Finite Group Databasebeta

← #13139895

Subgroups — #13139895

Order 1728.

934 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D9C211yesmaximal, characteristic, complemented
2C22×#6194C211yesmaximal, characteristic
3C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
5C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
6#11720572C211yesmaximal, characteristic, complemented
7#11720331C211yesmaximal, characteristic, complemented
8#10591381—31nomaximal
9#10588636—31nomaximal
10C23×D3×C9C2211yescharacteristic
11C23×C3×D9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C3⋊Dic9C2211yescharacteristic
15C22×C9×Dic3C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C2×C3×C4×D9—22no—
18C2×C3×C4×D9—22no—
19C2×C3×C4×D9—22no—
20C2×#6194—22no—
21C2×#6194—22no—
22C2×#6194C414yescomplemented
23C9×(C2×D3)⋊C4—22no—
24(C2×D3)⋊Dic9—22no—
25(C2×D9)⋊Dic3—22no—
26C22×C3×C4×D3—31no—
27C22×#625—31no—
28C2×C3×(C2×D3)⋊C4D311yescharacteristic
29C2×(C2×D3)⋊Dic3—31no—
30C2×(C2×D3)⋊Dic3—31no—
31C22×#611—31no—
32C22×C4×D9D311yescharacteristic, complemented
33#63658—31no—
34#63579—31no—
35C2×C9×C22⋊C4—31no—
36C2×#3676—31no—
37C2×(C2×D9)⋊C4—31no—
38C9⋊#95—31no—
39C9⋊#95—31no—
40C9⋊#95—61no—
41C23×C3×C9C2311yescharacteristic
42C22×D3×C9—21no—
43C22×D3×C9—21no—
44C22×D3×C9—21no—
45C22×D3×C9—21no—
46C22×D3×C9—21no—
47C22×D3×C9—21no—
48C22×D3×C9C2×C412yescomplemented
49C22×C3×D9—21no—
50C22×C3×D9—21no—
51C22×C3×D9—21no—
52C22×C3×D9—21no—
53C22×C3×D9C2×C412yes—
54C22×C3×D9D412yes—
55C22×C3×D9D412yes—
56C2×C3×C4×C9—21no—
57C2×C3×C4×C9—21no—
58C2×C3×C4×C9D412yescomplemented
59C2×C3⋊Dic9—21no—
60C2×C3⋊Dic9—21no—
61C2×C3⋊Dic9—21no—
62C2×C3⋊Dic9—21no—
63C2×C3⋊Dic9—21no—
64C2×C3⋊Dic9C2×C412yescomplemented
65C2×C9×Dic3—21no—
66C2×C9×Dic3—21no—
67C2×C9×Dic3—21no—
68C2×C3×Dic9—21no—
69C2×C3×Dic9—21no—
70C2×C3×Dic9D412yescomplemented
71C3×C4×D9—28no—
72#6194—28no—
73#5213—91no—
74#4956—91no—
75C23×C3×D3—31no—
76C23×C3×D3C2×D311yescharacteristic
77C22×C32×C4C2×D311yescharacteristic
78C22×C3⋊Dic3—31no—
79C22×C3⋊Dic3—31no—
80C22×C3×Dic3—31no—
81C22×C3×Dic3C2×D311yescharacteristic
82C2×C3×C4×D3—62no—
83C2×C3×C4×D3—62no—
84C2×C3×C4×D3—62no—
85C2×#625—34no—
86C2×#625—62no—
87C2×#625—62no—
88C24×C9—31no—
89C23×D9C2×D311yescharacteristic
90C3×(C2×D3)⋊C4—22no—
91(C2×D3)⋊Dic3—62no—
92(C2×D3)⋊Dic3—62no—
93C22×C4×C9—21no—
94C22×C4×C9—31no—
95C22×C4×C9C2×D311yescharacteristic
96C2×#611—34no—
97C2×#611—62no—
98C2×#611—62no—
99C22×Dic9—31no—
100C22×Dic9—31no—
101C22×Dic9—61no—
102C22×Dic9—61no—
103C22×Dic9C2×D311yescharacteristic
104C2×C4×D9—22no—
105C2×C4×D9—22no—
106C2×C4×D9—22no—
107C9×C22⋊C4—62no—
108#3676—62no—
109(C2×D9)⋊C4—62no—
110C22×C3×C9C22×C411yescharacteristic
