Finite Group Databasebeta

← #30571178

Subgroups — #30571178

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#21459681C211yesmaximal, characteristic, complemented
2C2×#16840495C211yesmaximal, characteristic, complemented
3#21458902C214yesmaximal, complemented
4#21458890C214yesmaximal, complemented
5#21458594C214yesmaximal, complemented
6#21458577C214yesmaximal, complemented
7#21456835C212yesmaximal, complemented
8#21456824C211yesmaximal, characteristic, complemented
9#21456802C211yesmaximal, characteristic, complemented
10#21456781C212yesmaximal, complemented
11#21455987C212yesmaximal, complemented
12#21455918C211yesmaximal, characteristic, complemented
13#21455863C212yesmaximal, complemented
14#21454903C211yesmaximal, characteristic, complemented
15C61×#3109C211yesmaximal, characteristic, complemented
16#16840498C2212yescomplemented
17#16840495—22no—
18#16840495—22no—
19#16840495C2214yes—
20#16840495C2214yes—
21#16840487C2212yescomplemented
22#16840482C2212yescomplemented
23#16840481—22no—
24#16840469C2212yescomplemented
25#16840452—22no—
26#16840357—21no—
27#16840357—21no—
28#16840333—21no—
29#16840319C2211yescharacteristic
30C2×#14519773C2211yescharacteristic
31#16840293C2212yes—
32#16840293C2212yes—
33C2×#14519765C2211yescharacteristic
34C2×#14519764C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519760—21no—
37C2×#14519759—21no—
38#16840245—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×#14519742C2211yescharacteristic
41C2×#14519739C2211yescharacteristic
42C2×C4×C22⋊D61—21no—
43#16840156C2212yescomplemented
44#16840150C2214yes—
45#16840149C2212yescomplemented
46#16840145C2214yescomplemented
47#16840125C2214yes—
48#16840124C2212yescomplemented
49#16840122C2212yescomplemented
50#16840115C2214yescomplemented
51#16840097C2212yes—
52#16840072C2214yescomplemented
53#16840061C2214yescomplemented
54#16840042C2212yescomplemented
55#16839985C2214yescomplemented
56#16839983C2214yescomplemented
57#16839983C2214yescomplemented
58#16839977C2214yescomplemented
59#16839976C2214yescomplemented
60#16839975C2214yescomplemented
61#16839967C2212yescomplemented
62#16839961C2214yes—
63#16839955C2214yes—
64#16839920C2212yes—
65#16839915C2212yes—
66#16839913C2212yes—
67#16839900C2212yes—
68#16839895C2212yes—
69#16839891C2214yescomplemented
70#16839890C2214yescomplemented
71#16839868C2214yescomplemented
72#16839862C2214yescomplemented
73#16839859C2214yescomplemented
74#16839849C2214yescomplemented
75#16839842C2214yescomplemented
76#16839819C2211yescharacteristic
77#16839816C2212yes—
78#16839812C2212yes—
79C61×#532C2211yescharacteristic
80C2×C4×D4×C61C2211yescharacteristic
81C61×#481C2212yes—
82C61×#476C2212yescomplemented
83C61×#459C2212yescomplemented
84C61×#447C2212yes—
85C61×#442C2214yescomplemented
86C61×#432C2211yescharacteristic
87C22×Dic122D411yescharacteristic
88C22×Dic122C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C4×D61—21no—
93C2×Dic244C2314yes—
94C2×#11758190C2314yes—
95C2×#11758200C2314yes—
96C2×#11758200C2314yes—
97C2×#11758199C2314yes—
98#14519777C2311yescharacteristic
99#14519777C2311yescharacteristic
100#14519775—22no—
101#14519773—22no—
102#14519773C2314yes—
103#14519770—22no—
104#14519770—22no—
105#14519770—22no—
106#14519770—22no—
107#14519769—21no—
108#14519768C2312yes—
109#14519768C2312yes—
110#14519767—22no—
111#14519767—22no—
112#14519765—21no—
113#14519765—21no—
114#14519765C2312yes—
115#14519765C2312yes—
116#14519764—22no—
117#14519764—22no—
118#14519764C2312yes—
119#14519764C2312yes—
120#14519764C2314yes—
121#14519763—24no—
122#14519763—24no—
123#14519760—24no—
124#14519760—24no—
125#14519759—24no—
126#14519759—24no—
127#14519758—22no—
128#14519758—22no—
129#14519758—22no—
130#14519758—22no—
131#14519756—21no—
132#14519756—22no—
133#14519756—22no—
134#14519756C2312yes—
135#14519754—22no—
136#14519754—22no—
137Q8×Dic61—22no—
138C4×Dic122—21no—
139C4×Dic122D412yes—
