C3⋊C8—31no—
57C22×C3⋊C8—31no—
58C22×C3⋊C8—61no—
59C8×A4—61no—
60C3×#103—121no—
61#835—32no—
62#835—31no—
63#835—31no—
64#835—31no—
65#835A411yescharacteristic, direct product factor
66C2×C3×A4C22⋊C411yescharacteristic
67C2×C3×A4SD1611yescharacteristic
68C2×C3×A4Q1611yescharacteristic
69C32×Q8—42no—
70C32×Q8—81no—
71C2×C32×C4—41no—
72C2×C32×C4—81no—
73C2×C3×Dic3—81no—
74C3×C3⋊C8—81no—
75C23×Q8C3×D311yescharacteristic
76C23×C8—31no—
77C22×C4⋊C4—31no—
78C2×#103—91no—
79C2×#103—91no—
80C2×#103—91no—
81C2×#103—91no—
82C24×C3C3×D411yescharacteristic
83C22×A4—21no—
84C22×A4#6711yescharacteristic
85C2×C3×Q8—32no—
86C2×C3×Q8—32no—
87C2×C3×Q8—32no—
88C2×C3×Q8—32no—
89C2×C3×Q8—31no—
90C2×C3×Q8—41no—
91C2×C3×Q8—61no—
92C2×C3×Q8—61no—
93C2×C3×Q8—61no—
94C2×C3×Q8—62no—
95C2×C3×Q8—61no—
96C2×C3×Q8—62no—
97C2×C3×Q8—61no—
98C2×C3×Q8—64no—
99C2×C3×Q8—61no—
100C2×C3×Q8—81no—
101C2×C3×Q8C2×A411yescharacteristic
102C22×C3×C4—22no—
103C22×C3×C4—31no—
104C22×C3×C4—31no—
105C22×C3×C4—31no—
106C22×C3×C4—31no—
107C22×C3×C4—61no—
108C22×C3×C4—62no—
109C22×C3×C4—61no—
110C22×C3×C4C2×C3×C411yescharacteristic
111C22×C3×C4C3×D411yescharacteristic
112C22×Dic3—41no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C22×Dic3—121no—
116C4×A4—24no—
117C4×A4—22no—
118C4×A4—21no—
119C4×A4—21no—
120C4×A4—121no—
121C4×A4C2×Dic311yescharacteristic
122C4×A4#6711yescharacteristic
123C2×C3×C8—121no—
124C3×C4⋊C4—121no—
125C4⋊Dic3—31no—
126C4⋊Dic3—61no—
127C4⋊Dic3—61no—
128C4⋊Dic3C2×A411yescharacteristic
129C2×C3⋊C8—31no—
130C2×C3⋊C8—61no—
131C2×C3⋊C8—61no—
132C2×C3⋊C8—61no—
133C2×C3⋊C8—61no—
134C2×C3⋊C8C2×A411yescharacteristic
135C22×C32—41no—
136C3×A4#10311yescharacteristic, complemented
137C32×C4—41no—
138C32×C4—41no—
139C32×C4—82no—
140C3×Dic3—161no—
141C22×Q8—21no—
142C22×Q8—31no—
143C22×Q8—32no—
144C22×Q8—31no—
145C22×Q8—61no—
146C22×Q8—61no—
147C22×Q8C3×Dic312yescomplemented
148C23×C4—21no—
149C23×C4—61no—
150C23×C4C2×C3×D311yescharacteristic
151C22×C8—61no—
152C22×C8—91no—
153C22×C8—91no—
154C22×C8—181no—
155C2×C4⋊C4—91no—
156C2×C4⋊C4—91no—
157C2×C4⋊C4—181no—
158#103—31no—
159#103—91no—
160#103—91no—
161#103—92no—
162#103—91no—
163C23×C3—31no—
164C23×C3—31no—
165C23×C3—31no—
166C23×C3—31no—
167C23×C3C3×C22⋊C411yescharacteristic
168C23×C3C3×SD1611yescharacteristic
169C23×C3C3×Q1611yescharacteristic
170C2×A4—21no—
171C2×A4—21no—
172C2×A4—21no—
173C2×A4#21511yescharacteristic
174C2×A4#21611yescharacteristic
175C2×A4#21711yescharacteristic
176C3×Q8—21no—
177C3×Q8—32no—
178C3×Q8—42no—
179C3×Q8—62no—
180C3×Q8—62no—
181C3×Q8—62no—
182C3×Q8—62no—
183C3×Q8—61no—
184C3×Q8—81no—
185C3×Q8—82no—
186C3×Q8—82no—
187C3×Q8C4×A412yescomplemented
188C2×C3×C4—21no—
189C2×C3×C4—32no—
190C2×C3×C4—31no—
191C2×C3×C4—31no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—31no—
196C2×C3×C4—31no—
197C2×C3×C4—41no—
198C2×C3×C4—62no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4—61no—
202C2×C3×C4—62no—
203C2×C3×C4—81no—
204C2×C3×C4—82no—
205C2×C3×C4—81no—
206C2×C3×C4—241no—
207C2×C3×C4C22×A411yescharacteristic
208C2×Dic3—21no—
209C2×Dic3—61no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212C2×Dic3—121no—
213C2×Dic3—121no—
214C3×C8—241no—
215C3⋊C8—21no—
216C3⋊C8—61no—
217C2×C32—41no—
218C2×C32—41no—
219C2×C32—41no—
220C24C3×#6711yescharacteristic
221C2×Q8—32no—
222C2×Q8—32no—
223C2×Q8—32no—
224C2×Q8—32no—
225C2×Q8—31no—
