Finite Group Databasebeta

← #10584948

Subgroups — #10584948

Order 512.

5843 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63034C212yesmaximal, complemented
2#62495C212yesmaximal, complemented
3#62490C214yesmaximal, complemented
4#62476C212yesmaximal, complemented
5#62474C211yesmaximal, characteristic, complemented
6#62473C211yesmaximal, characteristic, complemented
7#62379C212yesmaximal, complemented
8#62375C211yesmaximal, characteristic, complemented
9#62361C212yesmaximal, complemented
10#62219C214yesmaximal, complemented
11#62210C218yesmaximal, complemented
12#62145C212yesmaximal, complemented
13#62142C214yesmaximal, complemented
14#62135C212yesmaximal, complemented
15#61871C212yesmaximal, complemented
16#61865C214yesmaximal, complemented
17#61839C214yesmaximal, complemented
18#61488C214yesmaximal, complemented
19#61478C212yesmaximal, complemented
20#61436C211yesmaximal, characteristic, complemented
21#61433C211yesmaximal, characteristic, complemented
22#61430C212yesmaximal, complemented
23#61373C211yesmaximal, characteristic, complemented
24#61372C212yesmaximal, complemented
25Q8×#135C212yesmaximal, complemented
26#60331C211yesmaximal, characteristic, complemented
27#3565—28no—
28#3565C2218yes—
29#3554—24no—
30#3554C2214yes—
31#3550—22no—
32#3550C2212yes—
33#3547—24no—
34#3547C2214yes—
35#3524C2218yes—
36#3518—24no—
37#3518C2214yes—
38#3518C2214yes—
39#3511—22no—
40#3511C2212yes—
41#3509—22no—
42#3509C2212yes—
43#3507—24no—
44#3507C2214yes—
45#3503C2212yes—
46#3502C2214yes—
47#3483C2212yes—
48#3482—22no—
49#3482C2212yes—
50#3482C2211yescharacteristic
51#3480C2214yes—
52Q8×#41C2214yes—
53#3396C2214yes—
54#3396C2212yes—
55#3393C2212yes—
56#3393C2211yescharacteristic
57#3391C2211yescharacteristic
58#3390C2218yes—
59#3388C2218yes—
60#3387C2214yes—
61#3387C2214yes—
62#3386C2214yes—
63#3385C2214yes—
64#3384C2214yes—
65#3383C2212yes—
66#3383C2212yes—
67#3383C2214yes—
68#3383C2214yes—
69#3383C2211yescharacteristic
70#3383C2212yes—
71Q8×Q16C2212yes—
72Q8×Q16C2212yes—
73Q8×Q16C2211yescharacteristic
74#3381C2218yes—
75#3381C2214yes—
76#3380C2212yes—
77#3380C2212yes—
78#3380C2214yes—
79#3380C2212yes—
80Q8×SD16C2214yes—
81Q8×SD16C2214yes—
82Q8×D8C2212yes—
83Q8×D8C2212yes—
84#3375C2214yes—
85#3373C2214yes—
86#3371C2218yes—
87#3370C2218yes—
88#3369C2214yes—
89#3368C2214yes—
90#3367C2214yes—
91#3365C2218yes—
92#3365C2214yes—
93#3364C2212yes—
94#3362C2212yes—
95#3360C2214yes—
96#3360C2214yes—
97#3354C2214yes—
98#3351C2218yes—
99#3350C2218yes—
100#3348C2218yes—
101#3347C2218yes—
102#3342C2212yes—
103#3342C2212yes—
104#3342C2214yes—
105#3341C2212yes—
106#3341C2212yes—
107#3341C2211yescharacteristic
108#3341C2214yes—
109#3341C2212yes—
110#3340C2218yes—
111#3340C2214yes—
112#3339C2214yes—
113#3339C2214yes—
114#3339C2214yes—
115#3336C2214yes—
116#3336C2214yes—
117#3336C2212yes—
118#3334C2211yescharacteristic
119#3329C2214yes—
120#3326C2218yes—
121#3321C2218yes—
122#3317C2218yes—
123#3313C2218yes—
124#3305C2214yes—
125#3305C2212yes—
126#3304C2214yes—
127#3301C2218yes—
128#3300C2214yes—
129#3298C2212yes—
130#3287C2212yes—
131#3287C2211yescharacteristic
132D4×Q16C2211yescharacteristic
133#3285C2214yes—
134#3285C2212yes—
135#3262C2214yes—
136#3257C2218yes—
137#3254C2212yes—
138#3251C2214yes—
139#3250C2218yes—
140#3246C2214yes—
141#3244C2218yes—
142#3244C2218yes—
143#3241C2218yes—
144#3240C2218yes—
