Finite Group Databasebeta

← #29669856

Subgroups — #29669856

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458522C211yesmaximal, characteristic, complemented
2#21457645C211yesmaximal, characteristic, complemented
3#21457626C211yesmaximal, characteristic, complemented
4#21445456C211yesmaximal, characteristic, complemented
5#21445389C211yesmaximal, characteristic, complemented
6#21445228C211yesmaximal, characteristic, complemented
7#21445226C211yesmaximal, characteristic, complemented
8#21445157C211yesmaximal, characteristic, complemented
9#21445031C211yesmaximal, characteristic, complemented
10#21444970C211yesmaximal, characteristic, complemented
11#21444884C211yesmaximal, characteristic, complemented
12#21444872C211yesmaximal, characteristic, complemented
13#21444656C211yesmaximal, characteristic, complemented
14#21444641C211yesmaximal, characteristic, complemented
15C61×#3284C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840138C2211yescharacteristic
19#16840126—21no—
20#16840114C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840108C2211yescharacteristic, complemented
24#16840082—21no—
25#16840075—21no—
26#16840062—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic, complemented
29#16840039C2211yescharacteristic
30#16839996—21no—
31#16839994—21no—
32#16839962C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839954—21no—
35#16839954C2211yescharacteristic
36#16839911—21no—
37#16839895—21no—
38#16839893C2211yescharacteristic, complemented
39#16839872—21no—
40C4×#11758199C2211yescharacteristic
41C8×D244C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43C2×#14519697—21no—
44#102×D61—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C2×#135×C61—21no—
57C61×#550C2211yescharacteristic, complemented
58C61×#547C2211yescharacteristic
59C61×#492C2211yescharacteristic, complemented
60C61×#465—21no—
61C61×#462C2211yescharacteristic, complemented
62C61×#459C2211yescharacteristic
63C61×#452—21no—
64C61×#449—21no—
65C4×SD16×C61C2211yescharacteristic
66C8×D4×C61C2211yescharacteristic, complemented
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758201—21no—
70C2×#11758199—21no—
71C2×#11758199—21no—
72C2×#11758199—41no—
73C2×#11758199D411yescharacteristic
74C22×#92418—21no—
75C2×C8×D61—21no—
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519769—21no—
79#14519755—41no—
80#14519753—21no—
81#14519752—21no—
82#14519751—21no—
83#14519747—41no—
84C4×D244—21no—
85C4×D244C2311yescharacteristic
86C4⋊C4×D61—21no—
87#14519710—21no—
88#14519710D411yescharacteristic
89#14519708—21no—
90#14519708—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519700—41no—
96#14519699—21no—
97#14519699—21no—
98#14519698—21no—
99#14519698—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698D411yescharacteristic
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117#135×C61—44no—
118C2×Q16×C61—21no—
119C2×SD16×C61—21no—
120C2×SD16×C61—21no—
121C2×SD16×C61D411yescharacteristic
122C2×D8×C61—21no—
123C22×C8×C61—21no—
124C4⋊Q8×C61C2311yescharacteristic
125#127×C61—21no—
126#127×C61C2311yescharacteristic
127#123×C61—41no—
128C22⋊Q8×C61—21no—
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—41no—
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136C2×C4⋊C4×C61—21no—
137#106×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146#41×C61—42no—
147#41×C61—42no—
148#41×C61—81no—
149#41×C61—81no—
150C2×Q8×C61—21no—
151C2×Q8×C61C2×D411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C2×C22⋊D61—41no—
165D4×D61—42no—
166D4×D61—81no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—42no—
171C2×D244—41no—
172C2×D244—81no—
173C2×D244C2×D411yescharacteristic
174C2×C4×D61—21no—
175C2×C4×D61—41no—
176C2×Dic122—21no—
177Q16×C61—42no—
178SD16×C61—22no—
179SD16×C61—42no—
180SD16×C61—81no—
181D8×C61—42no—
182C2×C8×C61—21no—
183C2×C8×C61—42no—
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61C2×D411yescharacteristic
191C4⋊C4×C61C2×D411yescharacteristic
192C4⋊C4×C61C2×D411yescharacteristic
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C42×C61—21no—
198C42×C61C2411yescharacteristic
199#11758201—81no—
200#11758199—22no—
201#11758199—42no—
202#11758199—81no—
203#11758199—82no—
204#11758198—21no—
205#11758198—41no—
206#11758198—41no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61C2×D411yescharacteristic
210#11758196—41no—
211#11758196—41no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—81no—
217C2×#92418C2×D411yescharacteristic
218C2×#92418C2×D411yescharacteristic
219C8×D61—81no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—41no—
223C22×D61—21no—
224C22×D61—41no—
225C22×D61—82no—
226C22×D61—82no—
227C22×D61—161no—
228Q8×C61—21no—
229Q8×C61—21no—
230Q8×C61—41no—
231Q8×C61—41no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—81no—
240D4×C61—82no—
241D4×C61—82no—
242D4×C61—161no—
243D4×C61AGL(1,ℤ/8)12yes—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—82no—
254C2×C4×C61—82no—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C22⋊D61—82no—
259C2×Dic61—21no—
260C2×Dic61—41no—
261D244—21no—
262D244—41no—
263D244—41no—
264D244—41no—
265D244—41no—
266D244—81no—
267D244—82no—
268D244#13512yescomplemented
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—161no—
272Dic122—81no—
273C8×C61—21no—
274C8×C61—21no—
275C8×C61—41no—
276#92418—21no—
277#92418—21no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#19788—611nomaximal, Sylow
283C22×C61—22no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61D4211yescharacteristic
293C2×D61—22no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—164no—
300C4×C61—21no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—81no—
306C4×C61C2×#13511yescharacteristic
