Finite Group Databasebeta

← C9×#4959 #13142487

Subgroups — C9×#4959 #13142487

Order 1728.

846 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×#67C211yesmaximal, characteristic
2C2×C3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C9×#217C211yesmaximal, characteristic, complemented
4C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C9×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4959C311yesmaximal, characteristic
9C9×#394—31nomaximal
10C24×C3×C9C2211yescharacteristic
11C23×D3×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3×C4×C9C2211yescharacteristic
14C2×C9×#67—22no—
15C2×C9×#67—22no—
16C2×C9×#67—22no—
17C22×C9×Dic3C2211yescharacteristic
18C22×C9×Dic3C2211yescharacteristic
19C22×C9×Dic3C2211yescharacteristic
20C3×C9×C22⋊C4—22no—
21C9×#217—22no—
22C9×(C2×D3)⋊C4—22no—
23C9×(C2×D3)⋊C4—22no—
24C9×Dic3⋊C4—22no—
25C22×C3×#67C2×C311yescharacteristic
26C2×C32×C22⋊C4C2×C311yescharacteristic
27C2×C3×#217C2×C311yescharacteristic
28C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
29C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
30C2×C3×Dic3⋊C4C2×C311yescharacteristic
31C22×D4×C9—31no—
32C3×C3⋊#95C2×C311yescharacteristic
33C2×C9×C4⋊C4—31no—
34C2×C9×C22⋊C4—21no—
35C2×C9×C22⋊C4—31no—
36C2×C9×C22⋊C4—31no—
37C2×C9×C22⋊C4—31no—
38C2×C9×C22⋊C4D311yescharacteristic, complemented
39C9×#95—31no—
40C23×C3×C9—21no—
41C23×C3×C9—21no—
42C23×C3×C9—21no—
43C23×C3×C9—21no—
44C23×C3×C9—21no—
45C23×C3×C9—21no—
46C23×C3×C9D412yes—
47C23×C3×C9C2311yescharacteristic
48C22×D3×C9—21no—
49C22×D3×C9—21no—
50C22×D3×C9—21no—
51C22×D3×C9—21no—
52C22×D3×C9—21no—
53C22×D3×C9—21no—
54C22×D3×C9D412yes—
55C2×C3×C4×C9—21no—
56C2×C3×C4×C9—21no—
57C2×C3×C4×C9—21no—
58C2×C3×C4×C9—21no—
59C2×C3×C4×C9—21no—
60C2×C3×C4×C9—21no—
61C9×#67—28no—
62C2×C9×Dic3—21no—
63C2×C9×Dic3—21no—
64C2×C9×Dic3—21no—
65C2×C9×Dic3—21no—
66C2×C9×Dic3—21no—
67C2×C9×Dic3—21no—
68C2×C9×Dic3—21no—
69C2×C9×Dic3D412yes—
70C2×C9×Dic3D412yescomplemented
71C3×#394—31no—
72#4959C911yescharacteristic, direct product factor
73C24×C32C22×C311yescharacteristic
74C23×C3×D3C22×C311yescharacteristic
75C22×C32×C4C22×C311yescharacteristic
76C22×C32×C4C22×C311yescharacteristic
77C2×C3×#67—22no—
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C22×C3×Dic3C22×C311yescharacteristic
81C22×C3×Dic3C22×C311yescharacteristic
82C22×C3×Dic3C22×C311yescharacteristic
83C24×C9—21no—
84C24×C9—31no—
85C24×C9C2×D311yescharacteristic
86C32×C22⋊C4—22no—
87C3×#217—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C2×D4×C9—62no—
92C2×D4×C9—62no—
93C2×D4×C9—62no—
94C22×C4×C9—21no—
95C22×C4×C9—21no—
96C22×C4×C9—31no—
97C22×C4×C9—31no—
98C22×C4×C9—31no—
99C22×C4×C9C2×D311yescharacteristic
100C22×C4×C9C2×D311yescharacteristic
101C9×C4⋊C4—62no—
102C9×C22⋊C4—24no—
103C9×C22⋊C4—22no—
104C9×C22⋊C4—62no—
105C9×C22⋊C4—62no—
106C9×C22⋊C4—62no—
107C22×C3×C9—22no—
108C22×C3×C9—22no—
109C22×C3×C9—22no—
110C22×C3×C9—41no—
111C22×C3×C9—41no—
112C22×C3×C9—41no—
113C22×C3×C9—41no—
114C22×C3×C9C2×D411yescharacteristic
115C22×C3×C9C2×D411yescharacteristic
116C22×C3×C9C2×D411yescharacteristic
117C22×C3×C9C2×D411yescharacteristic
118C22×C3×C9#4111yescharacteristic
119C22×C3×C9#4111yescharacteristic
