Finite Group Databasebeta

← D61×#2643 #29846460

Subgroups — D61×#2643 #29846460

Order 15616.

2546 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451777C211yesmaximal, characteristic, complemented
2#21451776C211yesmaximal, characteristic, complemented
3#21451775C213yesmaximal, complemented
4#21451774C213yesmaximal, complemented
5#21451773C213yesmaximal, complemented
6#21451772C211yesmaximal, characteristic, complemented
7#21451771C213yesmaximal, complemented
8#401×D61C211yesmaximal, characteristic, complemented
9#400×D61C213yesmaximal, complemented
10#397×D61C213yesmaximal, complemented
11#396×D61C211yesmaximal, characteristic, complemented
12#386×D61C213yesmaximal
13#385×D61C213yesmaximal, complemented
14C2×#95×D61C211yesmaximal, characteristic, complemented
15C61×#2643C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C23×C4×D61C2213yes—
18C2×C4⋊C4×D61C2213yes—
19C2×C4⋊C4×D61C2213yes—
20C2×C22⋊C4×D61C2213yes—
21C2×C22⋊C4×D61C2213yes—
22C2×C22⋊C4×D61C2213yes—
23C61⋊#401C2211yescharacteristic, complemented
24C61⋊#401C2213yescomplemented
25C61⋊#401C2213yescomplemented
26#16839704C2213yescomplemented
27#16839704C2213yescomplemented
28#16839703C2213yescomplemented
29#16839703C2213yescomplemented
30#16839702C2213yescomplemented
31#16839701C2213yescomplemented
32#16839700C2213yescomplemented
33#16839691C2213yescomplemented
34#16839691C2213yescomplemented
35#16839690C2213yescomplemented
36#16839690C2213yescomplemented
37#16839689C2213yescomplemented
38#16839688C2213yescomplemented
39#16839687C2213yescomplemented
40#16839686C2211yescharacteristic, complemented
41#16839685C2213yescomplemented
42#16839684C2213yescomplemented
43#16839642C2213yes—
44#16839641C2213yes—
45#16839640C2213yes—
46#16839640C2213yes—
47#16839639C2213yes—
48#16839638C2213yes—
49#16839638C2213yes—
50#16839637C2213yescomplemented
51#16839636C2213yescomplemented
52#16839636C2213yescomplemented
53#16839635C2213yescomplemented
54#16839634C2213yescomplemented
55#16839633C2213yescomplemented
56#16839633C2213yescomplemented
57C2×#14519684C2213yescomplemented
58#95×D61C2213yes—
59#95×D61C2213yes—
60#95×D61C2213yes—
61#95×D61C2213yes—
62#95×D61C2211yescharacteristic
63#95×D61C2213yes—
64#95×D61C2211yescharacteristic, complemented
65#95×D61C2213yescomplemented
66C61×#401C2211yescharacteristic, complemented
67C61×#400C2213yescomplemented
68C61×#397C2213yescomplemented
69C61×#396C2211yescharacteristic, complemented
70C61×#386C2213yes—
71C61×#385C2213yescomplemented
72C2×#95×C61C2211yescharacteristic, complemented
73C24×D61C2311yescharacteristic
74C24×D61C2311yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61C2311yescharacteristic
77C22×C22⋊D61C2311yescharacteristic
78C2×D4×D61—212no—
79C23×Dic61C2313yes—
80C22×C4×D61—212no—
81C22×C4×D61—46no—
82C22×C4×D61—46no—
83C22×C4×D61C2313yes—
84C22×C4×D61C2313yes—
85C22×C4×D61C2313yes—
86C22×C4×D61C2313yes—
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2313yes—
89C22×C4×D61C2313yes—
90C2×C4⋊Dic61C2313yes—
91C2×C4⋊Dic61C2313yes—
92C2×#11758196C2313yes—
93C2×#11758196C2313yes—
94C2×#11758196C2313yes—
95C2×#11758196C2313yes—
96C4⋊C4×D61—46no—
97C4⋊C4×D61—46no—
98C2×C22⋊Dic61C2313yes—
99C2×C22⋊Dic61C2313yes—
100C2×C22⋊Dic61C2313yes—
101C2×#11758198C2313yes—
102C2×#11758198C2313yes—
103C2×#11758198C2313yes—
104C2×#11758198C2313yes—
