Finite Group Databasebeta

← #30564917

Subgroups — #30564917

Order 15616.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459658C211yesmaximal, characteristic, complemented
2C2×#16840417C211yesmaximal, characteristic, complemented
3#21457917C214yesmaximal, complemented
4#21457797C214yesmaximal, complemented
5#21457379C214yesmaximal, complemented
6#21457349C214yesmaximal, complemented
7#21456848C212yesmaximal, complemented
8#21456643C211yesmaximal, characteristic, complemented
9#21456626C211yesmaximal, characteristic, complemented
10#21456602C212yesmaximal, complemented
11#21455959C212yesmaximal, complemented
12#21455081C211yesmaximal, characteristic, complemented
13#21455073C211yesmaximal, characteristic, complemented
14#21455041C212yesmaximal, complemented
15C61×#2973C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758222C2211yescharacteristic, complemented
18C2×#14519810C2212yescomplemented
19C2×#14519805C2212yescomplemented
20C2×#14519799C2214yescomplemented
21#16840461—22no—
22#16840458C2212yescomplemented
23#16840452C2212yescomplemented
24#16840441—22no—
25#16840421C2212yescomplemented
26#16840417—22no—
27#16840417—22no—
28#16840417C2214yes—
29#16840417C2214yescomplemented
30#16840408C2212yescomplemented
31#16840359—21no—
32#16840350—21no—
33#16840321—21no—
34C2×#14519777C2211yescharacteristic, complemented
35#16840296C2212yes—
36#16840273C2212yes—
37C2×#14519759—21no—
38C2×#14519759—21no—
39C2×#14519756C2211yescharacteristic
40C2×#14519756C2211yescharacteristic
41C2×#14519756C2211yescharacteristic, complemented
42C2×#14519751C2211yescharacteristic
43C2×#14519748—21no—
44#16840235—21no—
45C2×C4×D244C2211yescharacteristic, complemented
46C2×C4⋊C4×D61—21no—
47#16840156C2214yescomplemented
48#16840131C2214yescomplemented
49#16840104C2214yescomplemented
50#16840098C2212yescomplemented
51#16840093C2212yescomplemented
52#16840093C2212yescomplemented
53#16840076C2212yes—
54#16840063C2214yescomplemented
55#16840020C2214yescomplemented
56#16840008C2214yescomplemented
57#16840003C2214yescomplemented
58#16839991C2214yescomplemented
59#16839978C2214yescomplemented
60#16839973C2214yescomplemented
61#16839968C2214yescomplemented
62#16839926C2214yescomplemented
63#16839926C2214yescomplemented
64#16839926C2214yescomplemented
65#16839920C2212yescomplemented
66#16839920C2212yescomplemented
67#16839920C2212yescomplemented
68#16839915C2212yescomplemented
69#16839915C2212yescomplemented
70#16839909C2214yescomplemented
71#16839909C2214yescomplemented
72#16839903C2212yes—
73#16839903C2212yes—
74#16839898C2212yes—
75#16839875C2214yescomplemented
76#16839864C2214yescomplemented
77#16839764C2212yescomplemented
78#16839764C2212yescomplemented
79#16839759C2214yescomplemented
80C2×C4×D4×C61C2211yescharacteristic
81C61×#435C2214yescomplemented
82C61×#435C2214yescomplemented
83C61×#432C2212yescomplemented
84C61×#407C2211yescharacteristic
85C61×#407C2211yescharacteristic
86C2×C22⋊C8×C61C2212yescomplemented
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—22no—
90C2×#11758222—44no—
91C2×#11758222—44no—
92C2×#11758222C2314yes—
93C2×#11758222C2312yes—
94C2×#11758222C2312yes—
95C2×#11758222C2312yes—
96C22×Dic122C2311yescharacteristic
97C22×Dic122C2311yescharacteristic
98C22×Dic122C2311yescharacteristic
99C22×D244C2311yescharacteristic
100C22×D244C2311yescharacteristic
101C22×C22⋊D61—21no—
