Finite Group Databasebeta

← D61×#2064 #29708549

Subgroups — D61×#2064 #29708549

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D61C211yesmaximal, characteristic
2#428×D61C211yesmaximal, characteristic
3#424×D61C211yesmaximal, characteristic
4#419×D61C211yesmaximal, characteristic
5C2×#103×D61C211yesmaximal, characteristic
6C2×#101×D61C211yesmaximal, characteristic
7#21447187C211yesmaximal, characteristic, complemented
8#21447186C211yesmaximal, characteristic, complemented
9#21447185C211yesmaximal, characteristic, complemented
10#21447184C211yesmaximal, characteristic, complemented
11#21447183C211yesmaximal, characteristic, complemented
12#21447182C211yesmaximal, characteristic, complemented
13#21447181C211yesmaximal, characteristic, complemented
14#343×D61C211yesmaximal, characteristic
15C61×#2064C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#117×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×#14519713C2211yescharacteristic
24C2×#14519712C2211yescharacteristic
25C2×#14519712C2211yescharacteristic
26#108×D61—24no—
27#16839805C2211yescharacteristic
28#16839804C2211yescharacteristic
29#16839803—21no—
30#16839802C2211yescharacteristic
31#16839801—21no—
32#107×D61—21no—
33#106×D61—21no—
34#16839790C2211yescharacteristic
35#16839789C2211yescharacteristic
36#16839788C2211yescharacteristic
37#16839787—22no—
38C4⋊C8×D61—22no—
39#16839772C2211yescharacteristic
40#16839771C2211yescharacteristic
41#16839770C2211yescharacteristic
42#16839769—21no—
43#16839769—21no—
44C2×#14519702C2211yescharacteristic
45C2×#14519701C2211yescharacteristic
46C2×#14519700C2211yescharacteristic
47#103×D61—22no—
48#103×D61—22no—
49#103×D61—21no—
50#103×D61—21no—
51C2×#14519696C2211yescharacteristic
52C2×#14519695C2211yescharacteristic
53C2×#14519695C2211yescharacteristic
54#101×D61—24no—
55#16839531C2211yescharacteristic
56#16839530C2211yescharacteristic
57#16839530C2211yescharacteristic
58C2×#108×C61C2211yescharacteristic
59C61×#428C2211yescharacteristic
60C61×#424C2211yescharacteristic
61C61×#419C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×#101×C61C2211yescharacteristic
64C61×#343C2211yescharacteristic
65C22×Dic122—21no—
66C22×Dic122C2311yescharacteristic
67C2×Q8×D61—22no—
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70C2×Q8×D61—21no—
71C2×Q8×D61—21no—
72C2×Q8×D61—22no—
73C2×Q8×D61—22no—
74C2×Q8×D61Q814yes—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758189—21no—
82C2×#11758189—21no—
83C2×#11758189—21no—
84M16×D61—22no—
85M16×D61—22no—
86M16×D61—22no—
87M16×D61—22no—
88M16×D61—22no—
89M16×D61D414yes—
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—21no—
93C2×C8×D61—22no—
94C2×C8×D61—21no—
95C2×C8×D61—21no—
96C2×C8×D61D412yes—
97C2×C8×D61D412yes—
98#14519736C2311yescharacteristic
99#14519735D411yescharacteristic
100#14519735D411yescharacteristic
101#14519734—21no—
102#14519733—21no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C4⋊C4×D61—21no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61D411yescharacteristic
110C4⋊C4×D61D411yescharacteristic
111C22⋊C4×D61—21no—
112C42×D61—21no—
113#14519713—22no—
114#14519712—22no—
115#14519712—22no—
116#14519711—21no—
117#14519710—21no—
118#14519710—21no—
119#14519709—21no—
120#14519708—21no—
121#14519708—21no—
122C4⋊#92418—22no—
123#14519706—22no—
124#14519706—22no—
125#14519702—22no—
126#14519702—21no—
127#14519702—21no—
128#14519701—21no—
129#14519701—21no—
130#14519701—22no—
131#14519700—21no—
132#14519700—21no—
133#14519700—22no—
134#14519696—22no—
135#14519695—22no—
136#14519695—22no—
