Finite Group Databasebeta

← D9×D9⋊H(3,𝔽3) #72244029

Subgroups — D9×D9⋊H(3,𝔽3) #72244029

Order 8748.

1175 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D9×H(3,𝔽3)—31nomaximal
2D3×D9⋊H(3,𝔽3)—31nomaximal
3D9×C9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
4C9×D9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
5#72243650C211yesmaximal, characteristic, complemented
6C3×D9×AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
7C3×D9×AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
8C3×D9×AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
9C32×D92C311yesmaximal, characteristic, complemented
10C9×C9⋊H(3,𝔽3)C2211yescharacteristic, complemented, Sylow
11C3⋊(D9⋊H(3,𝔽3))—31no—
12C3×D9⋊H(3,𝔽3)D311yescharacteristic
13D3×C9⋊H(3,𝔽3)—31no—
14C3×#92299C2×C311yescharacteristic, complemented
15C3×#92299C2×C311yescharacteristic, complemented
16C3×#92299C2×C311yescharacteristic, complemented
17C3×D9×3−1+2C2×C311yescharacteristic, complemented
18C3×D9×3−1+2C2×C311yescharacteristic, complemented
19C3×D9×3−1+2C2×C311yescharacteristic, complemented
20C3×C9×AGL(1,ℤ/9)C2×C311yescharacteristic, complemented
21C3×C9×AGL(1,ℤ/9)C2×C311yescharacteristic, complemented
22C3×C9×AGL(1,ℤ/9)C2×C311yescharacteristic, complemented
23H(3,𝔽3)×C3⋊D9—31no—
24C3×D9×H(3,𝔽3)D311yescharacteristic
25D3×C9×H(3,𝔽3)—31no—
26C32×C9⋊D9C2×C311yescharacteristic, complemented
27C32×C9×D9C2×C311yescharacteristic, complemented
28C32×C9×D9C2×C311yescharacteristic, complemented
29(C3×AGL(1,ℤ/9))⋊C9—21no—
30(C3×AGL(1,ℤ/9))⋊C9—21no—
31(C3×AGL(1,ℤ/9))⋊C9—21no—
32#13090639—61no—
33#13090623—21no—
34D9×C32⋊C9—21no—
35D9×C32⋊C9—21no—
36D9×C32⋊C9—21no—
37D9×C32⋊C9—21no—
38C3×D3×AGL(1,ℤ/9)—31no—
39C3×D3×AGL(1,ℤ/9)—31no—
40C3×D3×AGL(1,ℤ/9)—31no—
41D32×H(3,𝔽3)—91no—
42C32×D3×D9—31no—
43C32×D3×D9—31no—
44C32×D3×D9—31no—
45C32×D3×D9—31no—
46C32×D3×D9—31no—
47C2×D9⋊H(3,𝔽3)—91no—
48C2×D9×H(3,𝔽3)—91no—
49D9×AGL(1,ℤ/9)—31no—
50D9×AGL(1,ℤ/9)—31no—
51D9×AGL(1,ℤ/9)—31no—
52C3×D92—31no—
53C3×D92C3211yescharacteristic
54C3×C9⋊H(3,𝔽3)C2×D311yescharacteristic
55C3×C9×3−1+2C22×C311yescharacteristic, complemented
56C3×C9×3−1+2C22×C311yescharacteristic, complemented
57C3×C9×3−1+2C22×C311yescharacteristic, complemented
58C3×C9×H(3,𝔽3)C2×D311yescharacteristic
59C32×C92C22×C311yescharacteristic, complemented
60#10624560—21no—
61#10624560—21no—
62#10624560—21no—
63#10624557—41no—
64#10624557—41no—
65#10624557—41no—
66#10624556—41no—
67#10624555—21no—
68#10624548—21no—
69C9×C32⋊C9—21no—
70C9×C32⋊C9—21no—
71C9×C32⋊C9—21no—
72C9×C32⋊C9—21no—
73C3×C3⋊AGL(1,ℤ/9)—31no—
74C3×C3⋊AGL(1,ℤ/9)—31no—
75C3×C3⋊AGL(1,ℤ/9)—31no—
76C3⋊D3×H(3,𝔽3)—91no—
77C32×C3⋊D9—31no—
78C32×C3⋊D9—31no—
79C32×C3⋊D9—31no—
80C32×C3⋊D9—31no—
81C32×C3⋊D9—31no—
82C32×C3⋊D9—61no—
83C3×D3×3−1+2—31no—
84C3×D3×3−1+2—31no—
85C3×D3×3−1+2—31no—
86C32×AGL(1,ℤ/9)C3×D311yescharacteristic
87C32×AGL(1,ℤ/9)C3×D311yescharacteristic
88C32×AGL(1,ℤ/9)C3×D311yescharacteristic
89C3×D3×H(3,𝔽3)—31no—
90C3×D3×H(3,𝔽3)—31no—
91C32×D3×C9—31no—
92C32×D3×C9—31no—
93C32×D3×C9—31no—
94C32×D3×C9—31no—
