Finite Group Databasebeta

← A4×#4033 #14513992

Subgroups — A4×#4033 #14513992

Order 1920.

788 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 129 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×A4×Dic10C211yesmaximal, characteristic
2C5×A4×C4⋊C4C211yesmaximal, characteristic
3A4×#683C212yesmaximal
4C4×A4×Dic5C211yesmaximal, characteristic
5C4×A4×Dic5C212yesmaximal
6C22×#4033C311yesmaximal, characteristic, complemented, Hall
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4×Dic5C2211yescharacteristic
10C2×A4×Dic5C2212yes—
11C2×A4×Dic5C2211yescharacteristic
12A4×Dic10C414yescomplemented
13C3×#4033—41nomaximal
14C4×Q8×A4—51nomaximal, Hall
15C23×Dic10C2×C311yescharacteristic
16C22×C5×C4⋊C4C2×C311yescharacteristic
17C22×#683C2×C312yes—
18C22×C4×Dic5C2×C311yescharacteristic
19C22×C4×Dic5C2×C312yes—
20C2×#4033—31no—
21C2×#4033—31no—
22C2×#4033—31no—
23C2×#4033—32no—
24C2×#4033—31no—
25C2×#4033—32no—
26C22×C5×A4C2311yescharacteristic
27C2×C3×Dic10—41no—
28C4×C5×A4—22no—
29C4×C5×A4C2×C412yes—
30A4×Dic5—21no—
31A4×Dic5C2×C414yes—
32A4×Dic5Q812yescomplemented
33C3×C5×C4⋊C4—41no—
34C3×#683—42no—
35C3×C4×Dic5—42no—
36C3×C4×Dic5—41no—
37C2×Q8×A4—51no—
38A4×C4⋊C4—52no—
39A4×C4⋊C4D511yescharacteristic
40C42×A4—52no—
41C42×A4—51no—
42C23×C4×C5C22×C312yes—
43C23×C4×C5C22×C311yescharacteristic
44C23×Dic5C22×C311yescharacteristic
45C23×Dic5C22×C312yes—
46C23×Dic5C22×C311yescharacteristic
47C22×Dic10—31no—
48C22×Dic10—31no—
49C22×Dic10—32no—
50C22×Dic10—34no—
51C22×Dic10C3×C414yescomplemented
52C2×C5×C4⋊C4—31no—
53C2×C5×C4⋊C4—31no—
54C2×C5×C4⋊C4—32no—
55C2×#683—32no—
56C2×#683—32no—
57C2×#683—32no—
58C2×#683—32no—
59C2×C4×Dic5—32no—
60C2×C4×Dic5—31no—
61C2×C4×Dic5—32no—
62C2×C4×Dic5—31no—
63C2×C4×Dic5—32no—
64C2×C4×Dic5—32no—
65C2×C4×Dic5—31no—
66C2×C4×Dic5—31no—
67#4033—32no—
68#4033—34no—
69#4033—34no—
70#4033—32no—
71#4033—32no—
72#4033—31no—
73#4033—31no—
74#4033—32no—
75#4033—32no—
76#4033—31no—
77#4033A411yescharacteristic, direct product factor
78C22×C4×Q8—51noSylow
79C2×C5×A4C22×C411yescharacteristic
80C2×C5×A4C2×Q811yescharacteristic
81C2×C5×A4#4111yescharacteristic
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—42no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5—42no—
86C2×C3×Dic5—41no—
87C3×Dic10—44no—
88Q8×A4—54no—
89C2×C4×A4—52no—
90C2×C4×A4—51no—
91C2×C4×A4—51no—
92C2×C4×A4C2×D512yes—
93C2×C4×A4C2×D511yescharacteristic
94C3×C4×Q8—201no—
95C24×C5C23×C311yescharacteristic
96C22×C4×C5—22no—
97C22×C4×C5—31no—
98C22×C4×C5—31no—
99C22×C4×C5—32no—
100C22×C4×C5—32no—
101C22×C4×C5—32no—
102C22×C4×C5—62no—
103C22×C4×C5C2×C3×C412yes—
104C22×Dic5—21no—
105C22×Dic5—32no—
106C22×Dic5—31no—
107C22×Dic5—34no—
108C22×Dic5—32no—
109C22×Dic5—32no—
110C22×Dic5—31no—
111C22×Dic5—31no—
112C22×Dic5—31no—
113C22×Dic5—61no—
114C22×Dic5C2×C3×C414yes—
115C22×Dic5C3×Q812yescomplemented
116C2×Dic10—34no—
117C2×Dic10—38no—
118C2×Dic10—32no—
119C2×Dic10—31no—
120C2×Dic10—32no—
121C2×Dic10—34no—
122C2×Dic10—34no—
123C2×Dic10—34no—
124C2×Dic10—38no—
125C2×Dic10C2×A411yescharacteristic
126C5×C4⋊C4—32no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4C2×A411yescharacteristic
