Finite Group Databasebeta

← #30571187

Subgroups — #30571187

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459684C211yesmaximal, characteristic, complemented
2#21458903C214yesmaximal, complemented
3#21458879C214yesmaximal, complemented
4#21458581C214yesmaximal, complemented
5#21458566C214yesmaximal, complemented
6#21456837C212yesmaximal, complemented
7#21456822C211yesmaximal, characteristic, complemented
8#21456806C211yesmaximal, characteristic, complemented
9#21456784C212yesmaximal, complemented
10#21455990C212yesmaximal, complemented
11#21455918C211yesmaximal, characteristic, complemented
12#21455910C211yesmaximal, characteristic, complemented
13#21455866C212yesmaximal, complemented
14#21454904C211yesmaximal, characteristic, complemented
15C2×C61×#559C211yesmaximal, characteristic, complemented
16#16840497C2212yescomplemented
17#16840490C2212yescomplemented
18#16840485C2212yescomplemented
19#16840484—22no—
20#16840472C2212yescomplemented
21#16840453—22no—
22#16840359—21no—
23#16840359—21no—
24#16840336—21no—
25#16840319C2211yescharacteristic
26#16840312C2211yescharacteristic
27#16840296C2212yes—
28#16840296C2212yes—
29#16840243—21no—
30#16840157C2212yescomplemented
31#16840152C2212yescomplemented
32#16840149C2214yes—
33#16840144C2214yescomplemented
34#16840126C2214yes—
35#16840121C2212yescomplemented
36#16840121C2212yescomplemented
37#16840116C2214yescomplemented
38#16840097C2212yes—
39#16840080C2212yes—
40#16840069C2214yescomplemented
41#16840062C2214yescomplemented
42#16840052C2212yescomplemented
43#16840042C2212yescomplemented
44#16839984C2214yescomplemented
45#16839981C2214yescomplemented
46#16839981C2214yescomplemented
47#16839977C2214yescomplemented
48#16839974C2214yescomplemented
49#16839974C2214yescomplemented
50#16839967C2212yescomplemented
51#16839959C2214yes—
52#16839957C2212yescomplemented
53#16839954C2214yes—
54#16839918C2212yes—
55#16839913C2212yes—
56#16839913C2212yes—
57#16839901C2212yes—
58#16839896C2212yes—
59#16839896C2212yes—
60#16839893C2214yescomplemented
61#16839893C2214yescomplemented
62#16839872C2214yescomplemented
63#16839867C2214yescomplemented
64#16839862C2214yescomplemented
65#16839860C2214yescomplemented
66C4×#11758200C2214yescomplemented
67C4×#11758199C2214yescomplemented
68#16839819C2211yescharacteristic
69#16839819C2211yescharacteristic
70#16839819C2212yes—
71#16839815C2212yes—
72C61×#559—22no—
73C61×#559—22no—
74C61×#559C2214yes—
75C61×#559C2214yes—
76C2×#127×C61C2211yescharacteristic
77C2×#124×C61—21no—
78C2×#124×C61C2211yescharacteristic
79C2×#124×C61C2211yescharacteristic
80C2×#123×C61—21no—
81C2×#123×C61—21no—
82C2×C4×Q8×C61C2211yescharacteristic
83C2×C4×Q8×C61C2211yescharacteristic
84C2×C4×D4×C61—21no—
85C2×C4×D4×C61C2211yescharacteristic
86C2×C4×D4×C61C2211yescharacteristic
87C2×#11758222—21no—
88C2×#11758202C2314yes—
89C2×#11758200C2314yes—
90C2×#11758200C2314yes—
91C2×#11758201C2314yes—
92C2×#11758199C2314yes—
93C2×#11758199C2314yes—
94#14519777C2311yescharacteristic
95#14519777C2311yescharacteristic
96#14519777C2311yescharacteristic
97#14519775—22no—
98#14519774C2311yescharacteristic
99#14519772—22no—
100#14519772—22no—
101#14519771—22no—
102#14519771—22no—
103#14519769—21no—
104#14519769C2312yes—
105#14519769C2312yes—
106#14519767—22no—
107#14519767—22no—
108#14519766—22no—
109#14519765—21no—
110#14519765C2312yes—
111#14519765C2312yes—
112#14519762—22no—
113#14519762—22no—
114#14519760—22no—
115#14519760—22no—
116#14519756—21no—
117#14519756C2312yes—
118#14519755—22no—
119#14519755—22no—
