Finite Group Databasebeta

← #30550440

Subgroups — #30550440

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459731C211yesmaximal, characteristic, complemented
2#21459688C211yesmaximal, characteristic, complemented
3#21456558C211yesmaximal, characteristic, complemented
4#21456553C211yesmaximal, characteristic, complemented
5#21456538C211yesmaximal, characteristic, complemented
6#21456535C211yesmaximal, characteristic, complemented
7#21456498C214yesmaximal, complemented
8#21456497C214yesmaximal, complemented
9#21456398C211yesmaximal, characteristic, complemented
10#21456397C211yesmaximal, characteristic, complemented
11#21456381C211yesmaximal, characteristic, complemented
12#21456360C211yesmaximal, characteristic, complemented
13#21456266C211yesmaximal, characteristic, complemented
14#21456143C211yesmaximal, characteristic, complemented
15#486×D61C211yesmaximal, characteristic, complemented
16#21455492C214yesmaximal, complemented
17#21454646C214yesmaximal, complemented
18C4×#14519783C211yesmaximal, characteristic, complemented
19C61×#3167C211yesmaximal, characteristic, complemented
20C2×#14519804C2214yes—
21C2×#14519783C2212yes—
22#16840495—21no—
23#16840494—21no—
24#16840484—21no—
25#16840475—21no—
26#16840468—21no—
27#16840465—21no—
28#16840456—21no—
29#16840431—21no—
30#16840430—21no—
31#16840424—21no—
32#16840422—21no—
33#16840414—21no—
34#16840409—21no—
35#16840407—21no—
36#16840405—21no—
37#16840400—21no—
38#16840385C2212yescomplemented
39#16840384C2212yescomplemented
40#16840365C2212yes—
41#16840363C2212yes—
42#16840342C2212yes—
43#16840328C2212yes—
44#16840317C2211yescharacteristic
45#16840317C2211yescharacteristic, complemented
46#16840313C2211yescharacteristic
47#16840313C2211yescharacteristic
48#16840313C2211yescharacteristic, complemented
49#16840312C2211yescharacteristic
50#16840312C2211yescharacteristic, complemented
51#16840310C2211yescharacteristic
52C4⋊Q8×D61C2211yescharacteristic
53#127×D61C2211yescharacteristic
54#16840244C2212yes—
55#16840234C2212yes—
56C4×#11758222C2211yescharacteristic
57#16840169C2214yescomplemented
58#16840167C2211yescharacteristic, complemented
59#16840165C2211yescharacteristic, complemented
60#16840158C2211yescharacteristic, complemented
61#16840148C2214yes—
62#16840139C2211yescharacteristic
63#16840138C2211yescharacteristic
64#16840136C2211yescharacteristic
65#16840118C2214yescomplemented
66#16840112C2211yescharacteristic, complemented
67#16840110C2211yescharacteristic
68#16840110C2211yescharacteristic, complemented
69#16840109C2211yescharacteristic
70#16840109C2211yescharacteristic, complemented
71#16840108C2211yescharacteristic
72#16840107C2214yes—
73#16840016C2214yescomplemented
74#16840013C2214yescomplemented
75#16840010C2214yescomplemented
76#16840005C2214yescomplemented
77#16839998C2214yescomplemented
78#16839997C2214yescomplemented
79#16839994C2214yescomplemented
80#16839873C2214yescomplemented
81#16839872C2214yescomplemented
82#16839863C2214yescomplemented
83#16839860C2214yescomplemented
