Finite Group Databasebeta

← #10581799

Subgroups — #10581799

Order 512.

6523 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62800C211yesmaximal, characteristic, complemented
2#62800C211yesmaximal, characteristic, complemented
3#62594C212yesmaximal, complemented
4#62592C216yesmaximal, complemented
5#62455C216yesmaximal, complemented
6#62453C212yesmaximal, complemented
7#62002C212yesmaximal, complemented
8#62001C212yesmaximal, complemented
9#61996C216yesmaximal, complemented
10#61995C216yesmaximal, complemented
11#61886C214yesmaximal, complemented
12#61590C2112yesmaximal, complemented
13#60953C213yesmaximal, complemented
14#60951C213yesmaximal, complemented
15#60803C213yesmaximal, complemented
16#60802C213yesmaximal, complemented
17#60284C211yesmaximal, characteristic, complemented
18#3522—21no—
19#3522C2212yescomplemented
20#3519—23no—
21#3519C2216yescomplemented
22#3517—21no—
23#3517C2212yes—
24#3514—23no—
25#3514C2216yescomplemented
26#3511C2213yescomplemented
27#3511C2213yescomplemented
28#3508C2213yescomplemented
29#3508C2213yescomplemented
30#3503C2211yescharacteristic, complemented
31#3503C2211yescharacteristic, complemented
32#3498C2211yescharacteristic, complemented
33#3498C2211yescharacteristic, complemented
34#3494—23no—
35#3494—23no—
36#3488—21no—
37#3488—21no—
38#3483—21no—
39#3483C2212yes—
40#3481—23no—
41#3481C2216yescomplemented
42#3480—21no—
43#3480C2212yescomplemented
44D4×#41—23no—
45D4×#41C2216yescomplemented
46#3460—23no—
47#3460—23no—
48#3444C2213yescomplemented
49#3444C2213yescomplemented
50C2×#532C2213yescomplemented
51C2×#532C2213yescomplemented
52C4×H(5,𝔽2)—21no—
53C4×H(5,𝔽2)—21no—
54C2×C4×#41C2211yescharacteristic
55#3396C22112yescomplemented
56#3394C22112yescomplemented
57#3392C2214yescomplemented
58#3391C2214yescomplemented
59#3363C2214yescomplemented
60#3362C2214yescomplemented
61#3361C22112yescomplemented
62#3360C22112yescomplemented
63#3333C22112yescomplemented
64#3331C22112yescomplemented
65#3329C22112yescomplemented
66#3326C22124yescomplemented
67#3325C22112yescomplemented
68#3322C22124yescomplemented
69#3278C22112yescomplemented
70#3275C22124yescomplemented
71#3274C22112yescomplemented
72#3274C22112yescomplemented
73#3273C22124yescomplemented
74#3272C22112yescomplemented
75#3254C2216yescomplemented
76#3253C2216yescomplemented
77#3252C2216yescomplemented
78#3251C2216yescomplemented
79#3240C2216yescomplemented
80#3238C2216yescomplemented
81#3237C2211yescharacteristic, complemented
82#3235C2213yescomplemented
83#3219C2216yescomplemented
84#3217C2216yescomplemented
85#3216C2213yescomplemented
86#3216C2216yescomplemented
87#3214C2216yescomplemented