111C22×C3×C9C2×D411yescharacteristic
112C22×C3×C9C2×D411yescharacteristic
113C22×C3×C9C2×D411yescharacteristic
114C22×C3×C9C2×D411yescharacteristic
115C22×C3×C9#4111yescharacteristic
116C22×C3×C9#4111yescharacteristic
117C2×D3×C9—22no—
118C2×D3×C9—22no—
119C2×D3×C9—22no—
120C2×D3×C9—41no—
121C2×D3×C9—41no—
122C2×D3×C9—41no—
123C2×D3×C9—41no—
124C2×C3×D9—22no—
125C2×C3×D9—22no—
126C2×C3×D9—22no—
127C2×C3×D9—22no—
128C2×C3×D9—22no—
129C2×C3×D9—22no—
130C2×C3×D9C22⋊C414yescomplemented
131C3×C4×C9—22no—
132C3⋊Dic9—22no—
133C3⋊Dic9—41no—
134C9×Dic3—41no—
135C3×Dic9—22no—
136C23×C3×C4—91no—
137C22×#67—91no—
138C22×#67—91no—
139C22×C4×D3—31no—
140C2×C3×C22⋊C4—31no—
141C2×#217—91no—
142C2×#217—91no—
143C2×(C2×D3)⋊C4—91no—
144C2×(C2×D3)⋊C4—91no—
145C2×(C2×D3)⋊C4D911yescharacteristic, complemented
146C3⋊#95—91no—
147C3⋊#95—91no—
148C3⋊#95—91no—
149C3⋊#95—91no—
150C3⋊#95—181no—
151C23×C32C22×D311yescharacteristic
152C22×C3×D3—21no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—32no—
159C22×C3×D3—32no—
160C22×C3×D3—32no—
161C22×C3×D3—61no—
162C22×C3×D3—61no—
163C22×C3×D3—61no—
164C22×C3×D3—61no—
165C22×C3×D3C4×D312yes—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4#6712yes—
169C2×C3⋊Dic3—32no—
170C2×C3⋊Dic3—61no—
171C2×C3⋊Dic3—61no—
172C2×C3⋊Dic3—61no—
173C2×C3⋊Dic3—61no—
174C2×C3⋊Dic3—61no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—32no—
179C2×C3×Dic3—61no—
180C2×C3×Dic3—61no—
181C3×C4×D3—68no—
182#625—68no—
183C23×C9—21no—
184C23×C9—32no—
185C23×C9—61no—
186C23×C9—61no—
187C23×C9—61no—
188C23×C9—61no—
189C23×C9—61no—
190C23×C9—61no—
191C23×C9C22×D311yescharacteristic
192C22×D9—21no—
193C22×D9—21no—
194C22×D9—21no—
195C22×D9—21no—
196C22×D9C4×D312yes—
197C22×D9D1212yes—
198C22×D9#6712yes—
199C2×C4×C9—21no—
200C2×C4×C9—21no—
201C2×C4×C9—22no—
202C2×C4×C9—41no—
203C2×C4×C9—41no—
204C2×C4×C9—61no—
205C2×C4×C9—61no—
206C2×C4×C9—61no—
207C2×C4×C9#6712yescomplemented
208#611—68no—
209C2×Dic9—21no—
210C2×Dic9—21no—
211C2×Dic9—32no—
212C2×Dic9—62no—
213C2×Dic9—61no—
214C2×Dic9—61no—
215C2×Dic9—62no—
216C2×Dic9—61no—
217C2×Dic9—61no—
218C2×Dic9—61no—
219C2×Dic9—121no—
220C2×Dic9—121no—
221C2×Dic9—121no—
222C2×Dic9—121no—
223C2×Dic9#6712yescomplemented
224C4×D9—28no—
225#386—271noSylow
226C2×C3×C9C2×C22⋊C411yescharacteristic
227C2×C3×C9C4×D411yescharacteristic
228C2×C3×C9C4×D411yescharacteristic
229C2×C3×C9#12011yescharacteristic
230C2×C3×C9#12111yescharacteristic
231C2×C3×C9#12111yescharacteristic
232C2×C3×C9#12311yescharacteristic
233D3×C9—42no—
234C3×D9—24no—
235C24×C3—31no—
236C24×C3—91no—
237C23×D3—31no—
238C23×D3C2×D911yescharacteristic
239C22×C3×C4—21no—
240C22×C3×C4—31no—
241C22×C3×C4—91no—
242C22×C3×C4—182no—
243C22×C3×C4—182no—
