Finite Group Databasebeta

← #10579839

Subgroups — #10579839

Order 512.

6099 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic, complemented
2C2×#3518C211yesmaximal, characteristic, complemented
3#62510C212yesmaximal, complemented
4#62509C212yesmaximal, complemented
5#62508C216yesmaximal, complemented
6#62507C216yesmaximal, complemented
7#62485C2112yesmaximal, complemented
8#62476C214yesmaximal, complemented
9Q8×#137C212yesmaximal, complemented
10Q8×AGL(1,ℤ/8)C212yesmaximal, complemented
11#61257C216yesmaximal, complemented
12#61256C216yesmaximal, complemented
13#60866C213yesmaximal, complemented
14#60863C213yesmaximal, complemented
15#60702C213yesmaximal, complemented
16#60663C213yesmaximal, complemented
17M16×#41C211yesmaximal, characteristic, complemented
18#3523—21no—
19#3520—23no—
20#3518—21no—
21#3518—23no—
22#3518—23no—
23#3518—21no—
24#3518C2212yes—
25#3518C2216yes—
26#3518C2216yes—
27#3518C2212yes—
28#3518C2212yescomplemented
29#3515C2216yescomplemented
30#3511C2213yescomplemented
31#3509C2213yescomplemented
32#3503C2211yescharacteristic, complemented
33#3499C2211yescharacteristic, complemented
34#3495—23no—
35#3489—21no—
36#3482—21no—
37#3482—23no—
38Q8×#41C2212yes—
39C2×Q82C2211yescharacteristic
40#3475C2216yes—
41C2×#556—23no—
42C2×#556C2213yes—
43C2×#555C2213yes—
44C2×D4×Q8C2211yescharacteristic
45C2×#548—21no—
46#3461—23no—
47C2×#542—23no—
48#3444C2213yes—
49C2×#533C2213yes—
50C2×#533C2213yes—
51C2×#529C2213yes—
52C4×2−1+4—21no—
53C2×#519—21no—
54C2×C4×#41C2211yescharacteristic
55#3387C22112yescomplemented
56#3386C22112yescomplemented
57#3385C22112yescomplemented
58#3384C22112yescomplemented
59Q8×Q16C2214yescomplemented
60Q8×SD16C2214yescomplemented
61Q8×SD16C2214yescomplemented
62Q8×D8C2214yescomplemented
63#3357C22112yescomplemented
64#3356C22112yescomplemented
65#3354C22112yescomplemented
66#3353C22112yescomplemented
67#3350C22124yescomplemented
68#3349C22124yescomplemented
69#3348C22124yescomplemented
70#3347C22124yescomplemented
71#3342C22112yescomplemented
72#3341C22112yescomplemented
73#3340C22112yescomplemented
74#3340C22112yescomplemented
75#3240C22112yescomplemented
76#3239C2216yescomplemented
77#3238C2216yescomplemented
78#3237C2216yescomplemented
79#3237C2216yescomplemented
80#3235C2216yescomplemented
81#3235C2216yescomplemented
82#3233C22112yescomplemented
83#3233C22112yescomplemented
84#3233C22112yescomplemented
85#3232C22112yescomplemented
86#3183C22112yescomplemented
87#3181C2216yescomplemented
88#3180C2216yescomplemented
89#3172C2216yescomplemented
90#3171C2216yescomplemented
91#3168C22112yescomplemented
92#3166C2213yes—
