Finite Group Databasebeta

← #30571189

Subgroups — #30571189

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#21459686C211yesmaximal, characteristic, complemented
2C2×#16840495C211yesmaximal, characteristic, complemented
3#21458908C214yesmaximal, complemented
4#21458892C214yesmaximal, complemented
5#21458592C214yesmaximal, complemented
6#21458579C214yesmaximal, complemented
7#21456840C212yesmaximal, complemented
8#21456818C211yesmaximal, characteristic, complemented
9#21456808C211yesmaximal, characteristic, complemented
10#21456787C212yesmaximal, complemented
11#21455993C212yesmaximal, complemented
12#21455910C211yesmaximal, characteristic, complemented
13#21455869C212yesmaximal, complemented
14#21454903C211yesmaximal, characteristic, complemented
15C61×#3110C211yesmaximal, characteristic, complemented
16#16840497C2212yescomplemented
17#16840495—22no—
18#16840495—22no—
19#16840495C2214yes—
20#16840495C2214yes—
21#16840491C2212yescomplemented
22#16840486C2212yescomplemented
23#16840485—22no—
24#16840473C2212yescomplemented
25#16840450—22no—
26#16840361—21no—
27#16840361—21no—
28#16840338—21no—
29#16840312C2211yescharacteristic
30C2×#14519773C2211yescharacteristic
31#16840298C2212yes—
32#16840298C2212yes—
33C2×#14519765C2211yescharacteristic
34C2×#14519764C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519760—21no—
37C2×#14519759—21no—
38#16840242—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×#14519742C2211yescharacteristic
41C2×#14519739C2211yescharacteristic
42C2×C4×C22⋊D61—21no—
43#16840154C2212yescomplemented
44#16840151C2212yescomplemented
45#16840148C2214yes—
46#16840143C2214yescomplemented
47#16840125C2214yes—
48#16840124C2212yescomplemented
49#16840122C2212yescomplemented
50#16840115C2214yescomplemented
51#16840080C2212yes—
52#16840068C2214yescomplemented
53#16840065C2214yescomplemented
54#16840052C2212yescomplemented
55#16839987C2214yescomplemented
56#16839984C2214yescomplemented
57#16839982C2214yescomplemented
58#16839980C2214yescomplemented
59#16839978C2214yescomplemented
60#16839976C2214yescomplemented
61#16839960C2214yes—
62#16839957C2212yescomplemented
63#16839956C2214yes—
64#16839917C2212yes—
65#16839912C2212yes—
66#16839903C2212yes—
67#16839898C2212yes—
68#16839896C2212yes—
69#16839891C2214yescomplemented
70#16839890C2214yescomplemented
71#16839872C2214yescomplemented
72#16839866C2214yescomplemented
73#16839861C2214yescomplemented
74#16839847C2214yescomplemented
75#16839844C2214yescomplemented
76#16839819C2211yescharacteristic
77#16839816C2212yes—
78#16839812C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×D4×C61C2211yescharacteristic
81C61×#484C2212yes—
82C61×#474C2212yescomplemented
83C61×#461C2212yescomplemented
84C61×#450C2212yes—
85C61×#440C2214yescomplemented
86C61×#432C2211yescharacteristic
87C2×#11758222—21no—
88C22×Dic122D411yescharacteristic
89C22×Dic122C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C4×D61—21no—
94C2×#11758202C2314yes—
95C2×#11758190C2314yes—
96C2×#11758201C2314yes—
97C2×D488C2314yes—
98C2×#11758199C2314yes—
99#14519777—22no—
100#14519777C2311yescharacteristic
101#14519774C2311yescharacteristic
102#14519773—22no—
103#14519773C2314yes—
104#14519772—22no—
105#14519772—22no—
106#14519772—22no—
107#14519772—22no—
108#14519768—22no—
109#14519768—22no—
110#14519768C2312yes—
111#14519768C2312yes—
112#14519766C2312yes—
113#14519766C2312yes—
114#14519765—22no—
115#14519765—21no—
116#14519765—21no—
117#14519765—21no—
118#14519765C2312yes—
119#14519765C2312yes—
120#14519764—22no—
121#14519764C2314yes—
122#14519763—24no—
123#14519763—24no—
124#14519762—22no—
125#14519762—22no—
126#14519761—22no—
127#14519761—22no—
128#14519760—24no—
129#14519760—24no—
130#14519759—24no—
131#14519759—24no—
132#14519757—22no—
133#14519757—22no—
134#14519753—22no—
135#14519753—22no—
136#14519751—21no—
137#14519751C2312yes—
138Q8×Dic61C2312yes—
139Q8×Dic61C2312yes—
