Finite Group Databasebeta

← #10581798

Subgroups — #10581798

Order 512.

6335 conjugacy classes of subgroups.

The subgroup lattice has 1053 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic, complemented
2#62800C211yesmaximal, characteristic, complemented
3#62595C212yesmaximal, complemented
4#62593C216yesmaximal, complemented
5#62456C216yesmaximal, complemented
6#62454C212yesmaximal, complemented
7#62000C212yesmaximal, complemented
8#61999C212yesmaximal, complemented
9#61998C216yesmaximal, complemented
10#61997C216yesmaximal, complemented
11#61887C214yesmaximal, complemented
12#61589C2112yesmaximal, complemented
13#60953C213yesmaximal, complemented
14#60952C213yesmaximal, complemented
15#60804C213yesmaximal, complemented
16#60802C213yesmaximal, complemented
17#60284C211yesmaximal, characteristic, complemented
18#3523C2212yescomplemented
19#3522—21no—
20#3520C2216yescomplemented
21#3519—23no—
22#3518—21no—
23#3517C2212yes—
24#3515—23no—
25#3514C2216yes—
26#3511C2213yes—
27#3511C2213yescomplemented
28#3509C2213yescomplemented
29#3508C2213yes—
30#3503C2211yescharacteristic
31#3503C2211yescharacteristic, complemented
32#3499C2211yescharacteristic, complemented
33#3498C2211yescharacteristic
34#3495—23no—
35#3494—23no—
36#3489—21no—
37#3488—21no—
38#3483—21no—
39#3482C2212yes—
40#3482C2216yescomplemented
41#3481—23no—
42#3480C2212yes—
43Q8×#41—21no—
44#3475—23no—
45D4×#41C2216yes—
46#3461—23no—
47#3460—23no—
48#3444C2213yes—
49#3444C2213yescomplemented
50C2×#533C2213yescomplemented
51C2×#532C2213yes—
52C4×2−1+4—21no—
53C4×H(5,𝔽2)—21no—
54C2×C4×#41C2211yescharacteristic
55#3395C2214yescomplemented
56#3394C22112yescomplemented
57#3393C22112yescomplemented
58#3392C2214yescomplemented
59#3365C22112yescomplemented
60#3364C22112yescomplemented
61#3359C2214yescomplemented
62#3358C2214yescomplemented
63#3332C22112yescomplemented
64#3330C22112yescomplemented
65#3328C22112yescomplemented
66#3327C22124yescomplemented
67#3324C22112yescomplemented
68#3323C22124yescomplemented
69#3278C22112yescomplemented
70#3277C22124yescomplemented
71#3276C22112yescomplemented
72#3276C22112yescomplemented
73#3275C22124yescomplemented
74#3272C22112yescomplemented
75#3255C2216yescomplemented
76#3254C2216yescomplemented
77#3252C2216yescomplemented
78#3251C2216yescomplemented
79#3240C2216yescomplemented
80#3239C2216yescomplemented
81#3237C2213yescomplemented
82#3235C2211yescharacteristic, complemented
83#3219C2216yescomplemented
84#3218C2216yescomplemented
85#3216C2216yescomplemented
86#3216C2213yescomplemented
87#3216C2216yescomplemented
88#3215C22112yescomplemented
89#3214C2213yescomplemented
90#3214C2216yescomplemented
91#3212C22112yescomplemented
92#3212C22112yescomplemented
