Finite Group Databasebeta

← #10581624

Subgroups — #10581624

Order 512.

6270 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62835C211yesmaximal, characteristic, complemented
2C2×#3548C211yesmaximal, characteristic, complemented
3#62405C218yesmaximal, complemented
4#62381C214yesmaximal, complemented
5#62373C214yesmaximal, complemented
6#61932C214yesmaximal, complemented
7#61910C214yesmaximal, complemented
8#61907C214yesmaximal, complemented
9#61890C212yesmaximal, complemented
10#61880C212yesmaximal, complemented
11#61868C214yesmaximal, complemented
12#61847C214yesmaximal, complemented
13#61835C214yesmaximal, complemented
14#61825C212yesmaximal, complemented
15#61819C212yesmaximal, complemented
16#60978C218yesmaximal, complemented
17#60968C211yesmaximal, characteristic, complemented
18#60951C211yesmaximal, characteristic, complemented
19#60946C211yesmaximal, characteristic, complemented
20#60940C211yesmaximal, characteristic, complemented
21#60250C211yesmaximal, characteristic, complemented
22#3561—22no—
23#3559—22no—
24#3554C2214yescomplemented
25#3550C2212yescomplemented
26#3548—22no—
27#3548—22no—
28#3548—22no—
29#3548—22no—
30#3548C2214yes—
31#3548C2214yes—
32#3548C2214yescomplemented
33#3548C2214yescomplemented
34#3548C2212yescomplemented
35#3547—22no—
36#3536—22no—
37C2×#562—22no—
38#3522C2214yes—
39#3520—22no—
40#3511—22no—
41#3511—21no—
42#3508C2212yescomplemented
43#3507C2212yes—
44#3506C2212yescomplemented
45#3503C2212yescomplemented
46#3501C2212yescomplemented
47#3499—21no—
48#3497C2212yes—
49#3494C2214yes—
50#3489—22no—
51C2×#554C2212yescomplemented
52C2×#554C2212yescomplemented
53C2×#550C2212yescomplemented
54C2×#550C2212yescomplemented
55C2×#547—21no—
56C2×#547—21no—
57C2×#540C2214yes—
58C2×#537—22no—
59C2×#537—22no—
60#3444C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#532C2211yescharacteristic
63C2×#532C2211yescharacteristic
64C2×#532C2211yescharacteristic
65#3399C2218yescomplemented
66#3399C2218yescomplemented
67#3399C22116yescomplemented
68#3397C2218yescomplemented
69#3391C2218yescomplemented
70#3391C2218yescomplemented
71#3391C2218yescomplemented
72#3389C22116yescomplemented
73#3385C2218yescomplemented
74#3384C2218yescomplemented
75#3384C2218yescomplemented
76#3381C2218yescomplemented
77#3380C2218yescomplemented
78#3380C2218yescomplemented
79#3370C22116yescomplemented
80#3368C2218yescomplemented
81#3366C2218yescomplemented
82#3366C2218yescomplemented
83#3366C2218yescomplemented
84#3366C2218yescomplemented
85#3366C22116yescomplemented
86#3366C2218yescomplemented
87#3362C2218yescomplemented
88#3361C2218yescomplemented
89#3361C2218yescomplemented
90#3360C2218yescomplemented
91#3358C2218yescomplemented
92#3358C2218yescomplemented
93#3259C22116yescomplemented
94#3257C22116yescomplemented
95#3254C2212yescomplemented
96#3253C2212yescomplemented
97#3253C2214yescomplemented
98#3247C2214yescomplemented
99#3245C2214yescomplemented
100#3241C22116yescomplemented
101#3238C2212yescomplemented
102#3235C2212yescomplemented
103#3234C2218yescomplemented
104#3232C2218yescomplemented
105#3230C2211yescharacteristic, complemented
106#3228C2212yescomplemented
107#3227C2212yes—
108#3227C2211yescharacteristic, complemented
109#3227C2212yescomplemented
110#3226C2212yes—
111#3226C2212yescomplemented
112#3220C22116yescomplemented
113#3217C2212yescomplemented
114#3217C2218yescomplemented
115#3214C2212yescomplemented
116#3208C2211yescharacteristic, complemented
117#3207C2212yescomplemented