95C32×D3×C9—31no—
96C33×D9C3×D311yescharacteristic
97C33×D9C3×D311yescharacteristic
98C33×D9C3×D311yescharacteristic
99C33×D9C3×D311yescharacteristic
100C33×D9C3×D311yescharacteristic
101C2×C9⋊H(3,𝔽3)—91no—
102C2×C9×H(3,𝔽3)—91no—
103#92299—31no—
104#92299—31no—
105#92299—31no—
106C3×C9⋊D9—31no—
107C3×C9⋊D9C2×C3211yescharacteristic
108D9⋊H(3,𝔽3)—21no—
109D9⋊H(3,𝔽3)—21no—
110D9⋊H(3,𝔽3)—21no—
111D9⋊H(3,𝔽3)—21no—
112D9⋊H(3,𝔽3)—91no—
113D9⋊H(3,𝔽3)—181no—
114D9⋊H(3,𝔽3)D911yescharacteristic, direct product factor
115D9×3−1+2—31no—
116D9×3−1+2—31no—
117D9×3−1+2—31no—
118D9×3−1+2—61no—
119D9×3−1+2—61no—
120D9×3−1+2—61no—
121C9×AGL(1,ℤ/9)—31no—
122C9×AGL(1,ℤ/9)—31no—
123C9×AGL(1,ℤ/9)—31no—
124C9×AGL(1,ℤ/9)—61no—
125C9×AGL(1,ℤ/9)—61no—
126C9×AGL(1,ℤ/9)—61no—
127D9×H(3,𝔽3)—61no—
128D9×H(3,𝔽3)—61no—
129D9×H(3,𝔽3)—91no—
130D9×H(3,𝔽3)—181no—
131C3×D9⋊C9—21no—
132C3×D9⋊C9—21no—
133C3×D9⋊C9—21no—
134D3×C32⋊C9—61no—
135D3×C32⋊C9—61no—
136D3×C32⋊C9—61no—
137D3×C32⋊C9—61no—
138D3×C32⋊C9—61no—
139D3×C32⋊C9—61no—
140D3×C32⋊C9—61no—
141D3×C32⋊C9—61no—
142C3×#4169—61no—
143C3×#4169—61no—
144C3×#4169—61no—
145C3×C9×D9—21no—
146C3×C9×D9—21no—
147C3×C9×D9—21no—
148C3×C9×D9—21no—
149C3×C9×D9—21no—
150C3×C9×D9—31no—
151C3×C9×D9—31no—
152C3×C9×D9—61no—
153C3×C9×D9—61no—
154C3×C9×D9C2×C3211yescharacteristic
155C3×C9×D9C2×C3211yescharacteristic
156C32×D32—91no—
157C32×D32—91no—
158C32×D32—91no—
159C32×D32—91no—
160C2×C3×AGL(1,ℤ/9)—91no—
161C2×C3×AGL(1,ℤ/9)—91no—
162C2×C3×AGL(1,ℤ/9)—91no—
163C2×D3×H(3,𝔽3)—271no—
164C2×D3×H(3,𝔽3)—271no—
165C2×C32×D9—91no—
166C2×C32×D9—91no—
167C2×C32×D9—91no—
168C2×C32×D9—91no—
169C2×C32×D9—91no—
170D3×AGL(1,ℤ/9)—91no—
171D3×AGL(1,ℤ/9)—91no—
172D3×AGL(1,ℤ/9)—91no—
173C3×D3×D9—31no—
174C3×D3×D9—31no—
175C3×D3×D9—91no—
176C3×D3×D9—91no—
177C3×D3×D9—91no—
178C3×D3×D9—91no—
179C3×D3×D9—91no—
180D92H(3,𝔽3)11yescharacteristic, complemented
181C32×3−1+2C2×C3×D311yescharacteristic
182C32×3−1+2C2×C3×D311yescharacteristic
183C32×3−1+2C2×C3×D311yescharacteristic
184C32×H(3,𝔽3)D3211yescharacteristic
185C33×C9—21no—
186C33×C9C2×C3×D311yescharacteristic
187C33×C9C2×C3×D311yescharacteristic
188C33×C9C2×C3×D311yescharacteristic
189C33×C9C2×C3×D311yescharacteristic
190C33×C9C2×C3×D311yescharacteristic
191C9⋊H(3,𝔽3)—21no—
192C9⋊H(3,𝔽3)—21no—
193C9⋊H(3,𝔽3)—21no—
194C9⋊H(3,𝔽3)—21no—
195C9⋊H(3,𝔽3)—21no—
196C9⋊H(3,𝔽3)—41no—
197C9⋊H(3,𝔽3)—41no—
198C9⋊H(3,𝔽3)—41no—
199C9⋊H(3,𝔽3)—41no—
200C9⋊H(3,𝔽3)C2×D911yescharacteristic, complemented
201C9×3−1+2—31no—
202C9×3−1+2—31no—
203C9×3−1+2—31no—
204C9×3−1+2—61no—
205C9×3−1+2—61no—
206C9×3−1+2—61no—
207C9×3−1+2—61no—
208C9×3−1+2—61no—
209C9×3−1+2—61no—
210C9×3−1+2—121no—
211C9×3−1+2—121no—
212C9×3−1+2—121no—
213C9×H(3,𝔽3)—61no—
214C9×H(3,𝔽3)—61no—
215C9×H(3,𝔽3)—61no—
216C9×H(3,𝔽3)—121no—
217C3×C9⋊C9—21no—
218C3×C9⋊C9—21no—
219C3×C9⋊C9—21no—
220C3×C9⋊C9—41no—
221C3×C9⋊C9—41no—
222C3×C9⋊C9—41no—
223C3×C32⋊C9—21no—
224C3×C32⋊C9—21no—
225C3×C32⋊C9—21no—
226C3×C32⋊C9—21no—
227C3×C32⋊C9—21no—
228C3×C32⋊C9—21no—
229C3×C32⋊C9—21no—
230C3×C32⋊C9—21no—
231C3×C32⋊C9—21no—
