Finite Group Databasebeta

← A4×#611⋊C3 #72269090

Subgroups — A4×#611⋊C3 #72269090

Order 2592.

611 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 611 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×A4×3−1+2C211yesmaximal, characteristic, complemented
2C2×A4×AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
3A4×3−1+2⋊C4C211yesmaximal, characteristic, complemented
4C3×A4×#67—31nomaximal
5C22×#611⋊C3C311yesmaximal, characteristic, complemented
6A4×#611C311yesmaximal, characteristic, complemented
7#611⋊A4C312yesmaximal, complemented
8C2×A4×3−1+2—21no—
9C2×A4×3−1+2C2211yescharacteristic
10A4×AGL(1,ℤ/9)—21no—
11C3×#611⋊C3—41nomaximal
12C22×C32×A4D311yescharacteristic
13C2×C3×D3×A4—31no—
14C3×Dic3×A4—31no—
15C24×3−1+2C2×C311yescharacteristic, complemented
16C23×AGL(1,ℤ/9)C2×C311yescharacteristic, complemented
17C22×#1094—21no—
18C22×C9⋊A4—22no—
19C22×C9⋊A4C2×C312yescomplemented
20C22×C9×A4—21no—
21C22×C9×A4C2×C311yescharacteristic, complemented
22C2×A4×D9C2×C311yescharacteristic, complemented
23C2×D9⋊A4C2×C312yescomplemented
24C2×#611⋊C3—31no—
25C2×#611⋊C3—31no—
26C2×#611⋊C3—31no—
27C2×#611⋊C3—31no—
28C22×3−1+2⋊C4C2×C311yescharacteristic, complemented
29A4×Dic9C2×C311yescharacteristic, complemented
30Dic9⋊A4C2×C312yescomplemented
31C22×C3×3−1+2—41no—
32C2×C3×AGL(1,ℤ/9)—41no—
33A4×3−1+2D411yescharacteristic, complemented
34C3×3−1+2⋊C4—41no—
35C22×C3×#67—31no—
36C3×D4×A4—91no—
37A4×#67—32no—
38A4×#67—31no—
39C22×#611C3211yescharacteristic, complemented
40C2×C32×A4—21no—
41C2×C32×A4C2×D311yescharacteristic
42C3×D3×A4—61no—
43C32×#67—121no—
44C23×3−1+2—21no—
45C23×3−1+2—31no—
46C23×3−1+2—31no—
47C23×3−1+2—61no—
48C23×3−1+2C22×C311yescharacteristic
49C22×AGL(1,ℤ/9)—21no—
50C22×AGL(1,ℤ/9)—31no—
51C22×AGL(1,ℤ/9)—31no—
52C22×AGL(1,ℤ/9)—61no—
53C2×#1094—22no—
54C2×#1094—21no—
55C2×C9⋊A4—24no—
56C2×C9⋊A4—22no—
57C2×C9⋊A4—22no—
58C2×C9⋊A4C22×C312yes—
59C2×C9×A4—22no—
60C2×C9×A4—21no—
61C2×C9×A4—21no—
62C2×C9×A4C22×C311yescharacteristic
63A4×D9—21no—
64D9⋊A4—22no—
65#611⋊C3—32no—
66#611⋊C3—31no—
67#611⋊C3—31no—
68#611⋊C3—31no—
69#611⋊C3—42no—
70#611⋊C3A411yescharacteristic, direct product factor
71C2×3−1+2⋊C4—31no—
72C2×3−1+2⋊C4—31no—
73C3×#611—41no—
74C2×C3×3−1+2—41no—
75C2×C3×3−1+2—81no—
76C3×AGL(1,ℤ/9)—81no—
77C24×C32C3×D311yescharacteristic
78C23×C3×D3—31no—
79C22×C3×A4—31no—
80C22×C3×A4—61no—
81C22×C3×A4—91no—
82C22×C3×A4C3×D311yescharacteristic
83C22×C3×A4C3×D312yes—