93#3210C22112yescomplemented
94#3209C2216yescomplemented
95#3208C2216yescomplemented
96#3197C22112yescomplemented
97#3196C22112yescomplemented
98#3172C22112yescomplemented
99#3172C2216yescomplemented
100#3171C2216yescomplemented
101#3153C2216yescomplemented
102#3152C2216yescomplemented
103#3141C2216yescomplemented
104#3140C2216yescomplemented
105#3107C22112yescomplemented
106#3107C2216yescomplemented
107#3106C2216yescomplemented
108#3104C2216yescomplemented
109#3103C2216yescomplemented
110#3102C22112yescomplemented
111#3039C2216yescomplemented
112#3038C2216yescomplemented
113#3037C22112yescomplemented
114#3007C22112yescomplemented
115#3005C22112yescomplemented
116#2991C2212yes—
117#2991C2216yescomplemented
118#2982C2212yescomplemented
119#2975C2216yescomplemented
120#2971C2216yescomplemented
121#2971C2212yescomplemented
122#2920C2213yescomplemented
123#2920C2213yescomplemented
124C2×2−1+4—21no—
125C2×H(5,𝔽2)—21no—
126C22×#41D411yescharacteristic
127C22×#41C2316yes—
128C2×#137C23124yes—
129C2×#137C23112yes—
130C2×AGL(1,ℤ/8)C23112yes—
131#559—23no—
132#559C2316yes—
133Q82—21no—
134Q82—21no—
135#557—23no—
136#557C2312yes—
137#557C2312yes—
138#557C2316yes—
139#556—23no—
140#556—26no—
141#556C2316yes—
142#556C2316yes—
143#556C2316yes—
144#555—23no—
145#555—23no—
146#555—26no—
147#554—23no—
148#554—23no—
149#554—23no—
150#554—23no—
151#554—26no—
152#553—26no—
153#553—26no—
154#553—26no—
155#553—26no—
156#552—26no—
157#552—26no—
158#552—212no—
159#552—26no—
160#552C23112yes—
161#551—212no—
162#551—212no—
163#550—22no—
164#550—21no—
165#550—23no—
166#550C2316yes—
167#550C2312yes—
168D4×Q8—22no—
169D4×Q8—21no—
170D4×Q8C2316yes—
171D4×Q8C2316yes—
172D4×Q8C2312yes—
173#548—22no—
174#548—22no—
175#548C23112yes—
176#548C23112yes—
177#547—26no—
178#547—23no—
179#547—26no—
180#547C2316yes—
181#547C2316yes—
182#547C2316yes—
183#546—26no—
184#546—26no—
185#546—26no—
186#546—212no—
187#546C23112yes—
188D42—26no—
189D42—23no—
190D42C2316yes—
191#544—23no—
192#544—23no—
193#542—26no—
194#542—26no—
195#542—26no—
196#542—26no—
197#541—26no—
198#541—26no—
199#540—26no—
200#540—26no—
201#539—212no—
202#538—212no—
203#537—23no—
204#537—23no—
205#536—23no—
206#536—23no—
207#535—23no—
208#535—23no—
209#533—26no—
210#533—23no—
211#533—23no—
212#533—23no—
213#533—23no—
214#533C2313yes—
215#533C2316yes—
216#533C2313yes—
217#533C2316yes—
218#533C2313yes—
219#533C2313yes—
220#533C2316yes—
221#533C2313yes—
222#533C2311yescharacteristic
223#532—26no—
224#532—23no—
225#532—23no—
226#532—23no—
227#532—23no—
228#532C2316yes—
229#532C2313yes—
230#532C2313yes—
231#532C2316yes—
232#532C2316yes—
233#532C2313yes—
234#532C2313yes—
235#532C2313yes—
236#532C2311yescharacteristic
