Finite Group Databasebeta

← D9×#935 #13150977

Subgroups — D9×#935 #13150977

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×D9C211yesmaximal, characteristic
2C22×Dic3×D9C211yesmaximal, characteristic, complemented
3#11721835C211yesmaximal, characteristic, complemented
4C9×#935C211yesmaximal, characteristic, complemented
5#11721269C212yesmaximal, complemented
6D9×#217C212yesmaximal, complemented
7D9×#217C211yesmaximal, characteristic, complemented
8#11721260C211yesmaximal, characteristic, complemented
9#11721259C211yesmaximal, characteristic, complemented
10#11720981C212yesmaximal, complemented
11D9×Dic3⋊C4C212yesmaximal, complemented
12D3×#935—31nomaximal
13D9×#123—31nomaximal
14C23×C3×D9C2211yescharacteristic
15C23×C3×D9C2211yescharacteristic
16C2×C3×D4×C9C2211yescharacteristic
17C22×C3⋊Dic9C2211yescharacteristic, complemented
18C2×C3×#611C2211yescharacteristic
19C2×C3×#611C2211yescharacteristic
20C22×C9×Dic3C2211yescharacteristic, complemented
21C3×D4×D9—24no—
22C2×C3×D36C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×Dic3×D9—24no—
25C2×Dic3×D9C2212yes—
26C2×Dic3×D9C2212yes—
27C2×Dic3×D9C2212yescomplemented
28#88551C2211yescharacteristic, complemented
29#88551C2212yescomplemented
30#88534C2212yescomplemented
31C9×#217C2211yescharacteristic, complemented
32C9×#217C2212yescomplemented
33C9×Dic3⋊C4C2212yescomplemented
34(C2×D9)⋊Dic3C2212yescomplemented
35(C2×D9)⋊Dic3C2212yescomplemented
36(C2×D9)⋊Dic3C2212yescomplemented
37Dic3⋊Dic9C2212yescomplemented
38#88442C2212yescomplemented
39C2×C3×D3×D4—31no—
40C22×D3×Dic3—31no—
41#64144—31no—
42C3×#935D311yescharacteristic
43#63969—32no—
44D3×#217—31no—
45D3×#217—32no—
46#63962—31no—
47#63961—31no—
48#63884—32no—
49D3×Dic3⋊C4—32no—
50C2×D4×D9D311yescharacteristic
51C22×C4×D9—31no—
52C9×#123—31no—
53#63497—31no—
54#63497—61no—
55#63491—31no—
56#63456—32no—
57C4⋊C4×D9—32no—
58#63448—31no—
59#63445—32no—
60C22⋊C4×D9—32no—
61C22⋊C4×D9—31no—
62C23×C3×C9C2311yescharacteristic
63C23×C3×C9C2311yescharacteristic
64C22×C3×D9—24no—
65C22×C3×D9—22no—
66C22×C3×D9—24no—
67C22×C3×D9D414yes—
68C22×C3×D9C2311yescharacteristic
69C22×C3×D9C2311yescharacteristic
70C22×C3×D9C2311yescharacteristic
71C3×D4×C9—22no—
72C2×C3×C4×C9C2311yescharacteristic
73C2×C3⋊Dic9—22no—
74C2×C3⋊Dic9C2312yes—
75C2×C3⋊Dic9C2312yes—
76C3×#611—22no—
77C3×#611—22no—
78C2×C9×Dic3—22no—
79C2×C9×Dic3C2312yes—
80C2×C9×Dic3C2312yes—
81C2×C3×Dic9C2311yescharacteristic
82C3×D36—22no—
83C3×C4×D9—22no—
84Dic3×D9—24no—
85Dic3×D9—24no—
86Dic3×D9—24no—
87C2×#935—91no—
88D3×#123—91no—
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C2×C32×D4C2×D311yescharacteristic