140C4×Dic122—22no—
141C4×Dic122D412yes—
142C4×Dic122D412yes—
143C4×Dic122C2312yes—
144C4×Dic122C2312yes—
145#14519742—22no—
146#14519742C2314yes—
147C4×D244—21no—
148C4×D244—22no—
149C4×D244C2312yes—
150#14519739—22no—
151#14519739C2312yes—
152#14519739C2312yes—
153#14519739C2314yes—
154C4×C22⋊D61—24no—
155C4×C22⋊D61—24no—
156#14519737—22no—
157#14519737—22no—
158#14519735—22no—
159#14519735—22no—
160#14519735—22no—
161C2×C4⋊Dic61D411yescharacteristic
162C2×#11758196—21no—
163C2×#11758196D411yescharacteristic
164C2×#11758196D411yescharacteristic
165C4⋊C4×D61—22no—
166C2×C22⋊Dic61—21no—
167C2×C22⋊Dic61—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C2×#11758198—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61C2311yescharacteristic
173C2×C4×Dic61C2311yescharacteristic
174#14519708C2314yes—
175C4⋊#92418C2312yes—
176#14519706C2314yes—
177#14519706C2314yes—
178#14519702C2314yes—
179#14519700C2314yes—
180#14519699C2314yes—
181#14519698C2314yes—
182#14519697C2314yes—
183#14519697C2314yes—
184C22⋊#92418C2312yes—
185#14519688C2312yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×D4×C61C2311yescharacteristic
189C23×C4×C61—21no—
190C2×SD16×C61C2314yes—
191C4⋊Q8×C61C2311yescharacteristic
192C4⋊Q8×C61C2311yescharacteristic
193#125×C61—21no—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61C2312yes—
196C4×Q8×C61—21no—
197C4×Q8×C61C2312yes—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2312yes—
201C4×D4×C61C2312yes—
202#117×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#107×C61C2314yes—
207C4⋊C8×C61C2312yes—
208#103×C61C2314yes—
209#102×C61C2314yes—
210C22⋊C8×C61C2312yes—
211#97×C61C2312yes—
212C24×C61—21no—
213C23×D61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61C2412yes—
216C2×D4×C61—21no—
217C2×D4×C61—42no—
218C2×D4×C61C2412yes—
219C22×C4×C61—21no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—82no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—22no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—82no—
231C22×Dic61—21no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236#11758222—44no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—42no—
241C2×D244C2412yes—
242C2×D244C2412yes—
243C2×C4×D61—22no—
244C2×C4×D61—24no—
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—82no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—42no—
251C2×Dic122—42no—
252C2×Dic122C2×D412yes—
253C2×Dic122C2×D412yes—
254C2×Dic122C2412yes—
255SD16×C61—44no—
256C2×C8×C61C2414yes—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61C2412yes—
264C4⋊C4×C61C2412yes—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—22no—
267C22⋊C4×C61—22no—
268C42×C61—22no—
269C42×C61C2×D411yescharacteristic
270C42×C61C2×D411yescharacteristic
271C42×C61C2411yescharacteristic
272C42×C61C2411yescharacteristic
273C22⋊Dic61—24no—
274C22⋊Dic61—24no—
275#11758202—44no—
276#11758201—44no—
277#11758199—44no—
278#11758198—22no—
279#11758198—22no—
280#11758198—22no—
281#11758198—22no—
282#11758198—22no—
283#11758198—22no—
284#11758198—24no—
285#11758198—22no—
286#11758198—22no—
287#11758198—22no—
288#11758198—22no—
289#11758198—22no—
290#11758198—22no—
291C4⋊Dic61—21no—
292C4⋊Dic61—22no—
293C4⋊Dic61—22no—
294C4⋊Dic61—22no—
295C4⋊Dic61—22no—
296C4⋊Dic61C2×D412yes—
297C4⋊Dic61C2×D412yes—
298C4⋊Dic61C2412yes—
299#11758196—22no—
300#11758196—22no—
301#11758196—24no—
302#11758196C2×D412yes—
303#11758196C2×D412yes—
304#11758196C2×D412yes—
305#11758196C2×D412yes—
306C4×Dic61—24no—
307C4×Dic61—22no—
308C4×Dic61—22no—
309C4×Dic61C2×D412yes—
310C4×Dic61C2×D412yes—
311C4×Dic61C2412yes—
312C4×Dic61C2412yes—
313C2×#92418C2414yes—
314D488—44no—
315#11758190—44no—
316C23×C61—22no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61C22×D411yescharacteristic
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326Q8×C61—24no—
327Q8×C61—81no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—42no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—41no—
