Finite Group Databasebeta

← #29669474

Subgroups — #29669474

Order 15616.

756 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457637C211yesmaximal, characteristic, complemented
2D4×#11758201C211yesmaximal, characteristic, complemented
3D8×D244C211yesmaximal, characteristic
4#21445448C211yesmaximal, characteristic, complemented
5#21445303C211yesmaximal, characteristic, complemented
6#21445230C211yesmaximal, characteristic, complemented
7#21445191C211yesmaximal, characteristic, complemented
8#21445162C211yesmaximal, characteristic, complemented
9#21444997C211yesmaximal, characteristic, complemented
10#21444934C211yesmaximal, characteristic, complemented
11#21444922C211yesmaximal, characteristic, complemented
12#21444891C211yesmaximal, characteristic, complemented
13#21444653C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3384C211yesmaximal, characteristic, complemented
16C22×#11758201—21no—
17C2×D8×D61—21no—
18D4×D244C2211yescharacteristic
19D4×D244C2211yescharacteristic
20#16840139C2211yescharacteristic
21#16840136C2211yescharacteristic, complemented
22#16840136C2211yescharacteristic, complemented
23#16840110C2211yescharacteristic, complemented
24#16840110C2211yescharacteristic, complemented
25#16840080—21no—
26#16840049C2211yescharacteristic
27#16839999—21no—
28#16839993—21no—
29#16839993—21no—
30#16839964C2211yescharacteristic
31#16839962C2211yescharacteristic, complemented
32#16839962C2211yescharacteristic, complemented
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839912—21no—
36#16839912—21no—
37#16839901—21no—
38#16839897—21no—
39#16839897—21no—
40C4×#11758201C2211yescharacteristic
41C8×D244C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43D4×#92418C2211yescharacteristic, complemented
44C2×#14519697—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839505C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C61×#554C2211yescharacteristic, complemented
57D4×Q8×C61C2211yescharacteristic, complemented
58C61×#501—21no—
59C61×#498C2211yescharacteristic, complemented
60C61×#478—21no—
61C61×#476—21no—
62C61×#476C2211yescharacteristic, complemented
63C61×#474C2211yescharacteristic, complemented
64C61×#446C2211yescharacteristic, complemented
65C61×#442—21no—
66C4×D8×C61C2211yescharacteristic
67C22×D244—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758201—21no—
75C2×#11758201—21no—
76C2×#11758201—41no—
77C2×#11758201—44no—
78C2×#11758201D411yescharacteristic
79C2×D488—21no—
80C2×D488—21no—
81C2×#11758199—21no—
82C2×#11758199—21no—
83D8×D61—44no—
84C22×#92418—21no—
85C22×#92418—21no—
86C2×C8×D61—21no—
87#14519774C2311yescharacteristic
88#14519774C2311yescharacteristic
89#14519752—21no—
90#14519752—21no—
91#14519751—21no—
92#14519751—21no—
93#14519747—41no—
94#14519747—41no—
95C4×D244C2311yescharacteristic
96#14519708—21no—
97#14519708D411yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701—21no—
102#14519701D411yescharacteristic
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697—41no—
111#14519697D411yescharacteristic
112C22⋊#92418—21no—
113C22⋊#92418—21no—
114#14519689—21no—
115C4×#92418C2311yescharacteristic
116C4×#92418C2311yescharacteristic
117C22×Q8×C61—21no—
118C2×D8×C61D411yescharacteristic
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#125×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137#106×C61—21no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#102×C61D411yescharacteristic
