Finite Group Databasebeta

← #7650922

Subgroups — #7650922

Order 512.

4262 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42961C211yesmaximal, characteristic
2#42941C211yesmaximal, characteristic, complemented
3#42700C212yesmaximal, complemented
4#42695C211yesmaximal, characteristic, complemented
5#42526C212yesmaximal, complemented
6#42522C211yesmaximal, characteristic
7#41527C214yesmaximal, complemented
8#41523C214yesmaximal, complemented
9#41489C214yesmaximal, complemented
10#41479C214yesmaximal, complemented
11#40181C214yesmaximal, complemented
12#40034C212yesmaximal, complemented
13#40025C212yesmaximal, complemented
14#38993C214yesmaximal, complemented
15#38986C212yesmaximal, complemented
16#38983C212yesmaximal, complemented
17#37929C214yesmaximal, complemented
18#37918C214yesmaximal, complemented
19#35669C212yesmaximal, complemented
20#35658C212yesmaximal, complemented
21#35656C212yesmaximal, complemented
22#35331C211yesmaximal, characteristic
23#35219C212yesmaximal, complemented
24#34945C212yesmaximal, complemented
25#34882C211yesmaximal, characteristic, complemented
26#34284C212yesmaximal, complemented
27#34254C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#519C2211yescharacteristic
30#2862C2211yescharacteristic
31#2858C2211yescharacteristic
32#2853C2214yes—
33#2852C2214yes—
34#2850C2212yes—
35#2838C2214yes—
36#2834C2212yes—
37#2833C2212yes—
38#2832C2212yes—
39#2831C2214yes—
40#2826C2212yes—
41#2800C2214yes—
42#2796C2214yes—
43#2795C2212yes—
44#2791C2214yes—
45#2789C2214yes—
46#2789C2214yes—
47#2789C2212yes—
48#2788C2214yes—
49#2782C2214yes—
50#2781C2214yes—
51#2780C2214yes—
52#2775C2214yes—
53#2775C2214yes—
54#2772C2214yes—
55#2771C2212yes—
56#2770C2214yes—
57#2769C2212yes—
58#2765C2214yes—
59#2764C2214yes—
60#2764C2212yes—
61#2763C2214yes—
62#2761C2214yes—
63#2760C2212yes—
64#2759C2214yes—
65#2759C2214yes—
66#2758C2214yes—
67#2758C2214yes—
68#2754C2214yes—
69#2752C2212yes—
70#2750C2214yes—
71#2749C2214yes—
72#2745C2214yes—
73#2723C2214yes—
74#2707C2214yes—
75#2698C2214yes—
76#2680C2212yes—
77#2666C2214yes—
78#2665C2214yes—
79#2653C2214yes—
80#2653C2214yes—
81#2652C2214yes—
82#2652C2214yes—
83#2651C2214yes—
84#2650C2214yes—
85#2650C2214yes—
86#2649C2214yes—
87#2645C2214yes—
88#2643C2214yes—
89#2640C2212yes—
90#2637C2214yes—
91#2630C2214yes—
92#2621C2211yescharacteristic
93#2619C2211yescharacteristic
94#2596C2214yes—
95#2596C2214yes—
96#2594C2214yes—
97#2592C2212yes—
98#2592C2212yes—
99#2590C2214yes—
100#2588C2214yes—
101#2586C2212yes—
102#2586C2212yes—
103#2585C2212yes—
104#2582C2212yes—
105#2581C2212yes—
106#2580C2212yes—
107#2578C2214yes—
108#2576C2214yes—
109#2575C2214yes—
110#2574C2212yes—
111#2573C2214yes—
112#2573C2214yes—
113#2572C2212yes—
114#2572C2214yes—
115#2571C2212yes—
116#2571C2212yes—
117#2570C2212yes—
118#2570C2212yes—
119#2568C2212yes—
120#2568C2212yes—
121#2568C2212yes—
122#2567C2212yes—
123#2560C2214yes—
124#2560C2214yes—
125#2557C2214yes—
126#2557C2214yes—
127#2556C2212yes—
128#2553C2214yes—
129#2547C2212yes—
130#2546C2212yes—
131#2545C2212yes—
132#2545C2212yes—
133#2545C2212yes—
134#2544C2212yes—
135#2538C2212yes—
136#2533C2214yes—
137#2533C2214yes—
138#2532C2214yes—
139#2531C2214yes—
140#2530C2214yes—
141#2529C2214yes—
142#2528C2214yes—
143#2528C2214yes—
144#2527C2214yes—
145#2526C2214yes—
146#2524C2214yes—
147#2523C2212yes—
148#2522C2212yes—
149#2522C2214yes—
150#2520C2212yes—
151#2520C2214yes—
152#2515C2214yes—
153#2515C2214yes—
154#2514C2214yes—
155#2514C2212yes—
156#2514C2212yes—
157#2514C2212yes—
158#2514C2212yes—
159#2514C2212yes—
160#2513C2212yes—
161#2512C2212yes—
162#2511C2212yes—
163#2510C2214yes—
164#2500C2212yes—
165#2499C2212yes—
166#2494C2214yes—
167#2474C2214yes—
168#2474C2214yes—
169#2470C2214yes—
170#2470C2214yes—
171#2469C2214yes—
172#2469C2214yes—
173#2465C2214yes—
174#2465C2214yes—
175#2465C2214yes—
176#2465C2212yes—
177#2463C2212yes—
178#2462C2212yes—
179#2453C2214yes—
180#2450C2214yes—
181#2448C2212yes—
182#2447C2212yes—
183#2447C2212yes—
184#2447C2212yes—
185#2446C2212yes—
186#2446C2212yes—
187#2446C2212yes—
188#2445C2212yes—
189#2436C2212yes—
190#2434C2212yes—
191#2421C2214yes—
192#2401C2214yes—
193#2401C2214yes—
194#2399C2211yescharacteristic
195#2399C2211yescharacteristic
196#2396C2211yescharacteristic
197#2396C2211yescharacteristic
198#2373C2214yes—
199#2373C2214yes—
200#2372C2214yes—
201#2369C2212yes—
202#2367C2212yes—
203#2367C2214yes—
204#2367C2212yes—
205#2365C2212yes—
206#2363C2212yes—
207#2362C2212yes—