244C22×C3×C4—182no—
245C22×C3×C4C2×D911yescharacteristic
246C22×C3×C4D3211yescharacteristic
247C2×#67—94no—
248C2×#67—94no—
249C2×#67—182no—
250C2×#67—182no—
251C2×#67—182no—
252C2×#67—182no—
253C22×Dic3—31no—
254C22×Dic3—91no—
255C22×Dic3—91no—
256C22×Dic3—91no—
257C22×Dic3—91no—
258C22×Dic3—181no—
259C22×Dic3—181no—
260C22×Dic3C2×D911yescharacteristic
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C3×C22⋊C4—62no—
265#217—182no—
266#217—182no—
267(C2×D3)⋊C4—22no—
268(C2×D3)⋊C4—182no—
269(C2×D3)⋊C4—182no—
270C22×C32C2×C4×D311yescharacteristic
271C22×C32#23511yescharacteristic
272C22×C32D3×D411yescharacteristic
273C22×C32D3×D411yescharacteristic
274C22×C32D3×D411yescharacteristic
275C22×C32#23711yescharacteristic
276C22×C32C2×#6711yescharacteristic
277C2×C3×D3—22no—
278C2×C3×D3—22no—
279C2×C3×D3—22no—
280C2×C3×D3—34no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—62no—
286C2×C3×D3—62no—
287C2×C3×D3—62no—
288C2×C3×D3—62no—
289C2×C3×D3—62no—
290C2×C3×D3—62no—
291C32×C4—22no—
292C3⋊Dic3—62no—
293C3⋊Dic3—121no—
294C3×Dic3—41no—
295C3×Dic3—62no—
296C22×C9—21no—
297C22×C9—21no—
298C22×C9—21no—
299C22×C9—21no—
300C22×C9—21no—
301C22×C9—21no—
302C22×C9—21no—
303C22×C9—62no—
304C22×C9—62no—
305C22×C9—62no—
306C22×C9—121no—
307C22×C9—121no—
308C22×C9—121no—
309C22×C9—121no—
310C22×C9C2×C4×D311yescharacteristic
311C22×C9C2×D1211yescharacteristic
312C22×C9#23511yescharacteristic
313C22×C9#23511yescharacteristic
314C22×C9C2×#6711yescharacteristic
315C22×C9C2×#6711yescharacteristic
316C22×C9C2×#6711yescharacteristic
317C2×D9—22no—
318C2×D9—22no—
319C2×D9—22no—
320C2×D9—22no—
321C2×D9—22no—
322C2×D9—22no—
323C2×D9(C2×D3)⋊C414yescomplemented
324C4×C9—22no—
325C4×C9—42no—
326C4×C9—121no—
327Dic9—22no—
328Dic9—62no—
329Dic9—122no—
330Dic9—122no—
331Dic9—121no—
332C22×D4—271no—
333C23×C4—91no—
334C2×C22⋊C4—31no—
335C2×C22⋊C4—271no—
336C2×C22⋊C4—271no—
337#95—271no—
338#95—271no—
339C3×C9#38611yescharacteristic, complemented, Sylow
340C23×C3—21no—
341C23×C3—32no—
342C23×C3—61no—
343C23×C3—61no—
344C23×C3—61no—
345C23×C3—61no—
346C23×C3—61no—
347C23×C3—61no—
348C23×C3—92no—
349C23×C3—92no—
350C23×C3—92no—
351C23×C3—181no—
352C23×C3—181no—
353C23×C3—181no—
354C23×C3—181no—
355C23×C3C22×D911yescharacteristic
356C23×C3C2×D3211yescharacteristic
357C22×D3—21no—
358C22×D3—21no—
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—21no—
362C22×D3—21no—
363C22×D3—32no—
364C22×D3—32no—
365C22×D3—32no—
366C22×D3—61no—
367C22×D3—61no—
368C22×D3—61no—
369C22×D3—61no—
370C22×D3C4×D912yescomplemented
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—92no—
382C2×C3×C4—188no—
383C2×C3×C4—181no—
384C2×C3×C4—181no—
385C2×C3×C4#61112yescomplemented
