Finite Group Databasebeta

← #29663800

Subgroups — #29663800

Order 15616.

798 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#21456397C211yesmaximal, characteristic, complemented
2#21455284C211yesmaximal, characteristic, complemented
3#21455278C211yesmaximal, characteristic, complemented
4C8×D4×D61C211yesmaximal, characteristic, complemented
5#21445257C211yesmaximal, characteristic, complemented
6#21445256C211yesmaximal, characteristic, complemented
7#21445253C211yesmaximal, characteristic, complemented
8#21445207C211yesmaximal, characteristic, complemented
9#21445206C211yesmaximal, characteristic, complemented
10#21445173C211yesmaximal, characteristic, complemented
11#21445172C211yesmaximal, characteristic, complemented
12#21444576C211yesmaximal, characteristic, complemented
13#21444495C211yesmaximal, characteristic, complemented
14#21444493C211yesmaximal, characteristic, complemented
15C61×#1681C211yesmaximal, characteristic, complemented
16C2×#14519804—21no—
17C2×#14519801—21no—
18C22×C8×D61—21no—
19#16840313C2211yescharacteristic
20#16840310C2211yescharacteristic
21C4×D4×D61C2211yescharacteristic
22#16840165C2211yescharacteristic, complemented
23#16840138C2211yescharacteristic, complemented
24#16840109C2211yescharacteristic, complemented
25#16839997—21no—
26#16839997—21no—
27#16839980—21no—
28#16839979—21no—
29#16839976—21no—
30#16839975—21no—
31#16839968C2211yescharacteristic
32#16839967C2211yescharacteristic
33#16839964C2211yescharacteristic
34#16839958C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839954C2211yescharacteristic
37#16839842—21no—
38#16839842—21no—
39C8×D244C2211yescharacteristic
40D4×#92418C2211yescharacteristic
41#16839827C2211yescharacteristic
42C8×C22⋊D61—21no—
43#16839825—21no—
44#16839784C2211yescharacteristic
45#16839784C2211yescharacteristic
46C4⋊C8×D61C2211yescharacteristic
47#16839762—21no—
48#16839760—21no—
49C22⋊C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic, complemented
52#16839514C2211yescharacteristic, complemented
53#16839514C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839508C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839506C2211yescharacteristic, complemented
58#16839505C2211yescharacteristic, complemented
59#16839505C2211yescharacteristic, complemented
60C61×#486C2211yescharacteristic, complemented
61C61×#461C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#331C2211yescharacteristic, complemented
67C2×#11758226—21no—
68C2×#11758224—21no—
69C2×D4×D61D411yescharacteristic
70C22×C4×D61—21no—
71#14519804—44no—
72#14519801—44no—
73C2×#11758190—21no—
74C2×#11758200—21no—
75C2×#11758201—21no—
76C2×D488—21no—
77C2×#11758199—21no—
78C2×#11758199—21no—
79C2×#11758199—21no—
80C2×#11758199—21no—
81C2×#11758189—21no—
82C2×#11758189—21no—
83C22×#92418—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87C2×C8×D61—44no—
88C2×C8×D61D411yescharacteristic
89C2×C8×D61D411yescharacteristic
90#14519777C2311yescharacteristic
91#14519774C2311yescharacteristic
92#14519766—21no—
93#14519764—21no—
94#14519752—21no—
95#14519752—21no—
96#14519748—21no—
97#14519748—21no—
98C4×D244C2311yescharacteristic
99D4×Dic61—21no—
100D4×Dic61—21no—
101D4×Dic61D411yescharacteristic
102#14519739—21no—
103#14519739—21no—
104#14519739D411yescharacteristic
105C4×C22⋊D61—21no—
106#14519737—21no—
107C4⋊C4×D61D411yescharacteristic
108C22⋊C4×D61—21no—
109C42×D61C2311yescharacteristic
110#14519710—21no—
111#14519710—21no—
112C4⋊#92418C2311yescharacteristic
113C4⋊#92418C2311yescharacteristic
114C4⋊#92418C2311yescharacteristic
115#14519706—21no—
116#14519706—21no—
117#14519706—21no—
118#14519702—21no—
119#14519701—21no—
120#14519700—21no—
121#14519699—21no—
122#14519699—21no—
123#14519699—21no—
124#14519698—21no—
125#14519697—21no—
126C22⋊#92418—21no—
127#14519689—21no—
128#14519689—21no—
129C4×#92418C2311yescharacteristic
130C8×Dic61D411yescharacteristic
131C8×Dic61D411yescharacteristic
132C2×SD16×C61—21no—
133C2×D8×C61—21no—
134C22×C8×C61—21no—
135C4⋊Q8×C61C2311yescharacteristic
136#127×C61C2311yescharacteristic
137C4×D4×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141#103×C61—21no—
142#102×C61—21no—
143#102×C61—21no—
144#102×C61—21no—
145C22⋊C8×C61—21no—
146C4×C8×C61C2311yescharacteristic
147C23×D61—21no—
148C2×Q8×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—41no—
156C22×Dic61—21no—
157C22×Dic61—41no—
158#11758226—42no—
159#11758226—42no—
160#11758224—42no—
161#11758224—42no—
162D4×D61—22no—
163D4×D61D814yescomplemented