145#3235C2214yes—
146#3233C2218yes—
147#3233C2214yes—
148#3231C2214yes—
149#3229C2212yes—
150#3228C2214yes—
151#3227C2212yes—
152#3176C2214yes—
153#3175C2214yes—
154#3175C2214yes—
155#3170C2212yes—
156#3170C2211yescharacteristic
157#3169C2211yescharacteristic
158#3169C2212yes—
159#3169C2212yes—
160#3168C2214yes—
161#3168C2212yes—
162#3168C2214yes—
163#3164C2212yes—
164#3164C2214yes—
165#3160C2212yes—
166#3160C2212yes—
167#3160C2214yes—
168C2×#500C2211yescharacteristic
169#3126C2218yes—
170#3125C2218yes—
171#3121C2218yes—
172#3116C2214yes—
173#3111C2218yes—
174#3108C2214yes—
175#3107C2212yes—
176#3106C2214yes—
177#3106C2212yes—
178#3103C2214yes—
179#3102C2218yes—
180#3083C2214yes—
181#3082C2218yes—
182#3079C2212yes—
183#3078C2214yes—
184#3076C2218yes—
185#3076C2214yes—
186#2994C2214yes—
187#2994C2212yes—
188#2991C2211yescharacteristic
189#2990C2211yescharacteristic
190#2990C2212yes—
191#2986C2212yes—
192#2986C2211yescharacteristic
193#2984C2212yes—
194#2966C2214yes—
195#2966C2212yes—
196C8×#41C2211yescharacteristic
197C8×#41C2211yescharacteristic
198C8×#41C2212yes—
199#2960C2211yescharacteristic
200#2960C2212yes—
201C2×C8×Q8C2212yes—
202#2951C2212yes—
203#2950C2214yes—
204C4×#135C2212yes—
205C4×#135C2214yes—
206C4×#135C2211yescharacteristic
207C2×C4×Q16C2212yes—
208C2×#135C2312yes—
209C2×#135C2311yescharacteristic
210C22×Q16C2312yes—
211#563—24no—
212#563—28no—
213#562—28no—
214#562—28no—
215#562—28no—
216#559—28no—
217#559—24no—
218#559C2318yes—
219#559C2314yes—
220Q82—24no—
221Q82C2312yes—
222Q82C2314yes—
223Q82C2314yes—
224#557—24no—
225#557—28no—
226#557—22no—
227#557D411yescharacteristic
228#557C2312yes—
229#557C2314yes—
230#557C2318yes—
231#557C2314yes—
232#557C2318yes—
233#556—22no—
234#556—28no—
235#556—28no—
236#556—24no—
237#556—24no—
238#556—28no—
239#556—22no—
240#556—22no—
241#556—24no—
242#556—22no—
243#556—28no—
244#556D411yescharacteristic
245#556D412yes—
246#556C2312yes—
247#556C2314yes—
248#556C2314yes—
249#556C2318yes—
250#555—28no—
251#555—24no—
252#555—22no—
253#555—24no—
254#555C2314yes—
255#555C2312yes—
256#555C2318yes—
257#555C2314yes—
258#554—24no—
259#554—24no—
260#554—28no—
261#554C2314yes—
262#554C2314yes—
263#554C2318yes—
264#553—28no—
265#553—28no—
266#553C2318yes—
267#553C2318yes—
268#552—28no—
269#552—24no—
270#552—28no—
271#552—24no—
272#552—24no—
273#552—24no—
274#552—24no—
275#552D412yes—
276#552D414yes—
277#552C2318yes—
278#552C2314yes—
279#550—22no—
280#550C2312yes—
281#550C2314yes—
282#550C2312yes—
283D4×Q8—24no—
284D4×Q8—22no—
285D4×Q8—24no—
286D4×Q8D411yescharacteristic
287D4×Q8C2312yes—
288D4×Q8C2314yes—
289D4×Q8C2314yes—
290#548—24no—
291#548—24no—
292#548—24no—
293#548—24no—
294#548D412yes—
295#548C2318yes—
296#548C2314yes—
297#547—22no—
298#547—24no—
299#547—22no—
300#547D411yescharacteristic
301#547D412yes—
302#547C2312yes—
303#544—24no—
304#544—28no—
305#544C2318yes—
306#544C2314yes—
307#542—24no—
308#542—28no—
309#542—28no—
310#542—28no—
311#542—28no—
312#542—24no—
313#542—28no—
314#542—28no—
315#542—24no—
316#542—24no—
317#542C2318yes—
318#542C2318yes—
319#541—28no—
320#541—24no—
321#540—28no—
322#540C2318yes—
323#539—28no—
324#539—28no—
325#539—28no—
326#537—22no—
327#537—24no—
328#536—22no—
329#536—24no—
330#536—24no—
331#536—24no—
332#536—24no—
333#533—22no—
334#533—24no—
335#533—24no—
336#533—24no—
337#533—24no—
338#533—28no—
339#533—22no—