84C2×D3×A4—32no—
85C2×D3×A4—31no—
86C2×C3×#67—91no—
87C2×C3×#67—91no—
88C2×C3×#67—91no—
89C2×C3×#67—91no—
90C22×C3×Dic3—31no—
91C3×C4×A4—91no—
92Dic3×A4—32no—
93Dic3×A4—31no—
94C24×C9—21no—
95C24×C9C2×C3211yescharacteristic, complemented
96C23×D9C2×C3211yescharacteristic, complemented
97C22×C22⋊C9—22no—
98C22×C22⋊C9—21no—
99C2×#611—31no—
100C2×#611—31no—
101C2×#611—31no—
102C2×#611—31no—
103C22×Dic9C2×C3211yescharacteristic, complemented
104C22×C33—41no—
105C2×C32×D3—121no—
106C32×A4#6711yescharacteristic
107C32×Dic3—121no—
108C22×3−1+2—31no—
109C22×3−1+2—31no—
110C22×3−1+2—31no—
111C22×3−1+2—42no—
112C22×3−1+2—61no—
113C22×3−1+2—61no—
114C22×3−1+2—61no—
115C22×3−1+2—61no—
116C22×3−1+2—82no—
117C22×3−1+2—81no—
118C22×3−1+2C3×D411yescharacteristic, complemented
119C22×3−1+2C2×A411yescharacteristic, complemented
120C22×C3×C9—41no—
121C22×C3×C9—81no—
122C2×AGL(1,ℤ/9)—31no—
123C2×AGL(1,ℤ/9)—42no—
124C2×AGL(1,ℤ/9)—61no—
125C2×AGL(1,ℤ/9)—61no—
126C2×AGL(1,ℤ/9)—61no—
127C2×AGL(1,ℤ/9)—61no—
128C2×AGL(1,ℤ/9)C2×A411yescharacteristic, complemented
129C2×C3×D9—41no—
130#1094—21no—
131C9⋊A4—22no—
132C9⋊A4C3×D412yescomplemented
133C9×A4—21no—
134C9×A4C3×D411yescharacteristic, complemented
1353−1+2⋊C4—31no—
1363−1+2⋊C4—42no—
1373−1+2⋊C4C2×A411yescharacteristic, complemented
138C3×Dic9—41no—
139C22×C3×D4—91no—
140C22×#67—31no—
141D4×A4—92no—
142D4×A4—91no—
143C3×3−1+2—41noSylow
144C23×C32—21no—
145C23×C32—31no—
146C23×C32—31no—
147C23×C32—61no—
148C23×C32C2×C3×D311yescharacteristic
149C22×C3×D3—61no—
150C22×C3×D3—91no—
151C22×C3×D3—91no—
152C22×C3×D3—181no—
153C2×C3×A4—21no—
154C2×C3×A4—22no—
155C2×C3×A4—31no—
156C2×C3×A4—61no—
157C2×C3×A4—61no—
158C2×C3×A4—62no—
159C2×C3×A4—181no—
160C2×C3×A4C2×C3×D311yescharacteristic
161C2×C3×A4C2×C3×D312yes—
162D3×A4—62no—
163D3×A4—61no—
164C32×D4—361no—
165C3×#67—31no—
166C3×#67—91no—
167C3×#67—91no—
168C3×#67—92no—
169C3×#67—91no—
170C3×#67—121no—
171C3×#67—122no—
172C2×C3×Dic3—91no—
173C2×C3×Dic3—91no—
174C23×C9—22no—
175C23×C9—21no—
176C23×C9—21no—
177C23×C9—31no—
178C23×C9—31no—
179C23×C9—61no—
180C23×C9—61no—
181C23×C9—61no—
182C23×C9—62no—
183C23×C9C22×C3211yescharacteristic
184C22×D9—21no—
185C22×D9—31no—
186C22×D9—31no—
187C22×D9—61no—
188C2×C22⋊C9—24no—
189C2×C22⋊C9—22no—
190C2×C22⋊C9—22no—
191C2×C22⋊C9—21no—
192#611—32no—
193#611—31no—
194#611—31no—
195#611—31no—
196#611C3×A411yescharacteristic, complemented
197C2×Dic9—31no—
198C2×Dic9—31no—