105C2×#11758198C2313yes—
106C2×#11758198C2313yes—
107C22⋊C4×D61—212no—
108C22⋊C4×D61—46no—
109C22⋊C4×D61—46no—
110#14519684C2313yes—
111#14519684C2313yes—
112#14519684C2313yes—
113#14519684C2313yes—
114#14519684C2313yes—
115#14519684C2313yes—
116#14519684C2313yes—
117#14519684C2313yes—
118#14519684C2313yes—
119#14519684C2313yes—
120#14519684C2313yes—
121#14519684C2313yes—
122#14519684C2313yes—
123#14519684C2313yes—
124#14519684C2313yes—
125#14519684C2313yes—
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61C2313yes—
128C2×C4⋊C4×C61C2313yes—
129C2×C4⋊C4×C61C2313yes—
130C2×C22⋊C4×C61C2313yes—
131C2×C22⋊C4×C61C2313yes—
132C2×C22⋊C4×C61C2313yes—
133#95×C61C2311yescharacteristic
134#95×C61C2313yes—
135#95×C61C2313yes—
136#95×C61C2313yes—
137#95×C61C2313yes—
138#95×C61C2313yes—
139C24×C61C2411yescharacteristic
140C24×C61C2411yescharacteristic
141C23×D61—26no—
142C23×D61—22no—
143C23×D61—26no—
144C23×D61—26no—
145C23×D61—22no—
146C23×D61#41112yes—
147C23×D61C2411yescharacteristic
148C23×D61C2411yescharacteristic
149C23×D61C2411yescharacteristic
150C2×D4×C61—26no—
151C22×C4×C61—26no—
152C22×C4×C61—43no—
153C22×C4×C61—43no—
154C22×C4×C61C2413yes—
155C22×C4×C61C2413yes—
156C22×C4×C61C2411yescharacteristic
157C22×C4×C61C2413yes—
158C22×C4×C61C2413yes—
159C2×C22⋊D61—26no—
160C2×C22⋊D61—26no—
161C22×Dic61—26no—
162C22×Dic61—43no—
163C22×Dic61—43no—
164C22×Dic61C2413yes—
165C22×Dic61C2413yes—
166C22×Dic61C2411yescharacteristic
167C22×Dic61C2413yes—
168C22×Dic61C2413yes—
169D4×D61—416no—
170C2×D244—26no—
171C2×C4×D61—26no—
172C2×C4×D61—26no—
173C2×C4×D61—26no—
174C2×C4×D61—26no—
175C2×C4×D61—26no—
176C2×C4×D61—26no—
177C2×C4×D61—26no—
178C2×C4×D61—26no—
179C2×C4×D61—26no—
180C2×C4×D61—26no—
181C2×C4×D61—26no—
182C2×C4×D61—26no—
183C2×C4×D61—26no—
184C2×C4×D61—26no—
185C2×C4×D61—26no—
186C2×C4×D61—43no—
187C2×C4×D61—43no—
188C2×C4×D61—43no—
189C2×C4×D61—43no—
190C2×C4×D61—448no—
191C4⋊C4×C61—43no—
192C4⋊C4×C61—43no—
193C22⋊C4×C61—26no—
194C22⋊C4×C61—43no—
195C22⋊C4×C61—43no—
196C22⋊Dic61—26no—
197C22⋊Dic61—43no—
198C22⋊Dic61—43no—
199#11758198—26no—
200#11758198—26no—
201#11758198—43no—
202#11758198—43no—
203#11758198—43no—
204#11758198—43no—
205C4⋊Dic61—43no—
206C4⋊Dic61—43no—
207#11758196—43no—
208#11758196—43no—
209#11758196—43no—
210#11758196—43no—
211C23×C61—23no—
212C23×C61—21no—
213C23×C61—23no—
214C23×C61—23no—
215C23×C61—21no—
216C23×C61C2×#4116yes—
217C23×C61C2511yescharacteristic
218C22×D61—23no—
219C22×D61—21no—
220C22×D61—224no—
221C22×D61—224no—
222C22×D61—23no—
223C22×D61—23no—
224C22×D61—21no—
225C22×D61—44no—
226C22×D61—412no—
227C22×D61—412no—
228C22×D61#126116yes—
229C22×D61C2×#4116yes—
230C22×D61C2×#4116yes—
231C22×D61H(5,𝔽2)16yes—
232C22×D612−1+412yes—
233D4×C61—44no—
234C2×C4×C61—23no—
235C2×C4×C61—23no—
236C2×C4×C61—23no—
237C2×C4×C61—23no—
238C2×C4×C61—23no—
239C2×C4×C61—23no—
240C2×C4×C61—23no—
241C2×C4×C61—23no—
242C2×C4×C61—23no—
243C2×C4×C61—23no—
244C2×C4×C61—23no—
245C2×C4×C61—23no—
246C2×C4×C61—23no—
247C2×C4×C61—412no—
248C22⋊D61—44no—
249C22⋊D61—44no—
250C2×Dic61—23no—
251C2×Dic61—23no—
252C2×Dic61—23no—
253C2×Dic61—23no—
254C2×Dic61—23no—
255C2×Dic61—23no—
256C2×Dic61—23no—
257C2×Dic61—23no—
258C2×Dic61—23no—
259C2×Dic61—23no—
260C2×Dic61—23no—
261C2×Dic61—23no—
262C2×Dic61—23no—
263C2×Dic61—412no—
