Finite Group Databasebeta

← #30550449

Subgroups — #30550449

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#21459720C211yesmaximal, characteristic, complemented
2#21459688C211yesmaximal, characteristic, complemented
3#21456555C211yesmaximal, characteristic, complemented
4#21456553C211yesmaximal, characteristic, complemented
5#21456539C211yesmaximal, characteristic, complemented
6#21456533C211yesmaximal, characteristic, complemented
7#21456506C214yesmaximal, complemented
8#21456505C214yesmaximal, complemented
9#21456397C211yesmaximal, characteristic, complemented
10#21456378C211yesmaximal, characteristic, complemented
11#21456377C211yesmaximal, characteristic, complemented
12#21456362C211yesmaximal, characteristic, complemented
13#21456270C211yesmaximal, characteristic, complemented
14#21456138C211yesmaximal, characteristic, complemented
15#486×D61C211yesmaximal, characteristic, complemented
16#21455498C214yesmaximal, complemented
17#21454644C214yesmaximal, complemented
18C4×#14519783C211yesmaximal, characteristic, complemented
19C61×#3169C211yesmaximal, characteristic, complemented
20C2×#14519801C2214yes—
21C2×#14519783C2212yes—
22#16840495—21no—
23#16840494—21no—
24#16840481—21no—
25#16840476—21no—
26#16840471—21no—
27#16840462—21no—
28#16840459—21no—
29#16840431—21no—
30#16840430—21no—
31#16840420—21no—
32#16840419—21no—
33#16840411—21no—
34#16840409—21no—
35#16840407—21no—
36#16840405—21no—
37#16840400—21no—
38#16840379C2212yescomplemented
39#16840377C2212yescomplemented
40#16840365C2212yes—
41#16840363C2212yes—
42#16840341C2212yes—
43#16840328C2212yes—
44#16840319C2211yescharacteristic, complemented
45#16840317C2211yescharacteristic
46#16840317C2211yescharacteristic, complemented
47#16840313C2211yescharacteristic
48#16840312C2211yescharacteristic
49#16840310C2211yescharacteristic
50#16840310C2211yescharacteristic
51#16840310C2211yescharacteristic, complemented
52C4⋊Q8×D61C2211yescharacteristic
53#127×D61C2211yescharacteristic
54#16840241C2212yes—
55#16840234C2212yes—
56C4×#11758222C2211yescharacteristic
57#16840170C2214yescomplemented
58#16840165C2211yescharacteristic, complemented
59#16840160C2211yescharacteristic, complemented
60#16840158C2211yescharacteristic, complemented
61#16840150C2214yes—
62#16840138C2211yescharacteristic
63#16840135C2211yescharacteristic
64#16840134C2211yescharacteristic
65#16840115C2214yescomplemented
66#16840114C2211yescharacteristic, complemented
67#16840113C2211yescharacteristic, complemented
68#16840110C2211yescharacteristic
69#16840109C2211yescharacteristic
70#16840108C2211yescharacteristic
71#16840108C2211yescharacteristic, complemented
72#16840107C2214yes—
73#16840013C2214yescomplemented
74#16840012C2214yescomplemented
75#16840009C2214yescomplemented
76#16840006C2214yescomplemented
77#16839997C2214yescomplemented
78#16839991C2214yescomplemented
79#16839990C2214yescomplemented
80#16839874C2214yescomplemented
81#16839872C2214yescomplemented