199C2×C33—41no—
200C2×C33—81no—
201C32×D3—241no—
202C2×3−1+2—21no—
203C2×3−1+2—31no—
204C2×3−1+2—31no—
205C2×3−1+2—42no—
206C2×3−1+2—61no—
207C2×3−1+2—82no—
208C2×3−1+2—82no—
209C2×3−1+2—84no—
210C2×3−1+2—82no—
211C2×3−1+2—81no—
212C2×3−1+2C22×A411yescharacteristic
213C2×C3×C9—41no—
214C2×C3×C9—81no—
215C2×C3×C9—81no—
216C2×C3×C9—82no—
217AGL(1,ℤ/9)—21no—
218AGL(1,ℤ/9)—61no—
219AGL(1,ℤ/9)—82no—
220C3×D9—81no—
221C24×C3—31no—
222C24×C3—91no—
223C24×C3C32×D311yescharacteristic
224C23×D3—31no—
225C22×A4—21no—
226C22×A4—32no—
227C22×A4—92no—
228C22×A4—91no—
229C22×A4AGL(1,ℤ/9)11yescharacteristic, complemented
230C2×C3×D4—271no—
231C2×C3×D4—271no—
232C2×C3×D4—271no—
233C2×C3×D4—271no—
234C22×C3×C4—91no—
235C2×#67—91no—
236C2×#67—91no—
237C2×#67—91no—
238C2×#67—91no—
239C22×Dic3—31no—
240C4×A4—92no—
241C4×A4—91no—
242C22×C32—31no—
243C22×C32—31no—
244C22×C32—31no—
245C22×C32—41no—
246C22×C32—42no—
247C22×C32—61no—
248C22×C32—61no—
249C22×C32—61no—
250C22×C32—61no—
251C22×C32—121no—
252C22×C32—241no—
253C22×C32—361no—
254C22×C32C3×#6711yescharacteristic
255C22×C32D3×A411yescharacteristic
256C2×C3×D3—31no—
257C2×C3×D3—91no—
258C2×C3×D3—121no—
259C2×C3×D3—122no—
260C2×C3×D3—181no—
261C2×C3×D3—181no—
262C2×C3×D3—181no—
263C2×C3×D3—181no—
264C3×A4—31no—
265C3×A4—61no—
266C3×A4C3×#6711yescharacteristic
267C3×A4C3×#6712yes—
268C32×C4—361no—
269C3×Dic3—31no—
270C3×Dic3—91no—
271C3×Dic3—121no—
272C3×Dic3—122no—
273C22×C9—21no—
274C22×C9—21no—
275C22×C9—31no—
276C22×C9—31no—
277C22×C9—31no—
278C22×C9—61no—
279C22×C9—61no—
280C22×C9—61no—
281C22×C9—61no—
282C22×C9—61no—
283C22×C9—62no—
284C22×C9—62no—
285C22×C9—61no—
286C22×C9—61no—
287C22×C9—62no—
288C22×C9—62no—
289C22×C9—81no—
290C22×C9—82no—
291C22×C9C32×D411yescharacteristic, complemented
292C22×C9C2×C3×A411yescharacteristic, complemented
293C2×D9—31no—
294C2×D9—61no—
295C2×D9—61no—
296C2×D9—61no—
297C2×D9—61no—
298C2×D9C2×C3×A411yescharacteristic, complemented
299C22⋊C9—22no—
300C22⋊C9—21no—
301Dic9—31no—
302Dic9C2×C3×A411yescharacteristic, complemented
303C22×D4—91noSylow
304C33—41no—
3053−1+2—42no—
3063−1+2—82no—
3073−1+2—81no—
3083−1+2D4×A411yescharacteristic, complemented
309C3×C9—41no—
310C3×C9—81no—
311C23×C3—21no—
312C23×C3—31no—
313C23×C3—31no—
314C23×C3—31no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3—91no—
318C23×C3—91no—
319C23×C3—181no—
320C23×C3—181no—
321C23×C3—271no—
322C23×C3—271no—
323C23×C3—541no—