340#533C2312yes—
341#533C2314yes—
342#533C2314yes—
343#533C2318yes—
344#533C2314yes—
345#533C2312yes—
346#533C2311yescharacteristic
347#532—24no—
348#532—24no—
349#532—22no—
350#532C2314yes—
351#532C2312yes—
352#532C2314yes—
353C2×C4⋊Q8—22no—
354C2×C4⋊Q8C2312yes—
355#529—28no—
356#529—28no—
357#529—24no—
358#529—24no—
359#529—28no—
360#529C2318yes—
361#529C2314yes—
362#529C2318yes—
363#529C2312yes—
364#529C2314yes—
365#520—22no—
366#520—24no—
367#520C2314yes—
368#519—24no—
369#519—22no—
370#519C2318yes—
371C4×#41—22no—
372C4×#41—22no—
373C4×#41—24no—
374C4×#41C2318yes—
375C4×#41C2314yes—
376C4×#41C2312yes—
377C4×#41C2312yes—
378C4×#41C2311yescharacteristic
379C4×#41C2311yescharacteristic
380C2×C4×Q8—24no—
381C2×C4×Q8C2314yes—
382C2×C4×Q8C2312yes—
383#501C2318yes—
384#501C2318yes—
385#501C2318yes—
386#500C2311yescharacteristic
387#500C2314yes—
388#500C2312yes—
389#500C2312yes—
390#500C2311yescharacteristic
391#500C2312yes—
392#500C2314yes—
393#500C2312yes—
394#500C2312yes—
395#499C2312yes—
396#499C2314yes—
397#499C2314yes—
398#499C2314yes—
399#499C2314yes—
400#499C2314yes—
401#499C2318yes—
402#498C2318yes—
403#498C2314yes—
404#498C2314yes—
405#495C2312yes—
406#495C2314yes—
407#494C2311yescharacteristic
408#493C2311yescharacteristic
409#493C2312yes—
410#490C2318yes—
411#489C2318yes—
412#489C2318yes—
413#488C2318yes—
414#488C2318yes—
415#488C2314yes—
416#487C2314yes—
417#487C2312yes—
418#486C2314yes—
419#486C2312yes—
420#486C2314yes—
421#485C2318yes—
422#485C2318yes—
423#485C2318yes—
424#485C2314yes—
425#485C2318yes—
426#483C2318yes—
427#483C2314yes—
428#482C2318yes—
429#482C2318yes—
430#482C2318yes—
431#482C2314yes—
432#482C2318yes—
433#482C2318yes—
434#482C2314yes—
435#482C2314yes—
436#481C2318yes—
437#481C2318yes—
438#480C2314yes—
439#479C2314yes—
440#479C2318yes—
441#479C2318yes—
442#479C2318yes—
443#479C2318yes—
444#479C2314yes—
445#479C2318yes—
446#479C2318yes—
447#479C2318yes—
448#478C2318yes—
449#478C2318yes—
450#478C2318yes—
451#478C2318yes—
452#478C2318yes—
453#478C2318yes—
454#477C2314yes—
455#477C2318yes—
456#477C2312yes—
457#477C2314yes—
458#477C2314yes—
459#477C2318yes—
460#476C2314yes—
461#476C2318yes—
462#476C2314yes—
463#476C2312yes—
464#476C2314yes—
465#476C2314yes—
466#476C2318yes—
467#475C2312yes—
468#475C2318yes—
469#475C2314yes—
470#475C2314yes—
471#475C2318yes—
472#475C2314yes—
473#475C2318yes—
474#474C2318yes—
475#474C2314yes—
476#474C2312yes—
477#474C2314yes—
478#474C2318yes—
479#469C2318yes—
480#468C2318yes—
481#468C2318yes—
482#467C2312yes—
483#467C2312yes—
484#467C2314yes—
485#467C2312yes—
486#467C2314yes—
487#466C2312yes—
488#466C2312yes—
489#466C2312yes—
490#466C2314yes—
491#466C2312yes—
492#466C2314yes—
493#466C2312yes—
494#466C2314yes—
495#465C2318yes—
496#465C2314yes—
497#465C2318yes—
498#464C2318yes—
499#464C2314yes—
500#464C2314yes—
501#464C2318yes—
502#463C2318yes—
503#463C2318yes—
504#463C2318yes—
505#462C2312yes—
506#461C2314yes—
507#461C2312yes—
508#460C2312yes—
509#460C2314yes—
510#460C2314yes—
511#460C2318yes—
512#459C2314yes—
513#459C2312yes—
514#452C2318yes—
515#452C2314yes—
516#451C2314yes—
517#449C2314yes—
518#449C2314yes—
519#449C2314yes—
520#448C2318yes—
521#448C2314yes—
522#446C2312yes—
523#446C2312yes—
524#446C2312yes—
525#446C2314yes—
526#446C2314yes—
527#446C2312yes—
528#446C2312yes—
529C8×Q8C2312yes—
530C8×Q8C2312yes—
531C8×Q8C2311yescharacteristic
