Finite Group Databasebeta

← D4×A4⋊AGL(1,ℤ/9) #72268959

Subgroups — D4×A4⋊AGL(1,ℤ/9) #72268959

Order 5184.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72268947C211yesmaximal, characteristic, complemented
2#72268942C212yesmaximal, complemented
3D4×A4×3−1+2C211yesmaximal, characteristic, complemented
4C4×A4⋊AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
5C22×A4⋊AGL(1,ℤ/9)C212yesmaximal, complemented
6C3×D4×C3⋊S4—31nomaximal
7D4×C9⋊S4C311yesmaximal, characteristic, complemented
8D4×((C22⋊C9)⋊C2)⋊C3—32nomaximal
9D4×#611⋊C3—31nomaximal
10C22×A4×3−1+2C2212yescomplemented
11C2×A4⋊AGL(1,ℤ/9)—24no—
12C2×A4⋊AGL(1,ℤ/9)C2211yescharacteristic
13C2×A4⋊AGL(1,ℤ/9)C2212yescomplemented
14D4×C3⋊AGL(1,ℤ/9)—41nomaximal
15C4×A4×3−1+2C2211yescharacteristic, complemented
16A4⋊(3−1+2⋊C4)C2211yescharacteristic, complemented
17C22×C3×C3⋊S4—32no—
18C32×D4×A4D311yescharacteristic
19C3×#64269—32no—
20C3×C4⋊(C3⋊S4)—31no—
21C3×C4×C3⋊S4—31no—
22C22×C9⋊S4C2×C312yescomplemented
23C22×((C22⋊C9)⋊C2)⋊C3—34no—
24C22×D4×3−1+2D311yescharacteristic, complemented
25C22×#611⋊C3—32no—
26C2×D4×AGL(1,ℤ/9)—31no—
27D4×#1094D312yescomplemented
28D4×C9⋊A4—21no—
29D4×C9⋊A4—22no—
30D4×C9×A4—21no—
31D4×C9×A4C2×C311yescharacteristic, complemented
32#11722376C2×C312yescomplemented
33C4⋊(C9⋊S4)C2×C311yescharacteristic, complemented
34C4×C9⋊S4C2×C311yescharacteristic, complemented
35#63694⋊C3—34no—
36C4⋊(((C22⋊C9)⋊C2)⋊C3)—32no—
37C4×((C22⋊C9)⋊C2)⋊C3—32no—
38#11721704—32no—
39#63502⋊C3—31no—
40#63501⋊C3—32no—
41#63500⋊C3—31no—
42#63499⋊C3—32no—
43D4×3−1+2⋊C4—31no—
44#63492⋊C3—31no—
45C4×#611⋊C3—31no—
46C22×C3⋊AGL(1,ℤ/9)—42no—
47C2×A4×3−1+2—22no—
48C2×A4×3−1+2C2311yescharacteristic
49A4⋊AGL(1,ℤ/9)—22no—
50A4⋊AGL(1,ℤ/9)D412yesdirect product factor
51C3×D4×3−1+2—41no—
52#10619980—42no—
53C4⋊(C3⋊AGL(1,ℤ/9))—41no—
54C4×C3⋊AGL(1,ℤ/9)—41no—
55D4×C3⋊S4—31no—
56C3×D4×S4—93no—
57C3×D4×#67—91no—
58D4×(C22⋊C9)⋊C2—32no—
59D4×#611—31no—
60C22×C32×A4C2×D312yes—
61C2×C3×C3⋊S4—31no—
62C2×C3×C3⋊S4—32no—
63C2×C3×C3⋊S4—64no—
64C3×D4×C3⋊D3—121no—
65C32×C4×A4C2×D311yescharacteristic
66C3×C3⋊SL(2,ℤ/4)—31no—
67C24×3−1+2C2×D312yescomplemented
68C23×AGL(1,ℤ/9)—32no—
69C22×#1094C2×D314yescomplemented
70C22×C9⋊A4—22no—
71C22×C9⋊A4—24no—
72C22×C9×A4—22no—
73C22×C9×A4C22×C312yescomplemented
74C2×C9⋊S4—24no—
75C2×C9⋊S4C22×C311yescharacteristic
76C2×C9⋊S4C22×C312yescomplemented
77C2×((C22⋊C9)⋊C2)⋊C3—32no—
78C2×((C22⋊C9)⋊C2)⋊C3—34no—
79C2×((C22⋊C9)⋊C2)⋊C3—68no—
80C2×D4×3−1+2—31no—
81C2×D4×3−1+2—32no—
82C2×D4×3−1+2—31no—
83C22×C4×3−1+2C2×D311yescharacteristic, complemented
84D4×C3⋊D9—41no—
85C2×#611⋊C3—31no—
86C2×#611⋊C3—32no—
87C2×#611⋊C3—32no—
88C2×#611⋊C3—32no—
89C2×#611⋊C3—32no—
90C2×#611⋊C3—32no—
91C2×#611⋊C3—64no—
92C2×#611⋊C3—64no—
93C22×3−1+2⋊C4—32no—
94D4×AGL(1,ℤ/9)—62no—
95D4×AGL(1,ℤ/9)—61no—
96D4×AGL(1,ℤ/9)—61no—
