Finite Group Databasebeta

← A4×#806 #11921253

Subgroups — A4×#806 #11921253

Order 1152.

578 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 57 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×#67C211yesmaximal, characteristic
2C3×A4×C22⋊C4C211yesmaximal, characteristic, complemented
3A4×#217C211yesmaximal, characteristic, complemented
4C22×#806C311yesmaximal, characteristic, complemented
5A4×#99—31nomaximal
6C23×C3×A4C2211yescharacteristic
7C22×D3×A4C411yescharacteristic, complemented
8C2×C3×C4×A4—21no—
9A4×#67—21no—
10A4×#67—21no—
11C2×Dic3×A4—21no—
12C2×Dic3×A4C411yescharacteristic, complemented
13C3×#806—41nomaximal
14C23×#67C2×C311yescharacteristic
15C2×D4×A4—31no—
16C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
17C22×#217C2×C311yescharacteristic, complemented
18A4×C22⋊C4—21no—
19A4×C22⋊C4—31no—
20A4×C22⋊C4D311yescharacteristic, complemented
21C2×#806—31no—
22C2×#806—31no—
23C2×#806—31no—
24C2×#806—31no—
25C22×C3×A4—41no—
26C22×C3×A4C2×C411yescharacteristic
27C22×C3×A4D411yescharacteristic
28C22×C3×A4D411yescharacteristic
29C2×D3×A4—21no—
30C2×D3×A4—41no—
31C2×C3×#67—41no—
32C3×C4×A4—41no—
33Dic3×A4—21no—
34Dic3×A4—41no—
35C32×C22⋊C4—41no—
36C3×#217—41no—
37C22×#99—31noSylow
38C25×C3C22×C311yescharacteristic
39C24×D3C3×C411yescharacteristic, complemented
40C23×A4—21no—
41C23×A4—31no—
42C23×A4C2×D311yescharacteristic
43C23×C3×C4—21no—
44C22×#67—21no—
45C22×#67—21no—
46C22×#67—31no—
47C22×#67—31no—
48C22×#67—31no—
49C22×#67—31no—
50C22×#67—61no—
51C22×#67—61no—
52C23×Dic3—21no—
53C23×Dic3C3×C411yescharacteristic, complemented
54D4×A4—61no—
55D4×A4—61no—
56C2×C4×A4—22no—
57C2×C4×A4—21no—
58C2×C4×A4—31no—
59C2×C4×A4—61no—
60C2×C3×C22⋊C4—31no—
61C2×C3×C22⋊C4—31no—
62C2×C3×C22⋊C4—61no—
63C2×#217—31no—
64C2×#217—31no—
65C2×#217—61no—
66C3×#99—121no—
67#806—32no—
68#806—31no—
69#806—31no—
70#806—31no—
71#806A411yescharacteristic, direct product factor
72C23×C32—41no—
73C22×C3×D3—41no—
74C2×C3×A4—21no—
75C2×C3×A4—21no—
76C2×C3×A4—21no—
77C2×C3×A4C22⋊C411yescharacteristic
78D3×A4—41no—
79C2×C32×C4—81no—
80C3×#67—81no—
81C3×#67—81no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—81no—
84C23×D4—31no—
85C22×C22⋊C4—31no—
86C22×C22⋊C4C3×D311yescharacteristic, complemented
87C2×#99—91no—
88C2×#99—91no—
89C2×#99—91no—
90C2×#99—91no—
91C24×C3—31no—
92C24×C3—31no—
93C24×C3—31no—
94C24×C3—31no—
95C24×C3—41no—
96C24×C3—121no—
97C24×C3C2×C3×C411yescharacteristic
98C24×C3C3×D411yescharacteristic
99C24×C3C3×D411yescharacteristic
100C23×D3—21no—
101C23×D3—31no—
102C23×D3—31no—
103C23×D3—41no—
104C23×D3—61no—
105C23×D3—121no—
106C22×A4—21no—
107C22×A4—21no—
108C22×A4—21no—
109C22×A4—41no—
110C22×A4—42no—
111C22×A4—61no—
112C22×A4—121no—
113C22×A4C4×D311yescharacteristic