337C2×C4×C61—42no—
338C2×C4×C61—82no—
339C2×C4×C61—82no—
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C2511yescharacteristic
346C22⋊D61—48no—
347C22⋊D61—44no—
348C22⋊D61—84no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—42no—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D412yes—
360D244—24no—
361D244—24no—
362D244—42no—
363D244—42no—
364D244—81no—
365C4×D61—44no—
366C4×D61—82no—
367C4×D61—82no—
368C4×D61—84no—
369Dic122—24no—
370Dic122—42no—
371Dic122—42no—
372Dic122—42no—
373Dic122—42no—
374C8×C61—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—84no—
383C22×C61#57512yes—
384C22×C61C23×D411yescharacteristic
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—84no—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—42no—
398C4×C61—42no—
399C4×C61—42no—
400C4×C61#58512yes—
401Dic61—22no—
402Dic61—22no—
403Dic61—22no—
404Dic61—22no—
405Dic61—42no—
406Dic61—42no—
407#3507—611no—
408C2×#559—611no—
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#3110D6111yescharacteristic, complemented
419#3109—611no—
420#3105—612no—
421#2983—611no—
422C2×C61—22no—
423C2×C61—82no—
424C2×C61#348711yescharacteristic
425C2×C61C2×#57511yescharacteristic
426C2×C61#358511yescharacteristic
427D61—82no—
428D61—82no—
429#559—612no—
430#559—614no—
431#559—614no—
432#559—1222no—
433#559—1222no—
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#533C2×D6111yescharacteristic
443#532—611no—
444C2×#127—611no—
445#529—612no—
446#529—612no—
447C2×#124—611no—
448C2×#124—611no—
449C2×#124—1221no—
450C2×#123—1221no—
451C2×#123—1221no—
452#520—1221no—
453C2×C4×Q8—611no—
454C2×C4×Q8—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
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#484C2×D6112yes—
467#481—612no—
468#479—614no—
469#478—614no—
470#476—612no—
471#474C2×D6112yescomplemented
472#464—614no—
473#464—614no—
474#464—614no—
475#463—614no—
476#463—614no—
477#463—614no—
478#461C2×D6112yescomplemented
479#460—614no—
480#459—612no—
481#459—614no—
482#451—612no—
483#450—612no—
484#450C2×D6112yes—
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#440C2×D6114yescomplemented
494C4×SD16—614no—
495C4×D8—614no—
496#432—611no—
497#432—612no—
498#432C2×D6111yescharacteristic
499#431—612no—
500C61#6189511yescharacteristic, complemented, Sylow
501C2×#41—1221no—
502C22×Q8—611no—
503C22×Q8—611no—
504C22×D4—611no—
505C22×D4—1221no—
506C22×D4—1221no—
507C22×D4C22×D6111yescharacteristic
508C23×C4—21no—
509C23×C4—1221no—
510C2×Q16—614no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16C22×D6114yes—
514C2×D8—614no—
515C2×D8—614no—
516C4⋊Q8—611no—
517C4⋊Q8—1222no—
518C4⋊Q8C22×D6111yescharacteristic
519C4⋊Q8C22×D6111yescharacteristic
520#127—614no—
521#127—611no—
522#127—1222no—
523#126—1222no—
524#126—1222no—
525#126—1222no—
526#126—1222no—
527#125—21no—
528#125—612no—
529#125—612no—
530#125—1222no—
531#125—1222no—
532#124—612no—
533#124—612no—
534#124—614no—
535#124—612no—
536#124—612no—
537#124—1222no—
538#124—1222no—
539#124—1224no—
540#124—1224no—
541#124—1221no—
542#124—1221no—
543#124—1221no—
544#123—1224no—
545#123—1224no—
546#123—1222no—
547#123—1222no—
548#123—1222no—
549#123—1222no—
550#123—1224no—
551#123—1224no—
552C22⋊Q8—21no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555C22⋊Q8—1222no—
556C22⋊Q8—1222no—
557C22⋊Q8C22×D6112yes—
558#121—612no—
559#121—1221no—
560C4×Q8—21no—
561C4×Q8—612no—
562C4×Q8—612no—
563C4×Q8—612no—
564C4×Q8—612no—
565C4×Q8—612no—
566C4×Q8—612no—
567C4×Q8—614no—
568C4×Q8—1222no—
569C4×Q8—1222no—
570C4×Q8C22×D6112yes—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—614no—
574C4×D4—612no—
575C4×D4—612no—
576C4×D4—612no—
577C4×D4—1222no—
578C4×D4—1222no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1224no—
582C4×D4—1224no—
583C4×D4—1221no—
584C4×D4C22×D6112yes—
585C4×D4C22×D6112yes—
586#117—21no—