532C8×Q8C2311yescharacteristic
533C8×Q8C2312yes—
534C8×Q8C2314yes—
535C8×Q8C2312yes—
536C8×Q8C2312yes—
537C8×Q8C2311yescharacteristic
538C8×Q8C2314yes—
539C8×Q8C2311yescharacteristic
540#442C2318yes—
541#441C2318yes—
542#441C2318yes—
543#440C2318yes—
544#440C2318yes—
545#440C2318yes—
546C4×Q16C2314yes—
547C4×Q16C2312yes—
548C4×Q16C2314yes—
549C4×Q16C2312yes—
550C4×Q16C2314yes—
551C4×Q16C2312yes—
552C4×Q16C2314yes—
553C4×Q16C2314yes—
554C4×Q16C2311yescharacteristic
555C4×Q16C2311yescharacteristic
556C4×Q16C2312yes—
557C4×Q16C2314yes—
558C4×Q16C2312yes—
559C4×SD16C2314yes—
560C4×SD16C2318yes—
561C4×SD16C2314yes—
562C4×SD16C2318yes—
563C4×SD16C2318yes—
564C4×SD16C2312yes—
565C4×SD16C2312yes—
566C4×SD16C2314yes—
567C4×SD16C2318yes—
568C4×D8C2311yescharacteristic
569C4×D8C2314yes—
570C4×D8C2314yes—
571C4×D8C2314yes—
572C4×D8C2312yes—
573C4×D8C2311yescharacteristic
574C4×D8C2312yes—
575C4×D8C2314yes—
576C4×D8C2312yes—
577C4×D8C2314yes—
578#436C2312yes—
579#436C2314yes—
580#435C2314yes—
581#435C2314yes—
582#435C2314yes—
583C8×D4C2311yescharacteristic
584C8×D4C2312yes—
585C8×D4C2312yes—
586C8×D4C2312yes—
587C8×D4C2312yes—
588C8×D4C2314yes—
589C8×D4C2312yes—
590C8×D4C2314yes—
591C8×D4C2311yescharacteristic
592C8×D4C2311yescharacteristic
593C8×D4C2311yescharacteristic
594#433C2314yes—
595#433C2314yes—
596#433C2314yes—
597#432C2314yes—
598#432C2312yes—
599#431C2314yes—
600#431C2312yes—
601#431C2311yescharacteristic
602#431C2312yes—
603#431C2311yescharacteristic
604#431C2312yes—
605#428C2318yes—
606#428C2314yes—
607#427C2314yes—
608#427C2318yes—
609#427C2311yescharacteristic
610#427C2314yes—
611#427C2314yes—
612#427C2314yes—
613#427C2312yes—
614C2×#107C2312yes—
615C2×#107C2312yes—
616C2×#107C2312yes—
617#424C2314yes—
618#424C2312yes—
619#423C2312yes—
620#423C2311yescharacteristic
621C2×C4⋊C8C2312yes—
622C2×C4⋊C8C2314yes—
623#419C2318yes—
624#417C2314yes—
625#416C2318yes—
626#416C2314yes—
627#416C2312yes—
628C2×#103C2314yes—
629#405C2312yes—
630#405C2314yes—
631C2×C4×C8C2311yescharacteristic
632C2×C4×C8C2314yes—
633C2×C4×C8C2312yes—
634C2×C4×C8C2312yes—
635C2×#41—22no—
636C2×#41—22no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—22no—
640C2×#41C2×D412yes—
641C2×#41C2×D411yescharacteristic
642C2×#41C2×D411yescharacteristic
643C2×#41C2414yes—
644C2×#41C2412yes—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—22no—
648C22×Q8C2×D412yes—
649C22×Q8C2414yes—
650#135—28no—
651#135—24no—
652C2×Q16—28no—
653C2×Q16C2412yes—
654C2×Q16C2414yes—
655C2×Q16C2412yes—
656C2×Q16C2411yescharacteristic
657C2×SD16C2414yes—
658C2×SD16C2412yes—
659C2×SD16C2414yes—
660C2×SD16C2418yes—
661C2×D8C2412yes—
662C2×D8C2411yescharacteristic
663C2×D8C2412yes—
664C2×D8C2414yes—
665C2×M16C2412yes—
666C2×M16C2414yes—
667C22×C8C2412yes—
668C22×C8C2412yes—
669C22×C8C2411yescharacteristic
670C22×C8C2412yes—
671C22×C8C2414yes—
672C22×C8C2412yes—
673C22×C8C2411yescharacteristic
674C4⋊Q8—24no—
675C4⋊Q8—22no—
676C4⋊Q8—24no—
677C4⋊Q8—28no—
678C4⋊Q8—28no—
679C4⋊Q8—24no—
680C4⋊Q8—24no—
681C4⋊Q8—22no—
682C4⋊Q8—24no—
683C4⋊Q8—22no—
684C4⋊Q8—24no—
685C4⋊Q8—28no—
686C4⋊Q8—28no—
687C4⋊Q8—28no—
688C4⋊Q8—22no—
689C4⋊Q8—22no—
690C4⋊Q8C2×D411yescharacteristic
691C4⋊Q8C2×D411yescharacteristic
692C4⋊Q8C2×D412yes—
693C4⋊Q8C2×D412yes—
694C4⋊Q8C2412yes—
695C4⋊Q8C2414yes—
696C4⋊Q8C2414yes—
697C4⋊Q8C2412yes—
698C4⋊Q8C2414yes—
699C4⋊Q8C2412yes—
