Finite Group Databasebeta

← C9×#92303 #72243881

Subgroups — C9×#92303 #72243881

Order 4374.

1033 conjugacy classes of subgroups.

The subgroup lattice has 989 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×C9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented, Sylow
2C3×#92303C311yesmaximal, characteristic
3C9×C3⋊AGL(1,ℤ/9)—31nomaximal
4C9×C3⋊((C3⋊D3)⋊C3)—31nomaximal
5C9×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
6#13090624C311yesmaximal, characteristic, complemented
7#13090624C311yesmaximal, characteristic, complemented
8C9×#4169—31nomaximal
9C9×#4169—31nomaximal
10C3×C9⋊H(3,𝔽3)C2×C311yescharacteristic
11C3×C9×3−1+2—21no—
12C3×C9×3−1+2D311yescharacteristic, complemented
13C3×C9×H(3,𝔽3)D311yescharacteristic
14C32×C92C2×C311yescharacteristic, complemented
15#10624560—21no—
16#10624560—21no—
17#10624560—21no—
18#10624557—21no—
19#10624557—21no—
20#10624557—21no—
21#10624557—21no—
22#10624557—21no—
23#10624557—21no—
24#10624556—21no—
25#10624556—21no—
26#10624555—21no—
27#10624548C2×C311yescharacteristic, complemented
28#10624548C2×C311yescharacteristic, complemented
29C9×C32⋊C9—21no—
30C9×C32⋊C9—21no—
31C9×C32⋊C9—21no—
32C9×C32⋊C9D311yescharacteristic, complemented
33C9×C32⋊C9D311yescharacteristic, complemented
34C9×C3⋊(C3⋊D3)—31no—
35C3×C3⋊(C3⋊D9)C3211yescharacteristic
36C3×C3⋊AGL(1,ℤ/9)—31no—
37C3×C3⋊((C3⋊D3)⋊C3)—31no—
38C3×C9×C3⋊D3—91no—
39#92303C911yescharacteristic, direct product factor
40#92303C911yescharacteristic, direct product factor
41#92303C911yescharacteristic, direct product factor
42C3⋊(D9⋊C9)—31no—
43C3⋊(D9⋊C9)—31no—
44C3⋊((C3⋊D3)⋊C9)—31no—
45C3⋊((C3⋊D3)⋊C9)—31no—
46C9×C3⋊D9—31no—
47C9×C3⋊D9—31no—
48C9×C3⋊D9—31no—
49C9×C3⋊D9—91no—
50C9×C3⋊D9—91no—
51C9×C3⋊D9—91no—
52C9×AGL(1,ℤ/9)—91no—
53C9×AGL(1,ℤ/9)—91no—
54C9×AGL(1,ℤ/9)—91no—
55C9×(C3⋊D3)⋊C3—91no—
56C9×(C3⋊D3)⋊C3—91no—
57C9×(C3⋊D3)⋊C3—91no—
58C3×#4169—31no—
59C3×#4169—31no—
60#92158—31no—
61#92158—31no—
62#92158—31no—
63#92158—31no—
64C32×3−1+2—21no—
65C32×3−1+2C3×D311yescharacteristic
66C32×H(3,𝔽3)C3×D311yescharacteristic
67C33×C9—21no—
68C33×C9—21no—
69C33×C9C3×D311yescharacteristic
70C33×C9C3⋊D311yescharacteristic
71C33×C9C2×C3211yescharacteristic
72C9⋊H(3,𝔽3)—21no—
73C9⋊H(3,𝔽3)—21no—
74C9⋊H(3,𝔽3)—21no—
75C9⋊H(3,𝔽3)—21no—
76C9⋊H(3,𝔽3)—21no—
77C9⋊H(3,𝔽3)—21no—
78C9⋊H(3,𝔽3)—21no—
79C9⋊H(3,𝔽3)—21no—
80C9⋊H(3,𝔽3)—21no—
81C9⋊H(3,𝔽3)—21no—
82C9⋊H(3,𝔽3)—21no—
83C9⋊H(3,𝔽3)—21no—
84C9⋊H(3,𝔽3)C2×C911yescharacteristic, complemented
85C9⋊H(3,𝔽3)C2×C911yescharacteristic, complemented