102C22×C22⋊D61—21no—
103C22×C22⋊D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61—21no—
106C22×C4×D61—21no—
107#14519810—44no—
108#14519805—44no—
109#14519799—48no—
110C2×Dic244C2314yes—
111C2×Dic244C2314yes—
112C2×#11758190C2314yes—
113C2×#11758190C2314yes—
114C2×#11758190C2314yes—
115C2×D488C2314yes—
116#14519777—22no—
117#14519777C2314yes—
118#14519772—22no—
119#14519771—22no—
120#14519770—22no—
121#14519769C2312yes—
122#14519767—22no—
123#14519765C2312yes—
124#14519763—22no—
125#14519762—22no—
126#14519760—22no—
127#14519760—22no—
128#14519759—22no—
129#14519759—24no—
130#14519759—24no—
131#14519759—24no—
132#14519759—24no—
133#14519758—22no—
134#14519756—21no—
135#14519756—21no—
136#14519756—21no—
137#14519756—21no—
138#14519756—22no—
139#14519756C2312yes—
140#14519756C2312yes—
141#14519756C2314yes—
142#14519756C2312yes—
143#14519756C2312yes—
144#14519756C2312yes—
145#14519755—22no—
146#14519751—21no—
147#14519751—21no—
148#14519751C2312yes—
149#14519751C2312yes—
150#14519751C2312yes—
151#14519750—22no—
152#14519749—22no—
153#14519749—22no—
154#14519748—24no—
155#14519748—24no—
156#14519746—22no—
157#14519745—22no—
158C4×Dic122C2312yes—
159C4×D244—22no—
160C4×D244C2312yes—
161C4×D244C2314yes—
162C4×C22⋊D61—22no—
163C4×C22⋊D61—22no—
164C4×C22⋊D61—22no—
165#14519737—22no—
166#14519737—22no—
167#14519736C2312yes—
168#14519734—22no—
169#14519733—22no—
170C2×C4⋊Dic61—21no—
171C2×C4⋊Dic61—21no—
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2311yescharacteristic
174C2×C4⋊Dic61C2311yescharacteristic
175C2×#11758196—21no—
176C2×#11758196—21no—
177C2×#11758196—21no—
178C4⋊C4×D61—24no—
179C4⋊C4×D61—24no—
180C2×C22⋊Dic61—21no—
181C2×C22⋊Dic61—21no—
182C2×C22⋊Dic61—21no—
183C2×#11758198—21no—
184C2×#11758198—21no—
185C22⋊C4×D61—22no—
186#14519711C2314yes—
187#14519709C2314yes—
188#14519702C2314yes—
189#14519702C2314yes—
190#14519702C2314yes—
191#14519702C2314yes—
192#14519702C2314yes—
193#14519699C2314yes—
194#14519699C2314yes—
195#14519699C2314yes—
196C22×D4×C61D411yescharacteristic
197C23×C4×C61C2311yescharacteristic
198C23×C4×C61C2311yescharacteristic
199C2×M16×C61C2312yes—
200C2×M16×C61C2312yes—
201C22×C8×C61C2314yes—
202C4×D4×C61D412yes—
203C4×D4×C61D412yes—
204C4×D4×C61C2312yes—
205C4×D4×C61C2312yes—
206C2×C4⋊C4×C61D411yescharacteristic
207C2×C22⋊C4×C61D411yescharacteristic
208C2×C22⋊C4×C61D411yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C4⋊C8×C61C2314yes—
211C22⋊C8×C61C2312yes—
212C22⋊C8×C61C2312yes—
213C22⋊C8×C61C2314yes—
214C22⋊C8×C61C2312yes—
215C22⋊C8×C61C2312yes—
216#97×C61C2314yes—
217C24×C61C2×D411yescharacteristic
218C24×C61C2×D411yescharacteristic
219C23×D61—21no—
220C23×D61—21no—
221C2×D4×C61—42no—
222C2×D4×C61C2×D412yes—
223C2×D4×C61C2×D412yes—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C22×C4×C61C2412yes—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—24no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—22no—
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61—44no—
246C2×C22⋊D61—44no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253#11758222—24no—
254#11758222—28no—
255#11758222—24no—
256#11758222—42no—
257#11758222—44no—
258#11758222—42no—
259#11758222—44no—
260#11758222—44no—
261#11758222—44no—
262#11758222—48no—
263C2×D244—21no—
264C2×D244—24no—
265C2×D244—21no—
266C2×D244—42no—
267C2×D244C2412yes—
268C2×D244C2412yes—