88#3214C2213yescomplemented
89#3214C2216yescomplemented
90#3213C22112yescomplemented
91#3212C22112yescomplemented
92#3212C22112yescomplemented
93#3207C22112yescomplemented
94#3206C2216yescomplemented
95#3205C2216yescomplemented
96#3197C22112yescomplemented
97#3194C22112yescomplemented
98#3172C2216yescomplemented
99#3171C22112yescomplemented
100#3171C2216yescomplemented
101#3153C2216yescomplemented
102#3151C2216yescomplemented
103#3141C2216yescomplemented
104#3140C2216yescomplemented
105#3107C2216yescomplemented
106#3106C22112yescomplemented
107#3106C2216yescomplemented
108#3102C22112yescomplemented
109#3101C2216yescomplemented
110#3100C2216yescomplemented
111#3039C2216yescomplemented
112#3038C2216yescomplemented
113#3036C22112yescomplemented
114#3006C22112yescomplemented
115#3005C22112yescomplemented
116#2991C2216yescomplemented
117#2991C2212yescomplemented
118#2982C2212yescomplemented
119#2975C2216yescomplemented
120#2971C2216yescomplemented
121#2971C2212yescomplemented
122#2920C2213yescomplemented
123#2920C2213yescomplemented
124C2×H(5,𝔽2)—21no—
125C2×H(5,𝔽2)—21no—
126C22×#41—23no—
127C22×#41D411yescharacteristic
128C22×#41C2316yes—
129C2×#137C23112yes—
130C2×AGL(1,ℤ/8)C23124yes—
131C2×AGL(1,ℤ/8)C23112yes—
132#559—23no—
133#559—23no—
134#559C2316yes—
135#559C2316yes—
136Q82—21no—
137Q82C2312yes—
138#557—21no—
139#557C2312yes—
140#556—23no—
141#556C2316yes—
142#555—23no—
143#555—26no—
144#555—26no—
145#555C2316yes—
146#554—23no—
147#554—23no—
148#554C2316yes—
149#554C2316yes—
150#553—26no—
151#553—26no—
152#553—26no—
153#553—26no—
154#553—26no—
155#553C23112yes—
156#551—212no—
157#551—212no—
158#550—22no—
159#550—22no—
160#550—21no—
161#550—21no—
162#550—23no—
163#550—23no—
164#550C2316yes—
165#550C2316yes—
166#550C2312yes—
167#550C2312yes—
168D4×Q8—23no—
169D4×Q8C2316yes—
170#548—22no—
171#548—22no—
172#548—26no—
173#548C23112yes—
174#547—23no—
175#547—26no—
176#547—26no—
177#547C2316yes—
178#546—26no—
179#546—26no—
180#546—26no—
181#546—26no—
182#546—212no—
183#546—212no—
184#546C23112yes—
185#546C23112yes—
186D42—26no—
187D42—26no—
188D42—23no—
189D42—23no—
190D42C2316yes—
191D42C2316yes—
192#544—23no—
193#544—23no—
194#542—26no—
195#542—26no—
196#542—26no—
197#542—26no—
198#540—26no—
199#540—26no—
200#540—26no—
201#540—26no—
202#538—212no—
203#538—212no—
204#537—23no—
205#537—23no—
206#535—23no—
207#535—23no—
208#535—23no—
209#535—23no—
210#533C2313yes—
211#533C2313yes—
212#533C2313yes—
213#533C2311yescharacteristic
214#533C2313yes—
215#533C2311yescharacteristic
216#532—26no—
217#532—26no—
218#532—23no—
219#532—23no—
220#532—23no—
221#532—23no—
222#532—23no—
223#532—23no—
224#532—23no—
225#532—23no—
