Finite Group Databasebeta

← D61×#2082 #29708954

Subgroups — D61×#2082 #29708954

Order 15616.

878 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#430×D61C211yesmaximal, characteristic
2#419×D61C211yesmaximal, characteristic
3#419×D61C211yesmaximal, characteristic
4C2×#101×D61C211yesmaximal, characteristic
5#21447289C211yesmaximal, characteristic, complemented
6#21447288C211yesmaximal, characteristic, complemented
7#21447287C211yesmaximal, characteristic, complemented
8#21447286C211yesmaximal, characteristic, complemented
9#21447285C211yesmaximal, characteristic, complemented
10#21447284C211yesmaximal, characteristic, complemented
11#21447283C211yesmaximal, characteristic, complemented
12#344×D61C211yesmaximal, characteristic
13#344×D61C211yesmaximal, characteristic
14H(3,ℤ/4)×D61C211yesmaximal, characteristic
15C61×#2082C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21#117×D61C2211yescharacteristic
22#117×D61C2211yescharacteristic
23#16839811C2211yescharacteristic
24#16839810C2211yescharacteristic
25#16839810C2211yescharacteristic
26#16839809—22no—
27#108×D61—22no—
28#16839772C2211yescharacteristic
29#16839772C2211yescharacteristic
30#16839771C2211yescharacteristic
31#16839771C2211yescharacteristic
32#16839770C2211yescharacteristic
33#16839770C2211yescharacteristic
34#16839769—22no—
35#16839769—22no—
36#103×D61—22no—
37#103×D61—22no—
38C2×#14519696C2211yescharacteristic
39C2×#14519695C2211yescharacteristic
40C2×#14519695C2211yescharacteristic
41#101×D61—22no—
42#101×D61—22no—
43#16839534C2211yescharacteristic
44#16839534C2211yescharacteristic
45#16839533C2211yescharacteristic
46#16839533C2211yescharacteristic
47#16839532C2211yescharacteristic
48#16839532C2211yescharacteristic
49#16839519C2211yescharacteristic
50#16839518C2211yescharacteristic
51#16839518C2211yescharacteristic
52C61×#430C2211yescharacteristic
53C61×#419C2211yescharacteristic
54C61×#419C2211yescharacteristic
55C2×#101×C61C2211yescharacteristic
56C61×#344C2211yescharacteristic
57C61×#344C2211yescharacteristic
58C61×H(3,ℤ/4)C2211yescharacteristic
59C22×Dic122—21no—
60C22×Dic122C2311yescharacteristic
61C2×Q8×D61—21no—
62C2×Q8×D61—21no—
63C2×Q8×D61—21no—
64C2×Q8×D61—21no—
65C2×Q8×D61—21no—
66C2×Q8×D61—21no—
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70C2×Q8×D61—21no—
71C2×Q8×D61D412yes—
72C2×Q8×D61D412yes—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758189—21no—
80C2×#11758189—21no—
81C2×#11758189—21no—
82C2×#11758189D412yes—
83M16×D61—21no—
84M16×D61—21no—
85M16×D61—21no—
86M16×D61—21no—
87M16×D61—21no—
88M16×D61—21no—
89M16×D61—21no—
90M16×D61—21no—
91M16×D61—21no—
92M16×D61—21no—
93M16×D61—21no—
94M16×D61—21no—
95M16×D61—21no—
96M16×D61—21no—
97M16×D61—21no—
98M16×D61—21no—
99C2×C8×D61—21no—
100C2×C8×D61—21no—
101C2×C8×D61—21no—
102C2×C8×D61D412yes—
103#14519736C2311yescharacteristic
104#14519736C2311yescharacteristic
105#14519735—21no—
106#14519735—21no—
107#14519734—21no—
108#14519734—21no—
109#14519733—21no—
110#14519733—21no—
111C4⋊C4×D61—21no—