82#16839862C2214yescomplemented
83#16839861C2214yescomplemented
84#16839853C2214yescomplemented
85C4×#11758190C2214yescomplemented
86#16839842C2214yescomplemented
87#16839803C2214yes—
88#16839755C2214yes—
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×#532C2211yescharacteristic
99C61×#532C2211yescharacteristic, complemented
100C61×#500C2211yescharacteristic, complemented
101C61×#493C2211yescharacteristic
102C61×#486C2211yescharacteristic
103C61×#486C2211yescharacteristic, complemented
104C61×#466C2214yescomplemented
105C4×D8×C61C2214yescomplemented
106C2×C4×C8×C61C2211yescharacteristic, complemented
107C2×#11758226—21no—
108C2×#11758222—21no—
109C2×#11758222C2311yescharacteristic
110C2×#11758224—21no—
111C2×#11758224—21no—
112C2×#11758224C2312yes—
113C2×Q8×D61—21no—
114C2×D4×D61—21no—
115C2×D4×D61—21no—
116C2×D4×D61C2312yes—
117#14519801—216no—
118C2×#11758190C2314yes—
119C2×#11758200C2314yes—
120C2×#11758199C2314yes—
121#14519783—28no—
122C2×#11758194C2312yes—
123C2×#11758189C2312yes—
124C2×#11758189C2312yes—
125C2×C8×D61C2312yes—
126C2×C8×D61C2312yes—
127#14519777C2311yescharacteristic
128#14519777C2311yescharacteristic
129#14519777C2311yescharacteristic
130#14519776—21no—
131#14519776C2312yes—
132#14519775—21no—
133#14519774C2311yescharacteristic
134#14519773—22no—
135#14519773—21no—
136#14519773—21no—
137#14519773C2312yes—
138#14519770—22no—
139#14519770—22no—
140#14519769—21no—
141#14519768—21no—
142#14519768C2312yes—
143#14519766—21no—
144#14519765—21no—
145#14519764—22no—
146#14519764—21no—
147#14519764—21no—
148#14519764C2312yes—
149#14519763—22no—
150#14519763—22no—
151#14519761—22no—
152#14519760—22no—
153#14519760—22no—
154#14519759—22no—
155#14519759—22no—
156#14519758—22no—
157#14519757—21no—
158#14519757C2312yes—
159#14519756—21no—
160#14519756—22no—
161#14519756C2312yes—
162#14519754—22no—
163#14519754—22no—
164#14519753—21no—
165#14519753—21no—
166#14519752—21no—
167#14519752C2312yes—
168#14519751—21no—
169#14519751—22no—
170#14519751C2312yes—
171#14519750—22no—
172#14519750—22no—
173#14519749—22no—
174#14519749—22no—
175#14519748—22no—
176#14519748—21no—
177#14519748—21no—
178#14519748—21no—
179#14519748—21no—
180#14519748—22no—
181#14519748C2312yes—
182#14519748C2312yes—
183#14519747—22no—
184#14519745—22no—
185Q8×Dic61—21no—
186Q8×Dic61—21no—
187C4×Dic122—21no—
188C4×Dic122D411yescharacteristic
189C4×Dic122D411yescharacteristic
190C4×Dic122C2312yes—
191#14519742—21no—
192#14519742C2312yes—
193C4×D244—21no—
194C4×D244D411yescharacteristic
195C4×D244D411yescharacteristic
196C4×D244C2312yes—
197D4×Dic61—21no—
198D4×Dic61—21no—
199D4×Dic61—21no—
200D4×Dic61—21no—
201D4×Dic61C2312yes—
202D4×Dic61C2312yes—
203#14519739—21no—
204#14519739C2312yes—
205C4×C22⋊D61—22no—
206C4×C22⋊D61—22no—
207C4×C22⋊D61D411yescharacteristic
208C4×C22⋊D61D411yescharacteristic
209C4×C22⋊D61D411yescharacteristic
210C4×C22⋊D61D411yescharacteristic
211#14519737—22no—
212#14519737—22no—
213#14519736—21no—