97D4×AGL(1,ℤ/9)—122no—
98C2×C4⋊AGL(1,ℤ/9)—31no—
99C2×C4×AGL(1,ℤ/9)—31no—
100C4×#1094C2×D312yescomplemented
101C4×C9⋊A4—21no—
102C4×C9⋊A4—22no—
103C4×C9×A4—21no—
104C4×C9×A4C22×C311yescharacteristic, complemented
105C9⋊SL(2,ℤ/4)C22×C311yescharacteristic, complemented
106#1094⋊C4—32no—
107#3676⋊C3—32no—
108#3676⋊C3—32no—
109#3676⋊C3—31no—
110(C2×AGL(1,ℤ/9))⋊C4—31no—
111(C2×AGL(1,ℤ/9))⋊C4—32no—
112C4⋊(3−1+2⋊C4)—31no—
113(3−1+2⋊C4)⋊C4—31no—
114C4×3−1+2⋊C4—31no—
115C22×C3×3−1+2—42no—
116C2×C3⋊AGL(1,ℤ/9)—41no—
117C2×C3⋊AGL(1,ℤ/9)—42no—
118C2×C3⋊AGL(1,ℤ/9)—84no—
119A4×3−1+2C2×D411yescharacteristic, complemented
120C3×C4×3−1+2—41no—
121C3⋊(3−1+2⋊C4)—41no—
122C22×C3⋊S4—32no—
123C22×C3×S4—96no—
124C22×C32×D4C3⋊D311yescharacteristic
125C22×C3×#67—92no—
126C2×C3×D3×D4—91no—
127C3×D4×A4—21no—
128C3×D4×A4—33no—
129C3×D4×A4C3×D311yescharacteristic
130#64269—32no—
131C4⋊(C3⋊S4)—31no—
132C4×C3⋊S4—31no—
133C3×GL(2,ℤ/4)—96no—
134C3×C4⋊S4—93no—
135C3×C4×S4—93no—
136C22×(C22⋊C9)⋊C2—34no—
137C3×#953—92no—
138C3×#940—91no—
139C3×#939—92no—
140C3×#938—91no—
141C3×#937—92no—
142C3×D4×Dic3—91no—
143C3×#930—91no—
144C3×C4×#67—91no—
145C22×D4×C9—21no—
146C22×D4×C9C3×D311yescharacteristic, complemented
147C22×#611—32no—
148C2×D4×D9—31no—
149D4×C22⋊C9—22no—
150D4×C22⋊C9C3×D312yescomplemented
151#63694—34no—
152C4⋊((C22⋊C9)⋊C2)—32no—
153C4×(C22⋊C9)⋊C2—32no—
154#63515—32no—
155#63502—31no—
156#63501—32no—
157#63500—31no—
158#63499—32no—
159D4×Dic9—31no—
160#63492—31no—
161C4×#611—31no—
162C22×C3×C3⋊D3—122no—
163C2×C32×A4—22no—
164C2×C32×A4C22×D311yescharacteristic
165C3×C3⋊S4—32no—
166C3×C3⋊S4—62no—
167C33×D4—41no—
168C3×#638—122no—
169C3×C4⋊(C3⋊D3)—121no—
170C3×C4×C3⋊D3—121no—
171C23×3−1+2—22no—
172C23×3−1+2—32no—
173C23×3−1+2—32no—
174C23×3−1+2—62no—
175C23×3−1+2C22×D311yescharacteristic
176C22×C3⋊D9—42no—
177C22×AGL(1,ℤ/9)—31no—
178C22×AGL(1,ℤ/9)—32no—
179C22×AGL(1,ℤ/9)—64no—
180C22×AGL(1,ℤ/9)—62no—
181C22×AGL(1,ℤ/9)—62no—
182C22×AGL(1,ℤ/9)—122no—
183C22×AGL(1,ℤ/9)—124no—
184C2×#1094—24no—
185C2×#1094C22×D312yes—
186C2×C9⋊A4—21no—
187C2×C9⋊A4—22no—
188C2×C9⋊A4—44no—
189C2×C9⋊A4—42no—
190C2×C9×A4—21no—
191C2×C9×A4—22no—
192C2×C9×A4—42no—
193C2×C9×A4C23×C311yescharacteristic
194C9⋊S4—22no—
195C9⋊S4C3×D412yescomplemented
196((C22⋊C9)⋊C2)⋊C3—34no—
197((C22⋊C9)⋊C2)⋊C3—64no—
198D4×3−1+2—32no—
199D4×3−1+2—31no—
200D4×3−1+2—42no—
201D4×3−1+2—61no—
202D4×3−1+2—82no—
203D4×3−1+2—81no—
204D4×3−1+2S411yescharacteristic, complemented
205C3×D4×C9—41no—
206C3×D4×C9—81no—
207C2×C4×3−1+2—31no—
208C2×C4×3−1+2—31no—
209#6233—42no—
210C4⋊(C3⋊D9)—41no—
211C4×C3⋊D9—41no—
212#611⋊C3—32no—
213#611⋊C3—32no—
214#611⋊C3—64no—
215#611⋊C3—64no—
216#611⋊C3—62no—
217#611⋊C3—62no—
218#611⋊C3—62no—
219#611⋊C3—62no—
220#611⋊C3—122no—
221#611⋊C3—124no—
222C2×3−1+2⋊C4—31no—
223C2×3−1+2⋊C4—31no—
224C2×3−1+2⋊C4—32no—