232C3×C32⋊C9—21no—
233C3×C32⋊C9—21no—
234C3×C32⋊C9—41no—
235C3×C32⋊C9—41no—
236C3×C32⋊C9—41no—
237C3×C32⋊C9—41no—
238C3×C92—21no—
239C3×C92—21no—
240C3×C92—21no—
241C3×C92—21no—
242C3×C92—21no—
243C3×C92—31no—
244C3×C92—41no—
245C3×C92—61no—
246C3×C92—61no—
247C3×C92—121no—
248C3×C92C22×C3211yescharacteristic
249#6855—41no—
250#6855—41no—
251#6855—41no—
252#6855—41no—
253#6855—41no—
254#6855—41no—
255#6855—41no—
256#6855—41no—
257#6855—41no—
258#6855—41no—
259#6855—41no—
260#6855—41no—
261C32×C3⋊D3—91no—
262C32×C3⋊D3—91no—
263C32×C3⋊D3—91no—
264C32×C3⋊D3—91no—
265C33×D3—31no—
266C33×D3—31no—
267C33×D3—31no—
268C33×D3—31no—
269C33×D3—31no—
270C33×D3—31no—
271C33×D3—31no—
272C33×D3—31no—
273C2×C3×3−1+2—91no—
274C2×C3×3−1+2—91no—
275C2×C3×3−1+2—91no—
276C2×C3×H(3,𝔽3)—91no—
277C2×C3×H(3,𝔽3)—91no—
278C2×C32×C9—91no—
279C2×C32×C9—91no—
280C2×C32×C9—91no—
281C2×C32×C9—91no—
282C2×C32×C9—91no—
283C3⋊AGL(1,ℤ/9)—91no—
284C3⋊AGL(1,ℤ/9)—91no—
285C3⋊AGL(1,ℤ/9)—91no—
286C3×C3⋊D9—31no—
287C3×C3⋊D9—31no—
288C3×C3⋊D9—61no—
289C3×C3⋊D9—91no—
290C3×C3⋊D9—91no—
291C3×C3⋊D9—91no—
292C3×C3⋊D9—91no—
293C3×C3⋊D9—91no—
294C3×C3⋊D9—181no—
295D3×3−1+2—91no—
296D3×3−1+2—91no—
297D3×3−1+2—91no—
298D3×3−1+2—181no—
299D3×3−1+2—181no—
300D3×3−1+2—181no—
301C3×AGL(1,ℤ/9)—21no—
302C3×AGL(1,ℤ/9)—21no—
303C3×AGL(1,ℤ/9)—21no—
304C3×AGL(1,ℤ/9)—31no—
305C3×AGL(1,ℤ/9)—31no—
306C3×AGL(1,ℤ/9)—31no—
307C3×AGL(1,ℤ/9)—61no—
308C3×AGL(1,ℤ/9)—61no—
309C3×AGL(1,ℤ/9)—61no—
310C3×AGL(1,ℤ/9)—91no—
311C3×AGL(1,ℤ/9)—91no—
312C3×AGL(1,ℤ/9)—91no—
313C3×AGL(1,ℤ/9)—181no—
314C3×AGL(1,ℤ/9)—181no—
315C3×AGL(1,ℤ/9)—181no—
316C3×AGL(1,ℤ/9)C3×D911yescharacteristic, complemented
317C3×AGL(1,ℤ/9)C3×D911yescharacteristic, complemented
318C3×AGL(1,ℤ/9)C3×D911yescharacteristic, complemented
319D3×H(3,𝔽3)—31no—
320D3×H(3,𝔽3)—61no—
321D3×H(3,𝔽3)—61no—
322D3×H(3,𝔽3)—61no—
323D3×H(3,𝔽3)—61no—
324D3×H(3,𝔽3)—181no—
325D3×H(3,𝔽3)—181no—
326D3×H(3,𝔽3)—271no—
327D3×H(3,𝔽3)—271no—
328D3×H(3,𝔽3)—541no—
329C3×D3×C9—31no—
330C3×D3×C9—31no—
331C3×D3×C9—61no—
332C3×D3×C9—61no—
333C3×D3×C9—61no—
334C3×D3×C9—61no—
335C3×D3×C9—61no—
336C3×D3×C9—61no—
337C3×D3×C9—61no—
338C3×D3×C9—61no—
339C3×D3×C9—91no—
340C3×D3×C9—91no—
341C3×D3×C9—91no—
342C3×D3×C9—91no—
343C3×D3×C9—91no—
344C3×D3×C9—181no—
345C3×D3×C9—181no—
346C3×D3×C9—181no—
347C3×D3×C9—181no—
348C3×D3×C9—181no—
349C32×D9—21no—
350C32×D9—21no—
351C32×D9—31no—
352C32×D9—31no—
353C32×D9—31no—
354C32×D9—31no—
355C32×D9—31no—
356C32×D9—31no—
357C32×D9—61no—
358C32×D9—61no—
359C32×D9—61no—
360C32×D9—61no—
361C32×D9—61no—
362C32×D9—61no—
363C32×D9—61no—
364C32×D9—91no—
365C32×D9—91no—
366C32×D9—91no—
367C32×D9—91no—
368C32×D9—91no—
369C32×D9—181no—
370C32×D9—181no—
371C32×D9—181no—
372C32×D9—181no—
373C32×D9—181no—
374C32×D9—541no—
375C32×D9C3×D911yescharacteristic, complemented
376C32×D9AGL(1,ℤ/9)11yescharacteristic, complemented
377C32×D9C32×D311yescharacteristic
378C32×D9C32×D311yescharacteristic
379C2×C32⋊C9—181no—
380C2×C32⋊C9—181no—
381C2×C32⋊C9—181no—
382C2×C32⋊C9—181no—
383C2×C32⋊C9—181no—
384C2×C32⋊C9—181no—
