Finite Group Databasebeta

← D61×#1590 #29649743

Subgroups — D61×#1590 #29649743

Order 15616.

746 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
1#446×D61C211yesmaximal, characteristic, complemented
2C4×SD16×D61C211yesmaximal, characteristic
3#436×D61C211yesmaximal, characteristic
4#21444712C211yesmaximal, characteristic, complemented
5#21444711C211yesmaximal, characteristic, complemented
6#21444710C211yesmaximal, characteristic, complemented
7#21444709C211yesmaximal, characteristic, complemented
8#21444708C211yesmaximal, characteristic, complemented
9#21444707C211yesmaximal, characteristic, complemented
10#21444706C211yesmaximal, characteristic, complemented
11#334×D61C211yesmaximal, characteristic, complemented
12Q8⋊C8×D61C211yesmaximal, characteristic, complemented
13D4⋊C8×D61C211yesmaximal, characteristic
14C82×D61C211yesmaximal, characteristic, complemented
15C61×#1590C211yesmaximal, characteristic, complemented
16C2×SD16×D61C411yescharacteristic
17C2×M16×D61—21no—
18C4×Q8×D61C2211yescharacteristic
19C4×D4×D61C2211yescharacteristic
20#16839893C2211yescharacteristic, complemented
21#16839892C2211yescharacteristic, complemented
22#16839891—21no—
23#16839890—21no—
24#16839889C2211yescharacteristic, complemented
25#16839853C411yescharacteristic
26C4×#11758190C2211yescharacteristic
27SD16×Dic61C411yescharacteristic
28C4×#11758201C2211yescharacteristic
29#16839849C411yescharacteristic
30C4×#11758200C2211yescharacteristic
31#16839847C411yescharacteristic
32#16839841C2211yescharacteristic
33#16839840C2211yescharacteristic
34#16839839C2211yescharacteristic
35#16839838—21no—
36#16839837—21no—
37#106×D61C411yescharacteristic
38C4⋊C8×D61—21no—
39C4⋊C8×D61C2211yescharacteristic
40C4⋊C8×D61C2211yescharacteristic
41#103×D61C411yescharacteristic
42#102×D61C411yescharacteristic
43C22⋊C8×D61—21no—
44#97×D61—21no—
45C4×C8×D61C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839513C2211yescharacteristic, complemented
49#16839512C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51#16839494C2211yescharacteristic, complemented
52Q8⋊#92418C2211yescharacteristic, complemented
53#16839492C2211yescharacteristic, complemented
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57C8×#92418C2211yescharacteristic, complemented
58C8×#92418C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C61×#446C2211yescharacteristic, complemented
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#334C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic, complemented
67C2×Q8×D61C2×C411yescharacteristic
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C2×#11758190C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758201C2×C411yescharacteristic
73SD16×D61—24no—
74C2×#11758194—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77M16×D61—44no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61C2×C411yescharacteristic
82C2×C8×D61C2×C411yescharacteristic
83C2×C8×D61D411yescharacteristic
84C2×C8×D61D411yescharacteristic
85Q8×Dic61C2×C411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122C2311yescharacteristic
88#14519742—21no—
89#14519742C2×C411yescharacteristic
90C4×D244C2311yescharacteristic
91D4×Dic61C2×C411yescharacteristic
92#14519739C2×C411yescharacteristic
93C4×C22⋊D61—21no—
94#14519737—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61C2×C411yescharacteristic
97C4⋊C4×D61C2×C411yescharacteristic
98C22⋊C4×D61—21no—
99C42×D61—21no—
100C42×D61C2311yescharacteristic
101#14519709C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103#14519708C2×C411yescharacteristic
104C4⋊#92418—21no—