137C22×Q8×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142#117×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144#108×C61—22no—
145#107×C61—21no—
146#106×C61—21no—
147C4⋊C8×C61—22no—
148#103×C61—22no—
149#103×C61—21no—
150#103×C61—21no—
151#101×C61—22no—
152C23×D61#4111yescharacteristic
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61C2×Q812yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C2411yescharacteristic
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61#4111yescharacteristic
165Q8×D61—24no—
166Q8×D61—24no—
167Q8×D61—24no—
168Q8×D61—24no—
169Q8×D61—42no—
170Q8×D61—42no—
171Q8×D61—42no—
172Q8×D61—42no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—24no—
176C2×C4×D61—41no—
177C2×C4×D61—41no—
178C2×C4×D61—42no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61—82no—
182C2×C4×D61C2×D412yes—
183C2×C4×D61C2×D411yescharacteristic
184C2×C4×D61C2×D411yescharacteristic
185C2×C4×D61C2×D411yescharacteristic
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×Q812yes—
188C2×C4×D61#4112yes—
189C2×C4×D61#4112yes—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—24no—
196C2×Dic122—41no—
197C2×Dic122—41no—
198C2×Dic122—42no—
199C2×Dic122C2×Q812yes—
200M16×C61—21no—
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—21no—
205M16×C61C2×D412yes—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61C2×D412yes—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C2×D411yescharacteristic
215C4⋊C4×C61C2×D411yescharacteristic
216C22⋊C4×C61—21no—
217C42×C61—21no—
218C22⋊Dic61—21no—
219#11758198—21no—
220#11758198—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61C2×D411yescharacteristic
224C4⋊Dic61C2×D411yescharacteristic
225#11758196—21no—
226#11758196—21no—
227#11758196—41no—
228#11758196—41no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232#11758194—21no—
233#11758194—21no—
234#11758194—21no—
235#11758194—21no—
236#11758194—21no—
237#11758194C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418C2×D412yes—
244#11758189—24no—
245#11758189—42no—
246#11758189—42no—
247C8×D61—24no—
248C8×D61—24no—
249C8×D61—24no—
250C8×D61—42no—
251C8×D61—42no—
252C23×C61C2×#4111yescharacteristic
253C22×D61—22no—
254C22×D61—22no—
255C22×D61#12111yescharacteristic
256C22×D61#12111yescharacteristic
257C22×D61C22⋊Q812yes—
258C22×D61#12612yes—
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—41no—
262Q8×C61—41no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—81no—
270C2×C4×C61C22×D411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C22×Q811yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—22no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—81no—
283C2×Dic61#12111yescharacteristic
284C2×Dic61#12111yescharacteristic
285C2×Dic61C22⋊Q812yes—
286C2×Dic61#12612yes—
287C4×D61—44no—
288C4×D61—44no—
289C4×D61—42no—
290C4×D61—42no—
291C4×D61—82no—
292C4×D61—82no—
293C4×D61#12112yes—
294C4×D61#12112yes—
295C4×D61#12112yes—
296C4×D61#12112yes—
297C4×D61C22⋊Q812yes—
298C4×D61C22⋊Q812yes—
299C4×D61C22⋊Q812yes—
300C4×D61C22⋊Q812yes—
301Dic122—22no—
302Dic122—22no—
303Dic122—41no—
304Dic122—41no—
305Dic122—44no—
306Dic122—44no—
307C8×C61—22no—
308C8×C61—22no—
309C8×C61—41no—
310C8×C61—41no—
311#92418—22no—
312#92418—22no—
313#92418—41no—
314#92418—41no—
315C2×#2064—611nomaximal, Sylow
316C22×C61—21no—
317C22×C61—21no—
318C22×C61C2×#12111yescharacteristic
319C22×C61C2×C22⋊Q811yescharacteristic
320C22×C61C2×#12611yescharacteristic
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—24no—
324C2×D61—24no—
325C2×D61#39612yes—
326C2×D61#39612yes—
327C2×D61#47112yes—
328C2×D61#47312yes—
329C4×C61—42no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—81no—