385C2×C32⋊C9—181no—
386C2×C32⋊C9—181no—
387C9⋊D9C2×H(3,𝔽3)11yescharacteristic, complemented
388D9⋊C9—61no—
389D9⋊C9—61no—
390D9⋊C9—61no—
391#4169—181no—
392#4169—181no—
393#4169—181no—
394C9×D9—21no—
395C9×D9—21no—
396C9×D9—61no—
397C9×D9—61no—
398C9×D9—61no—
399C9×D9—61no—
400C9×D9—61no—
401C9×D9C2×H(3,𝔽3)11yescharacteristic, complemented
402C9×D9C2×H(3,𝔽3)11yescharacteristic, complemented
403C2×C32×D3—271no—
404C2×C32×D3—271no—
405C2×C32×D3—271no—
406C2×C32×D3—271no—
407C2×C32×D3—271no—
408C2×C32×D3—271no—
409C2×C32×D3—271no—
410C2×C32×D3—271no—
411C3×D32—91no—
412C3×D32—271no—
413C3×D32—271no—
414C3×D32—271no—
415C3×D32—271no—
416C22×H(3,𝔽3)—811no—
417C2×AGL(1,ℤ/9)—271no—
418C2×AGL(1,ℤ/9)—271no—
419C2×AGL(1,ℤ/9)—271no—
420C2×C3×D9—91no—
421C2×C3×D9—91no—
422C2×C3×D9—271no—
423C2×C3×D9—271no—
424C2×C3×D9—271no—
425C2×C3×D9—271no—
426C2×C3×D9—271no—
427D3×D9—31no—
428D3×D9—31no—
429C34C3×D3211yescharacteristic
430C34C3×D3211yescharacteristic
431C34C3×D3211yescharacteristic
432C34C3×D3211yescharacteristic
433C3×3−1+2—21no—
434C3×3−1+2—21no—
435C3×3−1+2—21no—
436C3×3−1+2—21no—
437C3×3−1+2—21no—
438C3×3−1+2—21no—
439C3×3−1+2—31no—
440C3×3−1+2—31no—
441C3×3−1+2—31no—
442C3×3−1+2—41no—
443C3×3−1+2—41no—
444C3×3−1+2—41no—
445C3×3−1+2—61no—
446C3×3−1+2—61no—
447C3×3−1+2—61no—
448C3×3−1+2—61no—
449C3×3−1+2—61no—
450C3×3−1+2—61no—
451C3×3−1+2—121no—
452C3×3−1+2—121no—
453C3×3−1+2—121no—
454C3×3−1+2C2×C3×D911yescharacteristic, complemented
455C3×3−1+2C2×C3×D911yescharacteristic, complemented
456C3×3−1+2C2×C3×D911yescharacteristic, complemented
457C3×H(3,𝔽3)—21no—
458C3×H(3,𝔽3)—21no—
459C3×H(3,𝔽3)—21no—
460C3×H(3,𝔽3)—21no—
461C3×H(3,𝔽3)—61no—
462C3×H(3,𝔽3)—61no—
463C3×H(3,𝔽3)—121no—
464C3×H(3,𝔽3)—121no—
465C3×H(3,𝔽3)D3×D911yescharacteristic
466C32×C9—21no—
467C32×C9—21no—
468C32×C9—21no—
469C32×C9—21no—
470C32×C9—21no—
471C32×C9—21no—
472C32×C9—21no—
473C32×C9—21no—
474C32×C9—21no—
475C32×C9—21no—
476C32×C9—21no—
477C32×C9—21no—
478C32×C9—21no—
479C32×C9—31no—
480C32×C9—31no—
481C32×C9—31no—
482C32×C9—31no—
483C32×C9—31no—
484C32×C9—31no—
485C32×C9—41no—
486C32×C9—41no—
487C32×C9—41no—
488C32×C9—41no—
489C32×C9—41no—
490C32×C9—41no—
491C32×C9—61no—
492C32×C9—61no—
493C32×C9—61no—
494C32×C9—61no—
495C32×C9—61no—
496C32×C9—61no—
497C32×C9—61no—
498C32×C9—61no—
499C32×C9—61no—
500C32×C9—61no—
501C32×C9—61no—
502C32×C9—61no—
503C32×C9—61no—
504C32×C9—61no—
505C32×C9—61no—
506C32×C9—61no—
507C32×C9—121no—
508C32×C9—121no—
509C32×C9—121no—
510C32×C9—123no—
511C32×C9—121no—
512C32×C9—121no—
513C32×C9—121no—
514C32×C9—121no—
515C32×C9—121no—
516C32×C9C2×C3×D911yescharacteristic, complemented
517C32×C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
518C32×C9C2×C32×D311yescharacteristic
519C32×C9C2×C32×D311yescharacteristic
520C9⋊C9—61no—
521C9⋊C9—61no—
522C9⋊C9—61no—
523C9⋊C9—121no—
524C9⋊C9—121no—
525C9⋊C9—121no—
526C9⋊C9—121no—
527C9⋊C9—121no—
528C9⋊C9—121no—
529C9⋊C9—122no—
530C9⋊C9—122no—
531C9⋊C9—122no—
532C32⋊C9—21no—
533C32⋊C9—21no—
534C32⋊C9—21no—
535C32⋊C9—21no—
536C32⋊C9—41no—