93#3166C2216yes—
94#3166C22112yescomplemented
95#3165C2216yes—
96#3165C2216yes—
97#3165C2216yescomplemented
98#3165C2216yescomplemented
99#3162C22112yescomplemented
100#3160C22112yescomplemented
101#3153C2211yescharacteristic
102#3142C2213yes—
103#3140C2213yes—
104#3095C2216yes—
105#3094C2216yes—
106#3093C22112yes—
107#3079C2216yes—
108#3079C2216yes—
109#3078C2216yes—
110#3077C2216yes—
111#3056C2216yes—
112#3055C2216yes—
113#2971C2212yescomplemented
114#2970C2216yescomplemented
115#2965C2216yescomplemented
116C8×#41C2212yescomplemented
117Q8×M16C2212yes—
118C4×#137C2216yes—
119C4×AGL(1,ℤ/8)C2216yes—
120D4×M16C2216yes—
121#2920C2213yes—
122#2911C22112yes—
123C2×C4×M16C2213yes—
124C2×2−1+4—21no—
125C22×#41D411yescharacteristic
126C23×Q8—21no—
127C2×#137C2312yes—
128C2×AGL(1,ℤ/8)C2312yes—
129C22×M16C2316yes—
130Q82—21no—
131Q82—23no—
132Q82C2312yes—
133Q82C2312yes—
134Q82C2316yes—
135#557—21no—
136#557—23no—
137#557C2316yes—
138#556—23no—
139#556—23no—
140#556—26no—
141#556—23no—
142#556—23no—
143#556—26no—
144#556—26no—
145#556—212no—
146#556—26no—
147#556—212no—
148#556—26no—
149#556—26no—
150#556C2316yes—
151#556C2316yes—
152#556C23112yes—
153#556C2316yes—
154#555—23no—
155#555—26no—
156#555—23no—
157#555C2316yes—
158#555C2316yes—
159#555C23112yes—
160#555C2316yes—
161#554—26no—
162#554C2316yes—
163#554C2316yes—
164#553C23112yes—
165#552—26no—
166#552—212no—
167#552—26no—
168#552—26no—
169#552C23112yes—
170#551—212no—
171D4×Q8—22no—
172D4×Q8—21no—
173D4×Q8—23no—
174D4×Q8—21no—
175D4×Q8—23no—
176D4×Q8C2312yes—
177D4×Q8C2312yes—
178D4×Q8C2316yes—
179#548—22no—
180#548—22no—
181#548—26no—
182#548—26no—
183#548—22no—
184#548—26no—
185#547—26no—
186#547—23no—
187#547—23no—
188#547C2316yes—
189#546—26no—
190#544—23no—
191#542—26no—
192#542—212no—
193#542—26no—
194#542—26no—
195#542—26no—
196#542—212no—
197#542—26no—
198#542—26no—
199#541—26no—
200#541—26no—
201#539—212no—
202#537—23no—
203#536—23no—
204#536—23no—
205#533—26no—
206#533—23no—
207#533—23no—
208#533—23no—
209#533—23no—
210#533—23no—
211#533—23no—
212#533—23no—
213#533—23no—
214#533C2313yes—
215#533C2313yes—
216#533C2316yes—
217#533C2313yes—
218#533C2316yes—
219#533C2316yes—
220#533C2316yes—
221#533C2316yes—
222#533C2316yes—
223#533C2316yes—
224#532C2311yescharacteristic
225#532C2313yes—
226#532C2313yes—
227C2×C4⋊Q8—23no—
228C2×C4⋊Q8C2313yes—
229C2×C4⋊Q8C2313yes—
230C2×C4⋊Q8C2313yes—
231C2×C4⋊Q8C2313yes—
232#529—212no—
233#529—26no—
234#529—23no—
235#529—23no—
236#529—23no—
237#529—23no—
238#529—23no—
239#529—23no—
240#529—23no—
241#529—23no—
242#529C2316yes—
243#529C2316yes—
244#529C2316yes—
245#529C2316yes—