86C9⋊H(3,𝔽3)C2×C911yescharacteristic, complemented
87C9×3−1+2—31no—
88C9×3−1+2—61no—
89C9×3−1+2—61no—
90C9×3−1+2—61no—
91C9×3−1+2—61no—
92C9×3−1+2—61no—
93C9×3−1+2—61no—
94C9×3−1+2—61no—
95C9×3−1+2—61no—
96C9×3−1+2—61no—
97C9×3−1+2—61no—
98C9×3−1+2—61no—
99C9×3−1+2—61no—
100C9×3−1+2—61no—
101C9×3−1+2—61no—
102C9×H(3,𝔽3)—31no—
103C9×H(3,𝔽3)—61no—
104C9×H(3,𝔽3)—61no—
105C9×H(3,𝔽3)—61no—
106C9×H(3,𝔽3)—61no—
107C9×H(3,𝔽3)—61no—
108C3×C9⋊C9—21no—
109C3×C9⋊C9—21no—
110C3×C9⋊C9—21no—
111C3×C9⋊C9—21no—
112C3×C9⋊C9—21no—
113C3×C9⋊C9—21no—
114C3×C9⋊C9—21no—
115C3×C9⋊C9—21no—
116C3×C9⋊C9C3×D311yescharacteristic
117C3×C9⋊C9C3×D311yescharacteristic
118C3×C32⋊C9—21no—
119C3×C32⋊C9—21no—
120C3×C32⋊C9—21no—
121C3×C32⋊C9—21no—
122C3×C32⋊C9—21no—
123C3×C32⋊C9—21no—
124C3×C32⋊C9—21no—
125C3×C32⋊C9—21no—
126C3×C32⋊C9—21no—
127C3×C32⋊C9—21no—
128C3×C32⋊C9—21no—
129C3×C32⋊C9—21no—
130C3×C32⋊C9—21no—
131C3×C32⋊C9—21no—
132C3×C32⋊C9—21no—
133C3×C32⋊C9—21no—
134C3×C32⋊C9—21no—
135C3×C32⋊C9C3×D311yescharacteristic
136C3×C32⋊C9C3×D311yescharacteristic
137C3×C32⋊C9C3×D311yescharacteristic
138C3×C32⋊C9C3×D311yescharacteristic
139C3×C92—21no—
140C3×C92—21no—
141C3×C92—21no—
142C3×C92—21no—
143C3×C92—21no—
144C3×C92—21no—
145C3×C92—31no—
146C3×C92—31no—
147C3×C92—31no—
148C3×C92—61no—
149C3×C92—61no—
150C3×C92—61no—
151C3×C92C3×D311yescharacteristic
152C3×C92C3×D311yescharacteristic
153C3×C92C3×D311yescharacteristic
154#6855—21no—
155#6855—21no—
156#6855—21no—
157#6855—21no—
158#6855—21no—
159#6855—21no—
160#6855—21no—
161#6855—21no—
162#6855—21no—
163#6855—21no—
164#6855—21no—
165#6855—21no—
166#6855—21no—
167#6855—21no—
168#6855—21no—
169#6855—21no—
170#6855—21no—
171#6855—21no—
172#6855—21no—
173#6855—21no—
174#6855—21no—
175#6855—21no—
176#6855C3×D311yescharacteristic
177#6855C3×D311yescharacteristic
178#6855C3×D311yescharacteristic
179#6855C3×D311yescharacteristic
180C3×C3⋊(C3⋊D3)—31no—
181C32×C3⋊D3—91no—
182C3⋊(C3⋊D9)C3×C911yescharacteristic, complemented
183C3⋊AGL(1,ℤ/9)—31no—
184C3⋊AGL(1,ℤ/9)—31no—
185C3⋊AGL(1,ℤ/9)—31no—
186C3⋊((C3⋊D3)⋊C3)—31no—
187C3⋊((C3⋊D3)⋊C3)—31no—
188C3⋊((C3⋊D3)⋊C3)—31no—
189C9×C3⋊D3—91no—
190C9×C3⋊D3—91no—
191C9×C3⋊D3—91no—
192C9×C3⋊D3—91no—
193C9×C3⋊D3—91no—
194C9×C3⋊D3—91no—
195C9×C3⋊D3—271no—
196C9×C3⋊D3—271no—
197C9×C3⋊D3—271no—
198C3×C3⋊D9—31no—
199C3×C3⋊D9—31no—
200C3×C3⋊D9—31no—
201C3×C3⋊D9—91no—
202C3×C3⋊D9—91no—
203C3×C3⋊D9—91no—
204C3×AGL(1,ℤ/9)—91no—
205C3×AGL(1,ℤ/9)—91no—
206C3×AGL(1,ℤ/9)—91no—
207C3×(C3⋊D3)⋊C3—91no—
208C3×(C3⋊D3)⋊C3—91no—
209C3×(C3⋊D3)⋊C3—91no—