225C2×3−1+2⋊C4—31no—
226C2×3−1+2⋊C4—64no—
227C4⋊AGL(1,ℤ/9)—61no—
228C4⋊AGL(1,ℤ/9)—61no—
229C4⋊AGL(1,ℤ/9)—122no—
230C4×AGL(1,ℤ/9)—61no—
231C4×AGL(1,ℤ/9)—61no—
232C4×AGL(1,ℤ/9)—122no—
233D4×S4—93no—
234C3×D42—271no—
235D4×#67—91no—
236C2×C3×3−1+2—41no—
237C2×C3×3−1+2—82no—
238C3⋊AGL(1,ℤ/9)—42no—
239C3⋊AGL(1,ℤ/9)—82no—
240C24×C32C2×C3⋊D312yes—
241C23×C3×D3—92no—
242C22×C3×A4—22no—
243C22×C3×A4—36no—
244C22×C3×A4C2×C3×D312yes—
245C2×C3⋊S4—31no—
246C2×C3⋊S4—32no—
247C2×C3⋊S4—64no—
248C2×C3×S4—93no—
249C2×C3×S4—96no—
250C2×C3×S4—1812no—
251C2×C32×D4—31no—
252C2×C32×D4—32no—
253C2×C32×D4—31no—
254C22×C32×C4C2×C3⋊D311yescharacteristic
255D4×C3⋊D3—121no—
256C2×C3×#67—91no—
257C2×C3×#67—92no—
258C2×C3×#67—92no—
259C2×C3×#67—92no—
260C2×C3×#67—92no—
261C2×C3×#67—92no—
262C2×C3×#67—184no—
263C2×C3×#67—184no—
264C22×C3×Dic3—92no—
265C3×D3×D4—182no—
266C3×D3×D4—181no—
267C3×D3×D4—181no—
268C3×D3×D4—363no—
269C2×C3×D12—91no—
270C2×C3×C4×D3—91no—
271C3×C4×A4—21no—
272C3×C4×A4—33no—
273C3×C4×A4C2×C3×D311yescharacteristic
274C3⋊SL(2,ℤ/4)—31no—
275C3×SL(2,ℤ/4)—93no—
276C24×C9—22no—
277C24×C9C2×C3×D312yescomplemented
278C23×D9—32no—
279C22×C22⋊C9—24no—
280C22×C22⋊C9C2×C3×D314yescomplemented
281C2×(C22⋊C9)⋊C2—32no—
282C2×(C22⋊C9)⋊C2—34no—
283C2×(C22⋊C9)⋊C2—68no—
284C3×#217—92no—
285C3×#217—92no—
286C3×#217—91no—
287C3×(C2×D3)⋊C4—91no—
288C3×(C2×D3)⋊C4—92no—
289C3×C4⋊Dic3—91no—
290C3×Dic3⋊C4—91no—
291C3×C4×Dic3—91no—
292C2×D4×C9—31no—
293C2×D4×C9—32no—
294C2×D4×C9—31no—
295C2×D4×C9—61no—
296C2×D4×C9—61no—
297C2×D4×C9—62no—
298C22×C4×C9—21no—
299C22×C4×C9C2×C3×D311yescharacteristic, complemented
300C2×#611—31no—
301C2×#611—32no—
302C2×#611—32no—
303C2×#611—32no—
304C2×#611—32no—
305C2×#611—32no—
306C2×#611—64no—
307C2×#611—64no—
308C22×Dic9—32no—
309D4×D9—62no—
310D4×D9—61no—
311D4×D9—61no—
312D4×D9—122no—
313C2×D36—31no—
314C2×C4×D9—31no—
315C4×C22⋊C9—22no—
316C4×C22⋊C9C2×C3×D312yescomplemented
317(C22⋊C9)⋊C4—32no—
318#3676—32no—
319#3676—32no—
320#3676—31no—
321(C2×D9)⋊C4—31no—
322(C2×D9)⋊C4—32no—
323C4⋊Dic9—31no—
324Dic9⋊C4—31no—
325C4×Dic9—31no—
326C22×C33—42no—
327C2×C3×C3⋊D3—121no—
328C2×C3×C3⋊D3—122no—
329C2×C3×C3⋊D3—244no—
330C32×A4D3×D411yescharacteristic
331C33×C4—41no—
332C3×C3⋊Dic3—121no—
333C22×3−1+2—31no—
334C22×3−1+2—31no—
335C22×3−1+2—32no—
336C22×3−1+2—44no—
337C22×3−1+2—62no—
338C22×3−1+2—62no—
339C22×3−1+2—62no—
340C22×3−1+2—62no—
341C22×3−1+2—84no—
342C22×3−1+2—82no—
343C22×3−1+2D3×D411yescharacteristic, complemented
344C22×3−1+2C2×S412yescomplemented
345C22×C3×C9—42no—
346C22×C3×C9—82no—
347C2×C3⋊D9—41no—
348C2×C3⋊D9—42no—
349C2×C3⋊D9—84no—
350C2×AGL(1,ℤ/9)—32no—
351C2×AGL(1,ℤ/9)—61no—
352C2×AGL(1,ℤ/9)—61no—
353C2×AGL(1,ℤ/9)—62no—
354C2×AGL(1,ℤ/9)—62no—
355C2×AGL(1,ℤ/9)—62no—
356C2×AGL(1,ℤ/9)—124no—
357C2×AGL(1,ℤ/9)—124no—
358C2×AGL(1,ℤ/9)—122no—