92C22×C3⋊Dic3—31no—
93C2×C3×#67—31no—
94C2×C3×#67—31no—
95C22×C3×Dic3C2×D311yescharacteristic
96C3×D3×D4—64no—
97C2×C3×D12—31no—
98C2×C3×C4×D3—31no—
99C2×D3×Dic3—32no—
100C2×D3×Dic3—32no—
101C2×D3×Dic3—32no—
102C2×D3×Dic3—64no—
103C23×D9C2×D311yescharacteristic
104C23×D9C2×D311yescharacteristic
105#3757—31no—
106#3757—32no—
107#3750—32no—
108C3×#217C2×D311yescharacteristic
109C3×#217C2×D312yes—
110C3×Dic3⋊C4C2×D312yes—
111#3724—32no—
112Dic3⋊Dic3—32no—
113(C2×D3)⋊Dic3—32no—
114(C2×D3)⋊Dic3—32no—
115(C2×D3)⋊Dic3—32no—
116C2×D4×C9—21no—
117C2×D4×C9C2×D311yescharacteristic
118C22×C4×C9—31no—
119C2×#611C2×D311yescharacteristic
120C2×#611C2×D311yescharacteristic
121C22×Dic9—31no—
122C22×Dic9—61no—
123D4×D9—24no—
124C2×D36C2×D311yescharacteristic
125C2×C4×D9—32no—
126C2×C4×D9—32no—
127C2×C4×D9—32no—
128C2×C4×D9—64no—
129C2×C4×D9C2×D311yescharacteristic
130C9×C4⋊C4—32no—
131C9×C22⋊C4—32no—
132C9×C22⋊C4—31no—
133#3676—31no—
134#3676—32no—
135#3676—61no—
136#3676—62no—
137(C2×D9)⋊C4—32no—
138(C2×D9)⋊C4—32no—
139(C2×D9)⋊C4—32no—
140C4⋊Dic9—32no—
141Dic9⋊C4—32no—
142Dic9⋊C4—32no—
143Dic9⋊C4—62no—
144C22×C3×C9—22no—
145C22×C3×C9—21no—
146C22×C3×C9—22no—
147C22×C3×C9C2×D412yes—
148C22×C3×C9C2411yescharacteristic
149C2×C3×D9—22no—
150C2×C3×D9—28no—
151C2×C3×D9—21no—
152C2×C3×D9—22no—
153C2×C3×D9—44no—
154C2×C3×D9C2×D412yes—
155C2×C3×D9C2×D412yes—
156C2×C3×D9#4114yes—
157C3×C4×C9—21no—
158C3⋊Dic9—22no—
159C3⋊Dic9—22no—
160C9×Dic3—22no—
161C9×Dic3—22no—
162C3×Dic9—21no—
163C22×C3×D4—91no—
164C23×Dic3—91no—
165C2×D3×D4—31no—
166C22×C4×D3—91no—
167C3×#123—31no—
168C2×#217—91no—
169C2×#217—92no—
170#935—91no—
171#935—91no—
172#935—91no—
173#935—91no—
174#935—92no—
175#935—92no—
176#935—181no—
177#935D911yescharacteristic, direct product factor
178#929—91no—
179C2×Dic3⋊C4—92no—
180#894—92no—
181D3×C4⋊C4—92no—
182#886—91no—
183#883—92no—
184D3×C22⋊C4—91no—
185D3×C22⋊C4—92no—
186C23×C32C22×D311yescharacteristic
187C23×C32C22×D311yescharacteristic
188C22×C3×D3—31no—
189C22×C3×D3—34no—
190C22×C3×D3—31no—
191C22×C3×D3—31no—
192C22×C3×D3—64no—
193C22×C3×D3—64no—
194C22×C3×D3—62no—
195C32×D4—22no—
196C2×C32×C4C22×D311yescharacteristic
197C2×C3⋊Dic3—32no—
198C2×C3⋊Dic3—32no—
199C2×C3⋊Dic3—62no—
200C3×#67—62no—
201C3×#67—62no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—31no—
204C2×C3×Dic3C22×D312yes—
205C2×C3×Dic3C22×D312yes—
206C3×D12—62no—
207C3×C4×D3—62no—
208D3×Dic3—64no—
209D3×Dic3—64no—
210D3×Dic3—64no—
211C23×C9—21no—
212C23×C9—21no—
213C23×C9C22×D311yescharacteristic
214C23×C9C22×D311yescharacteristic
215C22×D9—24no—
216C22×D9—24no—
217C22×D9—22no—
218C22×D9#6714yes—