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519702C2×C411yescharacteristic
112#14519701C2×C411yescharacteristic
113#14519700C2×C411yescharacteristic
114#14519699C2×C411yescharacteristic
115#14519698C2×C411yescharacteristic
116#14519697C2×C411yescharacteristic
117C22⋊#92418—21no—
118#14519689—21no—
119#14519689—21no—
120#14519688—21no—
121#14519687—21no—
122#14519687—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61C2×C411yescharacteristic
129C8×Dic61D411yescharacteristic
130C8×Dic61D411yescharacteristic
131C2×SD16×C61C2×C411yescharacteristic
132C2×M16×C61—21no—
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#106×C61C2×C411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61C2×C411yescharacteristic
140#102×C61C2×C411yescharacteristic
141C22⋊C8×C61—21no—
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C4×C8×C61C2311yescharacteristic
146C23×D61—21no—
147C2×Q8×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152Q8×D61—22no—
153Q8×D61—22no—
154D4×D61—22no—
155D4×D61—22no—
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61#4111yescharacteristic
167C2×Dic122—21no—
168C2×Dic122C22×C411yescharacteristic
169SD16×C61—22no—
170M16×C61—42no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61C22×C411yescharacteristic
175C2×C8×C61C22×C411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C4⋊C4×C61—21no—
179C4⋊C4×C61C22×C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—21no—
182C42×C61—21no—
183C42×C61C2411yescharacteristic
184C22⋊Dic61—21no—
185#11758201—22no—
186#11758200—22no—
187#11758198—21no—
188#11758198—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61C22×C411yescharacteristic
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61C22×C411yescharacteristic
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61#4111yescharacteristic
202#11758194—42no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210#11758190—22no—
211#11758189—42no—
212#11758189—42no—
213C8×D61—24no—
214C8×D61—22no—
215C8×D61—22no—
216C8×D61—42no—
217C8×D61—42no—
218C8×D61M1614yescomplemented
219C8×D61SD1614yescomplemented
220C23×C61—21no—
221C22×D61—21no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61C4×D411yescharacteristic
226Q8×C61—21no—
227Q8×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61C23×C411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C22⋊D61—42no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—42no—
243C2×Dic61C4×D411yescharacteristic
244C2×Dic61C4×D411yescharacteristic
245C2×Dic61C4×D411yescharacteristic
246D244—21no—
247D244—21no—
248C4×D61—22no—
249C4×D61—42no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—42no—
255C4×D61C2×M1612yes—
256C4×D61#13112yes—
257C4×D61C2×SD1612yes—
258C4×D61#13512yes—
259Dic122—21no—
260Dic122—21no—
261Dic122—42no—
262C8×C61—22no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—41no—
266C8×C61—41no—
267C8×C61C2×M1612yescomplemented
268C8×C61C2×SD1612yescomplemented
269#92418—22no—
270#92418—21no—
271#92418—21no—
272#92418—41no—
273#92418—41no—
274#92418C2×M1612yescomplemented
275#92418C2×SD1612yescomplemented
276C2×#1590—611nomaximal, Sylow
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61C2×C4×D411yescharacteristic
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—84no—
285C2×D61#43612yes—
286C2×D61C4×SD1612yes—
287C2×D61#44312yes—
288C4×C61—21no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61C22×M1611yescharacteristic
293C4×C61C2×#13111yescharacteristic
294C4×C61C22×SD1611yescharacteristic
295C4×C61C2×#13511yescharacteristic
296Dic61—21no—
297Dic61—41no—
298Dic61—41no—
299Dic61—41no—
300Dic61#43612yes—
301Dic61C4×SD1612yes—