210C3×D3×C9—271no—
211C3×D3×C9—271no—
212C3×D3×C9—271no—
213C3×D3×C9—271no—
214D9⋊C9—91no—
215D9⋊C9—91no—
216D9⋊C9—91no—
217D9⋊C9—91no—
218D9⋊C9—91no—
219D9⋊C9—91no—
220#4169—31no—
221#4169—31no—
222#4169—31no—
223#4169—31no—
224#4169—31no—
225#4169—31no—
226(C3⋊D3)⋊C9—91no—
227(C3⋊D3)⋊C9—91no—
228(C3⋊D3)⋊C9—91no—
229(C3⋊D3)⋊C9—91no—
230(C3⋊D3)⋊C9—91no—
231(C3⋊D3)⋊C9—91no—
232C9×D9—91no—
233C9×D9—91no—
234C9×D9—91no—
235C9×D9—271no—
236C9×D9—271no—
237C34—21no—
238C34C32×D311yescharacteristic
239C34C3×C3⋊D311yescharacteristic
240C3×3−1+2—21no—
241C3×3−1+2—21no—
242C3×3−1+2—21no—
243C3×3−1+2—21no—
244C3×3−1+2—21no—
245C3×3−1+2—21no—
246C3×3−1+2—21no—
247C3×3−1+2—21no—
248C3×3−1+2—21no—
249C3×3−1+2—21no—
250C3×3−1+2—21no—
251C3×3−1+2—21no—
252C3×3−1+2—31no—
253C3×3−1+2—31no—
254C3×3−1+2—61no—
255C3×3−1+2—61no—
256C3×3−1+2—61no—
257C3×3−1+2—61no—
258C3×3−1+2—61no—
259C3×3−1+2—61no—
260C3×3−1+2—61no—
261C3×3−1+2—61no—
262C3×3−1+2—61no—
263C3×3−1+2—61no—
264C3×3−1+2—61no—
265C3×3−1+2—61no—
266C3×3−1+2—61no—
267C3×3−1+2D3×C911yescharacteristic, complemented
268C3×3−1+2D3×C911yescharacteristic, complemented
269C3×3−1+2D3×C911yescharacteristic, complemented
270C3×H(3,𝔽3)—21no—
271C3×H(3,𝔽3)—21no—
272C3×H(3,𝔽3)—21no—
273C3×H(3,𝔽3)—31no—
274C3×H(3,𝔽3)—61no—
275C3×H(3,𝔽3)—61no—
276C3×H(3,𝔽3)—61no—
277C3×H(3,𝔽3)—61no—
278C3×H(3,𝔽3)—61no—
279C3×H(3,𝔽3)D3×C911yescharacteristic
280C3×H(3,𝔽3)D3×C911yescharacteristic
281C3×H(3,𝔽3)D3×C911yescharacteristic
282C32×C9—21no—
283C32×C9—21no—
284C32×C9—21no—
285C32×C9—21no—
286C32×C9—21no—
287C32×C9—21no—
288C32×C9—21no—
289C32×C9—21no—
290C32×C9—21no—
291C32×C9—21no—
292C32×C9—21no—
293C32×C9—21no—
294C32×C9—21no—
295C32×C9—21no—
296C32×C9—21no—
297C32×C9—21no—
298C32×C9—21no—
299C32×C9—21no—
300C32×C9—21no—
301C32×C9—21no—
302C32×C9—21no—
303C32×C9—21no—
304C32×C9—31no—
305C32×C9—31no—
306C32×C9—31no—
307C32×C9—31no—
308C32×C9—31no—
309C32×C9—31no—
310C32×C9—31no—
311C32×C9—31no—
312C32×C9—31no—
313C32×C9—61no—
314C32×C9—61no—
315C32×C9—61no—
316C32×C9—61no—
317C32×C9—61no—
318C32×C9—61no—
319C32×C9—61no—
320C32×C9—61no—
321C32×C9—61no—
322C32×C9—63no—
323C32×C9—63no—
324C32×C9—61no—
325C32×C9—61no—
326C32×C9—61no—
327C32×C9—61no—
328C32×C9—61no—
329C32×C9—61no—
330C32×C9—61no—
331C32×C9—61no—
332C32×C9—61no—
333C32×C9—61no—
334C32×C9—61no—
335C32×C9—61no—
336C32×C9—61no—
337C32×C9—61no—
338C32×C9—61no—
339C32×C9—61no—
340C32×C9—61no—
341C32×C9—61no—
342C32×C9—61no—
343C32×C9—61no—
344C32×C9AGL(1,ℤ/9)11yescharacteristic, complemented