264D244—44no—
265C4×D61—412no—
266C4×D61—412no—
267C4×D61—44no—
268C4×D61—412no—
269C4×D61—412no—
270C4×D61—412no—
271C4×D61—412no—
272C2×#2643—611nomaximal, Sylow
273C22×C61—26no—
274C22×C61—26no—
275C22×C61—41no—
276C22×C61—43no—
277C22×C61—43no—
278C22×C61C2×#12614yes—
279C22×C61C22×#4113yes—
280C22×C61C2×H(5,𝔽2)13yes—
281C22×C61C2×2−1+411yescharacteristic
282C2×D61—26no—
283C2×D61—26no—
284C2×D61—232no—
285C2×D61—41no—
286C2×D61—43no—
287C2×D61—43no—
288C2×D61—88no—
289C2×D61C2×#12614yes—
290C2×D61C2×#12614yes—
291C2×D61#538112yes—
292C2×D61#539112yes—
293C4×C61—41no—
294C4×C61—43no—
295C4×C61—43no—
296C4×C61—43no—
297C4×C61—43no—
298Dic61—41no—
299Dic61—43no—
300Dic61—43no—
301Dic61—43no—
302Dic61—43no—
303#2643—611no—
304#2643—613no—
305#2643—613no—
306#2643—611no—
307#2643—613no—
308#2643—613no—
309#2643—611no—
310#2643D6111yescharacteristic, direct product factor
311C2×#401—611no—
312C2×#400—613no—
313C2×#397—613no—
314C2×#396—611no—
315C2×#386—613no—
316C2×#385—613no—
317C22×#95—611no—
318C2×C61—24no—
319C2×C61—81no—
320C2×C61C22×#12611yescharacteristic
321C2×C61C2×#53813yes—
322C2×C61C2×#53913yes—
323D61—24no—
324D61—81no—
325D61#264318yesdirect product factor
326C23×D4—611no—
327C24×C4—613no—
328C22×C4⋊C4—613no—
329C22×C4⋊C4—613no—
330C22×C22⋊C4—613no—
331C22×C22⋊C4—613no—
332C22×C22⋊C4—613no—
333#401—613no—
334#401—613no—
335#401—611no—
336#401C2×D6111yescharacteristic, complemented
337#400—613no—
338#400—613no—
339#400—613no—
340#400—613no—
341#400—613no—
342#400—613no—
343#400—613no—
344#400C2×D6113yescomplemented
345#397—613no—
346#397—613no—
347#397—613no—
348#397—613no—
349#397—613no—
350#397—613no—
351#397—613no—
352#397C2×D6113yescomplemented
353#396—613no—
354#396—613no—
355#396—611no—
356#396C2×D6111yescharacteristic, complemented
357#386—613no—
358#386—613no—
359#386—613no—
360#386—613no—
361#386—613no—
362#386—613no—
363#386—613no—
364#386C2×D6113yes—
365#385—613no—
366#385—613no—
367#385—613no—
368#385—613no—
369#385—613no—
370#385—613no—
371#385—613no—
372#385C2×D6113yescomplemented
373C2×#95—613no—
374C2×#95—613no—
375C2×#95—611no—
376C2×#95—611no—
377C2×#95—613no—
378C2×#95—613no—
379C2×#95—613no—
380C2×#95—613no—
381C2×#95—613no—
382C2×#95C2×D6111yescharacteristic, complemented
383C61C2×#264311yescharacteristic, complemented, Sylow
384C25—611no—
385C25—611no—
386C22×D4—611no—
387C22×D4—611no—
388C22×D4—611no—
389C22×D4—12212no—
390C22×D4C22×D6111yescharacteristic
391C23×C4—613no—
392C23×C4—613no—
393C23×C4—613no—
394C23×C4—613no—
395C23×C4—613no—
396C23×C4—611no—
397C23×C4—613no—
398C23×C4—613no—
399C23×C4—12212no—
400C23×C4—2446no—
401C23×C4—2446no—
402C23×C4C22×D6113yes—
403C2×C4⋊C4—613no—
404C2×C4⋊C4—613no—
405C2×C4⋊C4—613no—
406C2×C4⋊C4—613no—
407C2×C4⋊C4—613no—
408C2×C4⋊C4—613no—
409C2×C4⋊C4—2446no—
410C2×C4⋊C4—2446no—
411C2×C4⋊C4C22×D6113yes—
412C2×C4⋊C4C22×D6113yes—
413C2×C22⋊C4—613no—
414C2×C22⋊C4—613no—
415C2×C22⋊C4—613no—
416C2×C22⋊C4—613no—
417C2×C22⋊C4—613no—
418C2×C22⋊C4—613no—
419C2×C22⋊C4—613no—
420C2×C22⋊C4—613no—
421C2×C22⋊C4—613no—
422C2×C22⋊C4—12212no—
423C2×C22⋊C4—2446no—
424C2×C22⋊C4—2446no—
425C2×C22⋊C4C22×D6113yes—
426C2×C22⋊C4C22×D6113yes—
427C2×C22⋊C4C22×D6113yes—
428#95—613no—
429#95—613no—
430#95—613no—
431#95—613no—
432#95—613no—
433#95—613no—
434#95—613no—
435#95—613no—
436#95—613no—