144#97×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147C23×D61—41no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—41no—
151C2×Q8×C61—42no—
152C2×Q8×C61—81no—
153C2×Q8×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162D4×D61—42no—
163D4×D61—42no—
164D4×D61—81no—
165D4×D61—81no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—42no—
173C2×D244—42no—
174C2×D244—41no—
175C2×D244—41no—
176C2×D244—81no—
177C2×D244—81no—
178C2×D244C2×D411yescharacteristic
179C2×C4×D61—21no—
180D8×C61SD1614yescomplemented
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×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61C2×D411yescharacteristic
193C4⋊C4×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C42×C61—21no—
200C42×C61C2411yescharacteristic
201#11758201—22no—
202#11758201—42no—
203#11758201—42no—
204#11758201—42no—
205#11758201—81no—
206#11758201—81no—
207#11758201—82no—
208#11758199—42no—
209#11758199—42no—
210#11758198—21no—
211#11758198—41no—
212#11758198—41no—
213C4⋊Dic61C2×D411yescharacteristic
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—42no—
219C2×#92418—81no—
220C2×#92418C2×D411yescharacteristic
221C2×#92418C2×D411yescharacteristic
222D488—42no—
223D488—81no—
224C8×D61—42no—
225C23×C61—21no—
226C23×C61—21no—
227C22×D61—21no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—82no—
231C22×D61—82no—
232C22×D61—82no—
233C22×D61—82no—
234C22×D61—161no—
235C22×D61—161no—
236Q8×C61—21no—
237Q8×C61—21no—
238Q8×C61—41no—
239Q8×C61—41no—
240Q8×C61—81no—
241Q8×C61—82no—
242D4×C61—21no—
243D4×C61—21no—
244D4×C61C2×SD1612yes—
245D4×C61C2×SD1612yescomplemented
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—82no—
257C2×C4×C61—161no—
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61H(5,𝔽2)11yescharacteristic
261C22⋊D61—82no—
262C22⋊D61—82no—
263C2×Dic61—21no—
264D244—21no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—41no—
269D244—41no—
270D244—41no—
271D244—41no—
272D244—41no—
273D244—81no—
274D244—81no—
275D244—82no—
276D244—82no—
277D244AGL(1,ℤ/8)12yes—
278C4×D61—41no—
279C4×D61—41no—
280C8×C61—21no—
281C8×C61—41no—
282C8×C61C2×SD1612yescomplemented
283#92418—21no—
284#92418—21no—
285#92418—41no—
286#92418—41no—
287#92418—41no—
288#92418—41no—
289#19763—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61D4211yescharacteristic
297C2×D61—22no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—81no—
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—164no—
307C2×D61—164no—
308C4×C61—21no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—81no—
314C4×C61—81no—
315C4×C61C22×SD1611yescharacteristic
316C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
317C4×C61#57611yescharacteristic
318C4×C61#57711yescharacteristic
319Dic61—41no—
320#3384D6111yescharacteristic, complemented
321#3295—611no—
322D4×SD16—611no—
323D4×D8—611no—
324#1715—611no—
325#1688—611no—
326#1677—611no—
327#1671—611no—
328#1665—611no—
329#1639—611no—
330#1629—611no—
331#1627—611no—
332#1622—611no—
333#1582—611no—
334#1580—611no—
335C2×C61—42no—
336C2×C61—42no—
337C2×C61#326411yescharacteristic
338C2×C61D4×SD1611yescharacteristic
339C2×C61#328811yescharacteristic
340D61—42no—
341D61—161no—
342D61—161no—
343C22×SD16—1221no—
344C22×D8—1221no—
345#554C2×D6111yescharacteristic, complemented
346D4×Q8C2×D6111yescharacteristic, complemented
347D42—611no—
348D42—611no—
349#501—21no—
350#498C2×D6111yescharacteristic, complemented
