Finite Group Databasebeta

← #29669420

Subgroups — #29669420

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458791C211yesmaximal, characteristic, complemented
2#21457626C211yesmaximal, characteristic, complemented
3#21457440C211yesmaximal, characteristic, complemented
4#21445483C211yesmaximal, characteristic, complemented
5#21445281C211yesmaximal, characteristic, complemented
6#21445265C211yesmaximal, characteristic, complemented
7#21445174C211yesmaximal, characteristic, complemented
8#21445172C211yesmaximal, characteristic, complemented
9#21445010C211yesmaximal, characteristic, complemented
10#21444908C211yesmaximal, characteristic, complemented
11#21444884C211yesmaximal, characteristic, complemented
12#21444872C211yesmaximal, characteristic, complemented
13#21444648C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3284C211yesmaximal, characteristic, complemented
16C2×#14519804—21no—
17#16840434C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840139C2211yescharacteristic
20#16840138—21no—
21#16840138C2211yescharacteristic
22#16840138C2211yescharacteristic, complemented
23#16840110C2211yescharacteristic
24#16840110C2211yescharacteristic, complemented
25#16840075—21no—
26#16840039C2211yescharacteristic
27#16840016—21no—
28#16839996—21no—
29#16839962C2211yescharacteristic
30#16839957—21no—
31#16839957C2211yescharacteristic
32#16839957C2211yescharacteristic
33#16839957C2211yescharacteristic, complemented
34#16839954—21no—
35#16839954C2211yescharacteristic
36#16839910—21no—
37#16839897—21no—
38#16839895—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758199—21no—
41C4×#11758199C2211yescharacteristic
42#16839841C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44C2×#14519697—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839508C2211yescharacteristic, complemented
48#16839506C2211yescharacteristic, complemented
49#16839505C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic, 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
67C2×#11758226—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70#14519804—44no—
71C2×#11758201—21no—
72C2×D488—21no—
73C2×D488—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199—21no—
78C2×#11758199—21no—
79C2×#11758199—21no—
80C2×#11758199—41no—
81C2×#11758199D411yescharacteristic
82C2×#11758189—21no—
83C22×#92418—21no—
84#14519774—21no—
85#14519774C2311yescharacteristic
86#14519774C2311yescharacteristic
87#14519752—21no—
88#14519752—21no—
89#14519752—41no—
90#14519751—21no—
91#14519747—41no—
92C4×D244—21no—
93C4×D244C2311yescharacteristic
94#14519710—21no—
95#14519710D411yescharacteristic
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519698—21no—
101#14519698D411yescharacteristic
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118#135×C61—44no—
119C2×Q16×C61—21no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×SD16×C61D411yescharacteristic
123C2×D8×C61—21no—
124C22×C8×C61—21no—
125C4⋊Q8×C61C2311yescharacteristic
126#127×C61—21no—
127#127×C61C2311yescharacteristic
128#123×C61—41no—
129C22⋊Q8×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—41no—
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61—21no—
135C4×D4×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—21no—
138#106×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61D411yescharacteristic
142#102×C61—21no—
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147#41×C61—42no—
148#41×C61—42no—
149#41×C61—81no—
