Finite Group Databasebeta

← #30548499

Subgroups — #30548499

Order 15616.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459208C211yesmaximal, characteristic, complemented
2C2×#16840241C211yesmaximal, characteristic, complemented
3#21456093C214yesmaximal, complemented
4#21456078C214yesmaximal, complemented
5#21456030C214yesmaximal, complemented
6#21456015C214yesmaximal, complemented
7#21455740C212yesmaximal, complemented
8#21455626C211yesmaximal, characteristic, complemented
9#21455616C211yesmaximal, characteristic, complemented
10#21455287C211yesmaximal, characteristic, complemented
11#21455058C212yesmaximal, complemented
12#21454643C212yesmaximal, complemented
13AGL(1,ℤ/8)×Dic61C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3036C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C2×#14519807C2212yes—
18#16840381C2212yescomplemented
19#16840381C2212yescomplemented
20#16840373C2212yescomplemented
21#16840366C2212yescomplemented
22#16840357—21no—
23#16840357—21no—
24#16840349—21no—
25#16840349—21no—
26#16840319C2211yescharacteristic
27#16840292—22no—
28#16840292—22no—
29#16840269C2212yes—
30#16840241—22no—
31#16840241—22no—
32#16840241C2214yes—
33#16840241C2214yes—
34#41×Dic61C2212yes—
35C2×C4×Dic122C2211yescharacteristic
36C2×#14519742C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×#14519737—21no—
40C2×#14519734C2211yescharacteristic
41C2×#14519733—21no—
42C22×#11758196—21no—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840096C2214yescomplemented
45#16840091C2214yescomplemented
46#16840079C2214yescomplemented
47#16840074C2214yescomplemented
48#16840070C2214yescomplemented
49#16840062C2214yescomplemented
50#16840058C2212yescomplemented
51#16840052C2212yescomplemented
52#16840048C2212yescomplemented
53#16840042C2212yescomplemented
54#16839981C2214yescomplemented
55#16839969C2212yescomplemented
56#16839959C2212yescomplemented
57#16839921C2214yes—
58#16839921C2214yes—
59#16839904C2214yes—
60#16839904C2214yes—
61#16839874C2214yescomplemented
62#16839866C2214yescomplemented
63#16839863C2214yescomplemented
64#16839859C2214yescomplemented
65#16839854C2214yescomplemented
66#16839853C2214yescomplemented
67SD16×Dic61C2214yescomplemented
68D8×Dic61C2214yescomplemented
69#16839822C2214yescomplemented
70#16839822C2214yescomplemented
71#16839804C2212yes—
72#16839802C2212yes—
73#16839786C2211yescharacteristic
74#16839772C2212yes—
75#16839767C2212yes—
76#16839763C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C2×AGL(1,ℤ/8)×C61C2212yes—
80C61×#532C2211yescharacteristic
81C2×C4×D4×C61C2211yescharacteristic
82C61×#463C2214yescomplemented
83C61×#461C2212yescomplemented
84C61×#459C2212yescomplemented
85C61×#423C2211yescharacteristic
86C61×#417C2212yes—
87C2×#11758224—24no—
88C2×#11758224—22no—
89C2×#11758224—24no—
90C2×#11758224C2314yes—
91C22×Dic122C2311yescharacteristic
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C23×Dic61—21no—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97#14519807—28no—
98C2×#11758202C2314yes—
99C2×#11758200C2314yes—
100C2×#11758194C2312yes—
101#14519777C2311yescharacteristic
102#14519777C2311yescharacteristic
103#14519772—22no—
104#14519772—22no—
105#14519770—22no—
106#14519770—22no—
107#14519769C2312yes—
108#14519767—22no—
109#14519767—22no—
110#14519763—22no—
111#14519763—22no—
112#14519761—22no—
113#14519761—22no—
114#14519758—22no—
115#14519758—22no—
116#14519758—22no—
117#14519756—21no—
118#14519756—21no—
119#14519754—22no—
120#14519754—22no—
121#14519753C2312yes—
122#14519753C2312yes—
123#14519749—22no—
124#14519749—22no—
125#14519748C2312yes—
126#14519748C2312yes—
127#14519745—22no—
128Q8×Dic61C2312yes—
129Q8×Dic61C2312yes—
