Finite Group Databasebeta

← D61×#1702 #29662673

Subgroups — D61×#1702 #29662673

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D61C211yesmaximal, characteristic
2#462×D61C211yesmaximal, characteristic, complemented
3#460×D61C211yesmaximal, characteristic
4#446×D61C211yesmaximal, characteristic, complemented
5#21445390C211yesmaximal, characteristic, complemented
6#21445389C211yesmaximal, characteristic, complemented
7#21445388C211yesmaximal, characteristic, complemented
8#21445387C211yesmaximal, characteristic, complemented
9#21445386C211yesmaximal, characteristic, complemented
10#21445385C211yesmaximal, characteristic, complemented
11#21445384C211yesmaximal, characteristic, complemented
12#334×D61C211yesmaximal, characteristic, complemented
13#332×D61C211yesmaximal, characteristic, complemented
14#331×D61C211yesmaximal, characteristic
15C61×#1702C211yesmaximal, characteristic, complemented
16C2×Q16×D61—21no—
17C2×SD16×D61—21no—
18C4⋊Q8×D61C2211yescharacteristic
19#127×D61C2211yescharacteristic
20C4×Q8×D61C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840107—21no—
25#16840107—21no—
26#16839973C2211yescharacteristic, complemented
27#16839972C2211yescharacteristic, complemented
28#16839971—21no—
29#16839970—21no—
30#16839969C2211yescharacteristic, complemented
31#16839963C2211yescharacteristic
32#16839962C2211yescharacteristic
33#16839961—21no—
34#16839960—21no—
35#16839959C2211yescharacteristic
36#16839893C2211yescharacteristic, complemented
37#16839892C2211yescharacteristic, complemented
38#16839891—21no—
39#16839890—21no—
40#16839889C2211yescharacteristic, complemented
41C4⋊C8×D61—21no—
42C4⋊C8×D61C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44C4⋊C8×D61C2211yescharacteristic
45#103×D61—21no—
46#102×D61—21no—
47#102×D61—21no—
48#102×D61—21no—
49#97×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839513C2211yescharacteristic, complemented
52#16839512C2211yescharacteristic, complemented
53#16839512C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839508C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839506C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C61×#486C2211yescharacteristic
61C61×#462C2211yescharacteristic, complemented
62C61×#460C2211yescharacteristic
63C61×#446C2211yescharacteristic, complemented
64C61×#334C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#331C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61D411yescharacteristic
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61—21no—
72C2×Dic244—21no—
73C2×#11758202—21no—
74C2×#11758202—21no—
75Q16×D61—44no—
76C2×#11758190—21no—
77C2×#11758200—21no—
78C2×#11758201—21no—
79SD16×D61—44no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61D411yescharacteristic
84C2×C8×D61D411yescharacteristic
85#14519777C2311yescharacteristic
86#14519776—21no—
87#14519776—21no—
88#14519775—21no—
89#14519774C2311yescharacteristic
90#14519773—21no—
91#14519773—21no—
92#14519773—21no—
93Q8×Dic61D411yescharacteristic
94C4×Dic122—21no—
95C4×Dic122C2311yescharacteristic
96#14519742—21no—
97#14519742D411yescharacteristic
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61D411yescharacteristic
102C42×D61—21no—
103C42×D61C2311yescharacteristic
104C4⋊#92418—21no—
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2311yescharacteristic
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519702—21no—
114#14519701—21no—
115#14519700—21no—
116#14519699—21no—
117#14519699—21no—
118#14519699—21no—
119#14519698—21no—
120#14519698—21no—
121#14519698—21no—
122#14519697—21no—
123#14519697—21no—
124#14519697—21no—
125#14519688—21no—
126#14519687—21no—
127#14519687—21no—
128C4×#92418C2311yescharacteristic
129C8×Dic61D411yescharacteristic
130C8×Dic61D411yescharacteristic
131C2×Q16×C61—21no—
132C2×SD16×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134#127×C61C2311yescharacteristic
135C4×Q8×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#102×C61—21no—
142#102×C61—21no—
143#102×C61—21no—
144#97×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×C22⋊D61—41no—
153C2×C22⋊D61—41no—
154C2×C22⋊D61—41no—
155Q8×D61—22no—
156Q8×D61—22no—
157Q8×D61—42no—
158Q8×D61—42no—
159D4×D61—42no—
160D4×D61—42no—
161D4×D61—42no—
162D4×D61—42no—
163D4×D61—82no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—41no—
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61#4111yescharacteristic
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—41no—
176C2×Dic122C2×D411yescharacteristic
177Q16×C61—42no—
178SD16×C61—42no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61C2×D411yescharacteristic
188C42×C61—21no—
189C42×C61C2411yescharacteristic
190#11758202—42no—
191#11758202—42no—
192#11758201—42no—
193#11758200—42no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—21no—
200#11758196—21no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61#4111yescharacteristic
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418C2×D411yescharacteristic
213C2×#92418C2×D411yescharacteristic
214Dic244—42no—
215#11758190—42no—
216C8×D61—22no—
217C8×D61—22no—
218C8×D61—42no—
219C8×D61—42no—
220C8×D61—42no—
221C23×C61—41no—
222C22×D61—41no—
223C22×D61—82no—
224C22×D61—82no—
225C22×D61—82no—
226C22×D61#12111yescharacteristic
227Q8×C61—21no—
228Q8×C61—21no—
229Q8×C61—41no—
230Q8×C61—41no—
231D4×C61—41no—
232D4×C61—41no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—81no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—41no—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C22⋊D61—82no—
243C22⋊D61—82no—
244C22⋊D61—82no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—41no—
248C2×Dic61#12111yescharacteristic
249C2×Dic61#12111yescharacteristic
250C2×Dic61#12111yescharacteristic
251D244—41no—
252D244—41no—
253D244—41no—
254D244—41no—
255D244—81no—
256C4×D61—22no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—82no—
260C4×D61#13512yes—
261C4×D61AGL(1,ℤ/8)12yes—
262C4×D61AGL(1,ℤ/8)12yes—
263C4×D61#13712yes—
264Dic122—21no—
265Dic122—21no—
266Dic122—42no—
267Dic122—41no—
268Dic122—41no—
269Dic122—82no—
270C8×C61—21no—
271C8×C61—21no—
272C8×C61—41no—
273C8×C61—41no—
274C8×C61—41no—
275#92418—21no—