150#41×C61—81no—
151C2×Q8×C61—21no—
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61C2×D411yescharacteristic
160C2×D4×C61C2×D411yescharacteristic
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—41no—
164C22×C4×C61—41no—
165C2×C22⋊D61—41no—
166#11758226—42no—
167#11758226—81no—
168D4×D61—42no—
169D4×D61—81no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—42no—
177C2×D244—41no—
178C2×D244—41no—
179C2×D244—41no—
180C2×D244—81no—
181C2×D244C2×D411yescharacteristic
182C2×C4×D61—21no—
183C2×C4×D61—41no—
184Q16×C61—42no—
185SD16×C61—42no—
186SD16×C61—81no—
187SD16×C61D814yescomplemented
188D8×C61—42no—
189C2×C8×C61—21no—
190C2×C8×C61—42no—
191C2×C8×C61C2×D411yescharacteristic
192C2×C8×C61C2×D411yescharacteristic
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—41no—
197C4⋊C4×C61C2×D411yescharacteristic
198C4⋊C4×C61C2×D411yescharacteristic
199C4⋊C4×C61C2×D411yescharacteristic
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C42×C61—21no—
205C42×C61C2411yescharacteristic
206#11758201—42no—
207#11758199—41no—
208#11758199—42no—
209#11758199—42no—
210#11758199—81no—
211#11758199—81no—
212#11758199—81no—
213#11758199—81no—
214#11758199—82no—
215#11758198—21no—
216#11758198—41no—
217#11758198—41no—
218C4⋊Dic61C2×D411yescharacteristic
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—81no—
224C2×#92418C2×D411yescharacteristic
225C2×#92418C2×D411yescharacteristic
226D488—42no—
227D488—81no—
228#11758189—42no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—41no—
232C22×D61—21no—
233C22×D61—41no—
234C22×D61—41no—
235C22×D61—82no—
236C22×D61—82no—
237C22×D61—161no—
238Q8×C61—21no—
239Q8×C61—41no—
240Q8×C61—41no—
241Q8×C61C2×D812yes—
242D4×C61—21no—
243D4×C61—21no—
244D4×C61—21no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—41no—
249D4×C61—82no—
250D4×C61—81no—
251D4×C61—82no—
252D4×C61—161no—
253D4×C61C2×D812yes—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—82no—
264C2×C4×C61—82no—
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C22⋊D61—82no—
269C2×Dic61—21no—
270D244—21no—
271D244—21no—
272D244—41no—
273D244—41no—
274D244—41no—
275D244—41no—
276D244—41no—
277D244—41no—
278D244—41no—
279D244—41no—
280D244—82no—
281D244—81no—
282D244—81no—
283D244—82no—
284D244—161no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—82no—
288C8×C61—21no—
289C8×C61—41no—
290C8×C61C2×D812yes—
291#92418—21no—
292#92418—21no—
293#92418—41no—
294#92418—41no—
295#92418—41no—
296#92418—41no—
297#19759—611nomaximal, Sylow
298C22×C61—22no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61D4211yescharacteristic
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—81no—
312C2×D61—81no—
313C2×D61—81no—
314C2×D61—81no—
315C2×D61—81no—
316C2×D61—81no—
317C2×D61—164no—
318C4×C61—22no—
319C4×C61—21no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61—81no—
324C4×C61C22×D811yescharacteristic
325C4×C61#57511yescharacteristic
326C4×C61#57611yescharacteristic
327C4×C61#57611yescharacteristic
328Dic61—41no—
329#3391—611no—
330#3294—611no—
331#3284D6111yescharacteristic, complemented
332#3274—611no—
333#1721—611no—
334#1685—611no—
335#1682—611no—
336#1667—611no—
337#1667—611no—
338#1641—611no—
339#1625—611no—
340#1621—611no—
341#1619—611no—
342#1581—611no—
343SD16⋊C8—611no—
344C2×C61—42no—
345C2×C61—81no—
346C2×C61—161no—
347C2×C61#326811yescharacteristic
348C2×C61D4×D811yescharacteristic
349C2×C61#328811yescharacteristic
350D61—81no—
351D61—161no—
352D61—161no—
