Finite Group Databasebeta

← #10582810

Subgroups — #10582810

Order 512.

5799 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62841C211yesmaximal, characteristic, complemented
2#62825C211yesmaximal, characteristic, complemented
3#62547C218yesmaximal, complemented
4#62485C218yesmaximal, complemented
5#62240C214yesmaximal, complemented
6#62239C214yesmaximal, complemented
7#62236C214yesmaximal, complemented
8#62235C214yesmaximal, complemented
9#61878C214yesmaximal, complemented
10#61798C212yesmaximal, complemented
11#61797C212yesmaximal, complemented
12#61775C218yesmaximal, complemented
13#61010C214yesmaximal, complemented
14#60967C212yesmaximal, complemented
15#60879C214yesmaximal, complemented
16#60861C212yesmaximal, complemented
17#60281C211yesmaximal, characteristic, complemented
18#3568—24no—
19#3563—22no—
20#3563C2214yescomplemented
21#3559—22no—
22#3559C2214yescomplemented
23#3553—24no—
24#3550C2212yes—
25#3550C2211yescharacteristic
26#3549C2211yescharacteristic
27#3540—24no—
28#3540C2214yes—
29#3518—22no—
30#3518C2214yes—
31#3518C2214yes—
32#3515—24no—
33#3515C2218yescomplemented
34#3514—22no—
35#3514C2214yes—
36#3514C2214yes—
37#3512C2212yes—
38#3512C2212yescomplemented
39#3510—24no—
40#3510C2214yes—
41#3504C2212yescomplemented
42#3504C2212yescomplemented
43#3492—24no—
44#3492C2214yescomplemented
45#3444C2212yes—
46#3444C2211yescharacteristic
47#3444C2211yescharacteristic, complemented
48C22×#125C2211yescharacteristic, complemented
49#3387C2218yescomplemented
50#3386C2218yescomplemented
51#3385C2218yescomplemented
52#3384C2218yescomplemented
53#3377C2218yescomplemented
54#3376C2218yescomplemented
55#3371C2218yescomplemented
56#3370C2218yescomplemented
57#3357C2218yescomplemented
58#3356C2218yescomplemented
59#3354C2218yescomplemented
60#3353C2218yescomplemented
61#3350C2218yescomplemented
62#3350C2218yescomplemented
63#3349C2218yescomplemented
64#3349C2218yescomplemented
65#3348C2218yescomplemented
66#3348C2218yescomplemented
67#3347C2218yescomplemented
68#3347C2218yescomplemented
69#3327C2218yescomplemented
70#3326C2218yescomplemented
71#3323C2218yescomplemented
72#3322C2218yescomplemented
73#3320C2218yescomplemented
74#3318C2218yescomplemented
75#3316C2218yescomplemented
76#3314C2218yescomplemented
77#3312C2218yescomplemented
78#3310C2218yescomplemented
79#3308C2218yescomplemented
80#3306C2218yescomplemented
81#3258C2218yescomplemented
82#3257C2218yescomplemented
83#3255C2212yescomplemented
84#3254C2212yes—
85#3254C2212yescomplemented
86#3253C2212yes—
87#3244C2218yescomplemented
88#3244C2218yescomplemented
89#3243C2218yescomplemented
90#3243C2218yescomplemented
91#3236C2214yescomplemented
92#3236C2214yescomplemented
93#3234C2214yes—
94#3234C2214yes—
95#3233C2214yescomplemented
96#3233C2218yescomplemented
97#3233C2218yescomplemented
98#3233C2214yescomplemented
99#3232C2218yescomplemented
100#3232C2218yescomplemented
101#3232C2218yescomplemented
102#3212C2214yes—
103#3212C2214yescomplemented
104#3211C2218yescomplemented
105#3201C2218yescomplemented
106#3198C2218yes—
107#3197C2218yescomplemented
108#3183C2218yescomplemented
109#3183C2218yescomplemented