237C2×C4⋊Q8C2313yes—
238C2×C4⋊Q8C2313yes—
239C2×C4⋊Q8C2313yes—
240C2×#127C2313yes—
241#529—26no—
242#529—26no—
243#529—212no—
244#529—23no—
245#529—23no—
246#529—23no—
247#529—23no—
248#529—23no—
249#529—23no—
250#529—23no—
251#529—23no—
252#529C2316yes—
253#529C2316yes—
254#529C2316yes—
255#529C2316yes—
256C2×#125—23no—
257C2×#124C2316yes—
258#525—23no—
259#525—23no—
260#525—23no—
261#525—23no—
262#525—212no—
263#525C2316yes—
264#525C2316yes—
265C2×C22⋊Q8—23no—
266C2×C22⋊Q8C2316yes—
267C2×#121—23no—
268C2×#121—23no—
269#520—21no—
270#520—21no—
271#520—22no—
272#520—26no—
273#520—23no—
274#520—23no—
275#519—22no—
276#519—23no—
277#518—26no—
278#518—23no—
279C4×#41—22no—
280C4×#41—26no—
281C4×#41—23no—
282C4×#41—23no—
283C4×#41—23no—
284C4×#41—23no—
285C4×#41D411yescharacteristic
286C4×#41D411yescharacteristic
287C4×#41D413yes—
288C4×#41D413yes—
289C4×#41C2316yes—
290C4×#41C2316yes—
291C4×#41C2311yescharacteristic
292C4×#41C2313yes—
293C4×#41C2311yescharacteristic
294C4×#41C2313yes—
295C2×C4×Q8—22no—
296C2×C4×Q8—23no—
297C2×C4×Q8D411yescharacteristic
298C2×C4×Q8C2316yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4—26no—
301C2×C4×D4—23no—
302C2×C4×D4—23no—
303C2×C4×D4D413yes—
304C2×C4×D4C2313yes—
305C2×#117—23no—
306C2×#117D413yes—
307C22×C42C2313yes—
308#501C2316yes—
309#501C2312yes—
310#497C2316yes—
311#497C23112yes—
312#496C2316yes—
313#495C23124yes—
314#494C23112yes—
315#492C23112yes—
316#491C2316yes—
317#490C2312yes—
318#489C2316yes—
319#489C23112yes—
320#489C2316yes—
321#488C23124yes—
322#487C23112yes—
323#486C23112yes—
324#485C23112yes—
325#485C23112yes—
326#484C23112yes—
327#482C2314yes—
328#482C23112yes—
329#481C23112yes—
330#479C23112yes—
331#478C23112yes—
332#477C2316yes—
333#476C2312yes—
334#475C23112yes—
335#475C2316yes—
336#474C23112yes—
337#474C2312yes—
338#470C23124yes—
339#470C23112yes—
340#469C23112yes—
341#468C23112yes—
342#468C23124yes—
343#468C23112yes—
344#464C23112yes—
345#464C23124yes—
346#464C23124yes—
347#463C23112yes—
348#462C23112yes—
349#462C23112yes—
350#462C23112yes—
351#462C2316yes—
352#461C23112yes—
353#461C23112yes—
354#461C2316yes—
355#460C23112yes—
356#460C2316yes—
357#460C23112yes—
358#459C23112yes—
359#459C2316yes—
360#452C23112yes—
361#452C23124yes—
362#452C23112yes—
363#452C23124yes—
364#451C23124yes—
365#451C23112yes—
366#450C23124yes—
367#449C23124yes—
368#449C23112yes—
369#449C23112yes—
370#448C23112yes—
371C8×Q8C2314yes—
372C8×Q8C23112yes—
373C4×Q16C23112yes—
374C4×Q16C23124yes—
375C4×SD16C23112yes—
376C4×SD16C23112yes—
377C4×SD16C23124yes—
378C4×D8C23112yes—
379#436C23112yes—
380#436C23112yes—
381#436C23124yes—
382#432C2313yes—
383#432C2311yescharacteristic
384#432C2316yes—
385#432C2316yes—
