Finite Group Databasebeta

← C9×#4948 #13142474

Subgroups — C9×#4948 #13142474

Order 1728.

690 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C9×C22⋊C4C211yesmaximal, characteristic
2C2×C9×#217C211yesmaximal, characteristic
3C2×C9×#217C211yesmaximal, characteristic
4C2×C9×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C9×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4948C311yesmaximal, characteristic
9C9×#396—31nomaximal
10C24×C3×C9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C9×Dic3C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C9×Dic3C2211yescharacteristic
16C22×C9×Dic3C2211yescharacteristic
17C3×C9×C22⋊C4—22no—
18C9×#217—22no—
19C9×#217—22no—
20C9×C4⋊Dic3—22no—
21C9×Dic3⋊C4—22no—
22C9×Dic3⋊C4—22no—
23C2×C32×C22⋊C4C2×C311yescharacteristic
24C2×C3×#217C2×C311yescharacteristic
25C2×C3×#217C2×C311yescharacteristic
26C2×C3×C4⋊Dic3C2×C311yescharacteristic
27C2×C3×Dic3⋊C4C2×C311yescharacteristic
28C2×C3×Dic3⋊C4C2×C311yescharacteristic
29C3×C3⋊#95C2×C311yescharacteristic
30C2×C9×C4⋊C4—31no—
31C2×C9×C4⋊C4—31no—
32C2×C9×C4⋊C4—31no—
33C2×C9×C22⋊C4—21no—
34C2×C9×C22⋊C4—31no—
35C2×C9×C22⋊C4—31no—
36C2×C9×C22⋊C4D311yescharacteristic
37C9×#95—31no—
38C23×C3×C9—21no—
39C23×C3×C9—21no—
40C23×C3×C9—21no—
41C23×C3×C9—21no—
42C23×C3×C9—21no—
43C23×C3×C9—21no—
44C23×C3×C9Q812yes—
45C23×C3×C9C2311yescharacteristic
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9—21no—
48C2×C3×C4×C9—21no—
49C2×C3×C4×C9—21no—
50C2×C3×C4×C9—21no—
51C2×C3×C4×C9D412yes—
52C2×C9×Dic3—21no—
53C2×C9×Dic3—21no—
54C2×C9×Dic3—21no—
55C2×C9×Dic3—21no—
56C2×C9×Dic3—21no—
57C2×C9×Dic3—21no—
58C2×C9×Dic3—21no—
59C2×C9×Dic3—21no—
60C2×C9×Dic3—21no—
61C2×C9×Dic3—21no—
62C2×C9×Dic3D412yes—
63C2×C9×Dic3D412yes—
64C3×#396—31no—
65#4948C911yescharacteristic, direct product factor
66C24×C32C22×C311yescharacteristic
67C22×C32×C4C22×C311yescharacteristic
68C22×C32×C4C22×C311yescharacteristic
69C22×C3×Dic3C22×C311yescharacteristic
70C22×C3×Dic3C22×C311yescharacteristic
71C22×C3×Dic3C22×C311yescharacteristic
72C22×C3×Dic3C22×C311yescharacteristic
73C24×C9—21no—
74C24×C9C2×D311yescharacteristic
75C32×C22⋊C4—22no—
76C3×#217—22no—
77C3×#217—22no—
78C3×C4⋊Dic3—22no—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C22×C4×C9—21no—
82C22×C4×C9—21no—
83C22×C4×C9—31no—
84C22×C4×C9—31no—
85C22×C4×C9—31no—
86C22×C4×C9—31no—
87C22×C4×C9C2×D311yescharacteristic
88C22×C4×C9C2×D311yescharacteristic
89C9×C4⋊C4—62no—
90C9×C4⋊C4—62no—
91C9×C4⋊C4—62no—
92C9×C22⋊C4—24no—
93C9×C22⋊C4—22no—
94C9×C22⋊C4—62no—
95C9×C22⋊C4—62no—
96C22×C3×C9—22no—
97C22×C3×C9—22no—
98C22×C3×C9—22no—
99C22×C3×C9—41no—
100C22×C3×C9—41no—
101C22×C3×C9—41no—
102C22×C3×C9—41no—
103C22×C3×C9C2×D411yescharacteristic
104C22×C3×C9C2×D411yescharacteristic
105C22×C3×C9C2×D411yescharacteristic
106C22×C3×C9C2×Q811yescharacteristic