353C2×AGL(1,ℤ/8)—1221no—
354C2×#135—21no—
355#550—611no—
356#550C2×D6111yescharacteristic, complemented
357#547C2×D6111yescharacteristic
358D42—611no—
359#493—611no—
360#493—611no—
361#493—611no—
362#493—1221no—
363#492C2×D6111yescharacteristic, complemented
364#486—611no—
365#486—611no—
366#480—1221no—
367#474—611no—
368#469—1221no—
369#466—1221no—
370#465—21no—
371#462C2×D6111yescharacteristic, complemented
372#460—611no—
373#459—611no—
374#459—611no—
375#459—611no—
376#459—611no—
377#459—1221no—
378#459—1221no—
379#459C2×D6111yescharacteristic
380#452—21no—
381#449—21no—
382#449—1221no—
383#447—1221no—
384#447—1221no—
385C8×Q8—611no—
386C4×SD16C2×D6111yescharacteristic
387C4×D8—611no—
388C4×D8—1221no—
389#436—611no—
390C8×D4—611no—
391C8×D4C2×D6111yescharacteristic, complemented
392C2×#102—1221no—
393#335—611no—
394#335—611no—
395#332—611no—
396#331—611no—
397#331—611no—
398#331—611no—
399Q8⋊C8—611no—
400D4⋊C8—611no—
401D4⋊C8—611no—
402D4⋊C8—611no—
403#322—611no—
404C61#1975911yescharacteristic, complemented, Sylow
405C2×#41—21no—
406C2×#41—21no—
407C2×#41—1221no—
408C22×D4—1221no—
409C22×D4—1221no—
410AGL(1,ℤ/8)—2444no—
411#135—44no—
412C2×Q16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16—1221no—
416C2×SD16C22⋊D6111yescharacteristic
417C2×D8—21no—
418C2×D8—611no—
419C2×D8—1221no—
420C2×D8—1221no—
421C2×D8—1221no—
422C2×D8—1221no—
423C2×D8—1221no—
424C2×D8—1221no—
425C2×D8—1221no—
426C2×D8—1221no—
427C2×D8—2441no—
428C2×M16—1221no—
429C22×C8—21no—
430C22×C8—1221no—
431C4⋊Q8C22×D6111yescharacteristic
432#127—21no—
433#127—611no—
434#127—611no—
435#127—1221no—
436#127C22×D6111yescharacteristic
437#123—41no—
438C22⋊Q8—21no—
439#121—21no—
440#121—21no—
441#121—41no—
442#121—1221no—
443#121—1221no—
444#121—1221no—
445#121—2441no—
446#120—2441no—
447C4×Q8C22×D6111yescharacteristic
448C4×D4—21no—
449C4×D4—611no—
450C4×D4—1221no—
451C4×D4C22×D6111yescharacteristic
452C4×D4C22×D6111yescharacteristic
453C2×C4⋊C4—21no—
454#107—611no—
455#107—1221no—
456#106C22⋊D6111yescharacteristic
457C4⋊C8—611no—
458C4⋊C8—611no—
459C4⋊C8—611no—
460C4⋊C8—1221no—
461C4⋊C8C22×D6111yescharacteristic
462#103—21no—
463#103C22⋊D6111yescharacteristic
464#102—21no—
465#102—611no—
466#102—611no—
467#102—1221no—
468#102—1221no—
469#102—1221no—
470#102—1221no—
471#102—1221no—
472#102—1221no—
473#102—1221no—
474#102—1221no—
475#102—2441no—
476#102C22⋊D6111yescharacteristic
477C22⋊C8—21no—
478C22⋊C8—1221no—
479C22⋊C8—1221no—
480C4×C8—611no—
481C4×C8—611no—
482C4×C8—1221no—
483C4×C8C22×D6111yescharacteristic
484C24—2441no—
485#41—42no—
486#41—42no—
487#41—81no—
488#41—81no—
489#41—4881no—
490#41—2442no—
491C2×Q8—21no—
492C2×Q8C2×C22⋊D6111yescharacteristic
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—611no—
500C2×D4—1221no—
501C2×D4—1221no—
502C2×D4—1221no—
503C2×D4—1221no—
504C2×D4—1221no—
505C2×D4—1221no—
506C2×D4—4881no—
507C2×D4—4881no—
508C2×D4—2441no—
509C2×D4—2441no—
510C2×D4—2441no—
511C2×D4—2442no—
512C2×D4—2441no—
513C2×D4—2442no—
514C2×D4D4×D6111yescharacteristic
515C2×D4C2×C22⋊D6111yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—1221no—
521C22×C4—2441no—
522Q16—42no—
523SD16—42no—
524SD16—81no—
525SD16—2442no—
526SD16#1175819914yescomplemented
527D8—42no—
528D8—4881no—
529D8—4881no—
530D8—4881no—
531D8—4881no—
532D8—4881no—
533D8—4882no—
534D8—2441no—
535D8—2442no—
536D8—2442no—
537D8—2442no—
538M16—2442no—
539C2×C8—21no—
540C2×C8—42no—
541C2×C8—611no—