269C2×C4×D61—24no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—24no—
273C2×C4×D61—22no—
274C2×C4×D61—22no—
275C2×C4×D61—44no—
276C2×C4×D61—44no—
277C2×C4×D61—44no—
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—21no—
281C2×Dic122—42no—
282C2×Dic122—42no—
283C2×Dic122—42no—
284C2×Dic122C2412yes—
285C2×Dic122C2412yes—
286C2×Dic122C2412yes—
287M16×C61—42no—
288M16×C61—42no—
289C2×C8×C61—44no—
290C2×C8×C61C2414yes—
291C2×C8×C61C2414yes—
292C4⋊C4×C61C2×D412yes—
293C4⋊C4×C61C2×D412yes—
294C22⋊C4×C61C2×D412yes—
295C22⋊C4×C61C2×D412yes—
296C22⋊C4×C61C2×D412yes—
297C22⋊C4×C61C2×D412yes—
298C42×C61C2×D412yes—
299C42×C61C2412yes—
300C22⋊Dic61—22no—
301C22⋊Dic61—22no—
302C22⋊Dic61—22no—
303C22⋊Dic61—24no—
304C22⋊Dic61—22no—
305C22⋊Dic61—22no—
306C22⋊Dic61—22no—
307#11758198—22no—
308#11758198—22no—
309#11758198—22no—
310#11758198—24no—
311#11758198—22no—
312#11758198—22no—
313#11758198—22no—
314C4⋊Dic61—24no—
315C4⋊Dic61—24no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61C2412yes—
320C4⋊Dic61C2412yes—
321C4⋊Dic61C2412yes—
322#11758196—24no—
323#11758196—22no—
324#11758196—22no—
325#11758196—22no—
326#11758196—22no—
327#11758196—22no—
328#11758196—22no—
329#11758196—22no—
330#11758196—22no—
331C4×Dic61—22no—
332C4×Dic61—22no—
333Dic244—44no—
334Dic244—44no—
335D488—28no—
336#11758190—28no—
337#11758190—44no—
338#11758190—44no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61C22×D411yescharacteristic
346C23×C61C22×D412yes—
347C23×C61C22×D411yescharacteristic
348C23×C61C22×D411yescharacteristic
349C22×D61—24no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—81no—
356C22×D61—81no—
357D4×C61—42no—
358D4×C61—42no—
359C2×C4×C61—22no—
360C2×C4×C61—24no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—42no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61C22×D412yes—
371C2×C4×C61C22×D412yes—
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D412yes—
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C2511yescharacteristic
377C22⋊D61—44no—
378C22⋊D61—48no—
379C22⋊D61—44no—
380C22⋊D61—44no—
381C22⋊D61—44no—
382C22⋊D61—82no—
383C22⋊D61—82no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—42no—
391C2×Dic61—42no—
392C2×Dic61—42no—
393C2×Dic61—42no—
394C2×Dic61—81no—
395C2×Dic61—81no—
396D244—24no—
397D244—22no—
398D244—24no—
399D244—81no—
400D244H(5,𝔽2)14yes—
401C4×D61—44no—
402C4×D61—48no—
403C4×D61—44no—
404C4×D61—48no—
405C4×D61—82no—
406C4×D61—82no—
407Dic122—24no—
408Dic122—22no—
409Dic122—24no—
410Dic122—22no—
411Dic122—42no—
412Dic122—42no—
413Dic122—81no—
414C8×C61—24no—
415C8×C61—24no—
416#61575—611nomaximal, Sylow
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—22no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—22no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—22no—
428C22×C61—82no—
429C22×C61—82no—
430C22×C61#57512yes—
431C22×C61C23×D411yescharacteristic
432C2×D61—24no—
433C2×D61—48no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—42no—
439C2×D61—162no—
440C4×C61—22no—
441C4×C61—21no—
442C4×C61—21no—
443C4×C61—22no—
444C4×C61—21no—
445C4×C61—22no—
446C4×C61C2×H(5,𝔽2)12yes—
447Dic61—42no—
448Dic61—42no—
449Dic61—42no—
450Dic61—42no—
451Dic61—42no—
452Dic61—42no—
453#3505—611no—
454C2×#547—611no—
455#3315—614no—
456#3307—614no—
457#3269—614no—
458#3267—614no—
459#3218—612no—
460#3195—611no—
461#3193—611no—
462#3190—612no—
463#3114—612no—