345C32×C9AGL(1,ℤ/9)11yescharacteristic, complemented
346C32×C9AGL(1,ℤ/9)11yescharacteristic, complemented
347C32×C9C2×C3×C911yescharacteristic, complemented
348C32×C9C32×D311yescharacteristic
349C32×C9C32×D311yescharacteristic
350C32×C9C32×D311yescharacteristic
351C32×C9C3×C3⋊D311yescharacteristic
352C32×C9C3×C3⋊D311yescharacteristic
353C32×C9C3×C3⋊D311yescharacteristic
354C9⋊C9—61no—
355C9⋊C9—61no—
356C9⋊C9—61no—
357C9⋊C9—61no—
358C9⋊C9—61no—
359C9⋊C9—61no—
360C9⋊C9—61no—
361C9⋊C9—61no—
362C9⋊C9—61no—
363C9⋊C9—61no—
364C9⋊C9—61no—
365C9⋊C9—61no—
366C9⋊C9—61no—
367C9⋊C9—61no—
368C9⋊C9—61no—
369C9⋊C9—61no—
370C9⋊C9—61no—
371C9⋊C9—61no—
372C9⋊C9—61no—
373C9⋊C9—61no—
374C9⋊C9—61no—
375C9⋊C9—61no—
376C9⋊C9—61no—
377C9⋊C9—61no—
378C9⋊C9—61no—
379C9⋊C9—61no—
380C9⋊C9—61no—
381C9⋊C9—61no—
382C9⋊C9—61no—
383C9⋊C9—61no—
384C32⋊C9—21no—
385C32⋊C9—21no—
386C32⋊C9—21no—
387C32⋊C9—21no—
388C32⋊C9—21no—
389C32⋊C9—21no—
390C32⋊C9—21no—
391C32⋊C9—21no—
392C32⋊C9—21no—
393C32⋊C9—21no—
394C32⋊C9—21no—
395C32⋊C9—21no—
396C32⋊C9—21no—
397C32⋊C9—21no—
398C32⋊C9—21no—
399C32⋊C9—21no—
400C32⋊C9—21no—
401C32⋊C9—21no—
402C32⋊C9—21no—
403C32⋊C9—21no—
404C32⋊C9—21no—
405C32⋊C9—21no—
406C32⋊C9—21no—
407C32⋊C9—21no—
408C32⋊C9—21no—
409C32⋊C9—21no—
410C32⋊C9—21no—
411C32⋊C9—21no—
412C32⋊C9—21no—
413C32⋊C9—21no—
414C32⋊C9—21no—
415C32⋊C9—21no—
416C32⋊C9—21no—
417C32⋊C9—31no—
418C32⋊C9—31no—
419C32⋊C9—31no—
420C32⋊C9—61no—
421C32⋊C9—61no—
422C32⋊C9—61no—
423C32⋊C9—63no—
424C32⋊C9—63no—
425C32⋊C9—63no—
426C32⋊C9—63no—
427C32⋊C9—63no—
428C32⋊C9—63no—
429C32⋊C9—61no—
430C32⋊C9—61no—
431C32⋊C9—61no—
432C32⋊C9—61no—
433C32⋊C9—61no—
434C32⋊C9—61no—
435C32⋊C9—61no—
436C32⋊C9—61no—
437C32⋊C9—61no—
438C32⋊C9—61no—
439C32⋊C9—61no—
440C32⋊C9—61no—
441C32⋊C9—61no—
442C32⋊C9—61no—
443C32⋊C9—61no—
444C32⋊C9—61no—
445C32⋊C9—61no—
446C32⋊C9—61no—
447C32⋊C9—61no—
448C32⋊C9—61no—
449C32⋊C9—61no—
450C32⋊C9—61no—
451C32⋊C9—61no—
452C32⋊C9—61no—
453C32⋊C9D3×C911yescharacteristic, complemented
454C32⋊C9D3×C911yescharacteristic, complemented
455C32⋊C9D3×C911yescharacteristic, complemented
456C32⋊C9D3×C911yescharacteristic, complemented
457C32⋊C9D3×C911yescharacteristic, complemented
458C32⋊C9D3×C911yescharacteristic, complemented
459C92—21no—
460C92—21no—
461C92—21no—
462C92—31no—
463C92—31no—
464C92—61no—
465C92—61no—
466C92—61no—
467C92—61no—
468C92—61no—
469C92—61no—
470C92—61no—
471C92—61no—
472C92—62no—
473C92—61no—
474C92—61no—
475C92—61no—
476C92—61no—
477C92—61no—
478C92—61no—
479C92—61no—
480C92—61no—
481C92—61no—
482C92—61no—