118#3205C2212yes—
119#3205C2212yes—
120#3205C2212yescomplemented
121#3205C2211yescharacteristic, complemented
122#3205C2212yescomplemented
123#3205C2218yescomplemented
124#3194C2214yes—
125#3192C2214yes—
126#3188C2214yes—
127#3186C2214yes—
128#3184C2214yescomplemented
129#3179C22116yescomplemented
130#3176C22116yescomplemented
131#3171C2214yescomplemented
132#3169C2214yescomplemented
133#3169C2212yescomplemented
134#3167C2212yescomplemented
135#3122C22116yescomplemented
136#3119C22116yescomplemented
137#3114C2218yescomplemented
138#3109C2214yes—
139#3109C2214yescomplemented
140#3109C2218yescomplemented
141#3106C2214yescomplemented
142#3106C2214yescomplemented
143#3105C2214yescomplemented
144#3105C2218yescomplemented
145#3101C2212yescomplemented
146#3100C2212yes—
147#3100C2212yes—
148#3100C2214yescomplemented
149#3100C2212yescomplemented
150#3100C2218yescomplemented
151#2986C2214yescomplemented
152#2985C2214yescomplemented
153#2984C2214yescomplemented
154#2983C2212yescomplemented
155#2982C2212yescomplemented
156#2962C2214yescomplemented
157#2960C2214yescomplemented
158#2924C2214yes—
159#2920C2211yescharacteristic
160C2×#431C2211yescharacteristic
161C2×2−1+4—22no—
162C22×#41—22no—
163C22×#41—22no—
164C22×#41—21no—
165C22×#41—21no—
166C22×#41—21no—
167#563—24no—
168#562—28no—
169#562—28no—
170#562—28no—
171#562—28no—
172#562—24no—
173#562—28no—
174#559C2314yes—
175#559C2314yes—
176#559C2318yes—
177Q82C2314yes—
178#557C2314yes—
179#556—22no—
180#556—24no—
181#556C2314yes—
182#555—22no—
183#555—24no—
184#554—22no—
185#554—24no—
186#554—24no—
187#554—24no—
188#554—24no—
189#554—24no—
190#554—24no—
191#554C2318yes—
192#554C2318yes—
193#554C2318yes—
194#554C2314yes—
195#554C2314yes—
196#554C2318yes—
197#554C2318yes—
198#553—24no—
199#553—24no—
200#553—24no—
201#552—24no—
202#551—28no—
203#550—24no—
204#550—24no—
205#550—24no—
206#550—24no—
207#550C2318yes—
208#550C2318yes—
209#550C2318yes—
210#550C2314yes—
211#550C2314yes—
212#550C2314yes—
213#550C2318yes—
214D4×Q8—22no—
215D4×Q8—22no—
216D4×Q8—24no—
217D4×Q8C2314yes—
218D4×Q8C2314yes—
219#548—24no—
220#548—24no—
221#548—24no—
222#548—24no—
223#547—24no—
224#547—24no—
225#547—24no—
226#547—24no—
227#547—24no—
228#547—24no—
229#547—24no—
230#547—24no—
231#547—22no—
232#547—22no—
233#547—22no—
234#547—24no—
235#547—28no—
236#547—24no—
237#547—24no—
238#546—24no—
239#546—24no—
240#546—28no—
241#544—24no—
242#544C2314yes—
243#543—24no—
244#542—24no—
245#542—24no—
246#542—24no—
247#542—28no—
248#542C2318yes—
249#540—24no—
250#540—28no—
251#540—28no—
252#540C23116yes—
253#540C2318yes—
254#540C23116yes—
255#539—28no—
256#539—24no—
257#538—24no—
258#537—28no—
259#537—28no—
260#537—28no—
261#537—28no—
262#537—28no—
263#537—28no—
264#537—28no—
265#537—28no—
266#537—24no—
267#537—24no—
268#537—22no—
269#537—24no—
270#536—22no—
271#536—24no—
272#536—24no—
273#535C2314yes—
274#533—22no—
275#533D412yes—
276#533D412yes—
277#533D412yes—
278#533D412yes—
279#533C2311yescharacteristic
280#533C2311yescharacteristic
281#533C2311yescharacteristic
282#533C2312yes—
283#533C2312yes—
284#533C2312yes—
285#533C2312yes—
286#532—22no—
287#532—22no—
288#532—21no—
289#532—21no—
290#532—21no—
291#532—21no—
292#532—21no—
293#532—21no—
294#532—21no—
295#532—21no—
296#532—21no—
297#532—21no—
298#532—21no—
299#532—21no—
300#532C2311yescharacteristic
301#532C2312yes—
302#532C2312yes—
303#532C2311yescharacteristic
304#532C2318yes—
305#532C2312yes—
306#532C2312yes—
307#532C2312yes—