214#14519736C2311yescharacteristic
215#14519735—21no—
216#14519735C2312yes—
217#14519734C2311yescharacteristic
218#14519734C2311yescharacteristic
219#14519733—22no—
220C2×#11758196—22no—
221C4⋊C4×D61—21no—
222C4⋊C4×D61C2312yes—
223C2×#11758198—22no—
224C22⋊C4×D61—22no—
225C42×D61C2311yescharacteristic
226C42×D61C2311yescharacteristic
227#14519710C2314yes—
228#14519709C2314yes—
229#14519708C2314yes—
230#14519702C2314yes—
231#14519700C2314yes—
232#14519699C2314yes—
233#14519698C2314yes—
234#14519698C2314yes—
235#14519697C2314yes—
236#14519688C2312yes—
237#14519687C2312yes—
238#14519687C2312yes—
239C4×#92418C2311yescharacteristic
240C4×#92418C2311yescharacteristic
241C8×Dic61C2312yes—
242C8×Dic61C2312yes—
243C2×#41×C61—21no—
244C2×#41×C61—21no—
245C2×D8×C61C2314yes—
246C22×C8×C61C2312yes—
247C4⋊Q8×C61C2311yescharacteristic
248C4⋊Q8×C61C2311yescharacteristic
249#127×C61C2311yescharacteristic
250#127×C61C2311yescharacteristic
251#124×C61—21no—
252#124×C61—21no—
253#121×C61—21no—
254#121×C61—21no—
255#121×C61C2312yes—
256#121×C61C2312yes—
257C4×D4×C61—21no—
258C4×D4×C61—21no—
259C4×D4×C61C2312yes—
260C4×D4×C61C2312yes—
261C2×C42×C61C2311yescharacteristic
262#107×C61C2314yes—
263#102×C61C2314yes—
264#102×C61C2314yes—
265C4×C8×C61C2311yescharacteristic
266C4×C8×C61C2311yescharacteristic
267C4×C8×C61C2312yes—
268C23×D61—22no—
269#41×C61—82no—
270#41×C61—82no—
271C2×Q8×C61—21no—
272C2×Q8×C61—21no—
273C2×D4×C61—22no—
274C2×D4×C61—22no—
275C2×D4×C61—21no—
276C2×D4×C61—21no—
277C2×D4×C61—21no—
278C2×D4×C61—21no—
279C2×D4×C61C2412yes—
280C2×D4×C61C2412yes—
281C22×C4×C61—22no—
282C22×C4×C61—22no—
283C22×C4×C61C2×D411yescharacteristic
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2411yescharacteristic
286C2×C22⋊D61—22no—
287C2×C22⋊D61—22no—
288C2×C22⋊D61—22no—
289C2×C22⋊D61—22no—
290C2×C22⋊D61—22no—
291C2×C22⋊D61—22no—
292C2×C22⋊D61—22no—
293C2×C22⋊D61C2×D411yescharacteristic
294C2×C22⋊D61C2×D411yescharacteristic
295C22×Dic61—22no—
296C22×Dic61—22no—
297C22×Dic61—22no—
298#11758226—82no—
299Q8×D61—82no—
300#11758224—28no—
301#11758224—82no—
302#11758224—82no—
303D4×D61—28no—
304D4×D61—82no—
305D4×D61—82no—
306#11758222—24no—
307#11758222—82no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244—22no—
311C2×D244C2×D411yescharacteristic
312C2×D244C2412yes—
313C2×C4×D61—22no—
314C2×C4×D61—22no—
315C2×C4×D61—22no—
316C2×C4×D61C2×D411yescharacteristic
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2411yescharacteristic
321C2×C4×D61C2411yescharacteristic
322C2×Dic122—21no—
323C2×Dic122—21no—
324C2×Dic122—22no—
325C2×Dic122C2×D411yescharacteristic
326C2×Dic122C2412yes—
327D8×C61—28no—
328C2×C8×C61—24no—
329C2×C8×C61C2412yes—
330C2×C8×C61C2412yes—
331C4⋊C4×C61—21no—
332C4⋊C4×C61—21no—
333C4⋊C4×C61C2412yes—
334C4⋊C4×C61C2412yes—
335C22⋊C4×C61—22no—
336C22⋊C4×C61—22no—
337C22⋊C4×C61—22no—
338C22⋊C4×C61—22no—
339C42×C61C2×D411yescharacteristic
340C42×C61C2×D411yescharacteristic
341C42×C61C2411yescharacteristic