276#92418—21no—
277#92418—41no—
278#92418—41no—
279#92418—41no—
280C2×#1702—611nomaximal, Sylow
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61C2×#12111yescharacteristic
285C2×D61—81no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—164no—
289C2×D61#46412yes—
290C2×D61#46912yes—
291C2×D61#47112yes—
292C4×C61—21no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—81no—
296C4×C61C2×#13511yescharacteristic
297C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C61C2×#13711yescharacteristic
300Dic61—21no—
301Dic61—41no—
302Dic61—41no—
303Dic61—81no—
304Dic61#46412yes—
305Dic61#46912yes—
306C2×#486—611no—
307C2×#462—611no—
308C2×#460—611no—
309C2×#446—611no—
310#1702—611no—
311#1702—611no—
312#1702—611no—
313#1702—611no—
314#1702—611no—
315#1702—611no—
316#1702—611no—
317#1702D6111yescharacteristic, direct product factor
318C2×#334—611no—
319C2×#332—611no—
320C2×#331—611no—
321C2×C61—161no—
322C2×C61C2×#46411yescharacteristic
323C2×C61C2×#46911yescharacteristic
324C2×C61C2×#47111yescharacteristic
325D61—161no—
326D61#170214yesdirect product factor
327C22×Q16—1221no—
328C22×SD16—1221no—
329C2×C4⋊Q8—611no—
330C2×#127—611no—
331C2×C4×Q8—611no—
332#486—611no—
333#486—611no—
334#486—611no—
335#486—1221no—
336#486—1221no—
337#486C2×D6111yescharacteristic
338#462—611no—
339#462—611no—
340#462—611no—
341#462—1221no—
342#462—1221no—
343#462C2×D6111yescharacteristic, complemented
344#460—611no—
345#460—611no—
346#460—611no—
347#460—1221no—
348#460—1221no—
349#460C2×D6111yescharacteristic
350#446—611no—
351#446—611no—
352#446—611no—
353#446—1221no—
354#446—1221no—
355#446C2×D6111yescharacteristic, complemented
356C2×C4⋊C8—611no—
357C2×C4⋊C8—611no—
358C2×C4⋊C8—611no—
359C2×C4⋊C8—1221no—
360C2×#103—1221no—
361C2×#102—1221no—
362C2×#102—1221no—
363C2×#102—1221no—
364C2×#97—1221no—
365C2×C4×C8—611no—
366#334—611no—
367#334—611no—
368#334—611no—
369#334C2×D6111yescharacteristic, complemented
370#332—611no—
371#332—611no—
372#332—611no—
373#332C2×D6111yescharacteristic, complemented
374#331—611no—
375#331—611no—
376#331—611no—
377#331C2×D6111yescharacteristic
378C61C2×#170211yescharacteristic, complemented, Sylow
379C22×Q8—611no—
380C22×Q8—1221no—
381C22×D4—1221no—
382C22×D4—1221no—
383C22×D4—1221no—
384C2×Q16—21no—
385C2×Q16—1221no—
386C2×Q16—1221no—
387C2×Q16—1221no—
388C2×Q16—2444no—
389C2×SD16—21no—
390C2×SD16—1221no—
391C2×SD16—1221no—
392C2×SD16—1221no—
393C2×SD16—2444no—
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—1221no—
397C22×C8—1221no—
398C22×C8—1221no—
399C4⋊Q8—611no—
400C4⋊Q8—1221no—
401C4⋊Q8—1221no—
402C4⋊Q8—1221no—
403C4⋊Q8C22×D6111yescharacteristic
404#127—611no—
405#127—1221no—
406#127—1221no—
407#127—1221no—
408#127C22×D6111yescharacteristic
409C4×Q8—611no—
410C4×Q8—611no—
411C4×Q8—611no—
412C4×Q8—1221no—
413C4×Q8—1221no—
414C4×Q8C22×D6111yescharacteristic
415C2×C4⋊C4—611no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C42—611no—
420C2×C42—1221no—
421C4⋊C8—21no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—1221no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8—1221no—
429C4⋊C8—1221no—
430C4⋊C8—1221no—
431C4⋊C8C22×D6111yescharacteristic
432C4⋊C8C22×D6111yescharacteristic
433C4⋊C8C22×D6111yescharacteristic
434#103—21no—
435#103—1221no—
436#103—1221no—
437#103—1221no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—1221no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447#102—1221no—
448#102—1221no—
449#102—1221no—
450#97—21no—
451#97—1221no—
452#97—1221no—
453#97—1221no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8C22×D6111yescharacteristic
458C24—2441no—
459C2×Q8—21no—
460C2×Q8—611no—
461C2×Q8—1221no—
462C2×Q8—1222no—
463C2×Q8—1222no—
464C2×Q8—1221no—
465C2×Q8—2441no—
466C2×Q8—2442no—
467C2×Q8—2442no—
468C2×Q8D4×D6111yescharacteristic
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4—4882no—
476C2×D4—2442no—
477C2×D4—2442no—
478C2×D4—2442no—
479C2×D4—2442no—
480C2×D4—2441no—
481C2×D4—2441no—
482C2×D4—2441no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—2441no—
489Q16—42no—
490Q16—2442no—
491Q16—2442no—
492Q16—2442no—
493SD16—42no—
494SD16—2442no—
495SD16—2442no—
496SD16—2442no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—2442no—
508C2×C8—2442no—
509C2×C8—2442no—
510C2×C8D4×D6111yescharacteristic
511C2×C8D4×D6111yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—611no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—2441no—
523C4⋊C4—2441no—
524C4⋊C4D4×D6111yescharacteristic
525C42—21no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—1221no—
530C42—1221no—
531C42—1221no—
532C42C23×D6111yescharacteristic
533C23—41no—
534C23—611no—
535C23—4882no—
536C23—4882no—
537C23—4882no—
538C23—2441no—
539Q8—21no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8—1221no—
544Q8—1221no—
545Q8—4882no—
546Q8—2442no—
547Q8—2441no—
548Q8—2441no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—4881no—
555D4—4882no—
556D4—4882no—
557D4—4882no—
558D4—2441no—
559D4—2441no—
560D4—2441no—
561D4—2441no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—611no—
572C2×C4—1222no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—4882no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2441no—
579C2×C4C2×D4×D6111yescharacteristic
580C2×C4C2×D4×D6111yescharacteristic
581C2×C4#41×D6111yescharacteristic
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—1221no—
588C8—1221no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—612no—
596C22—612no—
597C22—612no—
598C22—9764no—
599C22—4881no—
600C22—4881no—
601C22—4881no—
602C22#121×D6111yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—612no—
608C4—612no—
609C4—1221no—
610C4—4881no—
611C4—2441no—
612C4—2441no—
613C4#135×D6111yescharacteristic
614C4AGL(1,ℤ/8)×D6111yescharacteristic
615C4AGL(1,ℤ/8)×D6111yescharacteristic
616C4#137×D6111yescharacteristic
617C2—161no—
618C2—614no—
619C2—9761no—
620C2#464×D6111yescharacteristic
621C2#469×D6111yescharacteristic
622C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1702C2
socleC22×C61C2×#121
prime radical#127×D61C22
hypercenter#1702D61
hypocenterC61C2×#1702
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1702

