Finite Group Databasebeta

← #10580255

Subgroups — #10580255

Order 512.

6456 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#62150C212yesmaximal, complemented
4#62135C216yesmaximal, complemented
5#62002C212yesmaximal, complemented
6#61987C216yesmaximal, complemented
7#61901C212yesmaximal, complemented
8#61838C212yesmaximal, complemented
9#61731C216yesmaximal, complemented
10#61596C216yesmaximal, complemented
11#61450C2112yesmaximal, complemented
12#61434C214yesmaximal, complemented
13#60951C213yesmaximal, complemented
14#60941C213yesmaximal, complemented
15#60562C213yesmaximal, complemented
16#60536C213yesmaximal, complemented
17#60278C211yesmaximal, characteristic, complemented
18#3523C2212yes—
19#3520C2216yes—
20#3518—21no—
21#3515—23no—
22#3511C2213yescomplemented
23#3509C2213yescomplemented
24#3503C2211yescharacteristic, complemented
25#3499C2211yescharacteristic, complemented
26#3495—23no—
27#3489—21no—
28#3483—21no—
29#3483—23no—
30#3483—23no—
31#3483—21no—
32#3483C2216yes—
33#3483C2216yes—
34#3483C2212yes—
35#3483C2212yes—
36#3482C2212yescomplemented
37#3482C2216yescomplemented
38Q8×#41—21no—
39C2×Q82C2211yescharacteristic
40#3475—23no—
41C2×#555—23no—
42C2×#555C2213yes—
43C2×#550—21no—
44C2×#550C2213yes—
45C2×#550C2211yescharacteristic
46#3461—23no—
47#3444C2213yes—
48C2×#533C2213yes—
49C2×#532—23no—
50C2×#532C2213yes—
51C4×2−1+4—21no—
52C2×C4×#41—21no—
53C2×C4×#41C2213yes—
54C2×C4×#41C2211yescharacteristic
55#3397C22112yescomplemented
56#3392C2214yescomplemented
57#3387C22112yescomplemented
58Q8×SD16C2214yescomplemented
59#3369C22112yescomplemented
60#3368C22112yescomplemented
61#3363C2214yescomplemented
62#3358C2214yescomplemented
63#3354C22112yescomplemented
64#3348C22124yescomplemented
65#3340C22112yescomplemented
66#3332C22112yescomplemented
67#3329C22112yescomplemented
68#3321C22124yescomplemented
69#3317C22124yescomplemented
70#3304C22112yescomplemented
71#3303C22112yescomplemented
72#3284C22112yescomplemented
73#3278C22112yescomplemented
74#3271C22124yescomplemented
75#3254C2216yescomplemented
76#3253C2216yescomplemented
77#3246C22112yescomplemented
78#3238C2216yes—
79#3235C2216yescomplemented
80#3229C2216yes—
81#3227C2216yescomplemented
82#3217C2216yes—
83#3214C2216yescomplemented
84#3208C2216yes—
85#3206C2216yescomplemented
86#3194C22112yes—
87#3187C22112yes—
88#3171C22112yescomplemented
89#3167C22112yescomplemented
90#3116C22112yescomplemented
91#3113C2216yes—
92#3110C2216yes—
93#3108C2216yes—
94#3107C22112yescomplemented
95#3107C2216yescomplemented
96#3106C22112yescomplemented
97#3106C2216yescomplemented
98#3105C2216yes—
99#3104C2213yes—
100#3103C2211yescharacteristic