130C4×Dic122—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122C2312yes—
135C4×Dic122C2312yes—
136#14519742—22no—
137#14519742C2314yes—
138D4×Dic61—22no—
139D4×Dic61—22no—
140D4×Dic61—22no—
141D4×Dic61C2314yes—
142D4×Dic61C2312yes—
143D4×Dic61C2312yes—
144C4×C22⋊D61—22no—
145C4×C22⋊D61—22no—
146C4×C22⋊D61—24no—
147C4×C22⋊D61—24no—
148#14519737—24no—
149#14519737—24no—
150#14519736—22no—
151#14519736C2312yes—
152#14519734D412yes—
153#14519734D412yes—
154#14519734C2312yes—
155#14519734C2312yes—
156#14519733—24no—
157#14519733—24no—
158C2×C4⋊Dic61C2311yescharacteristic
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196—21no—
162C2×#11758196—24no—
163C2×#11758196—24no—
164C2×#11758196D411yescharacteristic
165C2×#11758196D411yescharacteristic
166C4⋊C4×D61—22no—
167C4⋊C4×D61C2314yes—
168C2×C22⋊Dic61—21no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61—22no—
174C2×C4×Dic61C2311yescharacteristic
175#14519711C2314yes—
176#14519710C2314yes—
177#14519709C2314yes—
178#14519708C2314yes—
179C4⋊#92418C2312yes—
180C4⋊#92418C2312yes—
181#14519702C2314yes—
182#14519702C2314yes—
183#14519701C2314yes—
184#14519698C2314yes—
185#14519698C2314yes—
186#14519698C2314yes—
187#14519689C2314yes—
188#14519689C2314yes—
189#14519687C2314yes—
190C8×Dic61C2314yes—
191C2×#41×C61C2312yes—
192C22×D4×C61C2311yescharacteristic
193C23×C4×C61—21no—
194AGL(1,ℤ/8)×C61—28no—
195C2×SD16×C61C2314yes—
196C2×D8×C61C2314yes—
197C2×M16×C61C2312yes—
198C4⋊Q8×C61C2311yescharacteristic
199#127×C61C2311yescharacteristic
200#124×C61C2312yes—
201#121×C61—21no—
202#121×C61—21no—
203C4×D4×C61—21no—
204C4×D4×C61—21no—
205C4×D4×C61—21no—
206C4×D4×C61—21no—
207C4×D4×C61C2312yes—
208C4×D4×C61C2312yes—
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61—21no—
211C2×C42×C61C2311yescharacteristic
212C4⋊C8×C61C2312yes—
213C4⋊C8×C61C2312yes—
214#103×C61C2314yes—
215#102×C61C2314yes—
216C24×C61—21no—
217C23×D61C2×D411yescharacteristic
218#41×C61—24no—
219#41×C61—24no—
220C2×Q8×C61C2412yes—
221C2×D4×C61—22no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—22no—
226C2×D4×C61#4114yes—
227C2×D4×C61C2412yes—
228C2×D4×C61C2412yes—
229C22×C4×C61—21no—
230C22×C4×C61—22no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—82no—
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C2×C22⋊D61—28no—
238C2×C22⋊D61—24no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—22no—
241C22×Dic61—28no—
242C22×Dic61—21no—
243C22×Dic61—24no—
244C22×Dic61—21no—
245C22×Dic61—24no—
246C22×Dic61—22no—
247C22×Dic61—22no—
248C22×Dic61—82no—
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251C22×Dic61C2×D411yescharacteristic
252#11758224—216no—
253#11758224—28no—
254#11758224—28no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—24no—
258C2×C4×D61—82no—
259C2×C4×D61C2×D412yes—
260C2×C4×D61C2412yes—
261C2×Dic122—21no—
262C2×Dic122—22no—
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122#4114yes—
266C2×Dic122C2412yes—
267SD16×C61—28no—
268D8×C61—28no—
269M16×C61—24no—
270C2×C8×C61C2414yes—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C2412yes—
275C22⋊C4×C61—22no—
276C22⋊C4×C61—22no—
277C22⋊C4×C61—22no—
278C22⋊C4×C61—22no—
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2411yescharacteristic
282C42×C61C2411yescharacteristic
283C22⋊Dic61—22no—
284C22⋊Dic61—24no—
285C22⋊Dic61—22no—
286C22⋊Dic61—22no—
287C22⋊Dic61—22no—
288C22⋊Dic61—22no—
289#11758202—28no—
290#11758200—28no—
291#11758198—22no—
292#11758198—22no—
293#11758198C2×D412yes—
294#11758198C2×D412yes—
295#11758198C2×D412yes—
296#11758198C2×D412yes—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—22no—
301C4⋊Dic61—22no—
302C4⋊Dic61C2412yes—
303C4⋊Dic61C2412yes—
304C4⋊Dic61C2412yes—
305#11758196—22no—