307C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C61#57611yescharacteristic
309C4×C61#57711yescharacteristic
310Dic61—41no—
311Dic61—81no—
312#3366—611no—
313#3295—611no—
314#3294—611no—
315#3284D6111yescharacteristic, complemented
316#1717—611no—
317#1702—611no—
318#1677—611no—
319#1677—611no—
320#1665—611no—
321#1644—611no—
322#1635—611no—
323#1621—611no—
324#1619—611no—
325#1582—611no—
326#1580—611no—
327C2×C61—42no—
328C2×C61—81no—
329C2×C61—161no—
330C2×C61#326411yescharacteristic
331C2×C61#328211yescharacteristic
332C2×C61#328811yescharacteristic
333D61—42no—
334D61—161no—
335C2×#135—21no—
336#554—611no—
337#550C2×D6111yescharacteristic, complemented
338#547C2×D6111yescharacteristic
339D42—611no—
340#493—611no—
341#492C2×D6111yescharacteristic, complemented
342#490—1221no—
343#487—611no—
344#486—611no—
345#486—611no—
346#486—611no—
347#481—1221no—
348#480—1221no—
349#478—1221no—
350#476—611no—
351#476—611no—
352#474—611no—
353#466—1221no—
354#465—21no—
355#465—1221no—
356#462C2×D6111yescharacteristic, complemented
357#460—611no—
358#459—611no—
359#459—611no—
360#459—1221no—
361#459C2×D6111yescharacteristic
362#452—21no—
363#450—1221no—
364#449—21no—
365#447—1221no—
366#446—611no—
367#442—1221no—
368C4×SD16C2×D6111yescharacteristic
369C4×D8—611no—
370C8×D4—611no—
371C8×D4—611no—
372C8×D4C2×D6111yescharacteristic, complemented
373C2×#102—1221no—
374C2×#102—1221no—
375#334—611no—
376#334—611no—
377#333—611no—
378#332—611no—
379#331—611no—
380#331—611no—
381Q8⋊C8—611no—
382D4⋊C8—611no—
383D4⋊C8—611no—
384D4⋊C8—611no—
385#322—611no—
386C61#1978811yescharacteristic, complemented, Sylow
387C2×#41—21no—
388C2×#41—21no—
389C22×D4—1221no—
390C22×D4—1221no—
391#135—44no—
392C2×Q16—21no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×SD16—1221no—
396C2×SD16C22⋊D6111yescharacteristic
397C2×D8—21no—
398C2×D8—611no—
399C2×D8—1221no—
400C2×D8—1221no—
401C2×D8—2441no—
402C22×C8—21no—
403C22×C8—1221no—
404C22×C8—1221no—
405C4⋊Q8—611no—
406C4⋊Q8C22×D6111yescharacteristic
407#127—21no—
408#127—611no—
409#127C22×D6111yescharacteristic
410#125—1221no—
411#123—41no—
412C22⋊Q8—21no—
413C22⋊Q8—1221no—
414C22⋊Q8—2441no—
415#121—21no—
416#121—21no—
417#121—41no—
418#121—1221no—
419#121—1221no—
420#120—2441no—
421C4×Q8C22×D6111yescharacteristic
422C4×D4—21no—
423C4×D4—611no—
424C4×D4—1221no—
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427C2×C4⋊C4—21no—
428C2×C4⋊C4—1221no—
429#107—611no—
430#107—1221no—
431#106—1221no—
432#106—1221no—
433#106C22⋊D6111yescharacteristic
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—1221no—
438C4⋊C8C22×D6111yescharacteristic
439#103—21no—
440#103—2441no—
441#103C22⋊D6111yescharacteristic
442#102—21no—
443#102—611no—
444#102—611no—
445#102—1221no—
446#102—1221no—
447#102—1221no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#102C22⋊D6111yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—1221no—
460C22⋊C8—1221no—
461#97—1221no—
462C4×C8—611no—
463C4×C8—611no—
464C4×C8C22×D6111yescharacteristic
465C24—2441no—
466#41—42no—
467#41—42no—
468#41—81no—
469#41—81no—
470C2×Q8—21no—
471C2×Q8—1221no—
472C2×Q8C2×C22⋊D6111yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—611no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—4881no—
484C2×D4—4881no—
485C2×D4—2441no—
486C2×D4—2442no—
487C2×D4—2441no—
488C2×D4—2442no—
489C2×D4D4×D6111yescharacteristic
490C2×D4C2×C22⋊D6111yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—1221no—
496C22×C4—2441no—
497Q16—42no—
498SD16—22no—
499SD16—42no—
500SD16—81no—
501SD16—4881no—
502D8—42no—
503D8—1222no—
504D8—4881no—
505D8—4882no—
506D8—2442no—
507C2×C8—21no—
508C2×C8—42no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—4881no—
516C2×C8—4881no—
517C2×C8C2×C22⋊D6111yescharacteristic
518C2×C8C2×C22⋊D6111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—41no—
523C4⋊C4—611no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—2441no—
527C4⋊C4—2441no—
528C4⋊C4D4×D6111yescharacteristic
529C4⋊C4C2×C22⋊D6111yescharacteristic
530C4⋊C4C2×C22⋊D6111yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—1221no—
536C22⋊C4—2441no—
537C22⋊C4—2441no—
538C42—21no—
539C42C23×D6111yescharacteristic
540C23—21no—
541C23—21no—
542C23—41no—
543C23—1221no—
544C23—9761no—
545C23—4882no—
546C23—4882no—
547C23—2441no—
548Q8—21no—
549Q8—21no—
550Q8—41no—
551Q8—41no—
552Q8—4881no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—161no—
564D4—612no—
565D4—1221no—
566D4—4881no—
567D4—4882no—
568D4—4882no—
569D4—2441no—
570D4—2441no—
571D4—2441no—
572D4—2441no—
573D4#1451980312yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—82no—
584C2×C4—82no—
585C2×C4—1221no—
586C2×C4—9761no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4C2×D4×D6111yescharacteristic
591C2×C4C22×C22⋊D6111yescharacteristic
592C2×C4#1451982211yescharacteristic
593C8—21no—
594C8—21no—
595C8—41no—
596C8—1221no—
597C8—1221no—
598C8—2441no—
599C8—2441no—
600C8—2441no—
601C8—2441no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—1222no—
612C22—9764no—
613C22—4881no—
614C22—4881no—
615C22—4881no—
616C22—2441no—
617C22—2441no—
618C22D4×C22⋊D6111yescharacteristic
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—4881no—
626C4—2441no—
627C4#135×D6111yescharacteristic
628C4C2×#1451980311yescharacteristic
629C4#1684056511yescharacteristic
630C4#1684056911yescharacteristic
631C2—42no—
632C2—81no—
633C2—161no—
634C2—9761no—
635C2—2442no—
636C2#2145729511yescharacteristic
637C2#2145752011yescharacteristic
638C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3284C2
socleC22×C61D42
hypercenter#3284D61
hypocenterC61#19788
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3284

