Finite Group Databasebeta

← #13148270

Subgroups — #13148270

Order 1728.

1146 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6195C211yesmaximal, characteristic
2C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
3D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×#63439C211yesmaximal, characteristic, complemented
5D3×#3676C211yesmaximal, characteristic, complemented
6#11721274C211yesmaximal, characteristic, complemented
7#11721245C211yesmaximal, characteristic, complemented
8#11721030C212yesmaximal, complemented
9C4×#6195C212yesmaximal, complemented
10#11721014C212yesmaximal, complemented
11#11721013C212yesmaximal, complemented
12#10594182—31nomaximal
13#10589588—31nomaximal
14C23×C3⋊D9C2211yescharacteristic
15C23×D3×C9C2211yescharacteristic
16C2×C4×C3⋊D9C2212yescomplemented
17C22×C3×Dic9C2211yescharacteristic
18C2×C4×D3×C9C2212yescomplemented
19C2×#6195C418yescomplemented
20C2×#6195C2211yescharacteristic
21C2×#6195C2211yescharacteristic
22C2×#6195C2211yescharacteristic
23C2×#6195C2211yescharacteristic
24C2×D3×Dic9C2212yescomplemented
25C2×(C3⋊D9)⋊C4C2212yescomplemented
26C3×C9×C22⋊C4C2211yescharacteristic
27#88551C2211yescharacteristic
28#88536C2212yescomplemented
29C9×#217C2211yescharacteristic
30C3×#3676C2211yescharacteristic
31C9×(C2×D3)⋊C4C2212yescomplemented
32C3×Dic9⋊C4C2212yescomplemented
33C3×C4×Dic9C2212yescomplemented
34(C2×D3)⋊Dic9C2212yescomplemented
35#88445C2212yescomplemented
36Dic9⋊Dic3C2212yescomplemented
37Dic3×Dic9C2212yescomplemented
38C22×#626—31no—
39C22⋊C4×C3⋊D3—31no—
40C3×D3×C22⋊C4D311yescharacteristic
41C3×#877—31no—
42#63974—31no—
43D3×#217—31no—
44#63955—31no—
45#63904—32no—
46C4×#626—32no—
47#63881—32no—
48#63880—32no—
49C22×#611—31no—
50C2×C9×C22⋊C4—31no—
51C2×#3676—31no—
52C4×#611—32no—
53C4×#611—32no—
54#611⋊C4—32no—
55#611⋊C4—32no—
56C22⋊C4×D9—31no—
57C22⋊C4×D9—31no—
58C22⋊C4×D9—61no—
59#63439—31no—
60#63439D311yescharacteristic, complemented
61C23×C3×C9C2311yescharacteristic
62C22×C3⋊D9—42no—
63C22×C3⋊D9C2×C414yescomplemented
64C22×C3⋊D9C2311yescharacteristic
65C22×C3⋊D9C2311yescharacteristic
66C22×D3×C9—42no—
67C22×D3×C9C2×C414yescomplemented
68C22×D3×C9C2311yescharacteristic
69C22×D3×C9C2311yescharacteristic
70C2×C3×C4×C9C2312yes—
71C2×C3⋊Dic9C2312yes—
72C4×C3⋊D9—42no—
73C2×C9×Dic3C2312yes—
74C2×C3×Dic9C2×C414yescomplemented
75C2×C3×Dic9C2312yes—
76C2×C3×Dic9C2311yescharacteristic
77C2×C3×Dic9C2311yescharacteristic
78C4×D3×C9—42no—
79#6195C2×C414yescomplemented
80#6195C2×C414yescomplemented
81#6195C2×C414yescomplemented
82#6195C2×C414yescomplemented
83D3×Dic9—42no—
84(C3⋊D9)⋊C4—42no—
85#5521—91no—
86#5486—91no—
87C23×C3⋊D3—31no—
88C23×C3×D3C2×D311yescharacteristic