110#3168C2218yescomplemented
111#3166C2214yescomplemented
112#3166C2214yescomplemented
113#3160C2214yescomplemented
114#3142C2214yes—
115#3140C2214yescomplemented
116C2×#488C2214yescomplemented
117#3127C2214yescomplemented
118#3126C2214yescomplemented
119#3125C2218yescomplemented
120#3124C2218yescomplemented
121#3123C2214yescomplemented
122#3122C2214yescomplemented
123#3116C2214yescomplemented
124#3116C2214yescomplemented
125#3115C2214yes—
126#3115C2214yescomplemented
127#3097C2218yescomplemented
128#3096C2218yes—
129#3092C2214yescomplemented
130#3092C2214yescomplemented
131#3082C2218yescomplemented
132#3081C2218yescomplemented
133#3080C2214yescomplemented
134#3080C2214yescomplemented
135#2995C2214yescomplemented
136#2995C2214yescomplemented
137#2987C2212yescomplemented
138#2980C2212yes—
139#2978C2214yescomplemented
140#2965C2218yescomplemented
141#2922C2214yescomplemented
142#2920C2212yescomplemented
143#564—24no—
144#563—24no—
145#563—24no—
146#563—22no—
147#563—24no—
148#562—24no—
149H(3,𝔽4)—22no—
150H(3,𝔽4)—24no—
151#560—24no—
152#559—21no—
153#559—24no—
154#559—28no—
155#559C2314yes—
156Q82—21no—
157Q82C2314yes—
158#557—24no—
159#557C2318yes—
160#556—22no—
161#556—28no—
162#556—24no—
163#556—28no—
164#556—28no—
165#556—24no—
166#556C2314yes—
167#556C2314yes—
168#556C2318yes—
169#555—21no—
170#555—24no—
171#555—24no—
172#555C2314yes—
173#555C2318yes—
174#554—28no—
175#554—24no—
176#554—28no—
177#554—24no—
178#554C2318yes—
179#554C2318yes—
180#553—28no—
181#553—24no—
182#553—28no—
183#553—24no—
184#553C2318yes—
185#553C2318yes—
186#552—28no—
187#552—24no—
188#552—24no—
189#552—28no—
190#552—28no—
191#552—28no—
192#552C2318yes—
193#552C2318yes—
194#551—28no—
195#551—24no—
196#551—28no—
197#551—28no—
198#551—28no—
199D4×Q8—22no—
200D4×Q8C2314yes—
201D4×Q8C2314yes—
202#548—24no—
203#548—24no—
204#548C2318yes—
205#547—28no—
206#547—28no—
207#547—24no—
208#547C2318yes—
209#546—24no—
210#546—24no—
211#546C2318yes—
212D42—21no—
213D42C2314yes—
214#544—24no—
215#544—24no—
216#544C2318yes—
217#544C2314yes—
218#542—28no—
219#542—24no—
220#542—28no—
221#542—24no—
222#542—24no—
223#542—24no—
224#542—28no—
225#542C2318yes—
226#542C2318yes—
227#541—22no—
228#541—28no—
229#541—28no—
230#541C2314yes—
231#540—22no—
232#540C2314yes—
233#539—28no—
234#539—28no—
235#539—24no—
236#539—24no—
237#539—28no—
238#539—28no—
239#538—28no—
240#538—28no—
241#538—28no—
242#537—24no—
243#537C2314yes—
244#536—24no—
245#536C2314yes—
246#535—24no—
247#535C2314yes—
248#533—22no—
249#533—24no—
250#533D412yes—
251#533C2312yes—
252#533C2312yes—
253#533C2312yes—
254#533C2314yes—
255#533C2314yes—
256#533C2312yes—
257#533C2311yescharacteristic
258#533C2311yescharacteristic
259#532D412yes—
260#532C2312yes—
261#532C2311yescharacteristic
262#532C2312yes—
263#532C2312yes—
264#532C2312yes—
265#532C2311yescharacteristic
266#529—24no—
267#529—24no—
268#529—24no—
269#529—22no—
270#529—22no—
271#529—22no—
272#529—22no—
273#529—22no—
274#529—22no—
275#529D414yes—
276#529D414yes—
277#529C2318yes—
278#529C2318yes—
279#529C2314yes—
280#529C2314yes—
281#529C2314yes—
282#529C2314yes—
283C2×#125—22no—
284C2×#125—22no—
285C2×#125—22no—