120#14519753—22no—
121#14519753—22no—
122#14519751—21no—
123#14519751C2312yes—
124C4×Dic122—21no—
125C4×Dic122C2312yes—
126C4×Dic122C2312yes—
127C4×Dic122C2312yes—
128#14519742—22no—
129C4×D244—21no—
130C4×D244C2312yes—
131C4×D244C2312yes—
132C4×D244C2312yes—
133#14519739—22no—
134C4×C22⋊D61—22no—
135C4×C22⋊D61—22no—
136#14519736—21no—
137#14519735—22no—
138#14519734—22no—
139#14519734—22no—
140C4⋊C4×D61—22no—
141#14519710C2314yes—
142#14519708C2314yes—
143C4⋊#92418C2314yes—
144C4⋊#92418C2312yes—
145C4⋊#92418C2312yes—
146C4⋊#92418C2314yes—
147#14519701C2314yes—
148#14519701C2314yes—
149#14519700C2314yes—
150#14519698C2314yes—
151#14519698C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519697C2314yes—
155C22⋊#92418C2312yes—
156C22⋊#92418C2312yes—
157#14519688C2314yes—
158#14519688C2312yes—
159#14519688C2312yes—
160C4×#92418C2314yes—
161C22×Q8×C61D411yescharacteristic
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C23×C4×C61—21no—
169#127×C61—22no—
170#127×C61C2314yes—
171#124×C61—24no—
172#124×C61—24no—
173#124×C61—22no—
174#124×C61—21no—
175#124×C61—21no—
176#124×C61C2312yes—
177#124×C61C2314yes—
178#124×C61C2312yes—
179#123×C61—24no—
180#123×C61—24no—
181#123×C61—24no—
182#123×C61—24no—
183C4×Q8×C61—22no—
184C4×Q8×C61D412yes—
185C4×Q8×C61D412yes—
186C4×Q8×C61C2314yes—
187C4×Q8×C61C2312yes—
188C4×Q8×C61C2312yes—
189C4×D4×C61—24no—
190C4×D4×C61—24no—
191C4×D4×C61—22no—
192C4×D4×C61—21no—
193C4×D4×C61—21no—
194C4×D4×C61C2312yes—
195C4×D4×C61C2312yes—
196C4×D4×C61C2314yes—
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61D411yescharacteristic
199C2×C4⋊C4×C61D411yescharacteristic
200C2×C4⋊C4×C61D411yescharacteristic
201C2×C4⋊C4×C61C2311yescharacteristic
202C2×C22⋊C4×C61—21no—
203C2×C22⋊C4×C61—21no—
204C2×C22⋊C4×C61—21no—
205C2×C22⋊C4×C61—21no—
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C42×C61—21no—
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212C24×C61—21no—
213C24×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—42no—
216C2×Q8×C61—42no—
217C2×Q8×C61C2×D412yes—
218C2×Q8×C61C2×D412yes—
219C2×Q8×C61C2412yes—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—24no—
223C2×D4×C61—24no—
224C2×D4×C61—42no—
225C2×D4×C61—42no—
226C2×D4×C61—44no—
227C2×D4×C61—82no—
228C2×D4×C61C2412yes—
229C2×D4×C61C2412yes—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—24no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—82no—
236C22×C4×C61—82no—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2411yescharacteristic
244C2×C22⋊D61—22no—
245#11758222—44no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244C2412yes—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122C2412yes—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2×D412yes—
258C4⋊C4×C61C2×D412yes—
259C4⋊C4×C61C2×D412yes—
260C4⋊C4×C61C2×D412yes—
261C4⋊C4×C61C2×D412yes—
262C4⋊C4×C61C2×D412yes—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—22no—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—24no—
269C22⋊C4×C61—22no—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—24no—
272C22⋊C4×C61—22no—
273C42×C61—24no—
274C42×C61C2×D412yes—
275C42×C61C2×D411yescharacteristic
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D412yes—
278C42×C61C2412yes—
279C42×C61C2411yescharacteristic
280C42×C61C2411yescharacteristic
281C42×C61C2412yes—
282C22⋊Dic61—22no—
283#11758202—44no—
284#11758201—44no—
285#11758200—44no—
286#11758200—44no—
287#11758199—44no—
288#11758199—44no—
289#11758198—22no—
290#11758198—22no—
291#11758198—22no—
292#11758198—22no—