537C32⋊C9—41no—
538C32⋊C9—41no—
539C32⋊C9—41no—
540C32⋊C9—41no—
541C32⋊C9—41no—
542C32⋊C9—41no—
543C32⋊C9—41no—
544C32⋊C9—41no—
545C32⋊C9—41no—
546C32⋊C9—41no—
547C32⋊C9—41no—
548C32⋊C9—41no—
549C32⋊C9—41no—
550C32⋊C9—41no—
551C32⋊C9—41no—
552C32⋊C9—61no—
553C32⋊C9—61no—
554C32⋊C9—61no—
555C32⋊C9—61no—
556C32⋊C9—61no—
557C32⋊C9—61no—
558C32⋊C9—121no—
559C32⋊C9—121no—
560C32⋊C9—121no—
561C32⋊C9—121no—
562C32⋊C9—123no—
563C32⋊C9—123no—
564C32⋊C9—123no—
565C32⋊C9—121no—
566C32⋊C9—121no—
567C32⋊C9—121no—
568C32⋊C9—121no—
569C32⋊C9—121no—
570C32⋊C9—122no—
571C92—21no—
572C92—21no—
573C92—41no—
574C92—61no—
575C92—61no—
576C92—61no—
577C92—61no—
578C92—61no—
579C92—121no—
580C92—121no—
581C92—121no—
582C92—121no—
583C92—121no—
584C92—121no—
585C92—122no—
586C92C22×H(3,𝔽3)11yescharacteristic, complemented
587C2×C33—91no—
588C2×C33—91no—
589C2×C33—91no—
590C2×C33—91no—
591C2×C33—91no—
592C2×C33—91no—
593C2×C33—91no—
594C2×C33—91no—
595C3×C3⋊D3—91no—
596C3×C3⋊D3—271no—
597C3×C3⋊D3—271no—
598C3×C3⋊D3—271no—
599C3×C3⋊D3—271no—
600C32×D3—31no—
601C32×D3—31no—
602C32×D3—31no—
603C32×D3—31no—
604C32×D3—31no—
605C32×D3—31no—
606C32×D3—31no—
607C32×D3—61no—
608C32×D3—61no—
609C32×D3—61no—
610C32×D3—61no—
611C32×D3—61no—
612C32×D3—91no—
613C32×D3—91no—
614C32×D3—91no—
615C32×D3—91no—
616C32×D3—91no—
617C32×D3—91no—
618C32×D3—91no—
619C32×D3—91no—
620C32×D3—181no—
621C32×D3—181no—
622C32×D3—181no—
623C32×D3—181no—
624C32×D3—181no—
625C32×D3—181no—
626C32×D3—181no—
627C32×D3—181no—
628C32×D3—181no—
629C32×D3—181no—
630C32×D3—181no—
631C32×D3—271no—
632C32×D3—271no—
633C32×D3—271no—
634C32×D3—271no—
635C32×D3—271no—
636C32×D3—271no—
637C32×D3—271no—
638C32×D3—271no—
639C32×D3—541no—
640C32×D3—541no—
641C32×D3—541no—
642C32×D3—541no—
643C2×3−1+2—271no—
644C2×3−1+2—271no—
645C2×3−1+2—271no—
646C2×3−1+2—541no—
647C2×3−1+2—541no—
648C2×3−1+2—541no—
649C2×H(3,𝔽3)—91no—
650C2×H(3,𝔽3)—181no—
651C2×H(3,𝔽3)—181no—
652C2×H(3,𝔽3)—181no—
653C2×H(3,𝔽3)—181no—
654C2×H(3,𝔽3)—541no—
655C2×H(3,𝔽3)—541no—
656C2×H(3,𝔽3)—811no—
657C2×C3×C9—91no—
658C2×C3×C9—91no—
659C2×C3×C9—181no—
660C2×C3×C9—181no—
661C2×C3×C9—181no—
662C2×C3×C9—181no—
663C2×C3×C9—181no—
664C2×C3×C9—181no—
665C2×C3×C9—181no—
666C2×C3×C9—181no—
667C2×C3×C9—271no—
668C2×C3×C9—271no—
669C2×C3×C9—271no—
670C2×C3×C9—271no—
671C2×C3×C9—271no—
672C2×C3×C9—541no—
673C2×C3×C9—541no—
674C2×C3×C9—541no—
675C2×C3×C9—541no—
676C2×C3×C9—541no—
677C3⋊D9—31no—
678C3⋊D9—31no—
679C3⋊D9—61no—
680AGL(1,ℤ/9)—31no—
681AGL(1,ℤ/9)—31no—
682AGL(1,ℤ/9)—31no—
683AGL(1,ℤ/9)—61no—
684AGL(1,ℤ/9)—61no—
685AGL(1,ℤ/9)—61no—
686AGL(1,ℤ/9)—271no—
687AGL(1,ℤ/9)—271no—
688AGL(1,ℤ/9)—271no—
689AGL(1,ℤ/9)—541no—
690AGL(1,ℤ/9)—541no—
691AGL(1,ℤ/9)—541no—
692D3×C9—31no—
693D3×C9—31no—
694D3×C9—61no—
695D3×C9—61no—
696D3×C9—181no—
697D3×C9—181no—
698D3×C9—181no—
699D3×C9—181no—
700D3×C9—181no—
701D3×C9—181no—
702D3×C9—181no—
703D3×C9—181no—
704C3×D9—21no—
705C3×D9—21no—
706C3×D9—31no—
707C3×D9—31no—
708C3×D9—61no—
709C3×D9—61no—
710C3×D9—91no—
711C3×D9—91no—
712C3×D9—181no—
713C3×D9—181no—