226#532C2316yes—
227#532C2313yes—
228#532C2313yes—
229#532C2316yes—
230#532C2316yes—
231#532C2313yes—
232#532C2316yes—
233#532C2313yes—
234#532C2316yes—
235#532C2313yes—
236#532C2313yes—
237#532C2316yes—
238C2×C4⋊Q8C2313yes—
239C2×C4⋊Q8C2313yes—
240C2×#127C2313yes—
241C2×#127C2313yes—
242#529—26no—
243#529—26no—
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×#124—23no—
257C2×#124C2316yes—
258#525—23no—
259#525—23no—
260#525—23no—
261#525—23no—
262#525—212no—
263#525—212no—
264#525C2316yes—
265#525C2316yes—
266C2×#121—23no—
267C2×#121—23no—
268C2×#121—23no—
269C2×#121C2316yes—
270#520—21no—
271#520—21no—
272#520—22no—
273#520—22no—
274#520—23no—
275#520—23no—
276#518—26no—
277#518—26no—
278#518—23no—
279#518—23no—
280C4×#41—22no—
281C4×#41—22no—
282C4×#41—23no—
283C4×#41—23no—
284C4×#41—23no—
285C4×#41—23no—
286C4×#41D411yescharacteristic
287C4×#41D411yescharacteristic
288C4×#41D413yes—
289C4×#41D413yes—
290C4×#41C2316yes—
291C4×#41C2316yes—
292C4×#41C2313yes—
293C4×#41C2311yescharacteristic
294C4×#41C2313yes—
295C4×#41C2311yescharacteristic
296C2×C4×Q8D411yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×D4—26no—
299C2×C4×D4—26no—
300C2×C4×D4—23no—
301C2×C4×D4—23no—
302C2×C4×D4—23no—
303C2×C4×D4D413yes—
304C2×C4×D4C2316yes—
305C2×C4×D4C2313yes—
306C2×#117D413yes—
307C22×C42C2313yes—
308#501C2312yes—
309#501C2316yes—
310#497C2316yes—
311#496C2316yes—
312#496C23112yes—
313#495C23124yes—
314#493C23112yes—
315#492C23112yes—
316#491C2312yes—
317#490C2316yes—
318#489C2316yes—
319#489C23112yes—
320#489C2316yes—
321#488C23124yes—
322#487C23112yes—
323#486C23112yes—
324#485C23112yes—
325#485C2314yes—
326#483C23112yes—
327#482C23112yes—
328#482C23112yes—
329#480C23112yes—
330#479C23112yes—
331#478C23112yes—
332#477C23112yes—
333#477C2312yes—
334#476C23112yes—
335#476C2316yes—
336#475C2312yes—
337#474C2316yes—
338#470C23112yes—
339#469C23124yes—
340#469C23112yes—
341#468C23124yes—
342#468C23112yes—
343#468C23112yes—
344#464C23112yes—
345#463C23112yes—
346#463C23124yes—
347#463C23124yes—
348#462C23112yes—
349#462C2316yes—
350#461C23112yes—
351#461C23112yes—
352#461C2316yes—
353#460C23112yes—
354#460C23112yes—
355#460C2316yes—
356#459C23112yes—
357#459C23112yes—
358#459C23112yes—
359#459C2316yes—
360#452C23124yes—
361#452C23112yes—
362#452C23112yes—
363#450C23112yes—
364#449C23112yes—
365#449C23124yes—
366#449C23112yes—
367#449C23124yes—
368#448C23124yes—
369#447C23112yes—
370#447C23124yes—
371C8×Q8C23112yes—
372C8×Q8C2314yes—
373C4×Q16C23112yes—
374C4×SD16C23112yes—
375C4×SD16C23112yes—
376C4×SD16C23124yes—
377C4×D8C23124yes—
378C4×D8C23112yes—
379#436C23112yes—
380#436C23112yes—
381#436C23124yes—