302C2×#446—611no—
303C2×C4×SD16—611no—
304C2×#436—611no—
305#1590—611no—
306#1590—611no—
307#1590—611no—
308#1590—611no—
309#1590—611no—
310#1590—611no—
311#1590—611no—
312#1590D6111yescharacteristic, direct product factor
313C2×#334—611no—
314C2×Q8⋊C8—611no—
315C2×D4⋊C8—611no—
316C2×C82—611no—
317C2×C61—81no—
318C2×C61C2×#43611yescharacteristic
319C2×C61C2×C4×SD1611yescharacteristic
320C2×C61C2×#44311yescharacteristic
321D61—81no—
322D61#159014yesdirect product factor
323C22×SD16—611no—
324C22×M16—1221no—
325C2×C4×Q8—611no—
326C2×C4×D4—611no—
327#446—611no—
328#446—611no—
329#446—611no—
330#446—1221no—
331#446—1221no—
332#446C2×D6111yescharacteristic, complemented
333C4×SD16—611no—
334C4×SD16—611no—
335C4×SD16—611no—
336C4×SD16—611no—
337C4×SD16—611no—
338C4×SD16—611no—
339C4×SD16—611no—
340C4×SD16C2×D6111yescharacteristic
341#436—611no—
342#436—611no—
343#436—611no—
344#436—1221no—
345#436—1221no—
346#436C2×D6111yescharacteristic
347C2×#106—611no—
348C2×C4⋊C8—611no—
349C2×C4⋊C8—611no—
350C2×C4⋊C8—1221no—
351C2×#103—611no—
352C2×#102—611no—
353C2×C22⋊C8—1221no—
354C2×#97—1221no—
355C2×C4×C8—611no—
356C2×C4×C8—611no—
357C2×C4×C8—611no—
358#334—611no—
359#334—611no—
360#334—611no—
361#334C2×D6111yescharacteristic, complemented
362Q8⋊C8—611no—
363Q8⋊C8—611no—
364Q8⋊C8—611no—
365Q8⋊C8C2×D6111yescharacteristic, complemented
366D4⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8—611no—
369D4⋊C8C2×D6111yescharacteristic
370C82—611no—
371C82—611no—
372C82—611no—
373C82C2×D6111yescharacteristic, complemented
374C61C2×#159011yescharacteristic, complemented, Sylow
375C22×Q8—611no—
376C22×D4—611no—
377C23×C4—1221no—
378C2×SD16—611no—
379C2×SD16—611no—
380C2×SD16—611no—
381C2×SD16—1224no—
382C2×SD16C4×D6111yescharacteristic
383C2×M16—21no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C2×M16—2444no—
388C22×C8—611no—
389C22×C8—611no—
390C22×C8—611no—
391C22×C8—611no—
392C22×C8—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C4×Q8—611no—
396C4×Q8—611no—
397C4×Q8—611no—
398C4×Q8—1221no—
399C4×Q8—1221no—
400C4×Q8C22×D6111yescharacteristic
401C4×D4—611no—
402C4×D4—611no—
403C4×D4—611no—
404C4×D4—1221no—
405C4×D4—1221no—
406C4×D4C22×D6111yescharacteristic
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C42—611no—
412C2×C42—1221no—
413#106—611no—
414#106—611no—
415#106—611no—
416#106C4×D6111yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—611no—
419C4⋊C8—611no—
420C4⋊C8—1221no—
421C4⋊C8—1221no—
422C4⋊C8—1221no—
423C4⋊C8—1221no—
424C4⋊C8—1221no—
425C4⋊C8C22×D6111yescharacteristic
426C4⋊C8C22×D6111yescharacteristic
427#103—611no—
428#103—611no—
429#103—611no—
430#103C4×D6111yescharacteristic
431#102—611no—
432#102—611no—
433#102—611no—
434#102C4×D6111yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439#97—21no—
440#97—1221no—
441#97—1221no—
442#97—1221no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8—611no—
449C4×C8—611no—
450C4×C8—1221no—
451C4×C8C22×D6111yescharacteristic
452C4×C8C22×D6111yescharacteristic
453C4×C8C22×D6111yescharacteristic
454C24—1221no—
455C2×Q8—611no—
456C2×Q8—1221no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8C2×C4×D6111yescharacteristic
460C2×D4—611no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1221no—
464C2×D4C2×C4×D6111yescharacteristic
465C22×C4—21no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—2442no—
476C22×C4—2442no—
477SD16—22no—
478SD16—1222no—
479SD16—1222no—
480SD16—1222no—
481M16—42no—
482M16—2442no—
483M16—2442no—
484M16—2442no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—611no—
489C2×C8—611no—
490C2×C8—614no—
491C2×C8—614no—
