Finite Group Databasebeta

← #13150566

Subgroups — #13150566

Order 1728.

1262 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×#88668C211yesmaximal, characteristic
3C9×#929C211yesmaximal, characteristic, complemented
4C3×#63491C211yesmaximal, characteristic, complemented
5#11721274C211yesmaximal, characteristic, complemented
6#11721266C211yesmaximal, characteristic, complemented
7#11721260C211yesmaximal, characteristic, complemented
8#11721048C212yesmaximal, complemented
9#11720980C212yesmaximal, complemented
10#11720957C212yesmaximal, complemented
11#11720941C212yesmaximal, complemented
12#10595079—31nomaximal
13D9×#123—31nomaximal
14C23×C3⋊D9C2211yescharacteristic
15C22×D3×D9C2211yescharacteristic
16C22×C3×C4×C9C2211yescharacteristic, complemented
17C22×C3⋊Dic9C2211yescharacteristic, complemented
18C2×C4×C3⋊D9—24no—
19C2×C4×C3⋊D9C2212yes—
20C2×C4×C3⋊D9C2212yescomplemented
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23#88668—24no—
24C2×#6195C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2212yes—
28C9×#217C2211yescharacteristic, complemented
29C3×#3676C2211yescharacteristic, complemented
30C9×(C2×D3)⋊C4C2212yescomplemented
31C3×(C2×D9)⋊C4C2212yescomplemented
32C9×Dic3⋊C4C2212yescomplemented
33C3×Dic9⋊C4C2212yescomplemented
34(C2×D3)⋊Dic9C2212yescomplemented
35#88445C2212yescomplemented
36(C2×D9)⋊Dic3C2212yescomplemented
37Dic3⋊Dic9C2212yescomplemented
38Dic9⋊Dic3C2212yescomplemented
39C22×C4×C3⋊D3—31no—
40C2×#3811—31no—
41C3×#929—31no—
42C3×#929D311yescharacteristic
43#63974—31no—
44#63962—31no—
45#63962—31no—
46#63921—32no—
47#63883—32no—
48#63853—32no—
49#63853—32no—
50C2×D4×D9—31no—
51C22×C4×D9—31no—
52C22×C4×D9—61no—
53C9×#123—31no—
54#63497—31no—
55#63491D311yescharacteristic, complemented
56#63456—32no—
57C4⋊C4×D9—32no—
58#63448—31no—
59#63445—32no—
60C22⋊C4×D9—31no—
61C22⋊C4×D9—32no—
62C23×C3×C9C2311yescharacteristic
63C22×C3⋊D9—24no—
64C22×C3⋊D9D414yes—
65C22×C3⋊D9C2311yescharacteristic
66C22×C3⋊D9C2311yescharacteristic
67C22×D3×C9C2311yescharacteristic
68C22×C3×D9C2311yescharacteristic
69C2×D3×D9—22no—
70C2×D3×D9—24no—
71C2×C3×C4×C9—22no—
72C2×C3×C4×C9C2312yes—
73C2×C3⋊Dic9—22no—
74C2×C3⋊Dic9C2312yes—
75C4×C3⋊D9—24no—
76C4×C3⋊D9—24no—
77C9×#67—22no—
78C3×#611—22no—
79C2×C9×Dic3C2311yescharacteristic
80C2×C9×Dic3C2312yes—
81C2×C3×Dic9C2311yescharacteristic
82C2×C3×Dic9C2312yes—
83#6195—22no—
84#6192—22no—
85(C3⋊D9)⋊C4—22no—
86(C3⋊D9)⋊C4—24no—
87D3×#123—91no—
88D3×#123—91no—
89C23×C3⋊D3—31no—
90C22×D32—31no—
91C22×C32×C4C2×D311yescharacteristic
92C22×C3⋊Dic3—31no—
93C2×C4×C3⋊D3—32no—
94C2×C4×C3⋊D3—32no—
95C2×C4×C3⋊D3—64no—
96C2×C3×#67—31no—
97C2×C3×#67C2×D311yescharacteristic