324C23×C3C2×C32×D311yescharacteristic
325C22×D3—61no—
326C22×D3—91no—
327C22×D3—91no—
328C22×D3—181no—
329C2×A4—22no—
330C2×A4—21no—
331C2×A4—21no—
332C2×A4—32no—
333C2×A4—62no—
334C2×A4—182no—
335C2×A4—181no—
336C2×A4C2×AGL(1,ℤ/9)11yescharacteristic
337C3×D4—91no—
338C3×D4—271no—
339C3×D4—271no—
340C3×D4—271no—
341C3×D4—272no—
342C3×D4—361no—
343C3×D4—362no—
344C2×C3×C4—271no—
345C2×C3×C4—271no—
346#67—31no—
347#67—91no—
348#67—91no—
349#67—92no—
350#67—91no—
351C2×Dic3—91no—
352C2×Dic3—91no—
353C2×C32—21no—
354C2×C32—31no—
355C2×C32—31no—
356C2×C32—41no—
357C2×C32—42no—
358C2×C32—61no—
359C2×C32—81no—
360C2×C32—82no—
361C2×C32—121no—
362C2×C32—241no—
363C2×C32—241no—
364C2×C32—242no—
365C2×C32—721no—
366C2×C32C2×D3×A411yescharacteristic
367C3×D3—61no—
368C3×D3—181no—
369C3×D3—241no—
370C3×D3—242no—
371C2×C9—22no—
372C2×C9—21no—
373C2×C9—21no—
374C2×C9—31no—
375C2×C9—31no—
376C2×C9—61no—
377C2×C9—61no—
378C2×C9—62no—
379C2×C9—61no—
380C2×C9—82no—
381C2×C9—84no—
382C2×C9—81no—
383C2×C9—82no—
384C2×C9C22×C3×A411yescharacteristic
385D9—21no—
386D9—61no—
387C24—91no—
388C24C3×AGL(1,ℤ/9)11yescharacteristic, complemented
389C2×D4—271no—
390C2×D4—271no—
391C2×D4—271no—
392C2×D4—271no—
393C22×C4—91no—
394C22×C3—31no—
395C22×C3—31no—
396C22×C3—31no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—41no—
400C22×C3—61no—
401C22×C3—61no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—81no—
405C22×C3—91no—
406C22×C3—91no—
407C22×C3—91no—
408C22×C3—91no—
409C22×C3—122no—
410C22×C3—181no—
411C22×C3—181no—
412C22×C3—181no—
413C22×C3—181no—
414C22×C3—271no—
415C22×C3—361no—
416C22×C3—362no—
417C22×C3—541no—
418C22×C3—541no—
419C22×C3—541no—
420C22×C3—541no—
421C22×C3C32×#6711yescharacteristic
422C22×C3C3×D3×A411yescharacteristic
423C2×D3—31no—
424C2×D3—91no—
425C2×D3—181no—
426C2×D3—181no—
427C2×D3—181no—
428C2×D3—181no—
429A4—21no—
430A4—32no—
431A4#611⋊C311yescharacteristic, direct product factor
432C3×C4—91no—
433C3×C4—271no—
434C3×C4—361no—
435C3×C4—362no—
436Dic3—31no—
437Dic3—91no—
438C32—41no—
439C32—42no—
440C32—121no—
441C32—241no—
442C32A4×#6711yescharacteristic
443C9—21no—
444C9—81no—
445C9—82no—
446C9C3×D4×A411yescharacteristic, complemented
447C23—21no—
448C23—31no—
449C23—31no—
450C23—61no—
451C23—181no—
452C23—271no—
453C23—271no—
454C23—541no—
455C23C2×C3×AGL(1,ℤ/9)11yescharacteristic
456D4—91no—
457D4—271no—
458D4—271no—
459D4—272no—
460D4—271no—
461C2×C4—271no—
462C2×C4—271no—