107C22×C3×C9#4111yescharacteristic
108C22×C3×C9#4111yescharacteristic
109C22×C3×C9#4111yescharacteristic
110C3×C4×C9—22no—
111C3×C4×C9—41no—
112C9×Dic3—22no—
113C9×Dic3—22no—
114C9×Dic3—41no—
115C9×Dic3—41no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—31no—
121C2×C3×C22⋊C4—31no—
122C2×C3×C22⋊C4C2×C911yescharacteristic
123C2×C3×C22⋊C4C3×D311yescharacteristic
124C2×#217C2×C911yescharacteristic
125C2×#217C2×C911yescharacteristic
126C2×C4⋊Dic3C2×C911yescharacteristic, complemented
127C2×Dic3⋊C4C2×C911yescharacteristic, complemented
128C2×Dic3⋊C4C2×C911yescharacteristic, complemented
129C3×#95—31no—
130C3⋊#95C2×C911yescharacteristic, complemented
131C23×C32—21no—
132C23×C32—21no—
133C23×C32—21no—
134C23×C32—21no—
135C23×C32—21no—
136C23×C32—21no—
137C23×C32C3×Q812yes—
138C23×C32C23×C311yescharacteristic
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4C3×D412yes—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3C3×D412yes—
156C2×C3×Dic3C3×D412yes—
157C23×C9—22no—
158C23×C9—22no—
159C23×C9—21no—
160C23×C9—21no—
161C23×C9—21no—
162C23×C9—21no—
163C23×C9—21no—
164C23×C9—21no—
165C23×C9—22no—
166C23×C9—21no—
167C23×C9—41no—
168C23×C9—41no—
169C23×C9—41no—
170C23×C9—41no—
171C23×C9Dic612yes—
172C23×C9C22×D311yescharacteristic
173C2×C4×C9—21no—
174C2×C4×C9—21no—
175C2×C4×C9—22no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—22no—
180C2×C4×C9—32no—
181C2×C4×C9—32no—
182C2×C4×C9—41no—
183C2×C4×C9—41no—
184C2×C4×C9—41no—
185C2×C4×C9—41no—
186C2×C4×C9—61no—
187C2×C4×C9—61no—
188C2×C4×C9—61no—
189C2×C4×C9—61no—
190C2×C4×C9—61no—
191C2×C4×C9—61no—
192C2×C4×C9—61no—
193C2×C4×C9—61no—
194C2×C4×C9—61no—
195C2×C4×C9—61no—
196C2×C4×C9#6712yes—
197#396—31noSylow
198C2×C3×C9—42no—
199C2×C3×C9#12111yescharacteristic
200C2×C3×C9#12111yescharacteristic
201C2×C3×C9#12111yescharacteristic
202C2×C3×C9C22⋊Q811yescharacteristic
203C2×C3×C9C22⋊Q811yescharacteristic
204C2×C3×C9C22⋊Q811yescharacteristic
205C2×C3×C9#12611yescharacteristic
206C24×C3—21no—
207C24×C3C22×C911yescharacteristic
208C24×C3C2×C3×D311yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4C22×C911yescharacteristic
216C22×C3×C4C22×C911yescharacteristic
217C22×C3×C4C2×C3×D311yescharacteristic
218C22×C3×C4C2×C3×D311yescharacteristic
219C22×Dic3C22×C911yescharacteristic
220C22×Dic3C22×C911yescharacteristic
221C22×Dic3C22×C911yescharacteristic
222C22×Dic3C22×C911yescharacteristic
223C3×C4⋊C4—62no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—62no—
226C3×C22⋊C4—24no—
227C3×C22⋊C4—22no—
228C3×C22⋊C4—22no—
229C3×C22⋊C4—62no—
230C3×C22⋊C4—62no—
231#217—22no—
232#217—22no—
233C4⋊Dic3—22no—
234Dic3⋊C4—22no—
235Dic3⋊C4—22no—
236C22×C32—22no—
237C22×C32—22no—
238C22×C32—22no—
239C22×C32—41no—
240C22×C32—41no—
241C22×C32—41no—
242C22×C32—41no—
243C22×C32C2×C3×D411yescharacteristic
244C22×C32C2×C3×D411yescharacteristic