700C4⋊Q8C2418yes—
701C4⋊Q8C2418yes—
702#127—22no—
703#127—24no—
704#127C2412yes—
705#127C2414yes—
706#126—24no—
707#126—28no—
708#126—28no—
709#126—28no—
710#126—28no—
711#126—28no—
712#126—24no—
713#126—28no—
714#126—28no—
715#126—28no—
716#126—28no—
717#126—28no—
718#126—24no—
719#126—28no—
720#126C2×D414yes—
721#126C2×D414yes—
722#126C2×D414yes—
723#125—24no—
724#125—28no—
725#125—28no—
726#125—28no—
727#125—28no—
728#125—28no—
729#125—24no—
730#125—24no—
731#125—28no—
732#125—28no—
733#125—28no—
734#125—24no—
735#125—22no—
736#125C2×D412yes—
737#125C2×D414yes—
738#125C2×D414yes—
739#125C2×D412yes—
740#125C2414yes—
741#125C2418yes—
742#125C2418yes—
743#125C2418yes—
744#124—24no—
745#124—28no—
746#124—24no—
747#124—28no—
748#124—24no—
749#124—28no—
750#124—28no—
751#124—24no—
752#124—24no—
753#124—24no—
754#124—28no—
755#124—28no—
756#124—28no—
757#124—28no—
758#124—24no—
759#124—24no—
760#124—22no—
761#124C2×D412yes—
762#124C2×D414yes—
763#124C2414yes—
764#124C2418yes—
765#123—24no—
766#123—28no—
767#123—28no—
768#123—28no—
769#123—24no—
770#123—28no—
771#123—28no—
772#123—28no—
773#123—28no—
774#123—28no—
775#123—28no—
776#123—28no—
777#123—28no—
778#123—24no—
779#123—28no—
780#123C2×D414yes—
781#123C2×D414yes—
782#123C2×D414yes—
783C22⋊Q8—24no—
784C22⋊Q8—22no—
785C22⋊Q8—24no—
786C22⋊Q8—24no—
787C22⋊Q8—28no—
788C22⋊Q8—24no—
789C22⋊Q8—22no—
790C22⋊Q8—24no—
791C22⋊Q8—24no—
792C22⋊Q8—24no—
793C22⋊Q8—24no—
794C22⋊Q8—28no—
795C22⋊Q8—28no—
796C22⋊Q8—28no—
797C22⋊Q8—28no—
798C22⋊Q8—22no—
799C22⋊Q8—24no—
800C22⋊Q8—28no—
801C22⋊Q8—28no—
802C22⋊Q8—28no—
803C22⋊Q8—28no—
804C22⋊Q8—24no—
805C22⋊Q8—24no—
806C22⋊Q8—28no—
807C22⋊Q8—28no—
808C22⋊Q8—28no—
809C22⋊Q8—24no—
810C22⋊Q8—28no—
811C22⋊Q8—28no—
812C22⋊Q8—28no—
813C22⋊Q8C2×D412yes—
814C22⋊Q8C2×D414yes—
815C22⋊Q8C2×D412yes—
816C22⋊Q8C2×D412yes—
817C22⋊Q8C2×D412yes—
818C22⋊Q8C2×D412yes—
819C22⋊Q8C2×D414yes—
820C22⋊Q8C2418yes—
821C22⋊Q8C2414yes—
822C22⋊Q8C2414yes—
823#121—24no—
824#121—24no—
825#121—28no—
826#121—24no—
827#121—28no—
828#121—22no—
829#121—28no—
830#121—28no—
831#121—24no—
832#121—24no—
833#121—22no—
834#121—24no—
835#121—22no—
836#121—24no—
837#121—24no—
838#121—28no—
839#121—24no—
840#121—28no—
841#121C2×D412yes—
842#121C2×D414yes—
843#121C2414yes—
844#121C2414yes—
845#121C2414yes—
846#121C2418yes—
847#121C2414yes—
848C4×Q8—24no—
849C4×Q8—22no—
850C4×Q8—24no—
851C4×Q8—22no—
852C4×Q8—28no—
853C4×Q8—24no—
854C4×Q8—24no—
855C4×Q8—28no—
856C4×Q8—24no—
857C4×Q8—28no—
858C4×Q8—28no—
859C4×Q8—28no—
860C4×Q8—24no—
861C4×Q8—28no—
862C4×Q8—24no—
863C4×Q8—24no—
864C4×Q8—22no—
865C4×Q8—24no—
866C4×Q8—28no—
867C4×Q8—24no—
868C4×Q8—24no—
869C4×Q8—24no—
870C4×Q8C2×D412yes—
871C4×Q8C2×D412yes—
872C4×Q8C2×D414yes—
873C4×Q8C2×D411yescharacteristic
874C4×Q8C2×D412yes—
875C4×Q8C2×D411yescharacteristic
876C4×Q8C2412yes—
877C4×Q8C2414yes—
878C4×Q8C2414yes—
879C4×Q8C2414yes—
880C4×Q8C2412yes—
881C4×Q8C2414yes—
882C4×Q8C2418yes—
883C4×Q8C2418yes—
884C4×Q8C2418yes—
885C4×Q8C2411yescharacteristic
886C4×Q8C2412yes—
887C4×Q8C2414yes—
888C4×Q8C2412yes—
889C4×Q8C2411yescharacteristic
890C4×D4—22no—
891C4×D4—24no—
892C4×D4—22no—
893C4×D4—28no—
894C4×D4—22no—
895C4×D4—24no—
896C4×D4—28no—
897C4×D4—24no—
898C4×D4—28no—
899C4×D4—28no—
900C4×D4—22no—
901C4×D4—24no—
902C4×D4—24no—
903C4×D4—28no—
904C4×D4—24no—
905C4×D4—28no—
906C4×D4—28no—
907C4×D4—28no—
908C4×D4—28no—