386#431C2316yes—
387#431C2316yes—
388#431C2316yes—
389#431C2316yes—
390#423C2316yes—
391#423C2316yes—
392#419C23112yes—
393#418C23112yes—
394#417C23124yes—
395#407C2316yes—
396#407C2316yes—
397C4×M16C2316yes—
398C4×M16C2316yes—
3992−1+4—48no—
400H(5,𝔽2)—48no—
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—44no—
410C2×#41—812no—
411C2×#41C2×D411yescharacteristic
412C2×#41C2×D411yescharacteristic
413C2×#41C2×D413yes—
414C2×#41C2×D413yes—
415C2×#41C2416yes—
416C2×#41C2416yes—
417C2×#41C24112yes—
418C22×Q8—22no—
419C22×Q8—23no—
420C22×Q8C2×D411yescharacteristic
421C22×Q8C2416yes—
422C22×Q8C2416yes—
423C22×D4—26no—
424C22×D4—26no—
425C22×D4—23no—
426C22×D4—23no—
427C22×D4C2×D413yes—
428C22×D4C2416yes—
429C23×C4—26no—
430C23×C4C2×D413yes—
431C23×C4C2×D413yes—
432C23×C4C2413yes—
433#137—812no—
434#137—824no—
435AGL(1,ℤ/8)—812no—
436C2×Q16C24124yes—
437C2×Q16C24112yes—
438C2×SD16C24124yes—
439C2×SD16C24112yes—
440C2×SD16C24112yes—
441C2×D8C24112yes—
442C2×M16C24112yes—
443C2×M16C24112yes—
444C4⋊Q8—26no—
445C4⋊Q8—26no—
446C4⋊Q8—26no—
447C4⋊Q8—23no—
448C4⋊Q8—23no—
449C4⋊Q8—23no—
450C4⋊Q8—23no—
451C4⋊Q8—23no—
452C4⋊Q8—23no—
453C4⋊Q8C2413yes—
454C4⋊Q8C2413yes—
455C4⋊Q8C2416yes—
456C4⋊Q8C2416yes—
457C4⋊Q8C2413yes—
458C4⋊Q8C2416yes—
459C4⋊Q8C2411yescharacteristic
460C4⋊Q8C2411yescharacteristic
461C4⋊Q8C2411yescharacteristic
462#127—26no—
463#127—23no—
464#127—23no—
465#127C2413yes—
466#127C2416yes—
467#127C2411yescharacteristic
468#126—212no—
469#126—212no—
470#126—212no—
471#126—212no—
472#126—26no—
473#126—26no—
474#126—26no—
475#126—26no—
476#125—26no—
477#125—212no—
478#125—26no—
479#125—212no—
480#125—23no—
481#125—26no—
482#125—26no—
483#125—26no—
484#125—23no—
485#125—23no—
486#125—23no—
487#125C2412yes—
488#125C2416yes—
489#124—26no—
490#124—26no—
491#124—212no—
492#124—212no—
493#124—26no—
494#124—26no—
495#124—21no—
496#124—23no—
497#124—23no—
498#124—23no—
499#124C2416yes—
500#124C24112yes—
501#124C2416yes—
502#123—212no—
503#123—26no—
504#123—26no—
505#123—26no—
506#123—26no—
507#123—26no—
508#123—26no—
509#123—212no—
510#123—212no—
511#123—212no—
512#123—212no—
513#123—212no—
514C22⋊Q8—26no—
515C22⋊Q8—26no—
516C22⋊Q8—23no—
517C22⋊Q8—26no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—26no—
521C22⋊Q8—26no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—23no—
525C22⋊Q8—23no—
526C22⋊Q8—23no—
527C22⋊Q8—23no—
528C22⋊Q8—23no—
529C22⋊Q8—212no—
530C22⋊Q8—26no—
531C22⋊Q8—26no—
532C22⋊Q8—212no—
533C22⋊Q8—212no—
534C22⋊Q8—212no—
535C22⋊Q8C2416yes—
536C22⋊Q8C24112yes—
537C22⋊Q8C2416yes—
538C22⋊Q8C2416yes—
539C22⋊Q8C2416yes—
540#121—212no—
541#121—212no—
542#121—26no—
543#121—26no—
544#121—23no—
545#121—23no—
546#121—26no—
547#121—26no—