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—41no—
168C2×D244C2×D411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—42no—
173C2×C4×D61—42no—
174C2×C4×D61—41no—
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61#4111yescharacteristic
178C2×Dic122—21no—
179SD16×C61—42no—
180D8×C61—42no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—42no—
185C2×C8×C61C2×D411yescharacteristic
186C2×C8×C61C2×D411yescharacteristic
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C2×D411yescharacteristic
190C22⋊C4×C61—21no—
191C42×C61C2411yescharacteristic
192C22⋊Dic61—21no—
193C22⋊Dic61—41no—
194C22⋊Dic61—41no—
195#11758201—42no—
196#11758200—42no—
197#11758199—42no—
198#11758199—42no—
199#11758199—42no—
200#11758199—42no—
201#11758198—21no—
202#11758198—21no—
203#11758198—41no—
204#11758198—41no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61C2×D411yescharacteristic
208#11758196—21no—
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61#4111yescharacteristic
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—42no—
216C2×#92418C2×D411yescharacteristic
217C2×#92418C2×D411yescharacteristic
218D488—42no—
219#11758190—42no—
220#11758189—42no—
221#11758189—42no—
222C8×D61—22no—
223C8×D61—41no—
224C8×D61—42no—
225C8×D61—42no—
226C8×D61—42no—
227C23×C61—21no—
228C23×C61—41no—
229C22×D61—21no—
230C22×D61—24no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61—41no—
234C22×D61#12111yescharacteristic
235Q8×C61—41no—
236Q8×C61—41no—
237D4×C61—21no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—81no—
243D4×C61C2×D812yes—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C22⋊D61—24no—
252C22⋊D61—82no—
253C2×Dic61—21no—
254C2×Dic61—42no—
255C2×Dic61—41no—
256C2×Dic61—82no—
257C2×Dic61#12111yescharacteristic
258C2×Dic61#12111yescharacteristic
259C2×Dic61#12111yescharacteristic
260D244—21no—
261D244—41no—
262D244—41no—
263D244—41no—
264D244—41no—
265D244—81no—
266D244—82no—
267D244C2×D812yes—
268C4×D61—21no—
269C4×D61—21no—
270C4×D61—41no—
271C4×D61—42no—
272C4×D61—42no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—82no—
276C4×D61C2×D812yes—
277C4×D61#13512yes—
278Dic122—41no—
279Dic122—41no—
280C8×C61—21no—
281C8×C61—21no—
282C8×C61—41no—
283C8×C61—41no—
284C8×C61—41no—
285#92418—21no—
286#92418—41no—
287#92418—41no—
288#92418—41no—
289#92418AGL(1,ℤ/8)12yescomplemented
290#19255—611nomaximal, Sylow
291C22×C61—22no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—81no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61C2×#12111yescharacteristic
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—22no—
301C2×D61—48no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61#46612yes—
308C4×C61—21no—
309C4×C61—41no—
310C4×C61—81no—
311C4×C61C22×D811yescharacteristic
312C4×C61C2×#13511yescharacteristic
313C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C61#57511yescharacteristic
315Dic61—21no—
316Dic61—21no—
317Dic61—41no—
318Dic61—81no—
319Dic61#46612yes—
320#3169—611no—
321#3036—611no—
322#3036—611no—
323C2×C8×D4—611no—
324#1681—611no—
325#1681—611no—
326#1681—611no—
327#1681D6111yescharacteristic, complemented
328#1673—611no—
329#1673—611no—
330#1667—611no—
331#1667—611no—
332#1567—611no—
333#1547—611no—
334#1547—611no—
335C2×C61—42no—
336C2×C61—161no—
337C2×C61#303611yescharacteristic
338C2×C61C2×#46611yescharacteristic
339C2×C61#306711yescharacteristic
340D61—22no—
341D61—42no—
342D61—161no—
343C2×AGL(1,ℤ/8)—1221no—
344C2×AGL(1,ℤ/8)—1221no—
345C23×C8—1221no—
346#532—611no—
347#532—611no—
348C2×C4×D4—611no—
349#500—611no—
350#493—611no—
351#486—611no—
352#486C2×D6111yescharacteristic, complemented
353#466—1221no—
354#466—1221no—
355#463—1221no—
356#463—1221no—
357#463—1221no—
358#463—1221no—
359#461—611no—
360#461—611no—
361#461—611no—
362#461C2×D6111yescharacteristic
363#459—611no—
364#459—611no—
365#459—611no—
366#459C2×D6111yescharacteristic
367C4×D8—1221no—
368C4×D8—1221no—
369C8×D4—611no—
370C8×D4—611no—
371C8×D4—611no—
372C8×D4—1221no—
373C8×D4—1221no—
374C8×D4C2×D6111yescharacteristic
375#423—611no—
376#423—611no—
377C2×C4⋊C8—611no—
378#417—1221no—
379#417—1221no—
380C2×C22⋊C8—1221no—
381C2×C4×C8—611no—
382#335—611no—
383#335—611no—
384#335—611no—
385#335C2×D6111yescharacteristic, complemented
386#332—611no—
387#332—611no—
388#332—611no—
389#332C2×D6111yescharacteristic, complemented
390#331—611no—
391#331—611no—
392#331—611no—
393#331C2×D6111yescharacteristic, complemented
394C61#1925511yescharacteristic, complemented, Sylow