101#3103C22112yescomplemented
102#3102C22112yescomplemented
103#3101C2213yes—
104#3101C2216yes—
105#3100C2213yes—
106#3095C2216yes—
107#3091C2216yes—
108#3079C2216yescomplemented
109#3076C2216yescomplemented
110#3039C2216yescomplemented
111#3035C2216yescomplemented
112#3007C2216yes—
113#3002C2216yes—
114#2991C2212yescomplemented
115#2990C2216yescomplemented
116#2984C2212yes—
117#2974C2216yes—
118#2965C2216yescomplemented
119C8×#41C2212yescomplemented
120C4×#137C22112yescomplemented
121C4×#135C22112yescomplemented
122#2920C2213yes—
123C2×#431C2213yes—
124C2×2−1+4—21no—
125C22×#41—21no—
126C22×#41—23no—
127C22×#41D411yescharacteristic
128C22×#41C2313yes—
129C2×#137C23112yes—
130C2×#135C23112yes—
131Q82—21no—
132Q82—23no—
133Q82—21no—
134Q82C2312yes—
135Q82C2316yes—
136#557—23no—
137#557C2312yes—
138#557C2316yes—
139#556—23no—
140#556—26no—
141#556C2316yes—
142#556C2316yes—
143#555—23no—
144#555—26no—
145#555—23no—
146#555—23no—
147#555—26no—
148#555—26no—
149#555—212no—
150#555—212no—
151#555—26no—
152#555—26no—
153#555C2316yes—
154#555C2316yes—
155#555C23112yes—
156#554—23no—
157#554—23no—
158#554—26no—
159#553—26no—
160#552—26no—
161#552—212no—
162#552—26no—
163#552—26no—
164#552C23112yes—
165#551—212no—
166#550—22no—
167#550—22no—
168#550—26no—
169#550—26no—
170#550—21no—
171#550—23no—
172#550—23no—
173#550—26no—
174#550—23no—
175#550C2316yes—
176#550C23112yes—
177#550C2316yes—
178#550C2312yes—
179#550C2316yes—
180D4×Q8—22no—
181D4×Q8—21no—
182D4×Q8C2316yes—
183D4×Q8C2312yes—
184#548—22no—
185#548C23112yes—
186#547—26no—
187#547—23no—
188#547C2316yes—
189#547C2316yes—
190#546—26no—
191#544—23no—
192#542—26no—
193#542—26no—
194#541—26no—
195#541—26no—
196#539—212no—
197#537—23no—
198#536—23no—
199#536—23no—
200#533—26no—
201#533—23no—
202#533—23no—
203#533—23no—
204#533—23no—
205#533C2313yes—
206#533C2316yes—
207#533C2313yes—
208#533C2316yes—
209#533C2316yes—
210#533C2313yes—
211#532—26no—
212#532—212no—
213#532—26no—
214#532—26no—
215#532—212no—
216#532—26no—
217#532—23no—
218#532—23no—
219#532—23no—
220#532—23no—
221#532C2313yes—
222#532C2311yescharacteristic
223#532C2316yes—
224#532C2316yes—
225#532C2313yes—
226#532C2316yes—
227#532C2316yes—
228C2×C4⋊Q8—23no—
229C2×C4⋊Q8C2313yes—
230C2×C4⋊Q8C2313yes—
231C2×C4⋊Q8C2313yes—
232C2×#127—23no—
233C2×#127C2313yes—
234#529—212no—
235#529—26no—
236#529—23no—
237#529—23no—
238#529—23no—
239#529—23no—
240#529C2316yes—
241#529C2316yes—
242C2×#125—23no—
243C2×#124—26no—
244C2×#124—23no—
245#525—23no—
246#525—23no—
247#525C2316yes—
248C2×C22⋊Q8—23no—
249C2×C22⋊Q8C2316yes—
250C2×#121—23no—
251C2×#121—23no—
252C2×#121—23no—