306#11758196—22no—
307#11758196—22no—
308#11758196—22no—
309#11758196—24no—
310#11758196—24no—
311#11758196—22no—
312#11758196—22no—
313#11758196C2×D412yes—
314#11758196C2×D412yes—
315#11758196C2×D412yes—
316#11758196C2×D412yes—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—24no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323C4×Dic61C2×D412yes—
324C4×Dic61C2412yes—
325#11758194—24no—
326C2×#92418C2414yes—
327C23×C61—24no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61C22×D411yescharacteristic
333C22×D61—22no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61C22×D412yes—
337Q8×C61—22no—
338Q8×C61—22no—
339D4×C61—24no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—44no—
344D4×C61—81no—
345D4×C61—81no—
346D4×C61C2×#4114yes—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—42no—
352C2×C4×C61—44no—
353C2×C4×C61—82no—
354C2×C4×C61—82no—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4112yes—
361C2×C4×C61C2×#4112yes—
362C2×C4×C61C2511yescharacteristic
363C22⋊D61—216no—
364C22⋊D61—82no—
365C22⋊D61—82no—
366C2×Dic61—216no—
367C2×Dic61—24no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—42no—
376C2×Dic61—82no—
377C2×Dic61—82no—
378C2×Dic61—84no—
379C2×Dic61C22×D412yes—
380C2×Dic61C22×D412yes—
381C2×Dic61C22×D412yes—
382C4×D61—24no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—84no—
386Dic122—24no—
387Dic122—22no—
388Dic122—81no—
389Dic122—81no—
390Dic122C2×#4114yes—
391C8×C61—24no—
392#92418—24no—
393#60565—611nomaximal, Sylow
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—24no—
397C22×C61—48no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61#52512yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—44no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—42no—
414C4×C61—42no—
415C4×C61#52512yes—
416C4×C61C22×#4111yescharacteristic
417C4×C61C22×#4111yescharacteristic
418Dic61—22no—
419Dic61—22no—
420Dic61—24no—
421Dic61—22no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425#3455—611no—
426C2×#520—611no—
427#3125—614no—
428#3124—614no—
429#3120—614no—
430#3119—614no—
431#3092—612no—
432#3078—611no—
433#3077—611no—
434#3037—611no—
435#3036D6111yescharacteristic, complemented
436#3005—612no—
437C4×#137—612no—
438C4×AGL(1,ℤ/8)—612no—
439#2921—611no—
440C2×C61—22no—
441C2×C61—44no—
442C2×C61—82no—
443C2×C61C2×#52511yescharacteristic
444C2×C61#358511yescharacteristic
445C2×C61#358611yescharacteristic
446D61—42no—
447C22×#41—611no—
448C2×#137—612no—
449C2×AGL(1,ℤ/8)C2×D6112yes—
450#542—612no—
451#542—612no—
452#541—612no—
453#540—612no—
454#539—1221no—
455#539—1221no—
456#538—1221no—
457#538—1221no—
458#533—611no—
459#532C2×D6111yescharacteristic
460#529—1222no—
461#529—1222no—
462#525—612no—
463#520—614no—
464#520—614no—
465#520—1222no—
466#520—1222no—
467C4×#41—612no—
468C2×C4×Q8—611no—
469C2×C4×Q8—611no—
470C2×C4×D4—611no—
471C2×C4×D4—1221no—
472C2×C4×D4—1221no—
473C2×C4×D4C2×D6111yescharacteristic
474C2×#117—611no—
475C2×#117—1221no—
476C22×C4⋊C4—611no—
477C22×C4⋊C4—1221no—
478#484—614no—
479#483—614no—
480#481—614no—
481#480—614no—
482#479—614no—
483#478—614no—
484#477—612no—
485#476—612no—
486#475—612no—
487#474—612no—
488#464—614no—
489#463C2×D6114yescomplemented
490#462—612no—
491#461C2×D6112yescomplemented
492#460—612no—
493#459C2×D6112yescomplemented
494#452—614no—
495#452—614no—
496#449—614no—
497#449—614no—
498#442—614no—
499#441—614no—
500#440—614no—
501#440—614no—
502C4×Q16—614no—
503C4×SD16—614no—
504C4×SD16—614no—
505C4×D8—614no—
506#433—614no—
507#433—614no—
508#428—612no—
509#428—612no—
510#423—611no—
511#423C2×D6111yescharacteristic
512#419—612no—
513#418—612no—
514#417—612no—
515#417C2×D6112yes—
516#407—612no—
517C4×M16—612no—
