Finite Group Databasebeta

← #8757196

Subgroups — #8757196

Order 512.

4244 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57051C214yesmaximal, complemented
2#55037C214yesmaximal, complemented
3#54991C214yesmaximal, complemented
4#54001C214yesmaximal, complemented
5#53958C214yesmaximal, complemented
6#53665C214yesmaximal, complemented
7#50096C214yesmaximal, complemented
8#49593C212yesmaximal, complemented
9#49592C212yesmaximal, complemented
10#48551C214yesmaximal, complemented
11#47807C212yesmaximal, complemented
12#47695C212yesmaximal, complemented
13#47071C214yesmaximal, complemented
14#46497C214yesmaximal, complemented
15#46241C212yesmaximal, complemented
16#46241C212yesmaximal, complemented
17#46232C212yesmaximal, complemented
18#46017C212yesmaximal, complemented
19#46017C212yesmaximal, complemented
20#45991C211yesmaximal, characteristic, complemented
21#45991C211yesmaximal, characteristic, complemented
22#35339C211yesmaximal, characteristic, complemented
23#35136C212yesmaximal, complemented
24#2864C2212yes—
25#2864C2212yes—
26#2864C2212yes—
27#2858C2212yes—
28#2850C2212yes—
29#2850C2212yes—
30#2844C2212yes—
31#2844C2211yescharacteristic
32#2844C2211yescharacteristic
33#2843C2212yes—
34#2839C2214yes—
35#2836C2214yes—
36#2832C2214yes—
37#2824C2214yes—
38#2819C2212yes—
39#2819C2211yescharacteristic
40#2819C2211yescharacteristic
41#2819C2212yes—
42#2814C2214yes—
43#2813C2214yes—
44#2803C2214yes—
45#2803C2214yes—
46#2799C2214yes—
47#2799C2214yes—
48#2795C2214yes—
49#2795C2212yes—
50#2788C2214yes—
51#2788C2214yes—
52#2788C2214yes—
53#2788C2214yes—
54#2785C2212yes—
55#2785C2212yes—
56#2785C2212yes—
57#2784C2214yes—
58#2784C2214yes—
59#2782C2212yes—
60#2782C2212yes—
61#2782C2212yes—
62#2781C2214yes—
63#2781C2214yes—
64#2775C2214yes—
65#2772C2214yes—
66#2767C2214yes—
67#2763C2214yes—
68#2763C2214yes—
69#2761C2214yes—
70#2754C2214yes—
71#2753C2214yes—
72#2753C2214yes—
73#2751C2214yes—
74#2751C2214yes—
75#2751C2214yes—
76#2750C2214yes—
77#2744C2214yes—
78#2743C2214yes—
79#2742C2214yes—
80#2742C2214yes—
81#2742C2214yes—
82#2742C2214yes—
83#2738C2214yes—
84#2718C2214yes—
85#2716C2214yes—
86#2716C2214yes—
87#2714C2214yes—
88#2714C2214yes—
89#2710C2214yes—
90#2708C2214yes—
91#2706C2214yes—
92#2705C2214yes—
93#2703C2214yes—
94#2703C2214yes—
95#2702C2214yes—
96#2701C2214yes—
97#2701C2214yes—
98#2698C2214yes—
99#2696C2214yes—
100#2696C2214yes—
101#2695C2214yes—
102#2693C2214yes—
103#2693C2214yes—
104#2692C2214yes—
105#2692C2214yes—
106#2687C2214yes—
107#2682C2214yes—
108#2681C2214yes—
109#2680C2214yes—
110#2680C2212yes—
111#2673C2214yes—
112#2673C2214yes—
113#2672C2214yes—
114#2671C2214yes—
115#2671C2214yes—
116#2667C2212yes—
117#2665C2212yes—
118#2652C2214yes—
119#2651C2214yes—
120#2648C2214yes—
121#2647C2212yes—
122#2647C2212yes—
123#2639C2214yes—
124#2637C2214yes—
125#2630C2214yes—
126#2615C2212yes—
127#2615C2212yes—
128#2612C2212yes—
129#2610C2214yes—
130#2604C2214yes—
131#2602C2214yes—
132#2602C2214yes—
133#2598C2214yes—
134#2591C2212yes—
135#2591C2212yes—
136#2581C2214yes—
137#2581C2214yes—
138#2570C2214yes—
139#2570C2214yes—
140#2569C2214yes—
141#2569C2214yes—
142#2564C2214yes—
143#2564C2214yes—
144#2559C2214yes—
145#2559C2214yes—
146#2557C2214yes—
147#2557C2214yes—
148#2553C2214yes—
149#2537C2212yes—
150#2536C2214yes—
151#2532C2214yes—
152#2532C2214yes—
153#2531C2214yes—
154#2530C2214yes—
155#2526C2214yes—
156#2505C2214yes—
157#2505C2214yes—
158#2505C2214yes—
159#2505C2214yes—
160#2488C2214yes—
161#2488C2214yes—
162#2488C2214yes—
163#2476C2214yes—
164#2471C2214yes—
165#2465C2214yes—
166#2465C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2461C2214yes—
170#2461C2214yes—
171#2459C2214yes—
172#2459C2214yes—
173#2458C2214yes—
174#2458C2214yes—
175#2458C2214yes—
176#2458C2214yes—
177#2456C2214yes—
178#2456C2214yes—
179#2455C2214yes—
180#2448C2212yes—
181#2447C2212yes—
182#2446C2212yes—
183#2445C2212yes—
184#2430C2214yes—
185#2430C2214yes—
186#2430C2214yes—
187#2429C2212yes—
188#2428C2212yes—
189#2427C2212yes—
190#2426C2212yes—
191#2425C2214yes—
192#2425C2214yes—
193#2421C2214yes—
194#2419C2214yes—