253C2×#121—26no—
254C2×#121C2316yes—
255#520—21no—
256#520—26no—
257#520—23no—
258#519—22no—
259#519—23no—
260C4×#41—22no—
261C4×#41—26no—
262C4×#41—22no—
263C4×#41—26no—
264C4×#41—26no—
265C4×#41—23no—
266C4×#41—23no—
267C4×#41—23no—
268C4×#41—23no—
269C4×#41—23no—
270C4×#41—23no—
271C4×#41D411yescharacteristic
272C4×#41D413yes—
273C4×#41D413yes—
274C4×#41D411yescharacteristic
275C4×#41C2316yes—
276C4×#41C2316yes—
277C4×#41C2316yes—
278C4×#41C2316yes—
279C4×#41C2316yes—
280C4×#41C2311yescharacteristic
281C4×#41C2313yes—
282C4×#41C2311yescharacteristic
283C4×#41C2313yes—
284C2×C4×Q8—21no—
285C2×C4×Q8—22no—
286C2×C4×Q8—23no—
287C2×C4×Q8D411yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2316yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×D4—23no—
293C2×C4×D4—23no—
294C2×C4×D4—23no—
295C2×C4×D4—23no—
296C2×C4×D4D413yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×#117—23no—
301C2×#117—23no—
302C2×#117—23no—
303C2×#117D413yes—
304C2×#117C2313yes—
305C22×C42—23no—
306C22×C42C2313yes—
307#501C23112yes—
308#498C23112yes—
309#496C23112yes—
310#492C23112yes—
311#490C23112yes—
312#489C23112yes—
313#487C23112yes—
314#486C23112yes—
315#485C23112yes—
316#485C23124yes—
317#484C2316yes—
318#483C2316yes—
319#483C23112yes—
320#482C23124yes—
321#482C23112yes—
322#481C23124yes—
323#481C2312yes—
324#480C2316yes—
325#479C23112yes—
326#478C23112yes—
327#477C23112yes—
328#477C2316yes—
329#476C2316yes—
330#476C23112yes—
331#476C23112yes—
332#475C2312yes—
333#475C23112yes—
334#475C23124yes—
335#474C2316yes—
336#474C23112yes—
337#469C23124yes—
338#468C23124yes—
339#465C23124yes—
340#465C23124yes—
341#464C23112yes—
342#463C23112yes—
343#462C2316yes—
344#462C23112yes—
345#461C23112yes—
346#461C2316yes—
347#461C23112yes—
348#460C2312yes—
349#460C23124yes—
350#460C23112yes—
351#459C23112yes—
352#459C2316yes—
353#452C23112yes—
354#452C23124yes—
355#451C2316yes—
356#450C2316yes—
357#450C23112yes—
358#449C23112yes—
359#449C23124yes—
360#448C23124yes—
361#448C2312yes—
362#447C2316yes—
363#446C23112yes—
364C8×Q8C2314yes—
365#441C23124yes—
366#440C23124yes—
367C4×Q16C23112yes—
368C4×Q16C23112yes—
369C4×SD16C23112yes—
370C4×SD16C23112yes—
371C4×SD16C23112yes—
372C4×SD16C23124yes—
373C4×SD16C2314yes—
374C4×D8C23112yes—
375C4×D8C23112yes—
376#436C23112yes—
377#435C23124yes—
378C8×D4C23112yes—
379#432C2316yes—
380#432C2316yes—
381#431C2313yes—
382#431C2311yescharacteristic
383#431C2316yes—
384#431C2316yes—
385#431C2316yes—
386#431C2316yes—
387#428C23112yes—
388#427C23112yes—
389#423C2316yes—
390C2×C4⋊C8C2316yes—
391#419C23112yes—
392#417C23112yes—
393#416C23112yes—
394#416C23112yes—
395#407C2316yes—