548#121—26no—
549#121—26no—
550#121—26no—
551#121—26no—
552#121—21no—
553#121—23no—
554#121—23no—
555#121—23no—
556#121—23no—
557#121—23no—
558#121—26no—
559#121—26no—
560#121—212no—
561#121—212no—
562#121C2412yes—
563#121C2416yes—
564#121C2416yes—
565#121C2416yes—
566#120—26no—
567#120—26no—
568#120—212no—
569#120—212no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—26no—
573C4×Q8—26no—
574C4×Q8—26no—
575C4×Q8—23no—
576C4×Q8—26no—
577C4×Q8—26no—
578C4×Q8—26no—
579C4×Q8—26no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—23no—
583C4×Q8—23no—
584C4×Q8—23no—
585C4×Q8—23no—
586C4×Q8—23no—
587C4×Q8C2×D411yescharacteristic
588C4×Q8C2×D411yescharacteristic
589C4×Q8C2×D413yes—
590C4×Q8C2×D413yes—
591C4×Q8C2×D411yescharacteristic
592C4×Q8C2×D413yes—
593C4×Q8C2416yes—
594C4×Q8C24112yes—
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—26no—
612C4×D4—26no—
613C4×D4—26no—
614C4×D4—26no—
615C4×D4—26no—
616C4×D4—212no—
617C4×D4—212no—
618C4×D4—26no—
619C4×D4—23no—
620C4×D4—23no—
621C4×D4—26no—
622C4×D4—26no—
623C4×D4—26no—
624C4×D4—26no—
625C4×D4—26no—
626C4×D4—21no—
627C4×D4—23no—
628C4×D4—23no—
629C4×D4—23no—
630C4×D4—23no—
631C4×D4—23no—
632C4×D4C2×D413yes—
633C4×D4C2×D413yes—
634C4×D4C2×D413yes—
635C4×D4C2×D413yes—
636C4×D4C2×D416yes—
637C4×D4C2×D416yes—
638C4×D4C2×D413yes—
639C4×D4C2×D413yes—
640C4×D4C2×D416yes—
641C4×D4C2412yes—
642C4×D4C2416yes—
643C4×D4C2416yes—
644C4×D4C2416yes—
645C4×D4C2413yes—
646C4×D4C2416yes—
647C4×D4C2413yes—
648#117—23no—
649#117—26no—
650#117—26no—
651#117—26no—
652#117—23no—
653#117—23no—
654#117—23no—
655#117—26no—
656#117—26no—
657#117—212no—
658#117—26no—
659#117—26no—
660#117—26no—
661#117—26no—
662#117—26no—
663#117—26no—
664#117C2×D413yes—
665#117C2×D413yes—
666#117C2×D413yes—
667#117C2×D413yes—
668#117C2×D416yes—
669#117C2×D416yes—
670#117C2412yes—
671#117C2416yes—
672C2×C4⋊C4—23no—
673C2×C4⋊C4—23no—
674C2×C4⋊C4—23no—
675C2×C4⋊C4—23no—
676C2×C4⋊C4—23no—
677C2×C4⋊C4—26no—
678C2×C4⋊C4—26no—
679C2×C4⋊C4—26no—
680C2×C4⋊C4—26no—
681C2×C4⋊C4C2×D413yes—
682C2×C4⋊C4C2×D413yes—
683C2×C4⋊C4C2416yes—
684C2×C22⋊C4—26no—
685C2×C22⋊C4—26no—
686C2×C22⋊C4—26no—
687C2×C22⋊C4—212no—
688C2×C22⋊C4C2×D416yes—
689C2×C42—26no—
690C2×C42—26no—
691C2×C42—26no—
692C2×C42C2×D413yes—
693C2×C42C2×D413yes—
694C2×C42C2×D413yes—
695C2×C42C2×D413yes—
696C2×C42C2×D413yes—
697C2×C42C2×D413yes—
698C2×C42C2413yes—
699C2×C42C2413yes—
700C2×C42C2413yes—
701C2×C42C2413yes—
702C2×C42C2413yes—
703C2×C42C2411yescharacteristic
704#107C24112yes—
705#107C2414yes—
706#106C24112yes—
707#106C2414yes—
708C4⋊C8C2416yes—
709C4⋊C8C2412yes—
710C4⋊C8C24112yes—
711C4⋊C8C24112yes—
712#103C24112yes—
713#103C24124yes—
714#103C24112yes—
715#103C24112yes—