286C2×#125—22no—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#124—24no—
293C2×#124C2314yes—
294#525—22no—
295#525—22no—
296#525—22no—
297#525—28no—
298#525D414yes—
299#525C2314yes—
300#525C2312yes—
301#525C2312yes—
302#520—28no—
303#520C2314yes—
304#520C2314yes—
305#519—24no—
306#519C2314yes—
307#518—24no—
308#518C2314yes—
309C4×#41—22no—
310C4×#41—22no—
311C4×#41—22no—
312C4×#41C2314yes—
313C4×#41C2312yes—
314C4×#41C2314yes—
315C4×#41C2312yes—
316C22×C4⋊C4—22no—
317C22×C4⋊C4C2312yes—
318C22×C42C2311yescharacteristic
319#501C2318yes—
320#501C2318yes—
321#501C2318yes—
322#501C2318yes—
323#500C2318yes—
324#499C2318yes—
325#499C2318yes—
326#499C2318yes—
327#498C2318yes—
328#495C2318yes—
329#491C2318yes—
330#490C2318yes—
331#489C2318yes—
332#489C2318yes—
333#488C2318yes—
334#488C2318yes—
335#488C2318yes—
336#488C2318yes—
337#488C2318yes—
338#488C2318yes—
339#485C2318yes—
340#485C2318yes—
341#485C2318yes—
342#485C2318yes—
343#485C2318yes—
344#485C2318yes—
345#484C2318yes—
346#484C2318yes—
347#484C2318yes—
348#483C2318yes—
349#483C2318yes—
350#483C2318yes—
351#482C2318yes—
352#482C2318yes—
353#482C2318yes—
354#482C2318yes—
355#482C2318yes—
356#482C2318yes—
357#481C2318yes—
358#481C2318yes—
359#481C2318yes—
360#480C2318yes—
361#480C2318yes—
362#480C2318yes—
363#479C2318yes—
364#479C2318yes—
365#479C2318yes—
366#479C2318yes—
367#479C2318yes—
368#479C2318yes—
369#478C2318yes—
370#478C2318yes—
371#478C2318yes—
372#478C2318yes—
373#478C2318yes—
374#478C2318yes—
375#477C2314yes—
376#477C2318yes—
377#477C2314yes—
378#477C2318yes—
379#476C2314yes—
380#476C2318yes—
381#476C2314yes—
382#476C2318yes—
383#475C2314yes—
384#475C2318yes—
385#475C2314yes—
386#475C2318yes—
387#474C2314yes—
388#474C2318yes—
389#474C2314yes—
390#474C2318yes—
391#470C2318yes—
392#470C2318yes—
393#469C2318yes—
394#469C2318yes—
395#468C2318yes—
396#468C2318yes—
397#468C2318yes—
398#468C2318yes—
399#467C2318yes—
400#466C2318yes—
401#465C2318yes—
402#465C2318yes—
403#464C2318yes—
404#464C2318yes—
405#463C2318yes—
406#463C2318yes—
407#462C2314yes—
408#462C2314yes—
409#461C2314yes—
410#461C2314yes—
411#460C2314yes—
412#460C2314yes—
413#459C2314yes—
414#459C2314yes—
415#452C2318yes—
416#452C2318yes—
417#451C2318yes—
418#450C2318yes—
419#449C2318yes—
420#449C2318yes—
421#448C2318yes—
422#447C2318yes—
423#446C2318yes—
424#446C2318yes—
425#442C2318yes—
426#442C2318yes—
427#441C2318yes—
428#441C2318yes—
429#440C2318yes—
430#440C2318yes—
431#440C2318yes—
432#440C2318yes—
433C4×Q16C2318yes—
434C4×SD16C2318yes—
435C4×SD16C2318yes—
436C4×D8C2318yes—
437#436C2318yes—
438#436C2318yes—
439#435C2318yes—
440#435C2318yes—
441#435C2318yes—
442#435C2318yes—
443#433C2314yes—
444#433C2314yes—
445#433C2314yes—
446#433C2314yes—
447#432C2314yes—
448#432C2314yes—
449#431C2314yes—
450#431C2314yes—
451#431C2318yes—
452#428C2314yes—
453#428C2314yes—
454#428C2314yes—
455#428C2314yes—
456#428C2318yes—
457#428C2318yes—
458#427C2318yes—
459#427C2318yes—
460#424C2318yes—
461#423C2312yes—
462#423C2312yes—
463#419C2318yes—
464#418C2318yes—
465#417C2314yes—
466#417C2314yes—
467#417C2314yes—
468#417C2314yes—
469C2×#103C2318yes—
470C2×#102C2318yes—
471#408C2318yes—