89C2×C4×C3⋊D3—32no—
90C22×C3×Dic3—31no—
91C2×C3×C4×D3C2×D312yes—
92C2×#626—38no—
93C2×#626—31no—
94C2×#626—31no—
95C2×#626—31no—
96C2×#626—31no—
97C2×#624—32no—
98C2×D3×Dic3—32no—
99C24×C9—31no—
100C23×D9—31no—
101C23×D9—61no—
102C32×C22⋊C4C2×D311yescharacteristic
103#3757—31no—
104#3752—32no—
105C3×#217—31no—
106C3×#217C2×D311yescharacteristic
107C3×(C2×D3)⋊C4C2×D312yes—
108C3×Dic3⋊C4—32no—
109C3×C4×Dic3—32no—
110Dic3⋊Dic3—32no—
111#3722—32no—
112(C2×D3)⋊Dic3—32no—
113Dic32—32no—
114C22×C4×C9—32no—
115C2×#611—38no—
116C2×#611—31no—
117C2×#611—31no—
118C2×#611—31no—
119C2×#611—31no—
120C22×Dic9—32no—
121C22×Dic9C2×D311yescharacteristic
122C2×C4×D9—32no—
123C2×C4×D9—32no—
124C2×C4×D9—62no—
125C9×C22⋊C4—21no—
126C9×C22⋊C4—31no—
127C9×C22⋊C4—32no—
128C9×C22⋊C4C2×D311yescharacteristic
129#3676—31no—
130#3676—32no—
131#3676—61no—
132#3676C2×D311yescharacteristic
133(C2×D9)⋊C4—32no—
134(C2×D9)⋊C4—32no—
135(C2×D9)⋊C4—62no—
136Dic9⋊C4—32no—
137Dic9⋊C4C2×D312yescomplemented
138C4×Dic9—32no—
139C4×Dic9C2×D312yescomplemented
140C22×C3×C9—22no—
141C22×C3×C9C22×C412yes—
142C22×C3×C9C2411yescharacteristic
143C2×C3⋊D9—22no—
144C2×C3⋊D9—22no—
145C2×C3⋊D9—44no—
146C2×C3⋊D9C22×C412yes—
147C2×C3⋊D9C22×C412yes—
148C2×D3×C9—22no—
149C2×D3×C9—22no—
150C2×D3×C9—44no—
151C2×D3×C9C22×C412yes—
152C2×D3×C9C22×C412yes—
153C3×C4×C9—22no—
154C3⋊Dic9—22no—
155C9×Dic3—22no—
156C3×Dic9—22no—
157C3×Dic9C22×C412yes—
158C3×Dic9C22×C412yes—
159C22×#67—91no—
160C22×D12—91no—
161C3×#117—91no—
162C2×C3×C22⋊C4—31no—
163C2×#217—91no—
164C4×#67—92no—
165C4×#67—92no—
166#926—91no—
167#893—92no—
168#893—92no—
169#67⋊C4—92no—
170#67⋊C4—92no—
171D3×C22⋊C4—91no—
172D3×C22⋊C4—91no—
173D3×C22⋊C4—91no—
174D3×C22⋊C4—91no—
175D3×C22⋊C4—91no—
176D3×C22⋊C4—181no—
177D3×C22⋊C4D911yescharacteristic, complemented
178#877—31no—
179#877—91no—
180C4×D12—92no—
181C4×D12—92no—
182C23×C32C22×D311yescharacteristic
183C22×C3⋊D3—31no—
184C22×C3⋊D3—31no—
185C22×C3⋊D3—34no—
186C22×C3⋊D3—122no—
187C22×C3×D3—42no—
188C22×C3×D3C4×D314yes—
189C22×C3×D3C22×D311yescharacteristic
190C22×C3×D3C22×D311yescharacteristic
191C2×C32×C4C22×D312yes—
192C2×C3⋊Dic3—32no—
193C4×C3⋊D3—122no—
194C2×C3×Dic3—34no—
195C2×C3×Dic3—31no—
196C2×C3×Dic3—31no—
197C2×C3×Dic3—32no—
198C2×C3×Dic3C22×D312yes—
199C3×C4×D3—42no—
200#626—34no—
201#626—34no—
202#626—34no—
203#626—34no—
204#624—122no—
205D3×Dic3—122no—
206C23×C9—21no—
207C23×C9—31no—
208C23×C9—31no—
209C23×C9—34no—
210C23×C9—122no—
211C23×C9C22×D311yescharacteristic
212C22×D9—31no—
213C22×D9—31no—
214C22×D9—34no—
215C22×D9—61no—
216C22×D9—61no—
217C22×D9—64no—
218C22×D9—122no—
219C22×D9—124no—
220C2×C4×C9—22no—
221C2×C4×C9—32no—
222C2×C4×C9—122no—