Complements

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

NH ≅ G/Ntype
2. #462×D61C2semidirect
4. #446×D61C2semidirect
5. #21445390C2semidirect
6. #21445389C2semidirect
7. #21445388C2semidirect
8. #21445387C2semidirect
9. #21445386C2semidirect
10. #21445385C2semidirect
11. #21445384C2semidirect
12. #334×D61C2semidirect
13. #332×D61C2semidirect
15. C61×#1702C2semidirect
26. #16839973C22semidirect
27. #16839972C22semidirect
30. #16839969C22semidirect
36. #16839893C22semidirect
37. #16839892C22semidirect
40. #16839889C22semidirect
51. #16839513C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839509C22semidirect
55. #16839508C22semidirect
56. #16839507C22semidirect
61. C61×#462C22semidirect
63. C61×#446C22semidirect
64. C61×#334C22semidirect
65. C61×#332C22semidirect
317. #1702D61direct (N × H)
326. D61#1702direct (N × H)
343. #462C2×D61semidirect
355. #446C2×D61semidirect
369. #334C2×D61semidirect
373. #332C2×D61semidirect
378. C61C2×#1702semidirect

Maximal subgroups

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

subgroupindex
#486×D612
#462×D612
#460×D612
#446×D612
#214453902
#214453892
#214453882
#214453872
#214453862
#214453852
#214453842
#334×D612
#332×D612
#331×D612
C61×#17022
C2×#170261