464#3007—611no—
465#3006—611no—
466#3002—612no—
467#2973D6111yescharacteristic, complemented
468C2×C61—22no—
469C2×C61—41no—
470C2×C61—41no—
471C2×C61—42no—
472C2×C61#348411yescharacteristic
473C2×C61C2×#57511yescharacteristic
474C2×C61#358611yescharacteristic
475D61—44no—
476D61—82no—
477C22×#41—611no—
478C22×#41—611no—
479C2×#137—612no—
480C2×AGL(1,ℤ/8)—612no—
481C2×#135—614no—
482#553—612no—
483#553—1222no—
484#552—612no—
485#551—1222no—
486#548—612no—
487#547—614no—
488#547—614no—
489#547—1222no—
490#547—1222no—
491#546—612no—
492#539—1221no—
493#538—1221no—
494#534—1221no—
495C2×C4⋊Q8—611no—
496#529—612no—
497#525—612no—
498C2×#123—1221no—
499C2×#123—1221no—
500C2×C22⋊Q8—611no—
501C2×C22⋊Q8—611no—
502C2×C22⋊Q8—611no—
503C2×#121—611no—
504C2×#121—1221no—
505#518—1221no—
506C2×C4×D4—611no—
507C2×C4×D4C2×D6111yescharacteristic
508C22×C4⋊C4—1221no—
509#497—614no—
510#491—614no—
511#485—614no—
512#484—612no—
513#483—612no—
514#483—612no—
515#480—612no—
516#478—614no—
517#470—614no—
518#468—614no—
519#467—614no—
520#465—614no—
521#463—614no—
522#462—614no—
523#461—614no—
524#452—614no—
525#452—614no—
526#452—614no—
527#451—612no—
528#451—612no—
529#451—612no—
530#450—612no—
531#450—612no—
532#449—614no—
533#449—614no—
534#448—612no—
535#448—612no—
536#447—612no—
537#442—614no—
538#440—614no—
539#435C2×D6114yescomplemented
540#435C2×D6114yescomplemented
541#432C2×D6112yescomplemented
542#417—612no—
543#417—612no—
544#416—614no—
545#407C2×D6111yescharacteristic
546#407C2×D6111yescharacteristic
547C2×C22⋊C8C2×D6112yescomplemented
548C61#6157511yescharacteristic, complemented, Sylow
549C2×#41—614no—
550C2×#41—612no—
551C2×#41—612no—
552C2×#41—612no—
553C2×#41—1221no—
554C2×#41—1221no—
555C2×#41—1222no—
556C2×#41—2444no—
557C2×#41—2444no—
558C22×Q8—611no—
559C22×Q8—611no—
560C22×Q8—611no—
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—1221no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4D24411yescharacteristic
567C23×C4—1221no—
568C23×C4—1221no—
569C23×C4—1221no—
570C23×C4C22×D6111yescharacteristic
571C23×C4C22×D6111yescharacteristic
572#137—2444no—
573AGL(1,ℤ/8)—2444no—
574#135—2448no—
575C2×Q16—614no—
576C2×Q16—614no—
577C2×SD16—614no—
578C2×SD16—614no—
579C2×SD16—614no—
580C2×D8—614no—
581C2×M16C22×D6112yes—
582C2×M16C22×D6112yes—
583C22×C8C22×D6114yes—
584C4⋊Q8—614no—
585C4⋊Q8—1222no—
586#126—1222no—
587#126—1222no—
588#126—1222no—
589#125—612no—
590#125—1222no—
591#124—612no—
592#124—1222no—
593#123—1222no—
594#123—1222no—
595#123—1222no—
596#123—1222no—
597#123—1224no—
598#123—1224no—
599#123—1224no—
600#123—1224no—
601#123—1222no—
602C22⋊Q8—612no—
603C22⋊Q8—612no—
604C22⋊Q8—612no—
605C22⋊Q8—612no—
606C22⋊Q8—614no—
607C22⋊Q8—612no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1222no—
612C22⋊Q8—1221no—
613C22⋊Q8—1222no—
614#121—612no—
615#121—612no—
616#121—612no—
617#121—1224no—
618#121—1224no—
619#121—1222no—
620#121—1222no—
621#121—1221no—
622#121—1221no—
623#121—1222no—
624#120—1222no—
625#120—1222no—
626C4×Q8—612no—
627C4×D4—614no—
628C4×D4—612no—
629C4×D4—1222no—
630C4×D4—1222no—
631C4×D4—1222no—
632C4×D4—1222no—
633C4×D4—1222no—
634C4×D4—1222no—
635C4×D4D24412yes—
636C4×D4D24412yes—
637C4×D4C22×D6112yes—
638C4×D4C22×D6112yes—
639#117—612no—
640#117—1222no—
641#117—1222no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4—1221no—
