Finite Group Databasebeta

← #8757616

Subgroups — #8757616

Order 512.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1243 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58622C214yesmaximal, complemented
2#57599C212yesmaximal, complemented
3#57597C212yesmaximal, complemented
4#56837C214yesmaximal, complemented
5#56663C212yesmaximal, complemented
6#56661C212yesmaximal, complemented
7#54541C214yesmaximal, complemented
8#54296C214yesmaximal, complemented
9#52076C212yesmaximal, complemented
10#52071C212yesmaximal, complemented
11#51720C214yesmaximal, complemented
12#51580C214yesmaximal, complemented
13#47567C212yesmaximal, complemented
14#47531C214yesmaximal, complemented
15#47487C214yesmaximal, complemented
16#47036C211yesmaximal, characteristic, complemented
17#47034C211yesmaximal, characteristic, complemented
18#46325C212yesmaximal, complemented
19#46311C212yesmaximal, complemented
20#46139C214yesmaximal, complemented
21#45969C214yesmaximal, complemented
22#35316C211yesmaximal, characteristic, complemented
23#35210C212yesmaximal, complemented
24C2×#563C2212yes—
25C2×#563C2212yes—
26C2×#554C2212yes—
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#529C2212yes—
31C2×C4×#41C2211yescharacteristic
32#2857C2214yes—
33#2852C2214yes—
34#2852C2214yes—
35#2843C2212yes—
36#2841C2212yes—
37#2838C2214yes—
38#2836C2214yes—
39#2836C2214yes—
40#2832C2214yes—
41#2829C2214yes—
42#2828C2214yes—
43#2823C2212yes—
44#2821C2214yes—
45#2817C2211yescharacteristic
46#2815C2211yescharacteristic
47#2802C2214yes—
48#2788C2214yes—
49#2786C2214yes—
50#2785C2212yes—
51#2784C2214yes—
52#2775C2214yes—
53#2772C2214yes—
54#2772C2214yes—
55#2771C2212yes—
56#2770C2214yes—
57#2769C2212yes—
58#2768C2214yes—
59#2766C2214yes—
60#2764C2212yes—
61#2764C2212yes—
62#2761C2214yes—
63#2760C2212yes—
64#2759C2214yes—
65#2758C2214yes—
66#2757C2214yes—
67#2756C2214yes—
68#2756C2214yes—
69#2754C2214yes—
70#2752C2212yes—
71#2752C2212yes—
72#2751C2214yes—
73#2750C2214yes—
74#2749C2214yes—
75#2745C2214yes—
76#2744C2214yes—
77#2743C2214yes—
78#2740C2214yes—
79#2740C2214yes—
80#2738C2214yes—
81#2734C2212yes—
82#2733C2212yes—
83#2731C2212yes—
84#2731C2212yes—
85#2730C2214yes—
86#2729C2214yes—
87#2729C2214yes—
88#2729C2214yes—
89#2726C2214yes—
90#2719C2214yes—
91#2716C2214yes—
92#2713C2214yes—
93#2713C2214yes—
94#2712C2214yes—
95#2705C2214yes—
96#2704C2214yes—
97#2704C2214yes—
98#2704C2214yes—
99#2704C2214yes—
100#2703C2214yes—
101#2702C2214yes—
102#2702C2214yes—
103#2702C2214yes—
104#2700C2214yes—
105#2698C2214yes—
106#2698C2214yes—
107#2696C2214yes—
108#2694C2214yes—
109#2694C2214yes—
110#2693C2214yes—
111#2692C2214yes—
112#2692C2214yes—
113#2691C2214yes—
114#2690C2214yes—
115#2687C2214yes—
116#2687C2214yes—
117#2682C2214yes—
118#2681C2214yes—
119#2677C2214yes—
120#2674C2214yes—
121#2666C2214yes—
122#2662C2214yes—
123#2655C2214yes—
124#2638C2212yes—
125#2638C2212yes—
126#2635C2212yes—
127#2635C2212yes—
128#2632C2212yes—
129#2631C2212yes—
130#2630C2214yes—
131#2627C2214yes—
132#2621C2214yes—
133#2612C2214yes—
134#2611C2212yes—
135#2611C2212yes—
136#2610C2212yes—
137#2610C2212yes—
138#2607C2211yescharacteristic
139#2607C2211yescharacteristic
140#2606C2214yes—
141#2605C2214yes—
142#2602C2214yes—
143#2602C2214yes—
144#2601C2214yes—
145#2600C2212yes—
146#2599C2212yes—
147#2598C2212yes—
148#2590C2214yes—
149#2586C2214yes—
150#2581C2212yes—
151#2580C2212yes—
152#2578C2214yes—
153#2574C2214yes—
154#2558C2214yes—
155#2556C2214yes—
156#2554C2214yes—
157#2547C2214yes—
158#2546C2214yes—
159#2536C2212yes—
160#2535C2212yes—
161#2533C2214yes—
162#2532C2214yes—
163#2532C2214yes—
164#2531C2214yes—
165#2527C2214yes—
166#2526C2214yes—
167#2525C2214yes—
168#2525C2214yes—
169#2524C2214yes—
170#2522C2214yes—
171#2519C2214yes—
172#2513C2214yes—
173#2486C2212yes—
174#2486C2212yes—
175#2486C2212yes—
176#2486C2212yes—
177#2485C2214yes—
178#2481C2214yes—
179#2478C2214yes—
180#2475C2214yes—
181#2473C2214yes—
182#2469C2214yes—
183#2469C2214yes—
184#2468C2214yes—
185#2468C2214yes—