308#532C2312yes—
309#532C2312yes—
310#532C2312yes—
311#532C2312yes—
312#532C2311yescharacteristic
313#532C2312yes—
314#532C2312yes—
315#532C2312yes—
316C2×C4⋊Q8—22no—
317C2×C4⋊Q8D411yescharacteristic
318C2×C4⋊Q8D411yescharacteristic
319C2×C4⋊Q8C2311yescharacteristic
320C2×C4⋊Q8C2311yescharacteristic
321C2×C4⋊Q8C2311yescharacteristic
322C2×#127C2311yescharacteristic
323C2×#127C2311yescharacteristic
324C2×#127C2311yescharacteristic
325C2×#127C2314yes—
326#529—21no—
327#529—21no—
328#529—21no—
329#529—21no—
330#529C2312yes—
331#529C2318yes—
332#529C2312yes—
333C2×#125D412yes—
334C2×#125C2314yes—
335C2×#124—21no—
336C2×#124—21no—
337C2×#124—21no—
338#525—21no—
339#525—21no—
340#525—24no—
341#525C2312yes—
342C2×#123—24no—
343C2×#123—24no—
344C2×C22⋊Q8—22no—
345C2×C22⋊Q8—22no—
346C2×C22⋊Q8—24no—
347C2×C22⋊Q8—24no—
348C2×C22⋊Q8—24no—
349C2×C22⋊Q8D412yes—
350C2×C22⋊Q8D412yes—
351C2×#121—21no—
352C2×#121—21no—
353C2×#121—21no—
354C2×#121—22no—
355C2×#121—22no—
356C2×#121—24no—
357C2×#121—24no—
358C2×#121—24no—
359C2×#121—24no—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363#520—24no—
364#520—22no—
365#520C2314yes—
366#518C2314yes—
367C4×#41—21no—
368C4×#41—21no—
369C4×#41C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×D4—21no—
373C2×C4×D4—21no—
374C2×C4×D4—21no—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2314yes—
380C2×#117C2312yes—
381C22×C4⋊C4—22no—
382C22×C4⋊C4—22no—
383C22×C42C2311yescharacteristic
384#501C23116yes—
385#501C2314yes—
386#500C2312yes—
387#500C2314yes—
388#499C23116yes—
389#498C2314yes—
390#498C2312yes—
391#496C23116yes—
392#496C2314yes—
393#493C2312yes—
394#493C23116yes—
395#493C2314yes—
396#493C2314yes—
397#492C2312yes—
398#490C2314yes—
399#490C23116yes—
400#490C23116yes—
401#489C2314yes—
402#488C23116yes—
403#487C2312yes—
404#486C2312yes—
405#486C23116yes—
406#486C2314yes—
407#486C2314yes—
408#486C2314yes—
409#486C2314yes—
410#486C2312yes—
411#486C2312yes—
412#484C2314yes—
413#483C2314yes—
414#482C2318yes—
415#482C2318yes—
416#481C2318yes—
417#481C2314yes—
418#481C2318yes—
419#480C2314yes—
420#480C2314yes—
421#480C2314yes—
422#480C2318yes—
423#479C23116yes—
424#478C23116yes—
425#478C2318yes—
426#478C23116yes—
427#478C23116yes—
428#478C23116yes—
429#478C23116yes—
430#477C2314yes—
431#477C2314yes—
432#476C2314yes—
433#476C2318yes—
434#476C2314yes—
435#476C2314yes—
436#476C2318yes—
437#476C23116yes—
438#474C2314yes—
439#474C2314yes—
440#474C2314yes—
441#474C23116yes—
442#474C2318yes—
443#469C2318yes—
444#469C23116yes—
445#468C2318yes—
446#466C2318yes—
447#466C2318yes—
448#466C2318yes—
449#465C2318yes—
450#463C23116yes—
451#463C2318yes—
452#463C23116yes—
453#461C2314yes—
454#460C2314yes—
455#460C2314yes—
456#460C23116yes—
457#459C2314yes—
458#459C2314yes—
459#459C2314yes—
460#459C2318yes—
461#459C23116yes—
462#459C2314yes—
463#459C2318yes—
464#459C23116yes—
465#459C23116yes—
466#459C2318yes—
467#459C2314yes—
468#459C23116yes—
469#459C23116yes—
470#450C2314yes—
471#450C2314yes—
472#449C2318yes—
473#449C2318yes—
474#447C2314yes—
475#447C2314yes—
476#447C2314yes—
477#447C2318yes—
478#447C2314yes—
479#447C2318yes—
480#447C2318yes—
481#446C2318yes—
482#446C2318yes—
483#446C2318yes—
484#446C23116yes—
485C8×Q8C2318yes—
486C8×Q8C2318yes—
487C8×Q8C2318yes—
488#442C23116yes—
489#442C23116yes—
490#442C23116yes—
491#442C23116yes—
492#440C23116yes—
493C4×SD16C2318yes—
494C4×SD16C23116yes—
495C4×SD16C2318yes—
496C4×D8C2318yes—
497C4×D8C2318yes—
498C4×D8C23116yes—