114C22×A4D1211yescharacteristic
115C22×A4#6711yescharacteristic
116C2×C3×D4—121no—
117C22×C3×C4—41no—
118C22×C3×C4—61no—
119C22×C3×C4—61no—
120C22×C3×C4—121no—
121C2×#67—32no—
122C2×#67—31no—
123C2×#67—31no—
124C2×#67—31no—
125C2×#67—61no—
126C2×#67—61no—
127C2×#67—61no—
128C2×#67—61no—
129C2×#67—62no—
130C2×#67—62no—
131C2×#67—61no—
132C2×#67—61no—
133C2×#67—61no—
134C2×#67—61no—
135C2×#67—61no—
136C2×#67—61no—
137C2×#67—61no—
138C2×#67—61no—
139C2×#67C2×A411yescharacteristic
140C22×Dic3—21no—
141C22×Dic3—31no—
142C22×Dic3—31no—
143C22×Dic3—41no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—121no—
148C4×A4—42no—
149C4×A4—41no—
150C4×A4—61no—
151C4×A4—121no—
152C3×C22⋊C4—31no—
153C3×C22⋊C4—41no—
154C3×C22⋊C4—61no—
155C3×C22⋊C4—61no—
156C3×C22⋊C4—81no—
157C3×C22⋊C4—121no—
158C3×C22⋊C4C2×A411yescharacteristic, complemented
159#217—31no—
160#217—61no—
161#217—61no—
162#217C2×A411yescharacteristic, complemented
163C22×C32—41no—
164C22×C32—41no—
165C22×C32—41no—
166C22×C32—161no—
167C2×C3×D3—81no—
168C2×C3×D3—161no—
169C3×A4#9911yescharacteristic, complemented
170C32×C4—161no—
171C3×Dic3—81no—
172C3×Dic3—161no—
173C25—31no—
174C25C2×C3×D311yescharacteristic
175C22×D4—61no—
176C22×D4—61no—
177C22×D4—91no—
178C22×D4—91no—
179C22×D4—91no—
180C22×D4—91no—
181C22×D4—181no—
182C22×D4—181no—
183C23×C4—21no—
184C23×C4—31no—
185C23×C4—61no—
186C2×C22⋊C4—31no—
187C2×C22⋊C4—31no—
188C2×C22⋊C4—61no—
189C2×C22⋊C4—91no—
190C2×C22⋊C4—91no—
191C2×C22⋊C4—181no—
192#99—31no—
193#99—91no—
194#99—91no—
195#99—92no—
196#99—91no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—32no—
201C23×C3—31no—
202C23×C3—31no—
203C23×C3—31no—
204C23×C3—31no—
205C23×C3—31no—
206C23×C3—31no—
207C23×C3—31no—
208C23×C3—31no—
209C23×C3—31no—
210C23×C3—41no—
211C23×C3—61no—
212C23×C3—61no—
213C23×C3—61no—
214C23×C3—81no—
215C23×C3—121no—
216C23×C3—121no—
217C23×C3—121no—
218C23×C3—121no—
219C23×C3—121no—
220C23×C3—121no—
221C23×C3—121no—
222C23×C3—121no—
223C23×C3—121no—
224C23×C3C3×C22⋊C411yescharacteristic
225C23×C3C22×A411yescharacteristic
226C22×D3—31no—
227C22×D3—41no—
228C22×D3—61no—
229C22×D3—61no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—121no—
233C22×D3—121no—
234C22×D3—122no—
235C22×D3—122no—
236C22×D3—121no—
237C22×D3—121no—
238C22×D3—121no—
239C22×D3C4×A411yescharacteristic, complemented
240C2×A4—22no—
241C2×A4—21no—
242C2×A4—21no—
243C2×A4—21no—
244C2×A4—21no—
245C2×A4—41no—
246C2×A4—41no—
247C2×A4—121no—
248C2×A4(C2×D3)⋊C411yescharacteristic
249C3×D4—241no—
250C3×D4—241no—
251C2×C3×C4—21no—
252C2×C3×C4—61no—
253C2×C3×C4—81no—
254C2×C3×C4—82no—
255C2×C3×C4—121no—
256C2×C3×C4—121no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4—241no—
261#67—21no—
262#67—21no—
263#67—61no—
264#67—61no—
