Finite Group Databasebeta

← C2×C22⋊A4×AGL(1,ℤ/9) #72269022

Subgroups — C2×C22⋊A4×AGL(1,ℤ/9) #72269022

Order 5184.

6470 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 6470 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C2×3−1+2×C22⋊A4C211yesmaximal, characteristic, complemented
2C22⋊A4×AGL(1,ℤ/9)C212yesmaximal, direct product factor
3C2×C3×D3×C22⋊A4—31nomaximal
4C25×AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
5C2×D9⋊(C22⋊A4)C312yesmaximal, complemented
6C2×D9×C22⋊A4C311yesmaximal, characteristic, complemented
73−1+2×C22⋊A4C2211yescharacteristic, complemented
8C2×A4×AGL(1,ℤ/9)—45nomaximal
9C2×C32×C22⋊A4D311yescharacteristic
10C3×D3×C22⋊A4—32no—
11C25×3−1+2C2×C311yescharacteristic, complemented
12C24×AGL(1,ℤ/9)—35no—
13C24×AGL(1,ℤ/9)—35no—
14C24×AGL(1,ℤ/9)—310no—
15C24×AGL(1,ℤ/9)C2×C312yescomplemented
16C2×#88907—21no—
17C2×C9⋊(C22⋊A4)—22no—
18C2×C9⋊(C22⋊A4)C2×C312yescomplemented
19C2×C9×C22⋊A4—21no—
20C2×C9×C22⋊A4C2×C311yescharacteristic, complemented
21D9×C22⋊A4C2×C312yescomplemented
22D9⋊(C22⋊A4)C2×C314yescomplemented
23C2×A4×3−1+2—45no—
24A4×AGL(1,ℤ/9)—410no—
25C25×C3×D3—31no—
26C22×C3×C22⋊A4—91no—
27C2×D3×C22⋊A4—31no—
28C2×D3×C22⋊A4—32no—
29C25×D9C3211yescharacteristic, complemented
30C32×C22⋊A4C2×D311yescharacteristic
31C2×C3×D3×A4—125no—
32C24×3−1+2—35no—
33C24×3−1+2—35no—
34C24×3−1+2C22×C311yescharacteristic, complemented
35C23×AGL(1,ℤ/9)—360no—
36C23×AGL(1,ℤ/9)—360no—
37C23×AGL(1,ℤ/9)—330no—
38C23×AGL(1,ℤ/9)—310no—
39C23×AGL(1,ℤ/9)—310no—
40C23×AGL(1,ℤ/9)—35no—
41C23×AGL(1,ℤ/9)—310no—
42C23×AGL(1,ℤ/9)—310no—
43C23×AGL(1,ℤ/9)—310no—
44C23×AGL(1,ℤ/9)A415yescomplemented
45#88907—21no—
46C9⋊(C22⋊A4)—22no—
47C9⋊(C22⋊A4)C22×C312yescomplemented
48C9×C22⋊A4—21no—
49C9×C22⋊A4C22×C311yescharacteristic, complemented
50C2×A4×D9—45no—
51C2×D9⋊A4—410no—
52C2×C3×AGL(1,ℤ/9)—161no—
53A4×3−1+2—45no—
54C25×C32C3×D311yescharacteristic
55C24×C3×D3—32no—
56C24×C3×D3—95no—
57C24×C3×D3—910no—
58C24×C3×D3—95no—
59C2×C3×C22⋊A4—31no—
60C2×C3×C22⋊A4—61no—
61C2×C3×C22⋊A4—92no—
62C2×C3×C22⋊A4C3×D311yescharacteristic
63C2×C3×C22⋊A4C3×D312yes—
64D3×C22⋊A4—34no—
65D3×C22⋊A4—32no—
66C25×C9—21no—
67C25×C9C2×C3211yescharacteristic, complemented
68C24×D9—35no—
69C24×D9—35no—
70C24×D9—310no—
71C24×D9C2×C3212yescomplemented
72C2×C22⋊(C22⋊C9)—22no—
73C2×C22⋊(C22⋊C9)—21no—
74C2×C32×A4—45no—
75C3×D3×A4—1210no—
76C23×3−1+2—330no—
77C23×3−1+2—310no—
78C23×3−1+2—35no—
79C23×3−1+2—35no—
