Finite Group Databasebeta

← #29649591

Subgroups — #29649591

Order 15616.

748 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454782C211yesmaximal, characteristic, complemented
2C4×#14519801C211yesmaximal, characteristic
3C8×D4×D61C211yesmaximal, characteristic, complemented
4#21444686C211yesmaximal, characteristic, complemented
5#21444684C211yesmaximal, characteristic, complemented
6#21444675C211yesmaximal, characteristic, complemented
7#21444673C211yesmaximal, characteristic, complemented
8#21444657C211yesmaximal, characteristic, complemented
9#21444655C211yesmaximal, characteristic, complemented
10#21444646C211yesmaximal, characteristic, complemented
11#21444570C211yesmaximal, characteristic, complemented
12#21444208C211yesmaximal, characteristic, complemented
13#21444203C211yesmaximal, characteristic, complemented
14#21444105C211yesmaximal, characteristic, complemented
15C61×#1581C211yesmaximal, characteristic, complemented
16C2×#14519801C411yescharacteristic
17C22×C8×D61—21no—
18C4×#11758224C2211yescharacteristic
19C4×D4×D61C2211yescharacteristic
20#16839892C2211yescharacteristic, complemented
21#16839889C2211yescharacteristic, complemented
22#16839874C411yescharacteristic
23#16839871C411yescharacteristic
24#16839861C411yescharacteristic
25#16839859C411yescharacteristic
26C4×#11758190C2211yescharacteristic
27C4×#11758200C2211yescharacteristic
28C4×#11758199C2211yescharacteristic
29#16839840C2211yescharacteristic, complemented
30#16839836—21no—
31#16839831—21no—
32C8×D244C2211yescharacteristic
33D4×#92418C2211yescharacteristic
34#16839827C2211yescharacteristic
35C8×C22⋊D61—21no—
36#16839825—21no—
37#16839814C2211yescharacteristic
38#16839813C2211yescharacteristic
39#16839812—21no—
40#16839803C411yescharacteristic
41C4⋊C8×D61C2211yescharacteristic
42#16839765C411yescharacteristic
43#16839760C411yescharacteristic
44C22⋊C8×D61—21no—
45M16×Dic61—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic, complemented
49#16839513C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51#16839494C2211yescharacteristic, complemented
52#16839492C2211yescharacteristic, complemented
53#16839491C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic, complemented
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59#16839483C2211yescharacteristic, complemented
60C4×D8×C61C2211yescharacteristic
61C61×#436C2211yescharacteristic, complemented
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic, complemented
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic, complemented
66C61×#322C2211yescharacteristic, complemented
67C2×#11758224C2×C411yescharacteristic
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70#14519801—24no—
71C2×#11758190C2×C411yescharacteristic
72C2×#11758200C2×C411yescharacteristic
73C2×#11758199C2×C411yescharacteristic
74C2×#11758194—21no—
75C2×#11758189C2×C411yescharacteristic
76C2×#11758189C2×C411yescharacteristic
77C22×#92418—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61—44no—
82C2×C8×D61D411yescharacteristic
83C2×C8×D61D411yescharacteristic
84C4×Dic122C2311yescharacteristic
85#14519742C2×C411yescharacteristic
86C4×D244C2311yescharacteristic
87D4×Dic61C2×C411yescharacteristic
88D4×Dic61C2×C411yescharacteristic
89#14519739C2×C411yescharacteristic
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92#14519737—21no—
93#14519737—21no—
94#14519735C2×C411yescharacteristic
95#14519733—21no—
96C4⋊C4×D61C2×C411yescharacteristic
97C22⋊C4×D61—21no—
98C2×C4×Dic61—21no—
99C42×D61C2311yescharacteristic
100#14519710C2×C411yescharacteristic
101#14519709C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519702C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519698C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519697C2×C411yescharacteristic
115C22⋊#92418—21no—
116C22⋊#92418—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519687—21no—
122#14519687—21no—
123#14519687C2×C411yescharacteristic
124#14519687C2×C411yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C8×Dic61D411yescharacteristic
130C8×Dic61D411yescharacteristic
131C2×D8×C61C2×C411yescharacteristic
132C2×M16×C61—21no—
133C22×C8×C61—21no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136#107×C61C2×C411yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#102×C61C2×C411yescharacteristic
140#102×C61C2×C411yescharacteristic
141C22⋊C8×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C4×C8×C61C2311yescharacteristic
146C23×D61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156#11758224—22no—
157#11758224—22no—