219C22×D9C22×D311yescharacteristic
220C22×D9C22×D311yescharacteristic
221C22×D9C22×D311yescharacteristic
222D4×C9—22no—
223D4×C9—42no—
224C2×C4×C9—21no—
225C2×C4×C9—32no—
226C2×C4×C9—32no—
227C2×C4×C9—62no—
228C2×C4×C9C22×D311yescharacteristic
229#611—22no—
230#611—22no—
231C2×Dic9—32no—
232C2×Dic9—32no—
233C2×Dic9—62no—
234C2×Dic9—62no—
235C2×Dic9—62no—
236C2×Dic9—122no—
237C2×Dic9C22×D311yescharacteristic
238D36—22no—
239C4×D9—22no—
240C4×D9—64no—
241C4×D9—64no—
242C4×D9—64no—
243C2×#123—271noSylow
244C2×C3×C9—22no—
245C2×C3×C9—41no—
246C2×C3×C9C22×D411yescharacteristic
247C2×C3×C9C2×#4112yes—
248C3×D9—22no—
249C3×D9—41no—
250C3×D9#12314yescomplemented
251C24×C3—91no—
252C24×C3—91no—
253C23×D3—31no—
254C23×D3—31no—
255C2×C3×D4—21no—
256C2×C3×D4—91no—
257C2×C3×D4—91no—
258C2×C3×D4—91no—
259C2×C3×D4—184no—
260C2×C3×D4C2×D911yescharacteristic
261C2×C3×D4D3211yescharacteristic
262C22×C3×C4—31no—
263C22×C3×C4—91no—
264C2×#67—31no—
265C2×#67—31no—
266C22×Dic3—91no—
267C22×Dic3—91no—
268C22×Dic3—92no—
269C22×Dic3—92no—
270C22×Dic3—92no—
271C22×Dic3—181no—
272C22×Dic3—184no—
273C22×Dic3C2×D911yescharacteristic, complemented
274D3×D4—64no—
275C2×D12—31no—
276C2×C4×D3—31no—
277C2×C4×D3—92no—
278C2×C4×D3—92no—
279C2×C4×D3—92no—
280C2×C4×D3—184no—
281C3×C4⋊C4—32no—
282C3×C22⋊C4—32no—
283C3×C22⋊C4—31no—
284#217—91no—
285#217—92no—
286#217—92no—
287#217—91no—
288#217—92no—
289#217—92no—
290#217—92no—
291#217—181no—
292#217—182no—
293#217C2×D911yescharacteristic, complemented
294#217C2×D912yescomplemented
295(C2×D3)⋊C4—92no—
296(C2×D3)⋊C4—92no—
297(C2×D3)⋊C4—92no—
298C4⋊Dic3—92no—
299Dic3⋊C4—92no—
300Dic3⋊C4—92no—
301Dic3⋊C4—92no—
302Dic3⋊C4—92no—
303Dic3⋊C4—92no—
304Dic3⋊C4—182no—
305Dic3⋊C4C2×D912yescomplemented
306C22×C32—22no—
307C22×C32—21no—
308C22×C32—22no—
309C22×C32D3×D412yes—
310C22×C32C23×D311yescharacteristic
311C2×C3×D3—32no—
312C2×C3×D3—34no—
313C2×C3×D3—32no—
314C2×C3×D3—68no—
315C2×C3×D3—62no—
316C2×C3×D3—61no—
317C2×C3×D3—62no—
318C2×C3×D3—124no—
319C32×C4—21no—
320C3⋊Dic3—62no—
321C3⋊Dic3—62no—
322C3×Dic3—22no—
323C3×Dic3—22no—
324C3×Dic3—61no—
325C22×C9—22no—
326C22×C9—22no—
327C22×C9—21no—
328C22×C9—21no—
329C22×C9—22no—
330C22×C9—42no—
331C22×C9—41no—
332C22×C9—42no—
333C22×C9C2×#6712yes—
334C22×C9C23×D311yescharacteristic
335C2×D9—22no—
336C2×D9—28no—
337C2×D9—22no—
338C2×D9—21no—
339C2×D9—44no—
340C2×D9#23714yes—
341C2×D9C2×#6712yes—
342C2×D9C2×#6712yes—
343C4×C9—21no—
344C4×C9—41no—
345C4×C9—62no—
346C4×C9—62no—
347Dic9—21no—
348Dic9—62no—
349Dic9—62no—
350Dic9—122no—
351Dic9—122no—
352C22×D4—91no—
353C23×C4—271no—
354#123—31no—
355#123—272no—
356#123—271no—
357#123—272no—