84#16839847C2214yescomplemented
85C4×D488C2214yescomplemented
86#16839842C2214yescomplemented
87#16839801C2214yes—
88#16839757C2214yes—
89#102×D61C2214yes—
90#16839717C2212yescomplemented
91#16839716C2212yes—
92#16839716C2212yescomplemented
93C4×#11758194C2211yescharacteristic, complemented
94C4×#11758189C2211yescharacteristic
95C4×#11758189C2211yescharacteristic, complemented
96C4×C8×D61C2211yescharacteristic
97C4×C8×D61C2211yescharacteristic, complemented
98C61×#533C2211yescharacteristic, complemented
99C61×#532C2211yescharacteristic
100C61×#498C2211yescharacteristic, complemented
101C61×#492C2211yescharacteristic
102C61×#487C2211yescharacteristic, complemented
103C61×#486C2211yescharacteristic
104C61×#465C2214yescomplemented
105C4×SD16×C61C2214yescomplemented
106C2×C4×C8×C61C2211yescharacteristic, complemented
107C2×#11758226—21no—
108C2×#11758226—21no—
109C2×#11758226C2312yes—
110C2×#11758222—21no—
111C2×#11758222—21no—
112C2×#11758222C2311yescharacteristic
113C2×#11758224—21no—
114C2×Q8×D61—21no—
115C2×D4×D61—21no—
116C2×D4×D61—21no—
117C2×D4×D61C2312yes—
118#14519804—216no—
119C2×#11758201C2314yes—
120C2×D488C2314yes—
121C2×#11758199C2314yes—
122#14519783—28no—
123C2×#11758194C2312yes—
124C2×#11758189C2312yes—
125C2×#11758189C2312yes—
126C2×C8×D61C2312yes—
127C2×C8×D61C2312yes—
128#14519777C2311yescharacteristic
129#14519777C2311yescharacteristic
130#14519776—21no—
131#14519776C2312yes—
132#14519775—21no—
133#14519774C2311yescharacteristic
134#14519774C2311yescharacteristic
135#14519773—22no—
136#14519773—21no—
137#14519773—21no—
138#14519773C2312yes—
139#14519772—22no—
140#14519771—22no—
141#14519768—21no—
142#14519768C2312yes—
143#14519766—21no—
144#14519766—21no—
145#14519766C2312yes—
146#14519765—21no—
147#14519765—21no—
148#14519765—22no—
149#14519764—21no—
150#14519763—22no—
151#14519763—22no—
152#14519762—22no—
153#14519761—22no—
154#14519760—22no—
155#14519759—22no—
156#14519759—22no—
157#14519759—22no—
158#14519757—21no—
159#14519757—21no—
160#14519757—22no—
161#14519755—22no—
162#14519755—22no—
163#14519753—21no—
164#14519753C2312yes—
165#14519752—22no—
166#14519752—21no—
167#14519752—21no—
168#14519752—21no—
169#14519752—21no—
170#14519752C2312yes—
171#14519752C2312yes—
172#14519751—21no—
173#14519751—21no—
174#14519751—22no—
175#14519751C2312yes—
176#14519751C2312yes—
177#14519750—22no—
178#14519750—22no—
179#14519750—22no—
180#14519749—22no—
181#14519748—21no—
182#14519748—22no—
183#14519748C2312yes—
184#14519747—22no—
185#14519745—22no—
186Q8×Dic61—21no—
187Q8×Dic61C2312yes—
188C4×Dic122D411yescharacteristic
189C4×Dic122D411yescharacteristic
190#14519742—21no—
191#14519742—21no—
192C4×D244—21no—
193C4×D244—21no—
194C4×D244—22no—
195C4×D244D411yescharacteristic
196C4×D244D411yescharacteristic
197C4×D244C2312yes—
198C4×D244C2312yes—
199D4×Dic61—21no—
200D4×Dic61C2312yes—
201#14519739—22no—
202#14519739—21no—
203#14519739—21no—
204#14519739—21no—
205#14519739—21no—
206#14519739C2312yes—
207#14519739C2312yes—
208C4×C22⋊D61—22no—