223C2×C4×C9C22×D312yes—
224#611—34no—
225#611—34no—
226#611—34no—
227#611—34no—
228C2×Dic9—32no—
229C2×Dic9—62no—
230C2×Dic9—122no—
231C2×Dic9C4×D314yescomplemented
232C2×Dic9C22×D312yes—
233C2×Dic9C22×D311yescharacteristic
234C2×Dic9C22×D311yescharacteristic
235C4×D9—122no—
236C4×D9—122no—
237C4×D9—124no—
238#518—271noSylow
239C2×C3×C9—22no—
240C2×C3×C9C23×C411yescharacteristic
241C2×C3×C9H(5,𝔽2)12yes—
242C3⋊D9—22no—
243C3⋊D9—22no—
244D3×C9—22no—
245D3×C9—22no—
246C24×C3—31no—
247C23×D3—91no—
248C23×D3—91no—
249C23×D3—181no—
250C23×D3C2×D911yescharacteristic
251C22×C3×C4—32no—
252C22×C3×C4—91no—
253C2×#67—91no—
254C2×#67—91no—
255C2×#67—91no—
256C2×#67—91no—
257C2×#67—98no—
258C22×Dic3—31no—
259C22×Dic3—92no—
260C2×D12—98no—
261C2×D12—91no—
262C2×D12—91no—
263C2×D12—91no—
264C2×D12—91no—
265C2×C4×D3—92no—
266C2×C4×D3—92no—
267C2×C4×D3—92no—
268C2×C4×D3—92no—
269C2×C4×D3—92no—
270C2×C4×D3—182no—
271C2×C4×D3C2×D912yescomplemented
272C3×C4⋊C4—92no—
273C3×C22⋊C4—21no—
274C3×C22⋊C4—31no—
275C3×C22⋊C4—32no—
276C3×C22⋊C4—91no—
277C3×C22⋊C4C2×D911yescharacteristic
278C3×C22⋊C4D3211yescharacteristic
279C3×C42—92no—
280#217—31no—
281#217—92no—
282#217—91no—
283#217—91no—
284#217—181no—
285#217C2×D911yescharacteristic
286(C2×D3)⋊C4—92no—
287(C2×D3)⋊C4—92no—
288(C2×D3)⋊C4—92no—
289(C2×D3)⋊C4—92no—
290(C2×D3)⋊C4—92no—
291(C2×D3)⋊C4—182no—
292(C2×D3)⋊C4C2×D912yescomplemented
293C4⋊Dic3—92no—
294Dic3⋊C4—32no—
295Dic3⋊C4—92no—
296C4×Dic3—32no—
297C4×Dic3—92no—
298C4×Dic3—92no—
299C22×C32—22no—
300C22×C32C2×C4×D312yes—
301C22×C32C23×D311yescharacteristic
302C2×C3⋊D3—32no—
303C2×C3⋊D3—32no—
304C2×C3⋊D3—62no—
305C2×C3⋊D3—62no—
306C2×C3⋊D3—124no—
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3—44no—
310C2×C3×D3C2×C4×D312yes—
311C2×C3×D3C2×C4×D312yes—
312C32×C4—22no—
313C3⋊Dic3—62no—
314C3×Dic3—22no—
315C3×Dic3—32no—
316C3×Dic3—32no—
317C3×Dic3—62no—
318C22×C9—22no—
319C22×C9—21no—
320C22×C9—22no—
321C22×C9—32no—
322C22×C9—32no—
323C22×C9—42no—
324C22×C9—62no—
325C22×C9—62no—
326C22×C9—124no—
327C22×C9C2×C4×D312yes—
328C22×C9C23×D311yescharacteristic
329C2×D9—32no—
330C2×D9—32no—
331C2×D9—62no—
332C2×D9—62no—
333C2×D9—64no—
334C2×D9—62no—
335C2×D9—62no—
336C2×D9—122no—
337C2×D9—124no—
338C2×D9—128no—
339C4×C9—22no—
340C4×C9—42no—
341C4×C9—62no—
342Dic9—22no—
343Dic9—62no—
344Dic9—122no—
345Dic9C2×C4×D312yes—
346Dic9C2×C4×D312yes—
347C22×D4—271no—
348C4×D4—272no—
349C4×D4—272no—
350C4×D4—272no—
351C4×D4—272no—
352#117—91no—
353#117—271no—
354C2×C22⋊C4—31no—
355C2×C22⋊C4—271no—
356C2×C22⋊C4—271no—
357C2×C22⋊C4—271no—
358C3×C9#51811yescharacteristic, complemented, Sylow
359C23×C3—21no—
360C23×C3—31no—
361C23×C3—31no—