483C92(C3⋊D3)⋊C311yescharacteristic, complemented
484C92(C3⋊D3)⋊C311yescharacteristic, complemented
485C92(C3⋊D3)⋊C311yescharacteristic, complemented
486C3⋊(C3⋊D3)—31no—
487C3×C3⋊D3—91no—
488C3×C3⋊D3—91no—
489C3×C3⋊D3—91no—
490C3×C3⋊D3—91no—
491C3×C3⋊D3—91no—
492C3×C3⋊D3—91no—
493C3×C3⋊D3—91no—
494C3×C3⋊D3—271no—
495C3×C3⋊D3—271no—
496C3×C3⋊D3—271no—
497C32×D3—271no—
498C32×D3—271no—
499C32×D3—271no—
500C32×D3—271no—
501C2×C3×C9—811no—
502C3⋊D9—31no—
503C3⋊D9—31no—
504C3⋊D9—31no—
505C3⋊D9—91no—
506C3⋊D9—91no—
507C3⋊D9—91no—
508AGL(1,ℤ/9)—91no—
509AGL(1,ℤ/9)—91no—
510AGL(1,ℤ/9)—91no—
511AGL(1,ℤ/9)—91no—
512AGL(1,ℤ/9)—91no—
513AGL(1,ℤ/9)—91no—
514AGL(1,ℤ/9)—91no—
515AGL(1,ℤ/9)—91no—
516AGL(1,ℤ/9)—91no—
517(C3⋊D3)⋊C3—91no—
518(C3⋊D3)⋊C3—91no—
519(C3⋊D3)⋊C3—91no—
520(C3⋊D3)⋊C3—91no—
521(C3⋊D3)⋊C3—91no—
522(C3⋊D3)⋊C3—91no—
523(C3⋊D3)⋊C3—91no—
524(C3⋊D3)⋊C3—91no—
525(C3⋊D3)⋊C3—91no—
526D3×C9—271no—
527D3×C9—271no—
528D3×C9—271no—
529D3×C9—271no—
530D3×C9—271no—
531D3×C9—271no—
532D3×C9—271no—
533D3×C9—271no—
534D3×C9—271no—
535D3×C9—271no—
536D3×C9—271no—
537D3×C9—271no—
538D3×C9—811no—
539D3×C9—811no—
540D3×C9—811no—
541C3×D9—91no—
542C3×D9—91no—
543C3×D9—91no—
544C3×D9—271no—
545C3×D9—271no—
546C33—21no—
547C33—21no—
548C33—21no—
549C33—21no—
550C33—21no—
551C33—21no—
552C33—21no—
553C33—31no—
554C33—31no—
555C33—31no—
556C33—31no—
557C33—61no—
558C33—61no—
559C33—61no—
560C33—61no—
561C33—61no—
562C33—61no—
563C33—61no—
564C33—61no—
565C33—61no—
566C33—61no—
567C33—61no—
568C33—61no—
569C33—61no—
570C33—61no—
571C33—61no—
572C33—61no—
573C33—61no—
574C33—61no—
575C33—61no—
576C33—61no—
577C33—61no—
578C33—61no—
579C33C3×D3×C911yescharacteristic
580C33C3×AGL(1,ℤ/9)11yescharacteristic
581C33C3×AGL(1,ℤ/9)11yescharacteristic
582C33C3×AGL(1,ℤ/9)11yescharacteristic
583C33C9×C3⋊D311yescharacteristic
584C33C9×C3⋊D311yescharacteristic
585C33C9×C3⋊D311yescharacteristic
586C33C32×C3⋊D311yescharacteristic
5873−1+2—31no—
5883−1+2—31no—
5893−1+2—61no—
5903−1+2—61no—
5913−1+2—61no—
5923−1+2—61no—
5933−1+2—61no—
5943−1+2—61no—
5953−1+2—61no—
5963−1+2—61no—
5973−1+2—61no—
5983−1+2—61no—
5993−1+2—61no—
6003−1+2—61no—
6013−1+2—61no—
6023−1+2—61no—
6033−1+2—61no—
6043−1+2—61no—
6053−1+2—61no—
6063−1+2—61no—
6073−1+2—61no—
6083−1+2—61no—
6093−1+2—61no—
6103−1+2—61no—
6113−1+2—61no—
6123−1+2—61no—
6133−1+2—61no—
6143−1+2—61no—
6153−1+2—61no—
6163−1+2—61no—
6173−1+2—61no—
6183−1+2—61no—
6193−1+2—61no—
6203−1+2—61no—
6213−1+2—61no—
6223−1+2—61no—
6233−1+2—61no—
6243−1+2—61no—
6253−1+2—61no—
6263−1+2—61no—