342C42×C61C2411yescharacteristic
343C22⋊Dic61—22no—
344C22⋊Dic61—22no—
345C22⋊Dic61—22no—
346C22⋊Dic61—22no—
347C22⋊Dic61—22no—
348C22⋊Dic61—22no—
349C22⋊Dic61—22no—
350C22⋊Dic61C2×D411yescharacteristic
351C22⋊Dic61C2×D411yescharacteristic
352#11758200—28no—
353#11758199—28no—
354#11758198—22no—
355#11758198—22no—
356#11758198—22no—
357#11758198—22no—
358#11758198—22no—
359#11758198—22no—
360#11758198C2×D411yescharacteristic
361#11758198C2×D411yescharacteristic
362#11758198C2×D411yescharacteristic
363#11758198C2×D411yescharacteristic
364C4⋊Dic61—21no—
365C4⋊Dic61—21no—
366C4⋊Dic61—21no—
367C4⋊Dic61—21no—
368C4⋊Dic61—22no—
369C4⋊Dic61—22no—
370C4⋊Dic61C2×D411yescharacteristic
371C4⋊Dic61C2×D411yescharacteristic
372C4⋊Dic61C2412yes—
373C4⋊Dic61C2412yes—
374#11758196—22no—
375#11758196—22no—
376#11758196—22no—
377#11758196—22no—
378#11758196—22no—
379#11758196—22no—
380#11758196C2×D411yescharacteristic
381#11758196C2×D411yescharacteristic
382#11758196C2×D411yescharacteristic
383#11758196C2×D411yescharacteristic
384C4×Dic61—22no—
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—
396#11758190—28no—
397#11758189—24no—
398#11758189#4118yescomplemented
399C8×D61—24no—
400C8×D61—24no—
401C23×C61—22no—
402C23×C61—22no—
403C23×C61C22×D411yescharacteristic
404C22×D61—22no—
405C22×D61—44no—
406C22×D61—82no—
407C22×D61—82no—
408C22×D61C22×D411yescharacteristic
409C22×D61C22×D411yescharacteristic
410Q8×C61—42no—
411Q8×C61—42no—
412D4×C61—24no—
413D4×C61—24no—
414D4×C61—42no—
415D4×C61—42no—
416D4×C61—42no—
417D4×C61—42no—
418D4×C61—82no—
419D4×C61—82no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—82no—
426C2×C4×C61—82no—
427C2×C4×C61C22×D411yescharacteristic
428C2×C4×C61C22×D411yescharacteristic
429C2×C4×C61C22×D411yescharacteristic
430C2×C4×C61C22×D411yescharacteristic
431C2×C4×C61C22×D411yescharacteristic
432C2×C4×C61C2511yescharacteristic
433C22⋊D61—22no—
434C22⋊D61—22no—
435C22⋊D61—44no—
436C22⋊D61—44no—
437C22⋊D61—82no—
438C22⋊D61—82no—
439C22⋊D61—82no—
440C22⋊D61—82no—
441C22⋊D61—82no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—44no—
446C2×Dic61—82no—
447C2×Dic61—82no—
448C2×Dic61C22×D411yescharacteristic
449C2×Dic61C22×D411yescharacteristic
450C2×Dic61C22×D411yescharacteristic
451C2×Dic61C22×D411yescharacteristic
452C2×Dic61C22×D411yescharacteristic
453C2×Dic61C22×D411yescharacteristic
454D244—22no—
455D244—24no—
456D244—42no—
457D244—42no—
458D244—82no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—22no—
462C4×D61—22no—
463C4×D61—22no—
464C4×D61—82no—
465C4×D61—82no—
466C4×D61—82no—
467C4×D61C2×#4114yes—
468Dic122—22no—
469Dic122—24no—
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×C61—42no—
485C22×C61—42no—
486C22×C61—42no—
487C22×C61C23×D411yescharacteristic
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
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#57612yes—
504C4×C61#57712yes—
505C4×C61C22×#4112yes—
506Dic61—21no—
507Dic61—21no—
508Dic61—21no—
509Dic61—21no—