437#95—613no—
438#95—613no—
439#95—613no—
440#95—613no—
441#95—613no—
442#95—613no—
443#95—613no—
444#95C22×D6111yescharacteristic
445#95C22×D6113yes—
446#95C22×D6113yes—
447#95C22×D6113yes—
448#95C22×D6113yes—
449#95C22×D6113yes—
450C24—611no—
451C24—6112no—
452C24—611no—
453C24—611no—
454C24—1226no—
455C24—1222no—
456C24—1226no—
457C24—1226no—
458C24—1222no—
459C24C23×D6111yescharacteristic
460C24C23×D6111yescharacteristic
461C2×D4—26no—
462C2×D4—1226no—
463C2×D4—1226no—
464C2×D4—1226no—
465C2×D4—24416no—
466C22×C4—26no—
467C22×C4—43no—
468C22×C4—43no—
469C22×C4—611no—
470C22×C4—613no—
471C22×C4—613no—
472C22×C4—613no—
473C22×C4—613no—
474C22×C4—1226no—
475C22×C4—1226no—
476C22×C4—1226no—
477C22×C4—1226no—
478C22×C4—1226no—
479C22×C4—1226no—
480C22×C4—1226no—
481C22×C4—1226no—
482C22×C4—1226no—
483C22×C4—1226no—
484C22×C4—1226no—
485C22×C4—1226no—
486C22×C4—1226no—
487C22×C4—1226no—
488C22×C4—1226no—
489C22×C4—1226no—
490C22×C4—2443no—
491C22×C4—2443no—
492C22×C4—2443no—
493C22×C4—2443no—
494C22×C4—24448no—
495C22×C4—2443no—
496C22×C4—2443no—
497C22×C4C23×D6111yescharacteristic
498C22×C4C23×D6113yes—
499C22×C4C23×D6113yes—
500C22×C4C23×D6113yes—
501C22×C4C23×D6113yes—
502C4⋊C4—43no—
503C4⋊C4—43no—
504C4⋊C4—2443no—
505C4⋊C4—2443no—
506C4⋊C4—2443no—
507C4⋊C4—2443no—
508C4⋊C4—2443no—
509C4⋊C4—2443no—
510C22⋊C4—26no—
511C22⋊C4—43no—
512C22⋊C4—43no—
513C22⋊C4—1226no—
514C22⋊C4—1226no—
515C22⋊C4—1226no—
516C22⋊C4—2443no—
517C22⋊C4—2443no—
518C22⋊C4—2443no—
519C22⋊C4—2443no—
520C22⋊C4—2443no—
521C22⋊C4—2443no—
522C23—23no—
523C23—21no—
524C23—23no—
525C23—23no—
526C23—21no—
527C23—616no—
528C23—616no—
529C23—612no—
530C23—6116no—
531C23—616no—
532C23—12224no—
533C23—12224no—
534C23—1223no—
535C23—1221no—
536C23—1223no—
537C23—1223no—
538C23—1221no—
539C23—2444no—
540C23—24412no—
541C23—24412no—
542C23#41×D6116yes—
543C23C24×D6111yescharacteristic
544D4—44no—
545D4—2444no—
546D4—2444no—
547D4—2444no—
548C2×C4—23no—
549C2×C4—23no—
550C2×C4—23no—
551C2×C4—23no—
552C2×C4—23no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—23no—
556C2×C4—23no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—412no—
562C2×C4—1223no—
563C2×C4—1223no—
564C2×C4—1223no—
565C2×C4—1223no—
566C2×C4—1223no—
567C2×C4—1223no—
568C2×C4—1223no—
569C2×C4—1223no—
570C2×C4—1223no—
571C2×C4—1223no—
572C2×C4—1223no—
573C2×C4—1223no—
574C2×C4—1223no—
575C2×C4—24412no—
576C2×C4—24412no—
577C2×C4—24412no—
578C2×C4—24412no—
579C2×C4—2444no—
580C2×C4—24412no—
581C2×C4—24412no—
582C2×C4—24412no—
583C22—26no—
584C22—26no—
585C22—41no—
586C22—43no—
587C22—43no—
588C22—614no—
589C22—6112no—
590C22—6112no—
591C22—614no—
592C22—12232no—
593C22—1226no—
594C22—1226no—
595C22—4888no—
596C22—2441no—
597C22—2443no—
598C22—2443no—
599C22#126×D6114yes—
600C22C2×#41×D6113yes—
601C22H(5,𝔽2)×D6113yes—
602C222−1+4×D6111yescharacteristic
603C4—41no—
604C4—43no—
605C4—43no—
606C4—43no—
607C4—43no—
608C4—2441no—
609C4—2443no—
610C4—2443no—
611C4—2443no—
612C4—2443no—
613C2—24no—
614C2—81no—
615C2—618no—
616C2—1224no—
617C2—4881no—
618C2C2×#126×D6111yescharacteristic
619C2#538×D6113yes—
620C2#539×D6113yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2643C2
prime radicalC22×D4×D61C22
hypercenter#2643D61
hypocenterC61C2×#2643
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2643