499C4×D8C2318yes—
500C4×D8C23116yes—
501C4×D8C23116yes—
502C4×D8C2318yes—
503#433C23116yes—
504#432C2312yes—
505#432C2312yes—
506#432C2318yes—
507#431C2311yescharacteristic
508#431C2311yescharacteristic
509#431C2312yes—
510#431C2312yes—
511#431C2318yes—
512#431C2312yes—
513#431C2312yes—
514#431C2312yes—
515#424C2318yes—
516#423C2312yes—
517C2×C4⋊C8C2312yes—
518#407C2312yes—
519C2×C22⋊C8C2312yes—
520#405C2318yes—
521C4×M16C2312yes—
522C2×C4×C8C2312yes—
5232−1+4—88no—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—28no—
531C2×#41—21no—
532C2×#41—22no—
533C2×#41—21no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—28no—
546C2×#41—84no—
547C2×#41—84no—
548C2×#41—84no—
549C2×#41—88no—
550C2×#41—88no—
551C2×#41C2412yes—
552C22×Q8—24no—
553C22×Q8—24no—
554C22×Q8—21no—
555C22×Q8—21no—
556C22×Q8—21no—
557C22×Q8C2×D412yes—
558C22×Q8C2×D412yes—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—24no—
566C22×D4—24no—
567C22×D4—21no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4C2412yes—
571C22×D4C2412yes—
572C22×D4C2412yes—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—24no—
576C23×C4—24no—
577C23×C4—22no—
578C23×C4C2×D411yescharacteristic
579C23×C4C2×D411yescharacteristic
580C23×C4C2411yescharacteristic
581C2×SD16C2418yes—
582C2×SD16C2418yes—
583C2×D8C2418yes—
584C2×D8C2418yes—
585C2×D8C2418yes—
586C2×D8C24116yes—
587C2×D8C2418yes—
588C2×M16C2414yes—
589C22×C8C2414yes—
590C4⋊Q8—24no—
591C4⋊Q8—24no—
592C4⋊Q8—24no—
593C4⋊Q8—28no—
594C4⋊Q8—21no—
595C4⋊Q8—21no—
596C4⋊Q8—21no—
597C4⋊Q8—21no—
598C4⋊Q8—21no—
599C4⋊Q8—21no—
600C4⋊Q8C2×D412yes—
601C4⋊Q8C2×D412yes—
602C4⋊Q8C2×D412yes—
603C4⋊Q8C2×D412yes—
604C4⋊Q8C2×D412yes—
605C4⋊Q8C2×D412yes—
606C4⋊Q8C2×D412yes—
607C4⋊Q8C2×D412yes—
608C4⋊Q8C2411yescharacteristic
609C4⋊Q8C2412yes—
610C4⋊Q8C2412yes—
611C4⋊Q8C2412yes—
612C4⋊Q8C2412yes—
613C4⋊Q8C2412yes—
614C4⋊Q8C2412yes—
615C4⋊Q8C2411yescharacteristic
616C4⋊Q8C2411yescharacteristic
617C4⋊Q8C2418yes—
618#127—21no—
619#127—21no—
620#127—21no—
621#127—21no—
622#127—21no—
623#127—21no—
624#127—28no—
625#127C2412yes—
626#127C2412yes—
627#127C2412yes—
628#127C2412yes—
629#127C2412yes—
630#127C2412yes—
631#127C24116yes—
632#127C2411yescharacteristic
633#127C2418yes—
634#126—28no—
635#126—28no—
636#126—22no—
637#126—22no—
638#126—28no—
639#125—24no—
640#125—28no—
641#125—28no—
642#125—21no—
643#125—21no—
644#125C2×D414yes—
645#125C2×D414yes—
646#125C2×D414yes—
647#125C2×D414yes—
648#125C24116yes—
649#125C2412yes—
650#125C2418yes—
651#124—24no—
652#124—24no—
653#124—28no—
654#124—28no—
655#124—22no—
656#124—22no—
657#124—22no—
658#124—22no—
659#124—22no—
660#124—22no—
661#124—22no—
662#124—22no—
663#124—22no—
664#124—22no—
665#124—22no—
666#124—22no—
667#124—21no—
668#124—21no—
669#124—28no—
670#124C2412yes—
671#124C2418yes—
672#123—22no—
673#123—22no—
674#123—22no—
675#123—28no—
676#123—216no—
677#123—216no—
678#123—216no—
679#123—216no—
680#123—28no—
681#123—28no—
682#123—28no—
683#123—28no—
684#123—28no—
685#123—28no—
686#123—28no—
687C22⋊Q8—24no—
688C22⋊Q8—28no—
689C22⋊Q8—28no—
690C22⋊Q8—28no—
691C22⋊Q8—28no—
692C22⋊Q8—24no—
693C22⋊Q8—24no—
694C22⋊Q8—28no—
695C22⋊Q8—21no—
696C22⋊Q8—21no—
697C22⋊Q8—21no—
698C22⋊Q8—21no—
699C22⋊Q8—24no—
700C22⋊Q8—216no—
701C22⋊Q8—216no—
702C22⋊Q8—216no—
703C22⋊Q8—216no—
704C22⋊Q8—28no—
705C22⋊Q8—24no—
706C22⋊Q8—28no—
707C22⋊Q8—28no—
708C22⋊Q8—28no—
709C22⋊Q8—28no—
710C22⋊Q8—28no—
711C22⋊Q8—28no—
712C22⋊Q8—28no—
713C22⋊Q8C2×D414yes—
714C22⋊Q8C2×D414yes—
