Finite Group Databasebeta

← A4×#4092 #14514202

Subgroups — A4×#4092 #14514202

Order 1920.

860 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 860 conjugacy classes of subgroups — too many to draw. Only its 105 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×C5×Q8×A4C211yesmaximal, characteristic, complemented
2C2×C4×D5×A4C211yesmaximal, characteristic
3A4×#685C212yesmaximal
4A4×C4⋊Dic5C211yesmaximal, characteristic, complemented
5A4×#683C212yesmaximal, complemented
6C22×#4092C311yesmaximal, characteristic, complemented, Hall
7C22×D5×A4C2211yescharacteristic
8C5×Q8×A4—22no—
9C2×C4×C5×A4C2212yes—
10C2×C4×C5×A4C2211yescharacteristic
11C2×A4×Dic5C2211yescharacteristic
12C2×A4×Dic5C2212yes—
13C4×D5×A4—22no—
14C3×#4092—41nomaximal
15A4×C22⋊Q8—51nomaximal, Hall
16C23×C5×Q8C2×C311yescharacteristic, complemented
17C23×C4×D5C2×C311yescharacteristic
18C2×#4092—31no—
19C2×#4092—32no—
20C2×#4092—31no—
21C2×#4092—32no—
22C2×#4092—31no—
23C2×#4092—31no—
24C22×#685C2×C312yes—
25C22×C4⋊Dic5C2×C311yescharacteristic, complemented
26C22×#683C2×C312yescomplemented
27C22×C5×A4C2311yescharacteristic
28C2×D5×A4—21no—
29C2×D5×A4—21no—
30C2×D5×A4Q812yescomplemented
31C2×C3×C5×Q8—41no—
32C2×C3×C4×D5—41no—
33C4×C5×A4—22no—
34C4×C5×A4D412yes—
35A4×Dic5—21no—
36A4×Dic5—22no—
37C3×#685—42no—
38C3×C4⋊Dic5—41no—
39C3×#683—42no—
40C2×Q8×A4D511yescharacteristic, complemented
41C22×C4×A4—51no—
42A4×C4⋊C4—52no—
43A4×C4⋊C4—51no—
44A4×C22⋊C4—52no—
45C24×D5C22×C311yescharacteristic
46C22×C5×Q8—22no—
47C22×C5×Q8—31no—
48C22×C5×Q8—32no—
49C22×C5×Q8—31no—
50C22×C5×Q8—62no—
51C23×C4×C5C22×C312yes—
52C23×C4×C5C22×C311yescharacteristic
53C23×Dic5C22×C311yescharacteristic
54C23×Dic5C22×C312yes—
55C22×C4×D5—22no—
56C22×C4×D5—31no—
57C22×C4×D5—31no—
58C22×C4×D5—31no—
59C22×C4×D5—31no—
60C22×C4×D5—62no—
61#4092—32no—
62#4092—32no—
63#4092—34no—
64#4092—34no—
65#4092—32no—
66#4092—31no—
67#4092—31no—
68#4092—32no—
69#4092—31no—
70#4092—32no—
71#4092A411yescharacteristic, direct product factor
72C2×#685—32no—
73C2×#685—32no—
74C2×#685—32no—
75C2×#685—32no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—31no—
78C2×C4⋊Dic5—32no—
79C2×#683—32no—
80C2×#683—32no—
81C2×#683—32no—
82C2×#683—32no—
83C22×C22⋊Q8—51noSylow
84C22×C3×D5—41no—
85C2×C5×A4C2×D411yescharacteristic
86C2×C5×A4C2×Q811yescharacteristic
87C2×C5×A4#4111yescharacteristic
88D5×A4—22no—
89C3×C5×Q8—82no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—42no—
92C2×C3×Dic5—41no—
93C2×C3×Dic5—42no—
94C3×C4×D5—82no—
95C23×A4—51no—
96Q8×A4—22no—
97C2×C4×A4—51no—
98C2×C4×A4—52no—
99C2×C4×A4—102no—
100C2×C4×A4C2×D512yes—
101C2×C4×A4C2×D511yescharacteristic
102C3×C22⋊Q8—201no—
103C24×C5C23×C311yescharacteristic
104C23×D5—21no—
105C23×D5—21no—
106C23×D5—31no—
107C23×D5—31no—
108C23×D5—32no—
109C23×D5—61no—
110C23×D5—61no—
111C23×D5C3×Q812yescomplemented
112C2×C5×Q8—32no—