245C22×C32C2×C3×D411yescharacteristic
246C22×C32C2×C3×Q811yescharacteristic
247C22×C32C3×#4111yescharacteristic
248C22×C32C3×#4111yescharacteristic
249C22×C32C3×#4111yescharacteristic
250C32×C4—22no—
251C32×C4—41no—
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—41no—
255C3×Dic3—41no—
256C22×C9—24no—
257C22×C9—22no—
258C22×C9—22no—
259C22×C9—22no—
260C22×C9—21no—
261C22×C9—21no—
262C22×C9—21no—
263C22×C9—21no—
264C22×C9—21no—
265C22×C9—21no—
266C22×C9—21no—
267C22×C9—42no—
268C22×C9—42no—
269C22×C9—42no—
270C22×C9—42no—
271C22×C9—42no—
272C22×C9—42no—
273C22×C9—41no—
274C22×C9—41no—
275C22×C9—41no—
276C22×C9—41no—
277C22×C9C2×Dic611yescharacteristic
278C22×C9#23511yescharacteristic
279C22×C9D3×D411yescharacteristic
280C22×C9D3×D411yescharacteristic
281C22×C9#23711yescharacteristic
282C22×C9#23711yescharacteristic
283C22×C9C2×#6711yescharacteristic
284C4×C9—22no—
285C4×C9—42no—
286C4×C9—42no—
287C4×C9—41no—
288C4×C9—62no—
289C4×C9—62no—
290C4×C9—121no—
291C4×C9—121no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—31no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4D3×C911yescharacteristic
298#95—31no—
299C3×C9#39611yescharacteristic, complemented, Sylow
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—22no—
315C23×C3—21no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3Q8×C912yes—
321C23×C3C23×C911yescharacteristic
322C23×C3C3×Dic612yes—
323C23×C3C22×C3×D311yescharacteristic
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4D4×C912yes—
353C2×C3×C4C3×#6712yes—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3D4×C912yes—
365C2×Dic3D4×C912yes—
366C2×C32—42no—
367C2×C32C3×#12111yescharacteristic
368C2×C32C3×#12111yescharacteristic
369C2×C32C3×#12111yescharacteristic
370C2×C32C3×C22⋊Q811yescharacteristic
371C2×C32C3×C22⋊Q811yescharacteristic
372C2×C32C3×C22⋊Q811yescharacteristic
373C2×C32C3×#12611yescharacteristic
374C2×C9—21no—
375C2×C9—21no—
376C2×C9—21no—
377C2×C9—21no—
378C2×C9—21no—
379C2×C9—21no—
380C2×C9—21no—
381C2×C9—44no—
382C2×C9—42no—
383C2×C9#87811yescharacteristic
384C2×C9#87811yescharacteristic
385C2×C9#87911yescharacteristic
386C2×C9#88411yescharacteristic
387C2×C9#92411yescharacteristic
388C2×C9#93811yescharacteristic
389C2×C9#93911yescharacteristic
390C24C2×D3×C911yescharacteristic
391C22×C4—31no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—31no—
395C22×C4C2×D3×C911yescharacteristic
396C22×C4C2×D3×C911yescharacteristic
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C22⋊C4—22no—
401C22⋊C4—62no—
402C22⋊C4—62no—
403C22×C3—24no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3C2×D4×C911yescharacteristic
432C22×C3C2×D4×C911yescharacteristic
433C22×C3C2×D4×C911yescharacteristic
434C22×C3C2×Q8×C911yescharacteristic
435C22×C3C9×#4111yescharacteristic
436C22×C3C9×#4111yescharacteristic
437C22×C3C9×#4111yescharacteristic
