Finite Group Databasebeta

← C9×#4675 #13141330

Subgroups — C9×#4675 #13141330

Order 1728.

586 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C3×C9×#95C211yesmaximal, characteristic, complemented
6C9×C3⋊#95C211yesmaximal, characteristic, complemented
7C9×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4675C311yesmaximal, characteristic
9C9×#397—31nomaximal
10C23×D3×C9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3×C4×C9C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C9×Dic3C2211yescharacteristic
16C22×C9×Dic3C2211yescharacteristic
17C9×(C2×D3)⋊C4—22no—
18C9×(C2×D3)⋊C4—22no—
19C9×(C2×D3)⋊C4—22no—
20C9×Dic3⋊C4—22no—
21C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
22C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
23C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
24C2×C3×Dic3⋊C4C2×C311yescharacteristic
25C32×#95C2×C311yescharacteristic
26C3×C3⋊#95C2×C311yescharacteristic
27C3×C3⋊#95C2×C311yescharacteristic
28C2×C9×C4⋊C4—31no—
29C2×C9×C22⋊C4—31no—
30C2×C9×C22⋊C4—31no—
31C2×C9×C22⋊C4—31no—
32C9×#95—21no—
33C9×#95—31no—
34C9×#95—31no—
35C9×#95D311yescharacteristic, complemented
36C23×C3×C9C2311yescharacteristic
37C22×D3×C9—21no—
38C22×D3×C9—21no—
39C22×D3×C9—21no—
40C22×D3×C9—21no—
41C22×D3×C9—21no—
42C22×D3×C9—21no—
43C22×D3×C9D412yes—
44C2×C3×C4×C9—21no—
45C2×C3×C4×C9—21no—
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×C9—21no—
52C2×C3×C4×C9—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×Dic3D412yes—
62C3×#397—31no—
63#4675C911yescharacteristic, direct product factor
64C23×C3×D3C22×C311yescharacteristic
65C22×C32×C4C22×C311yescharacteristic
66C22×C32×C4C22×C311yescharacteristic
67C22×C32×C4C22×C311yescharacteristic
68C22×C3×Dic3C22×C311yescharacteristic
69C22×C3×Dic3C22×C311yescharacteristic
70C22×C3×Dic3C22×C311yescharacteristic
71C24×C9—31no—
72C3×(C2×D3)⋊C4—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×(C2×D3)⋊C4—22no—
75C3×Dic3⋊C4—22no—
76C22×C4×C9—21no—
77C22×C4×C9—21no—
78C22×C4×C9—21no—
79C22×C4×C9—31no—
80C22×C4×C9—31no—
81C22×C4×C9—31no—
82C22×C4×C9C2×D311yescharacteristic
83C22×C4×C9C2×D311yescharacteristic
84C22×C4×C9C2×D311yescharacteristic
85C9×C4⋊C4—62no—
86C9×C22⋊C4—62no—
87C9×C22⋊C4—62no—
88C9×C22⋊C4—62no—
89C22×C3×C9C2×D411yescharacteristic
90C22×C3×C9C2×D411yescharacteristic
91C22×C3×C9#4111yescharacteristic
92C22×C3×C9#4111yescharacteristic
93C22×C3×C9#4111yescharacteristic
94C22×C3×C9#4111yescharacteristic
95C22×C3×C9#4111yescharacteristic
96C2×D3×C9—22no—
97C2×D3×C9—22no—
98C2×D3×C9—22no—
99C2×D3×C9—41no—
100C2×D3×C9—41no—
101C2×D3×C9—41no—
102C2×D3×C9—41no—
103C3×C4×C9—41no—
104C3×C4×C9—41no—
105C3×C4×C9—41no—
106C9×Dic3—22no—
107C9×Dic3—41no—
108C9×Dic3—41no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C22⋊C4—31no—
113C2×(C2×D3)⋊C4C2×C911yescharacteristic
114C2×(C2×D3)⋊C4C2×C911yescharacteristic
115C2×(C2×D3)⋊C4C2×C911yescharacteristic
116C2×Dic3⋊C4C2×C911yescharacteristic, complemented
117C3×#95—21no—
118C3×#95—31no—
119C3×#95—31no—
120C3×#95C2×C911yescharacteristic, complemented
121C3×#95C3×D311yescharacteristic
122C3⋊#95C2×C911yescharacteristic, complemented
123C3⋊#95C2×C911yescharacteristic, complemented
124C23×C32C23×C311yescharacteristic
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3C3×D412yes—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3C3×D412yes—
150C23×C9—21no—
151C23×C9—32no—
152C23×C9—61no—
153C23×C9—61no—
154C23×C9—61no—
155C23×C9—61no—
156C23×C9—61no—
157C23×C9—61no—
158C23×C9C22×D311yescharacteristic
159C2×C4×C9—22no—
160C2×C4×C9—22no—
161C2×C4×C9—22no—
162C2×C4×C9—21no—