396C2×C22⋊C8C2316yes—
397C4×M16C2316yes—
398C2×C4×C8C2316yes—
3992−1+4—48no—
400C2×#41—26no—
401C2×#41—22no—
402C2×#41—26no—
403C2×#41—21no—
404C2×#41—23no—
405C2×#41—23no—
406C2×#41—23no—
407C2×#41—26no—
408C2×#41—26no—
409C2×#41—26no—
410C2×#41—26no—
411C2×#41—44no—
412C2×#41—412no—
413C2×#41—48no—
414C2×#41—812no—
415C2×#41C2×D411yescharacteristic
416C2×#41C2×D411yescharacteristic
417C2×#41C2×D413yes—
418C2×#41C2×D413yes—
419C2×#41C2416yes—
420C2×#41C2416yes—
421C2×#41C2416yes—
422C22×Q8—22no—
423C22×Q8—23no—
424C22×Q8—23no—
425C22×Q8C2×D411yescharacteristic
426C22×Q8C2411yescharacteristic
427C22×Q8C2416yes—
428C22×D4—23no—
429C22×D4—26no—
430C22×D4—23no—
431C22×D4—23no—
432C22×D4C2×D413yes—
433C22×D4C2413yes—
434C23×C4—23no—
435C23×C4—23no—
436C23×C4—23no—
437C23×C4C2×D413yes—
438C23×C4C2×D413yes—
439C23×C4C2413yes—
440#137—424no—
441#135—424no—
442C2×Q16C24112yes—
443C2×SD16C2414yes—
444C2×SD16C24112yes—
445C2×SD16C24124yes—
446C2×D8C24112yes—
447C2×M16C24112yes—
448C22×C8C24112yes—
449C4⋊Q8—26no—
450C4⋊Q8—26no—
451C4⋊Q8—26no—
452C4⋊Q8—212no—
453C4⋊Q8—26no—
454C4⋊Q8—23no—
455C4⋊Q8—23no—
456C4⋊Q8—23no—
457C4⋊Q8—23no—
458C4⋊Q8—23no—
459C4⋊Q8—23no—
460C4⋊Q8C2413yes—
461C4⋊Q8C2416yes—
462C4⋊Q8C2413yes—
463C4⋊Q8C2416yes—
464C4⋊Q8C2416yes—
465C4⋊Q8C2416yes—
466C4⋊Q8C2411yescharacteristic
467#127—26no—
468#127—26no—
469#127—212no—
470#127—23no—
471#127—23no—
472#127C2416yes—
473#127C2416yes—
474#127C2411yescharacteristic
475#126—212no—
476#126—212no—
477#126—212no—
478#126—26no—
479#126—26no—
480#125—212no—
481#125—26no—
482#125—212no—
483#125—23no—
484#125—26no—
485#125—26no—
486#125—26no—
487#125—23no—
488#125C2416yes—
489#124—26no—
490#124—212no—
491#124—212no—
492#124—212no—
493#124—212no—
494#124—212no—
495#124—26no—
496#124—26no—
497#124—26no—
498#124—26no—
499#124—21no—
500#124—23no—
501#124C2416yes—
502#123—212no—
503#123—26no—
504#123—26no—
505#123—26no—
506#123—212no—
507#123—212no—
508C22⋊Q8—26no—
509C22⋊Q8—23no—
510C22⋊Q8—26no—
511C22⋊Q8—26no—
512C22⋊Q8—26no—
513C22⋊Q8—26no—
514C22⋊Q8—26no—
515C22⋊Q8—23no—
516C22⋊Q8—23no—
517C22⋊Q8—23no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—212no—
521C22⋊Q8—212no—
522C22⋊Q8C2416yes—
523C22⋊Q8C24112yes—
524C22⋊Q8C2416yes—
525#121—26no—
526#121—26no—
527#121—212no—
528#121—212no—
529#121—26no—
530#121—26no—
531#121—26no—
532#121—26no—
533#121—26no—
534#121—26no—
535#121—26no—
536#121—21no—
537#121—23no—
538#121—23no—
539#121—23no—
540#121—26no—
541#121—26no—
542#121—212no—
543#121—212no—
544#121—212no—
545#121—212no—
546#121—212no—
547#121C24112yes—
548#121C24112yes—
549#121C2412yes—
550#121C2416yes—
551#120—26no—
