Finite Group Databasebeta

← #29645932

Subgroups — #29645932

Order 15616.

1346 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840234C211yesmaximal, characteristic
2#21454858C212yesmaximal, complemented
3#21444157C211yesmaximal, characteristic, complemented
4#21444156C212yesmaximal, complemented
5#21444145C212yesmaximal, complemented
6#21444144C212yesmaximal, complemented
7#21444138C212yesmaximal, complemented
8#21444132C212yesmaximal, complemented
9C61×#1465C211yesmaximal, characteristic, complemented
10C22×D4×D61C411yescharacteristic
11#16840234—24no—
12#16840234—24no—
13C2×C4×D244C411yescharacteristic
14C2×D4×Dic61C411yescharacteristic
15C2×#14519739C2211yescharacteristic
16C2×C4×C22⋊D61C411yescharacteristic
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519737C411yescharacteristic
19C2×#14519737C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519734C411yescharacteristic
22C22×#11758198C411yescharacteristic
23C22×#11758198C2211yescharacteristic
24C2×C22⋊C4×D61C411yescharacteristic
25C2×C22⋊C4×D61C2211yescharacteristic
26#16839838—24no—
27#16839837—24no—
28#16839812C2214yescomplemented
29#16839726C2212yescomplemented
30#16839724C2214yescomplemented
31#16839488C2212yescomplemented
32#16839486C2212yescomplemented
33#16839485C2214yes—
34#16839485C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C61×#407C2212yescomplemented
37C61×#324C2212yescomplemented
38C61×#323C2212yescomplemented
39C24×D61C2×C411yescharacteristic
40C24×D61C2×C411yescharacteristic
41C22×D244C2×C411yescharacteristic
42C22×C22⋊D61C2×C411yescharacteristic
43C22×C22⋊D61C2×C411yescharacteristic
44C2×D4×D61—24no—
45C2×D4×D61—24no—
46C2×D4×D61—24no—
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C2×#11758194—22no—
55C2×#11758189—24no—
56C4×D244—22no—
57C4×D244—22no—
58D4×Dic61—24no—
59#14519739—24no—
60C4×C22⋊D61—22no—
61C4×C22⋊D61—22no—
62C4×C22⋊D61D414yes—
63C4×C22⋊D61D414yes—
64#14519737—24no—
65#14519737—24no—
66#14519735—24no—
67#14519734—22no—
68#14519734—22no—
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2×C411yescharacteristic
72C2×C22⋊Dic61C2×C411yescharacteristic
73C2×C22⋊Dic61C2×C411yescharacteristic
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2311yescharacteristic
85C2×#11758198C2311yescharacteristic
86C22⋊C4×D61—24no—
87C22⋊C4×D61—24no—
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519706—24no—
92C22⋊#92418—22no—
93C22⋊#92418C2314yes—
94#14519689—24no—
95C8×Dic61—24no—
96C22×D4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C2×M16×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2311yescharacteristic
105C2×C42×C61C2×C411yescharacteristic
106C22⋊C8×C61—22no—
107C22⋊C8×C61C2314yes—
108C24×C61C22×C411yescharacteristic
109C24×C61C22×C411yescharacteristic
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—81no—
117C23×D61—81no—
118C23×D61—81no—
119C23×D61—81no—
120C23×D61C22×C411yescharacteristic
121C23×D61C22×C411yescharacteristic
122C23×D61C22×C411yescharacteristic
123C2×D4×C61—22no—
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—81no—
129C22×C4×C61—81no—
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2411yescharacteristic
137C2×C22⋊D61—22no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61C22⋊C414yes—
142C2×C22⋊D61M1614yescomplemented
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—81no—
146C22×Dic61—81no—
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152D4×D61—232no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—81no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×C4×D61—81no—
165C2×C4×D61M1614yescomplemented
166C2×C4×D61C2×D414yes—
167M16×C61—82no—
168C2×C8×C61—24no—
169C4⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C42×C61—21no—
173C42×C61—21no—
174C22⋊Dic61—22no—
175C22⋊Dic61C22⋊C414yes—
176#11758198—22no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—22no—
182#11758198—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198C22⋊C412yes—
186#11758198C22⋊C412yes—
187C4⋊Dic61—22no—
188#11758196—22no—
189#11758196C22⋊C412yes—