246#529C2316yes—
247#529C2316yes—
248C2×#126—26no—
249C2×#126—23no—
250C2×#125C2313yes—
251C2×#125C2316yes—
252C2×#124—23no—
253C2×#124—26no—
254C2×#124C2311yescharacteristic
255#525—23no—
256#525—23no—
257#525C2316yes—
258C2×#123—23no—
259C2×C22⋊Q8—23no—
260C2×C22⋊Q8—23no—
261C2×C22⋊Q8—23no—
262C2×C22⋊Q8—23no—
263C2×C22⋊Q8—23no—
264C2×C22⋊Q8C2313yes—
265C2×#121—23no—
266C2×#121C2313yes—
267#520—21no—
268#520—26no—
269#520—23no—
270#519—22no—
271#519—26no—
272#519—22no—
273#519—26no—
274#519—22no—
275#519—23no—
276C4×#41—26no—
277C4×#41—23no—
278C4×#41—23no—
279C4×#41D411yescharacteristic
280C4×#41D413yes—
281C4×#41D413yes—
282C4×#41D411yescharacteristic
283C4×#41C2316yes—
284C4×#41C2311yescharacteristic
285C4×#41C2313yes—
286C4×#41C2313yes—
287C4×#41C2311yescharacteristic
288C2×C4×Q8—21no—
289C2×C4×Q8—22no—
290C2×C4×Q8—23no—
291C2×C4×Q8—23no—
292C2×C4×Q8—23no—
293C2×C4×Q8—23no—
294C2×C4×Q8—23no—
295C2×C4×Q8D411yescharacteristic
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×D4—23no—
299C2×C4×D4D413yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×#117—23no—
303C2×#117—23no—
304C2×#117D413yes—
305C2×#117C2316yes—
306C2×#117C2316yes—
307C22×C42C2313yes—
308#501C23124yes—
309#501C23124yes—
310#501C2316yes—
311#501C2316yes—
312#501C23112yes—
313#501C23112yes—
314#500C23112yes—
315#500C23112yes—
316#499C23112yes—
317#499C23124yes—
318#498C23112yes—
319#498C23112yes—
320#497C2312yes—
321#496C2312yes—
322#495C2314yes—
323#491C2316yes—
324#490C2316yes—
325#489C2316yes—
326#489C2316yes—
327#488C23112yes—
328#488C23112yes—
329#485C23124yes—
330#485C23124yes—
331#485C23124yes—
332#484C23112yes—
333#483C23112yes—
334#482C23124yes—
335#482C23124yes—
336#482C23124yes—
337#481C23112yes—
338#480C23112yes—
339#479C23124yes—
340#478C23124yes—
341#477C23112yes—
342#477C23112yes—
343#477C23112yes—
344#476C23112yes—
345#476C23112yes—
346#476C23112yes—
347#475C23112yes—
348#475C23112yes—
349#475C23112yes—
350#474C23112yes—
351#474C23112yes—
352#474C23112yes—
353#470C23112yes—
354#469C23112yes—
355#468C23112yes—
356#468C23112yes—
357#467C23112yes—
358#466C23112yes—
359#465C23112yes—
360#465C23112yes—
361#446C23112yes—
362C8×Q8C2314yes—
363#442C23112yes—
364#441C23112yes—
365#440C23112yes—
366#440C23112yes—
367C4×Q16C23112yes—
368C4×SD16C23112yes—
369C4×SD16C23112yes—
370C4×D8C23112yes—
371#436C23112yes—
372#435C23124yes—
373C8×D4C23112yes—
374#432C2316yes—
375#432C2316yes—
376#431C2316yes—
377#431C2316yes—
378#428C23112yes—
379#428C23112yes—
380#428C23124yes—
381#428C23124yes—
382#428C2316yes—
383#428C2316yes—
384#427C23124yes—
385#427C23124yes—
386#423C2316yes—