716#103C24112yes—
717#102C24112yes—
718#102C24124yes—
719#102C24112yes—
720#102C2414yes—
721#102C2414yes—
722C22⋊C8C2416yes—
723C22⋊C8C2412yes—
724C22⋊C8C24112yes—
725C22⋊C8C24112yes—
726#97C2412yes—
727#97C2416yes—
728C4×C8C24112yes—
729C4×C8C24112yes—
730C24—26no—
731C24C22×D413yes—
732#41—24no—
733#41—24no—
734#41—46no—
735#41—46no—
736#41—412no—
737#41—44no—
738#41—412no—
739#41—412no—
740#41—46no—
741#41—46no—
742#41—424no—
743#41—424no—
744#41—48no—
745#41—86no—
746#41—812no—
747#41—812no—
748C2×Q8—24no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—23no—
753C2×Q8—26no—
754C2×Q8—26no—
755C2×Q8—26no—
756C2×Q8—412no—
757C2×Q8—412no—
758C2×Q8—412no—
759C2×Q8—48no—
760C2×Q8C22×D413yes—
761C2×Q8C22×D411yescharacteristic
762C2×Q8C2516yes—
763C2×Q8C2516yes—
764C2×D4—22no—
765C2×D4—26no—
766C2×D4—26no—
767C2×D4—26no—
768C2×D4—26no—
769C2×D4—26no—
770C2×D4—212no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—23no—
774C2×D4—23no—
775C2×D4—26no—
776C2×D4—26no—
777C2×D4—26no—
778C2×D4—46no—
779C2×D4—412no—
780C2×D4—412no—
781C2×D4—424no—
782C2×D4—86no—
783C2×D4—812no—
784C2×D4C22×D413yes—
785C2×D4C22×D413yes—
786C2×D4C22×D416yes—
787C2×D4C2516yes—
788C2×D4C2512yes—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—26no—
792C22×C4—22no—
793C22×C4—26no—
794C22×C4—26no—
795C22×C4—26no—
796C22×C4—26no—
797C22×C4—26no—
798C22×C4—212no—
799C22×C4—46no—
800C22×C4—46no—
801C22×C4—46no—
802C22×C4—812no—
803C22×C4C22×D413yes—
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D413yes—
806C22×C4C22×D413yes—
807C22×C4C22×D413yes—
808C22×C4C22×D413yes—
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D413yes—
811C22×C4C22×D413yes—
812C22×C4C22×D413yes—
813C22×C4C22×D413yes—
814C22×C4C22×D413yes—
815C22×C4C22×D413yes—
816C22×C4C22×D413yes—
817C22×C4C22×D413yes—
818C22×C4C2511yescharacteristic
819C22×C4C2513yes—
820C22×C4C2513yes—
821Q16—424no—
822Q16—412no—
823SD16—424no—
824SD16—412no—
825SD16—412no—
826D8—412no—
827M16—412no—
828M16—412no—
829C2×C8C2514yes—
830C2×C8C25112yes—
831C4⋊C4—23no—
832C4⋊C4—23no—
833C4⋊C4—23no—
834C4⋊C4—23no—
835C4⋊C4—26no—
836C4⋊C4—26no—
837C4⋊C4—23no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—212no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—26no—
844C4⋊C4—26no—
845C4⋊C4—212no—
846C4⋊C4—26no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—21no—
852C4⋊C4—26no—
853C4⋊C4—26no—
854C4⋊C4—26no—
855C4⋊C4—26no—
856C4⋊C4—26no—
857C4⋊C4—26no—
858C4⋊C4—26no—
859C4⋊C4C22×D413yes—
860C4⋊C4C22×D413yes—
861C4⋊C4C22×D413yes—
862C4⋊C4C22×D413yes—
863C4⋊C4C22×D416yes—
864C4⋊C4C22×D416yes—
865C4⋊C4C2516yes—
866C4⋊C4C2512yes—
867C4⋊C4C2512yes—
868C4⋊C4C2512yes—
869C22⋊C4—26no—
870C22⋊C4—26no—
871C22⋊C4—212no—