80C23×3−1+2C2×A415yescomplemented
81C22×AGL(1,ℤ/9)—3120no—
82C22×AGL(1,ℤ/9)—330no—
83C22×AGL(1,ℤ/9)—360no—
84C22×AGL(1,ℤ/9)—360no—
85C22×AGL(1,ℤ/9)—330no—
86C22×AGL(1,ℤ/9)—360no—
87C22×AGL(1,ℤ/9)—320no—
88C22×AGL(1,ℤ/9)—310no—
89C22×AGL(1,ℤ/9)—35no—
90C22×AGL(1,ℤ/9)—35no—
91C22×AGL(1,ℤ/9)—310no—
92C22×AGL(1,ℤ/9)C2×A4110yescomplemented
93C2×#1094—85no—
94C2×C9⋊A4—410no—
95C2×C9⋊A4—810no—
96C2×C9×A4—45no—
97C2×C9×A4—85no—
98A4×D9—410no—
99D9⋊A4—420no—
100C26×C3—91no—
101C25×D3—31no—
102C22×C22⋊A4—92no—
103C22×C22⋊A4—91no—
104C2×C3×3−1+2—161no—
105C3×AGL(1,ℤ/9)—162no—
106C24×C32—35no—
107C24×C32—35no—
108C24×C32C2×C3×D311yescharacteristic
109C23×C3×D3—35no—
110C23×C3×D3—910no—
111C23×C3×D3—910no—
112C23×C3×D3—910no—
113C23×C3×D3—960no—
114C23×C3×D3—960no—
115C23×C3×D3—930no—
116C23×C3×D3—910no—
117C23×C3×D3—95no—
118C23×C3×D3—910no—
119C3×C22⋊A4—31no—
120C3×C22⋊A4—61no—
121C3×C22⋊A4C2×C3×D311yescharacteristic
122C3×C22⋊A4C2×C3×D312yes—
123C22×C3×A4—365no—
124C2×D3×A4—1210no—
125C2×D3×A4—125no—
126C24×C9—21no—
127C24×C9—35no—
128C24×C9—35no—
129C24×C9—65no—
130C24×C9—65no—
131C24×C9C22×C3211yescharacteristic, complemented
132C23×D9—360no—
133C23×D9—360no—
134C23×D9—330no—
135C23×D9—310no—
136C23×D9—310no—
137C23×D9—35no—
138C23×D9—310no—
139C23×D9—310no—
140C23×D9—310no—
141C23×D9C3×A415yescomplemented
142C22⋊(C22⋊C9)—22no—
143C22⋊(C22⋊C9)—21no—
144C2×C32×D3—481no—
145C32×A4—45no—
146C22×3−1+2—330no—
147C22×3−1+2—310no—
148C22×3−1+2—35no—
149C22×3−1+2—35no—
150C22×3−1+2C22×A415yescomplemented
151C2×AGL(1,ℤ/9)—360no—
152C2×AGL(1,ℤ/9)—310no—
153C2×AGL(1,ℤ/9)—360no—
154C2×AGL(1,ℤ/9)—35no—
155C2×AGL(1,ℤ/9)—310no—
156C2×AGL(1,ℤ/9)—310no—
157C2×AGL(1,ℤ/9)—310no—
158C2×AGL(1,ℤ/9)—162no—
159C2×AGL(1,ℤ/9)C22⋊A411yescharacteristic, direct product factor
160C2×C3×D9—161no—
161#1094—85no—
162C9⋊A4—410no—
163C9⋊A4—810no—
164C9×A4—45no—
165C9×A4—85no—
166C25×C3—31no—
167C25×C3—92no—
168C25×C3—275no—
169C25×C3—275no—
170C25×C3—2710no—
171C25×C3C32×D311yescharacteristic
172C24×D3—32no—
173C24×D3—95no—
174C24×D3—910no—
175C24×D3—95no—
176C2×C22⋊A4—21no—
177C2×C22⋊A4—32no—
178C2×C22⋊A4—94no—
179C2×C22⋊A4—92no—
180C2×C22⋊A4AGL(1,ℤ/9)11yescharacteristic, direct product factor
181C3×3−1+2—161noSylow
182C23×C32—330no—
183C23×C32—310no—
184C23×C32—35no—
185C23×C32—35no—
186C23×C32D3×A415yes—
187C22×C3×D3—310no—
188C22×C3×D3—95no—
189C22×C3×D3—920no—
190C22×C3×D3—960no—
191C22×C3×D3—930no—
192C22×C3×D3—9120no—