6273−1+2—61no—
6283−1+2—61no—
6293−1+2—61no—
6303−1+2—61no—
6313−1+2—61no—
632H(3,𝔽3)—31no—
633H(3,𝔽3)—31no—
634H(3,𝔽3)—31no—
635H(3,𝔽3)—31no—
636H(3,𝔽3)—61no—
637H(3,𝔽3)—61no—
638H(3,𝔽3)—61no—
639H(3,𝔽3)—61no—
640H(3,𝔽3)—61no—
641H(3,𝔽3)—61no—
642H(3,𝔽3)—61no—
643H(3,𝔽3)—61no—
644H(3,𝔽3)—61no—
645H(3,𝔽3)—61no—
646H(3,𝔽3)—61no—
647H(3,𝔽3)—61no—
648H(3,𝔽3)—61no—
649H(3,𝔽3)—61no—
650C3×C9—21no—
651C3×C9—21no—
652C3×C9—21no—
653C3×C9—21no—
654C3×C9—21no—
655C3×C9—21no—
656C3×C9—21no—
657C3×C9—21no—
658C3×C9—23no—
659C3×C9—23no—
660C3×C9—21no—
661C3×C9—21no—
662C3×C9—21no—
663C3×C9—21no—
664C3×C9—21no—
665C3×C9—21no—
666C3×C9—21no—
667C3×C9—21no—
668C3×C9—21no—
669C3×C9—21no—
670C3×C9—21no—
671C3×C9—21no—
672C3×C9—21no—
673C3×C9—21no—
674C3×C9—21no—
675C3×C9—21no—
676C3×C9—21no—
677C3×C9—31no—
678C3×C9—31no—
679C3×C9—31no—
680C3×C9—31no—
681C3×C9—31no—
682C3×C9—31no—
683C3×C9—31no—
684C3×C9—31no—
685C3×C9—31no—
686C3×C9—31no—
687C3×C9—31no—
688C3×C9—31no—
689C3×C9—61no—
690C3×C9—61no—
691C3×C9—61no—
692C3×C9—61no—
693C3×C9—61no—
694C3×C9—61no—
695C3×C9—61no—
696C3×C9—61no—
697C3×C9—61no—
698C3×C9—61no—
699C3×C9—61no—
700C3×C9—61no—
701C3×C9—61no—
702C3×C9—61no—
703C3×C9—61no—
704C3×C9—61no—
705C3×C9—61no—
706C3×C9—61no—
707C3×C9—61no—
708C3×C9—61no—
709C3×C9—61no—
710C3×C9—61no—
711C3×C9—61no—
712C3×C9—61no—
713C3×C9—61no—
714C3×C9—61no—
715C3×C9—61no—
716C3×C9—61no—
717C3×C9—61no—
718C3×C9—61no—
719C3×C9—62no—
720C3×C9—61no—
721C3×C9—61no—
722C3×C9—61no—
723C3×C9—61no—
724C3×C9—63no—
725C3×C9—63no—
726C3×C9—63no—
727C3×C9—63no—
728C3×C9—63no—
729C3×C9—63no—
730C3×C9—63no—
731C3×C9—63no—
732C3×C9—63no—
733C3×C9—61no—
734C3×C9—61no—
735C3×C9—61no—
736C3×C9—61no—
737C3×C9—61no—
738C3×C9—61no—
739C3×C9—61no—
740C3×C9—61no—
741C3×C9—61no—
742C3×C9—61no—
743C3×C9—61no—
744C3×C9—61no—
745C3×C9—61no—
746C3×C9—61no—
747C3×C9—61no—
748C3×C9—61no—
749C3×C9—61no—
750C3×C9—61no—
751C3×C9—61no—
752C3×C9—61no—
753C3×C9—61no—
754C3×C9—61no—
755C3×C9—61no—
756C3×C9—61no—
757C3×C9—61no—
758C3×C9—61no—
759C3×C9—61no—
760C3×C9—61no—
761C3×C9—61no—
762C3×C9—61no—
763C3×C9—61no—
764C3×C9—61no—
765C3×C9—61no—
766C3×C9—61no—
767C3×C9—61no—
768C3×C9—61no—
769C3×C9—61no—
770C3×C9—61no—
771C3×C9—61no—
772C3×C9—61no—
773C3×C9—61no—
774C3×C9—61no—
775C3×C9—61no—
776C3×C9—61no—
777C3×C9—61no—
778C3×C9—61no—
779C3×C9—61no—
780C3×C9—181no—
781C3×C9—181no—
782C3×C9—181no—
783C3×C9—181no—
784C3×C9—181no—
785C3×C9—181no—
786C3×C9—181no—
787C3×C9—181no—
788C3×C9—181no—
789C3×C9—181no—
790C3×C9—181no—