382#432C2311yescharacteristic
383#432C2313yes—
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—
399H(5,𝔽2)—48no—
400H(5,𝔽2)—48no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—23no—
404C2×#41—23no—
405C2×#41—23no—
406C2×#41—23no—
407C2×#41—26no—
408C2×#41—26no—
409C2×#41—26no—
410C2×#41—26no—
411C2×#41—26no—
412C2×#41—44no—
413C2×#41—812no—
414C2×#41—812no—
415C2×#41C2×D411yescharacteristic
416C2×#41C2×D411yescharacteristic
417C2×#41C2×D413yes—
418C2×#41C2×D413yes—
419C2×#41C2416yes—
420C2×#41C2416yes—
421C2×#41C24112yes—
422C22×Q8—23no—
423C22×Q8C2×D411yescharacteristic
424C22×Q8C2416yes—
425C22×D4—26no—
426C22×D4—26no—
427C22×D4—26no—
428C22×D4—26no—
429C22×D4—23no—
430C22×D4—23no—
431C22×D4—23no—
432C22×D4—23no—
433C22×D4C2×D413yes—
434C22×D4C2416yes—
435C22×D4C2416yes—
436C23×C4—26no—
437C23×C4—26no—
438C23×C4C2×D413yes—
439C23×C4C2×D413yes—
440C23×C4C2413yes—
441#137—812no—
442AGL(1,ℤ/8)—824no—
443AGL(1,ℤ/8)—812no—
444C2×Q16C24112yes—
445C2×SD16C24112yes—
446C2×SD16C24112yes—
447C2×SD16C24124yes—
448C2×D8C24124yes—
449C2×D8C24112yes—
450C2×M16C24112yes—
451C2×M16C24112yes—
452C4⋊Q8—26no—
453C4⋊Q8—26no—
454C4⋊Q8—23no—
455C4⋊Q8—23no—
456C4⋊Q8—23no—
457C4⋊Q8—23no—
458C4⋊Q8C2413yes—
459C4⋊Q8C2416yes—
460C4⋊Q8C2411yescharacteristic
461C4⋊Q8C2413yes—
462C4⋊Q8C2416yes—
463C4⋊Q8C2411yescharacteristic
464C4⋊Q8C2411yescharacteristic
465C4⋊Q8C2411yescharacteristic
466#127—26no—
467#127—26no—
468#127—23no—
469#127—23no—
470#127—23no—
471#127—23no—
472#127C2413yes—
473#127C2413yes—
474#127C2416yes—
475#127C2416yes—
476#126—212no—
477#126—212no—
478#126—26no—
479#126—26no—
480#126—26no—
481#126—26no—
482#125—26no—
483#125—26no—
484#125—21no—
485#125—23no—
486#125—23no—
487#125—23no—
488#125C2412yes—
489#125C2416yes—
490#124—26no—
491#124—26no—
492#124—212no—
493#124—212no—
494#124—23no—
495#124—26no—
496#124—26no—
497#124—26no—
498#124—26no—
499#124—26no—
500#124—23no—
501#124—23no—
502#124—23no—
503#124C2416yes—
504#124C24112yes—
505#124C2416yes—
506#123—26no—
507#123—26no—
508#123—26no—
509#123—26no—
510#123—26no—
511#123—26no—
512#123—212no—
513#123—212no—
514#123—212no—
515#123—212no—
516#123—212no—
517#123—212no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—23no—
524C22⋊Q8—23no—
525C22⋊Q8—23no—
526C22⋊Q8—23no—
527C22⋊Q8—23no—
528C22⋊Q8—212no—
529C22⋊Q8—212no—
530C22⋊Q8—212no—
531C22⋊Q8—212no—
532C22⋊Q8C2412yes—
533C22⋊Q8C2416yes—
534C22⋊Q8C2416yes—
535C22⋊Q8C2416yes—
536#121—212no—
537#121—212no—
538#121—26no—
539#121—26no—
540#121—23no—
541#121—23no—
542#121—23no—
543#121—26no—
544#121—26no—
545#121—26no—
546#121—26no—
547#121—26no—
548#121—26no—
549#121—26no—
550#121—26no—
551#121—26no—