715C22⋊Q8C2×D414yes—
716C22⋊Q8C2×D414yes—
717C22⋊Q8C2×D414yes—
718C22⋊Q8C2×D414yes—
719C22⋊Q8C2×D414yes—
720C22⋊Q8C2×D414yes—
721C22⋊Q8C2412yes—
722C22⋊Q8C2412yes—
723#121—22no—
724#121—22no—
725#121—22no—
726#121—22no—
727#121—22no—
728#121—22no—
729#121—22no—
730#121—22no—
731#121—22no—
732#121—22no—
733#121—22no—
734#121—22no—
735#121—22no—
736#121—22no—
737#121—22no—
738#121—22no—
739#121—22no—
740#121—22no—
741#121—21no—
742#121—21no—
743#121—21no—
744#121—21no—
745#121—28no—
746#121—28no—
747#121—28no—
748#121—28no—
749#121—28no—
750#121—216no—
751#121—216no—
752#121—216no—
753#121—216no—
754#121—24no—
755#121—24no—
756#121—24no—
757#121—24no—
758#121—24no—
759#121—28no—
760#121—28no—
761#121—28no—
762#121—216no—
763#121—216no—
764#121—216no—
765#121—216no—
766#121—28no—
767#121—28no—
768#121C2414yes—
769#121C2414yes—
770#121C2414yes—
771#121C2414yes—
772#121C2414yes—
773#121C2414yes—
774#121C2412yes—
775#121C2412yes—
776#120—22no—
777#120—28no—
778C4×Q8—24no—
779C4×Q8—24no—
780C4×Q8—21no—
781C4×Q8—21no—
782C4×Q8—21no—
783C4×Q8—21no—
784C4×Q8C2×D414yes—
785C4×Q8C2×D414yes—
786C4×Q8C2×D414yes—
787C4×Q8C2×D414yes—
788C4×Q8C2412yes—
789C4×Q8C2412yes—
790C4×Q8C2418yes—
791C4×Q8C2414yes—
792C4×Q8C2414yes—
793C4×Q8C2414yes—
794C4×Q8C2414yes—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—22no—
799C4×D4—22no—
800C4×D4—22no—
801C4×D4—28no—
802C4×D4—24no—
803C4×D4—24no—
804C4×D4—28no—
805C4×D4—24no—
806C4×D4—24no—
807C4×D4—28no—
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—22no—
811C4×D4—22no—
812C4×D4—22no—
813C4×D4—22no—
814C4×D4—22no—
815C4×D4—22no—
816C4×D4—22no—
817C4×D4—22no—
818C4×D4—22no—
819C4×D4—22no—
820C4×D4—22no—
821C4×D4—22no—
822C4×D4—22no—
823C4×D4—22no—
824C4×D4—22no—
825C4×D4—22no—
826C4×D4—28no—
827C4×D4—28no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—21no—
832C4×D4—28no—
833C4×D4C2414yes—
834C4×D4C2414yes—
835C4×D4C2414yes—
836C4×D4C2414yes—
837C4×D4C2414yes—
838C4×D4C2414yes—
839C4×D4C24116yes—
840C4×D4C24116yes—
841C4×D4C2412yes—
842C4×D4C2412yes—
843C4×D4C2418yes—
844C4×D4C2418yes—
845C4×D4C2418yes—
846#117—21no—
847#117—21no—
848#117—24no—
849#117—24no—
850#117—22no—
851#117—22no—
852#117—22no—
853#117—28no—
854#117C2×D414yes—
855#117C2×D414yes—
856#117C2412yes—
857#117C2414yes—
858#117C2414yes—
859C2×C4⋊C4—21no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—24no—
862C2×C4⋊C4—24no—
863C2×C4⋊C4—21no—
864C2×C4⋊C4—28no—
865C2×C4⋊C4—28no—
866C2×C4⋊C4—28no—
867C2×C4⋊C4—28no—
868C2×C4⋊C4—24no—
869C2×C4⋊C4—28no—
870C2×C4⋊C4—24no—
871C2×C4⋊C4—24no—
872C2×C4⋊C4C2×D412yes—
873C2×C4⋊C4C2×D412yes—
874C2×C4⋊C4C2×D412yes—
875C2×C4⋊C4C2×D412yes—
876C2×C4⋊C4C2×D414yes—
877C2×C4⋊C4C2×D414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C22⋊C4—22no—
882C2×C22⋊C4—22no—
883C2×C22⋊C4—22no—
884C2×C22⋊C4—24no—
885C2×C22⋊C4—24no—
886C2×C22⋊C4—22no—
887C2×C22⋊C4—22no—
888C2×C22⋊C4—22no—
889C2×C22⋊C4—28no—
890C2×C22⋊C4C2×D414yes—
891C2×C42—22no—
892C2×C42C2×D411yescharacteristic
893C2×C42C2×D411yescharacteristic
894C2×C42C2×D411yescharacteristic
895C2×C42C2×D411yescharacteristic
896C2×C42C2×D411yescharacteristic
897C2×C42C2×D411yescharacteristic
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905#107C2418yes—
906#107C2418yes—
907#107C2418yes—
908#107C2418yes—
909#106C2418yes—
910#106C24116yes—
911#106C2418yes—
912C4⋊C8C2412yes—
913C4⋊C8C2412yes—
914C4⋊C8C2414yes—
915C4⋊C8C2414yes—
916C4⋊C8C2414yes—
917C4⋊C8C24116yes—
918C4⋊C8C24116yes—
919#103C2418yes—