130#683—34no—
131#683—32no—
132#683—32no—
133#683—32no—
134#683C2×A412yes—
135C4×Dic5—34no—
136C4×Dic5—32no—
137C4×Dic5—32no—
138C4×Dic5—31no—
139C4×Dic5—31no—
140C4×Dic5—32no—
141C4×Dic5—32no—
142C4×Dic5—31no—
143C4×Dic5C2×A411yescharacteristic
144C4×Dic5C2×A412yes—
145C23×Q8—51no—
146C2×C4×Q8—151no—
147C2×C4×Q8—151no—
148C2×C4×Q8—152no—
149C2×C4×Q8—151no—
150C2×C4×Q8—152no—
151C2×C4×Q8—151no—
152C22×C4⋊C4—52no—
153C22×C4⋊C4C3×D511yescharacteristic
154C22×C42—52no—
155C22×C42—51no—
156C22×C3×C5—41no—
157C5×A4C4×Q811yescharacteristic, complemented
158C3×C4×C5—42no—
159C3×C4×C5—82no—
160C3×Dic5—44no—
161C3×Dic5—42no—
162C3×Dic5—81no—
163C22×A4C22×D511yescharacteristic
164C2×C3×Q8—201no—
165C4×A4—22no—
166C4×A4—54no—
167C4×A4—52no—
168C4×A4—101no—
169C4×A4C4×D512yes—
170C3×C4⋊C4—41no—
171C3×C4⋊C4—202no—
172C3×C42—201no—
173C3×C42—202no—
174C23×C5—31no—
175C23×C5—31no—
176C23×C5—31no—
177C23×C5—31no—
178C23×C5C22×C3×C411yescharacteristic
179C23×C5C2×C3×Q811yescharacteristic
180C23×C5C3×#4111yescharacteristic
181C2×C4×C5—32no—
182C2×C4×C5—31no—
183C2×C4×C5—32no—
184C2×C4×C5—32no—
185C2×C4×C5—32no—
186C2×C4×C5—32no—
187C2×C4×C5—62no—
188C2×C4×C5—62no—
189C2×C4×C5—62no—
190C2×C4×C5—62no—
191C2×C4×C5C22×A412yes—
192C2×C4×C5C22×A411yescharacteristic
193C2×Dic5—34no—
194C2×Dic5—32no—
195C2×Dic5—31no—
196C2×Dic5—32no—
197C2×Dic5—34no—
198C2×Dic5—34no—
199C2×Dic5—32no—
200C2×Dic5—32no—
201C2×Dic5—34no—
202C2×Dic5—32no—
203C2×Dic5—31no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5—61no—
207C2×Dic5—61no—
208C2×Dic5C22×A411yescharacteristic
209C2×Dic5C22×A412yes—
210C2×Dic5C22×A411yescharacteristic
211Dic10—38no—
212Dic10—34no—
213Dic10—38no—
214Dic10C4×A414yescomplemented
215C22×Q8—54no—
216C22×Q8—151no—
217C22×Q8—151no—
218C22×Q8—152no—
219C22×Q8—154no—
220C23×C4—52no—
221C23×C4—51no—
222C23×C4—51no—
223C23×C4C2×C3×D512yes—
224C23×C4C2×C3×D511yescharacteristic
225C4×Q8—51no—
226C4×Q8—151no—
227C4×Q8—152no—
228C4×Q8—152no—
229C4×Q8—151no—
230C4×Q8—152no—
231C4×Q8—152no—
232C4×Q8—154no—
233C4×Q8—152no—
234C4×Q8—154no—
235C4×Q8—151no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—31no—
238C2×C4⋊C4—32no—
239C2×C4⋊C4—152no—
240C2×C4⋊C4—152no—
241C2×C4⋊C4—152no—
242C2×C4⋊C4—152no—
243C2×C42—151no—
244C2×C42—152no—
245C2×C42—151no—
246C2×C42—151no—
247C2×C42—152no—
248C2×C42—152no—
249C2×C42—151no—
250C2×C42—152no—
251C2×C3×C5—41no—
252C2×C3×C5—41no—
253C2×C3×C5—41no—
254C2×A4C2×C4×D511yescharacteristic
255C2×A4#71111yescharacteristic
256C2×A4Q8×D511yescharacteristic
257C3×Q8—204no—
258C2×C3×C4—41no—
259C2×C3×C4—42no—
260C2×C3×C4—201no—
261C2×C3×C4—202no—
262C2×C3×C4—201no—
263C22×C5—31no—
264C22×C5—31no—
265C22×C5—31no—
266C22×C5—32no—
267C22×C5—31no—
268C22×C5—31no—
269C22×C5—31no—
270C22×C5—31no—
271C22×C5—31no—
272C22×C5—31no—
273C22×C5C3×C4×Q811yescharacteristic, complemented
274C22×C5C23×A411yescharacteristic
275C4×C5—22no—
276C4×C5—32no—
277C4×C5—62no—
278C4×C5C2×C4×A412yes—
279Dic5—21no—
280Dic5—34no—
281Dic5—32no—
282Dic5—61no—
283Dic5C2×C4×A414yes—
284Dic5Q8×A412yescomplemented
285C24C22×C3×D511yescharacteristic
286C2×Q8—51no—
287C2×Q8—152no—
288C2×Q8—154no—