472#407C2314yes—
473C4×M16C2314yes—
474C4×M16C2314yes—
475C2×C4×C8C2314yes—
476C2×#41—28no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—22no—
480C2×#41C2×D414yes—
481C2×#41C2412yes—
482C2×#41C2414yes—
483C2×#41C2412yes—
484C22×Q8—24no—
485C22×Q8C2414yes—
486C22×D4—24no—
487C22×D4C2414yes—
488C23×C4—22no—
489C23×C4C2×D412yes—
490C23×C4C2411yescharacteristic
491C2×Q16C2418yes—
492C2×SD16C2418yes—
493C2×SD16C2418yes—
494C2×D8C2418yes—
495C2×M16C2414yes—
496C2×M16C2414yes—
497C2×M16C2418yes—
498C22×C8C2418yes—
499C4⋊Q8—24no—
500C4⋊Q8—28no—
501C4⋊Q8—24no—
502C4⋊Q8—24no—
503C4⋊Q8—24no—
504C4⋊Q8—28no—
505C4⋊Q8—28no—
506C4⋊Q8C2×D412yes—
507C4⋊Q8C2×D411yescharacteristic
508C4⋊Q8C2411yescharacteristic
509C4⋊Q8C2412yes—
510C4⋊Q8C2412yes—
511C4⋊Q8C2412yes—
512C4⋊Q8C2412yes—
513C4⋊Q8C2418yes—
514C4⋊Q8C2418yes—
515#127—24no—
516#127C2×D411yescharacteristic
517#127C2411yescharacteristic
518#127C2412yes—
519#126—28no—
520#126—28no—
521#126—28no—
522#126—28no—
523#126—28no—
524#126—28no—
525#126—28no—
526#126—28no—
527#126—28no—
528#126—28no—
529#126—28no—
530#126—24no—
531#126—24no—
532#126—24no—
533#126—28no—
534#126—28no—
535#126C2×D418yes—
536#125—28no—
537#125—24no—
538#125—28no—
539#125—28no—
540#125—28no—
541#125—28no—
542#125—28no—
543#125—28no—
544#125—22no—
545#125—24no—
546#125—24no—
547#125—22no—
548#125—24no—
549#125—24no—
550#125—24no—
551#125—28no—
552#125—22no—
553#125—22no—
554#125—22no—
555#125C2×D412yes—
556#125C2×D414yes—
557#125C2414yes—
558#125C2414yes—
559#125C2418yes—
560#125C2412yes—
561#125C2418yes—
562#125C2414yes—
563#124—24no—
564#124—24no—
565#124—24no—
566#124—24no—
567#124—28no—
568#124—28no—
569#124—28no—
570#124—28no—
571#124—28no—
572#124—28no—
573#124—28no—
574#124—22no—
575#124—28no—
576#124—22no—
577#124—22no—
578#124C2×D414yes—
579#124C2×D412yes—
580#124C2414yes—
581#124C2418yes—
582#124C2412yes—
583#123—28no—
584#123—24no—
585#123—24no—
586#123—28no—
587#123—24no—
588#123—24no—
589#123—24no—
590#123—24no—
591#123—22no—
592#123—28no—
593#123—28no—
594#123—28no—
595#123—28no—
596#123—28no—
597#123—28no—
598#123—28no—
599#123—28no—
600#123—28no—
601#123—28no—
602#123—28no—
603#123C2×D418yes—
604#123C2×D414yes—
605C22⋊Q8—24no—
606C22⋊Q8—24no—
607C22⋊Q8—28no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—22no—
613C22⋊Q8—22no—
614C22⋊Q8—28no—
615C22⋊Q8—28no—
616C22⋊Q8—24no—
617C22⋊Q8—28no—
618C22⋊Q8—28no—
619C22⋊Q8—28no—
620C22⋊Q8—28no—
621C22⋊Q8—28no—
622C22⋊Q8—28no—
623C22⋊Q8—28no—
624C22⋊Q8—28no—
625C22⋊Q8—28no—
626C22⋊Q8—28no—
627C22⋊Q8—28no—
628C22⋊Q8—28no—
629C22⋊Q8—28no—
630C22⋊Q8C2×D414yes—
631C22⋊Q8C2×D414yes—
632C22⋊Q8C2×D414yes—
633C22⋊Q8C2414yes—
634C22⋊Q8C2414yes—
635C22⋊Q8C2414yes—
636C22⋊Q8C2418yes—
637C22⋊Q8C2418yes—
638#121—28no—
639#121—28no—
640#121—24no—
641#121—24no—
642#121—28no—
643#121—28no—
644#121—28no—
645#121—22no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—22no—
650#121—22no—
651#121—24no—
652#121—28no—
653#121—28no—
654#121C2×D414yes—
655#121C2×D414yes—
656#121C2×D414yes—
657#121C2414yes—
658#121C2414yes—
659#121C2414yes—
660#121C2418yes—
661#121C2418yes—
662#120—22no—
663#120—24no—
664#120—24no—
665#120—24no—