226C2×Q8—61no—
227C2×Q8—61no—
228C2×Q8—61no—
229C2×Q8—62no—
230C2×Q8—61no—
231C2×Q8—62no—
232C2×Q8—61no—
233C2×Q8—64no—
234C2×Q8—61no—
235C2×Q8D3×A411yescharacteristic
236C22×C4—22no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—61no—
242C22×C4—62no—
243C22×C4—61no—
244C22×C4—121no—
245C22×C4—181no—
246C22×C4—181no—
247C22×C4—361no—
248C22×C4C2×C3×Dic311yescharacteristic
249C22×C4C3×#6711yescharacteristic
250C2×C8—31no—
251C2×C8—91no—
252C2×C8—181no—
253C2×C8—181no—
254C2×C8—181no—
255C2×C8—181no—
256C4⋊C4—31no—
257C4⋊C4—91no—
258C4⋊C4—181no—
259C4⋊C4—181no—
260C22×C3—31no—
261C22×C3—31no—
262C22×C3—31no—
263C22×C3—32no—
264C22×C3—31no—
265C22×C3—31no—
266C22×C3—31no—
267C22×C3—31no—
268C22×C3—31no—
269C22×C3—31no—
270C22×C3—41no—
271C22×C3—81no—
272C22×C3C3×#10311yescharacteristic, complemented
273C22×C3D4×A411yescharacteristic
274A4—21no—
275A4#83511yescharacteristic, direct product factor
276C3×C4—22no—
277C3×C4—31no—
278C3×C4—31no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—62no—
282C3×C4—82no—
283C3×C4—84no—
284C3×C4—81no—
285C3×C4—81no—
286C3×C4—481no—
287C3×C4C2×C4×A411yescharacteristic
288C3×C4D4×A411yescharacteristic
289Dic3—41no—
290Dic3—121no—
291C32—41noSylow
292C23—31no—
293C23—31no—
294C23—31no—
295C23—31no—
296C23C3×#21511yescharacteristic
297C23C3×#21611yescharacteristic
298C23C3×#21711yescharacteristic
299Q8—21no—
300Q8—32no—
301Q8—62no—
302Q8—62no—
303Q8—62no—
304Q8—62no—
305Q8—61no—
306Q8Dic3×A412yescomplemented
307C2×C4—21no—
308C2×C4—32no—
309C2×C4—31no—
310C2×C4—31no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—31no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—61no—
320C2×C4—62no—
321C2×C4—61no—
322C2×C4—181no—
323C2×C4—361no—
324C2×C4—361no—
325C2×C4—361no—
326C2×C4—361no—
327C2×C4C2×D3×A411yescharacteristic
328C8—61no—
329C8—181no—
330C2×C3—31no—
331C2×C3—31no—
332C2×C3—31no—
333C2×C3—31no—
334C2×C3—41no—
335C2×C3—41no—
336C2×C3—41no—
337C2×C3—81no—
338C2×C3—81no—
339C2×C3—81no—
340C2×C3A4×C22⋊C411yescharacteristic
341C2×C3A4×SD1611yescharacteristic
342C2×C3A4×Q1611yescharacteristic
343C22—31no—
344C22—31no—
345C22—31no—
346C22—32no—
347C22—31no—
348C22—31no—
349C22—31no—
350C22—31no—
351C22—31no—
352C22—31no—
353C22C3×#83511yescharacteristic, complemented
354C22A4×#6711yescharacteristic
355C4—22no—
356C4—31no—
357C4—31no—
358C4—62no—
359C4—121no—
360C4—361no—
361C4C2×Dic3×A411yescharacteristic
362C4A4×#6711yescharacteristic
363C3—41no—
364C3—81no—
365C3A4×#10311yescharacteristic, complemented
366C2—31no—
367C2—31no—
368C2—31no—
369C2—31no—
370C2A4×#21511yescharacteristic
371C2A4×#21611yescharacteristic
372C2A4×#21711yescharacteristic
subgroupG/H
centerC22A4×#67
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC23×C3×Q8C2×C3
socleC24×C3C3×D4
prime radicalC22×C3×A4D4
cosocleC23×C3×C4C22×C3
hypercenterC2×Q8D3×A4
hypocenterC22×C3C3×#103
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
4. C22×#835C3semidirect
7. C3×Q8×A4C4semidirect
39. C22×C3×Q8C3×C4semidirect
46. Q8×A4Dic3semidirect
65. #835A4direct (N × H)
136. C3×A4#103semidirect
147. C22×Q8C3×Dic3semidirect
187. C3×Q8C4×A4semidirect
272. C22×C3C3×#103semidirect
275. A4#835direct (N × H)
306. Q8Dic3×A4semidirect
353. C22C3×#835semidirect
365. C3A4×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
A4×C4⋊Dic32
C2×A4×C3⋊C82
C22×#8353
A4×#1033
C3×#8354