872C22⋊C4—26no—
873C22⋊C4—26no—
874C22⋊C4—22no—
875C22⋊C4—26no—
876C22⋊C4—212no—
877C22⋊C4—26no—
878C22⋊C4—26no—
879C22⋊C4—26no—
880C22⋊C4—212no—
881C22⋊C4—26no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—26no—
885C22⋊C4—26no—
886C22⋊C4—26no—
887C22⋊C4—26no—
888C22⋊C4—26no—
889C22⋊C4—26no—
890C22⋊C4C22×D416yes—
891C22⋊C4C22×D416yes—
892C22⋊C4C22×D416yes—
893C22⋊C4C22×D416yes—
894C42—26no—
895C42—22no—
896C42—26no—
897C42—212no—
898C42—26no—
899C42—26no—
900C42—26no—
901C42C22×D413yes—
902C42C22×D413yes—
903C42C22×D411yescharacteristic
904C42C22×D411yescharacteristic
905C42C22×D413yes—
906C42C22×D413yes—
907C42C22×D413yes—
908C42C22×D413yes—
909C42C22×D413yes—
910C42C22×D413yes—
911C42C22×D413yes—
912C42C22×D413yes—
913C42C2513yes—
914C42C2513yes—
915C42C2511yescharacteristic
916C42C2511yescharacteristic
917C23—22no—
918C23—26no—
919C23—43no—
920C23—43no—
921C23—43no—
922C23—412no—
923C23—86no—
924C23—86no—
925C23C23×D413yes—
926C23C23×D411yescharacteristic
927C23C23×D413yes—
928Q8—26no—
929Q8—26no—
930Q8—26no—
931Q8—212no—
932Q8—46no—
933Q8—42no—
934Q8—42no—
935Q8—42no—
936Q8—412no—
937Q8—86no—
938Q8—86no—
939Q8#57514yes—
940D4—22no—
941D4—212no—
942D4—22no—
943D4—26no—
944D4—26no—
945D4—46no—
946D4—46no—
947D4—42no—
948D4—42no—
949D4—412no—
950D4—412no—
951D4—44no—
952D4—412no—
953D4—46no—
954D4—412no—
955D4—86no—
956D4—86no—
957D4—812no—
958D4—86no—
959D4—86no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—22no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—26no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—26no—
973C2×C4—26no—
974C2×C4—26no—
975C2×C4—41no—
976C2×C4—43no—
977C2×C4—43no—
978C2×C4—43no—
979C2×C4—43no—
980C2×C4—43no—
981C2×C4—43no—
982C2×C4—43no—
983C2×C4—43no—
984C2×C4—412no—
985C2×C4—412no—
986C2×C4—44no—
987C2×C4—412no—
988C2×C4—412no—
989C2×C4—812no—
990C2×C4—86no—
991C2×C4—86no—
992C2×C4—86no—
993C2×C4—86no—
994C2×C4C23×D413yes—
995C2×C4C23×D411yescharacteristic
996C2×C4C23×D413yes—
997C2×C4C23×D411yescharacteristic
998C2×C4C23×D411yescharacteristic
999C2×C4C23×D411yescharacteristic
1000C2×C4C23×D413yes—
1001C2×C4C23×D413yes—
1002C2×C4C23×D413yes—
1003C2×C4C23×D411yescharacteristic
1004C2×C4C23×D413yes—
1005C2×C4C2611yescharacteristic
1006C8—212no—
1007C8—24no—
1008C22—21no—
1009C22—23no—
1010C22—23no—
1011C22—21no—
1012C22—23no—
1013C22—23no—
1014C22—21no—
1015C22—23no—
1016C22—23no—
1017C22—42no—
1018C22—46no—
1019C22—42no—
1020C22—46no—
1021C22—46no—
1022C22—42no—
1023C22—86no—
1024C22—1612no—
1025C22C24×D411yescharacteristic
1026C4—21no—
1027C4—21no—
1028C4—23no—
1029C4—21no—
1030C4—23no—
1031C4—23no—
1032C4—21no—
1033C4—23no—
1034C4—23no—
1035C4—42no—
1036C4—46no—
1037C4—42no—