359C2×AGL(1,ℤ/9)—124no—
360C2×AGL(1,ℤ/9)—248no—
361#1094D3×D412yescomplemented
362C9⋊A4—21no—
363C9⋊A4—22no—
364C9×A4—21no—
365C9×A4C2×C3×D411yescharacteristic, complemented
366C4×3−1+2—31no—
367C4×3−1+2—42no—
368C4×3−1+2—82no—
369C4×3−1+2—81no—
370C4×3−1+2C2×S411yescharacteristic, complemented
371C3×C4×C9—41no—
372C3×C4×C9—81no—
373C3⋊Dic9—41no—
3743−1+2⋊C4—32no—
3753−1+2⋊C4—62no—
3763−1+2⋊C4—61no—
3773−1+2⋊C4—61no—
3783−1+2⋊C4—122no—
379C22×S4—96no—
380C22×C3×D4—31no—
381C22×C3×D4—271no—
382C22×C3×D4—272no—
383C22×C3×D4C3×C3⋊D311yescharacteristic
384C22×#67—92no—
385C2×D3×D4—91no—
386D4×A4—61no—
387D4×A4AGL(1,ℤ/9)13yescomplemented
388GL(2,ℤ/4)—96no—
389C4⋊S4—93no—
390C4×S4—93no—
391C3×#127—271no—
392C3×#121—271no—
393C3×#121—271no—
394C3×#121—272no—
395C3×#120—272no—
396C3×#120—272no—
397C3×C4×D4—271no—
398C3×C4×D4—271no—
399#953—92no—
400#940—91no—
401#939—92no—
402#938—91no—
403#937—92no—
404D4×Dic3—91no—
405#930—91no—
406C4×#67—91no—
407C3×3−1+2—41noSylow
408C23×C32—22no—
409C23×C32—32no—
410C23×C32—32no—
411C23×C32—62no—
412C23×C32C22×C3⋊D311yescharacteristic
413C22×C3⋊D3—122no—
414C22×C3×D3—91no—
415C22×C3×D3—92no—
416C22×C3×D3—184no—
417C22×C3×D3—182no—
418C22×C3×D3—182no—
419C22×C3×D3—366no—
420C22×C3×D3—362no—
421C2×C3×A4—22no—
422C2×C3×A4—21no—
423C2×C3×A4—33no—
424C2×C3×A4—42no—
425C2×C3×A4—66no—
426C2×C3×A4C22×C3×D311yescharacteristic
427C3⋊S4—32no—
428C3⋊S4—62no—
429C3×S4—96no—
430C3×S4—186no—
431C32×D4—32no—
432C32×D4—31no—
433C32×D4—41no—
434C32×D4—61no—
435C32×D4—81no—
436C32×D4—123no—
437C32×D4C3⋊S411yescharacteristic
438C2×C32×C4—31no—
439C2×C32×C4—31no—
440#638—122no—
441C4⋊(C3⋊D3)—121no—
442C4×C3⋊D3—121no—
443C3×#67—92no—
444C3×#67—92no—
445C3×#67—184no—
446C3×#67—184no—
447C3×#67—182no—
448C3×#67—182no—
449C3×#67—182no—
450C3×#67—182no—
451C3×#67—366no—
452C3×#67—362no—
453C2×C3×Dic3—91no—
454C2×C3×Dic3—91no—
455C2×C3×Dic3—91no—
456C2×C3×Dic3—92no—
457C2×C3×Dic3—184no—
458C3×D12—181no—
459C3×D12—181no—
460C3×D12—363no—
461C3×C4×D3—181no—
462C3×C4×D3—181no—
463C3×C4×D3—363no—
464C23×C9—22no—
465C23×C9—21no—
466C23×C9—32no—
467C23×C9—32no—
468C23×C9—42no—
469C23×C9—62no—
470C23×C9—62no—
471C23×C9—62no—
472C23×C9—122no—
473C23×C9C22×C3×D311yescharacteristic
474C22×D9—31no—
475C22×D9—32no—
476C22×D9—64no—
477C22×D9—62no—
478C22×D9—62no—
479C22×D9—124no—
480C22×D9—122no—
481C2×C22⋊C9—24no—
482C2×C22⋊C9—22no—
483C2×C22⋊C9—44no—
484C2×C22⋊C9C22×C3×D312yes—
485(C22⋊C9)⋊C2—34no—
486(C22⋊C9)⋊C2—64no—
487D4×C9—21no—
488D4×C9—32no—
489D4×C9—31no—
490D4×C9—42no—
491D4×C9—61no—
492D4×C9—62no—
493D4×C9—61no—
494D4×C9—62no—
495D4×C9—82no—
496D4×C9C3×S411yescharacteristic, complemented
497C2×C4×C9—31no—
498C2×C4×C9—31no—
499C2×C4×C9—61no—
500C2×C4×C9—61no—
501#611—32no—
502#611—32no—
503#611—64no—
504#611—64no—
505#611—62no—
506#611—62no—
507#611—62no—
