Finite Group Databasebeta

← A4×#889 #11923163

Subgroups — A4×#889 #11923163

Order 1152.

610 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C3×A4×C4⋊C4C211yesmaximal, characteristic
2A4×C4⋊Dic3C211yesmaximal, characteristic
3A4×Dic3⋊C4C211yesmaximal, characteristic
4A4×Dic3⋊C4C211yesmaximal, characteristic
5A4×Dic3⋊C4C211yesmaximal, characteristic
6A4×Dic3⋊C4C211yesmaximal, characteristic
7C4×Dic3×A4C211yesmaximal, characteristic
8C22×#889C311yesmaximal, characteristic, complemented
9A4×#125—31nomaximal
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×Dic3×A4C2211yescharacteristic
14C2×Dic3×A4C2211yescharacteristic
15C2×Dic3×A4C2211yescharacteristic
16C2×Dic3×A4C2211yescharacteristic
17C3×#889—41nomaximal
18C22×C3×C4⋊C4C2×C311yescharacteristic
19C22×C4⋊Dic3C2×C311yescharacteristic
20C22×Dic3⋊C4C2×C311yescharacteristic
21C22×Dic3⋊C4C2×C311yescharacteristic
22C22×Dic3⋊C4C2×C311yescharacteristic
23C22×Dic3⋊C4C2×C311yescharacteristic
24C22×C4×Dic3C2×C311yescharacteristic
25C2×#889—31no—
26C2×#889—31no—
27C2×#889—31no—
28C2×#889—31no—
29C2×#889—31no—
30C2×#889—31no—
31C2×#889—31no—
32C2×#889—31no—
33A4×C4⋊C4—21no—
34A4×C4⋊C4—31no—
35A4×C4⋊C4—31no—
36A4×C4⋊C4—31no—
37A4×C4⋊C4—31no—
38A4×C4⋊C4—31no—
39A4×C4⋊C4D311yescharacteristic
40C42×A4—31no—
41C22×C3×A4C2311yescharacteristic
42C3×C4×A4—21no—
43C3×C4×A4—21no—
44C3×C4×A4—21no—
45Dic3×A4—21no—
46Dic3×A4—21no—
47Dic3×A4—21no—
48Dic3×A4Q812yes—
49C32×C4⋊C4—41no—
50C3×C4⋊Dic3—41no—
51C3×Dic3⋊C4—41no—
52C3×Dic3⋊C4—41no—
53C3×Dic3⋊C4—41no—
54C3×Dic3⋊C4—41no—
55C3×C4×Dic3—41no—
56C22×#125—31noSylow
57C23×C3×C4C22×C311yescharacteristic
58C23×C3×C4C22×C311yescharacteristic
59C23×C3×C4C22×C311yescharacteristic
60C23×Dic3C22×C311yescharacteristic
61C23×Dic3C22×C311yescharacteristic
62C23×Dic3C22×C311yescharacteristic
63C23×Dic3C22×C311yescharacteristic
64C2×C4×A4—21no—
65C2×C4×A4—21no—
66C2×C4×A4—21no—
67C2×C4×A4—31no—
68C2×C4×A4—31no—
69C2×C4×A4—31no—
70C2×C4×A4—31no—
71C2×C4×A4C2×D311yescharacteristic
72C2×C4×A4C2×D311yescharacteristic
73C2×C4×A4C2×D311yescharacteristic
74C3×#125—121no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—31no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×Dic3⋊C4—31no—
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—31no—
87C2×Dic3⋊C4—31no—
88C2×Dic3⋊C4—31no—
89C2×Dic3⋊C4—31no—
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—31no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103#889—32no—
104#889—32no—
105#889—32no—
106#889—32no—
107#889—32no—
108#889—32no—
109#889—32no—
110#889—31no—
111#889—31no—
112#889—31no—
113#889—31no—
114#889—31no—
115#889—31no—
116#889—31no—
117#889A411yescharacteristic, direct product factor
118C2×C3×A4C2×Q811yescharacteristic
119C2×C3×A4#4111yescharacteristic
120C2×C3×A4#4111yescharacteristic
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×#125—91no—
129C2×#125—91no—
130C2×#125—91no—
131C2×#125—91no—
132C2×#125—91no—
133C2×#125—91no—
134C2×#125—91no—
135C2×#125—91no—
136C22×C4⋊C4—31no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4—31no—
141C22×C4⋊C4C3×D311yescharacteristic
142C22×C42—31no—
143C24×C3C23×C311yescharacteristic
144C22×A4—21no—