209C4×C22⋊D61D411yescharacteristic
210C4×C22⋊D61D411yescharacteristic
211C4×C22⋊D61D411yescharacteristic
212C4×C22⋊D61D411yescharacteristic
213#14519737—22no—
214#14519736C2311yescharacteristic
215#14519735—21no—
216#14519735C2312yes—
217#14519734—22no—
218#14519734C2311yescharacteristic
219#14519734C2311yescharacteristic
220C4⋊C4×D61—21no—
221C4⋊C4×D61—22no—
222C4⋊C4×D61C2312yes—
223C2×#11758198—22no—
224C22⋊C4×D61—22no—
225C42×D61C2311yescharacteristic
226C42×D61C2311yescharacteristic
227#14519711C2314yes—
228#14519710C2314yes—
229#14519708C2314yes—
230#14519701C2314yes—
231#14519699C2314yes—
232#14519699C2314yes—
233#14519698C2314yes—
234#14519697C2314yes—
235#14519697C2314yes—
236#14519688C2312yes—
237#14519687C2312yes—
238#14519687C2312yes—
239C4×#92418C2311yescharacteristic
240C4×#92418C2311yescharacteristic
241C8×Dic61C2312yes—
242C8×Dic61C2312yes—
243C2×#41×C61—21no—
244C2×SD16×C61C2314yes—
245C22×C8×C61C2312yes—
246C4⋊Q8×C61C2311yescharacteristic
247C4⋊Q8×C61C2311yescharacteristic
248C4⋊Q8×C61C2311yescharacteristic
249#127×C61C2311yescharacteristic
250#125×C61—21no—
251#124×C61—21no—
252C22⋊Q8×C61—21no—
253C22⋊Q8×C61C2312yes—
254#121×C61—21no—
255#121×C61C2312yes—
256C4×Q8×C61—21no—
257C4×Q8×C61C2312yes—
258C4×D4×C61—21no—
259C4×D4×C61C2312yes—
260#117×C61—21no—
261C2×C42×C61C2311yescharacteristic
262#106×C61C2314yes—
263#103×C61C2314yes—
264#102×C61C2314yes—
265C4×C8×C61C2311yescharacteristic
266C4×C8×C61C2311yescharacteristic
267C4×C8×C61C2312yes—
268C23×D61—22no—
269#41×C61—82no—
270C2×Q8×C61—21no—
271C2×Q8×C61—21no—
272C2×Q8×C61C2412yes—
273C2×D4×C61—22no—
274C2×D4×C61—21no—
275C2×D4×C61—21no—
276C2×D4×C61C2412yes—
277C22×C4×C61—22no—
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2411yescharacteristic
281C2×C22⋊D61—22no—
282C2×C22⋊D61—22no—
283C2×C22⋊D61—22no—
284C2×C22⋊D61—22no—
285C2×C22⋊D61—22no—
286C2×C22⋊D61—22no—
287C2×C22⋊D61C2×D411yescharacteristic
288C2×C22⋊D61C2×D411yescharacteristic
289C22×Dic61—22no—
290#11758226—28no—
291#11758226—82no—
292#11758226—82no—
293Q8×D61—82no—
294#11758224—82no—
295D4×D61—28no—
296D4×D61—82no—
297D4×D61—82no—
298#11758222—24no—
299#11758222—82no—
300#11758222—82no—
301C2×D244—22no—
302C2×D244—21no—
303C2×D244—21no—
304C2×D244—21no—
305C2×D244—21no—
306C2×D244—22no—
307C2×D244—22no—
308C2×D244C2×D411yescharacteristic
309C2×D244C2412yes—
310C2×D244C2412yes—
311C2×C4×D61—22no—
312C2×C4×D61—22no—
313C2×C4×D61—22no—
314C2×C4×D61—22no—
315C2×C4×D61—22no—
316C2×C4×D61—22no—
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2×D411yescharacteristic
321C2×C4×D61C2411yescharacteristic
322C2×C4×D61C2411yescharacteristic
323C2×Dic122—21no—
324C2×Dic122—21no—
325C2×Dic122—22no—
326C2×Dic122C2×D411yescharacteristic
327SD16×C61—28no—
328C2×C8×C61—24no—
329C2×C8×C61C2412yes—
330C2×C8×C61C2412yes—
331C4⋊C4×C61—21no—
332C4⋊C4×C61—21no—
333C4⋊C4×C61—21no—
334C4⋊C4×C61—21no—
335C4⋊C4×C61—22no—
336C4⋊C4×C61—22no—
337C4⋊C4×C61C2412yes—
338C4⋊C4×C61C2412yes—
339C22⋊C4×C61—22no—
340C22⋊C4×C61—22no—
341C22⋊C4×C61—22no—
