Finite Group Databasebeta

← #29645915

Subgroups — #29645915

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840236C211yesmaximal, characteristic
2#21454847C212yesmaximal, complemented
3#21444159C212yesmaximal, complemented
4#21444156C212yesmaximal, complemented
5#21444153C211yesmaximal, characteristic, complemented
6#21444144C212yesmaximal, complemented
7#21444136C212yesmaximal, complemented
8#323×D61C212yesmaximal, complemented
9C61×#1464C211yesmaximal, characteristic, complemented
10C23×D244C411yescharacteristic
11#16840236—24no—
12#16840236—24no—
13C2×C4×D244C411yescharacteristic
14C2×C4×D244C411yescharacteristic
15C2×C4×D244C2211yescharacteristic
16C2×C4×D244C2211yescharacteristic
17C2×#14519739C411yescharacteristic
18C2×#14519739C411yescharacteristic
19C2×#14519739C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C2×#14519736C411yescharacteristic
22C2×C22⋊C4×D61C411yescharacteristic
23C2×C22⋊C4×D61C411yescharacteristic
24C2×C22⋊C4×D61C2211yescharacteristic
25C2×C22⋊C4×D61C2211yescharacteristic
26#16839835—24no—
27#16839832—24no—
28#16839819C2212yescomplemented
29#16839724C2214yescomplemented
30C22⋊C8×D61C2214yescomplemented
31#16839488C2212yescomplemented
32#16839486C2212yes—
33#16839485C2214yescomplemented
34#16839485C2214yescomplemented
35C2×#117×C61C2211yescharacteristic
36C61×#432C2212yescomplemented
37C61×#324C2212yescomplemented
38C61×#323C2212yes—
39C24×D61C2×C411yescharacteristic
40C24×D61C2×C411yescharacteristic
41C22×D244—24no—
42C22×D244—22no—
43C22×D244—22no—
44C22×D244—24no—
45C22×D244C2×C411yescharacteristic
46C22×D244C2×C411yescharacteristic
47C22×D244C2×C411yescharacteristic
48C22×D244C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2311yescharacteristic
56C22×C4×D61C2311yescharacteristic
57C2×#11758189—24no—
58C2×C8×D61—24no—
59C4×D244—22no—
60C4×D244—22no—
61C4×D244—22no—
62C4×D244—22no—
63C4×D244—22no—
64C4×D244—22no—
65C4×D244D414yes—
66C4×D244D414yes—
67#14519739—24no—
68#14519739—24no—
69#14519739—24no—
70#14519739—24no—
71#14519736—22no—
72#14519736—22no—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×C22⋊Dic61C2×C411yescharacteristic
76C2×C22⋊Dic61C2×C411yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2311yescharacteristic
84C2×#11758198C2311yescharacteristic
85C22⋊C4×D61—24no—
86C22⋊C4×D61—24no—
87C22⋊C4×D61—24no—
88C22⋊C4×D61—24no—
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C4⋊#92418—22no—
92C22⋊#92418C2314yes—
93#14519689—24no—
94#14519689—24no—
95#14519688—22no—
96C23×C4×C61C2×C411yescharacteristic
97#117×C61—22no—
98#117×C61—22no—
99C2×C4⋊C4×C61C2×C411yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C22⋊C4×C61C2×C411yescharacteristic
102C2×C22⋊C4×C61C2311yescharacteristic
103C2×C42×C61C2×C411yescharacteristic
104C2×C42×C61C2311yescharacteristic
105C4⋊C8×C61—22no—
106C22⋊C8×C61C2314yes—
107#97×C61—22no—
108C24×C61C22×C411yescharacteristic
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—81no—
115C23×D61—81no—
116C23×D61—81no—
117C23×D61—81no—
118C23×D61M1614yescomplemented
119C23×D61C22×C411yescharacteristic
120C23×D61C22×C411yescharacteristic
121C23×D61C22×C411yescharacteristic
122C23×D61C22×C411yescharacteristic
123C22×C4×C61—22no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C2×D244—216no—
138C2×D244—216no—
139C2×D244—22no—
140C2×D244—22no—
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—22no—
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—22no—
150C2×D244C22⋊C412yes—
151C2×D244C22⋊C412yes—
152C2×D244M1614yescomplemented
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C2×C4×D61—81no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×C4×D61—81no—
165C2×C4×D61—81no—
166C2×C4×D61—81no—
167C2×C4×D61C2×D414yes—
168C2×C4×D61C2×D414yes—
169C2×C8×C61—24no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61C2×D412yes—