Complements

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

NH ≅ G/Ntype
1. #21451777C2semidirect
2. #21451776C2semidirect
3. #21451775C2semidirect
4. #21451774C2semidirect
5. #21451773C2semidirect
6. #21451772C2semidirect
7. #21451771C2semidirect
8. #401×D61C2semidirect
9. #400×D61C2semidirect
10. #397×D61C2semidirect
11. #396×D61C2semidirect
13. #385×D61C2semidirect
14. C2×#95×D61C2semidirect
15. C61×#2643C2semidirect
23. C61⋊#401C22semidirect
24. C61⋊#401C22semidirect
25. C61⋊#401C22semidirect
26. #16839704C22semidirect
27. #16839704C22semidirect
28. #16839703C22semidirect
29. #16839703C22semidirect
30. #16839702C22semidirect
31. #16839701C22semidirect
32. #16839700C22semidirect
33. #16839691C22semidirect
34. #16839691C22semidirect
35. #16839690C22semidirect
36. #16839690C22semidirect
37. #16839689C22semidirect
38. #16839688C22semidirect
39. #16839687C22semidirect
40. #16839686C22semidirect
41. #16839685C22semidirect
42. #16839684C22semidirect
50. #16839637C22semidirect
51. #16839636C22semidirect
52. #16839636C22semidirect
53. #16839635C22semidirect
54. #16839634C22semidirect
55. #16839633C22semidirect
56. #16839633C22semidirect
57. C2×#14519684C22semidirect
64. #95×D61C22semidirect
65. #95×D61C22semidirect
66. C61×#401C22semidirect
67. C61×#400C22semidirect
68. C61×#397C22semidirect
69. C61×#396C22semidirect
71. C61×#385C22semidirect
72. C2×#95×C61C22semidirect
310. #2643D61direct (N × H)
325. D61#2643direct (N × H)
336. #401C2×D61semidirect
344. #400C2×D61semidirect
352. #397C2×D61semidirect
356. #396C2×D61semidirect
372. #385C2×D61semidirect
382. C2×#95C2×D61semidirect
383. C61C2×#2643semidirect

Maximal subgroups

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

subgroupindex
#214517772
#214517762
#214517752
#214517742
#214517732
#214517722
#214517712
#401×D612
#400×D612
#397×D612
#396×D612
#386×D612
#385×D612
C2×#95×D612
C61×#26432
C2×#264361