Finite Group Databasebeta

← D61×#2085 #29708977

Subgroups — D61×#2085 #29708977

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D61C211yesmaximal, characteristic
2C2×#106×D61C211yesmaximal, characteristic
3#389×D61C211yesmaximal, characteristic
4#382×D61C211yesmaximal, characteristic
5#21447306C211yesmaximal, characteristic, complemented
6#21447305C211yesmaximal, characteristic, complemented
7#21447304C211yesmaximal, characteristic, complemented
8#21447303C211yesmaximal, characteristic, complemented
9#21447302C211yesmaximal, characteristic, complemented
10#21447301C211yesmaximal, characteristic, complemented
11#21447300C211yesmaximal, characteristic, complemented
12#340×D61C211yesmaximal, characteristic
13#340×D61C211yesmaximal, characteristic
14#336×D61C211yesmaximal, characteristic
15C61×#2085C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4⋊C4×D61—21no—
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C42×D61C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27#107×D61—24no—
28C2×#14519709C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31#106×D61—24no—
32#16839661C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839659—21no—
35#16839658C2211yescharacteristic
36#16839657—21no—
37#16839628C2211yescharacteristic
38#16839627C2211yescharacteristic
39#16839627C2211yescharacteristic
40#16839626—21no—
41#16839626—21no—
42#95×D61—21no—
43#95×D61—21no—
44#95×D61—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#382C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61Q814yes—
75C2×C8×D61Q814yes—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—22no—
91C4⋊C4×D61—22no—
92C4⋊C4×D61—22no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—44no—
95C4⋊C4×D61D414yes—
96C2×C4×Dic61D411yescharacteristic
97C2×C4×Dic61D411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C42×D61—22no—
100C42×D61—22no—
101#14519711—22no—
102#14519710—22no—
103#14519710—22no—
104#14519709—22no—
105#14519708—22no—
106#14519708—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124#107×C61—22no—
125#106×C61—22no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129C23×D61C2×D411yescharacteristic
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C2×C4×D61—24no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61C2×D412yes—
163C2×C4×D61C2×Q812yes—
164C2×C4×D61C2×Q812yes—
165C2×C4×D61#4112yes—
166C2×C4×D61#4112yes—
167C2×C4×D61#4112yes—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61C2×Q812yes—
173C2×C8×C61C2×Q812yes—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—42no—
182C4⋊C4×C61C2×D412yes—
183C42×C61—21no—
184C42×C61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—42no—
193C4⋊Dic61C2×D412yes—
194#11758196—24no—
195#11758196—42no—
196#11758196—42no—
197#11758196—42no—
198#11758196—42no—
199#11758196—42no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×Q812yes—
209C2×#92418C2×Q812yes—
210C8×D61—28no—
211C8×D61—28no—
212C23×C61C22×D411yescharacteristic
213C22×D61#12112yes—
214C22×D61#12312yes—
215C22×D61C4⋊Q812yes—
216C22×D61#13512yes—
217C22×D61#13512yes—
218C22×D61AGL(1,ℤ/8)12yes—
219C22×D61#13712yes—
220C2×C4×C61—22no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×Q811yescharacteristic
240C2×C4×C61C22×Q811yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61#12112yes—
263C2×Dic61#12312yes—
264C2×Dic61C4⋊Q812yes—
265C4×D61—48no—
266C4×D61—44no—
267C4×D61—44no—
268C4×D61—84no—
269C4×D61—84no—
270C4×D61—84no—
271C4×D61C22⋊Q814yes—
272C4×D61C22⋊Q814yes—
273C4×D61#12514yes—
274C4×D61#12514yes—
275C8×C61—22no—
276C8×C61—22no—
277#92418—22no—
278#92418—22no—
279C2×#2085—611nomaximal, Sylow
280C22×C61C2×#12111yescharacteristic
281C22×C61C2×#12311yescharacteristic
282C22×C61C2×C4⋊Q811yescharacteristic
283C22×C61C2×#13511yescharacteristic
284C22×C61C2×#13511yescharacteristic
285C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C61C2×#13711yescharacteristic
287C2×D61#39814yes—
288C2×D61#46314yes—
289C2×D61#46414yes—
290C2×D61#48214yes—
291C2×D61#48514yes—
292C2×D61#49914yes—
293C2×D61#50114yes—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—42no—
297C4×C61—81no—
298C4×C61—81no—
299C4×C61—81no—
300C4×C61C2×C22⋊Q811yescharacteristic
301C4×C61C2×C22⋊Q811yescharacteristic
302C4×C61C2×#12511yescharacteristic
303C4×C61C2×#12511yescharacteristic
304Dic61—41no—
305Dic61—41no—
306Dic61—42no—
307Dic61—81no—
308Dic61—81no—
309Dic61—81no—
310Dic61#39814yes—
311C22×#107—611no—
312C22×#106—611no—
313C2×#389—611no—
314C2×#382—611no—
315#2085—611no—
316#2085—611no—
317#2085—611no—
318#2085—611no—
319#2085—611no—
320#2085—611no—
321#2085—611no—
322#2085D6111yescharacteristic, direct product factor
323C2×#340—611no—
324C2×#340—611no—
325C2×#336—611no—
326C2×C61C2×#39811yescharacteristic
327C2×C61C2×#46311yescharacteristic
328C2×C61C2×#46411yescharacteristic
329C2×C61C2×#48211yescharacteristic
330C2×C61C2×#48511yescharacteristic