387#419C2316yes—
388#418C2316yes—
389#417C2316yes—
390#417C2316yes—
391#407C2316yes—
392C4×M16C2311yescharacteristic
393C4×M16C2313yes—
394C4×M16C2316yes—
395C4×M16C2316yes—
396C4×M16C2316yes—
397C2×#97C2316yes—
398C2×C4×C8C2316yes—
3992−1+4—48no—
400C2×#41—26no—
401C2×#41—23no—
402C2×#41—23no—
403C2×#41—44no—
404C2×#41C2×D411yescharacteristic
405C2×#41C2×D411yescharacteristic
406C2×#41C2×D413yes—
407C2×#41C2×D413yes—
408C2×#41C2412yes—
409C22×Q8—22no—
410C22×Q8—26no—
411C22×Q8—22no—
412C22×Q8—23no—
413C22×Q8—23no—
414C22×Q8—23no—
415C22×Q8—23no—
416C22×Q8—48no—
417C22×Q8C2×D411yescharacteristic
418C22×Q8C2411yescharacteristic
419C22×D4—23no—
420C22×D4C2×D413yes—
421C22×D4C2411yescharacteristic
422C23×C4—23no—
423C23×C4C2×D413yes—
424C23×C4C2×D413yes—
425C23×C4C2413yes—
426#137—28no—
427AGL(1,ℤ/8)—28no—
428C2×Q16C2414yes—
429C2×SD16C2414yes—
430C2×SD16C2414yes—
431C2×D8C2414yes—
432C2×M16—224no—
433C2×M16C2416yes—
434C2×M16C24112yes—
435C2×M16C2412yes—
436C22×C8C24112yes—
437C4⋊Q8—26no—
438C4⋊Q8—26no—
439C4⋊Q8—212no—
440C4⋊Q8—26no—
441C4⋊Q8—26no—
442C4⋊Q8—23no—
443C4⋊Q8—23no—
444C4⋊Q8—23no—
445C4⋊Q8—23no—
446C4⋊Q8—23no—
447C4⋊Q8—23no—
448C4⋊Q8—23no—
449C4⋊Q8—23no—
450C4⋊Q8C2411yescharacteristic
451C4⋊Q8C2413yes—
452C4⋊Q8C2413yes—
453C4⋊Q8C2416yes—
454C4⋊Q8C2416yes—
455C4⋊Q8C2416yes—
456C4⋊Q8C2416yes—
457C4⋊Q8C2416yes—
458C4⋊Q8C2416yes—
459#127C2411yescharacteristic
460#126—212no—
461#126—212no—
462#126—212no—
463#126—212no—
464#126—212no—
465#126—212no—
466#126—212no—
467#126—26no—
468#126—26no—
469#126—26no—
470#126—26no—
471#126—26no—
472#126—26no—
473#125—212no—
474#125—26no—
475#125—212no—
476#125—23no—
477#125—23no—
478#125—26no—
479#125—26no—
480#125—23no—
481#125—23no—
482#125C2416yes—
483#125C2416yes—
484#125C2416yes—
485#125C24112yes—
486#124—26no—
487#124—26no—
488#124—212no—
489#124—26no—
490#124—212no—
491#124—212no—
492#124—212no—
493#124—212no—
494#124—212no—
495#124—21no—
496#124—21no—
497#124—23no—
498#124—23no—
499#124C2412yes—
500#124C2412yes—
501#124C2412yes—
502#123—212no—
503#123—26no—
504#123—26no—
505#123—26no—
506#123—26no—
507#123—26no—
508#123—26no—
509#123—26no—
510#123—212no—
511#123—212no—
512C22⋊Q8—26no—
513C22⋊Q8—23no—
514C22⋊Q8—23no—
515C22⋊Q8—26no—
516C22⋊Q8—26no—
517C22⋊Q8—26no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—26no—
521C22⋊Q8—26no—
522C22⋊Q8—26no—
523C22⋊Q8—26no—
524C22⋊Q8—26no—
525C22⋊Q8—26no—
526C22⋊Q8—26no—
527C22⋊Q8—26no—
528C22⋊Q8—26no—
529C22⋊Q8—23no—
530C22⋊Q8—23no—
531C22⋊Q8—23no—
532C22⋊Q8—23no—
533C22⋊Q8—26no—
534C22⋊Q8—212no—
535C22⋊Q8—26no—
536C22⋊Q8—26no—
537C22⋊Q8—26no—
538C22⋊Q8—212no—