518C61#6056511yescharacteristic, complemented, Sylow
519C2×#41—614no—
520C2×#41—1222no—
521C2×#41—1224no—
522C2×#41—1224no—
523C2×#41C22×D6112yes—
524C22×Q8—611no—
525C22×D4—1221no—
526C22×D4C22×D6111yescharacteristic
527C23×C4—21no—
528C23×C4—611no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532#137—1228no—
533AGL(1,ℤ/8)—28no—
534C2×Q16—614no—
535C2×SD16—614no—
536C2×SD16C22×D6114yes—
537C2×D8C22×D6114yes—
538C2×M16—612no—
539C2×M16C22×D6112yes—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8C22×D6111yescharacteristic
543#127C22×D6111yescharacteristic
544#126—1222no—
545#126—1222no—
546#126—1222no—
547#126—1222no—
548#125—612no—
549#125—1222no—
550#125—1222no—
551#124—1222no—
552#124—1222no—
553#124C22×D6112yes—
554#123—1222no—
555#123—1222no—
556#123—1222no—
557#123—1222no—
558#123—1222no—
559C22⋊Q8—612no—
560C22⋊Q8—612no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8—1221no—
564C22⋊Q8—1221no—
565#121—21no—
566#121—21no—
567#121—612no—
568#121—612no—
569#121—1222no—
570#121—1222no—
571#120—1222no—
572C4×Q8—612no—
573C4×Q8—612no—
574C4×Q8—614no—
575C4×Q8—612no—
576C4×Q8—612no—
577C4×Q8—1222no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—614no—
587C4×D4—612no—
588C4×D4—612no—
589C4×D4—1222no—
590C4×D4—1224no—
591C4×D4—1224no—
592C4×D4—1224no—
593C4×D4—1224no—
594C4×D4—1222no—
595C4×D4—1222no—
596C4×D4—1222no—
597C4×D4—1222no—
598C4×D4C22×D6112yes—
599C4×D4C22×D6112yes—
600#117—612no—
601#117—612no—
602#117—612no—
603#117—612no—
604#117—612no—
605#117—1222no—
606#117—1224no—
607#117—1224no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—614no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1224no—
614C2×C4⋊C4—1224no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—1221no—
623C2×C42—611no—
624C2×C42—1222no—
625C2×C42—1221no—
626C2×C42—1221no—
627C2×C42C22×D6111yescharacteristic
628#107—614no—
629#107—614no—
630#106—614no—
631#106—614no—
632C4⋊C8—612no—
633C4⋊C8—612no—
634C4⋊C8C22×D6112yes—
635C4⋊C8C22×D6112yes—
636#103—614no—
637#103—614no—
638#103—614no—
639#103C22×D6114yes—
640#102—614no—
641#102—614no—
642#102—614no—
643#102C22×D6114yes—
644C22⋊C8—614no—
645C22⋊C8—614no—
646#97—614no—
647C4×C8—614no—
648C24—21no—
649C24—611no—
650#41—24no—
651#41—24no—
652#41—1228no—
653#41—12216no—
654#41—1228no—
655C2×Q8—614no—
656C2×Q8—612no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8—1221no—
660C2×Q8—1222no—
661C2×Q8C23×D6112yes—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—1224no—
668C2×D4—1228no—
669C2×D4—1222no—
670C2×D4—1222no—
671C2×D4#1175822414yes—
672C2×D4C23×D6112yes—
673C2×D4C23×D6112yes—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—82no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—1224no—
685C22×C4—1224no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1224no—
689C22×C4—1228no—
690C22×C4—1221no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1221no—
694C22×C4—4882no—
695C22×C4—4882no—
696C22×C4D4×D6111yescharacteristic
697C22×C4D4×D6111yescharacteristic
698C22×C4C23×D6111yescharacteristic
699Q16—1228no—
700SD16—28no—
701SD16—1228no—
702D8—28no—
703M16—24no—
704M16—1224no—
705C2×C8—614no—
706C2×C8C23×D6114yes—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—612no—
711C4⋊C4—612no—
712C4⋊C4—612no—
713C4⋊C4—612no—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—612no—
717C4⋊C4—1224no—
718C4⋊C4—1224no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1221no—
724C4⋊C4—1222no—
725C4⋊C4—1222no—
726C4⋊C4—1222no—
727C4⋊C4—1222no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4C23×D6112yes—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—612no—
736C22⋊C4—612no—
737C22⋊C4—612no—
738C22⋊C4—612no—
739C22⋊C4—1222no—
740C22⋊C4—1222no—