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9—21no—
166C2×C4×C9—21no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—32no—
172C2×C4×C9—41no—
173C2×C4×C9—41no—
174C2×C4×C9—41no—
175C2×C4×C9—41no—
176C2×C4×C9—41no—
177C2×C4×C9—41no—
178C2×C4×C9—61no—
179C2×C4×C9—61no—
180C2×C4×C9—61no—
181C2×C4×C9—61no—
182C2×C4×C9—61no—
183C2×C4×C9—61no—
184C2×C4×C9—61no—
185C2×C4×C9—61no—
186#397—31noSylow
187C2×C3×C9#12111yescharacteristic
188C2×C3×C9#12311yescharacteristic
189C2×C3×C9#12311yescharacteristic
190C2×C3×C9#12311yescharacteristic
191C2×C3×C9#12411yescharacteristic
192C2×C3×C9#12611yescharacteristic
193C2×C3×C9#12611yescharacteristic
194D3×C9—42no—
195C24×C3—31no—
196C23×D3C22×C911yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4C22×C911yescharacteristic
204C22×C3×C4C22×C911yescharacteristic
205C22×C3×C4C22×C911yescharacteristic
206C22×C3×C4C2×C3×D311yescharacteristic
207C22×C3×C4C2×C3×D311yescharacteristic
208C22×C3×C4C2×C3×D311yescharacteristic
209C22×Dic3C22×C911yescharacteristic
210C22×Dic3C22×C911yescharacteristic
211C22×Dic3C22×C911yescharacteristic
212C3×C4⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C22⋊C4—62no—
216(C2×D3)⋊C4—22no—
217(C2×D3)⋊C4—22no—
218(C2×D3)⋊C4—22no—
219Dic3⋊C4—22no—
220C22×C32C2×C3×D411yescharacteristic
221C22×C32C2×C3×D411yescharacteristic
222C22×C32C3×#4111yescharacteristic
223C22×C32C3×#4111yescharacteristic
224C22×C32C3×#4111yescharacteristic
225C22×C32C3×#4111yescharacteristic
226C22×C32C3×#4111yescharacteristic
227C2×C3×D3—22no—
228C2×C3×D3—22no—
229C2×C3×D3—22no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—41no—
235C32×C4—41no—
236C32×C4—41no—
237C3×Dic3—22no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C22×C9—21no—
241C22×C9—21no—
242C22×C9—21no—
243C22×C9—21no—
244C22×C9—21no—
245C22×C9—21no—
246C22×C9—21no—
247C22×C9—62no—
248C22×C9—62no—
249C22×C9—62no—
250C22×C9—121no—
251C22×C9—121no—
252C22×C9—121no—
253C22×C9—121no—
254C22×C9#23511yescharacteristic
255C22×C9#23511yescharacteristic
256C22×C9#23511yescharacteristic
257C22×C9D3×D411yescharacteristic
258C22×C9D3×D411yescharacteristic
259C22×C9#23711yescharacteristic
260C22×C9#23911yescharacteristic
261C4×C9—42no—
262C4×C9—42no—
263C4×C9—42no—
264C4×C9—41no—
265C4×C9—41no—
266C4×C9—41no—
267C4×C9—62no—
268C4×C9—121no—
269C4×C9—121no—
270C2×C4⋊C4—31no—
271C2×C22⋊C4—31no—
272C2×C22⋊C4—31no—
273C2×C22⋊C4—31no—
274#95—31no—
275#95—31no—
276#95D3×C911yescharacteristic, complemented
277C3×C9#39711yescharacteristic, complemented, Sylow
278C23×C3—21no—
279C23×C3—32no—
280C23×C3—61no—
281C23×C3—61no—
282C23×C3—61no—
283C23×C3—61no—
284C23×C3—61no—
285C23×C3—61no—
286C23×C3C23×C911yescharacteristic
287C23×C3C22×C3×D311yescharacteristic
288C22×D3—21no—
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—21no—
292C22×D3—21no—
293C22×D3—21no—
294C22×D3D4×C912yes—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—32no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3D4×C912yes—
340C2×C32C3×#12111yescharacteristic
341C2×C32C3×#12311yescharacteristic
342C2×C32C3×#12311yescharacteristic
343C2×C32C3×#12311yescharacteristic
344C2×C32C3×#12411yescharacteristic
345C2×C32C3×#12611yescharacteristic
346C2×C32C3×#12611yescharacteristic
347C3×D3—42no—
348C2×C9—21no—
349C2×C9—21no—
350C2×C9—21no—
351C2×C9—21no—
352C2×C9—21no—
353C2×C9—21no—
354C2×C9—21no—
355C2×C9—122no—
356C2×C9#87611yescharacteristic
357C2×C9#88311yescharacteristic
358C2×C9#88411yescharacteristic
359C2×C9#88511yescharacteristic
360C2×C9#89411yescharacteristic
361C2×C9#89411yescharacteristic
362C2×C9#89811yescharacteristic