342C42×C61—22no—
343C42×C61C2×D411yescharacteristic
344C42×C61C2×D411yescharacteristic
345C42×C61C2411yescharacteristic
346C42×C61C2411yescharacteristic
347C22⋊Dic61—22no—
348C22⋊Dic61—22no—
349C22⋊Dic61C2×D411yescharacteristic
350C22⋊Dic61C2×D411yescharacteristic
351#11758201—28no—
352#11758199—28no—
353#11758198—22no—
354#11758198—22no—
355#11758198—22no—
356#11758198—22no—
357#11758198—22no—
358#11758198—22no—
359#11758198—22no—
360#11758198—22no—
361#11758198—22no—
362#11758198—22no—
363#11758198—22no—
364#11758198—22no—
365#11758198C2×D411yescharacteristic
366#11758198C2×D411yescharacteristic
367#11758198C2×D411yescharacteristic
368#11758198C2×D411yescharacteristic
369C4⋊Dic61—21no—
370C4⋊Dic61—21no—
371C4⋊Dic61—22no—
372C4⋊Dic61—22no—
373C4⋊Dic61C2×D411yescharacteristic
374C4⋊Dic61C2×D411yescharacteristic
375C4⋊Dic61C2412yes—
376C4⋊Dic61C2412yes—
377#11758196—22no—
378#11758196—22no—
379#11758196—22no—
380#11758196—22no—
381#11758196C2×D411yescharacteristic
382#11758196C2×D411yescharacteristic
383#11758196C2×D411yescharacteristic
384#11758196C2×D411yescharacteristic
385C4×Dic61—22no—
386C4×Dic61—22no—
387C4×Dic61C2×D411yescharacteristic
388C4×Dic61C2×D411yescharacteristic
389C4×Dic61C2×D411yescharacteristic
390C4×Dic61C2×D411yescharacteristic
391C4×Dic61C2411yescharacteristic
392C4×Dic61C2411yescharacteristic
393#11758194—24no—
394C2×#92418C2412yes—
395C2×#92418C2412yes—
396D488—28no—
397#11758189—24no—
398#11758189#4118yescomplemented
399C8×D61—24no—
400C8×D61—24no—
401C23×C61—22no—
402C23×C61C22×D411yescharacteristic
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—44no—
406C22×D61—82no—
407C22×D61—82no—
408C22×D61C22×D411yescharacteristic
409C22×D61C22×D411yescharacteristic
410Q8×C61—24no—
411Q8×C61—42no—
412Q8×C61—42no—
413D4×C61—24no—
414D4×C61—42no—
415D4×C61—42no—
416D4×C61—82no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—82no—
424C2×C4×C61C22×D411yescharacteristic
425C2×C4×C61C22×D411yescharacteristic
426C2×C4×C61C22×D411yescharacteristic
427C2×C4×C61C22×D411yescharacteristic
428C2×C4×C61C22×D411yescharacteristic
429C2×C4×C61C2511yescharacteristic
430C22⋊D61—22no—
431C22⋊D61—22no—
432C22⋊D61—44no—
433C22⋊D61—82no—
434C22⋊D61—82no—
435C22⋊D61—82no—
436C22⋊D61—82no—
437C22⋊D61—82no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—82no—
441C2×Dic61C22×D411yescharacteristic
442C2×Dic61C22×D411yescharacteristic
443C2×Dic61C22×D411yescharacteristic
444C2×Dic61C22×D411yescharacteristic
445C2×Dic61C22×D411yescharacteristic
446C2×Dic61C22×D411yescharacteristic
447D244—22no—
448D244—24no—
449D244—24no—
450D244—44no—
451D244—42no—
452D244—42no—
453D244—42no—
454D244—42no—
455D244—82no—
456D244—82no—
457C4×D61—22no—
458C4×D61—22no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—22no—
462C4×D61—44no—
463C4×D61—82no—
464C4×D61—82no—
465C4×D61—82no—
466C4×D61—82no—
467C4×D61—82no—
468C4×D61C2×#4114yes—
469Dic122—22no—
470Dic122—42no—
471Dic122—42no—
472Dic122—82no—
473C8×C61—22no—
474C8×C61C2×#4114yes—
475#92418—22no—