552#121—26no—
553#121—26no—
554#121—23no—
555#121—23no—
556#121—23no—
557#121—23no—
558#121—23no—
559#121—26no—
560#121—26no—
561#121—26no—
562#121—26no—
563#121—212no—
564#121—212no—
565#121—212no—
566#121—212no—
567#121C2416yes—
568#121C24112yes—
569#121C2416yes—
570#121C2416yes—
571#121C2416yes—
572#120—26no—
573#120—26no—
574#120—212no—
575#120—212no—
576#120—212no—
577#120—212no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8—23no—
584C4×Q8—23no—
585C4×Q8—23no—
586C4×Q8—23no—
587C4×Q8—23no—
588C4×Q8C2×D411yescharacteristic
589C4×Q8C2×D411yescharacteristic
590C4×Q8C2×D413yes—
591C4×Q8C2×D413yes—
592C4×Q8C2×D411yescharacteristic
593C4×Q8C2×D413yes—
594C4×Q8C2412yes—
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—26no—
617C4×D4—26no—
618C4×D4—212no—
619C4×D4—212no—
620C4×D4—26no—
621C4×D4—26no—
622C4×D4—23no—
623C4×D4—23no—
624C4×D4—23no—
625C4×D4—26no—
626C4×D4—26no—
627C4×D4—26no—
628C4×D4—26no—
629C4×D4—26no—
630C4×D4—26no—
631C4×D4—26no—
632C4×D4—26no—
633C4×D4—26no—
634C4×D4—23no—
635C4×D4—23no—
636C4×D4—23no—
637C4×D4—23no—
638C4×D4—23no—
639C4×D4C2×D413yes—
640C4×D4C2×D413yes—
641C4×D4C2×D413yes—
642C4×D4C2×D416yes—
643C4×D4C2×D413yes—
644C4×D4C2×D416yes—
645C4×D4C2×D413yes—
646C4×D4C2×D413yes—
647C4×D4C2×D416yes—
648C4×D4C2416yes—
649C4×D4C24112yes—
650C4×D4C2416yes—
651C4×D4C2416yes—
652C4×D4C2416yes—
653C4×D4C2413yes—
654C4×D4C2413yes—
655C4×D4C2416yes—
656#117—21no—
657#117—23no—
658#117—23no—
659#117—23no—
660#117—26no—
661#117—26no—
662#117—26no—
663#117—26no—
664#117—26no—
665#117—26no—
666#117—26no—
667#117—26no—
668#117C2×D413yes—
669#117C2×D413yes—
670#117C2×D413yes—
671#117C2×D413yes—
672#117C2×D416yes—
673#117C2×D416yes—
674#117C2412yes—
675#117C2416yes—
676C2×C4⋊C4—23no—
677C2×C4⋊C4—23no—
678C2×C4⋊C4—23no—
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—26no—
688C2×C22⋊C4—212no—
689C2×C22⋊C4—212no—
690C2×C22⋊C4C2×D416yes—
691C2×C42—26no—
692C2×C42—26no—
693C2×C42C2×D413yes—
694C2×C42C2×D413yes—
695C2×C42C2×D413yes—
696C2×C42C2×D413yes—
697C2×C42C2×D413yes—
698C2×C42C2×D413yes—
699C2×C42C2413yes—
700C2×C42C2413yes—
701C2×C42C2413yes—
702C2×C42C2413yes—
703C2×C42C2413yes—
704C2×C42C2411yescharacteristic
705#107C2414yes—
706#107C24112yes—
707#106C2414yes—
708#106C24112yes—
709C4⋊C8C2412yes—
710C4⋊C8C2416yes—
711C4⋊C8C24112yes—
712C4⋊C8C24112yes—
713#103C24112yes—
714#103C24124yes—
715#103C24112yes—
716#103C2414yes—
717#103C2414yes—
718#102C24112yes—
719#102C24124yes—
720#102C24112yes—
721#102C24112yes—
722#102C24112yes—
723C22⋊C8C2412yes—
724C22⋊C8C2416yes—
725C22⋊C8C24112yes—
726C22⋊C8C24112yes—
727#97C2416yes—
728#97C2412yes—
729C4×C8C24112yes—
730C4×C8C24112yes—