193C22×C3×D3—960no—
194C22×C3×D3—960no—
195C22×C3×D3—930no—
196C22×C3×D3—910no—
197C22×C3×D3—910no—
198C22×C3×D3—95no—
199C2×C3×A4—45no—
200C2×C3×A4—410no—
201C2×C3×A4—125no—
202C2×C3×A4—245no—
203C2×C3×A4—3610no—
204D3×A4—1220no—
205D3×A4—1210no—
206C23×C9—25no—
207C23×C9—330no—
208C23×C9—310no—
209C23×C9—35no—
210C23×C9—35no—
211C23×C9—65no—
212C23×C9—65no—
213C23×C9—610no—
214C23×C9—630no—
215C23×C9C2×C3×A415yescomplemented
216C22×D9—330no—
217C22×D9—3120no—
218C22×D9—360no—
219C22×D9—360no—
220C22×D9—330no—
221C22×D9—360no—
222C22×D9—320no—
223C22×D9—310no—
224C22×D9—35no—
225C22×D9—35no—
226C22×D9—310no—
227C22×D9C2×C3×A4110yescomplemented
228C2×C22⋊C9—85no—
229C2×C22⋊C9—810no—
230C26—91noSylow
231C2×C33—161no—
232C32×D3—482no—
233C2×3−1+2—35no—
234C2×3−1+2—35no—
235C2×3−1+2—162no—
236C2×3−1+2—322no—
237C2×3−1+2—321no—
238C2×3−1+2C2×C22⋊A411yescharacteristic, complemented
239C2×C3×C9—161no—
240C2×C3×C9—321no—
241AGL(1,ℤ/9)—310no—
242AGL(1,ℤ/9)—164no—
243AGL(1,ℤ/9)C2×C22⋊A412yesdirect product factor
244C3×D9—162no—
245C24×C3—35no—
246C24×C3—35no—
247C24×C3—31no—
248C24×C3—95no—
249C24×C3—95no—
250C24×C3—95no—
251C24×C3—275no—
252C24×C3—2710no—
253C24×C3—2710no—
254C24×C3—2710no—
255C24×C3—2710no—
256C24×C3—2710no—
257C24×C3—2730no—
258C24×C3—2760no—
259C24×C3—2760no—
260C24×C3C2×C32×D311yescharacteristic
261C23×D3—35no—
262C23×D3—910no—
263C23×D3—910no—
264C23×D3—910no—
265C23×D3—960no—
266C23×D3—960no—
267C23×D3—930no—
268C23×D3—910no—
269C23×D3—95no—
270C23×D3—910no—
271C22⋊A4—21no—
272C22⋊A4—32no—
273C22⋊A4C2×AGL(1,ℤ/9)11yescharacteristic, direct product factor
274C22×A4—365no—
275C22×A4—3610no—
276C22×C32—35no—
277C22×C32—330no—
278C22×C32—310no—
279C22×C32—35no—
280C22×C32—1441no—
281C22×C32C2×D3×A415yes—
282C2×C3×D3—31no—
283C2×C3×D3—910no—
284C2×C3×D3—910no—
285C2×C3×D3—960no—
286C2×C3×D3—910no—
287C2×C3×D3—960no—
288C2×C3×D3—95no—
289C2×C3×D3—910no—
290C2×C3×D3—481no—
291C2×C3×D3—482no—
292C3×A4—45no—
293C3×A4—410no—
294C3×A4—125no—
295C3×A4—245no—
296C22×C9—25no—
297C22×C9—35no—
298C22×C9—330no—
299C22×C9—310no—
300C22×C9—35no—
301C22×C9—65no—
302C22×C9—65no—
303C22×C9—610no—
304C22×C9—630no—
305C22×C9C22×C3×A415yescomplemented
306C2×D9—360no—
307C2×D9—310no—
308C2×D9—360no—
309C2×D9—35no—
310C2×D9—310no—
311C2×D9—310no—
312C2×D9—310no—
313C2×D9C3×C22⋊A411yescharacteristic, complemented
314C22⋊C9—85no—
315C22⋊C9—810no—
316C25—92no—
317C25—275no—
318C25—2710no—
319C25—275no—