289C2×Q8—154no—
290C2×Q8—154no—
291C2×Q8—158no—
292C2×Q8—152no—
293C2×Q8—158no—
294C2×Q8—154no—
295C2×Q8—151no—
296C22×C4—22no—
297C22×C4—31no—
298C22×C4—31no—
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—54no—
303C22×C4—52no—
304C22×C4—62no—
305C22×C4—101no—
306C22×C4—151no—
307C22×C4—152no—
308C22×C4—151no—
309C22×C4—151no—
310C22×C4—152no—
311C22×C4—154no—
312C22×C4—152no—
313C22×C4—151no—
314C22×C4—301no—
315C22×C4C3×C4×D512yes—
316C4⋊C4—32no—
317C4⋊C4—32no—
318C4⋊C4—31no—
319C4⋊C4—52no—
320C4⋊C4—152no—
321C4⋊C4—152no—
322C4⋊C4—154no—
323C4⋊C4—152no—
324C4⋊C4D5×A411yescharacteristic
325C42—52no—
326C42—51no—
327C42—151no—
328C42—151no—
329C42—152no—
330C42—152no—
331C42—152no—
332C42—154no—
333C42—152no—
334C42—151no—
335C3×C5—41noHall
336C22×C3—41no—
337A4#403311yescharacteristic, direct product factor
338C3×C4—42no—
339C3×C4—82no—
340C3×C4—204no—
341C3×C4—202no—
342C3×C4—401no—
343C2×C5—31no—
344C2×C5—31no—
345C2×C5—31no—
346C2×C5—31no—
347C2×C5C22×C4×A411yescharacteristic
348C2×C5C2×Q8×A411yescharacteristic
349C2×C5A4×#4111yescharacteristic
350C23—31no—
351C23—31no—
352C23—31no—
353C23—31no—
354C23C2×C3×C4×D511yescharacteristic
355C23C3×#71111yescharacteristic
356C23C3×Q8×D511yescharacteristic
357Q8—54no—
358Q8—158no—
359Q8—158no—
360Q8—154no—
361C2×C4—32no—
362C2×C4—31no—
363C2×C4—32no—
364C2×C4—32no—
365C2×C4—32no—
366C2×C4—32no—
367C2×C4—51no—
368C2×C4—52no—
369C2×C4—51no—
370C2×C4—62no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—154no—
375C2×C4—152no—
376C2×C4—154no—
377C2×C4—152no—
378C2×C4—154no—
379C2×C4—152no—
380C2×C4—151no—
381C2×C4—152no—
382C2×C4—154no—
383C2×C4—152no—
384C2×C4—151no—
385C2×C4—301no—
386C2×C4—301no—
387C2×C4—301no—
388C2×C4—301no—
389C2×C4C2×D5×A412yes—
390C2×C4C2×D5×A411yescharacteristic
391C2×C3—41no—
392C2×C3—41no—
393C2×C3—41no—
394C5C4×Q8×A411yescharacteristic, complemented, Sylow
395C22—31no—
396C22—31no—
397C22—31no—
398C22—32no—
399C22—31no—
400C22—31no—
401C22—31no—
402C22—31no—
403C22—31no—
404C22—31no—
405C22C3×#403311yescharacteristic, complemented
406C22C22×D5×A411yescharacteristic
407C4—22no—
408C4—32no—
409C4—54no—
410C4—52no—
411C4—62no—
412C4—101no—
413C4—154no—
414C4—152no—
415C4—301no—
416C4C4×D5×A412yes—
417C3—41noSylow
418C2—31no—
419C2—31no—
420C2—31no—
421C2—31no—
422C2C2×C4×D5×A411yescharacteristic
423C2A4×#71111yescharacteristic
424C2Q8×D5×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutatorC23×C5C22×C3×C4
FittingC22×C5×C4⋊C4C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC22×C5×A4C23
hypercenterC4⋊C4D5×A4
hypocenterC22×C5C3×C4×Q8
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×#4033C3semidirect
12. A4×Dic10C4semidirect
32. A4×Dic5Q8semidirect
51. C22×Dic10C3×C4semidirect
77. #4033A4direct (N × H)
115. C22×Dic5C3×Q8semidirect
157. C5×A4C4×Q8semidirect
214. Dic10C4×A4semidirect
273. C22×C5C3×C4×Q8semidirect
284. Dic5Q8×A4semidirect
337. A4#4033direct (N × H)
394. C5C4×Q8×A4semidirect
405. C22C3×#4033semidirect

Maximal subgroups

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

subgroupindex
C2×A4×Dic102
C5×A4×C4⋊C42
A4×#6832
C4×A4×Dic52
C22×#40333
C3×#40334
C4×Q8×A45