539C22⋊Q8—212no—
540C22⋊Q8C2416yes—
541C22⋊Q8C2416yes—
542C22⋊Q8C2416yes—
543C22⋊Q8C2416yes—
544#121—26no—
545#121—26no—
546#121—212no—
547#121—212no—
548#121—26no—
549#121—23no—
550#121—23no—
551#121—21no—
552#121—21no—
553#121—23no—
554#121—23no—
555#121C2416yes—
556#121C2416yes—
557#121C2416yes—
558#121C2416yes—
559#120—26no—
560C4×Q8—26no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—26no—
564C4×Q8—26no—
565C4×Q8—212no—
566C4×Q8—26no—
567C4×Q8—26no—
568C4×Q8—26no—
569C4×Q8—23no—
570C4×Q8—23no—
571C4×Q8—26no—
572C4×Q8—26no—
573C4×Q8—26no—
574C4×Q8—26no—
575C4×Q8—26no—
576C4×Q8—26no—
577C4×Q8—26no—
578C4×Q8—26no—
579C4×Q8—26no—
580C4×Q8—26no—
581C4×Q8—26no—
582C4×Q8—26no—
583C4×Q8—26no—
584C4×Q8—23no—
585C4×Q8—23no—
586C4×Q8—23no—
587C4×Q8—23no—
588C4×Q8C2×D411yescharacteristic
589C4×Q8C2×D411yescharacteristic
590C4×Q8C2×D413yes—
591C4×Q8C2×D411yescharacteristic
592C4×Q8C2×D413yes—
593C4×Q8C2×D413yes—
594C4×Q8C2416yes—
595C4×Q8C2416yes—
596C4×Q8C2416yes—
597C4×Q8C2416yes—
598C4×Q8C2411yescharacteristic
599C4×Q8C2413yes—
600C4×D4—26no—
601C4×D4—26no—
602C4×D4—26no—
603C4×D4—26no—
604C4×D4—26no—
605C4×D4—26no—
606C4×D4—26no—
607C4×D4—26no—
608C4×D4—26no—
609C4×D4—26no—
610C4×D4—26no—
611C4×D4—212no—
612C4×D4—23no—
613C4×D4—23no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—23no—
617C4×D4—23no—
618C4×D4C2×D413yes—
619C4×D4C2×D416yes—
620C4×D4C2×D413yes—
621C4×D4C2×D413yes—
622C4×D4C2×D413yes—
623C4×D4C2×D416yes—
624C4×D4C2×D413yes—
625C4×D4C2×D413yes—
626C4×D4C2×D416yes—
627C4×D4C2416yes—
628C4×D4C2416yes—
629C4×D4C2416yes—
630C4×D4C2416yes—
631C4×D4C2413yes—
632C4×D4C2416yes—
633C4×D4C2413yes—
634#117—26no—
635#117—26no—
636#117—26no—
637#117—26no—
638#117—23no—
639#117—23no—
640#117—26no—
641#117—26no—
642#117—212no—
643#117—26no—
644#117—212no—
645#117—26no—
646#117—26no—
647#117—26no—
648#117—26no—
649#117—26no—
650#117—26no—
651#117—26no—
652#117C2×D413yes—
653#117C2×D413yes—
654#117C2×D416yes—
655#117C2×D413yes—
656#117C2×D416yes—
657#117C2×D413yes—
658#117C2416yes—
659#117C24112yes—
660#117C24112yes—
661#117C24112yes—
662C2×C4⋊C4—23no—
663C2×C4⋊C4—23no—
664C2×C4⋊C4—23no—
665C2×C4⋊C4—23no—
666C2×C4⋊C4—26no—
667C2×C4⋊C4—23no—
668C2×C4⋊C4—23no—
669C2×C4⋊C4—26no—
670C2×C4⋊C4—23no—
671C2×C4⋊C4—23no—
672C2×C4⋊C4—26no—
673C2×C4⋊C4C2×D413yes—
674C2×C4⋊C4C2×D413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2416yes—
678C2×C4⋊C4C2416yes—
679C2×C22⋊C4—26no—
680C2×C22⋊C4—26no—
681C2×C22⋊C4—23no—
682C2×C22⋊C4—23no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—23no—
686C2×C22⋊C4C2×D416yes—
687C2×C42—26no—
688C2×C42—23no—
689C2×C42—26no—