358#123—271no—
359#123—271no—
360C2×C4⋊C4—272no—
361C2×C22⋊C4—271no—
362C2×C22⋊C4—272no—
363C3×C9C2×#12311yescharacteristic, complemented, Sylow
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—91no—
367C23×C3—94no—
368C23×C3—91no—
369C23×C3—91no—
370C23×C3—184no—
371C23×C3—182no—
372C23×C3—184no—
373C23×C3C22×D911yescharacteristic
374C23×C3C22×D911yescharacteristic
375C23×C3C2×D3211yescharacteristic
376C23×C3C2×D3211yescharacteristic
377C22×D3—31no—
378C22×D3—31no—
379C22×D3—34no—
380C22×D3—31no—
381C22×D3—64no—
382C22×D3—62no—
383C22×D3—64no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—42no—
387C3×D4—182no—
388C3×D4—182no—
389C3×D4—182no—
390C2×C3×C4—21no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—62no—
394C2×C3×C4—91no—
395C2×C3×C4—182no—
396C2×C3×C4C22×D911yescharacteristic
397C2×C3×C4C2×D3211yescharacteristic
398#67—62no—
399#67—62no—
400C2×Dic3—22no—
401C2×Dic3—31no—
402C2×Dic3—92no—
403C2×Dic3—92no—
404C2×Dic3—92no—
405C2×Dic3—92no—
406C2×Dic3—182no—
407C2×Dic3—182no—
408C2×Dic3—184no—
409C2×Dic3—184no—
410C2×Dic3—184no—
411C2×Dic3—182no—
412C2×Dic3—182no—
413C2×Dic3—362no—
414C2×Dic3C22×D912yes—
415C2×Dic3C22×D912yes—
416D12—62no—
417C4×D3—62no—
418C4×D3—184no—
419C4×D3—184no—
420C4×D3—184no—
421C2×C32—22no—
422C2×C32—41no—
423C2×C32C2×D3×D411yescharacteristic
424C2×C32D3×#4112yes—
425C3×D3—34no—
426C3×D3—62no—
427C3×D3—121no—
428C2×C9—22no—
429C2×C9—22no—
430C2×C9—21no—
431C2×C9—42no—
432C2×C9—41no—
433C2×C9—81no—
434C2×C9C2×#23712yes—
435C2×C9C22×#6711yescharacteristic
436D9—22no—
437D9—41no—
438D9#93514yesdirect product factor
439C24—91no—
440C24—91no—
441C2×D4—91no—
442C2×D4—91no—
443C2×D4—91no—
444C2×D4—184no—
445C2×D4D3×D911yescharacteristic
446C22×C4—31no—
447C22×C4—91no—
448C22×C4—272no—
449C22×C4—272no—
450C22×C4—272no—
451C22×C4—271no—
452C22×C4—544no—
453C4⋊C4—32no—
454C4⋊C4—272no—
455C4⋊C4—272no—
456C4⋊C4—272no—
457C22⋊C4—31no—
458C22⋊C4—32no—
459C22⋊C4—272no—
460C22⋊C4—272no—
461C22⋊C4—272no—
462C22⋊C4—271no—
463C22⋊C4—272no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—42no—
473C22×C3—41no—
474C22×C3—42no—
475C22×C3—92no—
476C22×C3—94no—
477C22×C3—92no—
478C22×C3—188no—
479C22×C3—182no—
480C22×C3—181no—
481C22×C3—182no—
482C22×C3—364no—
483C22×C3D4×D912yes—
484C22×C3C23×D911yescharacteristic
485C22×C3D3×#6712yes—
486C22×C3C22×D3211yescharacteristic
487C2×D3—34no—
488C2×D3—32no—
489C2×D3—32no—
490C2×D3—68no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—61no—
494C2×D3—124no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—41no—
498C3×C4—62no—
499C3×C4—62no—
500C3×C4—181no—
501Dic3—22no—
502Dic3—22no—