463C2×C3—21no—
464C2×C3—31no—
465C2×C3—31no—
466C2×C3—31no—
467C2×C3—41no—
468C2×C3—61no—
469C2×C3—61no—
470C2×C3—81no—
471C2×C3—82no—
472C2×C3—81no—
473C2×C3—91no—
474C2×C3—91no—
475C2×C3—122no—
476C2×C3—181no—
477C2×C3—181no—
478C2×C3—242no—
479C2×C3—541no—
480C2×C3—721no—
481C2×C3—722no—
482C2×C3C2×C3×D3×A411yescharacteristic
483D3—61no—
484D3—181no—
485C22—31no—
486C22—31no—
487C22—31no—
488C22—61no—
489C22—61no—
490C22—61no—
491C22—61no—
492C22—91no—
493C22—271no—
494C22—541no—
495C22—541no—
496C22—541no—
497C22—541no—
498C22C3×#611⋊C311yescharacteristic, complemented
499C22A4×AGL(1,ℤ/9)11yescharacteristic, complemented
500C4—91no—
501C4—271no—
502C3—31no—
503C3—41no—
504C3—81no—
505C3—122no—
506C3C3×A4×#6711yescharacteristic
507C2—21no—
508C2—31no—
509C2—31no—
510C2—61no—
511C2—181no—
512C2—541no—
513C2C2×A4×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
centerC2C2×A4×AGL(1,ℤ/9)
commutator, cosocleC23×C9C22×C32
FrattiniC2×C3C2×C3×D3×A4
FittingC24×3−1+2C2×C3
socleC23×C3C2×C32×D3
hypercenterC22A4×AGL(1,ℤ/9)
hypocenterC22×C9C32×D4
LCSG ▷ C23×C9 ▷ C22×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×A4×3−1+2C2semidirect
2. C2×A4×AGL(1,ℤ/9)C2semidirect
3. A4×3−1+2⋊C4C2semidirect
5. C22×#611⋊C3C3semidirect
6. A4×#611C3semidirect
7. #611⋊A4C3semidirect
15. C24×3−1+2C2×C3semidirect
16. C23×AGL(1,ℤ/9)C2×C3semidirect
19. C22×C9⋊A4C2×C3semidirect
21. C22×C9×A4C2×C3semidirect
22. C2×A4×D9C2×C3semidirect
23. C2×D9⋊A4C2×C3semidirect
28. C22×3−1+2⋊C4C2×C3semidirect
29. A4×Dic9C2×C3semidirect
30. Dic9⋊A4C2×C3semidirect
33. A4×3−1+2D4semidirect
39. C22×#611C32semidirect
70. #611⋊C3A4direct (N × H)
95. C24×C9C2×C32semidirect
96. C23×D9C2×C32semidirect
103. C22×Dic9C2×C32semidirect
118. C22×3−1+2C3×D4semidirect
119. C22×3−1+2C2×A4semidirect
128. C2×AGL(1,ℤ/9)C2×A4semidirect
132. C9⋊A4C3×D4semidirect
134. C9×A4C3×D4semidirect
137. 3−1+2⋊C4C2×A4semidirect
196. #611C3×A4semidirect
229. C22×A4AGL(1,ℤ/9)semidirect
291. C22×C9C32×D4semidirect
292. C22×C9C2×C3×A4semidirect
298. C2×D9C2×C3×A4semidirect
302. Dic9C2×C3×A4semidirect
308. 3−1+2D4×A4semidirect
388. C24C3×AGL(1,ℤ/9)semidirect
431. A4#611⋊C3direct (N × H)
446. C9C3×D4×A4semidirect
498. C22C3×#611⋊C3semidirect
499. C22A4×AGL(1,ℤ/9)semidirect

Maximal subgroups

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

subgroupindex
C22×A4×3−1+22
C2×A4×AGL(1,ℤ/9)2
A4×3−1+2⋊C42
C3×A4×#673
C22×#611⋊C33
A4×#6113
#611⋊A43
C3×#611⋊C34