186#2463C2214yes—
187#2461C2214yes—
188#2459C2214yes—
189#2456C2214yes—
190#2455C2214yes—
191#2453C2214yes—
192#2452C2214yes—
193#2451C2214yes—
194#2449C2214yes—
195#2449C2214yes—
196#2449C2214yes—
197#2443C2214yes—
198#2443C2214yes—
199#2442C2214yes—
200#2436C2212yes—
201#2434C2212yes—
202#2415C2214yes—
203#2413C2214yes—
204#2409C2214yes—
205#2407C2214yes—
206#2383C2214yes—
207#2381C2212yes—
208#2381C2212yes—
209#2369C2212yes—
210#2333C2212yes—
211#2332C2212yes—
212#2324C2214yes—
213#2323C2214yes—
214#2319C2214yes—
215#2310C2211yescharacteristic
216#2310C2211yescharacteristic
217#2285C2211yescharacteristic
218#2283C2212yes—
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222#563—48no—
223#563—48no—
224#554—48no—
225#536—44no—
226#536—44no—
227C2×C4⋊Q8—44no—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235#529—48no—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2312yes—
269C4×#41—44no—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2314yes—
285C2×#117C2312yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C42C2311yescharacteristic
290C22×C42C2312yes—
291#401C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2312yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2312yes—
314#399C2312yes—
315#399C2314yes—
316#399C2312yes—
317#398C2314yes—
318#398C2314yes—
319#398C2312yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#397C2312yes—
345#397C2312yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2312yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2312yes—
382#395C2312yes—
383#395C2314yes—
384#395C2314yes—
385#395C2312yes—
386#395C2314yes—
387#394C2312yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2312yes—
403#394C2312yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2312yes—
408#393C2314yes—
409#393C2314yes—
410#393C2312yes—
411#393C2314yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#392C2312yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2312yes—
420#392C2312yes—
421#392C2314yes—
422#392C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
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#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#384C2312yes—
574#383C2314yes—
575#383C2314yes—
576#383C2312yes—
577#383C2312yes—
578#383C2314yes—
579#383C2314yes—
580#382C2314yes—
581#382C2312yes—
582#382C2312yes—
583#382C2312yes—
584#382C2314yes—
585#381C2311yescharacteristic
586#381C2312yes—
587#381C2312yes—
588#381C2311yescharacteristic
589#381C2311yescharacteristic
590#381C2311yescharacteristic
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2312yes—
595#381C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2312yes—
607#380C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619#376C2314yes—
620#376C2312yes—
621#376C2312yes—
622C2×#41—24no—
623C2×#41—42no—
624C2×#41—42no—
625C22×Q8—42no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×Q8C2411yescharacteristic
639C22×D4C2412yes—
640C22×D4C2411yescharacteristic
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C23×C4C2414yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C4⋊Q8—28no—
659C4⋊Q8—28no—
660C4⋊Q8—28no—
661C4⋊Q8—48no—
662C4⋊Q8—44no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665#126—216no—
666#126—48no—
667#126—48no—
668#126—48no—
669#125—44no—
670#125—48no—
671#125—48no—
672#125—48no—
673#124—44no—
674#124—44no—
675#124—44no—
676#124—44no—
677#124—44no—
678#123—48no—
679#123—48no—
680#123—48no—
681#123—44no—
682#123—44no—
683#123—44no—
684#123—44no—
685C22⋊Q8—216no—
686C22⋊Q8—44no—
687C22⋊Q8—48no—
688C22⋊Q8—48no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691C22⋊Q8—44no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695#121—44no—
696#121—48no—
697#121—44no—
698C4×Q8—44no—
699C4×Q8—44no—
700C4×Q8—44no—
701C4×D4—44no—
702C4×D4—44no—
703C4×D4—44no—
704C4×D4—44no—
705C4×D4—44no—
706C4×D4—48no—
707C4×D4—48no—
708C4×D4—48no—
709#117—42no—
710#117—44no—
711#117—42no—
712#117—42no—
713#117—48no—
714C2×C4⋊C4—44no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4—48no—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C42—28no—
