Finite Group Databasebeta

← #8095122

Subgroups — #8095122

Order 512.

4345 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53154C211yesmaximal, characteristic, complemented
2#53147C211yesmaximal, characteristic, complemented
3#53138C212yesmaximal, complemented
4#53032C211yesmaximal, characteristic, complemented
5#52985C211yesmaximal, characteristic, complemented
6#52962C212yesmaximal, complemented
7#52942C214yesmaximal, complemented
8#52937C214yesmaximal, complemented
9#52921C214yesmaximal, complemented
10#52919C214yesmaximal, complemented
11#46116C212yesmaximal, complemented
12#46048C212yesmaximal, complemented
13#45695C212yesmaximal, complemented
14#45685C214yesmaximal, complemented
15#45672C214yesmaximal, complemented
16#45669C212yesmaximal, complemented
17#45540C214yesmaximal, complemented
18#45534C214yesmaximal, complemented
19#35632C212yesmaximal, complemented
20#35570C212yesmaximal, complemented
21#35548C212yesmaximal, complemented
22#35332C211yesmaximal, characteristic, complemented
23#35323C211yesmaximal, characteristic, complemented
24#35246C212yesmaximal, complemented
25#35244C212yesmaximal, complemented
26#34879C211yesmaximal, characteristic, complemented
27#34708C212yesmaximal, complemented
28C2×#541C2211yescharacteristic
29C2×#540C2211yescharacteristic
30C2×#529C2212yes—
31C22×C4×Q8C2212yes—
32#2863C2212yes—
33#2859C2211yescharacteristic
34#2858C2211yescharacteristic
35#2857C2211yescharacteristic
36#2853C2214yes—
37#2853C2214yes—
38#2852C2214yes—
39#2851C2214yes—
40#2851C2211yescharacteristic
41#2850C2212yes—
42#2844C2214yes—
43#2841C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2839C2214yes—
47#2838C2214yes—
48#2837C2214yes—
49#2837C2214yes—
50#2836C2214yes—
51#2835C2214yes—
52#2831C2214yes—
53#2830C2214yes—
54#2830C2214yes—
55#2827C2214yes—
56#2827C2214yes—
57#2827C2214yes—
58#2827C2214yes—
59#2827C2214yes—
60#2824C2214yes—
61#2824C2214yes—
62#2808C2214yes—
63#2797C2214yes—
64#2794C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2787C2214yes—
68#2786C2214yes—
69#2784C2214yes—
70#2784C2214yes—
71#2784C2214yes—
72#2782C2214yes—
73#2779C2214yes—
74#2778C2214yes—
75#2770C2214yes—
76#2769C2214yes—
77#2768C2214yes—
78#2766C2214yes—
79#2763C2214yes—
80#2761C2214yes—
81#2761C2214yes—
82#2757C2214yes—
83#2749C2214yes—
84#2747C2214yes—
85#2744C2214yes—
86#2743C2214yes—
87#2742C2214yes—
88#2741C2214yes—
89#2739C2214yes—
90#2737C2214yes—
91#2737C2214yes—
92#2737C2214yes—
93#2722C2214yes—
94#2708C2214yes—
95#2708C2214yes—
96#2693C2214yes—
97#2691C2214yes—
98#2691C2214yes—
99#2691C2214yes—
100#2688C2214yes—
101#2671C2214yes—
102#2647C2211yescharacteristic
103#2642C2211yescharacteristic
104#2642C2211yescharacteristic
105#2641C2211yescharacteristic
106#2637C2214yes—
107#2637C2214yes—
108#2637C2214yes—
109#2634C2214yes—
110#2625C2212yes—
111#2620C2212yes—
112#2602C2214yes—
113#2599C2214yes—
114#2599C2214yes—
115#2590C2214yes—
116#2580C2212yes—
117#2579C2214yes—
118#2579C2214yes—
119#2578C2214yes—
120#2577C2214yes—
121#2577C2214yes—
122#2575C2214yes—
123#2574C2212yes—
124#2573C2212yes—
125#2572C2212yes—
126#2570C2212yes—
127#2568C2212yes—
128#2565C2212yes—
129#2565C2212yes—
130#2559C2214yes—
131#2559C2214yes—
132#2559C2214yes—
133#2558C2214yes—
134#2558C2214yes—
135#2553C2212yes—
136#2553C2214yes—
137#2553C2214yes—
138#2552C2212yes—
139#2547C2212yes—
140#2545C2212yes—
141#2545C2212yes—
142#2544C2212yes—
143#2543C2214yes—
144#2540C2212yes—
145#2537C2212yes—
146#2533C2214yes—
147#2530C2214yes—
148#2530C2214yes—
149#2527C2214yes—
150#2524C2212yes—
151#2523C2214yes—
152#2517C2214yes—
153#2517C2214yes—
154#2515C2212yes—
155#2515C2214yes—
156#2514C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2507C2212yes—
160#2505C2214yes—
161#2505C2214yes—
162#2504C2212yes—
163#2502C2212yes—
164#2500C2214yes—
165#2498C2214yes—
166#2496C2212yes—
167#2495C2214yes—
168#2493C2214yes—
169#2490C2212yes—
170#2489C2212yes—
171#2489C2212yes—
172#2481C2214yes—
173#2481C2214yes—
174#2473C2214yes—
175#2469C2214yes—
176#2469C2214yes—
177#2468C2212yes—
178#2466C2214yes—
179#2464C2214yes—
180#2462C2214yes—
181#2458C2214yes—
182#2457C2212yes—
183#2454C2212yes—
184#2453C2212yes—
185#2453C2212yes—
186#2448C2212yes—
187#2447C2212yes—
188#2447C2212yes—
189#2447C2212yes—
190#2446C2212yes—
191#2443C2214yes—
192#2442C2212yes—
193#2442C2212yes—
194#2436C2212yes—
195#2436C2212yes—
196#2434C2212yes—
197#2434C2212yes—
198#2429C2212yes—
199#2428C2212yes—