158D4×D61—22no—
159D4×D61M1614yescomplemented
160C2×D244C22×C411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61#4111yescharacteristic
169C2×Dic122C22×C411yescharacteristic
170D8×C61—22no—
171M16×C61—42no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—42no—
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C4⋊C4×C61C22×C411yescharacteristic
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C42×C61C2411yescharacteristic
185C22⋊Dic61—21no—
186C22⋊Dic61—21no—
187#11758200—22no—
188#11758199—22no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61C22×C411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61#4111yescharacteristic
203#11758194—42no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—42no—
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212#11758190—22no—
213#11758189—22no—
214#11758189—22no—
215C8×D61—22no—
216C8×D61—41no—
217C8×D61—42no—
218C8×D61—42no—
219C8×D61—42no—
220C23×C61—21no—
221C23×C61—21no—
222C22×D61—21no—
223C22×D61—24no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61C4×D411yescharacteristic
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61C2×M1612yes—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C22⋊D61—24no—
241C22⋊D61—42no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61C4×D411yescharacteristic
249C2×Dic61C4×D411yescharacteristic
250C2×Dic61C4×D411yescharacteristic
251D244—21no—
252D244C2×M1612yes—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—41no—
256C4×D61—42no—
257C4×D61—42no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61C2×M1612yes—
261C4×D61#13112yes—
262Dic122—21no—
263Dic122—21no—
264C8×C61—21no—
265C8×C61—21no—
266C8×C61—21no—
267C8×C61—41no—
268C8×C61—41no—
269C8×C61—41no—
270C8×C61AGL(1,ℤ/8)12yescomplemented
271#92418—21no—
272#92418—21no—
273#92418—21no—
274#92418—21no—
275#92418—41no—
276#92418—41no—
277#92418—41no—
278#17869—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61C2×C4×D411yescharacteristic
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—22no—
289C2×D61—48no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61#43512yes—
293C4×C61—21no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61C22×M1611yescharacteristic
297C4×C61C2×#13111yescharacteristic
298C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C61#57511yescharacteristic
300Dic61—21no—
301Dic61—21no—
302Dic61—41no—
303Dic61—41no—
304Dic61—41no—
305Dic61#43512yes—
306#2965—611no—
307C4×AGL(1,ℤ/8)—611no—
308C2×C8×D4—611no—
309#1586—611no—
310#1586—611no—
311#1585—611no—
312#1585—611no—
313#1582—611no—
314#1582—611no—
315#1581—611no—
316#1581D6111yescharacteristic, complemented
317#1565—611no—
318#1478—611no—
319#1477—611no—
320#1451—611no—
321C2×C61—42no—
322C2×C61—81no—
323C2×C61C2×#43511yescharacteristic
324C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
325C2×C61#295511yescharacteristic
326D61—22no—
327D61—42no—
328C2×AGL(1,ℤ/8)—611no—
329C23×C8—1221no—
330C4×#41—611no—
331C2×C4×D4—611no—
332#446—611no—
333#446—611no—
334#442—611no—
335#442—611no—
336#440—611no—
337#440—611no—
338C4×SD16—611no—
339C4×SD16—611no—
340C4×D8—611no—
341C4×D8C2×D6111yescharacteristic
342#436—611no—
343#436C2×D6111yescharacteristic, complemented
344#435—1221no—
345#435—1221no—
346C8×D4—611no—
347C8×D4—611no—
348C8×D4—611no—
349C8×D4—1221no—
350C8×D4—1221no—
351C8×D4C2×D6111yescharacteristic
352#431—611no—
353#431—611no—
354#431—1221no—
355#428—611no—
356C2×C4⋊C8—611no—
357#418—611no—
358#417—611no—
359C2×C22⋊C8—1221no—
360C4×M16—611no—
361C4×M16—1221no—
362C2×C4×C8—611no—
363#335—611no—
364#335C2×D6111yescharacteristic, complemented
365#334—611no—
366#334—611no—
367Q8⋊C8—611no—
368Q8⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8C2×D6111yescharacteristic
374D4⋊C8C2×D6111yescharacteristic, complemented
375#322—611no—
376#322—611no—
377#322—611no—
378#322C2×D6111yescharacteristic, complemented
379C61#1786911yescharacteristic, complemented, Sylow
380C2×#41—611no—
381C22×D4—611no—
382C23×C4—1221no—
383AGL(1,ℤ/8)—1224no—
384C2×SD16—611no—
385C2×SD16—611no—
386C2×D8—611no—
387C2×D8C4×D6111yescharacteristic
388C2×M16—21no—
389C2×M16—611no—
390C2×M16—611no—
391C2×M16—1221no—
392C22×C8—21no—
393C22×C8—611no—
394C22×C8—611no—
395C22×C8—1221no—
396C22×C8—1221no—
397C22×C8—1221no—
398C22×C8—1221no—
399C22×C8—2444no—
400C4×Q8—611no—
401C4×Q8—611no—
402C4×D4—611no—
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4C22×D6111yescharacteristic
411C4×D4C22×D6111yescharacteristic
412#117—611no—
413#117—1221no—
414C2×C4⋊C4—611no—