909C4×D4—22no—
910C4×D4—24no—
911C4×D4—24no—
912C4×D4C2×D411yescharacteristic
913C4×D4C2×D412yes—
914C4×D4C2×D411yescharacteristic
915C4×D4C2×D412yes—
916C4×D4C2×D412yes—
917C4×D4C2×D414yes—
918C4×D4C2412yes—
919C4×D4C2418yes—
920C4×D4C2412yes—
921C4×D4C2414yes—
922C4×D4C2418yes—
923C4×D4C2414yes—
924C4×D4C2418yes—
925C4×D4C2411yescharacteristic
926C4×D4C2411yescharacteristic
927C4×D4C2412yes—
928C4×D4C2414yes—
929C4×D4C2412yes—
930#117—22no—
931#117—24no—
932#117—22no—
933#117—22no—
934#117—24no—
935#117—28no—
936#117—24no—
937#117—24no—
938#117—24no—
939#117—24no—
940#117—28no—
941#117—28no—
942#117—28no—
943#117—28no—
944#117—28no—
945#117—24no—
946#117—22no—
947#117—24no—
948#117—28no—
949#117C2×D412yes—
950#117C2×D411yescharacteristic
951#117C2×D411yescharacteristic
952#117C2×D414yes—
953#117C2×D412yes—
954#117C2×D412yes—
955#117C2418yes—
956#117C2414yes—
957#117C2412yes—
958#117C2418yes—
959#117C2414yes—
960#117C2412yes—
961C2×C4⋊C4—24no—
962C2×C4⋊C4—22no—
963C2×C4⋊C4—24no—
964C2×C4⋊C4—28no—
965C2×C4⋊C4—24no—
966C2×C4⋊C4—24no—
967C2×C4⋊C4C2×D412yes—
968C2×C4⋊C4C2×D414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C42—24no—
972C2×C42—28no—
973C2×C42—24no—
974C2×C42—22no—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2412yes—
978C2×C42C2411yescharacteristic
979#107C2411yescharacteristic
980#107C2412yes—
981#107C2414yes—
982#107C2414yes—
983#107C2414yes—
984#107C2414yes—
985#107C2414yes—
986#107C2411yescharacteristic
987#107C2412yes—
988#107C2412yes—
989#107C2412yes—
990#107C2418yes—
991#107C2418yes—
992#107C2414yes—
993#106C2418yes—
994#106C2414yes—
995#106C2418yes—
996#106C2414yes—
997#106C2418yes—
998#106C2412yes—
999#106C2418yes—
1000#106C2418yes—
1001C4⋊C8C2411yescharacteristic
1002C4⋊C8C2412yes—
1003C4⋊C8C2412yes—
1004C4⋊C8C2414yes—
1005C4⋊C8C2414yes—
1006C4⋊C8C2414yes—
1007C4⋊C8C2414yes—
1008C4⋊C8C2411yescharacteristic
1009C4⋊C8C2412yes—
1010C4⋊C8C2412yes—
1011C4⋊C8C2414yes—
1012C4⋊C8C2411yescharacteristic
1013C4⋊C8C2411yescharacteristic
1014C4⋊C8C2412yes—
1015C4⋊C8C2412yes—
1016C4⋊C8C2414yes—
1017#103C2412yes—
1018#103C2414yes—
1019#103C2414yes—
1020#103C2414yes—
1021#103C2412yes—
1022#103C2418yes—
1023#103C2414yes—
1024#103C2418yes—
1025#103C2418yes—
1026#103C2418yes—
1027#103C2414yes—
1028#103C2414yes—
1029#102C2412yes—
1030#102C2414yes—
1031#102C2418yes—
1032#102C2418yes—
1033#102C2414yes—
1034#102C2412yes—
1035#102C2418yes—
1036#102C2414yes—
1037#102C2414yes—
1038#102C2414yes—
1039#102C2418yes—
1040#102C2414yes—
1041C22⋊C8C2412yes—
1042C22⋊C8C2412yes—
1043C22⋊C8C2414yes—
1044C22⋊C8C2412yes—
1045C22⋊C8C2412yes—
1046C22⋊C8C2412yes—
1047C22⋊C8C2414yes—
1048C22⋊C8C2412yes—
1049#97C2414yes—
1050#97C2414yes—
1051#97C2414yes—
1052C4×C8C2411yescharacteristic
1053C4×C8C2412yes—
1054C4×C8C2411yescharacteristic
1055C4×C8C2414yes—
1056C4×C8C2412yes—
1057C4×C8C2411yescharacteristic
1058C4×C8C2412yes—
1059C4×C8C2412yes—
1060C4×C8C2411yescharacteristic
1061C4×C8C2412yes—
1062C4×C8C2414yes—
1063C4×C8C2414yes—
1064C4×C8C2412yes—
1065#41—28no—
1066#41—24no—
1067#41—42no—
1068#41—44no—
1069#41—42no—
1070#41—44no—
1071#41—42no—
1072#41—88no—
1073#41—84no—
1074#41—88no—
1075#41—84no—
1076#41—84no—
1077C2×Q8—24no—
1078C2×Q8—22no—
1079C2×Q8—24no—
1080C2×Q8—28no—
1081C2×Q8—24no—
1082C2×Q8—28no—
1083C2×Q8—22no—
1084C2×Q8—24no—
1085C2×Q8—28no—
1086C2×Q8—44no—
1087C2×Q8—44no—
1088C2×Q8—84no—