508#611—62no—
509#611—124no—
510#611—122no—
511C2×Dic9—31no—
512C2×Dic9—31no—
513C2×Dic9—31no—
514C2×Dic9—32no—
515C2×Dic9—64no—
516D36—61no—
517D36—61no—
518D36—122no—
519C4×D9—61no—
520C4×D9—61no—
521C4×D9—122no—
522D42—271noSylow
523C2×C33—41no—
524C2×C33—82no—
525C3×C3⋊D3—122no—
526C3×C3⋊D3—242no—
527C2×3−1+2—22no—
528C2×3−1+2—31no—
529C2×3−1+2—31no—
530C2×3−1+2—42no—
531C2×3−1+2—62no—
532C2×3−1+2—82no—
533C2×3−1+2—81no—
534C2×3−1+2—84no—
535C2×3−1+2—162no—
536C2×3−1+2—164no—
537C2×3−1+2C22×S411yescharacteristic
538C2×C3×C9—41no—
539C2×C3×C9—81no—
540C2×C3×C9—82no—
541C2×C3×C9—162no—
542C3⋊D9—42no—
543C3⋊D9—82no—
544AGL(1,ℤ/9)—62no—
545AGL(1,ℤ/9)—124no—
546AGL(1,ℤ/9)—122no—
547AGL(1,ℤ/9)—244no—
548C24×C3—32no—
549C24×C3—272no—
550C24×C3C2×C3×C3⋊D312yes—
551C23×D3—92no—
552C22×A4—62no—
553C22×A4C2×AGL(1,ℤ/9)16yescomplemented
554C2×S4—93no—
555C2×S4—96no—
556C2×S4—1812no—
557C2×C3×D4—31no—
558C2×C3×D4—32no—
559C2×C3×D4—31no—
560C2×C3×D4—91no—
561C2×C3×D4—92no—
562C2×C3×D4—91no—
563C2×C3×D4—271no—
564C2×C3×D4—271no—
565C2×C3×D4—272no—
566C2×C3×D4—272no—
567C2×C3×D4—272no—
568C2×C3×D4—272no—
569C2×C3×D4—272no—
570C2×C3×D4—541no—
571C2×C3×D4—541no—
572C2×C3×D4—542no—
573C2×C3×D4—544no—
574C2×C3×D4—544no—
575C22×C3×C4—31no—
576C22×C3×C4—271no—
577C22×C3×C4—272no—
578C22×C3×C4C2×C3×C3⋊D311yescharacteristic
579C2×#67—91no—
580C2×#67—92no—
581C2×#67—92no—
582C2×#67—92no—
583C2×#67—92no—
584C2×#67—92no—
585C2×#67—184no—
586C2×#67—184no—
587C22×Dic3—92no—
588D3×D4—182no—
589D3×D4—181no—
590D3×D4—181no—
591D3×D4—363no—
592C2×D12—91no—
593C2×C4×D3—91no—
594C4×A4—61no—
595C4×A4C2×AGL(1,ℤ/9)13yescomplemented
596SL(2,ℤ/4)—93no—
597C3×C4⋊C4—271no—
598C3×C4⋊C4—271no—
599C3×C22⋊C4—271no—
600C3×C22⋊C4—272no—
601C3×C22⋊C4—271no—
602C3×C22⋊C4—272no—
603C3×C22⋊C4—272no—
604C3×C42—271no—
605#217—92no—
606#217—92no—
607#217—91no—
608(C2×D3)⋊C4—91no—
609(C2×D3)⋊C4—92no—
610C4⋊Dic3—91no—
611Dic3⋊C4—91no—
612C4×Dic3—91no—
613C22×C32—31no—
614C22×C32—31no—
615C22×C32—32no—
616C22×C32—42no—
617C22×C32—62no—
618C22×C32—62no—
619C22×C32—62no—
620C22×C32—62no—
621C22×C32—82no—
622C22×C32—126no—
623C22×C32D4×C3⋊D311yescharacteristic
624C22×C32C2×C3⋊S412yes—
625C2×C3⋊D3—121no—
626C2×C3⋊D3—122no—
627C2×C3⋊D3—244no—
628C2×C3×D3—92no—
629C2×C3×D3—181no—
630C2×C3×D3—181no—
631C2×C3×D3—182no—
632C2×C3×D3—182no—
633C2×C3×D3—182no—
634C2×C3×D3—363no—
635C2×C3×D3—366no—
636C2×C3×D3—364no—
637C2×C3×D3—364no—
638C2×C3×D3—7212no—
639C3×A4—21no—
640C3×A4—33no—
641C3×A4C3×D3×D411yescharacteristic
642C32×C4—31no—
643C32×C4—41no—
644C32×C4—81no—
645C32×C4—123no—
646C32×C4C2×C3⋊S411yescharacteristic
647C3⋊Dic3—121no—
648C3×Dic3—92no—
649C3×Dic3—182no—
650C3×Dic3—181no—
651C3×Dic3—181no—
652C3×Dic3—363no—
653C22×C9—22no—
654C22×C9—21no—
655C22×C9—31no—
656C22×C9—31no—
657C22×C9—32no—
658C22×C9—44no—