113C2×C5×Q8—32no—
114C2×C5×Q8—31no—
115C2×C5×Q8—62no—
116C2×C5×Q8—62no—
117C2×C5×Q8—62no—
118C2×C5×Q8—64no—
119C2×C5×Q8—62no—
120C2×C5×Q8—64no—
121C2×C5×Q8C2×A411yescharacteristic, complemented
122C22×C4×C5—22no—
123C22×C4×C5—31no—
124C22×C4×C5—31no—
125C22×C4×C5—32no—
126C22×C4×C5—32no—
127C22×C4×C5—32no—
128C22×C4×C5—62no—
129C22×C4×C5C3×D412yes—
130C22×Dic5—21no—
131C22×Dic5—22no—
132C22×Dic5—31no—
133C22×Dic5—32no—
134C22×Dic5—31no—
135C22×Dic5—32no—
136C22×Dic5—61no—
137C22×Dic5—62no—
138C2×C4×D5—32no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×C4×D5—31no—
142C2×C4×D5—62no—
143C2×C4×D5—62no—
144C2×C4×D5—62no—
145C2×C4×D5—62no—
146C2×C4×D5—62no—
147C2×C4×D5—62no—
148C2×C4×D5—62no—
149C2×C4×D5—62no—
150C2×C4×D5C2×A411yescharacteristic
151#685—34no—
152#685—32no—
153#685—32no—
154#685—32no—
155#685C2×A412yes—
156C4⋊Dic5—32no—
157C4⋊Dic5—31no—
158C4⋊Dic5—32no—
159C4⋊Dic5C2×A411yescharacteristic, complemented
160#683—34no—
161#683—32no—
162#683—32no—
163#683—32no—
164#683C2×A412yescomplemented
165C23×Q8C3×D511yescharacteristic, complemented
166C24×C4—51no—
167C2×C22⋊Q8—151no—
168C2×C22⋊Q8—152no—
169C2×C22⋊Q8—152no—
170C2×C22⋊Q8—151no—
171C2×C22⋊Q8—151no—
172C2×C22⋊Q8—151no—
173C22×C4⋊C4—52no—
174C22×C4⋊C4—51no—
175C22×C22⋊C4—52no—
176C22×C3×C5—41no—
177C2×C3×D5—42no—
178C2×C3×D5—81no—
179C2×C3×D5—81no—
180C5×A4C22⋊Q811yescharacteristic, complemented
181C3×C4×C5—42no—
182C3×C4×C5—82no—
183C3×Dic5—81no—
184C3×Dic5—82no—
185C22×A4—52no—
186C22×A4—101no—
187C22×A4—101no—
188C22×A4C22×D511yescharacteristic
189C2×C3×Q8—41no—
190C22×C3×C4—201no—
191C4×A4—22no—
192C4×A4—102no—
193C4×A4—101no—
194C4×A4C22⋊D512yes—
195C3×C4⋊C4—202no—
196C3×C4⋊C4—201no—
197C3×C22⋊C4—202no—
198C23×C5—31no—
199C23×C5—31no—
200C23×C5—31no—
201C23×C5—31no—
202C23×C5C2×C3×D411yescharacteristic
203C23×C5C2×C3×Q811yescharacteristic
204C23×C5C3×#4111yescharacteristic
205C22×D5—22no—
206C22×D5—32no—
207C22×D5—31no—
208C22×D5—32no—
209C22×D5—32no—
210C22×D5—32no—
211C22×D5—61no—
212C22×D5—61no—
213C22×D5—61no—
214C22×D5—61no—
215C22×D5—64no—
216C22×D5—61no—
217C22×D5—61no—
218C22×D5—62no—
219C22×D5—62no—
220C22×D5—61no—
221C22×D5—61no—
222C22×D5—62no—
223C22×D5C22×A411yescharacteristic
224C5×Q8—22no—
225C5×Q8—64no—
226C5×Q8—64no—
227C5×Q8—62no—
228C2×C4×C5—32no—
229C2×C4×C5—31no—
230C2×C4×C5—32no—
231C2×C4×C5—32no—
232C2×C4×C5—32no—
233C2×C4×C5—32no—
234C2×C4×C5—62no—
235C2×C4×C5—62no—
236C2×C4×C5—62no—
237C2×C4×C5—62no—
238C2×C4×C5C22×A412yes—
239C2×C4×C5C22×A411yescharacteristic
240C2×Dic5—31no—
241C2×Dic5—32no—
242C2×Dic5—61no—
243C2×Dic5—61no—
244C2×Dic5—62no—
245C2×Dic5—62no—
246C2×Dic5—61no—
247C2×Dic5—61no—
248C2×Dic5—62no—
249C2×Dic5—62no—
250C2×Dic5C22×A411yescharacteristic
251C2×Dic5C22×A412yes—
252C4×D5—22no—
253C4×D5—62no—
254C4×D5—62no—
255C4×D5—64no—
256C4×D5—62no—
257C25—51no—
258C22×Q8—22no—