145C22×A4C22×D311yescharacteristic
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×Dic3—21no—
159C22×Dic3—21no—
160C22×Dic3—21no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—32no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3C3×Q812yes—
174C4×A4—22no—
175C4×A4—21no—
176C4×A4—21no—
177C4×A4—21no—
178C4×A4—32no—
179C4×A4—41no—
180C4×A4—41no—
181C4×A4—61no—
182C4×A4—61no—
183C4×A4—61no—
184C3×C4⋊C4—32no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4—81no—
190C3×C4⋊C4—121no—
191C3×C4⋊C4—121no—
192C3×C4⋊C4—121no—
193C3×C4⋊C4—121no—
194C3×C4⋊C4—121no—
195C3×C4⋊C4C2×A411yescharacteristic
196C3×C42—121no—
197C4⋊Dic3—32no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—31no—
201C4⋊Dic3C2×A411yescharacteristic
202Dic3⋊C4—32no—
203Dic3⋊C4—32no—
204Dic3⋊C4—32no—
205Dic3⋊C4—32no—
206Dic3⋊C4—31no—
207Dic3⋊C4—31no—
208Dic3⋊C4—31no—
209Dic3⋊C4—31no—
210Dic3⋊C4—31no—
211Dic3⋊C4—31no—
212Dic3⋊C4—31no—
213Dic3⋊C4—31no—
214Dic3⋊C4—31no—
215Dic3⋊C4—31no—
216Dic3⋊C4—31no—
217Dic3⋊C4—31no—
218Dic3⋊C4C2×A411yescharacteristic
219Dic3⋊C4C2×A411yescharacteristic
220Dic3⋊C4C2×A411yescharacteristic
221Dic3⋊C4C2×A411yescharacteristic
222C4×Dic3—32no—
223C4×Dic3—31no—
224C4×Dic3—31no—
225C4×Dic3—31no—
226C4×Dic3C2×A411yescharacteristic
227C22×C32—41no—
228C3×A4#12511yescharacteristic, complemented
229C32×C4—81no—
230C32×C4—81no—
231C32×C4—81no—
232C3×Dic3—42no—
233C3×Dic3—81no—
234C3×Dic3—81no—
235C3×Dic3—81no—
236C23×C4—31no—
237C23×C4—31no—
238C23×C4—31no—
239C23×C4—31no—
240C23×C4C2×C3×D311yescharacteristic
241C23×C4C2×C3×D311yescharacteristic
242C23×C4C2×C3×D311yescharacteristic
243#125—31no—
244#125—91no—
245#125—91no—
246#125—91no—
247#125—91no—
248#125—91no—
249#125—91no—
250#125—92no—
251#125—92no—
252#125—92no—
253#125—92no—
254#125—92no—
255#125—92no—
256#125—92no—
257#125—91no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—91no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—91no—
282C2×C42—91no—
283C2×C42—91no—
284C2×C42—91no—
285C2×C42—91no—
286C23×C3—31no—
287C23×C3—31no—
288C23×C3—31no—
289C23×C3—31no—
290C23×C3C2×C3×Q811yescharacteristic
291C23×C3C3×#4111yescharacteristic
292C23×C3C3×#4111yescharacteristic
293C2×A4—21no—
294C2×A4—21no—
295C2×A4—21no—
296C2×A4#23511yescharacteristic
297C2×A4#23711yescharacteristic
298C2×A4D3×Q811yescharacteristic
299C2×C3×C4—31no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—81no—
318C2×C3×C4—81no—
319C2×C3×C4—81no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4C22×A411yescharacteristic
325C2×C3×C4C22×A411yescharacteristic
326C2×C3×C4C22×A411yescharacteristic
327C2×Dic3—32no—
328C2×Dic3—31no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3C22×A411yescharacteristic
348C2×Dic3C22×A411yescharacteristic
349C2×Dic3C22×A411yescharacteristic
350C2×Dic3C22×A411yescharacteristic
351C2×C32—41no—
352C2×C32—41no—
353C2×C32—41no—
354C24C22×C3×D311yescharacteristic
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—32no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—92no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—181no—
381C22×C4—181no—
382C22×C4—181no—
383C4⋊C4—32no—
384C4⋊C4—31no—
385C4⋊C4—31no—