659C22×C9—61no—
660C22×C9—62no—
661C22×C9—61no—
662C22×C9—62no—
663C22×C9—62no—
664C22×C9—62no—
665C22×C9—62no—
666C22×C9—84no—
667C22×C9—122no—
668C22×C9—122no—
669C22×C9—122no—
670C22×C9—122no—
671C22×C9C3×D3×D411yescharacteristic, complemented
672C22×C9C2×C3×S412yescomplemented
673C2×D9—32no—
674C2×D9—61no—
675C2×D9—61no—
676C2×D9—62no—
677C2×D9—62no—
678C2×D9—62no—
679C2×D9—122no—
680C2×D9—124no—
681C2×D9—124no—
682C2×D9—124no—
683C2×D9—248no—
684C22⋊C9—22no—
685C22⋊C9C3×D3×D412yescomplemented
686C4×C9—21no—
687C4×C9—31no—
688C4×C9—42no—
689C4×C9—61no—
690C4×C9—82no—
691C4×C9C2×C3×S411yescharacteristic, complemented
692Dic9—32no—
693Dic9—62no—
694Dic9—61no—
695Dic9—61no—
696Dic9—122no—
697C22×D4—271no—
698C22×D4—272no—
699C22×D4C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
700#127—271no—
701#121—271no—
702#121—272no—
703#121—271no—
704#120—272no—
705#120—272no—
706C4×D4—271no—
707C4×D4—271no—
708C33—41no—
7093−1+2—42no—
7103−1+2—82no—
7113−1+2—81no—
7123−1+2D4×S411yescharacteristic, complemented
713C3×C9—41no—
714C3×C9—81no—
715C23×C3—22no—
716C23×C3—32no—
717C23×C3—32no—
718C23×C3—31no—
719C23×C3—62no—
720C23×C3—62no—
721C23×C3—92no—
722C23×C3—92no—
723C23×C3—182no—
724C23×C3—271no—
725C23×C3—272no—
726C23×C3—542no—
727C23×C3—542no—
728C23×C3—544no—
729C23×C3—1082no—
730C23×C3C22×C3×C3⋊D311yescharacteristic
731C22×D3—91no—
732C22×D3—92no—
733C22×D3—184no—
734C22×D3—182no—
735C22×D3—182no—
736C22×D3—366no—
737C22×D3—362no—
738C2×A4—26no—
739C2×A4—61no—
740C2×A4—122no—
741C2×A4C22×AGL(1,ℤ/9)13yes—
742S4—96no—
743S4—186no—
744C3×D4—32no—
745C3×D4—31no—
746C3×D4—31no—
747C3×D4—43no—
748C3×D4—61no—
749C3×D4—91no—
750C3×D4—92no—
751C3×D4—181no—
752C3×D4—241no—
753C3×D4—272no—
754C3×D4—272no—
755C3×D4—541no—
756C3×D4—541no—
757C3×D4—544no—
758C3×D4—542no—
759C3×D4—542no—
760C3×D4—542no—
761C3×D4—542no—
762C3×D4—544no—
763C3×D4—1082no—
764C3×D4C3×C3⋊S411yescharacteristic
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—91no—
768C2×C3×C4—91no—
769C2×C3×C4—271no—
770C2×C3×C4—271no—
771C2×C3×C4—271no—
772C2×C3×C4—272no—
773C2×C3×C4—541no—
774C2×C3×C4—541no—
775C2×C3×C4—544no—
776#67—92no—
777#67—92no—
778#67—184no—
779#67—184no—
780#67—182no—
781#67—182no—
782#67—182no—
783#67—182no—
784#67—366no—
785#67—362no—
786C2×Dic3—91no—
787C2×Dic3—91no—
788C2×Dic3—91no—
789C2×Dic3—92no—
790C2×Dic3—184no—
791D12—181no—
792D12—181no—
793D12—363no—
794C4×D3—181no—
795C4×D3—181no—
796C4×D3—363no—
797C2×C32—22no—
798C2×C32—31no—
799C2×C32—31no—
800C2×C32—41no—
801C2×C32—62no—
802C2×C32—82no—
803C2×C32—81no—
804C2×C32—123no—
805C2×C32—162no—
806C2×C32—246no—
807C2×C32C22×C3⋊S411yescharacteristic
808C3⋊D3—122no—
809C3⋊D3—242no—
810C3×D3—182no—
811C3×D3—366no—
812C3×D3—362no—
813C3×D3—726no—
814C2×C9—22no—
815C2×C9—21no—
816C2×C9—31no—
817C2×C9—31no—
818C2×C9—42no—