293#11758198—22no—
294#11758198—22no—
295#11758198—22no—
296#11758198—22no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61C2412yes—
302C4⋊Dic61C2412yes—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307#11758196—22no—
308#11758196—22no—
309#11758196—22no—
310#11758196—22no—
311C4×Dic61—22no—
312C4×Dic61—22no—
313C4×Dic61—22no—
314C2×#92418C2414yes—
315C2×#92418C2414yes—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61—42no—
324C23×C61C22×D411yescharacteristic
325C22×D61—22no—
326Q8×C61—24no—
327Q8×C61—42no—
328Q8×C61—42no—
329Q8×C61—42no—
330D4×C61—22no—
331D4×C61—24no—
332D4×C61—22no—
333D4×C61—42no—
334D4×C61—42no—
335D4×C61—48no—
336D4×C61—84no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—82no—
349C2×C4×C61—84no—
350C2×C4×C61—82no—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D412yes—
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D412yes—
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2511yescharacteristic
361C22⋊D61—44no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365D244—24no—
366D244—42no—
367D244—81no—
368C4×D61—44no—
369C4×D61—82no—
370C4×D61—82no—
371Dic122—24no—
372Dic122—42no—
373Dic122—81no—
374#92418—24no—
375#92418—24no—
376#61895—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—84no—
386C22×C61—84no—
387C22×C61#57512yes—
388C22×C61C23×D411yescharacteristic
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C4×C61—21no—
393C4×C61—22no—
394C4×C61—22no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61#58512yes—
404Dic61—42no—
405Dic61—42no—
406Dic61—42no—
407#3507—611no—
408C2×#559D6111yescharacteristic, complemented
409#3403—614no—
410#3401—614no—
411#3371—614no—
412#3370—614no—
413#3217—612no—
414#3215—611no—
415#3213—611no—
416#3211—612no—
417#3117—612no—
418#3110—611no—
419#3109—611no—
420#3105—612no—
421#2983—611no—
422C2×C61—22no—
423C2×C61—82no—
424C2×C61—82no—
425C2×C61#348711yescharacteristic
426C2×C61C2×#57511yescharacteristic
427C2×C61#358511yescharacteristic
428D61—82no—
429#559—22no—
430#559—22no—
431#559—612no—
432#559C2×D6114yes—
433#559C2×D6114yes—
434#557—612no—
435#556—612no—
436#556—1222no—
437#554—612no—
438#552—1222no—
439#539—1221no—
440#539—1221no—
441#536—1221no—
442#533—611no—
443#532—611no—
444C2×#127C2×D6111yescharacteristic
445#529—612no—
446#529—612no—
447C2×#124—21no—
448C2×#124C2×D6111yescharacteristic
449C2×#124C2×D6111yescharacteristic
450C2×#123—21no—
451C2×#123—21no—
452#520—1221no—
453C2×C4×Q8C2×D6111yescharacteristic
454C2×C4×Q8C2×D6111yescharacteristic
455C2×C4×D4—21no—
456C2×C4×D4C2×D6111yescharacteristic
457C2×C4×D4C2×D6111yescharacteristic
458#497—612no—
459#496—614no—
460#496—612no—
461#495—614no—
462#490—614no—
463#489—612no—
464#489—612no—
465#488—614no—
466#484—612no—
467#481—612no—
468#479—614no—
469#478—614no—
470#476—612no—
471#474—612no—
472#464—614no—
473#464—614no—
474#464—614no—
475#463—614no—
476#463—614no—
477#463—614no—
478#461—612no—
479#460—614no—
480#459—614no—
481#459—612no—
482#451—612no—
483#450—612no—
484#450—612no—
485#448—612no—
486#447—612no—
487#447—612no—
488#446—614no—
489#446—614no—
490#442—614no—
491#441—614no—
492#440—614no—
493#440—614no—
494C4×SD16—614no—
495C4×D8—614no—
496#432—611no—
497#432—611no—
498#432—612no—
499#431—612no—
500C61#6189511yescharacteristic, complemented, Sylow
501C2×#41—1221no—
502C22×Q8C22⋊D6111yescharacteristic
503C22×Q8C22×D6111yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C22×D6111yescharacteristic