386C2×C3×C4#62512yes—
387#67—188no—
388#67—188no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—32no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—92no—
396C2×Dic3—92no—
397C2×Dic3—182no—
398C2×Dic3—181no—
399C2×Dic3—181no—
400C2×Dic3—181no—
401C2×Dic3—181no—
402C2×Dic3—182no—
403C2×Dic3—181no—
404C2×Dic3—181no—
405C2×Dic3—181no—
406C2×Dic3—181no—
407C2×Dic3—181no—
408C2×Dic3—181no—
409C2×Dic3—361no—
410C2×Dic3—361no—
411C2×Dic3—361no—
412C2×Dic3—361no—
413C4×D3—68no—
414C2×C32D3×C22⋊C411yescharacteristic
415C2×C32#67⋊C411yescharacteristic
416C2×C32#88311yescharacteristic
417C2×C32#88411yescharacteristic
418C2×C32C4×#6711yescharacteristic
419C2×C32#93711yescharacteristic
420C2×C32#93811yescharacteristic
421C3×D3—42no—
422C3×D3—64no—
423C2×C9—21no—
424C2×C9—21no—
425C2×C9—21no—
426C2×C9—21no—
427C2×C9—21no—
428C2×C9—21no—
429C2×C9—21no—
430C2×C9—122no—
431C2×C9C2×(C2×D3)⋊C411yescharacteristic
432C2×C9C4×#6711yescharacteristic
433C2×C9C4×#6711yescharacteristic
434C2×C9#92911yescharacteristic
435C2×C9#93011yescharacteristic
436C2×C9#93011yescharacteristic
437C2×C9#95311yescharacteristic
438D9—24no—
439C24—31no—
440C24—91no—
441C2×D4—274no—
442C2×D4—542no—
443C2×D4—542no—
444C22×C4—31no—
445C22×C4—91no—
446C22×C4—182no—
447C22×C4—182no—
448C22×C4—182no—
449C22×C4—271no—
450C22×C4—271no—
451C22×C4D3×D911yescharacteristic
452C22⋊C4—62no—
453C22⋊C4—542no—
454C22⋊C4—542no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—94no—
466C22×C3—121no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3—121no—
470C22×C3—182no—
471C22×C3—182no—
472C22×C3—182no—
473C22×C3—182no—
474C22×C3—182no—
475C22×C3—182no—
476C22×C3C2×C4×D911yescharacteristic
477C22×C3#369711yescharacteristic
478C22×C3D4×D911yescharacteristic
479C22×C3D4×D911yescharacteristic
480C22×C3D4×D911yescharacteristic
481C22×C3#369911yescharacteristic
482C22×C3C2×#61111yescharacteristic
483C22×C3#379511yescharacteristic
484C22×C3#379811yescharacteristic
485C22×C3C4×D3211yescharacteristic
486C22×C3D3×D1211yescharacteristic
487C22×C3C2×#62511yescharacteristic
488C22×C3D3×#6711yescharacteristic
489C22×C3D3×#6711yescharacteristic
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—22no—
493C2×D3—34no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—42no—
507C3×C4—121no—
508C3×C4—182no—
509Dic3—41no—
510Dic3—62no—
511Dic3—182no—
512Dic3—182no—
513Dic3—362no—
514Dic3—362no—
515Dic3—361no—
516Dic3—361no—
517C32#495611yescharacteristic
518C9—21no—
519C9#521311yescharacteristic, complemented
520C23—32no—
521C23—61no—
522C23—61no—
523C23—61no—
524C23—61no—
525C23—61no—
526C23—61no—
527C23—92no—
528C23—92no—
529C23—92no—
530C23—181no—
531C23—181no—
532C23—181no—
533C23—181no—