320C25C3×AGL(1,ℤ/9)11yescharacteristic, complemented
321C33—161no—
3223−1+2—162no—
3233−1+2—322no—
3243−1+2—321no—
3253−1+2C22×C22⋊A411yescharacteristic, complemented
326C3×C9—161no—
327C3×C9—321no—
328C23×C3—330no—
329C23×C3—310no—
330C23×C3—35no—
331C23×C3—35no—
332C23×C3—35no—
333C23×C3—95no—
334C23×C3—95no—
335C23×C3—910no—
336C23×C3—930no—
337C23×C3—910no—
338C23×C3—2710no—
339C23×C3—275no—
340C23×C3—275no—
341C23×C3—2710no—
342C23×C3—2730no—
343C23×C3—2730no—
344C23×C3—2720no—
345C23×C3—2760no—
346C23×C3—2760no—
347C23×C3—2760no—
348C23×C3—27120no—
349C23×C3C3×D3×A415yes—
350C22×D3—310no—
351C22×D3—95no—
352C22×D3—920no—
353C22×D3—960no—
354C22×D3—930no—
355C22×D3—9120no—
356C22×D3—960no—
357C22×D3—960no—
358C22×D3—930no—
359C22×D3—910no—
360C22×D3—910no—
361C22×D3—95no—
362C2×A4—45no—
363C2×A4—85no—
364C2×A4—1210no—
365C2×A4—3610no—
366C2×A4—3620no—
367C2×C32—35no—
368C2×C32—35no—
369C2×C32—161no—
370C2×C32—162no—
371C2×C32—481no—
372C2×C32—961no—
373C2×C32—1442no—
374C2×C32D3×C22⋊A411yescharacteristic
375C3×D3—32no—
376C3×D3—910no—
377C3×D3—482no—
378C3×D3—484no—
379C2×C9—21no—
380C2×C9—35no—
381C2×C9—35no—
382C2×C9—65no—
383C2×C9—65no—
384C2×C9—321no—
385C2×C9—322no—
386C2×C9C2×C3×C22⋊A411yescharacteristic, complemented
387D9—310no—
388D9C2×C3×C22⋊A412yescomplemented
389C24—35no—
390C24—35no—
391C24—95no—
392C24—2710no—
393C24—2710no—
394C24—2710no—
395C24—2710no—
396C24—2760no—
397C24—2730no—
398C24—2760no—
399C24—2710no—
400C24—275no—
401C24C2×C3×AGL(1,ℤ/9)11yescharacteristic, complemented
402C22×C3—35no—
403C22×C3—310no—
404C22×C3—330no—
405C22×C3—35no—
406C22×C3—35no—
407C22×C3—95no—
408C22×C3—95no—
409C22×C3—910no—
410C22×C3—930no—
411C22×C3—91no—
412C22×C3—275no—
413C22×C3—2710no—
414C22×C3—2710no—
415C22×C3—2710no—
416C22×C3—2760no—
417C22×C3—2710no—
418C22×C3—2760no—
419C22×C3—1441no—
420C22×C3—1442no—
421C22×C3C2×C3×D3×A415yes—
422C2×D3—31no—
423C2×D3—910no—
424C2×D3—910no—
425C2×D3—960no—
426C2×D3—960no—
427C2×D3—910no—
428C2×D3—95no—
429C2×D3—910no—
430A4—45no—
431A4—85no—
432A4—1210no—
433C32—161no—
434C32—162no—
435C32—481no—
436C32—961no—
437C32C2×D3×C22⋊A411yescharacteristic
438C9—21no—
439C9—321no—
440C9—322no—
441C9C22×C3×C22⋊A411yescharacteristic, complemented
442C23—330no—
443C23—310no—
444C23—35no—
445C23—35no—
446C23—910no—
447C23—275no—
448C23—2710no—
449C23—275no—
450C23—2730no—
451C23—2720no—
452C23—2760no—
453C23—2760no—
454C23—2760no—
455C23—27120no—