666#120—28no—
667#120—28no—
668#120C2×D414yes—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—22no—
676C4×Q8—22no—
677C4×Q8—22no—
678C4×Q8—22no—
679C4×Q8—22no—
680C4×Q8—22no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8C2×D414yes—
684C4×Q8C2×D414yes—
685C4×Q8C2414yes—
686C4×Q8C2414yes—
687C4×Q8C2414yes—
688C4×Q8C2418yes—
689C4×Q8C2418yes—
690C4×Q8C2414yes—
691C4×D4—24no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4—24no—
695C4×D4—24no—
696C4×D4—24no—
697C4×D4—24no—
698C4×D4—24no—
699C4×D4—24no—
700C4×D4—24no—
701C4×D4—24no—
702C4×D4—24no—
703C4×D4—24no—
704C4×D4—28no—
705C4×D4—28no—
706C4×D4—24no—
707C4×D4—28no—
708C4×D4—28no—
709C4×D4—28no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—22no—
713C4×D4—22no—
714C4×D4—22no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—22no—
718C4×D4C2×D414yes—
719C4×D4C2×D418yes—
720C4×D4C2×D418yes—
721C4×D4C2×D414yes—
722C4×D4C2414yes—
723C4×D4C2414yes—
724C4×D4C2414yes—
725C4×D4C2418yes—
726C4×D4C2418yes—
727C4×D4C2418yes—
728C4×D4C2414yes—
729#117—22no—
730#117—22no—
731#117—22no—
732#117—24no—
733#117—28no—
734#117—24no—
735#117—24no—
736#117—28no—
737#117—28no—
738#117—28no—
739#117—24no—
740#117—24no—
741#117—24no—
742#117—22no—
743#117—24no—
744#117—28no—
745#117—28no—
746#117C2×D414yes—
747#117C2×D418yes—
748#117C2412yes—
749#117C2414yes—
750#117C2414yes—
751#117C2414yes—
752#117C2418yes—
753#117C2414yes—
754#117C2412yes—
755C2×C4⋊C4—24no—
756C2×C4⋊C4—24no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—24no—
759C2×C4⋊C4—24no—
760C2×C4⋊C4—24no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—28no—
765C2×C4⋊C4—28no—
766C2×C4⋊C4—24no—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2418yes—
771C2×C22⋊C4—28no—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—28no—
774C2×C42—24no—
775C2×C42—22no—
776C2×C42C2×D412yes—
777C2×C42C2×D412yes—
778C2×C42C2×D412yes—
779C2×C42C2414yes—
780C2×C42C2412yes—
781C2×C42C2411yescharacteristic
782C2×C42C2412yes—
783C2×C42C2411yescharacteristic
784#107C2418yes—
785#107C2418yes—
786#107C2418yes—
787#107C2418yes—
788#107C2418yes—
789#107C2418yes—
790#106C2418yes—
791#106C2418yes—
792#106C2418yes—
793#106C2418yes—
794#106C2418yes—
795#106C2418yes—
796C4⋊C8C2414yes—
797C4⋊C8C2414yes—
798C4⋊C8C2414yes—
799C4⋊C8C2414yes—
800C4⋊C8C2418yes—
801C4⋊C8C2418yes—
802#103C2418yes—
803#103C2418yes—
804#103C2418yes—
805#103C2418yes—
806#103C2418yes—
807#103C2418yes—
808#103C2418yes—
809#103C2418yes—
810#102C2418yes—
811#102C2418yes—
812#102C2418yes—
813#102C2418yes—
814#102C2418yes—
815#102C2418yes—
816#102C2418yes—
817#102C2418yes—
818C22⋊C8C2418yes—
819C22⋊C8C2418yes—
820C22⋊C8C2418yes—
821C22⋊C8C2418yes—
822#97C2418yes—
823#97C2414yes—
824#97C2414yes—
825C4×C8C2418yes—
826C4×C8C2414yes—
827C4×C8C2414yes—
828C24—24no—
829C24C22×D411yescharacteristic
830#41—44no—
831#41—44no—
832#41—44no—
833#41—44no—
834#41—84no—
835#41—84no—
836#41—84no—
837#41—816no—
838#41—84no—
839C2×Q8—22no—
840C2×Q8—28no—
841C2×Q8—22no—
842C2×Q8—24no—
843C2×Q8—28no—
844C2×Q8—22no—
845C2×Q8—48no—
846C2×Q8—88no—
847C2×Q8C22×D412yes—
848C2×Q8C22×D414yes—
849C2×Q8C2514yes—
850C2×Q8C2512yes—