492C2×C8—611no—
493C2×C8—611no—
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—1224no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—2442no—
501C2×C8—2442no—
502C2×C8C2×C4×D6111yescharacteristic
503C2×C8C2×C4×D6111yescharacteristic
504C2×C8D4×D6111yescharacteristic
505C2×C8D4×D6111yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—611no—
508C4⋊C4—611no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4C2×C4×D6111yescharacteristic
515C4⋊C4C2×C4×D6111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C42—21no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—1221no—
525C42—1221no—
526C42—1221no—
527C42C23×D6111yescharacteristic
528C23—21no—
529C23—611no—
530C23—1221no—
531C23—2442no—
532C23—2442no—
533C23—2442no—
534Q8—21no—
535Q8—21no—
536Q8—1221no—
537Q8—1221no—
538Q8—2442no—
539D4—21no—
540D4—21no—
541D4—1221no—
542D4—1221no—
543D4—2442no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—612no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—611no—
556C2×C4—1222no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4C22×C4×D6111yescharacteristic
568C2×C4C2×D4×D6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C8—22no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—612no—
576C8—612no—
577C8—1222no—
578C8—1221no—
579C8—1221no—
580C8—2441no—
581C8—2441no—
582C8M16×D6112yescomplemented
583C8SD16×D6112yescomplemented
584C22—41no—
585C22—41no—
586C22—41no—
587C22—612no—
588C22—612no—
589C22—612no—
590C22—4884no—
591C22—2441no—
592C22—2441no—
593C22—2441no—
594C22C4×D4×D6111yescharacteristic
595C4—21no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—612no—
600C4—612no—
601C4—1221no—
602C4—2441no—
603C4—2441no—
604C4—2441no—
605C4C2×M16×D6111yescharacteristic
606C4#131×D6111yescharacteristic
607C4C2×SD16×D6111yescharacteristic
608C4#135×D6111yescharacteristic
609C2—81no—
610C2—614no—
611C2—4881no—
612C2#436×D6111yescharacteristic
613C2C4×SD16×D6111yescharacteristic
614C2#443×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1590C2
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C2×C4
cosocleC42×C61C24
hypercenter#1590D61
hypocenterC61C2×#1590
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #446×D61C2semidirect
4. #21444712C2semidirect
5. #21444711C2semidirect
6. #21444710C2semidirect
7. #21444709C2semidirect
8. #21444708C2semidirect
9. #21444707C2semidirect
10. #21444706C2semidirect
11. #334×D61C2semidirect
12. Q8⋊C8×D61C2semidirect
14. C82×D61C2semidirect
15. C61×#1590C2semidirect
20. #16839893C22semidirect
21. #16839892C22semidirect
24. #16839889C22semidirect
48. #16839513C22semidirect
49. #16839512C22semidirect
50. #16839512C22semidirect
51. #16839494C22semidirect
52. Q8⋊#92418C22semidirect
53. #16839492C22semidirect
57. C8×#92418C22semidirect
58. C8×#92418C22semidirect
59. C8×#92418C22semidirect
60. C61×#446C22semidirect
63. C61×#334C22semidirect
64. C61×Q8⋊C8C22semidirect
66. C82×C61C22semidirect
218. C8×D61M16semidirect
219. C8×D61SD16semidirect
267. C8×C61C2×M16semidirect
268. C8×C61C2×SD16semidirect
274. #92418C2×M16semidirect
275. #92418C2×SD16semidirect
312. #1590D61direct (N × H)
322. D61#1590direct (N × H)
332. #446C2×D61semidirect
361. #334C2×D61semidirect
365. Q8⋊C8C2×D61semidirect
373. C82C2×D61semidirect
374. C61C2×#1590semidirect
582. C8M16×D61semidirect
583. C8SD16×D61semidirect

Maximal subgroups

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

subgroupindex
#446×D612
C4×SD16×D612
#436×D612
#214447122
#214447112
#214447102
#214447092
#214447082
#214447072
#214447062
#334×D612
Q8⋊C8×D612
D4⋊C8×D612
C82×D612
C61×#15902
C2×#159061