395C2×#41—1221no—
396C2×#41—1221no—
397C22×D4—611no—
398C23×C4—1221no—
399AGL(1,ℤ/8)—2444no—
400AGL(1,ℤ/8)—2444no—
401C2×SD16—21no—
402C2×SD16—1221no—
403C2×SD16—1221no—
404C2×SD16—1221no—
405C2×D8—21no—
406C2×D8—1221no—
407C2×D8—1221no—
408C2×D8—1221no—
409C2×D8—1221no—
410C2×D8—1221no—
411C2×M16—1221no—
412C2×M16—1221no—
413C22×C8—21no—
414C22×C8—611no—
415C22×C8—611no—
416C22×C8—1221no—
417C22×C8—1221no—
418C22×C8—1221no—
419C22×C8—1221no—
420C22×C8—2444no—
421C4⋊Q8—611no—
422C4⋊Q8C22×D6111yescharacteristic
423#127—611no—
424#127C22×D6111yescharacteristic
425#124—1221no—
426#124—1221no—
427#121—1221no—
428#121—1221no—
429#121—1221no—
430#121—1221no—
431C4×D4—611no—
432C4×D4—611no—
433C4×D4—611no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1221no—
437C4×D4—1221no—
438C4×D4—1221no—
439C4×D4—1221no—
440C4×D4C22×D6111yescharacteristic
441C2×C4⋊C4—611no—
442C2×C22⋊C4—1221no—
443C2×C42—611no—
444#107—1221no—
445#107—1221no—
446C4⋊C8—611no—
447C4⋊C8—611no—
448C4⋊C8—611no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8—1221no—
452C4⋊C8C22×D6111yescharacteristic
453C4⋊C8C22×D6111yescharacteristic
454C4⋊C8C22×D6111yescharacteristic
455#103—21no—
456#103—1221no—
457#103—1221no—
458#103—1221no—
459#102—21no—
460#102—21no—
461#102—21no—
462#102—1221no—
463#102—1221no—
464#102—1221no—
465#102—1221no—
466#102—1221no—
467C22⋊C8—21no—
468C22⋊C8—1221no—
469C22⋊C8—1221no—
470C22⋊C8—1221no—
471C4×C8—611no—
472C4×C8—611no—
473C4×C8—611no—
474C4×C8C22×D6111yescharacteristic
475C24—1221no—
476#41—2442no—
477#41—2442no—
478#41—2442no—
479#41—2442no—
480C2×Q8—21no—
481C2×Q8—1221no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—614no—
486C2×D4—611no—
487C2×D4—1222no—
488C2×D4—1221no—
489C2×D4—1221no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—2441no—
493C2×D4—2441no—
494C2×D4D4×D6111yescharacteristic
495C22×C4—21no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—2441no—
504C22×C4—2442no—
505C22×C4—2442no—
506C22×C4—2441no—
507SD16—42no—
508SD16—2442no—
509SD16—2442no—
510SD16—2442no—
511D8—42no—
512D8—2442no—
513D8—2442no—
514D8—2442no—
515D8—2442no—
516D8—2442no—
517M16—2442no—
518M16—2442no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—42no—
523C2×C8—611no—
524C2×C8—611no—
525C2×C8—1222no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—2441no—
530C2×C8—2442no—
531C2×C8—2442no—
532C2×C8—2442no—
533C2×C8—2442no—
534C2×C8D4×D6111yescharacteristic
535C2×C8D4×D6111yescharacteristic
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—611no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4D4×D6111yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—1221no—
545C22⋊C4—1221no—
546C22⋊C4—1221no—
547C22⋊C4—2441no—
548C22⋊C4—2441no—
549C22⋊C4—2441no—
550C22⋊C4—2441no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42C23×D6111yescharacteristic
555C23—21no—
556C23—41no—
557C23—611no—
558C23—1224no—
559C23—1221no—
560C23—2442no—
561C23—2442no—
562C23—2441no—
563Q8—41no—
564Q8—41no—
565Q8—2441no—
566Q8—2441no—
567D4—21no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—81no—
573D4—612no—
574D4—1224no—
575D4—1221no—
576D4—4881no—
577D4—4882no—
578D4—4882no—
579D4—2441no—
580D4—2441no—
581D4—2441no—
582D4—2441no—
583D4D8×D6112yes—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—611no—
589C2×C4—612no—
590C2×C4—612no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—4882no—
597C2×C4—4882no—
598C2×C4—2441no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4C2×D4×D6111yescharacteristic
607C2×C4#41×D6111yescharacteristic
608C8—21no—
609C8—21no—
610C8—41no—
611C8—41no—
612C8—41no—
613C8—612no—
614C8—1221no—
615C8—2441no—
616C8—2441no—
617C8—2441no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—612no—
625C22—1221no—
626C22—1221no—
627C22—1222no—
628C22—4881no—
629C22—4881no—
630C22—4881no—
631C22—2448no—
632C22—2441no—
633C22—2441no—
634C22#121×D6111yescharacteristic
635C4—21no—
636C4—41no—
637C4—81no—
638C4—612no—
639C4—1221no—
640C4—1221no—
641C4—4881no—
642C4—2441no—
643C4C2×D8×D6111yescharacteristic
644C4#135×D6111yescharacteristic
645C4AGL(1,ℤ/8)×D6111yescharacteristic
646C4#1684055911yescharacteristic
647C2—42no—
648C2—161no—
649C2—1222no—
650C2—9761no—
651C2—2442no—
652C2#2145528111yescharacteristic
653C2#466×D6111yescharacteristic
654C2#2145553411yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1681C2
socleC22×C61C2×#121
hypercenter#1681D61
hypocenterC61#19255
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1681