714C3×D9—181no—
715C3×D9—181no—
716C3×D9—181no—
717C3×D9—271no—
718C3×D9—271no—
719C3×D9—271no—
720C3×D9—271no—
721C3×D9—271no—
722C3×D9—541no—
723C3×D9—541no—
724C3×D9—541no—
725C3×D9—541no—
726C3×D9—541no—
727C3×D9—541no—
728C3×D9—543no—
729C3×D9C32×D911yescharacteristic
730C3×D9D3×H(3,𝔽3)11yescharacteristic
731C3×D9D3×H(3,𝔽3)11yescharacteristic
732C3×D9C3×AGL(1,ℤ/9)11yescharacteristic
733C22×C32—811no—
734C22×C32—811no—
735C22×C32—811no—
736C22×C32—811no—
737C2×C3×D3—271no—
738C2×C3×D3—271no—
739C2×C3×D3—811no—
740C2×C3×D3—811no—
741C2×C3×D3—811no—
742C2×C3×D3—811no—
743C2×C3×D3—811no—
744C2×C3×D3—811no—
745C2×C3×D3—811no—
746C2×C3×D3—811no—
747D32—91no—
748C2×D9—91no—
749C2×D9—91no—
750C33—21no—
751C33—21no—
752C33—21no—
753C33—21no—
754C33—21no—
755C33—21no—
756C33—31no—
757C33—31no—
758C33—31no—
759C33—31no—
760C33—41no—
761C33—61no—
762C33—61no—
763C33—61no—
764C33—61no—
765C33—61no—
766C33—61no—
767C33—61no—
768C33—61no—
769C33—61no—
770C33—61no—
771C33—61no—
772C33—61no—
773C33—61no—
774C33—61no—
775C33—121no—
776C33—121no—
777C33—121no—
778C33—121no—
779C33C3×D3×D911yescharacteristic
780C33C3×D3×D911yescharacteristic
781C33C3×D3×D911yescharacteristic
782C33C3×D3×D911yescharacteristic
783C33D3×AGL(1,ℤ/9)11yescharacteristic
784C33C32×D3211yescharacteristic
7853−1+2—31no—
7863−1+2—31no—
7873−1+2—31no—
7883−1+2—61no—
7893−1+2—61no—
7903−1+2—61no—
7913−1+2—61no—
7923−1+2—61no—
7933−1+2—61no—
7943−1+2—61no—
7953−1+2—61no—
7963−1+2—61no—
7973−1+2—121no—
7983−1+2—121no—
7993−1+2—121no—
8003−1+2—121no—
8013−1+2—121no—
8023−1+2—121no—
8033−1+2—122no—
8043−1+2—122no—
8053−1+2—122no—
8063−1+2—121no—
8073−1+2—121no—
8083−1+2—121no—
809H(3,𝔽3)—61no—
810H(3,𝔽3)—61no—
811H(3,𝔽3)—61no—
812H(3,𝔽3)—121no—
813H(3,𝔽3)—121no—
814H(3,𝔽3)—121no—
815H(3,𝔽3)—121no—
816H(3,𝔽3)—121no—
817H(3,𝔽3)—121no—
818H(3,𝔽3)—121no—
819C3×C9—21no—
820C3×C9—21no—
821C3×C9—21no—
822C3×C9—21no—
823C3×C9—21no—
824C3×C9—21no—
825C3×C9—21no—
826C3×C9—21no—
827C3×C9—21no—
828C3×C9—21no—
829C3×C9—21no—
830C3×C9—21no—
831C3×C9—31no—
832C3×C9—31no—
833C3×C9—41no—
834C3×C9—41no—
835C3×C9—43no—
836C3×C9—41no—
837C3×C9—41no—
838C3×C9—41no—
839C3×C9—41no—
840C3×C9—41no—
841C3×C9—41no—
842C3×C9—61no—
843C3×C9—61no—
844C3×C9—61no—
845C3×C9—61no—
846C3×C9—61no—
847C3×C9—63no—
848C3×C9—61no—
849C3×C9—61no—
850C3×C9—61no—
851C3×C9—61no—
852C3×C9—61no—
853C3×C9—61no—
854C3×C9—61no—
855C3×C9—61no—
856C3×C9—61no—
857C3×C9—61no—
858C3×C9—121no—
859C3×C9—121no—
860C3×C9—121no—
861C3×C9—121no—
862C3×C9—122no—
863C3×C9—122no—
864C3×C9—121no—
865C3×C9—121no—
866C3×C9—123no—
867C3×C9—121no—
868C3×C9—121no—
869C3×C9—121no—
870C3×C9—121no—
871C3×C9—121no—
872C3×C9—121no—
873C3×C9—121no—
874C3×C9—121no—
875C3×C9—123no—
876C3×C9—123no—
877C3×C9—121no—
878C3×C9—123no—
879C3×C9—121no—
880C3×C9—121no—
881C3×C9—121no—
882C3×C9—121no—
883C3×C9—121no—
884C3×C9—121no—
885C3×C9—121no—
886C3×C9—121no—
887C3×C9—121no—
888C3×C9—121no—
889C3×C9—121no—
890C3×C9—121no—
891C3×C9—121no—
892C3×C9—121no—
893C3×C9—121no—
894C3×C9—121no—
895C3×C9—121no—