351#493—611no—
352#492—611no—
353#492—611no—
354#486—611no—
355#486—611no—
356#481—1221no—
357#478—21no—
358#476—21no—
359#476—611no—
360#476C2×D6111yescharacteristic, complemented
361#474C2×D6111yescharacteristic, complemented
362#466—1221no—
363#465—1221no—
364#465—1221no—
365#461—611no—
366#460—611no—
367#460—611no—
368#459—611no—
369#459—611no—
370#450—1221no—
371#450—1221no—
372#448—1221no—
373#447—1221no—
374#447—1221no—
375#446C2×D6111yescharacteristic, complemented
376#442—21no—
377C4×SD16—611no—
378C4×D8C2×D6111yescharacteristic
379C8×D4—611no—
380C8×D4—611no—
381C8×D4—611no—
382C2×#102—1221no—
383#334—611no—
384#334—611no—
385#333—611no—
386#332—611no—
387#331—611no—
388#331—611no—
389Q8⋊C8—611no—
390D4⋊C8—611no—
391D4⋊C8—611no—
392D4⋊C8—611no—
393#322—611no—
394C61#1976311yescharacteristic, complemented, Sylow
395C22×Q8—21no—
396C22×D4—1221no—
397C22×D4—1221no—
398C22×D4—1221no—
399C22×D4—1221no—
400C2×SD16—611no—
401C2×SD16—1221no—
402C2×SD16—1221no—
403C2×SD16—1221no—
404C2×SD16—1221no—
405C2×SD16—1221no—
406C2×SD16—2441no—
407C2×SD16—2444no—
408C2×D8—1221no—
409C2×D8—1221no—
410C2×D8—1221no—
411C2×D8—1221no—
412C2×D8—2444no—
413C2×D8C22⋊D6111yescharacteristic
414C22×C8—1221no—
415C22×C8—1221no—
416C22×C8—1221no—
417C4⋊Q8—21no—
418C4⋊Q8C22×D6111yescharacteristic
419C4⋊Q8C22×D6111yescharacteristic
420#127—611no—
421#127—611no—
422#125—21no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—41no—
426C22⋊Q8—41no—
427#121—1221no—
428#121—1221no—
429#121—1221no—
430#121—1221no—
431#120—2441no—
432#120—2441no—
433C4×Q8C22×D6111yescharacteristic
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—611no—
437C4×D4C22×D6111yescharacteristic
438C4×D4C22×D6111yescharacteristic
439C2×C4⋊C4—21no—
440#107—21no—
441#107C22⋊D6111yescharacteristic
442#106—21no—
443#106—21no—
444#106—21no—
445#106—611no—
446#106—1221no—
447C4⋊C8—21no—
448C4⋊C8—611no—
449C4⋊C8—611no—
450C4⋊C8—611no—
451C4⋊C8C22×D6111yescharacteristic
452#103—611no—
453#103—1221no—
454#102—21no—
455#102—21no—
456#102—611no—
457#102—1221no—
458#102—1221no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—1221no—
463#102—1221no—
464#102—2441no—
465#102C22⋊D6111yescharacteristic
466#102C22⋊D6111yescharacteristic
467C22⋊C8—1221no—
468C22⋊C8—1221no—
469C22⋊C8—1221no—
470#97—21no—
471C4×C8—611no—
472C4×C8—611no—
473C4×C8C22×D6111yescharacteristic
474C24—2441no—
475C24—2441no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—41no—
479C2×Q8—42no—
480C2×Q8—81no—
481C2×Q8D4×D6111yescharacteristic
482C2×D4—611no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—1221no—
487C2×D4—1221no—
488C2×D4—1221no—
489C2×D4—4881no—
490C2×D4—4881no—
491C2×D4—4881no—
492C2×D4—4881no—
493C2×D4—2441no—
494C2×D4—2441no—
495C2×D4—2442no—
496C2×D4—2442no—
497C2×D4—2441no—
498C2×D4—2441no—
499C2×D4—2442no—
500C2×D4—2442no—
501C2×D4C2×C22⋊D6111yescharacteristic
502C2×D4C2×C22⋊D6111yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—1221no—
508SD16—1222no—
509SD16—4881no—
510SD16—4882no—
511SD16—4881no—
512SD16—2442no—
513SD16—2442no—
514SD16—2442no—
515D8—4881no—
516D8—2442no—
517D8—2442no—
518D8—2442no—
519D8#1175820114yescomplemented
520C2×C8—21no—
521C2×C8—611no—
522C2×C8—611no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—4881no—
528C2×C8—2442no—
529C2×C8—2442no—
530C2×C8C2×C22⋊D6111yescharacteristic
531C2×C8C2×C22⋊D6111yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—611no—
541C4⋊C4D4×D6111yescharacteristic