791C3×C9—181no—
792C3×C9—181no—
793C3×C9—181no—
794C3×C9C3×D3×C911yescharacteristic
795C3×C9C3×D3×C911yescharacteristic
796C3×C9C3×D3×C911yescharacteristic
797C3×C9C3×(C3⋊D3)⋊C311yescharacteristic
798C3×C9C3×(C3⋊D3)⋊C311yescharacteristic
799C3×C9C3×(C3⋊D3)⋊C311yescharacteristic
800C3×C9C3⋊((C3⋊D3)⋊C3)11yescharacteristic
801C3×C9C3⋊AGL(1,ℤ/9)11yescharacteristic
802C3×C9#420711yescharacteristic
803C3×C9#420711yescharacteristic
804C2×C32—811no—
805C3⋊D3—91no—
806C3⋊D3—91no—
807C3⋊D3—91no—
808C3⋊D3—91no—
809C3⋊D3—271no—
810C3⋊D3—271no—
811C3⋊D3—271no—
812C3×D3—271no—
813C3×D3—271no—
814C3×D3—271no—
815C3×D3—271no—
816C3×D3—271no—
817C3×D3—271no—
818C3×D3—271no—
819C3×D3—271no—
820C3×D3—271no—
821C3×D3—271no—
822C3×D3—271no—
823C3×D3—271no—
824C3×D3—271no—
825C3×D3—271no—
826C3×D3—271no—
827C3×D3—271no—
828C3×D3—811no—
829C3×D3—811no—
830C3×D3—811no—
831C2×C9—811no—
832C2×C9—811no—
833C2×C9—811no—
834D9—91no—
835D9—91no—
836D9—91no—
837D9—271no—
838D9—271no—
839C32—21no—
840C32—21no—
841C32—21no—
842C32—21no—
843C32—21no—
844C32—21no—
845C32—21no—
846C32—31no—
847C32—31no—
848C32—31no—
849C32—31no—
850C32—31no—
851C32—31no—
852C32—31no—
853C32—31no—
854C32—31no—
855C32—31no—
856C32—31no—
857C32—31no—
858C32—61no—
859C32—61no—
860C32—61no—
861C32—61no—
862C32—61no—
863C32—61no—
864C32—61no—
865C32—61no—
866C32—61no—
867C32—61no—
868C32—61no—
869C32—61no—
870C32—61no—
871C32—61no—
872C32—61no—
873C32—61no—
874C32—61no—
875C32—61no—
876C32—61no—
877C32—61no—
878C32—61no—
879C32—61no—
880C32—61no—
881C32—61no—
882C32—61no—
883C32—61no—
884C32—61no—
885C32—61no—
886C32—61no—
887C32—61no—
888C32—61no—
889C32—61no—
890C32—61no—
891C32—91no—
892C32—181no—
893C32—181no—
894C32—181no—
895C32—181no—
896C32—181no—
897C32—181no—
898C32—181no—
899C32—181no—
900C32—181no—
901C32—181no—
902C32—181no—
903C32—181no—
904C32—181no—
905C32C9×AGL(1,ℤ/9)11yescharacteristic, complemented
906C32C9×AGL(1,ℤ/9)11yescharacteristic, complemented
907C32C9×AGL(1,ℤ/9)11yescharacteristic, complemented
908C32C3×C9×C3⋊D311yescharacteristic
909C32C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
910C32C3×C3⋊AGL(1,ℤ/9)11yescharacteristic
911C32C3×#420711yescharacteristic
912C32C3×#420711yescharacteristic
913C9—21no—
914C9—21no—
915C9—21no—
916C9—21no—
917C9—21no—
918C9—21no—
919C9—21no—
920C9—31no—
921C9—31no—
922C9—63no—
923C9—63no—
924C9—61no—
925C9—61no—
926C9—61no—
927C9—61no—
928C9—61no—
929C9—61no—
930C9—61no—
931C9—61no—
932C9—61no—
933C9—61no—
934C9—61no—
935C9—61no—
936C9—61no—
937C9—61no—
938C9—61no—