363C24—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4C2×D3×C911yescharacteristic
368C22×C4C2×D3×C911yescharacteristic
369C22×C4C2×D3×C911yescharacteristic
370C4⋊C4—62no—
371C22⋊C4—62no—
372C22⋊C4—62no—
373C22⋊C4—62no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—62no—
382C22×C3—62no—
383C22×C3—62no—
384C22×C3—121no—
385C22×C3—121no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3C2×D4×C911yescharacteristic
389C22×C3C2×D4×C911yescharacteristic
390C22×C3C9×#4111yescharacteristic
391C22×C3C9×#4111yescharacteristic
392C22×C3C9×#4111yescharacteristic
393C22×C3C9×#4111yescharacteristic
394C22×C3C9×#4111yescharacteristic
395C22×C3C3×#23511yescharacteristic
396C22×C3C3×#23511yescharacteristic
397C22×C3C3×#23511yescharacteristic
398C22×C3C3×D3×D411yescharacteristic
399C22×C3C3×D3×D411yescharacteristic
400C22×C3C3×#23711yescharacteristic
401C22×C3C3×#23911yescharacteristic
402C2×D3—22no—
403C2×D3—22no—
404C2×D3—22no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—41no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—62no—
419C3×C4—121no—
420C3×C4—121no—
421Dic3—22no—
422Dic3—41no—
423Dic3—41no—
424C32C3×#39711yescharacteristic
425C9—21no—
426C9#467511yescharacteristic, direct product factor
427C23—32no—
428C23—61no—
429C23—61no—
430C23—61no—
431C23—61no—
432C23—61no—
433C23—61no—
434C23C22×D3×C911yescharacteristic
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—32no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—122no—
461C2×C3C9×#12111yescharacteristic
462C2×C3C9×#12311yescharacteristic
463C2×C3C9×#12311yescharacteristic
464C2×C3C9×#12311yescharacteristic
465C2×C3C9×#12411yescharacteristic
466C2×C3C9×#12611yescharacteristic
467C2×C3C9×#12611yescharacteristic
468C2×C3C3×#87611yescharacteristic
469C2×C3C3×#88311yescharacteristic
470C2×C3C3×#88411yescharacteristic
471C2×C3C3×#88511yescharacteristic
472C2×C3C3×#89411yescharacteristic
473C2×C3C3×#89411yescharacteristic
474C2×C3C3×#89811yescharacteristic
475D3—42no—
476C22—62no—
477C22—62no—
478C22—62no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22—121no—
483C22C9×#23511yescharacteristic
484C22C9×#23511yescharacteristic
485C22C9×#23511yescharacteristic
486C22D3×D4×C911yescharacteristic
487C22D3×D4×C911yescharacteristic
488C22C9×#23711yescharacteristic
489C22C9×#23911yescharacteristic
490C4—41no—
491C4—41no—
492C4—41no—
493C4—62no—
494C4—121no—
495C4—121no—
496C3—21no—
497C3C9×#39711yescharacteristic, complemented
498C3C3×#467511yescharacteristic
499C2—122no—
500C2C9×#87611yescharacteristic
501C2C9×#88311yescharacteristic
502C2C9×#88411yescharacteristic
503C2C9×#88511yescharacteristic
504C2C9×#89411yescharacteristic
505C2C9×#89411yescharacteristic
506C2C9×#89811yescharacteristic
subgroupG/H
centerC23×C9C22×D3
commutatorC23×C3C23×C9
FrattiniC23×C3C22×C3×D3
FittingC3×C9×#95C2
socle, cosocleC23×C32C23×C3
prime radicalC23×C3×D3C22×C3
hypercenterC9×#95D3
hypocenterC3C9×#397
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C9 ◁ C9×#95

Complements

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

NH ≅ G/Ntype
4. C2×C9×Dic3⋊C4C2semidirect
5. C3×C9×#95C2semidirect
6. C9×C3⋊#95C2semidirect
7. C9×C3⋊#95C2semidirect
35. C9×#95D3semidirect
63. #4675C9direct (N × H)
116. C2×Dic3⋊C4C2×C9semidirect
120. C3×#95C2×C9semidirect
122. C3⋊#95C2×C9semidirect
123. C3⋊#95C2×C9semidirect
276. #95D3×C9semidirect
277. C3×C9#397semidirect
426. C9#4675direct (N × H)
497. C3C9×#397semidirect

Maximal subgroups

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

subgroupindex
C2×C9×(C2×D3)⋊C42
C2×C9×Dic3⋊C42
C3×C9×#952
C9×C3⋊#952
C3×#46753
C9×#3973