510Dic61—21no—
511Dic61—42no—
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#3169D6111yescharacteristic, complemented
525#3167—611no—
526#3167—611no—
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×C61—82no—
537C2×C61C2×#53211yescharacteristic
538C2×C61C2×#57611yescharacteristic
539C2×C61C2×#57711yescharacteristic
540D61—22no—
541D61—41no—
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#533—611no—
570#532—611no—
571#532—611no—
572#532—611no—
573#532—611no—
574#532—611no—
575#532C2×D6111yescharacteristic
576#532C2×D6111yescharacteristic, complemented
577C2×C4⋊Q8—611no—
578C2×#127—611no—
579#520—612no—
580#518—612no—
581C4×#41—611no—
582#501—614no—
583#500—611no—
584#500C2×D6111yescharacteristic, complemented
585#498—611no—
586#498—611no—
587#496—614no—
588#493—611no—
589#493C2×D6111yescharacteristic
590#492—611no—
591#492—611no—
592#488—614no—
593#487—611no—
594#487—611no—
595#486—611no—
596#486—611no—
597#486—611no—
598#486—614no—
599#486—611no—
600#486C2×D6111yescharacteristic
601#486C2×D6111yescharacteristic, complemented
602#469—614no—
603#469—614no—
604#468—614no—
605#468—614no—
606#466—614no—
607#466C2×D6114yescomplemented
608#465—614no—
609#465—614no—
610#442—614no—
611#442—614no—
612#440—614no—
613#440—614no—
614C4×SD16—614no—
615C4×SD16—614no—
616C4×D8—614no—
617C4×D8C2×D6114yescomplemented
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—21no—
633C2×#41—611no—
634C2×#41—612no—
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×SD16—614no—
646C2×D8—614no—
647C2×D8C22×D6114yes—
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—611no—
659C4⋊Q8—1221no—
660C4⋊Q8—1221no—
661C4⋊Q8C22×D6111yescharacteristic
662C4⋊Q8C22×D6111yescharacteristic
663#127—612no—
664#127—611no—
665#127—1221no—
666#127—1221no—
667#127—1222no—
668#127C22×D6111yescharacteristic
669#127C22×D6111yescharacteristic
670#126—1222no—
671#126—1222no—
672#125—612no—
673#125—1221no—
674#125—1221no—
675#124—21no—
676#124—21no—
677#124—612no—
678#124—1221no—
679#124—1221no—
680#124—1221no—
681#124—1222no—
682#124—1222no—
683#124—1222no—
684#124—1221no—
685#123—1222no—
686#123—1222no—
687#123—1222no—
688#123—1222no—
689#123—1222no—
690#123—1222no—
691C22⋊Q8—612no—
692C22⋊Q8—612no—
693C22⋊Q8—1222no—
694C22⋊Q8—1222no—
695C22⋊Q8—1221no—
696C22⋊Q8—1222no—
697C22⋊Q8—1221no—
698C22⋊Q8—1221no—
699C22⋊Q8—1221no—
700#121—21no—
701#121—21no—
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—1221no—
712#121—1221no—
713#121—1221no—
714#121—1221no—
715#121—1221no—
716#121—1222no—
717#121—1222no—
718#121—1221no—
719#121C22×D6112yes—
720#121C22×D6112yes—
721#120—1222no—
722#120—1222no—
723C4×Q8—611no—
724C4×Q8—611no—
725C4×Q8—612no—
726C4×Q8—612no—
727C4×Q8—1221no—
728C4×Q8—1221no—
729C4×Q8—1221no—
730C4×Q8—1221no—
731C4×D4—21no—
732C4×D4—21no—
733C4×D4—611no—
734C4×D4—611no—
735C4×D4—611no—
736C4×D4—611no—
737C4×D4—612no—
738C4×D4—612no—
739C4×D4—612no—
740C4×D4—611no—
741C4×D4—611no—
742C4×D4—612no—
743C4×D4—1221no—