809C2×C42—24no—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2411yescharacteristic
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2411yescharacteristic
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2412yes—
834#95C2412yes—
835#95C2412yes—
836#95C2412yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2412yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887C24C2514yes—
888C24C2512yes—
889C24C2511yescharacteristic
890#41—416no—
891C2×Q8—24no—
892C2×Q8—24no—
893C2×Q8—24no—
894C2×Q8—24no—
895C2×Q8—41no—
896C2×Q8—41no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—42no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—88no—
913C2×Q8—88no—
914C2×Q8H(5,𝔽2)14yes—
915C2×D4—24no—
916C2×D4—28no—
917C2×D4—24no—
918C2×D4—22no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—41no—
922C2×D4—44no—
923C2×D4—41no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—44no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—24no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—44no—
950C22×C4—42no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—42no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2511yescharacteristic
984C22×C4C2512yes—
985C22×C4C2511yescharacteristic
986C22×C4C2512yes—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
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—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—41no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—42no—
1062C22⋊C4—41no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C42—24no—
1079C42—24no—
1080C42—22no—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—24no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—42no—
1096C42H(5,𝔽2)14yes—
1097C23—21no—
1098C23—21no—
1099C23—24no—
1100C23—24no—
1101C23—24no—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—22no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23#58512yes—
1113C23C2611yescharacteristic
1114Q8—44no—
1115Q8—84no—
1116Q8—84no—
1117Q8—84no—
1118Q8—84no—
1119Q8—84no—
1120Q8—84no—
1121Q8—162no—
1122D4—48no—
1123D4—44no—
1124D4—48no—
1125D4—88no—
1126D4—84no—
1127D4—88no—
1128D4—164no—
1129D4—162no—
1130C2×C4—28no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—48no—
1182C2×C4—48no—
1183C2×C4—88no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4—82no—
1188C2×C4—82no—
1189C2×C4—88no—
1190C2×C4—164no—
1191C2×C4C2×H(5,𝔽2)12yes—
1192C2×C4C2×H(5,𝔽2)14yes—
1193C2×C4C2×H(5,𝔽2)12yes—
1194C2×C4C2×H(5,𝔽2)14yes—
1195C22—24no—
1196C22—22no—
1197C22—42no—
1198C22—42no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—44no—
1211C22C22×H(5,𝔽2)11yescharacteristic
1212C22C22×H(5,𝔽2)11yescharacteristic
1213C22C2×#58511yescharacteristic
1214C222−1+614yes—
1215C4—22no—
1216C4—22no—
1217C4—24no—
1218C4—24no—
1219C4—44no—
1220C4—44no—
1221C4—42no—
1222C4—42no—
1223C4—44no—
1224C4—44no—
1225C4—44no—
1226C4—44no—
1227C4—44no—
1228C4—42no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—44no—
1234C4—44no—
1235C2—42no—
1236C2—84no—
1237C2—82no—
1238C2#6281811yescharacteristic
1239C2#6288612yes—
1240C2#6304412yes—
1241C2#6306412yes—
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. #58622C2semidirect
2. #57599C2semidirect
3. #57597C2semidirect
4. #56837C2semidirect
5. #56663C2semidirect
6. #56661C2semidirect
7. #54541C2semidirect
8. #54296C2semidirect
9. #52076C2semidirect
10. #52071C2semidirect
11. #51720C2semidirect
12. #51580C2semidirect
13. #47567C2semidirect
14. #47531C2semidirect
15. #47487C2semidirect
16. #47036C2semidirect
17. #47034C2semidirect
18. #46325C2semidirect
19. #46311C2semidirect
20. #46139C2semidirect
21. #45969C2semidirect
22. #35316C2semidirect
23. #35210C2semidirect

Maximal subgroups

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

subgroupindex
#586222
#575992
#575972
#568372
#566632
#566612
#545412
#542962
#520762
#520712
#517202
#515802
#475672
#475312
#474872
#470362
#470342
#463252
#463112
#461392
#459692
#353162
#352102