112C4⋊C4×D61—21no—
113C22⋊C4×D61—21no—
114C22⋊C4×D61—21no—
115C42×D61—21no—
116C42×D61—21no—
117#14519713—22no—
118#14519712—22no—
119#14519712—22no—
120#14519702—22no—
121#14519702—22no—
122#14519701—22no—
123#14519701—22no—
124#14519700—22no—
125#14519700—22no—
126#14519696—22no—
127#14519695—22no—
128#14519695—22no—
129C22×Q8×C61C2311yescharacteristic
130C2×M16×C61C2311yescharacteristic
131C2×M16×C61C2311yescharacteristic
132C2×M16×C61C2311yescharacteristic
133C2×M16×C61C2311yescharacteristic
134#117×C61C2311yescharacteristic
135#117×C61C2311yescharacteristic
136#108×C61—22no—
137#103×C61—22no—
138#103×C61—22no—
139#101×C61—22no—
140C23×D61#4111yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D412yes—
147C22×C4×C61—21no—
148C22×C4×C61C2411yescharacteristic
149C22×Dic61—21no—
150C22×Dic61#4111yescharacteristic
151Q8×D61—22no—
152Q8×D61—22no—
153Q8×D61—22no—
154Q8×D61—22no—
155Q8×D61—22no—
156Q8×D61—22no—
157Q8×D61—22no—
158Q8×D61—22no—
159Q8×D61—41no—
160Q8×D61—41no—
161Q8×D61—41no—
162Q8×D61—41no—
163Q8×D61—41no—
164Q8×D61—41no—
165Q8×D61—41no—
166Q8×D61—41no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—41no—
170C2×C4×D61—41no—
171C2×C4×D61—41no—
172C2×C4×D61—41no—
173C2×C4×D61—41no—
174C2×C4×D61—41no—
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61#4111yescharacteristic
180C2×C4×D61#4111yescharacteristic
181C2×C4×D61#4111yescharacteristic
182C2×C4×D61#4111yescharacteristic
183C2×C4×D61#4111yescharacteristic
184C2×C4×D61#4111yescharacteristic
185C2×C4×D61#4111yescharacteristic
186C2×C4×D61#4111yescharacteristic
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—22no—
193C2×Dic122—22no—
194C2×Dic122—41no—
195C2×Dic122—41no—
196C2×Dic122—41no—
197C2×Dic122—41no—
198C2×Dic122C2×D412yes—
199M16×C61—21no—
200M16×C61—21no—
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—21no—
205M16×C61—21no—
206M16×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61C2×D412yes—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C22⋊C4×C61—21no—
214C22⋊C4×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—21no—
218C22⋊Dic61—21no—
219#11758198—41no—
220#11758198—41no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223#11758196—41no—
224#11758196—41no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—41no—
228C4×Dic61—41no—
229#11758194—21no—
230#11758194—21no—
231#11758194—21no—
232#11758194—21no—
233#11758194—21no—
234#11758194—21no—
235#11758194—21no—
236#11758194—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C2×D412yes—
241#11758189—22no—
242#11758189—22no—
243#11758189—41no—
244#11758189—41no—
245#11758189—41no—
246#11758189—41no—
247#11758189—41no—
248#11758189—41no—
249C8×D61—22no—
250C8×D61—22no—
251C8×D61—41no—
252C8×D61—41no—
253C8×D61—41no—
254C8×D61—41no—
255C8×D61—41no—
256C8×D61—41no—
257C23×C61C2×#4111yescharacteristic
258C22×D61—42no—
259C22×D61#12311yescharacteristic
260C22×D61#12311yescharacteristic
261C22×D61#12411yescharacteristic
262C22×D61#12411yescharacteristic
263C22×D61#12611yescharacteristic