744C4×D4—1221no—
745C4×D4—1221no—
746C4×D4—1221no—
747C4×D4—1221no—
748C4×D4—1222no—
749C4×D4—1222no—
750C4×D4—1222no—
751C4×D4—1222no—
752C4×D4—1221no—
753C4×D4C22×D6112yes—
754C4×D4C22×D6112yes—
755#117—611no—
756#117—611no—
757#117—611no—
758#117—612no—
759#117—1222no—
760#117—1221no—
761#117—1221no—
762C2×C4⋊C4—612no—
763C2×C4⋊C4—1221no—
764C2×C4⋊C4—1222no—
765C2×C22⋊C4—1222no—
766C2×C22⋊C4—1222no—
767C2×C42—611no—
768C2×C42—611no—
769C2×C42C22×D6111yescharacteristic
770#107—614no—
771#107C22×D6114yes—
772#106—614no—
773#106—614no—
774#103—614no—
775#103—614no—
776#102—614no—
777#102—614no—
778#102—614no—
779#102—614no—
780#102C22×D6114yes—
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—82no—
795#41—1224no—
796#41—1228no—
797#41—4882no—
798#41—4882no—
799#41—4882no—
800#41—4882no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—611no—
804C2×Q8—612no—
805C2×Q8—1222no—
806C2×Q8—1221no—
807C2×Q8—1221no—
808C2×Q8—4882no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—611no—
816C2×D4—611no—
817C2×D4—611no—
818C2×D4—612no—
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—1222no—
828C2×D4—1221no—
829C2×D4—1221no—
830C2×D4—4882no—
831C2×D4—4882no—
832C2×D4C23×D6112yes—
833C2×D4C23×D6112yes—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—611no—
837C22×C4—611no—
838C22×C4—611no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—611no—
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—1228no—
852SD16—1228no—
853D8—28no—
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—21no—
867C4⋊C4—611no—
868C4⋊C4—611no—
869C4⋊C4—611no—
870C4⋊C4—611no—
871C4⋊C4—611no—
872C4⋊C4—611no—
873C4⋊C4—612no—
874C4⋊C4—612no—
875C4⋊C4—1222no—
876C4⋊C4—1222no—
877C4⋊C4—1222no—
878C4⋊C4—1222no—
879C4⋊C4—1222no—
880C4⋊C4—1222no—
881C4⋊C4—1222no—
882C4⋊C4—1221no—
883C4⋊C4—1222no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—1221no—
887C4⋊C4C23×D6112yes—
888C4⋊C4C23×D6112yes—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—611no—
894C22⋊C4—611no—
895C22⋊C4—611no—
896C22⋊C4—611no—
897C22⋊C4—611no—
898C22⋊C4—611no—
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—611no—
913C42—611no—
914C42—611no—
915C42—611no—
916C42—611no—
917C42—611no—
918C42—1222no—
919C42—1222no—
920C42—1222no—
921C42D4×D6111yescharacteristic
922C42D4×D6111yescharacteristic
923C42C23×D6111yescharacteristic
924C42C23×D6111yescharacteristic
925C23—22no—
926C23—22no—
927C23—611no—
928C23—611no—
929C23—1222no—
930C23—4882no—
931C23—4882no—
932C23—2444no—
933C23C2×D4×D6111yescharacteristic
934Q8—42no—
935Q8—42no—
936Q8—1222no—
937Q8—1224no—
938Q8—4882no—
939Q8—2442no—
940Q8—2442no—
941D4—24no—
942D4—24no—
943D4—42no—
944D4—42no—
945D4—42no—
946D4—42no—
947D4—82no—
948D4—82no—
949D4—1222no—
950D4—1222no—
951D4—1222no—
952D4—1224no—
953D4—4882no—
954D4—4882no—
955D4—4882no—
956D4—4882no—
957D4—4882no—
958D4—4882no—
959D4—2444no—
960D4—2444no—
961D4—2442no—
962D4—2442no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—82no—