731C24—26no—
732C24—26no—
733C24C22×D413yes—
734#41—24no—
735#41—24no—
736#41—46no—
737#41—46no—
738#41—412no—
739#41—412no—
740#41—412no—
741#41—412no—
742#41—46no—
743#41—424no—
744#41—46no—
745#41—48no—
746#41—48no—
747#41—812no—
748#41—86no—
749#41—812no—
750#41—812no—
751#41—812no—
752#41—812no—
753C2×Q8—24no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—23no—
758C2×Q8—26no—
759C2×Q8—26no—
760C2×Q8—412no—
761C2×Q8—86no—
762C2×Q8C22×D413yes—
763C2×Q8C22×D411yescharacteristic
764C2×Q8C2516yes—
765C2×Q8C2512yes—
766C2×D4—26no—
767C2×D4—26no—
768C2×D4—26no—
769C2×D4—26no—
770C2×D4—26no—
771C2×D4—26no—
772C2×D4—212no—
773C2×D4—212no—
774C2×D4—23no—
775C2×D4—23no—
776C2×D4—23no—
777C2×D4—26no—
778C2×D4—26no—
779C2×D4—23no—
780C2×D4—26no—
781C2×D4—26no—
782C2×D4—26no—
783C2×D4—26no—
784C2×D4—46no—
785C2×D4—412no—
786C2×D4—412no—
787C2×D4—412no—
788C2×D4—412no—
789C2×D4—424no—
790C2×D4—424no—
791C2×D4—86no—
792C2×D4—86no—
793C2×D4—812no—
794C2×D4—812no—
795C2×D4C22×D413yes—
796C2×D4C22×D413yes—
797C2×D4C22×D416yes—
798C2×D4C2516yes—
799C2×D4C2516yes—
800C22×C4—26no—
801C22×C4—26no—
802C22×C4—26no—
803C22×C4—26no—
804C22×C4—26no—
805C22×C4—26no—
806C22×C4—26no—
807C22×C4—26no—
808C22×C4—212no—
809C22×C4—212no—
810C22×C4—46no—
811C22×C4—46no—
812C22×C4—46no—
813C22×C4—812no—
814C22×C4—812no—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D413yes—
817C22×C4C22×D413yes—
818C22×C4C22×D413yes—
819C22×C4C22×D413yes—
820C22×C4C22×D413yes—
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D413yes—
823C22×C4C22×D413yes—
824C22×C4C22×D413yes—
825C22×C4C22×D413yes—
826C22×C4C22×D413yes—
827C22×C4C22×D413yes—
828C22×C4C22×D413yes—
829C22×C4C22×D413yes—
830C22×C4C2511yescharacteristic
831C22×C4C2513yes—
832C22×C4C2513yes—
833Q16—412no—
834SD16—412no—
835SD16—412no—
836SD16—424no—
837D8—412no—
838D8—424no—
839M16—412no—
840M16—412no—
841C2×C8C25112yes—
842C2×C8C2514yes—
843C4⋊C4—23no—
844C4⋊C4—23no—
845C4⋊C4—26no—
846C4⋊C4—23no—
847C4⋊C4—26no—
848C4⋊C4—26no—
849C4⋊C4—26no—
850C4⋊C4—26no—
851C4⋊C4—26no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—26no—
862C4⋊C4—26no—
863C4⋊C4—26no—
864C4⋊C4—26no—
865C4⋊C4—26no—
866C4⋊C4—26no—
867C4⋊C4C22×D413yes—
868C4⋊C4C22×D413yes—
869C4⋊C4C22×D413yes—
870C4⋊C4C22×D413yes—
871C4⋊C4C22×D416yes—
872C4⋊C4C22×D416yes—
873C4⋊C4C2516yes—
874C4⋊C4C2512yes—
875C4⋊C4C2512yes—
876C4⋊C4C2512yes—
877C22⋊C4—26no—
878C22⋊C4—26no—
879C22⋊C4—22no—
880C22⋊C4—26no—
881C22⋊C4—22no—
882C22⋊C4—26no—
883C22⋊C4—26no—
884C22⋊C4—212no—
885C22⋊C4—26no—
886C22⋊C4—26no—
887C22⋊C4—26no—
888C22⋊C4—26no—
889C22⋊C4—212no—
890C22⋊C4—26no—
891C22⋊C4—212no—
892C22⋊C4—212no—
893C22⋊C4—26no—