476#92418C2×#4114yes—
477#60722—611nomaximal, Sylow
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—42no—
484C22×C61C23×D411yescharacteristic
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—42no—
493C2×D61—42no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—164no—
497C2×D61#53212yes—
498C4×C61—21no—
499C4×C61—21no—
500C4×C61—21no—
501C4×C61—42no—
502C4×C61—42no—
503C4×C61—42no—
504C4×C61#57612yes—
505C4×C61#57712yes—
506C4×C61C22×#4112yes—
507Dic61—21no—
508Dic61—21no—
509Dic61—21no—
510Dic61—21no—
511Dic61—21no—
512Dic61—42no—
513Dic61—42no—
514Dic61#53212yes—
515#3511—611no—
516#3508—611no—
517#3184—611no—
518#3184—611no—
519#3182—611no—
520#3182—611no—
521#3179—614no—
522#3179—614no—
523#3169—611no—
524#3169—611no—
525#3167—611no—
526#3167D6111yescharacteristic, complemented
527#3165—611no—
528#3151—611no—
529#3131—611no—
530C2×#486—611no—
531#3062—614no—
532#2946—614no—
533C4×#131—611no—
534C2×C61—41no—
535C2×C61—82no—
536C2×C61C2×#53211yescharacteristic
537C2×C61C2×#57611yescharacteristic
538C2×C61C2×#57711yescharacteristic
539D61—22no—
540D61—41no—
541D61—82no—
542D61—82no—
543C2×AGL(1,ℤ/8)—614no—
544C2×#131—612no—
545#559—1221no—
546#559—1221no—
547#556—1221no—
548#555—1221no—
549#554—1221no—
550#553—1221no—
551#553—1221no—
552#550—1221no—
553#550—1221no—
554#548—1221no—
555#548—1221no—
556#547—1221no—
557#546—1221no—
558#546—1221no—
559#546—1221no—
560#546—1221no—
561#542—612no—
562#542—612no—
563#540—612no—
564#540—612no—
565#537—612no—
566#535—612no—
567#533—611no—
568#533—611no—
569#533C2×D6111yescharacteristic, complemented
570#532—611no—
571#532—611no—
572#532—611no—
573#532—611no—
574#532—611no—
575#532—611no—
576#532C2×D6111yescharacteristic
577C2×C4⋊Q8—611no—
578C2×#127—611no—
579#520—612no—
580#518—612no—
581C4×#41—611no—
582#501—614no—
583#500—611no—
584#500—611no—
585#498—611no—
586#498C2×D6111yescharacteristic, complemented
587#496—614no—
588#493—611no—
589#493—611no—
590#492—611no—
591#492C2×D6111yescharacteristic
592#488—614no—
593#487—611no—
594#487C2×D6111yescharacteristic, complemented
595#486—611no—
596#486—611no—
597#486—611no—
598#486—614no—
599#486—611no—
600#486—611no—
601#486C2×D6111yescharacteristic
602#469—614no—
603#469—614no—
604#468—614no—
605#468—614no—
606#466—614no—
607#466—614no—
608#465—614no—
609#465C2×D6114yescomplemented
610#442—614no—
611#442—614no—
612#440—614no—
613#440—614no—
614C4×SD16—614no—
615C4×SD16C2×D6114yescomplemented
616C4×D8—614no—
617C4×D8—614no—
618#428—614no—
619#416—614no—
620C2×#102—614no—
621#405—612no—
622#405—612no—
623#405—612no—
624C4×M16—611no—
625C4×M16—611no—
626C4×M16—611no—
627C2×C4×C8—611no—
628C2×C4×C8—611no—
629C2×C4×C8C2×D6111yescharacteristic, complemented
630C61#6072211yescharacteristic, complemented, Sylow
631C2×#41—21no—
632C2×#41—611no—
633C2×#41—612no—
634C2×#41—1221no—
635C2×#41—1221no—
636C2×#41—1221no—
637C2×#41—1221no—
638C2×#41—1221no—
639C22×Q8—1221no—
640C22×D4—612no—
641C22×D4—1221no—
642C22×D4—1221no—
643AGL(1,ℤ/8)—12216no—
644C2×SD16—614no—