Complements

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

NH ≅ G/Ntype
1. #21456397C2semidirect
2. #21455284C2semidirect
3. #21455278C2semidirect
4. C8×D4×D61C2semidirect
5. #21445257C2semidirect
6. #21445256C2semidirect
7. #21445253C2semidirect
8. #21445207C2semidirect
9. #21445206C2semidirect
10. #21445173C2semidirect
11. #21445172C2semidirect
12. #21444576C2semidirect
13. #21444495C2semidirect
14. #21444493C2semidirect
15. C61×#1681C2semidirect
22. #16840165C22semidirect
23. #16840138C22semidirect
24. #16840109C22semidirect
51. #16839515C22semidirect
52. #16839514C22semidirect
53. #16839514C22semidirect
54. #16839509C22semidirect
55. #16839508C22semidirect
56. #16839507C22semidirect
57. #16839506C22semidirect
58. #16839505C22semidirect
59. #16839505C22semidirect
60. C61×#486C22semidirect
64. C61×#335C22semidirect
65. C61×#332C22semidirect
66. C61×#331C22semidirect
163. D4×D61D8semidirect
289. #92418AGL(1,ℤ/8)semidirect
327. #1681D61semidirect
352. #486C2×D61semidirect
385. #335C2×D61semidirect
389. #332C2×D61semidirect
393. #331C2×D61semidirect
394. C61#19255semidirect

Maximal subgroups

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

subgroupindex
#214563972
#214552842
#214552782
C8×D4×D612
#214452572
#214452562
#214452532
#214452072
#214452062
#214451732
#214451722
#214445762
#214444952
#214444932
C61×#16812
#1925561