1038C4—42no—
1039C4—46no—
1040C4—46no—
1041C4C2×#57516yes—
1042C4#358612yes—
1043C4H(7,𝔽2)12yes—
1044C2—43no—
1045C2—41no—
1046C2—43no—
1047C2—82no—
1048C2—86no—
1049C2#6285211yescharacteristic
1050C2C22×#57511yescharacteristic
1051C2C2×#358611yescharacteristic
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. #62800C2semidirect
3. #62595C2semidirect
4. #62593C2semidirect
5. #62456C2semidirect
6. #62454C2semidirect
7. #62000C2semidirect
8. #61999C2semidirect
9. #61998C2semidirect
10. #61997C2semidirect
11. #61887C2semidirect
12. #61589C2semidirect
13. #60953C2semidirect
14. #60952C2semidirect
15. #60804C2semidirect
16. #60802C2semidirect
17. #60284C2semidirect
18. #3523C22semidirect
20. #3520C22semidirect
27. #3511C22semidirect
28. #3509C22semidirect
31. #3503C22semidirect
32. #3499C22semidirect
40. #3482C22semidirect
49. #3444C22semidirect
50. C2×#533C22semidirect
55. #3395C22semidirect
56. #3394C22semidirect
57. #3393C22semidirect
58. #3392C22semidirect
59. #3365C22semidirect
60. #3364C22semidirect
61. #3359C22semidirect
62. #3358C22semidirect
63. #3332C22semidirect
64. #3330C22semidirect
65. #3328C22semidirect
66. #3327C22semidirect
67. #3324C22semidirect
68. #3323C22semidirect
69. #3278C22semidirect
70. #3277C22semidirect
71. #3276C22semidirect
72. #3276C22semidirect
73. #3275C22semidirect
74. #3272C22semidirect
75. #3255C22semidirect
76. #3254C22semidirect
77. #3252C22semidirect
78. #3251C22semidirect
79. #3240C22semidirect
80. #3239C22semidirect
81. #3237C22semidirect
82. #3235C22semidirect
83. #3219C22semidirect
84. #3218C22semidirect
85. #3216C22semidirect
86. #3216C22semidirect
87. #3216C22semidirect
88. #3215C22semidirect
89. #3214C22semidirect
90. #3214C22semidirect
91. #3212C22semidirect
92. #3212C22semidirect
93. #3210C22semidirect
94. #3209C22semidirect
95. #3208C22semidirect
96. #3197C22semidirect
97. #3196C22semidirect
98. #3172C22semidirect
99. #3172C22semidirect
100. #3171C22semidirect
101. #3153C22semidirect
102. #3152C22semidirect
103. #3141C22semidirect
104. #3140C22semidirect
105. #3107C22semidirect
106. #3107C22semidirect
107. #3106C22semidirect
108. #3104C22semidirect
109. #3103C22semidirect
110. #3102C22semidirect
111. #3039C22semidirect
112. #3038C22semidirect
113. #3037C22semidirect
114. #3007C22semidirect
115. #3005C22semidirect
117. #2991C22semidirect
118. #2982C22semidirect
119. #2975C22semidirect
120. #2971C22semidirect
121. #2971C22semidirect
122. #2920C22semidirect
123. #2920C22semidirect

Maximal subgroups

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

subgroupindex
#628052
#628002
#625952
#625932
#624562
#624542
#620002
#619992
#619982
#619972
#618872
#615892
#609532
#609522
#608042
#608022
#602842