542C4⋊C4C2×C22⋊D6111yescharacteristic
543C4⋊C4C2×C22⋊D6111yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—1221no—
549C22⋊C4—2441no—
550C22⋊C4—2441no—
551C42—21no—
552C42C23×D6111yescharacteristic
553C23—21no—
554C23—21no—
555C23—1221no—
556C23—9761no—
557C23—9761no—
558C23—4882no—
559C23—4882no—
560C23—4882no—
561C23—4882no—
562C23—2441no—
563C23—2441no—
564Q8—21no—
565Q8—21no—
566Q8—41no—
567Q8—41no—
568Q8—81no—
569Q8—82no—
570D4—21no—
571D4—21no—
572D4—612no—
573D4—1221no—
574D4—4881no—
575D4—4881no—
576D4—4882no—
577D4—4882no—
578D4—4882no—
579D4—4882no—
580D4—2441no—
581D4—2441no—
582D4—2441no—
583D4—2441no—
584D4—2441no—
585D4—2441no—
586D4—2441no—
587D4—2441no—
588D4C2×#1175820112yes—
589D4C2×#1175820112yescomplemented
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—82no—
601C2×C4—161no—
602C2×C4—1221no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4C22×C22⋊D6111yescharacteristic
607C2×C4#1451982211yescharacteristic
608C8—21no—
609C8—41no—
610C8—1221no—
611C8—1221no—
612C8—2441no—
613C8—2441no—
614C8—2441no—
615C8—2441no—
616C8C2×#1175820112yescomplemented
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—1222no—
624C22—9764no—
625C22—9764no—
626C22—4881no—
627C22—4881no—
628C22—4881no—
629C22—4881no—
630C22—4881no—
631C22—4881no—
632C22—2441no—
633C22—2441no—
634C22D4×C22⋊D6111yescharacteristic
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—2441no—
643C4C22×#1175820111yescharacteristic
644C4AGL(1,ℤ/8)×D6111yescharacteristic
645C4#1684056611yescharacteristic
646C4#1684057011yescharacteristic
647C2—42no—
648C2—42no—
649C2—9761no—
650C2—9761no—
651C2—2442no—
652C2#2145729311yescharacteristic
653C2D4×#1175820111yescharacteristic
654C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3384C2
socleC22×C61D42
prime radicalD8×D244C2
hypercenter#3384D61
hypocenterC61#19763
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #21457637C2semidirect
2. D4×#11758201C2semidirect
4. #21445448C2semidirect
5. #21445303C2semidirect
6. #21445230C2semidirect
7. #21445191C2semidirect
8. #21445162C2semidirect
9. #21444997C2semidirect
10. #21444934C2semidirect
11. #21444922C2semidirect
12. #21444891C2semidirect
13. #21444653C2semidirect
14. #21444643C2semidirect
15. C61×#3384C2semidirect
21. #16840136C22semidirect
22. #16840136C22semidirect
23. #16840110C22semidirect
24. #16840110C22semidirect
31. #16839962C22semidirect
32. #16839962C22semidirect
42. D4×#92418C22semidirect
43. D4×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839508C22semidirect
49. #16839505C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839483C22semidirect
56. C61×#554C22semidirect
57. D4×Q8×C61C22semidirect
59. C61×#498C22semidirect
62. C61×#476C22semidirect
63. C61×#474C22semidirect
64. C61×#446C22semidirect
180. D8×C61SD16semidirect
245. D4×C61C2×SD16semidirect
282. C8×C61C2×SD16semidirect
320. #3384D61semidirect
345. #554C2×D61semidirect
346. D4×Q8C2×D61semidirect
350. #498C2×D61semidirect
360. #476C2×D61semidirect
361. #474C2×D61semidirect
375. #446C2×D61semidirect
394. C61#19763semidirect
519. D8#11758201semidirect
589. D4C2×#11758201semidirect
616. C8C2×#11758201semidirect

Maximal subgroups

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

subgroupindex
#214576372
D4×#117582012
D8×D2442
#214454482
#214453032
#214452302
#214451912
#214451622
#214449972
#214449342
#214449222
#214448912
#214446532
#214446432
C61×#33842
#1976361