542C2×C8—611no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—4881no—
548C2×C8C2×C22⋊D6111yescharacteristic
549C2×C8C2×C22⋊D6111yescharacteristic
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—41no—
554C4⋊C4—611no—
555C4⋊C4D4×D6111yescharacteristic
556C4⋊C4C2×C22⋊D6111yescharacteristic
557C4⋊C4C2×C22⋊D6111yescharacteristic
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—1221no—
563C22⋊C4—2441no—
564C22⋊C4—2441no—
565C42—21no—
566C42C23×D6111yescharacteristic
567C23—21no—
568C23—21no—
569C23—41no—
570C23—1221no—
571C23—9761no—
572C23—4882no—
573C23—4882no—
574C23—2441no—
575C23—2441no—
576Q8—21no—
577Q8—41no—
578Q8—41no—
579Q8C2×#1175819912yes—
580D4—21no—
581D4—21no—
582D4—21no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—82no—
588D4—81no—
589D4—82no—
590D4—161no—
591D4—1221no—
592D4—1221no—
593D4—9761no—
594D4—4881no—
595D4—4881no—
596D4—4882no—
597D4—4882no—
598D4—4882no—
599D4—2441no—
600D4—2441no—
601D4—2441no—
602D4—2441no—
603D4—2441no—
604D4—2441no—
605D4—2441no—
606D4—2441no—
607D4C2×#1175819912yes—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—82no—
618C2×C4—82no—
619C2×C4—1221no—
620C2×C4—4882no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4C2×D4×D6111yescharacteristic
624C2×C4C22×C22⋊D6111yescharacteristic
625C2×C4#1451982211yescharacteristic
626C8—21no—
627C8—41no—
628C8—1221no—
629C8—1221no—
630C8—2441no—
631C8—2441no—
632C8—2441no—
633C8—2441no—
634C8C2×#1175819912yes—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—9764no—
645C22—4881no—
646C22—4881no—
647C22—4881no—
648C22—4881no—
649C22—4881no—
650C22—4881no—
651C22—2441no—
652C22—2441no—
653C22—2441no—
654C22D4×C22⋊D6111yescharacteristic
655C4—22no—
656C4—21no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—81no—
661C4—2441no—
662C4C22×#1175819911yescharacteristic
663C4#1684055911yescharacteristic
664C4#1684056411yescharacteristic
665C4#1684056511yescharacteristic
666C2—42no—
667C2—81no—
668C2—161no—
669C2—9761no—
670C2—9761no—
671C2—4881no—
672C2#2145735911yescharacteristic
673C2D4×#1175819911yescharacteristic
674C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3284C2
socleC22×C61D42
hypercenter#3284D61
hypocenterC61#19759
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. #21458791C2semidirect
2. #21457626C2semidirect
3. #21457440C2semidirect
4. #21445483C2semidirect
5. #21445281C2semidirect
6. #21445265C2semidirect
7. #21445174C2semidirect
8. #21445172C2semidirect
9. #21445010C2semidirect
10. #21444908C2semidirect
11. #21444884C2semidirect
12. #21444872C2semidirect
13. #21444648C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3284C2semidirect
22. #16840138C22semidirect
24. #16840110C22semidirect
33. #16839957C22semidirect
39. Q8×#92418C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839508C22semidirect
48. #16839506C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839483C22semidirect
57. C61×#550C22semidirect
59. C61×#492C22semidirect
61. C61×#462C22semidirect
66. C8×D4×C61C22semidirect
187. SD16×C61D8semidirect
331. #3284D61semidirect
356. #550C2×D61semidirect
363. #492C2×D61semidirect
371. #462C2×D61semidirect
391. C8×D4C2×D61semidirect
404. C61#19759semidirect
526. SD16#11758199semidirect

Maximal subgroups

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

subgroupindex
#214587912
#214576262
#214574402
#214454832
#214452812
#214452652
#214451742
#214451722
#214450102
#214449082
#214448842
#214448722
#214446482
SD16⋊#924182
C61×#32842
#1975961