Finite Group Databasebeta

← A4×#4036 #14513996

Subgroups — A4×#4036 #14513996

Order 1920.

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

normal subgroups only

This group has 584 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
1C5×A4×C4⋊C4C211yesmaximal, characteristic
2A4×C4⋊Dic5C212yesmaximal
3A4×C4⋊Dic5C211yesmaximal, characteristic
4A4×#683C212yesmaximal
5C4×A4×Dic5C211yesmaximal, characteristic
6C22×#4036C311yesmaximal, characteristic, complemented, Hall
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4×Dic5C2211yescharacteristic
10C2×A4×Dic5C2211yescharacteristic
11C2×A4×Dic5C2212yes—
12C3×#4036—41nomaximal
13A4×#125—51nomaximal, Hall
14C22×C5×C4⋊C4C2×C311yescharacteristic
15C22×C4⋊Dic5C2×C312yes—
16C22×C4⋊Dic5C2×C311yescharacteristic
17C22×#683C2×C312yes—
18C22×C4×Dic5C2×C311yescharacteristic
19C2×#4036—31no—
20C2×#4036—31no—
21C2×#4036—31no—
22C2×#4036—32no—
23C2×#4036—32no—
24C2×#4036—31no—
25C22×C5×A4C2311yescharacteristic
26C4×C5×A4—22no—
27C4×C5×A4Q812yes—
28A4×Dic5—21no—
29A4×Dic5—21no—
30A4×Dic5—22no—
31C3×C5×C4⋊C4—41no—
32C3×C4⋊Dic5—42no—
33C3×C4⋊Dic5—41no—
34C3×#683—42no—
35C3×C4×Dic5—41no—
36A4×C4⋊C4—52no—
37A4×C4⋊C4—52no—
38A4×C4⋊C4—51no—
39A4×C4⋊C4D511yescharacteristic
40C42×A4—51no—
41C23×C4×C5C22×C312yes—
42C23×C4×C5C22×C311yescharacteristic
43C23×Dic5C22×C311yescharacteristic
44C23×Dic5C22×C311yescharacteristic
45C23×Dic5C22×C312yes—
46C2×C5×C4⋊C4—31no—
47C2×C5×C4⋊C4—31no—
48C2×C5×C4⋊C4—32no—
49C2×C4⋊Dic5—32no—
50C2×C4⋊Dic5—31no—
51C2×C4⋊Dic5—32no—
52C2×C4⋊Dic5—31no—
53C2×C4⋊Dic5—32no—
54C2×C4⋊Dic5—32no—
55C2×C4⋊Dic5—32no—
56C2×#683—32no—
57C2×#683—32no—
58C2×#683—32no—
59C2×#683—32no—
60C2×C4×Dic5—31no—
61C2×C4×Dic5—31no—
62C2×C4×Dic5—31no—
63C2×C4×Dic5—31no—
64#4036—34no—
65#4036—34no—
66#4036—32no—
67#4036—32no—
68#4036—32no—
69#4036—31no—
70#4036—31no—
71#4036—32no—
72#4036—32no—
73#4036—31no—
74#4036A411yescharacteristic, direct product factor
75C22×#125—51noSylow
76C2×C5×A4C2×Q811yescharacteristic
77C2×C5×A4#4111yescharacteristic
78C2×C5×A4#4111yescharacteristic
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—42no—
81C2×C3×Dic5—41no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—42no—
84C2×C4×A4—51no—
85C2×C4×A4—51no—
86C2×C4×A4—52no—
87C2×C4×A4C2×D512yes—
88C2×C4×A4C2×D511yescharacteristic
89C3×#125—201no—
90C24×C5C23×C311yescharacteristic
91C22×C4×C5—22no—
92C22×C4×C5—31no—
93C22×C4×C5—31no—
94C22×C4×C5—32no—
95C22×C4×C5—32no—
96C22×C4×C5—32no—
97C22×C4×C5—62no—
98C22×C4×C5C3×Q812yes—
99C22×Dic5—21no—
100C22×Dic5—21no—
101C22×Dic5—22no—
102C22×Dic5—31no—
103C22×Dic5—31no—
104C22×Dic5—32no—
105C22×Dic5—31no—
106C22×Dic5—31no—
107C22×Dic5—32no—
108C22×Dic5—61no—
109C22×Dic5—62no—
110C22×Dic5—61no—
111C5×C4⋊C4—32no—
112C5×C4⋊C4—32no—
113C5×C4⋊C4—31no—
114C5×C4⋊C4C2×A411yescharacteristic
115C4⋊Dic5—34no—
116C4⋊Dic5—32no—
117C4⋊Dic5—32no—