120C22×C3×C9#4111yescharacteristic
121C2×D3×C9—22no—
122C2×D3×C9—22no—
123C2×D3×C9—22no—
124C2×D3×C9—41no—
125C2×D3×C9—41no—
126C2×D3×C9—41no—
127C2×D3×C9—41no—
128C3×C4×C9—41no—
129C3×C4×C9—41no—
130C9×Dic3—22no—
131C9×Dic3—22no—
132C9×Dic3—41no—
133C22×C3×D4—31no—
134C22×#67C2×C911yescharacteristic
135C2×C3×C4⋊C4—31no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4C2×C911yescharacteristic, complemented
141C2×C3×C22⋊C4C3×D311yescharacteristic
142C2×#217C2×C911yescharacteristic, complemented
143C2×(C2×D3)⋊C4C2×C911yescharacteristic, complemented
144C2×(C2×D3)⋊C4C2×C911yescharacteristic, complemented
145C2×Dic3⋊C4C2×C911yescharacteristic, complemented
146C3×#95—31no—
147C3⋊#95C2×C911yescharacteristic, complemented
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32C3×D412yes—
155C23×C32C23×C311yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3C3×D412yes—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C3×#67—28no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C3×D412yes—
178C2×C3×Dic3C3×D412yes—
179C23×C9—22no—
180C23×C9—22no—
181C23×C9—21no—
182C23×C9—21no—
183C23×C9—21no—
184C23×C9—21no—
185C23×C9—21no—
186C23×C9—21no—
187C23×C9—22no—
188C23×C9—21no—
189C23×C9—32no—
190C23×C9—41no—
191C23×C9—41no—
192C23×C9—41no—
193C23×C9—41no—
194C23×C9—61no—
195C23×C9—61no—
196C23×C9—61no—
197C23×C9—61no—
198C23×C9—61no—
199C23×C9—61no—
200C23×C9#6712yes—
201C23×C9C22×D311yescharacteristic
202D4×C9—68no—
203C2×C4×C9—22no—
204C2×C4×C9—22no—
205C2×C4×C9—21no—
206C2×C4×C9—21no—
207C2×C4×C9—21no—
208C2×C4×C9—21no—
209C2×C4×C9—21no—
210C2×C4×C9—21no—
211C2×C4×C9—32no—
212C2×C4×C9—32no—
213C2×C4×C9—41no—
214C2×C4×C9—41no—
215C2×C4×C9—41no—
216C2×C4×C9—41no—
217C2×C4×C9—61no—
218C2×C4×C9—61no—
219C2×C4×C9—61no—
220C2×C4×C9—61no—
221C2×C4×C9—61no—
222C2×C4×C9—61no—
223C2×C4×C9—61no—
224#394—31noSylow
225C2×C3×C9—42no—
226C2×C3×C9#12011yescharacteristic
227C2×C3×C9#12111yescharacteristic
228C2×C3×C9#12111yescharacteristic
229C2×C3×C9#12111yescharacteristic
230C2×C3×C9#12311yescharacteristic
231C2×C3×C9#12311yescharacteristic
232C2×C3×C9#12411yescharacteristic
233D3×C9—42no—
234C24×C3—21no—
235C24×C3—31no—
236C24×C3C22×C911yescharacteristic
237C24×C3C2×C3×D311yescharacteristic
238C23×D3C22×C911yescharacteristic
239C2×C3×D4—62no—
240C2×C3×D4—62no—
241C2×C3×D4—62no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4C22×C911yescharacteristic
248C22×C3×C4C22×C911yescharacteristic
249C22×C3×C4C2×C3×D311yescharacteristic
250C22×C3×C4C2×C3×D311yescharacteristic
251C2×#67—22no—
252C2×#67—22no—
253C2×#67—22no—
254C22×Dic3C22×C911yescharacteristic
255C22×Dic3C22×C911yescharacteristic
256C22×Dic3C22×C911yescharacteristic
257C3×C4⋊C4—62no—
258C3×C22⋊C4—24no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—62no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—62no—
264#217—22no—
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—22no—
267Dic3⋊C4—22no—
268C22×C32—22no—
269C22×C32—22no—
270C22×C32—22no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C2×C3×D411yescharacteristic
276C22×C32C2×C3×D411yescharacteristic
277C22×C32C2×C3×D411yescharacteristic
278C22×C32C2×C3×D411yescharacteristic
279C22×C32C3×#4111yescharacteristic