Complements

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

NH ≅ G/Ntype
1. #21458522C2semidirect
2. #21457645C2semidirect
3. #21457626C2semidirect
4. #21445456C2semidirect
5. #21445389C2semidirect
6. #21445228C2semidirect
7. #21445226C2semidirect
8. #21445157C2semidirect
9. #21445031C2semidirect
10. #21444970C2semidirect
11. #21444884C2semidirect
12. #21444872C2semidirect
13. #21444656C2semidirect
14. #21444641C2semidirect
15. C61×#3284C2semidirect
20. #16840114C22semidirect
23. #16840108C22semidirect
28. #16840052C22semidirect
38. #16839893C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
49. #16839506C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839484C22semidirect
57. C61×#550C22semidirect
59. C61×#492C22semidirect
61. C61×#462C22semidirect
66. C8×D4×C61C22semidirect
268. D244#135semidirect
315. #3284D61semidirect
337. #550C2×D61semidirect
341. #492C2×D61semidirect
356. #462C2×D61semidirect
372. C8×D4C2×D61semidirect
386. C61#19788semidirect

Maximal subgroups

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

subgroupindex
#214585222
#214576452
#214576262
#214454562
#214453892
#214452282
#214452262
#214451572
#214450312
#214449702
#214448842
#214448722
#214446562
#214446412
C61×#32842
#1978861