896C3×C9—121no—
897C3×C9—181no—
898C3×C9—181no—
899C3×C9—181no—
900C3×C9—181no—
901C3×C9—181no—
902C3×C9—361no—
903C3×C9—361no—
904C3×C9—361no—
905C3×C9—361no—
906C3×C9—361no—
907C3×C9—361no—
908C3×C9—361no—
909C3×C9C2×C32×D911yescharacteristic
910C3×C9C2×D3×H(3,𝔽3)11yescharacteristic
911C3×C9C2×D3×H(3,𝔽3)11yescharacteristic
912C3×C9C2×C3×AGL(1,ℤ/9)11yescharacteristic
913C2×C32—91no—
914C2×C32—91no—
915C2×C32—91no—
916C2×C32—91no—
917C2×C32—91no—
918C2×C32—91no—
919C2×C32—91no—
920C2×C32—181no—
921C2×C32—181no—
922C2×C32—181no—
923C2×C32—181no—
924C2×C32—181no—
925C2×C32—271no—
926C2×C32—271no—
927C2×C32—271no—
928C2×C32—271no—
929C2×C32—271no—
930C2×C32—271no—
931C2×C32—271no—
932C2×C32—271no—
933C2×C32—271no—
934C2×C32—271no—
935C2×C32—541no—
936C2×C32—541no—
937C2×C32—541no—
938C2×C32—541no—
939C2×C32—541no—
940C2×C32—541no—
941C2×C32—541no—
942C2×C32—541no—
943C2×C32—541no—
944C2×C32—811no—
945C2×C32—811no—
946C2×C32—811no—
947C2×C32—811no—
948C3⋊D3—91no—
949C3×D3—31no—
950C3×D3—31no—
951C3×D3—31no—
952C3×D3—31no—
953C3×D3—61no—
954C3×D3—61no—
955C3×D3—91no—
956C3×D3—91no—
957C3×D3—91no—
958C3×D3—91no—
959C3×D3—91no—
960C3×D3—181no—
961C3×D3—181no—
962C3×D3—181no—
963C3×D3—181no—
964C3×D3—181no—
965C3×D3—271no—
966C3×D3—271no—
967C3×D3—271no—
968C3×D3—541no—
969C3×D3—541no—
970C3×D3—541no—
971C3×D3—811no—
972C3×D3—811no—
973C3×D3—811no—
974C3×D3—811no—
975C3×D3—811no—
976C3×D3—811no—
977C3×D3—811no—
978C3×D3—811no—
979C3×D3—1621no—
980C3×D3—1621no—
981C3×D3—1621no—
982C3×D3—1621no—
983C2×C9—91no—
984C2×C9—91no—
985C2×C9—181no—
986C2×C9—181no—
987C2×C9—541no—
988C2×C9—541no—
989C2×C9—541no—
990C2×C9—541no—
991C2×C9—541no—
992C2×C9—541no—
993C2×C9—541no—
994C2×C9—541no—
995D9—91no—
996D9—91no—
997D9—181no—
998D9—181no—
999D9—541no—
1000D9D9×H(3,𝔽3)11yescharacteristic, complemented
1001D9D9⋊H(3,𝔽3)11yescharacteristic, direct product factor
1002C22×C3—811no—
1003C22×C3—2431no—
1004C22×C3—2431no—
1005C22×C3—2431no—
1006C22×C3—2431no—
1007C2×D3—271no—
1008C2×D3—271no—
1009C32—21no—
1010C32—21no—
1011C32—21no—
1012C32—21no—
1013C32—21no—
1014C32—31no—
1015C32—31no—
1016C32—31no—
1017C32—31no—
1018C32—31no—
1019C32—31no—
1020C32—31no—
1021C32—41no—
1022C32—41no—
1023C32—61no—
1024C32—61no—
1025C32—61no—
1026C32—61no—
1027C32—61no—
1028C32—61no—
1029C32—61no—
1030C32—61no—
1031C32—61no—
1032C32—61no—
1033C32—61no—
1034C32—61no—
1035C32—91no—
1036C32—121no—
1037C32—121no—
1038C32—121no—
1039C32—121no—
1040C32—121no—
1041C32—121no—
1042C32—121no—
1043C32—122no—
1044C32—121no—
1045C32—121no—
1046C32—121no—
1047C32—181no—
1048C32—181no—
1049C32—181no—
1050C32—361no—
1051C32—361no—
1052C32—361no—
1053C32—361no—
1054C32—361no—
1055C32—361no—
1056C32—361no—
1057C32—361no—
1058C32D9×AGL(1,ℤ/9)11yescharacteristic, complemented
1059C32C32×D3×D911yescharacteristic
1060C32D32×H(3,𝔽3)11yescharacteristic
1061C32C3×D3×AGL(1,ℤ/9)11yescharacteristic
1062C9—21no—
1063C9—21no—
1064C9—21no—
1065C9—21no—
1066C9—41no—
1067C9—41no—
1068C9—61no—
1069C9—61no—
1070C9—61no—
1071C9—61no—
1072C9—61no—
1073C9—61no—