195#2407C2214yes—
196#2406C2212yes—
197#2406C2212yes—
198#2379C2212yes—
199#2379C2212yes—
200#2379C2212yes—
201#2379C2212yes—
202#2377C2212yes—
203#2377C2212yes—
204#2341C2212yes—
205#2339C2212yes—
206#2335C2214yes—
207#2333C2214yes—
208#2326C2214yes—
209#2318C2214yes—
210#2317C2211yescharacteristic
211#2317C2211yescharacteristic
212#2316C2211yescharacteristic
213#2316C2211yescharacteristic
214C4×#124C2212yes—
215C4×#124C2212yes—
216#2285C2211yescharacteristic
217C2×#382C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×#127C2312yes—
223C2×#126C2314yes—
224C2×#126C2314yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×#121C2314yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×#121C2312yes—
249C2×#121C2312yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C42C2311yescharacteristic
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2312yes—
287#400C2314yes—
288#400C2312yes—
289#400C2312yes—
290#400C2314yes—
291#400C2312yes—
292#400C2314yes—
293#400C2314yes—
294#399C2314yes—
295#399C2314yes—
296#399C2314yes—
297#399C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2312yes—
343#395C2314yes—
344#395C2312yes—
345#395C2312yes—
346#395C2312yes—
347#394C2312yes—
348#394C2312yes—
349#394C2312yes—
350#394C2314yes—
351#394C2312yes—
352#394C2314yes—
353#394C2314yes—
354#394C2312yes—
355#394C2312yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2312yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2312yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#392C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#392C2314yes—
392#392C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#392C2314yes—
397#392C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#390C2314yes—
411#390C2314yes—
412#390C2314yes—
413#390C2314yes—
414#390C2312yes—
415#390C2312yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2314yes—
420#390C2314yes—
421#390C2312yes—
422#390C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#384C2312yes—
559#384C2312yes—
560#384C2312yes—
561#383C2314yes—
562#382C2312yes—
563#382C2311yescharacteristic
564#382C2311yescharacteristic
565#382C2312yes—
566#382C2312yes—
567#382C2314yes—
568#382C2314yes—
569#382C2314yes—
570#382C2312yes—
571#382C2312yes—
572#382C2314yes—
573#382C2311yescharacteristic
574#382C2311yescharacteristic
575#382C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2312yes—
580#381C2312yes—
581#380C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608#376C2314yes—
609#376C2312yes—
610C2×#95C2314yes—
611C2×#95C2314yes—
612C2×#95C2314yes—
613C43C2312yes—
614C2×#41—44no—
615C2×#41—44no—
616C2×#41—84no—
617C2×#41—84no—
618C22×Q8C2412yes—
619C22×Q8C2412yes—
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×D4C2412yes—
624C22×D4C2412yes—
625C22×D4C2414yes—
626C22×D4C2414yes—
627C22×D4C2412yes—
628C22×D4C2414yes—
629C22×D4C2414yes—
630C22×D4C2412yes—
631C22×D4C2412yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2412yes—
635C23×C4C2411yescharacteristic
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2414yes—
640C23×C4C2414yes—
641C23×C4C2414yes—
642C23×C4C2414yes—
643C23×C4C2414yes—
644C23×C4C2414yes—
645C4⋊Q8—82no—
646#127—82no—
647#126—84no—
648#126—84no—
649#124—28no—
650#124—28no—
651#124—48no—
652#124—82no—
653#124—82no—
654#123—48no—
655#123—84no—
656#123—84no—
657#123—84no—
658#123—84no—
659#123—84no—
660#123—84no—
661#123—84no—
662#123—84no—
663C22⋊Q8—84no—
664C22⋊Q8—82no—
665C22⋊Q8—84no—
666C22⋊Q8—82no—
667C22⋊Q8—84no—
668C22⋊Q8—84no—
669#121—48no—
670#121—44no—
671#121—44no—
672#121—84no—
673#121—84no—
674#121—84no—
675#121—84no—
676#121—82no—
677#121—82no—
678C4×Q8—84no—
679C4×Q8—82no—
680C4×Q8—82no—
681C4×Q8—84no—
682C4×D4—48no—
683C4×D4—82no—
684C4×D4—82no—
685C4×D4—84no—
686C4×D4—84no—
687#117—42no—
688#117—42no—
689#117—42no—
690#117—42no—
691C2×C4⋊C4—42no—
692C2×C4⋊C4—42no—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C42—24no—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2411yescharacteristic
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2412yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2414yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2411yescharacteristic