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417C2×C42—1221no—
418#107—611no—
419#107C4×D6111yescharacteristic
420#106—611no—
421#106—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—1221no—
425C4⋊C8—1221no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8C22×D6111yescharacteristic
429C4⋊C8C22×D6111yescharacteristic
430#103—611no—
431#103—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102—611no—
436#102C4×D6111yescharacteristic
437#102C4×D6111yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446#97—611no—
447#97—611no—
448#97—1221no—
449#97—1221no—
450C4×C8—611no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—1221no—
456C4×C8C22×D6111yescharacteristic
457C4×C8C22×D6111yescharacteristic
458C4×C8C22×D6111yescharacteristic
459C24—1221no—
460#41—1222no—
461#41—1222no—
462C2×Q8—611no—
463C2×D4—614no—
464C2×D4—611no—
465C2×D4—1222no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4C2×C4×D6111yescharacteristic
469C2×D4C2×C4×D6111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—2442no—
482C22×C4—2442no—
483SD16—1222no—
484SD16—1222no—
485D8—22no—
486D8—1222no—
487M16—42no—
488M16—1222no—
489M16—1222no—
490M16—2442no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—611no—
498C2×C8—611no—
499C2×C8—1222no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—2441no—
504C2×C8—2442no—
505C2×C8—2442no—
506C2×C8—2442no—
507C2×C8—2442no—
508C2×C8C2×C4×D6111yescharacteristic
509C2×C8C2×C4×D6111yescharacteristic
510C2×C8D4×D6111yescharacteristic
511C2×C8D4×D6111yescharacteristic
512C4⋊C4—611no—
513C4⋊C4—611no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4C2×C4×D6111yescharacteristic
518C4⋊C4C2×C4×D6111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—1221no—
530C42—1221no—
531C42—1221no—
532C42C23×D6111yescharacteristic
533C23—21no—
534C23—21no—
535C23—611no—
536C23—1224no—
537C23—1221no—
538C23—2442no—
539C23—2442no—
540Q8—1221no—
541Q8—1221no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—612no—
546D4—1224no—
547D4—1221no—
548D4—2442no—
549D4M16×D6112yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—611no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—2441no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4C22×C4×D6111yescharacteristic
575C2×C4C2×D4×D6111yescharacteristic
576C2×C4#41×D6111yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—1221no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C8#1451980112yescomplemented
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—612no—
598C22—1221no—
599C22—1221no—
600C22—1222no—
601C22—2448no—
602C22—2441no—
603C22—2441no—
604C22C4×D4×D6111yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—612no—
609C4—1221no—
610C4—1221no—
611C4—2441no—
612C4—2441no—
613C4—2441no—
614C4C2×M16×D6111yescharacteristic
615C4#131×D6111yescharacteristic
616C4C2×#1451980111yescharacteristic
617C4#1684055911yescharacteristic
618C2—42no—
619C2—81no—
620C2—1222no—
621C2—2442no—
622C2#435×D6111yescharacteristic
623C2C4×#1451980111yescharacteristic
624C2#2145471911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1581C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519801C4
cosocleC42×C61C24
hypercenter#1581D61
hypocenterC61#17869
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. #21454782C2semidirect
3. C8×D4×D61C2semidirect
4. #21444686C2semidirect
5. #21444684C2semidirect
6. #21444675C2semidirect
7. #21444673C2semidirect
8. #21444657C2semidirect
9. #21444655C2semidirect
10. #21444646C2semidirect
11. #21444570C2semidirect
12. #21444208C2semidirect
13. #21444203C2semidirect
14. #21444105C2semidirect
15. C61×#1581C2semidirect
20. #16839892C22semidirect
21. #16839889C22semidirect
29. #16839840C22semidirect
48. #16839514C22semidirect
49. #16839513C22semidirect
50. #16839512C22semidirect
51. #16839494C22semidirect
52. #16839492C22semidirect
55. D4⋊#92418C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. #16839483C22semidirect
61. C61×#436C22semidirect
63. C61×#335C22semidirect
65. C61×D4⋊C8C22semidirect
66. C61×#322C22semidirect
159. D4×D61M16semidirect
270. C8×C61AGL(1,ℤ/8)semidirect
316. #1581D61semidirect
343. #436C2×D61semidirect
364. #335C2×D61semidirect
374. D4⋊C8C2×D61semidirect
378. #322C2×D61semidirect
379. C61#17869semidirect
590. C8#14519801semidirect

Maximal subgroups

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

subgroupindex
#214547822
C4×#145198012
C8×D4×D612
#214446862
#214446842
#214446752
#214446732
#214446572
#214446552
#214446462
#214445702
#214442082
#214442032
#214441052
C61×#15812
#1786961