552C4×Q8—26no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—26no—
556C4×Q8—26no—
557C4×Q8—26no—
558C4×Q8—23no—
559C4×Q8—26no—
560C4×Q8—26no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—23no—
564C4×Q8—23no—
565C4×Q8—26no—
566C4×Q8—26no—
567C4×Q8—23no—
568C4×Q8—23no—
569C4×Q8—23no—
570C4×Q8C2×D411yescharacteristic
571C4×Q8C2×D413yes—
572C4×Q8C2×D411yescharacteristic
573C4×Q8C2×D413yes—
574C4×Q8C2×D411yescharacteristic
575C4×Q8C2×D413yes—
576C4×Q8C2416yes—
577C4×Q8C2412yes—
578C4×Q8C2412yes—
579C4×Q8C2416yes—
580C4×Q8C2416yes—
581C4×Q8C24112yes—
582C4×Q8C2416yes—
583C4×Q8C2411yescharacteristic
584C4×Q8C2413yes—
585C4×D4—26no—
586C4×D4—26no—
587C4×D4—26no—
588C4×D4—26no—
589C4×D4—26no—
590C4×D4—26no—
591C4×D4—26no—
592C4×D4—26no—
593C4×D4—26no—
594C4×D4—26no—
595C4×D4—26no—
596C4×D4—26no—
597C4×D4—26no—
598C4×D4—26no—
599C4×D4—26no—
600C4×D4—26no—
601C4×D4—212no—
602C4×D4—26no—
603C4×D4—212no—
604C4×D4—26no—
605C4×D4—26no—
606C4×D4—26no—
607C4×D4—26no—
608C4×D4—23no—
609C4×D4—23no—
610C4×D4—23no—
611C4×D4—23no—
612C4×D4—21no—
613C4×D4—23no—
614C4×D4—23no—
615C4×D4—23no—
616C4×D4C2×D413yes—
617C4×D4C2×D413yes—
618C4×D4C2×D416yes—
619C4×D4C2×D413yes—
620C4×D4C2×D416yes—
621C4×D4C2×D413yes—
622C4×D4C2×D413yes—
623C4×D4C2×D416yes—
624C4×D4C2×D413yes—
625C4×D4C2416yes—
626C4×D4C2416yes—
627C4×D4C2416yes—
628C4×D4C2416yes—
629C4×D4C2412yes—
630C4×D4C2416yes—
631C4×D4C2413yes—
632C4×D4C2413yes—
633C4×D4C2416yes—
634#117—23no—
635#117—26no—
636#117—26no—
637#117—26no—
638#117—23no—
639#117—23no—
640#117—23no—
641#117—26no—
642#117—212no—
643#117—26no—
644#117—26no—
645#117—212no—
646#117—26no—
647#117—26no—
648#117—26no—
649#117—26no—
650#117—26no—
651#117—26no—
652#117—26no—
653#117C2×D413yes—
654#117C2×D413yes—
655#117C2×D416yes—
656#117C2×D413yes—
657#117C2×D416yes—
658#117C2×D413yes—
659#117C2416yes—
660#117C2416yes—
661#117C2416yes—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—23no—
664C2×C4⋊C4—23no—
665C2×C4⋊C4—23no—
666C2×C4⋊C4—23no—
667C2×C4⋊C4—23no—
668C2×C4⋊C4—26no—
669C2×C4⋊C4—26no—
670C2×C4⋊C4—26no—
671C2×C4⋊C4C2×D413yes—
672C2×C4⋊C4C2×D413yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2416yes—
676C2×C22⋊C4—26no—
677C2×C22⋊C4—23no—
678C2×C22⋊C4—26no—
679C2×C22⋊C4—23no—
680C2×C22⋊C4—23no—
681C2×C22⋊C4C2×D416yes—
682C2×C42—23no—
683C2×C42—26no—
684C2×C42—21no—
685C2×C42—23no—
686C2×C42—26no—
687C2×C42—26no—
688C2×C42—26no—
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×C42C2411yescharacteristic
698C2×C42C2413yes—
699C2×C42C2413yes—
700C2×C42C2413yes—
701C2×C42C2413yes—
702C2×C42C2413yes—
703#107C24112yes—
704#107C24112yes—
705#106C2414yes—
706#106C24112yes—