386C4⋊C4—31no—
387C4⋊C4—31no—
388C4⋊C4—31no—
389C4⋊C4—31no—
390C4⋊C4—31no—
391C4⋊C4—31no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—91no—
395C4⋊C4—91no—
396C4⋊C4—91no—
397C4⋊C4—91no—
398C4⋊C4—91no—
399C4⋊C4—91no—
400C4⋊C4—91no—
401C4⋊C4—91no—
402C4⋊C4—92no—
403C4⋊C4—92no—
404C4⋊C4—92no—
405C4⋊C4—92no—
406C4⋊C4—92no—
407C4⋊C4—91no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—91no—
411C4⋊C4—91no—
412C4⋊C4D3×A411yescharacteristic
413C42—31no—
414C42—91no—
415C42—91no—
416C42—92no—
417C42—91no—
418C22×C3—31no—
419C22×C3—31no—
420C22×C3—31no—
421C22×C3—32no—
422C22×C3—31no—
423C22×C3—31no—
424C22×C3—31no—
425C22×C3—31no—
426C22×C3—31no—
427C22×C3—31no—
428C22×C3—41no—
429C22×C3—81no—
430C22×C3C3×#12511yescharacteristic, complemented
431C22×C3C23×A411yescharacteristic
432A4—21no—
433A4#88911yescharacteristic, direct product factor
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—61no—
438C3×C4—61no—
439C3×C4—61no—
440C3×C4—81no—
441C3×C4—81no—
442C3×C4—81no—
443C3×C4—82no—
444C3×C4—122no—
445C3×C4—161no—
446C3×C4—161no—
447C3×C4—241no—
448C3×C4—241no—
449C3×C4—241no—
450Dic3—21no—
451Dic3—21no—
452Dic3—21no—
453Dic3—32no—
454Dic3—61no—
455Dic3—61no—
456Dic3—61no—
457Dic3Q8×A412yes—
458C32—41noSylow
459C23—31no—
460C23—31no—
461C23—31no—
462C23—31no—
463C23C3×#23511yescharacteristic
464C23C3×#23711yescharacteristic
465C23C3×D3×Q811yescharacteristic
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—31no—
470C2×C4—31no—
471C2×C4—31no—
472C2×C4—31no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—91no—
489C2×C4—92no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—91no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4C2×D3×A411yescharacteristic
506C2×C4C2×D3×A411yescharacteristic
507C2×C4C2×D3×A411yescharacteristic
508C2×C3—31no—
509C2×C3—31no—
510C2×C3—31no—
511C2×C3—31no—
512C2×C3—41no—
513C2×C3—41no—
514C2×C3—41no—
515C2×C3—81no—
516C2×C3—81no—
517C2×C3—81no—
518C2×C3C2×Q8×A411yescharacteristic
519C2×C3A4×#4111yescharacteristic
520C2×C3A4×#4111yescharacteristic
521C22—31no—
522C22—31no—
523C22—31no—
524C22—32no—
525C22—31no—
526C22—31no—
527C22—31no—
528C22—31no—
529C22—31no—
530C22—31no—
531C22C3×#88911yescharacteristic, complemented
532C22C22×D3×A411yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—32no—
537C4—61no—
538C4—61no—
539C4—61no—
540C4—61no—
541C4—61no—
542C4—61no—
543C4—92no—
544C4—181no—
545C4—181no—
546C4—181no—
547C3—41no—
548C3—81no—
549C3A4×#12511yescharacteristic, complemented
550C2—31no—
551C2—31no—
552C2—31no—
553C2—31no—
554C2A4×#23511yescharacteristic
555C2A4×#23711yescharacteristic
556C2D3×Q8×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C4⋊C4C2×C3
prime radicalC22×C3×A4C23
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C3×#125
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
8. C22×#889C3semidirect
117. #889A4direct (N × H)
228. C3×A4#125semidirect
430. C22×C3C3×#125semidirect
433. A4#889direct (N × H)
531. C22C3×#889semidirect
549. C3A4×#125semidirect

Maximal subgroups

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

subgroupindex
C3×A4×C4⋊C42
A4×C4⋊Dic32
A4×Dic3⋊C42
C4×Dic3×A42
C22×#8893
A4×#1253
C3×#8894