647C2×C4⋊C4—1221no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1224no—
651C2×C4⋊C4—1224no—
652C2×C4⋊C4D24411yescharacteristic
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1222no—
659C2×C22⋊C4D24411yescharacteristic
660C2×C22⋊C4D24411yescharacteristic
661C2×C42C22×D6111yescharacteristic
662#107—614no—
663#106—614no—
664C4⋊C8C22×D6114yes—
665#103—614no—
666#103—614no—
667#103—614no—
668#103—614no—
669#103—614no—
670#102—614no—
671#102—614no—
672#102—614no—
673C22⋊C8C22×D6112yes—
674C22⋊C8C22×D6112yes—
675C22⋊C8C22×D6114yes—
676C22⋊C8C22×D6112yes—
677C22⋊C8C22×D6112yes—
678#97C22×D6114yes—
679C24—1221no—
680C24—1221no—
681C24C2×D24411yescharacteristic
682C24C2×D24411yescharacteristic
683#41—1228no—
684#41—1224no—
685#41—1224no—
686#41—2444no—
687#41—2444no—
688#41—2442no—
689#41—2442no—
690#41—2448no—
691#41—2444no—
692#41—2444no—
693C2×Q8—612no—
694C2×Q8—612no—
695C2×Q8—612no—
696C2×Q8—1221no—
697C2×Q8—1221no—
698C2×Q8—1221no—
699C2×Q8—2442no—
700C2×Q8—2442no—
701C2×Q8—2442no—
702C2×D4—42no—
703C2×D4—612no—
704C2×D4—612no—
705C2×D4—1224no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—1222no—
709C2×D4—1222no—
710C2×D4—1222no—
711C2×D4—1224no—
712C2×D4—1222no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—2442no—
716C2×D4—2444no—
717C2×D4—2444no—
718C2×D4—2444no—
719C2×D4C2×D24412yes—
720C2×D4C2×D24412yes—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1222no—
730C22×C4—1222no—
731C22×C4—1224no—
732C22×C4—1224no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—2444no—
736C22×C4—2444no—
737C22×C4—2444no—
738C22×C4C2×D24411yescharacteristic
739C22×C4C2×D24411yescharacteristic
740C22×C4C2×D24411yescharacteristic
741C22×C4C2×D24411yescharacteristic
742C22×C4C2×D24411yescharacteristic
743C22×C4C2×D24411yescharacteristic
744C22×C4C2×D24412yes—
745C22×C4C23×D6111yescharacteristic
746C22×C4C23×D6111yescharacteristic
747C22×C4C23×D6111yescharacteristic
748C22×C4C23×D6112yes—
749Q16—2444no—
750Q16—2444no—
751SD16—1228no—
752SD16—2444no—
753SD16—2444no—
754D8—1228no—
755M16—42no—
756M16—42no—
757C2×C8—44no—
758C2×C8C23×D6114yes—
759C2×C8C23×D6114yes—
760C4⋊C4—612no—
761C4⋊C4—612no—
762C4⋊C4—612no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1224no—
767C4⋊C4—1222no—
768C4⋊C4—1222no—
769C4⋊C4—1224no—
770C4⋊C4—1222no—
771C4⋊C4—1222no—
772C4⋊C4—1224no—
773C4⋊C4—1222no—
774C4⋊C4—1222no—
775C4⋊C4—1222no—
776C4⋊C4—1222no—
777C4⋊C4C2×D24412yes—
778C4⋊C4C2×D24412yes—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—1224no—
783C22⋊C4—1222no—
784C22⋊C4—1222no—
785C22⋊C4—1222no—
786C22⋊C4—1222no—
787C22⋊C4—1224no—
788C22⋊C4—1222no—
789C22⋊C4—1222no—
790C22⋊C4—1222no—
791C22⋊C4—1222no—
792C22⋊C4—1222no—
793C22⋊C4C2×D24412yes—
794C22⋊C4C2×D24412yes—
795C22⋊C4C2×D24412yes—
796C22⋊C4C2×D24412yes—
797C42—1222no—
798C42—1222no—
799C42C2×D24412yes—
800C42C23×D6112yes—
801C23—22no—
802C23—22no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—1224no—
808C23—1222no—
809C23—1222no—
810C23—4881no—
811C23—4881no—
812C23—2442no—
813C23—2442no—
814C23—2442no—
815C23C22×D24411yescharacteristic
816C23C22×D24412yes—
817C23C22×D24411yescharacteristic
818C23C22×D24411yescharacteristic
819Q8—1224no—
820Q8—1222no—
821Q8—1224no—
822Q8—1222no—
823Q8—4881no—
824Q8—2442no—
825Q8—2442no—
826D4—42no—
827D4—42no—
828D4—614no—
829D4—1224no—
830D4—1222no—
831D4—1224no—
832D4—4881no—
833D4—4882no—
834D4—4882no—