98#3811—64no—
99C2×#626—31no—
100C2×#626—31no—
101C2×#624—31no—
102C2×#624—32no—
103C23×D9—31no—
104C23×D9—31no—
105C23×D9—61no—
106C3×#217—31no—
107C3×#217C2×D311yescharacteristic
108C3×(C2×D3)⋊C4—32no—
109C3×(C2×D3)⋊C4C2×D312yes—
110C3×Dic3⋊C4—32no—
111C3×Dic3⋊C4C2×D312yes—
112Dic3⋊Dic3—32no—
113Dic3⋊Dic3—32no—
114#3722—32no—
115(C2×D3)⋊Dic3—32no—
116(C2×D3)⋊Dic3—32no—
117C2×D4×C9—31no—
118C22×C4×C9—21no—
119C22×C4×C9C2×D311yescharacteristic, complemented
120C2×#611—31no—
121C2×#611C2×D311yescharacteristic
122C22×Dic9—31no—
123C22×Dic9—61no—
124D4×D9—64no—
125C2×D36—31no—
126C2×C4×D9—32no—
127C2×C4×D9—32no—
128C2×C4×D9—32no—
129C2×C4×D9—31no—
130C2×C4×D9—64no—
131C2×C4×D9—62no—
132C2×C4×D9—62no—
133C2×C4×D9—68no—
134C9×C4⋊C4—32no—
135C9×C22⋊C4—31no—
136C9×C22⋊C4—32no—
137#3676—32no—
138#3676C2×D311yescharacteristic, complemented
139(C2×D9)⋊C4—32no—
140(C2×D9)⋊C4—32no—
141(C2×D9)⋊C4C2×D312yescomplemented
142C4⋊Dic9—32no—
143Dic9⋊C4—32no—
144Dic9⋊C4C2×D312yescomplemented
145C22×C3×C9—22no—
146C22×C3×C9C2×D412yes—
147C22×C3×C9C2411yescharacteristic
148C2×C3⋊D9—22no—
149C2×C3⋊D9—28no—
150C2×C3⋊D9C2×D412yes—
151C2×C3⋊D9C2×D412yes—
152C2×C3⋊D9#4114yes—
153C2×D3×C9—21no—
154C2×D3×C9—22no—
155C2×C3×D9—21no—
156C2×C3×D9—22no—
157D3×D9—44no—
158C3×C4×C9—22no—
159C3⋊Dic9—22no—
160C9×Dic3—21no—
161C9×Dic3—22no—
162C3×Dic9—21no—
163C3×Dic9—22no—
164C2×D3×D4—91no—
165C2×D3×D4—91no—
166C22×C4×D3—91no—
167C22×C4×D3—91no—
168C22×C4×D3—181no—
169C3×#123—31no—
170C3×#123—91no—
171#935—91no—
172#935—91no—
173#929—31no—
174#929D911yescharacteristic, complemented
175#894—92no—
176#894—92no—
177D3×C4⋊C4—92no—
178D3×C4⋊C4—92no—
179#886—91no—
180#886—91no—
181#883—92no—
182#883—92no—
183D3×C22⋊C4—92no—
184D3×C22⋊C4—91no—
185D3×C22⋊C4—91no—
186D3×C22⋊C4—92no—
187C23×C32C22×D311yescharacteristic
188C22×C3⋊D3—31no—
189C22×C3⋊D3—34no—
190C22×C3⋊D3—31no—
191C22×C3⋊D3—64no—
192C22×C3×D3—31no—
193C22×C3×D3C22×D311yescharacteristic
194C2×D32—64no—
195C2×D32—62no—
196C2×C32×C4—22no—
197C2×C32×C4C22×D312yes—
198C2×C3⋊Dic3—32no—
199C2×C3⋊Dic3—62no—
200C4×C3⋊D3—64no—
201C4×C3⋊D3—64no—
202C3×#67—22no—
203C3×#67—62no—
204C2×C3×Dic3—32no—
205C2×C3×Dic3—31no—
206C2×C3×Dic3C22×D312yes—
207C2×C3×Dic3C22×D311yescharacteristic
208#626—62no—
209#626—62no—
210#624—64no—
211#624—62no—
212C23×C9—21no—
213C23×C9—31no—
214C23×C9C22×D311yescharacteristic
215C22×D9—31no—
216C22×D9—34no—
217C22×D9—31no—
218C22×D9—64no—
219C22×D9—61no—
220C22×D9—61no—
221C22×D9—62no—
222C22×D9—64no—
223C22×D9—64no—
224C22×D9—68no—
225C22×D9C22×D311yescharacteristic
226D4×C9—62no—
227C2×C4×C9—24no—
228C2×C4×C9—22no—
229C2×C4×C9—22no—
230C2×C4×C9—31no—