208#2361C2212yes—
209#2360C2212yes—
210#2356C2214yes—
211#2355C2214yes—
212#2343C2214yes—
213#2343C2214yes—
214#2335C2214yes—
215#2335C2214yes—
216#2334C2214yes—
217#2332C2214yes—
218#2328C2211yescharacteristic
219#2327C2211yescharacteristic
220#2327C2212yes—
221#2326C2212yes—
222#2320C2214yes—
223#2320C2212yes—
224#2320C2212yes—
225#2319C2212yes—
226#2318C2214yes—
227#2317C2211yescharacteristic
228#2310C2211yescharacteristic
229C4×C4⋊Q8C2212yes—
230C4×#125C2212yes—
231C4×#124C2212yes—
232C4×#124C2212yes—
233C4×C22⋊Q8C2214yes—
234C4×C22⋊Q8C2212yes—
235C4×C22⋊Q8C2214yes—
236C4×#123C2214yes—
237#2298C2212yes—
238#2296C2211yescharacteristic
239#2295C2212yes—
240#2295C2211yescharacteristic
241#2295C2212yes—
242#2295C2212yes—
243#2295C2212yes—
244C2×#391C2211yescharacteristic
245#2283C2214yes—
246#2276C2212yes—
247#2274C2211yescharacteristic
248C42×Q8C2211yescharacteristic
249C42×D4C2212yes—
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252#542—216no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×#127C2311yescharacteristic
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2312yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×#121C2312yes—
273#519—28no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×#117C2311yescharacteristic
290C2×#117C2314yes—
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2314yes—
297#401C2314yes—
298#401C2314yes—
299#401C2314yes—
300#401C2314yes—
301#401C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2311yescharacteristic
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2311yescharacteristic
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#399C2311yescharacteristic
328#399C2314yes—
329#399C2311yescharacteristic
330#399C2314yes—
331#398C2312yes—
332#398C2312yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2312yes—
347#398C2312yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2312yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2312yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2312yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2312yes—
379#395C2314yes—
380#395C2314yes—
381#395C2312yes—
382#395C2311yescharacteristic
383#395C2314yes—
384#395C2314yes—
385#395C2312yes—
386#395C2311yescharacteristic
387#395C2314yes—
388#395C2312yes—
389#395C2312yes—
390#394C2312yes—
391#394C2312yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2311yescharacteristic
404#393C2314yes—
405#393C2314yes—
406#393C2311yescharacteristic
407#392C2312yes—
408#392C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#390C2312yes—
448#390C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2312yes—
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#388C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2312yes—
517#387C2312yes—
518#387C2312yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#385C2312yes—
582#385C2312yes—
583#385C2314yes—
584#385C2314yes—
585#385C2312yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2312yes—
598#385C2314yes—
599#384C2312yes—
600#384C2312yes—
601#384C2312yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2311yescharacteristic
615#382C2311yescharacteristic
616#382C2312yes—
617#382C2314yes—
618#382C2314yes—
619#382C2312yes—
620#382C2314yes—
621#382C2314yes—
622#381C2312yes—
623#381C2312yes—
624#381C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#380C2314yes—
629#380C2312yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681#376C2312yes—
682#376C2311yescharacteristic
683#376C2311yescharacteristic
684#376C2314yes—
685#376C2314yes—
686#376C2314yes—
687#376C2314yes—
688C2×#95C2314yes—
689C43C2311yescharacteristic
690C43C2312yes—
691C43C2311yescharacteristic
692C22×Q8—24no—
693C22×Q8—42no—
694C22×Q8—42no—
695C22×Q8C2412yes—
696C22×Q8C2412yes—
697C22×Q8C2411yescharacteristic
698C22×Q8C2412yes—
699C22×Q8C2414yes—
700C22×Q8C2412yes—
701C22×Q8C2411yescharacteristic
702C22×D4C2412yes—
703C22×D4C2414yes—
704C22×D4C2412yes—
705C22×D4C2412yes—
706C23×C4C2411yescharacteristic
707C23×C4C2412yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2412yes—
711C23×C4C2414yes—
712C23×C4C2412yes—
713C4⋊Q8—28no—
714C4⋊Q8—42no—
715C4⋊Q8—44no—
716C4⋊Q8—44no—
717#127—42no—
718#126—216no—
719#126—48no—
720#125—44no—
721#124—216no—
722#124—28no—
723#124—44no—
724#124—44no—
725#124—44no—
726#123—216no—
727#123—48no—
728C22⋊Q8—28no—
729C22⋊Q8—216no—
730C22⋊Q8—44no—
731C22⋊Q8—48no—
732#121—28no—
733C4×Q8—216no—
734C4×Q8—28no—
735C4×Q8—28no—
736C4×Q8—28no—
737C4×Q8—44no—
738C4×Q8—42no—
739C4×Q8—42no—
740C4×Q8—48no—