835D4—2444no—
836D4—2448no—
837D4—2444no—
838D4—2444no—
839D4—2444no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—4882no—
858C2×C4—4882no—
859C2×C4—4881no—
860C2×C4—4881no—
861C2×C4—2448no—
862C2×C4—2444no—
863C2×C4—2444no—
864C2×C4—2448no—
865C2×C4—2442no—
866C2×C4—2442no—
867C2×C4—2442no—
868C2×C4—2442no—
869C2×C4C22×D24412yes—
870C2×C4C22×D24412yes—
871C2×C4C22×D24411yescharacteristic
872C2×C4C22×D24412yes—
873C2×C4C22×D24411yescharacteristic
874C2×C4C22×D24411yescharacteristic
875C2×C4C24×D6111yescharacteristic
876C8—24no—
877C8—24no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—82no—
890C22—82no—
891C22—1224no—
892C22—9762no—
893C22—2448no—
894C22—2442no—
895C22—2442no—
896C22—2442no—
897C22—2442no—
898C22—2442no—
899C22#1684056212yes—
900C22C23×D24411yescharacteristic
901C4—22no—
902C4—22no—
903C4—21no—
904C4—22no—
905C4—21no—
906C4—21no—
907C4—2442no—
908C4—2442no—
909C4—2442no—
910C4—2442no—
911C4—2442no—
912C4—2442no—
913C4H(5,𝔽2)×D6112yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—4882no—
919C2—2444no—
920C2#2145945511yescharacteristic
921C2C2×#1684056211yescharacteristic
922C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2973C2
socleC22×C61C23×D4
hypercenter#2973D61
hypocenterC61#61575
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
1. #21459658C2semidirect
2. C2×#16840417C2semidirect
3. #21457917C2semidirect
4. #21457797C2semidirect
5. #21457379C2semidirect
6. #21457349C2semidirect
7. #21456848C2semidirect
8. #21456643C2semidirect
9. #21456626C2semidirect
10. #21456602C2semidirect
11. #21455959C2semidirect
12. #21455081C2semidirect
13. #21455073C2semidirect
14. #21455041C2semidirect
15. C61×#2973C2semidirect
17. C22×#11758222C22semidirect
18. C2×#14519810C22semidirect
19. C2×#14519805C22semidirect
20. C2×#14519799C22semidirect
22. #16840458C22semidirect
23. #16840452C22semidirect
25. #16840421C22semidirect
29. #16840417C22semidirect
30. #16840408C22semidirect
34. C2×#14519777C22semidirect
41. C2×#14519756C22semidirect
45. C2×C4×D244C22semidirect
47. #16840156C22semidirect
48. #16840131C22semidirect
49. #16840104C22semidirect
50. #16840098C22semidirect
51. #16840093C22semidirect
52. #16840093C22semidirect
54. #16840063C22semidirect
55. #16840020C22semidirect
56. #16840008C22semidirect
57. #16840003C22semidirect
58. #16839991C22semidirect
59. #16839978C22semidirect
60. #16839973C22semidirect
61. #16839968C22semidirect
62. #16839926C22semidirect
63. #16839926C22semidirect
64. #16839926C22semidirect
65. #16839920C22semidirect
66. #16839920C22semidirect
67. #16839920C22semidirect
68. #16839915C22semidirect
69. #16839915C22semidirect
70. #16839909C22semidirect
71. #16839909C22semidirect
75. #16839875C22semidirect
76. #16839864C22semidirect
77. #16839764C22semidirect
78. #16839764C22semidirect
79. #16839759C22semidirect
81. C61×#435C22semidirect
82. C61×#435C22semidirect
83. C61×#432C22semidirect
86. C2×C22⋊C8×C61C22semidirect
467. #2973D61semidirect
539. #435C2×D61semidirect
540. #435C2×D61semidirect
541. #432C2×D61semidirect
547. C2×C22⋊C8C2×D61semidirect
548. C61#61575semidirect

Maximal subgroups

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

subgroupindex
#214596582
C2×#168404172
#214579172
#214577972
#214573792
#214573492
#214568482
#214566432
#214566262
#214566022
#214559592
#214550812
#214550732
#214550412
C61×#29732
#6157561