645C2×SD16C22×D6114yes—
646C2×D8—614no—
647C2×D8—614no—
648#131—1228no—
649C2×M16—612no—
650C2×M16—612no—
651C2×M16—612no—
652C22×C8—612no—
653C22×C8—612no—
654C22×C8C22×D6112yes—
655C4⋊Q8—612no—
656C4⋊Q8—611no—
657C4⋊Q8—611no—
658C4⋊Q8—1221no—
659C4⋊Q8—1221no—
660C4⋊Q8C22×D6111yescharacteristic
661C4⋊Q8C22×D6111yescharacteristic
662C4⋊Q8C22×D6111yescharacteristic
663#127—612no—
664#127—611no—
665#127—611no—
666#127—1221no—
667#127—1221no—
668#127—1222no—
669#127C22×D6111yescharacteristic
670#126—1222no—
671#126—1222no—
672#125—21no—
673#125—612no—
674#125—1221no—
675#124—21no—
676#124—612no—
677#124—1222no—
678#124—1221no—
679#124—1221no—
680#124—1221no—
681#124—1222no—
682#124—1222no—
683#124—1221no—
684#124—1221no—
685#123—1222no—
686#123—1222no—
687#123—1222no—
688#123—1222no—
689#123—1222no—
690#123—1222no—
691C22⋊Q8—21no—
692C22⋊Q8—612no—
693C22⋊Q8—1222no—
694C22⋊Q8—1222no—
695C22⋊Q8—1221no—
696C22⋊Q8—1221no—
697C22⋊Q8—1222no—
698C22⋊Q8—1221no—
699C22⋊Q8C22×D6112yes—
700#121—21no—
701#121—612no—
702#121—612no—
703#121—612no—
704#121—612no—
705#121—612no—
706#121—1222no—
707#121—1222no—
708#121—1222no—
709#121—1222no—
710#121—1222no—
711#121—1222no—
712#121—1221no—
713#121—1221no—
714#121—1221no—
715#121—1221no—
716#121—1222no—
717#121—1221no—
718#121—1221no—
719#121—1221no—
720#121C22×D6112yes—
721#120—1222no—
722#120—1222no—
723C4×Q8—21no—
724C4×Q8—611no—
725C4×Q8—611no—
726C4×Q8—612no—
727C4×Q8—1221no—
728C4×Q8—1221no—
729C4×Q8—1221no—
730C4×Q8C22×D6112yes—
731C4×D4—21no—
732C4×D4—611no—
733C4×D4—611no—
734C4×D4—611no—
735C4×D4—611no—
736C4×D4—612no—
737C4×D4—612no—
738C4×D4—612no—
739C4×D4—611no—
740C4×D4—611no—
741C4×D4—612no—
742C4×D4—612no—
743C4×D4—1222no—
744C4×D4—1221no—
745C4×D4—1221no—
746C4×D4—1221no—
747C4×D4—1221no—
748C4×D4—1221no—
749C4×D4—1222no—
750C4×D4—1222no—
751C4×D4—1222no—
752C4×D4—1221no—
753C4×D4—1221no—
754C4×D4C22×D6112yes—
755#117—21no—
756#117—611no—
757#117—611no—
758#117—611no—
759#117—612no—
760#117—1222no—
761#117—1221no—
762C2×C4⋊C4—612no—
763C2×C4⋊C4—1222no—
764C2×C4⋊C4—1221no—
765C2×C22⋊C4—1222no—
766C2×C22⋊C4—1222no—
767C2×C42—611no—
768C2×C42—611no—
769C2×C42C22×D6111yescharacteristic
770#107—614no—
771#107—614no—
772#106—614no—
773#106C22×D6114yes—
774#103—614no—
775#103C22×D6114yes—
776#102—614no—
777#102—614no—
778#102—614no—
779#102—614no—
780#102—614no—
781#102C22×D6114yes—
782#97—612no—
783#97—612no—
784#97—612no—
785C4×C8—612no—
786C4×C8—612no—
787C4×C8—611no—
788C4×C8—611no—
789C4×C8C22×D6111yescharacteristic
790C4×C8C22×D6111yescharacteristic
791C4×C8C22×D6112yes—
792C24—1222no—
793#41—82no—
794#41—1224no—
795#41—1228no—
796#41—4882no—
797#41—4882no—
798#41—4882no—
799#41—4882no—
800#41—4882no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—611no—
804C2×Q8—1222no—
805C2×Q8—1221no—
806C2×Q8—1221no—
807C2×Q8—4882no—
808C2×Q8C23×D6112yes—
809C2×D4—22no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—611no—
813C2×D4—611no—
814C2×D4—611no—
815C2×D4—612no—
816C2×D4—612no—
817C2×D4—1222no—