264C22×D61#12611yescharacteristic
265Q8×C61—22no—
266Q8×C61—22no—
267Q8×C61—41no—
268Q8×C61—41no—
269C2×C4×C61—22no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61C22×D411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×Dic61—22no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61#12311yescharacteristic
286C2×Dic61#12311yescharacteristic
287C2×Dic61#12411yescharacteristic
288C2×Dic61#12411yescharacteristic
289C2×Dic61#12611yescharacteristic
290C2×Dic61#12611yescharacteristic
291C4×D61—42no—
292C4×D61—42no—
293C4×D61—42no—
294C4×D61—42no—
295C4×D61—82no—
296C4×D61—82no—
297C4×D61#12111yescharacteristic
298C4×D61#12111yescharacteristic
299C4×D61#12111yescharacteristic
300C4×D61#12111yescharacteristic
301C4×D61#12311yescharacteristic
302C4×D61#12311yescharacteristic
303C4×D61#12311yescharacteristic
304C4×D61#12311yescharacteristic
305C4×D61#12311yescharacteristic
306C4×D61#12311yescharacteristic
307C4×D61#12311yescharacteristic
308C4×D61#12311yescharacteristic
309C4×D61#12611yescharacteristic
310C4×D61#12611yescharacteristic
311C4×D61#12611yescharacteristic
312C4×D61#12611yescharacteristic
313Dic122—22no—
314Dic122—22no—
315Dic122—41no—
316Dic122—41no—
317Dic122—42no—
318Dic122—42no—
319Dic122—42no—
320Dic122—42no—
321C8×C61—22no—
322C8×C61—41no—
323C8×C61—41no—
324C8×C61—41no—
325#92418—22no—
326#92418—41no—
327#92418—41no—
328#92418—41no—
329C2×#2082—611nomaximal, Sylow
330C22×C61—41no—
331C22×C61C2×#12311yescharacteristic
332C22×C61C2×#12411yescharacteristic
333C22×C61C2×#12611yescharacteristic
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61#39711yescharacteristic
341C2×D61#39711yescharacteristic
342C2×D61#39711yescharacteristic
343C2×D61#39711yescharacteristic
344C4×C61—42no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61C2×#12111yescharacteristic
348C4×C61C2×#12311yescharacteristic
349C4×C61C2×#12311yescharacteristic
350C4×C61C2×#12611yescharacteristic
351Dic61—42no—
352Dic61—81no—
353Dic61—81no—
354Dic61#39711yescharacteristic
355Dic61#39711yescharacteristic
356Dic61#39711yescharacteristic
357Dic61#39711yescharacteristic
358C2×#430—611no—
359C2×#419—611no—
360C2×#419—611no—
361C22×#101—611no—
362#2082—611no—
363#2082—611no—
364#2082—611no—
365#2082—611no—
366#2082—611no—
367#2082—611no—
368#2082—611no—
369#2082D6111yescharacteristic, direct product factor
370C2×#344—611no—
371C2×#344—611no—
372C2×H(3,ℤ/4)—611no—
373C2×C61—21no—
374C2×C61—21no—
375C2×C61—21no—
376C2×C61C2×#39711yescharacteristic
377D61—21no—
378D61—21no—
379D61—21no—
380D61#208212yesdirect product factor
381C23×Q8—611no—
382C22×M16—611no—
383C22×M16—611no—
384C22×M16—611no—
385C22×M16—611no—
386C2×#117—611no—
387C2×#117—611no—
388#430—611no—
389#430—611no—
390#430—611no—
391#430—1222no—
392#430C2×D6111yescharacteristic
393C2×#108—1222no—
394#419—611no—
395#419—611no—
396#419—611no—
397#419—611no—
398#419—611no—
399#419—611no—
400#419—1222no—
401#419—1222no—
402#419C2×D6111yescharacteristic
403#419C2×D6111yescharacteristic
404C2×#103—1222no—