331C2×C61C2×#49911yescharacteristic
332C2×C61C2×#50111yescharacteristic
333D61#208518yesdirect product factor
334C23×C8—611no—
335C23×C8—611no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4—611no—
338C22×C4⋊C4—611no—
339C22×C4⋊C4—611no—
340C22×C4⋊C4—1221no—
341C22×C42—611no—
342C2×#107—611no—
343C2×#107—611no—
344C2×#107—611no—
345C2×#107—1224no—
346C2×#107C2×D6111yescharacteristic
347C2×#106—611no—
348C2×#106—611no—
349C2×#106—611no—
350C2×#106—1224no—
351C2×#106C2×D6111yescharacteristic
352#389—611no—
353#389—611no—
354#389—611no—
355#389—1221no—
356#389—1221no—
357#389C2×D6111yescharacteristic
358#382—611no—
359#382—611no—
360#382—611no—
361#382—1221no—
362#382—1221no—
363#382C2×D6111yescharacteristic
364C2×#95—1221no—
365C2×#95—1221no—
366C2×#95—1221no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340C2×D6111yescharacteristic
374#340C2×D6111yescharacteristic
375#336—611no—
376#336—611no—
377#336—611no—
378#336C2×D6111yescharacteristic
379C61C2×#208511yescharacteristic, complemented, Sylow
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—1221no—
384C23×C4—1221no—
385C23×C4—1221no—
386C23×C4—1221no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8—614no—
390C22×C8—614no—
391C22×C8—1222no—
392C22×C8—1222no—
393C22×C8—1222no—
394C22×C8—1222no—
395C22×C8C22×D6111yescharacteristic
396C22×C8C22×D6111yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—614no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1222no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—2444no—
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C4⋊C4C22×D6111yescharacteristic
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—1222no—
426C2×C42—1222no—
427C2×C42C22×D6111yescharacteristic
428#107—22no—
429#107—1222no—
430#107—1222no—
431#107—1222no—
432#106—22no—
433#106—1222no—
434#106—1222no—
435#106—1222no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448C24—611no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—611no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1224no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4D4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C22×C4C23×D6111yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—612no—
492C2×C8—612no—
493C2×C8—1228no—
494C2×C8—1228no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8Q8×D6112yes—
500C2×C8Q8×D6112yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—612no—
510C4⋊C4—1224no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—2442no—
519C4⋊C4—2442no—
520C4⋊C4—2442no—
521C4⋊C4—2442no—
522C4⋊C4—2442no—
523C4⋊C4—2442no—
524C4⋊C4D4×D6112yes—
525C42—21no—
526C42—21no—
527C42—1222no—
528C42—1222no—
529C42—1221no—
530C42—1221no—
531C23—612no—
532C23—612no—
533C23—612no—
534C23—612no—
535C23—612no—
536C23—612no—
537C23—612no—
538C23C2×D4×D6111yescharacteristic
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—612no—
560C2×C4—614no—
561C2×C4—614no—
562C2×C4—614no—
563C2×C4—614no—
564C2×C4—1222no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—4884no—
572C2×C4—4884no—
573C2×C4—4884no—
574C2×C4—2444no—
575C2×C4—2444no—
576C2×C4—2448no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4C2×D4×D6111yescharacteristic
589C2×C4C2×Q8×D6111yescharacteristic
590C2×C4C2×Q8×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C8—22no—
595C8—22no—
596C8—1222no—
597C8—1222no—
598C22—614no—
599C22—614no—
600C22—614no—
601C22—614no—
602C22—614no—
603C22—614no—
604C22—614no—
605C22#121×D6111yescharacteristic
606C22#123×D6111yescharacteristic
607C22C4⋊Q8×D6111yescharacteristic
608C22#135×D6111yescharacteristic
609C22#135×D6111yescharacteristic
610C22AGL(1,ℤ/8)×D6111yescharacteristic
611C22#137×D6111yescharacteristic
612C4—41no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—614no—
619C4—4881no—
620C4—4881no—
621C4—4881no—
622C4—2441no—
623C4—2441no—
624C4—2442no—
625C4C22⋊Q8×D6111yescharacteristic
626C4C22⋊Q8×D6111yescharacteristic
627C4#125×D6111yescharacteristic
628C4#125×D6111yescharacteristic
629C2—618no—
630C2#398×D6111yescharacteristic
631C2#463×D6111yescharacteristic
632C2#464×D6111yescharacteristic
633C2#482×D6111yescharacteristic
634C2#485×D6111yescharacteristic
635C2#499×D6111yescharacteristic
636C2#501×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2085C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2085D61
hypocenterC61C2×#2085
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #21447306C2semidirect
6. #21447305C2semidirect
7. #21447304C2semidirect
8. #21447303C2semidirect
9. #21447302C2semidirect
10. #21447301C2semidirect
11. #21447300C2semidirect
15. C61×#2085C2semidirect
322. #2085D61direct (N × H)
333. D61#2085direct (N × H)
379. C61C2×#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D612
C2×#106×D612
#389×D612
#382×D612
#214473062
#214473052
#214473042
#214473032
#214473022
#214473012
#214473002
#340×D612
#336×D612
C61×#20852
C2×#208561