177C42×C61C2×D412yes—
178C22⋊Dic61—22no—
179C22⋊Dic61—22no—
180#11758198—22no—
181#11758198—22no—
182#11758198—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186#11758198C22⋊C414yes—
187#11758198C22⋊C414yes—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61C22⋊C412yes—
191C4⋊Dic61C22⋊C412yes—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C2×#92418—24no—
195#11758189—84no—
196C8×D61—84no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61C2×M1612yes—
202C23×C61C23×C411yescharacteristic
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—28no—
210C22×D61—28no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—82no—
220C22×D61—82no—
221C22×D61—82no—
222C22×D61—82no—
223C22×D61—84no—
224C22×D61—84no—
225C22×D61—84no—
226C22×D61—84no—
227C22×D61C2×C22⋊C412yes—
228C22×D61C2×C22⋊C412yes—
229C22×D61C2×M1612yes—
230C22×D61C2×M1612yes—
231C22×D61C2×M1612yes—
232C22×D61C2×M1612yes—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C412yes—
248C2×C4×C61C2×M1612yes—
249C2×C4×C61C22×D412yes—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61C2×C22⋊C412yes—
258D244—24no—
259D244—24no—
260D244—28no—
261D244—24no—
262D244—24no—
263D244—28no—
264C4×D61—44no—
265C4×D61—44no—
266C4×D61—82no—
267C4×D61—82no—
268C4×D61—82no—
269C4×D61—82no—
270C4×D61—82no—
271C4×D61—82no—
272C8×C61—44no—
273#92418—44no—
274#17367—611nomaximal, Sylow
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—22no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61C22×C22⋊C411yescharacteristic
283C22×C61C22×M1611yescharacteristic
284C22×C61C22×M1611yescharacteristic
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—42no—
293C2×D61—42no—
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—
306C2×D61#40714yes—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—22no—
312C4×C61—41no—
313C4×C61—41no—
314Dic61—22no—
315Dic61—22no—
316Dic61—41no—
317Dic61—41no—
318C2×#518—611no—
319#2973—612no—
320#1466—612no—
321#1465—612no—
322#1464—611no—
323#1464D6111yescharacteristic, complemented
324#1462—612no—
325#1459—612no—
326C2×#323—612no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—42no—
330C2×C61C2×#40711yescharacteristic
331C2×C61#288311yescharacteristic
332C2×C61#288811yescharacteristic
333D61—24no—
334D61—42no—
335D61—42no—
336D61—42no—
337C23×D4—611no—
338#518—1224no—
339#518—1224no—
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×D4—611no—
347C2×C4×D4—611no—
348C2×#117—611no—
349C2×#117C2×D6111yescharacteristic
350C22×C22⋊C4—611no—
351C22×C22⋊C4—611no—
352C22×C22⋊C4—611no—
353C22×C22⋊C4—611no—
354#435—1224no—
355#435—1224no—
356#432—612no—
357#432C2×D6112yescomplemented
358#407—614no—
359C2×C22⋊C8—614no—
360#324—612no—
361#324C2×D6112yescomplemented
362#323—612no—
363#323—614no—
364#323—614no—
365#323C2×D6112yes—
366C61#1736711yescharacteristic, complemented, Sylow
367C25—611no—
368C25—611no—
369C22×D4—611no—
370C22×D4—611no—
371C22×D4—611no—
372C22×D4—611no—
373C22×D4—1222no—
374C22×D4—1222no—
375C22×D4—1224no—
376C22×D4—1224no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4C4×D6111yescharacteristic
386C2×M16—1224no—
387C22×C8—1224no—
388C4×D4—614no—
389C4×D4—614no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4—1224no—
395C4×D4—1224no—
396C4×D4—1224no—
397C4×D4—1224no—
398C4×D4—1222no—
399C4×D4—1222no—
400#117—22no—
401#117—22no—
402#117—1222no—
403#117—1222no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4C4×D6111yescharacteristic
407C2×C4⋊C4C22×D6111yescharacteristic
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—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—1224no—
419C2×C22⋊C4—1224no—
420C2×C22⋊C4—1224no—
421C2×C22⋊C4—1224no—
422C2×C22⋊C4C4×D6111yescharacteristic
423C2×C22⋊C4C22×D6111yescharacteristic
424C2×C42—611no—
425C2×C42—611no—