939C9—61no—
940C9—61no—
941C9—181no—
942C9—181no—
943C9—181no—
944C9—181no—
945C9—181no—
946C9—181no—
947C9—181no—
948C9—181no—
949C9—181no—
950C9—181no—
951C9C9×(C3⋊D3)⋊C311yescharacteristic, complemented
952C9C9×(C3⋊D3)⋊C311yescharacteristic, complemented
953C9C9×(C3⋊D3)⋊C311yescharacteristic, complemented
954C9#9230311yescharacteristic, direct product factor
955C2×C3—811no—
956C2×C3—811no—
957C2×C3—811no—
958C2×C3—811no—
959D3—271no—
960D3—271no—
961D3—271no—
962D3—271no—
963D3—811no—
964D3—811no—
965D3—811no—
966C3—21no—
967C3—21no—
968C3—21no—
969C3—21no—
970C3—31no—
971C3—31no—
972C3—31no—
973C3—61no—
974C3—61no—
975C3—61no—
976C3—91no—
977C3—181no—
978C3—181no—
979C3—181no—
980C3—181no—
981C3—181no—
982C3C9×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
983C3C9×C3⋊AGL(1,ℤ/9)11yescharacteristic
984C3C9×#420711yescharacteristic
985C3C9×#420711yescharacteristic
986C3C3×#9230311yescharacteristic
987C2—811noSylow
subgroupG/H
center, hypercenterC9#92303
commutator, hypocenterC32×C9C2×C3×C9
Frattini, socleC33C32×C3⋊D3
FittingC9×C9⋊H(3,𝔽3)C2
prime radicalC3×#92303C3
cosocleC33×C9C2×C32
LCSG ▷ C32×C9
UCSC1 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C9×C9⋊H(3,𝔽3)C2semidirect
5. C9×C3⋊(C3⋊D9)C3semidirect
6. #13090624C3semidirect
7. #13090624C3semidirect
12. C3×C9×3−1+2D3semidirect
14. C32×C92C2×C3semidirect
27. #10624548C2×C3semidirect
28. #10624548C2×C3semidirect
32. C9×C32⋊C9D3semidirect
33. C9×C32⋊C9D3semidirect
39. #92303C9direct (N × H)
40. #92303C9direct (N × H)
41. #92303C9direct (N × H)
84. C9⋊H(3,𝔽3)C2×C9semidirect
85. C9⋊H(3,𝔽3)C2×C9semidirect
86. C9⋊H(3,𝔽3)C2×C9semidirect
182. C3⋊(C3⋊D9)C3×C9semidirect
267. C3×3−1+2D3×C9semidirect
268. C3×3−1+2D3×C9semidirect
269. C3×3−1+2D3×C9semidirect
344. C32×C9AGL(1,ℤ/9)semidirect
345. C32×C9AGL(1,ℤ/9)semidirect
346. C32×C9AGL(1,ℤ/9)semidirect
347. C32×C9C2×C3×C9semidirect
453. C32⋊C9D3×C9semidirect
454. C32⋊C9D3×C9semidirect
455. C32⋊C9D3×C9semidirect
456. C32⋊C9D3×C9semidirect
457. C32⋊C9D3×C9semidirect
458. C32⋊C9D3×C9semidirect
483. C92(C3⋊D3)⋊C3semidirect
484. C92(C3⋊D3)⋊C3semidirect
485. C92(C3⋊D3)⋊C3semidirect
905. C32C9×AGL(1,ℤ/9)semidirect
906. C32C9×AGL(1,ℤ/9)semidirect
907. C32C9×AGL(1,ℤ/9)semidirect
951. C9C9×(C3⋊D3)⋊C3semidirect
952. C9C9×(C3⋊D3)⋊C3semidirect
953. C9C9×(C3⋊D3)⋊C3semidirect
954. C9#92303direct (N × H)

Maximal subgroups

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

subgroupindex
C9×C9⋊H(3,𝔽3)2
C3×#923033
C9×C3⋊AGL(1,ℤ/9)3
C9×C3⋊((C3⋊D3)⋊C3)3
C9×C3⋊(C3⋊D9)3
#130906243
C9×#41693