690C2×C42—26no—
691C2×C42C2×D413yes—
692C2×C42C2×D413yes—
693C2×C42C2×D413yes—
694C2×C42C2×D413yes—
695C2×C42C2×D413yes—
696C2×C42C2×D413yes—
697C2×C42C2413yes—
698C2×C42C2413yes—
699C2×C42C2413yes—
700C2×C42C2413yes—
701C2×C42C2413yes—
702C2×C42C2411yescharacteristic
703#107C24112yes—
704#107C24112yes—
705#107C24124yes—
706#107C24124yes—
707#106C24112yes—
708#106C24112yes—
709#106C24124yes—
710#106C24124yes—
711C4⋊C8C24112yes—
712C4⋊C8C24112yes—
713#103C24112yes—
714#103C24112yes—
715#103C24112yes—
716#103C24112yes—
717#102C24112yes—
718#102C24112yes—
719#102C24112yes—
720#102C24112yes—
721C22⋊C8C24112yes—
722C22⋊C8C24112yes—
723#97C2412yes—
724#97C2416yes—
725#97C24112yes—
726C4×C8C2412yes—
727C4×C8C2416yes—
728C4×C8C24112yes—
729C24—21no—
730C24C22×D413yes—
731#41—24no—
732#41—24no—
733#41—24no—
734#41—24no—
735#41—46no—
736#41—46no—
737#41—412no—
738#41—424no—
739#41—86no—
740C2×Q8—24no—
741C2×Q8—21no—
742C2×Q8—26no—
743C2×Q8—26no—
744C2×Q8—23no—
745C2×Q8—23no—
746C2×Q8—26no—
747C2×Q8—26no—
748C2×Q8—26no—
749C2×Q8—26no—
750C2×Q8—24no—
751C2×Q8—412no—
752C2×Q8—412no—
753C2×Q8—424no—
754C2×Q8—48no—
755C2×Q8—48no—
756C2×Q8—86no—
757C2×Q8—86no—
758C2×Q8C22×D413yes—
759C2×Q8C22×D411yescharacteristic
760C2×Q8C2512yes—
761C2×Q8C2512yes—
762C2×D4—22no—
763C2×D4—26no—
764C2×D4—26no—
765C2×D4—26no—
766C2×D4—26no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—24no—
771C2×D4—46no—
772C2×D4—86no—
773C2×D4C22×D413yes—
774C2×D4C22×D413yes—
775C2×D4C22×D416yes—
776C2×D4C2512yes—
777C2×D4C2512yes—
778C22×C4—212no—
779C22×C4—21no—
780C22×C4—23no—
781C22×C4—23no—
782C22×C4—26no—
783C22×C4—26no—
784C22×C4—22no—
785C22×C4—26no—
786C22×C4—26no—
787C22×C4—26no—
788C22×C4—26no—
789C22×C4—46no—
790C22×C4—412no—
791C22×C4—83no—
792C22×C4C22×D413yes—
793C22×C4C22×D413yes—
794C22×C4C22×D413yes—
795C22×C4C22×D413yes—
796C22×C4C22×D413yes—
797C22×C4C22×D413yes—
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D413yes—
801C22×C4C22×D413yes—
802C22×C4C22×D413yes—
803C22×C4C22×D413yes—
804C22×C4C22×D413yes—
805C22×C4C22×D413yes—
806C22×C4C22×D413yes—
807C22×C4C2513yes—
808C22×C4C2513yes—
809C22×C4C2511yescharacteristic
810Q16—28no—
811SD16—28no—
812SD16—28no—
813D8—28no—
814M16—212no—
815M16—224no—
816M162−1+418yescomplemented
817C2×C8—224no—
818C2×C8C25112yes—
819C2×C8C2514yes—
820C4⋊C4—23no—
821C4⋊C4—23no—
822C4⋊C4—26no—
823C4⋊C4—212no—
824C4⋊C4—26no—
825C4⋊C4—26no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—26no—
829C4⋊C4—26no—
830C4⋊C4—26no—
831C4⋊C4—26no—
832C4⋊C4—26no—
833C4⋊C4—26no—
834C4⋊C4—212no—
835C4⋊C4—26no—
836C4⋊C4—26no—
837C4⋊C4—26no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—23no—