280C22×C32C3×#4111yescharacteristic
281C22×C32C3×#4111yescharacteristic
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—41no—
290C32×C4—41no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C22×C9—24no—
295C22×C9—22no—
296C22×C9—22no—
297C22×C9—22no—
298C22×C9—21no—
299C22×C9—21no—
300C22×C9—21no—
301C22×C9—21no—
302C22×C9—21no—
303C22×C9—21no—
304C22×C9—21no—
305C22×C9—42no—
306C22×C9—42no—
307C22×C9—42no—
308C22×C9—42no—
309C22×C9—42no—
310C22×C9—42no—
311C22×C9—41no—
312C22×C9—41no—
313C22×C9—41no—
314C22×C9—41no—
315C22×C9—62no—
316C22×C9—62no—
317C22×C9—62no—
318C22×C9—121no—
319C22×C9—121no—
320C22×C9—121no—
321C22×C9—121no—
322C22×C9#23511yescharacteristic
323C22×C9#23511yescharacteristic
324C22×C9D3×D411yescharacteristic
325C22×C9D3×D411yescharacteristic
326C22×C9D3×D411yescharacteristic
327C22×C9#23711yescharacteristic
328C22×C9C2×#6711yescharacteristic
329C4×C9—42no—
330C4×C9—42no—
331C4×C9—41no—
332C4×C9—41no—
333C4×C9—62no—
334C4×C9—62no—
335C4×C9—121no—
336C22×D4—31no—
337C2×C4⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—31no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4D3×C911yescharacteristic, complemented
342#95—31no—
343C3×C9#39411yescharacteristic, complemented, Sylow
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—32no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—61no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3D4×C912yes—
372C23×C3C23×C911yescharacteristic
373C23×C3C3×#6712yes—
374C23×C3C22×C3×D311yescharacteristic
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—21no—
380C22×D3—21no—
381C22×D3D4×C912yes—
382C3×D4—68no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410#67—28no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3D4×C912yes—
419C2×Dic3D4×C912yescomplemented
420C2×C32—42no—
421C2×C32C3×#12011yescharacteristic
422C2×C32C3×#12111yescharacteristic
423C2×C32C3×#12111yescharacteristic
424C2×C32C3×#12111yescharacteristic
425C2×C32C3×#12311yescharacteristic
426C2×C32C3×#12311yescharacteristic
427C2×C32C3×#12411yescharacteristic
428C3×D3—42no—
429C2×C9—21no—
430C2×C9—21no—
431C2×C9—21no—
432C2×C9—21no—
433C2×C9—21no—
434C2×C9—21no—
435C2×C9—21no—
436C2×C9—44no—
437C2×C9—42no—
438C2×C9—122no—
439C2×C9#88311yescharacteristic
440C2×C9#88411yescharacteristic
441C2×C9#88411yescharacteristic
442C2×C9#88511yescharacteristic
443C2×C9#92911yescharacteristic
444C2×C9#93711yescharacteristic
445C2×C9#93911yescharacteristic
446C24—31no—
447C24C2×D3×C911yescharacteristic
448C2×D4—62no—
449C2×D4—62no—
450C2×D4—62no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4C2×D3×C911yescharacteristic
455C22×C4C2×D3×C911yescharacteristic
456C4⋊C4—62no—
457C22⋊C4—22no—
458C22⋊C4—62no—
459C22⋊C4—62no—
460C22⋊C4—62no—
461C22×C3—24no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3—121no—
493C22×C3—121no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3C2×D4×C911yescharacteristic
497C22×C3C2×D4×C911yescharacteristic
498C22×C3C2×D4×C911yescharacteristic
499C22×C3C2×D4×C911yescharacteristic
500C22×C3C9×#4111yescharacteristic
501C22×C3C9×#4111yescharacteristic
502C22×C3C9×#4111yescharacteristic
503C22×C3C3×#23511yescharacteristic