819C2×C9—42no—
820C2×C9—61no—
821C2×C9—61no—
822C2×C9—62no—
823C2×C9—84no—
824C2×C9—82no—
825C2×C9—122no—
826C2×C9—164no—
827C2×C9C22×C3×S411yescharacteristic
828D9—62no—
829D9—124no—
830D9—122no—
831D9—244no—
832C24—272no—
833C24C2×C3⋊AGL(1,ℤ/9)12yescomplemented
834C2×D4—31no—
835C2×D4—32no—
836C2×D4—31no—
837C2×D4—271no—
838C2×D4—271no—
839C2×D4—272no—
840C2×D4—272no—
841C2×D4—272no—
842C2×D4—272no—
843C2×D4—272no—
844C2×D4—542no—
845C2×D4—541no—
846C2×D4—544no—
847C2×D4—544no—
848C2×D4—541no—
849C22×C4—271no—
850C22×C4—272no—
851C22×C4C2×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
852C4⋊C4—271no—
853C4⋊C4—271no—
854C22⋊C4—271no—
855C22⋊C4—272no—
856C22⋊C4—272no—
857C22⋊C4—272no—
858C22⋊C4—271no—
859C42—271no—
860C22×C3—31no—
861C22×C3—31no—
862C22×C3—32no—
863C22×C3—31no—
864C22×C3—32no—
865C22×C3—46no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3—62no—
869C22×C3—62no—
870C22×C3—91no—
871C22×C3—92no—
872C22×C3—91no—
873C22×C3—182no—
874C22×C3—182no—
875C22×C3—182no—
876C22×C3—182no—
877C22×C3—242no—
878C22×C3—272no—
879C22×C3—541no—
880C22×C3—542no—
881C22×C3—541no—
882C22×C3—542no—
883C22×C3—542no—
884C22×C3—1084no—
885C22×C3—1084no—
886C22×C3C3×D4×C3⋊D311yescharacteristic
887C22×C3C2×C3×C3⋊S412yes—
888C2×D3—92no—
889C2×D3—181no—
890C2×D3—181no—
891C2×D3—182no—
892C2×D3—182no—
893C2×D3—182no—
894C2×D3—363no—
895C2×D3—366no—
896C2×D3—364no—
897C2×D3—364no—
898C2×D3—7212no—
899A4—61no—
900A4D4×AGL(1,ℤ/9)13yescomplemented
901C3×C4—31no—
902C3×C4—31no—
903C3×C4—43no—
904C3×C4—91no—
905C3×C4—241no—
906C3×C4—272no—
907C3×C4—541no—
908C3×C4—542no—
909C3×C4—541no—
910C3×C4C2×C3×C3⋊S411yescharacteristic
911Dic3—92no—
912Dic3—182no—
913Dic3—181no—
914Dic3—181no—
915Dic3—363no—
916C32—41no—
917C32—81no—
918C32—123no—
919C32D4×C3⋊S411yescharacteristic
920C9—21no—
921C9—42no—
922C9—82no—
923C9C3×D4×S411yescharacteristic, complemented
924C23—22no—
925C23—32no—
926C23—32no—
927C23—62no—
928C23—271no—
929C23—272no—
930C23—542no—
931C23—544no—
932C23—542no—
933C23—1082no—
934C23C22×C3⋊AGL(1,ℤ/9)11yescharacteristic
935D4—32no—
936D4—31no—
937D4—61no—
938D4—272no—
939D4—272no—
940D4—541no—
941D4—544no—
942D4—542no—
943D4—542no—
944D4—544no—
945D4—542no—
946D4—542no—
947D4—541no—
948D4—1082no—
949D4A4⋊AGL(1,ℤ/9)11yescharacteristic, direct product factor
950C2×C4—31no—
951C2×C4—31no—
952C2×C4—271no—
953C2×C4—271no—
954C2×C4—272no—
955C2×C4—271no—
956C2×C4—541no—
957C2×C4—544no—
958C2×C4—541no—
959C2×C3—22no—
960C2×C3—31no—
961C2×C3—31no—
962C2×C3—31no—
963C2×C3—43no—
964C2×C3—62no—
965C2×C3—62no—
966C2×C3—86no—
967C2×C3—91no—
968C2×C3—91no—
969C2×C3—182no—
970C2×C3—241no—
971C2×C3—482no—
972C2×C3—542no—
973C2×C3—1082no—
974C2×C3C22×C3×C3⋊S411yescharacteristic
975D3—182no—
976D3—366no—
977D3—362no—
978D3—726no—
979C22—31no—
980C22—31no—