259C22×Q8—31no—
260C22×Q8—32no—
261C22×Q8—31no—
262C22×Q8—62no—
263C23×C4—52no—
264C23×C4—51no—
265C23×C4—102no—
266C23×C4—151no—
267C23×C4—151no—
268C23×C4—151no—
269C23×C4—151no—
270C23×C4—302no—
271C23×C4C2×C3×D512yes—
272C23×C4C2×C3×D511yescharacteristic
273C22⋊Q8—51no—
274C22⋊Q8—152no—
275C22⋊Q8—151no—
276C22⋊Q8—152no—
277C22⋊Q8—151no—
278C22⋊Q8—154no—
279C22⋊Q8—152no—
280C22⋊Q8—152no—
281C22⋊Q8—152no—
282C22⋊Q8—154no—
283C22⋊Q8—151no—
284C2×C4⋊C4—152no—
285C2×C4⋊C4—151no—
286C2×C4⋊C4—152no—
287C2×C4⋊C4—152no—
288C2×C4⋊C4—152no—
289C2×C4⋊C4—152no—
290C2×C4⋊C4—151no—
291C2×C22⋊C4—152no—
292C2×C22⋊C4—152no—
293C2×C22⋊C4—152no—
294C2×C22⋊C4—152no—
295C2×C3×C5—41no—
296C2×C3×C5—41no—
297C2×C3×C5—41no—
298C3×D5—82no—
299C23×C3—201no—
300C2×A4—102no—
301C2×A4Q8×D511yescharacteristic
302C2×A4#71311yescharacteristic
303C2×A4C2×C22⋊D511yescharacteristic
304C3×Q8—82no—
305C2×C3×C4—41no—
306C2×C3×C4—42no—
307C2×C3×C4—202no—
308C2×C3×C4—201no—
309C2×C3×C4—402no—
310C22×C5—31no—
311C22×C5—31no—
312C22×C5—31no—
313C22×C5—32no—
314C22×C5—31no—
315C22×C5—31no—
316C22×C5—31no—
317C22×C5—31no—
318C22×C5—31no—
319C22×C5—31no—
320C22×C5C3×C22⋊Q811yescharacteristic, complemented
321C22×C5C23×A411yescharacteristic
322C2×D5—21no—
323C2×D5—21no—
324C2×D5—32no—
325C2×D5—62no—
326C2×D5—62no—
327C2×D5—62no—
328C2×D5—62no—
329C2×D5—62no—
330C2×D5—62no—
331C2×D5—61no—
332C2×D5—61no—
333C2×D5—62no—
334C2×D5—62no—
335C2×D5Q8×A412yescomplemented
336C4×C5—22no—
337C4×C5—32no—
338C4×C5—62no—
339C4×C5D4×A412yes—
340Dic5—21no—
341Dic5—22no—
342Dic5—61no—
343Dic5—62no—
344C24—52no—
345C24—101no—
346C24—101no—
347C24—151no—
348C24—151no—
349C24—152no—
350C24—301no—
351C24—301no—
352C24C22×C3×D511yescharacteristic
353C2×Q8—32no—
354C2×Q8—32no—
355C2×Q8—31no—
356C2×Q8—62no—
357C2×Q8—62no—
358C2×Q8—62no—
359C2×Q8—64no—
360C2×Q8—62no—
361C2×Q8—64no—
362C2×Q8D5×A411yescharacteristic, complemented
363C22×C4—22no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—32no—
368C22×C4—32no—
369C22×C4—51no—
370C22×C4—62no—
371C22×C4—102no—
372C22×C4—101no—
373C22×C4—151no—
374C22×C4—151no—
375C22×C4—152no—
376C22×C4—152no—
377C22×C4—151no—
378C22×C4—151no—
379C22×C4—152no—
380C22×C4—151no—
381C22×C4—302no—
382C22×C4—302no—
383C22×C4—302no—
384C22×C4—302no—
385C22×C4—302no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4—301no—
390C22×C4—302no—
391C22×C4C3×C22⋊D512yes—
392C4⋊C4—52no—
393C4⋊C4—51no—
394C4⋊C4—152no—
395C4⋊C4—152no—
396C4⋊C4—152no—
397C4⋊C4—154no—
398C4⋊C4—152no—
399C4⋊C4—152no—
400C4⋊C4—151no—
401C22⋊C4—52no—
402C22⋊C4—152no—
403C22⋊C4—152no—
404C22⋊C4—154no—
405C22⋊C4—152no—
406C3×C5—41noHall
407C22×C3—41no—
408C22×C3—202no—
409C22×C3—401no—
410C22×C3—401no—
411A4#409211yescharacteristic, direct product factor
412C3×C4—42no—
413C3×C4—82no—
414C3×C4—401no—
415C3×C4—402no—
416C2×C5—31no—
417C2×C5—31no—
418C2×C5—31no—