920#103C2418yes—
921#102C2418yes—
922#102C2418yes—
923#102C2418yes—
924#102C2418yes—
925#102C2418yes—
926#102C24116yes—
927#102C2418yes—
928#102C24116yes—
929#102C2418yes—
930#102C2418yes—
931#102C2418yes—
932#102C2418yes—
933C22⋊C8C2412yes—
934C22⋊C8C2412yes—
935C22⋊C8C2414yes—
936C22⋊C8C2414yes—
937C22⋊C8C2414yes—
938#97C2414yes—
939#97C24116yes—
940C4×C8C2412yes—
941C4×C8C2412yes—
942C4×C8C2414yes—
943C4×C8C2414yes—
944C4×C8C24116yes—
945C24—22no—
946C24—22no—
947C24—22no—
948C24C22×D411yescharacteristic
949#41—44no—
950#41—48no—
951#41—44no—
952#41—82no—
953#41—84no—
954#41—84no—
955#41—84no—
956#41—84no—
957#41—84no—
958#41—84no—
959#41—84no—
960#41—84no—
961#41—816no—
962#41—84no—
963#41—84no—
964#41—84no—
965#41—88no—
966#41—816no—
967#41—816no—
968#41—816no—
969#41—88no—
970#41—88no—
971#41—816no—
972C2×Q8—28no—
973C2×Q8—21no—
974C2×Q8—22no—
975C2×Q8—21no—
976C2×Q8—22no—
977C2×Q8—22no—
978C2×Q8—22no—
979C2×Q8—22no—
980C2×Q8—28no—
981C2×Q8—22no—
982C2×Q8—44no—
983C2×Q8—82no—
984C2×Q8—82no—
985C2×Q8—82no—
986C2×Q8—88no—
987C2×Q8—88no—
988C2×Q8C22×D414yes—
989C2×Q8C22×D414yes—
990C2×Q8C22×D414yes—
991C2×Q8C22×D414yes—
992C2×Q8C2512yes—
993C2×D4—22no—
994C2×D4—22no—
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—22no—
1005C2×D4—22no—
1006C2×D4—21no—
1007C2×D4—22no—
1008C2×D4—22no—
1009C2×D4—22no—
1010C2×D4—22no—
1011C2×D4—22no—
1012C2×D4—28no—
1013C2×D4—21no—
1014C2×D4—22no—
1015C2×D4—28no—
1016C2×D4—216no—
1017C2×D4—216no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C2×D4—22no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—82no—
1029C2×D4—82no—
1030C2×D4—82no—
1031C2×D4—88no—
1032C2×D4—84no—
1033C2×D4—82no—
1034C2×D4—88no—
1035C2×D4—84no—
1036C2×D4—84no—
1037C2×D4C2514yes—
1038C2×D4C2512yes—
1039C2×D4C2514yes—
1040C2×D4C2514yes—
1041C22×C4—24no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—28no—
1054C22×C4—28no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—216no—
1058C22×C4—216no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—48no—
1062C22×C4—48no—
1063C22×C4—84no—
1064C22×C4—88no—
1065C22×C4—88no—
1066C22×C4C22×D411yescharacteristic
1067C22×C4C22×D411yescharacteristic
1068C22×C4C22×D411yescharacteristic
1069C22×C4C22×D411yescharacteristic
1070C22×C4C22×D411yescharacteristic
1071C22×C4C22×D411yescharacteristic
1072C22×C4C22×D411yescharacteristic
1073C22×C4C22×D411yescharacteristic
1074C22×C4C22×D414yes—
1075C22×C4C22×D411yescharacteristic
1076C22×C4C22×D411yescharacteristic
1077C22×C4C22×D411yescharacteristic
1078C22×C4C22×D411yescharacteristic
1079C22×C4C22×D411yescharacteristic
1080C22×C4C22×D411yescharacteristic
1081C22×C4C22×D414yes—
1082C22×C4C22×D411yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086SD16—48no—
1087SD16—48no—
1088D8—48no—
1089D8—48no—
1090D8—48no—
1091D8—48no—
1092D8—416no—
1093M16—44no—
1094C2×C8—44no—
1095C2×C8C2514yes—
1096C2×C8C2518yes—
1097C2×C8C2514yes—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—21no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—216no—
1106C4⋊C4—216no—
1107C4⋊C4—22no—
1108C4⋊C4—28no—
1109C4⋊C4—22no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—22no—
1114C4⋊C4—22no—
1115C4⋊C4—21no—
1116C4⋊C4—22no—
1117C4⋊C4—21no—
1118C4⋊C4—21no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4C22×D414yes—
1124C4⋊C4C22×D414yes—
1125C4⋊C4C22×D414yes—
1126C4⋊C4C22×D414yes—
1127C4⋊C4C22×D414yes—
1128C4⋊C4C22×D418yes—
1129C4⋊C4C22×D414yes—
1130C4⋊C4C22×D414yes—
1131C4⋊C4C22×D414yes—