140C4×Dic122D412yes—
141C4×Dic122C2312yes—
142C4×Dic122C2312yes—
143C4×Dic122C2312yes—
144#14519742—22no—
145#14519742C2312yes—
146#14519742C2314yes—
147#14519742C2312yes—
148D4×Dic61—22no—
149D4×Dic61—22no—
150D4×Dic61—22no—
151D4×Dic61C2312yes—
152D4×Dic61C2312yes—
153#14519739—22no—
154#14519739C2314yes—
155C4×C22⋊D61—24no—
156C4×C22⋊D61—24no—
157#14519736—21no—
158#14519736—22no—
159#14519733—22no—
160#14519733—22no—
161C2×C4⋊Dic61—22no—
162C2×C4⋊Dic61D411yescharacteristic
163C2×#11758196—21no—
164C2×#11758196D411yescharacteristic
165C2×#11758196D411yescharacteristic
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#14519710C2314yes—
175C4⋊#92418C2312yes—
176#14519706C2314yes—
177#14519706C2314yes—
178#14519702C2314yes—
179#14519700C2314yes—
180#14519700C2314yes—
181#14519699C2314yes—
182#14519698C2314yes—
183#14519697C2314yes—
184C22⋊#92418C2312yes—
185#14519688C2312yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C2×#41×C61—21no—
189C22×D4×C61C2311yescharacteristic
190C23×C4×C61—21no—
191C2×D8×C61C2314yes—
192C4⋊Q8×C61C2311yescharacteristic
193#127×C61C2311yescharacteristic
194#124×C61—21no—
195#121×C61—21no—
196#121×C61C2312yes—
197C4×D4×C61—21no—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2312yes—
201C4×D4×C61C2312yes—
202C4×D4×C61C2312yes—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#106×C61C2314yes—
207C4⋊C8×C61C2312yes—
208#102×C61C2314yes—
209#102×C61C2314yes—
210C22⋊C8×C61C2312yes—
211#97×C61C2312yes—
212C24×C61—21no—
213C23×D61—21no—
214#41×C61—44no—
215C2×Q8×C61—21no—
216C2×D4×C61—22no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—42no—
221C2×D4×C61C2412yes—
222C2×D4×C61C2412yes—
223C22×C4×C61—21no—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61—82no—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C2×C22⋊D61—24no—
232C2×C22⋊D61—24no—
233C2×C22⋊D61—44no—
234C2×C22⋊D61—82no—
235C22×Dic61—21no—
236C22×Dic61—22no—
237C22×Dic61—22no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C2×D244—21no—
243C2×D244—42no—
244C2×D244C2412yes—
245C2×C4×D61—24no—
246C2×C4×D61—82no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—42no—
250C2×Dic122—42no—
251C2×Dic122C2×D412yes—
252C2×Dic122C2×D412yes—
253C2×Dic122C2412yes—
254C2×Dic122C2412yes—
255D8×C61—44no—
256C2×C8×C61C2414yes—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2412yes—
260C4⋊C4×C61C2412yes—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—22no—
265C42×C61C2×D411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2411yescharacteristic
268C42×C61C2411yescharacteristic
269C22⋊Dic61—22no—
270C22⋊Dic61—24no—
271C22⋊Dic61—24no—
272C22⋊Dic61—22no—
273C22⋊Dic61—22no—
274C22⋊Dic61—22no—
275C22⋊Dic61—22no—
276C22⋊Dic61—22no—
277C22⋊Dic61—22no—
278#11758200—44no—
279#11758200—44no—
280#11758199—44no—
281#11758198—22no—
282#11758198—22no—
283#11758198—22no—
284#11758198—22no—
285#11758198—24no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—22no—
290C4⋊Dic61—22no—
291C4⋊Dic61C2×D412yes—
292C4⋊Dic61C2×D412yes—
293C4⋊Dic61C2412yes—
294#11758196—22no—
295#11758196—22no—
296#11758196—24no—
297#11758196—22no—
298#11758196—22no—
299#11758196—22no—
300#11758196—22no—
301#11758196C2×D412yes—
302#11758196C2×D412yes—
303#11758196C2×D412yes—
304#11758196C2×D412yes—
305C4×Dic61—22no—
306C4×Dic61—24no—
307C4×Dic61—22no—
308C4×Dic61—22no—
309C4×Dic61C2×D412yes—
310C4×Dic61C2×D412yes—
311C4×Dic61C2412yes—
312C4×Dic61C2412yes—
313C2×#92418C2414yes—
314Dic244—44no—
315#11758190—44no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61C22×D411yescharacteristic
322C22×D61—22no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326Q8×C61—42no—
327D4×C61—24no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—42no—
331D4×C61—42no—
332D4×C61—44no—
333D4×C61—81no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—41no—
339C2×C4×C61—44no—
340C2×C4×C61—42no—
341C2×C4×C61—82no—