534C23C2×D3×D911yescharacteristic
535D4—548no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—92no—
542C2×C4—188no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4—272no—
546C2×C4—541no—
547C2×C4—541no—
548C2×C4—541no—
549C2×C4—541no—
550C2×C4—541no—
551C2×C4#619412yescomplemented
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—122no—
560C2×C3—184no—
561C2×C3C22⋊C4×D911yescharacteristic
562C2×C3#611⋊C411yescharacteristic
563C2×C3#6344511yescharacteristic
564C2×C3#6344611yescharacteristic
565C2×C3C4×#61111yescharacteristic
566C2×C3#6349911yescharacteristic
567C2×C3#6350011yescharacteristic
568C2×C3#6387911yescharacteristic
569C2×C3C4×#62511yescharacteristic
570C2×C3#6390511yescharacteristic
571C2×C3#6390611yescharacteristic
572C2×C3#6390811yescharacteristic
573C2×C3D3×(C2×D3)⋊C411yescharacteristic
574C2×C3#6397611yescharacteristic
575D3—42no—
576D3—64no—
577C22—62no—
578C22—62no—
579C22—62no—
580C22—94no—
581C22—121no—
582C22—121no—
583C22—121no—
584C22—121no—
585C22—182no—
586C22—182no—
587C22—182no—
588C22—182no—
589C22—182no—
590C22—182no—
591C22#8863811yescharacteristic
592C22#8864011yescharacteristic
593C22C4×D3×D911yescharacteristic
594C22D9×D1211yescharacteristic
595C22C2×#619411yescharacteristic
596C22D9×#6711yescharacteristic
597C22D9×#6711yescharacteristic
598C4—22no—
599C4—121no—
600C4—182no—
601C4—542no—
602C4—1081no—
603C3—21no—
604C3#1058863611yescharacteristic, complemented
605C3#1059138111yescharacteristic
606C2—122no—
607C2—184no—
608C2#1172101211yescharacteristic
609C2C4×#619411yescharacteristic
610C2#1172103111yescharacteristic
611C2#1172103311yescharacteristic
612C2#1172103611yescharacteristic
613C2D9×(C2×D3)⋊C411yescharacteristic
614C2#1172128511yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC22×#6194C2
cosocleC23×C3×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#386
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×D9C2semidirect
3. C2×C9×(C2×D3)⋊C4C2semidirect
4. C2×(C2×D3)⋊Dic9C2semidirect
5. C2×(C2×D9)⋊Dic3C2semidirect
6. #11720572C2semidirect
7. #11720331C2semidirect
22. C2×#6194C4semidirect
32. C22×C4×D9D3semidirect
48. C22×D3×C9C2×C4semidirect
58. C2×C3×C4×C9D4semidirect
64. C2×C3⋊Dic9C2×C4semidirect
70. C2×C3×Dic9D4semidirect
130. C2×C3×D9C22⋊C4semidirect
145. C2×(C2×D3)⋊C4D9semidirect
207. C2×C4×C9#67semidirect
223. C2×Dic9#67semidirect
323. C2×D9(C2×D3)⋊C4semidirect
339. C3×C9#386semidirect
370. C22×D3C4×D9semidirect
385. C2×C3×C4#611semidirect
519. C9#5213semidirect
551. C2×C4#6194semidirect
604. C3#10588636semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D92
C22×#61942
C2×C9×(C2×D3)⋊C42
C2×(C2×D3)⋊Dic92
C2×(C2×D9)⋊Dic32
#117205722
#117203312
#105913813
#105886363