507C22×D4C22×D6111yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C2×Q16—614no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×D8—614no—
515C2×D8—614no—
516C4⋊Q8—611no—
517C4⋊Q8—611no—
518C4⋊Q8—611no—
519C4⋊Q8—1222no—
520#127—22no—
521#127—611no—
522#127C22×D6114yes—
523#126—1222no—
524#126—1222no—
525#126—1222no—
526#126—1222no—
527#125—612no—
528#125—612no—
529#125—1222no—
530#125—1222no—
531#125—1221no—
532#124—24no—
533#124—24no—
534#124—22no—
535#124—21no—
536#124—21no—
537#124—612no—
538#124—612no—
539#124—1222no—
540#124—1221no—
541#124C22×D6112yes—
542#124C22×D6114yes—
543#124C22×D6112yes—
544#123—24no—
545#123—24no—
546#123—24no—
547#123—24no—
548#123—1222no—
549#123—1222no—
550#123—1222no—
551#123—1222no—
552C22⋊Q8—612no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555C22⋊Q8—1221no—
556C22⋊Q8—1222no—
557C22⋊Q8—1222no—
558#121—612no—
559#121—1221no—
560C4×Q8—22no—
561C4×Q8—612no—
562C4×Q8—612no—
563C4×Q8—612no—
564C4×Q8—1222no—
565C4×Q8—1221no—
566C4×Q8C22⋊D6112yes—
567C4×Q8C22⋊D6112yes—
568C4×Q8C22×D6114yes—
569C4×Q8C22×D6112yes—
570C4×Q8C22×D6112yes—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—22no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4—612no—
577C4×D4—612no—
578C4×D4—612no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1221no—
583C4×D4C22×D6114yes—
584C4×D4C22×D6112yes—
585C4×D4C22×D6112yes—
586#117—1221no—
587#117—1222no—
588#117—1222no—
589#117—1222no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—1222no—
592C2×C4⋊C4C22⋊D6111yescharacteristic
593C2×C4⋊C4C22⋊D6111yescharacteristic
594C2×C4⋊C4C22⋊D6111yescharacteristic
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C42—21no—
603C2×C42C22×D6111yescharacteristic
604C2×C42C22×D6111yescharacteristic
605C2×C42C22×D6111yescharacteristic
606#107—614no—
607#106—614no—
608C4⋊C8—614no—
609C4⋊C8—614no—
610C4⋊C8—612no—
611C4⋊C8—612no—
612#103—614no—
613#103—614no—
614#103—614no—
615#102—614no—
616#102—614no—
617#102—614no—
618#102—614no—
619#102—614no—
620C22⋊C8—612no—
621C22⋊C8—612no—
622#97—612no—
623#97—614no—
624#97—612no—
625C4×C8—614no—
626C24—21no—
627C24—21no—
628#41—2444no—
629C2×Q8—21no—
630C2×Q8—42no—
631C2×Q8—42no—
632C2×Q8—612no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8C2×C22⋊D6112yes—
636C2×Q8C2×C22⋊D6112yes—
637C2×Q8C23×D6112yes—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—44no—
645C2×D4—82no—
646C2×D4—612no—
647C2×D4—1222no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4C23×D6112yes—
651C2×D4C23×D6112yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—82no—
658C22×C4—82no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4C2×C22⋊D6111yescharacteristic
663C22×C4C2×C22⋊D6111yescharacteristic
664C22×C4C2×C22⋊D6111yescharacteristic
665C22×C4C2×C22⋊D6111yescharacteristic
666C22×C4C2×C22⋊D6111yescharacteristic
667C22×C4C2×C22⋊D6111yescharacteristic
668C22×C4C23×D6111yescharacteristic
669Q16—2444no—
670SD16—2444no—
671SD16—2444no—
672SD16—2444no—
673D8—2444no—
674D8—2444no—
675C2×C8—614no—
676C2×C8—614no—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—612no—
680C4⋊C4—612no—
681C4⋊C4—1221no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1222no—
688C4⋊C4—1222no—
689C4⋊C4—1222no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4C2×C22⋊D6112yes—
694C4⋊C4C2×C22⋊D6112yes—
695C4⋊C4C2×C22⋊D6112yes—
696C4⋊C4C2×C22⋊D6112yes—
697C4⋊C4C2×C22⋊D6112yes—
698C4⋊C4C2×C22⋊D6112yes—
699C4⋊C4C23×D6112yes—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—24no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—1222no—
710C22⋊C4—1222no—
711C22⋊C4—1222no—