342C2×C4×C61—82no—
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2511yescharacteristic
349C22⋊D61—48no—
350C22⋊D61—84no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—42no—
359C2×Dic61—82no—
360C2×Dic61—82no—
361C2×Dic61C22×D412yes—
362C2×Dic61C22×D412yes—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365D244—24no—
366D244—42no—
367C4×D61—84no—
368Dic122—24no—
369Dic122—24no—
370Dic122—42no—
371Dic122—42no—
372Dic122—42no—
373Dic122—81no—
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—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—84no—
386C22×C61#57512yes—
387C22×C61C23×D411yescharacteristic
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#58512yes—
400Dic61—22no—
401Dic61—22no—
402Dic61—22no—
403Dic61—22no—
404Dic61—42no—
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#3110—611no—
419#3109D6111yescharacteristic, complemented
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—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#533—611no—
443#532C2×D6111yescharacteristic
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#484—612no—
467#481C2×D6112yes—
468#479—614no—
469#478—614no—
470#476C2×D6112yescomplemented
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#459C2×D6112yescomplemented
482#451—612no—
483#450—612no—
484#450—612no—
485#448—612no—
486#447—612no—
487#447C2×D6112yes—
488#446—614no—
489#446—614no—
490#442C2×D6114yescomplemented
491#441—614no—
492#440—614no—
493#440—614no—
494C4×SD16—614no—
495C4×D8—614no—
496#432—611no—
497#432—612no—
498#432C2×D6111yescharacteristic
499#431—612no—
500C61#6189511yescharacteristic, complemented, Sylow
501C2×#41—21no—
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×SD16—614no—
514C2×D8—614no—
515C2×D8C22×D6114yes—
516C4⋊Q8—611no—
517C4⋊Q8—611no—
518C4⋊Q8—1222no—
519C4⋊Q8C22×D6111yescharacteristic
520#127—614no—
521#127—1222no—
522#127C22×D6111yescharacteristic
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—21no—
533#124—614no—
534#124—612no—
535#124—612no—
536#124—612no—
537#124—612no—
538#124—1222no—
539#124—1224no—
540#124—1224no—
541#124—1222no—
542#124—1221no—
543#124—1221no—
544#123—1224no—
545#123—1224no—
546#123—1224no—
547#123—1224no—
548#123—1222no—
549#123—1222no—
550#123—1222no—
551#123—1222no—
552C22⋊Q8—612no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555C22⋊Q8—1222no—
556C22⋊Q8—1222no—
557C22⋊Q8—1221no—
558#121—21no—
559#121C22×D6112yes—
560C4×Q8—612no—
561C4×Q8—612no—
562C4×Q8—612no—
563C4×Q8—612no—
564C4×Q8—614no—
565C4×Q8—612no—
566C4×Q8—612no—
567C4×Q8—612no—
568C4×Q8—1222no—
569C4×Q8—1222no—
570C4×Q8—1221no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—612no—
575C4×D4—612no—
576C4×D4—614no—
577C4×D4—1222no—
578C4×D4—1224no—
579C4×D4—1224no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4C22×D6112yes—
584C4×D4C22×D6112yes—
585C4×D4C22×D6112yes—
586#117—1222no—
587#117—1222no—
588#117—1222no—
589#117—1221no—
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#107—614no—
607#106C22×D6114yes—
608C4⋊C8—614no—
609C4⋊C8—614no—
610C4⋊C8—612no—
611C4⋊C8C22×D6112yes—
612#103—614no—
613#103—614no—
614#103—614no—
615#102—614no—
616#102—614no—
617#102—614no—
618#102C22×D6114yes—
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—44no—
629C2×Q8—21no—
630C2×Q8—612no—
631C2×Q8—612no—
632C2×Q8—612no—
633C2×Q8—612no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—2442no—
637C2×Q8—2442no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—42no—
643C2×D4—612no—
644C2×D4—1224no—
645C2×D4—1224no—
646C2×D4—1221no—
647C2×D4—4882no—
648C2×D4—2442no—
649C2×D4—2444no—
650C2×D4C23×D6112yes—
651C2×D4C23×D6112yes—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—82no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—1224no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1221no—
665C22×C4—4882no—
666C22×C4D4×D6111yescharacteristic
667C22×C4D4×D6111yescharacteristic