503Dic3—61no—
504Dic3—182no—
505Dic3—182no—
506Dic3—182no—
507Dic3—182no—
508Dic3—362no—
509Dic3—362no—
510C32D3×#12311yescharacteristic
511C9—21no—
512C9C2×#93511yescharacteristic, complemented
513C23—91no—
514C23—91no—
515C23—94no—
516C23—91no—
517C23—184no—
518C23—182no—
519C23—184no—
520C23C2×D3×D911yescharacteristic
521C23C2×D3×D911yescharacteristic
522D4—22no—
523D4—182no—
524D4—182no—
525D4—182no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—62no—
529C2×C4—91no—
530C2×C4—182no—
531C2×C4—272no—
532C2×C4—272no—
533C2×C4—544no—
534C2×C4—544no—
535C2×C4—544no—
536C2×C4—542no—
537C2×C4C2×D3×D911yescharacteristic
538C2×C3—22no—
539C2×C3—22no—
540C2×C3—22no—
541C2×C3—21no—
542C2×C3—42no—
543C2×C3—41no—
544C2×C3—41no—
545C2×C3—81no—
546C2×C3—94no—
547C2×C3—182no—
548C2×C3—361no—
549C2×C3C2×D4×D911yescharacteristic
550C2×C3#41×D912yes—
551C2×C3D3×#23712yes—
552C2×C3C2×D3×#6711yescharacteristic
553D3—34no—
554D3—62no—
555D3—121no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—94no—
560C22—92no—
561C22—92no—
562C22—188no—
563C22—182no—
564C22—182no—
565C22—181no—
566C22—364no—
567C22D9×#6712yes—
568C22C22×D3×D911yescharacteristic
569C4—21no—
570C4—62no—
571C4—62no—
572C4—181no—
573C4—542no—
574C4—542no—
575C3—21no—
576C3D9×#12311yescharacteristic, complemented
577C3D3×#93511yescharacteristic
578C2—22no—
579C2—41no—
580C2—94no—
581C2—182no—
582C2—361no—
583C2D9×#23712yes—
584C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
prime radicalC2×C3×D4×D9C2
hypercenterC2×D4D3×D9
hypocenterC3×C9C2×#123
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3×D9C2semidirect
3. #11721835C2semidirect
4. C9×#935C2semidirect
5. #11721269C2semidirect
6. D9×#217C2semidirect
7. D9×#217C2semidirect
8. #11721260C2semidirect
9. #11721259C2semidirect
10. #11720981C2semidirect
11. D9×Dic3⋊C4C2semidirect
17. C22×C3⋊Dic9C22semidirect
20. C22×C9×Dic3C22semidirect
27. C2×Dic3×D9C22semidirect
28. #88551C22semidirect
29. #88551C22semidirect
30. #88534C22semidirect
31. C9×#217C22semidirect
32. C9×#217C22semidirect
33. C9×Dic3⋊C4C22semidirect
34. (C2×D9)⋊Dic3C22semidirect
35. (C2×D9)⋊Dic3C22semidirect
36. (C2×D9)⋊Dic3C22semidirect
37. Dic3⋊Dic9C22semidirect
38. #88442C22semidirect
177. #935D9direct (N × H)
250. C3×D9#123semidirect
273. C22×Dic3C2×D9semidirect
293. #217C2×D9semidirect
294. #217C2×D9semidirect
305. Dic3⋊C4C2×D9semidirect
363. C3×C9C2×#123semidirect
438. D9#935direct (N × H)
512. C9C2×#935semidirect
576. C3D9×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×D92
C22×Dic3×D92
#117218352
C9×#9352
#117212692
D9×#2172
#117212602
#117212592
#117209812
D9×Dic3⋊C42
D3×#9353
D9×#1233