333C4×C61C2×#12111yescharacteristic
334C4×C61C2×#12111yescharacteristic
335C4×C61C2×C22⋊Q811yescharacteristic
336C4×C61C2×C22⋊Q811yescharacteristic
337Dic61—42no—
338Dic61—41no—
339Dic61—41no—
340Dic61—81no—
341Dic61#39612yes—
342Dic61#39612yes—
343C22×#108—611no—
344C2×#428—611no—
345C2×#424—611no—
346C2×#419—611no—
347C22×#103—611no—
348C22×#101—611no—
349#2064—611no—
350#2064—611no—
351#2064—611no—
352#2064—611no—
353#2064—611no—
354#2064—611no—
355#2064—611no—
356#2064D6111yescharacteristic, direct product factor
357C2×#343—611no—
358C2×C61—21no—
359C2×C61—21no—
360C2×C61C2×#39611yescharacteristic
361C2×C61C2×#47111yescharacteristic
362C2×C61C2×#47311yescharacteristic
363D61—22no—
364D61#206414yesdirect product factor
365C23×Q8—611no—
366C22×M16—611no—
367C22×M16—611no—
368C22×M16—611no—
369C23×C8—611no—
370C2×#117—611no—
371C22×C4⋊C4—611no—
372C2×#108—611no—
373C2×#108—611no—
374C2×#108—611no—
375C2×#108—1224no—
376C2×#108C2×D6111yescharacteristic
377#428—611no—
378#428—611no—
379#428—611no—
380#428—1221no—
381#428—1221no—
382#428C2×D6111yescharacteristic
383C2×#107—1221no—
384C2×#106—1221no—
385#424—611no—
386#424—611no—
387#424—611no—
388#424—1222no—
389#424C2×D6111yescharacteristic
390C2×C4⋊C8—1222no—
391#419—611no—
392#419—611no—
393#419—611no—
394#419—1221no—
395#419—1221no—
396#419C2×D6111yescharacteristic
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—1221no—
401C2×#103—1221no—
402C2×#103—1222no—
403C2×#103—1222no—
404C2×#103C2×D6111yescharacteristic
405C2×#101—611no—
406C2×#101—611no—
407C2×#101—611no—
408C2×#101—1224no—
409C2×#101C2×D6111yescharacteristic
410#343—611no—
411#343—611no—
412#343—611no—
413#343C2×D6111yescharacteristic
414C61C2×#206411yescharacteristic, complemented, Sylow
415C22×Q8—614no—
416C22×Q8—611no—
417C22×Q8—1221no—
418C22×Q8—1222no—
419C22×Q8—1222no—
420C22×Q8—1222no—
421C22×Q8—1221no—
422C22×Q8—1221no—
423C22×Q8—1221no—
424C22×Q8—1221no—
425C22×Q8C22×D6111yescharacteristic
426C23×C4—611no—
427C23×C4—1221no—
428C23×C4—1221no—
429C2×M16—611no—
430C2×M16—614no—
431C2×M16—611no—
432C2×M16—611no—
433C2×M16—1221no—
434C2×M16—1221no—
435C2×M16—1221no—
436C2×M16—1222no—
437C2×M16—1222no—
438C2×M16—1222no—
439C2×M16—1222no—
440C2×M16—1222no—
441C2×M16C22×D6111yescharacteristic
442C2×M16C22×D6111yescharacteristic
443C2×M16C22×D6111yescharacteristic
444C22×C8—611no—
445C22×C8—612no—
446C22×C8—612no—
447C22×C8—1222no—
448C22×C8—1222no—
449C22×C8—1221no—
450C22×C8—1221no—
451C22×C8—1221no—
452C22×C8C22×D6111yescharacteristic
453#117—611no—
454#117—611no—
455#117—611no—
456#117—1221no—
457#117—1221no—
458#117C22×D6111yescharacteristic
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4C22×D6111yescharacteristic
468C2×C22⋊C4—1221no—
469C2×C42—1221no—
470#108—22no—
471#108—1222no—
472#108—1222no—
473#108—1222no—
474#107—21no—
475#107—1221no—
476#107—1221no—
477#107—1221no—
478#106—21no—
479#106—1221no—
480#106—1221no—
481#106—1221no—
482C4⋊C8—22no—
483C4⋊C8—1222no—
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486#103—22no—
487#103—21no—
488#103—21no—
489#103—1222no—
490#103—1221no—
491#103—1221no—
492#103—1221no—
493#103—1221no—
494#103—1222no—
495#103—1222no—
496#103—1221no—
497#103—1221no—
498#101—22no—
499#101—1222no—
500#101—1222no—
501#101—1222no—
502C24—611no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—612no—
509C2×Q8—1224no—
510C2×Q8—1224no—
511C2×Q8—1224no—
512C2×Q8—1224no—
513C2×Q8—1224no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×Q8—1221no—
517C2×Q8—1221no—
518C2×Q8—1221no—
519C2×Q8—2441no—
520C2×Q8—2441no—
521C2×Q8—2442no—