851C2×D4—22no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—24no—
861C2×D4—22no—
862C2×D4—48no—
863C2×D4—88no—
864C2×D4C22×D412yes—
865C2×D4C22×D414yes—
866C2×D4C22×D418yes—
867C2×D4C22×D414yes—
868C2×D4C2514yes—
869C2×D4C2512yes—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—28no—
875C22×C4—22no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—28no—
881C22×C4—28no—
882C22×C4—42no—
883C22×C4—82no—
884C22×C4—84no—
885C22×C4C22×D412yes—
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D418yes—
894C22×C4C2511yescharacteristic
895C22×C4C2512yes—
896C22×C4C2514yes—
897Q16—48no—
898SD16—48no—
899SD16—48no—
900D8—48no—
901M16—44no—
902M16—48no—
903M16—44no—
904C2×C8—48no—
905C2×C8C2518yes—
906C2×C8C2518yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4C22×D414yes—
939C4⋊C4C22×D418yes—
940C4⋊C4C22×D414yes—
941C4⋊C4C22×D414yes—
942C4⋊C4C22×D418yes—
943C4⋊C4C22×D418yes—
944C4⋊C4C2518yes—
945C4⋊C4C2514yes—
946C4⋊C4C2514yes—
947C4⋊C4C2514yes—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—28no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—28no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—24no—
966C22⋊C4—28no—
967C22⋊C4—24no—
968C22⋊C4—28no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—28no—
973C22⋊C4C22×D418yes—
974C22⋊C4C22×D418yes—
975C22⋊C4C22×D418yes—
976C22⋊C4C22×D418yes—
977C22⋊C4C22×D414yes—
978C42—24no—
979C42—24no—
980C42—24no—
981C42—24no—
982C42—22no—
983C42—28no—
984C42—28no—
985C42—28no—
986C42—24no—
987C42—24no—
988C42C22×D412yes—
989C42C22×D411yescharacteristic
990C42C22×D412yes—
991C42C22×D412yes—
992C42C22×D411yescharacteristic
993C42C22×D412yes—
994C42C22×D412yes—
995C42C22×D418yes—
996C42C2511yescharacteristic
997C42C2514yes—
998C42C2512yes—
999C42C2511yescharacteristic
1000C23—22no—
1001C23—24no—
1002C23—41no—
1003C23—42no—
1004C23—84no—
1005C23—88no—
1006C23C23×D414yes—
1007C23C23×D412yes—
1008C23C23×D411yescharacteristic
1009Q8—24no—
1010Q8—24no—
1011Q8—24no—
1012Q8—44no—
1013Q8—42no—
1014Q8—44no—
1015Q8—84no—
1016Q8—88no—
1017Q8—82no—
1018Q8—82no—
1019Q8—88no—
1020D4—24no—
1021D4—24no—
1022D4—24no—
1023D4—44no—
1024D4—42no—
1025D4—44no—
1026D4—48no—
1027D4—44no—
1028D4—44no—
1029D4—48no—
1030D4—84no—
1031D4—82no—
1032D4—82no—
1033D4—88no—
1034D4—84no—
1035D4—88no—
1036D4—84no—
1037D4—84no—
1038C2×C4—28no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—28no—
1048C2×C4—42no—
1049C2×C4—41no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—88no—
1061C2×C4—84no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—88no—
1065C2×C4—84no—
1066C2×C4—84no—
1067C2×C4—84no—
1068C2×C4—88no—
1069C2×C4C23×D414yes—
1070C2×C4C23×D412yes—
1071C2×C4C23×D411yescharacteristic
1072C2×C4C23×D412yes—
1073C2×C4C23×D412yes—
1074C2×C4C23×D412yes—
1075C2×C4C23×D418yes—
1076C2×C4C23×D412yes—
1077C2×C4C2611yescharacteristic
1078C8—28no—
1079C8—28no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—28no—
1084C22—21no—
1085C22—22no—
1086C22—24no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—42no—
1092C22—44no—
1093C22—324no—
1094C22C24×D411yescharacteristic
1095C4—22no—
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—28no—
1100C4—21no—