841C4⋊C4—23no—
842C4⋊C4—26no—
843C4⋊C4—26no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—26no—
847C4⋊C4—26no—
848C4⋊C4—26no—
849C4⋊C4—26no—
850C4⋊C4C22×D413yes—
851C4⋊C4C22×D413yes—
852C4⋊C4C22×D413yes—
853C4⋊C4C22×D416yes—
854C4⋊C4C22×D416yes—
855C4⋊C4C22×D413yes—
856C4⋊C4C2516yes—
857C4⋊C4C2516yes—
858C4⋊C4C2516yes—
859C4⋊C4C2516yes—
860C22⋊C4—26no—
861C22⋊C4—212no—
862C22⋊C4—212no—
863C22⋊C4—212no—
864C22⋊C4—26no—
865C22⋊C4—26no—
866C22⋊C4—26no—
867C22⋊C4—26no—
868C22⋊C4—26no—
869C22⋊C4—26no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—26no—
875C22⋊C4—26no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—26no—
879C22⋊C4—26no—
880C22⋊C4—26no—
881C22⋊C4—26no—
882C22⋊C4C22×D416yes—
883C22⋊C4C22×D416yes—
884C22⋊C4C22×D416yes—
885C22⋊C4C22×D416yes—
886C42—26no—
887C42—26no—
888C42—212no—
889C42—212no—
890C42—212no—
891C42—26no—
892C42—26no—
893C42—26no—
894C42C22×D413yes—
895C42C22×D411yescharacteristic
896C42C22×D411yescharacteristic
897C42C22×D413yes—
898C42C22×D413yes—
899C42C22×D413yes—
900C42C22×D413yes—
901C42C22×D413yes—
902C42C22×D413yes—
903C42C22×D413yes—
904C42C22×D413yes—
905C42C22×D413yes—
906C42C2511yescharacteristic
907C42C2513yes—
908C42C2511yescharacteristic
909C42C2513yes—
910C23—26no—
911C23—22no—
912C23—22no—
913C23—43no—
914C23—43no—
915C23—42no—
916C23—42no—
917C23—42no—
918C23C23×D413yes—
919C23C23×D413yes—
920C23C23×D411yescharacteristic
921Q8—26no—
922Q8—22no—
923Q8—24no—
924Q8—22no—
925Q8—412no—
926Q8—46no—
927Q8—46no—
928Q8—42no—
929Q8—412no—
930Q8—412no—
931Q8—86no—
932Q8—86no—
933Q8—86no—
934Q8#57514yes—
935D4—22no—
936D4—24no—
937D4—22no—
938D4—26no—
939D4—26no—
940D4—46no—
941D4—42no—
942D4—42no—
943D4—412no—
944D4—44no—
945D4—42no—
946D4—86no—
947D4—86no—
948D4—86no—
949C2×C4—26no—
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—26no—
953C2×C4—26no—
954C2×C4—26no—
955C2×C4—26no—
956C2×C4—26no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—26no—
960C2×C4—26no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—41no—
964C2×C4—43no—
965C2×C4—43no—
966C2×C4—41no—
967C2×C4—43no—
968C2×C4—43no—
969C2×C4—43no—
970C2×C4—43no—
971C2×C4—43no—
972C2×C4—412no—
973C2×C4—46no—
974C2×C4—46no—
975C2×C4—412no—
976C2×C4—42no—
977C2×C4—44no—
978C2×C4—412no—
979C2×C4—412no—
980C2×C4—86no—
981C2×C4—86no—
982C2×C4C23×D413yes—
983C2×C4C23×D413yes—
984C2×C4C23×D413yes—
985C2×C4C23×D413yes—
986C2×C4C23×D411yescharacteristic
987C2×C4C23×D411yescharacteristic
988C2×C4C23×D411yescharacteristic
989C2×C4C23×D411yescharacteristic
990C2×C4C23×D413yes—
991C2×C4C23×D411yescharacteristic
992C2×C4C23×D413yes—