231C2×C4×C9—32no—
232C2×C4×C9C22×D312yes—
233#611—22no—
234#611—62no—
235C2×Dic9—32no—
236C2×Dic9—62no—
237C2×Dic9—64no—
238C2×Dic9—62no—
239C2×Dic9C22×D312yes—
240C2×Dic9C22×D311yescharacteristic
241D36—62no—
242C4×D9—64no—
243C4×D9—62no—
244C4×D9—64no—
245C4×D9—64no—
246C4×D9—68no—
247C4×D9—68no—
248C2×#123—271noSylow
249C2×C3×C9—22no—
250C2×C3×C9C22×D411yescharacteristic
251C2×C3×C9C2×#4112yes—
252C3⋊D9—22no—
253C3⋊D9#12314yescomplemented
254D3×C9—41no—
255C3×D9—41no—
256C23×D3—91no—
257C23×D3—91no—
258C23×D3—91no—
259C23×D3—91no—
260C23×D3—181no—
261C2×C3×D4—31no—
262C2×C3×D4—91no—
263C22×C3×C4—21no—
264C22×C3×C4C2×D911yescharacteristic, complemented
265C22×C3×C4D3211yescharacteristic
266C2×#67—31no—
267C2×#67—91no—
268C2×#67—91no—
269C2×#67C2×D911yescharacteristic
270C22×Dic3—91no—
271C22×Dic3—91no—
272C22×Dic3—181no—
273D3×D4—184no—
274D3×D4—184no—
275C2×D12—91no—
276C2×D12—91no—
277C2×C4×D3—92no—
278C2×C4×D3—91no—
279C2×C4×D3—92no—
280C2×C4×D3—92no—
281C2×C4×D3—92no—
282C2×C4×D3—92no—
283C2×C4×D3—92no—
284C2×C4×D3—91no—
285C2×C4×D3—182no—
286C2×C4×D3—182no—
287C2×C4×D3—184no—
288C2×C4×D3—184no—
289C2×C4×D3—188no—
290C3×C4⋊C4—32no—
291C3×C4⋊C4—92no—
292C3×C22⋊C4—31no—
293C3×C22⋊C4—32no—
294C3×C22⋊C4—91no—
295C3×C22⋊C4—92no—
296#217—31no—
297#217—92no—
298#217—92no—
299#217C2×D911yescharacteristic, complemented
300(C2×D3)⋊C4—32no—
301(C2×D3)⋊C4—92no—
302(C2×D3)⋊C4—92no—
303(C2×D3)⋊C4—92no—
304(C2×D3)⋊C4—92no—
305(C2×D3)⋊C4C2×D912yescomplemented
306C4⋊Dic3—92no—
307C4⋊Dic3—92no—
308Dic3⋊C4—32no—
309Dic3⋊C4—92no—
310Dic3⋊C4—92no—
311Dic3⋊C4C2×D912yescomplemented
312C22×C32—22no—
313C22×C32D3×D412yes—
314C22×C32C23×D311yescharacteristic
315C2×C3⋊D3—32no—
316C2×C3⋊D3—34no—
317C2×C3⋊D3—32no—
318C2×C3⋊D3—68no—
319C2×C3⋊D3—62no—
320C2×C3×D3—21no—
321C2×C3×D3—22no—
322C2×C3×D3—61no—
323C2×C3×D3—62no—
324D32—124no—
325C32×C4—22no—
326C3⋊Dic3—62no—
327C3×Dic3—21no—
328C3×Dic3—22no—
329C3×Dic3—61no—
330C3×Dic3—62no—
331C22×C9—24no—
332C22×C9—22no—
333C22×C9—21no—
334C22×C9—22no—
335C22×C9—61no—
336C22×C9—62no—
337C22×C9D3×D412yes—
338C22×C9C23×D311yescharacteristic
339C2×D9—21no—
340C2×D9—22no—
341C2×D9—32no—
342C2×D9—34no—
343C2×D9—32no—
344C2×D9—62no—
345C2×D9—62no—
346C2×D9—64no—
347C2×D9—68no—
348C2×D9—616no—
349C2×D9—64no—
350C2×D9—62no—
351C2×D9—124no—
352C4×C9—24no—
353C4×C9—22no—
354C4×C9—61no—
355C4×C9—62no—
356Dic9—21no—
357Dic9—22no—
358Dic9—64no—
359Dic9—62no—
360C22×D4—271no—
361C23×C4—271no—
362#123—31no—
363#123—91no—
364#123—272no—
365#123—271no—
366#123—272no—
367#123—271no—
368C2×C4⋊C4—272no—
369C2×C22⋊C4—271no—
370C2×C22⋊C4—272no—
371C3×C9C2×#12311yescharacteristic, complemented, Sylow