1101C4—22no—
1102C4—24no—
1103C4—48no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—42no—
1108C4—44no—
1109C42−1+612yes—
1110C2—42no—
1111C2—41no—
1112C2—44no—
1113C2—82no—
1114C2—84no—
1115C2#6285911yescharacteristic
1116C2#6309012yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3444 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62841C2semidirect
2. #62825C2semidirect
3. #62547C2semidirect
4. #62485C2semidirect
5. #62240C2semidirect
6. #62239C2semidirect
7. #62236C2semidirect
8. #62235C2semidirect
9. #61878C2semidirect
10. #61798C2semidirect
11. #61797C2semidirect
12. #61775C2semidirect
13. #61010C2semidirect
14. #60967C2semidirect
15. #60879C2semidirect
16. #60861C2semidirect
17. #60281C2semidirect
20. #3563C22semidirect
22. #3559C22semidirect
33. #3515C22semidirect
38. #3512C22semidirect
41. #3504C22semidirect
42. #3504C22semidirect
44. #3492C22semidirect
47. #3444C22semidirect
48. C22×#125C22semidirect
49. #3387C22semidirect
50. #3386C22semidirect
51. #3385C22semidirect
52. #3384C22semidirect
53. #3377C22semidirect
54. #3376C22semidirect
55. #3371C22semidirect
56. #3370C22semidirect
57. #3357C22semidirect
58. #3356C22semidirect
59. #3354C22semidirect
60. #3353C22semidirect
61. #3350C22semidirect
62. #3350C22semidirect
63. #3349C22semidirect
64. #3349C22semidirect
65. #3348C22semidirect
66. #3348C22semidirect
67. #3347C22semidirect
68. #3347C22semidirect
69. #3327C22semidirect
70. #3326C22semidirect
71. #3323C22semidirect
72. #3322C22semidirect
73. #3320C22semidirect
74. #3318C22semidirect
75. #3316C22semidirect
76. #3314C22semidirect
77. #3312C22semidirect
78. #3310C22semidirect
79. #3308C22semidirect
80. #3306C22semidirect
81. #3258C22semidirect
82. #3257C22semidirect
83. #3255C22semidirect
85. #3254C22semidirect
87. #3244C22semidirect
88. #3244C22semidirect
89. #3243C22semidirect
90. #3243C22semidirect
91. #3236C22semidirect
92. #3236C22semidirect
95. #3233C22semidirect
96. #3233C22semidirect
97. #3233C22semidirect
98. #3233C22semidirect
99. #3232C22semidirect
100. #3232C22semidirect
101. #3232C22semidirect
103. #3212C22semidirect
104. #3211C22semidirect
105. #3201C22semidirect
107. #3197C22semidirect
108. #3183C22semidirect
109. #3183C22semidirect
110. #3168C22semidirect
111. #3166C22semidirect
112. #3166C22semidirect
113. #3160C22semidirect
115. #3140C22semidirect
116. C2×#488C22semidirect
117. #3127C22semidirect
118. #3126C22semidirect
119. #3125C22semidirect
120. #3124C22semidirect
121. #3123C22semidirect
122. #3122C22semidirect
123. #3116C22semidirect
124. #3116C22semidirect
126. #3115C22semidirect
127. #3097C22semidirect
129. #3092C22semidirect
130. #3092C22semidirect
131. #3082C22semidirect
132. #3081C22semidirect
133. #3080C22semidirect
134. #3080C22semidirect
135. #2995C22semidirect
136. #2995C22semidirect
137. #2987C22semidirect
139. #2978C22semidirect
140. #2965C22semidirect
141. #2922C22semidirect
142. #2920C22semidirect

Maximal subgroups

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

subgroupindex
#628412
#628252
#625472
#624852
#622402
#622392
#622362
#622352
#618782
#617982
#617972
#617752
#610102
#609672
#608792
#608612
#602812