438C22×C3C2×C3×Dic611yescharacteristic
439C22×C3C3×#23511yescharacteristic
440C22×C3C3×D3×D411yescharacteristic
441C22×C3C3×D3×D411yescharacteristic
442C22×C3C3×#23711yescharacteristic
443C22×C3C3×#23711yescharacteristic
444C22×C3C2×C3×#6711yescharacteristic
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—41no—
450C3×C4—41no—
451C3×C4—62no—
452C3×C4—62no—
453C3×C4—121no—
454C3×C4—121no—
455Dic3—22no—
456Dic3—22no—
457Dic3—41no—
458Dic3—41no—
459C32C3×#39611yescharacteristic
460C9—21no—
461C9#494811yescharacteristic, direct product factor
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23C9×Dic612yes—
469C23C22×D3×C911yescharacteristic
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4C9×#6712yes—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—44no—
496C2×C3—42no—
497C2×C3—42no—
498C2×C3C9×#12111yescharacteristic
499C2×C3C9×#12111yescharacteristic
500C2×C3C9×#12111yescharacteristic
501C2×C3C9×C22⋊Q811yescharacteristic
502C2×C3C9×C22⋊Q811yescharacteristic
503C2×C3C9×C22⋊Q811yescharacteristic
504C2×C3C9×#12611yescharacteristic
505C2×C3C3×#87811yescharacteristic
506C2×C3C3×#87811yescharacteristic
507C2×C3C3×#87911yescharacteristic
508C2×C3C3×#88411yescharacteristic
509C2×C3C3×#92411yescharacteristic
510C2×C3C3×#93811yescharacteristic
511C2×C3C3×#93911yescharacteristic
512C22—22no—
513C22—22no—
514C22—22no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22C2×C9×Dic611yescharacteristic
520C22C9×#23511yescharacteristic
521C22D3×D4×C911yescharacteristic
522C22D3×D4×C911yescharacteristic
523C22C9×#23711yescharacteristic
524C22C9×#23711yescharacteristic
525C22C2×C9×#6711yescharacteristic
526C4—22no—
527C4—41no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—121no—
532C3—21no—
533C3C9×#39611yescharacteristic, complemented
534C3C3×#494811yescharacteristic
535C2—42no—
536C2C9×#87811yescharacteristic
537C2C9×#87811yescharacteristic
538C2C9×#87911yescharacteristic
539C2C9×#88411yescharacteristic
540C2C9×#92411yescharacteristic
541C2C9×#93811yescharacteristic
542C2C9×#93911yescharacteristic
subgroupG/H
centerC23×C9C22×D3
commutatorC23×C3C23×C9
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C9×C22⋊C4C2
socle, cosocleC23×C32C23×C3
prime radicalC24×C32C22×C3
hypercenterC2×C9×C22⋊C4D3
hypocenterC3C9×#396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C9 ◁ C2×C9×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C9×C4⋊Dic3C2semidirect
5. C2×C9×Dic3⋊C4C2semidirect
6. C2×C9×Dic3⋊C4C2semidirect
7. C9×C3⋊#95C2semidirect
65. #4948C9direct (N × H)
126. C2×C4⋊Dic3C2×C9semidirect
127. C2×Dic3⋊C4C2×C9semidirect
128. C2×Dic3⋊C4C2×C9semidirect
130. C3⋊#95C2×C9semidirect
299. C3×C9#396semidirect
461. C9#4948direct (N × H)
533. C3C9×#396semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C9×C22⋊C42
C2×C9×#2172
C2×C9×C4⋊Dic32
C2×C9×Dic3⋊C42
C9×C3⋊#952
C3×#49483
C9×#3963