818C2×D4—1222no—
819C2×D4—1222no—
820C2×D4—1228no—
821C2×D4—1222no—
822C2×D4—1222no—
823C2×D4—1222no—
824C2×D4—1222no—
825C2×D4—1222no—
826C2×D4—1222no—
827C2×D4—1221no—
828C2×D4—1221no—
829C2×D4—1221no—
830C2×D4—1221no—
831C2×D4—4882no—
832C2×D4—4882no—
833C2×D4C23×D6112yes—
834C22×C4—22no—
835C22×C4—611no—
836C22×C4—611no—
837C22×C4—611no—
838C22×C4—611no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—1222no—
842C22×C4—1222no—
843C22×C4—1222no—
844C22×C4—1222no—
845C22×C4—1222no—
846C22×C4—1222no—
847C22×C4—1222no—
848C22×C4D4×D6111yescharacteristic
849C22×C4D4×D6111yescharacteristic
850C22×C4C23×D6111yescharacteristic
851SD16—28no—
852SD16—1228no—
853D8—1228no—
854D8—1228no—
855M16—618no—
856M16—1224no—
857M16—1224no—
858C2×C8—24no—
859C2×C8—612no—
860C2×C8—612no—
861C2×C8—1224no—
862C2×C8—1224no—
863C2×C8C23×D6112yes—
864C2×C8C23×D6112yes—
865C4⋊C4—21no—
866C4⋊C4—22no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—22no—
871C4⋊C4—611no—
872C4⋊C4—611no—
873C4⋊C4—611no—
874C4⋊C4—611no—
875C4⋊C4—611no—
876C4⋊C4—611no—
877C4⋊C4—612no—
878C4⋊C4—612no—
879C4⋊C4—1222no—
880C4⋊C4—1222no—
881C4⋊C4—1222no—
882C4⋊C4—1222no—
883C4⋊C4—1222no—
884C4⋊C4—1222no—
885C4⋊C4—1221no—
886C4⋊C4—1221no—
887C4⋊C4C23×D6112yes—
888C4⋊C4C23×D6112yes—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—611no—
893C22⋊C4—611no—
894C22⋊C4—611no—
895C22⋊C4—611no—
896C22⋊C4—611no—
897C22⋊C4—611no—
898C22⋊C4—1222no—
899C22⋊C4—1222no—
900C22⋊C4—1222no—
901C22⋊C4—1222no—
902C22⋊C4—1222no—
903C22⋊C4—1222no—
904C22⋊C4—1222no—
905C22⋊C4—1222no—
906C22⋊C4—1222no—
907C22⋊C4—1222no—
908C22⋊C4—1222no—
909C22⋊C4—1222no—
910C22⋊C4—1222no—
911C22⋊C4—1222no—
912C42—22no—
913C42—611no—
914C42—611no—
915C42—611no—
916C42—611no—
917C42—611no—
918C42—611no—
919C42—1222no—
920C42—1222no—
921C42D4×D6111yescharacteristic
922C42D4×D6111yescharacteristic
923C42C23×D6111yescharacteristic
924C42C23×D6111yescharacteristic
925C23—22no—
926C23—611no—
927C23—611no—
928C23—1222no—
929C23—1222no—
930C23—4882no—
931C23—4882no—
932C23—2444no—
933C23C2×D4×D6111yescharacteristic
934Q8—24no—
935Q8—42no—
936Q8—42no—
937Q8—1222no—
938Q8—4882no—
939Q8—2442no—
940Q8—2442no—
941D4—24no—
942D4—42no—
943D4—42no—
944D4—82no—
945D4—1222no—
946D4—1222no—
947D4—1222no—
948D4—1224no—
949D4—1224no—
950D4—4882no—
951D4—4882no—
952D4—4882no—
953D4—4882no—
954D4—4882no—
955D4—4882no—
956D4—4882no—
957D4—2444no—
958D4—2444no—
959D4—2442no—
960D4—2442no—
961D4—2442no—
962D4—2442no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—82no—
970C2×C4—611no—
971C2×C4—614no—
972C2×C4—611no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—611no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—4882no—
985C2×C4—4882no—
986C2×C4—4882no—
987C2×C4—4882no—
988C2×C4—4882no—
989C2×C4—4882no—
990C2×C4—2444no—
991C2×C4C2×D4×D6111yescharacteristic
992C2×C4C2×D4×D6111yescharacteristic
993C2×C4C2×D4×D6111yescharacteristic
994C2×C4C2×D4×D6111yescharacteristic
995C2×C4C2×D4×D6111yescharacteristic
996C2×C4C24×D6111yescharacteristic