894C22⋊C4—26no—
895C22⋊C4—26no—
896C22⋊C4—26no—
897C22⋊C4—26no—
898C22⋊C4—26no—
899C22⋊C4C22×D416yes—
900C22⋊C4C22×D416yes—
901C22⋊C4C22×D416yes—
902C22⋊C4C22×D416yes—
903C42—22no—
904C42—22no—
905C42—26no—
906C42—26no—
907C42—26no—
908C42—26no—
909C42C22×D413yes—
910C42C22×D413yes—
911C42C22×D411yescharacteristic
912C42C22×D411yescharacteristic
913C42C22×D413yes—
914C42C22×D413yes—
915C42C22×D413yes—
916C42C22×D413yes—
917C42C22×D413yes—
918C42C22×D413yes—
919C42C22×D413yes—
920C42C22×D413yes—
921C42C2513yes—
922C42C2513yes—
923C42C2511yescharacteristic
924C42C2511yescharacteristic
925C23—26no—
926C23—26no—
927C23—43no—
928C23—43no—
929C23—43no—
930C23—412no—
931C23—412no—
932C23—86no—
933C23—86no—
934C23—86no—
935C23—86no—
936C23C23×D413yes—
937C23C23×D413yes—
938C23C23×D411yescharacteristic
939Q8—26no—
940Q8—22no—
941Q8—212no—
942Q8—22no—
943Q8—46no—
944Q8—42no—
945Q8—42no—
946Q8—42no—
947Q8—86no—
948Q8—86no—
949Q8#57514yes—
950D4—26no—
951D4—212no—
952D4—26no—
953D4—26no—
954D4—26no—
955D4—46no—
956D4—46no—
957D4—46no—
958D4—46no—
959D4—412no—
960D4—412no—
961D4—412no—
962D4—412no—
963D4—46no—
964D4—412no—
965D4—412no—
966D4—86no—
967D4—86no—
968D4—86no—
969D4—86no—
970D4—812no—
971D4—812no—
972D4—86no—
973D4—86no—
974C2×C4—22no—
975C2×C4—26no—
976C2×C4—26no—
977C2×C4—26no—
978C2×C4—26no—
979C2×C4—22no—
980C2×C4—26no—
981C2×C4—26no—
982C2×C4—26no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—26no—
988C2×C4—26no—
989C2×C4—41no—
990C2×C4—43no—
991C2×C4—43no—
992C2×C4—43no—
993C2×C4—43no—
994C2×C4—43no—
995C2×C4—43no—
996C2×C4—43no—
997C2×C4—43no—
998C2×C4—412no—
999C2×C4—412no—
1000C2×C4—412no—
1001C2×C4—412no—
1002C2×C4—812no—
1003C2×C4—812no—
1004C2×C4—86no—
1005C2×C4—86no—
1006C2×C4—86no—
1007C2×C4—86no—
1008C2×C4C23×D411yescharacteristic
1009C2×C4C23×D413yes—
1010C2×C4C23×D413yes—
1011C2×C4C23×D411yescharacteristic
1012C2×C4C23×D411yescharacteristic
1013C2×C4C23×D411yescharacteristic
1014C2×C4C23×D413yes—
1015C2×C4C23×D413yes—
1016C2×C4C23×D413yes—
1017C2×C4C23×D411yescharacteristic
1018C2×C4C23×D413yes—
1019C2×C4C2611yescharacteristic
1020C8—24no—
1021C8—212no—
1022C22—21no—
1023C22—23no—
1024C22—23no—
1025C22—21no—
1026C22—23no—
1027C22—23no—
1028C22—21no—
1029C22—23no—
1030C22—23no—
1031C22—46no—
1032C22—46no—
1033C22—46no—
1034C22—46no—
1035C22—46no—
1036C22—46no—
1037C22—86no—
1038C22—1612no—
1039C22—1612no—
1040C22C24×D411yescharacteristic
1041C4—21no—
1042C4—21no—
1043C4—23no—
1044C4—21no—
1045C4—23no—
1046C4—23no—
1047C4—21no—
1048C4—23no—
1049C4—23no—
1050C4—42no—
1051C4—42no—
1052C4—46no—
1053C4—42no—
1054C4—46no—
1055C4—42no—
1056C4C2×#57516yes—
1057C4#358512yes—
1058C4H(7,𝔽2)12yes—