456C23—2730no—
457C23—2710no—
458C23A4×AGL(1,ℤ/9)15yescomplemented
459C2×C3—35no—
460C2×C3—35no—
461C2×C3—31no—
462C2×C3—95no—
463C2×C3—95no—
464C2×C3—92no—
465C2×C3—161no—
466C2×C3—2710no—
467C2×C3—321no—
468C2×C3—482no—
469C2×C3—1442no—
470C2×C3—1444no—
471C2×C3C3×D3×C22⋊A411yescharacteristic
472D3—32no—
473D3—910no—
474C22—35no—
475C22—310no—
476C22—330no—
477C22—35no—
478C22—91no—
479C22—2710no—
480C22—2710no—
481C22—2710no—
482C22—2760no—
483C22—2710no—
484C22—2760no—
485C22—275no—
486C22C2×A4×AGL(1,ℤ/9)15yescomplemented
487C3—31no—
488C3—161no—
489C3—321no—
490C3—482no—
491C3C2×C3×D3×C22⋊A411yescharacteristic
492C2—35no—
493C2—35no—
494C2—92no—
495C2—2710no—
496C2C22⋊A4×AGL(1,ℤ/9)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C22⋊A4×AGL(1,ℤ/9)
commutator, cosocle, hypocenterC24×C9C22×C32
FrattiniC3C2×C3×D3×C22⋊A4
FittingC25×3−1+2C2×C3
socleC25×C3C32×D3
LCSG ▷ C24×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×3−1+2×C22⋊A4C2semidirect
2. C22⋊A4×AGL(1,ℤ/9)C2direct (N × H)
4. C25×AGL(1,ℤ/9)C3semidirect
5. C2×D9⋊(C22⋊A4)C3semidirect
6. C2×D9×C22⋊A4C3semidirect
7. 3−1+2×C22⋊A4C22semidirect
11. C25×3−1+2C2×C3semidirect
15. C24×AGL(1,ℤ/9)C2×C3semidirect
18. C2×C9⋊(C22⋊A4)C2×C3semidirect
20. C2×C9×C22⋊A4C2×C3semidirect
21. D9×C22⋊A4C2×C3semidirect
22. D9⋊(C22⋊A4)C2×C3semidirect
29. C25×D9C32semidirect
34. C24×3−1+2C22×C3semidirect
44. C23×AGL(1,ℤ/9)A4semidirect
47. C9⋊(C22⋊A4)C22×C3semidirect
49. C9×C22⋊A4C22×C3semidirect
67. C25×C9C2×C32semidirect
71. C24×D9C2×C32semidirect
80. C23×3−1+2C2×A4semidirect
92. C22×AGL(1,ℤ/9)C2×A4semidirect
131. C24×C9C22×C32semidirect
141. C23×D9C3×A4semidirect
150. C22×3−1+2C22×A4semidirect
159. C2×AGL(1,ℤ/9)C22⋊A4direct (N × H)
180. C2×C22⋊A4AGL(1,ℤ/9)direct (N × H)
215. C23×C9C2×C3×A4semidirect
227. C22×D9C2×C3×A4semidirect
238. C2×3−1+2C2×C22⋊A4semidirect
243. AGL(1,ℤ/9)C2×C22⋊A4direct (N × H)
273. C22⋊A4C2×AGL(1,ℤ/9)direct (N × H)
305. C22×C9C22×C3×A4semidirect
313. C2×D9C3×C22⋊A4semidirect
320. C25C3×AGL(1,ℤ/9)semidirect
325. 3−1+2C22×C22⋊A4semidirect
386. C2×C9C2×C3×C22⋊A4semidirect
388. D9C2×C3×C22⋊A4semidirect
401. C24C2×C3×AGL(1,ℤ/9)semidirect
441. C9C22×C3×C22⋊A4semidirect
458. C23A4×AGL(1,ℤ/9)semidirect
486. C22C2×A4×AGL(1,ℤ/9)semidirect
496. C2C22⋊A4×AGL(1,ℤ/9)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×3−1+2×C22⋊A42
C22⋊A4×AGL(1,ℤ/9)2
C2×C3×D3×C22⋊A43
C25×AGL(1,ℤ/9)3
C2×D9⋊(C22⋊A4)3
C2×D9×C22⋊A43
C2×A4×AGL(1,ℤ/9)4