587#117—1222no—
588#117—1222no—
589#117—1222no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—1221no—
605C2×C42C22×D6111yescharacteristic
606#107C22×D6114yes—
607#106—614no—
608C4⋊C8—614no—
609C4⋊C8—614no—
610C4⋊C8—612no—
611C4⋊C8C22×D6112yes—
612#103—614no—
613#103—614no—
614#103C22×D6114yes—
615#102—614no—
616#102—614no—
617#102—614no—
618#102—614no—
619#102C22×D6114yes—
620C22⋊C8—612no—
621C22⋊C8C22×D6112yes—
622#97—614no—
623#97—612no—
624#97C22×D6112yes—
625C4×C8—614no—
626C24—21no—
627C24—1221no—
628#41—2444no—
629C2×Q8—21no—
630C2×Q8—612no—
631C2×Q8—612no—
632C2×Q8—612no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—2442no—
636C2×Q8—2442no—
637C2×Q8C23×D6112yes—
638C2×D4—21no—
639C2×D4—42no—
640C2×D4—612no—
641C2×D4—612no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1222no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—4882no—
649C2×D4—2442no—
650C2×D4—2444no—
651C2×D4C23×D6112yes—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—82no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—1224no—
663C22×C4—1221no—
664C22×C4—1222no—
665C22×C4—4882no—
666C22×C4D4×D6111yescharacteristic
667C22×C4D4×D6111yescharacteristic
668C22×C4C23×D6111yescharacteristic
669Q16—2444no—
670SD16—44no—
671SD16—2444no—
672SD16—2444no—
673D8—2444no—
674D8—2444no—
675C2×C8—614no—
676C2×C8C23×D6114yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—22no—
683C4⋊C4—612no—
684C4⋊C4—612no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—612no—
688C4⋊C4—612no—
689C4⋊C4—612no—
690C4⋊C4—1222no—
691C4⋊C4—1222no—
692C4⋊C4—1224no—
693C4⋊C4—1222no—
694C4⋊C4—1222no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1221no—
698C4⋊C4C23×D6112yes—
699C4⋊C4C23×D6112yes—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—1224no—
704C22⋊C4—1222no—
705C22⋊C4—1222no—
706C22⋊C4—1222no—
707C22⋊C4—1222no—
708C22⋊C4—1222no—
709C22⋊C4—1222no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—1222no—
713C22⋊C4—1222no—
714C22⋊C4—1222no—
715C22⋊C4—1222no—
716C22⋊C4—1222no—
717C22⋊C4—1222no—
718C42—22no—
719C42—612no—
720C42—612no—
721C42—612no—
722C42—612no—
723C42—1224no—
724C42—1222no—
725C42—1222no—
726C42D4×D6111yescharacteristic
727C42D4×D6111yescharacteristic
728C42C23×D6111yescharacteristic
729C42C23×D6111yescharacteristic
730C23—22no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—1222no—
735C23—1222no—
736C23—2442no—
737C23—2442no—
738C23—2442no—
739C23C2×D4×D6111yescharacteristic
740Q8—24no—
741Q8—81no—
742Q8—1224no—
743Q8—2442no—
744Q8—2442no—
745Q8—2442no—
746Q8—2442no—
747D4—22no—
748D4—22no—
749D4—42no—
750D4—1224no—
751D4—1224no—
752D4—4881no—
753D4—4884no—
754D4—2442no—
755D4—2442no—
756D4—2448no—
757D4—2444no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—82no—
766C2×C4—82no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—612no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—4882no—
776C2×C4—4882no—
777C2×C4—4884no—
778C2×C4—2444no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2442no—
782C2×C4C2×D4×D6111yescharacteristic
783C2×C4C2×D4×D6111yescharacteristic
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4C2×D4×D6111yescharacteristic
787C2×C4C24×D6111yescharacteristic
788C8—24no—
789C8—1224no—
790C22—21no—
791C22—21no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—84no—
796C22—4884no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22#1684056112yes—
804C22C22×D4×D6111yescharacteristic
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—1222no—
814C4—1222no—
815C4—1222no—
816C4—1222no—
817C4—2442no—
818C4—2442no—
819C4#1684059812yes—
820C2—22no—
821C2—82no—
822C2—4882no—
823C2—4882no—
824C2#2145947311yescharacteristic
825C2C2×#1684056111yescharacteristic
826C2#2146059511yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3110C2
socleC22×C61C23×D4
hypercenter#3110D61
hypocenterC61#61895
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3110