1074C9—123no—
1075C9—121no—
1076C9—121no—
1077C9—121no—
1078C9—121no—
1079C9—121no—
1080C9—121no—
1081C9—361no—
1082C9—361no—
1083C9—361no—
1084C9—361no—
1085C9—361no—
1086C9—361no—
1087C9C2×D9×H(3,𝔽3)11yescharacteristic, complemented
1088C9C2×D9⋊H(3,𝔽3)11yescharacteristic, complemented
1089C2×C3—91no—
1090C2×C3—91no—
1091C2×C3—91no—
1092C2×C3—91no—
1093C2×C3—181no—
1094C2×C3—181no—
1095C2×C3—271no—
1096C2×C3—271no—
1097C2×C3—271no—
1098C2×C3—271no—
1099C2×C3—271no—
1100C2×C3—541no—
1101C2×C3—541no—
1102C2×C3—541no—
1103C2×C3—541no—
1104C2×C3—541no—
1105C2×C3—811no—
1106C2×C3—811no—
1107C2×C3—811no—
1108C2×C3—1621no—
1109C2×C3—2431no—
1110C2×C3—2431no—
1111C2×C3—2431no—
1112C2×C3—2431no—
1113D3—31no—
1114D3—31no—
1115D3—271no—
1116D3—271no—
1117D3—541no—
1118C22—811noSylow
1119C3—21no—
1120C3—21no—
1121C3—21no—
1122C3—31no—
1123C3—41no—
1124C3—61no—
1125C3—61no—
1126C3—91no—
1127C3—91no—
1128C3—121no—
1129C3—181no—
1130C3—361no—
1131C3—361no—
1132C3—361no—
1133C3C3×D9×AGL(1,ℤ/9)11yescharacteristic
1134C3D3×D9⋊H(3,𝔽3)11yescharacteristic
1135C3D3×D9×H(3,𝔽3)11yescharacteristic
1136C2—91no—
1137C2—91no—
1138C2—811no—
subgroupG/H
centerC3C3×D9×AGL(1,ℤ/9)
commutator, cosocleC3×C92C22×C32
Frattini, socleC33C32×D32
FittingC9×C9⋊H(3,𝔽3)C22
hypercenterC32D9×AGL(1,ℤ/9)
hypocenterC92C22×H(3,𝔽3)
LCSG ▷ C3×C92 ▷ C92
UCSC1 ◁ C3 ◁ C32

Complements

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

NH ≅ G/Ntype
3. D9×C9⋊H(3,𝔽3)C2semidirect
4. C9×D9⋊H(3,𝔽3)C2semidirect
5. #72243650C2semidirect
6. C3×D9×AGL(1,ℤ/9)C3semidirect
7. C3×D9×AGL(1,ℤ/9)C3semidirect
8. C3×D9×AGL(1,ℤ/9)C3semidirect
9. C32×D92C3semidirect
10. C9×C9⋊H(3,𝔽3)C22semidirect
14. C3×#92299C2×C3semidirect
15. C3×#92299C2×C3semidirect
16. C3×#92299C2×C3semidirect
17. C3×D9×3−1+2C2×C3semidirect
18. C3×D9×3−1+2C2×C3semidirect
19. C3×D9×3−1+2C2×C3semidirect
20. C3×C9×AGL(1,ℤ/9)C2×C3semidirect
21. C3×C9×AGL(1,ℤ/9)C2×C3semidirect
22. C3×C9×AGL(1,ℤ/9)C2×C3semidirect
26. C32×C9⋊D9C2×C3semidirect
27. C32×C9×D9C2×C3semidirect
28. C32×C9×D9C2×C3semidirect
55. C3×C9×3−1+2C22×C3semidirect
56. C3×C9×3−1+2C22×C3semidirect
57. C3×C9×3−1+2C22×C3semidirect
59. C32×C92C22×C3semidirect
114. D9⋊H(3,𝔽3)D9direct (N × H)
180. D92H(3,𝔽3)semidirect
200. C9⋊H(3,𝔽3)C2×D9semidirect
316. C3×AGL(1,ℤ/9)C3×D9semidirect
317. C3×AGL(1,ℤ/9)C3×D9semidirect
318. C3×AGL(1,ℤ/9)C3×D9semidirect
375. C32×D9C3×D9semidirect
376. C32×D9AGL(1,ℤ/9)semidirect
387. C9⋊D9C2×H(3,𝔽3)semidirect
401. C9×D9C2×H(3,𝔽3)semidirect
402. C9×D9C2×H(3,𝔽3)semidirect
454. C3×3−1+2C2×C3×D9semidirect
455. C3×3−1+2C2×C3×D9semidirect
456. C3×3−1+2C2×C3×D9semidirect
516. C32×C9C2×C3×D9semidirect
517. C32×C9C2×AGL(1,ℤ/9)semidirect
586. C92C22×H(3,𝔽3)semidirect
1000. D9D9×H(3,𝔽3)semidirect
1001. D9D9⋊H(3,𝔽3)direct (N × H)
1058. C32D9×AGL(1,ℤ/9)semidirect
1087. C9C2×D9×H(3,𝔽3)semidirect
1088. C9C2×D9⋊H(3,𝔽3)semidirect

Maximal subgroups

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

subgroupindex
D3×D9×H(3,𝔽3)3
D3×D9⋊H(3,𝔽3)3
D9×C9⋊H(3,𝔽3)2
C9×D9⋊H(3,𝔽3)2
#722436502
C3×D9×AGL(1,ℤ/9)3
C32×D923