372C23×C3—21no—
373C23×C3—31no—
374C23×C3—91no—
375C23×C3C22×D911yescharacteristic
376C23×C3C2×D3211yescharacteristic
377C22×D3—31no—
378C22×D3—91no—
379C22×D3—91no—
380C22×D3—91no—
381C22×D3—94no—
382C22×D3—91no—
383C22×D3—94no—
384C22×D3—181no—
385C22×D3—181no—
386C22×D3—184no—
387C22×D3—182no—
388C22×D3—184no—
389C22×D3—182no—
390C22×D3—184no—
391C22×D3—184no—
392C22×D3—184no—
393C22×D3—188no—
394C22×D3C22×D911yescharacteristic
395C3×D4—62no—
396C3×D4—182no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—31no—
402C2×C3×C4—32no—
403C2×C3×C4—91no—
404C2×C3×C4—92no—
405C2×C3×C4C22×D912yes—
406C2×C3×C4C2×D3212yes—
407#67—22no—
408#67—62no—
409#67—182no—
410#67—182no—
411C2×Dic3—31no—
412C2×Dic3—32no—
413C2×Dic3—92no—
414C2×Dic3—92no—
415C2×Dic3—182no—
416C2×Dic3—184no—
417C2×Dic3—182no—
418C2×Dic3—182no—
419C2×Dic3C22×D912yes—
420C2×Dic3C22×D911yescharacteristic
421D12—182no—
422D12—182no—
423C4×D3—184no—
424C4×D3—182no—
425C4×D3—184no—
426C4×D3—182no—
427C4×D3—184no—
428C4×D3—184no—
429C4×D3—184no—
430C4×D3—184no—
431C4×D3—188no—
432C4×D3—188no—
433C2×C32—22no—
434C2×C32C2×D3×D411yescharacteristic
435C2×C32D3×#4112yes—
436C3⋊D3—34no—
437C3⋊D3—62no—
438C3×D3—41no—
439C3×D3—121no—
440C2×C9—24no—
441C2×C9—22no—
442C2×C9—22no—
443C2×C9—21no—
444C2×C9—121no—
445C2×C9C2×D3×D411yescharacteristic
446C2×C9D3×#4112yes—
447D9—34no—
448D9—41no—
449D9—64no—
450D9—64no—
451D9—62no—
452C24—271no—
453C24—271no—
454C2×D4—31no—
455C2×D4—91no—
456C2×D4—271no—
457C2×D4—271no—
458C2×D4—544no—
459C22×C4—272no—
460C22×C4—271no—
461C22×C4—271no—
462C22×C4—272no—
463C22×C4—272no—
464C22×C4—544no—
465C22×C4D3×D911yescharacteristic, complemented
466C4⋊C4—32no—
467C4⋊C4—92no—
468C4⋊C4—272no—
469C4⋊C4—272no—
470C22⋊C4—31no—
471C22⋊C4—32no—
472C22⋊C4—91no—
473C22⋊C4—92no—
474C22⋊C4—272no—
475C22⋊C4—272no—
476C22⋊C4—272no—
477C22×C3—24no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—62no—
483C22×C3—61no—
484C22×C3—181no—
485C22×C3—182no—
486C22×C3D4×D912yes—
487C22×C3C23×D911yescharacteristic
488C22×C3#381112yes—
489C22×C3C22×D3211yescharacteristic
490C2×D3—21no—
491C2×D3—22no—
492C2×D3—62no—
493C2×D3—61no—
494C2×D3—94no—
495C2×D3—92no—
496C2×D3—92no—
497C2×D3—94no—
498C2×D3—92no—
499C2×D3—92no—
500C2×D3—182no—
501C2×D3—182no—
502C2×D3—184no—
503C2×D3—188no—
504C2×D3—188no—
505C2×D3—1816no—
506C2×D3—184no—
507C2×D3—182no—
508C2×D3—182no—
509C2×D3—364no—
510C2×D3—364no—
511C3×C4—24no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—62no—
515C3×C4—61no—
516C3×C4—181no—
517C3×C4—182no—
518Dic3—21no—
519Dic3—22no—
520Dic3—62no—
521Dic3—61no—
522Dic3—184no—
523Dic3—182no—
524Dic3—182no—