804#95C2412yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2412yes—
817#95C2412yes—
818#95C2412yes—
819#95C2412yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2412yes—
825#95C2412yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2412yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2412yes—
849#95C2412yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862C24C2514yes—
863C24C2514yes—
864C24C2511yescharacteristic
865#41—816no—
866#41—816no—
867C2×Q8—24no—
868C2×Q8—24no—
869C2×Q8—44no—
870C2×Q8—42no—
871C2×Q8—44no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—44no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—44no—
878C2×Q8—44no—
879C2×Q8—42no—
880C2×D4—28no—
881C2×D4—28no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—44no—
885C2×D4—42no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—42no—
902C2×D4—44no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—44no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4C2514yes—
941C22×C4C2512yes—
942C22×C4C2512yes—
943C22×C4C2514yes—
944C22×C4C2514yes—
945C22×C4C2512yes—
946C22×C4C2512yes—
947C22×C4C2512yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C4⋊C4—24no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—44no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C22⋊C4—24no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C42—24no—
1054C42—22no—
1055C42—24no—
1056C42—24no—
1057C42—42no—
1058C42—42no—
1059C42—42no—
1060C42—42no—
1061C42—44no—
1062C42—44no—
1063C42—44no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—42no—
1068C42—42no—
1069C422−1+414yes—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—24no—
1075C23—24no—
1076C23—24no—
1077C23—24no—
1078C23—24no—
1079C23—24no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—24no—
1087C23—24no—
1088C23#58512yes—
1089C23C2611yescharacteristic
1090Q8—48no—
1091Q8—84no—
1092Q8—84no—
1093Q8—88no—
1094Q8—84no—
1095D4—48no—
1096D4—84no—
1097D4—84no—
1098D4—88no—
1099D4—88no—
1100D4—88no—
1101D4—88no—
1102D4—84no—
1103D4—162no—
1104D4—162no—
1105D4—164no—
1106D4—164no—
1107C2×C4—28no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—84no—
1162C2×C4—84no—
1163C2×C4—84no—
1164C2×C4—88no—
1165C2×C4—88no—
1166C2×C4—164no—
1167C2×C4—164no—
1168C2×C4—164no—
1169C2×C4—164no—
1170C2×C4C2×2−1+412yes—
1171C2×C4C2×2−1+414yes—
1172C2×C4#58512yes—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—42no—
1177C22—42no—
1178C22—44no—
1179C22—44no—
1180C22—44no—
1181C22—44no—
1182C22—44no—
1183C22—44no—
1184C22—44no—
1185C22—44no—
1186C22—44no—
1187C22—44no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22C22×2−1+411yescharacteristic
1193C22C2×#58511yescharacteristic
1194C22C2×#58511yescharacteristic
1195C22H(7,𝔽2)12yes—
1196C22H(7,𝔽2)12yes—
1197C4—22no—
1198C4—22no—
1199C4—24no—
1200C4—42no—
1201C4—42no—
1202C4—44no—
1203C4—42no—
1204C4—42no—
1205C4—44no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—44no—
1210C4—44no—
1211C4—44no—
1212C4—44no—
1213C4—42no—
1214C4—42no—
1215C4—44no—
1216C4—44no—
1217C2—42no—
1218C2—84no—
1219C2—84no—
1220C2#6282511yescharacteristic
1221C2#6288112yes—
1222C2#6304611yescharacteristic
1223C2#6304611yescharacteristic
1224C2#6305112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57051C2semidirect
2. #55037C2semidirect
3. #54991C2semidirect
4. #54001C2semidirect
5. #53958C2semidirect
6. #53665C2semidirect
7. #50096C2semidirect
8. #49593C2semidirect
9. #49592C2semidirect
10. #48551C2semidirect
11. #47807C2semidirect
12. #47695C2semidirect
13. #47071C2semidirect
14. #46497C2semidirect
15. #46241C2semidirect
16. #46241C2semidirect
17. #46232C2semidirect
18. #46017C2semidirect
19. #46017C2semidirect
20. #45991C2semidirect
21. #45991C2semidirect
22. #35339C2semidirect
23. #35136C2semidirect

Maximal subgroups

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

subgroupindex
#570512
#550372
#549912
#540012
#539582
#536652
#500962
#495932
#495922
#485512
#478072
#476952
#470712
#464972
#462412
#462322
#460172
#459912
#353392
#351362