668C22×C4C23×D6111yescharacteristic
669Q16—2444no—
670SD16—2444no—
671SD16—2444no—
672SD16—2444no—
673D8—44no—
674D8—2444no—
675C2×C8—614no—
676C2×C8C23×D6114yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—612no—
680C4⋊C4—612no—
681C4⋊C4—612no—
682C4⋊C4—612no—
683C4⋊C4—612no—
684C4⋊C4—612no—
685C4⋊C4—612no—
686C4⋊C4—1224no—
687C4⋊C4—1222no—
688C4⋊C4—1222no—
689C4⋊C4—1222no—
690C4⋊C4—1222no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C4⋊C4—1221no—
694C4⋊C4—1222no—
695C4⋊C4—1222no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4C23×D6112yes—
699C4⋊C4C23×D6112yes—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1222no—
708C22⋊C4—1222no—
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—612no—
719C42—612no—
720C42—612no—
721C42—612no—
722C42—1224no—
723C42—1222no—
724C42—1222no—
725C42—1222no—
726C42D4×D6111yescharacteristic
727C42D4×D6111yescharacteristic
728C42C23×D6111yescharacteristic
729C42C23×D6111yescharacteristic
730C23—22no—
731C23—22no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—1222no—
736C23—2442no—
737C23—2442no—
738C23—2442no—
739C23C2×D4×D6111yescharacteristic
740Q8—42no—
741Q8—1224no—
742Q8—1224no—
743Q8—4881no—
744Q8—2442no—
745Q8—2442no—
746Q8—2442no—
747D4—22no—
748D4—24no—
749D4—22no—
750D4—42no—
751D4—42no—
752D4—44no—
753D4—81no—
754D4—1224no—
755D4—4884no—
756D4—2442no—
757D4—2448no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—41no—
763C2×C4—44no—
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—1222no—
776C2×C4—4884no—
777C2×C4—4882no—
778C2×C4—4882no—
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—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—4884no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22#1684055812yes—
804C22C22×D4×D6111yescharacteristic
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—42no—
811C4—42no—
812C4—1222no—
813C4—1222no—
814C4—1222no—
815C4—1222no—
816C4—2442no—
817C4—2442no—
818C4—2442no—
819C4#1684059812yes—
820C2—22no—
821C2—82no—
822C2—82no—
823C2—4882no—
824C2#2145947311yescharacteristic
825C2C2×#1684055811yescharacteristic
826C2#2146059511yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3109C2
socleC22×C61C23×D4
hypercenter#3109D61
hypocenterC61#61895
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #21459681C2semidirect
2. C2×#16840495C2semidirect
3. #21458902C2semidirect
4. #21458890C2semidirect
5. #21458594C2semidirect
6. #21458577C2semidirect
7. #21456835C2semidirect
8. #21456824C2semidirect
9. #21456802C2semidirect
10. #21456781C2semidirect
11. #21455987C2semidirect
12. #21455918C2semidirect
13. #21455863C2semidirect
14. #21454903C2semidirect
15. C61×#3109C2semidirect
16. #16840498C22semidirect
21. #16840487C22semidirect
22. #16840482C22semidirect
24. #16840469C22semidirect
43. #16840156C22semidirect
45. #16840149C22semidirect
46. #16840145C22semidirect
48. #16840124C22semidirect
49. #16840122C22semidirect
50. #16840115C22semidirect
52. #16840072C22semidirect
53. #16840061C22semidirect
54. #16840042C22semidirect
55. #16839985C22semidirect
56. #16839983C22semidirect
57. #16839983C22semidirect
58. #16839977C22semidirect
59. #16839976C22semidirect
60. #16839975C22semidirect
61. #16839967C22semidirect
69. #16839891C22semidirect
70. #16839890C22semidirect
71. #16839868C22semidirect
72. #16839862C22semidirect
73. #16839859C22semidirect
74. #16839849C22semidirect
75. #16839842C22semidirect
82. C61×#476C22semidirect
83. C61×#459C22semidirect
85. C61×#442C22semidirect
419. #3109D61semidirect
470. #476C2×D61semidirect
481. #459C2×D61semidirect
490. #442C2×D61semidirect
500. C61#61895semidirect

Maximal subgroups

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

subgroupindex
#214596812
C2×#168404952
#214589022
#214588902
#214585942
#214585772
#214568352
#214568242
#214568022
#214567812
#214559872
#214559182
#214558632
#214549032
C61×#31092
#6189561