362C23×C3—34no—
363C23×C3—122no—
364C23×C3C22×D911yescharacteristic
365C23×C3C2×D3211yescharacteristic
366C22×D3—42no—
367C22×D3—91no—
368C22×D3—91no—
369C22×D3—91no—
370C22×D3—91no—
371C22×D3—94no—
372C22×D3—94no—
373C22×D3—181no—
374C22×D3—181no—
375C22×D3—184no—
376C22×D3—362no—
377C22×D3—362no—
378C22×D3—364no—
379C22×D3C4×D914yescomplemented
380C22×D3C22×D911yescharacteristic
381C22×D3C22×D911yescharacteristic
382C2×C3×C4—22no—
383C2×C3×C4—32no—
384C2×C3×C4—94no—
385C2×C3×C4—91no—
386C2×C3×C4—91no—
387C2×C3×C4—92no—
388C2×C3×C4—122no—
389C2×C3×C4C22×D912yes—
390C2×C3×C4C2×D3212yes—
391#67—94no—
392#67—94no—
393#67—94no—
394#67—94no—
395C2×Dic3—31no—
396C2×Dic3—31no—
397C2×Dic3—34no—
398C2×Dic3—32no—
399C2×Dic3—92no—
400C2×Dic3—92no—
401C2×Dic3—182no—
402C2×Dic3—362no—
403C2×Dic3C22×D912yes—
404D12—94no—
405D12—94no—
406D12—94no—
407D12—94no—
408C4×D3—42no—
409C4×D3—362no—
410C4×D3—362no—
411C4×D3—362no—
412C4×D3—362no—
413C4×D3—362no—
414C4×D3—364no—
415C2×C32—22no—
416C2×C32C22×C4×D311yescharacteristic
417C2×C32#100412yes—
418C3⋊D3—62no—
419C3⋊D3—62no—
420C3×D3—22no—
421C3×D3—22no—
422C2×C9—22no—
423C2×C9—21no—
424C2×C9—22no—
425C2×C9—42no—
426C2×C9—62no—
427C2×C9—62no—
428C2×C9C22×C4×D311yescharacteristic
429C2×C9#100912yes—
430D9—64no—
431D9—62no—
432D9—62no—
433D9—122no—
434C24—31no—
435C24—271no—
436C2×D4—271no—
437C2×D4—271no—
438C2×D4—271no—
439C2×D4—271no—
440C2×D4—278no—
441C22×C4—32no—
442C22×C4—91no—
443C22×C4—272no—
444C22×C4—272no—
445C22×C4—272no—
446C4⋊C4—92no—
447C4⋊C4—272no—
448C22⋊C4—31no—
449C22⋊C4—32no—
450C22⋊C4—91no—
451C22⋊C4—272no—
452C22⋊C4—272no—
453C22⋊C4—271no—
454C22⋊C4—272no—
455C22⋊C4D3×D911yescharacteristic
456C42—92no—
457C42—272no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—32no—
463C22×C3—32no—
464C22×C3—42no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—124no—
468C22×C3C2×C4×D912yes—
469C22×C3C23×D911yescharacteristic
470C22×C3C4×D3212yes—
471C22×C3C22×D3211yescharacteristic
472C2×D3—22no—
473C2×D3—22no—
474C2×D3—44no—
475C2×D3—92no—
476C2×D3—92no—
477C2×D3—92no—
478C2×D3—92no—
479C2×D3—182no—
480C2×D3—182no—
481C2×D3—184no—
482C2×D3—182no—
483C2×D3—182no—
484C2×D3—182no—
485C2×D3—182no—
486C2×D3—362no—
487C2×D3—364no—
488C2×D3—364no—
489C2×D3—368no—
490C2×D3C2×C4×D912yes—
491C2×D3C2×C4×D912yes—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—42no—
495C3×C4—62no—
496C3×C4—92no—
497C3×C4—92no—
498C3×C4—182no—
499Dic3—22no—
500Dic3—32no—
501Dic3—32no—
502Dic3—62no—
503Dic3—182no—
504Dic3—182no—
505Dic3—362no—
506C32#548611yescharacteristic
507C9—21no—
508C9#552111yescharacteristic, complemented
509C23—31no—
510C23—31no—
511C23—34no—
512C23—122no—
513C23—271no—