265#67—61no—
266#67—61no—
267#67—62no—
268#67—62no—
269#67—61no—
270#67—61no—
271C2×Dic3—21no—
272C2×Dic3—31no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280C2×Dic3—121no—
281C2×Dic3—121no—
282C2×Dic3C4×A411yescharacteristic, complemented
283C2×C32—41no—
284C2×C32—81no—
285C2×C32—81no—
286C2×C32—81no—
287C3×D3—161no—
288C24—31no—
289C24—31no—
290C24—31no—
291C24—31no—
292C24—41no—
293C24—61no—
294C24—91no—
295C24—91no—
296C24—121no—
297C24—121no—
298C24—181no—
299C24—361no—
300C24C3×C4×D311yescharacteristic
301C24C3×D1211yescharacteristic
302C24C3×#6711yescharacteristic
303C2×D4—31no—
304C2×D4—91no—
305C2×D4—91no—
306C2×D4—92no—
307C2×D4—91no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—182no—
313C2×D4—182no—
314C2×D4—181no—
315C2×D4—181no—
316C2×D4—181no—
317C2×D4—181no—
318C2×D4—181no—
319C2×D4—181no—
320C2×D4—181no—
321C2×D4—181no—
322C22×C4—41no—
323C22×C4—61no—
324C22×C4—61no—
325C22×C4—61no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—121no—
329C22×C4—121no—
330C22×C4—181no—
331C22×C4—181no—
332C22×C4—181no—
333C22×C4—361no—
334C22⋊C4—31no—
335C22⋊C4—31no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C22⋊C4—91no—
339C22⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4D3×A411yescharacteristic, complemented
342C22×C3—31no—
343C22×C3—31no—
344C22×C3—31no—
345C22×C3—31no—
346C22×C3—31no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—61no—
352C22×C3—61no—
353C22×C3—61no—
354C22×C3—61no—
355C22×C3—61no—
356C22×C3—61no—
357C22×C3—61no—
358C22×C3—61no—
359C22×C3—61no—
360C22×C3—61no—
361C22×C3—61no—
362C22×C3—61no—
363C22×C3—81no—
364C22×C3—81no—
365C22×C3—81no—
366C22×C3—121no—
367C22×C3—121no—
368C22×C3—121no—
369C22×C3—122no—
370C22×C3—161no—
371C22×C3—162no—
372C22×C3—241no—
373C22×C3—481no—
374C22×C3C3×#9911yescharacteristic, complemented
375C22×C3C2×C4×A411yescharacteristic
376C22×C3D4×A411yescharacteristic
377C22×C3D4×A411yescharacteristic
378C2×D3—21no—
379C2×D3—41no—
380C2×D3—61no—
381C2×D3—121no—
382C2×D3—121no—
383C2×D3—122no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—121no—
387C2×D3—122no—
388A4—21no—
389A4#80611yescharacteristic, direct product factor
390C3×C4—41no—
391C3×C4—121no—
392C3×C4—161no—
393C3×C4—162no—
394C3×C4—241no—
395C3×C4—481no—
396Dic3—21no—
397Dic3—41no—
398Dic3—61no—
399Dic3—121no—
400C32—41noSylow
401C23—21no—
402C23—21no—
403C23—21no—
404C23—32no—
405C23—31no—
406C23—31no—
407C23—31no—
408C23—31no—
409C23—31no—
410C23—31no—
411C23—31no—
412C23—31no—
413C23—31no—
414C23—31no—
415C23—61no—
416C23—61no—
417C23—61no—
418C23—91no—
419C23—121no—
420C23—121no—
421C23—121no—
422C23—121no—
423C23—121no—
424C23—121no—
425C23—121no—
426C23—121no—
427C23—121no—
428C23—181no—
429C23—181no—
430C23—181no—
431C23—181no—