707#106C24124yes—
708C4⋊C8C2412yes—
709C4⋊C8C2416yes—
710C4⋊C8C24112yes—
711C4⋊C8C24112yes—
712#103C2414yes—
713#103C24112yes—
714#103C24112yes—
715#103C24112yes—
716#103C24124yes—
717#102C2414yes—
718#102C24112yes—
719#102C24112yes—
720#102C24112yes—
721#102C24124yes—
722C22⋊C8C2412yes—
723C22⋊C8C2416yes—
724C22⋊C8C24112yes—
725C22⋊C8C24112yes—
726#97C24112yes—
727C4×C8C2412yes—
728C4×C8C2416yes—
729C4×C8C24112yes—
730C24—23no—
731C24C22×D413yes—
732#41—24no—
733#41—24no—
734#41—212no—
735#41—212no—
736#41—46no—
737#41—46no—
738#41—46no—
739#41—46no—
740#41—412no—
741#41—412no—
742#41—424no—
743#41—412no—
744#41—412no—
745#41—424no—
746#41—48no—
747#41—44no—
748#41—812no—
749#41—812no—
750#41—812no—
751#41—812no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—23no—
757C2×Q8—26no—
758C2×Q8—26no—
759C2×Q8—26no—
760C2×Q8—26no—
761C2×Q8—412no—
762C2×Q8—412no—
763C2×Q8—48no—
764C2×Q8—86no—
765C2×Q8C22×D413yes—
766C2×Q8C22×D411yescharacteristic
767C2×Q8C2516yes—
768C2×Q8C2512yes—
769C2×D4—22no—
770C2×D4—26no—
771C2×D4—26no—
772C2×D4—26no—
773C2×D4—26no—
774C2×D4—212no—
775C2×D4—212no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—23no—
779C2×D4—26no—
780C2×D4—26no—
781C2×D4—26no—
782C2×D4—26no—
783C2×D4—46no—
784C2×D4—46no—
785C2×D4—412no—
786C2×D4—412no—
787C2×D4—86no—
788C2×D4—812no—
789C2×D4C22×D413yes—
790C2×D4C22×D413yes—
791C2×D4C22×D416yes—
792C2×D4C2512yes—
793C2×D4C2516yes—
794C22×C4—21no—
795C22×C4—212no—
796C22×C4—21no—
797C22×C4—23no—
798C22×C4—26no—
799C22×C4—26no—
800C22×C4—26no—
801C22×C4—26no—
802C22×C4—26no—
803C22×C4—26no—
804C22×C4—26no—
805C22×C4—26no—
806C22×C4—22no—
807C22×C4—26no—
808C22×C4—26no—
809C22×C4—46no—
810C22×C4—46no—
811C22×C4—412no—
812C22×C4—412no—
813C22×C4—412no—
814C22×C4C22×D413yes—
815C22×C4C22×D413yes—
816C22×C4C22×D413yes—
817C22×C4C22×D413yes—
818C22×C4C22×D413yes—
819C22×C4C22×D413yes—
820C22×C4C22×D413yes—
821C22×C4C22×D413yes—
822C22×C4C22×D413yes—
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D413yes—
825C22×C4C22×D413yes—
826C22×C4C22×D413yes—
827C22×C4C22×D413yes—
828C22×C4C22×D411yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2513yes—
831C22×C4C2513yes—
832Q16—224no—
833SD16—28no—
834SD16—412no—
835SD16—424no—
836D8—412no—
837M16—412no—
838C2×C8—412no—
839C2×C8C2514yes—
840C2×C8C25112yes—
841C4⋊C4—23no—
842C4⋊C4—23no—
843C4⋊C4—23no—
844C4⋊C4—26no—
845C4⋊C4—212no—
846C4⋊C4—26no—
847C4⋊C4—26no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—26no—
851C4⋊C4—26no—
852C4⋊C4—26no—
853C4⋊C4—26no—
854C4⋊C4—26no—
855C4⋊C4—26no—
856C4⋊C4—212no—
857C4⋊C4—21no—
858C4⋊C4—23no—
859C4⋊C4—26no—
860C4⋊C4—21no—
861C4⋊C4—26no—
862C4⋊C4—26no—