514C23—271no—
515C23—274no—
516C23—1082no—
517C23C2×D3×D911yescharacteristic
518D4—274no—
519D4—274no—
520D4—274no—
521D4—274no—
522C2×C4—32no—
523C2×C4—91no—
524C2×C4—91no—
525C2×C4—94no—
526C2×C4—92no—
527C2×C4—122no—
528C2×C4—272no—
529C2×C4—1082no—
530C2×C4—1082no—
531C2×C4—1082no—
532C2×C4C2×D3×D912yes—
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—42no—
538C2×C3—62no—
539C2×C3—62no—
540C2×C3C22×C4×D911yescharacteristic
541C2×C3#6371012yes—
542C2×C3C2×C4×D3211yescharacteristic
543C2×C3#6431412yes—
544D3—22no—
545D3—22no—
546D3—184no—
547D3—182no—
548D3—182no—
549D3—182no—
550D3—182no—
551D3—362no—
552C22—22no—
553C22—32no—
554C22—32no—
555C22—62no—
556C22—62no—
557C22—124no—
558C22—272no—
559C22—272no—
560C22—542no—
561C22—542no—
562C22—1084no—
563C22C4×D3×D912yes—
564C22C22×D3×D911yescharacteristic
565C4—22no—
566C4—62no—
567C4—92no—
568C4—92no—
569C4—182no—
570C4—542no—
571C3—21no—
572C3#1058958811yescharacteristic, complemented
573C3#1059418211yescharacteristic
574C2—22no—
575C2—62no—
576C2—62no—
577C2—542no—
578C2—542no—
579C2C2×C4×D3×D911yescharacteristic
580C2#1172250012yes—
subgroupG/H
centerC22C22×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC22×#6195C2
cosocleC22×C3×C9C24
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#518
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C3⋊D9C2semidirect
3. D3×C9×C22⋊C4C2semidirect
4. C3×#63439C2semidirect
5. D3×#3676C2semidirect
6. #11721274C2semidirect
7. #11721245C2semidirect
8. #11721030C2semidirect
9. C4×#6195C2semidirect
10. #11721014C2semidirect
11. #11721013C2semidirect
16. C2×C4×C3⋊D9C22semidirect
18. C2×C4×D3×C9C22semidirect
19. C2×#6195C4semidirect
24. C2×D3×Dic9C22semidirect
25. C2×(C3⋊D9)⋊C4C22semidirect
28. #88536C22semidirect
31. C9×(C2×D3)⋊C4C22semidirect
32. C3×Dic9⋊C4C22semidirect
33. C3×C4×Dic9C22semidirect
34. (C2×D3)⋊Dic9C22semidirect
35. #88445C22semidirect
36. Dic9⋊Dic3C22semidirect
37. Dic3×Dic9C22semidirect
60. #63439D3semidirect
63. C22×C3⋊D9C2×C4semidirect
67. C22×D3×C9C2×C4semidirect
74. C2×C3×Dic9C2×C4semidirect
79. #6195C2×C4semidirect
80. #6195C2×C4semidirect
81. #6195C2×C4semidirect
82. #6195C2×C4semidirect
137. Dic9⋊C4C2×D3semidirect
139. C4×Dic9C2×D3semidirect
177. D3×C22⋊C4D9semidirect
231. C2×Dic9C4×D3semidirect
271. C2×C4×D3C2×D9semidirect
292. (C2×D3)⋊C4C2×D9semidirect
358. C3×C9#518semidirect
379. C22×D3C4×D9semidirect
508. C9#5521semidirect
572. C3#10589588semidirect

Maximal subgroups

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

subgroupindex
C22×#61952
C22⋊C4×C3⋊D92
D3×C9×C22⋊C42
C3×#634392
D3×#36762
#117212742
#117212452
#117210302
C4×#61952
#117210142
#117210132
#105941823
#105895883