190#11758196C22⋊C412yes—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61C2×D414yes—
194#11758194—82no—
195C2×#92418—24no—
196#11758189—84no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61—21no—
200C23×C61—21no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61C2×C22⋊C412yes—
206C23×C61C2×M1612yes—
207C23×C61C23×C411yescharacteristic
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—28no—
215C22×D61—28no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—82no—
223C22×D61—82no—
224C22×D61—82no—
225C22×D61—82no—
226C22×D61—84no—
227C22×D61—84no—
228C22×D61—84no—
229C22×D61—84no—
230C22×D61C2×C22⋊C412yes—
231C22×D61C2×M1612yes—
232C22×D61C2×M1612yes—
233D4×C61—28no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—81no—
245C2×C4×C61—81no—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×M1612yes—
249C2×C4×C61C22×D412yes—
250C22⋊D61—28no—
251C22⋊D61—28no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—82no—
259C2×Dic61—82no—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C412yes—
263C2×Dic61C2×M1612yes—
264C2×Dic61C2×M1612yes—
265D244—28no—
266C4×D61—28no—
267C4×D61—44no—
268C4×D61—82no—
269C4×D61—82no—
270C4×D61—82no—
271C8×C61—44no—
272#92418—44no—
273#17369—611nomaximal, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61C22×C22⋊C411yescharacteristic
287C22×C61C22×M1611yescharacteristic
288C22×C61C22×M1611yescharacteristic
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—88no—
305C2×D61—88no—
306C4×C61—22no—
307C4×C61—22no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—41no—
311C4×C61—41no—
312Dic61—22no—
313Dic61—22no—
314Dic61—41no—
315Dic61—41no—
316Dic61#40714yes—
317C2×#518—611no—
318#2975—612no—
319#1465—612no—
320#1465—611no—
321#1465D6111yescharacteristic, complemented
322#1462—612no—
323#1462—612no—
324#1460—612no—
325#1458—612no—
326C2×C61—21no—
327C2×C61—21no—
328C2×C61—42no—
329C2×C61—42no—
330C2×C61C2×#40711yescharacteristic
331C2×C61#288311yescharacteristic
332C2×C61#288811yescharacteristic
333D61—42no—
334D61—42no—
335D61—42no—
336C23×D4—611no—
337#518—1224no—
338#518—1224no—
339C2×C4×D4—611no—
340C2×C4×D4—611no—
341C2×C4×D4—611no—
342C2×C4×D4—611no—
343C2×C4×D4—611no—
344C2×C4×D4—611no—
345C2×C4×D4—611no—
346C2×C4×D4C2×D6111yescharacteristic
347C2×#117—611no—
348C2×#117—611no—
349C22×C22⋊C4—611no—
350C22×C22⋊C4—611no—
351C22×C22⋊C4—611no—
352C22×C22⋊C4—611no—
353#436—1224no—
354#436—1224no—
355#431—614no—
356#407—612no—
357#407—614no—
358#407C2×D6112yescomplemented
359#324—612no—
360#324C2×D6112yescomplemented
361#323—612no—
362#323—614no—
363#323—614no—
364#323C2×D6112yescomplemented
365C61#1736911yescharacteristic, complemented, Sylow
366C25—611no—
367C25—611no—
368C22×D4—611no—
369C22×D4—611no—
370C22×D4—611no—
371C22×D4—1224no—
372C22×D4—1224no—
373C22×D4—1224no—
374C22×D4C4×D6111yescharacteristic
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4C4×D6111yescharacteristic
383C23×C4C22×D6111yescharacteristic
384C2×M16—22no—
385C2×M16—1224no—
386C2×M16—1222no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—614no—
390C4×D4—614no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1224no—
394C4×D4—1224no—
395C4×D4—1224no—
396C4×D4—1224no—
397C4×D4—1222no—
398C4×D4—1222no—
399#117—1222no—
400#117—1222no—
401#117—1224no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4C22×D6111yescharacteristic
406C2×C22⋊C4—611no—
407C2×C22⋊C4—611no—
408C2×C22⋊C4—611no—
409C2×C22⋊C4—611no—
410C2×C22⋊C4—611no—
411C2×C22⋊C4—611no—
412C2×C22⋊C4—611no—
413C2×C22⋊C4—611no—
414C2×C22⋊C4—611no—
415C2×C22⋊C4—611no—
416C2×C22⋊C4—1224no—
417C2×C22⋊C4—1224no—
418C2×C22⋊C4—1222no—
419C2×C22⋊C4—1222no—
420C2×C22⋊C4—1222no—
421C2×C22⋊C4—1222no—
422C2×C22⋊C4C4×D6111yescharacteristic
423C2×C22⋊C4C22×D6111yescharacteristic
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42C4×D6111yescharacteristic
428C4⋊C8—1224no—
429C22⋊C8—22no—
430C22⋊C8—614no—
431C22⋊C8—1224no—
432C22⋊C8—1222no—
433C22⋊C8C22×D6114yes—
434C4×C8—1224no—
435C24—611no—
436C24—611no—