419C2×C5—31no—
420C2×C5C2×D4×A411yescharacteristic
421C2×C5C2×Q8×A411yescharacteristic
422C2×C5A4×#4111yescharacteristic
423D5—22no—
424D5—62no—
425C23—31no—
426C23—31no—
427C23—31no—
428C23—31no—
429C23—51no—
430C23—102no—
431C23—152no—
432C23—152no—
433C23—152no—
434C23—152no—
435C23—151no—
436C23—301no—
437C23—301no—
438C23—301no—
439C23—301no—
440C23—302no—
441C23—301no—
442C23—301no—
443C23—302no—
444C23—302no—
445C23—301no—
446C23—301no—
447C23—304no—
448C23C3×Q8×D511yescharacteristic
449C23C3×#71311yescharacteristic
450C23C2×C3×C22⋊D511yescharacteristic
451Q8—22no—
452Q8—64no—
453Q8—64no—
454Q8—62no—
455C2×C4—32no—
456C2×C4—31no—
457C2×C4—32no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—52no—
462C2×C4—51no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—102no—
468C2×C4—152no—
469C2×C4—151no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—304no—
473C2×C4—301no—
474C2×C4—302no—
475C2×C4—301no—
476C2×C4—302no—
477C2×C4—302no—
478C2×C4—301no—
479C2×C4—302no—
480C2×C4—301no—
481C2×C4—302no—
482C2×C4C2×D5×A412yes—
483C2×C4C2×D5×A411yescharacteristic
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—41no—
487C2×C3—402no—
488C5A4×C22⋊Q811yescharacteristic, complemented, Sylow
489C22—31no—
490C22—31no—
491C22—31no—
492C22—32no—
493C22—31no—
494C22—31no—
495C22—31no—
496C22—31no—
497C22—31no—
498C22—31no—
499C22—52no—
500C22—101no—
501C22—101no—
502C22—152no—
503C22—302no—
504C22—302no—
505C22—302no—
506C22—302no—
507C22—302no—
508C22—302no—
509C22—302no—
510C22—302no—
511C22—301no—
512C22—301no—
513C22C3×#409211yescharacteristic, complemented
514C22C22×D5×A411yescharacteristic
515C4—22no—
516C4—32no—
517C4—62no—
518C4—102no—
519C4—101no—
520C4—302no—
521C4—301no—
522C4A4×C22⋊D512yes—
523C3—41noSylow
524C2—31no—
525C2—31no—
526C2—31no—
527C2—31no—
528C2—102no—
529C2—302no—
530C2Q8×D5×A411yescharacteristic
531C2A4×#71311yescharacteristic
532C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, socle, cosocleC24×C5C23×C3
FittingC23×C5×Q8C2×C3
prime radicalC22×D5×A4C22
hypercenterC2×Q8D5×A4
hypocenterC22×C5C3×C22⋊Q8
LCSG ▷ C24×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×Q8×A4C2semidirect
4. A4×C4⋊Dic5C2semidirect
5. A4×#683C2semidirect
6. C22×#4092C3semidirect
16. C23×C5×Q8C2×C3semidirect
25. C22×C4⋊Dic5C2×C3semidirect
26. C22×#683C2×C3semidirect
30. C2×D5×A4Q8semidirect
40. C2×Q8×A4D5semidirect
71. #4092A4direct (N × H)
111. C23×D5C3×Q8semidirect
121. C2×C5×Q8C2×A4semidirect
159. C4⋊Dic5C2×A4semidirect
164. #683C2×A4semidirect
165. C23×Q8C3×D5semidirect
180. C5×A4C22⋊Q8semidirect
320. C22×C5C3×C22⋊Q8semidirect
335. C2×D5Q8×A4semidirect
362. C2×Q8D5×A4semidirect
411. A4#4092direct (N × H)
488. C5A4×C22⋊Q8semidirect
513. C22C3×#4092semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Q8×A42
C2×C4×D5×A42
A4×#6852
A4×C4⋊Dic52
A4×#6832
C22×#40923
C3×#40924
A4×C22⋊Q85