522C2×Q8—2442no—
523C2×Q8—2442no—
524C2×Q8—2442no—
525C2×Q8—2442no—
526C2×Q8Q8×D6112yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1224no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—4882no—
544C22×C4—2441no—
545C22×C4—2441no—
546C22×C4—2441no—
547C22×C4—2441no—
548C22×C4—2442no—
549C22×C4C23×D6111yescharacteristic
550M16—21no—
551M16—21no—
552M16—21no—
553M16—21no—
554M16—21no—
555M16—612no—
556M16—1224no—
557M16—1221no—
558M16—1221no—
559M16—1221no—
560M16—1221no—
561M16—1221no—
562M16—2442no—
563M16—2442no—
564M16D4×D6112yes—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—612no—
571C2×C8—1224no—
572C2×C8—1224no—
573C2×C8—1224no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—2442no—
580C2×C8—2442no—
581C2×C8D4×D6112yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—611no—
585C4⋊C4—611no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—2441no—
591C4⋊C4—2441no—
592C4⋊C4D4×D6111yescharacteristic
593C4⋊C4D4×D6111yescharacteristic
594C22⋊C4—21no—
595C22⋊C4—1221no—
596C22⋊C4—1221no—
597C22⋊C4—1221no—
598C42—21no—
599C42—1221no—
600C42—1221no—
601C42—1221no—
602C23—611no—
603C23—611no—
604C23—612no—
605C23—612no—
606C23—1222no—
607C23—1222no—
608C23#41×D6111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613Q8—1222no—
614Q8—1222no—
615Q8—2444no—
616Q8—2444no—
617Q8—2441no—
618Q8—2441no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—81no—
626C2×C4—611no—
627C2×C4—611no—
628C2×C4—612no—
629C2×C4—612no—
630C2×C4—612no—
631C2×C4—612no—
632C2×C4—612no—
633C2×C4—612no—
634C2×C4—612no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—612no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1222no—
641C2×C4—4882no—
642C2×C4—4882no—
643C2×C4—4881no—
644C2×C4—2442no—
645C2×C4—2442no—
646C2×C4—2444no—
647C2×C4—2444no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4C2×D4×D6111yescharacteristic
652C2×C4C2×D4×D6111yescharacteristic
653C2×C4C2×D4×D6111yescharacteristic
654C2×C4C2×Q8×D6111yescharacteristic
655C2×C4#41×D6111yescharacteristic
656C2×C4#41×D6111yescharacteristic
657C8—22no—
658C8—22no—
659C8—41no—
660C8—41no—
661C8—1222no—
662C8—1222no—
663C8—2441no—
664C8—2441no—
665C22—21no—
666C22—21no—
667C22—612no—
668C22—612no—
669C22—612no—
670C22—612no—
671C22—1224no—
672C22—1224no—
673C22—1221no—
674C22—1221no—
675C22#121×D6111yescharacteristic
676C22C22⋊Q8×D6111yescharacteristic
677C22#126×D6111yescharacteristic
678C4—42no—
679C4—41no—
680C4—41no—
681C4—81no—
682C4—612no—
683C4—612no—
684C4—4881no—
685C4—2442no—
686C4—2441no—
687C4—2441no—
688C4#121×D6111yescharacteristic
689C4#121×D6111yescharacteristic
690C4C22⋊Q8×D6111yescharacteristic
691C4C22⋊Q8×D6111yescharacteristic
692C2—21no—
693C2—21no—
694C2—614no—
695C2—1222no—
696C2#396×D6111yescharacteristic
697C2#471×D6111yescharacteristic
698C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2064C2
socleC22×C61C2×#121
prime radicalC23×D61#41
hypercenter#2064D61
hypocenterC61C2×#2064
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2064

Complements

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

NH ≅ G/Ntype
7. #21447187C2semidirect
8. #21447186C2semidirect
9. #21447185C2semidirect
10. #21447184C2semidirect
11. #21447183C2semidirect
12. #21447182C2semidirect
13. #21447181C2semidirect
15. C61×#2064C2semidirect
356. #2064D61direct (N × H)
364. D61#2064direct (N × H)
414. C61C2×#2064semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D612
#428×D612
#424×D612
#419×D612
C2×#103×D612
C2×#101×D612
#214471872
#214471862
#214471852
#214471842
#214471832
#214471822
#214471812
#343×D612
C61×#20642
C2×#206461