200#2427C2212yes—
201#2427C2212yes—
202#2426C2212yes—
203#2422C2212yes—
204#2422C2214yes—
205#2421C2212yes—
206#2421C2212yes—
207#2419C2214yes—
208#2417C2212yes—
209#2416C2212yes—
210#2409C2212yes—
211#2409C2212yes—
212#2402C2211yescharacteristic
213#2398C2211yescharacteristic
214#2398C2214yes—
215#2396C2211yescharacteristic
216#2396C2214yes—
217#2392C2211yescharacteristic
218#2383C2214yes—
219#2377C2214yes—
220#2377C2214yes—
221#2376C2214yes—
222#2330C2211yescharacteristic
223#2327C2212yes—
224#2327C2211yescharacteristic
225#2326C2212yes—
226#2326C2212yes—
227#2323C2212yes—
228#2320C2212yes—
229C4×#126C2212yes—
230C4×#124C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×#123C2212yes—
233C4×#121C2214yes—
234C4×#121C2212yes—
235#2295C2211yescharacteristic
236#2295C2212yes—
237#2290C2212yes—
238#2290C2214yes—
239#2283C2212yes—
240#2275C2212yes—
241C42×D4C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C23×Q8C2312yes—
244#541—44no—
245#540—44no—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2311yescharacteristic
249C2×#127C2311yescharacteristic
250#529—48no—
251C2×#126C2312yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2314yes—
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×C4×Q8—48no—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×#117C2311yescharacteristic
296C2×#117C2314yes—
297C2×#117C2311yescharacteristic
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2312yes—
300C22×C42C2312yes—
301C22×C42C2311yescharacteristic
302C22×C42C2314yes—
303#401C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2312yes—
319#400C2311yescharacteristic
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#399C2311yescharacteristic
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2311yescharacteristic
360#398C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2311yescharacteristic
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#396C2312yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2312yes—
397#396C2314yes—
398#395C2311yescharacteristic
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#394C2312yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2311yescharacteristic
421#394C2312yes—
422#394C2314yes—
423#393C2312yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2311yescharacteristic
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2311yescharacteristic
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2312yes—
483#388C2312yes—
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#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#387C2312yes—
510#387C2312yes—
511#387C2312yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2312yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2312yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2312yes—
575#385C2314yes—
576#385C2314yes—
577#385C2312yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2312yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#384C2312yes—
602#384C2312yes—
603#384C2311yescharacteristic
604#384C2314yes—
605#383C2312yes—
606#383C2312yes—
607#383C2312yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#382C2311yescharacteristic
612#382C2312yes—
613#382C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2312yes—
620#381C2312yes—
621#381C2312yes—
622#381C2312yes—
623#381C2314yes—
624#381C2314yes—
625#381C2314yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2311yescharacteristic
674#376C2314yes—
675C2×#95C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C22×Q8—44no—
679C22×Q8—44no—
680C22×Q8—44no—
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2414yes—
684C22×Q8C2411yescharacteristic
685C22×D4C2412yes—
686C22×D4C2411yescharacteristic
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2412yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2412yes—
702C4⋊Q8—42no—
703C4⋊Q8—44no—
704C4⋊Q8—42no—
705#127—42no—
706#126—48no—
707#126—48no—
708#126—48no—
709#126—44no—
710#125—42no—
711#125—44no—
712#125—42no—
713#125—48no—
714#125—42no—
715#124—44no—
716#124—44no—
717#124—44no—
718#124—44no—
719#123—44no—
720#123—48no—
721#123—48no—
722#123—48no—
723C22⋊Q8—44no—
724C22⋊Q8—44no—
725C22⋊Q8—44no—
726C22⋊Q8—44no—
727#121—48no—
728#121—48no—
729#121—48no—
730#121—48no—
731#121—44no—
732#121—44no—
733#121—44no—
734C4×Q8—28no—
735C4×Q8—28no—
736C4×Q8—48no—
737C4×Q8—42no—
738C4×Q8—48no—
739C4×Q8—44no—
740C4×Q8—44no—
741C4×D4—28no—
742C4×D4—44no—
743C4×D4—44no—
744C4×D4—42no—
745C4×D4—44no—
746C4×D4—48no—