426C2×C42C4×D6111yescharacteristic
427C2×C42C22×D6111yescharacteristic
428C4⋊C8—22no—
429C4⋊C8—1222no—
430C22⋊C8—614no—
431C22⋊C8—1224no—
432C22⋊C8—1224no—
433C22⋊C8C22×D6114yes—
434#97—22no—
435#97—1222no—
436C24—611no—
437C24—614no—
438C24—611no—
439C24—611no—
440C24—611no—
441C24—1222no—
442C24—1222no—
443C24—1222no—
444C24—1222no—
445C24—1222no—
446C24—4881no—
447C24—4881no—
448C24—4881no—
449C24—4881no—
450C24C2×C4×D6111yescharacteristic
451C2×D4—612no—
452C2×D4—612no—
453C2×D4—614no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1222no—
462C2×D4—12216no—
463C2×D4—12216no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—1222no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—614no—
474C22×C4—614no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4—4881no—
487C22×C4—4881no—
488C22×C4—4881no—
489C22×C4—4881no—
490C22×C4—4881no—
491C22×C4C2×C4×D6111yescharacteristic
492C22×C4C2×C4×D6111yescharacteristic
493C22×C4C2×C4×D6111yescharacteristic
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4C23×D6111yescharacteristic
497M16—4884no—
498C2×C8—24no—
499C2×C8—1224no—
500C2×C8—4884no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—612no—
504C4⋊C4—612no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—614no—
510C22⋊C4—614no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C42—21no—
520C42—21no—
521C42—1222no—
522C42—1222no—
523C42D4×D6112yes—
524C42D4×D6112yes—
525C23—21no—
526C23—21no—
527C23—41no—
528C23—41no—
529C23—612no—
530C23—612no—
531C23—612no—
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—
557C23—2441no—
558C23—2441no—
559C23M16×D6112yes—
560C23C22×C4×D6111yescharacteristic
561D4—1224no—
562D4—1224no—
563D4—1228no—
564D4—1224no—
565D4—1224no—
566D4—1228no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—4882no—
584C2×C4—4882no—
585C2×C4—4882no—
586C2×C4—4882no—
587C2×C4—4882no—
588C2×C4—4882no—
589C2×C4—2444no—
590C2×C4—2444no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6111yescharacteristic
597C2×C4C22⋊C4×D6112yes—
598C2×C4M16×D6112yes—
599C2×C4C2×D4×D6112yes—
600C8—44no—
601C8—2444no—
602C22—21no—
603C22—21no—
604C22—22no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—614no—
610C22—1222no—
611C22—1222no—
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—2442no—
626C22—2442no—
627C22—2441no—
628C22—2441no—
629C22—2441no—
630C22—2441no—
631C22C2×C22⋊C4×D6111yescharacteristic
632C22C2×M16×D6111yescharacteristic
633C22C2×M16×D6111yescharacteristic
634C4—21no—
635C4—21no—
636C4—22no—
637C4—22no—
638C4—22no—
639C4—41no—
640C4—41no—
641C4—1222no—
642C4—1222no—
643C4—2441no—
644C4—2441no—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—1224no—
649C2—2442no—
650C2—2442no—
651C2—2442no—
652C2#407×D6111yescharacteristic
653C2#2145427811yescharacteristic
654C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1464C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D244C4
cosocleC22×C4×C61C24
hypercenter#1464D61
hypocenterC61#17367
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #21454847C2semidirect
3. #21444159C2semidirect
4. #21444156C2semidirect
5. #21444153C2semidirect
6. #21444144C2semidirect
7. #21444136C2semidirect
8. #323×D61C2semidirect
9. C61×#1464C2semidirect
28. #16839819C22semidirect
29. #16839724C22semidirect
30. C22⋊C8×D61C22semidirect
31. #16839488C22semidirect
33. #16839485C22semidirect
34. #16839485C22semidirect
36. C61×#432C22semidirect
37. C61×#324C22semidirect
118. C23×D61M16semidirect
152. C2×D244M16semidirect
323. #1464D61semidirect
357. #432C2×D61semidirect
361. #324C2×D61semidirect
366. C61#17367semidirect

Maximal subgroups

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

subgroupindex
C2×#168402362
#214548472
#214441592
#214441562
#214441532
#214441442
#214441362
#323×D612
C61×#14642
#1736761