1132C4⋊C4C22×D418yes—
1133C4⋊C4C22×D418yes—
1134C4⋊C4C22×D418yes—
1135C4⋊C4C2514yes—
1136C4⋊C4C2512yes—
1137C4⋊C4C2512yes—
1138C4⋊C4C2514yes—
1139C4⋊C4C2514yes—
1140C22⋊C4—22no—
1141C22⋊C4—22no—
1142C22⋊C4—22no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—216no—
1150C22⋊C4—216no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—24no—
1159C22⋊C4—22no—
1160C22⋊C4—22no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—22no—
1164C22⋊C4—22no—
1165C22⋊C4—22no—
1166C22⋊C4—22no—
1167C22⋊C4—28no—
1168C22⋊C4C22×D418yes—
1169C22⋊C4C22×D418yes—
1170C42—22no—
1171C42—22no—
1172C42—22no—
1173C42—28no—
1174C42C22×D411yescharacteristic
1175C42C22×D411yescharacteristic
1176C42C22×D411yescharacteristic
1177C42C22×D411yescharacteristic
1178C42C22×D411yescharacteristic
1179C42C22×D411yescharacteristic
1180C42C22×D411yescharacteristic
1181C42C22×D411yescharacteristic
1182C42C22×D411yescharacteristic
1183C42C22×D411yescharacteristic
1184C42C22×D411yescharacteristic
1185C42C22×D411yescharacteristic
1186C42C22×D418yes—
1187C42C2511yescharacteristic
1188C42C2511yescharacteristic
1189C42C2511yescharacteristic
1190C42C2518yes—
1191C42C2511yescharacteristic
1192C23—22no—
1193C23—24no—
1194C23—22no—
1195C23—24no—
1196C23—24no—
1197C23—41no—
1198C23—41no—
1199C23—44no—
1200C23—44no—
1201C23—44no—
1202C23—44no—
1203C23—44no—
1204C23—44no—
1205C23—44no—
1206C23—82no—
1207C23—82no—
1208C23C23×D411yescharacteristic
1209C23C23×D411yescharacteristic
1210C23C23×D411yescharacteristic
1211Q8—28no—
1212Q8—28no—
1213Q8—28no—
1214Q8—24no—
1215Q8—44no—
1216Q8—42no—
1217Q8—44no—
1218Q8—88no—
1219Q8—82no—
1220Q8—82no—
1221Q8—82no—
1222Q8—82no—
1223Q8—82no—
1224Q8—81no—
1225D4—28no—
1226D4—24no—
1227D4—24no—
1228D4—28no—
1229D4—24no—
1230D4—44no—
1231D4—44no—
1232D4—44no—
1233D4—44no—
1234D4—44no—
1235D4—48no—
1236D4—44no—
1237D4—44no—
1238D4—44no—
1239D4—44no—
1240D4—44no—
1241D4—44no—
1242D4—42no—
1243D4—82no—
1244D4—82no—
1245D4—82no—
1246D4—82no—
1247D4—816no—
1248D4—82no—
1249D4—82no—
1250D4—816no—
1251D4—81no—
1252D4—88no—
1253D4—88no—
1254D4—84no—
1255D4—84no—
1256D4—84no—
1257D4—84no—
1258D4—84no—
1259D4—82no—
1260C2×C4—22no—
1261C2×C4—28no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—44no—
1285C2×C4—48no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—44no—
1289C2×C4—48no—
1290C2×C4—44no—
1291C2×C4—48no—
1292C2×C4—48no—
1293C2×C4—48no—
1294C2×C4—44no—
1295C2×C4—84no—
1296C2×C4—816no—
1297C2×C4—816no—
1298C2×C4—88no—
1299C2×C4—88no—
1300C2×C4—88no—
1301C2×C4—82no—
1302C2×C4#57614yes—
1303C2×C4C23×D411yescharacteristic
1304C2×C4C23×D418yes—
1305C2×C4C23×D411yescharacteristic
1306C2×C4C23×D411yescharacteristic
1307C2×C4C23×D411yescharacteristic
1308C2×C4C23×D411yescharacteristic
1309C2×C4C23×D411yescharacteristic
1310C2×C4C23×D411yescharacteristic
1311C2×C4C23×D411yescharacteristic
1312C2×C4C23×D418yes—
1313C2×C4C23×D411yescharacteristic
1314C2×C4C23×D411yescharacteristic
1315C2×C4C23×D411yescharacteristic
1316C2×C4C2611yescharacteristic
1317C8—24no—
1318C8—24no—
1319C8—28no—
1320C22—21no—
1321C22—21no—
1322C22—21no—
1323C22—21no—
1324C22—21no—
1325C22—21no—
1326C22—21no—
1327C22—21no—
1328C22—44no—
1329C22—42no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—42no—
1334C22—44no—
1335C22—44no—
1336C22—42no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—82no—
1341C22—88no—
1342C22—88no—
1343C22—164no—
1344C22C2×#57612yes—
1345C22C24×D411yescharacteristic
1346C4—21no—
1347C4—21no—
1348C4—28no—