993C2×C4C2×2−1+414yes—
994C2×C4C2611yescharacteristic
995C8—212no—
996C8C2×2−1+418yes—
997C22—21no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—23no—
1004C22—23no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—86no—
1012C22—84no—
1013C22#349912yes—
1014C22C24×D411yescharacteristic
1015C4—23no—
1016C4—23no—
1017C4—21no—
1018C4—21no—
1019C4—23no—
1020C4—21no—
1021C4—21no—
1022C4—23no—
1023C4—23no—
1024C4—42no—
1025C4—42no—
1026C4—46no—
1027C4—46no—
1028C4—46no—
1029C4—46no—
1030C4#349912yes—
1031C4C2×#57516yes—
1032C4C22×2−1+412yes—
1033C2—22no—
1034C2—43no—
1035C2—43no—
1036C2—82no—
1037C2—82no—
1038C2C2×#349911yescharacteristic
1039C2C22×#57511yescharacteristic
1040C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62805C2semidirect
2. C2×#3518C2semidirect
3. #62510C2semidirect
4. #62509C2semidirect
5. #62508C2semidirect
6. #62507C2semidirect
7. #62485C2semidirect
8. #62476C2semidirect
9. Q8×#137C2semidirect
10. Q8×AGL(1,ℤ/8)C2semidirect
11. #61257C2semidirect
12. #61256C2semidirect
13. #60866C2semidirect
14. #60863C2semidirect
15. #60702C2semidirect
16. #60663C2semidirect
17. M16×#41C2semidirect
28. #3518C22semidirect
29. #3515C22semidirect
30. #3511C22semidirect
31. #3509C22semidirect
32. #3503C22semidirect
33. #3499C22semidirect
55. #3387C22semidirect
56. #3386C22semidirect
57. #3385C22semidirect
58. #3384C22semidirect
59. Q8×Q16C22semidirect
60. Q8×SD16C22semidirect
61. Q8×SD16C22semidirect
62. Q8×D8C22semidirect
63. #3357C22semidirect
64. #3356C22semidirect
65. #3354C22semidirect
66. #3353C22semidirect
67. #3350C22semidirect
68. #3349C22semidirect
69. #3348C22semidirect
70. #3347C22semidirect
71. #3342C22semidirect
72. #3341C22semidirect
73. #3340C22semidirect
74. #3340C22semidirect
75. #3240C22semidirect
76. #3239C22semidirect
77. #3238C22semidirect
78. #3237C22semidirect
79. #3237C22semidirect
80. #3235C22semidirect
81. #3235C22semidirect
82. #3233C22semidirect
83. #3233C22semidirect
84. #3233C22semidirect
85. #3232C22semidirect
86. #3183C22semidirect
87. #3181C22semidirect
88. #3180C22semidirect
89. #3172C22semidirect
90. #3171C22semidirect
91. #3168C22semidirect
94. #3166C22semidirect
97. #3165C22semidirect
98. #3165C22semidirect
99. #3162C22semidirect
100. #3160C22semidirect
113. #2971C22semidirect
114. #2970C22semidirect
115. #2965C22semidirect
116. C8×#41C22semidirect
816. M162−1+4semidirect

Maximal subgroups

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

subgroupindex
#628052
C2×#35182
#625102
#625092
#625082
#625072
#624852
#624762
Q8×#1372
Q8×AGL(1,ℤ/8)2
#612572
#612562
#608662
#608632
#607022
#606632
M16×#412