741C4×Q8—44no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×D4—28no—
745C4×D4—44no—
746C4×D4—44no—
747C4×D4—48no—
748#117—24no—
749#117—216no—
750#117—42no—
751#117—42no—
752#117#4118yes—
753C2×C4⋊C4—42no—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C42—48no—
846C2×C42—42no—
847C2×C42C2411yescharacteristic
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2411yescharacteristic
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2411yescharacteristic
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2412yes—
923#95C2411yescharacteristic
924#95C2412yes—
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2411yescharacteristic
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2411yescharacteristic
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961C24C2514yes—
962C24C2511yescharacteristic
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—28no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—24no—
972C2×Q8—41no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—44no—
976C2×Q8—41no—
977C2×Q8—42no—
978C2×Q8—42no—
979C2×Q8—44no—
980C2×Q8—42no—
981C2×Q8—42no—
982C2×Q8—416no—
983C2×D4—28no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—42no—
992C2×D4—44no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—28no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4C2×#4114yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2514yes—
1018C22×C4C2514yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2512yes—
1037C22×C4C2511yescharacteristic
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4C2×#4118yes—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—44no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—42no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—44no—
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⋊C4C2×#4118yes—
1129C42—24no—
1130C42—28no—
1131C42—28no—
1132C42—28no—
1133C42—24no—
1134C42—22no—
1135C42—28no—
1136C42—22no—
1137C42—22no—
1138C42—22no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—44no—
1144C42—42no—
1145C42—44no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—44no—
1152C42—42no—
1153C42—42no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—42no—
1159C42C2×#4114yes—
1160C42C2×#4114yes—
1161C23—22no—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23C22×#4112yes—
1173C23C2611yescharacteristic
1174Q8—44no—
1175Q8—48no—
1176Q8—48no—
1177Q8—48no—
1178Q8—88no—
1179Q8—82no—
1180Q8—84no—
1181D4—48no—
1182D4—88no—
1183D4—162no—
1184D4—162no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—28no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—48no—
1251C2×C4—88no—
1252C2×C4—88no—
1253C2×C4—88no—
1254C2×C4—84no—
1255C2×C4—162no—
1256C2×C4C22×#4114yes—
1257C2×C4C22×#4114yes—
1258C2×C4C22×#4112yes—
1259C2×C4C22×#4112yes—
1260C2×C4#58514yes—
1261C2×C4#58512yes—
1262C2×C4#58512yes—
1263C22—24no—
1264C22—22no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22C23×#4111yescharacteristic
1276C22C2×#58512yes—
1277C22C2×#58511yescharacteristic
1278C22C2×#58511yescharacteristic
1279C222−1+612yes—
1280C4—24no—
1281C4—24no—
1282C4—24no—
1283C4—22no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—42no—
1288C4—44no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—42no—
1294C4—41no—
1295C4—42no—
1296C4—44no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C4—44no—
1304C4#345514yes—
1305C2—42no—
1306C2—84no—
1307C2C2×#345511yescharacteristic
1308C2#6282911yescharacteristic
1309C2#6289111yescharacteristic
1310C2#6293612yes—
1311C2#6299512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2619C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42941C2semidirect
3. #42700C2semidirect
4. #42695C2semidirect
5. #42526C2semidirect
7. #41527C2semidirect
8. #41523C2semidirect
9. #41489C2semidirect
10. #41479C2semidirect
11. #40181C2semidirect
12. #40034C2semidirect
13. #40025C2semidirect
14. #38993C2semidirect
15. #38986C2semidirect
16. #38983C2semidirect
17. #37929C2semidirect
18. #37918C2semidirect
19. #35669C2semidirect
20. #35658C2semidirect
21. #35656C2semidirect
23. #35219C2semidirect
24. #34945C2semidirect
25. #34882C2semidirect
26. #34284C2semidirect
27. #34254C2semidirect

Maximal subgroups

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

subgroupindex
#429612
#429412
#427002
#426952
#425262
#425222
#415272
#415232
#414892
#414792
#401812
#400342
#400252
#389932
#389862
#389832
#379292
#379182
#356692
#356582
#356562
#353312
#352192
#349452
#348822
#342842
#342542