863C4⋊C4—26no—
864C4⋊C4—26no—
865C4⋊C4C22×D413yes—
866C4⋊C4C22×D416yes—
867C4⋊C4C22×D413yes—
868C4⋊C4C22×D413yes—
869C4⋊C4C22×D413yes—
870C4⋊C4C22×D416yes—
871C4⋊C4C2516yes—
872C4⋊C4C2512yes—
873C4⋊C4C2516yes—
874C4⋊C4C2512yes—
875C22⋊C4—26no—
876C22⋊C4—212no—
877C22⋊C4—26no—
878C22⋊C4—26no—
879C22⋊C4—26no—
880C22⋊C4—26no—
881C22⋊C4—212no—
882C22⋊C4—212no—
883C22⋊C4—26no—
884C22⋊C4—26no—
885C22⋊C4—26no—
886C22⋊C4—26no—
887C22⋊C4—26no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—26no—
891C22⋊C4—26no—
892C22⋊C4—26no—
893C22⋊C4C22×D416yes—
894C22⋊C4C22×D416yes—
895C22⋊C4C22×D416yes—
896C22⋊C4C22×D416yes—
897C42—22no—
898C42—26no—
899C42—26no—
900C42—26no—
901C42—26no—
902C42—212no—
903C42—26no—
904C42—26no—
905C42—22no—
906C42—26no—
907C42C22×D413yes—
908C42C22×D413yes—
909C42C22×D411yescharacteristic
910C42C22×D413yes—
911C42C22×D413yes—
912C42C22×D413yes—
913C42C22×D413yes—
914C42C22×D413yes—
915C42C22×D413yes—
916C42C22×D413yes—
917C42C22×D413yes—
918C42C22×D411yescharacteristic
919C42C2513yes—
920C42C2513yes—
921C42C2511yescharacteristic
922C42C2511yescharacteristic
923C23—26no—
924C23—22no—
925C23—26no—
926C23—43no—
927C23—43no—
928C23—46no—
929C23—46no—
930C23—46no—
931C23C23×D413yes—
932C23C23×D413yes—
933C23C23×D411yescharacteristic
934Q8—24no—
935Q8—22no—
936Q8—26no—
937Q8—212no—
938Q8—46no—
939Q8—412no—
940Q8—42no—
941Q8—86no—
942Q8—86no—
943Q8—86no—
944Q8#57514yes—
945Q8#58514yes—
946D4—24no—
947D4—26no—
948D4—26no—
949D4—26no—
950D4—26no—
951D4—46no—
952D4—412no—
953D4—412no—
954D4—46no—
955D4—412no—
956D4—42no—
957D4—412no—
958D4—44no—
959D4—412no—
960D4—42no—
961D4—86no—
962D4—86no—
963D4—812no—
964D4—812no—
965D4—86no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—26no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—22no—
972C2×C4—26no—
973C2×C4—26no—
974C2×C4—26no—
975C2×C4—26no—
976C2×C4—26no—
977C2×C4—26no—
978C2×C4—26no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—26no—
982C2×C4—26no—
983C2×C4—26no—
984C2×C4—43no—
985C2×C4—41no—
986C2×C4—43no—
987C2×C4—43no—
988C2×C4—43no—
989C2×C4—43no—
990C2×C4—412no—
991C2×C4—412no—
992C2×C4—412no—
993C2×C4—42no—
994C2×C4—412no—
995C2×C4—46no—
996C2×C4—412no—
997C2×C4—412no—
998C2×C4—412no—
999C2×C4—412no—
1000C2×C4—44no—
1001C2×C4—86no—
1002C2×C4—86no—
1003C2×C4#57714yes—
1004C2×C4C23×D413yes—
1005C2×C4C23×D413yes—
1006C2×C4C23×D413yes—
1007C2×C4C23×D413yes—
1008C2×C4C23×D411yescharacteristic
1009C2×C4C23×D411yescharacteristic
1010C2×C4C23×D411yescharacteristic
1011C2×C4C23×D413yes—
1012C2×C4C23×D413yes—
1013C2×C4C23×D411yescharacteristic
1014C2×C4C23×D411yescharacteristic
1015C2×C4C2611yescharacteristic