Complements

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

NH ≅ G/Ntype
1. #21459686C2semidirect
2. C2×#16840495C2semidirect
3. #21458908C2semidirect
4. #21458892C2semidirect
5. #21458592C2semidirect
6. #21458579C2semidirect
7. #21456840C2semidirect
8. #21456818C2semidirect
9. #21456808C2semidirect
10. #21456787C2semidirect
11. #21455993C2semidirect
12. #21455910C2semidirect
13. #21455869C2semidirect
14. #21454903C2semidirect
15. C61×#3110C2semidirect
16. #16840497C22semidirect
21. #16840491C22semidirect
22. #16840486C22semidirect
24. #16840473C22semidirect
43. #16840154C22semidirect
44. #16840151C22semidirect
46. #16840143C22semidirect
48. #16840124C22semidirect
49. #16840122C22semidirect
50. #16840115C22semidirect
52. #16840068C22semidirect
53. #16840065C22semidirect
54. #16840052C22semidirect
55. #16839987C22semidirect
56. #16839984C22semidirect
57. #16839982C22semidirect
58. #16839980C22semidirect
59. #16839978C22semidirect
60. #16839976C22semidirect
62. #16839957C22semidirect
69. #16839891C22semidirect
70. #16839890C22semidirect
71. #16839872C22semidirect
72. #16839866C22semidirect
73. #16839861C22semidirect
74. #16839847C22semidirect
75. #16839844C22semidirect
82. C61×#474C22semidirect
83. C61×#461C22semidirect
85. C61×#440C22semidirect
418. #3110D61semidirect
471. #474C2×D61semidirect
478. #461C2×D61semidirect
493. #440C2×D61semidirect
500. C61#61895semidirect

Maximal subgroups

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

subgroupindex
#214596862
C2×#168404952
#214589082
#214588922
#214585922
#214585792
#214568402
#214568182
#214568082
#214567872
#214559932
#214559102
#214558692
#214549032
C61×#31102
#6189561