405C2×#103—1222no—
406C2×#101—611no—
407C2×#101—611no—
408C2×#101—611no—
409C2×#101—1222no—
410C2×#101—1222no—
411C2×#101C2×D6111yescharacteristic
412#344—611no—
413#344—611no—
414#344—611no—
415#344—611no—
416#344—611no—
417#344—611no—
418#344C2×D6111yescharacteristic
419#344C2×D6111yescharacteristic
420H(3,ℤ/4)—611no—
421H(3,ℤ/4)—611no—
422H(3,ℤ/4)—611no—
423H(3,ℤ/4)C2×D6111yescharacteristic
424C61C2×#208211yescharacteristic, complemented, Sylow
425C22×Q8—612no—
426C22×Q8—612no—
427C22×Q8—611no—
428C22×Q8—1221no—
429C22×Q8—1221no—
430C22×Q8—1221no—
431C22×Q8—1221no—
432C22×Q8—1221no—
433C22×Q8—1221no—
434C22×Q8—1221no—
435C22×Q8—1221no—
436C22×Q8—1221no—
437C22×Q8—1221no—
438C22×Q8—1221no—
439C22×Q8C22×D6111yescharacteristic
440C23×C4—611no—
441C23×C4—1221no—
442C2×M16—611no—
443C2×M16—612no—
444C2×M16—611no—
445C2×M16—611no—
446C2×M16—611no—
447C2×M16—1221no—
448C2×M16—1221no—
449C2×M16—1221no—
450C2×M16—1221no—
451C2×M16—1221no—
452C2×M16—1221no—
453C2×M16—1221no—
454C2×M16—1221no—
455C2×M16—1221no—
456C2×M16—1221no—
457C2×M16—1221no—
458C2×M16—1221no—
459C2×M16—1221no—
460C2×M16—1221no—
461C2×M16—1221no—
462C2×M16—1221no—
463C2×M16—1221no—
464C2×M16—1221no—
465C2×M16—1221no—
466C2×M16C22×D6111yescharacteristic
467C2×M16C22×D6111yescharacteristic
468C2×M16C22×D6111yescharacteristic
469C2×M16C22×D6111yescharacteristic
470C22×C8—612no—
471C22×C8—1221no—
472C22×C8—1221no—
473C22×C8—1221no—
474#117—611no—
475#117—611no—
476#117—1221no—
477#117—1221no—
478#117—1221no—
479#117—1221no—
480#117—1221no—
481#117—1221no—
482#117C22×D6111yescharacteristic
483#117C22×D6111yescharacteristic
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490#108—22no—
491#108—1222no—
492#108—1222no—
493#108—1222no—
494#103—22no—
495#103—22no—
496#103—1222no—
497#103—1222no—
498#103—1222no—
499#103—1222no—
500#103—1222no—
501#103—1222no—
502#101—22no—
503#101—1222no—
504#101—1222no—
505#101—1222no—
506C24—611no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—612no—
513C2×Q8—1222no—
514C2×Q8—1222no—
515C2×Q8—1222no—
516C2×Q8—1222no—
517C2×Q8—1222no—
518C2×Q8—1222no—
519C2×Q8—1222no—
520C2×Q8—1222no—
521C2×Q8—1222no—
522C2×Q8—1222no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—2441no—
529C2×Q8—2441no—
530C2×Q8—2441no—
531C2×Q8—2441no—
532C2×Q8—2441no—
533C2×Q8—2441no—
534C2×Q8—2441no—
535C2×Q8—2441no—
536C2×Q8—2441no—
537C2×Q8—2441no—
538C2×Q8—2441no—
539C2×Q8—2441no—
540C2×Q8D4×D6112yes—
541C22×C4—21no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1221no—
558C22×C4—2441no—
559C22×C4—2441no—
560C22×C4—2441no—
561C22×C4—2441no—
562C22×C4—2441no—
563C22×C4—2441no—
564C22×C4C23×D6111yescharacteristic
565M16—21no—
566M16—21no—
567M16—21no—
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16—21no—
573M16—1222no—
574M16—1222no—
575M16—1221no—
576M16—1221no—
577M16—1221no—
578M16—1221no—
579M16—1221no—
580M16—1221no—
581M16—1221no—
582M16—1221no—
583M16—2441no—
584M16—2441no—
585M16—2441no—
586M16—2441no—
587M16—2441no—