1089C2×Q8—88no—
1090C2×Q8—88no—
1091C2×Q8C22×D412yes—
1092C2×Q8C22×D412yes—
1093C2×Q8C22×D411yescharacteristic
1094C2×Q8C22×D411yescharacteristic
1095C2×Q8C22×D414yes—
1096C2×Q8C2514yes—
1097C2×Q8C2512yes—
1098C2×D4—24no—
1099C2×D4—22no—
1100C2×D4—24no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—24no—
1104C2×D4—24no—
1105C2×D4—22no—
1106C2×D4—22no—
1107C2×D4—24no—
1108C2×D4—24no—
1109C2×D4C22×D411yescharacteristic
1110C2×D4C22×D411yescharacteristic
1111C2×D4C22×D412yes—
1112C2×D4C22×D414yes—
1113C2×D4C22×D412yes—
1114C2×D4C2512yes—
1115C2×D4C2514yes—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—22no—
1121C22×C4—22no—
1122C22×C4—24no—
1123C22×C4—22no—
1124C22×C4—28no—
1125C22×C4—24no—
1126C22×C4—28no—
1127C22×C4—28no—
1128C22×C4C22×D412yes—
1129C22×C4C22×D411yescharacteristic
1130C22×C4C22×D412yes—
1131C22×C4C22×D411yescharacteristic
1132C22×C4C22×D412yes—
1133C22×C4C22×D414yes—
1134C22×C4C22×D412yes—
1135C22×C4C22×D414yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139Q16—28no—
1140Q16—24no—
1141Q16—42no—
1142Q162−1+414yes—
1143SD16—28no—
1144SD16—24no—
1145SD16—44no—
1146SD16—48no—
1147D8—24no—
1148D8—22no—
1149D8—42no—
1150D8—44no—
1151M16—44no—
1152M16—42no—
1153C2×C8—24no—
1154C2×C8—24no—
1155C2×C8—22no—
1156C2×C8—42no—
1157C2×C8—41no—
1158C2×C8—44no—
1159C2×C8—42no—
1160C2×C8C2512yes—
1161C2×C8C2511yescharacteristic
1162C2×C8C2512yes—
1163C2×C8C2511yescharacteristic
1164C2×C8C2512yes—
1165C2×C8C2511yescharacteristic
1166C2×C8C2514yes—
1167C2×C8C2512yes—
1168C2×C8C2511yescharacteristic
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—28no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—22no—
1184C4⋊C4—22no—
1185C4⋊C4—28no—
1186C4⋊C4—24no—
1187C4⋊C4—22no—
1188C4⋊C4—24no—
1189C4⋊C4—28no—
1190C4⋊C4—24no—
1191C4⋊C4—28no—
1192C4⋊C4—28no—
1193C4⋊C4—28no—
1194C4⋊C4—22no—
1195C4⋊C4—24no—
1196C4⋊C4—22no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—28no—
1200C4⋊C4C22×D411yescharacteristic
1201C4⋊C4C22×D412yes—
1202C4⋊C4C22×D414yes—
1203C4⋊C4C22×D412yes—
1204C4⋊C4C22×D412yes—
1205C4⋊C4C22×D414yes—
1206C4⋊C4C22×D414yes—
1207C4⋊C4C22×D414yes—
1208C4⋊C4C22×D411yescharacteristic
1209C4⋊C4C22×D411yescharacteristic
1210C4⋊C4C22×D412yes—
1211C4⋊C4C22×D414yes—
1212C4⋊C4C22×D412yes—
1213C4⋊C4C22×D412yes—
1214C4⋊C4C22×D411yescharacteristic
1215C4⋊C4C22×D412yes—
1216C4⋊C4C22×D414yes—
1217C4⋊C4C22×D412yes—
1218C4⋊C4C22×D414yes—
1219C4⋊C4C22×D414yes—
1220C4⋊C4C2512yes—
1221C4⋊C4C2518yes—
1222C4⋊C4C2514yes—
1223C4⋊C4C2512yes—
1224C4⋊C4C2514yes—
1225C22⋊C4—24no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—24no—
1229C22⋊C4—22no—
1230C22⋊C4—28no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—22no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—22no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—28no—
1248C22⋊C4C22×D412yes—
1249C22⋊C4C22×D412yes—
1250C22⋊C4C22×D414yes—
1251C22⋊C4C22×D414yes—
1252C22⋊C4C22×D412yes—
1253C22⋊C4C22×D412yes—
1254C22⋊C4C22×D414yes—
1255C22⋊C4C22×D412yes—
1256C22⋊C4C22×D412yes—
1257C22⋊C4C22×D414yes—
1258C22⋊C4C22×D414yes—
1259C42—22no—
1260C42—24no—
1261C42—22no—
1262C42—22no—
1263C42—24no—
1264C42—28no—
1265C42—24no—
1266C42—28no—
1267C42—24no—
1268C42—24no—
1269C42—28no—
1270C42—28no—
1271C42—28no—
1272C42C22×D414yes—
1273C42C22×D411yescharacteristic
1274C42C22×D412yes—
1275C42C22×D414yes—
1276C42C22×D411yescharacteristic