1059C2—41no—
1060C2—43no—
1061C2—43no—
1062C2—86no—
1063C2—86no—
1064C2#6285211yescharacteristic
1065C2C22×#57511yescharacteristic
1066C2C2×#358511yescharacteristic
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. #62800C2semidirect
2. #62800C2semidirect
3. #62594C2semidirect
4. #62592C2semidirect
5. #62455C2semidirect
6. #62453C2semidirect
7. #62002C2semidirect
8. #62001C2semidirect
9. #61996C2semidirect
10. #61995C2semidirect
11. #61886C2semidirect
12. #61590C2semidirect
13. #60953C2semidirect
14. #60951C2semidirect
15. #60803C2semidirect
16. #60802C2semidirect
17. #60284C2semidirect
19. #3522C22semidirect
21. #3519C22semidirect
25. #3514C22semidirect
26. #3511C22semidirect
27. #3511C22semidirect
28. #3508C22semidirect
29. #3508C22semidirect
30. #3503C22semidirect
31. #3503C22semidirect
32. #3498C22semidirect
33. #3498C22semidirect
41. #3481C22semidirect
43. #3480C22semidirect
45. D4×#41C22semidirect
48. #3444C22semidirect
49. #3444C22semidirect
50. C2×#532C22semidirect
51. C2×#532C22semidirect
55. #3396C22semidirect
56. #3394C22semidirect
57. #3392C22semidirect
58. #3391C22semidirect
59. #3363C22semidirect
60. #3362C22semidirect
61. #3361C22semidirect
62. #3360C22semidirect
63. #3333C22semidirect
64. #3331C22semidirect
65. #3329C22semidirect
66. #3326C22semidirect
67. #3325C22semidirect
68. #3322C22semidirect
69. #3278C22semidirect
70. #3275C22semidirect
71. #3274C22semidirect
72. #3274C22semidirect
73. #3273C22semidirect
74. #3272C22semidirect
75. #3254C22semidirect
76. #3253C22semidirect
77. #3252C22semidirect
78. #3251C22semidirect
79. #3240C22semidirect
80. #3238C22semidirect
81. #3237C22semidirect
82. #3235C22semidirect
83. #3219C22semidirect
84. #3217C22semidirect
85. #3216C22semidirect
86. #3216C22semidirect
87. #3214C22semidirect
88. #3214C22semidirect
89. #3214C22semidirect
90. #3213C22semidirect
91. #3212C22semidirect
92. #3212C22semidirect
93. #3207C22semidirect
94. #3206C22semidirect
95. #3205C22semidirect
96. #3197C22semidirect
97. #3194C22semidirect
98. #3172C22semidirect
99. #3171C22semidirect
100. #3171C22semidirect
101. #3153C22semidirect
102. #3151C22semidirect
103. #3141C22semidirect
104. #3140C22semidirect
105. #3107C22semidirect
106. #3106C22semidirect
107. #3106C22semidirect
108. #3102C22semidirect
109. #3101C22semidirect
110. #3100C22semidirect
111. #3039C22semidirect
112. #3038C22semidirect
113. #3036C22semidirect
114. #3006C22semidirect
115. #3005C22semidirect
116. #2991C22semidirect
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
#628002
#625942
#625922
#624552
#624532
#620022
#620012
#619962
#619952
#618862
#615902
#609532
#609512
#608032
#608022
#602842