432C23—361no—
433C23—361no—
434C23—361no—
435C23—361no—
436C23—361no—
437C23—362no—
438C23—362no—
439C23C3×(C2×D3)⋊C411yescharacteristic
440C23C2×D3×A411yescharacteristic
441D4—61no—
442D4—61no—
443D4—181no—
444D4—181no—
445D4—181no—
446D4—181no—
447D4—182no—
448D4—182no—
449D4—181no—
450D4—181no—
451C2×C4—21no—
452C2×C4—31no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—91no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4—361no—
468C2×C4—361no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—31no—
473C2×C3—31no—
474C2×C3—41no—
475C2×C3—61no—
476C2×C3—61no—
477C2×C3—61no—
478C2×C3—81no—
479C2×C3—81no—
480C2×C3—81no—
481C2×C3—82no—
482C2×C3—81no—
483C2×C3—161no—
484C2×C3—161no—
485C2×C3—481no—
486C2×C3A4×C22⋊C411yescharacteristic
487D3—41no—
488D3—121no—
489C22—31no—
490C22—31no—
491C22—31no—
492C22—31no—
493C22—31no—
494C22—41no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—61no—
500C22—61no—
501C22—61no—
502C22—61no—
503C22—61no—
504C22—61no—
505C22—61no—
506C22—61no—
507C22—61no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—122no—
513C22—181no—
514C22—361no—
515C22—361no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22—362no—
520C22—362no—
521C22C3×#80611yescharacteristic, complemented
522C22C4×D3×A411yescharacteristic
523C22A4×D1211yescharacteristic
524C22A4×#6711yescharacteristic
525C4—41no—
526C4—61no—
527C4—121no—
528C4—121no—
529C4—181no—
530C4—361no—
531C3—41no—
532C3—81no—
533C3A4×#9911yescharacteristic, complemented
534C2—21no—
535C2—21no—
536C2—21no—
537C2—31no—
538C2—31no—
539C2—61no—
540C2—61no—
541C2—61no—
542C2—121no—
543C2—361no—
544C2A4×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2A4×(C2×D3)⋊C4
commutatorC24×C3C2×C3×C4
FrattiniC23C2×D3×A4
FittingC22×C3×C22⋊C4C2×C3
socleC23×C3C3×C22⋊C4
prime radicalC2×A4×#67C2
cosocleC25×C3C22×C3
hypercenterC22⋊C4D3×A4
hypocenterC22×C3C3×#99
LCSG ▷ C24×C3 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C23 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×A4×C22⋊C4C2semidirect
3. A4×#217C2semidirect
4. C22×#806C3semidirect
7. C22×D3×A4C4semidirect
12. C2×Dic3×A4C4semidirect
16. C22×C3×C22⋊C4C2×C3semidirect
17. C22×#217C2×C3semidirect
20. A4×C22⋊C4D3semidirect
39. C24×D3C3×C4semidirect
53. C23×Dic3C3×C4semidirect
71. #806A4direct (N × H)
86. C22×C22⋊C4C3×D3semidirect
158. C3×C22⋊C4C2×A4semidirect
162. #217C2×A4semidirect
169. C3×A4#99semidirect
239. C22×D3C4×A4semidirect
282. C2×Dic3C4×A4semidirect
341. C22⋊C4D3×A4semidirect
374. C22×C3C3×#99semidirect
389. A4#806direct (N × H)
521. C22C3×#806semidirect
533. C3A4×#99semidirect

Maximal subgroups

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

subgroupindex
C2×A4×#672
C3×A4×C22⋊C42
A4×#2172
C22×#8063
A4×#993
C3×#8064