741C22⋊C4—1224no—
742C22⋊C4—1222no—
743C22⋊C4—1222no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C42—612no—
748C42—612no—
749C42—1224no—
750C42—1222no—
751C42—1222no—
752C42—1222no—
753C42—1222no—
754C42—1222no—
755C42D4×D6111yescharacteristic
756C42D4×D6111yescharacteristic
757C42C23×D6111yescharacteristic
758C42C23×D6111yescharacteristic
759C23—24no—
760C23—22no—
761C23—22no—
762C23—42no—
763C23—42no—
764C23—612no—
765C23—1222no—
766C23—2441no—
767C23—2441no—
768C23C2×D4×D6111yescharacteristic
769Q8—22no—
770Q8—22no—
771Q8—614no—
772Q8—1224no—
773Q8—1222no—
774Q8—4881no—
775Q8—4881no—
776D4—24no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—44no—
781D4—81no—
782D4—81no—
783D4—12216no—
784D4—4882no—
785D4—4882no—
786D4C2×#1175822414yes—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—612no—
798C2×C4—12216no—
799C2×C4—1222no—
800C2×C4—1224no—
801C2×C4—1222no—
802C2×C4—1224no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—4884no—
809C2×C4—4882no—
810C2×C4—4882no—
811C2×C4—4884no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2442no—
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4C2×D4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4#41×D6112yes—
821C2×C4C2×#1175822412yes—
822C2×C4C24×D6111yescharacteristic
823C8—24no—
824C8—1224no—
825C22—21no—
826C22—21no—
827C22—24no—
828C22—48no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—1222no—
835C22—1222no—
836C22—1222no—
837C22—2444no—
838C22#1684027212yes—
839C22C22×D4×D6111yescharacteristic
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—42no—
845C4—42no—
846C4—1222no—
847C4—1222no—
848C4—1224no—
849C4—1222no—
850C4—2442no—
851C4—2442no—
852C4—2442no—
853C4#1684027212yes—
854C4C2×#41×D6111yescharacteristic
855C4C22×#1175822411yescharacteristic
856C2—22no—
857C2—44no—
858C2—82no—
859C2—2442no—
860C2C2×#1684027211yescharacteristic
861C2#2146059511yescharacteristic
862C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3036C2
socleC22×C61C23×D4
hypercenter#3036D61
hypocenterC61#60565
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #21459208C2semidirect
2. C2×#16840241C2semidirect
3. #21456093C2semidirect
4. #21456078C2semidirect
5. #21456030C2semidirect
6. #21456015C2semidirect
7. #21455740C2semidirect
8. #21455626C2semidirect
9. #21455616C2semidirect
10. #21455287C2semidirect
11. #21455058C2semidirect
12. #21454643C2semidirect
13. AGL(1,ℤ/8)×Dic61C2semidirect
14. #21454456C2semidirect
15. C61×#3036C2semidirect
18. #16840381C22semidirect
19. #16840381C22semidirect
20. #16840373C22semidirect
21. #16840366C22semidirect
44. #16840096C22semidirect
45. #16840091C22semidirect
46. #16840079C22semidirect
47. #16840074C22semidirect
48. #16840070C22semidirect
49. #16840062C22semidirect
50. #16840058C22semidirect
51. #16840052C22semidirect
52. #16840048C22semidirect
53. #16840042C22semidirect
54. #16839981C22semidirect
55. #16839969C22semidirect
56. #16839959C22semidirect
61. #16839874C22semidirect
62. #16839866C22semidirect
63. #16839863C22semidirect
64. #16839859C22semidirect
65. #16839854C22semidirect
66. #16839853C22semidirect
67. SD16×Dic61C22semidirect
68. D8×Dic61C22semidirect
69. #16839822C22semidirect
70. #16839822C22semidirect
82. C61×#463C22semidirect
83. C61×#461C22semidirect
84. C61×#459C22semidirect
435. #3036D61semidirect
489. #463C2×D61semidirect
491. #461C2×D61semidirect
493. #459C2×D61semidirect
518. C61#60565semidirect

Maximal subgroups

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

subgroupindex
#214592082
C2×#168402412
#214560932
#214560782
#214560302
#214560152
#214557402
#214556262
#214556162
#214552872
#214550582
#214546432
AGL(1,ℤ/8)×Dic612
#214544562
C61×#30362
#6056561