118C4⋊Dic5—31no—
119C4⋊Dic5—32no—
120C4⋊Dic5—32no—
121C4⋊Dic5—32no—
122C4⋊Dic5C2×A412yes—
123C4⋊Dic5C2×A411yescharacteristic
124#683—34no—
125#683—32no—
126#683—32no—
127#683—32no—
128#683C2×A412yes—
129C4×Dic5—32no—
130C4×Dic5—31no—
131C4×Dic5—31no—
132C4×Dic5—31no—
133C4×Dic5C2×A411yescharacteristic
134C2×#125—151no—
135C2×#125—151no—
136C2×#125—151no—
137C2×#125—152no—
138C2×#125—152no—
139C2×#125—151no—
140C22×C4⋊C4—52no—
141C22×C4⋊C4—51no—
142C22×C4⋊C4—52no—
143C22×C4⋊C4C3×D511yescharacteristic
144C22×C42—51no—
145C22×C3×C5—41no—
146C5×A4#12511yescharacteristic, complemented
147C3×C4×C5—42no—
148C3×C4×C5—82no—
149C3×Dic5—81no—
150C3×Dic5—82no—
151C3×Dic5—81no—
152C22×A4C22×D511yescharacteristic
153C4×A4—22no—
154C4×A4—101no—
155C4×A4—101no—
156C4×A4—102no—
157C4×A4Dic1012yes—
158C3×C4⋊C4—41no—
159C3×C4⋊C4—202no—
160C3×C4⋊C4—201no—
161C3×C4⋊C4—202no—
162C3×C42—201no—
163C23×C5—31no—
164C23×C5—31no—
165C23×C5—31no—
166C23×C5—31no—
167C23×C5C2×C3×Q811yescharacteristic
168C23×C5C3×#4111yescharacteristic
169C23×C5C3×#4111yescharacteristic
170C2×C4×C5—32no—
171C2×C4×C5—31no—
172C2×C4×C5—32no—
173C2×C4×C5—32no—
174C2×C4×C5—32no—
175C2×C4×C5—32no—
176C2×C4×C5—62no—
177C2×C4×C5—62no—
178C2×C4×C5—62no—
179C2×C4×C5—62no—
180C2×C4×C5C22×A412yes—
181C2×C4×C5C22×A411yescharacteristic
182C2×Dic5—31no—
183C2×Dic5—31no—
184C2×Dic5—32no—
185C2×Dic5—61no—
186C2×Dic5—62no—
187C2×Dic5—61no—
188C2×Dic5—61no—
189C2×Dic5—62no—
190C2×Dic5—61no—
191C2×Dic5—61no—
192C2×Dic5—62no—
193C2×Dic5—61no—
194C2×Dic5—61no—
195C2×Dic5—62no—
196C2×Dic5—61no—
197C2×Dic5C22×A411yescharacteristic
198C2×Dic5C22×A411yescharacteristic
199C2×Dic5C22×A412yes—
200C23×C4—52no—
201C23×C4—51no—
202C23×C4—51no—
203C23×C4C2×C3×D512yes—
204C23×C4C2×C3×D511yescharacteristic
205#125—51no—
206#125—151no—
207#125—152no—
208#125—152no—
209#125—151no—
210#125—152no—
211#125—152no—
212#125—154no—
213#125—154no—
214#125—152no—
215#125—151no—
216C2×C4⋊C4—31no—
217C2×C4⋊C4—31no—
218C2×C4⋊C4—32no—
219C2×C4⋊C4—152no—
220C2×C4⋊C4—151no—
221C2×C4⋊C4—152no—
222C2×C4⋊C4—152no—
223C2×C4⋊C4—152no—
224C2×C4⋊C4—152no—
225C2×C4⋊C4—152no—
226C2×C4⋊C4—152no—
227C2×C4⋊C4—152no—
228C2×C4⋊C4—151no—
229C2×C4⋊C4—152no—
230C2×C42—151no—
231C2×C42—151no—
232C2×C42—151no—
233C2×C42—151no—
234C2×C3×C5—41no—
235C2×C3×C5—41no—
236C2×C3×C5—41no—
237C2×A4C2×Dic1011yescharacteristic
238C2×A4#71111yescharacteristic
239C2×A4#71311yescharacteristic
240C2×C3×C4—41no—
241C2×C3×C4—42no—
242C2×C3×C4—201no—
243C2×C3×C4—201no—
244C2×C3×C4—202no—
245C22×C5—31no—
246C22×C5—31no—
247C22×C5—31no—
248C22×C5—32no—
249C22×C5—31no—
250C22×C5—31no—
251C22×C5—31no—
252C22×C5—31no—
253C22×C5—31no—
254C22×C5—31no—
255C22×C5C3×#12511yescharacteristic, complemented
256C22×C5C23×A411yescharacteristic
257C4×C5—22no—
258C4×C5—32no—
259C4×C5—62no—
260C4×C5Q8×A412yes—
261Dic5—21no—
262Dic5—21no—
263Dic5—22no—
264Dic5—61no—