712C22⋊C4—1222no—
713C22⋊C4—1222no—
714C22⋊C4—1222no—
715C22⋊C4—1222no—
716C22⋊C4—1222no—
717C22⋊C4—1222no—
718C42—24no—
719C42—1222no—
720C42—1222no—
721C42—1222no—
722C42C2×C22⋊D6112yes—
723C42C2×C22⋊D6112yes—
724C42C2×C22⋊D6111yescharacteristic
725C42C2×C22⋊D6111yescharacteristic
726C42C23×D6112yes—
727C42C23×D6111yescharacteristic
728C42C23×D6112yes—
729C42C23×D6111yescharacteristic
730C23—22no—
731C23—22no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—1222no—
739C23C22×C22⋊D6111yescharacteristic
740Q8—24no—
741Q8—42no—
742Q8—42no—
743Q8—42no—
744Q8—1224no—
745Q8—4881no—
746Q8—2442no—
747D4—22no—
748D4—24no—
749D4—22no—
750D4—42no—
751D4—42no—
752D4—48no—
753D4—84no—
754D4—1224no—
755D4—4881no—
756D4—2442no—
757D4—2444no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—84no—
770C2×C4—82no—
771C2×C4—82no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—4882no—
776C2×C4—4882no—
777C2×C4—2444no—
778C2×C4C22×C22⋊D6112yes—
779C2×C4C22×C22⋊D6111yescharacteristic
780C2×C4C22×C22⋊D6112yes—
781C2×C4C22×C22⋊D6112yes—
782C2×C4C22×C22⋊D6111yescharacteristic
783C2×C4C22×C22⋊D6112yes—
784C2×C4C22×C22⋊D6111yescharacteristic
785C2×C4C22×C22⋊D6111yescharacteristic
786C2×C4C22×C22⋊D6111yescharacteristic
787C2×C4C24×D6111yescharacteristic
788C8—1224no—
789C8—1224no—
790C22—21no—
791C22—21no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—84no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22#1684056012yes—
804C22C23×C22⋊D6111yescharacteristic
805C4—21no—
806C4—21no—
807C4—22no—
808C4—21no—
809C4—22no—
810C4—22no—
811C4—21no—
812C4—21no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—2442no—
817C4—2442no—
818C4—2442no—
819C4#1684059812yes—
820C2—22no—
821C2—82no—
822C2—82no—
823C2—4882no—
824C2#2145947711yescharacteristic
825C2C2×#1684056011yescharacteristic
826C2#2146059911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#559C2
socleC22×C61C23×D4
hypercenterC2×#559D61
hypocenterC61#61895
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #21459684C2semidirect
2. #21458903C2semidirect
3. #21458879C2semidirect
4. #21458581C2semidirect
5. #21458566C2semidirect
6. #21456837C2semidirect
7. #21456822C2semidirect
8. #21456806C2semidirect
9. #21456784C2semidirect
10. #21455990C2semidirect
11. #21455918C2semidirect
12. #21455910C2semidirect
13. #21455866C2semidirect
14. #21454904C2semidirect
15. C2×C61×#559C2semidirect
16. #16840497C22semidirect
17. #16840490C22semidirect
18. #16840485C22semidirect
20. #16840472C22semidirect
30. #16840157C22semidirect
31. #16840152C22semidirect
33. #16840144C22semidirect
35. #16840121C22semidirect
36. #16840121C22semidirect
37. #16840116C22semidirect
40. #16840069C22semidirect
41. #16840062C22semidirect
42. #16840052C22semidirect
43. #16840042C22semidirect
44. #16839984C22semidirect
45. #16839981C22semidirect
46. #16839981C22semidirect
47. #16839977C22semidirect
48. #16839974C22semidirect
49. #16839974C22semidirect
50. #16839967C22semidirect
52. #16839957C22semidirect
60. #16839893C22semidirect
61. #16839893C22semidirect
62. #16839872C22semidirect
63. #16839867C22semidirect
64. #16839862C22semidirect
65. #16839860C22semidirect
66. C4×#11758200C22semidirect
67. C4×#11758199C22semidirect
408. C2×#559D61semidirect
500. C61#61895semidirect

Maximal subgroups

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

subgroupindex
#214596842
#214589032
#214588792
#214585812
#214585662
#214568372
#214568222
#214568062
#214567842
#214559902
#214559182
#214559102
#214558662
#214549042
C2×C61×#5592
#6189561