1277C42C22×D412yes—
1278C42C22×D412yes—
1279C42C22×D412yes—
1280C42C2511yescharacteristic
1281C42C2512yes—
1282C42C2511yescharacteristic
1283C42C2514yes—
1284C42C2512yes—
1285C23—22no—
1286C23—24no—
1287C23C23×D412yes—
1288C23C23×D412yes—
1289C23C23×D411yescharacteristic
1290Q8—22no—
1291Q8—24no—
1292Q8—24no—
1293Q8—22no—
1294Q8—22no—
1295Q8—24no—
1296Q8—24no—
1297Q8—44no—
1298Q8—48no—
1299Q8—44no—
1300Q8—48no—
1301Q8—84no—
1302Q8—88no—
1303Q8—88no—
1304Q8—82no—
1305Q8—84no—
1306Q8C2×2−1+414yes—
1307D4—22no—
1308D4—22no—
1309D4—24no—
1310D4—22no—
1311D4—24no—
1312D4—22no—
1313D4—42no—
1314D4—42no—
1315D4—44no—
1316D4—48no—
1317D4—44no—
1318D4—44no—
1319D4—82no—
1320D4—84no—
1321D4—84no—
1322D4—84no—
1323D4—84no—
1324D4—84no—
1325D4—88no—
1326D4—84no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—28no—
1343C2×C4—22no—
1344C2×C4—44no—
1345C2×C4—44no—
1346C2×C4—42no—
1347C2×C4—42no—
1348C2×C4—48no—
1349C2×C4—44no—
1350C2×C4—48no—
1351C2×C4—44no—
1352C2×C4—48no—
1353C2×C4—44no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—88no—
1357C2×C4—84no—
1358C2×C4—84no—
1359C2×C4—84no—
1360C2×C4C23×D412yes—
1361C2×C4C23×D412yes—
1362C2×C4C23×D412yes—
1363C2×C4C23×D412yes—
1364C2×C4C23×D411yescharacteristic
1365C2×C4C23×D414yes—
1366C2×C4C23×D414yes—
1367C2×C4C23×D412yes—
1368C2×C4C23×D411yescharacteristic
1369C2×C4C23×D412yes—
1370C2×C4C23×D411yescharacteristic
1371C2×C4C23×D411yescharacteristic
1372C2×C4C23×D411yescharacteristic
1373C2×C4C2611yescharacteristic
1374C8—22no—
1375C8—21no—
1376C8—22no—
1377C8—21no—
1378C8—22no—
1379C8—21no—
1380C8—22no—
1381C8—24no—
1382C8C2×2−1+412yes—
1383C22—22no—
1384C22—22no—
1385C22—21no—
1386C22—22no—
1387C22—21no—
1388C22—22no—
1389C22—21no—
1390C22—22no—
1391C22—22no—
1392C22—42no—
1393C22—44no—
1394C22—42no—
1395C22—44no—
1396C22—42no—
1397C22—44no—
1398C22C24×D411yescharacteristic
1399C4—22no—
1400C4—21no—
1401C4—22no—
1402C4—24no—
1403C4—22no—
1404C4—21no—
1405C4—21no—
1406C4—22no—
1407C4—22no—
1408C4—22no—
1409C4—24no—
1410C4—24no—
1411C4—44no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—44no—
1416C4—48no—
1417C4#358412yes—
1418C4#358412yes—
1419C4C22×2−1+411yescharacteristic
1420C42−1+611yescharacteristic
1421C2—42no—
1422C2—42no—
1423C2—41no—
1424C2—82no—
1425C2—84no—
1426C2D4×2−1+411yescharacteristic
1427C2C2×#358411yescharacteristic
1428C2C2×#358411yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3482 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63034C2semidirect
2. #62495C2semidirect
3. #62490C2semidirect
4. #62476C2semidirect
5. #62474C2semidirect
6. #62473C2semidirect
7. #62379C2semidirect
8. #62375C2semidirect
9. #62361C2semidirect
10. #62219C2semidirect
11. #62210C2semidirect
12. #62145C2semidirect
13. #62142C2semidirect
14. #62135C2semidirect
15. #61871C2semidirect
16. #61865C2semidirect
17. #61839C2semidirect
18. #61488C2semidirect
19. #61478C2semidirect
20. #61436C2semidirect
21. #61433C2semidirect
22. #61430C2semidirect
23. #61373C2semidirect
24. #61372C2semidirect
25. Q8×#135C2semidirect
26. #60331C2semidirect

Maximal subgroups

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

subgroupindex
#630342
#624952
#624902
#624762
#624742
#624732
#623792
#623752
#623612
#622192
#622102
#621452
#621422
#621352
#618712
#618652
#618392
#614882
#614782
#614362
#614332
#614302
#613732
#613722
Q8×#1352
#603312