747C4×D4—48no—
748C4×D4—44no—
749#117—24no—
750#117—42no—
751#117—48no—
752C2×C4⋊C4—44no—
753C2×C4⋊C4—48no—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C42—28no—
853C2×C42—48no—
854C2×C42—42no—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2412yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2412yes—
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2414yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2414yes—
911#95C2412yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2411yescharacteristic
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2411yescharacteristic
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951C24C2511yescharacteristic
952C24C2514yes—
953C24C2512yes—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—41no—
964C2×Q8—42no—
965C2×Q8—432no—
966C2×D4—24no—
967C2×D4—28no—
968C2×D4—28no—
969C2×D4—24no—
970C2×D4—24no—
971C2×D4—24no—
972C2×D4—24no—
973C2×D4—41no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—28no—
996C22×C4—44no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4C2512yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—41no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—41no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C22⋊C4—28no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—44no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—42no—
1108C22⋊C4—44no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—42no—
1114C22⋊C4—44no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—42no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—42no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—28no—
1142C42—28no—
1143C42—22no—
1144C42—22no—
1145C42—22no—
1146C42—22no—
1147C42—22no—
1148C42—24no—
1149C42—24no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42—42no—
1154C42—44no—
1155C42—42no—
1156C42—42no—
1157C42—44no—
1158C42—42no—
1159C42—44no—
1160C42H(5,𝔽2)14yes—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—21no—
1168C23—24no—
1169C23—21no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—22no—
1174C23—21no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23#58514yes—
1180C23C2611yescharacteristic
1181Q8—416no—
1182Q8—48no—
1183Q8—48no—
1184Q8—82no—
1185D4—44no—
1186D4—48no—
1187D4—88no—
1188D4—88no—
1189D4—84no—
1190D4—164no—
1191D4—164no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—48no—
1257C2×C4—416no—
1258C2×C4—44no—
1259C2×C4—48no—
1260C2×C4—84no—
1261C2×C4—88no—
1262C2×C4—88no—
1263C2×C4—84no—
1264C2×C4—164no—
1265C2×C4—164no—
1266C2×C4C2×H(5,𝔽2)14yes—
1267C2×C4C2×H(5,𝔽2)12yes—
1268C2×C4#58512yes—
1269C2×C4#58512yes—
1270C22—24no—
1271C22—24no—
1272C22—24no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—44no—
1278C22—41no—
1279C22—41no—
1280C22—44no—
1281C22—41no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—42no—
1286C22—42no—
1287C22—44no—
1288C22—44no—
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22C2×#58512yes—
1292C22C2×#58511yescharacteristic
1293C222−1+612yes—
1294C4—24no—
1295C4—41no—
1296C4—42no—
1297C4—44no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—42no—
1302C4—41no—
1303C4—42no—
1304C4—44no—
1305C4—44no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—44no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—44no—
1316C4—42no—
1317C4#352914yes—
1318C2—44no—
1319C2—84no—
1320C2—81no—
1321C2C2×#352911yescharacteristic
1322C2#6282911yescharacteristic
1323C2#6289011yescharacteristic
1324C2#6295412yes—
1325C2#6297112yes—
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. #53154C2semidirect
2. #53147C2semidirect
3. #53138C2semidirect
4. #53032C2semidirect
5. #52985C2semidirect
6. #52962C2semidirect
7. #52942C2semidirect
8. #52937C2semidirect
9. #52921C2semidirect
10. #52919C2semidirect
11. #46116C2semidirect
12. #46048C2semidirect
13. #45695C2semidirect
14. #45685C2semidirect
15. #45672C2semidirect
16. #45669C2semidirect
17. #45540C2semidirect
18. #45534C2semidirect
19. #35632C2semidirect
20. #35570C2semidirect
21. #35548C2semidirect
22. #35332C2semidirect
23. #35323C2semidirect
24. #35246C2semidirect
25. #35244C2semidirect
26. #34879C2semidirect
27. #34708C2semidirect

Maximal subgroups

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

subgroupindex
#531542
#531472
#531382
#530322
#529852
#529622
#529422
#529372
#529212
#529192
#461162
#460482
#456952
#456852
#456722
#456692
#455402
#455342
#356322
#355702
#355482
#353322
#353232
#352462
#352442
#348792
#347082