997C8—22no—
998C8—614no—
999C8—1222no—
1000C8#41×D6114yes—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22—612no—
1008C22—1221no—
1009C22—1221no—
1010C22—1221no—
1011C22—1221no—
1012C22—1221no—
1013C22—9764no—
1014C22—2442no—
1015C22—2442no—
1016C22—2442no—
1017C22—2442no—
1018C22—2442no—
1019C22—2442no—
1020C22C22×D4×D6111yescharacteristic
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—612no—
1028C4—1221no—
1029C4—1221no—
1030C4—1221no—
1031C4—1221no—
1032C4—1221no—
1033C4—2442no—
1034C4—2442no—
1035C4#1684056412yes—
1036C4#1684056812yes—
1037C4C2×#41×D6112yes—
1038C2—41no—
1039C2—82no—
1040C2—1222no—
1041C2—4882no—
1042C2—4882no—
1043C2—2441no—
1044C2#532×D6111yescharacteristic
1045C2C2×#1684056411yescharacteristic
1046C2C2×#1684056811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3167C2
socleC22×C61C23×D4
hypercenter#3167D61
hypocenterC61#60722
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #21459731C2semidirect
2. #21459688C2semidirect
3. #21456558C2semidirect
4. #21456553C2semidirect
5. #21456538C2semidirect
6. #21456535C2semidirect
7. #21456498C2semidirect
8. #21456497C2semidirect
9. #21456398C2semidirect
10. #21456397C2semidirect
11. #21456381C2semidirect
12. #21456360C2semidirect
13. #21456266C2semidirect
14. #21456143C2semidirect
15. #486×D61C2semidirect
16. #21455492C2semidirect
17. #21454646C2semidirect
18. C4×#14519783C2semidirect
19. C61×#3167C2semidirect
38. #16840385C22semidirect
39. #16840384C22semidirect
45. #16840317C22semidirect
48. #16840313C22semidirect
50. #16840312C22semidirect
57. #16840169C22semidirect
58. #16840167C22semidirect
59. #16840165C22semidirect
60. #16840158C22semidirect
65. #16840118C22semidirect
66. #16840112C22semidirect
68. #16840110C22semidirect
70. #16840109C22semidirect
73. #16840016C22semidirect
74. #16840013C22semidirect
75. #16840010C22semidirect
76. #16840005C22semidirect
77. #16839998C22semidirect
78. #16839997C22semidirect
79. #16839994C22semidirect
80. #16839873C22semidirect
81. #16839872C22semidirect
82. #16839863C22semidirect
83. #16839860C22semidirect
84. #16839847C22semidirect
85. C4×D488C22semidirect
86. #16839842C22semidirect
90. #16839717C22semidirect
92. #16839716C22semidirect
93. C4×#11758194C22semidirect
95. C4×#11758189C22semidirect
97. C4×C8×D61C22semidirect
98. C61×#533C22semidirect
100. C61×#498C22semidirect
102. C61×#487C22semidirect
104. C61×#465C22semidirect
105. C4×SD16×C61C22semidirect
106. C2×C4×C8×C61C22semidirect
398. #11758189#41semidirect
526. #3167D61semidirect
569. #533C2×D61semidirect
586. #498C2×D61semidirect
594. #487C2×D61semidirect
609. #465C2×D61semidirect
615. C4×SD16C2×D61semidirect
629. C2×C4×C8C2×D61semidirect
630. C61#60722semidirect

Maximal subgroups

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

subgroupindex
#214597312
#214596882
#214565582
#214565532
#214565382
#214565352
#214564982
#214564972
#214563982
#214563972
#214563812
#214563602
#214562662
#214561432
#486×D612
#214554922
#214546462
C4×#145197832
C61×#31672
#6072261