1349C4—21no—
1350C4—21no—
1351C4—21no—
1352C4—28no—
1353C4—21no—
1354C4—21no—
1355C4—21no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—44no—
1360C4—42no—
1361C4—42no—
1362C4C2×#57612yes—
1363C4C2×#57612yes—
1364C4#358512yes—
1365C42−1+612yes—
1366C2—22no—
1367C2—41no—
1368C2—41no—
1369C2—82no—
1370C2—84no—
1371C2—84no—
1372C2—84no—
1373C2#6284811yescharacteristic
1374C2C22×#57611yescharacteristic
1375C2C2×#358511yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62835C2semidirect
2. C2×#3548C2semidirect
3. #62405C2semidirect
4. #62381C2semidirect
5. #62373C2semidirect
6. #61932C2semidirect
7. #61910C2semidirect
8. #61907C2semidirect
9. #61890C2semidirect
10. #61880C2semidirect
11. #61868C2semidirect
12. #61847C2semidirect
13. #61835C2semidirect
14. #61825C2semidirect
15. #61819C2semidirect
16. #60978C2semidirect
17. #60968C2semidirect
18. #60951C2semidirect
19. #60946C2semidirect
20. #60940C2semidirect
21. #60250C2semidirect
24. #3554C22semidirect
25. #3550C22semidirect
32. #3548C22semidirect
33. #3548C22semidirect
34. #3548C22semidirect
42. #3508C22semidirect
44. #3506C22semidirect
45. #3503C22semidirect
46. #3501C22semidirect
51. C2×#554C22semidirect
52. C2×#554C22semidirect
53. C2×#550C22semidirect
54. C2×#550C22semidirect
65. #3399C22semidirect
66. #3399C22semidirect
67. #3399C22semidirect
68. #3397C22semidirect
69. #3391C22semidirect
70. #3391C22semidirect
71. #3391C22semidirect
72. #3389C22semidirect
73. #3385C22semidirect
74. #3384C22semidirect
75. #3384C22semidirect
76. #3381C22semidirect
77. #3380C22semidirect
78. #3380C22semidirect
79. #3370C22semidirect
80. #3368C22semidirect
81. #3366C22semidirect
82. #3366C22semidirect
83. #3366C22semidirect
84. #3366C22semidirect
85. #3366C22semidirect
86. #3366C22semidirect
87. #3362C22semidirect
88. #3361C22semidirect
89. #3361C22semidirect
90. #3360C22semidirect
91. #3358C22semidirect
92. #3358C22semidirect
93. #3259C22semidirect
94. #3257C22semidirect
95. #3254C22semidirect
96. #3253C22semidirect
97. #3253C22semidirect
98. #3247C22semidirect
99. #3245C22semidirect
100. #3241C22semidirect
101. #3238C22semidirect
102. #3235C22semidirect
103. #3234C22semidirect
104. #3232C22semidirect
105. #3230C22semidirect
106. #3228C22semidirect
108. #3227C22semidirect
109. #3227C22semidirect
111. #3226C22semidirect
112. #3220C22semidirect
113. #3217C22semidirect
114. #3217C22semidirect
115. #3214C22semidirect
116. #3208C22semidirect
117. #3207C22semidirect
120. #3205C22semidirect
121. #3205C22semidirect
122. #3205C22semidirect
123. #3205C22semidirect
128. #3184C22semidirect
129. #3179C22semidirect
130. #3176C22semidirect
131. #3171C22semidirect
132. #3169C22semidirect
133. #3169C22semidirect
134. #3167C22semidirect
135. #3122C22semidirect
136. #3119C22semidirect
137. #3114C22semidirect
139. #3109C22semidirect
140. #3109C22semidirect
141. #3106C22semidirect
142. #3106C22semidirect
143. #3105C22semidirect
144. #3105C22semidirect
145. #3101C22semidirect
148. #3100C22semidirect
149. #3100C22semidirect
150. #3100C22semidirect
151. #2986C22semidirect
152. #2985C22semidirect
153. #2984C22semidirect
154. #2983C22semidirect
155. #2982C22semidirect
156. #2962C22semidirect
157. #2960C22semidirect

Maximal subgroups

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

subgroupindex
#628352
C2×#35482
#624052
#623812
#623732
#619322
#619102
#619072
#618902
#618802
#618682
#618472
#618352
#618252
#618192
#609782
#609682
#609512
#609462
#609402
#602502