265Dic5—61no—
266Dic5—62no—
267C24C22×C3×D511yescharacteristic
268C22×C4—22no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—32no—
272C22×C4—32no—
273C22×C4—32no—
274C22×C4—62no—
275C22×C4—101no—
276C22×C4—102no—
277C22×C4—101no—
278C22×C4—151no—
279C22×C4—151no—
280C22×C4—152no—
281C22×C4—151no—
282C22×C4—151no—
283C22×C4—152no—
284C22×C4—301no—
285C22×C4—302no—
286C22×C4—301no—
287C22×C4C3×Dic1012yes—
288C4⋊C4—32no—
289C4⋊C4—32no—
290C4⋊C4—31no—
291C4⋊C4—52no—
292C4⋊C4—52no—
293C4⋊C4—51no—
294C4⋊C4—152no—
295C4⋊C4—152no—
296C4⋊C4—152no—
297C4⋊C4—152no—
298C4⋊C4—152no—
299C4⋊C4—154no—
300C4⋊C4—152no—
301C4⋊C4—154no—
302C4⋊C4—152no—
303C4⋊C4—152no—
304C4⋊C4—151no—
305C4⋊C4D5×A411yescharacteristic
306C42—51no—
307C42—151no—
308C42—151no—
309C42—152no—
310C42—151no—
311C3×C5—41noHall
312C22×C3—41no—
313A4#403611yescharacteristic, direct product factor
314C3×C4—42no—
315C3×C4—82no—
316C3×C4—401no—
317C3×C4—401no—
318C3×C4—402no—
319C2×C5—31no—
320C2×C5—31no—
321C2×C5—31no—
322C2×C5—31no—
323C2×C5C2×Q8×A411yescharacteristic
324C2×C5A4×#4111yescharacteristic
325C2×C5A4×#4111yescharacteristic
326C23—31no—
327C23—31no—
328C23—31no—
329C23—31no—
330C23C2×C3×Dic1011yescharacteristic
331C23C3×#71111yescharacteristic
332C23C3×#71311yescharacteristic
333C2×C4—32no—
334C2×C4—31no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—52no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—62no—
345C2×C4—62no—
346C2×C4—151no—
347C2×C4—151no—
348C2×C4—152no—
349C2×C4—301no—
350C2×C4—301no—
351C2×C4—302no—
352C2×C4—301no—
353C2×C4—301no—
354C2×C4—302no—
355C2×C4—301no—
356C2×C4—301no—
357C2×C4—302no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—302no—
361C2×C4C2×D5×A412yes—
362C2×C4C2×D5×A411yescharacteristic
363C2×C3—41no—
364C2×C3—41no—
365C2×C3—41no—
366C5A4×#12511yescharacteristic, complemented, Sylow
367C22—31no—
368C22—31no—
369C22—31no—
370C22—32no—
371C22—31no—
372C22—31no—
373C22—31no—
374C22—31no—
375C22—31no—
376C22—31no—
377C22C3×#403611yescharacteristic, complemented
378C22C22×D5×A411yescharacteristic
379C4—22no—
380C4—32no—
381C4—62no—
382C4—101no—
383C4—101no—
384C4—102no—
385C4—301no—
386C4—301no—
387C4—302no—
388C4A4×Dic1012yes—
389C3—41noSylow
390C2—31no—
391C2—31no—
392C2—31no—
393C2—31no—
394C2C2×A4×Dic1011yescharacteristic
395C2A4×#71111yescharacteristic
396C2A4×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC22×C5×C4⋊C4C2×C3
prime radicalC22×C5×A4C23
hypercenterC4⋊C4D5×A4
hypocenterC22×C5C3×#125
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×#4036C3semidirect
74. #4036A4direct (N × H)
146. C5×A4#125semidirect
255. C22×C5C3×#125semidirect
313. A4#4036direct (N × H)
366. C5A4×#125semidirect
377. C22C3×#4036semidirect

Maximal subgroups

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

subgroupindex
C5×A4×C4⋊C42
A4×C4⋊Dic52
A4×#6832
C4×A4×Dic52
C22×#40363
C3×#40364
A4×#1255