981C22—32no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—272no—
987C22—541no—
988C22—542no—
989C22—542no—
990C22—541no—
991C22—542no—
992C22—1084no—
993C22—1084no—
994C22D4×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
995C22C2×A4⋊AGL(1,ℤ/9)12yescomplemented
996C4—31no—
997C4—272no—
998C4—542no—
999C4—541no—
1000C4—541no—
1001C4C2×A4⋊AGL(1,ℤ/9)11yescharacteristic, complemented
1002C3—31no—
1003C3—43no—
1004C3—241no—
1005C3C3×D4×C3⋊S411yescharacteristic
1006C2—22no—
1007C2—31no—
1008C2—31no—
1009C2—62no—
1010C2—542no—
1011C2—1082no—
1012C2C22×A4⋊AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
centerC2C22×A4⋊AGL(1,ℤ/9)
commutator, cosocleC2×C9×A4C23×C3
FrattiniC2×C3C22×C3×C3⋊S4
FittingC22×D4×3−1+2D3
socleC23×C3C22×C3×C3⋊D3
hypercenterD4A4⋊AGL(1,ℤ/9)
hypocenterC9×A4C2×C3×D4
LCSG ▷ C2×C9×A4 ▷ C9×A4
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. #72268947C2semidirect
2. #72268942C2semidirect
3. D4×A4×3−1+2C2semidirect
4. C4×A4⋊AGL(1,ℤ/9)C2semidirect
5. C22×A4⋊AGL(1,ℤ/9)C2semidirect
7. D4×C9⋊S4C3semidirect
10. C22×A4×3−1+2C22semidirect
13. C2×A4⋊AGL(1,ℤ/9)C22semidirect
15. C4×A4×3−1+2C22semidirect
16. A4⋊(3−1+2⋊C4)C22semidirect
22. C22×C9⋊S4C2×C3semidirect
24. C22×D4×3−1+2D3semidirect
27. D4×#1094D3semidirect
31. D4×C9×A4C2×C3semidirect
32. #11722376C2×C3semidirect
33. C4⋊(C9⋊S4)C2×C3semidirect
34. C4×C9⋊S4C2×C3semidirect
50. A4⋊AGL(1,ℤ/9)D4direct (N × H)
67. C24×3−1+2C2×D3semidirect
69. C22×#1094C2×D3semidirect
73. C22×C9×A4C22×C3semidirect
76. C2×C9⋊S4C22×C3semidirect
83. C22×C4×3−1+2C2×D3semidirect
100. C4×#1094C2×D3semidirect
104. C4×C9×A4C22×C3semidirect
105. C9⋊SL(2,ℤ/4)C22×C3semidirect
119. A4×3−1+2C2×D4semidirect
146. C22×D4×C9C3×D3semidirect
150. D4×C22⋊C9C3×D3semidirect
195. C9⋊S4C3×D4semidirect
204. D4×3−1+2S4semidirect
277. C24×C9C2×C3×D3semidirect
280. C22×C22⋊C9C2×C3×D3semidirect
299. C22×C4×C9C2×C3×D3semidirect
316. C4×C22⋊C9C2×C3×D3semidirect
343. C22×3−1+2D3×D4semidirect
344. C22×3−1+2C2×S4semidirect
361. #1094D3×D4semidirect
365. C9×A4C2×C3×D4semidirect
370. C4×3−1+2C2×S4semidirect
387. D4×A4AGL(1,ℤ/9)semidirect
496. D4×C9C3×S4semidirect
553. C22×A4C2×AGL(1,ℤ/9)semidirect
595. C4×A4C2×AGL(1,ℤ/9)semidirect
671. C22×C9C3×D3×D4semidirect
672. C22×C9C2×C3×S4semidirect
685. C22⋊C9C3×D3×D4semidirect
691. C4×C9C2×C3×S4semidirect
699. C22×D4C3⋊AGL(1,ℤ/9)semidirect
712. 3−1+2D4×S4semidirect
833. C24C2×C3⋊AGL(1,ℤ/9)semidirect
851. C22×C4C2×C3⋊AGL(1,ℤ/9)semidirect
900. A4D4×AGL(1,ℤ/9)semidirect
923. C9C3×D4×S4semidirect
949. D4A4⋊AGL(1,ℤ/9)direct (N × H)
994. C22D4×C3⋊AGL(1,ℤ/9)semidirect
995. C22C2×A4⋊AGL(1,ℤ/9)semidirect
1001. C4C2×A4⋊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
#722689472
#722689422
D4×A4×3−1+22
C4×A4⋊AGL(1,ℤ/9)2
C22×A4⋊AGL(1,ℤ/9)2
C3×D4×C3⋊S43
D4×C9⋊S43
D4×((C22⋊C9)⋊C2)⋊C33
D4×#611⋊C33
D4×C3⋊AGL(1,ℤ/9)4