1016C8—24no—
1017C8—212no—
1018C22—21no—
1019C22—21no—
1020C22—23no—
1021C22—23no—
1022C22—23no—
1023C22—23no—
1024C22—23no—
1025C22—23no—
1026C22—46no—
1027C22—42no—
1028C22—42no—
1029C22—46no—
1030C22—46no—
1031C22—42no—
1032C22—86no—
1033C22—812no—
1034C22C2×#57712yes—
1035C22C24×D411yescharacteristic
1036C4—24no—
1037C4—23no—
1038C4—21no—
1039C4—23no—
1040C4—21no—
1041C4—21no—
1042C4—23no—
1043C4—23no—
1044C4—23no—
1045C4—46no—
1046C4—42no—
1047C4—46no—
1048C4—46no—
1049C4—42no—
1050C4C2×#57516yes—
1051C4C2×#57712yes—
1052C4C2×#57712yes—
1053C4C2×#58512yes—
1054C2—22no—
1055C2—43no—
1056C2—43no—
1057C2—82no—
1058C2—86no—
1059C2#6281111yescharacteristic
1060C2C22×#57511yescharacteristic
1061C2C22×#57711yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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×#3483C2semidirect
3. #62150C2semidirect
4. #62135C2semidirect
5. #62002C2semidirect
6. #61987C2semidirect
7. #61901C2semidirect
8. #61838C2semidirect
9. #61731C2semidirect
10. #61596C2semidirect
11. #61450C2semidirect
12. #61434C2semidirect
13. #60951C2semidirect
14. #60941C2semidirect
15. #60562C2semidirect
16. #60536C2semidirect
17. #60278C2semidirect
22. #3511C22semidirect
23. #3509C22semidirect
24. #3503C22semidirect
25. #3499C22semidirect
36. #3482C22semidirect
37. #3482C22semidirect
55. #3397C22semidirect
56. #3392C22semidirect
57. #3387C22semidirect
58. Q8×SD16C22semidirect
59. #3369C22semidirect
60. #3368C22semidirect
61. #3363C22semidirect
62. #3358C22semidirect
63. #3354C22semidirect
64. #3348C22semidirect
65. #3340C22semidirect
66. #3332C22semidirect
67. #3329C22semidirect
68. #3321C22semidirect
69. #3317C22semidirect
70. #3304C22semidirect
71. #3303C22semidirect
72. #3284C22semidirect
73. #3278C22semidirect
74. #3271C22semidirect
75. #3254C22semidirect
76. #3253C22semidirect
77. #3246C22semidirect
79. #3235C22semidirect
81. #3227C22semidirect
83. #3214C22semidirect
85. #3206C22semidirect
88. #3171C22semidirect
89. #3167C22semidirect
90. #3116C22semidirect
94. #3107C22semidirect
95. #3107C22semidirect
96. #3106C22semidirect
97. #3106C22semidirect
101. #3103C22semidirect
102. #3102C22semidirect
108. #3079C22semidirect
109. #3076C22semidirect
110. #3039C22semidirect
111. #3035C22semidirect
114. #2991C22semidirect
115. #2990C22semidirect
118. #2965C22semidirect
119. C8×#41C22semidirect
120. C4×#137C22semidirect
121. C4×#135C22semidirect

Maximal subgroups

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

subgroupindex
#628052
C2×#34832
#621502
#621352
#620022
#619872
#619012
#618382
#617312
#615962
#614502
#614342
#609512
#609412
#605622
#605362
#602782