437C24—611no—
438C24—1222no—
439C24—1222no—
440C24—1222no—
441C24—1222no—
442C24—1222no—
443C24—1222no—
444C24—4881no—
445C24—4881no—
446C24—4881no—
447C24—4881no—
448C24C2×C4×D6111yescharacteristic
449C24C2×C4×D6111yescharacteristic
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—614no—
454C2×D4—614no—
455C2×D4—1222no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—12232no—
462C2×D4—1222no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—81no—
466C22×C4—81no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—614no—
471C22×C4—614no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—4881no—
482C22×C4—4881no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4—4881no—
487C22×C4C2×C4×D6111yescharacteristic
488C22×C4C2×C4×D6111yescharacteristic
489C22×C4C2×C4×D6111yescharacteristic
490C22×C4C2×C4×D6111yescharacteristic
491C22×C4D4×D6112yes—
492C22×C4D4×D6112yes—
493C22×C4C23×D6111yescharacteristic
494M16—82no—
495M16—4884no—
496M16—4882no—
497C2×C8—24no—
498C2×C8—1224no—
499C4⋊C4—22no—
500C4⋊C4—612no—
501C4⋊C4—612no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—614no—
507C22⋊C4—612no—
508C22⋊C4—612no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1221no—
516C22⋊C4—1221no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C42—21no—
520C42—21no—
521C42—614no—
522C42—1222no—
523C42—1222no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—612no—
533C23—612no—
534C23—612no—
535C23—1228no—
536C23—1228no—
537C23—1221no—
538C23—1221no—
539C23—1221no—
540C23—1221no—
541C23—1221no—
542C23—1221no—
543C23—4882no—
544C23—4882no—
545C23—4882no—
546C23—4882no—
547C23—4884no—
548C23—4884no—
549C23—4884no—
550C23—4884no—
551C23—2441no—
552C23—2441no—
553C23—2441no—
554C23—2441no—
555C23—2441no—
556C23—2441no—
557C23C22⋊C4×D6112yes—
558C23M16×D6112yes—
559C23C22×C4×D6111yescharacteristic
560D4—28no—
561D4—1228no—
562D4—1228no—
563D4—1228no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—612no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—1228no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—4882no—
585C2×C4—4882no—
586C2×C4—4882no—
587C2×C4—4882no—
588C2×C4—4882no—
589C2×C4—2444no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4M16×D6112yes—
597C2×C4C2×D4×D6112yes—
598C8—44no—
599C8—2444no—
600C22—21no—
601C22—21no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—1222no—
613C22—1222no—
614C22—1222no—
615C22—1222no—
616C22—1222no—
617C22—4888no—
618C22—4888no—
619C22—2442no—
620C22—2442no—
621C22—2442no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22C2×C22⋊C4×D6111yescharacteristic
630C22C2×M16×D6111yescharacteristic
631C22C2×M16×D6111yescharacteristic
632C4—22no—
633C4—22no—
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—614no—
639C4—1222no—
640C4—1222no—
641C4—2441no—
642C4—2441no—
643C2—21no—
644C2—21no—
645C2—42no—
646C2—42no—
647C2—2442no—
648C2—2442no—
649C2—2442no—
650C2#407×D6111yescharacteristic
651C2#2145427711yescharacteristic
652C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1465C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×C4×C61C24
hypercenter#1465D61
hypocenterC61#17369
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #21454858C2semidirect
3. #21444157C2semidirect
4. #21444156C2semidirect
5. #21444145C2semidirect
6. #21444144C2semidirect
7. #21444138C2semidirect
8. #21444132C2semidirect
9. C61×#1465C2semidirect
28. #16839812C22semidirect
29. #16839726C22semidirect
30. #16839724C22semidirect
31. #16839488C22semidirect
32. #16839486C22semidirect
34. #16839485C22semidirect
36. C61×#407C22semidirect
37. C61×#324C22semidirect
38. C61×#323C22semidirect
142. C2×C22⋊D61M16semidirect
165. C2×C4×D61M16semidirect
321. #1465D61semidirect
358. #407C2×D61semidirect
360. #324C2×D61semidirect
364. #323C2×D61semidirect
365. C61#17369semidirect

Maximal subgroups

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

subgroupindex
C2×#168402342
#214548582
#214441572
#214441562
#214441452
#214441442
#214441382
#214441322
C61×#14652
#1736961