525C32D3×#12311yescharacteristic
526C9—21no—
527C9D3×#12311yescharacteristic, complemented
528C23—31no—
529C23—91no—
530C23—271no—
531C23—271no—
532C23—274no—
533C23—544no—
534C23—542no—
535C23—544no—
536C23C2×D3×D911yescharacteristic
537D4—62no—
538D4—182no—
539D4—542no—
540D4—542no—
541C2×C4—22no—
542C2×C4—32no—
543C2×C4—31no—
544C2×C4—92no—
545C2×C4—91no—
546C2×C4—272no—
547C2×C4—544no—
548C2×C4—544no—
549C2×C4—542no—
550C2×C4—544no—
551C2×C4—542no—
552C2×C4C2×D3×D912yes—
553C2×C3—24no—
554C2×C3—22no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—121no—
559C2×C3—361no—
560C2×C3C2×D4×D911yescharacteristic
561C2×C3#41×D912yes—
562C2×C3#6430612yes—
563C2×C3C2×#381111yescharacteristic
564D3—41no—
565D3—94no—
566D3—94no—
567D3—121no—
568D3—184no—
569D3—184no—
570D3—182no—
571D3—182no—
572C22—22no—
573C22—61no—
574C22—62no—
575C22—181no—
576C22—182no—
577C22—272no—
578C22—274no—
579C22—272no—
580C22—548no—
581C22—542no—
582C22—1084no—
583C22#8866812yes—
584C22C22×D3×D911yescharacteristic
585C4—22no—
586C4—61no—
587C4—62no—
588C4—181no—
589C4—182no—
590C4—542no—
591C3—21no—
592C3D9×#12311yescharacteristic, complemented
593C3#1059507911yescharacteristic
594C2—22no—
595C2—121no—
596C2—274no—
597C2—361no—
598C2—542no—
599C2#1172247512yes—
600C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radicalC2×#88668C2
hypercenterC22×C4D3×D9
hypocenterC3×C9C2×#123
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊D9C2semidirect
3. C9×#929C2semidirect
4. C3×#63491C2semidirect
5. #11721274C2semidirect
6. #11721266C2semidirect
7. #11721260C2semidirect
8. #11721048C2semidirect
9. #11720980C2semidirect
10. #11720957C2semidirect
11. #11720941C2semidirect
16. C22×C3×C4×C9C22semidirect
17. C22×C3⋊Dic9C22semidirect
20. C2×C4×C3⋊D9C22semidirect
28. C9×#217C22semidirect
29. C3×#3676C22semidirect
30. C9×(C2×D3)⋊C4C22semidirect
31. C3×(C2×D9)⋊C4C22semidirect
32. C9×Dic3⋊C4C22semidirect
33. C3×Dic9⋊C4C22semidirect
34. (C2×D3)⋊Dic9C22semidirect
35. #88445C22semidirect
36. (C2×D9)⋊Dic3C22semidirect
37. Dic3⋊Dic9C22semidirect
38. Dic9⋊Dic3C22semidirect
55. #63491D3semidirect
119. C22×C4×C9C2×D3semidirect
138. #3676C2×D3semidirect
141. (C2×D9)⋊C4C2×D3semidirect
144. Dic9⋊C4C2×D3semidirect
174. #929D9semidirect
253. C3⋊D9#123semidirect
264. C22×C3×C4C2×D9semidirect
299. #217C2×D9semidirect
305. (C2×D3)⋊C4C2×D9semidirect
311. Dic3⋊C4C2×D9semidirect
371. C3×C9C2×#123semidirect
465. C22×C4D3×D9semidirect
527. C9D3×#123semidirect
592. C3D9×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊D92
C2×#886682
C9×#9292
C3×#634912
#117212742
#117212662
#117212602
#117210482
#117209802
#117209572
#117209412
#105950793
D9×#1233