588M16—2441no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—612no—
593C2×C8—1222no—
594C2×C8—1222no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—2441no—
599C2×C8—2441no—
600C2×C8—2441no—
601C2×C8—2441no—
602C2×C8—2441no—
603C2×C8—2441no—
604C2×C8D4×D6112yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—2441no—
610C4⋊C4—2441no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—1221no—
614C22⋊C4—1221no—
615C22⋊C4—2441no—
616C22⋊C4—2441no—
617C42—21no—
618C42—21no—
619C42—1221no—
620C42—1221no—
621C42—2441no—
622C42—2441no—
623C23—611no—
624C23—611no—
625C23—611no—
626C23—611no—
627C23—611no—
628C23—611no—
629C23—2442no—
630C23#41×D6111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635Q8—1222no—
636Q8—1222no—
637Q8—2442no—
638Q8—2442no—
639Q8—2442no—
640Q8—2442no—
641Q8—2441no—
642Q8—2441no—
643C2×C4—22no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—611no—
649C2×C4—611no—
650C2×C4—611no—
651C2×C4—611no—
652C2×C4—611no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—611no—
669C2×C4—611no—
670C2×C4—1222no—
671C2×C4—4882no—
672C2×C4—4882no—
673C2×C4—2442no—
674C2×C4—2442no—
675C2×C4—2442no—
676C2×C4—2442no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4C2×D4×D6111yescharacteristic
682C2×C4C2×D4×D6111yescharacteristic
683C2×C4#41×D6111yescharacteristic
684C2×C4#41×D6111yescharacteristic
685C2×C4#41×D6111yescharacteristic
686C2×C4#41×D6111yescharacteristic
687C8—22no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—1222no—
692C8—2441no—
693C8—2441no—
694C8—2441no—
695C22—41no—
696C22—611no—
697C22—611no—
698C22—611no—
699C22—611no—
700C22—1222no—
701C22—1222no—
702C22—1222no—
703C22—2441no—
704C22—2441no—
705C22—2441no—
706C22#123×D6111yescharacteristic
707C22#124×D6111yescharacteristic
708C22#126×D6111yescharacteristic
709C4—42no—
710C4—81no—
711C4—81no—
712C4—611no—
713C4—611no—
714C4—611no—
715C4—611no—
716C4—4881no—
717C4—4881no—
718C4—2442no—
719C4#121×D6111yescharacteristic
720C4#123×D6111yescharacteristic
721C4#123×D6111yescharacteristic
722C4#126×D6111yescharacteristic
723C2—21no—
724C2—21no—
725C2—21no—
726C2—612no—
727C2—1221no—
728C2—1221no—
729C2—1221no—
730C2#397×D6111yescharacteristic
subgroupG/H
centerC2#397×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2082C2
socleC2×C61C2×#397
prime radicalC23×D61#41
hypercenter#2082D61
hypocenterC61C2×#2082
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2082

Complements

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

NH ≅ G/Ntype
5. #21447289C2semidirect
6. #21447288C2semidirect
7. #21447287C2semidirect
8. #21447286C2semidirect
9. #21447285C2semidirect
10. #21447284C2semidirect
11. #21447283C2semidirect
15. C61×#2082C2semidirect
369. #2082D61direct (N × H)
380. D61#2082direct (N × H)
424. C61C2×#2082semidirect

Maximal subgroups

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

subgroupindex
#430×D612
#419×D612
C2×#101×D612
#214472892
#214472882
#214472872
#214472862
#214472852
#214472842
#214472832
#344×D612
H(3,ℤ/4)×D612
C61×#20822
C2×#208261