504C22×C3C3×#23511yescharacteristic
505C22×C3C3×D3×D411yescharacteristic
506C22×C3C3×D3×D411yescharacteristic
507C22×C3C3×D3×D411yescharacteristic
508C22×C3C3×#23711yescharacteristic
509C22×C3C2×C3×#6711yescharacteristic
510C2×D3—22no—
511C2×D3—22no—
512C2×D3—22no—
513C2×D3—41no—
514C2×D3—41no—
515C2×D3—41no—
516C2×D3—41no—
517C3×C4—42no—
518C3×C4—42no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—41no—
522C3×C4—41no—
523C3×C4—62no—
524C3×C4—62no—
525C3×C4—121no—
526Dic3—22no—
527Dic3—22no—
528Dic3—41no—
529C32C3×#39411yescharacteristic
530C9—21no—
531C9#495911yescharacteristic, direct product factor
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—32no—
539C23—61no—
540C23—61no—
541C23—61no—
542C23—61no—
543C23—61no—
544C23—61no—
545C23C9×#6712yes—
546C23C22×D3×C911yescharacteristic
547D4—68no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—44no—
571C2×C3—42no—
572C2×C3—42no—
573C2×C3—122no—
574C2×C3C9×#12011yescharacteristic
575C2×C3C9×#12111yescharacteristic
576C2×C3C9×#12111yescharacteristic
577C2×C3C9×#12111yescharacteristic
578C2×C3C9×#12311yescharacteristic
579C2×C3C9×#12311yescharacteristic
580C2×C3C9×#12411yescharacteristic
581C2×C3C3×#88311yescharacteristic
582C2×C3C3×#88411yescharacteristic
583C2×C3C3×#88411yescharacteristic
584C2×C3C3×#88511yescharacteristic
585C2×C3C3×#92911yescharacteristic
586C2×C3C3×#93711yescharacteristic
587C2×C3C3×#93911yescharacteristic
588D3—42no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—62no—
597C22—62no—
598C22—62no—
599C22—121no—
600C22—121no—
601C22—121no—
602C22—121no—
603C22C9×#23511yescharacteristic
604C22C9×#23511yescharacteristic
605C22D3×D4×C911yescharacteristic
606C22D3×D4×C911yescharacteristic
607C22D3×D4×C911yescharacteristic
608C22C9×#23711yescharacteristic
609C22C2×C9×#6711yescharacteristic
610C4—41no—
611C4—41no—
612C4—62no—
613C4—62no—
614C4—121no—
615C3—21no—
616C3C9×#39411yescharacteristic, complemented
617C3C3×#495911yescharacteristic
618C2—42no—
619C2—122no—
620C2C9×#88311yescharacteristic
621C2C9×#88411yescharacteristic
622C2C9×#88411yescharacteristic
623C2C9×#88511yescharacteristic
624C2C9×#92911yescharacteristic
625C2C9×#93711yescharacteristic
626C2C9×#93911yescharacteristic
subgroupG/H
centerC23×C9C22×D3
commutatorC23×C3C23×C9
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C9×C22⋊C4C2
socle, cosocleC23×C32C23×C3
prime radicalC22×C3×#67C2×C3
hypercenterC2×C9×C22⋊C4D3
hypocenterC3C9×#394
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
2. C2×C3×C9×C22⋊C4C2semidirect
3. C2×C9×#217C2semidirect
4. C2×C9×(C2×D3)⋊C4C2semidirect
5. C2×C9×(C2×D3)⋊C4C2semidirect
6. C2×C9×Dic3⋊C4C2semidirect
7. C9×C3⋊#95C2semidirect
38. C2×C9×C22⋊C4D3semidirect
70. C2×C9×Dic3D4semidirect
72. #4959C9direct (N × H)
140. C2×C3×C22⋊C4C2×C9semidirect
142. C2×#217C2×C9semidirect
143. C2×(C2×D3)⋊C4C2×C9semidirect
144. C2×(C2×D3)⋊C4C2×C9semidirect
145. C2×Dic3⋊C4C2×C9semidirect
147. C3⋊#95C2×C9semidirect
341. C2×C22⋊C4D3×C9semidirect
343. C3×C9#394semidirect
419. C2×Dic3D4×C9semidirect
531. C9#4959direct (N × H)
616. C3C9×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C9×#672
C2×C3×C9×C22⋊C42
C2×C9×#2172
C2×C9×(C2×D3)⋊C42
C2×C9×Dic3⋊C42
C9×C3⋊#952
C3×#49593
C9×#3943