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—1222no—
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—42no—
1008C22—42no—
1009C22—42no—
1010C22—612no—
1011C22—1221no—
1012C22—1221no—
1013C22—1221no—
1014C22—1221no—
1015C22—1221no—
1016C22—9764no—
1017C22—2442no—
1018C22—2442no—
1019C22—2442no—
1020C22C22×D4×D6111yescharacteristic
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—42no—
1025C4—42no—
1026C4—612no—
1027C4—1221no—
1028C4—1221no—
1029C4—1221no—
1030C4—1221no—
1031C4—1221no—
1032C4—2442no—
1033C4—2442no—
1034C4—2442no—
1035C4#1684056312yes—
1036C4#1684056912yes—
1037C4C2×#41×D6112yes—
1038C2—41no—
1039C2—82no—
1040C2—82no—
1041C2—1222no—
1042C2—4882no—
1043C2—2441no—
1044C2#532×D6111yescharacteristic
1045C2C2×#1684056311yescharacteristic
1046C2C2×#1684056911yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3169C2
socleC22×C61C23×D4
hypercenter#3169D61
hypocenterC61#60722
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #21459720C2semidirect
2. #21459688C2semidirect
3. #21456555C2semidirect
4. #21456553C2semidirect
5. #21456539C2semidirect
6. #21456533C2semidirect
7. #21456506C2semidirect
8. #21456505C2semidirect
9. #21456397C2semidirect
10. #21456378C2semidirect
11. #21456377C2semidirect
12. #21456362C2semidirect
13. #21456270C2semidirect
14. #21456138C2semidirect
15. #486×D61C2semidirect
16. #21455498C2semidirect
17. #21454644C2semidirect
18. C4×#14519783C2semidirect
19. C61×#3169C2semidirect
38. #16840379C22semidirect
39. #16840377C22semidirect
44. #16840319C22semidirect
46. #16840317C22semidirect
51. #16840310C22semidirect
57. #16840170C22semidirect
58. #16840165C22semidirect
59. #16840160C22semidirect
60. #16840158C22semidirect
65. #16840115C22semidirect
66. #16840114C22semidirect
67. #16840113C22semidirect
71. #16840108C22semidirect
73. #16840013C22semidirect
74. #16840012C22semidirect
75. #16840009C22semidirect
76. #16840006C22semidirect
77. #16839997C22semidirect
78. #16839991C22semidirect
79. #16839990C22semidirect
80. #16839874C22semidirect
81. #16839872C22semidirect
82. #16839862C22semidirect
83. #16839861C22semidirect
84. #16839853C22semidirect
85. C4×#11758190C22semidirect
86. #16839842C22semidirect
90. #16839717C22semidirect
92. #16839716C22semidirect
93. C4×#11758194C22semidirect
95. C4×#11758189C22semidirect
97. C4×C8×D61C22semidirect
99. C61×#532C22semidirect
100. C61×#500C22semidirect
103. C61×#486C22semidirect
104. C61×#466C22semidirect
105. C4×D8×C61C22semidirect
106. C2×C4×C8×C61C22semidirect
398. #11758189#41semidirect
524. #3169D61semidirect
576. #532C2×D61semidirect
584. #500C2×D61semidirect
601. #486C2×D61semidirect
607. #466C2×D61semidirect
617. C4×D8C2×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
#214597202
#214596882
#214565552
#214565532
#214565392
#214565332
#214565062
#214565052
#214563972
#214563782
#214563772
#214563622
#214562702
#214561382
#486×D612
#214554982
#214546442
C4×#145197832
C61×#31692
#6072261